Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [445,2,Mod(1,445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(445, 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("445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 445 = 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 445.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: | \(3.55334288995\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
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 | 1.1 | ||
Root | \(2.09529\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39026 | −1.69017 | −0.845083 | − | 0.534634i | \(-0.820449\pi\) | ||||
−0.845083 | + | 0.534634i | \(0.820449\pi\) | |||||||
\(3\) | 0.294963 | 0.170297 | 0.0851485 | − | 0.996368i | \(-0.472864\pi\) | ||||
0.0851485 | + | 0.996368i | \(0.472864\pi\) | |||||||
\(4\) | 3.71333 | 1.85666 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.705037 | −0.287830 | ||||||||
\(7\) | 1.95452 | 0.738739 | 0.369370 | − | 0.929283i | \(-0.379574\pi\) | ||||
0.369370 | + | 0.929283i | \(0.379574\pi\) | |||||||
\(8\) | −4.09529 | −1.44791 | ||||||||
\(9\) | −2.91300 | −0.970999 | ||||||||
\(10\) | 2.39026 | 0.755866 | ||||||||
\(11\) | −4.29496 | −1.29498 | −0.647490 | − | 0.762074i | \(-0.724181\pi\) | ||||
−0.647490 | + | 0.762074i | \(0.724181\pi\) | |||||||
\(12\) | 1.09529 | 0.316184 | ||||||||
\(13\) | 1.05377 | 0.292263 | 0.146132 | − | 0.989265i | \(-0.453318\pi\) | ||||
0.146132 | + | 0.989265i | \(0.453318\pi\) | |||||||
\(14\) | −4.67180 | −1.24859 | ||||||||
\(15\) | −0.294963 | −0.0761591 | ||||||||
\(16\) | 2.36215 | 0.590537 | ||||||||
\(17\) | 3.65443 | 0.886330 | 0.443165 | − | 0.896440i | \(-0.353856\pi\) | ||||
0.443165 | + | 0.896440i | \(0.353856\pi\) | |||||||
\(18\) | 6.96281 | 1.64115 | ||||||||
\(19\) | −3.07792 | −0.706124 | −0.353062 | − | 0.935600i | \(-0.614859\pi\) | ||||
−0.353062 | + | 0.935600i | \(0.614859\pi\) | |||||||
\(20\) | −3.71333 | −0.830325 | ||||||||
\(21\) | 0.576511 | 0.125805 | ||||||||
\(22\) | 10.2661 | 2.18873 | ||||||||
\(23\) | −1.46385 | −0.305233 | −0.152616 | − | 0.988286i | \(-0.548770\pi\) | ||||
−0.152616 | + | 0.988286i | \(0.548770\pi\) | |||||||
\(24\) | −1.20796 | −0.246574 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.51878 | −0.493974 | ||||||||
\(27\) | −1.74411 | −0.335655 | ||||||||
\(28\) | 7.25777 | 1.37159 | ||||||||
\(29\) | −8.44007 | −1.56728 | −0.783641 | − | 0.621214i | \(-0.786640\pi\) | ||||
−0.783641 | + | 0.621214i | \(0.786640\pi\) | |||||||
\(30\) | 0.705037 | 0.128722 | ||||||||
\(31\) | 4.24040 | 0.761599 | 0.380799 | − | 0.924658i | \(-0.375649\pi\) | ||||
0.380799 | + | 0.924658i | \(0.375649\pi\) | |||||||
\(32\) | 2.54445 | 0.449799 | ||||||||
\(33\) | −1.26685 | −0.220531 | ||||||||
\(34\) | −8.73503 | −1.49805 | ||||||||
\(35\) | −1.95452 | −0.330374 | ||||||||
\(36\) | −10.8169 | −1.80282 | ||||||||
\(37\) | −4.61163 | −0.758148 | −0.379074 | − | 0.925366i | \(-0.623757\pi\) | ||||
−0.379074 | + | 0.925366i | \(0.623757\pi\) | |||||||
\(38\) | 7.35702 | 1.19347 | ||||||||
\(39\) | 0.310823 | 0.0497716 | ||||||||
\(40\) | 4.09529 | 0.647523 | ||||||||
\(41\) | 0.785638 | 0.122696 | 0.0613480 | − | 0.998116i | \(-0.480460\pi\) | ||||
0.0613480 | + | 0.998116i | \(0.480460\pi\) | |||||||
\(42\) | −1.37801 | −0.212631 | ||||||||
\(43\) | −3.60895 | −0.550360 | −0.275180 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275180 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(44\) | −15.9486 | −2.40434 | ||||||||
\(45\) | 2.91300 | 0.434244 | ||||||||
\(46\) | 3.49897 | 0.515894 | ||||||||
\(47\) | −10.8220 | −1.57856 | −0.789278 | − | 0.614036i | \(-0.789545\pi\) | ||||
−0.789278 | + | 0.614036i | \(0.789545\pi\) | |||||||
\(48\) | 0.696746 | 0.100567 | ||||||||
\(49\) | −3.17985 | −0.454265 | ||||||||
\(50\) | −2.39026 | −0.338033 | ||||||||
\(51\) | 1.07792 | 0.150939 | ||||||||
\(52\) | 3.91300 | 0.542635 | ||||||||
\(53\) | −9.07035 | −1.24591 | −0.622954 | − | 0.782258i | \(-0.714068\pi\) | ||||
−0.622954 | + | 0.782258i | \(0.714068\pi\) | |||||||
\(54\) | 4.16888 | 0.567313 | ||||||||
\(55\) | 4.29496 | 0.579133 | ||||||||
\(56\) | −8.00433 | −1.06962 | ||||||||
\(57\) | −0.907873 | −0.120251 | ||||||||
\(58\) | 20.1739 | 2.64897 | ||||||||
\(59\) | −5.36459 | −0.698411 | −0.349205 | − | 0.937046i | \(-0.613548\pi\) | ||||
−0.349205 | + | 0.937046i | \(0.613548\pi\) | |||||||
\(60\) | −1.09529 | −0.141402 | ||||||||
\(61\) | −5.59950 | −0.716942 | −0.358471 | − | 0.933541i | \(-0.616702\pi\) | ||||
−0.358471 | + | 0.933541i | \(0.616702\pi\) | |||||||
\(62\) | −10.1356 | −1.28723 | ||||||||
\(63\) | −5.69351 | −0.717315 | ||||||||
\(64\) | −10.8062 | −1.35077 | ||||||||
\(65\) | −1.05377 | −0.130704 | ||||||||
\(66\) | 3.02811 | 0.372734 | ||||||||
\(67\) | −7.92129 | −0.967739 | −0.483870 | − | 0.875140i | \(-0.660769\pi\) | ||||
−0.483870 | + | 0.875140i | \(0.660769\pi\) | |||||||
\(68\) | 13.5701 | 1.64562 | ||||||||
\(69\) | −0.431780 | −0.0519802 | ||||||||
\(70\) | 4.67180 | 0.558387 | ||||||||
\(71\) | 10.0621 | 1.19415 | 0.597074 | − | 0.802187i | \(-0.296330\pi\) | ||||
0.597074 | + | 0.802187i | \(0.296330\pi\) | |||||||
\(72\) | 11.9296 | 1.40591 | ||||||||
\(73\) | 2.47330 | 0.289478 | 0.144739 | − | 0.989470i | \(-0.453766\pi\) | ||||
0.144739 | + | 0.989470i | \(0.453766\pi\) | |||||||
\(74\) | 11.0230 | 1.28140 | ||||||||
\(75\) | 0.294963 | 0.0340594 | ||||||||
\(76\) | −11.4293 | −1.31103 | ||||||||
\(77\) | −8.39459 | −0.956652 | ||||||||
\(78\) | −0.742948 | −0.0841222 | ||||||||
\(79\) | −11.6532 | −1.31108 | −0.655541 | − | 0.755159i | \(-0.727559\pi\) | ||||
−0.655541 | + | 0.755159i | \(0.727559\pi\) | |||||||
\(80\) | −2.36215 | −0.264096 | ||||||||
\(81\) | 8.22454 | 0.913838 | ||||||||
\(82\) | −1.87788 | −0.207377 | ||||||||
\(83\) | 12.5329 | 1.37567 | 0.687833 | − | 0.725869i | \(-0.258562\pi\) | ||||
0.687833 | + | 0.725869i | \(0.258562\pi\) | |||||||
\(84\) | 2.14077 | 0.233578 | ||||||||
\(85\) | −3.65443 | −0.396379 | ||||||||
\(86\) | 8.62632 | 0.930201 | ||||||||
\(87\) | −2.48951 | −0.266903 | ||||||||
\(88\) | 17.5891 | 1.87501 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | −6.96281 | −0.733945 | ||||||||
\(91\) | 2.05962 | 0.215906 | ||||||||
\(92\) | −5.43574 | −0.566715 | ||||||||
\(93\) | 1.25076 | 0.129698 | ||||||||
\(94\) | 25.8674 | 2.66802 | ||||||||
\(95\) | 3.07792 | 0.315788 | ||||||||
\(96\) | 0.750517 | 0.0765993 | ||||||||
\(97\) | 5.96756 | 0.605914 | 0.302957 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302957 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(98\) | 7.60066 | 0.767783 | ||||||||
\(99\) | 12.5112 | 1.25742 | ||||||||
\(100\) | 3.71333 | 0.371333 | ||||||||
\(101\) | 6.15863 | 0.612807 | 0.306403 | − | 0.951902i | \(-0.400874\pi\) | ||||
0.306403 | + | 0.951902i | \(0.400874\pi\) | |||||||
\(102\) | −2.57651 | −0.255113 | ||||||||
\(103\) | 15.0166 | 1.47963 | 0.739814 | − | 0.672812i | \(-0.234914\pi\) | ||||
0.739814 | + | 0.672812i | \(0.234914\pi\) | |||||||
\(104\) | −4.31550 | −0.423170 | ||||||||
\(105\) | −0.576511 | −0.0562617 | ||||||||
\(106\) | 21.6805 | 2.10579 | ||||||||
\(107\) | 2.68955 | 0.260009 | 0.130004 | − | 0.991513i | \(-0.458501\pi\) | ||||
0.130004 | + | 0.991513i | \(0.458501\pi\) | |||||||
\(108\) | −6.47647 | −0.623199 | ||||||||
\(109\) | −0.671805 | −0.0643472 | −0.0321736 | − | 0.999482i | \(-0.510243\pi\) | ||||
−0.0321736 | + | 0.999482i | \(0.510243\pi\) | |||||||
\(110\) | −10.2661 | −0.978831 | ||||||||
\(111\) | −1.36026 | −0.129110 | ||||||||
\(112\) | 4.61687 | 0.436253 | ||||||||
\(113\) | −8.72825 | −0.821085 | −0.410543 | − | 0.911841i | \(-0.634661\pi\) | ||||
−0.410543 | + | 0.911841i | \(0.634661\pi\) | |||||||
\(114\) | 2.17005 | 0.203244 | ||||||||
\(115\) | 1.46385 | 0.136504 | ||||||||
\(116\) | −31.3408 | −2.90992 | ||||||||
\(117\) | −3.06963 | −0.283788 | ||||||||
\(118\) | 12.8228 | 1.18043 | ||||||||
\(119\) | 7.14266 | 0.654767 | ||||||||
\(120\) | 1.20796 | 0.110271 | ||||||||
\(121\) | 7.44671 | 0.676973 | ||||||||
\(122\) | 13.3842 | 1.21175 | ||||||||
\(123\) | 0.231734 | 0.0208948 | ||||||||
\(124\) | 15.7460 | 1.41403 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 13.6090 | 1.21238 | ||||||||
\(127\) | −4.55006 | −0.403752 | −0.201876 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201876 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(128\) | 20.7406 | 1.83323 | ||||||||
\(129\) | −1.06451 | −0.0937246 | ||||||||
\(130\) | 2.51878 | 0.220912 | ||||||||
\(131\) | −9.12736 | −0.797461 | −0.398731 | − | 0.917068i | \(-0.630549\pi\) | ||||
−0.398731 | + | 0.917068i | \(0.630549\pi\) | |||||||
\(132\) | −4.70425 | −0.409452 | ||||||||
\(133\) | −6.01586 | −0.521641 | ||||||||
\(134\) | 18.9339 | 1.63564 | ||||||||
\(135\) | 1.74411 | 0.150109 | ||||||||
\(136\) | −14.9660 | −1.28332 | ||||||||
\(137\) | 16.8521 | 1.43978 | 0.719888 | − | 0.694090i | \(-0.244193\pi\) | ||||
0.719888 | + | 0.694090i | \(0.244193\pi\) | |||||||
\(138\) | 1.03207 | 0.0878552 | ||||||||
\(139\) | 3.20205 | 0.271594 | 0.135797 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135797 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(140\) | −7.25777 | −0.613394 | ||||||||
\(141\) | −3.19210 | −0.268823 | ||||||||
\(142\) | −24.0509 | −2.01831 | ||||||||
\(143\) | −4.52591 | −0.378475 | ||||||||
\(144\) | −6.88093 | −0.573411 | ||||||||
\(145\) | 8.44007 | 0.700910 | ||||||||
\(146\) | −5.91183 | −0.489267 | ||||||||
\(147\) | −0.937938 | −0.0773598 | ||||||||
\(148\) | −17.1245 | −1.40763 | ||||||||
\(149\) | 14.6448 | 1.19975 | 0.599874 | − | 0.800094i | \(-0.295217\pi\) | ||||
0.599874 | + | 0.800094i | \(0.295217\pi\) | |||||||
\(150\) | −0.705037 | −0.0575660 | ||||||||
\(151\) | −17.8411 | −1.45189 | −0.725943 | − | 0.687755i | \(-0.758596\pi\) | ||||
−0.725943 | + | 0.687755i | \(0.758596\pi\) | |||||||
\(152\) | 12.6050 | 1.02240 | ||||||||
\(153\) | −10.6454 | −0.860626 | ||||||||
\(154\) | 20.0652 | 1.61690 | ||||||||
\(155\) | −4.24040 | −0.340597 | ||||||||
\(156\) | 1.15419 | 0.0924091 | ||||||||
\(157\) | 15.4767 | 1.23518 | 0.617588 | − | 0.786502i | \(-0.288110\pi\) | ||||
0.617588 | + | 0.786502i | \(0.288110\pi\) | |||||||
\(158\) | 27.8540 | 2.21595 | ||||||||
\(159\) | −2.67542 | −0.212174 | ||||||||
\(160\) | −2.54445 | −0.201156 | ||||||||
\(161\) | −2.86111 | −0.225487 | ||||||||
\(162\) | −19.6588 | −1.54454 | ||||||||
\(163\) | −2.39177 | −0.187338 | −0.0936689 | − | 0.995603i | \(-0.529860\pi\) | ||||
−0.0936689 | + | 0.995603i | \(0.529860\pi\) | |||||||
\(164\) | 2.91733 | 0.227805 | ||||||||
\(165\) | 1.26685 | 0.0986245 | ||||||||
\(166\) | −29.9569 | −2.32511 | ||||||||
\(167\) | 0.644864 | 0.0499011 | 0.0249505 | − | 0.999689i | \(-0.492057\pi\) | ||||
0.0249505 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(168\) | −2.36098 | −0.182154 | ||||||||
\(169\) | −11.8896 | −0.914582 | ||||||||
\(170\) | 8.73503 | 0.669947 | ||||||||
\(171\) | 8.96598 | 0.685645 | ||||||||
\(172\) | −13.4012 | −1.02183 | ||||||||
\(173\) | −19.2152 | −1.46091 | −0.730453 | − | 0.682963i | \(-0.760691\pi\) | ||||
−0.730453 | + | 0.682963i | \(0.760691\pi\) | |||||||
\(174\) | 5.95056 | 0.451111 | ||||||||
\(175\) | 1.95452 | 0.147748 | ||||||||
\(176\) | −10.1453 | −0.764734 | ||||||||
\(177\) | −1.58236 | −0.118937 | ||||||||
\(178\) | 2.39026 | 0.179157 | ||||||||
\(179\) | −14.9898 | −1.12039 | −0.560193 | − | 0.828362i | \(-0.689273\pi\) | ||||
−0.560193 | + | 0.828362i | \(0.689273\pi\) | |||||||
\(180\) | 10.8169 | 0.806245 | ||||||||
\(181\) | 23.1716 | 1.72233 | 0.861167 | − | 0.508322i | \(-0.169734\pi\) | ||||
0.861167 | + | 0.508322i | \(0.169734\pi\) | |||||||
\(182\) | −4.92301 | −0.364918 | ||||||||
\(183\) | −1.65164 | −0.122093 | ||||||||
\(184\) | 5.99488 | 0.441948 | ||||||||
\(185\) | 4.61163 | 0.339054 | ||||||||
\(186\) | −2.98964 | −0.219211 | ||||||||
\(187\) | −15.6957 | −1.14778 | ||||||||
\(188\) | −40.1858 | −2.93085 | ||||||||
\(189\) | −3.40891 | −0.247962 | ||||||||
\(190\) | −7.35702 | −0.533735 | ||||||||
\(191\) | 0.390024 | 0.0282211 | 0.0141106 | − | 0.999900i | \(-0.495508\pi\) | ||||
0.0141106 | + | 0.999900i | \(0.495508\pi\) | |||||||
\(192\) | −3.18742 | −0.230032 | ||||||||
\(193\) | 9.91428 | 0.713645 | 0.356823 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356823 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(194\) | −14.2640 | −1.02410 | ||||||||
\(195\) | −0.310823 | −0.0222585 | ||||||||
\(196\) | −11.8078 | −0.843417 | ||||||||
\(197\) | −1.01097 | −0.0720286 | −0.0360143 | − | 0.999351i | \(-0.511466\pi\) | ||||
−0.0360143 | + | 0.999351i | \(0.511466\pi\) | |||||||
\(198\) | −29.9050 | −2.12526 | ||||||||
\(199\) | −13.3504 | −0.946384 | −0.473192 | − | 0.880959i | \(-0.656898\pi\) | ||||
−0.473192 | + | 0.880959i | \(0.656898\pi\) | |||||||
\(200\) | −4.09529 | −0.289581 | ||||||||
\(201\) | −2.33649 | −0.164803 | ||||||||
\(202\) | −14.7207 | −1.03575 | ||||||||
\(203\) | −16.4963 | −1.15781 | ||||||||
\(204\) | 4.00268 | 0.280244 | ||||||||
\(205\) | −0.785638 | −0.0548713 | ||||||||
\(206\) | −35.8935 | −2.50082 | ||||||||
\(207\) | 4.26418 | 0.296381 | ||||||||
\(208\) | 2.48916 | 0.172592 | ||||||||
\(209\) | 13.2196 | 0.914416 | ||||||||
\(210\) | 1.37801 | 0.0950917 | ||||||||
\(211\) | −25.4818 | −1.75424 | −0.877118 | − | 0.480274i | \(-0.840537\pi\) | ||||
−0.877118 | + | 0.480274i | \(0.840537\pi\) | |||||||
\(212\) | −33.6812 | −2.31323 | ||||||||
\(213\) | 2.96793 | 0.203360 | ||||||||
\(214\) | −6.42872 | −0.439459 | ||||||||
\(215\) | 3.60895 | 0.246129 | ||||||||
\(216\) | 7.14266 | 0.485997 | ||||||||
\(217\) | 8.28795 | 0.562623 | ||||||||
\(218\) | 1.60579 | 0.108758 | ||||||||
\(219\) | 0.729533 | 0.0492972 | ||||||||
\(220\) | 15.9486 | 1.07525 | ||||||||
\(221\) | 3.85094 | 0.259042 | ||||||||
\(222\) | 3.25137 | 0.218218 | ||||||||
\(223\) | 20.3456 | 1.36244 | 0.681222 | − | 0.732076i | \(-0.261449\pi\) | ||||
0.681222 | + | 0.732076i | \(0.261449\pi\) | |||||||
\(224\) | 4.97317 | 0.332284 | ||||||||
\(225\) | −2.91300 | −0.194200 | ||||||||
\(226\) | 20.8628 | 1.38777 | ||||||||
\(227\) | 16.0605 | 1.06597 | 0.532986 | − | 0.846124i | \(-0.321070\pi\) | ||||
0.532986 | + | 0.846124i | \(0.321070\pi\) | |||||||
\(228\) | −3.37123 | −0.223265 | ||||||||
\(229\) | 15.2661 | 1.00881 | 0.504405 | − | 0.863467i | \(-0.331712\pi\) | ||||
0.504405 | + | 0.863467i | \(0.331712\pi\) | |||||||
\(230\) | −3.49897 | −0.230715 | ||||||||
\(231\) | −2.47609 | −0.162915 | ||||||||
\(232\) | 34.5646 | 2.26928 | ||||||||
\(233\) | 18.5117 | 1.21274 | 0.606371 | − | 0.795182i | \(-0.292625\pi\) | ||||
0.606371 | + | 0.795182i | \(0.292625\pi\) | |||||||
\(234\) | 7.33721 | 0.479648 | ||||||||
\(235\) | 10.8220 | 0.705952 | ||||||||
\(236\) | −19.9205 | −1.29671 | ||||||||
\(237\) | −3.43725 | −0.223273 | ||||||||
\(238\) | −17.0728 | −1.10667 | ||||||||
\(239\) | −27.6511 | −1.78860 | −0.894300 | − | 0.447468i | \(-0.852326\pi\) | ||||
−0.894300 | + | 0.447468i | \(0.852326\pi\) | |||||||
\(240\) | −0.696746 | −0.0449748 | ||||||||
\(241\) | 27.2269 | 1.75384 | 0.876920 | − | 0.480636i | \(-0.159594\pi\) | ||||
0.876920 | + | 0.480636i | \(0.159594\pi\) | |||||||
\(242\) | −17.7995 | −1.14420 | ||||||||
\(243\) | 7.65828 | 0.491279 | ||||||||
\(244\) | −20.7928 | −1.33112 | ||||||||
\(245\) | 3.17985 | 0.203153 | ||||||||
\(246\) | −0.553904 | −0.0353156 | ||||||||
\(247\) | −3.24342 | −0.206374 | ||||||||
\(248\) | −17.3657 | −1.10272 | ||||||||
\(249\) | 3.69675 | 0.234272 | ||||||||
\(250\) | 2.39026 | 0.151173 | ||||||||
\(251\) | 12.9645 | 0.818310 | 0.409155 | − | 0.912465i | \(-0.365824\pi\) | ||||
0.409155 | + | 0.912465i | \(0.365824\pi\) | |||||||
\(252\) | −21.1419 | −1.33181 | ||||||||
\(253\) | 6.28716 | 0.395270 | ||||||||
\(254\) | 10.8758 | 0.682409 | ||||||||
\(255\) | −1.07792 | −0.0675021 | ||||||||
\(256\) | −27.9631 | −1.74769 | ||||||||
\(257\) | 18.9552 | 1.18240 | 0.591198 | − | 0.806527i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806527i | \(0.298655\pi\) | |||||||
\(258\) | 2.54445 | 0.158410 | ||||||||
\(259\) | −9.01353 | −0.560073 | ||||||||
\(260\) | −3.91300 | −0.242674 | ||||||||
\(261\) | 24.5859 | 1.52183 | ||||||||
\(262\) | 21.8167 | 1.34784 | ||||||||
\(263\) | −16.4109 | −1.01194 | −0.505971 | − | 0.862551i | \(-0.668866\pi\) | ||||
−0.505971 | + | 0.862551i | \(0.668866\pi\) | |||||||
\(264\) | 5.18814 | 0.319308 | ||||||||
\(265\) | 9.07035 | 0.557187 | ||||||||
\(266\) | 14.3795 | 0.881661 | ||||||||
\(267\) | −0.294963 | −0.0180514 | ||||||||
\(268\) | −29.4143 | −1.79677 | ||||||||
\(269\) | 28.9069 | 1.76248 | 0.881242 | − | 0.472664i | \(-0.156708\pi\) | ||||
0.881242 | + | 0.472664i | \(0.156708\pi\) | |||||||
\(270\) | −4.16888 | −0.253710 | ||||||||
\(271\) | 6.39573 | 0.388513 | 0.194256 | − | 0.980951i | \(-0.437771\pi\) | ||||
0.194256 | + | 0.980951i | \(0.437771\pi\) | |||||||
\(272\) | 8.63231 | 0.523411 | ||||||||
\(273\) | 0.607510 | 0.0367682 | ||||||||
\(274\) | −40.2810 | −2.43346 | ||||||||
\(275\) | −4.29496 | −0.258996 | ||||||||
\(276\) | −1.60334 | −0.0965098 | ||||||||
\(277\) | −2.90811 | −0.174731 | −0.0873656 | − | 0.996176i | \(-0.527845\pi\) | ||||
−0.0873656 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(278\) | −7.65371 | −0.459039 | ||||||||
\(279\) | −12.3523 | −0.739512 | ||||||||
\(280\) | 8.00433 | 0.478350 | ||||||||
\(281\) | −6.27691 | −0.374449 | −0.187225 | − | 0.982317i | \(-0.559949\pi\) | ||||
−0.187225 | + | 0.982317i | \(0.559949\pi\) | |||||||
\(282\) | 7.62994 | 0.454356 | ||||||||
\(283\) | 11.8814 | 0.706277 | 0.353139 | − | 0.935571i | \(-0.385114\pi\) | ||||
0.353139 | + | 0.935571i | \(0.385114\pi\) | |||||||
\(284\) | 37.3637 | 2.21713 | ||||||||
\(285\) | 0.907873 | 0.0537777 | ||||||||
\(286\) | 10.8181 | 0.639686 | ||||||||
\(287\) | 1.53554 | 0.0906403 | ||||||||
\(288\) | −7.41196 | −0.436754 | ||||||||
\(289\) | −3.64512 | −0.214419 | ||||||||
\(290\) | −20.1739 | −1.18465 | ||||||||
\(291\) | 1.76021 | 0.103185 | ||||||||
\(292\) | 9.18419 | 0.537464 | ||||||||
\(293\) | −15.4163 | −0.900630 | −0.450315 | − | 0.892870i | \(-0.648688\pi\) | ||||
−0.450315 | + | 0.892870i | \(0.648688\pi\) | |||||||
\(294\) | 2.24191 | 0.130751 | ||||||||
\(295\) | 5.36459 | 0.312339 | ||||||||
\(296\) | 18.8860 | 1.09773 | ||||||||
\(297\) | 7.49091 | 0.434667 | ||||||||
\(298\) | −35.0048 | −2.02777 | ||||||||
\(299\) | −1.54256 | −0.0892084 | ||||||||
\(300\) | 1.09529 | 0.0632368 | ||||||||
\(301\) | −7.05377 | −0.406573 | ||||||||
\(302\) | 42.6447 | 2.45393 | ||||||||
\(303\) | 1.81657 | 0.104359 | ||||||||
\(304\) | −7.27051 | −0.416992 | ||||||||
\(305\) | 5.59950 | 0.320626 | ||||||||
\(306\) | 25.4451 | 1.45460 | ||||||||
\(307\) | −13.1695 | −0.751623 | −0.375811 | − | 0.926696i | \(-0.622636\pi\) | ||||
−0.375811 | + | 0.926696i | \(0.622636\pi\) | |||||||
\(308\) | −31.1719 | −1.77618 | ||||||||
\(309\) | 4.42933 | 0.251976 | ||||||||
\(310\) | 10.1356 | 0.575666 | ||||||||
\(311\) | 13.6116 | 0.771841 | 0.385920 | − | 0.922532i | \(-0.373884\pi\) | ||||
0.385920 | + | 0.922532i | \(0.373884\pi\) | |||||||
\(312\) | −1.27291 | −0.0720645 | ||||||||
\(313\) | −20.0023 | −1.13059 | −0.565297 | − | 0.824887i | \(-0.691239\pi\) | ||||
−0.565297 | + | 0.824887i | \(0.691239\pi\) | |||||||
\(314\) | −36.9933 | −2.08765 | ||||||||
\(315\) | 5.69351 | 0.320793 | ||||||||
\(316\) | −43.2720 | −2.43424 | ||||||||
\(317\) | 17.9215 | 1.00657 | 0.503286 | − | 0.864120i | \(-0.332124\pi\) | ||||
0.503286 | + | 0.864120i | \(0.332124\pi\) | |||||||
\(318\) | 6.39494 | 0.358610 | ||||||||
\(319\) | 36.2498 | 2.02960 | ||||||||
\(320\) | 10.8062 | 0.604084 | ||||||||
\(321\) | 0.793319 | 0.0442787 | ||||||||
\(322\) | 6.83880 | 0.381111 | ||||||||
\(323\) | −11.2481 | −0.625859 | ||||||||
\(324\) | 30.5404 | 1.69669 | ||||||||
\(325\) | 1.05377 | 0.0584527 | ||||||||
\(326\) | 5.71694 | 0.316632 | ||||||||
\(327\) | −0.198158 | −0.0109581 | ||||||||
\(328\) | −3.21742 | −0.177652 | ||||||||
\(329\) | −21.1519 | −1.16614 | ||||||||
\(330\) | −3.02811 | −0.166692 | ||||||||
\(331\) | −20.2646 | −1.11384 | −0.556920 | − | 0.830566i | \(-0.688017\pi\) | ||||
−0.556920 | + | 0.830566i | \(0.688017\pi\) | |||||||
\(332\) | 46.5388 | 2.55415 | ||||||||
\(333\) | 13.4337 | 0.736160 | ||||||||
\(334\) | −1.54139 | −0.0843411 | ||||||||
\(335\) | 7.92129 | 0.432786 | ||||||||
\(336\) | 1.36180 | 0.0742925 | ||||||||
\(337\) | −16.1392 | −0.879158 | −0.439579 | − | 0.898204i | \(-0.644872\pi\) | ||||
−0.439579 | + | 0.898204i | \(0.644872\pi\) | |||||||
\(338\) | 28.4191 | 1.54580 | ||||||||
\(339\) | −2.57451 | −0.139828 | ||||||||
\(340\) | −13.5701 | −0.735942 | ||||||||
\(341\) | −18.2124 | −0.986255 | ||||||||
\(342\) | −21.4310 | −1.15886 | ||||||||
\(343\) | −19.8967 | −1.07432 | ||||||||
\(344\) | 14.7797 | 0.796869 | ||||||||
\(345\) | 0.431780 | 0.0232463 | ||||||||
\(346\) | 45.9293 | 2.46918 | ||||||||
\(347\) | 14.3396 | 0.769789 | 0.384895 | − | 0.922961i | \(-0.374238\pi\) | ||||
0.384895 | + | 0.922961i | \(0.374238\pi\) | |||||||
\(348\) | −9.24436 | −0.495550 | ||||||||
\(349\) | −31.8954 | −1.70732 | −0.853660 | − | 0.520830i | \(-0.825622\pi\) | ||||
−0.853660 | + | 0.520830i | \(0.825622\pi\) | |||||||
\(350\) | −4.67180 | −0.249718 | ||||||||
\(351\) | −1.83790 | −0.0980997 | ||||||||
\(352\) | −10.9283 | −0.582480 | ||||||||
\(353\) | 2.46050 | 0.130959 | 0.0654796 | − | 0.997854i | \(-0.479142\pi\) | ||||
0.0654796 | + | 0.997854i | \(0.479142\pi\) | |||||||
\(354\) | 3.78224 | 0.201024 | ||||||||
\(355\) | −10.0621 | −0.534039 | ||||||||
\(356\) | −3.71333 | −0.196806 | ||||||||
\(357\) | 2.10682 | 0.111505 | ||||||||
\(358\) | 35.8294 | 1.89364 | ||||||||
\(359\) | 4.79276 | 0.252952 | 0.126476 | − | 0.991970i | \(-0.459633\pi\) | ||||
0.126476 | + | 0.991970i | \(0.459633\pi\) | |||||||
\(360\) | −11.9296 | −0.628744 | ||||||||
\(361\) | −9.52640 | −0.501389 | ||||||||
\(362\) | −55.3862 | −2.91103 | ||||||||
\(363\) | 2.19650 | 0.115286 | ||||||||
\(364\) | 7.64803 | 0.400866 | ||||||||
\(365\) | −2.47330 | −0.129459 | ||||||||
\(366\) | 3.94785 | 0.206358 | ||||||||
\(367\) | −23.3647 | −1.21963 | −0.609813 | − | 0.792545i | \(-0.708755\pi\) | ||||
−0.609813 | + | 0.792545i | \(0.708755\pi\) | |||||||
\(368\) | −3.45782 | −0.180251 | ||||||||
\(369\) | −2.28856 | −0.119138 | ||||||||
\(370\) | −11.0230 | −0.573058 | ||||||||
\(371\) | −17.7282 | −0.920402 | ||||||||
\(372\) | 4.64449 | 0.240805 | ||||||||
\(373\) | 23.7500 | 1.22973 | 0.614863 | − | 0.788634i | \(-0.289211\pi\) | ||||
0.614863 | + | 0.788634i | \(0.289211\pi\) | |||||||
\(374\) | 37.5166 | 1.93994 | ||||||||
\(375\) | −0.294963 | −0.0152318 | ||||||||
\(376\) | 44.3194 | 2.28560 | ||||||||
\(377\) | −8.89390 | −0.458059 | ||||||||
\(378\) | 8.14816 | 0.419096 | ||||||||
\(379\) | −27.7001 | −1.42286 | −0.711429 | − | 0.702758i | \(-0.751952\pi\) | ||||
−0.711429 | + | 0.702758i | \(0.751952\pi\) | |||||||
\(380\) | 11.4293 | 0.586312 | ||||||||
\(381\) | −1.34210 | −0.0687578 | ||||||||
\(382\) | −0.932257 | −0.0476984 | ||||||||
\(383\) | 6.03526 | 0.308388 | 0.154194 | − | 0.988041i | \(-0.450722\pi\) | ||||
0.154194 | + | 0.988041i | \(0.450722\pi\) | |||||||
\(384\) | 6.11772 | 0.312194 | ||||||||
\(385\) | 8.39459 | 0.427828 | ||||||||
\(386\) | −23.6977 | −1.20618 | ||||||||
\(387\) | 10.5129 | 0.534399 | ||||||||
\(388\) | 22.1595 | 1.12498 | ||||||||
\(389\) | 8.53031 | 0.432504 | 0.216252 | − | 0.976338i | \(-0.430617\pi\) | ||||
0.216252 | + | 0.976338i | \(0.430617\pi\) | |||||||
\(390\) | 0.742948 | 0.0376206 | ||||||||
\(391\) | −5.34952 | −0.270537 | ||||||||
\(392\) | 13.0224 | 0.657732 | ||||||||
\(393\) | −2.69223 | −0.135805 | ||||||||
\(394\) | 2.41648 | 0.121740 | ||||||||
\(395\) | 11.6532 | 0.586334 | ||||||||
\(396\) | 46.4582 | 2.33461 | ||||||||
\(397\) | −14.6163 | −0.733572 | −0.366786 | − | 0.930305i | \(-0.619542\pi\) | ||||
−0.366786 | + | 0.930305i | \(0.619542\pi\) | |||||||
\(398\) | 31.9109 | 1.59955 | ||||||||
\(399\) | −1.77446 | −0.0888339 | ||||||||
\(400\) | 2.36215 | 0.118107 | ||||||||
\(401\) | 17.2987 | 0.863858 | 0.431929 | − | 0.901908i | \(-0.357833\pi\) | ||||
0.431929 | + | 0.901908i | \(0.357833\pi\) | |||||||
\(402\) | 5.58480 | 0.278545 | ||||||||
\(403\) | 4.46841 | 0.222587 | ||||||||
\(404\) | 22.8690 | 1.13778 | ||||||||
\(405\) | −8.22454 | −0.408681 | ||||||||
\(406\) | 39.4304 | 1.95690 | ||||||||
\(407\) | 19.8068 | 0.981786 | ||||||||
\(408\) | −4.41441 | −0.218546 | ||||||||
\(409\) | −2.78264 | −0.137592 | −0.0687962 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687962 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(410\) | 1.87788 | 0.0927417 | ||||||||
\(411\) | 4.97076 | 0.245189 | ||||||||
\(412\) | 55.7615 | 2.74717 | ||||||||
\(413\) | −10.4852 | −0.515943 | ||||||||
\(414\) | −10.1925 | −0.500933 | ||||||||
\(415\) | −12.5329 | −0.615217 | ||||||||
\(416\) | 2.68126 | 0.131460 | ||||||||
\(417\) | 0.944485 | 0.0462516 | ||||||||
\(418\) | −31.5981 | −1.54552 | ||||||||
\(419\) | −4.20691 | −0.205521 | −0.102761 | − | 0.994706i | \(-0.532768\pi\) | ||||
−0.102761 | + | 0.994706i | \(0.532768\pi\) | |||||||
\(420\) | −2.14077 | −0.104459 | ||||||||
\(421\) | 19.0766 | 0.929737 | 0.464869 | − | 0.885380i | \(-0.346102\pi\) | ||||
0.464869 | + | 0.885380i | \(0.346102\pi\) | |||||||
\(422\) | 60.9079 | 2.96495 | ||||||||
\(423\) | 31.5246 | 1.53278 | ||||||||
\(424\) | 37.1458 | 1.80396 | ||||||||
\(425\) | 3.65443 | 0.177266 | ||||||||
\(426\) | −7.09413 | −0.343712 | ||||||||
\(427\) | −10.9443 | −0.529633 | ||||||||
\(428\) | 9.98720 | 0.482749 | ||||||||
\(429\) | −1.33497 | −0.0644532 | ||||||||
\(430\) | −8.62632 | −0.415998 | ||||||||
\(431\) | −4.11651 | −0.198285 | −0.0991427 | − | 0.995073i | \(-0.531610\pi\) | ||||
−0.0991427 | + | 0.995073i | \(0.531610\pi\) | |||||||
\(432\) | −4.11986 | −0.198217 | ||||||||
\(433\) | −34.4248 | −1.65435 | −0.827176 | − | 0.561943i | \(-0.810054\pi\) | ||||
−0.827176 | + | 0.561943i | \(0.810054\pi\) | |||||||
\(434\) | −19.8103 | −0.950926 | ||||||||
\(435\) | 2.48951 | 0.119363 | ||||||||
\(436\) | −2.49463 | −0.119471 | ||||||||
\(437\) | 4.50560 | 0.215532 | ||||||||
\(438\) | −1.74377 | −0.0833206 | ||||||||
\(439\) | 15.1883 | 0.724896 | 0.362448 | − | 0.932004i | \(-0.381941\pi\) | ||||
0.362448 | + | 0.932004i | \(0.381941\pi\) | |||||||
\(440\) | −17.5891 | −0.838529 | ||||||||
\(441\) | 9.26290 | 0.441090 | ||||||||
\(442\) | −9.20472 | −0.437824 | ||||||||
\(443\) | 2.14752 | 0.102032 | 0.0510159 | − | 0.998698i | \(-0.483754\pi\) | ||||
0.0510159 | + | 0.998698i | \(0.483754\pi\) | |||||||
\(444\) | −5.05109 | −0.239714 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | −48.6313 | −2.30276 | ||||||||
\(447\) | 4.31967 | 0.204313 | ||||||||
\(448\) | −21.1209 | −0.997868 | ||||||||
\(449\) | 32.5132 | 1.53439 | 0.767197 | − | 0.641411i | \(-0.221651\pi\) | ||||
0.767197 | + | 0.641411i | \(0.221651\pi\) | |||||||
\(450\) | 6.96281 | 0.328230 | ||||||||
\(451\) | −3.37429 | −0.158889 | ||||||||
\(452\) | −32.4109 | −1.52448 | ||||||||
\(453\) | −5.26245 | −0.247252 | ||||||||
\(454\) | −38.3887 | −1.80167 | ||||||||
\(455\) | −2.05962 | −0.0965563 | ||||||||
\(456\) | 3.71801 | 0.174112 | ||||||||
\(457\) | −15.9654 | −0.746831 | −0.373415 | − | 0.927664i | \(-0.621813\pi\) | ||||
−0.373415 | + | 0.927664i | \(0.621813\pi\) | |||||||
\(458\) | −36.4898 | −1.70506 | ||||||||
\(459\) | −6.37375 | −0.297501 | ||||||||
\(460\) | 5.43574 | 0.253443 | ||||||||
\(461\) | −0.406983 | −0.0189551 | −0.00947754 | − | 0.999955i | \(-0.503017\pi\) | ||||
−0.00947754 | + | 0.999955i | \(0.503017\pi\) | |||||||
\(462\) | 5.91850 | 0.275353 | ||||||||
\(463\) | 28.6219 | 1.33017 | 0.665087 | − | 0.746766i | \(-0.268395\pi\) | ||||
0.665087 | + | 0.746766i | \(0.268395\pi\) | |||||||
\(464\) | −19.9367 | −0.925538 | ||||||||
\(465\) | −1.25076 | −0.0580027 | ||||||||
\(466\) | −44.2477 | −2.04974 | ||||||||
\(467\) | −38.5772 | −1.78514 | −0.892571 | − | 0.450907i | \(-0.851100\pi\) | ||||
−0.892571 | + | 0.450907i | \(0.851100\pi\) | |||||||
\(468\) | −11.3985 | −0.526898 | ||||||||
\(469\) | −15.4823 | −0.714907 | ||||||||
\(470\) | −25.8674 | −1.19318 | ||||||||
\(471\) | 4.56505 | 0.210347 | ||||||||
\(472\) | 21.9696 | 1.01123 | ||||||||
\(473\) | 15.5003 | 0.712705 | ||||||||
\(474\) | 8.21591 | 0.377369 | ||||||||
\(475\) | −3.07792 | −0.141225 | ||||||||
\(476\) | 26.5230 | 1.21568 | ||||||||
\(477\) | 26.4219 | 1.20978 | ||||||||
\(478\) | 66.0932 | 3.02303 | ||||||||
\(479\) | −14.1350 | −0.645843 | −0.322922 | − | 0.946426i | \(-0.604665\pi\) | ||||
−0.322922 | + | 0.946426i | \(0.604665\pi\) | |||||||
\(480\) | −0.750517 | −0.0342563 | ||||||||
\(481\) | −4.85960 | −0.221579 | ||||||||
\(482\) | −65.0793 | −2.96428 | ||||||||
\(483\) | −0.843923 | −0.0383998 | ||||||||
\(484\) | 27.6521 | 1.25691 | ||||||||
\(485\) | −5.96756 | −0.270973 | ||||||||
\(486\) | −18.3053 | −0.830343 | ||||||||
\(487\) | −12.5869 | −0.570369 | −0.285184 | − | 0.958473i | \(-0.592055\pi\) | ||||
−0.285184 | + | 0.958473i | \(0.592055\pi\) | |||||||
\(488\) | 22.9316 | 1.03806 | ||||||||
\(489\) | −0.705483 | −0.0319030 | ||||||||
\(490\) | −7.60066 | −0.343363 | ||||||||
\(491\) | −13.4541 | −0.607174 | −0.303587 | − | 0.952804i | \(-0.598184\pi\) | ||||
−0.303587 | + | 0.952804i | \(0.598184\pi\) | |||||||
\(492\) | 0.860504 | 0.0387945 | ||||||||
\(493\) | −30.8437 | −1.38913 | ||||||||
\(494\) | 7.75262 | 0.348807 | ||||||||
\(495\) | −12.5112 | −0.562337 | ||||||||
\(496\) | 10.0165 | 0.449752 | ||||||||
\(497\) | 19.6665 | 0.882163 | ||||||||
\(498\) | −8.83617 | −0.395958 | ||||||||
\(499\) | 17.5343 | 0.784945 | 0.392472 | − | 0.919764i | \(-0.371620\pi\) | ||||
0.392472 | + | 0.919764i | \(0.371620\pi\) | |||||||
\(500\) | −3.71333 | −0.166065 | ||||||||
\(501\) | 0.190211 | 0.00849800 | ||||||||
\(502\) | −30.9884 | −1.38308 | ||||||||
\(503\) | −32.4398 | −1.44642 | −0.723209 | − | 0.690629i | \(-0.757334\pi\) | ||||
−0.723209 | + | 0.690629i | \(0.757334\pi\) | |||||||
\(504\) | 23.3166 | 1.03860 | ||||||||
\(505\) | −6.15863 | −0.274056 | ||||||||
\(506\) | −15.0279 | −0.668073 | ||||||||
\(507\) | −3.50698 | −0.155751 | ||||||||
\(508\) | −16.8959 | −0.749632 | ||||||||
\(509\) | 37.9507 | 1.68214 | 0.841068 | − | 0.540929i | \(-0.181927\pi\) | ||||
0.841068 | + | 0.540929i | \(0.181927\pi\) | |||||||
\(510\) | 2.57651 | 0.114090 | ||||||||
\(511\) | 4.83412 | 0.213849 | ||||||||
\(512\) | 25.3577 | 1.12066 | ||||||||
\(513\) | 5.36825 | 0.237014 | ||||||||
\(514\) | −45.3079 | −1.99845 | ||||||||
\(515\) | −15.0166 | −0.661710 | ||||||||
\(516\) | −3.95286 | −0.174015 | ||||||||
\(517\) | 46.4802 | 2.04420 | ||||||||
\(518\) | 21.5446 | 0.946617 | ||||||||
\(519\) | −5.66778 | −0.248788 | ||||||||
\(520\) | 4.31550 | 0.189247 | ||||||||
\(521\) | −12.0211 | −0.526656 | −0.263328 | − | 0.964706i | \(-0.584820\pi\) | ||||
−0.263328 | + | 0.964706i | \(0.584820\pi\) | |||||||
\(522\) | −58.7666 | −2.57214 | ||||||||
\(523\) | −23.7443 | −1.03826 | −0.519132 | − | 0.854694i | \(-0.673745\pi\) | ||||
−0.519132 | + | 0.854694i | \(0.673745\pi\) | |||||||
\(524\) | −33.8929 | −1.48062 | ||||||||
\(525\) | 0.576511 | 0.0251610 | ||||||||
\(526\) | 39.2264 | 1.71035 | ||||||||
\(527\) | 15.4963 | 0.675028 | ||||||||
\(528\) | −2.99250 | −0.130232 | ||||||||
\(529\) | −20.8572 | −0.906833 | ||||||||
\(530\) | −21.6805 | −0.941740 | ||||||||
\(531\) | 15.6270 | 0.678156 | ||||||||
\(532\) | −22.3389 | −0.968513 | ||||||||
\(533\) | 0.827882 | 0.0358596 | ||||||||
\(534\) | 0.705037 | 0.0305099 | ||||||||
\(535\) | −2.68955 | −0.116280 | ||||||||
\(536\) | 32.4400 | 1.40119 | ||||||||
\(537\) | −4.42142 | −0.190798 | ||||||||
\(538\) | −69.0949 | −2.97889 | ||||||||
\(539\) | 13.6573 | 0.588263 | ||||||||
\(540\) | 6.47647 | 0.278703 | ||||||||
\(541\) | 3.22247 | 0.138545 | 0.0692725 | − | 0.997598i | \(-0.477932\pi\) | ||||
0.0692725 | + | 0.997598i | \(0.477932\pi\) | |||||||
\(542\) | −15.2874 | −0.656651 | ||||||||
\(543\) | 6.83477 | 0.293308 | ||||||||
\(544\) | 9.29851 | 0.398670 | ||||||||
\(545\) | 0.671805 | 0.0287770 | ||||||||
\(546\) | −1.45211 | −0.0621444 | ||||||||
\(547\) | −0.363571 | −0.0155452 | −0.00777259 | − | 0.999970i | \(-0.502474\pi\) | ||||
−0.00777259 | + | 0.999970i | \(0.502474\pi\) | |||||||
\(548\) | 62.5775 | 2.67318 | ||||||||
\(549\) | 16.3113 | 0.696150 | ||||||||
\(550\) | 10.2661 | 0.437746 | ||||||||
\(551\) | 25.9779 | 1.10669 | ||||||||
\(552\) | 1.76827 | 0.0752624 | ||||||||
\(553\) | −22.7763 | −0.968548 | ||||||||
\(554\) | 6.95112 | 0.295325 | ||||||||
\(555\) | 1.36026 | 0.0577398 | ||||||||
\(556\) | 11.8902 | 0.504259 | ||||||||
\(557\) | −10.6808 | −0.452561 | −0.226280 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226280 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(558\) | 29.5251 | 1.24990 | ||||||||
\(559\) | −3.80301 | −0.160850 | ||||||||
\(560\) | −4.61687 | −0.195098 | ||||||||
\(561\) | −4.62964 | −0.195463 | ||||||||
\(562\) | 15.0034 | 0.632882 | ||||||||
\(563\) | −16.3376 | −0.688549 | −0.344274 | − | 0.938869i | \(-0.611875\pi\) | ||||
−0.344274 | + | 0.938869i | \(0.611875\pi\) | |||||||
\(564\) | −11.8533 | −0.499114 | ||||||||
\(565\) | 8.72825 | 0.367200 | ||||||||
\(566\) | −28.3996 | −1.19373 | ||||||||
\(567\) | 16.0750 | 0.675088 | ||||||||
\(568\) | −41.2071 | −1.72901 | ||||||||
\(569\) | −40.6357 | −1.70354 | −0.851768 | − | 0.523919i | \(-0.824470\pi\) | ||||
−0.851768 | + | 0.523919i | \(0.824470\pi\) | |||||||
\(570\) | −2.17005 | −0.0908934 | ||||||||
\(571\) | −38.8677 | −1.62656 | −0.813281 | − | 0.581871i | \(-0.802321\pi\) | ||||
−0.813281 | + | 0.581871i | \(0.802321\pi\) | |||||||
\(572\) | −16.8062 | −0.702702 | ||||||||
\(573\) | 0.115043 | 0.00480597 | ||||||||
\(574\) | −3.67035 | −0.153197 | ||||||||
\(575\) | −1.46385 | −0.0610466 | ||||||||
\(576\) | 31.4784 | 1.31160 | ||||||||
\(577\) | −29.1209 | −1.21232 | −0.606158 | − | 0.795344i | \(-0.707290\pi\) | ||||
−0.606158 | + | 0.795344i | \(0.707290\pi\) | |||||||
\(578\) | 8.71277 | 0.362403 | ||||||||
\(579\) | 2.92434 | 0.121532 | ||||||||
\(580\) | 31.3408 | 1.30135 | ||||||||
\(581\) | 24.4958 | 1.01626 | ||||||||
\(582\) | −4.20735 | −0.174400 | ||||||||
\(583\) | 38.9568 | 1.61343 | ||||||||
\(584\) | −10.1289 | −0.419137 | ||||||||
\(585\) | 3.06963 | 0.126914 | ||||||||
\(586\) | 36.8489 | 1.52221 | ||||||||
\(587\) | −11.3820 | −0.469787 | −0.234894 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234894 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(588\) | −3.48287 | −0.143631 | ||||||||
\(589\) | −13.0516 | −0.537783 | ||||||||
\(590\) | −12.8228 | −0.527905 | ||||||||
\(591\) | −0.298198 | −0.0122662 | ||||||||
\(592\) | −10.8934 | −0.447714 | ||||||||
\(593\) | −5.10274 | −0.209544 | −0.104772 | − | 0.994496i | \(-0.533411\pi\) | ||||
−0.104772 | + | 0.994496i | \(0.533411\pi\) | |||||||
\(594\) | −17.9052 | −0.734659 | ||||||||
\(595\) | −7.14266 | −0.292821 | ||||||||
\(596\) | 54.3809 | 2.22753 | ||||||||
\(597\) | −3.93787 | −0.161166 | ||||||||
\(598\) | 3.68711 | 0.150777 | ||||||||
\(599\) | 22.6299 | 0.924631 | 0.462316 | − | 0.886715i | \(-0.347019\pi\) | ||||
0.462316 | + | 0.886715i | \(0.347019\pi\) | |||||||
\(600\) | −1.20796 | −0.0493148 | ||||||||
\(601\) | 27.2940 | 1.11335 | 0.556673 | − | 0.830732i | \(-0.312078\pi\) | ||||
0.556673 | + | 0.830732i | \(0.312078\pi\) | |||||||
\(602\) | 16.8603 | 0.687176 | ||||||||
\(603\) | 23.0747 | 0.939674 | ||||||||
\(604\) | −66.2497 | −2.69566 | ||||||||
\(605\) | −7.44671 | −0.302752 | ||||||||
\(606\) | −4.34207 | −0.176384 | ||||||||
\(607\) | 34.1969 | 1.38801 | 0.694004 | − | 0.719971i | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(608\) | −7.83161 | −0.317614 | ||||||||
\(609\) | −4.86579 | −0.197172 | ||||||||
\(610\) | −13.3842 | −0.541912 | ||||||||
\(611\) | −11.4039 | −0.461354 | ||||||||
\(612\) | −39.5297 | −1.59789 | ||||||||
\(613\) | 24.2886 | 0.981009 | 0.490504 | − | 0.871439i | \(-0.336813\pi\) | ||||
0.490504 | + | 0.871439i | \(0.336813\pi\) | |||||||
\(614\) | 31.4785 | 1.27037 | ||||||||
\(615\) | −0.231734 | −0.00934442 | ||||||||
\(616\) | 34.3783 | 1.38514 | ||||||||
\(617\) | 31.9292 | 1.28542 | 0.642711 | − | 0.766109i | \(-0.277810\pi\) | ||||
0.642711 | + | 0.766109i | \(0.277810\pi\) | |||||||
\(618\) | −10.5872 | −0.425882 | ||||||||
\(619\) | −29.1111 | −1.17007 | −0.585037 | − | 0.811007i | \(-0.698920\pi\) | ||||
−0.585037 | + | 0.811007i | \(0.698920\pi\) | |||||||
\(620\) | −15.7460 | −0.632375 | ||||||||
\(621\) | 2.55311 | 0.102453 | ||||||||
\(622\) | −32.5351 | −1.30454 | ||||||||
\(623\) | −1.95452 | −0.0783062 | ||||||||
\(624\) | 0.734211 | 0.0293920 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 47.8106 | 1.91089 | ||||||||
\(627\) | 3.89928 | 0.155722 | ||||||||
\(628\) | 57.4701 | 2.29331 | ||||||||
\(629\) | −16.8529 | −0.671969 | ||||||||
\(630\) | −13.6090 | −0.542194 | ||||||||
\(631\) | 26.7634 | 1.06543 | 0.532717 | − | 0.846293i | \(-0.321171\pi\) | ||||
0.532717 | + | 0.846293i | \(0.321171\pi\) | |||||||
\(632\) | 47.7231 | 1.89832 | ||||||||
\(633\) | −7.51617 | −0.298741 | ||||||||
\(634\) | −42.8370 | −1.70128 | ||||||||
\(635\) | 4.55006 | 0.180564 | ||||||||
\(636\) | −9.93470 | −0.393937 | ||||||||
\(637\) | −3.35084 | −0.132765 | ||||||||
\(638\) | −86.6463 | −3.43036 | ||||||||
\(639\) | −29.3108 | −1.15952 | ||||||||
\(640\) | −20.7406 | −0.819846 | ||||||||
\(641\) | −16.4357 | −0.649173 | −0.324586 | − | 0.945856i | \(-0.605225\pi\) | ||||
−0.324586 | + | 0.945856i | \(0.605225\pi\) | |||||||
\(642\) | −1.89624 | −0.0748384 | ||||||||
\(643\) | −28.2642 | −1.11463 | −0.557316 | − | 0.830300i | \(-0.688169\pi\) | ||||
−0.557316 | + | 0.830300i | \(0.688169\pi\) | |||||||
\(644\) | −10.6243 | −0.418654 | ||||||||
\(645\) | 1.06451 | 0.0419149 | ||||||||
\(646\) | 26.8858 | 1.05781 | ||||||||
\(647\) | 16.9725 | 0.667258 | 0.333629 | − | 0.942704i | \(-0.391727\pi\) | ||||
0.333629 | + | 0.942704i | \(0.391727\pi\) | |||||||
\(648\) | −33.6819 | −1.32315 | ||||||||
\(649\) | 23.0407 | 0.904428 | ||||||||
\(650\) | −2.51878 | −0.0987948 | ||||||||
\(651\) | 2.44464 | 0.0958129 | ||||||||
\(652\) | −8.88142 | −0.347823 | ||||||||
\(653\) | −39.2631 | −1.53648 | −0.768242 | − | 0.640160i | \(-0.778868\pi\) | ||||
−0.768242 | + | 0.640160i | \(0.778868\pi\) | |||||||
\(654\) | 0.473647 | 0.0185211 | ||||||||
\(655\) | 9.12736 | 0.356635 | ||||||||
\(656\) | 1.85579 | 0.0724566 | ||||||||
\(657\) | −7.20472 | −0.281083 | ||||||||
\(658\) | 50.5584 | 1.97097 | ||||||||
\(659\) | 3.77282 | 0.146968 | 0.0734841 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734841 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(660\) | 4.70425 | 0.183113 | ||||||||
\(661\) | 1.17732 | 0.0457923 | 0.0228962 | − | 0.999738i | \(-0.492711\pi\) | ||||
0.0228962 | + | 0.999738i | \(0.492711\pi\) | |||||||
\(662\) | 48.4375 | 1.88258 | ||||||||
\(663\) | 1.13588 | 0.0441140 | ||||||||
\(664\) | −51.3260 | −1.99183 | ||||||||
\(665\) | 6.01586 | 0.233285 | ||||||||
\(666\) | −32.1099 | −1.24423 | ||||||||
\(667\) | 12.3550 | 0.478386 | ||||||||
\(668\) | 2.39459 | 0.0926495 | ||||||||
\(669\) | 6.00121 | 0.232020 | ||||||||
\(670\) | −18.9339 | −0.731481 | ||||||||
\(671\) | 24.0496 | 0.928425 | ||||||||
\(672\) | 1.46690 | 0.0565869 | ||||||||
\(673\) | 45.6233 | 1.75865 | 0.879324 | − | 0.476224i | \(-0.157995\pi\) | ||||
0.879324 | + | 0.476224i | \(0.157995\pi\) | |||||||
\(674\) | 38.5768 | 1.48592 | ||||||||
\(675\) | −1.74411 | −0.0671310 | ||||||||
\(676\) | −44.1499 | −1.69807 | ||||||||
\(677\) | −43.1019 | −1.65654 | −0.828270 | − | 0.560329i | \(-0.810675\pi\) | ||||
−0.828270 | + | 0.560329i | \(0.810675\pi\) | |||||||
\(678\) | 6.15374 | 0.236333 | ||||||||
\(679\) | 11.6637 | 0.447612 | ||||||||
\(680\) | 14.9660 | 0.573919 | ||||||||
\(681\) | 4.73725 | 0.181532 | ||||||||
\(682\) | 43.5322 | 1.66694 | ||||||||
\(683\) | 24.1509 | 0.924108 | 0.462054 | − | 0.886852i | \(-0.347113\pi\) | ||||
0.462054 | + | 0.886852i | \(0.347113\pi\) | |||||||
\(684\) | 33.2936 | 1.27301 | ||||||||
\(685\) | −16.8521 | −0.643887 | ||||||||
\(686\) | 47.5583 | 1.81578 | ||||||||
\(687\) | 4.50292 | 0.171797 | ||||||||
\(688\) | −8.52488 | −0.325008 | ||||||||
\(689\) | −9.55807 | −0.364134 | ||||||||
\(690\) | −1.03207 | −0.0392900 | ||||||||
\(691\) | −31.4456 | −1.19625 | −0.598124 | − | 0.801404i | \(-0.704087\pi\) | ||||
−0.598124 | + | 0.801404i | \(0.704087\pi\) | |||||||
\(692\) | −71.3524 | −2.71241 | ||||||||
\(693\) | 24.4534 | 0.928909 | ||||||||
\(694\) | −34.2753 | −1.30107 | ||||||||
\(695\) | −3.20205 | −0.121461 | ||||||||
\(696\) | 10.1953 | 0.386451 | ||||||||
\(697\) | 2.87106 | 0.108749 | ||||||||
\(698\) | 76.2381 | 2.88566 | ||||||||
\(699\) | 5.46027 | 0.206526 | ||||||||
\(700\) | 7.25777 | 0.274318 | ||||||||
\(701\) | −45.2299 | −1.70831 | −0.854155 | − | 0.520019i | \(-0.825925\pi\) | ||||
−0.854155 | + | 0.520019i | \(0.825925\pi\) | |||||||
\(702\) | 4.39305 | 0.165805 | ||||||||
\(703\) | 14.1942 | 0.535346 | ||||||||
\(704\) | 46.4121 | 1.74922 | ||||||||
\(705\) | 3.19210 | 0.120221 | ||||||||
\(706\) | −5.88122 | −0.221343 | ||||||||
\(707\) | 12.0372 | 0.452705 | ||||||||
\(708\) | −5.87581 | −0.220826 | ||||||||
\(709\) | 11.5007 | 0.431919 | 0.215960 | − | 0.976402i | \(-0.430712\pi\) | ||||
0.215960 | + | 0.976402i | \(0.430712\pi\) | |||||||
\(710\) | 24.0509 | 0.902615 | ||||||||
\(711\) | 33.9456 | 1.27306 | ||||||||
\(712\) | 4.09529 | 0.153478 | ||||||||
\(713\) | −6.20729 | −0.232465 | ||||||||
\(714\) | −5.03584 | −0.188462 | ||||||||
\(715\) | 4.52591 | 0.169259 | ||||||||
\(716\) | −55.6619 | −2.08018 | ||||||||
\(717\) | −8.15604 | −0.304593 | ||||||||
\(718\) | −11.4559 | −0.427532 | ||||||||
\(719\) | −51.2805 | −1.91244 | −0.956220 | − | 0.292648i | \(-0.905463\pi\) | ||||
−0.956220 | + | 0.292648i | \(0.905463\pi\) | |||||||
\(720\) | 6.88093 | 0.256437 | ||||||||
\(721\) | 29.3502 | 1.09306 | ||||||||
\(722\) | 22.7705 | 0.847431 | ||||||||
\(723\) | 8.03093 | 0.298674 | ||||||||
\(724\) | 86.0439 | 3.19780 | ||||||||
\(725\) | −8.44007 | −0.313456 | ||||||||
\(726\) | −5.25020 | −0.194853 | ||||||||
\(727\) | 36.9416 | 1.37009 | 0.685044 | − | 0.728502i | \(-0.259783\pi\) | ||||
0.685044 | + | 0.728502i | \(0.259783\pi\) | |||||||
\(728\) | −8.43473 | −0.312612 | ||||||||
\(729\) | −22.4147 | −0.830175 | ||||||||
\(730\) | 5.91183 | 0.218807 | ||||||||
\(731\) | −13.1887 | −0.487801 | ||||||||
\(732\) | −6.13309 | −0.226686 | ||||||||
\(733\) | 14.0425 | 0.518673 | 0.259337 | − | 0.965787i | \(-0.416496\pi\) | ||||
0.259337 | + | 0.965787i | \(0.416496\pi\) | |||||||
\(734\) | 55.8476 | 2.06137 | ||||||||
\(735\) | 0.937938 | 0.0345964 | ||||||||
\(736\) | −3.72467 | −0.137293 | ||||||||
\(737\) | 34.0216 | 1.25320 | ||||||||
\(738\) | 5.47025 | 0.201363 | ||||||||
\(739\) | −18.4116 | −0.677282 | −0.338641 | − | 0.940916i | \(-0.609967\pi\) | ||||
−0.338641 | + | 0.940916i | \(0.609967\pi\) | |||||||
\(740\) | 17.1245 | 0.629509 | ||||||||
\(741\) | −0.956690 | −0.0351449 | ||||||||
\(742\) | 42.3749 | 1.55563 | ||||||||
\(743\) | −20.0671 | −0.736191 | −0.368096 | − | 0.929788i | \(-0.619990\pi\) | ||||
−0.368096 | + | 0.929788i | \(0.619990\pi\) | |||||||
\(744\) | −5.12224 | −0.187790 | ||||||||
\(745\) | −14.6448 | −0.536544 | ||||||||
\(746\) | −56.7685 | −2.07844 | ||||||||
\(747\) | −36.5084 | −1.33577 | ||||||||
\(748\) | −58.2831 | −2.13104 | ||||||||
\(749\) | 5.25679 | 0.192079 | ||||||||
\(750\) | 0.705037 | 0.0257443 | ||||||||
\(751\) | −17.5280 | −0.639607 | −0.319803 | − | 0.947484i | \(-0.603617\pi\) | ||||
−0.319803 | + | 0.947484i | \(0.603617\pi\) | |||||||
\(752\) | −25.5633 | −0.932196 | ||||||||
\(753\) | 3.82404 | 0.139356 | ||||||||
\(754\) | 21.2587 | 0.774196 | ||||||||
\(755\) | 17.8411 | 0.649303 | ||||||||
\(756\) | −12.6584 | −0.460381 | ||||||||
\(757\) | 21.0316 | 0.764406 | 0.382203 | − | 0.924078i | \(-0.375166\pi\) | ||||
0.382203 | + | 0.924078i | \(0.375166\pi\) | |||||||
\(758\) | 66.2103 | 2.40487 | ||||||||
\(759\) | 1.85448 | 0.0673133 | ||||||||
\(760\) | −12.6050 | −0.457231 | ||||||||
\(761\) | −37.2035 | −1.34863 | −0.674313 | − | 0.738445i | \(-0.735560\pi\) | ||||
−0.674313 | + | 0.738445i | \(0.735560\pi\) | |||||||
\(762\) | 3.20796 | 0.116212 | ||||||||
\(763\) | −1.31306 | −0.0475358 | ||||||||
\(764\) | 1.44829 | 0.0523972 | ||||||||
\(765\) | 10.6454 | 0.384884 | ||||||||
\(766\) | −14.4258 | −0.521227 | ||||||||
\(767\) | −5.65305 | −0.204120 | ||||||||
\(768\) | −8.24808 | −0.297627 | ||||||||
\(769\) | −15.2246 | −0.549013 | −0.274507 | − | 0.961585i | \(-0.588515\pi\) | ||||
−0.274507 | + | 0.961585i | \(0.588515\pi\) | |||||||
\(770\) | −20.0652 | −0.723101 | ||||||||
\(771\) | 5.59109 | 0.201358 | ||||||||
\(772\) | 36.8150 | 1.32500 | ||||||||
\(773\) | 26.7520 | 0.962202 | 0.481101 | − | 0.876665i | \(-0.340237\pi\) | ||||
0.481101 | + | 0.876665i | \(0.340237\pi\) | |||||||
\(774\) | −25.1285 | −0.903224 | ||||||||
\(775\) | 4.24040 | 0.152320 | ||||||||
\(776\) | −24.4389 | −0.877306 | ||||||||
\(777\) | −2.65866 | −0.0953787 | ||||||||
\(778\) | −20.3896 | −0.731004 | ||||||||
\(779\) | −2.41813 | −0.0866386 | ||||||||
\(780\) | −1.15419 | −0.0413266 | ||||||||
\(781\) | −43.2162 | −1.54640 | ||||||||
\(782\) | 12.7867 | 0.457253 | ||||||||
\(783\) | 14.7205 | 0.526066 | ||||||||
\(784\) | −7.51128 | −0.268260 | ||||||||
\(785\) | −15.4767 | −0.552387 | ||||||||
\(786\) | 6.43513 | 0.229533 | ||||||||
\(787\) | 28.4808 | 1.01523 | 0.507615 | − | 0.861584i | \(-0.330527\pi\) | ||||
0.507615 | + | 0.861584i | \(0.330527\pi\) | |||||||
\(788\) | −3.75406 | −0.133733 | ||||||||
\(789\) | −4.84062 | −0.172331 | ||||||||
\(790\) | −27.8540 | −0.991002 | ||||||||
\(791\) | −17.0595 | −0.606568 | ||||||||
\(792\) | −51.2371 | −1.82063 | ||||||||
\(793\) | −5.90058 | −0.209536 | ||||||||
\(794\) | 34.9367 | 1.23986 | ||||||||
\(795\) | 2.67542 | 0.0948873 | ||||||||
\(796\) | −49.5744 | −1.75712 | ||||||||
\(797\) | 44.0413 | 1.56002 | 0.780012 | − | 0.625764i | \(-0.215213\pi\) | ||||
0.780012 | + | 0.625764i | \(0.215213\pi\) | |||||||
\(798\) | 4.24140 | 0.150144 | ||||||||
\(799\) | −39.5484 | −1.39912 | ||||||||
\(800\) | 2.54445 | 0.0899597 | ||||||||
\(801\) | 2.91300 | 0.102926 | ||||||||
\(802\) | −41.3484 | −1.46006 | ||||||||
\(803\) | −10.6227 | −0.374869 | ||||||||
\(804\) | −8.67614 | −0.305984 | ||||||||
\(805\) | 2.86111 | 0.100841 | ||||||||
\(806\) | −10.6807 | −0.376210 | ||||||||
\(807\) | 8.52646 | 0.300146 | ||||||||
\(808\) | −25.2214 | −0.887286 | ||||||||
\(809\) | −30.2316 | −1.06289 | −0.531444 | − | 0.847094i | \(-0.678350\pi\) | ||||
−0.531444 | + | 0.847094i | \(0.678350\pi\) | |||||||
\(810\) | 19.6588 | 0.690739 | ||||||||
\(811\) | −34.5210 | −1.21220 | −0.606099 | − | 0.795389i | \(-0.707266\pi\) | ||||
−0.606099 | + | 0.795389i | \(0.707266\pi\) | |||||||
\(812\) | −61.2561 | −2.14967 | ||||||||
\(813\) | 1.88650 | 0.0661625 | ||||||||
\(814\) | −47.3433 | −1.65938 | ||||||||
\(815\) | 2.39177 | 0.0837800 | ||||||||
\(816\) | 2.54621 | 0.0891353 | ||||||||
\(817\) | 11.1081 | 0.388622 | ||||||||
\(818\) | 6.65121 | 0.232554 | ||||||||
\(819\) | −5.99966 | −0.209645 | ||||||||
\(820\) | −2.91733 | −0.101878 | ||||||||
\(821\) | 35.2307 | 1.22956 | 0.614780 | − | 0.788698i | \(-0.289245\pi\) | ||||
0.614780 | + | 0.788698i | \(0.289245\pi\) | |||||||
\(822\) | −11.8814 | −0.414411 | ||||||||
\(823\) | −40.5379 | −1.41306 | −0.706532 | − | 0.707681i | \(-0.749741\pi\) | ||||
−0.706532 | + | 0.707681i | \(0.749741\pi\) | |||||||
\(824\) | −61.4973 | −2.14236 | ||||||||
\(825\) | −1.26685 | −0.0441062 | ||||||||
\(826\) | 25.0623 | 0.872030 | ||||||||
\(827\) | −30.0036 | −1.04333 | −0.521664 | − | 0.853151i | \(-0.674688\pi\) | ||||
−0.521664 | + | 0.853151i | \(0.674688\pi\) | |||||||
\(828\) | 15.8343 | 0.550279 | ||||||||
\(829\) | 11.3949 | 0.395761 | 0.197881 | − | 0.980226i | \(-0.436594\pi\) | ||||
0.197881 | + | 0.980226i | \(0.436594\pi\) | |||||||
\(830\) | 29.9569 | 1.03982 | ||||||||
\(831\) | −0.857783 | −0.0297562 | ||||||||
\(832\) | −11.3872 | −0.394781 | ||||||||
\(833\) | −11.6206 | −0.402628 | ||||||||
\(834\) | −2.25756 | −0.0781729 | ||||||||
\(835\) | −0.644864 | −0.0223164 | ||||||||
\(836\) | 49.0886 | 1.69776 | ||||||||
\(837\) | −7.39575 | −0.255634 | ||||||||
\(838\) | 10.0556 | 0.347365 | ||||||||
\(839\) | 38.3055 | 1.32245 | 0.661226 | − | 0.750187i | \(-0.270037\pi\) | ||||
0.661226 | + | 0.750187i | \(0.270037\pi\) | |||||||
\(840\) | 2.36098 | 0.0814616 | ||||||||
\(841\) | 42.2348 | 1.45637 | ||||||||
\(842\) | −45.5980 | −1.57141 | ||||||||
\(843\) | −1.85146 | −0.0637675 | ||||||||
\(844\) | −94.6221 | −3.25703 | ||||||||
\(845\) | 11.8896 | 0.409014 | ||||||||
\(846\) | −75.3518 | −2.59065 | ||||||||
\(847\) | 14.5547 | 0.500107 | ||||||||
\(848\) | −21.4255 | −0.735755 | ||||||||
\(849\) | 3.50458 | 0.120277 | ||||||||
\(850\) | −8.73503 | −0.299609 | ||||||||
\(851\) | 6.75071 | 0.231412 | ||||||||
\(852\) | 11.0209 | 0.377570 | ||||||||
\(853\) | −5.70914 | −0.195477 | −0.0977386 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977386 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(854\) | 26.1597 | 0.895168 | ||||||||
\(855\) | −8.96598 | −0.306630 | ||||||||
\(856\) | −11.0145 | −0.376468 | ||||||||
\(857\) | −18.5138 | −0.632419 | −0.316210 | − | 0.948689i | \(-0.602410\pi\) | ||||
−0.316210 | + | 0.948689i | \(0.602410\pi\) | |||||||
\(858\) | 3.19093 | 0.108937 | ||||||||
\(859\) | 36.1682 | 1.23404 | 0.617021 | − | 0.786947i | \(-0.288339\pi\) | ||||
0.617021 | + | 0.786947i | \(0.288339\pi\) | |||||||
\(860\) | 13.4012 | 0.456978 | ||||||||
\(861\) | 0.452929 | 0.0154358 | ||||||||
\(862\) | 9.83952 | 0.335135 | ||||||||
\(863\) | −48.1408 | −1.63873 | −0.819366 | − | 0.573271i | \(-0.805674\pi\) | ||||
−0.819366 | + | 0.573271i | \(0.805674\pi\) | |||||||
\(864\) | −4.43781 | −0.150977 | ||||||||
\(865\) | 19.2152 | 0.653337 | ||||||||
\(866\) | 82.2842 | 2.79613 | ||||||||
\(867\) | −1.07517 | −0.0365149 | ||||||||
\(868\) | 30.7759 | 1.04460 | ||||||||
\(869\) | 50.0499 | 1.69783 | ||||||||
\(870\) | −5.95056 | −0.201743 | ||||||||
\(871\) | −8.34722 | −0.282835 | ||||||||
\(872\) | 2.75124 | 0.0931687 | ||||||||
\(873\) | −17.3835 | −0.588342 | ||||||||
\(874\) | −10.7695 | −0.364285 | ||||||||
\(875\) | −1.95452 | −0.0660748 | ||||||||
\(876\) | 2.70899 | 0.0915284 | ||||||||
\(877\) | 16.7949 | 0.567122 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(878\) | −36.3038 | −1.22519 | ||||||||
\(879\) | −4.54724 | −0.153374 | ||||||||
\(880\) | 10.1453 | 0.341999 | ||||||||
\(881\) | 10.4309 | 0.351425 | 0.175713 | − | 0.984442i | \(-0.443777\pi\) | ||||
0.175713 | + | 0.984442i | \(0.443777\pi\) | |||||||
\(882\) | −22.1407 | −0.745516 | ||||||||
\(883\) | 29.5575 | 0.994690 | 0.497345 | − | 0.867553i | \(-0.334308\pi\) | ||||
0.497345 | + | 0.867553i | \(0.334308\pi\) | |||||||
\(884\) | 14.2998 | 0.480954 | ||||||||
\(885\) | 1.58236 | 0.0531903 | ||||||||
\(886\) | −5.13313 | −0.172451 | ||||||||
\(887\) | 30.1297 | 1.01166 | 0.505828 | − | 0.862634i | \(-0.331187\pi\) | ||||
0.505828 | + | 0.862634i | \(0.331187\pi\) | |||||||
\(888\) | 5.57067 | 0.186939 | ||||||||
\(889\) | −8.89318 | −0.298268 | ||||||||
\(890\) | −2.39026 | −0.0801216 | ||||||||
\(891\) | −35.3241 | −1.18340 | ||||||||
\(892\) | 75.5500 | 2.52960 | ||||||||
\(893\) | 33.3094 | 1.11466 | ||||||||
\(894\) | −10.3251 | −0.345324 | ||||||||
\(895\) | 14.9898 | 0.501052 | ||||||||
\(896\) | 40.5380 | 1.35428 | ||||||||
\(897\) | −0.454997 | −0.0151919 | ||||||||
\(898\) | −77.7150 | −2.59338 | ||||||||
\(899\) | −35.7893 | −1.19364 | ||||||||
\(900\) | −10.8169 | −0.360564 | ||||||||
\(901\) | −33.1470 | −1.10429 | ||||||||
\(902\) | 8.06541 | 0.268549 | ||||||||
\(903\) | −2.08060 | −0.0692381 | ||||||||
\(904\) | 35.7448 | 1.18885 | ||||||||
\(905\) | −23.1716 | −0.770251 | ||||||||
\(906\) | 12.5786 | 0.417896 | ||||||||
\(907\) | 34.4041 | 1.14237 | 0.571185 | − | 0.820821i | \(-0.306484\pi\) | ||||
0.571185 | + | 0.820821i | \(0.306484\pi\) | |||||||
\(908\) | 59.6378 | 1.97915 | ||||||||
\(909\) | −17.9401 | −0.595035 | ||||||||
\(910\) | 4.92301 | 0.163196 | ||||||||
\(911\) | −48.0626 | −1.59239 | −0.796193 | − | 0.605043i | \(-0.793156\pi\) | ||||
−0.796193 | + | 0.605043i | \(0.793156\pi\) | |||||||
\(912\) | −2.14453 | −0.0710125 | ||||||||
\(913\) | −53.8284 | −1.78146 | ||||||||
\(914\) | 38.1615 | 1.26227 | ||||||||
\(915\) | 1.65164 | 0.0546016 | ||||||||
\(916\) | 56.6879 | 1.87302 | ||||||||
\(917\) | −17.8396 | −0.589116 | ||||||||
\(918\) | 15.2349 | 0.502827 | ||||||||
\(919\) | 9.64985 | 0.318319 | 0.159160 | − | 0.987253i | \(-0.449122\pi\) | ||||
0.159160 | + | 0.987253i | \(0.449122\pi\) | |||||||
\(920\) | −5.99488 | −0.197645 | ||||||||
\(921\) | −3.88451 | −0.127999 | ||||||||
\(922\) | 0.972793 | 0.0320372 | ||||||||
\(923\) | 10.6031 | 0.349006 | ||||||||
\(924\) | −9.19454 | −0.302478 | ||||||||
\(925\) | −4.61163 | −0.151630 | ||||||||
\(926\) | −68.4137 | −2.24822 | ||||||||
\(927\) | −43.7433 | −1.43672 | ||||||||
\(928\) | −21.4753 | −0.704961 | ||||||||
\(929\) | −4.87453 | −0.159928 | −0.0799641 | − | 0.996798i | \(-0.525481\pi\) | ||||
−0.0799641 | + | 0.996798i | \(0.525481\pi\) | |||||||
\(930\) | 2.98964 | 0.0980342 | ||||||||
\(931\) | 9.78734 | 0.320767 | ||||||||
\(932\) | 68.7400 | 2.25165 | ||||||||
\(933\) | 4.01491 | 0.131442 | ||||||||
\(934\) | 92.2095 | 3.01719 | ||||||||
\(935\) | 15.6957 | 0.513303 | ||||||||
\(936\) | 12.5710 | 0.410897 | ||||||||
\(937\) | 6.79035 | 0.221831 | 0.110916 | − | 0.993830i | \(-0.464622\pi\) | ||||
0.110916 | + | 0.993830i | \(0.464622\pi\) | |||||||
\(938\) | 37.0067 | 1.20831 | ||||||||
\(939\) | −5.89993 | −0.192537 | ||||||||
\(940\) | 40.1858 | 1.31072 | ||||||||
\(941\) | −26.9378 | −0.878147 | −0.439074 | − | 0.898451i | \(-0.644693\pi\) | ||||
−0.439074 | + | 0.898451i | \(0.644693\pi\) | |||||||
\(942\) | −10.9116 | −0.355521 | ||||||||
\(943\) | −1.15005 | −0.0374508 | ||||||||
\(944\) | −12.6720 | −0.412437 | ||||||||
\(945\) | 3.40891 | 0.110892 | ||||||||
\(946\) | −37.0497 | −1.20459 | ||||||||
\(947\) | 0.0394219 | 0.00128104 | 0.000640519 | − | 1.00000i | \(-0.499796\pi\) | ||||
0.000640519 | 1.00000i | \(0.499796\pi\) | ||||||||
\(948\) | −12.7636 | −0.414543 | ||||||||
\(949\) | 2.60629 | 0.0846039 | ||||||||
\(950\) | 7.35702 | 0.238693 | ||||||||
\(951\) | 5.28618 | 0.171416 | ||||||||
\(952\) | −29.2513 | −0.948040 | ||||||||
\(953\) | −3.27013 | −0.105930 | −0.0529650 | − | 0.998596i | \(-0.516867\pi\) | ||||
−0.0529650 | + | 0.998596i | \(0.516867\pi\) | |||||||
\(954\) | −63.1551 | −2.04472 | ||||||||
\(955\) | −0.390024 | −0.0126209 | ||||||||
\(956\) | −102.678 | −3.32083 | ||||||||
\(957\) | 10.6923 | 0.345634 | ||||||||
\(958\) | 33.7862 | 1.09158 | ||||||||
\(959\) | 32.9379 | 1.06362 | ||||||||
\(960\) | 3.18742 | 0.102874 | ||||||||
\(961\) | −13.0190 | −0.419967 | ||||||||
\(962\) | 11.6157 | 0.374505 | ||||||||
\(963\) | −7.83466 | −0.252468 | ||||||||
\(964\) | 101.102 | 3.25629 | ||||||||
\(965\) | −9.91428 | −0.319152 | ||||||||
\(966\) | 2.01719 | 0.0649021 | ||||||||
\(967\) | 47.5329 | 1.52855 | 0.764277 | − | 0.644888i | \(-0.223096\pi\) | ||||
0.764277 | + | 0.644888i | \(0.223096\pi\) | |||||||
\(968\) | −30.4965 | −0.980193 | ||||||||
\(969\) | −3.31776 | −0.106582 | ||||||||
\(970\) | 14.2640 | 0.457989 | ||||||||
\(971\) | −25.1811 | −0.808101 | −0.404050 | − | 0.914737i | \(-0.632398\pi\) | ||||
−0.404050 | + | 0.914737i | \(0.632398\pi\) | |||||||
\(972\) | 28.4377 | 0.912140 | ||||||||
\(973\) | 6.25846 | 0.200637 | ||||||||
\(974\) | 30.0860 | 0.964019 | ||||||||
\(975\) | 0.310823 | 0.00995431 | ||||||||
\(976\) | −13.2268 | −0.423381 | ||||||||
\(977\) | −33.1228 | −1.05969 | −0.529846 | − | 0.848094i | \(-0.677750\pi\) | ||||
−0.529846 | + | 0.848094i | \(0.677750\pi\) | |||||||
\(978\) | 1.68629 | 0.0539215 | ||||||||
\(979\) | 4.29496 | 0.137268 | ||||||||
\(980\) | 11.8078 | 0.377187 | ||||||||
\(981\) | 1.95697 | 0.0624811 | ||||||||
\(982\) | 32.1587 | 1.02623 | ||||||||
\(983\) | −22.3428 | −0.712625 | −0.356313 | − | 0.934367i | \(-0.615966\pi\) | ||||
−0.356313 | + | 0.934367i | \(0.615966\pi\) | |||||||
\(984\) | −0.949019 | −0.0302536 | ||||||||
\(985\) | 1.01097 | 0.0322122 | ||||||||
\(986\) | 73.7243 | 2.34786 | ||||||||
\(987\) | −6.23902 | −0.198590 | ||||||||
\(988\) | −12.0439 | −0.383167 | ||||||||
\(989\) | 5.28295 | 0.167988 | ||||||||
\(990\) | 29.9050 | 0.950444 | ||||||||
\(991\) | 37.5767 | 1.19366 | 0.596832 | − | 0.802366i | \(-0.296426\pi\) | ||||
0.596832 | + | 0.802366i | \(0.296426\pi\) | |||||||
\(992\) | 10.7895 | 0.342566 | ||||||||
\(993\) | −5.97729 | −0.189684 | ||||||||
\(994\) | −47.0080 | −1.49100 | ||||||||
\(995\) | 13.3504 | 0.423236 | ||||||||
\(996\) | 13.7272 | 0.434964 | ||||||||
\(997\) | 21.4843 | 0.680416 | 0.340208 | − | 0.940350i | \(-0.389502\pi\) | ||||
0.340208 | + | 0.940350i | \(0.389502\pi\) | |||||||
\(998\) | −41.9116 | −1.32669 | ||||||||
\(999\) | 8.04321 | 0.254476 |
(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 | 445.2.a.d.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 4005.2.a.l.1.4 | 4 | |||
4.3 | odd | 2 | 7120.2.a.bc.1.2 | 4 | |||
5.4 | even | 2 | 2225.2.a.i.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2225.2.a.i.1.4 | 4 | 5.4 | even | 2 | |||
4005.2.a.l.1.4 | 4 | 3.2 | odd | 2 | |||
7120.2.a.bc.1.2 | 4 | 4.3 | odd | 2 |