Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63094 | −1.86035 | −0.930177 | − | 0.367111i | \(-0.880347\pi\) | ||||
−0.930177 | + | 0.367111i | \(0.880347\pi\) | |||||||
\(3\) | −2.05461 | −1.18623 | −0.593116 | − | 0.805117i | \(-0.702102\pi\) | ||||
−0.593116 | + | 0.805117i | \(0.702102\pi\) | |||||||
\(4\) | 4.92184 | 2.46092 | ||||||||
\(5\) | −2.98457 | −1.33474 | −0.667369 | − | 0.744727i | \(-0.732580\pi\) | ||||
−0.667369 | + | 0.744727i | \(0.732580\pi\) | |||||||
\(6\) | 5.40556 | 2.20681 | ||||||||
\(7\) | 0.228878 | 0.0865078 | 0.0432539 | − | 0.999064i | \(-0.486228\pi\) | ||||
0.0432539 | + | 0.999064i | \(0.486228\pi\) | |||||||
\(8\) | −7.68717 | −2.71783 | ||||||||
\(9\) | 1.22144 | 0.407146 | ||||||||
\(10\) | 7.85221 | 2.48309 | ||||||||
\(11\) | −4.45205 | −1.34234 | −0.671172 | − | 0.741301i | \(-0.734209\pi\) | ||||
−0.671172 | + | 0.741301i | \(0.734209\pi\) | |||||||
\(12\) | −10.1125 | −2.91922 | ||||||||
\(13\) | −3.16946 | −0.879051 | −0.439526 | − | 0.898230i | \(-0.644853\pi\) | ||||
−0.439526 | + | 0.898230i | \(0.644853\pi\) | |||||||
\(14\) | −0.602164 | −0.160935 | ||||||||
\(15\) | 6.13213 | 1.58331 | ||||||||
\(16\) | 10.3808 | 2.59520 | ||||||||
\(17\) | 0.815402 | 0.197764 | 0.0988820 | − | 0.995099i | \(-0.468473\pi\) | ||||
0.0988820 | + | 0.995099i | \(0.468473\pi\) | |||||||
\(18\) | −3.21353 | −0.757436 | ||||||||
\(19\) | 2.49505 | 0.572405 | 0.286202 | − | 0.958169i | \(-0.407607\pi\) | ||||
0.286202 | + | 0.958169i | \(0.407607\pi\) | |||||||
\(20\) | −14.6895 | −3.28468 | ||||||||
\(21\) | −0.470256 | −0.102618 | ||||||||
\(22\) | 11.7131 | 2.49724 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 15.7942 | 3.22397 | ||||||||
\(25\) | 3.90763 | 0.781527 | ||||||||
\(26\) | 8.33867 | 1.63535 | ||||||||
\(27\) | 3.65426 | 0.703262 | ||||||||
\(28\) | 1.12650 | 0.212889 | ||||||||
\(29\) | −0.608467 | −0.112990 | −0.0564948 | − | 0.998403i | \(-0.517992\pi\) | ||||
−0.0564948 | + | 0.998403i | \(0.517992\pi\) | |||||||
\(30\) | −16.1333 | −2.94552 | ||||||||
\(31\) | −3.75357 | −0.674160 | −0.337080 | − | 0.941476i | \(-0.609439\pi\) | ||||
−0.337080 | + | 0.941476i | \(0.609439\pi\) | |||||||
\(32\) | −11.9369 | −2.11017 | ||||||||
\(33\) | 9.14725 | 1.59233 | ||||||||
\(34\) | −2.14527 | −0.367911 | ||||||||
\(35\) | −0.683102 | −0.115465 | ||||||||
\(36\) | 6.01172 | 1.00195 | ||||||||
\(37\) | 8.00206 | 1.31553 | 0.657766 | − | 0.753223i | \(-0.271502\pi\) | ||||
0.657766 | + | 0.753223i | \(0.271502\pi\) | |||||||
\(38\) | −6.56433 | −1.06488 | ||||||||
\(39\) | 6.51203 | 1.04276 | ||||||||
\(40\) | 22.9429 | 3.62759 | ||||||||
\(41\) | 10.8290 | 1.69121 | 0.845603 | − | 0.533812i | \(-0.179241\pi\) | ||||
0.845603 | + | 0.533812i | \(0.179241\pi\) | |||||||
\(42\) | 1.23721 | 0.190906 | ||||||||
\(43\) | −0.440332 | −0.0671500 | −0.0335750 | − | 0.999436i | \(-0.510689\pi\) | ||||
−0.0335750 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(44\) | −21.9123 | −3.30340 | ||||||||
\(45\) | −3.64546 | −0.543434 | ||||||||
\(46\) | −2.63094 | −0.387911 | ||||||||
\(47\) | −10.5002 | −1.53161 | −0.765806 | − | 0.643071i | \(-0.777660\pi\) | ||||
−0.765806 | + | 0.643071i | \(0.777660\pi\) | |||||||
\(48\) | −21.3285 | −3.07851 | ||||||||
\(49\) | −6.94761 | −0.992516 | ||||||||
\(50\) | −10.2807 | −1.45392 | ||||||||
\(51\) | −1.67534 | −0.234594 | ||||||||
\(52\) | −15.5996 | −2.16327 | ||||||||
\(53\) | 0.700230 | 0.0961839 | 0.0480920 | − | 0.998843i | \(-0.484686\pi\) | ||||
0.0480920 | + | 0.998843i | \(0.484686\pi\) | |||||||
\(54\) | −9.61413 | −1.30832 | ||||||||
\(55\) | 13.2874 | 1.79168 | ||||||||
\(56\) | −1.75943 | −0.235113 | ||||||||
\(57\) | −5.12637 | −0.679005 | ||||||||
\(58\) | 1.60084 | 0.210201 | ||||||||
\(59\) | −12.5183 | −1.62974 | −0.814872 | − | 0.579641i | \(-0.803193\pi\) | ||||
−0.814872 | + | 0.579641i | \(0.803193\pi\) | |||||||
\(60\) | 30.1813 | 3.89639 | ||||||||
\(61\) | 8.02118 | 1.02701 | 0.513503 | − | 0.858088i | \(-0.328347\pi\) | ||||
0.513503 | + | 0.858088i | \(0.328347\pi\) | |||||||
\(62\) | 9.87540 | 1.25418 | ||||||||
\(63\) | 0.279560 | 0.0352213 | ||||||||
\(64\) | 10.6437 | 1.33046 | ||||||||
\(65\) | 9.45948 | 1.17330 | ||||||||
\(66\) | −24.0659 | −2.96230 | ||||||||
\(67\) | 15.0315 | 1.83640 | 0.918198 | − | 0.396122i | \(-0.129644\pi\) | ||||
0.918198 | + | 0.396122i | \(0.129644\pi\) | |||||||
\(68\) | 4.01328 | 0.486681 | ||||||||
\(69\) | −2.05461 | −0.247346 | ||||||||
\(70\) | 1.79720 | 0.214806 | ||||||||
\(71\) | −16.7994 | −1.99372 | −0.996858 | − | 0.0792058i | \(-0.974762\pi\) | ||||
−0.996858 | + | 0.0792058i | \(0.974762\pi\) | |||||||
\(72\) | −9.38940 | −1.10655 | ||||||||
\(73\) | 3.78320 | 0.442791 | 0.221395 | − | 0.975184i | \(-0.428939\pi\) | ||||
0.221395 | + | 0.975184i | \(0.428939\pi\) | |||||||
\(74\) | −21.0529 | −2.44735 | ||||||||
\(75\) | −8.02868 | −0.927072 | ||||||||
\(76\) | 12.2802 | 1.40864 | ||||||||
\(77\) | −1.01898 | −0.116123 | ||||||||
\(78\) | −17.1327 | −1.93990 | ||||||||
\(79\) | −3.19883 | −0.359896 | −0.179948 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179948 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(80\) | −30.9822 | −3.46391 | ||||||||
\(81\) | −11.1724 | −1.24138 | ||||||||
\(82\) | −28.4905 | −3.14624 | ||||||||
\(83\) | −6.21259 | −0.681921 | −0.340960 | − | 0.940078i | \(-0.610752\pi\) | ||||
−0.340960 | + | 0.940078i | \(0.610752\pi\) | |||||||
\(84\) | −2.31452 | −0.252535 | ||||||||
\(85\) | −2.43362 | −0.263963 | ||||||||
\(86\) | 1.15849 | 0.124923 | ||||||||
\(87\) | 1.25017 | 0.134032 | ||||||||
\(88\) | 34.2237 | 3.64826 | ||||||||
\(89\) | 0.573084 | 0.0607468 | 0.0303734 | − | 0.999539i | \(-0.490330\pi\) | ||||
0.0303734 | + | 0.999539i | \(0.490330\pi\) | |||||||
\(90\) | 9.59099 | 1.01098 | ||||||||
\(91\) | −0.725421 | −0.0760448 | ||||||||
\(92\) | 4.92184 | 0.513137 | ||||||||
\(93\) | 7.71213 | 0.799711 | ||||||||
\(94\) | 27.6254 | 2.84934 | ||||||||
\(95\) | −7.44665 | −0.764010 | ||||||||
\(96\) | 24.5257 | 2.50315 | ||||||||
\(97\) | −8.68164 | −0.881487 | −0.440743 | − | 0.897633i | \(-0.645285\pi\) | ||||
−0.440743 | + | 0.897633i | \(0.645285\pi\) | |||||||
\(98\) | 18.2787 | 1.84643 | ||||||||
\(99\) | −5.43791 | −0.546530 | ||||||||
\(100\) | 19.2327 | 1.92327 | ||||||||
\(101\) | −2.87422 | −0.285996 | −0.142998 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142998 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(102\) | 4.40771 | 0.436428 | ||||||||
\(103\) | −4.19722 | −0.413564 | −0.206782 | − | 0.978387i | \(-0.566299\pi\) | ||||
−0.206782 | + | 0.978387i | \(0.566299\pi\) | |||||||
\(104\) | 24.3642 | 2.38911 | ||||||||
\(105\) | 1.40351 | 0.136969 | ||||||||
\(106\) | −1.84226 | −0.178936 | ||||||||
\(107\) | −4.71951 | −0.456252 | −0.228126 | − | 0.973632i | \(-0.573260\pi\) | ||||
−0.228126 | + | 0.973632i | \(0.573260\pi\) | |||||||
\(108\) | 17.9857 | 1.73067 | ||||||||
\(109\) | −10.5394 | −1.00949 | −0.504745 | − | 0.863269i | \(-0.668413\pi\) | ||||
−0.504745 | + | 0.863269i | \(0.668413\pi\) | |||||||
\(110\) | −34.9585 | −3.33316 | ||||||||
\(111\) | −16.4412 | −1.56052 | ||||||||
\(112\) | 2.37594 | 0.224505 | ||||||||
\(113\) | −11.7957 | −1.10964 | −0.554822 | − | 0.831969i | \(-0.687214\pi\) | ||||
−0.554822 | + | 0.831969i | \(0.687214\pi\) | |||||||
\(114\) | 13.4872 | 1.26319 | ||||||||
\(115\) | −2.98457 | −0.278312 | ||||||||
\(116\) | −2.99478 | −0.278058 | ||||||||
\(117\) | −3.87131 | −0.357902 | ||||||||
\(118\) | 32.9349 | 3.03190 | ||||||||
\(119\) | 0.186628 | 0.0171081 | ||||||||
\(120\) | −47.1387 | −4.30316 | ||||||||
\(121\) | 8.82078 | 0.801889 | ||||||||
\(122\) | −21.1032 | −1.91060 | ||||||||
\(123\) | −22.2494 | −2.00616 | ||||||||
\(124\) | −18.4744 | −1.65905 | ||||||||
\(125\) | 3.26024 | 0.291604 | ||||||||
\(126\) | −0.735506 | −0.0655241 | ||||||||
\(127\) | −9.67470 | −0.858491 | −0.429245 | − | 0.903188i | \(-0.641220\pi\) | ||||
−0.429245 | + | 0.903188i | \(0.641220\pi\) | |||||||
\(128\) | −4.12899 | −0.364954 | ||||||||
\(129\) | 0.904712 | 0.0796555 | ||||||||
\(130\) | −24.8873 | −2.18276 | ||||||||
\(131\) | 10.9994 | 0.961019 | 0.480510 | − | 0.876989i | \(-0.340452\pi\) | ||||
0.480510 | + | 0.876989i | \(0.340452\pi\) | |||||||
\(132\) | 45.0213 | 3.91860 | ||||||||
\(133\) | 0.571063 | 0.0495175 | ||||||||
\(134\) | −39.5471 | −3.41635 | ||||||||
\(135\) | −10.9064 | −0.938671 | ||||||||
\(136\) | −6.26813 | −0.537488 | ||||||||
\(137\) | 15.6571 | 1.33767 | 0.668837 | − | 0.743409i | \(-0.266792\pi\) | ||||
0.668837 | + | 0.743409i | \(0.266792\pi\) | |||||||
\(138\) | 5.40556 | 0.460152 | ||||||||
\(139\) | −17.2793 | −1.46561 | −0.732807 | − | 0.680437i | \(-0.761790\pi\) | ||||
−0.732807 | + | 0.680437i | \(0.761790\pi\) | |||||||
\(140\) | −3.36212 | −0.284151 | ||||||||
\(141\) | 21.5739 | 1.81685 | ||||||||
\(142\) | 44.1981 | 3.70902 | ||||||||
\(143\) | 14.1106 | 1.17999 | ||||||||
\(144\) | 12.6795 | 1.05663 | ||||||||
\(145\) | 1.81601 | 0.150811 | ||||||||
\(146\) | −9.95338 | −0.823747 | ||||||||
\(147\) | 14.2747 | 1.17735 | ||||||||
\(148\) | 39.3848 | 3.23741 | ||||||||
\(149\) | −8.30005 | −0.679967 | −0.339983 | − | 0.940431i | \(-0.610421\pi\) | ||||
−0.339983 | + | 0.940431i | \(0.610421\pi\) | |||||||
\(150\) | 21.1230 | 1.72468 | ||||||||
\(151\) | 8.26813 | 0.672851 | 0.336425 | − | 0.941710i | \(-0.390782\pi\) | ||||
0.336425 | + | 0.941710i | \(0.390782\pi\) | |||||||
\(152\) | −19.1799 | −1.55570 | ||||||||
\(153\) | 0.995963 | 0.0805189 | ||||||||
\(154\) | 2.68087 | 0.216030 | ||||||||
\(155\) | 11.2028 | 0.899828 | ||||||||
\(156\) | 32.0511 | 2.56614 | ||||||||
\(157\) | 21.4572 | 1.71247 | 0.856235 | − | 0.516587i | \(-0.172798\pi\) | ||||
0.856235 | + | 0.516587i | \(0.172798\pi\) | |||||||
\(158\) | 8.41591 | 0.669534 | ||||||||
\(159\) | −1.43870 | −0.114096 | ||||||||
\(160\) | 35.6265 | 2.81652 | ||||||||
\(161\) | 0.228878 | 0.0180381 | ||||||||
\(162\) | 29.3939 | 2.30940 | ||||||||
\(163\) | −5.12274 | −0.401244 | −0.200622 | − | 0.979669i | \(-0.564296\pi\) | ||||
−0.200622 | + | 0.979669i | \(0.564296\pi\) | |||||||
\(164\) | 53.2986 | 4.16192 | ||||||||
\(165\) | −27.3006 | −2.12535 | ||||||||
\(166\) | 16.3449 | 1.26861 | ||||||||
\(167\) | 22.3880 | 1.73244 | 0.866220 | − | 0.499663i | \(-0.166543\pi\) | ||||
0.866220 | + | 0.499663i | \(0.166543\pi\) | |||||||
\(168\) | 3.61494 | 0.278899 | ||||||||
\(169\) | −2.95449 | −0.227269 | ||||||||
\(170\) | 6.40271 | 0.491065 | ||||||||
\(171\) | 3.04755 | 0.233052 | ||||||||
\(172\) | −2.16724 | −0.165251 | ||||||||
\(173\) | −0.230581 | −0.0175308 | −0.00876538 | − | 0.999962i | \(-0.502790\pi\) | ||||
−0.00876538 | + | 0.999962i | \(0.502790\pi\) | |||||||
\(174\) | −3.28911 | −0.249347 | ||||||||
\(175\) | 0.894372 | 0.0676082 | ||||||||
\(176\) | −46.2159 | −3.48365 | ||||||||
\(177\) | 25.7203 | 1.93325 | ||||||||
\(178\) | −1.50775 | −0.113010 | ||||||||
\(179\) | −13.1701 | −0.984379 | −0.492190 | − | 0.870488i | \(-0.663803\pi\) | ||||
−0.492190 | + | 0.870488i | \(0.663803\pi\) | |||||||
\(180\) | −17.9424 | −1.33735 | ||||||||
\(181\) | −22.5609 | −1.67694 | −0.838470 | − | 0.544948i | \(-0.816549\pi\) | ||||
−0.838470 | + | 0.544948i | \(0.816549\pi\) | |||||||
\(182\) | 1.90854 | 0.141470 | ||||||||
\(183\) | −16.4804 | −1.21827 | ||||||||
\(184\) | −7.68717 | −0.566706 | ||||||||
\(185\) | −23.8827 | −1.75589 | ||||||||
\(186\) | −20.2901 | −1.48775 | ||||||||
\(187\) | −3.63021 | −0.265468 | ||||||||
\(188\) | −51.6803 | −3.76917 | ||||||||
\(189\) | 0.836380 | 0.0608377 | ||||||||
\(190\) | 19.5917 | 1.42133 | ||||||||
\(191\) | −11.5402 | −0.835021 | −0.417511 | − | 0.908672i | \(-0.637097\pi\) | ||||
−0.417511 | + | 0.908672i | \(0.637097\pi\) | |||||||
\(192\) | −21.8686 | −1.57823 | ||||||||
\(193\) | −1.13217 | −0.0814954 | −0.0407477 | − | 0.999169i | \(-0.512974\pi\) | ||||
−0.0407477 | + | 0.999169i | \(0.512974\pi\) | |||||||
\(194\) | 22.8408 | 1.63988 | ||||||||
\(195\) | −19.4356 | −1.39181 | ||||||||
\(196\) | −34.1950 | −2.44250 | ||||||||
\(197\) | 3.69105 | 0.262977 | 0.131488 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131488 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(198\) | 14.3068 | 1.01674 | ||||||||
\(199\) | −3.35641 | −0.237930 | −0.118965 | − | 0.992898i | \(-0.537958\pi\) | ||||
−0.118965 | + | 0.992898i | \(0.537958\pi\) | |||||||
\(200\) | −30.0387 | −2.12405 | ||||||||
\(201\) | −30.8840 | −2.17839 | ||||||||
\(202\) | 7.56191 | 0.532054 | ||||||||
\(203\) | −0.139265 | −0.00977447 | ||||||||
\(204\) | −8.24573 | −0.577317 | ||||||||
\(205\) | −32.3199 | −2.25732 | ||||||||
\(206\) | 11.0426 | 0.769376 | ||||||||
\(207\) | 1.22144 | 0.0848958 | ||||||||
\(208\) | −32.9016 | −2.28131 | ||||||||
\(209\) | −11.1081 | −0.768364 | ||||||||
\(210\) | −3.69255 | −0.254810 | ||||||||
\(211\) | 25.5631 | 1.75984 | 0.879920 | − | 0.475122i | \(-0.157596\pi\) | ||||
0.879920 | + | 0.475122i | \(0.157596\pi\) | |||||||
\(212\) | 3.44642 | 0.236701 | ||||||||
\(213\) | 34.5162 | 2.36501 | ||||||||
\(214\) | 12.4167 | 0.848790 | ||||||||
\(215\) | 1.31420 | 0.0896277 | ||||||||
\(216\) | −28.0909 | −1.91134 | ||||||||
\(217\) | −0.859109 | −0.0583201 | ||||||||
\(218\) | 27.7285 | 1.87801 | ||||||||
\(219\) | −7.77303 | −0.525252 | ||||||||
\(220\) | 65.3986 | 4.40918 | ||||||||
\(221\) | −2.58439 | −0.173845 | ||||||||
\(222\) | 43.2557 | 2.90313 | ||||||||
\(223\) | −23.6936 | −1.58664 | −0.793321 | − | 0.608804i | \(-0.791650\pi\) | ||||
−0.793321 | + | 0.608804i | \(0.791650\pi\) | |||||||
\(224\) | −2.73210 | −0.182546 | ||||||||
\(225\) | 4.77293 | 0.318196 | ||||||||
\(226\) | 31.0337 | 2.06433 | ||||||||
\(227\) | −6.21504 | −0.412506 | −0.206253 | − | 0.978499i | \(-0.566127\pi\) | ||||
−0.206253 | + | 0.978499i | \(0.566127\pi\) | |||||||
\(228\) | −25.2312 | −1.67097 | ||||||||
\(229\) | −17.7950 | −1.17593 | −0.587964 | − | 0.808887i | \(-0.700070\pi\) | ||||
−0.587964 | + | 0.808887i | \(0.700070\pi\) | |||||||
\(230\) | 7.85221 | 0.517759 | ||||||||
\(231\) | 2.09361 | 0.137749 | ||||||||
\(232\) | 4.67739 | 0.307086 | ||||||||
\(233\) | −17.0964 | −1.12002 | −0.560012 | − | 0.828485i | \(-0.689203\pi\) | ||||
−0.560012 | + | 0.828485i | \(0.689203\pi\) | |||||||
\(234\) | 10.1852 | 0.665825 | ||||||||
\(235\) | 31.3386 | 2.04430 | ||||||||
\(236\) | −61.6130 | −4.01067 | ||||||||
\(237\) | 6.57235 | 0.426920 | ||||||||
\(238\) | −0.491006 | −0.0318272 | ||||||||
\(239\) | −6.87581 | −0.444759 | −0.222380 | − | 0.974960i | \(-0.571382\pi\) | ||||
−0.222380 | + | 0.974960i | \(0.571382\pi\) | |||||||
\(240\) | 63.6564 | 4.10900 | ||||||||
\(241\) | −20.7952 | −1.33953 | −0.669767 | − | 0.742571i | \(-0.733606\pi\) | ||||
−0.669767 | + | 0.742571i | \(0.733606\pi\) | |||||||
\(242\) | −23.2069 | −1.49180 | ||||||||
\(243\) | 11.9922 | 0.769300 | ||||||||
\(244\) | 39.4789 | 2.52738 | ||||||||
\(245\) | 20.7356 | 1.32475 | ||||||||
\(246\) | 58.5369 | 3.73217 | ||||||||
\(247\) | −7.90798 | −0.503173 | ||||||||
\(248\) | 28.8543 | 1.83225 | ||||||||
\(249\) | 12.7645 | 0.808916 | ||||||||
\(250\) | −8.57748 | −0.542488 | ||||||||
\(251\) | −6.31715 | −0.398735 | −0.199368 | − | 0.979925i | \(-0.563889\pi\) | ||||
−0.199368 | + | 0.979925i | \(0.563889\pi\) | |||||||
\(252\) | 1.37595 | 0.0866768 | ||||||||
\(253\) | −4.45205 | −0.279898 | ||||||||
\(254\) | 25.4535 | 1.59710 | ||||||||
\(255\) | 5.00015 | 0.313122 | ||||||||
\(256\) | −10.4242 | −0.651512 | ||||||||
\(257\) | −30.5067 | −1.90295 | −0.951477 | − | 0.307719i | \(-0.900434\pi\) | ||||
−0.951477 | + | 0.307719i | \(0.900434\pi\) | |||||||
\(258\) | −2.38024 | −0.148187 | ||||||||
\(259\) | 1.83150 | 0.113804 | ||||||||
\(260\) | 46.5580 | 2.88740 | ||||||||
\(261\) | −0.743205 | −0.0460032 | ||||||||
\(262\) | −28.9387 | −1.78784 | ||||||||
\(263\) | 5.22419 | 0.322137 | 0.161069 | − | 0.986943i | \(-0.448506\pi\) | ||||
0.161069 | + | 0.986943i | \(0.448506\pi\) | |||||||
\(264\) | −70.3165 | −4.32768 | ||||||||
\(265\) | −2.08988 | −0.128380 | ||||||||
\(266\) | −1.50243 | −0.0921200 | ||||||||
\(267\) | −1.17747 | −0.0720597 | ||||||||
\(268\) | 73.9828 | 4.51922 | ||||||||
\(269\) | −15.4095 | −0.939534 | −0.469767 | − | 0.882790i | \(-0.655662\pi\) | ||||
−0.469767 | + | 0.882790i | \(0.655662\pi\) | |||||||
\(270\) | 28.6940 | 1.74626 | ||||||||
\(271\) | 22.6210 | 1.37413 | 0.687063 | − | 0.726598i | \(-0.258900\pi\) | ||||
0.687063 | + | 0.726598i | \(0.258900\pi\) | |||||||
\(272\) | 8.46453 | 0.513237 | ||||||||
\(273\) | 1.49046 | 0.0902067 | ||||||||
\(274\) | −41.1928 | −2.48855 | ||||||||
\(275\) | −17.3970 | −1.04908 | ||||||||
\(276\) | −10.1125 | −0.608699 | ||||||||
\(277\) | −9.40141 | −0.564876 | −0.282438 | − | 0.959286i | \(-0.591143\pi\) | ||||
−0.282438 | + | 0.959286i | \(0.591143\pi\) | |||||||
\(278\) | 45.4608 | 2.72656 | ||||||||
\(279\) | −4.58475 | −0.274482 | ||||||||
\(280\) | 5.25112 | 0.313814 | ||||||||
\(281\) | 7.07424 | 0.422014 | 0.211007 | − | 0.977485i | \(-0.432326\pi\) | ||||
0.211007 | + | 0.977485i | \(0.432326\pi\) | |||||||
\(282\) | −56.7595 | −3.37998 | ||||||||
\(283\) | −1.32472 | −0.0787466 | −0.0393733 | − | 0.999225i | \(-0.512536\pi\) | ||||
−0.0393733 | + | 0.999225i | \(0.512536\pi\) | |||||||
\(284\) | −82.6837 | −4.90637 | ||||||||
\(285\) | 15.3000 | 0.906293 | ||||||||
\(286\) | −37.1242 | −2.19520 | ||||||||
\(287\) | 2.47852 | 0.146303 | ||||||||
\(288\) | −14.5802 | −0.859146 | ||||||||
\(289\) | −16.3351 | −0.960889 | ||||||||
\(290\) | −4.77781 | −0.280563 | ||||||||
\(291\) | 17.8374 | 1.04565 | ||||||||
\(292\) | 18.6203 | 1.08967 | ||||||||
\(293\) | 31.7535 | 1.85506 | 0.927529 | − | 0.373751i | \(-0.121929\pi\) | ||||
0.927529 | + | 0.373751i | \(0.121929\pi\) | |||||||
\(294\) | −37.5558 | −2.19030 | ||||||||
\(295\) | 37.3617 | 2.17528 | ||||||||
\(296\) | −61.5132 | −3.57538 | ||||||||
\(297\) | −16.2690 | −0.944020 | ||||||||
\(298\) | 21.8369 | 1.26498 | ||||||||
\(299\) | −3.16946 | −0.183295 | ||||||||
\(300\) | −39.5159 | −2.28145 | ||||||||
\(301\) | −0.100782 | −0.00580900 | ||||||||
\(302\) | −21.7529 | −1.25174 | ||||||||
\(303\) | 5.90542 | 0.339258 | ||||||||
\(304\) | 25.9007 | 1.48550 | ||||||||
\(305\) | −23.9397 | −1.37079 | ||||||||
\(306\) | −2.62032 | −0.149794 | ||||||||
\(307\) | −4.30086 | −0.245463 | −0.122732 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122732 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(308\) | −5.01524 | −0.285770 | ||||||||
\(309\) | 8.62366 | 0.490583 | ||||||||
\(310\) | −29.4738 | −1.67400 | ||||||||
\(311\) | −13.9944 | −0.793547 | −0.396774 | − | 0.917916i | \(-0.629870\pi\) | ||||
−0.396774 | + | 0.917916i | \(0.629870\pi\) | |||||||
\(312\) | −50.0591 | −2.83404 | ||||||||
\(313\) | 9.97013 | 0.563545 | 0.281773 | − | 0.959481i | \(-0.409078\pi\) | ||||
0.281773 | + | 0.959481i | \(0.409078\pi\) | |||||||
\(314\) | −56.4525 | −3.18580 | ||||||||
\(315\) | −0.834367 | −0.0470112 | ||||||||
\(316\) | −15.7441 | −0.885675 | ||||||||
\(317\) | −22.8673 | −1.28435 | −0.642177 | − | 0.766556i | \(-0.721969\pi\) | ||||
−0.642177 | + | 0.766556i | \(0.721969\pi\) | |||||||
\(318\) | 3.78514 | 0.212260 | ||||||||
\(319\) | 2.70893 | 0.151671 | ||||||||
\(320\) | −31.7667 | −1.77581 | ||||||||
\(321\) | 9.69677 | 0.541221 | ||||||||
\(322\) | −0.602164 | −0.0335573 | ||||||||
\(323\) | 2.03447 | 0.113201 | ||||||||
\(324\) | −54.9887 | −3.05493 | ||||||||
\(325\) | −12.3851 | −0.687002 | ||||||||
\(326\) | 13.4776 | 0.746456 | ||||||||
\(327\) | 21.6544 | 1.19749 | ||||||||
\(328\) | −83.2444 | −4.59640 | ||||||||
\(329\) | −2.40327 | −0.132496 | ||||||||
\(330\) | 71.8261 | 3.95390 | ||||||||
\(331\) | 26.6590 | 1.46531 | 0.732655 | − | 0.680600i | \(-0.238281\pi\) | ||||
0.732655 | + | 0.680600i | \(0.238281\pi\) | |||||||
\(332\) | −30.5774 | −1.67815 | ||||||||
\(333\) | 9.77403 | 0.535613 | ||||||||
\(334\) | −58.9016 | −3.22295 | ||||||||
\(335\) | −44.8626 | −2.45111 | ||||||||
\(336\) | −4.88163 | −0.266315 | ||||||||
\(337\) | −19.7403 | −1.07532 | −0.537660 | − | 0.843161i | \(-0.680692\pi\) | ||||
−0.537660 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(338\) | 7.77309 | 0.422801 | ||||||||
\(339\) | 24.2356 | 1.31629 | ||||||||
\(340\) | −11.9779 | −0.649592 | ||||||||
\(341\) | 16.7111 | 0.904956 | ||||||||
\(342\) | −8.01793 | −0.433560 | ||||||||
\(343\) | −3.19230 | −0.172368 | ||||||||
\(344\) | 3.38491 | 0.182502 | ||||||||
\(345\) | 6.13213 | 0.330143 | ||||||||
\(346\) | 0.606645 | 0.0326134 | ||||||||
\(347\) | −13.8804 | −0.745138 | −0.372569 | − | 0.928004i | \(-0.621523\pi\) | ||||
−0.372569 | + | 0.928004i | \(0.621523\pi\) | |||||||
\(348\) | 6.15311 | 0.329841 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −2.35304 | −0.125775 | ||||||||
\(351\) | −11.5820 | −0.618204 | ||||||||
\(352\) | 53.1437 | 2.83257 | ||||||||
\(353\) | 9.75402 | 0.519154 | 0.259577 | − | 0.965722i | \(-0.416417\pi\) | ||||
0.259577 | + | 0.965722i | \(0.416417\pi\) | |||||||
\(354\) | −67.6684 | −3.59654 | ||||||||
\(355\) | 50.1388 | 2.66109 | ||||||||
\(356\) | 2.82062 | 0.149493 | ||||||||
\(357\) | −0.383448 | −0.0202942 | ||||||||
\(358\) | 34.6497 | 1.83129 | ||||||||
\(359\) | −16.4800 | −0.869782 | −0.434891 | − | 0.900483i | \(-0.643213\pi\) | ||||
−0.434891 | + | 0.900483i | \(0.643213\pi\) | |||||||
\(360\) | 28.0233 | 1.47696 | ||||||||
\(361\) | −12.7747 | −0.672353 | ||||||||
\(362\) | 59.3564 | 3.11970 | ||||||||
\(363\) | −18.1233 | −0.951226 | ||||||||
\(364\) | −3.57040 | −0.187140 | ||||||||
\(365\) | −11.2912 | −0.591010 | ||||||||
\(366\) | 43.3590 | 2.26641 | ||||||||
\(367\) | −7.70470 | −0.402182 | −0.201091 | − | 0.979573i | \(-0.564449\pi\) | ||||
−0.201091 | + | 0.979573i | \(0.564449\pi\) | |||||||
\(368\) | 10.3808 | 0.541137 | ||||||||
\(369\) | 13.2270 | 0.688568 | ||||||||
\(370\) | 62.8339 | 3.26658 | ||||||||
\(371\) | 0.160267 | 0.00832066 | ||||||||
\(372\) | 37.9578 | 1.96802 | ||||||||
\(373\) | 12.6023 | 0.652525 | 0.326262 | − | 0.945279i | \(-0.394211\pi\) | ||||
0.326262 | + | 0.945279i | \(0.394211\pi\) | |||||||
\(374\) | 9.55087 | 0.493864 | ||||||||
\(375\) | −6.69853 | −0.345910 | ||||||||
\(376\) | 80.7169 | 4.16266 | ||||||||
\(377\) | 1.92852 | 0.0993236 | ||||||||
\(378\) | −2.20046 | −0.113180 | ||||||||
\(379\) | 10.9700 | 0.563489 | 0.281745 | − | 0.959489i | \(-0.409087\pi\) | ||||
0.281745 | + | 0.959489i | \(0.409087\pi\) | |||||||
\(380\) | −36.6512 | −1.88017 | ||||||||
\(381\) | 19.8778 | 1.01837 | ||||||||
\(382\) | 30.3616 | 1.55344 | ||||||||
\(383\) | 24.1547 | 1.23425 | 0.617123 | − | 0.786867i | \(-0.288298\pi\) | ||||
0.617123 | + | 0.786867i | \(0.288298\pi\) | |||||||
\(384\) | 8.48347 | 0.432920 | ||||||||
\(385\) | 3.04121 | 0.154994 | ||||||||
\(386\) | 2.97867 | 0.151610 | ||||||||
\(387\) | −0.537838 | −0.0273399 | ||||||||
\(388\) | −42.7296 | −2.16927 | ||||||||
\(389\) | 7.28676 | 0.369454 | 0.184727 | − | 0.982790i | \(-0.440860\pi\) | ||||
0.184727 | + | 0.982790i | \(0.440860\pi\) | |||||||
\(390\) | 51.1338 | 2.58926 | ||||||||
\(391\) | 0.815402 | 0.0412367 | ||||||||
\(392\) | 53.4075 | 2.69749 | ||||||||
\(393\) | −22.5995 | −1.13999 | ||||||||
\(394\) | −9.71093 | −0.489230 | ||||||||
\(395\) | 9.54711 | 0.480367 | ||||||||
\(396\) | −26.7645 | −1.34497 | ||||||||
\(397\) | −10.8698 | −0.545542 | −0.272771 | − | 0.962079i | \(-0.587940\pi\) | ||||
−0.272771 | + | 0.962079i | \(0.587940\pi\) | |||||||
\(398\) | 8.83052 | 0.442634 | ||||||||
\(399\) | −1.17331 | −0.0587392 | ||||||||
\(400\) | 40.5644 | 2.02822 | ||||||||
\(401\) | −19.8380 | −0.990663 | −0.495331 | − | 0.868704i | \(-0.664953\pi\) | ||||
−0.495331 | + | 0.868704i | \(0.664953\pi\) | |||||||
\(402\) | 81.2540 | 4.05258 | ||||||||
\(403\) | 11.8968 | 0.592622 | ||||||||
\(404\) | −14.1465 | −0.703813 | ||||||||
\(405\) | 33.3448 | 1.65692 | ||||||||
\(406\) | 0.366397 | 0.0181840 | ||||||||
\(407\) | −35.6256 | −1.76590 | ||||||||
\(408\) | 12.8786 | 0.637586 | ||||||||
\(409\) | 16.4458 | 0.813193 | 0.406597 | − | 0.913608i | \(-0.366715\pi\) | ||||
0.406597 | + | 0.913608i | \(0.366715\pi\) | |||||||
\(410\) | 85.0316 | 4.19941 | ||||||||
\(411\) | −32.1692 | −1.58679 | ||||||||
\(412\) | −20.6580 | −1.01775 | ||||||||
\(413\) | −2.86516 | −0.140986 | ||||||||
\(414\) | −3.21353 | −0.157936 | ||||||||
\(415\) | 18.5419 | 0.910186 | ||||||||
\(416\) | 37.8336 | 1.85494 | ||||||||
\(417\) | 35.5023 | 1.73856 | ||||||||
\(418\) | 29.2248 | 1.42943 | ||||||||
\(419\) | 14.1447 | 0.691012 | 0.345506 | − | 0.938417i | \(-0.387707\pi\) | ||||
0.345506 | + | 0.938417i | \(0.387707\pi\) | |||||||
\(420\) | 6.90785 | 0.337069 | ||||||||
\(421\) | 2.57159 | 0.125332 | 0.0626658 | − | 0.998035i | \(-0.480040\pi\) | ||||
0.0626658 | + | 0.998035i | \(0.480040\pi\) | |||||||
\(422\) | −67.2551 | −3.27393 | ||||||||
\(423\) | −12.8254 | −0.623590 | ||||||||
\(424\) | −5.38278 | −0.261411 | ||||||||
\(425\) | 3.18629 | 0.154558 | ||||||||
\(426\) | −90.8100 | −4.39976 | ||||||||
\(427\) | 1.83587 | 0.0888441 | ||||||||
\(428\) | −23.2286 | −1.12280 | ||||||||
\(429\) | −28.9919 | −1.39974 | ||||||||
\(430\) | −3.45758 | −0.166739 | ||||||||
\(431\) | −39.6491 | −1.90983 | −0.954915 | − | 0.296879i | \(-0.904054\pi\) | ||||
−0.954915 | + | 0.296879i | \(0.904054\pi\) | |||||||
\(432\) | 37.9341 | 1.82511 | ||||||||
\(433\) | −30.4796 | −1.46476 | −0.732379 | − | 0.680897i | \(-0.761590\pi\) | ||||
−0.732379 | + | 0.680897i | \(0.761590\pi\) | |||||||
\(434\) | 2.26026 | 0.108496 | ||||||||
\(435\) | −3.73120 | −0.178897 | ||||||||
\(436\) | −51.8731 | −2.48427 | ||||||||
\(437\) | 2.49505 | 0.119355 | ||||||||
\(438\) | 20.4503 | 0.977155 | ||||||||
\(439\) | −15.9366 | −0.760615 | −0.380307 | − | 0.924860i | \(-0.624182\pi\) | ||||
−0.380307 | + | 0.924860i | \(0.624182\pi\) | |||||||
\(440\) | −102.143 | −4.86947 | ||||||||
\(441\) | −8.48608 | −0.404099 | ||||||||
\(442\) | 6.79937 | 0.323413 | ||||||||
\(443\) | −2.43015 | −0.115460 | −0.0577298 | − | 0.998332i | \(-0.518386\pi\) | ||||
−0.0577298 | + | 0.998332i | \(0.518386\pi\) | |||||||
\(444\) | −80.9207 | −3.84032 | ||||||||
\(445\) | −1.71041 | −0.0810810 | ||||||||
\(446\) | 62.3364 | 2.95172 | ||||||||
\(447\) | 17.0534 | 0.806598 | ||||||||
\(448\) | 2.43610 | 0.115095 | ||||||||
\(449\) | −19.9848 | −0.943143 | −0.471571 | − | 0.881828i | \(-0.656313\pi\) | ||||
−0.471571 | + | 0.881828i | \(0.656313\pi\) | |||||||
\(450\) | −12.5573 | −0.591957 | ||||||||
\(451\) | −48.2113 | −2.27018 | ||||||||
\(452\) | −58.0564 | −2.73074 | ||||||||
\(453\) | −16.9878 | −0.798157 | ||||||||
\(454\) | 16.3514 | 0.767408 | ||||||||
\(455\) | 2.16507 | 0.101500 | ||||||||
\(456\) | 39.4073 | 1.84542 | ||||||||
\(457\) | 0.626530 | 0.0293078 | 0.0146539 | − | 0.999893i | \(-0.495335\pi\) | ||||
0.0146539 | + | 0.999893i | \(0.495335\pi\) | |||||||
\(458\) | 46.8176 | 2.18764 | ||||||||
\(459\) | 2.97969 | 0.139080 | ||||||||
\(460\) | −14.6895 | −0.684904 | ||||||||
\(461\) | 19.4873 | 0.907616 | 0.453808 | − | 0.891099i | \(-0.350065\pi\) | ||||
0.453808 | + | 0.891099i | \(0.350065\pi\) | |||||||
\(462\) | −5.50815 | −0.256262 | ||||||||
\(463\) | 38.4685 | 1.78778 | 0.893892 | − | 0.448283i | \(-0.147964\pi\) | ||||
0.893892 | + | 0.448283i | \(0.147964\pi\) | |||||||
\(464\) | −6.31638 | −0.293230 | ||||||||
\(465\) | −23.0174 | −1.06740 | ||||||||
\(466\) | 44.9796 | 2.08364 | ||||||||
\(467\) | −33.6159 | −1.55556 | −0.777778 | − | 0.628539i | \(-0.783653\pi\) | ||||
−0.777778 | + | 0.628539i | \(0.783653\pi\) | |||||||
\(468\) | −19.0539 | −0.880768 | ||||||||
\(469\) | 3.44039 | 0.158863 | ||||||||
\(470\) | −82.4498 | −3.80313 | ||||||||
\(471\) | −44.0862 | −2.03139 | ||||||||
\(472\) | 96.2303 | 4.42936 | ||||||||
\(473\) | 1.96038 | 0.0901384 | ||||||||
\(474\) | −17.2915 | −0.794223 | ||||||||
\(475\) | 9.74976 | 0.447350 | ||||||||
\(476\) | 0.918551 | 0.0421017 | ||||||||
\(477\) | 0.855287 | 0.0391609 | ||||||||
\(478\) | 18.0898 | 0.827410 | ||||||||
\(479\) | 17.9263 | 0.819072 | 0.409536 | − | 0.912294i | \(-0.365691\pi\) | ||||
0.409536 | + | 0.912294i | \(0.365691\pi\) | |||||||
\(480\) | −73.1986 | −3.34105 | ||||||||
\(481\) | −25.3623 | −1.15642 | ||||||||
\(482\) | 54.7108 | 2.49201 | ||||||||
\(483\) | −0.470256 | −0.0213974 | ||||||||
\(484\) | 43.4144 | 1.97338 | ||||||||
\(485\) | 25.9109 | 1.17655 | ||||||||
\(486\) | −31.5507 | −1.43117 | ||||||||
\(487\) | −0.128777 | −0.00583546 | −0.00291773 | − | 0.999996i | \(-0.500929\pi\) | ||||
−0.00291773 | + | 0.999996i | \(0.500929\pi\) | |||||||
\(488\) | −61.6602 | −2.79122 | ||||||||
\(489\) | 10.5253 | 0.475969 | ||||||||
\(490\) | −54.5541 | −2.46450 | ||||||||
\(491\) | −15.6854 | −0.707872 | −0.353936 | − | 0.935270i | \(-0.615157\pi\) | ||||
−0.353936 | + | 0.935270i | \(0.615157\pi\) | |||||||
\(492\) | −109.508 | −4.93700 | ||||||||
\(493\) | −0.496145 | −0.0223453 | ||||||||
\(494\) | 20.8054 | 0.936080 | ||||||||
\(495\) | 16.2298 | 0.729475 | ||||||||
\(496\) | −38.9650 | −1.74958 | ||||||||
\(497\) | −3.84500 | −0.172472 | ||||||||
\(498\) | −33.5826 | −1.50487 | ||||||||
\(499\) | −3.37144 | −0.150926 | −0.0754632 | − | 0.997149i | \(-0.524044\pi\) | ||||
−0.0754632 | + | 0.997149i | \(0.524044\pi\) | |||||||
\(500\) | 16.0464 | 0.717615 | ||||||||
\(501\) | −45.9988 | −2.05507 | ||||||||
\(502\) | 16.6200 | 0.741789 | ||||||||
\(503\) | −30.0034 | −1.33779 | −0.668894 | − | 0.743358i | \(-0.733232\pi\) | ||||
−0.668894 | + | 0.743358i | \(0.733232\pi\) | |||||||
\(504\) | −2.14903 | −0.0957254 | ||||||||
\(505\) | 8.57831 | 0.381730 | ||||||||
\(506\) | 11.7131 | 0.520710 | ||||||||
\(507\) | 6.07035 | 0.269594 | ||||||||
\(508\) | −47.6173 | −2.11268 | ||||||||
\(509\) | −28.6795 | −1.27120 | −0.635598 | − | 0.772020i | \(-0.719246\pi\) | ||||
−0.635598 | + | 0.772020i | \(0.719246\pi\) | |||||||
\(510\) | −13.1551 | −0.582517 | ||||||||
\(511\) | 0.865893 | 0.0383048 | ||||||||
\(512\) | 35.6834 | 1.57700 | ||||||||
\(513\) | 9.11757 | 0.402550 | ||||||||
\(514\) | 80.2612 | 3.54017 | ||||||||
\(515\) | 12.5269 | 0.552000 | ||||||||
\(516\) | 4.45285 | 0.196026 | ||||||||
\(517\) | 46.7475 | 2.05595 | ||||||||
\(518\) | −4.81856 | −0.211715 | ||||||||
\(519\) | 0.473755 | 0.0207955 | ||||||||
\(520\) | −72.7166 | −3.18883 | ||||||||
\(521\) | −40.1973 | −1.76108 | −0.880538 | − | 0.473975i | \(-0.842819\pi\) | ||||
−0.880538 | + | 0.473975i | \(0.842819\pi\) | |||||||
\(522\) | 1.95533 | 0.0855823 | ||||||||
\(523\) | −17.7048 | −0.774175 | −0.387087 | − | 0.922043i | \(-0.626519\pi\) | ||||
−0.387087 | + | 0.922043i | \(0.626519\pi\) | |||||||
\(524\) | 54.1371 | 2.36499 | ||||||||
\(525\) | −1.83759 | −0.0801990 | ||||||||
\(526\) | −13.7445 | −0.599289 | ||||||||
\(527\) | −3.06067 | −0.133325 | ||||||||
\(528\) | 94.9558 | 4.13242 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.49835 | 0.238833 | ||||||||
\(531\) | −15.2903 | −0.663544 | ||||||||
\(532\) | 2.81068 | 0.121858 | ||||||||
\(533\) | −34.3222 | −1.48666 | ||||||||
\(534\) | 3.09784 | 0.134057 | ||||||||
\(535\) | 14.0857 | 0.608977 | ||||||||
\(536\) | −115.550 | −4.99100 | ||||||||
\(537\) | 27.0595 | 1.16770 | ||||||||
\(538\) | 40.5415 | 1.74787 | ||||||||
\(539\) | 30.9312 | 1.33230 | ||||||||
\(540\) | −53.6794 | −2.30999 | ||||||||
\(541\) | 5.59650 | 0.240612 | 0.120306 | − | 0.992737i | \(-0.461612\pi\) | ||||
0.120306 | + | 0.992737i | \(0.461612\pi\) | |||||||
\(542\) | −59.5144 | −2.55636 | ||||||||
\(543\) | 46.3540 | 1.98924 | ||||||||
\(544\) | −9.73337 | −0.417315 | ||||||||
\(545\) | 31.4555 | 1.34740 | ||||||||
\(546\) | −3.92131 | −0.167817 | ||||||||
\(547\) | −22.2762 | −0.952462 | −0.476231 | − | 0.879320i | \(-0.657997\pi\) | ||||
−0.476231 | + | 0.879320i | \(0.657997\pi\) | |||||||
\(548\) | 77.0616 | 3.29191 | ||||||||
\(549\) | 9.79737 | 0.418142 | ||||||||
\(550\) | 45.7704 | 1.95166 | ||||||||
\(551\) | −1.51816 | −0.0646757 | ||||||||
\(552\) | 15.7942 | 0.672244 | ||||||||
\(553\) | −0.732141 | −0.0311338 | ||||||||
\(554\) | 24.7345 | 1.05087 | ||||||||
\(555\) | 49.0697 | 2.08289 | ||||||||
\(556\) | −85.0460 | −3.60675 | ||||||||
\(557\) | 39.0311 | 1.65380 | 0.826900 | − | 0.562349i | \(-0.190102\pi\) | ||||
0.826900 | + | 0.562349i | \(0.190102\pi\) | |||||||
\(558\) | 12.0622 | 0.510633 | ||||||||
\(559\) | 1.39562 | 0.0590283 | ||||||||
\(560\) | −7.09114 | −0.299655 | ||||||||
\(561\) | 7.45869 | 0.314906 | ||||||||
\(562\) | −18.6119 | −0.785095 | ||||||||
\(563\) | −33.2073 | −1.39952 | −0.699761 | − | 0.714377i | \(-0.746710\pi\) | ||||
−0.699761 | + | 0.714377i | \(0.746710\pi\) | |||||||
\(564\) | 106.183 | 4.47111 | ||||||||
\(565\) | 35.2050 | 1.48108 | ||||||||
\(566\) | 3.48526 | 0.146497 | ||||||||
\(567\) | −2.55712 | −0.107389 | ||||||||
\(568\) | 129.140 | 5.41857 | ||||||||
\(569\) | 32.7635 | 1.37352 | 0.686759 | − | 0.726885i | \(-0.259033\pi\) | ||||
0.686759 | + | 0.726885i | \(0.259033\pi\) | |||||||
\(570\) | −40.2533 | −1.68603 | ||||||||
\(571\) | 41.6595 | 1.74339 | 0.871697 | − | 0.490044i | \(-0.163019\pi\) | ||||
0.871697 | + | 0.490044i | \(0.163019\pi\) | |||||||
\(572\) | 69.4502 | 2.90386 | ||||||||
\(573\) | 23.7107 | 0.990529 | ||||||||
\(574\) | −6.52084 | −0.272175 | ||||||||
\(575\) | 3.90763 | 0.162960 | ||||||||
\(576\) | 13.0006 | 0.541690 | ||||||||
\(577\) | −23.0819 | −0.960914 | −0.480457 | − | 0.877018i | \(-0.659529\pi\) | ||||
−0.480457 | + | 0.877018i | \(0.659529\pi\) | |||||||
\(578\) | 42.9767 | 1.78759 | ||||||||
\(579\) | 2.32617 | 0.0966725 | ||||||||
\(580\) | 8.93811 | 0.371135 | ||||||||
\(581\) | −1.42193 | −0.0589915 | ||||||||
\(582\) | −46.9291 | −1.94527 | ||||||||
\(583\) | −3.11746 | −0.129112 | ||||||||
\(584\) | −29.0821 | −1.20343 | ||||||||
\(585\) | 11.5542 | 0.477706 | ||||||||
\(586\) | −83.5414 | −3.45107 | ||||||||
\(587\) | 9.00552 | 0.371698 | 0.185849 | − | 0.982578i | \(-0.440497\pi\) | ||||
0.185849 | + | 0.982578i | \(0.440497\pi\) | |||||||
\(588\) | 70.2576 | 2.89737 | ||||||||
\(589\) | −9.36535 | −0.385892 | ||||||||
\(590\) | −98.2963 | −4.04679 | ||||||||
\(591\) | −7.58369 | −0.311951 | ||||||||
\(592\) | 83.0678 | 3.41407 | ||||||||
\(593\) | −25.9986 | −1.06763 | −0.533816 | − | 0.845600i | \(-0.679243\pi\) | ||||
−0.533816 | + | 0.845600i | \(0.679243\pi\) | |||||||
\(594\) | 42.8026 | 1.75621 | ||||||||
\(595\) | −0.557003 | −0.0228349 | ||||||||
\(596\) | −40.8515 | −1.67334 | ||||||||
\(597\) | 6.89613 | 0.282240 | ||||||||
\(598\) | 8.33867 | 0.340993 | ||||||||
\(599\) | 18.5189 | 0.756661 | 0.378330 | − | 0.925671i | \(-0.376498\pi\) | ||||
0.378330 | + | 0.925671i | \(0.376498\pi\) | |||||||
\(600\) | 61.7178 | 2.51962 | ||||||||
\(601\) | 35.6404 | 1.45380 | 0.726901 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726901 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(602\) | 0.265152 | 0.0108068 | ||||||||
\(603\) | 18.3601 | 0.747681 | ||||||||
\(604\) | 40.6944 | 1.65583 | ||||||||
\(605\) | −26.3262 | −1.07031 | ||||||||
\(606\) | −15.5368 | −0.631139 | ||||||||
\(607\) | −44.7603 | −1.81676 | −0.908381 | − | 0.418142i | \(-0.862681\pi\) | ||||
−0.908381 | + | 0.418142i | \(0.862681\pi\) | |||||||
\(608\) | −29.7832 | −1.20787 | ||||||||
\(609\) | 0.286135 | 0.0115948 | ||||||||
\(610\) | 62.9840 | 2.55015 | ||||||||
\(611\) | 33.2800 | 1.34637 | ||||||||
\(612\) | 4.90197 | 0.198150 | ||||||||
\(613\) | 25.3292 | 1.02304 | 0.511518 | − | 0.859272i | \(-0.329083\pi\) | ||||
0.511518 | + | 0.859272i | \(0.329083\pi\) | |||||||
\(614\) | 11.3153 | 0.456649 | ||||||||
\(615\) | 66.4049 | 2.67770 | ||||||||
\(616\) | 7.83305 | 0.315603 | ||||||||
\(617\) | 12.2873 | 0.494669 | 0.247334 | − | 0.968930i | \(-0.420445\pi\) | ||||
0.247334 | + | 0.968930i | \(0.420445\pi\) | |||||||
\(618\) | −22.6883 | −0.912658 | ||||||||
\(619\) | −8.52472 | −0.342637 | −0.171319 | − | 0.985216i | \(-0.554803\pi\) | ||||
−0.171319 | + | 0.985216i | \(0.554803\pi\) | |||||||
\(620\) | 55.1382 | 2.21440 | ||||||||
\(621\) | 3.65426 | 0.146640 | ||||||||
\(622\) | 36.8183 | 1.47628 | ||||||||
\(623\) | 0.131166 | 0.00525507 | ||||||||
\(624\) | 67.6000 | 2.70617 | ||||||||
\(625\) | −29.2686 | −1.17074 | ||||||||
\(626\) | −26.2308 | −1.04839 | ||||||||
\(627\) | 22.8229 | 0.911458 | ||||||||
\(628\) | 105.609 | 4.21425 | ||||||||
\(629\) | 6.52490 | 0.260165 | ||||||||
\(630\) | 2.19517 | 0.0874576 | ||||||||
\(631\) | −27.3594 | −1.08916 | −0.544581 | − | 0.838708i | \(-0.683311\pi\) | ||||
−0.544581 | + | 0.838708i | \(0.683311\pi\) | |||||||
\(632\) | 24.5899 | 0.978134 | ||||||||
\(633\) | −52.5224 | −2.08758 | ||||||||
\(634\) | 60.1624 | 2.38935 | ||||||||
\(635\) | 28.8748 | 1.14586 | ||||||||
\(636\) | −7.08105 | −0.280782 | ||||||||
\(637\) | 22.0202 | 0.872473 | ||||||||
\(638\) | −7.12702 | −0.282162 | ||||||||
\(639\) | −20.5194 | −0.811734 | ||||||||
\(640\) | 12.3232 | 0.487119 | ||||||||
\(641\) | 46.9265 | 1.85348 | 0.926742 | − | 0.375699i | \(-0.122597\pi\) | ||||
0.926742 | + | 0.375699i | \(0.122597\pi\) | |||||||
\(642\) | −25.5116 | −1.00686 | ||||||||
\(643\) | 20.9496 | 0.826171 | 0.413086 | − | 0.910692i | \(-0.364451\pi\) | ||||
0.413086 | + | 0.910692i | \(0.364451\pi\) | |||||||
\(644\) | 1.12650 | 0.0443903 | ||||||||
\(645\) | −2.70017 | −0.106319 | ||||||||
\(646\) | −5.35257 | −0.210594 | ||||||||
\(647\) | 19.8076 | 0.778718 | 0.389359 | − | 0.921086i | \(-0.372697\pi\) | ||||
0.389359 | + | 0.921086i | \(0.372697\pi\) | |||||||
\(648\) | 85.8842 | 3.37385 | ||||||||
\(649\) | 55.7321 | 2.18768 | ||||||||
\(650\) | 32.5845 | 1.27807 | ||||||||
\(651\) | 1.76514 | 0.0691812 | ||||||||
\(652\) | −25.2133 | −0.987429 | ||||||||
\(653\) | 1.13530 | 0.0444278 | 0.0222139 | − | 0.999753i | \(-0.492929\pi\) | ||||
0.0222139 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(654\) | −56.9713 | −2.22775 | ||||||||
\(655\) | −32.8283 | −1.28271 | ||||||||
\(656\) | 112.414 | 4.38902 | ||||||||
\(657\) | 4.62095 | 0.180280 | ||||||||
\(658\) | 6.32285 | 0.246490 | ||||||||
\(659\) | −41.2185 | −1.60564 | −0.802822 | − | 0.596218i | \(-0.796669\pi\) | ||||
−0.802822 | + | 0.596218i | \(0.796669\pi\) | |||||||
\(660\) | −134.369 | −5.23030 | ||||||||
\(661\) | 14.1319 | 0.549668 | 0.274834 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274834 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(662\) | −70.1381 | −2.72599 | ||||||||
\(663\) | 5.30992 | 0.206220 | ||||||||
\(664\) | 47.7573 | 1.85334 | ||||||||
\(665\) | −1.70438 | −0.0660929 | ||||||||
\(666\) | −25.7149 | −0.996431 | ||||||||
\(667\) | −0.608467 | −0.0235599 | ||||||||
\(668\) | 110.190 | 4.26339 | ||||||||
\(669\) | 48.6812 | 1.88213 | ||||||||
\(670\) | 118.031 | 4.55993 | ||||||||
\(671\) | −35.7107 | −1.37860 | ||||||||
\(672\) | 5.61340 | 0.216542 | ||||||||
\(673\) | 9.93640 | 0.383020 | 0.191510 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(674\) | 51.9354 | 2.00048 | ||||||||
\(675\) | 14.2795 | 0.549618 | ||||||||
\(676\) | −14.5415 | −0.559290 | ||||||||
\(677\) | 15.6518 | 0.601546 | 0.300773 | − | 0.953696i | \(-0.402755\pi\) | ||||
0.300773 | + | 0.953696i | \(0.402755\pi\) | |||||||
\(678\) | −63.7623 | −2.44877 | ||||||||
\(679\) | −1.98704 | −0.0762555 | ||||||||
\(680\) | 18.7077 | 0.717406 | ||||||||
\(681\) | 12.7695 | 0.489328 | ||||||||
\(682\) | −43.9658 | −1.68354 | ||||||||
\(683\) | 27.4149 | 1.04900 | 0.524501 | − | 0.851410i | \(-0.324252\pi\) | ||||
0.524501 | + | 0.851410i | \(0.324252\pi\) | |||||||
\(684\) | 14.9996 | 0.573523 | ||||||||
\(685\) | −46.7296 | −1.78545 | ||||||||
\(686\) | 8.39875 | 0.320666 | ||||||||
\(687\) | 36.5619 | 1.39492 | ||||||||
\(688\) | −4.57100 | −0.174268 | ||||||||
\(689\) | −2.21935 | −0.0845506 | ||||||||
\(690\) | −16.1333 | −0.614183 | ||||||||
\(691\) | −15.2052 | −0.578434 | −0.289217 | − | 0.957264i | \(-0.593395\pi\) | ||||
−0.289217 | + | 0.957264i | \(0.593395\pi\) | |||||||
\(692\) | −1.13488 | −0.0431418 | ||||||||
\(693\) | −1.24462 | −0.0472791 | ||||||||
\(694\) | 36.5184 | 1.38622 | ||||||||
\(695\) | 51.5713 | 1.95621 | ||||||||
\(696\) | −9.61023 | −0.364275 | ||||||||
\(697\) | 8.83000 | 0.334460 | ||||||||
\(698\) | 2.63094 | 0.0995825 | ||||||||
\(699\) | 35.1265 | 1.32861 | ||||||||
\(700\) | 4.40195 | 0.166378 | ||||||||
\(701\) | 23.8884 | 0.902252 | 0.451126 | − | 0.892460i | \(-0.351022\pi\) | ||||
0.451126 | + | 0.892460i | \(0.351022\pi\) | |||||||
\(702\) | 30.4716 | 1.15008 | ||||||||
\(703\) | 19.9656 | 0.753016 | ||||||||
\(704\) | −47.3861 | −1.78593 | ||||||||
\(705\) | −64.3886 | −2.42502 | ||||||||
\(706\) | −25.6622 | −0.965811 | ||||||||
\(707\) | −0.657847 | −0.0247409 | ||||||||
\(708\) | 126.591 | 4.75758 | ||||||||
\(709\) | −9.91002 | −0.372178 | −0.186089 | − | 0.982533i | \(-0.559581\pi\) | ||||
−0.186089 | + | 0.982533i | \(0.559581\pi\) | |||||||
\(710\) | −131.912 | −4.95057 | ||||||||
\(711\) | −3.90717 | −0.146530 | ||||||||
\(712\) | −4.40539 | −0.165099 | ||||||||
\(713\) | −3.75357 | −0.140572 | ||||||||
\(714\) | 1.00883 | 0.0377544 | ||||||||
\(715\) | −42.1141 | −1.57498 | ||||||||
\(716\) | −64.8210 | −2.42248 | ||||||||
\(717\) | 14.1271 | 0.527588 | ||||||||
\(718\) | 43.3579 | 1.61810 | ||||||||
\(719\) | −51.1979 | −1.90936 | −0.954680 | − | 0.297633i | \(-0.903803\pi\) | ||||
−0.954680 | + | 0.297633i | \(0.903803\pi\) | |||||||
\(720\) | −37.8428 | −1.41032 | ||||||||
\(721\) | −0.960651 | −0.0357765 | ||||||||
\(722\) | 33.6095 | 1.25081 | ||||||||
\(723\) | 42.7260 | 1.58900 | ||||||||
\(724\) | −111.041 | −4.12681 | ||||||||
\(725\) | −2.37767 | −0.0883044 | ||||||||
\(726\) | 47.6813 | 1.76962 | ||||||||
\(727\) | 31.7496 | 1.17753 | 0.588764 | − | 0.808305i | \(-0.299615\pi\) | ||||
0.588764 | + | 0.808305i | \(0.299615\pi\) | |||||||
\(728\) | 5.57644 | 0.206676 | ||||||||
\(729\) | 8.87787 | 0.328810 | ||||||||
\(730\) | 29.7065 | 1.09949 | ||||||||
\(731\) | −0.359048 | −0.0132799 | ||||||||
\(732\) | −81.1139 | −2.99806 | ||||||||
\(733\) | −3.16313 | −0.116833 | −0.0584165 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584165 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(734\) | 20.2706 | 0.748201 | ||||||||
\(735\) | −42.6037 | −1.57146 | ||||||||
\(736\) | −11.9369 | −0.440000 | ||||||||
\(737\) | −66.9212 | −2.46508 | ||||||||
\(738\) | −34.7993 | −1.28098 | ||||||||
\(739\) | −26.8997 | −0.989521 | −0.494760 | − | 0.869029i | \(-0.664744\pi\) | ||||
−0.494760 | + | 0.869029i | \(0.664744\pi\) | |||||||
\(740\) | −117.547 | −4.32110 | ||||||||
\(741\) | 16.2479 | 0.596880 | ||||||||
\(742\) | −0.421653 | −0.0154794 | ||||||||
\(743\) | 32.0968 | 1.17752 | 0.588760 | − | 0.808308i | \(-0.299616\pi\) | ||||
0.588760 | + | 0.808308i | \(0.299616\pi\) | |||||||
\(744\) | −59.2845 | −2.17347 | ||||||||
\(745\) | 24.7720 | 0.907578 | ||||||||
\(746\) | −33.1560 | −1.21393 | ||||||||
\(747\) | −7.58830 | −0.277641 | ||||||||
\(748\) | −17.8673 | −0.653294 | ||||||||
\(749\) | −1.08019 | −0.0394694 | ||||||||
\(750\) | 17.6234 | 0.643516 | ||||||||
\(751\) | 26.3161 | 0.960289 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(752\) | −109.001 | −3.97484 | ||||||||
\(753\) | 12.9793 | 0.472992 | ||||||||
\(754\) | −5.07380 | −0.184777 | ||||||||
\(755\) | −24.6768 | −0.898080 | ||||||||
\(756\) | 4.11652 | 0.149717 | ||||||||
\(757\) | −7.12245 | −0.258870 | −0.129435 | − | 0.991588i | \(-0.541316\pi\) | ||||
−0.129435 | + | 0.991588i | \(0.541316\pi\) | |||||||
\(758\) | −28.8613 | −1.04829 | ||||||||
\(759\) | 9.14725 | 0.332024 | ||||||||
\(760\) | 57.2437 | 2.07645 | ||||||||
\(761\) | 24.8606 | 0.901196 | 0.450598 | − | 0.892727i | \(-0.351211\pi\) | ||||
0.450598 | + | 0.892727i | \(0.351211\pi\) | |||||||
\(762\) | −52.2972 | −1.89453 | ||||||||
\(763\) | −2.41223 | −0.0873287 | ||||||||
\(764\) | −56.7991 | −2.05492 | ||||||||
\(765\) | −2.97252 | −0.107472 | ||||||||
\(766\) | −63.5494 | −2.29613 | ||||||||
\(767\) | 39.6763 | 1.43263 | ||||||||
\(768\) | 21.4177 | 0.772844 | ||||||||
\(769\) | −10.8611 | −0.391661 | −0.195831 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195831 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(770\) | −8.00122 | −0.288344 | ||||||||
\(771\) | 62.6795 | 2.25735 | ||||||||
\(772\) | −5.57236 | −0.200554 | ||||||||
\(773\) | 37.4718 | 1.34777 | 0.673884 | − | 0.738837i | \(-0.264625\pi\) | ||||
0.673884 | + | 0.738837i | \(0.264625\pi\) | |||||||
\(774\) | 1.41502 | 0.0508618 | ||||||||
\(775\) | −14.6676 | −0.526875 | ||||||||
\(776\) | 66.7372 | 2.39573 | ||||||||
\(777\) | −3.76302 | −0.134998 | ||||||||
\(778\) | −19.1710 | −0.687315 | ||||||||
\(779\) | 27.0190 | 0.968055 | ||||||||
\(780\) | −95.6587 | −3.42513 | ||||||||
\(781\) | 74.7916 | 2.67625 | ||||||||
\(782\) | −2.14527 | −0.0767148 | ||||||||
\(783\) | −2.22350 | −0.0794613 | ||||||||
\(784\) | −72.1218 | −2.57578 | ||||||||
\(785\) | −64.0404 | −2.28570 | ||||||||
\(786\) | 59.4578 | 2.12079 | ||||||||
\(787\) | 17.8744 | 0.637155 | 0.318577 | − | 0.947897i | \(-0.396795\pi\) | ||||
0.318577 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(788\) | 18.1668 | 0.647164 | ||||||||
\(789\) | −10.7337 | −0.382129 | ||||||||
\(790\) | −25.1178 | −0.893653 | ||||||||
\(791\) | −2.69977 | −0.0959928 | ||||||||
\(792\) | 41.8021 | 1.48537 | ||||||||
\(793\) | −25.4228 | −0.902791 | ||||||||
\(794\) | 28.5979 | 1.01490 | ||||||||
\(795\) | 4.29390 | 0.152289 | ||||||||
\(796\) | −16.5197 | −0.585526 | ||||||||
\(797\) | −35.6080 | −1.26130 | −0.630649 | − | 0.776068i | \(-0.717211\pi\) | ||||
−0.630649 | + | 0.776068i | \(0.717211\pi\) | |||||||
\(798\) | 3.08692 | 0.109276 | ||||||||
\(799\) | −8.56189 | −0.302898 | ||||||||
\(800\) | −46.6450 | −1.64915 | ||||||||
\(801\) | 0.699986 | 0.0247328 | ||||||||
\(802\) | 52.1926 | 1.84298 | ||||||||
\(803\) | −16.8430 | −0.594378 | ||||||||
\(804\) | −152.006 | −5.36084 | ||||||||
\(805\) | −0.683102 | −0.0240762 | ||||||||
\(806\) | −31.2997 | −1.10249 | ||||||||
\(807\) | 31.6606 | 1.11451 | ||||||||
\(808\) | 22.0947 | 0.777287 | ||||||||
\(809\) | 26.1925 | 0.920881 | 0.460440 | − | 0.887691i | \(-0.347692\pi\) | ||||
0.460440 | + | 0.887691i | \(0.347692\pi\) | |||||||
\(810\) | −87.7280 | −3.08245 | ||||||||
\(811\) | −31.0296 | −1.08960 | −0.544798 | − | 0.838567i | \(-0.683394\pi\) | ||||
−0.544798 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(812\) | −0.685439 | −0.0240542 | ||||||||
\(813\) | −46.4774 | −1.63003 | ||||||||
\(814\) | 93.7288 | 3.28519 | ||||||||
\(815\) | 15.2892 | 0.535556 | ||||||||
\(816\) | −17.3913 | −0.608818 | ||||||||
\(817\) | −1.09865 | −0.0384370 | ||||||||
\(818\) | −43.2679 | −1.51283 | ||||||||
\(819\) | −0.886057 | −0.0309613 | ||||||||
\(820\) | −159.073 | −5.55508 | ||||||||
\(821\) | 20.9002 | 0.729422 | 0.364711 | − | 0.931121i | \(-0.381168\pi\) | ||||
0.364711 | + | 0.931121i | \(0.381168\pi\) | |||||||
\(822\) | 84.6353 | 2.95199 | ||||||||
\(823\) | 16.2708 | 0.567165 | 0.283583 | − | 0.958948i | \(-0.408477\pi\) | ||||
0.283583 | + | 0.958948i | \(0.408477\pi\) | |||||||
\(824\) | 32.2647 | 1.12400 | ||||||||
\(825\) | 35.7441 | 1.24445 | ||||||||
\(826\) | 7.53807 | 0.262283 | ||||||||
\(827\) | 23.9242 | 0.831928 | 0.415964 | − | 0.909381i | \(-0.363444\pi\) | ||||
0.415964 | + | 0.909381i | \(0.363444\pi\) | |||||||
\(828\) | 6.01172 | 0.208922 | ||||||||
\(829\) | −1.51181 | −0.0525075 | −0.0262537 | − | 0.999655i | \(-0.508358\pi\) | ||||
−0.0262537 | + | 0.999655i | \(0.508358\pi\) | |||||||
\(830\) | −48.7826 | −1.69327 | ||||||||
\(831\) | 19.3163 | 0.670074 | ||||||||
\(832\) | −33.7347 | −1.16954 | ||||||||
\(833\) | −5.66510 | −0.196284 | ||||||||
\(834\) | −93.4045 | −3.23433 | ||||||||
\(835\) | −66.8186 | −2.31235 | ||||||||
\(836\) | −54.6723 | −1.89088 | ||||||||
\(837\) | −13.7165 | −0.474112 | ||||||||
\(838\) | −37.2137 | −1.28553 | ||||||||
\(839\) | 19.9387 | 0.688360 | 0.344180 | − | 0.938904i | \(-0.388157\pi\) | ||||
0.344180 | + | 0.938904i | \(0.388157\pi\) | |||||||
\(840\) | −10.7890 | −0.372257 | ||||||||
\(841\) | −28.6298 | −0.987233 | ||||||||
\(842\) | −6.76570 | −0.233161 | ||||||||
\(843\) | −14.5348 | −0.500606 | ||||||||
\(844\) | 125.818 | 4.33082 | ||||||||
\(845\) | 8.81789 | 0.303344 | ||||||||
\(846\) | 33.7427 | 1.16010 | ||||||||
\(847\) | 2.01888 | 0.0693697 | ||||||||
\(848\) | 7.26894 | 0.249617 | ||||||||
\(849\) | 2.72179 | 0.0934117 | ||||||||
\(850\) | −8.38294 | −0.287533 | ||||||||
\(851\) | 8.00206 | 0.274307 | ||||||||
\(852\) | 169.883 | 5.82010 | ||||||||
\(853\) | 43.3645 | 1.48477 | 0.742385 | − | 0.669973i | \(-0.233694\pi\) | ||||
0.742385 | + | 0.669973i | \(0.233694\pi\) | |||||||
\(854\) | −4.83007 | −0.165281 | ||||||||
\(855\) | −9.09563 | −0.311064 | ||||||||
\(856\) | 36.2797 | 1.24001 | ||||||||
\(857\) | 48.0809 | 1.64241 | 0.821206 | − | 0.570632i | \(-0.193302\pi\) | ||||
0.821206 | + | 0.570632i | \(0.193302\pi\) | |||||||
\(858\) | 76.2759 | 2.60402 | ||||||||
\(859\) | −16.5351 | −0.564169 | −0.282084 | − | 0.959390i | \(-0.591026\pi\) | ||||
−0.282084 | + | 0.959390i | \(0.591026\pi\) | |||||||
\(860\) | 6.46828 | 0.220566 | ||||||||
\(861\) | −5.09241 | −0.173549 | ||||||||
\(862\) | 104.314 | 3.55296 | ||||||||
\(863\) | 0.918753 | 0.0312747 | 0.0156374 | − | 0.999878i | \(-0.495022\pi\) | ||||
0.0156374 | + | 0.999878i | \(0.495022\pi\) | |||||||
\(864\) | −43.6205 | −1.48400 | ||||||||
\(865\) | 0.688185 | 0.0233990 | ||||||||
\(866\) | 80.1900 | 2.72497 | ||||||||
\(867\) | 33.5624 | 1.13984 | ||||||||
\(868\) | −4.22839 | −0.143521 | ||||||||
\(869\) | 14.2413 | 0.483104 | ||||||||
\(870\) | 9.81656 | 0.332812 | ||||||||
\(871\) | −47.6419 | −1.61429 | ||||||||
\(872\) | 81.0180 | 2.74362 | ||||||||
\(873\) | −10.6041 | −0.358894 | ||||||||
\(874\) | −6.56433 | −0.222042 | ||||||||
\(875\) | 0.746197 | 0.0252261 | ||||||||
\(876\) | −38.2576 | −1.29260 | ||||||||
\(877\) | −14.4453 | −0.487782 | −0.243891 | − | 0.969803i | \(-0.578424\pi\) | ||||
−0.243891 | + | 0.969803i | \(0.578424\pi\) | |||||||
\(878\) | 41.9283 | 1.41501 | ||||||||
\(879\) | −65.2411 | −2.20053 | ||||||||
\(880\) | 137.934 | 4.64977 | ||||||||
\(881\) | 32.9166 | 1.10899 | 0.554494 | − | 0.832188i | \(-0.312912\pi\) | ||||
0.554494 | + | 0.832188i | \(0.312912\pi\) | |||||||
\(882\) | 22.3264 | 0.751768 | ||||||||
\(883\) | 49.2930 | 1.65884 | 0.829420 | − | 0.558625i | \(-0.188671\pi\) | ||||
0.829420 | + | 0.558625i | \(0.188671\pi\) | |||||||
\(884\) | −12.7199 | −0.427818 | ||||||||
\(885\) | −76.7638 | −2.58039 | ||||||||
\(886\) | 6.39356 | 0.214796 | ||||||||
\(887\) | −42.2438 | −1.41841 | −0.709204 | − | 0.705003i | \(-0.750946\pi\) | ||||
−0.709204 | + | 0.705003i | \(0.750946\pi\) | |||||||
\(888\) | 126.386 | 4.24123 | ||||||||
\(889\) | −2.21433 | −0.0742661 | ||||||||
\(890\) | 4.49997 | 0.150839 | ||||||||
\(891\) | 49.7401 | 1.66636 | ||||||||
\(892\) | −116.616 | −3.90460 | ||||||||
\(893\) | −26.1986 | −0.876702 | ||||||||
\(894\) | −44.8664 | −1.50056 | ||||||||
\(895\) | 39.3070 | 1.31389 | ||||||||
\(896\) | −0.945035 | −0.0315714 | ||||||||
\(897\) | 6.51203 | 0.217430 | ||||||||
\(898\) | 52.5789 | 1.75458 | ||||||||
\(899\) | 2.28392 | 0.0761731 | ||||||||
\(900\) | 23.4916 | 0.783053 | ||||||||
\(901\) | 0.570969 | 0.0190217 | ||||||||
\(902\) | 126.841 | 4.22334 | ||||||||
\(903\) | 0.207069 | 0.00689082 | ||||||||
\(904\) | 90.6754 | 3.01582 | ||||||||
\(905\) | 67.3346 | 2.23828 | ||||||||
\(906\) | 44.6939 | 1.48485 | ||||||||
\(907\) | −42.6787 | −1.41712 | −0.708561 | − | 0.705650i | \(-0.750655\pi\) | ||||
−0.708561 | + | 0.705650i | \(0.750655\pi\) | |||||||
\(908\) | −30.5894 | −1.01514 | ||||||||
\(909\) | −3.51069 | −0.116442 | ||||||||
\(910\) | −5.69616 | −0.188826 | ||||||||
\(911\) | 20.8112 | 0.689507 | 0.344753 | − | 0.938693i | \(-0.387963\pi\) | ||||
0.344753 | + | 0.938693i | \(0.387963\pi\) | |||||||
\(912\) | −53.2158 | −1.76215 | ||||||||
\(913\) | 27.6588 | 0.915373 | ||||||||
\(914\) | −1.64836 | −0.0545230 | ||||||||
\(915\) | 49.1869 | 1.62607 | ||||||||
\(916\) | −87.5841 | −2.89386 | ||||||||
\(917\) | 2.51751 | 0.0831356 | ||||||||
\(918\) | −7.83938 | −0.258738 | ||||||||
\(919\) | 0.198263 | 0.00654009 | 0.00327005 | − | 0.999995i | \(-0.498959\pi\) | ||||
0.00327005 | + | 0.999995i | \(0.498959\pi\) | |||||||
\(920\) | 22.9429 | 0.756404 | ||||||||
\(921\) | 8.83661 | 0.291176 | ||||||||
\(922\) | −51.2700 | −1.68849 | ||||||||
\(923\) | 53.2450 | 1.75258 | ||||||||
\(924\) | 10.3044 | 0.338989 | ||||||||
\(925\) | 31.2691 | 1.02812 | ||||||||
\(926\) | −101.208 | −3.32591 | ||||||||
\(927\) | −5.12664 | −0.168381 | ||||||||
\(928\) | 7.26321 | 0.238427 | ||||||||
\(929\) | 13.5423 | 0.444309 | 0.222155 | − | 0.975011i | \(-0.428691\pi\) | ||||
0.222155 | + | 0.975011i | \(0.428691\pi\) | |||||||
\(930\) | 60.5573 | 1.98575 | ||||||||
\(931\) | −17.3347 | −0.568121 | ||||||||
\(932\) | −84.1457 | −2.75629 | ||||||||
\(933\) | 28.7530 | 0.941331 | ||||||||
\(934\) | 88.4413 | 2.89389 | ||||||||
\(935\) | 10.8346 | 0.354330 | ||||||||
\(936\) | 29.7594 | 0.972716 | ||||||||
\(937\) | −49.2146 | −1.60777 | −0.803885 | − | 0.594785i | \(-0.797237\pi\) | ||||
−0.803885 | + | 0.594785i | \(0.797237\pi\) | |||||||
\(938\) | −9.05146 | −0.295541 | ||||||||
\(939\) | −20.4848 | −0.668495 | ||||||||
\(940\) | 154.243 | 5.03086 | ||||||||
\(941\) | 25.0294 | 0.815935 | 0.407968 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407968 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(942\) | 115.988 | 3.77910 | ||||||||
\(943\) | 10.8290 | 0.352641 | ||||||||
\(944\) | −129.950 | −4.22951 | ||||||||
\(945\) | −2.49623 | −0.0812024 | ||||||||
\(946\) | −5.15764 | −0.167689 | ||||||||
\(947\) | −48.9624 | −1.59106 | −0.795532 | − | 0.605912i | \(-0.792808\pi\) | ||||
−0.795532 | + | 0.605912i | \(0.792808\pi\) | |||||||
\(948\) | 32.3480 | 1.05062 | ||||||||
\(949\) | −11.9907 | −0.389236 | ||||||||
\(950\) | −25.6510 | −0.832229 | ||||||||
\(951\) | 46.9834 | 1.52354 | ||||||||
\(952\) | −1.43464 | −0.0464969 | ||||||||
\(953\) | 38.3680 | 1.24286 | 0.621431 | − | 0.783469i | \(-0.286552\pi\) | ||||
0.621431 | + | 0.783469i | \(0.286552\pi\) | |||||||
\(954\) | −2.25021 | −0.0728532 | ||||||||
\(955\) | 34.4426 | 1.11454 | ||||||||
\(956\) | −33.8416 | −1.09452 | ||||||||
\(957\) | −5.56580 | −0.179917 | ||||||||
\(958\) | −47.1629 | −1.52377 | ||||||||
\(959\) | 3.58356 | 0.115719 | ||||||||
\(960\) | 65.2683 | 2.10652 | ||||||||
\(961\) | −16.9107 | −0.545508 | ||||||||
\(962\) | 66.7265 | 2.15135 | ||||||||
\(963\) | −5.76459 | −0.185761 | ||||||||
\(964\) | −102.350 | −3.29648 | ||||||||
\(965\) | 3.37904 | 0.108775 | ||||||||
\(966\) | 1.23721 | 0.0398067 | ||||||||
\(967\) | −25.1060 | −0.807356 | −0.403678 | − | 0.914901i | \(-0.632268\pi\) | ||||
−0.403678 | + | 0.914901i | \(0.632268\pi\) | |||||||
\(968\) | −67.8068 | −2.17939 | ||||||||
\(969\) | −4.18005 | −0.134283 | ||||||||
\(970\) | −68.1700 | −2.18881 | ||||||||
\(971\) | −6.37105 | −0.204457 | −0.102228 | − | 0.994761i | \(-0.532597\pi\) | ||||
−0.102228 | + | 0.994761i | \(0.532597\pi\) | |||||||
\(972\) | 59.0237 | 1.89318 | ||||||||
\(973\) | −3.95486 | −0.126787 | ||||||||
\(974\) | 0.338806 | 0.0108560 | ||||||||
\(975\) | 25.4466 | 0.814944 | ||||||||
\(976\) | 83.2662 | 2.66529 | ||||||||
\(977\) | 42.7400 | 1.36737 | 0.683686 | − | 0.729776i | \(-0.260376\pi\) | ||||
0.683686 | + | 0.729776i | \(0.260376\pi\) | |||||||
\(978\) | −27.6913 | −0.885470 | ||||||||
\(979\) | −2.55140 | −0.0815431 | ||||||||
\(980\) | 102.057 | 3.26010 | ||||||||
\(981\) | −12.8732 | −0.411010 | ||||||||
\(982\) | 41.2673 | 1.31689 | ||||||||
\(983\) | −4.74542 | −0.151356 | −0.0756778 | − | 0.997132i | \(-0.524112\pi\) | ||||
−0.0756778 | + | 0.997132i | \(0.524112\pi\) | |||||||
\(984\) | 171.035 | 5.45240 | ||||||||
\(985\) | −11.0162 | −0.351005 | ||||||||
\(986\) | 1.30533 | 0.0415701 | ||||||||
\(987\) | 4.93779 | 0.157171 | ||||||||
\(988\) | −38.9218 | −1.23827 | ||||||||
\(989\) | −0.440332 | −0.0140017 | ||||||||
\(990\) | −42.6996 | −1.35708 | ||||||||
\(991\) | −27.5281 | −0.874460 | −0.437230 | − | 0.899350i | \(-0.644041\pi\) | ||||
−0.437230 | + | 0.899350i | \(0.644041\pi\) | |||||||
\(992\) | 44.8060 | 1.42259 | ||||||||
\(993\) | −54.7739 | −1.73820 | ||||||||
\(994\) | 10.1160 | 0.320859 | ||||||||
\(995\) | 10.0174 | 0.317574 | ||||||||
\(996\) | 62.8247 | 1.99068 | ||||||||
\(997\) | −17.2609 | −0.546660 | −0.273330 | − | 0.961920i | \(-0.588125\pi\) | ||||
−0.273330 | + | 0.961920i | \(0.588125\pi\) | |||||||
\(998\) | 8.87005 | 0.280776 | ||||||||
\(999\) | 29.2416 | 0.925163 |
(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 | 8027.2.a.f.1.8 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.8 | ✓ | 176 | 1.1 | even | 1 | trivial |