Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20228 | −1.55725 | −0.778625 | − | 0.627490i | \(-0.784082\pi\) | ||||
−0.778625 | + | 0.627490i | \(0.784082\pi\) | |||||||
\(3\) | −3.01220 | −1.73909 | −0.869547 | − | 0.493851i | \(-0.835589\pi\) | ||||
−0.869547 | + | 0.493851i | \(0.835589\pi\) | |||||||
\(4\) | 2.85005 | 1.42503 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 6.63371 | 2.70820 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.87206 | −0.661872 | ||||||||
\(9\) | 6.07333 | 2.02444 | ||||||||
\(10\) | 2.20228 | 0.696423 | ||||||||
\(11\) | −3.78158 | −1.14019 | −0.570094 | − | 0.821580i | \(-0.693093\pi\) | ||||
−0.570094 | + | 0.821580i | \(0.693093\pi\) | |||||||
\(12\) | −8.58492 | −2.47825 | ||||||||
\(13\) | 4.33541 | 1.20243 | 0.601214 | − | 0.799088i | \(-0.294684\pi\) | ||||
0.601214 | + | 0.799088i | \(0.294684\pi\) | |||||||
\(14\) | 2.20228 | 0.588585 | ||||||||
\(15\) | 3.01220 | 0.777746 | ||||||||
\(16\) | −1.57731 | −0.394327 | ||||||||
\(17\) | 1.42225 | 0.344947 | 0.172473 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172473 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(18\) | −13.3752 | −3.15257 | ||||||||
\(19\) | −3.78650 | −0.868683 | −0.434341 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434341 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(20\) | −2.85005 | −0.637291 | ||||||||
\(21\) | 3.01220 | 0.657315 | ||||||||
\(22\) | 8.32810 | 1.77556 | ||||||||
\(23\) | −8.43662 | −1.75916 | −0.879578 | − | 0.475754i | \(-0.842175\pi\) | ||||
−0.879578 | + | 0.475754i | \(0.842175\pi\) | |||||||
\(24\) | 5.63900 | 1.15106 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.54781 | −1.87248 | ||||||||
\(27\) | −9.25749 | −1.78160 | ||||||||
\(28\) | −2.85005 | −0.538609 | ||||||||
\(29\) | −7.89528 | −1.46612 | −0.733058 | − | 0.680166i | \(-0.761908\pi\) | ||||
−0.733058 | + | 0.680166i | \(0.761908\pi\) | |||||||
\(30\) | −6.63371 | −1.21114 | ||||||||
\(31\) | −4.98465 | −0.895270 | −0.447635 | − | 0.894216i | \(-0.647734\pi\) | ||||
−0.447635 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(32\) | 7.21779 | 1.27594 | ||||||||
\(33\) | 11.3909 | 1.98289 | ||||||||
\(34\) | −3.13220 | −0.537168 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 17.3093 | 2.88489 | ||||||||
\(37\) | −2.71137 | −0.445747 | −0.222873 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222873 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(38\) | 8.33895 | 1.35276 | ||||||||
\(39\) | −13.0591 | −2.09113 | ||||||||
\(40\) | 1.87206 | 0.295998 | ||||||||
\(41\) | −1.56428 | −0.244299 | −0.122150 | − | 0.992512i | \(-0.538979\pi\) | ||||
−0.122150 | + | 0.992512i | \(0.538979\pi\) | |||||||
\(42\) | −6.63371 | −1.02360 | ||||||||
\(43\) | 5.07248 | 0.773545 | 0.386773 | − | 0.922175i | \(-0.373590\pi\) | ||||
0.386773 | + | 0.922175i | \(0.373590\pi\) | |||||||
\(44\) | −10.7777 | −1.62480 | ||||||||
\(45\) | −6.07333 | −0.905359 | ||||||||
\(46\) | 18.5798 | 2.73945 | ||||||||
\(47\) | −3.10936 | −0.453547 | −0.226773 | − | 0.973948i | \(-0.572818\pi\) | ||||
−0.226773 | + | 0.973948i | \(0.572818\pi\) | |||||||
\(48\) | 4.75116 | 0.685771 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.20228 | −0.311450 | ||||||||
\(51\) | −4.28410 | −0.599894 | ||||||||
\(52\) | 12.3562 | 1.71349 | ||||||||
\(53\) | 1.42151 | 0.195259 | 0.0976295 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976295 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(54\) | 20.3876 | 2.77440 | ||||||||
\(55\) | 3.78158 | 0.509908 | ||||||||
\(56\) | 1.87206 | 0.250164 | ||||||||
\(57\) | 11.4057 | 1.51072 | ||||||||
\(58\) | 17.3876 | 2.28311 | ||||||||
\(59\) | −9.60495 | −1.25046 | −0.625229 | − | 0.780441i | \(-0.714994\pi\) | ||||
−0.625229 | + | 0.780441i | \(0.714994\pi\) | |||||||
\(60\) | 8.58492 | 1.10831 | ||||||||
\(61\) | −10.5797 | −1.35460 | −0.677299 | − | 0.735708i | \(-0.736850\pi\) | ||||
−0.677299 | + | 0.735708i | \(0.736850\pi\) | |||||||
\(62\) | 10.9776 | 1.39416 | ||||||||
\(63\) | −6.07333 | −0.765168 | ||||||||
\(64\) | −12.7410 | −1.59263 | ||||||||
\(65\) | −4.33541 | −0.537742 | ||||||||
\(66\) | −25.0859 | −3.08786 | ||||||||
\(67\) | −0.748661 | −0.0914636 | −0.0457318 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457318 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(68\) | 4.05349 | 0.491558 | ||||||||
\(69\) | 25.4128 | 3.05934 | ||||||||
\(70\) | −2.20228 | −0.263223 | ||||||||
\(71\) | 1.44871 | 0.171930 | 0.0859650 | − | 0.996298i | \(-0.472603\pi\) | ||||
0.0859650 | + | 0.996298i | \(0.472603\pi\) | |||||||
\(72\) | −11.3696 | −1.33992 | ||||||||
\(73\) | 5.14212 | 0.601840 | 0.300920 | − | 0.953649i | \(-0.402706\pi\) | ||||
0.300920 | + | 0.953649i | \(0.402706\pi\) | |||||||
\(74\) | 5.97121 | 0.694139 | ||||||||
\(75\) | −3.01220 | −0.347819 | ||||||||
\(76\) | −10.7917 | −1.23790 | ||||||||
\(77\) | 3.78158 | 0.430950 | ||||||||
\(78\) | 28.7599 | 3.25642 | ||||||||
\(79\) | 9.81951 | 1.10478 | 0.552391 | − | 0.833585i | \(-0.313716\pi\) | ||||
0.552391 | + | 0.833585i | \(0.313716\pi\) | |||||||
\(80\) | 1.57731 | 0.176348 | ||||||||
\(81\) | 9.66538 | 1.07393 | ||||||||
\(82\) | 3.44499 | 0.380435 | ||||||||
\(83\) | 0.0758723 | 0.00832807 | 0.00416403 | − | 0.999991i | \(-0.498675\pi\) | ||||
0.00416403 | + | 0.999991i | \(0.498675\pi\) | |||||||
\(84\) | 8.58492 | 0.936692 | ||||||||
\(85\) | −1.42225 | −0.154265 | ||||||||
\(86\) | −11.1710 | −1.20460 | ||||||||
\(87\) | 23.7821 | 2.54971 | ||||||||
\(88\) | 7.07932 | 0.754658 | ||||||||
\(89\) | −14.5072 | −1.53776 | −0.768879 | − | 0.639395i | \(-0.779185\pi\) | ||||
−0.768879 | + | 0.639395i | \(0.779185\pi\) | |||||||
\(90\) | 13.3752 | 1.40987 | ||||||||
\(91\) | −4.33541 | −0.454475 | ||||||||
\(92\) | −24.0448 | −2.50684 | ||||||||
\(93\) | 15.0148 | 1.55696 | ||||||||
\(94\) | 6.84769 | 0.706285 | ||||||||
\(95\) | 3.78650 | 0.388487 | ||||||||
\(96\) | −21.7414 | −2.21897 | ||||||||
\(97\) | 8.60767 | 0.873976 | 0.436988 | − | 0.899467i | \(-0.356045\pi\) | ||||
0.436988 | + | 0.899467i | \(0.356045\pi\) | |||||||
\(98\) | −2.20228 | −0.222464 | ||||||||
\(99\) | −22.9668 | −2.30825 | ||||||||
\(100\) | 2.85005 | 0.285005 | ||||||||
\(101\) | −1.83398 | −0.182488 | −0.0912442 | − | 0.995829i | \(-0.529084\pi\) | ||||
−0.0912442 | + | 0.995829i | \(0.529084\pi\) | |||||||
\(102\) | 9.43481 | 0.934185 | ||||||||
\(103\) | −9.46639 | −0.932751 | −0.466375 | − | 0.884587i | \(-0.654440\pi\) | ||||
−0.466375 | + | 0.884587i | \(0.654440\pi\) | |||||||
\(104\) | −8.11614 | −0.795853 | ||||||||
\(105\) | −3.01220 | −0.293960 | ||||||||
\(106\) | −3.13056 | −0.304067 | ||||||||
\(107\) | 0.955305 | 0.0923528 | 0.0461764 | − | 0.998933i | \(-0.485296\pi\) | ||||
0.0461764 | + | 0.998933i | \(0.485296\pi\) | |||||||
\(108\) | −26.3843 | −2.53883 | ||||||||
\(109\) | 3.03723 | 0.290913 | 0.145457 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145457 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(110\) | −8.32810 | −0.794053 | ||||||||
\(111\) | 8.16719 | 0.775195 | ||||||||
\(112\) | 1.57731 | 0.149041 | ||||||||
\(113\) | 9.05115 | 0.851461 | 0.425730 | − | 0.904850i | \(-0.360017\pi\) | ||||
0.425730 | + | 0.904850i | \(0.360017\pi\) | |||||||
\(114\) | −25.1186 | −2.35257 | ||||||||
\(115\) | 8.43662 | 0.786719 | ||||||||
\(116\) | −22.5020 | −2.08925 | ||||||||
\(117\) | 26.3304 | 2.43425 | ||||||||
\(118\) | 21.1528 | 1.94728 | ||||||||
\(119\) | −1.42225 | −0.130378 | ||||||||
\(120\) | −5.63900 | −0.514768 | ||||||||
\(121\) | 3.30031 | 0.300028 | ||||||||
\(122\) | 23.2996 | 2.10945 | ||||||||
\(123\) | 4.71192 | 0.424859 | ||||||||
\(124\) | −14.2065 | −1.27578 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 13.3752 | 1.19156 | ||||||||
\(127\) | −15.2615 | −1.35424 | −0.677122 | − | 0.735871i | \(-0.736773\pi\) | ||||
−0.677122 | + | 0.735871i | \(0.736773\pi\) | |||||||
\(128\) | 13.6237 | 1.20418 | ||||||||
\(129\) | −15.2793 | −1.34527 | ||||||||
\(130\) | 9.54781 | 0.837398 | ||||||||
\(131\) | 3.03144 | 0.264858 | 0.132429 | − | 0.991192i | \(-0.457722\pi\) | ||||
0.132429 | + | 0.991192i | \(0.457722\pi\) | |||||||
\(132\) | 32.4645 | 2.82567 | ||||||||
\(133\) | 3.78650 | 0.328331 | ||||||||
\(134\) | 1.64876 | 0.142432 | ||||||||
\(135\) | 9.25749 | 0.796758 | ||||||||
\(136\) | −2.66254 | −0.228311 | ||||||||
\(137\) | 3.14462 | 0.268663 | 0.134332 | − | 0.990936i | \(-0.457111\pi\) | ||||
0.134332 | + | 0.990936i | \(0.457111\pi\) | |||||||
\(138\) | −55.9661 | −4.76415 | ||||||||
\(139\) | −11.8717 | −1.00695 | −0.503473 | − | 0.864011i | \(-0.667945\pi\) | ||||
−0.503473 | + | 0.864011i | \(0.667945\pi\) | |||||||
\(140\) | 2.85005 | 0.240873 | ||||||||
\(141\) | 9.36600 | 0.788760 | ||||||||
\(142\) | −3.19046 | −0.267738 | ||||||||
\(143\) | −16.3947 | −1.37099 | ||||||||
\(144\) | −9.57951 | −0.798292 | ||||||||
\(145\) | 7.89528 | 0.655667 | ||||||||
\(146\) | −11.3244 | −0.937215 | ||||||||
\(147\) | −3.01220 | −0.248442 | ||||||||
\(148\) | −7.72755 | −0.635201 | ||||||||
\(149\) | −18.1012 | −1.48291 | −0.741454 | − | 0.671004i | \(-0.765863\pi\) | ||||
−0.741454 | + | 0.671004i | \(0.765863\pi\) | |||||||
\(150\) | 6.63371 | 0.541640 | ||||||||
\(151\) | −6.14969 | −0.500455 | −0.250227 | − | 0.968187i | \(-0.580505\pi\) | ||||
−0.250227 | + | 0.968187i | \(0.580505\pi\) | |||||||
\(152\) | 7.08854 | 0.574957 | ||||||||
\(153\) | 8.63781 | 0.698326 | ||||||||
\(154\) | −8.32810 | −0.671097 | ||||||||
\(155\) | 4.98465 | 0.400377 | ||||||||
\(156\) | −37.2192 | −2.97992 | ||||||||
\(157\) | 17.3907 | 1.38793 | 0.693964 | − | 0.720009i | \(-0.255863\pi\) | ||||
0.693964 | + | 0.720009i | \(0.255863\pi\) | |||||||
\(158\) | −21.6253 | −1.72042 | ||||||||
\(159\) | −4.28186 | −0.339573 | ||||||||
\(160\) | −7.21779 | −0.570616 | ||||||||
\(161\) | 8.43662 | 0.664899 | ||||||||
\(162\) | −21.2859 | −1.67238 | ||||||||
\(163\) | −6.62045 | −0.518554 | −0.259277 | − | 0.965803i | \(-0.583484\pi\) | ||||
−0.259277 | + | 0.965803i | \(0.583484\pi\) | |||||||
\(164\) | −4.45828 | −0.348133 | ||||||||
\(165\) | −11.3909 | −0.886777 | ||||||||
\(166\) | −0.167092 | −0.0129689 | ||||||||
\(167\) | −20.9967 | −1.62478 | −0.812388 | − | 0.583118i | \(-0.801833\pi\) | ||||
−0.812388 | + | 0.583118i | \(0.801833\pi\) | |||||||
\(168\) | −5.63900 | −0.435058 | ||||||||
\(169\) | 5.79580 | 0.445831 | ||||||||
\(170\) | 3.13220 | 0.240229 | ||||||||
\(171\) | −22.9967 | −1.75860 | ||||||||
\(172\) | 14.4568 | 1.10232 | ||||||||
\(173\) | −15.8812 | −1.20742 | −0.603712 | − | 0.797202i | \(-0.706312\pi\) | ||||
−0.603712 | + | 0.797202i | \(0.706312\pi\) | |||||||
\(174\) | −52.3750 | −3.97054 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 5.96470 | 0.449606 | ||||||||
\(177\) | 28.9320 | 2.17466 | ||||||||
\(178\) | 31.9489 | 2.39467 | ||||||||
\(179\) | 8.25045 | 0.616668 | 0.308334 | − | 0.951278i | \(-0.400229\pi\) | ||||
0.308334 | + | 0.951278i | \(0.400229\pi\) | |||||||
\(180\) | −17.3093 | −1.29016 | ||||||||
\(181\) | 13.4586 | 1.00037 | 0.500184 | − | 0.865919i | \(-0.333266\pi\) | ||||
0.500184 | + | 0.865919i | \(0.333266\pi\) | |||||||
\(182\) | 9.54781 | 0.707731 | ||||||||
\(183\) | 31.8683 | 2.35577 | ||||||||
\(184\) | 15.7938 | 1.16434 | ||||||||
\(185\) | 2.71137 | 0.199344 | ||||||||
\(186\) | −33.0667 | −2.42457 | ||||||||
\(187\) | −5.37835 | −0.393304 | ||||||||
\(188\) | −8.86184 | −0.646316 | ||||||||
\(189\) | 9.25749 | 0.673383 | ||||||||
\(190\) | −8.33895 | −0.604971 | ||||||||
\(191\) | 9.46567 | 0.684912 | 0.342456 | − | 0.939534i | \(-0.388741\pi\) | ||||
0.342456 | + | 0.939534i | \(0.388741\pi\) | |||||||
\(192\) | 38.3784 | 2.76972 | ||||||||
\(193\) | −16.0525 | −1.15549 | −0.577743 | − | 0.816219i | \(-0.696066\pi\) | ||||
−0.577743 | + | 0.816219i | \(0.696066\pi\) | |||||||
\(194\) | −18.9565 | −1.36100 | ||||||||
\(195\) | 13.0591 | 0.935183 | ||||||||
\(196\) | 2.85005 | 0.203575 | ||||||||
\(197\) | −22.5002 | −1.60307 | −0.801535 | − | 0.597948i | \(-0.795983\pi\) | ||||
−0.801535 | + | 0.597948i | \(0.795983\pi\) | |||||||
\(198\) | 50.5793 | 3.59452 | ||||||||
\(199\) | −9.28637 | −0.658293 | −0.329147 | − | 0.944279i | \(-0.606761\pi\) | ||||
−0.329147 | + | 0.944279i | \(0.606761\pi\) | |||||||
\(200\) | −1.87206 | −0.132374 | ||||||||
\(201\) | 2.25512 | 0.159064 | ||||||||
\(202\) | 4.03895 | 0.284180 | ||||||||
\(203\) | 7.89528 | 0.554140 | ||||||||
\(204\) | −12.2099 | −0.854865 | ||||||||
\(205\) | 1.56428 | 0.109254 | ||||||||
\(206\) | 20.8477 | 1.45253 | ||||||||
\(207\) | −51.2384 | −3.56132 | ||||||||
\(208\) | −6.83827 | −0.474149 | ||||||||
\(209\) | 14.3189 | 0.990462 | ||||||||
\(210\) | 6.63371 | 0.457770 | ||||||||
\(211\) | −15.1645 | −1.04397 | −0.521985 | − | 0.852955i | \(-0.674808\pi\) | ||||
−0.521985 | + | 0.852955i | \(0.674808\pi\) | |||||||
\(212\) | 4.05137 | 0.278249 | ||||||||
\(213\) | −4.36379 | −0.299002 | ||||||||
\(214\) | −2.10385 | −0.143816 | ||||||||
\(215\) | −5.07248 | −0.345940 | ||||||||
\(216\) | 17.3305 | 1.17919 | ||||||||
\(217\) | 4.98465 | 0.338380 | ||||||||
\(218\) | −6.68883 | −0.453025 | ||||||||
\(219\) | −15.4891 | −1.04666 | ||||||||
\(220\) | 10.7777 | 0.726632 | ||||||||
\(221\) | 6.16605 | 0.414773 | ||||||||
\(222\) | −17.9865 | −1.20717 | ||||||||
\(223\) | −4.53894 | −0.303950 | −0.151975 | − | 0.988384i | \(-0.548563\pi\) | ||||
−0.151975 | + | 0.988384i | \(0.548563\pi\) | |||||||
\(224\) | −7.21779 | −0.482259 | ||||||||
\(225\) | 6.07333 | 0.404889 | ||||||||
\(226\) | −19.9332 | −1.32594 | ||||||||
\(227\) | 3.67431 | 0.243873 | 0.121936 | − | 0.992538i | \(-0.461090\pi\) | ||||
0.121936 | + | 0.992538i | \(0.461090\pi\) | |||||||
\(228\) | 32.5068 | 2.15282 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −18.5798 | −1.22512 | ||||||||
\(231\) | −11.3909 | −0.749463 | ||||||||
\(232\) | 14.7804 | 0.970381 | ||||||||
\(233\) | −16.8132 | −1.10147 | −0.550734 | − | 0.834681i | \(-0.685652\pi\) | ||||
−0.550734 | + | 0.834681i | \(0.685652\pi\) | |||||||
\(234\) | −57.9870 | −3.79073 | ||||||||
\(235\) | 3.10936 | 0.202832 | ||||||||
\(236\) | −27.3746 | −1.78194 | ||||||||
\(237\) | −29.5783 | −1.92132 | ||||||||
\(238\) | 3.13220 | 0.203030 | ||||||||
\(239\) | 17.7248 | 1.14652 | 0.573262 | − | 0.819372i | \(-0.305678\pi\) | ||||
0.573262 | + | 0.819372i | \(0.305678\pi\) | |||||||
\(240\) | −4.75116 | −0.306686 | ||||||||
\(241\) | 18.8485 | 1.21414 | 0.607070 | − | 0.794649i | \(-0.292345\pi\) | ||||
0.607070 | + | 0.794649i | \(0.292345\pi\) | |||||||
\(242\) | −7.26822 | −0.467219 | ||||||||
\(243\) | −1.34157 | −0.0860617 | ||||||||
\(244\) | −30.1528 | −1.93034 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −10.3770 | −0.661612 | ||||||||
\(247\) | −16.4160 | −1.04453 | ||||||||
\(248\) | 9.33155 | 0.592554 | ||||||||
\(249\) | −0.228542 | −0.0144833 | ||||||||
\(250\) | 2.20228 | 0.139285 | ||||||||
\(251\) | −4.97088 | −0.313759 | −0.156880 | − | 0.987618i | \(-0.550143\pi\) | ||||
−0.156880 | + | 0.987618i | \(0.550143\pi\) | |||||||
\(252\) | −17.3093 | −1.09038 | ||||||||
\(253\) | 31.9037 | 2.00577 | ||||||||
\(254\) | 33.6103 | 2.10889 | ||||||||
\(255\) | 4.28410 | 0.268281 | ||||||||
\(256\) | −4.52129 | −0.282581 | ||||||||
\(257\) | 2.41699 | 0.150768 | 0.0753840 | − | 0.997155i | \(-0.475982\pi\) | ||||
0.0753840 | + | 0.997155i | \(0.475982\pi\) | |||||||
\(258\) | 33.6493 | 2.09492 | ||||||||
\(259\) | 2.71137 | 0.168476 | ||||||||
\(260\) | −12.3562 | −0.766296 | ||||||||
\(261\) | −47.9507 | −2.96807 | ||||||||
\(262\) | −6.67608 | −0.412450 | ||||||||
\(263\) | −7.57986 | −0.467394 | −0.233697 | − | 0.972309i | \(-0.575082\pi\) | ||||
−0.233697 | + | 0.972309i | \(0.575082\pi\) | |||||||
\(264\) | −21.3243 | −1.31242 | ||||||||
\(265\) | −1.42151 | −0.0873224 | ||||||||
\(266\) | −8.33895 | −0.511294 | ||||||||
\(267\) | 43.6985 | 2.67430 | ||||||||
\(268\) | −2.13372 | −0.130338 | ||||||||
\(269\) | −15.2830 | −0.931820 | −0.465910 | − | 0.884832i | \(-0.654273\pi\) | ||||
−0.465910 | + | 0.884832i | \(0.654273\pi\) | |||||||
\(270\) | −20.3876 | −1.24075 | ||||||||
\(271\) | 1.98963 | 0.120861 | 0.0604307 | − | 0.998172i | \(-0.480753\pi\) | ||||
0.0604307 | + | 0.998172i | \(0.480753\pi\) | |||||||
\(272\) | −2.24333 | −0.136022 | ||||||||
\(273\) | 13.0591 | 0.790374 | ||||||||
\(274\) | −6.92535 | −0.418376 | ||||||||
\(275\) | −3.78158 | −0.228038 | ||||||||
\(276\) | 72.4277 | 4.35964 | ||||||||
\(277\) | −25.7457 | −1.54691 | −0.773455 | − | 0.633852i | \(-0.781473\pi\) | ||||
−0.773455 | + | 0.633852i | \(0.781473\pi\) | |||||||
\(278\) | 26.1449 | 1.56807 | ||||||||
\(279\) | −30.2734 | −1.81242 | ||||||||
\(280\) | −1.87206 | −0.111877 | ||||||||
\(281\) | 22.8797 | 1.36489 | 0.682445 | − | 0.730937i | \(-0.260917\pi\) | ||||
0.682445 | + | 0.730937i | \(0.260917\pi\) | |||||||
\(282\) | −20.6266 | −1.22830 | ||||||||
\(283\) | −6.63277 | −0.394277 | −0.197139 | − | 0.980376i | \(-0.563165\pi\) | ||||
−0.197139 | + | 0.980376i | \(0.563165\pi\) | |||||||
\(284\) | 4.12889 | 0.245005 | ||||||||
\(285\) | −11.4057 | −0.675615 | ||||||||
\(286\) | 36.1057 | 2.13498 | ||||||||
\(287\) | 1.56428 | 0.0923365 | ||||||||
\(288\) | 43.8360 | 2.58306 | ||||||||
\(289\) | −14.9772 | −0.881012 | ||||||||
\(290\) | −17.3876 | −1.02104 | ||||||||
\(291\) | −25.9280 | −1.51993 | ||||||||
\(292\) | 14.6553 | 0.857638 | ||||||||
\(293\) | −6.88190 | −0.402045 | −0.201023 | − | 0.979587i | \(-0.564426\pi\) | ||||
−0.201023 | + | 0.979587i | \(0.564426\pi\) | |||||||
\(294\) | 6.63371 | 0.386886 | ||||||||
\(295\) | 9.60495 | 0.559222 | ||||||||
\(296\) | 5.07584 | 0.295027 | ||||||||
\(297\) | 35.0079 | 2.03136 | ||||||||
\(298\) | 39.8640 | 2.30926 | ||||||||
\(299\) | −36.5762 | −2.11526 | ||||||||
\(300\) | −8.58492 | −0.495651 | ||||||||
\(301\) | −5.07248 | −0.292373 | ||||||||
\(302\) | 13.5434 | 0.779333 | ||||||||
\(303\) | 5.52432 | 0.317364 | ||||||||
\(304\) | 5.97247 | 0.342545 | ||||||||
\(305\) | 10.5797 | 0.605795 | ||||||||
\(306\) | −19.0229 | −1.08747 | ||||||||
\(307\) | 9.02278 | 0.514957 | 0.257479 | − | 0.966284i | \(-0.417108\pi\) | ||||
0.257479 | + | 0.966284i | \(0.417108\pi\) | |||||||
\(308\) | 10.7777 | 0.614116 | ||||||||
\(309\) | 28.5146 | 1.62214 | ||||||||
\(310\) | −10.9776 | −0.623487 | ||||||||
\(311\) | −24.3545 | −1.38102 | −0.690510 | − | 0.723323i | \(-0.742614\pi\) | ||||
−0.690510 | + | 0.723323i | \(0.742614\pi\) | |||||||
\(312\) | 24.4474 | 1.38406 | ||||||||
\(313\) | 2.98681 | 0.168824 | 0.0844122 | − | 0.996431i | \(-0.473099\pi\) | ||||
0.0844122 | + | 0.996431i | \(0.473099\pi\) | |||||||
\(314\) | −38.2992 | −2.16135 | ||||||||
\(315\) | 6.07333 | 0.342194 | ||||||||
\(316\) | 27.9861 | 1.57434 | ||||||||
\(317\) | −20.6349 | −1.15897 | −0.579487 | − | 0.814982i | \(-0.696747\pi\) | ||||
−0.579487 | + | 0.814982i | \(0.696747\pi\) | |||||||
\(318\) | 9.42986 | 0.528801 | ||||||||
\(319\) | 29.8566 | 1.67165 | ||||||||
\(320\) | 12.7410 | 0.712244 | ||||||||
\(321\) | −2.87757 | −0.160610 | ||||||||
\(322\) | −18.5798 | −1.03541 | ||||||||
\(323\) | −5.38536 | −0.299649 | ||||||||
\(324\) | 27.5468 | 1.53038 | ||||||||
\(325\) | 4.33541 | 0.240485 | ||||||||
\(326\) | 14.5801 | 0.807517 | ||||||||
\(327\) | −9.14872 | −0.505926 | ||||||||
\(328\) | 2.92842 | 0.161695 | ||||||||
\(329\) | 3.10936 | 0.171425 | ||||||||
\(330\) | 25.0859 | 1.38093 | ||||||||
\(331\) | −33.8801 | −1.86222 | −0.931110 | − | 0.364739i | \(-0.881158\pi\) | ||||
−0.931110 | + | 0.364739i | \(0.881158\pi\) | |||||||
\(332\) | 0.216240 | 0.0118677 | ||||||||
\(333\) | −16.4671 | −0.902389 | ||||||||
\(334\) | 46.2407 | 2.53018 | ||||||||
\(335\) | 0.748661 | 0.0409037 | ||||||||
\(336\) | −4.75116 | −0.259197 | ||||||||
\(337\) | −20.9479 | −1.14110 | −0.570552 | − | 0.821261i | \(-0.693271\pi\) | ||||
−0.570552 | + | 0.821261i | \(0.693271\pi\) | |||||||
\(338\) | −12.7640 | −0.694270 | ||||||||
\(339\) | −27.2639 | −1.48077 | ||||||||
\(340\) | −4.05349 | −0.219831 | ||||||||
\(341\) | 18.8498 | 1.02078 | ||||||||
\(342\) | 50.6452 | 2.73858 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −9.49596 | −0.511988 | ||||||||
\(345\) | −25.4128 | −1.36818 | ||||||||
\(346\) | 34.9749 | 1.88026 | ||||||||
\(347\) | −19.5114 | −1.04743 | −0.523714 | − | 0.851894i | \(-0.675454\pi\) | ||||
−0.523714 | + | 0.851894i | \(0.675454\pi\) | |||||||
\(348\) | 67.7803 | 3.63341 | ||||||||
\(349\) | 7.17450 | 0.384042 | 0.192021 | − | 0.981391i | \(-0.438496\pi\) | ||||
0.192021 | + | 0.981391i | \(0.438496\pi\) | |||||||
\(350\) | 2.20228 | 0.117717 | ||||||||
\(351\) | −40.1350 | −2.14225 | ||||||||
\(352\) | −27.2946 | −1.45481 | ||||||||
\(353\) | 9.41706 | 0.501219 | 0.250610 | − | 0.968088i | \(-0.419369\pi\) | ||||
0.250610 | + | 0.968088i | \(0.419369\pi\) | |||||||
\(354\) | −63.7165 | −3.38649 | ||||||||
\(355\) | −1.44871 | −0.0768894 | ||||||||
\(356\) | −41.3462 | −2.19134 | ||||||||
\(357\) | 4.28410 | 0.226739 | ||||||||
\(358\) | −18.1698 | −0.960306 | ||||||||
\(359\) | 9.33033 | 0.492436 | 0.246218 | − | 0.969214i | \(-0.420812\pi\) | ||||
0.246218 | + | 0.969214i | \(0.420812\pi\) | |||||||
\(360\) | 11.3696 | 0.599232 | ||||||||
\(361\) | −4.66241 | −0.245390 | ||||||||
\(362\) | −29.6396 | −1.55782 | ||||||||
\(363\) | −9.94119 | −0.521777 | ||||||||
\(364\) | −12.3562 | −0.647638 | ||||||||
\(365\) | −5.14212 | −0.269151 | ||||||||
\(366\) | −70.1830 | −3.66852 | ||||||||
\(367\) | 18.0824 | 0.943895 | 0.471948 | − | 0.881627i | \(-0.343551\pi\) | ||||
0.471948 | + | 0.881627i | \(0.343551\pi\) | |||||||
\(368\) | 13.3071 | 0.693682 | ||||||||
\(369\) | −9.50039 | −0.494571 | ||||||||
\(370\) | −5.97121 | −0.310428 | ||||||||
\(371\) | −1.42151 | −0.0738009 | ||||||||
\(372\) | 42.7928 | 2.21871 | ||||||||
\(373\) | 5.68094 | 0.294148 | 0.147074 | − | 0.989125i | \(-0.453014\pi\) | ||||
0.147074 | + | 0.989125i | \(0.453014\pi\) | |||||||
\(374\) | 11.8447 | 0.612473 | ||||||||
\(375\) | 3.01220 | 0.155549 | ||||||||
\(376\) | 5.82090 | 0.300190 | ||||||||
\(377\) | −34.2293 | −1.76290 | ||||||||
\(378\) | −20.3876 | −1.04863 | ||||||||
\(379\) | −18.6051 | −0.955681 | −0.477841 | − | 0.878447i | \(-0.658580\pi\) | ||||
−0.477841 | + | 0.878447i | \(0.658580\pi\) | |||||||
\(380\) | 10.7917 | 0.553604 | ||||||||
\(381\) | 45.9708 | 2.35516 | ||||||||
\(382\) | −20.8461 | −1.06658 | ||||||||
\(383\) | −21.3436 | −1.09060 | −0.545302 | − | 0.838239i | \(-0.683585\pi\) | ||||
−0.545302 | + | 0.838239i | \(0.683585\pi\) | |||||||
\(384\) | −41.0373 | −2.09418 | ||||||||
\(385\) | −3.78158 | −0.192727 | ||||||||
\(386\) | 35.3522 | 1.79938 | ||||||||
\(387\) | 30.8068 | 1.56600 | ||||||||
\(388\) | 24.5323 | 1.24544 | ||||||||
\(389\) | −33.8583 | −1.71668 | −0.858341 | − | 0.513079i | \(-0.828505\pi\) | ||||
−0.858341 | + | 0.513079i | \(0.828505\pi\) | |||||||
\(390\) | −28.7599 | −1.45631 | ||||||||
\(391\) | −11.9990 | −0.606815 | ||||||||
\(392\) | −1.87206 | −0.0945531 | ||||||||
\(393\) | −9.13129 | −0.460613 | ||||||||
\(394\) | 49.5517 | 2.49638 | ||||||||
\(395\) | −9.81951 | −0.494073 | ||||||||
\(396\) | −65.4565 | −3.28931 | ||||||||
\(397\) | 17.2818 | 0.867351 | 0.433675 | − | 0.901069i | \(-0.357216\pi\) | ||||
0.433675 | + | 0.901069i | \(0.357216\pi\) | |||||||
\(398\) | 20.4512 | 1.02513 | ||||||||
\(399\) | −11.4057 | −0.570999 | ||||||||
\(400\) | −1.57731 | −0.0788653 | ||||||||
\(401\) | −34.5449 | −1.72509 | −0.862545 | − | 0.505980i | \(-0.831131\pi\) | ||||
−0.862545 | + | 0.505980i | \(0.831131\pi\) | |||||||
\(402\) | −4.96641 | −0.247702 | ||||||||
\(403\) | −21.6105 | −1.07650 | ||||||||
\(404\) | −5.22695 | −0.260051 | ||||||||
\(405\) | −9.66538 | −0.480277 | ||||||||
\(406\) | −17.3876 | −0.862934 | ||||||||
\(407\) | 10.2533 | 0.508235 | ||||||||
\(408\) | 8.02008 | 0.397053 | ||||||||
\(409\) | 23.5760 | 1.16576 | 0.582879 | − | 0.812559i | \(-0.301926\pi\) | ||||
0.582879 | + | 0.812559i | \(0.301926\pi\) | |||||||
\(410\) | −3.44499 | −0.170136 | ||||||||
\(411\) | −9.47222 | −0.467230 | ||||||||
\(412\) | −26.9797 | −1.32919 | ||||||||
\(413\) | 9.60495 | 0.472629 | ||||||||
\(414\) | 112.841 | 5.54586 | ||||||||
\(415\) | −0.0758723 | −0.00372442 | ||||||||
\(416\) | 31.2921 | 1.53422 | ||||||||
\(417\) | 35.7600 | 1.75117 | ||||||||
\(418\) | −31.5344 | −1.54240 | ||||||||
\(419\) | −36.7564 | −1.79567 | −0.897833 | − | 0.440336i | \(-0.854859\pi\) | ||||
−0.897833 | + | 0.440336i | \(0.854859\pi\) | |||||||
\(420\) | −8.58492 | −0.418901 | ||||||||
\(421\) | 1.34267 | 0.0654375 | 0.0327188 | − | 0.999465i | \(-0.489583\pi\) | ||||
0.0327188 | + | 0.999465i | \(0.489583\pi\) | |||||||
\(422\) | 33.3966 | 1.62572 | ||||||||
\(423\) | −18.8842 | −0.918180 | ||||||||
\(424\) | −2.66114 | −0.129236 | ||||||||
\(425\) | 1.42225 | 0.0689893 | ||||||||
\(426\) | 9.61031 | 0.465621 | ||||||||
\(427\) | 10.5797 | 0.511990 | ||||||||
\(428\) | 2.72267 | 0.131605 | ||||||||
\(429\) | 49.3840 | 2.38428 | ||||||||
\(430\) | 11.1710 | 0.538715 | ||||||||
\(431\) | −7.49466 | −0.361005 | −0.180503 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180503 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(432\) | 14.6019 | 0.702534 | ||||||||
\(433\) | −7.35574 | −0.353495 | −0.176747 | − | 0.984256i | \(-0.556558\pi\) | ||||
−0.176747 | + | 0.984256i | \(0.556558\pi\) | |||||||
\(434\) | −10.9776 | −0.526942 | ||||||||
\(435\) | −23.7821 | −1.14027 | ||||||||
\(436\) | 8.65625 | 0.414559 | ||||||||
\(437\) | 31.9453 | 1.52815 | ||||||||
\(438\) | 34.1114 | 1.62990 | ||||||||
\(439\) | −9.15590 | −0.436987 | −0.218494 | − | 0.975838i | \(-0.570114\pi\) | ||||
−0.218494 | + | 0.975838i | \(0.570114\pi\) | |||||||
\(440\) | −7.07932 | −0.337493 | ||||||||
\(441\) | 6.07333 | 0.289206 | ||||||||
\(442\) | −13.5794 | −0.645906 | ||||||||
\(443\) | 17.1794 | 0.816216 | 0.408108 | − | 0.912934i | \(-0.366189\pi\) | ||||
0.408108 | + | 0.912934i | \(0.366189\pi\) | |||||||
\(444\) | 23.2769 | 1.10467 | ||||||||
\(445\) | 14.5072 | 0.687706 | ||||||||
\(446\) | 9.99602 | 0.473325 | ||||||||
\(447\) | 54.5244 | 2.57892 | ||||||||
\(448\) | 12.7410 | 0.601956 | ||||||||
\(449\) | −4.72940 | −0.223194 | −0.111597 | − | 0.993754i | \(-0.535597\pi\) | ||||
−0.111597 | + | 0.993754i | \(0.535597\pi\) | |||||||
\(450\) | −13.3752 | −0.630513 | ||||||||
\(451\) | 5.91544 | 0.278547 | ||||||||
\(452\) | 25.7963 | 1.21335 | ||||||||
\(453\) | 18.5241 | 0.870337 | ||||||||
\(454\) | −8.09188 | −0.379771 | ||||||||
\(455\) | 4.33541 | 0.203247 | ||||||||
\(456\) | −21.3521 | −0.999903 | ||||||||
\(457\) | 27.6705 | 1.29437 | 0.647185 | − | 0.762333i | \(-0.275946\pi\) | ||||
0.647185 | + | 0.762333i | \(0.275946\pi\) | |||||||
\(458\) | −2.20228 | −0.102906 | ||||||||
\(459\) | −13.1665 | −0.614559 | ||||||||
\(460\) | 24.0448 | 1.12109 | ||||||||
\(461\) | −29.1383 | −1.35711 | −0.678553 | − | 0.734551i | \(-0.737393\pi\) | ||||
−0.678553 | + | 0.734551i | \(0.737393\pi\) | |||||||
\(462\) | 25.0859 | 1.16710 | ||||||||
\(463\) | −34.8120 | −1.61785 | −0.808926 | − | 0.587910i | \(-0.799951\pi\) | ||||
−0.808926 | + | 0.587910i | \(0.799951\pi\) | |||||||
\(464\) | 12.4533 | 0.578129 | ||||||||
\(465\) | −15.0148 | −0.696293 | ||||||||
\(466\) | 37.0274 | 1.71526 | ||||||||
\(467\) | −3.58396 | −0.165846 | −0.0829228 | − | 0.996556i | \(-0.526426\pi\) | ||||
−0.0829228 | + | 0.996556i | \(0.526426\pi\) | |||||||
\(468\) | 75.0430 | 3.46887 | ||||||||
\(469\) | 0.748661 | 0.0345700 | ||||||||
\(470\) | −6.84769 | −0.315860 | ||||||||
\(471\) | −52.3842 | −2.41374 | ||||||||
\(472\) | 17.9810 | 0.827643 | ||||||||
\(473\) | −19.1819 | −0.881987 | ||||||||
\(474\) | 65.1398 | 2.99197 | ||||||||
\(475\) | −3.78650 | −0.173737 | ||||||||
\(476\) | −4.05349 | −0.185792 | ||||||||
\(477\) | 8.63328 | 0.395291 | ||||||||
\(478\) | −39.0351 | −1.78543 | ||||||||
\(479\) | 24.9792 | 1.14133 | 0.570664 | − | 0.821184i | \(-0.306686\pi\) | ||||
0.570664 | + | 0.821184i | \(0.306686\pi\) | |||||||
\(480\) | 21.7414 | 0.992355 | ||||||||
\(481\) | −11.7549 | −0.535978 | ||||||||
\(482\) | −41.5098 | −1.89072 | ||||||||
\(483\) | −25.4128 | −1.15632 | ||||||||
\(484\) | 9.40606 | 0.427548 | ||||||||
\(485\) | −8.60767 | −0.390854 | ||||||||
\(486\) | 2.95451 | 0.134020 | ||||||||
\(487\) | 4.02620 | 0.182445 | 0.0912223 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912223 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(488\) | 19.8059 | 0.896570 | ||||||||
\(489\) | 19.9421 | 0.901813 | ||||||||
\(490\) | 2.20228 | 0.0994890 | ||||||||
\(491\) | −18.3784 | −0.829407 | −0.414703 | − | 0.909957i | \(-0.636115\pi\) | ||||
−0.414703 | + | 0.909957i | \(0.636115\pi\) | |||||||
\(492\) | 13.4292 | 0.605436 | ||||||||
\(493\) | −11.2291 | −0.505732 | ||||||||
\(494\) | 36.1528 | 1.62659 | ||||||||
\(495\) | 22.9668 | 1.03228 | ||||||||
\(496\) | 7.86232 | 0.353029 | ||||||||
\(497\) | −1.44871 | −0.0649834 | ||||||||
\(498\) | 0.503315 | 0.0225541 | ||||||||
\(499\) | −3.51102 | −0.157175 | −0.0785874 | − | 0.996907i | \(-0.525041\pi\) | ||||
−0.0785874 | + | 0.996907i | \(0.525041\pi\) | |||||||
\(500\) | −2.85005 | −0.127458 | ||||||||
\(501\) | 63.2463 | 2.82564 | ||||||||
\(502\) | 10.9473 | 0.488601 | ||||||||
\(503\) | 19.7903 | 0.882405 | 0.441202 | − | 0.897408i | \(-0.354552\pi\) | ||||
0.441202 | + | 0.897408i | \(0.354552\pi\) | |||||||
\(504\) | 11.3696 | 0.506443 | ||||||||
\(505\) | 1.83398 | 0.0816113 | ||||||||
\(506\) | −70.2610 | −3.12348 | ||||||||
\(507\) | −17.4581 | −0.775341 | ||||||||
\(508\) | −43.4962 | −1.92983 | ||||||||
\(509\) | 38.5748 | 1.70980 | 0.854899 | − | 0.518795i | \(-0.173619\pi\) | ||||
0.854899 | + | 0.518795i | \(0.173619\pi\) | |||||||
\(510\) | −9.43481 | −0.417780 | ||||||||
\(511\) | −5.14212 | −0.227474 | ||||||||
\(512\) | −17.2903 | −0.764129 | ||||||||
\(513\) | 35.0535 | 1.54765 | ||||||||
\(514\) | −5.32291 | −0.234783 | ||||||||
\(515\) | 9.46639 | 0.417139 | ||||||||
\(516\) | −43.5468 | −1.91704 | ||||||||
\(517\) | 11.7583 | 0.517128 | ||||||||
\(518\) | −5.97121 | −0.262360 | ||||||||
\(519\) | 47.8373 | 2.09982 | ||||||||
\(520\) | 8.11614 | 0.355916 | ||||||||
\(521\) | −27.2196 | −1.19251 | −0.596256 | − | 0.802794i | \(-0.703346\pi\) | ||||
−0.596256 | + | 0.802794i | \(0.703346\pi\) | |||||||
\(522\) | 105.601 | 4.62203 | ||||||||
\(523\) | 6.38232 | 0.279079 | 0.139540 | − | 0.990216i | \(-0.455438\pi\) | ||||
0.139540 | + | 0.990216i | \(0.455438\pi\) | |||||||
\(524\) | 8.63976 | 0.377429 | ||||||||
\(525\) | 3.01220 | 0.131463 | ||||||||
\(526\) | 16.6930 | 0.727849 | ||||||||
\(527\) | −7.08943 | −0.308820 | ||||||||
\(528\) | −17.9669 | −0.781907 | ||||||||
\(529\) | 48.1765 | 2.09463 | ||||||||
\(530\) | 3.13056 | 0.135983 | ||||||||
\(531\) | −58.3341 | −2.53148 | ||||||||
\(532\) | 10.7917 | 0.467881 | ||||||||
\(533\) | −6.78180 | −0.293752 | ||||||||
\(534\) | −96.2364 | −4.16456 | ||||||||
\(535\) | −0.955305 | −0.0413014 | ||||||||
\(536\) | 1.40154 | 0.0605371 | ||||||||
\(537\) | −24.8520 | −1.07244 | ||||||||
\(538\) | 33.6575 | 1.45108 | ||||||||
\(539\) | −3.78158 | −0.162884 | ||||||||
\(540\) | 26.3843 | 1.13540 | ||||||||
\(541\) | −26.9115 | −1.15702 | −0.578508 | − | 0.815677i | \(-0.696365\pi\) | ||||
−0.578508 | + | 0.815677i | \(0.696365\pi\) | |||||||
\(542\) | −4.38173 | −0.188211 | ||||||||
\(543\) | −40.5399 | −1.73973 | ||||||||
\(544\) | 10.2655 | 0.440130 | ||||||||
\(545\) | −3.03723 | −0.130100 | ||||||||
\(546\) | −28.7599 | −1.23081 | ||||||||
\(547\) | 28.9162 | 1.23637 | 0.618183 | − | 0.786034i | \(-0.287869\pi\) | ||||
0.618183 | + | 0.786034i | \(0.287869\pi\) | |||||||
\(548\) | 8.96234 | 0.382852 | ||||||||
\(549\) | −64.2543 | −2.74231 | ||||||||
\(550\) | 8.32810 | 0.355111 | ||||||||
\(551\) | 29.8955 | 1.27359 | ||||||||
\(552\) | −47.5741 | −2.02489 | ||||||||
\(553\) | −9.81951 | −0.417568 | ||||||||
\(554\) | 56.6993 | 2.40892 | ||||||||
\(555\) | −8.16719 | −0.346678 | ||||||||
\(556\) | −33.8350 | −1.43493 | ||||||||
\(557\) | −14.7611 | −0.625449 | −0.312725 | − | 0.949844i | \(-0.601242\pi\) | ||||
−0.312725 | + | 0.949844i | \(0.601242\pi\) | |||||||
\(558\) | 66.6707 | 2.82240 | ||||||||
\(559\) | 21.9913 | 0.930132 | ||||||||
\(560\) | −1.57731 | −0.0666534 | ||||||||
\(561\) | 16.2007 | 0.683992 | ||||||||
\(562\) | −50.3877 | −2.12548 | ||||||||
\(563\) | −10.9805 | −0.462774 | −0.231387 | − | 0.972862i | \(-0.574326\pi\) | ||||
−0.231387 | + | 0.972862i | \(0.574326\pi\) | |||||||
\(564\) | 26.6936 | 1.12400 | ||||||||
\(565\) | −9.05115 | −0.380785 | ||||||||
\(566\) | 14.6072 | 0.613988 | ||||||||
\(567\) | −9.66538 | −0.405908 | ||||||||
\(568\) | −2.71206 | −0.113796 | ||||||||
\(569\) | 33.1740 | 1.39073 | 0.695363 | − | 0.718659i | \(-0.255244\pi\) | ||||
0.695363 | + | 0.718659i | \(0.255244\pi\) | |||||||
\(570\) | 25.1186 | 1.05210 | ||||||||
\(571\) | −14.6394 | −0.612640 | −0.306320 | − | 0.951929i | \(-0.599098\pi\) | ||||
−0.306320 | + | 0.951929i | \(0.599098\pi\) | |||||||
\(572\) | −46.7257 | −1.95370 | ||||||||
\(573\) | −28.5125 | −1.19113 | ||||||||
\(574\) | −3.44499 | −0.143791 | ||||||||
\(575\) | −8.43662 | −0.351831 | ||||||||
\(576\) | −77.3804 | −3.22418 | ||||||||
\(577\) | −36.5018 | −1.51959 | −0.759794 | − | 0.650164i | \(-0.774700\pi\) | ||||
−0.759794 | + | 0.650164i | \(0.774700\pi\) | |||||||
\(578\) | 32.9840 | 1.37196 | ||||||||
\(579\) | 48.3534 | 2.00950 | ||||||||
\(580\) | 22.5020 | 0.934343 | ||||||||
\(581\) | −0.0758723 | −0.00314771 | ||||||||
\(582\) | 57.1008 | 2.36690 | ||||||||
\(583\) | −5.37553 | −0.222632 | ||||||||
\(584\) | −9.62635 | −0.398341 | ||||||||
\(585\) | −26.3304 | −1.08863 | ||||||||
\(586\) | 15.1559 | 0.626085 | ||||||||
\(587\) | 10.5598 | 0.435848 | 0.217924 | − | 0.975966i | \(-0.430071\pi\) | ||||
0.217924 | + | 0.975966i | \(0.430071\pi\) | |||||||
\(588\) | −8.58492 | −0.354036 | ||||||||
\(589\) | 18.8744 | 0.777705 | ||||||||
\(590\) | −21.1528 | −0.870848 | ||||||||
\(591\) | 67.7749 | 2.78789 | ||||||||
\(592\) | 4.27666 | 0.175770 | ||||||||
\(593\) | 36.9143 | 1.51589 | 0.757945 | − | 0.652318i | \(-0.226203\pi\) | ||||
0.757945 | + | 0.652318i | \(0.226203\pi\) | |||||||
\(594\) | −77.0973 | −3.16334 | ||||||||
\(595\) | 1.42225 | 0.0583066 | ||||||||
\(596\) | −51.5894 | −2.11318 | ||||||||
\(597\) | 27.9724 | 1.14483 | ||||||||
\(598\) | 80.5512 | 3.29398 | ||||||||
\(599\) | −32.5743 | −1.33095 | −0.665475 | − | 0.746420i | \(-0.731771\pi\) | ||||
−0.665475 | + | 0.746420i | \(0.731771\pi\) | |||||||
\(600\) | 5.63900 | 0.230211 | ||||||||
\(601\) | 18.4055 | 0.750776 | 0.375388 | − | 0.926868i | \(-0.377509\pi\) | ||||
0.375388 | + | 0.926868i | \(0.377509\pi\) | |||||||
\(602\) | 11.1710 | 0.455297 | ||||||||
\(603\) | −4.54687 | −0.185163 | ||||||||
\(604\) | −17.5269 | −0.713161 | ||||||||
\(605\) | −3.30031 | −0.134177 | ||||||||
\(606\) | −12.1661 | −0.494215 | ||||||||
\(607\) | −18.7941 | −0.762830 | −0.381415 | − | 0.924404i | \(-0.624563\pi\) | ||||
−0.381415 | + | 0.924404i | \(0.624563\pi\) | |||||||
\(608\) | −27.3302 | −1.10838 | ||||||||
\(609\) | −23.7821 | −0.963701 | ||||||||
\(610\) | −23.2996 | −0.943373 | ||||||||
\(611\) | −13.4804 | −0.545357 | ||||||||
\(612\) | 24.6182 | 0.995132 | ||||||||
\(613\) | 16.8509 | 0.680601 | 0.340300 | − | 0.940317i | \(-0.389471\pi\) | ||||
0.340300 | + | 0.940317i | \(0.389471\pi\) | |||||||
\(614\) | −19.8707 | −0.801917 | ||||||||
\(615\) | −4.71192 | −0.190003 | ||||||||
\(616\) | −7.07932 | −0.285234 | ||||||||
\(617\) | 19.4653 | 0.783645 | 0.391822 | − | 0.920041i | \(-0.371845\pi\) | ||||
0.391822 | + | 0.920041i | \(0.371845\pi\) | |||||||
\(618\) | −62.7973 | −2.52608 | ||||||||
\(619\) | 21.4252 | 0.861152 | 0.430576 | − | 0.902554i | \(-0.358310\pi\) | ||||
0.430576 | + | 0.902554i | \(0.358310\pi\) | |||||||
\(620\) | 14.2065 | 0.570547 | ||||||||
\(621\) | 78.1019 | 3.13412 | ||||||||
\(622\) | 53.6356 | 2.15059 | ||||||||
\(623\) | 14.5072 | 0.581218 | ||||||||
\(624\) | 20.5982 | 0.824589 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.57780 | −0.262902 | ||||||||
\(627\) | −43.1315 | −1.72250 | ||||||||
\(628\) | 49.5644 | 1.97783 | ||||||||
\(629\) | −3.85625 | −0.153759 | ||||||||
\(630\) | −13.3752 | −0.532881 | ||||||||
\(631\) | 6.59963 | 0.262727 | 0.131364 | − | 0.991334i | \(-0.458064\pi\) | ||||
0.131364 | + | 0.991334i | \(0.458064\pi\) | |||||||
\(632\) | −18.3827 | −0.731223 | ||||||||
\(633\) | 45.6786 | 1.81556 | ||||||||
\(634\) | 45.4440 | 1.80481 | ||||||||
\(635\) | 15.2615 | 0.605636 | ||||||||
\(636\) | −12.2035 | −0.483901 | ||||||||
\(637\) | 4.33541 | 0.171775 | ||||||||
\(638\) | −65.7527 | −2.60317 | ||||||||
\(639\) | 8.79848 | 0.348063 | ||||||||
\(640\) | −13.6237 | −0.538525 | ||||||||
\(641\) | −1.68300 | −0.0664747 | −0.0332373 | − | 0.999447i | \(-0.510582\pi\) | ||||
−0.0332373 | + | 0.999447i | \(0.510582\pi\) | |||||||
\(642\) | 6.33722 | 0.250110 | ||||||||
\(643\) | 40.3837 | 1.59258 | 0.796289 | − | 0.604916i | \(-0.206793\pi\) | ||||
0.796289 | + | 0.604916i | \(0.206793\pi\) | |||||||
\(644\) | 24.0448 | 0.947498 | ||||||||
\(645\) | 15.2793 | 0.601622 | ||||||||
\(646\) | 11.8601 | 0.466629 | ||||||||
\(647\) | 20.9387 | 0.823183 | 0.411592 | − | 0.911368i | \(-0.364973\pi\) | ||||
0.411592 | + | 0.911368i | \(0.364973\pi\) | |||||||
\(648\) | −18.0941 | −0.710805 | ||||||||
\(649\) | 36.3219 | 1.42576 | ||||||||
\(650\) | −9.54781 | −0.374496 | ||||||||
\(651\) | −15.0148 | −0.588475 | ||||||||
\(652\) | −18.8686 | −0.738952 | ||||||||
\(653\) | −29.4081 | −1.15083 | −0.575414 | − | 0.817863i | \(-0.695159\pi\) | ||||
−0.575414 | + | 0.817863i | \(0.695159\pi\) | |||||||
\(654\) | 20.1481 | 0.787852 | ||||||||
\(655\) | −3.03144 | −0.118448 | ||||||||
\(656\) | 2.46735 | 0.0963337 | ||||||||
\(657\) | 31.2298 | 1.21839 | ||||||||
\(658\) | −6.84769 | −0.266951 | ||||||||
\(659\) | 16.2680 | 0.633712 | 0.316856 | − | 0.948474i | \(-0.397373\pi\) | ||||
0.316856 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(660\) | −32.4645 | −1.26368 | ||||||||
\(661\) | −23.2298 | −0.903534 | −0.451767 | − | 0.892136i | \(-0.649206\pi\) | ||||
−0.451767 | + | 0.892136i | \(0.649206\pi\) | |||||||
\(662\) | 74.6136 | 2.89994 | ||||||||
\(663\) | −18.5734 | −0.721329 | ||||||||
\(664\) | −0.142037 | −0.00551211 | ||||||||
\(665\) | −3.78650 | −0.146834 | ||||||||
\(666\) | 36.2651 | 1.40525 | ||||||||
\(667\) | 66.6095 | 2.57913 | ||||||||
\(668\) | −59.8418 | −2.31535 | ||||||||
\(669\) | 13.6722 | 0.528597 | ||||||||
\(670\) | −1.64876 | −0.0636973 | ||||||||
\(671\) | 40.0081 | 1.54450 | ||||||||
\(672\) | 21.7414 | 0.838693 | ||||||||
\(673\) | 13.4306 | 0.517712 | 0.258856 | − | 0.965916i | \(-0.416654\pi\) | ||||
0.258856 | + | 0.965916i | \(0.416654\pi\) | |||||||
\(674\) | 46.1332 | 1.77698 | ||||||||
\(675\) | −9.25749 | −0.356321 | ||||||||
\(676\) | 16.5183 | 0.635321 | ||||||||
\(677\) | 31.6062 | 1.21473 | 0.607363 | − | 0.794424i | \(-0.292227\pi\) | ||||
0.607363 | + | 0.794424i | \(0.292227\pi\) | |||||||
\(678\) | 60.0427 | 2.30593 | ||||||||
\(679\) | −8.60767 | −0.330332 | ||||||||
\(680\) | 2.66254 | 0.102104 | ||||||||
\(681\) | −11.0678 | −0.424118 | ||||||||
\(682\) | −41.5127 | −1.58960 | ||||||||
\(683\) | 24.8793 | 0.951981 | 0.475991 | − | 0.879450i | \(-0.342090\pi\) | ||||
0.475991 | + | 0.879450i | \(0.342090\pi\) | |||||||
\(684\) | −65.5417 | −2.50605 | ||||||||
\(685\) | −3.14462 | −0.120150 | ||||||||
\(686\) | 2.20228 | 0.0840836 | ||||||||
\(687\) | −3.01220 | −0.114923 | ||||||||
\(688\) | −8.00085 | −0.305029 | ||||||||
\(689\) | 6.16282 | 0.234785 | ||||||||
\(690\) | 55.9661 | 2.13059 | ||||||||
\(691\) | 0.365424 | 0.0139014 | 0.00695069 | − | 0.999976i | \(-0.497788\pi\) | ||||
0.00695069 | + | 0.999976i | \(0.497788\pi\) | |||||||
\(692\) | −45.2622 | −1.72061 | ||||||||
\(693\) | 22.9668 | 0.872435 | ||||||||
\(694\) | 42.9697 | 1.63111 | ||||||||
\(695\) | 11.8717 | 0.450320 | ||||||||
\(696\) | −44.5215 | −1.68758 | ||||||||
\(697\) | −2.22480 | −0.0842703 | ||||||||
\(698\) | −15.8003 | −0.598050 | ||||||||
\(699\) | 50.6446 | 1.91556 | ||||||||
\(700\) | −2.85005 | −0.107722 | ||||||||
\(701\) | 23.3790 | 0.883012 | 0.441506 | − | 0.897258i | \(-0.354444\pi\) | ||||
0.441506 | + | 0.897258i | \(0.354444\pi\) | |||||||
\(702\) | 88.3887 | 3.33602 | ||||||||
\(703\) | 10.2666 | 0.387212 | ||||||||
\(704\) | 48.1811 | 1.81589 | ||||||||
\(705\) | −9.36600 | −0.352744 | ||||||||
\(706\) | −20.7390 | −0.780524 | ||||||||
\(707\) | 1.83398 | 0.0689741 | ||||||||
\(708\) | 82.4578 | 3.09895 | ||||||||
\(709\) | 7.45475 | 0.279969 | 0.139984 | − | 0.990154i | \(-0.455295\pi\) | ||||
0.139984 | + | 0.990154i | \(0.455295\pi\) | |||||||
\(710\) | 3.19046 | 0.119736 | ||||||||
\(711\) | 59.6371 | 2.23657 | ||||||||
\(712\) | 27.1582 | 1.01780 | ||||||||
\(713\) | 42.0536 | 1.57492 | ||||||||
\(714\) | −9.43481 | −0.353089 | ||||||||
\(715\) | 16.3947 | 0.613127 | ||||||||
\(716\) | 23.5142 | 0.878768 | ||||||||
\(717\) | −53.3907 | −1.99391 | ||||||||
\(718\) | −20.5480 | −0.766846 | ||||||||
\(719\) | −41.4309 | −1.54511 | −0.772555 | − | 0.634947i | \(-0.781022\pi\) | ||||
−0.772555 | + | 0.634947i | \(0.781022\pi\) | |||||||
\(720\) | 9.57951 | 0.357007 | ||||||||
\(721\) | 9.46639 | 0.352547 | ||||||||
\(722\) | 10.2680 | 0.382134 | ||||||||
\(723\) | −56.7754 | −2.11150 | ||||||||
\(724\) | 38.3576 | 1.42555 | ||||||||
\(725\) | −7.89528 | −0.293223 | ||||||||
\(726\) | 21.8933 | 0.812537 | ||||||||
\(727\) | −10.5579 | −0.391569 | −0.195785 | − | 0.980647i | \(-0.562725\pi\) | ||||
−0.195785 | + | 0.980647i | \(0.562725\pi\) | |||||||
\(728\) | 8.11614 | 0.300804 | ||||||||
\(729\) | −24.9551 | −0.924262 | ||||||||
\(730\) | 11.3244 | 0.419135 | ||||||||
\(731\) | 7.21434 | 0.266832 | ||||||||
\(732\) | 90.8263 | 3.35704 | ||||||||
\(733\) | 38.9965 | 1.44037 | 0.720184 | − | 0.693783i | \(-0.244057\pi\) | ||||
0.720184 | + | 0.693783i | \(0.244057\pi\) | |||||||
\(734\) | −39.8226 | −1.46988 | ||||||||
\(735\) | 3.01220 | 0.111107 | ||||||||
\(736\) | −60.8937 | −2.24457 | ||||||||
\(737\) | 2.83112 | 0.104286 | ||||||||
\(738\) | 20.9225 | 0.770170 | ||||||||
\(739\) | 6.56544 | 0.241514 | 0.120757 | − | 0.992682i | \(-0.461468\pi\) | ||||
0.120757 | + | 0.992682i | \(0.461468\pi\) | |||||||
\(740\) | 7.72755 | 0.284070 | ||||||||
\(741\) | 49.4484 | 1.81653 | ||||||||
\(742\) | 3.13056 | 0.114926 | ||||||||
\(743\) | 11.5345 | 0.423161 | 0.211581 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211581 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(744\) | −28.1085 | −1.03051 | ||||||||
\(745\) | 18.1012 | 0.663177 | ||||||||
\(746\) | −12.5110 | −0.458062 | ||||||||
\(747\) | 0.460798 | 0.0168597 | ||||||||
\(748\) | −15.3286 | −0.560469 | ||||||||
\(749\) | −0.955305 | −0.0349061 | ||||||||
\(750\) | −6.63371 | −0.242229 | ||||||||
\(751\) | 15.9499 | 0.582019 | 0.291010 | − | 0.956720i | \(-0.406009\pi\) | ||||
0.291010 | + | 0.956720i | \(0.406009\pi\) | |||||||
\(752\) | 4.90441 | 0.178846 | ||||||||
\(753\) | 14.9733 | 0.545657 | ||||||||
\(754\) | 75.3826 | 2.74527 | ||||||||
\(755\) | 6.14969 | 0.223810 | ||||||||
\(756\) | 26.3843 | 0.959589 | ||||||||
\(757\) | −36.4971 | −1.32651 | −0.663255 | − | 0.748394i | \(-0.730825\pi\) | ||||
−0.663255 | + | 0.748394i | \(0.730825\pi\) | |||||||
\(758\) | 40.9738 | 1.48823 | ||||||||
\(759\) | −96.1003 | −3.48822 | ||||||||
\(760\) | −7.08854 | −0.257128 | ||||||||
\(761\) | 29.2799 | 1.06140 | 0.530698 | − | 0.847561i | \(-0.321930\pi\) | ||||
0.530698 | + | 0.847561i | \(0.321930\pi\) | |||||||
\(762\) | −101.241 | −3.66756 | ||||||||
\(763\) | −3.03723 | −0.109955 | ||||||||
\(764\) | 26.9777 | 0.976017 | ||||||||
\(765\) | −8.63781 | −0.312301 | ||||||||
\(766\) | 47.0046 | 1.69834 | ||||||||
\(767\) | −41.6414 | −1.50358 | ||||||||
\(768\) | 13.6190 | 0.491434 | ||||||||
\(769\) | 31.3181 | 1.12936 | 0.564680 | − | 0.825310i | \(-0.309000\pi\) | ||||
0.564680 | + | 0.825310i | \(0.309000\pi\) | |||||||
\(770\) | 8.32810 | 0.300124 | ||||||||
\(771\) | −7.28046 | −0.262199 | ||||||||
\(772\) | −45.7505 | −1.64660 | ||||||||
\(773\) | 1.29537 | 0.0465911 | 0.0232956 | − | 0.999729i | \(-0.492584\pi\) | ||||
0.0232956 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(774\) | −67.8454 | −2.43865 | ||||||||
\(775\) | −4.98465 | −0.179054 | ||||||||
\(776\) | −16.1140 | −0.578460 | ||||||||
\(777\) | −8.16719 | −0.292996 | ||||||||
\(778\) | 74.5655 | 2.67330 | ||||||||
\(779\) | 5.92314 | 0.212219 | ||||||||
\(780\) | 37.2192 | 1.33266 | ||||||||
\(781\) | −5.47840 | −0.196032 | ||||||||
\(782\) | 26.4252 | 0.944963 | ||||||||
\(783\) | 73.0904 | 2.61204 | ||||||||
\(784\) | −1.57731 | −0.0563324 | ||||||||
\(785\) | −17.3907 | −0.620700 | ||||||||
\(786\) | 20.1097 | 0.717289 | ||||||||
\(787\) | 41.5502 | 1.48111 | 0.740553 | − | 0.671998i | \(-0.234564\pi\) | ||||
0.740553 | + | 0.671998i | \(0.234564\pi\) | |||||||
\(788\) | −64.1267 | −2.28442 | ||||||||
\(789\) | 22.8320 | 0.812842 | ||||||||
\(790\) | 21.6253 | 0.769395 | ||||||||
\(791\) | −9.05115 | −0.321822 | ||||||||
\(792\) | 42.9951 | 1.52776 | ||||||||
\(793\) | −45.8676 | −1.62881 | ||||||||
\(794\) | −38.0595 | −1.35068 | ||||||||
\(795\) | 4.28186 | 0.151862 | ||||||||
\(796\) | −26.4666 | −0.938085 | ||||||||
\(797\) | −21.9005 | −0.775756 | −0.387878 | − | 0.921711i | \(-0.626792\pi\) | ||||
−0.387878 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(798\) | 25.1186 | 0.889187 | ||||||||
\(799\) | −4.42229 | −0.156449 | ||||||||
\(800\) | 7.21779 | 0.255187 | ||||||||
\(801\) | −88.1069 | −3.11310 | ||||||||
\(802\) | 76.0777 | 2.68640 | ||||||||
\(803\) | −19.4453 | −0.686211 | ||||||||
\(804\) | 6.42720 | 0.226670 | ||||||||
\(805\) | −8.43662 | −0.297352 | ||||||||
\(806\) | 47.5925 | 1.67637 | ||||||||
\(807\) | 46.0354 | 1.62052 | ||||||||
\(808\) | 3.43332 | 0.120784 | ||||||||
\(809\) | 9.39275 | 0.330232 | 0.165116 | − | 0.986274i | \(-0.447200\pi\) | ||||
0.165116 | + | 0.986274i | \(0.447200\pi\) | |||||||
\(810\) | 21.2859 | 0.747910 | ||||||||
\(811\) | −31.7952 | −1.11648 | −0.558240 | − | 0.829680i | \(-0.688523\pi\) | ||||
−0.558240 | + | 0.829680i | \(0.688523\pi\) | |||||||
\(812\) | 22.5020 | 0.789664 | ||||||||
\(813\) | −5.99316 | −0.210189 | ||||||||
\(814\) | −22.5806 | −0.791449 | ||||||||
\(815\) | 6.62045 | 0.231904 | ||||||||
\(816\) | 6.75734 | 0.236554 | ||||||||
\(817\) | −19.2069 | −0.671965 | ||||||||
\(818\) | −51.9210 | −1.81538 | ||||||||
\(819\) | −26.3304 | −0.920059 | ||||||||
\(820\) | 4.45828 | 0.155690 | ||||||||
\(821\) | −28.5619 | −0.996818 | −0.498409 | − | 0.866942i | \(-0.666082\pi\) | ||||
−0.498409 | + | 0.866942i | \(0.666082\pi\) | |||||||
\(822\) | 20.8605 | 0.727594 | ||||||||
\(823\) | −7.52021 | −0.262138 | −0.131069 | − | 0.991373i | \(-0.541841\pi\) | ||||
−0.131069 | + | 0.991373i | \(0.541841\pi\) | |||||||
\(824\) | 17.7216 | 0.617361 | ||||||||
\(825\) | 11.3909 | 0.396579 | ||||||||
\(826\) | −21.1528 | −0.736001 | ||||||||
\(827\) | −29.9178 | −1.04034 | −0.520171 | − | 0.854062i | \(-0.674132\pi\) | ||||
−0.520171 | + | 0.854062i | \(0.674132\pi\) | |||||||
\(828\) | −146.032 | −5.07497 | ||||||||
\(829\) | −30.9662 | −1.07550 | −0.537750 | − | 0.843104i | \(-0.680726\pi\) | ||||
−0.537750 | + | 0.843104i | \(0.680726\pi\) | |||||||
\(830\) | 0.167092 | 0.00579986 | ||||||||
\(831\) | 77.5511 | 2.69022 | ||||||||
\(832\) | −55.2375 | −1.91502 | ||||||||
\(833\) | 1.42225 | 0.0492781 | ||||||||
\(834\) | −78.7536 | −2.72701 | ||||||||
\(835\) | 20.9967 | 0.726622 | ||||||||
\(836\) | 40.8097 | 1.41143 | ||||||||
\(837\) | 46.1453 | 1.59502 | ||||||||
\(838\) | 80.9479 | 2.79630 | ||||||||
\(839\) | 29.6014 | 1.02196 | 0.510978 | − | 0.859594i | \(-0.329284\pi\) | ||||
0.510978 | + | 0.859594i | \(0.329284\pi\) | |||||||
\(840\) | 5.63900 | 0.194564 | ||||||||
\(841\) | 33.3354 | 1.14950 | ||||||||
\(842\) | −2.95693 | −0.101903 | ||||||||
\(843\) | −68.9183 | −2.37367 | ||||||||
\(844\) | −43.2197 | −1.48768 | ||||||||
\(845\) | −5.79580 | −0.199382 | ||||||||
\(846\) | 41.5883 | 1.42984 | ||||||||
\(847\) | −3.30031 | −0.113400 | ||||||||
\(848\) | −2.24215 | −0.0769958 | ||||||||
\(849\) | 19.9792 | 0.685685 | ||||||||
\(850\) | −3.13220 | −0.107434 | ||||||||
\(851\) | 22.8748 | 0.784138 | ||||||||
\(852\) | −12.4370 | −0.426086 | ||||||||
\(853\) | −3.48457 | −0.119309 | −0.0596547 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596547 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(854\) | −23.2996 | −0.797296 | ||||||||
\(855\) | 22.9967 | 0.786470 | ||||||||
\(856\) | −1.78838 | −0.0611257 | ||||||||
\(857\) | −5.86120 | −0.200215 | −0.100107 | − | 0.994977i | \(-0.531919\pi\) | ||||
−0.100107 | + | 0.994977i | \(0.531919\pi\) | |||||||
\(858\) | −108.758 | −3.71292 | ||||||||
\(859\) | −13.8263 | −0.471746 | −0.235873 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235873 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(860\) | −14.4568 | −0.492973 | ||||||||
\(861\) | −4.71192 | −0.160582 | ||||||||
\(862\) | 16.5054 | 0.562175 | ||||||||
\(863\) | −46.9250 | −1.59735 | −0.798673 | − | 0.601766i | \(-0.794464\pi\) | ||||
−0.798673 | + | 0.601766i | \(0.794464\pi\) | |||||||
\(864\) | −66.8186 | −2.27321 | ||||||||
\(865\) | 15.8812 | 0.539977 | ||||||||
\(866\) | 16.1994 | 0.550479 | ||||||||
\(867\) | 45.1143 | 1.53216 | ||||||||
\(868\) | 14.2065 | 0.482201 | ||||||||
\(869\) | −37.1332 | −1.25966 | ||||||||
\(870\) | 52.3750 | 1.77568 | ||||||||
\(871\) | −3.24576 | −0.109978 | ||||||||
\(872\) | −5.68586 | −0.192547 | ||||||||
\(873\) | 52.2772 | 1.76932 | ||||||||
\(874\) | −70.3525 | −2.37971 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −44.1447 | −1.49151 | ||||||||
\(877\) | −49.1993 | −1.66134 | −0.830671 | − | 0.556763i | \(-0.812043\pi\) | ||||
−0.830671 | + | 0.556763i | \(0.812043\pi\) | |||||||
\(878\) | 20.1639 | 0.680498 | ||||||||
\(879\) | 20.7297 | 0.699194 | ||||||||
\(880\) | −5.96470 | −0.201070 | ||||||||
\(881\) | 26.5334 | 0.893934 | 0.446967 | − | 0.894550i | \(-0.352504\pi\) | ||||
0.446967 | + | 0.894550i | \(0.352504\pi\) | |||||||
\(882\) | −13.3752 | −0.450366 | ||||||||
\(883\) | 26.7806 | 0.901238 | 0.450619 | − | 0.892716i | \(-0.351203\pi\) | ||||
0.450619 | + | 0.892716i | \(0.351203\pi\) | |||||||
\(884\) | 17.5736 | 0.591063 | ||||||||
\(885\) | −28.9320 | −0.972539 | ||||||||
\(886\) | −37.8338 | −1.27105 | ||||||||
\(887\) | 22.7884 | 0.765158 | 0.382579 | − | 0.923923i | \(-0.375036\pi\) | ||||
0.382579 | + | 0.923923i | \(0.375036\pi\) | |||||||
\(888\) | −15.2894 | −0.513080 | ||||||||
\(889\) | 15.2615 | 0.511856 | ||||||||
\(890\) | −31.9489 | −1.07093 | ||||||||
\(891\) | −36.5504 | −1.22448 | ||||||||
\(892\) | −12.9362 | −0.433136 | ||||||||
\(893\) | 11.7736 | 0.393988 | ||||||||
\(894\) | −120.078 | −4.01601 | ||||||||
\(895\) | −8.25045 | −0.275782 | ||||||||
\(896\) | −13.6237 | −0.455137 | ||||||||
\(897\) | 110.175 | 3.67863 | ||||||||
\(898\) | 10.4155 | 0.347569 | ||||||||
\(899\) | 39.3552 | 1.31257 | ||||||||
\(900\) | 17.3093 | 0.576977 | ||||||||
\(901\) | 2.02174 | 0.0673539 | ||||||||
\(902\) | −13.0275 | −0.433767 | ||||||||
\(903\) | 15.2793 | 0.508463 | ||||||||
\(904\) | −16.9443 | −0.563558 | ||||||||
\(905\) | −13.4586 | −0.447378 | ||||||||
\(906\) | −40.7953 | −1.35533 | ||||||||
\(907\) | −36.1619 | −1.20074 | −0.600368 | − | 0.799724i | \(-0.704979\pi\) | ||||
−0.600368 | + | 0.799724i | \(0.704979\pi\) | |||||||
\(908\) | 10.4720 | 0.347525 | ||||||||
\(909\) | −11.1384 | −0.369437 | ||||||||
\(910\) | −9.54781 | −0.316507 | ||||||||
\(911\) | −47.5345 | −1.57489 | −0.787444 | − | 0.616387i | \(-0.788596\pi\) | ||||
−0.787444 | + | 0.616387i | \(0.788596\pi\) | |||||||
\(912\) | −17.9903 | −0.595717 | ||||||||
\(913\) | −0.286917 | −0.00949556 | ||||||||
\(914\) | −60.9382 | −2.01566 | ||||||||
\(915\) | −31.8683 | −1.05353 | ||||||||
\(916\) | 2.85005 | 0.0941684 | ||||||||
\(917\) | −3.03144 | −0.100107 | ||||||||
\(918\) | 28.9963 | 0.957021 | ||||||||
\(919\) | −7.87020 | −0.259614 | −0.129807 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129807 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(920\) | −15.7938 | −0.520707 | ||||||||
\(921\) | −27.1784 | −0.895558 | ||||||||
\(922\) | 64.1708 | 2.11335 | ||||||||
\(923\) | 6.28074 | 0.206733 | ||||||||
\(924\) | −32.4645 | −1.06800 | ||||||||
\(925\) | −2.71137 | −0.0891493 | ||||||||
\(926\) | 76.6660 | 2.51940 | ||||||||
\(927\) | −57.4925 | −1.88830 | ||||||||
\(928\) | −56.9864 | −1.87067 | ||||||||
\(929\) | 56.1990 | 1.84383 | 0.921915 | − | 0.387392i | \(-0.126624\pi\) | ||||
0.921915 | + | 0.387392i | \(0.126624\pi\) | |||||||
\(930\) | 33.0667 | 1.08430 | ||||||||
\(931\) | −3.78650 | −0.124098 | ||||||||
\(932\) | −47.9185 | −1.56962 | ||||||||
\(933\) | 73.3607 | 2.40172 | ||||||||
\(934\) | 7.89289 | 0.258263 | ||||||||
\(935\) | 5.37835 | 0.175891 | ||||||||
\(936\) | −49.2920 | −1.61116 | ||||||||
\(937\) | 40.8418 | 1.33424 | 0.667122 | − | 0.744948i | \(-0.267526\pi\) | ||||
0.667122 | + | 0.744948i | \(0.267526\pi\) | |||||||
\(938\) | −1.64876 | −0.0538341 | ||||||||
\(939\) | −8.99686 | −0.293601 | ||||||||
\(940\) | 8.86184 | 0.289041 | ||||||||
\(941\) | −32.4457 | −1.05770 | −0.528850 | − | 0.848715i | \(-0.677377\pi\) | ||||
−0.528850 | + | 0.848715i | \(0.677377\pi\) | |||||||
\(942\) | 115.365 | 3.75879 | ||||||||
\(943\) | 13.1972 | 0.429761 | ||||||||
\(944\) | 15.1500 | 0.493089 | ||||||||
\(945\) | −9.25749 | −0.301146 | ||||||||
\(946\) | 42.2441 | 1.37347 | ||||||||
\(947\) | 17.9499 | 0.583292 | 0.291646 | − | 0.956526i | \(-0.405797\pi\) | ||||
0.291646 | + | 0.956526i | \(0.405797\pi\) | |||||||
\(948\) | −84.2997 | −2.73793 | ||||||||
\(949\) | 22.2932 | 0.723669 | ||||||||
\(950\) | 8.33895 | 0.270551 | ||||||||
\(951\) | 62.1565 | 2.01556 | ||||||||
\(952\) | 2.66254 | 0.0862933 | ||||||||
\(953\) | −1.98786 | −0.0643929 | −0.0321965 | − | 0.999482i | \(-0.510250\pi\) | ||||
−0.0321965 | + | 0.999482i | \(0.510250\pi\) | |||||||
\(954\) | −19.0129 | −0.615566 | ||||||||
\(955\) | −9.46567 | −0.306302 | ||||||||
\(956\) | 50.5167 | 1.63383 | ||||||||
\(957\) | −89.9339 | −2.90715 | ||||||||
\(958\) | −55.0112 | −1.77733 | ||||||||
\(959\) | −3.14462 | −0.101545 | ||||||||
\(960\) | −38.3784 | −1.23866 | ||||||||
\(961\) | −6.15325 | −0.198492 | ||||||||
\(962\) | 25.8876 | 0.834651 | ||||||||
\(963\) | 5.80189 | 0.186963 | ||||||||
\(964\) | 53.7192 | 1.73018 | ||||||||
\(965\) | 16.0525 | 0.516749 | ||||||||
\(966\) | 55.9661 | 1.80068 | ||||||||
\(967\) | 47.0012 | 1.51146 | 0.755728 | − | 0.654885i | \(-0.227283\pi\) | ||||
0.755728 | + | 0.654885i | \(0.227283\pi\) | |||||||
\(968\) | −6.17837 | −0.198580 | ||||||||
\(969\) | 16.2218 | 0.521118 | ||||||||
\(970\) | 18.9565 | 0.608657 | ||||||||
\(971\) | −53.3009 | −1.71051 | −0.855254 | − | 0.518210i | \(-0.826599\pi\) | ||||
−0.855254 | + | 0.518210i | \(0.826599\pi\) | |||||||
\(972\) | −3.82354 | −0.122640 | ||||||||
\(973\) | 11.8717 | 0.380590 | ||||||||
\(974\) | −8.86684 | −0.284112 | ||||||||
\(975\) | −13.0591 | −0.418226 | ||||||||
\(976\) | 16.6875 | 0.534154 | ||||||||
\(977\) | −18.5001 | −0.591871 | −0.295935 | − | 0.955208i | \(-0.595631\pi\) | ||||
−0.295935 | + | 0.955208i | \(0.595631\pi\) | |||||||
\(978\) | −43.9182 | −1.40435 | ||||||||
\(979\) | 54.8600 | 1.75333 | ||||||||
\(980\) | −2.85005 | −0.0910416 | ||||||||
\(981\) | 18.4461 | 0.588938 | ||||||||
\(982\) | 40.4745 | 1.29159 | ||||||||
\(983\) | −38.3996 | −1.22476 | −0.612379 | − | 0.790564i | \(-0.709787\pi\) | ||||
−0.612379 | + | 0.790564i | \(0.709787\pi\) | |||||||
\(984\) | −8.82097 | −0.281202 | ||||||||
\(985\) | 22.5002 | 0.716915 | ||||||||
\(986\) | 24.7296 | 0.787551 | ||||||||
\(987\) | −9.36600 | −0.298123 | ||||||||
\(988\) | −46.7866 | −1.48848 | ||||||||
\(989\) | −42.7945 | −1.36079 | ||||||||
\(990\) | −50.5793 | −1.60752 | ||||||||
\(991\) | −36.0994 | −1.14673 | −0.573367 | − | 0.819298i | \(-0.694363\pi\) | ||||
−0.573367 | + | 0.819298i | \(0.694363\pi\) | |||||||
\(992\) | −35.9782 | −1.14231 | ||||||||
\(993\) | 102.054 | 3.23857 | ||||||||
\(994\) | 3.19046 | 0.101195 | ||||||||
\(995\) | 9.28637 | 0.294398 | ||||||||
\(996\) | −0.651358 | −0.0206391 | ||||||||
\(997\) | 2.67421 | 0.0846931 | 0.0423465 | − | 0.999103i | \(-0.486517\pi\) | ||||
0.0423465 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(998\) | 7.73226 | 0.244761 | ||||||||
\(999\) | 25.1005 | 0.794144 |
(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 | 8015.2.a.l.1.9 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.9 | ✓ | 62 | 1.1 | even | 1 | trivial |