Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39066 | −1.69045 | −0.845226 | − | 0.534409i | \(-0.820534\pi\) | ||||
−0.845226 | + | 0.534409i | \(0.820534\pi\) | |||||||
\(3\) | −3.44347 | −1.98809 | −0.994045 | − | 0.108970i | \(-0.965245\pi\) | ||||
−0.994045 | + | 0.108970i | \(0.965245\pi\) | |||||||
\(4\) | 3.71525 | 1.85763 | ||||||||
\(5\) | −1.21628 | −0.543937 | −0.271969 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271969 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(6\) | 8.23217 | 3.36077 | ||||||||
\(7\) | −4.84430 | −1.83097 | −0.915487 | − | 0.402349i | \(-0.868194\pi\) | ||||
−0.915487 | + | 0.402349i | \(0.868194\pi\) | |||||||
\(8\) | −4.10059 | −1.44978 | ||||||||
\(9\) | 8.85751 | 2.95250 | ||||||||
\(10\) | 2.90771 | 0.919499 | ||||||||
\(11\) | −0.135468 | −0.0408453 | −0.0204226 | − | 0.999791i | \(-0.506501\pi\) | ||||
−0.0204226 | + | 0.999791i | \(0.506501\pi\) | |||||||
\(12\) | −12.7934 | −3.69313 | ||||||||
\(13\) | −2.82151 | −0.782546 | −0.391273 | − | 0.920275i | \(-0.627965\pi\) | ||||
−0.391273 | + | 0.920275i | \(0.627965\pi\) | |||||||
\(14\) | 11.5811 | 3.09517 | ||||||||
\(15\) | 4.18823 | 1.08140 | ||||||||
\(16\) | 2.37260 | 0.593149 | ||||||||
\(17\) | −1.47149 | −0.356889 | −0.178445 | − | 0.983950i | \(-0.557107\pi\) | ||||
−0.178445 | + | 0.983950i | \(0.557107\pi\) | |||||||
\(18\) | −21.1753 | −4.99106 | ||||||||
\(19\) | 2.49646 | 0.572726 | 0.286363 | − | 0.958121i | \(-0.407554\pi\) | ||||
0.286363 | + | 0.958121i | \(0.407554\pi\) | |||||||
\(20\) | −4.51879 | −1.01043 | ||||||||
\(21\) | 16.6812 | 3.64014 | ||||||||
\(22\) | 0.323859 | 0.0690470 | ||||||||
\(23\) | 2.68073 | 0.558971 | 0.279485 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279485 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(24\) | 14.1203 | 2.88228 | ||||||||
\(25\) | −3.52066 | −0.704132 | ||||||||
\(26\) | 6.74527 | 1.32286 | ||||||||
\(27\) | −20.1702 | −3.88175 | ||||||||
\(28\) | −17.9978 | −3.40126 | ||||||||
\(29\) | −9.84315 | −1.82783 | −0.913913 | − | 0.405909i | \(-0.866955\pi\) | ||||
−0.913913 | + | 0.405909i | \(0.866955\pi\) | |||||||
\(30\) | −10.0126 | −1.82805 | ||||||||
\(31\) | 2.01105 | 0.361195 | 0.180597 | − | 0.983557i | \(-0.442197\pi\) | ||||
0.180597 | + | 0.983557i | \(0.442197\pi\) | |||||||
\(32\) | 2.52910 | 0.447085 | ||||||||
\(33\) | 0.466482 | 0.0812041 | ||||||||
\(34\) | 3.51784 | 0.603304 | ||||||||
\(35\) | 5.89203 | 0.995934 | ||||||||
\(36\) | 32.9079 | 5.48465 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −5.96818 | −0.968166 | ||||||||
\(39\) | 9.71580 | 1.55577 | ||||||||
\(40\) | 4.98746 | 0.788587 | ||||||||
\(41\) | 3.23832 | 0.505741 | 0.252870 | − | 0.967500i | \(-0.418625\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418625\pi\) | |||||||
\(42\) | −39.8791 | −6.15348 | ||||||||
\(43\) | 9.12887 | 1.39214 | 0.696069 | − | 0.717974i | \(-0.254931\pi\) | ||||
0.696069 | + | 0.717974i | \(0.254931\pi\) | |||||||
\(44\) | −0.503300 | −0.0758753 | ||||||||
\(45\) | −10.7732 | −1.60598 | ||||||||
\(46\) | −6.40871 | −0.944913 | ||||||||
\(47\) | −0.500209 | −0.0729629 | −0.0364815 | − | 0.999334i | \(-0.511615\pi\) | ||||
−0.0364815 | + | 0.999334i | \(0.511615\pi\) | |||||||
\(48\) | −8.16998 | −1.17923 | ||||||||
\(49\) | 16.4672 | 2.35246 | ||||||||
\(50\) | 8.41670 | 1.19030 | ||||||||
\(51\) | 5.06704 | 0.709528 | ||||||||
\(52\) | −10.4826 | −1.45368 | ||||||||
\(53\) | −0.367546 | −0.0504863 | −0.0252431 | − | 0.999681i | \(-0.508036\pi\) | ||||
−0.0252431 | + | 0.999681i | \(0.508036\pi\) | |||||||
\(54\) | 48.2200 | 6.56191 | ||||||||
\(55\) | 0.164768 | 0.0222173 | ||||||||
\(56\) | 19.8645 | 2.65450 | ||||||||
\(57\) | −8.59648 | −1.13863 | ||||||||
\(58\) | 23.5316 | 3.08985 | ||||||||
\(59\) | −3.17992 | −0.413990 | −0.206995 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206995 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(60\) | 15.5603 | 2.00883 | ||||||||
\(61\) | 4.45697 | 0.570657 | 0.285328 | − | 0.958430i | \(-0.407897\pi\) | ||||
0.285328 | + | 0.958430i | \(0.407897\pi\) | |||||||
\(62\) | −4.80773 | −0.610582 | ||||||||
\(63\) | −42.9084 | −5.40595 | ||||||||
\(64\) | −10.7914 | −1.34893 | ||||||||
\(65\) | 3.43175 | 0.425656 | ||||||||
\(66\) | −1.11520 | −0.137272 | ||||||||
\(67\) | −5.70935 | −0.697508 | −0.348754 | − | 0.937214i | \(-0.613395\pi\) | ||||
−0.348754 | + | 0.937214i | \(0.613395\pi\) | |||||||
\(68\) | −5.46696 | −0.662967 | ||||||||
\(69\) | −9.23102 | −1.11128 | ||||||||
\(70\) | −14.0858 | −1.68358 | ||||||||
\(71\) | −10.2470 | −1.21610 | −0.608050 | − | 0.793899i | \(-0.708048\pi\) | ||||
−0.608050 | + | 0.793899i | \(0.708048\pi\) | |||||||
\(72\) | −36.3210 | −4.28047 | ||||||||
\(73\) | 11.3144 | 1.32425 | 0.662126 | − | 0.749393i | \(-0.269654\pi\) | ||||
0.662126 | + | 0.749393i | \(0.269654\pi\) | |||||||
\(74\) | −2.39066 | −0.277909 | ||||||||
\(75\) | 12.1233 | 1.39988 | ||||||||
\(76\) | 9.27497 | 1.06391 | ||||||||
\(77\) | 0.656250 | 0.0747866 | ||||||||
\(78\) | −23.2272 | −2.62996 | ||||||||
\(79\) | −14.1824 | −1.59564 | −0.797821 | − | 0.602894i | \(-0.794014\pi\) | ||||
−0.797821 | + | 0.602894i | \(0.794014\pi\) | |||||||
\(80\) | −2.88574 | −0.322636 | ||||||||
\(81\) | 42.8829 | 4.76476 | ||||||||
\(82\) | −7.74172 | −0.854930 | ||||||||
\(83\) | −1.22978 | −0.134986 | −0.0674931 | − | 0.997720i | \(-0.521500\pi\) | ||||
−0.0674931 | + | 0.997720i | \(0.521500\pi\) | |||||||
\(84\) | 61.9749 | 6.76202 | ||||||||
\(85\) | 1.78975 | 0.194125 | ||||||||
\(86\) | −21.8240 | −2.35334 | ||||||||
\(87\) | 33.8946 | 3.63388 | ||||||||
\(88\) | 0.555500 | 0.0592165 | ||||||||
\(89\) | 14.6789 | 1.55596 | 0.777979 | − | 0.628290i | \(-0.216245\pi\) | ||||
0.777979 | + | 0.628290i | \(0.216245\pi\) | |||||||
\(90\) | 25.7551 | 2.71482 | ||||||||
\(91\) | 13.6682 | 1.43282 | ||||||||
\(92\) | 9.95959 | 1.03836 | ||||||||
\(93\) | −6.92498 | −0.718087 | ||||||||
\(94\) | 1.19583 | 0.123340 | ||||||||
\(95\) | −3.03639 | −0.311527 | ||||||||
\(96\) | −8.70888 | −0.888846 | ||||||||
\(97\) | −18.6249 | −1.89107 | −0.945535 | − | 0.325521i | \(-0.894460\pi\) | ||||
−0.945535 | + | 0.325521i | \(0.894460\pi\) | |||||||
\(98\) | −39.3676 | −3.97672 | ||||||||
\(99\) | −1.19991 | −0.120596 | ||||||||
\(100\) | −13.0801 | −1.30801 | ||||||||
\(101\) | 8.84752 | 0.880361 | 0.440180 | − | 0.897909i | \(-0.354914\pi\) | ||||
0.440180 | + | 0.897909i | \(0.354914\pi\) | |||||||
\(102\) | −12.1136 | −1.19942 | ||||||||
\(103\) | −14.8523 | −1.46344 | −0.731722 | − | 0.681603i | \(-0.761283\pi\) | ||||
−0.731722 | + | 0.681603i | \(0.761283\pi\) | |||||||
\(104\) | 11.5698 | 1.13452 | ||||||||
\(105\) | −20.2890 | −1.98001 | ||||||||
\(106\) | 0.878676 | 0.0853446 | ||||||||
\(107\) | −16.7233 | −1.61670 | −0.808349 | − | 0.588704i | \(-0.799638\pi\) | ||||
−0.808349 | + | 0.588704i | \(0.799638\pi\) | |||||||
\(108\) | −74.9372 | −7.21084 | ||||||||
\(109\) | 2.43512 | 0.233242 | 0.116621 | − | 0.993176i | \(-0.462794\pi\) | ||||
0.116621 | + | 0.993176i | \(0.462794\pi\) | |||||||
\(110\) | −0.393903 | −0.0375572 | ||||||||
\(111\) | −3.44347 | −0.326840 | ||||||||
\(112\) | −11.4936 | −1.08604 | ||||||||
\(113\) | 2.09540 | 0.197119 | 0.0985593 | − | 0.995131i | \(-0.468577\pi\) | ||||
0.0985593 | + | 0.995131i | \(0.468577\pi\) | |||||||
\(114\) | 20.5513 | 1.92480 | ||||||||
\(115\) | −3.26052 | −0.304045 | ||||||||
\(116\) | −36.5698 | −3.39542 | ||||||||
\(117\) | −24.9916 | −2.31047 | ||||||||
\(118\) | 7.60210 | 0.699830 | ||||||||
\(119\) | 7.12835 | 0.653454 | ||||||||
\(120\) | −17.1742 | −1.56778 | ||||||||
\(121\) | −10.9816 | −0.998332 | ||||||||
\(122\) | −10.6551 | −0.964667 | ||||||||
\(123\) | −11.1511 | −1.00546 | ||||||||
\(124\) | 7.47154 | 0.670964 | ||||||||
\(125\) | 10.3635 | 0.926941 | ||||||||
\(126\) | 102.579 | 9.13850 | ||||||||
\(127\) | 8.66784 | 0.769147 | 0.384573 | − | 0.923094i | \(-0.374349\pi\) | ||||
0.384573 | + | 0.923094i | \(0.374349\pi\) | |||||||
\(128\) | 20.7404 | 1.83321 | ||||||||
\(129\) | −31.4350 | −2.76770 | ||||||||
\(130\) | −8.20414 | −0.719551 | ||||||||
\(131\) | 14.4173 | 1.25964 | 0.629821 | − | 0.776740i | \(-0.283128\pi\) | ||||
0.629821 | + | 0.776740i | \(0.283128\pi\) | |||||||
\(132\) | 1.73310 | 0.150847 | ||||||||
\(133\) | −12.0936 | −1.04865 | ||||||||
\(134\) | 13.6491 | 1.17910 | ||||||||
\(135\) | 24.5326 | 2.11143 | ||||||||
\(136\) | 6.03398 | 0.517409 | ||||||||
\(137\) | 16.4247 | 1.40326 | 0.701630 | − | 0.712542i | \(-0.252456\pi\) | ||||
0.701630 | + | 0.712542i | \(0.252456\pi\) | |||||||
\(138\) | 22.0682 | 1.87857 | ||||||||
\(139\) | −8.16156 | −0.692255 | −0.346127 | − | 0.938188i | \(-0.612503\pi\) | ||||
−0.346127 | + | 0.938188i | \(0.612503\pi\) | |||||||
\(140\) | 21.8904 | 1.85007 | ||||||||
\(141\) | 1.72245 | 0.145057 | ||||||||
\(142\) | 24.4972 | 2.05576 | ||||||||
\(143\) | 0.382226 | 0.0319633 | ||||||||
\(144\) | 21.0153 | 1.75127 | ||||||||
\(145\) | 11.9720 | 0.994223 | ||||||||
\(146\) | −27.0489 | −2.23858 | ||||||||
\(147\) | −56.7045 | −4.67691 | ||||||||
\(148\) | 3.71525 | 0.305392 | ||||||||
\(149\) | −4.82510 | −0.395288 | −0.197644 | − | 0.980274i | \(-0.563329\pi\) | ||||
−0.197644 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(150\) | −28.9827 | −2.36643 | ||||||||
\(151\) | −1.38176 | −0.112446 | −0.0562232 | − | 0.998418i | \(-0.517906\pi\) | ||||
−0.0562232 | + | 0.998418i | \(0.517906\pi\) | |||||||
\(152\) | −10.2369 | −0.830325 | ||||||||
\(153\) | −13.0337 | −1.05372 | ||||||||
\(154\) | −1.56887 | −0.126423 | ||||||||
\(155\) | −2.44600 | −0.196467 | ||||||||
\(156\) | 36.0966 | 2.89004 | ||||||||
\(157\) | 3.19329 | 0.254852 | 0.127426 | − | 0.991848i | \(-0.459328\pi\) | ||||
0.127426 | + | 0.991848i | \(0.459328\pi\) | |||||||
\(158\) | 33.9053 | 2.69736 | ||||||||
\(159\) | 1.26563 | 0.100371 | ||||||||
\(160\) | −3.07609 | −0.243186 | ||||||||
\(161\) | −12.9863 | −1.02346 | ||||||||
\(162\) | −102.518 | −8.05460 | ||||||||
\(163\) | −1.00000 | −0.0783260 | ||||||||
\(164\) | 12.0312 | 0.939478 | ||||||||
\(165\) | −0.567373 | −0.0441699 | ||||||||
\(166\) | 2.93999 | 0.228188 | ||||||||
\(167\) | −3.16645 | −0.245028 | −0.122514 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122514 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(168\) | −68.4027 | −5.27739 | ||||||||
\(169\) | −5.03907 | −0.387621 | ||||||||
\(170\) | −4.27867 | −0.328159 | ||||||||
\(171\) | 22.1124 | 1.69098 | ||||||||
\(172\) | 33.9160 | 2.58607 | ||||||||
\(173\) | −18.5326 | −1.40901 | −0.704503 | − | 0.709701i | \(-0.748830\pi\) | ||||
−0.704503 | + | 0.709701i | \(0.748830\pi\) | |||||||
\(174\) | −81.0305 | −6.14290 | ||||||||
\(175\) | 17.0551 | 1.28925 | ||||||||
\(176\) | −0.321412 | −0.0242274 | ||||||||
\(177\) | 10.9500 | 0.823050 | ||||||||
\(178\) | −35.0922 | −2.63027 | ||||||||
\(179\) | −21.6275 | −1.61652 | −0.808258 | − | 0.588829i | \(-0.799589\pi\) | ||||
−0.808258 | + | 0.588829i | \(0.799589\pi\) | |||||||
\(180\) | −40.0252 | −2.98330 | ||||||||
\(181\) | −8.83530 | −0.656722 | −0.328361 | − | 0.944552i | \(-0.606496\pi\) | ||||
−0.328361 | + | 0.944552i | \(0.606496\pi\) | |||||||
\(182\) | −32.6761 | −2.42212 | ||||||||
\(183\) | −15.3475 | −1.13452 | ||||||||
\(184\) | −10.9926 | −0.810382 | ||||||||
\(185\) | −1.21628 | −0.0894227 | ||||||||
\(186\) | 16.5553 | 1.21389 | ||||||||
\(187\) | 0.199341 | 0.0145772 | ||||||||
\(188\) | −1.85840 | −0.135538 | ||||||||
\(189\) | 97.7103 | 7.10738 | ||||||||
\(190\) | 7.25898 | 0.526622 | ||||||||
\(191\) | −9.98659 | −0.722604 | −0.361302 | − | 0.932449i | \(-0.617668\pi\) | ||||
−0.361302 | + | 0.932449i | \(0.617668\pi\) | |||||||
\(192\) | 37.1599 | 2.68179 | ||||||||
\(193\) | −10.4260 | −0.750479 | −0.375239 | − | 0.926928i | \(-0.622439\pi\) | ||||
−0.375239 | + | 0.926928i | \(0.622439\pi\) | |||||||
\(194\) | 44.5257 | 3.19676 | ||||||||
\(195\) | −11.8171 | −0.846243 | ||||||||
\(196\) | 61.1800 | 4.37000 | ||||||||
\(197\) | −5.41021 | −0.385462 | −0.192731 | − | 0.981252i | \(-0.561734\pi\) | ||||
−0.192731 | + | 0.981252i | \(0.561734\pi\) | |||||||
\(198\) | 2.86858 | 0.203861 | ||||||||
\(199\) | −25.5069 | −1.80813 | −0.904067 | − | 0.427390i | \(-0.859433\pi\) | ||||
−0.904067 | + | 0.427390i | \(0.859433\pi\) | |||||||
\(200\) | 14.4368 | 1.02083 | ||||||||
\(201\) | 19.6600 | 1.38671 | ||||||||
\(202\) | −21.1514 | −1.48821 | ||||||||
\(203\) | 47.6832 | 3.34670 | ||||||||
\(204\) | 18.8253 | 1.31804 | ||||||||
\(205\) | −3.93871 | −0.275091 | ||||||||
\(206\) | 35.5069 | 2.47388 | ||||||||
\(207\) | 23.7446 | 1.65036 | ||||||||
\(208\) | −6.69431 | −0.464167 | ||||||||
\(209\) | −0.338191 | −0.0233932 | ||||||||
\(210\) | 48.5042 | 3.34711 | ||||||||
\(211\) | −15.3996 | −1.06015 | −0.530075 | − | 0.847951i | \(-0.677836\pi\) | ||||
−0.530075 | + | 0.847951i | \(0.677836\pi\) | |||||||
\(212\) | −1.36552 | −0.0937846 | ||||||||
\(213\) | 35.2854 | 2.41772 | ||||||||
\(214\) | 39.9796 | 2.73295 | ||||||||
\(215\) | −11.1033 | −0.757236 | ||||||||
\(216\) | 82.7095 | 5.62767 | ||||||||
\(217\) | −9.74211 | −0.661337 | ||||||||
\(218\) | −5.82154 | −0.394284 | ||||||||
\(219\) | −38.9609 | −2.63273 | ||||||||
\(220\) | 0.612154 | 0.0412714 | ||||||||
\(221\) | 4.15183 | 0.279282 | ||||||||
\(222\) | 8.23217 | 0.552507 | ||||||||
\(223\) | −15.6357 | −1.04705 | −0.523523 | − | 0.852012i | \(-0.675382\pi\) | ||||
−0.523523 | + | 0.852012i | \(0.675382\pi\) | |||||||
\(224\) | −12.2517 | −0.818601 | ||||||||
\(225\) | −31.1843 | −2.07895 | ||||||||
\(226\) | −5.00939 | −0.333219 | ||||||||
\(227\) | −16.7705 | −1.11310 | −0.556550 | − | 0.830814i | \(-0.687875\pi\) | ||||
−0.556550 | + | 0.830814i | \(0.687875\pi\) | |||||||
\(228\) | −31.9381 | −2.11515 | ||||||||
\(229\) | −21.1078 | −1.39484 | −0.697420 | − | 0.716662i | \(-0.745669\pi\) | ||||
−0.697420 | + | 0.716662i | \(0.745669\pi\) | |||||||
\(230\) | 7.79479 | 0.513973 | ||||||||
\(231\) | −2.25978 | −0.148683 | ||||||||
\(232\) | 40.3627 | 2.64994 | ||||||||
\(233\) | −3.81406 | −0.249868 | −0.124934 | − | 0.992165i | \(-0.539872\pi\) | ||||
−0.124934 | + | 0.992165i | \(0.539872\pi\) | |||||||
\(234\) | 59.7463 | 3.90574 | ||||||||
\(235\) | 0.608394 | 0.0396873 | ||||||||
\(236\) | −11.8142 | −0.769039 | ||||||||
\(237\) | 48.8367 | 3.17228 | ||||||||
\(238\) | −17.0414 | −1.10463 | ||||||||
\(239\) | −15.0787 | −0.975357 | −0.487679 | − | 0.873023i | \(-0.662156\pi\) | ||||
−0.487679 | + | 0.873023i | \(0.662156\pi\) | |||||||
\(240\) | 9.93698 | 0.641430 | ||||||||
\(241\) | 29.5507 | 1.90353 | 0.951763 | − | 0.306833i | \(-0.0992694\pi\) | ||||
0.951763 | + | 0.306833i | \(0.0992694\pi\) | |||||||
\(242\) | 26.2534 | 1.68763 | ||||||||
\(243\) | −87.1556 | −5.59103 | ||||||||
\(244\) | 16.5588 | 1.06007 | ||||||||
\(245\) | −20.0288 | −1.27959 | ||||||||
\(246\) | 26.6584 | 1.69968 | ||||||||
\(247\) | −7.04378 | −0.448185 | ||||||||
\(248\) | −8.24647 | −0.523651 | ||||||||
\(249\) | 4.23472 | 0.268365 | ||||||||
\(250\) | −24.7756 | −1.56695 | ||||||||
\(251\) | 6.38933 | 0.403291 | 0.201645 | − | 0.979459i | \(-0.435371\pi\) | ||||
0.201645 | + | 0.979459i | \(0.435371\pi\) | |||||||
\(252\) | −159.416 | −10.0422 | ||||||||
\(253\) | −0.363154 | −0.0228313 | ||||||||
\(254\) | −20.7219 | −1.30021 | ||||||||
\(255\) | −6.16294 | −0.385939 | ||||||||
\(256\) | −28.0004 | −1.75002 | ||||||||
\(257\) | 8.97001 | 0.559534 | 0.279767 | − | 0.960068i | \(-0.409743\pi\) | ||||
0.279767 | + | 0.960068i | \(0.409743\pi\) | |||||||
\(258\) | 75.1504 | 4.67866 | ||||||||
\(259\) | −4.84430 | −0.301010 | ||||||||
\(260\) | 12.7498 | 0.790710 | ||||||||
\(261\) | −87.1857 | −5.39666 | ||||||||
\(262\) | −34.4668 | −2.12936 | ||||||||
\(263\) | −9.09313 | −0.560706 | −0.280353 | − | 0.959897i | \(-0.590452\pi\) | ||||
−0.280353 | + | 0.959897i | \(0.590452\pi\) | |||||||
\(264\) | −1.91285 | −0.117728 | ||||||||
\(265\) | 0.447038 | 0.0274614 | ||||||||
\(266\) | 28.9116 | 1.77269 | ||||||||
\(267\) | −50.5463 | −3.09338 | ||||||||
\(268\) | −21.2117 | −1.29571 | ||||||||
\(269\) | −21.9185 | −1.33639 | −0.668197 | − | 0.743984i | \(-0.732934\pi\) | ||||
−0.668197 | + | 0.743984i | \(0.732934\pi\) | |||||||
\(270\) | −58.6490 | −3.56927 | ||||||||
\(271\) | −4.44341 | −0.269918 | −0.134959 | − | 0.990851i | \(-0.543090\pi\) | ||||
−0.134959 | + | 0.990851i | \(0.543090\pi\) | |||||||
\(272\) | −3.49126 | −0.211689 | ||||||||
\(273\) | −47.0662 | −2.84858 | ||||||||
\(274\) | −39.2659 | −2.37214 | ||||||||
\(275\) | 0.476939 | 0.0287605 | ||||||||
\(276\) | −34.2956 | −2.06435 | ||||||||
\(277\) | −28.1067 | −1.68877 | −0.844384 | − | 0.535738i | \(-0.820034\pi\) | ||||
−0.844384 | + | 0.535738i | \(0.820034\pi\) | |||||||
\(278\) | 19.5115 | 1.17022 | ||||||||
\(279\) | 17.8129 | 1.06643 | ||||||||
\(280\) | −24.1608 | −1.44388 | ||||||||
\(281\) | 18.0490 | 1.07671 | 0.538356 | − | 0.842718i | \(-0.319046\pi\) | ||||
0.538356 | + | 0.842718i | \(0.319046\pi\) | |||||||
\(282\) | −4.11780 | −0.245212 | ||||||||
\(283\) | −14.5187 | −0.863047 | −0.431524 | − | 0.902102i | \(-0.642024\pi\) | ||||
−0.431524 | + | 0.902102i | \(0.642024\pi\) | |||||||
\(284\) | −38.0703 | −2.25906 | ||||||||
\(285\) | 10.4557 | 0.619344 | ||||||||
\(286\) | −0.913772 | −0.0540325 | ||||||||
\(287\) | −15.6874 | −0.925998 | ||||||||
\(288\) | 22.4015 | 1.32002 | ||||||||
\(289\) | −14.8347 | −0.872630 | ||||||||
\(290\) | −28.6210 | −1.68069 | ||||||||
\(291\) | 64.1343 | 3.75962 | ||||||||
\(292\) | 42.0359 | 2.45996 | ||||||||
\(293\) | −5.66495 | −0.330950 | −0.165475 | − | 0.986214i | \(-0.552916\pi\) | ||||
−0.165475 | + | 0.986214i | \(0.552916\pi\) | |||||||
\(294\) | 135.561 | 7.90609 | ||||||||
\(295\) | 3.86767 | 0.225185 | ||||||||
\(296\) | −4.10059 | −0.238342 | ||||||||
\(297\) | 2.73242 | 0.158551 | ||||||||
\(298\) | 11.5352 | 0.668214 | ||||||||
\(299\) | −7.56371 | −0.437421 | ||||||||
\(300\) | 45.0411 | 2.60045 | ||||||||
\(301\) | −44.2230 | −2.54897 | ||||||||
\(302\) | 3.30333 | 0.190085 | ||||||||
\(303\) | −30.4662 | −1.75024 | ||||||||
\(304\) | 5.92309 | 0.339712 | ||||||||
\(305\) | −5.42093 | −0.310401 | ||||||||
\(306\) | 31.1592 | 1.78126 | ||||||||
\(307\) | 2.50243 | 0.142821 | 0.0714105 | − | 0.997447i | \(-0.477250\pi\) | ||||
0.0714105 | + | 0.997447i | \(0.477250\pi\) | |||||||
\(308\) | 2.43813 | 0.138926 | ||||||||
\(309\) | 51.1436 | 2.90946 | ||||||||
\(310\) | 5.84754 | 0.332118 | ||||||||
\(311\) | −0.198251 | −0.0112418 | −0.00562090 | − | 0.999984i | \(-0.501789\pi\) | ||||
−0.00562090 | + | 0.999984i | \(0.501789\pi\) | |||||||
\(312\) | −39.8405 | −2.25552 | ||||||||
\(313\) | −3.47697 | −0.196530 | −0.0982650 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982650 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(314\) | −7.63407 | −0.430815 | ||||||||
\(315\) | 52.1887 | 2.94050 | ||||||||
\(316\) | −52.6911 | −2.96411 | ||||||||
\(317\) | 1.46768 | 0.0824330 | 0.0412165 | − | 0.999150i | \(-0.486877\pi\) | ||||
0.0412165 | + | 0.999150i | \(0.486877\pi\) | |||||||
\(318\) | −3.02570 | −0.169673 | ||||||||
\(319\) | 1.33344 | 0.0746581 | ||||||||
\(320\) | 13.1254 | 0.733731 | ||||||||
\(321\) | 57.5861 | 3.21414 | ||||||||
\(322\) | 31.0457 | 1.73011 | ||||||||
\(323\) | −3.67352 | −0.204400 | ||||||||
\(324\) | 159.321 | 8.85115 | ||||||||
\(325\) | 9.93359 | 0.551016 | ||||||||
\(326\) | 2.39066 | 0.132406 | ||||||||
\(327\) | −8.38526 | −0.463706 | ||||||||
\(328\) | −13.2790 | −0.733211 | ||||||||
\(329\) | 2.42316 | 0.133593 | ||||||||
\(330\) | 1.35640 | 0.0746671 | ||||||||
\(331\) | −17.5039 | −0.962099 | −0.481049 | − | 0.876693i | \(-0.659744\pi\) | ||||
−0.481049 | + | 0.876693i | \(0.659744\pi\) | |||||||
\(332\) | −4.56895 | −0.250754 | ||||||||
\(333\) | 8.85751 | 0.485388 | ||||||||
\(334\) | 7.56991 | 0.414207 | ||||||||
\(335\) | 6.94417 | 0.379400 | ||||||||
\(336\) | 39.5778 | 2.15915 | ||||||||
\(337\) | 7.41249 | 0.403784 | 0.201892 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201892 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(338\) | 12.0467 | 0.655255 | ||||||||
\(339\) | −7.21545 | −0.391890 | ||||||||
\(340\) | 6.64936 | 0.360612 | ||||||||
\(341\) | −0.272433 | −0.0147531 | ||||||||
\(342\) | −52.8632 | −2.85851 | ||||||||
\(343\) | −45.8621 | −2.47632 | ||||||||
\(344\) | −37.4337 | −2.01829 | ||||||||
\(345\) | 11.2275 | 0.604469 | ||||||||
\(346\) | 44.3051 | 2.38186 | ||||||||
\(347\) | 6.47808 | 0.347762 | 0.173881 | − | 0.984767i | \(-0.444369\pi\) | ||||
0.173881 | + | 0.984767i | \(0.444369\pi\) | |||||||
\(348\) | 125.927 | 6.75040 | ||||||||
\(349\) | −11.1506 | −0.596880 | −0.298440 | − | 0.954428i | \(-0.596466\pi\) | ||||
−0.298440 | + | 0.954428i | \(0.596466\pi\) | |||||||
\(350\) | −40.7730 | −2.17941 | ||||||||
\(351\) | 56.9103 | 3.03765 | ||||||||
\(352\) | −0.342613 | −0.0182613 | ||||||||
\(353\) | 0.676731 | 0.0360188 | 0.0180094 | − | 0.999838i | \(-0.494267\pi\) | ||||
0.0180094 | + | 0.999838i | \(0.494267\pi\) | |||||||
\(354\) | −26.1776 | −1.39133 | ||||||||
\(355\) | 12.4633 | 0.661482 | ||||||||
\(356\) | 54.5357 | 2.89039 | ||||||||
\(357\) | −24.5463 | −1.29913 | ||||||||
\(358\) | 51.7040 | 2.73264 | ||||||||
\(359\) | −19.1354 | −1.00993 | −0.504965 | − | 0.863140i | \(-0.668494\pi\) | ||||
−0.504965 | + | 0.863140i | \(0.668494\pi\) | |||||||
\(360\) | 44.1765 | 2.32830 | ||||||||
\(361\) | −12.7677 | −0.671984 | ||||||||
\(362\) | 21.1222 | 1.11016 | ||||||||
\(363\) | 37.8150 | 1.98477 | ||||||||
\(364\) | 50.7810 | 2.66165 | ||||||||
\(365\) | −13.7615 | −0.720310 | ||||||||
\(366\) | 36.6905 | 1.91785 | ||||||||
\(367\) | 7.68946 | 0.401386 | 0.200693 | − | 0.979654i | \(-0.435681\pi\) | ||||
0.200693 | + | 0.979654i | \(0.435681\pi\) | |||||||
\(368\) | 6.36029 | 0.331553 | ||||||||
\(369\) | 28.6835 | 1.49320 | ||||||||
\(370\) | 2.90771 | 0.151165 | ||||||||
\(371\) | 1.78050 | 0.0924390 | ||||||||
\(372\) | −25.7281 | −1.33394 | ||||||||
\(373\) | 21.3883 | 1.10744 | 0.553722 | − | 0.832702i | \(-0.313207\pi\) | ||||
0.553722 | + | 0.832702i | \(0.313207\pi\) | |||||||
\(374\) | −0.476556 | −0.0246421 | ||||||||
\(375\) | −35.6865 | −1.84284 | ||||||||
\(376\) | 2.05115 | 0.105780 | ||||||||
\(377\) | 27.7726 | 1.43036 | ||||||||
\(378\) | −233.592 | −12.0147 | ||||||||
\(379\) | 10.4266 | 0.535579 | 0.267789 | − | 0.963477i | \(-0.413707\pi\) | ||||
0.267789 | + | 0.963477i | \(0.413707\pi\) | |||||||
\(380\) | −11.2810 | −0.578701 | ||||||||
\(381\) | −29.8475 | −1.52913 | ||||||||
\(382\) | 23.8745 | 1.22153 | ||||||||
\(383\) | 24.8371 | 1.26912 | 0.634559 | − | 0.772874i | \(-0.281182\pi\) | ||||
0.634559 | + | 0.772874i | \(0.281182\pi\) | |||||||
\(384\) | −71.4189 | −3.64458 | ||||||||
\(385\) | −0.798184 | −0.0406792 | ||||||||
\(386\) | 24.9250 | 1.26865 | ||||||||
\(387\) | 80.8590 | 4.11029 | ||||||||
\(388\) | −69.1961 | −3.51290 | ||||||||
\(389\) | 19.6415 | 0.995862 | 0.497931 | − | 0.867217i | \(-0.334093\pi\) | ||||
0.497931 | + | 0.867217i | \(0.334093\pi\) | |||||||
\(390\) | 28.2507 | 1.43053 | ||||||||
\(391\) | −3.94467 | −0.199491 | ||||||||
\(392\) | −67.5253 | −3.41054 | ||||||||
\(393\) | −49.6454 | −2.50428 | ||||||||
\(394\) | 12.9340 | 0.651604 | ||||||||
\(395\) | 17.2498 | 0.867929 | ||||||||
\(396\) | −4.45798 | −0.224022 | ||||||||
\(397\) | −23.2987 | −1.16933 | −0.584665 | − | 0.811275i | \(-0.698774\pi\) | ||||
−0.584665 | + | 0.811275i | \(0.698774\pi\) | |||||||
\(398\) | 60.9783 | 3.05656 | ||||||||
\(399\) | 41.6439 | 2.08480 | ||||||||
\(400\) | −8.35311 | −0.417656 | ||||||||
\(401\) | 29.8234 | 1.48931 | 0.744654 | − | 0.667451i | \(-0.232615\pi\) | ||||
0.744654 | + | 0.667451i | \(0.232615\pi\) | |||||||
\(402\) | −47.0003 | −2.34416 | ||||||||
\(403\) | −5.67419 | −0.282651 | ||||||||
\(404\) | 32.8708 | 1.63538 | ||||||||
\(405\) | −52.1576 | −2.59173 | ||||||||
\(406\) | −113.994 | −5.65744 | ||||||||
\(407\) | −0.135468 | −0.00671492 | ||||||||
\(408\) | −20.7778 | −1.02866 | ||||||||
\(409\) | 21.0010 | 1.03843 | 0.519217 | − | 0.854642i | \(-0.326224\pi\) | ||||
0.519217 | + | 0.854642i | \(0.326224\pi\) | |||||||
\(410\) | 9.41611 | 0.465028 | ||||||||
\(411\) | −56.5581 | −2.78981 | ||||||||
\(412\) | −55.1802 | −2.71853 | ||||||||
\(413\) | 15.4045 | 0.758005 | ||||||||
\(414\) | −56.7652 | −2.78986 | ||||||||
\(415\) | 1.49576 | 0.0734240 | ||||||||
\(416\) | −7.13588 | −0.349865 | ||||||||
\(417\) | 28.1041 | 1.37626 | ||||||||
\(418\) | 0.808500 | 0.0395450 | ||||||||
\(419\) | 36.8214 | 1.79884 | 0.899421 | − | 0.437084i | \(-0.143989\pi\) | ||||
0.899421 | + | 0.437084i | \(0.143989\pi\) | |||||||
\(420\) | −75.3789 | −3.67811 | ||||||||
\(421\) | −1.82707 | −0.0890461 | −0.0445230 | − | 0.999008i | \(-0.514177\pi\) | ||||
−0.0445230 | + | 0.999008i | \(0.514177\pi\) | |||||||
\(422\) | 36.8151 | 1.79213 | ||||||||
\(423\) | −4.43060 | −0.215423 | ||||||||
\(424\) | 1.50715 | 0.0731938 | ||||||||
\(425\) | 5.18062 | 0.251297 | ||||||||
\(426\) | −84.3554 | −4.08703 | ||||||||
\(427\) | −21.5909 | −1.04486 | ||||||||
\(428\) | −62.1311 | −3.00322 | ||||||||
\(429\) | −1.31618 | −0.0635460 | ||||||||
\(430\) | 26.5441 | 1.28007 | ||||||||
\(431\) | 6.28909 | 0.302935 | 0.151467 | − | 0.988462i | \(-0.451600\pi\) | ||||
0.151467 | + | 0.988462i | \(0.451600\pi\) | |||||||
\(432\) | −47.8557 | −2.30246 | ||||||||
\(433\) | 18.3178 | 0.880300 | 0.440150 | − | 0.897924i | \(-0.354925\pi\) | ||||
0.440150 | + | 0.897924i | \(0.354925\pi\) | |||||||
\(434\) | 23.2901 | 1.11796 | ||||||||
\(435\) | −41.2254 | −1.97660 | ||||||||
\(436\) | 9.04708 | 0.433276 | ||||||||
\(437\) | 6.69233 | 0.320137 | ||||||||
\(438\) | 93.1422 | 4.45051 | ||||||||
\(439\) | −33.6213 | −1.60466 | −0.802330 | − | 0.596881i | \(-0.796406\pi\) | ||||
−0.802330 | + | 0.596881i | \(0.796406\pi\) | |||||||
\(440\) | −0.675644 | −0.0322101 | ||||||||
\(441\) | 145.859 | 6.94565 | ||||||||
\(442\) | −9.92561 | −0.472113 | ||||||||
\(443\) | 33.0363 | 1.56960 | 0.784801 | − | 0.619748i | \(-0.212765\pi\) | ||||
0.784801 | + | 0.619748i | \(0.212765\pi\) | |||||||
\(444\) | −12.7934 | −0.607147 | ||||||||
\(445\) | −17.8536 | −0.846343 | ||||||||
\(446\) | 37.3797 | 1.76998 | ||||||||
\(447\) | 16.6151 | 0.785867 | ||||||||
\(448\) | 52.2768 | 2.46985 | ||||||||
\(449\) | −7.93248 | −0.374357 | −0.187178 | − | 0.982326i | \(-0.559934\pi\) | ||||
−0.187178 | + | 0.982326i | \(0.559934\pi\) | |||||||
\(450\) | 74.5510 | 3.51437 | ||||||||
\(451\) | −0.438691 | −0.0206571 | ||||||||
\(452\) | 7.78494 | 0.366173 | ||||||||
\(453\) | 4.75807 | 0.223553 | ||||||||
\(454\) | 40.0927 | 1.88164 | ||||||||
\(455\) | −16.6244 | −0.779365 | ||||||||
\(456\) | 35.2506 | 1.65076 | ||||||||
\(457\) | 11.2727 | 0.527313 | 0.263657 | − | 0.964617i | \(-0.415071\pi\) | ||||
0.263657 | + | 0.964617i | \(0.415071\pi\) | |||||||
\(458\) | 50.4615 | 2.35791 | ||||||||
\(459\) | 29.6802 | 1.38535 | ||||||||
\(460\) | −12.1137 | −0.564802 | ||||||||
\(461\) | −26.7251 | −1.24471 | −0.622357 | − | 0.782733i | \(-0.713825\pi\) | ||||
−0.622357 | + | 0.782733i | \(0.713825\pi\) | |||||||
\(462\) | 5.40236 | 0.251341 | ||||||||
\(463\) | −12.4635 | −0.579230 | −0.289615 | − | 0.957143i | \(-0.593527\pi\) | ||||
−0.289615 | + | 0.957143i | \(0.593527\pi\) | |||||||
\(464\) | −23.3538 | −1.08417 | ||||||||
\(465\) | 8.42272 | 0.390594 | ||||||||
\(466\) | 9.11813 | 0.422389 | ||||||||
\(467\) | −17.3791 | −0.804208 | −0.402104 | − | 0.915594i | \(-0.631721\pi\) | ||||
−0.402104 | + | 0.915594i | \(0.631721\pi\) | |||||||
\(468\) | −92.8499 | −4.29199 | ||||||||
\(469\) | 27.6578 | 1.27712 | ||||||||
\(470\) | −1.45446 | −0.0670894 | ||||||||
\(471\) | −10.9960 | −0.506669 | ||||||||
\(472\) | 13.0395 | 0.600193 | ||||||||
\(473\) | −1.23667 | −0.0568623 | ||||||||
\(474\) | −116.752 | −5.36259 | ||||||||
\(475\) | −8.78918 | −0.403275 | ||||||||
\(476\) | 26.4836 | 1.21387 | ||||||||
\(477\) | −3.25554 | −0.149061 | ||||||||
\(478\) | 36.0479 | 1.64879 | ||||||||
\(479\) | 25.8020 | 1.17892 | 0.589462 | − | 0.807796i | \(-0.299340\pi\) | ||||
0.589462 | + | 0.807796i | \(0.299340\pi\) | |||||||
\(480\) | 10.5924 | 0.483476 | ||||||||
\(481\) | −2.82151 | −0.128650 | ||||||||
\(482\) | −70.6456 | −3.21782 | ||||||||
\(483\) | 44.7178 | 2.03473 | ||||||||
\(484\) | −40.7996 | −1.85453 | ||||||||
\(485\) | 22.6531 | 1.02862 | ||||||||
\(486\) | 208.359 | 9.45137 | ||||||||
\(487\) | −15.4927 | −0.702043 | −0.351021 | − | 0.936367i | \(-0.614166\pi\) | ||||
−0.351021 | + | 0.936367i | \(0.614166\pi\) | |||||||
\(488\) | −18.2762 | −0.827324 | ||||||||
\(489\) | 3.44347 | 0.155719 | ||||||||
\(490\) | 47.8820 | 2.16309 | ||||||||
\(491\) | 16.1284 | 0.727863 | 0.363931 | − | 0.931426i | \(-0.381434\pi\) | ||||
0.363931 | + | 0.931426i | \(0.381434\pi\) | |||||||
\(492\) | −41.4291 | −1.86777 | ||||||||
\(493\) | 14.4841 | 0.652331 | ||||||||
\(494\) | 16.8393 | 0.757635 | ||||||||
\(495\) | 1.45943 | 0.0655965 | ||||||||
\(496\) | 4.77140 | 0.214242 | ||||||||
\(497\) | 49.6397 | 2.22665 | ||||||||
\(498\) | −10.1238 | −0.453657 | ||||||||
\(499\) | 20.3846 | 0.912541 | 0.456271 | − | 0.889841i | \(-0.349185\pi\) | ||||
0.456271 | + | 0.889841i | \(0.349185\pi\) | |||||||
\(500\) | 38.5031 | 1.72191 | ||||||||
\(501\) | 10.9036 | 0.487137 | ||||||||
\(502\) | −15.2747 | −0.681743 | ||||||||
\(503\) | 24.6042 | 1.09705 | 0.548523 | − | 0.836135i | \(-0.315190\pi\) | ||||
0.548523 | + | 0.836135i | \(0.315190\pi\) | |||||||
\(504\) | 175.950 | 7.83742 | ||||||||
\(505\) | −10.7611 | −0.478861 | ||||||||
\(506\) | 0.868178 | 0.0385952 | ||||||||
\(507\) | 17.3519 | 0.770625 | ||||||||
\(508\) | 32.2032 | 1.42879 | ||||||||
\(509\) | −26.0142 | −1.15306 | −0.576529 | − | 0.817077i | \(-0.695593\pi\) | ||||
−0.576529 | + | 0.817077i | \(0.695593\pi\) | |||||||
\(510\) | 14.7335 | 0.652410 | ||||||||
\(511\) | −54.8104 | −2.42467 | ||||||||
\(512\) | 25.4586 | 1.12512 | ||||||||
\(513\) | −50.3539 | −2.22318 | ||||||||
\(514\) | −21.4442 | −0.945865 | ||||||||
\(515\) | 18.0646 | 0.796022 | ||||||||
\(516\) | −116.789 | −5.14135 | ||||||||
\(517\) | 0.0677625 | 0.00298019 | ||||||||
\(518\) | 11.5811 | 0.508843 | ||||||||
\(519\) | 63.8165 | 2.80123 | ||||||||
\(520\) | −14.0722 | −0.617106 | ||||||||
\(521\) | 25.9645 | 1.13752 | 0.568762 | − | 0.822502i | \(-0.307423\pi\) | ||||
0.568762 | + | 0.822502i | \(0.307423\pi\) | |||||||
\(522\) | 208.431 | 9.12279 | ||||||||
\(523\) | −8.46869 | −0.370310 | −0.185155 | − | 0.982709i | \(-0.559279\pi\) | ||||
−0.185155 | + | 0.982709i | \(0.559279\pi\) | |||||||
\(524\) | 53.5638 | 2.33994 | ||||||||
\(525\) | −58.7289 | −2.56314 | ||||||||
\(526\) | 21.7386 | 0.947847 | ||||||||
\(527\) | −2.95924 | −0.128906 | ||||||||
\(528\) | 1.10677 | 0.0481662 | ||||||||
\(529\) | −15.8137 | −0.687552 | ||||||||
\(530\) | −1.06872 | −0.0464221 | ||||||||
\(531\) | −28.1662 | −1.22231 | ||||||||
\(532\) | −44.9307 | −1.94799 | ||||||||
\(533\) | −9.13696 | −0.395766 | ||||||||
\(534\) | 120.839 | 5.22922 | ||||||||
\(535\) | 20.3402 | 0.879382 | ||||||||
\(536\) | 23.4117 | 1.01123 | ||||||||
\(537\) | 74.4737 | 3.21378 | ||||||||
\(538\) | 52.3997 | 2.25911 | ||||||||
\(539\) | −2.23079 | −0.0960870 | ||||||||
\(540\) | 91.1447 | 3.92224 | ||||||||
\(541\) | −37.9044 | −1.62964 | −0.814820 | − | 0.579714i | \(-0.803164\pi\) | ||||
−0.814820 | + | 0.579714i | \(0.803164\pi\) | |||||||
\(542\) | 10.6227 | 0.456283 | ||||||||
\(543\) | 30.4241 | 1.30562 | ||||||||
\(544\) | −3.72155 | −0.159560 | ||||||||
\(545\) | −2.96179 | −0.126869 | ||||||||
\(546\) | 112.519 | 4.81538 | ||||||||
\(547\) | −9.37223 | −0.400727 | −0.200364 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200364 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(548\) | 61.0220 | 2.60673 | ||||||||
\(549\) | 39.4776 | 1.68486 | ||||||||
\(550\) | −1.14020 | −0.0486182 | ||||||||
\(551\) | −24.5730 | −1.04684 | ||||||||
\(552\) | 37.8526 | 1.61111 | ||||||||
\(553\) | 68.7037 | 2.92158 | ||||||||
\(554\) | 67.1936 | 2.85478 | ||||||||
\(555\) | 4.18823 | 0.177780 | ||||||||
\(556\) | −30.3223 | −1.28595 | ||||||||
\(557\) | −24.1449 | −1.02305 | −0.511526 | − | 0.859268i | \(-0.670920\pi\) | ||||
−0.511526 | + | 0.859268i | \(0.670920\pi\) | |||||||
\(558\) | −42.5845 | −1.80274 | ||||||||
\(559\) | −25.7572 | −1.08941 | ||||||||
\(560\) | 13.9794 | 0.590738 | ||||||||
\(561\) | −0.686424 | −0.0289809 | ||||||||
\(562\) | −43.1489 | −1.82013 | ||||||||
\(563\) | −41.0577 | −1.73038 | −0.865188 | − | 0.501448i | \(-0.832801\pi\) | ||||
−0.865188 | + | 0.501448i | \(0.832801\pi\) | |||||||
\(564\) | 6.39936 | 0.269461 | ||||||||
\(565\) | −2.54859 | −0.107220 | ||||||||
\(566\) | 34.7093 | 1.45894 | ||||||||
\(567\) | −207.738 | −8.72416 | ||||||||
\(568\) | 42.0189 | 1.76307 | ||||||||
\(569\) | −10.7259 | −0.449654 | −0.224827 | − | 0.974399i | \(-0.572182\pi\) | ||||
−0.224827 | + | 0.974399i | \(0.572182\pi\) | |||||||
\(570\) | −24.9961 | −1.04697 | ||||||||
\(571\) | −4.91688 | −0.205765 | −0.102882 | − | 0.994694i | \(-0.532807\pi\) | ||||
−0.102882 | + | 0.994694i | \(0.532807\pi\) | |||||||
\(572\) | 1.42007 | 0.0593759 | ||||||||
\(573\) | 34.3886 | 1.43660 | ||||||||
\(574\) | 37.5032 | 1.56535 | ||||||||
\(575\) | −9.43794 | −0.393589 | ||||||||
\(576\) | −95.5849 | −3.98271 | ||||||||
\(577\) | −33.8928 | −1.41098 | −0.705488 | − | 0.708722i | \(-0.749272\pi\) | ||||
−0.705488 | + | 0.708722i | \(0.749272\pi\) | |||||||
\(578\) | 35.4647 | 1.47514 | ||||||||
\(579\) | 35.9016 | 1.49202 | ||||||||
\(580\) | 44.4791 | 1.84689 | ||||||||
\(581\) | 5.95743 | 0.247156 | ||||||||
\(582\) | −153.323 | −6.35545 | ||||||||
\(583\) | 0.0497908 | 0.00206213 | ||||||||
\(584\) | −46.3957 | −1.91987 | ||||||||
\(585\) | 30.3967 | 1.25675 | ||||||||
\(586\) | 13.5430 | 0.559455 | ||||||||
\(587\) | 3.47997 | 0.143634 | 0.0718169 | − | 0.997418i | \(-0.477120\pi\) | ||||
0.0718169 | + | 0.997418i | \(0.477120\pi\) | |||||||
\(588\) | −210.672 | −8.68795 | ||||||||
\(589\) | 5.02049 | 0.206866 | ||||||||
\(590\) | −9.24629 | −0.380664 | ||||||||
\(591\) | 18.6299 | 0.766333 | ||||||||
\(592\) | 2.37260 | 0.0975132 | ||||||||
\(593\) | −42.5094 | −1.74565 | −0.872825 | − | 0.488033i | \(-0.837715\pi\) | ||||
−0.872825 | + | 0.488033i | \(0.837715\pi\) | |||||||
\(594\) | −6.53229 | −0.268023 | ||||||||
\(595\) | −8.67007 | −0.355438 | ||||||||
\(596\) | −17.9265 | −0.734297 | ||||||||
\(597\) | 87.8322 | 3.59473 | ||||||||
\(598\) | 18.0823 | 0.739438 | ||||||||
\(599\) | 29.1479 | 1.19095 | 0.595476 | − | 0.803373i | \(-0.296963\pi\) | ||||
0.595476 | + | 0.803373i | \(0.296963\pi\) | |||||||
\(600\) | −49.7126 | −2.02951 | ||||||||
\(601\) | −4.18290 | −0.170624 | −0.0853120 | − | 0.996354i | \(-0.527189\pi\) | ||||
−0.0853120 | + | 0.996354i | \(0.527189\pi\) | |||||||
\(602\) | 105.722 | 4.30891 | ||||||||
\(603\) | −50.5706 | −2.05939 | ||||||||
\(604\) | −5.13360 | −0.208883 | ||||||||
\(605\) | 13.3568 | 0.543030 | ||||||||
\(606\) | 72.8343 | 2.95869 | ||||||||
\(607\) | 6.05556 | 0.245788 | 0.122894 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122894 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(608\) | 6.31378 | 0.256058 | ||||||||
\(609\) | −164.196 | −6.65354 | ||||||||
\(610\) | 12.9596 | 0.524718 | ||||||||
\(611\) | 1.41134 | 0.0570969 | ||||||||
\(612\) | −48.4237 | −1.95741 | ||||||||
\(613\) | 25.6424 | 1.03569 | 0.517844 | − | 0.855475i | \(-0.326735\pi\) | ||||
0.517844 | + | 0.855475i | \(0.326735\pi\) | |||||||
\(614\) | −5.98245 | −0.241432 | ||||||||
\(615\) | 13.5628 | 0.546906 | ||||||||
\(616\) | −2.69101 | −0.108424 | ||||||||
\(617\) | 30.6352 | 1.23333 | 0.616663 | − | 0.787227i | \(-0.288484\pi\) | ||||
0.616663 | + | 0.787227i | \(0.288484\pi\) | |||||||
\(618\) | −122.267 | −4.91830 | ||||||||
\(619\) | −24.5398 | −0.986336 | −0.493168 | − | 0.869934i | \(-0.664161\pi\) | ||||
−0.493168 | + | 0.869934i | \(0.664161\pi\) | |||||||
\(620\) | −9.08749 | −0.364963 | ||||||||
\(621\) | −54.0707 | −2.16978 | ||||||||
\(622\) | 0.473951 | 0.0190037 | ||||||||
\(623\) | −71.1089 | −2.84892 | ||||||||
\(624\) | 23.0517 | 0.922806 | ||||||||
\(625\) | 4.99837 | 0.199935 | ||||||||
\(626\) | 8.31226 | 0.332225 | ||||||||
\(627\) | 1.16455 | 0.0465077 | ||||||||
\(628\) | 11.8639 | 0.473420 | ||||||||
\(629\) | −1.47149 | −0.0586722 | ||||||||
\(630\) | −124.765 | −4.97077 | ||||||||
\(631\) | −38.2059 | −1.52095 | −0.760476 | − | 0.649366i | \(-0.775034\pi\) | ||||
−0.760476 | + | 0.649366i | \(0.775034\pi\) | |||||||
\(632\) | 58.1561 | 2.31332 | ||||||||
\(633\) | 53.0280 | 2.10767 | ||||||||
\(634\) | −3.50872 | −0.139349 | ||||||||
\(635\) | −10.5425 | −0.418367 | ||||||||
\(636\) | 4.70215 | 0.186452 | ||||||||
\(637\) | −46.4625 | −1.84091 | ||||||||
\(638\) | −3.18779 | −0.126206 | ||||||||
\(639\) | −90.7632 | −3.59054 | ||||||||
\(640\) | −25.2261 | −0.997150 | ||||||||
\(641\) | 0.879418 | 0.0347349 | 0.0173675 | − | 0.999849i | \(-0.494471\pi\) | ||||
0.0173675 | + | 0.999849i | \(0.494471\pi\) | |||||||
\(642\) | −137.669 | −5.43335 | ||||||||
\(643\) | −14.1166 | −0.556702 | −0.278351 | − | 0.960479i | \(-0.589788\pi\) | ||||
−0.278351 | + | 0.960479i | \(0.589788\pi\) | |||||||
\(644\) | −48.2472 | −1.90121 | ||||||||
\(645\) | 38.2338 | 1.50545 | ||||||||
\(646\) | 8.78212 | 0.345528 | ||||||||
\(647\) | 39.5192 | 1.55366 | 0.776831 | − | 0.629710i | \(-0.216826\pi\) | ||||
0.776831 | + | 0.629710i | \(0.216826\pi\) | |||||||
\(648\) | −175.845 | −6.90784 | ||||||||
\(649\) | 0.430779 | 0.0169096 | ||||||||
\(650\) | −23.7478 | −0.931466 | ||||||||
\(651\) | 33.5467 | 1.31480 | ||||||||
\(652\) | −3.71525 | −0.145501 | ||||||||
\(653\) | 5.16929 | 0.202290 | 0.101145 | − | 0.994872i | \(-0.467749\pi\) | ||||
0.101145 | + | 0.994872i | \(0.467749\pi\) | |||||||
\(654\) | 20.0463 | 0.783872 | ||||||||
\(655\) | −17.5354 | −0.685166 | ||||||||
\(656\) | 7.68323 | 0.299980 | ||||||||
\(657\) | 100.217 | 3.90986 | ||||||||
\(658\) | −5.79295 | −0.225833 | ||||||||
\(659\) | −16.1383 | −0.628659 | −0.314329 | − | 0.949314i | \(-0.601780\pi\) | ||||
−0.314329 | + | 0.949314i | \(0.601780\pi\) | |||||||
\(660\) | −2.10793 | −0.0820512 | ||||||||
\(661\) | 36.1994 | 1.40799 | 0.703996 | − | 0.710204i | \(-0.251397\pi\) | ||||
0.703996 | + | 0.710204i | \(0.251397\pi\) | |||||||
\(662\) | 41.8458 | 1.62638 | ||||||||
\(663\) | −14.2967 | −0.555238 | ||||||||
\(664\) | 5.04283 | 0.195700 | ||||||||
\(665\) | 14.7092 | 0.570398 | ||||||||
\(666\) | −21.1753 | −0.820525 | ||||||||
\(667\) | −26.3868 | −1.02170 | ||||||||
\(668\) | −11.7642 | −0.455170 | ||||||||
\(669\) | 53.8412 | 2.08162 | ||||||||
\(670\) | −16.6011 | −0.641358 | ||||||||
\(671\) | −0.603779 | −0.0233086 | ||||||||
\(672\) | 42.1884 | 1.62745 | ||||||||
\(673\) | −1.69631 | −0.0653879 | −0.0326940 | − | 0.999465i | \(-0.510409\pi\) | ||||
−0.0326940 | + | 0.999465i | \(0.510409\pi\) | |||||||
\(674\) | −17.7207 | −0.682577 | ||||||||
\(675\) | 71.0123 | 2.73327 | ||||||||
\(676\) | −18.7214 | −0.720055 | ||||||||
\(677\) | 38.6560 | 1.48567 | 0.742835 | − | 0.669474i | \(-0.233481\pi\) | ||||
0.742835 | + | 0.669474i | \(0.233481\pi\) | |||||||
\(678\) | 17.2497 | 0.662470 | ||||||||
\(679\) | 90.2245 | 3.46250 | ||||||||
\(680\) | −7.33901 | −0.281438 | ||||||||
\(681\) | 57.7489 | 2.21294 | ||||||||
\(682\) | 0.651295 | 0.0249394 | ||||||||
\(683\) | −48.6319 | −1.86085 | −0.930425 | − | 0.366483i | \(-0.880562\pi\) | ||||
−0.930425 | + | 0.366483i | \(0.880562\pi\) | |||||||
\(684\) | 82.1531 | 3.14120 | ||||||||
\(685\) | −19.9771 | −0.763285 | ||||||||
\(686\) | 109.641 | 4.18610 | ||||||||
\(687\) | 72.6840 | 2.77307 | ||||||||
\(688\) | 21.6591 | 0.825746 | ||||||||
\(689\) | 1.03703 | 0.0395078 | ||||||||
\(690\) | −26.8412 | −1.02183 | ||||||||
\(691\) | 9.63903 | 0.366686 | 0.183343 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183343 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(692\) | −68.8533 | −2.61741 | ||||||||
\(693\) | 5.81274 | 0.220808 | ||||||||
\(694\) | −15.4869 | −0.587874 | ||||||||
\(695\) | 9.92675 | 0.376543 | ||||||||
\(696\) | −138.988 | −5.26832 | ||||||||
\(697\) | −4.76516 | −0.180493 | ||||||||
\(698\) | 26.6574 | 1.00900 | ||||||||
\(699\) | 13.1336 | 0.496759 | ||||||||
\(700\) | 63.3642 | 2.39494 | ||||||||
\(701\) | 26.9865 | 1.01927 | 0.509633 | − | 0.860392i | \(-0.329781\pi\) | ||||
0.509633 | + | 0.860392i | \(0.329781\pi\) | |||||||
\(702\) | −136.053 | −5.13500 | ||||||||
\(703\) | 2.49646 | 0.0941557 | ||||||||
\(704\) | 1.46190 | 0.0550973 | ||||||||
\(705\) | −2.09499 | −0.0789018 | ||||||||
\(706\) | −1.61783 | −0.0608880 | ||||||||
\(707\) | −42.8600 | −1.61192 | ||||||||
\(708\) | 40.6819 | 1.52892 | ||||||||
\(709\) | 4.55408 | 0.171032 | 0.0855160 | − | 0.996337i | \(-0.472746\pi\) | ||||
0.0855160 | + | 0.996337i | \(0.472746\pi\) | |||||||
\(710\) | −29.7954 | −1.11820 | ||||||||
\(711\) | −125.621 | −4.71114 | ||||||||
\(712\) | −60.1920 | −2.25579 | ||||||||
\(713\) | 5.39107 | 0.201897 | ||||||||
\(714\) | 58.6818 | 2.19611 | ||||||||
\(715\) | −0.464894 | −0.0173860 | ||||||||
\(716\) | −80.3516 | −3.00288 | ||||||||
\(717\) | 51.9229 | 1.93910 | ||||||||
\(718\) | 45.7463 | 1.70724 | ||||||||
\(719\) | 16.1375 | 0.601828 | 0.300914 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300914 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(720\) | −25.5605 | −0.952584 | ||||||||
\(721\) | 71.9492 | 2.67953 | ||||||||
\(722\) | 30.5232 | 1.13596 | ||||||||
\(723\) | −101.757 | −3.78438 | ||||||||
\(724\) | −32.8254 | −1.21994 | ||||||||
\(725\) | 34.6544 | 1.28703 | ||||||||
\(726\) | −90.4028 | −3.35516 | ||||||||
\(727\) | 49.2264 | 1.82570 | 0.912852 | − | 0.408290i | \(-0.133875\pi\) | ||||
0.912852 | + | 0.408290i | \(0.133875\pi\) | |||||||
\(728\) | −56.0478 | −2.07727 | ||||||||
\(729\) | 171.469 | 6.35071 | ||||||||
\(730\) | 32.8991 | 1.21765 | ||||||||
\(731\) | −13.4330 | −0.496839 | ||||||||
\(732\) | −57.0197 | −2.10751 | ||||||||
\(733\) | 11.6928 | 0.431885 | 0.215943 | − | 0.976406i | \(-0.430718\pi\) | ||||
0.215943 | + | 0.976406i | \(0.430718\pi\) | |||||||
\(734\) | −18.3829 | −0.678524 | ||||||||
\(735\) | 68.9686 | 2.54394 | ||||||||
\(736\) | 6.77983 | 0.249908 | ||||||||
\(737\) | 0.773437 | 0.0284899 | ||||||||
\(738\) | −68.5724 | −2.52418 | ||||||||
\(739\) | −35.9020 | −1.32068 | −0.660338 | − | 0.750969i | \(-0.729587\pi\) | ||||
−0.660338 | + | 0.750969i | \(0.729587\pi\) | |||||||
\(740\) | −4.51879 | −0.166114 | ||||||||
\(741\) | 24.2551 | 0.891032 | ||||||||
\(742\) | −4.25657 | −0.156264 | ||||||||
\(743\) | −10.8646 | −0.398582 | −0.199291 | − | 0.979940i | \(-0.563864\pi\) | ||||
−0.199291 | + | 0.979940i | \(0.563864\pi\) | |||||||
\(744\) | 28.3965 | 1.04107 | ||||||||
\(745\) | 5.86867 | 0.215012 | ||||||||
\(746\) | −51.1321 | −1.87208 | ||||||||
\(747\) | −10.8928 | −0.398547 | ||||||||
\(748\) | 0.740601 | 0.0270791 | ||||||||
\(749\) | 81.0124 | 2.96013 | ||||||||
\(750\) | 85.3142 | 3.11524 | ||||||||
\(751\) | 10.4183 | 0.380171 | 0.190085 | − | 0.981768i | \(-0.439124\pi\) | ||||
0.190085 | + | 0.981768i | \(0.439124\pi\) | |||||||
\(752\) | −1.18679 | −0.0432779 | ||||||||
\(753\) | −22.0015 | −0.801778 | ||||||||
\(754\) | −66.3947 | −2.41795 | ||||||||
\(755\) | 1.68061 | 0.0611638 | ||||||||
\(756\) | 363.018 | 13.2029 | ||||||||
\(757\) | −3.71037 | −0.134856 | −0.0674278 | − | 0.997724i | \(-0.521479\pi\) | ||||
−0.0674278 | + | 0.997724i | \(0.521479\pi\) | |||||||
\(758\) | −24.9265 | −0.905370 | ||||||||
\(759\) | 1.25051 | 0.0453907 | ||||||||
\(760\) | 12.4510 | 0.451645 | ||||||||
\(761\) | 14.2602 | 0.516932 | 0.258466 | − | 0.966020i | \(-0.416783\pi\) | ||||
0.258466 | + | 0.966020i | \(0.416783\pi\) | |||||||
\(762\) | 71.3552 | 2.58492 | ||||||||
\(763\) | −11.7964 | −0.427060 | ||||||||
\(764\) | −37.1027 | −1.34233 | ||||||||
\(765\) | 15.8527 | 0.573155 | ||||||||
\(766\) | −59.3772 | −2.14538 | ||||||||
\(767\) | 8.97218 | 0.323967 | ||||||||
\(768\) | 96.4186 | 3.47920 | ||||||||
\(769\) | −11.1981 | −0.403814 | −0.201907 | − | 0.979405i | \(-0.564714\pi\) | ||||
−0.201907 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(770\) | 1.90819 | 0.0687663 | ||||||||
\(771\) | −30.8880 | −1.11240 | ||||||||
\(772\) | −38.7352 | −1.39411 | ||||||||
\(773\) | 11.7467 | 0.422500 | 0.211250 | − | 0.977432i | \(-0.432247\pi\) | ||||
0.211250 | + | 0.977432i | \(0.432247\pi\) | |||||||
\(774\) | −193.306 | −6.94825 | ||||||||
\(775\) | −7.08021 | −0.254329 | ||||||||
\(776\) | 76.3729 | 2.74163 | ||||||||
\(777\) | 16.6812 | 0.598435 | ||||||||
\(778\) | −46.9561 | −1.68346 | ||||||||
\(779\) | 8.08433 | 0.289651 | ||||||||
\(780\) | −43.9036 | −1.57200 | ||||||||
\(781\) | 1.38815 | 0.0496719 | ||||||||
\(782\) | 9.43037 | 0.337229 | ||||||||
\(783\) | 198.538 | 7.09516 | ||||||||
\(784\) | 39.0701 | 1.39536 | ||||||||
\(785\) | −3.88394 | −0.138624 | ||||||||
\(786\) | 118.685 | 4.23337 | ||||||||
\(787\) | 32.6730 | 1.16467 | 0.582333 | − | 0.812950i | \(-0.302140\pi\) | ||||
0.582333 | + | 0.812950i | \(0.302140\pi\) | |||||||
\(788\) | −20.1003 | −0.716044 | ||||||||
\(789\) | 31.3119 | 1.11473 | ||||||||
\(790\) | −41.2383 | −1.46719 | ||||||||
\(791\) | −10.1507 | −0.360919 | ||||||||
\(792\) | 4.92035 | 0.174837 | ||||||||
\(793\) | −12.5754 | −0.446565 | ||||||||
\(794\) | 55.6993 | 1.97670 | ||||||||
\(795\) | −1.53936 | −0.0545956 | ||||||||
\(796\) | −94.7645 | −3.35884 | ||||||||
\(797\) | 22.2309 | 0.787457 | 0.393729 | − | 0.919227i | \(-0.371185\pi\) | ||||
0.393729 | + | 0.919227i | \(0.371185\pi\) | |||||||
\(798\) | −99.5565 | −3.52426 | ||||||||
\(799\) | 0.736053 | 0.0260397 | ||||||||
\(800\) | −8.90410 | −0.314807 | ||||||||
\(801\) | 130.018 | 4.59397 | ||||||||
\(802\) | −71.2975 | −2.51760 | ||||||||
\(803\) | −1.53275 | −0.0540894 | ||||||||
\(804\) | 73.0418 | 2.57599 | ||||||||
\(805\) | 15.7949 | 0.556698 | ||||||||
\(806\) | 13.5651 | 0.477809 | ||||||||
\(807\) | 75.4758 | 2.65687 | ||||||||
\(808\) | −36.2800 | −1.27633 | ||||||||
\(809\) | −20.5211 | −0.721485 | −0.360742 | − | 0.932665i | \(-0.617477\pi\) | ||||
−0.360742 | + | 0.932665i | \(0.617477\pi\) | |||||||
\(810\) | 124.691 | 4.38120 | ||||||||
\(811\) | −47.1246 | −1.65477 | −0.827385 | − | 0.561635i | \(-0.810172\pi\) | ||||
−0.827385 | + | 0.561635i | \(0.810172\pi\) | |||||||
\(812\) | 177.155 | 6.21692 | ||||||||
\(813\) | 15.3008 | 0.536621 | ||||||||
\(814\) | 0.323859 | 0.0113513 | ||||||||
\(815\) | 1.21628 | 0.0426044 | ||||||||
\(816\) | 12.0221 | 0.420856 | ||||||||
\(817\) | 22.7898 | 0.797315 | ||||||||
\(818\) | −50.2063 | −1.75542 | ||||||||
\(819\) | 121.067 | 4.23041 | ||||||||
\(820\) | −14.6333 | −0.511017 | ||||||||
\(821\) | −0.239658 | −0.00836413 | −0.00418206 | − | 0.999991i | \(-0.501331\pi\) | ||||
−0.00418206 | + | 0.999991i | \(0.501331\pi\) | |||||||
\(822\) | 135.211 | 4.71603 | ||||||||
\(823\) | −47.4038 | −1.65239 | −0.826197 | − | 0.563381i | \(-0.809500\pi\) | ||||
−0.826197 | + | 0.563381i | \(0.809500\pi\) | |||||||
\(824\) | 60.9033 | 2.12167 | ||||||||
\(825\) | −1.64233 | −0.0571784 | ||||||||
\(826\) | −36.8269 | −1.28137 | ||||||||
\(827\) | 10.0816 | 0.350571 | 0.175286 | − | 0.984518i | \(-0.443915\pi\) | ||||
0.175286 | + | 0.984518i | \(0.443915\pi\) | |||||||
\(828\) | 88.2171 | 3.06576 | ||||||||
\(829\) | −29.4496 | −1.02283 | −0.511413 | − | 0.859335i | \(-0.670878\pi\) | ||||
−0.511413 | + | 0.859335i | \(0.670878\pi\) | |||||||
\(830\) | −3.57585 | −0.124120 | ||||||||
\(831\) | 96.7847 | 3.35742 | ||||||||
\(832\) | 30.4481 | 1.05560 | ||||||||
\(833\) | −24.2314 | −0.839568 | ||||||||
\(834\) | −67.1874 | −2.32651 | ||||||||
\(835\) | 3.85130 | 0.133280 | ||||||||
\(836\) | −1.25647 | −0.0434558 | ||||||||
\(837\) | −40.5631 | −1.40207 | ||||||||
\(838\) | −88.0273 | −3.04085 | ||||||||
\(839\) | −3.79823 | −0.131129 | −0.0655647 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655647 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(840\) | 83.1969 | 2.87057 | ||||||||
\(841\) | 67.8875 | 2.34095 | ||||||||
\(842\) | 4.36791 | 0.150528 | ||||||||
\(843\) | −62.1511 | −2.14060 | ||||||||
\(844\) | −57.2133 | −1.96936 | ||||||||
\(845\) | 6.12893 | 0.210841 | ||||||||
\(846\) | 10.5921 | 0.364162 | ||||||||
\(847\) | 53.1984 | 1.82792 | ||||||||
\(848\) | −0.872038 | −0.0299459 | ||||||||
\(849\) | 49.9948 | 1.71582 | ||||||||
\(850\) | −12.3851 | −0.424806 | ||||||||
\(851\) | 2.68073 | 0.0918942 | ||||||||
\(852\) | 131.094 | 4.49121 | ||||||||
\(853\) | −9.19968 | −0.314991 | −0.157496 | − | 0.987520i | \(-0.550342\pi\) | ||||
−0.157496 | + | 0.987520i | \(0.550342\pi\) | |||||||
\(854\) | 51.6165 | 1.76628 | ||||||||
\(855\) | −26.8949 | −0.919785 | ||||||||
\(856\) | 68.5751 | 2.34385 | ||||||||
\(857\) | 31.8111 | 1.08665 | 0.543324 | − | 0.839523i | \(-0.317166\pi\) | ||||
0.543324 | + | 0.839523i | \(0.317166\pi\) | |||||||
\(858\) | 3.14655 | 0.107421 | ||||||||
\(859\) | −21.1043 | −0.720068 | −0.360034 | − | 0.932939i | \(-0.617235\pi\) | ||||
−0.360034 | + | 0.932939i | \(0.617235\pi\) | |||||||
\(860\) | −41.2514 | −1.40666 | ||||||||
\(861\) | 54.0191 | 1.84097 | ||||||||
\(862\) | −15.0351 | −0.512096 | ||||||||
\(863\) | −3.17301 | −0.108010 | −0.0540052 | − | 0.998541i | \(-0.517199\pi\) | ||||
−0.0540052 | + | 0.998541i | \(0.517199\pi\) | |||||||
\(864\) | −51.0123 | −1.73547 | ||||||||
\(865\) | 22.5408 | 0.766411 | ||||||||
\(866\) | −43.7917 | −1.48810 | ||||||||
\(867\) | 51.0829 | 1.73487 | ||||||||
\(868\) | −36.1944 | −1.22852 | ||||||||
\(869\) | 1.92127 | 0.0651745 | ||||||||
\(870\) | 98.5558 | 3.34135 | ||||||||
\(871\) | 16.1090 | 0.545832 | ||||||||
\(872\) | −9.98541 | −0.338149 | ||||||||
\(873\) | −164.970 | −5.58339 | ||||||||
\(874\) | −15.9991 | −0.541177 | ||||||||
\(875\) | −50.2040 | −1.69720 | ||||||||
\(876\) | −144.749 | −4.89063 | ||||||||
\(877\) | 15.6874 | 0.529726 | 0.264863 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264863 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(878\) | 80.3772 | 2.71260 | ||||||||
\(879\) | 19.5071 | 0.657959 | ||||||||
\(880\) | 0.390927 | 0.0131782 | ||||||||
\(881\) | 19.3735 | 0.652709 | 0.326355 | − | 0.945247i | \(-0.394180\pi\) | ||||
0.326355 | + | 0.945247i | \(0.394180\pi\) | |||||||
\(882\) | −348.698 | −11.7413 | ||||||||
\(883\) | 55.2554 | 1.85949 | 0.929747 | − | 0.368200i | \(-0.120026\pi\) | ||||
0.929747 | + | 0.368200i | \(0.120026\pi\) | |||||||
\(884\) | 15.4251 | 0.518802 | ||||||||
\(885\) | −13.3182 | −0.447687 | ||||||||
\(886\) | −78.9786 | −2.65334 | ||||||||
\(887\) | 30.0646 | 1.00947 | 0.504735 | − | 0.863274i | \(-0.331590\pi\) | ||||
0.504735 | + | 0.863274i | \(0.331590\pi\) | |||||||
\(888\) | 14.1203 | 0.473845 | ||||||||
\(889\) | −41.9896 | −1.40829 | ||||||||
\(890\) | 42.6820 | 1.43070 | ||||||||
\(891\) | −5.80928 | −0.194618 | ||||||||
\(892\) | −58.0907 | −1.94502 | ||||||||
\(893\) | −1.24875 | −0.0417878 | ||||||||
\(894\) | −39.7210 | −1.32847 | ||||||||
\(895\) | 26.3051 | 0.879283 | ||||||||
\(896\) | −100.473 | −3.35655 | ||||||||
\(897\) | 26.0454 | 0.869632 | ||||||||
\(898\) | 18.9639 | 0.632832 | ||||||||
\(899\) | −19.7950 | −0.660201 | ||||||||
\(900\) | −115.857 | −3.86192 | ||||||||
\(901\) | 0.540840 | 0.0180180 | ||||||||
\(902\) | 1.04876 | 0.0349199 | ||||||||
\(903\) | 152.281 | 5.06758 | ||||||||
\(904\) | −8.59236 | −0.285778 | ||||||||
\(905\) | 10.7462 | 0.357216 | ||||||||
\(906\) | −11.3749 | −0.377906 | ||||||||
\(907\) | −0.0685022 | −0.00227458 | −0.00113729 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113729 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(908\) | −62.3068 | −2.06772 | ||||||||
\(909\) | 78.3669 | 2.59927 | ||||||||
\(910\) | 39.7433 | 1.31748 | ||||||||
\(911\) | −10.2965 | −0.341139 | −0.170570 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170570 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(912\) | −20.3960 | −0.675379 | ||||||||
\(913\) | 0.166597 | 0.00551355 | ||||||||
\(914\) | −26.9491 | −0.891398 | ||||||||
\(915\) | 18.6668 | 0.617106 | ||||||||
\(916\) | −78.4207 | −2.59109 | ||||||||
\(917\) | −69.8415 | −2.30637 | ||||||||
\(918\) | −70.9553 | −2.34187 | ||||||||
\(919\) | 33.7802 | 1.11430 | 0.557152 | − | 0.830410i | \(-0.311894\pi\) | ||||
0.557152 | + | 0.830410i | \(0.311894\pi\) | |||||||
\(920\) | 13.3700 | 0.440797 | ||||||||
\(921\) | −8.61704 | −0.283941 | ||||||||
\(922\) | 63.8907 | 2.10413 | ||||||||
\(923\) | 28.9121 | 0.951655 | ||||||||
\(924\) | −8.39565 | −0.276197 | ||||||||
\(925\) | −3.52066 | −0.115759 | ||||||||
\(926\) | 29.7961 | 0.979160 | ||||||||
\(927\) | −131.555 | −4.32082 | ||||||||
\(928\) | −24.8943 | −0.817195 | ||||||||
\(929\) | −48.7448 | −1.59927 | −0.799633 | − | 0.600489i | \(-0.794973\pi\) | ||||
−0.799633 | + | 0.600489i | \(0.794973\pi\) | |||||||
\(930\) | −20.1359 | −0.660281 | ||||||||
\(931\) | 41.1097 | 1.34732 | ||||||||
\(932\) | −14.1702 | −0.464161 | ||||||||
\(933\) | 0.682673 | 0.0223497 | ||||||||
\(934\) | 41.5475 | 1.35947 | ||||||||
\(935\) | −0.242454 | −0.00792910 | ||||||||
\(936\) | 102.480 | 3.34966 | ||||||||
\(937\) | 32.7285 | 1.06919 | 0.534597 | − | 0.845107i | \(-0.320463\pi\) | ||||
0.534597 | + | 0.845107i | \(0.320463\pi\) | |||||||
\(938\) | −66.1204 | −2.15891 | ||||||||
\(939\) | 11.9729 | 0.390720 | ||||||||
\(940\) | 2.26034 | 0.0737241 | ||||||||
\(941\) | 59.1937 | 1.92966 | 0.964829 | − | 0.262877i | \(-0.0846713\pi\) | ||||
0.964829 | + | 0.262877i | \(0.0846713\pi\) | |||||||
\(942\) | 26.2877 | 0.856500 | ||||||||
\(943\) | 8.68106 | 0.282694 | ||||||||
\(944\) | −7.54467 | −0.245558 | ||||||||
\(945\) | −118.843 | −3.86597 | ||||||||
\(946\) | 2.95647 | 0.0961230 | ||||||||
\(947\) | −0.381041 | −0.0123822 | −0.00619109 | − | 0.999981i | \(-0.501971\pi\) | ||||
−0.00619109 | + | 0.999981i | \(0.501971\pi\) | |||||||
\(948\) | 181.441 | 5.89291 | ||||||||
\(949\) | −31.9237 | −1.03629 | ||||||||
\(950\) | 21.0119 | 0.681717 | ||||||||
\(951\) | −5.05391 | −0.163884 | ||||||||
\(952\) | −29.2304 | −0.947363 | ||||||||
\(953\) | −21.4792 | −0.695779 | −0.347889 | − | 0.937536i | \(-0.613101\pi\) | ||||
−0.347889 | + | 0.937536i | \(0.613101\pi\) | |||||||
\(954\) | 7.78288 | 0.251980 | ||||||||
\(955\) | 12.1465 | 0.393051 | ||||||||
\(956\) | −56.0210 | −1.81185 | ||||||||
\(957\) | −4.59165 | −0.148427 | ||||||||
\(958\) | −61.6838 | −1.99291 | ||||||||
\(959\) | −79.5663 | −2.56933 | ||||||||
\(960\) | −45.1969 | −1.45872 | ||||||||
\(961\) | −26.9557 | −0.869539 | ||||||||
\(962\) | 6.74527 | 0.217476 | ||||||||
\(963\) | −148.126 | −4.77330 | ||||||||
\(964\) | 109.788 | 3.53604 | ||||||||
\(965\) | 12.6809 | 0.408213 | ||||||||
\(966\) | −106.905 | −3.43961 | ||||||||
\(967\) | −18.5038 | −0.595041 | −0.297521 | − | 0.954715i | \(-0.596160\pi\) | ||||
−0.297521 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(968\) | 45.0312 | 1.44736 | ||||||||
\(969\) | 12.6497 | 0.406365 | ||||||||
\(970\) | −54.1558 | −1.73884 | ||||||||
\(971\) | −22.8473 | −0.733203 | −0.366602 | − | 0.930378i | \(-0.619479\pi\) | ||||
−0.366602 | + | 0.930378i | \(0.619479\pi\) | |||||||
\(972\) | −323.805 | −10.3860 | ||||||||
\(973\) | 39.5371 | 1.26750 | ||||||||
\(974\) | 37.0378 | 1.18677 | ||||||||
\(975\) | −34.2060 | −1.09547 | ||||||||
\(976\) | 10.5746 | 0.338485 | ||||||||
\(977\) | −50.9207 | −1.62910 | −0.814549 | − | 0.580095i | \(-0.803016\pi\) | ||||
−0.814549 | + | 0.580095i | \(0.803016\pi\) | |||||||
\(978\) | −8.23217 | −0.263236 | ||||||||
\(979\) | −1.98853 | −0.0635535 | ||||||||
\(980\) | −74.4120 | −2.37700 | ||||||||
\(981\) | 21.5691 | 0.688647 | ||||||||
\(982\) | −38.5574 | −1.23042 | ||||||||
\(983\) | −33.2930 | −1.06188 | −0.530940 | − | 0.847409i | \(-0.678161\pi\) | ||||
−0.530940 | + | 0.847409i | \(0.678161\pi\) | |||||||
\(984\) | 45.7259 | 1.45769 | ||||||||
\(985\) | 6.58034 | 0.209667 | ||||||||
\(986\) | −34.6266 | −1.10273 | ||||||||
\(987\) | −8.34409 | −0.265595 | ||||||||
\(988\) | −26.1694 | −0.832560 | ||||||||
\(989\) | 24.4720 | 0.778165 | ||||||||
\(990\) | −3.48900 | −0.110888 | ||||||||
\(991\) | 14.1141 | 0.448350 | 0.224175 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224175 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(992\) | 5.08613 | 0.161485 | ||||||||
\(993\) | 60.2741 | 1.91274 | ||||||||
\(994\) | −118.672 | −3.76404 | ||||||||
\(995\) | 31.0235 | 0.983512 | ||||||||
\(996\) | 15.7331 | 0.498521 | ||||||||
\(997\) | 36.7574 | 1.16412 | 0.582059 | − | 0.813147i | \(-0.302247\pi\) | ||||
0.582059 | + | 0.813147i | \(0.302247\pi\) | |||||||
\(998\) | −48.7327 | −1.54261 | ||||||||
\(999\) | −20.1702 | −0.638156 |
(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 | 6031.2.a.e.1.15 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.e.1.15 | ✓ | 134 | 1.1 | even | 1 | trivial |