Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0372 | −1.77435 | −0.887174 | − | 0.461435i | \(-0.847335\pi\) | ||||
−0.887174 | + | 0.461435i | \(0.847335\pi\) | |||||||
\(3\) | −21.3301 | −1.36833 | −0.684165 | − | 0.729327i | \(-0.739833\pi\) | ||||
−0.684165 | + | 0.729327i | \(0.739833\pi\) | |||||||
\(4\) | 68.7460 | 2.14831 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 214.096 | 2.42789 | ||||||||
\(7\) | 45.5863 | 0.351633 | 0.175816 | − | 0.984423i | \(-0.443744\pi\) | ||||
0.175816 | + | 0.984423i | \(0.443744\pi\) | |||||||
\(8\) | −368.828 | −2.03750 | ||||||||
\(9\) | 211.975 | 0.872326 | ||||||||
\(10\) | 250.931 | 0.793513 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −1466.36 | −2.93960 | ||||||||
\(13\) | 590.564 | 0.969189 | 0.484594 | − | 0.874739i | \(-0.338967\pi\) | ||||
0.484594 | + | 0.874739i | \(0.338967\pi\) | |||||||
\(14\) | −457.560 | −0.623919 | ||||||||
\(15\) | 533.254 | 0.611936 | ||||||||
\(16\) | 1502.14 | 1.46693 | ||||||||
\(17\) | 545.397 | 0.457710 | 0.228855 | − | 0.973460i | \(-0.426502\pi\) | ||||
0.228855 | + | 0.973460i | \(0.426502\pi\) | |||||||
\(18\) | −2127.64 | −1.54781 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −1718.65 | −0.960754 | ||||||||
\(21\) | −972.363 | −0.481149 | ||||||||
\(22\) | −1214.50 | −0.534986 | ||||||||
\(23\) | 253.238 | 0.0998182 | 0.0499091 | − | 0.998754i | \(-0.484107\pi\) | ||||
0.0499091 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(24\) | 7867.15 | 2.78798 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −5927.62 | −1.71968 | ||||||||
\(27\) | 661.762 | 0.174700 | ||||||||
\(28\) | 3133.87 | 0.755416 | ||||||||
\(29\) | 6044.62 | 1.33467 | 0.667335 | − | 0.744758i | \(-0.267435\pi\) | ||||
0.667335 | + | 0.744758i | \(0.267435\pi\) | |||||||
\(30\) | −5352.39 | −1.08579 | ||||||||
\(31\) | −6500.02 | −1.21482 | −0.607408 | − | 0.794390i | \(-0.707791\pi\) | ||||
−0.607408 | + | 0.794390i | \(0.707791\pi\) | |||||||
\(32\) | −3274.80 | −0.565340 | ||||||||
\(33\) | −2580.95 | −0.412567 | ||||||||
\(34\) | −5474.28 | −0.812137 | ||||||||
\(35\) | −1139.66 | −0.157255 | ||||||||
\(36\) | 14572.4 | 1.87403 | ||||||||
\(37\) | 13571.0 | 1.62969 | 0.814847 | − | 0.579676i | \(-0.196821\pi\) | ||||
0.814847 | + | 0.579676i | \(0.196821\pi\) | |||||||
\(38\) | −3623.44 | −0.407063 | ||||||||
\(39\) | −12596.8 | −1.32617 | ||||||||
\(40\) | 9220.69 | 0.911199 | ||||||||
\(41\) | −15169.1 | −1.40929 | −0.704646 | − | 0.709559i | \(-0.748894\pi\) | ||||
−0.704646 | + | 0.709559i | \(0.748894\pi\) | |||||||
\(42\) | 9759.83 | 0.853727 | ||||||||
\(43\) | −11437.9 | −0.943359 | −0.471680 | − | 0.881770i | \(-0.656352\pi\) | ||||
−0.471680 | + | 0.881770i | \(0.656352\pi\) | |||||||
\(44\) | 8318.26 | 0.647740 | ||||||||
\(45\) | −5299.38 | −0.390116 | ||||||||
\(46\) | −2541.81 | −0.177112 | ||||||||
\(47\) | −6287.49 | −0.415176 | −0.207588 | − | 0.978216i | \(-0.566561\pi\) | ||||
−0.207588 | + | 0.978216i | \(0.566561\pi\) | |||||||
\(48\) | −32040.8 | −2.00724 | ||||||||
\(49\) | −14728.9 | −0.876354 | ||||||||
\(50\) | −6273.27 | −0.354870 | ||||||||
\(51\) | −11633.4 | −0.626299 | ||||||||
\(52\) | 40598.9 | 2.08212 | ||||||||
\(53\) | 13921.0 | 0.680742 | 0.340371 | − | 0.940291i | \(-0.389447\pi\) | ||||
0.340371 | + | 0.940291i | \(0.389447\pi\) | |||||||
\(54\) | −6642.26 | −0.309978 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −16813.5 | −0.716453 | ||||||||
\(57\) | −7700.18 | −0.313916 | ||||||||
\(58\) | −60671.2 | −2.36817 | ||||||||
\(59\) | −16958.1 | −0.634231 | −0.317116 | − | 0.948387i | \(-0.602714\pi\) | ||||
−0.317116 | + | 0.948387i | \(0.602714\pi\) | |||||||
\(60\) | 36659.0 | 1.31463 | ||||||||
\(61\) | 7640.48 | 0.262903 | 0.131452 | − | 0.991323i | \(-0.458036\pi\) | ||||
0.131452 | + | 0.991323i | \(0.458036\pi\) | |||||||
\(62\) | 65242.2 | 2.15551 | ||||||||
\(63\) | 9663.17 | 0.306738 | ||||||||
\(64\) | −15198.4 | −0.463820 | ||||||||
\(65\) | −14764.1 | −0.433434 | ||||||||
\(66\) | 25905.6 | 0.732037 | ||||||||
\(67\) | −22736.3 | −0.618776 | −0.309388 | − | 0.950936i | \(-0.600124\pi\) | ||||
−0.309388 | + | 0.950936i | \(0.600124\pi\) | |||||||
\(68\) | 37493.9 | 0.983304 | ||||||||
\(69\) | −5401.61 | −0.136584 | ||||||||
\(70\) | 11439.0 | 0.279025 | ||||||||
\(71\) | −63586.6 | −1.49699 | −0.748496 | − | 0.663139i | \(-0.769224\pi\) | ||||
−0.748496 | + | 0.663139i | \(0.769224\pi\) | |||||||
\(72\) | −78182.3 | −1.77737 | ||||||||
\(73\) | 72895.7 | 1.60101 | 0.800506 | − | 0.599324i | \(-0.204564\pi\) | ||||
0.800506 | + | 0.599324i | \(0.204564\pi\) | |||||||
\(74\) | −136215. | −2.89164 | ||||||||
\(75\) | −13331.3 | −0.273666 | ||||||||
\(76\) | 24817.3 | 0.492856 | ||||||||
\(77\) | 5515.94 | 0.106021 | ||||||||
\(78\) | 126437. | 2.35309 | ||||||||
\(79\) | −57519.5 | −1.03693 | −0.518463 | − | 0.855100i | \(-0.673496\pi\) | ||||
−0.518463 | + | 0.855100i | \(0.673496\pi\) | |||||||
\(80\) | −37553.4 | −0.656031 | ||||||||
\(81\) | −65625.5 | −1.11137 | ||||||||
\(82\) | 152256. | 2.50057 | ||||||||
\(83\) | −101694. | −1.62032 | −0.810159 | − | 0.586211i | \(-0.800619\pi\) | ||||
−0.810159 | + | 0.586211i | \(0.800619\pi\) | |||||||
\(84\) | −66846.0 | −1.03366 | ||||||||
\(85\) | −13634.9 | −0.204694 | ||||||||
\(86\) | 114805. | 1.67385 | ||||||||
\(87\) | −128933. | −1.82627 | ||||||||
\(88\) | −44628.1 | −0.614330 | ||||||||
\(89\) | −18016.6 | −0.241100 | −0.120550 | − | 0.992707i | \(-0.538466\pi\) | ||||
−0.120550 | + | 0.992707i | \(0.538466\pi\) | |||||||
\(90\) | 53191.1 | 0.692202 | ||||||||
\(91\) | 26921.6 | 0.340798 | ||||||||
\(92\) | 17409.1 | 0.214441 | ||||||||
\(93\) | 138646. | 1.66227 | ||||||||
\(94\) | 63108.9 | 0.736667 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | 69852.0 | 0.773571 | ||||||||
\(97\) | −51497.8 | −0.555724 | −0.277862 | − | 0.960621i | \(-0.589626\pi\) | ||||
−0.277862 | + | 0.960621i | \(0.589626\pi\) | |||||||
\(98\) | 147837. | 1.55496 | ||||||||
\(99\) | 25649.0 | 0.263016 | ||||||||
\(100\) | 42966.2 | 0.429662 | ||||||||
\(101\) | 52377.3 | 0.510904 | 0.255452 | − | 0.966822i | \(-0.417776\pi\) | ||||
0.255452 | + | 0.966822i | \(0.417776\pi\) | |||||||
\(102\) | 116767. | 1.11127 | ||||||||
\(103\) | 33807.9 | 0.313997 | 0.156999 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156999 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(104\) | −217816. | −1.97473 | ||||||||
\(105\) | 24309.1 | 0.215177 | ||||||||
\(106\) | −139729. | −1.20787 | ||||||||
\(107\) | 58041.7 | 0.490095 | 0.245048 | − | 0.969511i | \(-0.421196\pi\) | ||||
0.245048 | + | 0.969511i | \(0.421196\pi\) | |||||||
\(108\) | 45493.5 | 0.375309 | ||||||||
\(109\) | 166191. | 1.33981 | 0.669904 | − | 0.742448i | \(-0.266335\pi\) | ||||
0.669904 | + | 0.742448i | \(0.266335\pi\) | |||||||
\(110\) | 30362.6 | 0.239253 | ||||||||
\(111\) | −289471. | −2.22996 | ||||||||
\(112\) | 68476.8 | 0.515820 | ||||||||
\(113\) | −189618. | −1.39696 | −0.698480 | − | 0.715630i | \(-0.746140\pi\) | ||||
−0.698480 | + | 0.715630i | \(0.746140\pi\) | |||||||
\(114\) | 77288.5 | 0.556997 | ||||||||
\(115\) | −6330.96 | −0.0446401 | ||||||||
\(116\) | 415543. | 2.86729 | ||||||||
\(117\) | 125185. | 0.845449 | ||||||||
\(118\) | 170212. | 1.12535 | ||||||||
\(119\) | 24862.6 | 0.160946 | ||||||||
\(120\) | −196679. | −1.24682 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −76689.3 | −0.466482 | ||||||||
\(123\) | 323560. | 1.92838 | ||||||||
\(124\) | −446850. | −2.60980 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −96991.4 | −0.544261 | ||||||||
\(127\) | 281147. | 1.54676 | 0.773381 | − | 0.633941i | \(-0.218564\pi\) | ||||
0.773381 | + | 0.633941i | \(0.218564\pi\) | |||||||
\(128\) | 257344. | 1.38832 | ||||||||
\(129\) | 243973. | 1.29083 | ||||||||
\(130\) | 148191. | 0.769063 | ||||||||
\(131\) | −362543. | −1.84578 | −0.922892 | − | 0.385058i | \(-0.874181\pi\) | ||||
−0.922892 | + | 0.385058i | \(0.874181\pi\) | |||||||
\(132\) | −177430. | −0.886322 | ||||||||
\(133\) | 16456.7 | 0.0806701 | ||||||||
\(134\) | 228210. | 1.09792 | ||||||||
\(135\) | −16544.0 | −0.0781281 | ||||||||
\(136\) | −201158. | −0.932586 | ||||||||
\(137\) | 188089. | 0.856174 | 0.428087 | − | 0.903738i | \(-0.359188\pi\) | ||||
0.428087 | + | 0.903738i | \(0.359188\pi\) | |||||||
\(138\) | 54217.2 | 0.242348 | ||||||||
\(139\) | 356004. | 1.56285 | 0.781427 | − | 0.623997i | \(-0.214492\pi\) | ||||
0.781427 | + | 0.623997i | \(0.214492\pi\) | |||||||
\(140\) | −78346.8 | −0.337832 | ||||||||
\(141\) | 134113. | 0.568098 | ||||||||
\(142\) | 638233. | 2.65619 | ||||||||
\(143\) | 71458.2 | 0.292221 | ||||||||
\(144\) | 318416. | 1.27964 | ||||||||
\(145\) | −151115. | −0.596883 | ||||||||
\(146\) | −731671. | −2.84075 | ||||||||
\(147\) | 314169. | 1.19914 | ||||||||
\(148\) | 932948. | 3.50109 | ||||||||
\(149\) | 283119. | 1.04473 | 0.522364 | − | 0.852723i | \(-0.325050\pi\) | ||||
0.522364 | + | 0.852723i | \(0.325050\pi\) | |||||||
\(150\) | 133810. | 0.485579 | ||||||||
\(151\) | 523212. | 1.86739 | 0.933695 | − | 0.358069i | \(-0.116565\pi\) | ||||
0.933695 | + | 0.358069i | \(0.116565\pi\) | |||||||
\(152\) | −133147. | −0.467435 | ||||||||
\(153\) | 115611. | 0.399273 | ||||||||
\(154\) | −55364.8 | −0.188119 | ||||||||
\(155\) | 162500. | 0.543282 | ||||||||
\(156\) | −865980. | −2.84902 | ||||||||
\(157\) | −434996. | −1.40843 | −0.704216 | − | 0.709985i | \(-0.748701\pi\) | ||||
−0.704216 | + | 0.709985i | \(0.748701\pi\) | |||||||
\(158\) | 577337. | 1.83987 | ||||||||
\(159\) | −296938. | −0.931479 | ||||||||
\(160\) | 81870.0 | 0.252828 | ||||||||
\(161\) | 11544.2 | 0.0350994 | ||||||||
\(162\) | 658698. | 1.97196 | ||||||||
\(163\) | 360460. | 1.06264 | 0.531322 | − | 0.847170i | \(-0.321695\pi\) | ||||
0.531322 | + | 0.847170i | \(0.321695\pi\) | |||||||
\(164\) | −1.04282e6 | −3.02760 | ||||||||
\(165\) | 64523.7 | 0.184506 | ||||||||
\(166\) | 1.02073e6 | 2.87501 | ||||||||
\(167\) | −67930.4 | −0.188483 | −0.0942416 | − | 0.995549i | \(-0.530043\pi\) | ||||
−0.0942416 | + | 0.995549i | \(0.530043\pi\) | |||||||
\(168\) | 358634. | 0.980344 | ||||||||
\(169\) | −22527.6 | −0.0606735 | ||||||||
\(170\) | 136857. | 0.363199 | ||||||||
\(171\) | 76523.1 | 0.200125 | ||||||||
\(172\) | −786313. | −2.02663 | ||||||||
\(173\) | −176616. | −0.448659 | −0.224329 | − | 0.974513i | \(-0.572019\pi\) | ||||
−0.224329 | + | 0.974513i | \(0.572019\pi\) | |||||||
\(174\) | 1.29413e6 | 3.24044 | ||||||||
\(175\) | 28491.4 | 0.0703265 | ||||||||
\(176\) | 181758. | 0.442296 | ||||||||
\(177\) | 361719. | 0.867837 | ||||||||
\(178\) | 180837. | 0.427796 | ||||||||
\(179\) | 236326. | 0.551287 | 0.275644 | − | 0.961260i | \(-0.411109\pi\) | ||||
0.275644 | + | 0.961260i | \(0.411109\pi\) | |||||||
\(180\) | −364311. | −0.838091 | ||||||||
\(181\) | 481024. | 1.09137 | 0.545683 | − | 0.837992i | \(-0.316270\pi\) | ||||
0.545683 | + | 0.837992i | \(0.316270\pi\) | |||||||
\(182\) | −270218. | −0.604695 | ||||||||
\(183\) | −162973. | −0.359738 | ||||||||
\(184\) | −93401.3 | −0.203380 | ||||||||
\(185\) | −339274. | −0.728821 | ||||||||
\(186\) | −1.39163e6 | −2.94944 | ||||||||
\(187\) | 65993.1 | 0.138005 | ||||||||
\(188\) | −432239. | −0.891927 | ||||||||
\(189\) | 30167.3 | 0.0614302 | ||||||||
\(190\) | 90586.0 | 0.182044 | ||||||||
\(191\) | −565416. | −1.12146 | −0.560731 | − | 0.827998i | \(-0.689480\pi\) | ||||
−0.560731 | + | 0.827998i | \(0.689480\pi\) | |||||||
\(192\) | 324185. | 0.634658 | ||||||||
\(193\) | 425197. | 0.821670 | 0.410835 | − | 0.911710i | \(-0.365237\pi\) | ||||
0.410835 | + | 0.911710i | \(0.365237\pi\) | |||||||
\(194\) | 516895. | 0.986048 | ||||||||
\(195\) | 314920. | 0.593081 | ||||||||
\(196\) | −1.01255e6 | −1.88268 | ||||||||
\(197\) | −620404. | −1.13896 | −0.569481 | − | 0.822005i | \(-0.692856\pi\) | ||||
−0.569481 | + | 0.822005i | \(0.692856\pi\) | |||||||
\(198\) | −257445. | −0.466682 | ||||||||
\(199\) | −946338. | −1.69400 | −0.847000 | − | 0.531593i | \(-0.821594\pi\) | ||||
−0.847000 | + | 0.531593i | \(0.821594\pi\) | |||||||
\(200\) | −230517. | −0.407501 | ||||||||
\(201\) | 484969. | 0.846689 | ||||||||
\(202\) | −525723. | −0.906522 | ||||||||
\(203\) | 275552. | 0.469314 | ||||||||
\(204\) | −799750. | −1.34548 | ||||||||
\(205\) | 379228. | 0.630255 | ||||||||
\(206\) | −339338. | −0.557140 | ||||||||
\(207\) | 53680.3 | 0.0870741 | ||||||||
\(208\) | 887107. | 1.42173 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | −243996. | −0.381798 | ||||||||
\(211\) | 171167. | 0.264676 | 0.132338 | − | 0.991205i | \(-0.457752\pi\) | ||||
0.132338 | + | 0.991205i | \(0.457752\pi\) | |||||||
\(212\) | 957016. | 1.46244 | ||||||||
\(213\) | 1.35631e6 | 2.04838 | ||||||||
\(214\) | −582577. | −0.869599 | ||||||||
\(215\) | 285949. | 0.421883 | ||||||||
\(216\) | −244076. | −0.355951 | ||||||||
\(217\) | −296312. | −0.427169 | ||||||||
\(218\) | −1.66810e6 | −2.37728 | ||||||||
\(219\) | −1.55488e6 | −2.19071 | ||||||||
\(220\) | −207957. | −0.289678 | ||||||||
\(221\) | 322092. | 0.443608 | ||||||||
\(222\) | 2.90548e6 | 3.95672 | ||||||||
\(223\) | 484865. | 0.652918 | 0.326459 | − | 0.945211i | \(-0.394144\pi\) | ||||
0.326459 | + | 0.945211i | \(0.394144\pi\) | |||||||
\(224\) | −149286. | −0.198792 | ||||||||
\(225\) | 132485. | 0.174465 | ||||||||
\(226\) | 1.90324e6 | 2.47869 | ||||||||
\(227\) | −451755. | −0.581887 | −0.290943 | − | 0.956740i | \(-0.593969\pi\) | ||||
−0.290943 | + | 0.956740i | \(0.593969\pi\) | |||||||
\(228\) | −529357. | −0.674390 | ||||||||
\(229\) | 77974.4 | 0.0982570 | 0.0491285 | − | 0.998792i | \(-0.484356\pi\) | ||||
0.0491285 | + | 0.998792i | \(0.484356\pi\) | |||||||
\(230\) | 63545.3 | 0.0792070 | ||||||||
\(231\) | −117656. | −0.145072 | ||||||||
\(232\) | −2.22942e6 | −2.71939 | ||||||||
\(233\) | −1.11386e6 | −1.34413 | −0.672063 | − | 0.740494i | \(-0.734592\pi\) | ||||
−0.672063 | + | 0.740494i | \(0.734592\pi\) | |||||||
\(234\) | −1.25651e6 | −1.50012 | ||||||||
\(235\) | 157187. | 0.185672 | ||||||||
\(236\) | −1.16580e6 | −1.36253 | ||||||||
\(237\) | 1.22690e6 | 1.41886 | ||||||||
\(238\) | −249552. | −0.285574 | ||||||||
\(239\) | 1.24063e6 | 1.40490 | 0.702452 | − | 0.711731i | \(-0.252089\pi\) | ||||
0.702452 | + | 0.711731i | \(0.252089\pi\) | |||||||
\(240\) | 801020. | 0.897666 | ||||||||
\(241\) | −163443. | −0.181269 | −0.0906344 | − | 0.995884i | \(-0.528889\pi\) | ||||
−0.0906344 | + | 0.995884i | \(0.528889\pi\) | |||||||
\(242\) | −146955. | −0.161304 | ||||||||
\(243\) | 1.23899e6 | 1.34603 | ||||||||
\(244\) | 525252. | 0.564798 | ||||||||
\(245\) | 368222. | 0.391918 | ||||||||
\(246\) | −3.24764e6 | −3.42161 | ||||||||
\(247\) | 213193. | 0.222347 | ||||||||
\(248\) | 2.39739e6 | 2.47519 | ||||||||
\(249\) | 2.16915e6 | 2.21713 | ||||||||
\(250\) | 156832. | 0.158703 | ||||||||
\(251\) | 894322. | 0.896004 | 0.448002 | − | 0.894033i | \(-0.352136\pi\) | ||||
0.448002 | + | 0.894033i | \(0.352136\pi\) | |||||||
\(252\) | 664304. | 0.658970 | ||||||||
\(253\) | 30641.8 | 0.0300963 | ||||||||
\(254\) | −2.82193e6 | −2.74449 | ||||||||
\(255\) | 290835. | 0.280089 | ||||||||
\(256\) | −2.09667e6 | −1.99954 | ||||||||
\(257\) | 1.40041e6 | 1.32258 | 0.661291 | − | 0.750129i | \(-0.270009\pi\) | ||||
0.661291 | + | 0.750129i | \(0.270009\pi\) | |||||||
\(258\) | −2.44881e6 | −2.29038 | ||||||||
\(259\) | 618650. | 0.573054 | ||||||||
\(260\) | −1.01497e6 | −0.931152 | ||||||||
\(261\) | 1.28131e6 | 1.16427 | ||||||||
\(262\) | 3.63892e6 | 3.27506 | ||||||||
\(263\) | 26892.4 | 0.0239740 | 0.0119870 | − | 0.999928i | \(-0.496184\pi\) | ||||
0.0119870 | + | 0.999928i | \(0.496184\pi\) | |||||||
\(264\) | 951925. | 0.840607 | ||||||||
\(265\) | −348026. | −0.304437 | ||||||||
\(266\) | −165179. | −0.143137 | ||||||||
\(267\) | 384297. | 0.329905 | ||||||||
\(268\) | −1.56303e6 | −1.32932 | ||||||||
\(269\) | −750989. | −0.632780 | −0.316390 | − | 0.948629i | \(-0.602471\pi\) | ||||
−0.316390 | + | 0.948629i | \(0.602471\pi\) | |||||||
\(270\) | 166056. | 0.138626 | ||||||||
\(271\) | −794375. | −0.657056 | −0.328528 | − | 0.944494i | \(-0.606552\pi\) | ||||
−0.328528 | + | 0.944494i | \(0.606552\pi\) | |||||||
\(272\) | 819261. | 0.671429 | ||||||||
\(273\) | −574242. | −0.466325 | ||||||||
\(274\) | −1.88789e6 | −1.51915 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −371339. | −0.293425 | ||||||||
\(277\) | 1.14572e6 | 0.897177 | 0.448588 | − | 0.893738i | \(-0.351927\pi\) | ||||
0.448588 | + | 0.893738i | \(0.351927\pi\) | |||||||
\(278\) | −3.57330e6 | −2.77305 | ||||||||
\(279\) | −1.37784e6 | −1.05972 | ||||||||
\(280\) | 420337. | 0.320407 | ||||||||
\(281\) | −2.26321e6 | −1.70986 | −0.854928 | − | 0.518747i | \(-0.826399\pi\) | ||||
−0.854928 | + | 0.518747i | \(0.826399\pi\) | |||||||
\(282\) | −1.34612e6 | −1.00800 | ||||||||
\(283\) | −1.90850e6 | −1.41653 | −0.708267 | − | 0.705944i | \(-0.750523\pi\) | ||||
−0.708267 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(284\) | −4.37132e6 | −3.21601 | ||||||||
\(285\) | 192505. | 0.140388 | ||||||||
\(286\) | −717242. | −0.518502 | ||||||||
\(287\) | −691504. | −0.495553 | ||||||||
\(288\) | −694176. | −0.493161 | ||||||||
\(289\) | −1.12240e6 | −0.790501 | ||||||||
\(290\) | 1.51678e6 | 1.05908 | ||||||||
\(291\) | 1.09846e6 | 0.760414 | ||||||||
\(292\) | 5.01129e6 | 3.43947 | ||||||||
\(293\) | −633883. | −0.431360 | −0.215680 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215680 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(294\) | −3.15339e6 | −2.12770 | ||||||||
\(295\) | 423953. | 0.283637 | ||||||||
\(296\) | −5.00534e6 | −3.32051 | ||||||||
\(297\) | 80073.2 | 0.0526740 | ||||||||
\(298\) | −2.84173e6 | −1.85371 | ||||||||
\(299\) | 149553. | 0.0967427 | ||||||||
\(300\) | −916476. | −0.587920 | ||||||||
\(301\) | −521414. | −0.331716 | ||||||||
\(302\) | −5.25160e6 | −3.31340 | ||||||||
\(303\) | −1.11722e6 | −0.699085 | ||||||||
\(304\) | 542271. | 0.336537 | ||||||||
\(305\) | −191012. | −0.117574 | ||||||||
\(306\) | −1.16041e6 | −0.708449 | ||||||||
\(307\) | 2.02564e6 | 1.22664 | 0.613318 | − | 0.789836i | \(-0.289835\pi\) | ||||
0.613318 | + | 0.789836i | \(0.289835\pi\) | |||||||
\(308\) | 379199. | 0.227767 | ||||||||
\(309\) | −721129. | −0.429652 | ||||||||
\(310\) | −1.63105e6 | −0.963971 | ||||||||
\(311\) | −1.57896e6 | −0.925700 | −0.462850 | − | 0.886437i | \(-0.653173\pi\) | ||||
−0.462850 | + | 0.886437i | \(0.653173\pi\) | |||||||
\(312\) | 4.64605e6 | 2.70208 | ||||||||
\(313\) | 24442.2 | 0.0141020 | 0.00705098 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00705098 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(314\) | 4.36615e6 | 2.49905 | ||||||||
\(315\) | −241579. | −0.137178 | ||||||||
\(316\) | −3.95423e6 | −2.22764 | ||||||||
\(317\) | −2.40458e6 | −1.34398 | −0.671988 | − | 0.740562i | \(-0.734559\pi\) | ||||
−0.671988 | + | 0.740562i | \(0.734559\pi\) | |||||||
\(318\) | 2.98043e6 | 1.65277 | ||||||||
\(319\) | 731399. | 0.402418 | ||||||||
\(320\) | 379961. | 0.207426 | ||||||||
\(321\) | −1.23804e6 | −0.670612 | ||||||||
\(322\) | −115872. | −0.0622785 | ||||||||
\(323\) | 196888. | 0.105006 | ||||||||
\(324\) | −4.51149e6 | −2.38758 | ||||||||
\(325\) | 369102. | 0.193838 | ||||||||
\(326\) | −3.61802e6 | −1.88550 | ||||||||
\(327\) | −3.54489e6 | −1.83330 | ||||||||
\(328\) | 5.59479e6 | 2.87144 | ||||||||
\(329\) | −286623. | −0.145989 | ||||||||
\(330\) | −647639. | −0.327377 | ||||||||
\(331\) | 548401. | 0.275124 | 0.137562 | − | 0.990493i | \(-0.456073\pi\) | ||||
0.137562 | + | 0.990493i | \(0.456073\pi\) | |||||||
\(332\) | −6.99105e6 | −3.48095 | ||||||||
\(333\) | 2.87671e6 | 1.42162 | ||||||||
\(334\) | 681833. | 0.334435 | ||||||||
\(335\) | 568408. | 0.276725 | ||||||||
\(336\) | −1.46062e6 | −0.705812 | ||||||||
\(337\) | 3.75593e6 | 1.80154 | 0.900768 | − | 0.434301i | \(-0.143005\pi\) | ||||
0.900768 | + | 0.434301i | \(0.143005\pi\) | |||||||
\(338\) | 226115. | 0.107656 | ||||||||
\(339\) | 4.04458e6 | 1.91150 | ||||||||
\(340\) | −937346. | −0.439747 | ||||||||
\(341\) | −786502. | −0.366281 | ||||||||
\(342\) | −768080. | −0.355092 | ||||||||
\(343\) | −1.43760e6 | −0.659788 | ||||||||
\(344\) | 4.21863e6 | 1.92210 | ||||||||
\(345\) | 135040. | 0.0610823 | ||||||||
\(346\) | 1.77274e6 | 0.796076 | ||||||||
\(347\) | 3.78299e6 | 1.68660 | 0.843299 | − | 0.537445i | \(-0.180611\pi\) | ||||
0.843299 | + | 0.537445i | \(0.180611\pi\) | |||||||
\(348\) | −8.86360e6 | −3.92339 | ||||||||
\(349\) | −3.33353e6 | −1.46501 | −0.732506 | − | 0.680760i | \(-0.761650\pi\) | ||||
−0.732506 | + | 0.680760i | \(0.761650\pi\) | |||||||
\(350\) | −285975. | −0.124784 | ||||||||
\(351\) | 390812. | 0.169317 | ||||||||
\(352\) | −396251. | −0.170456 | ||||||||
\(353\) | −2.81059e6 | −1.20049 | −0.600247 | − | 0.799815i | \(-0.704931\pi\) | ||||
−0.600247 | + | 0.799815i | \(0.704931\pi\) | |||||||
\(354\) | −3.63066e6 | −1.53985 | ||||||||
\(355\) | 1.58966e6 | 0.669476 | ||||||||
\(356\) | −1.23857e6 | −0.517958 | ||||||||
\(357\) | −530324. | −0.220227 | ||||||||
\(358\) | −2.37205e6 | −0.978176 | ||||||||
\(359\) | −1.77609e6 | −0.727324 | −0.363662 | − | 0.931531i | \(-0.618474\pi\) | ||||
−0.363662 | + | 0.931531i | \(0.618474\pi\) | |||||||
\(360\) | 1.95456e6 | 0.794863 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −4.82815e6 | −1.93646 | ||||||||
\(363\) | −312295. | −0.124394 | ||||||||
\(364\) | 1.85075e6 | 0.732141 | ||||||||
\(365\) | −1.82239e6 | −0.715995 | ||||||||
\(366\) | 1.63579e6 | 0.638301 | ||||||||
\(367\) | −4.59659e6 | −1.78144 | −0.890720 | − | 0.454553i | \(-0.849799\pi\) | ||||
−0.890720 | + | 0.454553i | \(0.849799\pi\) | |||||||
\(368\) | 380398. | 0.146426 | ||||||||
\(369\) | −3.21548e6 | −1.22936 | ||||||||
\(370\) | 3.40537e6 | 1.29318 | ||||||||
\(371\) | 634609. | 0.239371 | ||||||||
\(372\) | 9.53138e6 | 3.57107 | ||||||||
\(373\) | 2.34753e6 | 0.873653 | 0.436827 | − | 0.899546i | \(-0.356102\pi\) | ||||
0.436827 | + | 0.899546i | \(0.356102\pi\) | |||||||
\(374\) | −662387. | −0.244869 | ||||||||
\(375\) | 333284. | 0.122387 | ||||||||
\(376\) | 2.31900e6 | 0.845923 | ||||||||
\(377\) | 3.56973e6 | 1.29355 | ||||||||
\(378\) | −302796. | −0.108998 | ||||||||
\(379\) | 107669. | 0.0385029 | 0.0192515 | − | 0.999815i | \(-0.493872\pi\) | ||||
0.0192515 | + | 0.999815i | \(0.493872\pi\) | |||||||
\(380\) | −620432. | −0.220412 | ||||||||
\(381\) | −5.99690e6 | −2.11648 | ||||||||
\(382\) | 5.67521e6 | 1.98986 | ||||||||
\(383\) | 3.60665e6 | 1.25634 | 0.628170 | − | 0.778076i | \(-0.283804\pi\) | ||||
0.628170 | + | 0.778076i | \(0.283804\pi\) | |||||||
\(384\) | −5.48918e6 | −1.89968 | ||||||||
\(385\) | −137899. | −0.0474141 | ||||||||
\(386\) | −4.26780e6 | −1.45793 | ||||||||
\(387\) | −2.42456e6 | −0.822917 | ||||||||
\(388\) | −3.54027e6 | −1.19387 | ||||||||
\(389\) | 2.46669e6 | 0.826497 | 0.413248 | − | 0.910618i | \(-0.364394\pi\) | ||||
0.413248 | + | 0.910618i | \(0.364394\pi\) | |||||||
\(390\) | −3.16093e6 | −1.05233 | ||||||||
\(391\) | 138115. | 0.0456878 | ||||||||
\(392\) | 5.43242e6 | 1.78558 | ||||||||
\(393\) | 7.73309e6 | 2.52564 | ||||||||
\(394\) | 6.22714e6 | 2.02091 | ||||||||
\(395\) | 1.43799e6 | 0.463727 | ||||||||
\(396\) | 1.76327e6 | 0.565041 | ||||||||
\(397\) | 346619. | 0.110376 | 0.0551882 | − | 0.998476i | \(-0.482424\pi\) | ||||
0.0551882 | + | 0.998476i | \(0.482424\pi\) | |||||||
\(398\) | 9.49861e6 | 3.00575 | ||||||||
\(399\) | −351023. | −0.110383 | ||||||||
\(400\) | 938835. | 0.293386 | ||||||||
\(401\) | −3.29568e6 | −1.02349 | −0.511746 | − | 0.859137i | \(-0.671001\pi\) | ||||
−0.511746 | + | 0.859137i | \(0.671001\pi\) | |||||||
\(402\) | −4.86775e6 | −1.50232 | ||||||||
\(403\) | −3.83867e6 | −1.17739 | ||||||||
\(404\) | 3.60073e6 | 1.09758 | ||||||||
\(405\) | 1.64064e6 | 0.497021 | ||||||||
\(406\) | −2.76578e6 | −0.832726 | ||||||||
\(407\) | 1.64209e6 | 0.491371 | ||||||||
\(408\) | 4.29072e6 | 1.27609 | ||||||||
\(409\) | 2.54411e6 | 0.752017 | 0.376008 | − | 0.926616i | \(-0.377296\pi\) | ||||
0.376008 | + | 0.926616i | \(0.377296\pi\) | |||||||
\(410\) | −3.80640e6 | −1.11829 | ||||||||
\(411\) | −4.01197e6 | −1.17153 | ||||||||
\(412\) | 2.32416e6 | 0.674564 | ||||||||
\(413\) | −773058. | −0.223016 | ||||||||
\(414\) | −538801. | −0.154500 | ||||||||
\(415\) | 2.54235e6 | 0.724628 | ||||||||
\(416\) | −1.93398e6 | −0.547921 | ||||||||
\(417\) | −7.59363e6 | −2.13850 | ||||||||
\(418\) | −438436. | −0.122734 | ||||||||
\(419\) | −330591. | −0.0919933 | −0.0459966 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459966 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(420\) | 1.67115e6 | 0.462266 | ||||||||
\(421\) | −2.41740e6 | −0.664726 | −0.332363 | − | 0.943152i | \(-0.607846\pi\) | ||||
−0.332363 | + | 0.943152i | \(0.607846\pi\) | |||||||
\(422\) | −1.71804e6 | −0.469627 | ||||||||
\(423\) | −1.33279e6 | −0.362169 | ||||||||
\(424\) | −5.13447e6 | −1.38701 | ||||||||
\(425\) | 340873. | 0.0915420 | ||||||||
\(426\) | −1.36136e7 | −3.63454 | ||||||||
\(427\) | 348301. | 0.0924454 | ||||||||
\(428\) | 3.99013e6 | 1.05288 | ||||||||
\(429\) | −1.52421e6 | −0.399855 | ||||||||
\(430\) | −2.87013e6 | −0.748567 | ||||||||
\(431\) | −3.07852e6 | −0.798267 | −0.399134 | − | 0.916893i | \(-0.630689\pi\) | ||||
−0.399134 | + | 0.916893i | \(0.630689\pi\) | |||||||
\(432\) | 994056. | 0.256272 | ||||||||
\(433\) | 4.19886e6 | 1.07625 | 0.538123 | − | 0.842866i | \(-0.319133\pi\) | ||||
0.538123 | + | 0.842866i | \(0.319133\pi\) | |||||||
\(434\) | 2.97415e6 | 0.757946 | ||||||||
\(435\) | 3.22332e6 | 0.816732 | ||||||||
\(436\) | 1.14250e7 | 2.87832 | ||||||||
\(437\) | 91419.0 | 0.0228999 | ||||||||
\(438\) | 1.56066e7 | 3.88709 | ||||||||
\(439\) | 3.40182e6 | 0.842461 | 0.421230 | − | 0.906954i | \(-0.361598\pi\) | ||||
0.421230 | + | 0.906954i | \(0.361598\pi\) | |||||||
\(440\) | 1.11570e6 | 0.274737 | ||||||||
\(441\) | −3.12216e6 | −0.764467 | ||||||||
\(442\) | −3.23291e6 | −0.787114 | ||||||||
\(443\) | −1.04038e6 | −0.251874 | −0.125937 | − | 0.992038i | \(-0.540194\pi\) | ||||
−0.125937 | + | 0.992038i | \(0.540194\pi\) | |||||||
\(444\) | −1.98999e7 | −4.79065 | ||||||||
\(445\) | 450415. | 0.107823 | ||||||||
\(446\) | −4.86670e6 | −1.15850 | ||||||||
\(447\) | −6.03896e6 | −1.42953 | ||||||||
\(448\) | −692841. | −0.163094 | ||||||||
\(449\) | 5.72758e6 | 1.34077 | 0.670387 | − | 0.742012i | \(-0.266128\pi\) | ||||
0.670387 | + | 0.742012i | \(0.266128\pi\) | |||||||
\(450\) | −1.32978e6 | −0.309562 | ||||||||
\(451\) | −1.83546e6 | −0.424918 | ||||||||
\(452\) | −1.30355e7 | −3.00110 | ||||||||
\(453\) | −1.11602e7 | −2.55521 | ||||||||
\(454\) | 4.53437e6 | 1.03247 | ||||||||
\(455\) | −673040. | −0.152410 | ||||||||
\(456\) | 2.84004e6 | 0.639606 | ||||||||
\(457\) | −7.20308e6 | −1.61335 | −0.806673 | − | 0.590998i | \(-0.798734\pi\) | ||||
−0.806673 | + | 0.590998i | \(0.798734\pi\) | |||||||
\(458\) | −782647. | −0.174342 | ||||||||
\(459\) | 360923. | 0.0799619 | ||||||||
\(460\) | −435228. | −0.0959008 | ||||||||
\(461\) | 757304. | 0.165966 | 0.0829828 | − | 0.996551i | \(-0.473555\pi\) | ||||
0.0829828 | + | 0.996551i | \(0.473555\pi\) | |||||||
\(462\) | 1.18094e6 | 0.257408 | ||||||||
\(463\) | −6.04775e6 | −1.31112 | −0.655559 | − | 0.755144i | \(-0.727567\pi\) | ||||
−0.655559 | + | 0.755144i | \(0.727567\pi\) | |||||||
\(464\) | 9.07984e6 | 1.95787 | ||||||||
\(465\) | −3.46616e6 | −0.743389 | ||||||||
\(466\) | 1.11800e7 | 2.38495 | ||||||||
\(467\) | 2.77561e6 | 0.588934 | 0.294467 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294467 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(468\) | 8.60595e6 | 1.81629 | ||||||||
\(469\) | −1.03646e6 | −0.217582 | ||||||||
\(470\) | −1.57772e6 | −0.329447 | ||||||||
\(471\) | 9.27853e6 | 1.92720 | ||||||||
\(472\) | 6.25462e6 | 1.29225 | ||||||||
\(473\) | −1.38399e6 | −0.284433 | ||||||||
\(474\) | −1.23147e7 | −2.51754 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | 1.70921e6 | 0.345762 | ||||||||
\(477\) | 2.95092e6 | 0.593829 | ||||||||
\(478\) | −1.24525e7 | −2.49279 | ||||||||
\(479\) | −9.05636e6 | −1.80350 | −0.901748 | − | 0.432263i | \(-0.857715\pi\) | ||||
−0.901748 | + | 0.432263i | \(0.857715\pi\) | |||||||
\(480\) | −1.74630e6 | −0.345952 | ||||||||
\(481\) | 8.01451e6 | 1.57948 | ||||||||
\(482\) | 1.64051e6 | 0.321634 | ||||||||
\(483\) | −246239. | −0.0480275 | ||||||||
\(484\) | 1.00651e6 | 0.195301 | ||||||||
\(485\) | 1.28745e6 | 0.248527 | ||||||||
\(486\) | −1.24361e7 | −2.38832 | ||||||||
\(487\) | −918773. | −0.175544 | −0.0877720 | − | 0.996141i | \(-0.527975\pi\) | ||||
−0.0877720 | + | 0.996141i | \(0.527975\pi\) | |||||||
\(488\) | −2.81802e6 | −0.535667 | ||||||||
\(489\) | −7.68867e6 | −1.45405 | ||||||||
\(490\) | −3.69593e6 | −0.695398 | ||||||||
\(491\) | −2.99635e6 | −0.560905 | −0.280452 | − | 0.959868i | \(-0.590485\pi\) | ||||
−0.280452 | + | 0.959868i | \(0.590485\pi\) | |||||||
\(492\) | 2.22434e7 | 4.14275 | ||||||||
\(493\) | 3.29672e6 | 0.610892 | ||||||||
\(494\) | −2.13987e6 | −0.394521 | ||||||||
\(495\) | −641225. | −0.117624 | ||||||||
\(496\) | −9.76391e6 | −1.78205 | ||||||||
\(497\) | −2.89868e6 | −0.526392 | ||||||||
\(498\) | −2.17722e7 | −3.93396 | ||||||||
\(499\) | 350713. | 0.0630523 | 0.0315262 | − | 0.999503i | \(-0.489963\pi\) | ||||
0.0315262 | + | 0.999503i | \(0.489963\pi\) | |||||||
\(500\) | −1.07416e6 | −0.192151 | ||||||||
\(501\) | 1.44896e6 | 0.257907 | ||||||||
\(502\) | −8.97652e6 | −1.58982 | ||||||||
\(503\) | 9.61222e6 | 1.69396 | 0.846981 | − | 0.531623i | \(-0.178418\pi\) | ||||
0.846981 | + | 0.531623i | \(0.178418\pi\) | |||||||
\(504\) | −3.56404e6 | −0.624981 | ||||||||
\(505\) | −1.30943e6 | −0.228483 | ||||||||
\(506\) | −307559. | −0.0534014 | ||||||||
\(507\) | 480518. | 0.0830213 | ||||||||
\(508\) | 1.93277e7 | 3.32293 | ||||||||
\(509\) | 1.28850e6 | 0.220440 | 0.110220 | − | 0.993907i | \(-0.464844\pi\) | ||||
0.110220 | + | 0.993907i | \(0.464844\pi\) | |||||||
\(510\) | −2.91918e6 | −0.496976 | ||||||||
\(511\) | 3.32305e6 | 0.562968 | ||||||||
\(512\) | 1.28097e7 | 2.15956 | ||||||||
\(513\) | 238896. | 0.0400789 | ||||||||
\(514\) | −1.40562e7 | −2.34672 | ||||||||
\(515\) | −845199. | −0.140424 | ||||||||
\(516\) | 1.67722e7 | 2.77310 | ||||||||
\(517\) | −760786. | −0.125180 | ||||||||
\(518\) | −6.20953e6 | −1.01680 | ||||||||
\(519\) | 3.76726e6 | 0.613913 | ||||||||
\(520\) | 5.44540e6 | 0.883124 | ||||||||
\(521\) | 8.39869e6 | 1.35556 | 0.677778 | − | 0.735267i | \(-0.262943\pi\) | ||||
0.677778 | + | 0.735267i | \(0.262943\pi\) | |||||||
\(522\) | −1.28608e7 | −2.06582 | ||||||||
\(523\) | −1.61748e6 | −0.258573 | −0.129287 | − | 0.991607i | \(-0.541269\pi\) | ||||
−0.129287 | + | 0.991607i | \(0.541269\pi\) | |||||||
\(524\) | −2.49234e7 | −3.96532 | ||||||||
\(525\) | −607727. | −0.0962299 | ||||||||
\(526\) | −269925. | −0.0425382 | ||||||||
\(527\) | −3.54509e6 | −0.556033 | ||||||||
\(528\) | −3.87693e6 | −0.605207 | ||||||||
\(529\) | −6.37221e6 | −0.990036 | ||||||||
\(530\) | 3.49322e6 | 0.540177 | ||||||||
\(531\) | −3.59470e6 | −0.553256 | ||||||||
\(532\) | 1.13133e6 | 0.173304 | ||||||||
\(533\) | −8.95833e6 | −1.36587 | ||||||||
\(534\) | −3.85727e6 | −0.585366 | ||||||||
\(535\) | −1.45104e6 | −0.219177 | ||||||||
\(536\) | 8.38578e6 | 1.26076 | ||||||||
\(537\) | −5.04086e6 | −0.754343 | ||||||||
\(538\) | 7.53785e6 | 1.12277 | ||||||||
\(539\) | −1.78220e6 | −0.264231 | ||||||||
\(540\) | −1.13734e6 | −0.167844 | ||||||||
\(541\) | 6.19660e6 | 0.910250 | 0.455125 | − | 0.890428i | \(-0.349595\pi\) | ||||
0.455125 | + | 0.890428i | \(0.349595\pi\) | |||||||
\(542\) | 7.97332e6 | 1.16585 | ||||||||
\(543\) | −1.02603e7 | −1.49335 | ||||||||
\(544\) | −1.78607e6 | −0.258762 | ||||||||
\(545\) | −4.15479e6 | −0.599180 | ||||||||
\(546\) | 5.76380e6 | 0.827422 | ||||||||
\(547\) | 1.46936e6 | 0.209971 | 0.104985 | − | 0.994474i | \(-0.466520\pi\) | ||||
0.104985 | + | 0.994474i | \(0.466520\pi\) | |||||||
\(548\) | 1.29304e7 | 1.83933 | ||||||||
\(549\) | 1.61959e6 | 0.229337 | ||||||||
\(550\) | −759065. | −0.106997 | ||||||||
\(551\) | 2.18211e6 | 0.306194 | ||||||||
\(552\) | 1.99226e6 | 0.278291 | ||||||||
\(553\) | −2.62210e6 | −0.364617 | ||||||||
\(554\) | −1.14998e7 | −1.59190 | ||||||||
\(555\) | 7.23676e6 | 0.997268 | ||||||||
\(556\) | 2.44739e7 | 3.35750 | ||||||||
\(557\) | −1.79425e6 | −0.245044 | −0.122522 | − | 0.992466i | \(-0.539098\pi\) | ||||
−0.122522 | + | 0.992466i | \(0.539098\pi\) | |||||||
\(558\) | 1.38297e7 | 1.88030 | ||||||||
\(559\) | −6.75484e6 | −0.914293 | ||||||||
\(560\) | −1.71192e6 | −0.230682 | ||||||||
\(561\) | −1.40764e6 | −0.188836 | ||||||||
\(562\) | 2.27164e7 | 3.03388 | ||||||||
\(563\) | −1.48352e7 | −1.97253 | −0.986264 | − | 0.165177i | \(-0.947180\pi\) | ||||
−0.986264 | + | 0.165177i | \(0.947180\pi\) | |||||||
\(564\) | 9.21973e6 | 1.22045 | ||||||||
\(565\) | 4.74045e6 | 0.624739 | ||||||||
\(566\) | 1.91561e7 | 2.51343 | ||||||||
\(567\) | −2.99162e6 | −0.390795 | ||||||||
\(568\) | 2.34525e7 | 3.05013 | ||||||||
\(569\) | 9.29345e6 | 1.20336 | 0.601681 | − | 0.798736i | \(-0.294498\pi\) | ||||
0.601681 | + | 0.798736i | \(0.294498\pi\) | |||||||
\(570\) | −1.93221e6 | −0.249097 | ||||||||
\(571\) | 4.53135e6 | 0.581618 | 0.290809 | − | 0.956781i | \(-0.406076\pi\) | ||||
0.290809 | + | 0.956781i | \(0.406076\pi\) | |||||||
\(572\) | 4.91246e6 | 0.627782 | ||||||||
\(573\) | 1.20604e7 | 1.53453 | ||||||||
\(574\) | 6.94079e6 | 0.879284 | ||||||||
\(575\) | 158274. | 0.0199636 | ||||||||
\(576\) | −3.22169e6 | −0.404602 | ||||||||
\(577\) | 7.13723e6 | 0.892463 | 0.446231 | − | 0.894918i | \(-0.352766\pi\) | ||||
0.446231 | + | 0.894918i | \(0.352766\pi\) | |||||||
\(578\) | 1.12658e7 | 1.40262 | ||||||||
\(579\) | −9.06952e6 | −1.12432 | ||||||||
\(580\) | −1.03886e7 | −1.28229 | ||||||||
\(581\) | −4.63585e6 | −0.569756 | ||||||||
\(582\) | −1.10255e7 | −1.34924 | ||||||||
\(583\) | 1.68445e6 | 0.205251 | ||||||||
\(584\) | −2.68859e7 | −3.26207 | ||||||||
\(585\) | −3.12962e6 | −0.378096 | ||||||||
\(586\) | 6.36242e6 | 0.765383 | ||||||||
\(587\) | 8.27785e6 | 0.991567 | 0.495784 | − | 0.868446i | \(-0.334881\pi\) | ||||
0.495784 | + | 0.868446i | \(0.334881\pi\) | |||||||
\(588\) | 2.15979e7 | 2.57613 | ||||||||
\(589\) | −2.34651e6 | −0.278698 | ||||||||
\(590\) | −4.25531e6 | −0.503270 | ||||||||
\(591\) | 1.32333e7 | 1.55848 | ||||||||
\(592\) | 2.03854e7 | 2.39065 | ||||||||
\(593\) | 348773. | 0.0407292 | 0.0203646 | − | 0.999793i | \(-0.493517\pi\) | ||||
0.0203646 | + | 0.999793i | \(0.493517\pi\) | |||||||
\(594\) | −803713. | −0.0934619 | ||||||||
\(595\) | −621566. | −0.0719772 | ||||||||
\(596\) | 1.94633e7 | 2.24440 | ||||||||
\(597\) | 2.01855e7 | 2.31795 | ||||||||
\(598\) | −1.50110e6 | −0.171655 | ||||||||
\(599\) | −1.17454e7 | −1.33753 | −0.668763 | − | 0.743476i | \(-0.733176\pi\) | ||||
−0.668763 | + | 0.743476i | \(0.733176\pi\) | |||||||
\(600\) | 4.91697e6 | 0.557595 | ||||||||
\(601\) | −883129. | −0.0997328 | −0.0498664 | − | 0.998756i | \(-0.515880\pi\) | ||||
−0.0498664 | + | 0.998756i | \(0.515880\pi\) | |||||||
\(602\) | 5.23355e6 | 0.588579 | ||||||||
\(603\) | −4.81954e6 | −0.539774 | ||||||||
\(604\) | 3.59687e7 | 4.01174 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 1.12137e7 | 1.24042 | ||||||||
\(607\) | −8.44501e6 | −0.930312 | −0.465156 | − | 0.885229i | \(-0.654002\pi\) | ||||
−0.465156 | + | 0.885229i | \(0.654002\pi\) | |||||||
\(608\) | −1.18220e6 | −0.129698 | ||||||||
\(609\) | −5.87756e6 | −0.642176 | ||||||||
\(610\) | 1.91723e6 | 0.208617 | ||||||||
\(611\) | −3.71316e6 | −0.402384 | ||||||||
\(612\) | 7.94777e6 | 0.857762 | ||||||||
\(613\) | 8.48065e6 | 0.911545 | 0.455773 | − | 0.890096i | \(-0.349363\pi\) | ||||
0.455773 | + | 0.890096i | \(0.349363\pi\) | |||||||
\(614\) | −2.03318e7 | −2.17648 | ||||||||
\(615\) | −8.08899e6 | −0.862396 | ||||||||
\(616\) | −2.03443e6 | −0.216019 | ||||||||
\(617\) | −7.16224e6 | −0.757418 | −0.378709 | − | 0.925516i | \(-0.623632\pi\) | ||||
−0.378709 | + | 0.925516i | \(0.623632\pi\) | |||||||
\(618\) | 7.23813e6 | 0.762352 | ||||||||
\(619\) | 4.60337e6 | 0.482891 | 0.241445 | − | 0.970414i | \(-0.422379\pi\) | ||||
0.241445 | + | 0.970414i | \(0.422379\pi\) | |||||||
\(620\) | 1.11712e7 | 1.16714 | ||||||||
\(621\) | 167583. | 0.0174382 | ||||||||
\(622\) | 1.58484e7 | 1.64251 | ||||||||
\(623\) | −821310. | −0.0847787 | ||||||||
\(624\) | −1.89221e7 | −1.94540 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −245332. | −0.0250218 | ||||||||
\(627\) | −931722. | −0.0946493 | ||||||||
\(628\) | −2.99042e7 | −3.02575 | ||||||||
\(629\) | 7.40156e6 | 0.745928 | ||||||||
\(630\) | 2.42479e6 | 0.243401 | ||||||||
\(631\) | −3.82415e6 | −0.382351 | −0.191175 | − | 0.981556i | \(-0.561230\pi\) | ||||
−0.191175 | + | 0.981556i | \(0.561230\pi\) | |||||||
\(632\) | 2.12148e7 | 2.11274 | ||||||||
\(633\) | −3.65102e6 | −0.362164 | ||||||||
\(634\) | 2.41353e7 | 2.38468 | ||||||||
\(635\) | −7.02867e6 | −0.691733 | ||||||||
\(636\) | −2.04133e7 | −2.00111 | ||||||||
\(637\) | −8.69835e6 | −0.849353 | ||||||||
\(638\) | −7.34122e6 | −0.714030 | ||||||||
\(639\) | −1.34788e7 | −1.30587 | ||||||||
\(640\) | −6.43359e6 | −0.620874 | ||||||||
\(641\) | 768138. | 0.0738404 | 0.0369202 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369202 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(642\) | 1.24265e7 | 1.18990 | ||||||||
\(643\) | −1.09863e7 | −1.04791 | −0.523955 | − | 0.851746i | \(-0.675544\pi\) | ||||
−0.523955 | + | 0.851746i | \(0.675544\pi\) | |||||||
\(644\) | 793617. | 0.0754043 | ||||||||
\(645\) | −6.09933e6 | −0.577275 | ||||||||
\(646\) | −1.97621e6 | −0.186317 | ||||||||
\(647\) | −2.16555e6 | −0.203380 | −0.101690 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101690 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(648\) | 2.42045e7 | 2.26443 | ||||||||
\(649\) | −2.05193e6 | −0.191228 | ||||||||
\(650\) | −3.70476e6 | −0.343936 | ||||||||
\(651\) | 6.32037e6 | 0.584508 | ||||||||
\(652\) | 2.47802e7 | 2.28289 | ||||||||
\(653\) | 1.26384e7 | 1.15987 | 0.579936 | − | 0.814662i | \(-0.303078\pi\) | ||||
0.579936 | + | 0.814662i | \(0.303078\pi\) | |||||||
\(654\) | 3.55808e7 | 3.25291 | ||||||||
\(655\) | 9.06357e6 | 0.825460 | ||||||||
\(656\) | −2.27861e7 | −2.06733 | ||||||||
\(657\) | 1.54521e7 | 1.39661 | ||||||||
\(658\) | 2.87690e6 | 0.259036 | ||||||||
\(659\) | −4.36646e6 | −0.391666 | −0.195833 | − | 0.980637i | \(-0.562741\pi\) | ||||
−0.195833 | + | 0.980637i | \(0.562741\pi\) | |||||||
\(660\) | 4.43574e6 | 0.396375 | ||||||||
\(661\) | −1.45290e7 | −1.29340 | −0.646698 | − | 0.762746i | \(-0.723850\pi\) | ||||
−0.646698 | + | 0.762746i | \(0.723850\pi\) | |||||||
\(662\) | −5.50443e6 | −0.488166 | ||||||||
\(663\) | −6.87027e6 | −0.607001 | ||||||||
\(664\) | 3.75075e7 | 3.30140 | ||||||||
\(665\) | −411416. | −0.0360768 | ||||||||
\(666\) | −2.88742e7 | −2.52246 | ||||||||
\(667\) | 1.53073e6 | 0.133224 | ||||||||
\(668\) | −4.66994e6 | −0.404921 | ||||||||
\(669\) | −1.03422e7 | −0.893408 | ||||||||
\(670\) | −5.70524e6 | −0.491006 | ||||||||
\(671\) | 924498. | 0.0792683 | ||||||||
\(672\) | 3.18429e6 | 0.272013 | ||||||||
\(673\) | 1.80978e7 | 1.54024 | 0.770120 | − | 0.637900i | \(-0.220197\pi\) | ||||
0.770120 | + | 0.637900i | \(0.220197\pi\) | |||||||
\(674\) | −3.76991e7 | −3.19655 | ||||||||
\(675\) | 413601. | 0.0349400 | ||||||||
\(676\) | −1.54868e6 | −0.130346 | ||||||||
\(677\) | 1.02308e7 | 0.857904 | 0.428952 | − | 0.903327i | \(-0.358883\pi\) | ||||
0.428952 | + | 0.903327i | \(0.358883\pi\) | |||||||
\(678\) | −4.05964e7 | −3.39167 | ||||||||
\(679\) | −2.34759e6 | −0.195411 | ||||||||
\(680\) | 5.02894e6 | 0.417065 | ||||||||
\(681\) | 9.63600e6 | 0.796213 | ||||||||
\(682\) | 7.89430e6 | 0.649909 | ||||||||
\(683\) | 1.88068e7 | 1.54263 | 0.771317 | − | 0.636451i | \(-0.219598\pi\) | ||||
0.771317 | + | 0.636451i | \(0.219598\pi\) | |||||||
\(684\) | 5.26065e6 | 0.429932 | ||||||||
\(685\) | −4.70223e6 | −0.382893 | ||||||||
\(686\) | 1.44296e7 | 1.17069 | ||||||||
\(687\) | −1.66321e6 | −0.134448 | ||||||||
\(688\) | −1.71814e7 | −1.38384 | ||||||||
\(689\) | 8.22126e6 | 0.659767 | ||||||||
\(690\) | −1.35543e6 | −0.108381 | ||||||||
\(691\) | 8.82043e6 | 0.702740 | 0.351370 | − | 0.936237i | \(-0.385716\pi\) | ||||
0.351370 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(692\) | −1.21417e7 | −0.963858 | ||||||||
\(693\) | 1.16924e6 | 0.0924851 | ||||||||
\(694\) | −3.79707e7 | −2.99261 | ||||||||
\(695\) | −8.90011e6 | −0.698930 | ||||||||
\(696\) | 4.75539e7 | 3.72103 | ||||||||
\(697\) | −8.27320e6 | −0.645047 | ||||||||
\(698\) | 3.34594e7 | 2.59944 | ||||||||
\(699\) | 2.37588e7 | 1.83921 | ||||||||
\(700\) | 1.95867e6 | 0.151083 | ||||||||
\(701\) | 1.53235e7 | 1.17778 | 0.588888 | − | 0.808214i | \(-0.299566\pi\) | ||||
0.588888 | + | 0.808214i | \(0.299566\pi\) | |||||||
\(702\) | −3.92267e6 | −0.300427 | ||||||||
\(703\) | 4.89911e6 | 0.373877 | ||||||||
\(704\) | −1.83901e6 | −0.139847 | ||||||||
\(705\) | −3.35283e6 | −0.254061 | ||||||||
\(706\) | 2.82105e7 | 2.13009 | ||||||||
\(707\) | 2.38769e6 | 0.179651 | ||||||||
\(708\) | 2.48667e7 | 1.86438 | ||||||||
\(709\) | 8.01222e6 | 0.598601 | 0.299300 | − | 0.954159i | \(-0.403247\pi\) | ||||
0.299300 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(710\) | −1.59558e7 | −1.18788 | ||||||||
\(711\) | −1.21927e7 | −0.904537 | ||||||||
\(712\) | 6.64501e6 | 0.491243 | ||||||||
\(713\) | −1.64605e6 | −0.121261 | ||||||||
\(714\) | 5.32298e6 | 0.390759 | ||||||||
\(715\) | −1.78645e6 | −0.130685 | ||||||||
\(716\) | 1.62464e7 | 1.18434 | ||||||||
\(717\) | −2.64628e7 | −1.92237 | ||||||||
\(718\) | 1.78270e7 | 1.29053 | ||||||||
\(719\) | 2.83978e6 | 0.204863 | 0.102431 | − | 0.994740i | \(-0.467338\pi\) | ||||
0.102431 | + | 0.994740i | \(0.467338\pi\) | |||||||
\(720\) | −7.96039e6 | −0.572273 | ||||||||
\(721\) | 1.54118e6 | 0.110412 | ||||||||
\(722\) | −1.30806e6 | −0.0933867 | ||||||||
\(723\) | 3.48626e6 | 0.248035 | ||||||||
\(724\) | 3.30684e7 | 2.34459 | ||||||||
\(725\) | 3.77789e6 | 0.266934 | ||||||||
\(726\) | 3.13457e6 | 0.220718 | ||||||||
\(727\) | −5.14911e6 | −0.361323 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(728\) | −9.92943e6 | −0.694378 | ||||||||
\(729\) | −1.04809e7 | −0.730433 | ||||||||
\(730\) | 1.82918e7 | 1.27042 | ||||||||
\(731\) | −6.23823e6 | −0.431785 | ||||||||
\(732\) | −1.12037e7 | −0.772830 | ||||||||
\(733\) | −6.56744e6 | −0.451477 | −0.225739 | − | 0.974188i | \(-0.572480\pi\) | ||||
−0.225739 | + | 0.974188i | \(0.572480\pi\) | |||||||
\(734\) | 4.61371e7 | 3.16089 | ||||||||
\(735\) | −7.85424e6 | −0.536273 | ||||||||
\(736\) | −829305. | −0.0564312 | ||||||||
\(737\) | −2.75109e6 | −0.186568 | ||||||||
\(738\) | 3.22745e7 | 2.18132 | ||||||||
\(739\) | −1.85326e7 | −1.24832 | −0.624159 | − | 0.781297i | \(-0.714558\pi\) | ||||
−0.624159 | + | 0.781297i | \(0.714558\pi\) | |||||||
\(740\) | −2.33237e7 | −1.56574 | ||||||||
\(741\) | −4.54745e6 | −0.304244 | ||||||||
\(742\) | −6.36972e6 | −0.424727 | ||||||||
\(743\) | −2.11163e7 | −1.40329 | −0.701643 | − | 0.712529i | \(-0.747550\pi\) | ||||
−0.701643 | + | 0.712529i | \(0.747550\pi\) | |||||||
\(744\) | −5.11366e7 | −3.38688 | ||||||||
\(745\) | −7.07797e6 | −0.467216 | ||||||||
\(746\) | −2.35627e7 | −1.55017 | ||||||||
\(747\) | −2.15566e7 | −1.41345 | ||||||||
\(748\) | 4.53676e6 | 0.296477 | ||||||||
\(749\) | 2.64590e6 | 0.172333 | ||||||||
\(750\) | −3.34524e6 | −0.217157 | ||||||||
\(751\) | −1.42227e7 | −0.920199 | −0.460100 | − | 0.887867i | \(-0.652186\pi\) | ||||
−0.460100 | + | 0.887867i | \(0.652186\pi\) | |||||||
\(752\) | −9.44466e6 | −0.609034 | ||||||||
\(753\) | −1.90760e7 | −1.22603 | ||||||||
\(754\) | −3.58302e7 | −2.29520 | ||||||||
\(755\) | −1.30803e7 | −0.835122 | ||||||||
\(756\) | 2.07388e6 | 0.131971 | ||||||||
\(757\) | −2.88203e7 | −1.82792 | −0.913962 | − | 0.405800i | \(-0.866993\pi\) | ||||
−0.913962 | + | 0.405800i | \(0.866993\pi\) | |||||||
\(758\) | −1.08070e6 | −0.0683176 | ||||||||
\(759\) | −653595. | −0.0411817 | ||||||||
\(760\) | 3.32867e6 | 0.209043 | ||||||||
\(761\) | −1.53179e6 | −0.0958823 | −0.0479412 | − | 0.998850i | \(-0.515266\pi\) | ||||
−0.0479412 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(762\) | 6.01922e7 | 3.75537 | ||||||||
\(763\) | 7.57605e6 | 0.471120 | ||||||||
\(764\) | −3.88700e7 | −2.40925 | ||||||||
\(765\) | −2.89027e6 | −0.178560 | ||||||||
\(766\) | −3.62008e7 | −2.22918 | ||||||||
\(767\) | −1.00148e7 | −0.614690 | ||||||||
\(768\) | 4.47222e7 | 2.73603 | ||||||||
\(769\) | −1.87825e7 | −1.14535 | −0.572675 | − | 0.819782i | \(-0.694094\pi\) | ||||
−0.572675 | + | 0.819782i | \(0.694094\pi\) | |||||||
\(770\) | 1.38412e6 | 0.0841292 | ||||||||
\(771\) | −2.98710e7 | −1.80973 | ||||||||
\(772\) | 2.92306e7 | 1.76520 | ||||||||
\(773\) | −9.97295e6 | −0.600309 | −0.300155 | − | 0.953891i | \(-0.597038\pi\) | ||||
−0.300155 | + | 0.953891i | \(0.597038\pi\) | |||||||
\(774\) | 2.43359e7 | 1.46014 | ||||||||
\(775\) | −4.06251e6 | −0.242963 | ||||||||
\(776\) | 1.89938e7 | 1.13229 | ||||||||
\(777\) | −1.31959e7 | −0.784126 | ||||||||
\(778\) | −2.47588e7 | −1.46649 | ||||||||
\(779\) | −5.47606e6 | −0.323314 | ||||||||
\(780\) | 2.16495e7 | 1.27412 | ||||||||
\(781\) | −7.69398e6 | −0.451360 | ||||||||
\(782\) | −1.38630e6 | −0.0810661 | ||||||||
\(783\) | 4.00010e6 | 0.233167 | ||||||||
\(784\) | −2.21248e7 | −1.28555 | ||||||||
\(785\) | 1.08749e7 | 0.629870 | ||||||||
\(786\) | −7.76188e7 | −4.48137 | ||||||||
\(787\) | −2.21631e7 | −1.27554 | −0.637770 | − | 0.770227i | \(-0.720143\pi\) | ||||
−0.637770 | + | 0.770227i | \(0.720143\pi\) | |||||||
\(788\) | −4.26503e7 | −2.44684 | ||||||||
\(789\) | −573619. | −0.0328043 | ||||||||
\(790\) | −1.44334e7 | −0.822813 | ||||||||
\(791\) | −8.64399e6 | −0.491217 | ||||||||
\(792\) | −9.46006e6 | −0.535897 | ||||||||
\(793\) | 4.51219e6 | 0.254803 | ||||||||
\(794\) | −3.47910e6 | −0.195846 | ||||||||
\(795\) | 7.42345e6 | 0.416570 | ||||||||
\(796\) | −6.50569e7 | −3.63924 | ||||||||
\(797\) | −2.27378e7 | −1.26795 | −0.633976 | − | 0.773353i | \(-0.718578\pi\) | ||||
−0.633976 | + | 0.773353i | \(0.718578\pi\) | |||||||
\(798\) | 3.52330e6 | 0.195858 | ||||||||
\(799\) | −3.42918e6 | −0.190030 | ||||||||
\(800\) | −2.04675e6 | −0.113068 | ||||||||
\(801\) | −3.81907e6 | −0.210318 | ||||||||
\(802\) | 3.30795e7 | 1.81603 | ||||||||
\(803\) | 8.82038e6 | 0.482724 | ||||||||
\(804\) | 3.33397e7 | 1.81895 | ||||||||
\(805\) | −288605. | −0.0156969 | ||||||||
\(806\) | 3.85296e7 | 2.08909 | ||||||||
\(807\) | 1.60187e7 | 0.865852 | ||||||||
\(808\) | −1.93182e7 | −1.04097 | ||||||||
\(809\) | −1.89079e7 | −1.01571 | −0.507857 | − | 0.861441i | \(-0.669562\pi\) | ||||
−0.507857 | + | 0.861441i | \(0.669562\pi\) | |||||||
\(810\) | −1.64674e7 | −0.881889 | ||||||||
\(811\) | 2.13760e7 | 1.14123 | 0.570617 | − | 0.821216i | \(-0.306704\pi\) | ||||
0.570617 | + | 0.821216i | \(0.306704\pi\) | |||||||
\(812\) | 1.89431e7 | 1.00823 | ||||||||
\(813\) | 1.69441e7 | 0.899069 | ||||||||
\(814\) | −1.64820e7 | −0.871864 | ||||||||
\(815\) | −9.01150e6 | −0.475229 | ||||||||
\(816\) | −1.74750e7 | −0.918736 | ||||||||
\(817\) | −4.12910e6 | −0.216421 | ||||||||
\(818\) | −2.55358e7 | −1.33434 | ||||||||
\(819\) | 5.70672e6 | 0.297287 | ||||||||
\(820\) | 2.60704e7 | 1.35398 | ||||||||
\(821\) | −3.59719e6 | −0.186254 | −0.0931269 | − | 0.995654i | \(-0.529686\pi\) | ||||
−0.0931269 | + | 0.995654i | \(0.529686\pi\) | |||||||
\(822\) | 4.02690e7 | 2.07870 | ||||||||
\(823\) | 1.79216e7 | 0.922308 | 0.461154 | − | 0.887320i | \(-0.347436\pi\) | ||||
0.461154 | + | 0.887320i | \(0.347436\pi\) | |||||||
\(824\) | −1.24693e7 | −0.639770 | ||||||||
\(825\) | −1.61309e6 | −0.0825134 | ||||||||
\(826\) | 7.75936e6 | 0.395709 | ||||||||
\(827\) | −9.95628e6 | −0.506213 | −0.253106 | − | 0.967438i | \(-0.581452\pi\) | ||||
−0.253106 | + | 0.967438i | \(0.581452\pi\) | |||||||
\(828\) | 3.69030e6 | 0.187062 | ||||||||
\(829\) | −1.70509e7 | −0.861711 | −0.430855 | − | 0.902421i | \(-0.641788\pi\) | ||||
−0.430855 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(830\) | −2.55181e7 | −1.28574 | ||||||||
\(831\) | −2.44383e7 | −1.22763 | ||||||||
\(832\) | −8.97565e6 | −0.449529 | ||||||||
\(833\) | −8.03310e6 | −0.401116 | ||||||||
\(834\) | 7.62190e7 | 3.79444 | ||||||||
\(835\) | 1.69826e6 | 0.0842923 | ||||||||
\(836\) | 3.00289e6 | 0.148602 | ||||||||
\(837\) | −4.30146e6 | −0.212228 | ||||||||
\(838\) | 3.31822e6 | 0.163228 | ||||||||
\(839\) | 833322. | 0.0408703 | 0.0204352 | − | 0.999791i | \(-0.493495\pi\) | ||||
0.0204352 | + | 0.999791i | \(0.493495\pi\) | |||||||
\(840\) | −8.96585e6 | −0.438423 | ||||||||
\(841\) | 1.60263e7 | 0.781344 | ||||||||
\(842\) | 2.42640e7 | 1.17946 | ||||||||
\(843\) | 4.82746e7 | 2.33965 | ||||||||
\(844\) | 1.17670e7 | 0.568606 | ||||||||
\(845\) | 563191. | 0.0271340 | ||||||||
\(846\) | 1.33775e7 | 0.642614 | ||||||||
\(847\) | 667429. | 0.0319666 | ||||||||
\(848\) | 2.09113e7 | 0.998600 | ||||||||
\(849\) | 4.07087e7 | 1.93829 | ||||||||
\(850\) | −3.42142e6 | −0.162427 | ||||||||
\(851\) | 3.43669e6 | 0.162673 | ||||||||
\(852\) | 9.32409e7 | 4.40056 | ||||||||
\(853\) | 3.98036e7 | 1.87305 | 0.936525 | − | 0.350600i | \(-0.114022\pi\) | ||||
0.936525 | + | 0.350600i | \(0.114022\pi\) | |||||||
\(854\) | −3.49598e6 | −0.164030 | ||||||||
\(855\) | −1.91308e6 | −0.0894988 | ||||||||
\(856\) | −2.14074e7 | −0.998570 | ||||||||
\(857\) | −2.44196e7 | −1.13576 | −0.567880 | − | 0.823111i | \(-0.692236\pi\) | ||||
−0.567880 | + | 0.823111i | \(0.692236\pi\) | |||||||
\(858\) | 1.52989e7 | 0.709482 | ||||||||
\(859\) | 1.05741e7 | 0.488946 | 0.244473 | − | 0.969656i | \(-0.421385\pi\) | ||||
0.244473 | + | 0.969656i | \(0.421385\pi\) | |||||||
\(860\) | 1.96578e7 | 0.906336 | ||||||||
\(861\) | 1.47499e7 | 0.678080 | ||||||||
\(862\) | 3.08998e7 | 1.41640 | ||||||||
\(863\) | −1.89897e7 | −0.867941 | −0.433971 | − | 0.900927i | \(-0.642888\pi\) | ||||
−0.433971 | + | 0.900927i | \(0.642888\pi\) | |||||||
\(864\) | −2.16714e6 | −0.0987648 | ||||||||
\(865\) | 4.41541e6 | 0.200646 | ||||||||
\(866\) | −4.21449e7 | −1.90964 | ||||||||
\(867\) | 2.39409e7 | 1.08167 | ||||||||
\(868\) | −2.03702e7 | −0.917691 | ||||||||
\(869\) | −6.95986e6 | −0.312645 | ||||||||
\(870\) | −3.23532e7 | −1.44917 | ||||||||
\(871\) | −1.34272e7 | −0.599710 | ||||||||
\(872\) | −6.12960e7 | −2.72986 | ||||||||
\(873\) | −1.09163e7 | −0.484773 | ||||||||
\(874\) | −917594. | −0.0406323 | ||||||||
\(875\) | −712286. | −0.0314510 | ||||||||
\(876\) | −1.06891e8 | −4.70633 | ||||||||
\(877\) | −5.23888e6 | −0.230006 | −0.115003 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115003 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(878\) | −3.41448e7 | −1.49482 | ||||||||
\(879\) | 1.35208e7 | 0.590243 | ||||||||
\(880\) | −4.54396e6 | −0.197801 | ||||||||
\(881\) | 3.24651e7 | 1.40922 | 0.704608 | − | 0.709597i | \(-0.251123\pi\) | ||||
0.704608 | + | 0.709597i | \(0.251123\pi\) | |||||||
\(882\) | 3.13378e7 | 1.35643 | ||||||||
\(883\) | 1.58932e7 | 0.685979 | 0.342990 | − | 0.939339i | \(-0.388560\pi\) | ||||
0.342990 | + | 0.939339i | \(0.388560\pi\) | |||||||
\(884\) | 2.21425e7 | 0.953007 | ||||||||
\(885\) | −9.04298e6 | −0.388109 | ||||||||
\(886\) | 1.04425e7 | 0.446911 | ||||||||
\(887\) | −3.41180e7 | −1.45604 | −0.728022 | − | 0.685553i | \(-0.759560\pi\) | ||||
−0.728022 | + | 0.685553i | \(0.759560\pi\) | |||||||
\(888\) | 1.06765e8 | 4.54355 | ||||||||
\(889\) | 1.28164e7 | 0.543892 | ||||||||
\(890\) | −4.52092e6 | −0.191316 | ||||||||
\(891\) | −7.94068e6 | −0.335092 | ||||||||
\(892\) | 3.33325e7 | 1.40267 | ||||||||
\(893\) | −2.26978e6 | −0.0952479 | ||||||||
\(894\) | 6.06145e7 | 2.53649 | ||||||||
\(895\) | −5.90814e6 | −0.246543 | ||||||||
\(896\) | 1.17314e7 | 0.488178 | ||||||||
\(897\) | −3.19000e6 | −0.132376 | ||||||||
\(898\) | −5.74890e7 | −2.37900 | ||||||||
\(899\) | −3.92901e7 | −1.62138 | ||||||||
\(900\) | 9.10778e6 | 0.374806 | ||||||||
\(901\) | 7.59250e6 | 0.311582 | ||||||||
\(902\) | 1.84230e7 | 0.753952 | ||||||||
\(903\) | 1.11218e7 | 0.453897 | ||||||||
\(904\) | 6.99364e7 | 2.84631 | ||||||||
\(905\) | −1.20256e7 | −0.488073 | ||||||||
\(906\) | 1.12017e8 | 4.53382 | ||||||||
\(907\) | 3.87957e7 | 1.56590 | 0.782952 | − | 0.622082i | \(-0.213713\pi\) | ||||
0.782952 | + | 0.622082i | \(0.213713\pi\) | |||||||
\(908\) | −3.10563e7 | −1.25007 | ||||||||
\(909\) | 1.11027e7 | 0.445675 | ||||||||
\(910\) | 6.75546e6 | 0.270428 | ||||||||
\(911\) | −1.64385e7 | −0.656244 | −0.328122 | − | 0.944635i | \(-0.606416\pi\) | ||||
−0.328122 | + | 0.944635i | \(0.606416\pi\) | |||||||
\(912\) | −1.15667e7 | −0.460493 | ||||||||
\(913\) | −1.23050e7 | −0.488544 | ||||||||
\(914\) | 7.22989e7 | 2.86264 | ||||||||
\(915\) | 4.07432e6 | 0.160880 | ||||||||
\(916\) | 5.36043e6 | 0.211087 | ||||||||
\(917\) | −1.65270e7 | −0.649038 | ||||||||
\(918\) | −3.62267e6 | −0.141880 | ||||||||
\(919\) | 4.37235e7 | 1.70776 | 0.853879 | − | 0.520472i | \(-0.174244\pi\) | ||||
0.853879 | + | 0.520472i | \(0.174244\pi\) | |||||||
\(920\) | 2.33503e6 | 0.0909543 | ||||||||
\(921\) | −4.32071e7 | −1.67844 | ||||||||
\(922\) | −7.60123e6 | −0.294481 | ||||||||
\(923\) | −3.75519e7 | −1.45087 | ||||||||
\(924\) | −8.08837e6 | −0.311660 | ||||||||
\(925\) | 8.48185e6 | 0.325939 | ||||||||
\(926\) | 6.07027e7 | 2.32638 | ||||||||
\(927\) | 7.16645e6 | 0.273908 | ||||||||
\(928\) | −1.97949e7 | −0.754542 | ||||||||
\(929\) | 1.15292e6 | 0.0438288 | 0.0219144 | − | 0.999760i | \(-0.493024\pi\) | ||||
0.0219144 | + | 0.999760i | \(0.493024\pi\) | |||||||
\(930\) | 3.47906e7 | 1.31903 | ||||||||
\(931\) | −5.31713e6 | −0.201050 | ||||||||
\(932\) | −7.65733e7 | −2.88760 | ||||||||
\(933\) | 3.36794e7 | 1.26666 | ||||||||
\(934\) | −2.78595e7 | −1.04497 | ||||||||
\(935\) | −1.64983e6 | −0.0617176 | ||||||||
\(936\) | −4.61716e7 | −1.72260 | ||||||||
\(937\) | −3.33100e7 | −1.23944 | −0.619719 | − | 0.784823i | \(-0.712754\pi\) | ||||
−0.619719 | + | 0.784823i | \(0.712754\pi\) | |||||||
\(938\) | 1.04032e7 | 0.386066 | ||||||||
\(939\) | −521356. | −0.0192961 | ||||||||
\(940\) | 1.08060e7 | 0.398882 | ||||||||
\(941\) | −1.53770e7 | −0.566107 | −0.283053 | − | 0.959104i | \(-0.591347\pi\) | ||||
−0.283053 | + | 0.959104i | \(0.591347\pi\) | |||||||
\(942\) | −9.31307e7 | −3.41952 | ||||||||
\(943\) | −3.84140e6 | −0.140673 | ||||||||
\(944\) | −2.54734e7 | −0.930372 | ||||||||
\(945\) | −754182. | −0.0274724 | ||||||||
\(946\) | 1.38914e7 | 0.504684 | ||||||||
\(947\) | −1.30035e7 | −0.471177 | −0.235589 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235589 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(948\) | 8.43444e7 | 3.04814 | ||||||||
\(949\) | 4.30496e7 | 1.55168 | ||||||||
\(950\) | −2.26465e6 | −0.0814127 | ||||||||
\(951\) | 5.12901e7 | 1.83900 | ||||||||
\(952\) | −9.17003e6 | −0.327928 | ||||||||
\(953\) | 1.56383e7 | 0.557772 | 0.278886 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278886 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(954\) | −2.96190e7 | −1.05366 | ||||||||
\(955\) | 1.41354e7 | 0.501533 | ||||||||
\(956\) | 8.52881e7 | 3.01817 | ||||||||
\(957\) | −1.56008e7 | −0.550641 | ||||||||
\(958\) | 9.09008e7 | 3.20003 | ||||||||
\(959\) | 8.57428e6 | 0.301059 | ||||||||
\(960\) | −8.10463e6 | −0.283828 | ||||||||
\(961\) | 1.36211e7 | 0.475776 | ||||||||
\(962\) | −8.04435e7 | −2.80255 | ||||||||
\(963\) | 1.23034e7 | 0.427523 | ||||||||
\(964\) | −1.12360e7 | −0.389422 | ||||||||
\(965\) | −1.06299e7 | −0.367462 | ||||||||
\(966\) | 2.47156e6 | 0.0852175 | ||||||||
\(967\) | 3.26283e7 | 1.12209 | 0.561046 | − | 0.827785i | \(-0.310399\pi\) | ||||
0.561046 | + | 0.827785i | \(0.310399\pi\) | |||||||
\(968\) | −5.40000e6 | −0.185228 | ||||||||
\(969\) | −4.19966e6 | −0.143683 | ||||||||
\(970\) | −1.29224e7 | −0.440974 | ||||||||
\(971\) | 2.99551e7 | 1.01958 | 0.509792 | − | 0.860298i | \(-0.329722\pi\) | ||||
0.509792 | + | 0.860298i | \(0.329722\pi\) | |||||||
\(972\) | 8.51758e7 | 2.89168 | ||||||||
\(973\) | 1.62289e7 | 0.549551 | ||||||||
\(974\) | 9.22194e6 | 0.311476 | ||||||||
\(975\) | −7.87301e6 | −0.265234 | ||||||||
\(976\) | 1.14770e7 | 0.385661 | ||||||||
\(977\) | 2.68540e7 | 0.900063 | 0.450031 | − | 0.893013i | \(-0.351413\pi\) | ||||
0.450031 | + | 0.893013i | \(0.351413\pi\) | |||||||
\(978\) | 7.71729e7 | 2.57999 | ||||||||
\(979\) | −2.18001e6 | −0.0726944 | ||||||||
\(980\) | 2.53138e7 | 0.841961 | ||||||||
\(981\) | 3.52285e7 | 1.16875 | ||||||||
\(982\) | 3.00751e7 | 0.995241 | ||||||||
\(983\) | 4.78145e6 | 0.157825 | 0.0789125 | − | 0.996882i | \(-0.474855\pi\) | ||||
0.0789125 | + | 0.996882i | \(0.474855\pi\) | |||||||
\(984\) | −1.19338e8 | −3.92907 | ||||||||
\(985\) | 1.55101e7 | 0.509359 | ||||||||
\(986\) | −3.30899e7 | −1.08394 | ||||||||
\(987\) | 6.11372e6 | 0.199762 | ||||||||
\(988\) | 1.46562e7 | 0.477671 | ||||||||
\(989\) | −2.89653e6 | −0.0941644 | ||||||||
\(990\) | 6.43612e6 | 0.208707 | ||||||||
\(991\) | −5.75490e7 | −1.86146 | −0.930730 | − | 0.365706i | \(-0.880827\pi\) | ||||
−0.930730 | + | 0.365706i | \(0.880827\pi\) | |||||||
\(992\) | 2.12863e7 | 0.686784 | ||||||||
\(993\) | −1.16975e7 | −0.376460 | ||||||||
\(994\) | 2.90947e7 | 0.934002 | ||||||||
\(995\) | 2.36584e7 | 0.757580 | ||||||||
\(996\) | 1.49120e8 | 4.76308 | ||||||||
\(997\) | −1.55769e7 | −0.496298 | −0.248149 | − | 0.968722i | \(-0.579822\pi\) | ||||
−0.248149 | + | 0.968722i | \(0.579822\pi\) | |||||||
\(998\) | −3.52019e6 | −0.111877 | ||||||||
\(999\) | 8.98074e6 | 0.284707 |
(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 | 1045.6.a.a.1.2 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.a.1.2 | ✓ | 35 | 1.1 | even | 1 | trivial |