Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36619 | −1.67315 | −0.836575 | − | 0.547853i | \(-0.815445\pi\) | ||||
−0.836575 | + | 0.547853i | \(0.815445\pi\) | |||||||
\(3\) | −2.12839 | −1.22883 | −0.614414 | − | 0.788984i | \(-0.710607\pi\) | ||||
−0.614414 | + | 0.788984i | \(0.710607\pi\) | |||||||
\(4\) | 3.59886 | 1.79943 | ||||||||
\(5\) | 0.442767 | 0.198012 | 0.0990058 | − | 0.995087i | \(-0.468434\pi\) | ||||
0.0990058 | + | 0.995087i | \(0.468434\pi\) | |||||||
\(6\) | 5.03618 | 2.05601 | ||||||||
\(7\) | −4.08071 | −1.54236 | −0.771182 | − | 0.636615i | \(-0.780334\pi\) | ||||
−0.771182 | + | 0.636615i | \(0.780334\pi\) | |||||||
\(8\) | −3.78320 | −1.33756 | ||||||||
\(9\) | 1.53005 | 0.510017 | ||||||||
\(10\) | −1.04767 | −0.331303 | ||||||||
\(11\) | 6.07255 | 1.83094 | 0.915471 | − | 0.402384i | \(-0.131818\pi\) | ||||
0.915471 | + | 0.402384i | \(0.131818\pi\) | |||||||
\(12\) | −7.65978 | −2.21119 | ||||||||
\(13\) | −2.05816 | −0.570831 | −0.285416 | − | 0.958404i | \(-0.592132\pi\) | ||||
−0.285416 | + | 0.958404i | \(0.592132\pi\) | |||||||
\(14\) | 9.65574 | 2.58061 | ||||||||
\(15\) | −0.942382 | −0.243322 | ||||||||
\(16\) | 1.75406 | 0.438516 | ||||||||
\(17\) | −7.35382 | −1.78356 | −0.891781 | − | 0.452467i | \(-0.850544\pi\) | ||||
−0.891781 | + | 0.452467i | \(0.850544\pi\) | |||||||
\(18\) | −3.62039 | −0.853335 | ||||||||
\(19\) | −7.65712 | −1.75666 | −0.878332 | − | 0.478052i | \(-0.841343\pi\) | ||||
−0.878332 | + | 0.478052i | \(0.841343\pi\) | |||||||
\(20\) | 1.59346 | 0.356308 | ||||||||
\(21\) | 8.68535 | 1.89530 | ||||||||
\(22\) | −14.3688 | −3.06344 | ||||||||
\(23\) | 3.46771 | 0.723068 | 0.361534 | − | 0.932359i | \(-0.382253\pi\) | ||||
0.361534 | + | 0.932359i | \(0.382253\pi\) | |||||||
\(24\) | 8.05214 | 1.64364 | ||||||||
\(25\) | −4.80396 | −0.960791 | ||||||||
\(26\) | 4.87000 | 0.955086 | ||||||||
\(27\) | 3.12863 | 0.602104 | ||||||||
\(28\) | −14.6859 | −2.77537 | ||||||||
\(29\) | 1.30887 | 0.243051 | 0.121525 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121525 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(30\) | 2.22986 | 0.407114 | ||||||||
\(31\) | 2.51535 | 0.451770 | 0.225885 | − | 0.974154i | \(-0.427473\pi\) | ||||
0.225885 | + | 0.974154i | \(0.427473\pi\) | |||||||
\(32\) | 3.41596 | 0.603862 | ||||||||
\(33\) | −12.9248 | −2.24991 | ||||||||
\(34\) | 17.4005 | 2.98417 | ||||||||
\(35\) | −1.80681 | −0.305406 | ||||||||
\(36\) | 5.50644 | 0.917740 | ||||||||
\(37\) | 8.78489 | 1.44423 | 0.722114 | − | 0.691774i | \(-0.243171\pi\) | ||||
0.722114 | + | 0.691774i | \(0.243171\pi\) | |||||||
\(38\) | 18.1182 | 2.93916 | ||||||||
\(39\) | 4.38058 | 0.701453 | ||||||||
\(40\) | −1.67508 | −0.264853 | ||||||||
\(41\) | 1.66699 | 0.260340 | 0.130170 | − | 0.991492i | \(-0.458448\pi\) | ||||
0.130170 | + | 0.991492i | \(0.458448\pi\) | |||||||
\(42\) | −20.5512 | −3.17112 | ||||||||
\(43\) | −12.6010 | −1.92163 | −0.960814 | − | 0.277193i | \(-0.910596\pi\) | ||||
−0.960814 | + | 0.277193i | \(0.910596\pi\) | |||||||
\(44\) | 21.8542 | 3.29465 | ||||||||
\(45\) | 0.677457 | 0.100989 | ||||||||
\(46\) | −8.20527 | −1.20980 | ||||||||
\(47\) | 0.421122 | 0.0614270 | 0.0307135 | − | 0.999528i | \(-0.490222\pi\) | ||||
0.0307135 | + | 0.999528i | \(0.490222\pi\) | |||||||
\(48\) | −3.73333 | −0.538860 | ||||||||
\(49\) | 9.65220 | 1.37889 | ||||||||
\(50\) | 11.3671 | 1.60755 | ||||||||
\(51\) | 15.6518 | 2.19169 | ||||||||
\(52\) | −7.40703 | −1.02717 | ||||||||
\(53\) | 11.6200 | 1.59612 | 0.798062 | − | 0.602576i | \(-0.205859\pi\) | ||||
0.798062 | + | 0.602576i | \(0.205859\pi\) | |||||||
\(54\) | −7.40293 | −1.00741 | ||||||||
\(55\) | 2.68873 | 0.362548 | ||||||||
\(56\) | 15.4382 | 2.06301 | ||||||||
\(57\) | 16.2973 | 2.15864 | ||||||||
\(58\) | −3.09703 | −0.406660 | ||||||||
\(59\) | 12.7502 | 1.65994 | 0.829970 | − | 0.557808i | \(-0.188357\pi\) | ||||
0.829970 | + | 0.557808i | \(0.188357\pi\) | |||||||
\(60\) | −3.39150 | −0.437841 | ||||||||
\(61\) | −3.33656 | −0.427203 | −0.213601 | − | 0.976921i | \(-0.568519\pi\) | ||||
−0.213601 | + | 0.976921i | \(0.568519\pi\) | |||||||
\(62\) | −5.95179 | −0.755878 | ||||||||
\(63\) | −6.24370 | −0.786632 | ||||||||
\(64\) | −11.5909 | −1.44887 | ||||||||
\(65\) | −0.911287 | −0.113031 | ||||||||
\(66\) | 30.5824 | 3.76444 | ||||||||
\(67\) | −10.2681 | −1.25444 | −0.627222 | − | 0.778840i | \(-0.715808\pi\) | ||||
−0.627222 | + | 0.778840i | \(0.715808\pi\) | |||||||
\(68\) | −26.4653 | −3.20939 | ||||||||
\(69\) | −7.38065 | −0.888526 | ||||||||
\(70\) | 4.27525 | 0.510990 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −5.78850 | −0.682181 | ||||||||
\(73\) | −8.36381 | −0.978910 | −0.489455 | − | 0.872029i | \(-0.662804\pi\) | ||||
−0.489455 | + | 0.872029i | \(0.662804\pi\) | |||||||
\(74\) | −20.7867 | −2.41641 | ||||||||
\(75\) | 10.2247 | 1.18065 | ||||||||
\(76\) | −27.5569 | −3.16099 | ||||||||
\(77\) | −24.7803 | −2.82398 | ||||||||
\(78\) | −10.3653 | −1.17364 | ||||||||
\(79\) | 6.19979 | 0.697531 | 0.348766 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348766 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(80\) | 0.776642 | 0.0868312 | ||||||||
\(81\) | −11.2491 | −1.24990 | ||||||||
\(82\) | −3.94441 | −0.435588 | ||||||||
\(83\) | −5.89730 | −0.647313 | −0.323657 | − | 0.946175i | \(-0.604912\pi\) | ||||
−0.323657 | + | 0.946175i | \(0.604912\pi\) | |||||||
\(84\) | 31.2573 | 3.41046 | ||||||||
\(85\) | −3.25603 | −0.353166 | ||||||||
\(86\) | 29.8163 | 3.21517 | ||||||||
\(87\) | −2.78578 | −0.298667 | ||||||||
\(88\) | −22.9737 | −2.44900 | ||||||||
\(89\) | 10.3247 | 1.09442 | 0.547210 | − | 0.836995i | \(-0.315690\pi\) | ||||
0.547210 | + | 0.836995i | \(0.315690\pi\) | |||||||
\(90\) | −1.60299 | −0.168970 | ||||||||
\(91\) | 8.39877 | 0.880430 | ||||||||
\(92\) | 12.4798 | 1.30111 | ||||||||
\(93\) | −5.35364 | −0.555147 | ||||||||
\(94\) | −0.996455 | −0.102777 | ||||||||
\(95\) | −3.39032 | −0.347840 | ||||||||
\(96\) | −7.27050 | −0.742042 | ||||||||
\(97\) | 12.9648 | 1.31638 | 0.658189 | − | 0.752852i | \(-0.271323\pi\) | ||||
0.658189 | + | 0.752852i | \(0.271323\pi\) | |||||||
\(98\) | −22.8390 | −2.30708 | ||||||||
\(99\) | 9.29131 | 0.933812 | ||||||||
\(100\) | −17.2888 | −1.72888 | ||||||||
\(101\) | −13.2816 | −1.32157 | −0.660783 | − | 0.750577i | \(-0.729776\pi\) | ||||
−0.660783 | + | 0.750577i | \(0.729776\pi\) | |||||||
\(102\) | −37.0352 | −3.66703 | ||||||||
\(103\) | −8.06131 | −0.794305 | −0.397152 | − | 0.917753i | \(-0.630002\pi\) | ||||
−0.397152 | + | 0.917753i | \(0.630002\pi\) | |||||||
\(104\) | 7.78645 | 0.763524 | ||||||||
\(105\) | 3.84559 | 0.375291 | ||||||||
\(106\) | −27.4950 | −2.67055 | ||||||||
\(107\) | 8.88851 | 0.859285 | 0.429642 | − | 0.902999i | \(-0.358640\pi\) | ||||
0.429642 | + | 0.902999i | \(0.358640\pi\) | |||||||
\(108\) | 11.2595 | 1.08344 | ||||||||
\(109\) | 10.0984 | 0.967253 | 0.483627 | − | 0.875274i | \(-0.339319\pi\) | ||||
0.483627 | + | 0.875274i | \(0.339319\pi\) | |||||||
\(110\) | −6.36204 | −0.606596 | ||||||||
\(111\) | −18.6977 | −1.77471 | ||||||||
\(112\) | −7.15783 | −0.676351 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | −38.5626 | −3.61172 | ||||||||
\(115\) | 1.53539 | 0.143176 | ||||||||
\(116\) | 4.71043 | 0.437352 | ||||||||
\(117\) | −3.14909 | −0.291134 | ||||||||
\(118\) | −30.1695 | −2.77733 | ||||||||
\(119\) | 30.0088 | 2.75090 | ||||||||
\(120\) | 3.56522 | 0.325459 | ||||||||
\(121\) | 25.8758 | 2.35235 | ||||||||
\(122\) | 7.89493 | 0.714774 | ||||||||
\(123\) | −3.54801 | −0.319913 | ||||||||
\(124\) | 9.05238 | 0.812927 | ||||||||
\(125\) | −4.34087 | −0.388259 | ||||||||
\(126\) | 14.7738 | 1.31615 | ||||||||
\(127\) | −6.65856 | −0.590852 | −0.295426 | − | 0.955366i | \(-0.595462\pi\) | ||||
−0.295426 | + | 0.955366i | \(0.595462\pi\) | |||||||
\(128\) | 20.5944 | 1.82031 | ||||||||
\(129\) | 26.8198 | 2.36135 | ||||||||
\(130\) | 2.15628 | 0.189118 | ||||||||
\(131\) | 9.11938 | 0.796764 | 0.398382 | − | 0.917220i | \(-0.369572\pi\) | ||||
0.398382 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(132\) | −46.5144 | −4.04856 | ||||||||
\(133\) | 31.2465 | 2.70941 | ||||||||
\(134\) | 24.2962 | 2.09887 | ||||||||
\(135\) | 1.38525 | 0.119224 | ||||||||
\(136\) | 27.8210 | 2.38563 | ||||||||
\(137\) | 5.12922 | 0.438219 | 0.219109 | − | 0.975700i | \(-0.429685\pi\) | ||||
0.219109 | + | 0.975700i | \(0.429685\pi\) | |||||||
\(138\) | 17.4640 | 1.48664 | ||||||||
\(139\) | 3.16049 | 0.268069 | 0.134034 | − | 0.990977i | \(-0.457207\pi\) | ||||
0.134034 | + | 0.990977i | \(0.457207\pi\) | |||||||
\(140\) | −6.50244 | −0.549556 | ||||||||
\(141\) | −0.896313 | −0.0754832 | ||||||||
\(142\) | 2.36619 | 0.198566 | ||||||||
\(143\) | −12.4983 | −1.04516 | ||||||||
\(144\) | 2.68381 | 0.223651 | ||||||||
\(145\) | 0.579524 | 0.0481268 | ||||||||
\(146\) | 19.7904 | 1.63786 | ||||||||
\(147\) | −20.5437 | −1.69441 | ||||||||
\(148\) | 31.6156 | 2.59879 | ||||||||
\(149\) | 17.2508 | 1.41324 | 0.706620 | − | 0.707593i | \(-0.250219\pi\) | ||||
0.706620 | + | 0.707593i | \(0.250219\pi\) | |||||||
\(150\) | −24.1936 | −1.97540 | ||||||||
\(151\) | −13.1367 | −1.06905 | −0.534526 | − | 0.845152i | \(-0.679510\pi\) | ||||
−0.534526 | + | 0.845152i | \(0.679510\pi\) | |||||||
\(152\) | 28.9684 | 2.34965 | ||||||||
\(153\) | −11.2517 | −0.909648 | ||||||||
\(154\) | 58.6349 | 4.72494 | ||||||||
\(155\) | 1.11371 | 0.0894556 | ||||||||
\(156\) | 15.7651 | 1.26222 | ||||||||
\(157\) | −13.5724 | −1.08319 | −0.541597 | − | 0.840639i | \(-0.682180\pi\) | ||||
−0.541597 | + | 0.840639i | \(0.682180\pi\) | |||||||
\(158\) | −14.6699 | −1.16707 | ||||||||
\(159\) | −24.7318 | −1.96136 | ||||||||
\(160\) | 1.51247 | 0.119572 | ||||||||
\(161\) | −14.1507 | −1.11523 | ||||||||
\(162\) | 26.6175 | 2.09127 | ||||||||
\(163\) | 12.6027 | 0.987120 | 0.493560 | − | 0.869712i | \(-0.335695\pi\) | ||||
0.493560 | + | 0.869712i | \(0.335695\pi\) | |||||||
\(164\) | 5.99926 | 0.468463 | ||||||||
\(165\) | −5.72266 | −0.445508 | ||||||||
\(166\) | 13.9541 | 1.08305 | ||||||||
\(167\) | 0.771686 | 0.0597149 | 0.0298574 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298574 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(168\) | −32.8585 | −2.53508 | ||||||||
\(169\) | −8.76397 | −0.674151 | ||||||||
\(170\) | 7.70439 | 0.590899 | ||||||||
\(171\) | −11.7158 | −0.895929 | ||||||||
\(172\) | −45.3491 | −3.45783 | ||||||||
\(173\) | −12.5847 | −0.956796 | −0.478398 | − | 0.878143i | \(-0.658782\pi\) | ||||
−0.478398 | + | 0.878143i | \(0.658782\pi\) | |||||||
\(174\) | 6.59170 | 0.499715 | ||||||||
\(175\) | 19.6036 | 1.48189 | ||||||||
\(176\) | 10.6516 | 0.802897 | ||||||||
\(177\) | −27.1375 | −2.03978 | ||||||||
\(178\) | −24.4303 | −1.83113 | ||||||||
\(179\) | 2.97475 | 0.222343 | 0.111172 | − | 0.993801i | \(-0.464540\pi\) | ||||
0.111172 | + | 0.993801i | \(0.464540\pi\) | |||||||
\(180\) | 2.43807 | 0.181723 | ||||||||
\(181\) | −14.3982 | −1.07021 | −0.535106 | − | 0.844785i | \(-0.679728\pi\) | ||||
−0.535106 | + | 0.844785i | \(0.679728\pi\) | |||||||
\(182\) | −19.8731 | −1.47309 | ||||||||
\(183\) | 7.10150 | 0.524958 | ||||||||
\(184\) | −13.1191 | −0.967150 | ||||||||
\(185\) | 3.88966 | 0.285974 | ||||||||
\(186\) | 12.6677 | 0.928844 | ||||||||
\(187\) | −44.6564 | −3.26560 | ||||||||
\(188\) | 1.51556 | 0.110534 | ||||||||
\(189\) | −12.7670 | −0.928664 | ||||||||
\(190\) | 8.02215 | 0.581988 | ||||||||
\(191\) | −17.7644 | −1.28539 | −0.642695 | − | 0.766122i | \(-0.722184\pi\) | ||||
−0.642695 | + | 0.766122i | \(0.722184\pi\) | |||||||
\(192\) | 24.6700 | 1.78041 | ||||||||
\(193\) | −4.14988 | −0.298715 | −0.149358 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149358 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(194\) | −30.6773 | −2.20250 | ||||||||
\(195\) | 1.93958 | 0.138896 | ||||||||
\(196\) | 34.7369 | 2.48121 | ||||||||
\(197\) | 19.1210 | 1.36231 | 0.681157 | − | 0.732138i | \(-0.261477\pi\) | ||||
0.681157 | + | 0.732138i | \(0.261477\pi\) | |||||||
\(198\) | −21.9850 | −1.56241 | ||||||||
\(199\) | 8.73906 | 0.619496 | 0.309748 | − | 0.950819i | \(-0.399755\pi\) | ||||
0.309748 | + | 0.950819i | \(0.399755\pi\) | |||||||
\(200\) | 18.1743 | 1.28512 | ||||||||
\(201\) | 21.8545 | 1.54150 | ||||||||
\(202\) | 31.4268 | 2.21118 | ||||||||
\(203\) | −5.34111 | −0.374873 | ||||||||
\(204\) | 56.3286 | 3.94379 | ||||||||
\(205\) | 0.738088 | 0.0515503 | ||||||||
\(206\) | 19.0746 | 1.32899 | ||||||||
\(207\) | 5.30578 | 0.368777 | ||||||||
\(208\) | −3.61015 | −0.250319 | ||||||||
\(209\) | −46.4982 | −3.21635 | ||||||||
\(210\) | −9.09940 | −0.627918 | ||||||||
\(211\) | 9.50402 | 0.654284 | 0.327142 | − | 0.944975i | \(-0.393915\pi\) | ||||
0.327142 | + | 0.944975i | \(0.393915\pi\) | |||||||
\(212\) | 41.8186 | 2.87211 | ||||||||
\(213\) | 2.12839 | 0.145835 | ||||||||
\(214\) | −21.0319 | −1.43771 | ||||||||
\(215\) | −5.57929 | −0.380505 | ||||||||
\(216\) | −11.8362 | −0.805353 | ||||||||
\(217\) | −10.2644 | −0.696793 | ||||||||
\(218\) | −23.8948 | −1.61836 | ||||||||
\(219\) | 17.8015 | 1.20291 | ||||||||
\(220\) | 9.67634 | 0.652379 | ||||||||
\(221\) | 15.1353 | 1.01811 | ||||||||
\(222\) | 44.2423 | 2.96935 | ||||||||
\(223\) | 22.6442 | 1.51637 | 0.758185 | − | 0.652039i | \(-0.226086\pi\) | ||||
0.758185 | + | 0.652039i | \(0.226086\pi\) | |||||||
\(224\) | −13.9395 | −0.931374 | ||||||||
\(225\) | −7.35030 | −0.490020 | ||||||||
\(226\) | 2.36619 | 0.157397 | ||||||||
\(227\) | 23.4338 | 1.55536 | 0.777679 | − | 0.628661i | \(-0.216397\pi\) | ||||
0.777679 | + | 0.628661i | \(0.216397\pi\) | |||||||
\(228\) | 58.6518 | 3.88431 | ||||||||
\(229\) | −10.4501 | −0.690562 | −0.345281 | − | 0.938499i | \(-0.612216\pi\) | ||||
−0.345281 | + | 0.938499i | \(0.612216\pi\) | |||||||
\(230\) | −3.63302 | −0.239555 | ||||||||
\(231\) | 52.7422 | 3.47018 | ||||||||
\(232\) | −4.95171 | −0.325096 | ||||||||
\(233\) | −0.628158 | −0.0411520 | −0.0205760 | − | 0.999788i | \(-0.506550\pi\) | ||||
−0.0205760 | + | 0.999788i | \(0.506550\pi\) | |||||||
\(234\) | 7.45136 | 0.487110 | ||||||||
\(235\) | 0.186459 | 0.0121633 | ||||||||
\(236\) | 45.8863 | 2.98694 | ||||||||
\(237\) | −13.1956 | −0.857146 | ||||||||
\(238\) | −71.0065 | −4.60267 | ||||||||
\(239\) | 12.5760 | 0.813475 | 0.406737 | − | 0.913545i | \(-0.366666\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366666\pi\) | |||||||
\(240\) | −1.65300 | −0.106701 | ||||||||
\(241\) | 12.6444 | 0.814499 | 0.407250 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407250 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(242\) | −61.2271 | −3.93583 | ||||||||
\(243\) | 14.5566 | 0.933807 | ||||||||
\(244\) | −12.0078 | −0.768721 | ||||||||
\(245\) | 4.27368 | 0.273035 | ||||||||
\(246\) | 8.39526 | 0.535262 | ||||||||
\(247\) | 15.7596 | 1.00276 | ||||||||
\(248\) | −9.51607 | −0.604271 | ||||||||
\(249\) | 12.5518 | 0.795436 | ||||||||
\(250\) | 10.2713 | 0.649616 | ||||||||
\(251\) | 24.1268 | 1.52287 | 0.761434 | − | 0.648243i | \(-0.224496\pi\) | ||||
0.761434 | + | 0.648243i | \(0.224496\pi\) | |||||||
\(252\) | −22.4702 | −1.41549 | ||||||||
\(253\) | 21.0579 | 1.32390 | ||||||||
\(254\) | 15.7554 | 0.988584 | ||||||||
\(255\) | 6.93011 | 0.433980 | ||||||||
\(256\) | −25.5485 | −1.59678 | ||||||||
\(257\) | −2.28458 | −0.142508 | −0.0712542 | − | 0.997458i | \(-0.522700\pi\) | ||||
−0.0712542 | + | 0.997458i | \(0.522700\pi\) | |||||||
\(258\) | −63.4607 | −3.95089 | ||||||||
\(259\) | −35.8486 | −2.22752 | ||||||||
\(260\) | −3.27959 | −0.203392 | ||||||||
\(261\) | 2.00264 | 0.123960 | ||||||||
\(262\) | −21.5782 | −1.33311 | ||||||||
\(263\) | −6.37142 | −0.392879 | −0.196439 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196439 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(264\) | 48.8970 | 3.00940 | ||||||||
\(265\) | 5.14493 | 0.316051 | ||||||||
\(266\) | −73.9352 | −4.53325 | ||||||||
\(267\) | −21.9751 | −1.34485 | ||||||||
\(268\) | −36.9533 | −2.25728 | ||||||||
\(269\) | −14.6742 | −0.894701 | −0.447351 | − | 0.894359i | \(-0.647632\pi\) | ||||
−0.447351 | + | 0.894359i | \(0.647632\pi\) | |||||||
\(270\) | −3.27777 | −0.199479 | ||||||||
\(271\) | −4.61315 | −0.280229 | −0.140115 | − | 0.990135i | \(-0.544747\pi\) | ||||
−0.140115 | + | 0.990135i | \(0.544747\pi\) | |||||||
\(272\) | −12.8991 | −0.782120 | ||||||||
\(273\) | −17.8759 | −1.08190 | ||||||||
\(274\) | −12.1367 | −0.733205 | ||||||||
\(275\) | −29.1723 | −1.75915 | ||||||||
\(276\) | −26.5619 | −1.59884 | ||||||||
\(277\) | 31.6588 | 1.90219 | 0.951095 | − | 0.308898i | \(-0.0999603\pi\) | ||||
0.951095 | + | 0.308898i | \(0.0999603\pi\) | |||||||
\(278\) | −7.47831 | −0.448519 | ||||||||
\(279\) | 3.84861 | 0.230410 | ||||||||
\(280\) | 6.83551 | 0.408500 | ||||||||
\(281\) | 4.80563 | 0.286680 | 0.143340 | − | 0.989674i | \(-0.454216\pi\) | ||||
0.143340 | + | 0.989674i | \(0.454216\pi\) | |||||||
\(282\) | 2.12085 | 0.126295 | ||||||||
\(283\) | −20.3995 | −1.21262 | −0.606311 | − | 0.795228i | \(-0.707351\pi\) | ||||
−0.606311 | + | 0.795228i | \(0.707351\pi\) | |||||||
\(284\) | −3.59886 | −0.213553 | ||||||||
\(285\) | 7.21593 | 0.427435 | ||||||||
\(286\) | 29.5733 | 1.74871 | ||||||||
\(287\) | −6.80250 | −0.401539 | ||||||||
\(288\) | 5.22659 | 0.307980 | ||||||||
\(289\) | 37.0786 | 2.18110 | ||||||||
\(290\) | −1.37126 | −0.0805234 | ||||||||
\(291\) | −27.5942 | −1.61760 | ||||||||
\(292\) | −30.1002 | −1.76148 | ||||||||
\(293\) | 12.9704 | 0.757740 | 0.378870 | − | 0.925450i | \(-0.376313\pi\) | ||||
0.378870 | + | 0.925450i | \(0.376313\pi\) | |||||||
\(294\) | 48.6102 | 2.83501 | ||||||||
\(295\) | 5.64539 | 0.328687 | ||||||||
\(296\) | −33.2350 | −1.93175 | ||||||||
\(297\) | 18.9987 | 1.10242 | ||||||||
\(298\) | −40.8186 | −2.36456 | ||||||||
\(299\) | −7.13712 | −0.412750 | ||||||||
\(300\) | 36.7973 | 2.12449 | ||||||||
\(301\) | 51.4209 | 2.96385 | ||||||||
\(302\) | 31.0840 | 1.78868 | ||||||||
\(303\) | 28.2684 | 1.62398 | ||||||||
\(304\) | −13.4311 | −0.770325 | ||||||||
\(305\) | −1.47732 | −0.0845910 | ||||||||
\(306\) | 26.6237 | 1.52198 | ||||||||
\(307\) | 20.9522 | 1.19580 | 0.597902 | − | 0.801569i | \(-0.296001\pi\) | ||||
0.597902 | + | 0.801569i | \(0.296001\pi\) | |||||||
\(308\) | −89.1808 | −5.08155 | ||||||||
\(309\) | 17.1576 | 0.976064 | ||||||||
\(310\) | −2.63526 | −0.149673 | ||||||||
\(311\) | −2.33388 | −0.132342 | −0.0661711 | − | 0.997808i | \(-0.521078\pi\) | ||||
−0.0661711 | + | 0.997808i | \(0.521078\pi\) | |||||||
\(312\) | −16.5726 | −0.938239 | ||||||||
\(313\) | −21.6269 | −1.22242 | −0.611212 | − | 0.791467i | \(-0.709318\pi\) | ||||
−0.611212 | + | 0.791467i | \(0.709318\pi\) | |||||||
\(314\) | 32.1148 | 1.81234 | ||||||||
\(315\) | −2.76451 | −0.155762 | ||||||||
\(316\) | 22.3122 | 1.25516 | ||||||||
\(317\) | −33.5458 | −1.88412 | −0.942061 | − | 0.335442i | \(-0.891114\pi\) | ||||
−0.942061 | + | 0.335442i | \(0.891114\pi\) | |||||||
\(318\) | 58.5202 | 3.28165 | ||||||||
\(319\) | 7.94816 | 0.445012 | ||||||||
\(320\) | −5.13209 | −0.286892 | ||||||||
\(321\) | −18.9182 | −1.05591 | ||||||||
\(322\) | 33.4833 | 1.86595 | ||||||||
\(323\) | 56.3090 | 3.13312 | ||||||||
\(324\) | −40.4839 | −2.24911 | ||||||||
\(325\) | 9.88732 | 0.548450 | ||||||||
\(326\) | −29.8204 | −1.65160 | ||||||||
\(327\) | −21.4934 | −1.18859 | ||||||||
\(328\) | −6.30656 | −0.348221 | ||||||||
\(329\) | −1.71848 | −0.0947428 | ||||||||
\(330\) | 13.5409 | 0.745402 | ||||||||
\(331\) | 35.2081 | 1.93521 | 0.967605 | − | 0.252467i | \(-0.0812420\pi\) | ||||
0.967605 | + | 0.252467i | \(0.0812420\pi\) | |||||||
\(332\) | −21.2236 | −1.16479 | ||||||||
\(333\) | 13.4413 | 0.736581 | ||||||||
\(334\) | −1.82596 | −0.0999119 | ||||||||
\(335\) | −4.54637 | −0.248395 | ||||||||
\(336\) | 15.2347 | 0.831119 | ||||||||
\(337\) | 8.92467 | 0.486157 | 0.243079 | − | 0.970007i | \(-0.421843\pi\) | ||||
0.243079 | + | 0.970007i | \(0.421843\pi\) | |||||||
\(338\) | 20.7372 | 1.12796 | ||||||||
\(339\) | 2.12839 | 0.115598 | ||||||||
\(340\) | −11.7180 | −0.635497 | ||||||||
\(341\) | 15.2746 | 0.827164 | ||||||||
\(342\) | 27.7218 | 1.49902 | ||||||||
\(343\) | −10.8229 | −0.584380 | ||||||||
\(344\) | 47.6720 | 2.57030 | ||||||||
\(345\) | −3.26791 | −0.175938 | ||||||||
\(346\) | 29.7778 | 1.60086 | ||||||||
\(347\) | −16.0283 | −0.860445 | −0.430223 | − | 0.902723i | \(-0.641565\pi\) | ||||
−0.430223 | + | 0.902723i | \(0.641565\pi\) | |||||||
\(348\) | −10.0256 | −0.537431 | ||||||||
\(349\) | −12.4523 | −0.666559 | −0.333279 | − | 0.942828i | \(-0.608155\pi\) | ||||
−0.333279 | + | 0.942828i | \(0.608155\pi\) | |||||||
\(350\) | −46.3858 | −2.47942 | ||||||||
\(351\) | −6.43922 | −0.343700 | ||||||||
\(352\) | 20.7436 | 1.10564 | ||||||||
\(353\) | 3.79464 | 0.201968 | 0.100984 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100984 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(354\) | 64.2125 | 3.41286 | ||||||||
\(355\) | −0.442767 | −0.0234996 | ||||||||
\(356\) | 37.1573 | 1.96933 | ||||||||
\(357\) | −63.8705 | −3.38038 | ||||||||
\(358\) | −7.03883 | −0.372013 | ||||||||
\(359\) | 32.8685 | 1.73473 | 0.867366 | − | 0.497671i | \(-0.165811\pi\) | ||||
0.867366 | + | 0.497671i | \(0.165811\pi\) | |||||||
\(360\) | −2.56296 | −0.135080 | ||||||||
\(361\) | 39.6315 | 2.08587 | ||||||||
\(362\) | 34.0690 | 1.79062 | ||||||||
\(363\) | −55.0739 | −2.89063 | ||||||||
\(364\) | 30.2260 | 1.58427 | ||||||||
\(365\) | −3.70322 | −0.193835 | ||||||||
\(366\) | −16.8035 | −0.878334 | ||||||||
\(367\) | 5.35795 | 0.279683 | 0.139841 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139841 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(368\) | 6.08259 | 0.317077 | ||||||||
\(369\) | 2.55058 | 0.132778 | ||||||||
\(370\) | −9.20369 | −0.478477 | ||||||||
\(371\) | −47.4177 | −2.46180 | ||||||||
\(372\) | −19.2670 | −0.998948 | ||||||||
\(373\) | −21.9639 | −1.13725 | −0.568623 | − | 0.822598i | \(-0.692524\pi\) | ||||
−0.568623 | + | 0.822598i | \(0.692524\pi\) | |||||||
\(374\) | 105.666 | 5.46384 | ||||||||
\(375\) | 9.23907 | 0.477104 | ||||||||
\(376\) | −1.59319 | −0.0821625 | ||||||||
\(377\) | −2.69386 | −0.138741 | ||||||||
\(378\) | 30.2092 | 1.55379 | ||||||||
\(379\) | 2.02462 | 0.103998 | 0.0519989 | − | 0.998647i | \(-0.483441\pi\) | ||||
0.0519989 | + | 0.998647i | \(0.483441\pi\) | |||||||
\(380\) | −12.2013 | −0.625913 | ||||||||
\(381\) | 14.1720 | 0.726055 | ||||||||
\(382\) | 42.0341 | 2.15065 | ||||||||
\(383\) | −5.91063 | −0.302019 | −0.151010 | − | 0.988532i | \(-0.548252\pi\) | ||||
−0.151010 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(384\) | −43.8330 | −2.23685 | ||||||||
\(385\) | −10.9719 | −0.559180 | ||||||||
\(386\) | 9.81942 | 0.499795 | ||||||||
\(387\) | −19.2801 | −0.980064 | ||||||||
\(388\) | 46.6586 | 2.36873 | ||||||||
\(389\) | −32.5830 | −1.65202 | −0.826011 | − | 0.563653i | \(-0.809395\pi\) | ||||
−0.826011 | + | 0.563653i | \(0.809395\pi\) | |||||||
\(390\) | −4.58941 | −0.232394 | ||||||||
\(391\) | −25.5009 | −1.28964 | ||||||||
\(392\) | −36.5162 | −1.84435 | ||||||||
\(393\) | −19.4096 | −0.979086 | ||||||||
\(394\) | −45.2439 | −2.27935 | ||||||||
\(395\) | 2.74507 | 0.138119 | ||||||||
\(396\) | 33.4381 | 1.68033 | ||||||||
\(397\) | −7.99867 | −0.401442 | −0.200721 | − | 0.979648i | \(-0.564328\pi\) | ||||
−0.200721 | + | 0.979648i | \(0.564328\pi\) | |||||||
\(398\) | −20.6783 | −1.03651 | ||||||||
\(399\) | −66.5048 | −3.32940 | ||||||||
\(400\) | −8.42645 | −0.421322 | ||||||||
\(401\) | −17.5912 | −0.878463 | −0.439232 | − | 0.898374i | \(-0.644749\pi\) | ||||
−0.439232 | + | 0.898374i | \(0.644749\pi\) | |||||||
\(402\) | −51.7119 | −2.57915 | ||||||||
\(403\) | −5.17699 | −0.257884 | ||||||||
\(404\) | −47.7985 | −2.37807 | ||||||||
\(405\) | −4.98073 | −0.247495 | ||||||||
\(406\) | 12.6381 | 0.627218 | ||||||||
\(407\) | 53.3467 | 2.64430 | ||||||||
\(408\) | −59.2140 | −2.93153 | ||||||||
\(409\) | −12.6318 | −0.624602 | −0.312301 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312301 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(410\) | −1.74646 | −0.0862514 | ||||||||
\(411\) | −10.9170 | −0.538495 | ||||||||
\(412\) | −29.0115 | −1.42930 | ||||||||
\(413\) | −52.0301 | −2.56023 | ||||||||
\(414\) | −12.5545 | −0.617019 | ||||||||
\(415\) | −2.61113 | −0.128176 | ||||||||
\(416\) | −7.03060 | −0.344703 | ||||||||
\(417\) | −6.72675 | −0.329410 | ||||||||
\(418\) | 110.024 | 5.38143 | ||||||||
\(419\) | 9.63409 | 0.470656 | 0.235328 | − | 0.971916i | \(-0.424384\pi\) | ||||
0.235328 | + | 0.971916i | \(0.424384\pi\) | |||||||
\(420\) | 13.8397 | 0.675310 | ||||||||
\(421\) | 17.1770 | 0.837157 | 0.418578 | − | 0.908181i | \(-0.362529\pi\) | ||||
0.418578 | + | 0.908181i | \(0.362529\pi\) | |||||||
\(422\) | −22.4883 | −1.09471 | ||||||||
\(423\) | 0.644339 | 0.0313288 | ||||||||
\(424\) | −43.9606 | −2.13492 | ||||||||
\(425\) | 35.3274 | 1.71363 | ||||||||
\(426\) | −5.03618 | −0.244004 | ||||||||
\(427\) | 13.6155 | 0.658902 | ||||||||
\(428\) | 31.9885 | 1.54622 | ||||||||
\(429\) | 26.6013 | 1.28432 | ||||||||
\(430\) | 13.2017 | 0.636641 | ||||||||
\(431\) | 10.8666 | 0.523423 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(432\) | 5.48781 | 0.264032 | ||||||||
\(433\) | 14.6337 | 0.703250 | 0.351625 | − | 0.936141i | \(-0.385629\pi\) | ||||
0.351625 | + | 0.936141i | \(0.385629\pi\) | |||||||
\(434\) | 24.2875 | 1.16584 | ||||||||
\(435\) | −1.23345 | −0.0591396 | ||||||||
\(436\) | 36.3428 | 1.74050 | ||||||||
\(437\) | −26.5527 | −1.27019 | ||||||||
\(438\) | −42.1217 | −2.01265 | ||||||||
\(439\) | 17.7050 | 0.845012 | 0.422506 | − | 0.906360i | \(-0.361150\pi\) | ||||
0.422506 | + | 0.906360i | \(0.361150\pi\) | |||||||
\(440\) | −10.1720 | −0.484931 | ||||||||
\(441\) | 14.7684 | 0.703256 | ||||||||
\(442\) | −35.8131 | −1.70346 | ||||||||
\(443\) | 16.7633 | 0.796449 | 0.398225 | − | 0.917288i | \(-0.369626\pi\) | ||||
0.398225 | + | 0.917288i | \(0.369626\pi\) | |||||||
\(444\) | −67.2904 | −3.19346 | ||||||||
\(445\) | 4.57146 | 0.216708 | ||||||||
\(446\) | −53.5806 | −2.53711 | ||||||||
\(447\) | −36.7164 | −1.73663 | ||||||||
\(448\) | 47.2993 | 2.23468 | ||||||||
\(449\) | 13.5333 | 0.638677 | 0.319339 | − | 0.947641i | \(-0.396539\pi\) | ||||
0.319339 | + | 0.947641i | \(0.396539\pi\) | |||||||
\(450\) | 17.3922 | 0.819877 | ||||||||
\(451\) | 10.1229 | 0.476667 | ||||||||
\(452\) | −3.59886 | −0.169276 | ||||||||
\(453\) | 27.9601 | 1.31368 | ||||||||
\(454\) | −55.4489 | −2.60235 | ||||||||
\(455\) | 3.71870 | 0.174335 | ||||||||
\(456\) | −61.6562 | −2.88732 | ||||||||
\(457\) | −37.9060 | −1.77317 | −0.886585 | − | 0.462567i | \(-0.846929\pi\) | ||||
−0.886585 | + | 0.462567i | \(0.846929\pi\) | |||||||
\(458\) | 24.7269 | 1.15541 | ||||||||
\(459\) | −23.0073 | −1.07389 | ||||||||
\(460\) | 5.52565 | 0.257635 | ||||||||
\(461\) | −0.753289 | −0.0350841 | −0.0175421 | − | 0.999846i | \(-0.505584\pi\) | ||||
−0.0175421 | + | 0.999846i | \(0.505584\pi\) | |||||||
\(462\) | −124.798 | −5.80613 | ||||||||
\(463\) | 27.9872 | 1.30067 | 0.650337 | − | 0.759645i | \(-0.274627\pi\) | ||||
0.650337 | + | 0.759645i | \(0.274627\pi\) | |||||||
\(464\) | 2.29584 | 0.106582 | ||||||||
\(465\) | −2.37042 | −0.109925 | ||||||||
\(466\) | 1.48634 | 0.0688534 | ||||||||
\(467\) | 35.1515 | 1.62662 | 0.813310 | − | 0.581831i | \(-0.197664\pi\) | ||||
0.813310 | + | 0.581831i | \(0.197664\pi\) | |||||||
\(468\) | −11.3331 | −0.523875 | ||||||||
\(469\) | 41.9010 | 1.93481 | ||||||||
\(470\) | −0.441198 | −0.0203509 | ||||||||
\(471\) | 28.8873 | 1.33106 | ||||||||
\(472\) | −48.2368 | −2.22028 | ||||||||
\(473\) | −76.5199 | −3.51839 | ||||||||
\(474\) | 31.2233 | 1.43413 | ||||||||
\(475\) | 36.7845 | 1.68779 | ||||||||
\(476\) | 107.997 | 4.95005 | ||||||||
\(477\) | 17.7791 | 0.814050 | ||||||||
\(478\) | −29.7572 | −1.36106 | ||||||||
\(479\) | −4.71072 | −0.215238 | −0.107619 | − | 0.994192i | \(-0.534323\pi\) | ||||
−0.107619 | + | 0.994192i | \(0.534323\pi\) | |||||||
\(480\) | −3.21914 | −0.146933 | ||||||||
\(481\) | −18.0807 | −0.824411 | ||||||||
\(482\) | −29.9191 | −1.36278 | ||||||||
\(483\) | 30.1183 | 1.37043 | ||||||||
\(484\) | 93.1234 | 4.23288 | ||||||||
\(485\) | 5.74040 | 0.260658 | ||||||||
\(486\) | −34.4437 | −1.56240 | ||||||||
\(487\) | 40.4490 | 1.83292 | 0.916459 | − | 0.400129i | \(-0.131035\pi\) | ||||
0.916459 | + | 0.400129i | \(0.131035\pi\) | |||||||
\(488\) | 12.6229 | 0.571411 | ||||||||
\(489\) | −26.8235 | −1.21300 | ||||||||
\(490\) | −10.1123 | −0.456829 | ||||||||
\(491\) | −18.8191 | −0.849293 | −0.424647 | − | 0.905359i | \(-0.639602\pi\) | ||||
−0.424647 | + | 0.905359i | \(0.639602\pi\) | |||||||
\(492\) | −12.7688 | −0.575661 | ||||||||
\(493\) | −9.62517 | −0.433496 | ||||||||
\(494\) | −37.2902 | −1.67777 | ||||||||
\(495\) | 4.11389 | 0.184906 | ||||||||
\(496\) | 4.41208 | 0.198108 | ||||||||
\(497\) | 4.08071 | 0.183045 | ||||||||
\(498\) | −29.6999 | −1.33088 | ||||||||
\(499\) | −39.0292 | −1.74719 | −0.873593 | − | 0.486657i | \(-0.838216\pi\) | ||||
−0.873593 | + | 0.486657i | \(0.838216\pi\) | |||||||
\(500\) | −15.6222 | −0.698645 | ||||||||
\(501\) | −1.64245 | −0.0733793 | ||||||||
\(502\) | −57.0885 | −2.54799 | ||||||||
\(503\) | −16.8751 | −0.752423 | −0.376212 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376212 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(504\) | 23.6212 | 1.05217 | ||||||||
\(505\) | −5.88065 | −0.261685 | ||||||||
\(506\) | −49.8269 | −2.21508 | ||||||||
\(507\) | 18.6532 | 0.828416 | ||||||||
\(508\) | −23.9632 | −1.06320 | ||||||||
\(509\) | 9.70641 | 0.430229 | 0.215115 | − | 0.976589i | \(-0.430988\pi\) | ||||
0.215115 | + | 0.976589i | \(0.430988\pi\) | |||||||
\(510\) | −16.3980 | −0.726114 | ||||||||
\(511\) | 34.1303 | 1.50984 | ||||||||
\(512\) | 19.2638 | 0.851346 | ||||||||
\(513\) | −23.9563 | −1.05769 | ||||||||
\(514\) | 5.40576 | 0.238438 | ||||||||
\(515\) | −3.56929 | −0.157282 | ||||||||
\(516\) | 96.5206 | 4.24908 | ||||||||
\(517\) | 2.55728 | 0.112469 | ||||||||
\(518\) | 84.8247 | 3.72698 | ||||||||
\(519\) | 26.7852 | 1.17574 | ||||||||
\(520\) | 3.44758 | 0.151187 | ||||||||
\(521\) | 30.8855 | 1.35312 | 0.676559 | − | 0.736389i | \(-0.263471\pi\) | ||||
0.676559 | + | 0.736389i | \(0.263471\pi\) | |||||||
\(522\) | −4.73862 | −0.207404 | ||||||||
\(523\) | −34.9363 | −1.52766 | −0.763828 | − | 0.645420i | \(-0.776682\pi\) | ||||
−0.763828 | + | 0.645420i | \(0.776682\pi\) | |||||||
\(524\) | 32.8194 | 1.43372 | ||||||||
\(525\) | −41.7241 | −1.82099 | ||||||||
\(526\) | 15.0760 | 0.657345 | ||||||||
\(527\) | −18.4974 | −0.805759 | ||||||||
\(528\) | −22.6708 | −0.986622 | ||||||||
\(529\) | −10.9750 | −0.477172 | ||||||||
\(530\) | −12.1739 | −0.528800 | ||||||||
\(531\) | 19.5085 | 0.846598 | ||||||||
\(532\) | 112.452 | 4.87540 | ||||||||
\(533\) | −3.43093 | −0.148610 | ||||||||
\(534\) | 51.9972 | 2.25014 | ||||||||
\(535\) | 3.93554 | 0.170148 | ||||||||
\(536\) | 38.8462 | 1.67790 | ||||||||
\(537\) | −6.33143 | −0.273221 | ||||||||
\(538\) | 34.7219 | 1.49697 | ||||||||
\(539\) | 58.6135 | 2.52466 | ||||||||
\(540\) | 4.98533 | 0.214534 | ||||||||
\(541\) | −26.3746 | −1.13393 | −0.566965 | − | 0.823742i | \(-0.691883\pi\) | ||||
−0.566965 | + | 0.823742i | \(0.691883\pi\) | |||||||
\(542\) | 10.9156 | 0.468865 | ||||||||
\(543\) | 30.6451 | 1.31511 | ||||||||
\(544\) | −25.1203 | −1.07703 | ||||||||
\(545\) | 4.47125 | 0.191527 | ||||||||
\(546\) | 42.2977 | 1.81017 | ||||||||
\(547\) | −26.8385 | −1.14753 | −0.573766 | − | 0.819019i | \(-0.694518\pi\) | ||||
−0.573766 | + | 0.819019i | \(0.694518\pi\) | |||||||
\(548\) | 18.4593 | 0.788543 | ||||||||
\(549\) | −5.10511 | −0.217881 | ||||||||
\(550\) | 69.0271 | 2.94333 | ||||||||
\(551\) | −10.0222 | −0.426958 | ||||||||
\(552\) | 27.9225 | 1.18846 | ||||||||
\(553\) | −25.2996 | −1.07585 | ||||||||
\(554\) | −74.9106 | −3.18265 | ||||||||
\(555\) | −8.27873 | −0.351412 | ||||||||
\(556\) | 11.3741 | 0.482371 | ||||||||
\(557\) | 11.2130 | 0.475109 | 0.237554 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237554 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(558\) | −9.10655 | −0.385511 | ||||||||
\(559\) | 25.9348 | 1.09693 | ||||||||
\(560\) | −3.16925 | −0.133925 | ||||||||
\(561\) | 95.0463 | 4.01286 | ||||||||
\(562\) | −11.3710 | −0.479658 | ||||||||
\(563\) | −29.7705 | −1.25468 | −0.627338 | − | 0.778747i | \(-0.715856\pi\) | ||||
−0.627338 | + | 0.778747i | \(0.715856\pi\) | |||||||
\(564\) | −3.22570 | −0.135827 | ||||||||
\(565\) | −0.442767 | −0.0186274 | ||||||||
\(566\) | 48.2690 | 2.02890 | ||||||||
\(567\) | 45.9043 | 1.92780 | ||||||||
\(568\) | 3.78320 | 0.158740 | ||||||||
\(569\) | −7.74289 | −0.324599 | −0.162299 | − | 0.986742i | \(-0.551891\pi\) | ||||
−0.162299 | + | 0.986742i | \(0.551891\pi\) | |||||||
\(570\) | −17.0743 | −0.715163 | ||||||||
\(571\) | −13.2941 | −0.556343 | −0.278171 | − | 0.960531i | \(-0.589728\pi\) | ||||
−0.278171 | + | 0.960531i | \(0.589728\pi\) | |||||||
\(572\) | −44.9796 | −1.88069 | ||||||||
\(573\) | 37.8097 | 1.57952 | ||||||||
\(574\) | 16.0960 | 0.671835 | ||||||||
\(575\) | −16.6587 | −0.694718 | ||||||||
\(576\) | −17.7347 | −0.738947 | ||||||||
\(577\) | 15.7063 | 0.653860 | 0.326930 | − | 0.945049i | \(-0.393986\pi\) | ||||
0.326930 | + | 0.945049i | \(0.393986\pi\) | |||||||
\(578\) | −87.7351 | −3.64930 | ||||||||
\(579\) | 8.83258 | 0.367069 | ||||||||
\(580\) | 2.08562 | 0.0866008 | ||||||||
\(581\) | 24.0652 | 0.998393 | ||||||||
\(582\) | 65.2932 | 2.70649 | ||||||||
\(583\) | 70.5627 | 2.92241 | ||||||||
\(584\) | 31.6420 | 1.30935 | ||||||||
\(585\) | −1.39432 | −0.0576479 | ||||||||
\(586\) | −30.6905 | −1.26781 | ||||||||
\(587\) | 39.8682 | 1.64554 | 0.822768 | − | 0.568377i | \(-0.192428\pi\) | ||||
0.822768 | + | 0.568377i | \(0.192428\pi\) | |||||||
\(588\) | −73.9338 | −3.04898 | ||||||||
\(589\) | −19.2603 | −0.793607 | ||||||||
\(590\) | −13.3581 | −0.549943 | ||||||||
\(591\) | −40.6969 | −1.67405 | ||||||||
\(592\) | 15.4093 | 0.633317 | ||||||||
\(593\) | −16.1606 | −0.663636 | −0.331818 | − | 0.943343i | \(-0.607662\pi\) | ||||
−0.331818 | + | 0.943343i | \(0.607662\pi\) | |||||||
\(594\) | −44.9546 | −1.84451 | ||||||||
\(595\) | 13.2869 | 0.544710 | ||||||||
\(596\) | 62.0831 | 2.54302 | ||||||||
\(597\) | −18.6001 | −0.761253 | ||||||||
\(598\) | 16.8878 | 0.690593 | ||||||||
\(599\) | −9.69394 | −0.396084 | −0.198042 | − | 0.980194i | \(-0.563458\pi\) | ||||
−0.198042 | + | 0.980194i | \(0.563458\pi\) | |||||||
\(600\) | −38.6821 | −1.57919 | ||||||||
\(601\) | 27.1552 | 1.10768 | 0.553841 | − | 0.832622i | \(-0.313161\pi\) | ||||
0.553841 | + | 0.832622i | \(0.313161\pi\) | |||||||
\(602\) | −121.672 | −4.95897 | ||||||||
\(603\) | −15.7107 | −0.639788 | ||||||||
\(604\) | −47.2772 | −1.92368 | ||||||||
\(605\) | 11.4570 | 0.465792 | ||||||||
\(606\) | −66.8885 | −2.71716 | ||||||||
\(607\) | 15.5194 | 0.629912 | 0.314956 | − | 0.949106i | \(-0.398010\pi\) | ||||
0.314956 | + | 0.949106i | \(0.398010\pi\) | |||||||
\(608\) | −26.1564 | −1.06078 | ||||||||
\(609\) | 11.3680 | 0.460654 | ||||||||
\(610\) | 3.49562 | 0.141533 | ||||||||
\(611\) | −0.866738 | −0.0350645 | ||||||||
\(612\) | −40.4933 | −1.63685 | ||||||||
\(613\) | 40.0318 | 1.61687 | 0.808435 | − | 0.588585i | \(-0.200315\pi\) | ||||
0.808435 | + | 0.588585i | \(0.200315\pi\) | |||||||
\(614\) | −49.5769 | −2.00076 | ||||||||
\(615\) | −1.57094 | −0.0633465 | ||||||||
\(616\) | 93.7489 | 3.77725 | ||||||||
\(617\) | 9.15416 | 0.368533 | 0.184266 | − | 0.982876i | \(-0.441009\pi\) | ||||
0.184266 | + | 0.982876i | \(0.441009\pi\) | |||||||
\(618\) | −40.5982 | −1.63310 | ||||||||
\(619\) | −22.7056 | −0.912617 | −0.456308 | − | 0.889822i | \(-0.650829\pi\) | ||||
−0.456308 | + | 0.889822i | \(0.650829\pi\) | |||||||
\(620\) | 4.00810 | 0.160969 | ||||||||
\(621\) | 10.8492 | 0.435363 | ||||||||
\(622\) | 5.52240 | 0.221428 | ||||||||
\(623\) | −42.1323 | −1.68799 | ||||||||
\(624\) | 7.68381 | 0.307598 | ||||||||
\(625\) | 22.0978 | 0.883912 | ||||||||
\(626\) | 51.1734 | 2.04530 | ||||||||
\(627\) | 98.9664 | 3.95234 | ||||||||
\(628\) | −48.8450 | −1.94913 | ||||||||
\(629\) | −64.6025 | −2.57587 | ||||||||
\(630\) | 6.54135 | 0.260613 | ||||||||
\(631\) | 3.81869 | 0.152020 | 0.0760099 | − | 0.997107i | \(-0.475782\pi\) | ||||
0.0760099 | + | 0.997107i | \(0.475782\pi\) | |||||||
\(632\) | −23.4551 | −0.932993 | ||||||||
\(633\) | −20.2283 | −0.804002 | ||||||||
\(634\) | 79.3758 | 3.15242 | ||||||||
\(635\) | −2.94819 | −0.116996 | ||||||||
\(636\) | −89.0063 | −3.52933 | ||||||||
\(637\) | −19.8658 | −0.787112 | ||||||||
\(638\) | −18.8069 | −0.744571 | ||||||||
\(639\) | −1.53005 | −0.0605279 | ||||||||
\(640\) | 9.11855 | 0.360442 | ||||||||
\(641\) | 29.3557 | 1.15948 | 0.579740 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579740 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(642\) | 44.7641 | 1.76670 | ||||||||
\(643\) | −29.3639 | −1.15800 | −0.578999 | − | 0.815329i | \(-0.696556\pi\) | ||||
−0.578999 | + | 0.815329i | \(0.696556\pi\) | |||||||
\(644\) | −50.9265 | −2.00678 | ||||||||
\(645\) | 11.8749 | 0.467575 | ||||||||
\(646\) | −133.238 | −5.24218 | ||||||||
\(647\) | 35.3270 | 1.38885 | 0.694423 | − | 0.719567i | \(-0.255660\pi\) | ||||
0.694423 | + | 0.719567i | \(0.255660\pi\) | |||||||
\(648\) | 42.5576 | 1.67182 | ||||||||
\(649\) | 77.4265 | 3.03925 | ||||||||
\(650\) | −23.3953 | −0.917639 | ||||||||
\(651\) | 21.8467 | 0.856239 | ||||||||
\(652\) | 45.3553 | 1.77625 | ||||||||
\(653\) | −45.1762 | −1.76788 | −0.883940 | − | 0.467601i | \(-0.845119\pi\) | ||||
−0.883940 | + | 0.467601i | \(0.845119\pi\) | |||||||
\(654\) | 50.8575 | 1.98868 | ||||||||
\(655\) | 4.03776 | 0.157768 | ||||||||
\(656\) | 2.92401 | 0.114163 | ||||||||
\(657\) | −12.7971 | −0.499261 | ||||||||
\(658\) | 4.06625 | 0.158519 | ||||||||
\(659\) | 6.73244 | 0.262259 | 0.131129 | − | 0.991365i | \(-0.458140\pi\) | ||||
0.131129 | + | 0.991365i | \(0.458140\pi\) | |||||||
\(660\) | −20.5950 | −0.801661 | ||||||||
\(661\) | −30.5092 | −1.18667 | −0.593336 | − | 0.804955i | \(-0.702189\pi\) | ||||
−0.593336 | + | 0.804955i | \(0.702189\pi\) | |||||||
\(662\) | −83.3090 | −3.23790 | ||||||||
\(663\) | −32.2140 | −1.25109 | ||||||||
\(664\) | 22.3107 | 0.865823 | ||||||||
\(665\) | 13.8349 | 0.536495 | ||||||||
\(666\) | −31.8048 | −1.23241 | ||||||||
\(667\) | 4.53878 | 0.175742 | ||||||||
\(668\) | 2.77719 | 0.107453 | ||||||||
\(669\) | −48.1958 | −1.86336 | ||||||||
\(670\) | 10.7576 | 0.415601 | ||||||||
\(671\) | −20.2614 | −0.782183 | ||||||||
\(672\) | 29.6688 | 1.14450 | ||||||||
\(673\) | −44.9978 | −1.73454 | −0.867268 | − | 0.497841i | \(-0.834126\pi\) | ||||
−0.867268 | + | 0.497841i | \(0.834126\pi\) | |||||||
\(674\) | −21.1175 | −0.813414 | ||||||||
\(675\) | −15.0298 | −0.578497 | ||||||||
\(676\) | −31.5403 | −1.21309 | ||||||||
\(677\) | −31.0734 | −1.19425 | −0.597125 | − | 0.802149i | \(-0.703690\pi\) | ||||
−0.597125 | + | 0.802149i | \(0.703690\pi\) | |||||||
\(678\) | −5.03618 | −0.193413 | ||||||||
\(679\) | −52.9057 | −2.03033 | ||||||||
\(680\) | 12.3182 | 0.472382 | ||||||||
\(681\) | −49.8764 | −1.91127 | ||||||||
\(682\) | −36.1425 | −1.38397 | ||||||||
\(683\) | 15.9081 | 0.608708 | 0.304354 | − | 0.952559i | \(-0.401559\pi\) | ||||
0.304354 | + | 0.952559i | \(0.401559\pi\) | |||||||
\(684\) | −42.1635 | −1.61216 | ||||||||
\(685\) | 2.27105 | 0.0867723 | ||||||||
\(686\) | 25.6090 | 0.977756 | ||||||||
\(687\) | 22.2419 | 0.848582 | ||||||||
\(688\) | −22.1029 | −0.842665 | ||||||||
\(689\) | −23.9157 | −0.911117 | ||||||||
\(690\) | 7.73250 | 0.294371 | ||||||||
\(691\) | −5.80557 | −0.220854 | −0.110427 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110427 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(692\) | −45.2905 | −1.72169 | ||||||||
\(693\) | −37.9152 | −1.44028 | ||||||||
\(694\) | 37.9261 | 1.43965 | ||||||||
\(695\) | 1.39936 | 0.0530807 | ||||||||
\(696\) | 10.5392 | 0.399487 | ||||||||
\(697\) | −12.2587 | −0.464333 | ||||||||
\(698\) | 29.4646 | 1.11525 | ||||||||
\(699\) | 1.33697 | 0.0505687 | ||||||||
\(700\) | 70.5504 | 2.66656 | ||||||||
\(701\) | −13.4768 | −0.509012 | −0.254506 | − | 0.967071i | \(-0.581913\pi\) | ||||
−0.254506 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(702\) | 15.2364 | 0.575062 | ||||||||
\(703\) | −67.2670 | −2.53702 | ||||||||
\(704\) | −70.3865 | −2.65279 | ||||||||
\(705\) | −0.396858 | −0.0149465 | ||||||||
\(706\) | −8.97884 | −0.337923 | ||||||||
\(707\) | 54.1983 | 2.03834 | ||||||||
\(708\) | −97.6641 | −3.67044 | ||||||||
\(709\) | −14.4289 | −0.541887 | −0.270943 | − | 0.962595i | \(-0.587336\pi\) | ||||
−0.270943 | + | 0.962595i | \(0.587336\pi\) | |||||||
\(710\) | 1.04767 | 0.0393184 | ||||||||
\(711\) | 9.48600 | 0.355753 | ||||||||
\(712\) | −39.0606 | −1.46386 | ||||||||
\(713\) | 8.72250 | 0.326660 | ||||||||
\(714\) | 151.130 | 5.65589 | ||||||||
\(715\) | −5.53383 | −0.206954 | ||||||||
\(716\) | 10.7057 | 0.400091 | ||||||||
\(717\) | −26.7667 | −0.999620 | ||||||||
\(718\) | −77.7731 | −2.90246 | ||||||||
\(719\) | −49.9060 | −1.86118 | −0.930590 | − | 0.366064i | \(-0.880705\pi\) | ||||
−0.930590 | + | 0.366064i | \(0.880705\pi\) | |||||||
\(720\) | 1.18830 | 0.0442854 | ||||||||
\(721\) | 32.8959 | 1.22511 | ||||||||
\(722\) | −93.7756 | −3.48997 | ||||||||
\(723\) | −26.9123 | −1.00088 | ||||||||
\(724\) | −51.8172 | −1.92577 | ||||||||
\(725\) | −6.28775 | −0.233521 | ||||||||
\(726\) | 130.315 | 4.83646 | ||||||||
\(727\) | −12.2743 | −0.455229 | −0.227615 | − | 0.973751i | \(-0.573093\pi\) | ||||
−0.227615 | + | 0.973751i | \(0.573093\pi\) | |||||||
\(728\) | −31.7742 | −1.17763 | ||||||||
\(729\) | 2.76513 | 0.102412 | ||||||||
\(730\) | 8.76253 | 0.324316 | ||||||||
\(731\) | 92.6652 | 3.42735 | ||||||||
\(732\) | 25.5573 | 0.944625 | ||||||||
\(733\) | −24.4649 | −0.903633 | −0.451817 | − | 0.892111i | \(-0.649224\pi\) | ||||
−0.451817 | + | 0.892111i | \(0.649224\pi\) | |||||||
\(734\) | −12.6779 | −0.467951 | ||||||||
\(735\) | −9.09606 | −0.335513 | ||||||||
\(736\) | 11.8456 | 0.436633 | ||||||||
\(737\) | −62.3534 | −2.29682 | ||||||||
\(738\) | −6.03516 | −0.222157 | ||||||||
\(739\) | −21.2934 | −0.783289 | −0.391645 | − | 0.920117i | \(-0.628094\pi\) | ||||
−0.391645 | + | 0.920117i | \(0.628094\pi\) | |||||||
\(740\) | 13.9983 | 0.514589 | ||||||||
\(741\) | −33.5426 | −1.23222 | ||||||||
\(742\) | 112.199 | 4.11896 | ||||||||
\(743\) | −29.2966 | −1.07479 | −0.537394 | − | 0.843331i | \(-0.680591\pi\) | ||||
−0.537394 | + | 0.843331i | \(0.680591\pi\) | |||||||
\(744\) | 20.2539 | 0.742545 | ||||||||
\(745\) | 7.63808 | 0.279838 | ||||||||
\(746\) | 51.9707 | 1.90278 | ||||||||
\(747\) | −9.02318 | −0.330141 | ||||||||
\(748\) | −160.712 | −5.87621 | ||||||||
\(749\) | −36.2714 | −1.32533 | ||||||||
\(750\) | −21.8614 | −0.798266 | ||||||||
\(751\) | −13.5655 | −0.495011 | −0.247505 | − | 0.968887i | \(-0.579611\pi\) | ||||
−0.247505 | + | 0.968887i | \(0.579611\pi\) | |||||||
\(752\) | 0.738675 | 0.0269367 | ||||||||
\(753\) | −51.3512 | −1.87134 | ||||||||
\(754\) | 6.37419 | 0.232134 | ||||||||
\(755\) | −5.81651 | −0.211685 | ||||||||
\(756\) | −45.9467 | −1.67107 | ||||||||
\(757\) | 14.8883 | 0.541125 | 0.270563 | − | 0.962702i | \(-0.412790\pi\) | ||||
0.270563 | + | 0.962702i | \(0.412790\pi\) | |||||||
\(758\) | −4.79064 | −0.174004 | ||||||||
\(759\) | −44.8194 | −1.62684 | ||||||||
\(760\) | 12.8263 | 0.465258 | ||||||||
\(761\) | −20.8990 | −0.757589 | −0.378795 | − | 0.925481i | \(-0.623661\pi\) | ||||
−0.378795 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(762\) | −33.5337 | −1.21480 | ||||||||
\(763\) | −41.2087 | −1.49186 | ||||||||
\(764\) | −63.9317 | −2.31297 | ||||||||
\(765\) | −4.98189 | −0.180121 | ||||||||
\(766\) | 13.9857 | 0.505323 | ||||||||
\(767\) | −26.2421 | −0.947546 | ||||||||
\(768\) | 54.3772 | 1.96217 | ||||||||
\(769\) | −28.2988 | −1.02048 | −0.510241 | − | 0.860031i | \(-0.670444\pi\) | ||||
−0.510241 | + | 0.860031i | \(0.670444\pi\) | |||||||
\(770\) | 25.9616 | 0.935592 | ||||||||
\(771\) | 4.86249 | 0.175118 | ||||||||
\(772\) | −14.9348 | −0.537517 | ||||||||
\(773\) | −29.1467 | −1.04833 | −0.524166 | − | 0.851616i | \(-0.675623\pi\) | ||||
−0.524166 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(774\) | 45.6204 | 1.63979 | ||||||||
\(775\) | −12.0836 | −0.434056 | ||||||||
\(776\) | −49.0486 | −1.76074 | ||||||||
\(777\) | 76.2999 | 2.73724 | ||||||||
\(778\) | 77.0976 | 2.76408 | ||||||||
\(779\) | −12.7643 | −0.457330 | ||||||||
\(780\) | 6.98026 | 0.249933 | ||||||||
\(781\) | −6.07255 | −0.217293 | ||||||||
\(782\) | 60.3401 | 2.15776 | ||||||||
\(783\) | 4.09496 | 0.146342 | ||||||||
\(784\) | 16.9306 | 0.604663 | ||||||||
\(785\) | −6.00940 | −0.214485 | ||||||||
\(786\) | 45.9269 | 1.63816 | ||||||||
\(787\) | 17.5048 | 0.623978 | 0.311989 | − | 0.950086i | \(-0.399005\pi\) | ||||
0.311989 | + | 0.950086i | \(0.399005\pi\) | |||||||
\(788\) | 68.8137 | 2.45139 | ||||||||
\(789\) | 13.5609 | 0.482780 | ||||||||
\(790\) | −6.49535 | −0.231094 | ||||||||
\(791\) | 4.08071 | 0.145093 | ||||||||
\(792\) | −35.1509 | −1.24903 | ||||||||
\(793\) | 6.86718 | 0.243861 | ||||||||
\(794\) | 18.9264 | 0.671672 | ||||||||
\(795\) | −10.9504 | −0.388372 | ||||||||
\(796\) | 31.4506 | 1.11474 | ||||||||
\(797\) | 11.2022 | 0.396801 | 0.198401 | − | 0.980121i | \(-0.436425\pi\) | ||||
0.198401 | + | 0.980121i | \(0.436425\pi\) | |||||||
\(798\) | 157.363 | 5.57059 | ||||||||
\(799\) | −3.09686 | −0.109559 | ||||||||
\(800\) | −16.4101 | −0.580185 | ||||||||
\(801\) | 15.7974 | 0.558173 | ||||||||
\(802\) | 41.6242 | 1.46980 | ||||||||
\(803\) | −50.7896 | −1.79233 | ||||||||
\(804\) | 78.6512 | 2.77381 | ||||||||
\(805\) | −6.26548 | −0.220829 | ||||||||
\(806\) | 12.2497 | 0.431479 | ||||||||
\(807\) | 31.2324 | 1.09943 | ||||||||
\(808\) | 50.2469 | 1.76768 | ||||||||
\(809\) | 28.3606 | 0.997106 | 0.498553 | − | 0.866859i | \(-0.333865\pi\) | ||||
0.498553 | + | 0.866859i | \(0.333865\pi\) | |||||||
\(810\) | 11.7854 | 0.414095 | ||||||||
\(811\) | 43.2481 | 1.51865 | 0.759323 | − | 0.650714i | \(-0.225530\pi\) | ||||
0.759323 | + | 0.650714i | \(0.225530\pi\) | |||||||
\(812\) | −19.2219 | −0.674557 | ||||||||
\(813\) | 9.81859 | 0.344353 | ||||||||
\(814\) | −126.228 | −4.42430 | ||||||||
\(815\) | 5.58006 | 0.195461 | ||||||||
\(816\) | 27.4543 | 0.961091 | ||||||||
\(817\) | 96.4871 | 3.37566 | ||||||||
\(818\) | 29.8892 | 1.04505 | ||||||||
\(819\) | 12.8505 | 0.449034 | ||||||||
\(820\) | 2.65628 | 0.0927612 | ||||||||
\(821\) | −41.6063 | −1.45207 | −0.726036 | − | 0.687657i | \(-0.758639\pi\) | ||||
−0.726036 | + | 0.687657i | \(0.758639\pi\) | |||||||
\(822\) | 25.8317 | 0.900983 | ||||||||
\(823\) | 17.8613 | 0.622606 | 0.311303 | − | 0.950311i | \(-0.399235\pi\) | ||||
0.311303 | + | 0.950311i | \(0.399235\pi\) | |||||||
\(824\) | 30.4976 | 1.06243 | ||||||||
\(825\) | 62.0900 | 2.16170 | ||||||||
\(826\) | 123.113 | 4.28365 | ||||||||
\(827\) | −36.9493 | −1.28485 | −0.642427 | − | 0.766347i | \(-0.722072\pi\) | ||||
−0.642427 | + | 0.766347i | \(0.722072\pi\) | |||||||
\(828\) | 19.0947 | 0.663588 | ||||||||
\(829\) | −2.88194 | −0.100094 | −0.0500469 | − | 0.998747i | \(-0.515937\pi\) | ||||
−0.0500469 | + | 0.998747i | \(0.515937\pi\) | |||||||
\(830\) | 6.17844 | 0.214457 | ||||||||
\(831\) | −67.3822 | −2.33746 | ||||||||
\(832\) | 23.8560 | 0.827059 | ||||||||
\(833\) | −70.9805 | −2.45933 | ||||||||
\(834\) | 15.9168 | 0.551153 | ||||||||
\(835\) | 0.341678 | 0.0118242 | ||||||||
\(836\) | −167.340 | −5.78759 | ||||||||
\(837\) | 7.86958 | 0.272012 | ||||||||
\(838\) | −22.7961 | −0.787478 | ||||||||
\(839\) | −50.3066 | −1.73678 | −0.868388 | − | 0.495885i | \(-0.834844\pi\) | ||||
−0.868388 | + | 0.495885i | \(0.834844\pi\) | |||||||
\(840\) | −14.5486 | −0.501976 | ||||||||
\(841\) | −27.2869 | −0.940926 | ||||||||
\(842\) | −40.6441 | −1.40069 | ||||||||
\(843\) | −10.2283 | −0.352280 | ||||||||
\(844\) | 34.2036 | 1.17734 | ||||||||
\(845\) | −3.88040 | −0.133490 | ||||||||
\(846\) | −1.52463 | −0.0524178 | ||||||||
\(847\) | −105.592 | −3.62818 | ||||||||
\(848\) | 20.3821 | 0.699925 | ||||||||
\(849\) | 43.4180 | 1.49010 | ||||||||
\(850\) | −83.5914 | −2.86716 | ||||||||
\(851\) | 30.4635 | 1.04428 | ||||||||
\(852\) | 7.65978 | 0.262420 | ||||||||
\(853\) | 1.14137 | 0.0390797 | 0.0195399 | − | 0.999809i | \(-0.493780\pi\) | ||||
0.0195399 | + | 0.999809i | \(0.493780\pi\) | |||||||
\(854\) | −32.2169 | −1.10244 | ||||||||
\(855\) | −5.18737 | −0.177404 | ||||||||
\(856\) | −33.6270 | −1.14935 | ||||||||
\(857\) | 22.3373 | 0.763028 | 0.381514 | − | 0.924363i | \(-0.375403\pi\) | ||||
0.381514 | + | 0.924363i | \(0.375403\pi\) | |||||||
\(858\) | −62.9436 | −2.14886 | ||||||||
\(859\) | −46.2928 | −1.57949 | −0.789745 | − | 0.613435i | \(-0.789787\pi\) | ||||
−0.789745 | + | 0.613435i | \(0.789787\pi\) | |||||||
\(860\) | −20.0791 | −0.684691 | ||||||||
\(861\) | 14.4784 | 0.493422 | ||||||||
\(862\) | −25.7123 | −0.875766 | ||||||||
\(863\) | 30.6372 | 1.04290 | 0.521451 | − | 0.853281i | \(-0.325391\pi\) | ||||
0.521451 | + | 0.853281i | \(0.325391\pi\) | |||||||
\(864\) | 10.6873 | 0.363588 | ||||||||
\(865\) | −5.57209 | −0.189457 | ||||||||
\(866\) | −34.6261 | −1.17664 | ||||||||
\(867\) | −78.9178 | −2.68019 | ||||||||
\(868\) | −36.9401 | −1.25383 | ||||||||
\(869\) | 37.6485 | 1.27714 | ||||||||
\(870\) | 2.91859 | 0.0989494 | ||||||||
\(871\) | 21.1334 | 0.716077 | ||||||||
\(872\) | −38.2044 | −1.29376 | ||||||||
\(873\) | 19.8369 | 0.671376 | ||||||||
\(874\) | 62.8287 | 2.12521 | ||||||||
\(875\) | 17.7138 | 0.598837 | ||||||||
\(876\) | 64.0649 | 2.16455 | ||||||||
\(877\) | 30.4664 | 1.02878 | 0.514388 | − | 0.857558i | \(-0.328019\pi\) | ||||
0.514388 | + | 0.857558i | \(0.328019\pi\) | |||||||
\(878\) | −41.8934 | −1.41383 | ||||||||
\(879\) | −27.6061 | −0.931131 | ||||||||
\(880\) | 4.71619 | 0.158983 | ||||||||
\(881\) | 39.1199 | 1.31798 | 0.658991 | − | 0.752151i | \(-0.270983\pi\) | ||||
0.658991 | + | 0.752151i | \(0.270983\pi\) | |||||||
\(882\) | −34.9448 | −1.17665 | ||||||||
\(883\) | −49.0245 | −1.64981 | −0.824903 | − | 0.565275i | \(-0.808770\pi\) | ||||
−0.824903 | + | 0.565275i | \(0.808770\pi\) | |||||||
\(884\) | 54.4700 | 1.83202 | ||||||||
\(885\) | −12.0156 | −0.403900 | ||||||||
\(886\) | −39.6652 | −1.33258 | ||||||||
\(887\) | −2.47273 | −0.0830260 | −0.0415130 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415130 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(888\) | 70.7372 | 2.37378 | ||||||||
\(889\) | 27.1717 | 0.911309 | ||||||||
\(890\) | −10.8169 | −0.362584 | ||||||||
\(891\) | −68.3107 | −2.28849 | ||||||||
\(892\) | 81.4934 | 2.72860 | ||||||||
\(893\) | −3.22458 | −0.107907 | ||||||||
\(894\) | 86.8781 | 2.90564 | ||||||||
\(895\) | 1.31712 | 0.0440265 | ||||||||
\(896\) | −84.0400 | −2.80758 | ||||||||
\(897\) | 15.1906 | 0.507199 | ||||||||
\(898\) | −32.0224 | −1.06860 | ||||||||
\(899\) | 3.29226 | 0.109803 | ||||||||
\(900\) | −26.4527 | −0.881756 | ||||||||
\(901\) | −85.4510 | −2.84679 | ||||||||
\(902\) | −23.9526 | −0.797536 | ||||||||
\(903\) | −109.444 | −3.64206 | ||||||||
\(904\) | 3.78320 | 0.125827 | ||||||||
\(905\) | −6.37506 | −0.211914 | ||||||||
\(906\) | −66.1589 | −2.19798 | ||||||||
\(907\) | −8.09294 | −0.268722 | −0.134361 | − | 0.990932i | \(-0.542898\pi\) | ||||
−0.134361 | + | 0.990932i | \(0.542898\pi\) | |||||||
\(908\) | 84.3351 | 2.79876 | ||||||||
\(909\) | −20.3215 | −0.674022 | ||||||||
\(910\) | −8.79915 | −0.291689 | ||||||||
\(911\) | 40.8838 | 1.35454 | 0.677271 | − | 0.735734i | \(-0.263162\pi\) | ||||
0.677271 | + | 0.735734i | \(0.263162\pi\) | |||||||
\(912\) | 28.5866 | 0.946596 | ||||||||
\(913\) | −35.8117 | −1.18519 | ||||||||
\(914\) | 89.6929 | 2.96678 | ||||||||
\(915\) | 3.14431 | 0.103948 | ||||||||
\(916\) | −37.6084 | −1.24262 | ||||||||
\(917\) | −37.2136 | −1.22890 | ||||||||
\(918\) | 54.4398 | 1.79678 | ||||||||
\(919\) | 8.89358 | 0.293372 | 0.146686 | − | 0.989183i | \(-0.453139\pi\) | ||||
0.146686 | + | 0.989183i | \(0.453139\pi\) | |||||||
\(920\) | −5.80869 | −0.191507 | ||||||||
\(921\) | −44.5945 | −1.46944 | ||||||||
\(922\) | 1.78242 | 0.0587010 | ||||||||
\(923\) | 2.05816 | 0.0677452 | ||||||||
\(924\) | 189.812 | 6.24435 | ||||||||
\(925\) | −42.2023 | −1.38760 | ||||||||
\(926\) | −66.2230 | −2.17622 | ||||||||
\(927\) | −12.3342 | −0.405109 | ||||||||
\(928\) | 4.47104 | 0.146769 | ||||||||
\(929\) | −40.2545 | −1.32071 | −0.660354 | − | 0.750955i | \(-0.729594\pi\) | ||||
−0.660354 | + | 0.750955i | \(0.729594\pi\) | |||||||
\(930\) | 5.60886 | 0.183922 | ||||||||
\(931\) | −73.9081 | −2.42224 | ||||||||
\(932\) | −2.26065 | −0.0740501 | ||||||||
\(933\) | 4.96741 | 0.162626 | ||||||||
\(934\) | −83.1752 | −2.72158 | ||||||||
\(935\) | −19.7724 | −0.646626 | ||||||||
\(936\) | 11.9137 | 0.389410 | ||||||||
\(937\) | −39.6863 | −1.29650 | −0.648248 | − | 0.761430i | \(-0.724498\pi\) | ||||
−0.648248 | + | 0.761430i | \(0.724498\pi\) | |||||||
\(938\) | −99.1459 | −3.23723 | ||||||||
\(939\) | 46.0305 | 1.50215 | ||||||||
\(940\) | 0.671040 | 0.0218869 | ||||||||
\(941\) | 34.2656 | 1.11703 | 0.558514 | − | 0.829495i | \(-0.311372\pi\) | ||||
0.558514 | + | 0.829495i | \(0.311372\pi\) | |||||||
\(942\) | −68.3529 | −2.22706 | ||||||||
\(943\) | 5.78064 | 0.188244 | ||||||||
\(944\) | 22.3647 | 0.727910 | ||||||||
\(945\) | −5.65282 | −0.183886 | ||||||||
\(946\) | 181.061 | 5.88679 | ||||||||
\(947\) | −36.4741 | −1.18525 | −0.592625 | − | 0.805478i | \(-0.701908\pi\) | ||||
−0.592625 | + | 0.805478i | \(0.701908\pi\) | |||||||
\(948\) | −47.4890 | −1.54237 | ||||||||
\(949\) | 17.2141 | 0.558793 | ||||||||
\(950\) | −87.0391 | −2.82392 | ||||||||
\(951\) | 71.3987 | 2.31526 | ||||||||
\(952\) | −113.529 | −3.67951 | ||||||||
\(953\) | −12.0291 | −0.389660 | −0.194830 | − | 0.980837i | \(-0.562415\pi\) | ||||
−0.194830 | + | 0.980837i | \(0.562415\pi\) | |||||||
\(954\) | −42.0688 | −1.36203 | ||||||||
\(955\) | −7.86551 | −0.254522 | ||||||||
\(956\) | 45.2593 | 1.46379 | ||||||||
\(957\) | −16.9168 | −0.546843 | ||||||||
\(958\) | 11.1465 | 0.360126 | ||||||||
\(959\) | −20.9309 | −0.675893 | ||||||||
\(960\) | 10.9231 | 0.352541 | ||||||||
\(961\) | −24.6730 | −0.795904 | ||||||||
\(962\) | 42.7825 | 1.37936 | ||||||||
\(963\) | 13.5999 | 0.438250 | ||||||||
\(964\) | 45.5055 | 1.46563 | ||||||||
\(965\) | −1.83743 | −0.0591490 | ||||||||
\(966\) | −71.2657 | −2.29293 | ||||||||
\(967\) | −13.0230 | −0.418790 | −0.209395 | − | 0.977831i | \(-0.567150\pi\) | ||||
−0.209395 | + | 0.977831i | \(0.567150\pi\) | |||||||
\(968\) | −97.8935 | −3.14642 | ||||||||
\(969\) | −119.848 | −3.85006 | ||||||||
\(970\) | −13.5829 | −0.436120 | ||||||||
\(971\) | 8.32769 | 0.267248 | 0.133624 | − | 0.991032i | \(-0.457338\pi\) | ||||
0.133624 | + | 0.991032i | \(0.457338\pi\) | |||||||
\(972\) | 52.3872 | 1.68032 | ||||||||
\(973\) | −12.8970 | −0.413460 | ||||||||
\(974\) | −95.7100 | −3.06674 | ||||||||
\(975\) | −21.0441 | −0.673950 | ||||||||
\(976\) | −5.85254 | −0.187335 | ||||||||
\(977\) | 21.2680 | 0.680424 | 0.340212 | − | 0.940349i | \(-0.389501\pi\) | ||||
0.340212 | + | 0.940349i | \(0.389501\pi\) | |||||||
\(978\) | 63.4695 | 2.02953 | ||||||||
\(979\) | 62.6974 | 2.00382 | ||||||||
\(980\) | 15.3804 | 0.491308 | ||||||||
\(981\) | 15.4511 | 0.493316 | ||||||||
\(982\) | 44.5295 | 1.42099 | ||||||||
\(983\) | −36.4184 | −1.16157 | −0.580783 | − | 0.814058i | \(-0.697253\pi\) | ||||
−0.580783 | + | 0.814058i | \(0.697253\pi\) | |||||||
\(984\) | 13.4228 | 0.427904 | ||||||||
\(985\) | 8.46614 | 0.269754 | ||||||||
\(986\) | 22.7750 | 0.725304 | ||||||||
\(987\) | 3.65759 | 0.116423 | ||||||||
\(988\) | 56.7165 | 1.80439 | ||||||||
\(989\) | −43.6965 | −1.38947 | ||||||||
\(990\) | −9.73424 | −0.309375 | ||||||||
\(991\) | −9.99182 | −0.317401 | −0.158700 | − | 0.987327i | \(-0.550730\pi\) | ||||
−0.158700 | + | 0.987327i | \(0.550730\pi\) | |||||||
\(992\) | 8.59232 | 0.272806 | ||||||||
\(993\) | −74.9366 | −2.37804 | ||||||||
\(994\) | −9.65574 | −0.306261 | ||||||||
\(995\) | 3.86937 | 0.122667 | ||||||||
\(996\) | 45.1721 | 1.43133 | ||||||||
\(997\) | −7.06723 | −0.223821 | −0.111911 | − | 0.993718i | \(-0.535697\pi\) | ||||
−0.111911 | + | 0.993718i | \(0.535697\pi\) | |||||||
\(998\) | 92.3505 | 2.92330 | ||||||||
\(999\) | 27.4846 | 0.869576 |
(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 | 8023.2.a.c.1.20 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.20 | ✓ | 158 | 1.1 | even | 1 | trivial |