Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1418073786\) |
Analytic rank: | \(1\) |
Dimension: | \(234\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51561 | −1.77881 | −0.889403 | − | 0.457124i | \(-0.848880\pi\) | ||||
−0.889403 | + | 0.457124i | \(0.848880\pi\) | |||||||
\(3\) | 0.109654 | 0.0633089 | 0.0316544 | − | 0.999499i | \(-0.489922\pi\) | ||||
0.0316544 | + | 0.999499i | \(0.489922\pi\) | |||||||
\(4\) | 4.32830 | 2.16415 | ||||||||
\(5\) | −3.06491 | −1.37067 | −0.685334 | − | 0.728229i | \(-0.740344\pi\) | ||||
−0.685334 | + | 0.728229i | \(0.740344\pi\) | |||||||
\(6\) | −0.275847 | −0.112614 | ||||||||
\(7\) | 2.34212 | 0.885237 | 0.442619 | − | 0.896710i | \(-0.354050\pi\) | ||||
0.442619 | + | 0.896710i | \(0.354050\pi\) | |||||||
\(8\) | −5.85711 | −2.07080 | ||||||||
\(9\) | −2.98798 | −0.995992 | ||||||||
\(10\) | 7.71012 | 2.43815 | ||||||||
\(11\) | 5.97568 | 1.80174 | 0.900868 | − | 0.434094i | \(-0.142931\pi\) | ||||
0.900868 | + | 0.434094i | \(0.142931\pi\) | |||||||
\(12\) | 0.474617 | 0.137010 | ||||||||
\(13\) | 1.37139 | 0.380355 | 0.190178 | − | 0.981750i | \(-0.439094\pi\) | ||||
0.190178 | + | 0.981750i | \(0.439094\pi\) | |||||||
\(14\) | −5.89186 | −1.57467 | ||||||||
\(15\) | −0.336080 | −0.0867755 | ||||||||
\(16\) | 6.07760 | 1.51940 | ||||||||
\(17\) | 1.44330 | 0.350051 | 0.175025 | − | 0.984564i | \(-0.443999\pi\) | ||||
0.175025 | + | 0.984564i | \(0.443999\pi\) | |||||||
\(18\) | 7.51659 | 1.77168 | ||||||||
\(19\) | −7.12936 | −1.63559 | −0.817794 | − | 0.575511i | \(-0.804803\pi\) | ||||
−0.817794 | + | 0.575511i | \(0.804803\pi\) | |||||||
\(20\) | −13.2659 | −2.96634 | ||||||||
\(21\) | 0.256823 | 0.0560434 | ||||||||
\(22\) | −15.0325 | −3.20494 | ||||||||
\(23\) | 0.0744293 | 0.0155196 | 0.00775979 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00775979 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(24\) | −0.642256 | −0.131100 | ||||||||
\(25\) | 4.39366 | 0.878733 | ||||||||
\(26\) | −3.44989 | −0.676578 | ||||||||
\(27\) | −0.656607 | −0.126364 | ||||||||
\(28\) | 10.1374 | 1.91579 | ||||||||
\(29\) | 4.48625 | 0.833075 | 0.416538 | − | 0.909119i | \(-0.363243\pi\) | ||||
0.416538 | + | 0.909119i | \(0.363243\pi\) | |||||||
\(30\) | 0.845447 | 0.154357 | ||||||||
\(31\) | 2.15670 | 0.387354 | 0.193677 | − | 0.981065i | \(-0.437959\pi\) | ||||
0.193677 | + | 0.981065i | \(0.437959\pi\) | |||||||
\(32\) | −3.57468 | −0.631920 | ||||||||
\(33\) | 0.655258 | 0.114066 | ||||||||
\(34\) | −3.63077 | −0.622673 | ||||||||
\(35\) | −7.17838 | −1.21337 | ||||||||
\(36\) | −12.9329 | −2.15548 | ||||||||
\(37\) | −9.59831 | −1.57795 | −0.788976 | − | 0.614424i | \(-0.789389\pi\) | ||||
−0.788976 | + | 0.614424i | \(0.789389\pi\) | |||||||
\(38\) | 17.9347 | 2.90939 | ||||||||
\(39\) | 0.150379 | 0.0240799 | ||||||||
\(40\) | 17.9515 | 2.83838 | ||||||||
\(41\) | 8.99353 | 1.40455 | 0.702276 | − | 0.711904i | \(-0.252167\pi\) | ||||
0.702276 | + | 0.711904i | \(0.252167\pi\) | |||||||
\(42\) | −0.646067 | −0.0996903 | ||||||||
\(43\) | −3.85591 | −0.588020 | −0.294010 | − | 0.955802i | \(-0.594990\pi\) | ||||
−0.294010 | + | 0.955802i | \(0.594990\pi\) | |||||||
\(44\) | 25.8646 | 3.89923 | ||||||||
\(45\) | 9.15787 | 1.36518 | ||||||||
\(46\) | −0.187235 | −0.0276063 | ||||||||
\(47\) | 3.94668 | 0.575682 | 0.287841 | − | 0.957678i | \(-0.407063\pi\) | ||||
0.287841 | + | 0.957678i | \(0.407063\pi\) | |||||||
\(48\) | 0.666435 | 0.0961916 | ||||||||
\(49\) | −1.51449 | −0.216355 | ||||||||
\(50\) | −11.0528 | −1.56310 | ||||||||
\(51\) | 0.158264 | 0.0221613 | ||||||||
\(52\) | 5.93580 | 0.823147 | ||||||||
\(53\) | 3.97955 | 0.546633 | 0.273317 | − | 0.961924i | \(-0.411879\pi\) | ||||
0.273317 | + | 0.961924i | \(0.411879\pi\) | |||||||
\(54\) | 1.65177 | 0.224777 | ||||||||
\(55\) | −18.3149 | −2.46958 | ||||||||
\(56\) | −13.7180 | −1.83315 | ||||||||
\(57\) | −0.781765 | −0.103547 | ||||||||
\(58\) | −11.2857 | −1.48188 | ||||||||
\(59\) | −11.3592 | −1.47884 | −0.739418 | − | 0.673246i | \(-0.764899\pi\) | ||||
−0.739418 | + | 0.673246i | \(0.764899\pi\) | |||||||
\(60\) | −1.45466 | −0.187795 | ||||||||
\(61\) | −12.8104 | −1.64021 | −0.820105 | − | 0.572213i | \(-0.806085\pi\) | ||||
−0.820105 | + | 0.572213i | \(0.806085\pi\) | |||||||
\(62\) | −5.42541 | −0.689028 | ||||||||
\(63\) | −6.99819 | −0.881689 | ||||||||
\(64\) | −3.16271 | −0.395338 | ||||||||
\(65\) | −4.20319 | −0.521341 | ||||||||
\(66\) | −1.64838 | −0.202901 | ||||||||
\(67\) | −2.39098 | −0.292104 | −0.146052 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146052 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(68\) | 6.24703 | 0.757563 | ||||||||
\(69\) | 0.00816148 | 0.000982527 0 | ||||||||
\(70\) | 18.0580 | 2.15834 | ||||||||
\(71\) | −3.03894 | −0.360656 | −0.180328 | − | 0.983607i | \(-0.557716\pi\) | ||||
−0.180328 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(72\) | 17.5009 | 2.06250 | ||||||||
\(73\) | 2.90445 | 0.339940 | 0.169970 | − | 0.985449i | \(-0.445633\pi\) | ||||
0.169970 | + | 0.985449i | \(0.445633\pi\) | |||||||
\(74\) | 24.1456 | 2.80687 | ||||||||
\(75\) | 0.481784 | 0.0556316 | ||||||||
\(76\) | −30.8580 | −3.53966 | ||||||||
\(77\) | 13.9957 | 1.59496 | ||||||||
\(78\) | −0.378295 | −0.0428334 | ||||||||
\(79\) | 13.4125 | 1.50902 | 0.754512 | − | 0.656287i | \(-0.227874\pi\) | ||||
0.754512 | + | 0.656287i | \(0.227874\pi\) | |||||||
\(80\) | −18.6273 | −2.08260 | ||||||||
\(81\) | 8.89193 | 0.987992 | ||||||||
\(82\) | −22.6242 | −2.49843 | ||||||||
\(83\) | −13.7443 | −1.50863 | −0.754315 | − | 0.656512i | \(-0.772031\pi\) | ||||
−0.754315 | + | 0.656512i | \(0.772031\pi\) | |||||||
\(84\) | 1.11161 | 0.121286 | ||||||||
\(85\) | −4.42357 | −0.479804 | ||||||||
\(86\) | 9.69996 | 1.04597 | ||||||||
\(87\) | 0.491936 | 0.0527410 | ||||||||
\(88\) | −35.0002 | −3.73103 | ||||||||
\(89\) | −0.765554 | −0.0811486 | −0.0405743 | − | 0.999177i | \(-0.512919\pi\) | ||||
−0.0405743 | + | 0.999177i | \(0.512919\pi\) | |||||||
\(90\) | −23.0377 | −2.42838 | ||||||||
\(91\) | 3.21196 | 0.336705 | ||||||||
\(92\) | 0.322153 | 0.0335867 | ||||||||
\(93\) | 0.236491 | 0.0245230 | ||||||||
\(94\) | −9.92830 | −1.02403 | ||||||||
\(95\) | 21.8508 | 2.24185 | ||||||||
\(96\) | −0.391978 | −0.0400061 | ||||||||
\(97\) | 16.1047 | 1.63518 | 0.817591 | − | 0.575800i | \(-0.195309\pi\) | ||||
0.817591 | + | 0.575800i | \(0.195309\pi\) | |||||||
\(98\) | 3.80986 | 0.384854 | ||||||||
\(99\) | −17.8552 | −1.79451 | ||||||||
\(100\) | 19.0171 | 1.90171 | ||||||||
\(101\) | 2.41605 | 0.240406 | 0.120203 | − | 0.992749i | \(-0.461645\pi\) | ||||
0.120203 | + | 0.992749i | \(0.461645\pi\) | |||||||
\(102\) | −0.398130 | −0.0394207 | ||||||||
\(103\) | −12.8673 | −1.26786 | −0.633929 | − | 0.773391i | \(-0.718559\pi\) | ||||
−0.633929 | + | 0.773391i | \(0.718559\pi\) | |||||||
\(104\) | −8.03238 | −0.787640 | ||||||||
\(105\) | −0.787139 | −0.0768169 | ||||||||
\(106\) | −10.0110 | −0.972354 | ||||||||
\(107\) | −3.77762 | −0.365196 | −0.182598 | − | 0.983188i | \(-0.558451\pi\) | ||||
−0.182598 | + | 0.983188i | \(0.558451\pi\) | |||||||
\(108\) | −2.84199 | −0.273471 | ||||||||
\(109\) | −14.1078 | −1.35129 | −0.675643 | − | 0.737229i | \(-0.736134\pi\) | ||||
−0.675643 | + | 0.737229i | \(0.736134\pi\) | |||||||
\(110\) | 46.0732 | 4.39291 | ||||||||
\(111\) | −1.05250 | −0.0998984 | ||||||||
\(112\) | 14.2345 | 1.34503 | ||||||||
\(113\) | 5.62655 | 0.529301 | 0.264650 | − | 0.964344i | \(-0.414743\pi\) | ||||
0.264650 | + | 0.964344i | \(0.414743\pi\) | |||||||
\(114\) | 1.96662 | 0.184190 | ||||||||
\(115\) | −0.228119 | −0.0212722 | ||||||||
\(116\) | 19.4178 | 1.80290 | ||||||||
\(117\) | −4.09768 | −0.378831 | ||||||||
\(118\) | 28.5752 | 2.63056 | ||||||||
\(119\) | 3.38037 | 0.309878 | ||||||||
\(120\) | 1.96846 | 0.179695 | ||||||||
\(121\) | 24.7088 | 2.24625 | ||||||||
\(122\) | 32.2261 | 2.91762 | ||||||||
\(123\) | 0.986178 | 0.0889207 | ||||||||
\(124\) | 9.33484 | 0.838293 | ||||||||
\(125\) | 1.85836 | 0.166217 | ||||||||
\(126\) | 17.6047 | 1.56835 | ||||||||
\(127\) | −4.50963 | −0.400165 | −0.200082 | − | 0.979779i | \(-0.564121\pi\) | ||||
−0.200082 | + | 0.979779i | \(0.564121\pi\) | |||||||
\(128\) | 15.1055 | 1.33515 | ||||||||
\(129\) | −0.422816 | −0.0372269 | ||||||||
\(130\) | 10.5736 | 0.927365 | ||||||||
\(131\) | −9.42940 | −0.823851 | −0.411925 | − | 0.911218i | \(-0.635144\pi\) | ||||
−0.411925 | + | 0.911218i | \(0.635144\pi\) | |||||||
\(132\) | 2.83616 | 0.246856 | ||||||||
\(133\) | −16.6978 | −1.44788 | ||||||||
\(134\) | 6.01477 | 0.519597 | ||||||||
\(135\) | 2.01244 | 0.173203 | ||||||||
\(136\) | −8.45354 | −0.724885 | ||||||||
\(137\) | 11.2200 | 0.958592 | 0.479296 | − | 0.877653i | \(-0.340892\pi\) | ||||
0.479296 | + | 0.877653i | \(0.340892\pi\) | |||||||
\(138\) | −0.0205311 | −0.00174773 | ||||||||
\(139\) | 20.5009 | 1.73886 | 0.869432 | − | 0.494052i | \(-0.164485\pi\) | ||||
0.869432 | + | 0.494052i | \(0.164485\pi\) | |||||||
\(140\) | −31.0702 | −2.62591 | ||||||||
\(141\) | 0.432769 | 0.0364458 | ||||||||
\(142\) | 7.64480 | 0.641537 | ||||||||
\(143\) | 8.19499 | 0.685300 | ||||||||
\(144\) | −18.1597 | −1.51331 | ||||||||
\(145\) | −13.7499 | −1.14187 | ||||||||
\(146\) | −7.30646 | −0.604687 | ||||||||
\(147\) | −0.166070 | −0.0136972 | ||||||||
\(148\) | −41.5444 | −3.41493 | ||||||||
\(149\) | −0.179490 | −0.0147044 | −0.00735218 | − | 0.999973i | \(-0.502340\pi\) | ||||
−0.00735218 | + | 0.999973i | \(0.502340\pi\) | |||||||
\(150\) | −1.21198 | −0.0989578 | ||||||||
\(151\) | 7.30082 | 0.594132 | 0.297066 | − | 0.954857i | \(-0.403992\pi\) | ||||
0.297066 | + | 0.954857i | \(0.403992\pi\) | |||||||
\(152\) | 41.7575 | 3.38698 | ||||||||
\(153\) | −4.31254 | −0.348648 | ||||||||
\(154\) | −35.2079 | −2.83713 | ||||||||
\(155\) | −6.61008 | −0.530934 | ||||||||
\(156\) | 0.650885 | 0.0521125 | ||||||||
\(157\) | −2.39448 | −0.191101 | −0.0955503 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955503 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(158\) | −33.7406 | −2.68426 | ||||||||
\(159\) | 0.436374 | 0.0346067 | ||||||||
\(160\) | 10.9561 | 0.866153 | ||||||||
\(161\) | 0.174322 | 0.0137385 | ||||||||
\(162\) | −22.3686 | −1.75745 | ||||||||
\(163\) | −11.5948 | −0.908171 | −0.454086 | − | 0.890958i | \(-0.650034\pi\) | ||||
−0.454086 | + | 0.890958i | \(0.650034\pi\) | |||||||
\(164\) | 38.9267 | 3.03967 | ||||||||
\(165\) | −2.00831 | −0.156346 | ||||||||
\(166\) | 34.5753 | 2.68356 | ||||||||
\(167\) | −15.7489 | −1.21869 | −0.609343 | − | 0.792907i | \(-0.708567\pi\) | ||||
−0.609343 | + | 0.792907i | \(0.708567\pi\) | |||||||
\(168\) | −1.50424 | −0.116055 | ||||||||
\(169\) | −11.1193 | −0.855330 | ||||||||
\(170\) | 11.1280 | 0.853478 | ||||||||
\(171\) | 21.3024 | 1.62903 | ||||||||
\(172\) | −16.6895 | −1.27256 | ||||||||
\(173\) | 10.3400 | 0.786134 | 0.393067 | − | 0.919510i | \(-0.371414\pi\) | ||||
0.393067 | + | 0.919510i | \(0.371414\pi\) | |||||||
\(174\) | −1.23752 | −0.0938161 | ||||||||
\(175\) | 10.2905 | 0.777887 | ||||||||
\(176\) | 36.3178 | 2.73756 | ||||||||
\(177\) | −1.24558 | −0.0936235 | ||||||||
\(178\) | 1.92584 | 0.144348 | ||||||||
\(179\) | −1.71846 | −0.128444 | −0.0642220 | − | 0.997936i | \(-0.520457\pi\) | ||||
−0.0642220 | + | 0.997936i | \(0.520457\pi\) | |||||||
\(180\) | 39.6381 | 2.95445 | ||||||||
\(181\) | −6.60119 | −0.490662 | −0.245331 | − | 0.969439i | \(-0.578897\pi\) | ||||
−0.245331 | + | 0.969439i | \(0.578897\pi\) | |||||||
\(182\) | −8.08004 | −0.598932 | ||||||||
\(183\) | −1.40472 | −0.103840 | ||||||||
\(184\) | −0.435940 | −0.0321380 | ||||||||
\(185\) | 29.4179 | 2.16285 | ||||||||
\(186\) | −0.594919 | −0.0436216 | ||||||||
\(187\) | 8.62468 | 0.630699 | ||||||||
\(188\) | 17.0824 | 1.24586 | ||||||||
\(189\) | −1.53785 | −0.111862 | ||||||||
\(190\) | −54.9682 | −3.98782 | ||||||||
\(191\) | 9.45777 | 0.684340 | 0.342170 | − | 0.939638i | \(-0.388838\pi\) | ||||
0.342170 | + | 0.939638i | \(0.388838\pi\) | |||||||
\(192\) | −0.346804 | −0.0250284 | ||||||||
\(193\) | 23.2393 | 1.67280 | 0.836399 | − | 0.548121i | \(-0.184657\pi\) | ||||
0.836399 | + | 0.548121i | \(0.184657\pi\) | |||||||
\(194\) | −40.5131 | −2.90867 | ||||||||
\(195\) | −0.460897 | −0.0330055 | ||||||||
\(196\) | −6.55516 | −0.468225 | ||||||||
\(197\) | −1.04491 | −0.0744467 | −0.0372234 | − | 0.999307i | \(-0.511851\pi\) | ||||
−0.0372234 | + | 0.999307i | \(0.511851\pi\) | |||||||
\(198\) | 44.9167 | 3.19209 | ||||||||
\(199\) | −26.9437 | −1.90999 | −0.954994 | − | 0.296626i | \(-0.904138\pi\) | ||||
−0.954994 | + | 0.296626i | \(0.904138\pi\) | |||||||
\(200\) | −25.7342 | −1.81968 | ||||||||
\(201\) | −0.262181 | −0.0184928 | ||||||||
\(202\) | −6.07784 | −0.427635 | ||||||||
\(203\) | 10.5073 | 0.737469 | ||||||||
\(204\) | 0.685013 | 0.0479605 | ||||||||
\(205\) | −27.5643 | −1.92518 | ||||||||
\(206\) | 32.3693 | 2.25527 | ||||||||
\(207\) | −0.222393 | −0.0154574 | ||||||||
\(208\) | 8.33477 | 0.577912 | ||||||||
\(209\) | −42.6028 | −2.94690 | ||||||||
\(210\) | 1.98014 | 0.136642 | ||||||||
\(211\) | −16.5729 | −1.14093 | −0.570463 | − | 0.821323i | \(-0.693236\pi\) | ||||
−0.570463 | + | 0.821323i | \(0.693236\pi\) | |||||||
\(212\) | 17.2247 | 1.18300 | ||||||||
\(213\) | −0.333233 | −0.0228327 | ||||||||
\(214\) | 9.50303 | 0.649613 | ||||||||
\(215\) | 11.8180 | 0.805981 | ||||||||
\(216\) | 3.84582 | 0.261675 | ||||||||
\(217\) | 5.05124 | 0.342900 | ||||||||
\(218\) | 35.4898 | 2.40368 | ||||||||
\(219\) | 0.318485 | 0.0215212 | ||||||||
\(220\) | −79.2725 | −5.34455 | ||||||||
\(221\) | 1.97932 | 0.133144 | ||||||||
\(222\) | 2.64767 | 0.177700 | ||||||||
\(223\) | 3.08329 | 0.206472 | 0.103236 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103236 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(224\) | −8.37232 | −0.559399 | ||||||||
\(225\) | −13.1282 | −0.875211 | ||||||||
\(226\) | −14.1542 | −0.941524 | ||||||||
\(227\) | 3.64014 | 0.241605 | 0.120802 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120802 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(228\) | −3.38371 | −0.224092 | ||||||||
\(229\) | −8.09614 | −0.535008 | −0.267504 | − | 0.963557i | \(-0.586199\pi\) | ||||
−0.267504 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(230\) | 0.573859 | 0.0378391 | ||||||||
\(231\) | 1.53469 | 0.100975 | ||||||||
\(232\) | −26.2764 | −1.72513 | ||||||||
\(233\) | −28.9808 | −1.89860 | −0.949298 | − | 0.314378i | \(-0.898204\pi\) | ||||
−0.949298 | + | 0.314378i | \(0.898204\pi\) | |||||||
\(234\) | 10.3082 | 0.673867 | ||||||||
\(235\) | −12.0962 | −0.789069 | ||||||||
\(236\) | −49.1659 | −3.20043 | ||||||||
\(237\) | 1.47074 | 0.0955346 | ||||||||
\(238\) | −8.50370 | −0.551213 | ||||||||
\(239\) | 27.9834 | 1.81009 | 0.905047 | − | 0.425312i | \(-0.139836\pi\) | ||||
0.905047 | + | 0.425312i | \(0.139836\pi\) | |||||||
\(240\) | −2.04256 | −0.131847 | ||||||||
\(241\) | 14.9674 | 0.964137 | 0.482068 | − | 0.876134i | \(-0.339886\pi\) | ||||
0.482068 | + | 0.876134i | \(0.339886\pi\) | |||||||
\(242\) | −62.1577 | −3.99565 | ||||||||
\(243\) | 2.94486 | 0.188913 | ||||||||
\(244\) | −55.4475 | −3.54966 | ||||||||
\(245\) | 4.64176 | 0.296551 | ||||||||
\(246\) | −2.48084 | −0.158173 | ||||||||
\(247\) | −9.77714 | −0.622105 | ||||||||
\(248\) | −12.6320 | −0.802133 | ||||||||
\(249\) | −1.50712 | −0.0955097 | ||||||||
\(250\) | −4.67492 | −0.295668 | ||||||||
\(251\) | 12.3891 | 0.781991 | 0.390996 | − | 0.920393i | \(-0.372131\pi\) | ||||
0.390996 | + | 0.920393i | \(0.372131\pi\) | |||||||
\(252\) | −30.2903 | −1.90811 | ||||||||
\(253\) | 0.444766 | 0.0279622 | ||||||||
\(254\) | 11.3445 | 0.711816 | ||||||||
\(255\) | −0.485063 | −0.0303758 | ||||||||
\(256\) | −31.6742 | −1.97963 | ||||||||
\(257\) | −6.37361 | −0.397575 | −0.198788 | − | 0.980043i | \(-0.563700\pi\) | ||||
−0.198788 | + | 0.980043i | \(0.563700\pi\) | |||||||
\(258\) | 1.06364 | 0.0662194 | ||||||||
\(259\) | −22.4804 | −1.39686 | ||||||||
\(260\) | −18.1927 | −1.12826 | ||||||||
\(261\) | −13.4048 | −0.829736 | ||||||||
\(262\) | 23.7207 | 1.46547 | ||||||||
\(263\) | 28.2867 | 1.74423 | 0.872116 | − | 0.489299i | \(-0.162747\pi\) | ||||
0.872116 | + | 0.489299i | \(0.162747\pi\) | |||||||
\(264\) | −3.83792 | −0.236208 | ||||||||
\(265\) | −12.1970 | −0.749253 | ||||||||
\(266\) | 42.0052 | 2.57550 | ||||||||
\(267\) | −0.0839463 | −0.00513743 | ||||||||
\(268\) | −10.3489 | −0.632158 | ||||||||
\(269\) | −13.8923 | −0.847026 | −0.423513 | − | 0.905890i | \(-0.639203\pi\) | ||||
−0.423513 | + | 0.905890i | \(0.639203\pi\) | |||||||
\(270\) | −5.06252 | −0.308095 | ||||||||
\(271\) | 22.1281 | 1.34419 | 0.672093 | − | 0.740467i | \(-0.265396\pi\) | ||||
0.672093 | + | 0.740467i | \(0.265396\pi\) | |||||||
\(272\) | 8.77179 | 0.531868 | ||||||||
\(273\) | 0.352205 | 0.0213164 | ||||||||
\(274\) | −28.2252 | −1.70515 | ||||||||
\(275\) | 26.2551 | 1.58324 | ||||||||
\(276\) | 0.0353254 | 0.00212634 | ||||||||
\(277\) | −5.50198 | −0.330582 | −0.165291 | − | 0.986245i | \(-0.552856\pi\) | ||||
−0.165291 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(278\) | −51.5723 | −3.09310 | ||||||||
\(279\) | −6.44416 | −0.385802 | ||||||||
\(280\) | 42.0445 | 2.51264 | ||||||||
\(281\) | −24.7559 | −1.47682 | −0.738408 | − | 0.674354i | \(-0.764422\pi\) | ||||
−0.738408 | + | 0.674354i | \(0.764422\pi\) | |||||||
\(282\) | −1.08868 | −0.0648300 | ||||||||
\(283\) | 18.0241 | 1.07142 | 0.535710 | − | 0.844402i | \(-0.320044\pi\) | ||||
0.535710 | + | 0.844402i | \(0.320044\pi\) | |||||||
\(284\) | −13.1535 | −0.780515 | ||||||||
\(285\) | 2.39604 | 0.141929 | ||||||||
\(286\) | −20.6154 | −1.21902 | ||||||||
\(287\) | 21.0639 | 1.24336 | ||||||||
\(288\) | 10.6811 | 0.629387 | ||||||||
\(289\) | −14.9169 | −0.877464 | ||||||||
\(290\) | 34.5895 | 2.03117 | ||||||||
\(291\) | 1.76594 | 0.103521 | ||||||||
\(292\) | 12.5713 | 0.735681 | ||||||||
\(293\) | 16.4441 | 0.960677 | 0.480338 | − | 0.877083i | \(-0.340514\pi\) | ||||
0.480338 | + | 0.877083i | \(0.340514\pi\) | |||||||
\(294\) | 0.417767 | 0.0243647 | ||||||||
\(295\) | 34.8148 | 2.02700 | ||||||||
\(296\) | 56.2184 | 3.26763 | ||||||||
\(297\) | −3.92367 | −0.227675 | ||||||||
\(298\) | 0.451526 | 0.0261562 | ||||||||
\(299\) | 0.102072 | 0.00590296 | ||||||||
\(300\) | 2.08531 | 0.120395 | ||||||||
\(301\) | −9.03098 | −0.520537 | ||||||||
\(302\) | −18.3660 | −1.05685 | ||||||||
\(303\) | 0.264930 | 0.0152198 | ||||||||
\(304\) | −43.3295 | −2.48511 | ||||||||
\(305\) | 39.2628 | 2.24818 | ||||||||
\(306\) | 10.8487 | 0.620177 | ||||||||
\(307\) | −7.36738 | −0.420479 | −0.210239 | − | 0.977650i | \(-0.567424\pi\) | ||||
−0.210239 | + | 0.977650i | \(0.567424\pi\) | |||||||
\(308\) | 60.5778 | 3.45174 | ||||||||
\(309\) | −1.41096 | −0.0802666 | ||||||||
\(310\) | 16.6284 | 0.944429 | ||||||||
\(311\) | −4.52462 | −0.256568 | −0.128284 | − | 0.991737i | \(-0.540947\pi\) | ||||
−0.128284 | + | 0.991737i | \(0.540947\pi\) | |||||||
\(312\) | −0.880785 | −0.0498646 | ||||||||
\(313\) | 11.3604 | 0.642130 | 0.321065 | − | 0.947057i | \(-0.395959\pi\) | ||||
0.321065 | + | 0.947057i | \(0.395959\pi\) | |||||||
\(314\) | 6.02359 | 0.339931 | ||||||||
\(315\) | 21.4488 | 1.20850 | ||||||||
\(316\) | 58.0533 | 3.26576 | ||||||||
\(317\) | 5.13238 | 0.288263 | 0.144131 | − | 0.989559i | \(-0.453961\pi\) | ||||
0.144131 | + | 0.989559i | \(0.453961\pi\) | |||||||
\(318\) | −1.09775 | −0.0615587 | ||||||||
\(319\) | 26.8084 | 1.50098 | ||||||||
\(320\) | 9.69340 | 0.541878 | ||||||||
\(321\) | −0.414232 | −0.0231202 | ||||||||
\(322\) | −0.438527 | −0.0244381 | ||||||||
\(323\) | −10.2898 | −0.572539 | ||||||||
\(324\) | 38.4870 | 2.13816 | ||||||||
\(325\) | 6.02543 | 0.334231 | ||||||||
\(326\) | 29.1679 | 1.61546 | ||||||||
\(327\) | −1.54698 | −0.0855484 | ||||||||
\(328\) | −52.6761 | −2.90855 | ||||||||
\(329\) | 9.24358 | 0.509615 | ||||||||
\(330\) | 5.05212 | 0.278110 | ||||||||
\(331\) | −13.9866 | −0.768771 | −0.384386 | − | 0.923173i | \(-0.625587\pi\) | ||||
−0.384386 | + | 0.923173i | \(0.625587\pi\) | |||||||
\(332\) | −59.4894 | −3.26491 | ||||||||
\(333\) | 28.6795 | 1.57163 | ||||||||
\(334\) | 39.6181 | 2.16781 | ||||||||
\(335\) | 7.32813 | 0.400378 | ||||||||
\(336\) | 1.56087 | 0.0851524 | ||||||||
\(337\) | 22.5592 | 1.22888 | 0.614438 | − | 0.788965i | \(-0.289383\pi\) | ||||
0.614438 | + | 0.788965i | \(0.289383\pi\) | |||||||
\(338\) | 27.9718 | 1.52147 | ||||||||
\(339\) | 0.616974 | 0.0335094 | ||||||||
\(340\) | −19.1466 | −1.03837 | ||||||||
\(341\) | 12.8877 | 0.697910 | ||||||||
\(342\) | −53.5885 | −2.89773 | ||||||||
\(343\) | −19.9419 | −1.07676 | ||||||||
\(344\) | 22.5845 | 1.21767 | ||||||||
\(345\) | −0.0250142 | −0.00134672 | ||||||||
\(346\) | −26.0114 | −1.39838 | ||||||||
\(347\) | −32.9515 | −1.76893 | −0.884464 | − | 0.466609i | \(-0.845476\pi\) | ||||
−0.884464 | + | 0.466609i | \(0.845476\pi\) | |||||||
\(348\) | 2.12925 | 0.114140 | ||||||||
\(349\) | −19.1978 | −1.02763 | −0.513817 | − | 0.857900i | \(-0.671769\pi\) | ||||
−0.513817 | + | 0.857900i | \(0.671769\pi\) | |||||||
\(350\) | −25.8868 | −1.38371 | ||||||||
\(351\) | −0.900464 | −0.0480632 | ||||||||
\(352\) | −21.3611 | −1.13855 | ||||||||
\(353\) | −18.1307 | −0.964998 | −0.482499 | − | 0.875897i | \(-0.660271\pi\) | ||||
−0.482499 | + | 0.875897i | \(0.660271\pi\) | |||||||
\(354\) | 3.13339 | 0.166538 | ||||||||
\(355\) | 9.31408 | 0.494340 | ||||||||
\(356\) | −3.31355 | −0.175618 | ||||||||
\(357\) | 0.370672 | 0.0196180 | ||||||||
\(358\) | 4.32299 | 0.228477 | ||||||||
\(359\) | 33.5414 | 1.77025 | 0.885125 | − | 0.465353i | \(-0.154073\pi\) | ||||
0.885125 | + | 0.465353i | \(0.154073\pi\) | |||||||
\(360\) | −53.6387 | −2.82701 | ||||||||
\(361\) | 31.8278 | 1.67515 | ||||||||
\(362\) | 16.6060 | 0.872793 | ||||||||
\(363\) | 2.70942 | 0.142208 | ||||||||
\(364\) | 13.9023 | 0.728680 | ||||||||
\(365\) | −8.90186 | −0.465945 | ||||||||
\(366\) | 3.53373 | 0.184711 | ||||||||
\(367\) | −9.55097 | −0.498557 | −0.249278 | − | 0.968432i | \(-0.580193\pi\) | ||||
−0.249278 | + | 0.968432i | \(0.580193\pi\) | |||||||
\(368\) | 0.452352 | 0.0235805 | ||||||||
\(369\) | −26.8724 | −1.39892 | ||||||||
\(370\) | −74.0041 | −3.84729 | ||||||||
\(371\) | 9.32057 | 0.483900 | ||||||||
\(372\) | 1.02360 | 0.0530714 | ||||||||
\(373\) | 20.9958 | 1.08712 | 0.543560 | − | 0.839370i | \(-0.317076\pi\) | ||||
0.543560 | + | 0.839370i | \(0.317076\pi\) | |||||||
\(374\) | −21.6963 | −1.12189 | ||||||||
\(375\) | 0.203777 | 0.0105230 | ||||||||
\(376\) | −23.1161 | −1.19212 | ||||||||
\(377\) | 6.15240 | 0.316865 | ||||||||
\(378\) | 3.86863 | 0.198981 | ||||||||
\(379\) | −24.0977 | −1.23782 | −0.618909 | − | 0.785463i | \(-0.712425\pi\) | ||||
−0.618909 | + | 0.785463i | \(0.712425\pi\) | |||||||
\(380\) | 94.5771 | 4.85170 | ||||||||
\(381\) | −0.494500 | −0.0253340 | ||||||||
\(382\) | −23.7921 | −1.21731 | ||||||||
\(383\) | −29.8732 | −1.52645 | −0.763225 | − | 0.646133i | \(-0.776385\pi\) | ||||
−0.763225 | + | 0.646133i | \(0.776385\pi\) | |||||||
\(384\) | 1.65638 | 0.0845268 | ||||||||
\(385\) | −42.8957 | −2.18617 | ||||||||
\(386\) | −58.4609 | −2.97558 | ||||||||
\(387\) | 11.5214 | 0.585663 | ||||||||
\(388\) | 69.7059 | 3.53878 | ||||||||
\(389\) | −25.5557 | −1.29572 | −0.647862 | − | 0.761758i | \(-0.724336\pi\) | ||||
−0.647862 | + | 0.761758i | \(0.724336\pi\) | |||||||
\(390\) | 1.15944 | 0.0587104 | ||||||||
\(391\) | 0.107424 | 0.00543264 | ||||||||
\(392\) | 8.87051 | 0.448028 | ||||||||
\(393\) | −1.03397 | −0.0521571 | ||||||||
\(394\) | 2.62859 | 0.132426 | ||||||||
\(395\) | −41.1081 | −2.06837 | ||||||||
\(396\) | −77.2827 | −3.88360 | ||||||||
\(397\) | 1.03331 | 0.0518603 | 0.0259301 | − | 0.999664i | \(-0.491745\pi\) | ||||
0.0259301 | + | 0.999664i | \(0.491745\pi\) | |||||||
\(398\) | 67.7799 | 3.39750 | ||||||||
\(399\) | −1.83098 | −0.0916639 | ||||||||
\(400\) | 26.7030 | 1.33515 | ||||||||
\(401\) | 0.885632 | 0.0442264 | 0.0221132 | − | 0.999755i | \(-0.492961\pi\) | ||||
0.0221132 | + | 0.999755i | \(0.492961\pi\) | |||||||
\(402\) | 0.659545 | 0.0328951 | ||||||||
\(403\) | 2.95767 | 0.147332 | ||||||||
\(404\) | 10.4574 | 0.520275 | ||||||||
\(405\) | −27.2529 | −1.35421 | ||||||||
\(406\) | −26.4323 | −1.31181 | ||||||||
\(407\) | −57.3564 | −2.84305 | ||||||||
\(408\) | −0.926967 | −0.0458917 | ||||||||
\(409\) | −29.9718 | −1.48201 | −0.741004 | − | 0.671501i | \(-0.765650\pi\) | ||||
−0.741004 | + | 0.671501i | \(0.765650\pi\) | |||||||
\(410\) | 69.3412 | 3.42452 | ||||||||
\(411\) | 1.23032 | 0.0606874 | ||||||||
\(412\) | −55.6938 | −2.74384 | ||||||||
\(413\) | −26.6045 | −1.30912 | ||||||||
\(414\) | 0.559454 | 0.0274957 | ||||||||
\(415\) | 42.1250 | 2.06783 | ||||||||
\(416\) | −4.90228 | −0.240354 | ||||||||
\(417\) | 2.24801 | 0.110086 | ||||||||
\(418\) | 107.172 | 5.24196 | ||||||||
\(419\) | −12.9675 | −0.633505 | −0.316753 | − | 0.948508i | \(-0.602592\pi\) | ||||
−0.316753 | + | 0.948508i | \(0.602592\pi\) | |||||||
\(420\) | −3.40698 | −0.166243 | ||||||||
\(421\) | 21.3185 | 1.03900 | 0.519501 | − | 0.854470i | \(-0.326118\pi\) | ||||
0.519501 | + | 0.854470i | \(0.326118\pi\) | |||||||
\(422\) | 41.6910 | 2.02949 | ||||||||
\(423\) | −11.7926 | −0.573374 | ||||||||
\(424\) | −23.3086 | −1.13197 | ||||||||
\(425\) | 6.34136 | 0.307601 | ||||||||
\(426\) | 0.838284 | 0.0406150 | ||||||||
\(427\) | −30.0036 | −1.45197 | ||||||||
\(428\) | −16.3507 | −0.790340 | ||||||||
\(429\) | 0.898615 | 0.0433856 | ||||||||
\(430\) | −29.7295 | −1.43368 | ||||||||
\(431\) | 5.94836 | 0.286522 | 0.143261 | − | 0.989685i | \(-0.454241\pi\) | ||||
0.143261 | + | 0.989685i | \(0.454241\pi\) | |||||||
\(432\) | −3.99060 | −0.191998 | ||||||||
\(433\) | 14.2140 | 0.683082 | 0.341541 | − | 0.939867i | \(-0.389051\pi\) | ||||
0.341541 | + | 0.939867i | \(0.389051\pi\) | |||||||
\(434\) | −12.7070 | −0.609953 | ||||||||
\(435\) | −1.50774 | −0.0722905 | ||||||||
\(436\) | −61.0630 | −2.92439 | ||||||||
\(437\) | −0.530633 | −0.0253836 | ||||||||
\(438\) | −0.801184 | −0.0382820 | ||||||||
\(439\) | 3.57191 | 0.170478 | 0.0852391 | − | 0.996361i | \(-0.472835\pi\) | ||||
0.0852391 | + | 0.996361i | \(0.472835\pi\) | |||||||
\(440\) | 107.272 | 5.11401 | ||||||||
\(441\) | 4.52525 | 0.215488 | ||||||||
\(442\) | −4.97921 | −0.236837 | ||||||||
\(443\) | 21.2486 | 1.00955 | 0.504775 | − | 0.863251i | \(-0.331576\pi\) | ||||
0.504775 | + | 0.863251i | \(0.331576\pi\) | |||||||
\(444\) | −4.55552 | −0.216195 | ||||||||
\(445\) | 2.34635 | 0.111228 | ||||||||
\(446\) | −7.75635 | −0.367274 | ||||||||
\(447\) | −0.0196818 | −0.000930917 0 | ||||||||
\(448\) | −7.40743 | −0.349968 | ||||||||
\(449\) | −9.34568 | −0.441050 | −0.220525 | − | 0.975381i | \(-0.570777\pi\) | ||||
−0.220525 | + | 0.975381i | \(0.570777\pi\) | |||||||
\(450\) | 33.0254 | 1.55683 | ||||||||
\(451\) | 53.7424 | 2.53063 | ||||||||
\(452\) | 24.3534 | 1.14549 | ||||||||
\(453\) | 0.800565 | 0.0376138 | ||||||||
\(454\) | −9.15719 | −0.429768 | ||||||||
\(455\) | −9.84436 | −0.461511 | ||||||||
\(456\) | 4.57888 | 0.214426 | ||||||||
\(457\) | −18.4164 | −0.861483 | −0.430742 | − | 0.902475i | \(-0.641748\pi\) | ||||
−0.430742 | + | 0.902475i | \(0.641748\pi\) | |||||||
\(458\) | 20.3668 | 0.951676 | ||||||||
\(459\) | −0.947678 | −0.0442338 | ||||||||
\(460\) | −0.987368 | −0.0460363 | ||||||||
\(461\) | −31.8181 | −1.48192 | −0.740959 | − | 0.671550i | \(-0.765629\pi\) | ||||
−0.740959 | + | 0.671550i | \(0.765629\pi\) | |||||||
\(462\) | −3.86069 | −0.179616 | ||||||||
\(463\) | 8.98406 | 0.417525 | 0.208762 | − | 0.977966i | \(-0.433056\pi\) | ||||
0.208762 | + | 0.977966i | \(0.433056\pi\) | |||||||
\(464\) | 27.2656 | 1.26578 | ||||||||
\(465\) | −0.724823 | −0.0336128 | ||||||||
\(466\) | 72.9045 | 3.37723 | ||||||||
\(467\) | −3.05723 | −0.141472 | −0.0707358 | − | 0.997495i | \(-0.522535\pi\) | ||||
−0.0707358 | + | 0.997495i | \(0.522535\pi\) | |||||||
\(468\) | −17.7360 | −0.819848 | ||||||||
\(469\) | −5.59995 | −0.258582 | ||||||||
\(470\) | 30.4293 | 1.40360 | ||||||||
\(471\) | −0.262565 | −0.0120984 | ||||||||
\(472\) | 66.5318 | 3.06238 | ||||||||
\(473\) | −23.0417 | −1.05946 | ||||||||
\(474\) | −3.69980 | −0.169938 | ||||||||
\(475\) | −31.3240 | −1.43724 | ||||||||
\(476\) | 14.6313 | 0.670623 | ||||||||
\(477\) | −11.8908 | −0.544442 | ||||||||
\(478\) | −70.3953 | −3.21981 | ||||||||
\(479\) | −10.4524 | −0.477581 | −0.238790 | − | 0.971071i | \(-0.576751\pi\) | ||||
−0.238790 | + | 0.971071i | \(0.576751\pi\) | |||||||
\(480\) | 1.20138 | 0.0548352 | ||||||||
\(481\) | −13.1630 | −0.600183 | ||||||||
\(482\) | −37.6522 | −1.71501 | ||||||||
\(483\) | 0.0191152 | 0.000869770 0 | ||||||||
\(484\) | 106.947 | 4.86123 | ||||||||
\(485\) | −49.3593 | −2.24129 | ||||||||
\(486\) | −7.40812 | −0.336039 | ||||||||
\(487\) | −34.8112 | −1.57745 | −0.788723 | − | 0.614749i | \(-0.789257\pi\) | ||||
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(488\) | 75.0322 | 3.39655 | ||||||||
\(489\) | −1.27141 | −0.0574953 | ||||||||
\(490\) | −11.6769 | −0.527507 | ||||||||
\(491\) | 10.6515 | 0.480694 | 0.240347 | − | 0.970687i | \(-0.422739\pi\) | ||||
0.240347 | + | 0.970687i | \(0.422739\pi\) | |||||||
\(492\) | 4.26848 | 0.192438 | ||||||||
\(493\) | 6.47498 | 0.291619 | ||||||||
\(494\) | 24.5955 | 1.10660 | ||||||||
\(495\) | 54.7245 | 2.45968 | ||||||||
\(496\) | 13.1075 | 0.588546 | ||||||||
\(497\) | −7.11756 | −0.319266 | ||||||||
\(498\) | 3.79132 | 0.169893 | ||||||||
\(499\) | 27.4772 | 1.23005 | 0.615023 | − | 0.788509i | \(-0.289147\pi\) | ||||
0.615023 | + | 0.788509i | \(0.289147\pi\) | |||||||
\(500\) | 8.04357 | 0.359719 | ||||||||
\(501\) | −1.72693 | −0.0771537 | ||||||||
\(502\) | −31.1661 | −1.39101 | ||||||||
\(503\) | −23.3475 | −1.04101 | −0.520507 | − | 0.853857i | \(-0.674257\pi\) | ||||
−0.520507 | + | 0.853857i | \(0.674257\pi\) | |||||||
\(504\) | 40.9892 | 1.82580 | ||||||||
\(505\) | −7.40497 | −0.329517 | ||||||||
\(506\) | −1.11886 | −0.0497393 | ||||||||
\(507\) | −1.21928 | −0.0541500 | ||||||||
\(508\) | −19.5190 | −0.866018 | ||||||||
\(509\) | −25.7282 | −1.14038 | −0.570191 | − | 0.821512i | \(-0.693131\pi\) | ||||
−0.570191 | + | 0.821512i | \(0.693131\pi\) | |||||||
\(510\) | 1.22023 | 0.0540327 | ||||||||
\(511\) | 6.80255 | 0.300927 | ||||||||
\(512\) | 49.4689 | 2.18624 | ||||||||
\(513\) | 4.68119 | 0.206679 | ||||||||
\(514\) | 16.0335 | 0.707209 | ||||||||
\(515\) | 39.4372 | 1.73781 | ||||||||
\(516\) | −1.83008 | −0.0805646 | ||||||||
\(517\) | 23.5841 | 1.03723 | ||||||||
\(518\) | 56.5519 | 2.48475 | ||||||||
\(519\) | 1.13382 | 0.0497693 | ||||||||
\(520\) | 24.6185 | 1.07959 | ||||||||
\(521\) | −22.5748 | −0.989021 | −0.494510 | − | 0.869172i | \(-0.664653\pi\) | ||||
−0.494510 | + | 0.869172i | \(0.664653\pi\) | |||||||
\(522\) | 33.7213 | 1.47594 | ||||||||
\(523\) | −25.6577 | −1.12193 | −0.560967 | − | 0.827838i | \(-0.689571\pi\) | ||||
−0.560967 | + | 0.827838i | \(0.689571\pi\) | |||||||
\(524\) | −40.8133 | −1.78294 | ||||||||
\(525\) | 1.12839 | 0.0492471 | ||||||||
\(526\) | −71.1583 | −3.10265 | ||||||||
\(527\) | 3.11275 | 0.135594 | ||||||||
\(528\) | 3.98240 | 0.173312 | ||||||||
\(529\) | −22.9945 | −0.999759 | ||||||||
\(530\) | 30.6828 | 1.33278 | ||||||||
\(531\) | 33.9409 | 1.47291 | ||||||||
\(532\) | −72.2732 | −3.13344 | ||||||||
\(533\) | 12.3336 | 0.534229 | ||||||||
\(534\) | 0.211176 | 0.00913849 | ||||||||
\(535\) | 11.5781 | 0.500563 | ||||||||
\(536\) | 14.0042 | 0.604890 | ||||||||
\(537\) | −0.188437 | −0.00813164 | ||||||||
\(538\) | 34.9476 | 1.50670 | ||||||||
\(539\) | −9.05009 | −0.389815 | ||||||||
\(540\) | 8.71045 | 0.374838 | ||||||||
\(541\) | −25.9268 | −1.11468 | −0.557341 | − | 0.830284i | \(-0.688178\pi\) | ||||
−0.557341 | + | 0.830284i | \(0.688178\pi\) | |||||||
\(542\) | −55.6657 | −2.39105 | ||||||||
\(543\) | −0.723848 | −0.0310633 | ||||||||
\(544\) | −5.15932 | −0.221204 | ||||||||
\(545\) | 43.2392 | 1.85217 | ||||||||
\(546\) | −0.886010 | −0.0379177 | ||||||||
\(547\) | 15.3858 | 0.657849 | 0.328925 | − | 0.944356i | \(-0.393314\pi\) | ||||
0.328925 | + | 0.944356i | \(0.393314\pi\) | |||||||
\(548\) | 48.5637 | 2.07454 | ||||||||
\(549\) | 38.2773 | 1.63364 | ||||||||
\(550\) | −66.0477 | −2.81628 | ||||||||
\(551\) | −31.9841 | −1.36257 | ||||||||
\(552\) | −0.0478027 | −0.00203462 | ||||||||
\(553\) | 31.4136 | 1.33584 | ||||||||
\(554\) | 13.8409 | 0.588041 | ||||||||
\(555\) | 3.22580 | 0.136928 | ||||||||
\(556\) | 88.7342 | 3.76317 | ||||||||
\(557\) | 29.7817 | 1.26189 | 0.630946 | − | 0.775827i | \(-0.282667\pi\) | ||||
0.630946 | + | 0.775827i | \(0.282667\pi\) | |||||||
\(558\) | 16.2110 | 0.686266 | ||||||||
\(559\) | −5.28795 | −0.223657 | ||||||||
\(560\) | −43.6273 | −1.84359 | ||||||||
\(561\) | 0.945732 | 0.0399288 | ||||||||
\(562\) | 62.2764 | 2.62697 | ||||||||
\(563\) | 39.0349 | 1.64512 | 0.822562 | − | 0.568675i | \(-0.192544\pi\) | ||||
0.822562 | + | 0.568675i | \(0.192544\pi\) | |||||||
\(564\) | 1.87316 | 0.0788742 | ||||||||
\(565\) | −17.2448 | −0.725496 | ||||||||
\(566\) | −45.3415 | −1.90585 | ||||||||
\(567\) | 20.8259 | 0.874607 | ||||||||
\(568\) | 17.7994 | 0.746847 | ||||||||
\(569\) | 36.9995 | 1.55110 | 0.775550 | − | 0.631286i | \(-0.217473\pi\) | ||||
0.775550 | + | 0.631286i | \(0.217473\pi\) | |||||||
\(570\) | −6.02750 | −0.252464 | ||||||||
\(571\) | 6.04832 | 0.253114 | 0.126557 | − | 0.991959i | \(-0.459607\pi\) | ||||
0.126557 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(572\) | 35.4704 | 1.48309 | ||||||||
\(573\) | 1.03708 | 0.0433248 | ||||||||
\(574\) | −52.9886 | −2.21170 | ||||||||
\(575\) | 0.327017 | 0.0136376 | ||||||||
\(576\) | 9.45009 | 0.393754 | ||||||||
\(577\) | −38.2544 | −1.59255 | −0.796276 | − | 0.604933i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604933i | \(0.793200\pi\) | |||||||
\(578\) | 37.5251 | 1.56084 | ||||||||
\(579\) | 2.54828 | 0.105903 | ||||||||
\(580\) | −59.5139 | −2.47118 | ||||||||
\(581\) | −32.1907 | −1.33550 | ||||||||
\(582\) | −4.44243 | −0.184145 | ||||||||
\(583\) | 23.7805 | 0.984888 | ||||||||
\(584\) | −17.0117 | −0.703947 | ||||||||
\(585\) | 12.5590 | 0.519252 | ||||||||
\(586\) | −41.3671 | −1.70886 | ||||||||
\(587\) | 33.9792 | 1.40247 | 0.701236 | − | 0.712929i | \(-0.252632\pi\) | ||||
0.701236 | + | 0.712929i | \(0.252632\pi\) | |||||||
\(588\) | −0.718800 | −0.0296428 | ||||||||
\(589\) | −15.3759 | −0.633552 | ||||||||
\(590\) | −87.5805 | −3.60563 | ||||||||
\(591\) | −0.114579 | −0.00471314 | ||||||||
\(592\) | −58.3347 | −2.39754 | ||||||||
\(593\) | −18.4718 | −0.758546 | −0.379273 | − | 0.925285i | \(-0.623826\pi\) | ||||
−0.379273 | + | 0.925285i | \(0.623826\pi\) | |||||||
\(594\) | 9.87044 | 0.404989 | ||||||||
\(595\) | −10.3605 | −0.424740 | ||||||||
\(596\) | −0.776886 | −0.0318225 | ||||||||
\(597\) | −2.95449 | −0.120919 | ||||||||
\(598\) | −0.256773 | −0.0105002 | ||||||||
\(599\) | −34.0234 | −1.39016 | −0.695079 | − | 0.718934i | \(-0.744630\pi\) | ||||
−0.695079 | + | 0.718934i | \(0.744630\pi\) | |||||||
\(600\) | −2.82186 | −0.115202 | ||||||||
\(601\) | −13.1688 | −0.537168 | −0.268584 | − | 0.963256i | \(-0.586556\pi\) | ||||
−0.268584 | + | 0.963256i | \(0.586556\pi\) | |||||||
\(602\) | 22.7185 | 0.925935 | ||||||||
\(603\) | 7.14419 | 0.290934 | ||||||||
\(604\) | 31.6002 | 1.28579 | ||||||||
\(605\) | −75.7301 | −3.07887 | ||||||||
\(606\) | −0.666461 | −0.0270731 | ||||||||
\(607\) | −21.0334 | −0.853719 | −0.426860 | − | 0.904318i | \(-0.640380\pi\) | ||||
−0.426860 | + | 0.904318i | \(0.640380\pi\) | |||||||
\(608\) | 25.4852 | 1.03356 | ||||||||
\(609\) | 1.15217 | 0.0466883 | ||||||||
\(610\) | −98.7701 | −3.99908 | ||||||||
\(611\) | 5.41243 | 0.218964 | ||||||||
\(612\) | −18.6660 | −0.754527 | ||||||||
\(613\) | −30.8704 | −1.24684 | −0.623422 | − | 0.781885i | \(-0.714258\pi\) | ||||
−0.623422 | + | 0.781885i | \(0.714258\pi\) | |||||||
\(614\) | 18.5335 | 0.747950 | ||||||||
\(615\) | −3.02254 | −0.121881 | ||||||||
\(616\) | −81.9746 | −3.30285 | ||||||||
\(617\) | 32.8924 | 1.32420 | 0.662100 | − | 0.749416i | \(-0.269666\pi\) | ||||
0.662100 | + | 0.749416i | \(0.269666\pi\) | |||||||
\(618\) | 3.54942 | 0.142779 | ||||||||
\(619\) | 23.1323 | 0.929767 | 0.464884 | − | 0.885372i | \(-0.346096\pi\) | ||||
0.464884 | + | 0.885372i | \(0.346096\pi\) | |||||||
\(620\) | −28.6104 | −1.14902 | ||||||||
\(621\) | −0.0488708 | −0.00196112 | ||||||||
\(622\) | 11.3822 | 0.456385 | ||||||||
\(623\) | −1.79302 | −0.0718358 | ||||||||
\(624\) | 0.913943 | 0.0365870 | ||||||||
\(625\) | −27.6640 | −1.10656 | ||||||||
\(626\) | −28.5785 | −1.14223 | ||||||||
\(627\) | −4.67158 | −0.186565 | ||||||||
\(628\) | −10.3641 | −0.413571 | ||||||||
\(629\) | −13.8532 | −0.552364 | ||||||||
\(630\) | −53.9569 | −2.14969 | ||||||||
\(631\) | −19.9797 | −0.795377 | −0.397689 | − | 0.917520i | \(-0.630188\pi\) | ||||
−0.397689 | + | 0.917520i | \(0.630188\pi\) | |||||||
\(632\) | −78.5584 | −3.12489 | ||||||||
\(633\) | −1.81729 | −0.0722308 | ||||||||
\(634\) | −12.9111 | −0.512764 | ||||||||
\(635\) | 13.8216 | 0.548494 | ||||||||
\(636\) | 1.88876 | 0.0748942 | ||||||||
\(637\) | −2.07695 | −0.0822918 | ||||||||
\(638\) | −67.4395 | −2.66995 | ||||||||
\(639\) | 9.08029 | 0.359211 | ||||||||
\(640\) | −46.2970 | −1.83005 | ||||||||
\(641\) | −41.7437 | −1.64878 | −0.824388 | − | 0.566025i | \(-0.808480\pi\) | ||||
−0.824388 | + | 0.566025i | \(0.808480\pi\) | |||||||
\(642\) | 1.04205 | 0.0411263 | ||||||||
\(643\) | −17.2286 | −0.679431 | −0.339716 | − | 0.940528i | \(-0.610331\pi\) | ||||
−0.339716 | + | 0.940528i | \(0.610331\pi\) | |||||||
\(644\) | 0.754519 | 0.0297322 | ||||||||
\(645\) | 1.29589 | 0.0510257 | ||||||||
\(646\) | 25.8851 | 1.01844 | ||||||||
\(647\) | −30.4198 | −1.19593 | −0.597963 | − | 0.801524i | \(-0.704023\pi\) | ||||
−0.597963 | + | 0.801524i | \(0.704023\pi\) | |||||||
\(648\) | −52.0810 | −2.04593 | ||||||||
\(649\) | −67.8787 | −2.66447 | ||||||||
\(650\) | −15.1576 | −0.594532 | ||||||||
\(651\) | 0.553889 | 0.0217086 | ||||||||
\(652\) | −50.1856 | −1.96542 | ||||||||
\(653\) | 11.3656 | 0.444769 | 0.222385 | − | 0.974959i | \(-0.428616\pi\) | ||||
0.222385 | + | 0.974959i | \(0.428616\pi\) | |||||||
\(654\) | 3.89161 | 0.152174 | ||||||||
\(655\) | 28.9003 | 1.12923 | ||||||||
\(656\) | 54.6591 | 2.13408 | ||||||||
\(657\) | −8.67841 | −0.338577 | ||||||||
\(658\) | −23.2533 | −0.906506 | ||||||||
\(659\) | −38.4595 | −1.49817 | −0.749085 | − | 0.662474i | \(-0.769506\pi\) | ||||
−0.749085 | + | 0.662474i | \(0.769506\pi\) | |||||||
\(660\) | −8.69256 | −0.338358 | ||||||||
\(661\) | −19.1525 | −0.744948 | −0.372474 | − | 0.928043i | \(-0.621490\pi\) | ||||
−0.372474 | + | 0.928043i | \(0.621490\pi\) | |||||||
\(662\) | 35.1848 | 1.36750 | ||||||||
\(663\) | 0.217041 | 0.00842918 | ||||||||
\(664\) | 80.5017 | 3.12407 | ||||||||
\(665\) | 51.1772 | 1.98457 | ||||||||
\(666\) | −72.1466 | −2.79562 | ||||||||
\(667\) | 0.333908 | 0.0129290 | ||||||||
\(668\) | −68.1660 | −2.63742 | ||||||||
\(669\) | 0.338095 | 0.0130715 | ||||||||
\(670\) | −18.4347 | −0.712196 | ||||||||
\(671\) | −76.5511 | −2.95522 | ||||||||
\(672\) | −0.918060 | −0.0354149 | ||||||||
\(673\) | −3.04424 | −0.117347 | −0.0586734 | − | 0.998277i | \(-0.518687\pi\) | ||||
−0.0586734 | + | 0.998277i | \(0.518687\pi\) | |||||||
\(674\) | −56.7501 | −2.18593 | ||||||||
\(675\) | −2.88491 | −0.111040 | ||||||||
\(676\) | −48.1277 | −1.85106 | ||||||||
\(677\) | 35.6688 | 1.37086 | 0.685432 | − | 0.728137i | \(-0.259613\pi\) | ||||
0.685432 | + | 0.728137i | \(0.259613\pi\) | |||||||
\(678\) | −1.55207 | −0.0596068 | ||||||||
\(679\) | 37.7190 | 1.44752 | ||||||||
\(680\) | 25.9093 | 0.993578 | ||||||||
\(681\) | 0.399157 | 0.0152957 | ||||||||
\(682\) | −32.4205 | −1.24145 | ||||||||
\(683\) | −9.68229 | −0.370482 | −0.185241 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185241 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(684\) | 92.2031 | 3.52547 | ||||||||
\(685\) | −34.3884 | −1.31391 | ||||||||
\(686\) | 50.1661 | 1.91535 | ||||||||
\(687\) | −0.887776 | −0.0338708 | ||||||||
\(688\) | −23.4347 | −0.893438 | ||||||||
\(689\) | 5.45752 | 0.207915 | ||||||||
\(690\) | 0.0629260 | 0.00239555 | ||||||||
\(691\) | −25.1219 | −0.955680 | −0.477840 | − | 0.878447i | \(-0.658580\pi\) | ||||
−0.477840 | + | 0.878447i | \(0.658580\pi\) | |||||||
\(692\) | 44.7546 | 1.70131 | ||||||||
\(693\) | −41.8190 | −1.58857 | ||||||||
\(694\) | 82.8931 | 3.14658 | ||||||||
\(695\) | −62.8334 | −2.38341 | ||||||||
\(696\) | −2.88132 | −0.109216 | ||||||||
\(697\) | 12.9803 | 0.491665 | ||||||||
\(698\) | 48.2942 | 1.82796 | ||||||||
\(699\) | −3.17787 | −0.120198 | ||||||||
\(700\) | 44.5403 | 1.68347 | ||||||||
\(701\) | −27.2124 | −1.02780 | −0.513899 | − | 0.857851i | \(-0.671799\pi\) | ||||
−0.513899 | + | 0.857851i | \(0.671799\pi\) | |||||||
\(702\) | 2.26522 | 0.0854952 | ||||||||
\(703\) | 68.4299 | 2.58088 | ||||||||
\(704\) | −18.8993 | −0.712295 | ||||||||
\(705\) | −1.32640 | −0.0499551 | ||||||||
\(706\) | 45.6097 | 1.71654 | ||||||||
\(707\) | 5.65867 | 0.212816 | ||||||||
\(708\) | −5.39125 | −0.202615 | ||||||||
\(709\) | −44.8116 | −1.68293 | −0.841467 | − | 0.540309i | \(-0.818307\pi\) | ||||
−0.841467 | + | 0.540309i | \(0.818307\pi\) | |||||||
\(710\) | −23.4306 | −0.879335 | ||||||||
\(711\) | −40.0762 | −1.50298 | ||||||||
\(712\) | 4.48394 | 0.168043 | ||||||||
\(713\) | 0.160521 | 0.00601157 | ||||||||
\(714\) | −0.932466 | −0.0348967 | ||||||||
\(715\) | −25.1169 | −0.939319 | ||||||||
\(716\) | −7.43803 | −0.277972 | ||||||||
\(717\) | 3.06849 | 0.114595 | ||||||||
\(718\) | −84.3773 | −3.14893 | ||||||||
\(719\) | −27.3245 | −1.01903 | −0.509515 | − | 0.860462i | \(-0.670175\pi\) | ||||
−0.509515 | + | 0.860462i | \(0.670175\pi\) | |||||||
\(720\) | 55.6579 | 2.07425 | ||||||||
\(721\) | −30.1368 | −1.12235 | ||||||||
\(722\) | −80.0664 | −2.97976 | ||||||||
\(723\) | 1.64124 | 0.0610384 | ||||||||
\(724\) | −28.5719 | −1.06187 | ||||||||
\(725\) | 19.7111 | 0.732050 | ||||||||
\(726\) | −6.81585 | −0.252960 | ||||||||
\(727\) | 8.10796 | 0.300708 | 0.150354 | − | 0.988632i | \(-0.451959\pi\) | ||||
0.150354 | + | 0.988632i | \(0.451959\pi\) | |||||||
\(728\) | −18.8128 | −0.697248 | ||||||||
\(729\) | −26.3529 | −0.976032 | ||||||||
\(730\) | 22.3936 | 0.828825 | ||||||||
\(731\) | −5.56522 | −0.205837 | ||||||||
\(732\) | −6.08005 | −0.224725 | ||||||||
\(733\) | 15.4156 | 0.569389 | 0.284694 | − | 0.958618i | \(-0.408108\pi\) | ||||
0.284694 | + | 0.958618i | \(0.408108\pi\) | |||||||
\(734\) | 24.0265 | 0.886836 | ||||||||
\(735\) | 0.508989 | 0.0187743 | ||||||||
\(736\) | −0.266061 | −0.00980713 | ||||||||
\(737\) | −14.2877 | −0.526295 | ||||||||
\(738\) | 67.6006 | 2.48841 | ||||||||
\(739\) | −30.0721 | −1.10622 | −0.553111 | − | 0.833108i | \(-0.686559\pi\) | ||||
−0.553111 | + | 0.833108i | \(0.686559\pi\) | |||||||
\(740\) | 127.330 | 4.68074 | ||||||||
\(741\) | −1.07210 | −0.0393847 | ||||||||
\(742\) | −23.4469 | −0.860764 | ||||||||
\(743\) | −20.6158 | −0.756322 | −0.378161 | − | 0.925740i | \(-0.623443\pi\) | ||||
−0.378161 | + | 0.925740i | \(0.623443\pi\) | |||||||
\(744\) | −1.38515 | −0.0507821 | ||||||||
\(745\) | 0.550119 | 0.0201548 | ||||||||
\(746\) | −52.8172 | −1.93378 | ||||||||
\(747\) | 41.0676 | 1.50258 | ||||||||
\(748\) | 37.3302 | 1.36493 | ||||||||
\(749\) | −8.84763 | −0.323285 | ||||||||
\(750\) | −0.512625 | −0.0187184 | ||||||||
\(751\) | 26.8436 | 0.979537 | 0.489768 | − | 0.871853i | \(-0.337081\pi\) | ||||
0.489768 | + | 0.871853i | \(0.337081\pi\) | |||||||
\(752\) | 23.9863 | 0.874691 | ||||||||
\(753\) | 1.35851 | 0.0495070 | ||||||||
\(754\) | −15.4770 | −0.563641 | ||||||||
\(755\) | −22.3763 | −0.814358 | ||||||||
\(756\) | −6.65628 | −0.242087 | ||||||||
\(757\) | −24.1265 | −0.876892 | −0.438446 | − | 0.898758i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898758i | \(0.644471\pi\) | |||||||
\(758\) | 60.6206 | 2.20184 | ||||||||
\(759\) | 0.0487704 | 0.00177025 | ||||||||
\(760\) | −127.983 | −4.64242 | ||||||||
\(761\) | 28.1515 | 1.02049 | 0.510245 | − | 0.860029i | \(-0.329555\pi\) | ||||
0.510245 | + | 0.860029i | \(0.329555\pi\) | |||||||
\(762\) | 1.24397 | 0.0450643 | ||||||||
\(763\) | −33.0422 | −1.19621 | ||||||||
\(764\) | 40.9361 | 1.48102 | ||||||||
\(765\) | 13.2175 | 0.477881 | ||||||||
\(766\) | 75.1494 | 2.71526 | ||||||||
\(767\) | −15.5778 | −0.562483 | ||||||||
\(768\) | −3.47320 | −0.125328 | ||||||||
\(769\) | −2.87899 | −0.103819 | −0.0519096 | − | 0.998652i | \(-0.516531\pi\) | ||||
−0.0519096 | + | 0.998652i | \(0.516531\pi\) | |||||||
\(770\) | 107.909 | 3.88877 | ||||||||
\(771\) | −0.698893 | −0.0251700 | ||||||||
\(772\) | 100.587 | 3.62019 | ||||||||
\(773\) | 5.87427 | 0.211283 | 0.105641 | − | 0.994404i | \(-0.466310\pi\) | ||||
0.105641 | + | 0.994404i | \(0.466310\pi\) | |||||||
\(774\) | −28.9833 | −1.04178 | ||||||||
\(775\) | 9.47580 | 0.340381 | ||||||||
\(776\) | −94.3268 | −3.38613 | ||||||||
\(777\) | −2.46507 | −0.0884338 | ||||||||
\(778\) | 64.2881 | 2.30484 | ||||||||
\(779\) | −64.1181 | −2.29727 | ||||||||
\(780\) | −1.99490 | −0.0714290 | ||||||||
\(781\) | −18.1598 | −0.649807 | ||||||||
\(782\) | −0.270236 | −0.00966362 | ||||||||
\(783\) | −2.94570 | −0.105271 | ||||||||
\(784\) | −9.20445 | −0.328730 | ||||||||
\(785\) | 7.33887 | 0.261936 | ||||||||
\(786\) | 2.60108 | 0.0927773 | ||||||||
\(787\) | 1.10544 | 0.0394046 | 0.0197023 | − | 0.999806i | \(-0.493728\pi\) | ||||
0.0197023 | + | 0.999806i | \(0.493728\pi\) | |||||||
\(788\) | −4.52268 | −0.161114 | ||||||||
\(789\) | 3.10175 | 0.110425 | ||||||||
\(790\) | 103.412 | 3.67923 | ||||||||
\(791\) | 13.1780 | 0.468557 | ||||||||
\(792\) | 104.580 | 3.71608 | ||||||||
\(793\) | −17.5681 | −0.623862 | ||||||||
\(794\) | −2.59940 | −0.0922494 | ||||||||
\(795\) | −1.33745 | −0.0474344 | ||||||||
\(796\) | −116.620 | −4.13350 | ||||||||
\(797\) | −40.5711 | −1.43710 | −0.718551 | − | 0.695474i | \(-0.755194\pi\) | ||||
−0.718551 | + | 0.695474i | \(0.755194\pi\) | |||||||
\(798\) | 4.60605 | 0.163052 | ||||||||
\(799\) | 5.69622 | 0.201518 | ||||||||
\(800\) | −15.7059 | −0.555289 | ||||||||
\(801\) | 2.28746 | 0.0808234 | ||||||||
\(802\) | −2.22791 | −0.0786701 | ||||||||
\(803\) | 17.3560 | 0.612481 | ||||||||
\(804\) | −1.13480 | −0.0400212 | ||||||||
\(805\) | −0.534281 | −0.0188309 | ||||||||
\(806\) | −7.44036 | −0.262075 | ||||||||
\(807\) | −1.52335 | −0.0536243 | ||||||||
\(808\) | −14.1511 | −0.497833 | ||||||||
\(809\) | 37.6019 | 1.32201 | 0.661007 | − | 0.750380i | \(-0.270129\pi\) | ||||
0.661007 | + | 0.750380i | \(0.270129\pi\) | |||||||
\(810\) | 68.5578 | 2.40888 | ||||||||
\(811\) | −35.4190 | −1.24373 | −0.621864 | − | 0.783125i | \(-0.713624\pi\) | ||||
−0.621864 | + | 0.783125i | \(0.713624\pi\) | |||||||
\(812\) | 45.4789 | 1.59599 | ||||||||
\(813\) | 2.42644 | 0.0850989 | ||||||||
\(814\) | 144.287 | 5.05724 | ||||||||
\(815\) | 35.5369 | 1.24480 | ||||||||
\(816\) | 0.961863 | 0.0336719 | ||||||||
\(817\) | 27.4902 | 0.961759 | ||||||||
\(818\) | 75.3973 | 2.63621 | ||||||||
\(819\) | −9.59725 | −0.335355 | ||||||||
\(820\) | −119.307 | −4.16637 | ||||||||
\(821\) | −25.1654 | −0.878278 | −0.439139 | − | 0.898419i | \(-0.644716\pi\) | ||||
−0.439139 | + | 0.898419i | \(0.644716\pi\) | |||||||
\(822\) | −3.09502 | −0.107951 | ||||||||
\(823\) | 16.2066 | 0.564926 | 0.282463 | − | 0.959278i | \(-0.408849\pi\) | ||||
0.282463 | + | 0.959278i | \(0.408849\pi\) | |||||||
\(824\) | 75.3655 | 2.62548 | ||||||||
\(825\) | 2.87899 | 0.100233 | ||||||||
\(826\) | 66.9266 | 2.32867 | ||||||||
\(827\) | 10.5401 | 0.366516 | 0.183258 | − | 0.983065i | \(-0.441336\pi\) | ||||
0.183258 | + | 0.983065i | \(0.441336\pi\) | |||||||
\(828\) | −0.962584 | −0.0334521 | ||||||||
\(829\) | −30.8998 | −1.07319 | −0.536597 | − | 0.843838i | \(-0.680291\pi\) | ||||
−0.536597 | + | 0.843838i | \(0.680291\pi\) | |||||||
\(830\) | −105.970 | −3.67827 | ||||||||
\(831\) | −0.603315 | −0.0209288 | ||||||||
\(832\) | −4.33731 | −0.150369 | ||||||||
\(833\) | −2.18585 | −0.0757353 | ||||||||
\(834\) | −5.65512 | −0.195821 | ||||||||
\(835\) | 48.2689 | 1.67042 | ||||||||
\(836\) | −184.398 | −6.37753 | ||||||||
\(837\) | −1.41610 | −0.0489476 | ||||||||
\(838\) | 32.6213 | 1.12688 | ||||||||
\(839\) | −25.6649 | −0.886051 | −0.443025 | − | 0.896509i | \(-0.646095\pi\) | ||||
−0.443025 | + | 0.896509i | \(0.646095\pi\) | |||||||
\(840\) | 4.61036 | 0.159072 | ||||||||
\(841\) | −8.87359 | −0.305986 | ||||||||
\(842\) | −53.6291 | −1.84818 | ||||||||
\(843\) | −2.71459 | −0.0934956 | ||||||||
\(844\) | −71.7326 | −2.46914 | ||||||||
\(845\) | 34.0796 | 1.17237 | ||||||||
\(846\) | 29.6655 | 1.01992 | ||||||||
\(847\) | 57.8708 | 1.98846 | ||||||||
\(848\) | 24.1861 | 0.830555 | ||||||||
\(849\) | 1.97641 | 0.0678303 | ||||||||
\(850\) | −15.9524 | −0.547163 | ||||||||
\(851\) | −0.714396 | −0.0244892 | ||||||||
\(852\) | −1.44233 | −0.0494135 | ||||||||
\(853\) | 47.9373 | 1.64134 | 0.820670 | − | 0.571402i | \(-0.193600\pi\) | ||||
0.820670 | + | 0.571402i | \(0.193600\pi\) | |||||||
\(854\) | 75.4773 | 2.58278 | ||||||||
\(855\) | −65.2898 | −2.23286 | ||||||||
\(856\) | 22.1259 | 0.756249 | ||||||||
\(857\) | −21.2849 | −0.727077 | −0.363539 | − | 0.931579i | \(-0.618432\pi\) | ||||
−0.363539 | + | 0.931579i | \(0.618432\pi\) | |||||||
\(858\) | −2.26057 | −0.0771745 | ||||||||
\(859\) | −2.47244 | −0.0843585 | −0.0421792 | − | 0.999110i | \(-0.513430\pi\) | ||||
−0.0421792 | + | 0.999110i | \(0.513430\pi\) | |||||||
\(860\) | 51.1519 | 1.74426 | ||||||||
\(861\) | 2.30974 | 0.0787159 | ||||||||
\(862\) | −14.9638 | −0.509668 | ||||||||
\(863\) | −13.3682 | −0.455058 | −0.227529 | − | 0.973771i | \(-0.573065\pi\) | ||||
−0.227529 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(864\) | 2.34716 | 0.0798519 | ||||||||
\(865\) | −31.6911 | −1.07753 | ||||||||
\(866\) | −35.7570 | −1.21507 | ||||||||
\(867\) | −1.63570 | −0.0555513 | ||||||||
\(868\) | 21.8633 | 0.742088 | ||||||||
\(869\) | 80.1488 | 2.71886 | ||||||||
\(870\) | 3.79288 | 0.128591 | ||||||||
\(871\) | −3.27897 | −0.111104 | ||||||||
\(872\) | 82.6311 | 2.79824 | ||||||||
\(873\) | −48.1204 | −1.62863 | ||||||||
\(874\) | 1.33487 | 0.0451526 | ||||||||
\(875\) | 4.35251 | 0.147142 | ||||||||
\(876\) | 1.37850 | 0.0465751 | ||||||||
\(877\) | 48.4913 | 1.63744 | 0.818718 | − | 0.574195i | \(-0.194685\pi\) | ||||
0.818718 | + | 0.574195i | \(0.194685\pi\) | |||||||
\(878\) | −8.98555 | −0.303248 | ||||||||
\(879\) | 1.80317 | 0.0608194 | ||||||||
\(880\) | −111.311 | −3.75229 | ||||||||
\(881\) | 38.7922 | 1.30694 | 0.653471 | − | 0.756952i | \(-0.273312\pi\) | ||||
0.653471 | + | 0.756952i | \(0.273312\pi\) | |||||||
\(882\) | −11.3838 | −0.383311 | ||||||||
\(883\) | −59.3659 | −1.99782 | −0.998911 | − | 0.0466624i | \(-0.985141\pi\) | ||||
−0.998911 | + | 0.0466624i | \(0.985141\pi\) | |||||||
\(884\) | 8.56711 | 0.288143 | ||||||||
\(885\) | 3.81759 | 0.128327 | ||||||||
\(886\) | −53.4531 | −1.79579 | ||||||||
\(887\) | −33.5285 | −1.12578 | −0.562888 | − | 0.826533i | \(-0.690310\pi\) | ||||
−0.562888 | + | 0.826533i | \(0.690310\pi\) | |||||||
\(888\) | 6.16458 | 0.206870 | ||||||||
\(889\) | −10.5621 | −0.354241 | ||||||||
\(890\) | −5.90252 | −0.197853 | ||||||||
\(891\) | 53.1353 | 1.78010 | ||||||||
\(892\) | 13.3454 | 0.446837 | ||||||||
\(893\) | −28.1373 | −0.941578 | ||||||||
\(894\) | 0.0495118 | 0.00165592 | ||||||||
\(895\) | 5.26693 | 0.176054 | ||||||||
\(896\) | 35.3788 | 1.18192 | ||||||||
\(897\) | 0.0111926 | 0.000373709 0 | ||||||||
\(898\) | 23.5101 | 0.784542 | ||||||||
\(899\) | 9.67547 | 0.322695 | ||||||||
\(900\) | −56.8227 | −1.89409 | ||||||||
\(901\) | 5.74367 | 0.191349 | ||||||||
\(902\) | −135.195 | −4.50151 | ||||||||
\(903\) | −0.990285 | −0.0329546 | ||||||||
\(904\) | −32.9553 | −1.09608 | ||||||||
\(905\) | 20.2320 | 0.672536 | ||||||||
\(906\) | −2.01391 | −0.0669077 | ||||||||
\(907\) | −4.45849 | −0.148042 | −0.0740209 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740209 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(908\) | 15.7556 | 0.522869 | ||||||||
\(909\) | −7.21910 | −0.239442 | ||||||||
\(910\) | 24.7646 | 0.820938 | ||||||||
\(911\) | −12.1205 | −0.401570 | −0.200785 | − | 0.979635i | \(-0.564349\pi\) | ||||
−0.200785 | + | 0.979635i | \(0.564349\pi\) | |||||||
\(912\) | −4.75126 | −0.157330 | ||||||||
\(913\) | −82.1314 | −2.71815 | ||||||||
\(914\) | 46.3285 | 1.53241 | ||||||||
\(915\) | 4.30534 | 0.142330 | ||||||||
\(916\) | −35.0426 | −1.15784 | ||||||||
\(917\) | −22.0848 | −0.729303 | ||||||||
\(918\) | 2.38399 | 0.0786834 | ||||||||
\(919\) | −33.1316 | −1.09291 | −0.546455 | − | 0.837488i | \(-0.684023\pi\) | ||||
−0.546455 | + | 0.837488i | \(0.684023\pi\) | |||||||
\(920\) | 1.33612 | 0.0440505 | ||||||||
\(921\) | −0.807864 | −0.0266200 | ||||||||
\(922\) | 80.0421 | 2.63605 | ||||||||
\(923\) | −4.16758 | −0.137177 | ||||||||
\(924\) | 6.64261 | 0.218526 | ||||||||
\(925\) | −42.1718 | −1.38660 | ||||||||
\(926\) | −22.6004 | −0.742696 | ||||||||
\(927\) | 38.4473 | 1.26278 | ||||||||
\(928\) | −16.0369 | −0.526437 | ||||||||
\(929\) | −19.9837 | −0.655644 | −0.327822 | − | 0.944739i | \(-0.606315\pi\) | ||||
−0.327822 | + | 0.944739i | \(0.606315\pi\) | |||||||
\(930\) | 1.82337 | 0.0597907 | ||||||||
\(931\) | 10.7973 | 0.353868 | ||||||||
\(932\) | −125.438 | −4.10885 | ||||||||
\(933\) | −0.496144 | −0.0162430 | ||||||||
\(934\) | 7.69080 | 0.251651 | ||||||||
\(935\) | −26.4339 | −0.864479 | ||||||||
\(936\) | 24.0006 | 0.784483 | ||||||||
\(937\) | 53.3853 | 1.74402 | 0.872011 | − | 0.489487i | \(-0.162816\pi\) | ||||
0.872011 | + | 0.489487i | \(0.162816\pi\) | |||||||
\(938\) | 14.0873 | 0.459967 | ||||||||
\(939\) | 1.24572 | 0.0406525 | ||||||||
\(940\) | −52.3560 | −1.70766 | ||||||||
\(941\) | −14.4740 | −0.471839 | −0.235920 | − | 0.971773i | \(-0.575810\pi\) | ||||
−0.235920 | + | 0.971773i | \(0.575810\pi\) | |||||||
\(942\) | 0.660512 | 0.0215206 | ||||||||
\(943\) | 0.669382 | 0.0217981 | ||||||||
\(944\) | −69.0365 | −2.24695 | ||||||||
\(945\) | 4.71337 | 0.153326 | ||||||||
\(946\) | 57.9639 | 1.88457 | ||||||||
\(947\) | 18.5202 | 0.601827 | 0.300913 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300913 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(948\) | 6.36579 | 0.206751 | ||||||||
\(949\) | 3.98313 | 0.129298 | ||||||||
\(950\) | 78.7991 | 2.55658 | ||||||||
\(951\) | 0.562786 | 0.0182496 | ||||||||
\(952\) | −19.7992 | −0.641696 | ||||||||
\(953\) | −54.7246 | −1.77270 | −0.886352 | − | 0.463012i | \(-0.846769\pi\) | ||||
−0.886352 | + | 0.463012i | \(0.846769\pi\) | |||||||
\(954\) | 29.9126 | 0.968457 | ||||||||
\(955\) | −28.9872 | −0.938003 | ||||||||
\(956\) | 121.121 | 3.91732 | ||||||||
\(957\) | 2.93965 | 0.0950254 | ||||||||
\(958\) | 26.2941 | 0.849524 | ||||||||
\(959\) | 26.2786 | 0.848581 | ||||||||
\(960\) | 1.06292 | 0.0343057 | ||||||||
\(961\) | −26.3487 | −0.849957 | ||||||||
\(962\) | 33.1131 | 1.06761 | ||||||||
\(963\) | 11.2874 | 0.363733 | ||||||||
\(964\) | 64.7836 | 2.08654 | ||||||||
\(965\) | −71.2262 | −2.29285 | ||||||||
\(966\) | −0.0480863 | −0.00154715 | ||||||||
\(967\) | −14.1338 | −0.454511 | −0.227255 | − | 0.973835i | \(-0.572975\pi\) | ||||
−0.227255 | + | 0.973835i | \(0.572975\pi\) | |||||||
\(968\) | −144.722 | −4.65154 | ||||||||
\(969\) | −1.12832 | −0.0362468 | ||||||||
\(970\) | 124.169 | 3.98682 | ||||||||
\(971\) | 45.2229 | 1.45127 | 0.725636 | − | 0.688078i | \(-0.241546\pi\) | ||||
0.725636 | + | 0.688078i | \(0.241546\pi\) | |||||||
\(972\) | 12.7462 | 0.408836 | ||||||||
\(973\) | 48.0155 | 1.53931 | ||||||||
\(974\) | 87.5715 | 2.80597 | ||||||||
\(975\) | 0.660714 | 0.0211598 | ||||||||
\(976\) | −77.8568 | −2.49214 | ||||||||
\(977\) | −9.71934 | −0.310949 | −0.155475 | − | 0.987840i | \(-0.549691\pi\) | ||||
−0.155475 | + | 0.987840i | \(0.549691\pi\) | |||||||
\(978\) | 3.19838 | 0.102273 | ||||||||
\(979\) | −4.57471 | −0.146208 | ||||||||
\(980\) | 20.0910 | 0.641782 | ||||||||
\(981\) | 42.1539 | 1.34587 | ||||||||
\(982\) | −26.7950 | −0.855062 | ||||||||
\(983\) | 36.4697 | 1.16320 | 0.581602 | − | 0.813474i | \(-0.302426\pi\) | ||||
0.581602 | + | 0.813474i | \(0.302426\pi\) | |||||||
\(984\) | −5.77615 | −0.184137 | ||||||||
\(985\) | 3.20255 | 0.102042 | ||||||||
\(986\) | −16.2885 | −0.518733 | ||||||||
\(987\) | 1.01360 | 0.0322631 | ||||||||
\(988\) | −42.3184 | −1.34633 | ||||||||
\(989\) | −0.286992 | −0.00912583 | ||||||||
\(990\) | −137.666 | −4.37530 | ||||||||
\(991\) | 40.8078 | 1.29630 | 0.648151 | − | 0.761512i | \(-0.275543\pi\) | ||||
0.648151 | + | 0.761512i | \(0.275543\pi\) | |||||||
\(992\) | −7.70950 | −0.244777 | ||||||||
\(993\) | −1.53369 | −0.0486700 | ||||||||
\(994\) | 17.9050 | 0.567913 | ||||||||
\(995\) | 82.5799 | 2.61796 | ||||||||
\(996\) | −6.52326 | −0.206697 | ||||||||
\(997\) | −17.1690 | −0.543749 | −0.271874 | − | 0.962333i | \(-0.587644\pi\) | ||||
−0.271874 | + | 0.962333i | \(0.587644\pi\) | |||||||
\(998\) | −69.1219 | −2.18801 | ||||||||
\(999\) | 6.30232 | 0.199396 |
(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 | 6029.2.a.a.1.15 | ✓ | 234 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.a.1.15 | ✓ | 234 | 1.1 | even | 1 | trivial |