Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,6,Mod(1,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("363.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(58.2193265921\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 363.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.176777 | −0.0883883 | − | 0.996086i | \(-0.528172\pi\) | ||||
−0.0883883 | + | 0.996086i | \(0.528172\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −31.0000 | −0.968750 | ||||||||
\(5\) | −92.0000 | −1.64575 | −0.822873 | − | 0.568225i | \(-0.807630\pi\) | ||||
−0.822873 | + | 0.568225i | \(0.807630\pi\) | |||||||
\(6\) | −9.00000 | −0.102062 | ||||||||
\(7\) | 26.0000 | 0.200553 | 0.100276 | − | 0.994960i | \(-0.468027\pi\) | ||||
0.100276 | + | 0.994960i | \(0.468027\pi\) | |||||||
\(8\) | 63.0000 | 0.348029 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 92.0000 | 0.290930 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −279.000 | −0.559308 | ||||||||
\(13\) | 692.000 | 1.13566 | 0.567829 | − | 0.823146i | \(-0.307783\pi\) | ||||
0.567829 | + | 0.823146i | \(0.307783\pi\) | |||||||
\(14\) | −26.0000 | −0.0354530 | ||||||||
\(15\) | −828.000 | −0.950172 | ||||||||
\(16\) | 929.000 | 0.907227 | ||||||||
\(17\) | 1442.00 | 1.21016 | 0.605080 | − | 0.796165i | \(-0.293141\pi\) | ||||
0.605080 | + | 0.796165i | \(0.293141\pi\) | |||||||
\(18\) | −81.0000 | −0.0589256 | ||||||||
\(19\) | −2160.00 | −1.37268 | −0.686341 | − | 0.727280i | \(-0.740784\pi\) | ||||
−0.686341 | + | 0.727280i | \(0.740784\pi\) | |||||||
\(20\) | 2852.00 | 1.59432 | ||||||||
\(21\) | 234.000 | 0.115789 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1582.00 | −0.623572 | −0.311786 | − | 0.950152i | \(-0.600927\pi\) | ||||
−0.311786 | + | 0.950152i | \(0.600927\pi\) | |||||||
\(24\) | 567.000 | 0.200935 | ||||||||
\(25\) | 5339.00 | 1.70848 | ||||||||
\(26\) | −692.000 | −0.200758 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −806.000 | −0.194285 | ||||||||
\(29\) | 5526.00 | 1.22016 | 0.610079 | − | 0.792341i | \(-0.291138\pi\) | ||||
0.610079 | + | 0.792341i | \(0.291138\pi\) | |||||||
\(30\) | 828.000 | 0.167968 | ||||||||
\(31\) | 4792.00 | 0.895597 | 0.447798 | − | 0.894135i | \(-0.352208\pi\) | ||||
0.447798 | + | 0.894135i | \(0.352208\pi\) | |||||||
\(32\) | −2945.00 | −0.508406 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1442.00 | −0.213928 | ||||||||
\(35\) | −2392.00 | −0.330059 | ||||||||
\(36\) | −2511.00 | −0.322917 | ||||||||
\(37\) | −10194.0 | −1.22417 | −0.612083 | − | 0.790794i | \(-0.709668\pi\) | ||||
−0.612083 | + | 0.790794i | \(0.709668\pi\) | |||||||
\(38\) | 2160.00 | 0.242658 | ||||||||
\(39\) | 6228.00 | 0.655673 | ||||||||
\(40\) | −5796.00 | −0.572768 | ||||||||
\(41\) | 10622.0 | 0.986840 | 0.493420 | − | 0.869791i | \(-0.335747\pi\) | ||||
0.493420 | + | 0.869791i | \(0.335747\pi\) | |||||||
\(42\) | −234.000 | −0.0204688 | ||||||||
\(43\) | −8580.00 | −0.707646 | −0.353823 | − | 0.935312i | \(-0.615119\pi\) | ||||
−0.353823 | + | 0.935312i | \(0.615119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7452.00 | −0.548582 | ||||||||
\(46\) | 1582.00 | 0.110233 | ||||||||
\(47\) | −2362.00 | −0.155968 | −0.0779840 | − | 0.996955i | \(-0.524848\pi\) | ||||
−0.0779840 | + | 0.996955i | \(0.524848\pi\) | |||||||
\(48\) | 8361.00 | 0.523788 | ||||||||
\(49\) | −16131.0 | −0.959779 | ||||||||
\(50\) | −5339.00 | −0.302019 | ||||||||
\(51\) | 12978.0 | 0.698686 | ||||||||
\(52\) | −21452.0 | −1.10017 | ||||||||
\(53\) | −30804.0 | −1.50632 | −0.753160 | − | 0.657837i | \(-0.771472\pi\) | ||||
−0.753160 | + | 0.657837i | \(0.771472\pi\) | |||||||
\(54\) | −729.000 | −0.0340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1638.00 | 0.0697981 | ||||||||
\(57\) | −19440.0 | −0.792518 | ||||||||
\(58\) | −5526.00 | −0.215695 | ||||||||
\(59\) | 6416.00 | 0.239957 | 0.119979 | − | 0.992776i | \(-0.461717\pi\) | ||||
0.119979 | + | 0.992776i | \(0.461717\pi\) | |||||||
\(60\) | 25668.0 | 0.920479 | ||||||||
\(61\) | −42096.0 | −1.44849 | −0.724246 | − | 0.689541i | \(-0.757812\pi\) | ||||
−0.724246 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(62\) | −4792.00 | −0.158321 | ||||||||
\(63\) | 2106.00 | 0.0668509 | ||||||||
\(64\) | −26783.0 | −0.817352 | ||||||||
\(65\) | −63664.0 | −1.86901 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −28444.0 | −0.774112 | −0.387056 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387056 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(68\) | −44702.0 | −1.17234 | ||||||||
\(69\) | −14238.0 | −0.360020 | ||||||||
\(70\) | 2392.00 | 0.0583467 | ||||||||
\(71\) | 45690.0 | 1.07566 | 0.537830 | − | 0.843053i | \(-0.319244\pi\) | ||||
0.537830 | + | 0.843053i | \(0.319244\pi\) | |||||||
\(72\) | 5103.00 | 0.116010 | ||||||||
\(73\) | 18374.0 | 0.403549 | 0.201775 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201775 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(74\) | 10194.0 | 0.216404 | ||||||||
\(75\) | 48051.0 | 0.986391 | ||||||||
\(76\) | 66960.0 | 1.32979 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6228.00 | −0.115908 | ||||||||
\(79\) | 105214. | 1.89673 | 0.948366 | − | 0.317179i | \(-0.102736\pi\) | ||||
0.948366 | + | 0.317179i | \(0.102736\pi\) | |||||||
\(80\) | −85468.0 | −1.49306 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −10622.0 | −0.174450 | ||||||||
\(83\) | −62292.0 | −0.992515 | −0.496257 | − | 0.868175i | \(-0.665293\pi\) | ||||
−0.496257 | + | 0.868175i | \(0.665293\pi\) | |||||||
\(84\) | −7254.00 | −0.112171 | ||||||||
\(85\) | −132664. | −1.99162 | ||||||||
\(86\) | 8580.00 | 0.125095 | ||||||||
\(87\) | 49734.0 | 0.704458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −72246.0 | −0.966805 | −0.483402 | − | 0.875398i | \(-0.660599\pi\) | ||||
−0.483402 | + | 0.875398i | \(0.660599\pi\) | |||||||
\(90\) | 7452.00 | 0.0969765 | ||||||||
\(91\) | 17992.0 | 0.227759 | ||||||||
\(92\) | 49042.0 | 0.604086 | ||||||||
\(93\) | 43128.0 | 0.517073 | ||||||||
\(94\) | 2362.00 | 0.0275715 | ||||||||
\(95\) | 198720. | 2.25908 | ||||||||
\(96\) | −26505.0 | −0.293528 | ||||||||
\(97\) | 79262.0 | 0.855334 | 0.427667 | − | 0.903936i | \(-0.359336\pi\) | ||||
0.427667 | + | 0.903936i | \(0.359336\pi\) | |||||||
\(98\) | 16131.0 | 0.169667 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −165509. | −1.65509 | ||||||||
\(101\) | 24958.0 | 0.243448 | 0.121724 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121724 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(102\) | −12978.0 | −0.123511 | ||||||||
\(103\) | −56812.0 | −0.527651 | −0.263826 | − | 0.964570i | \(-0.584984\pi\) | ||||
−0.263826 | + | 0.964570i | \(0.584984\pi\) | |||||||
\(104\) | 43596.0 | 0.395242 | ||||||||
\(105\) | −21528.0 | −0.190559 | ||||||||
\(106\) | 30804.0 | 0.266282 | ||||||||
\(107\) | 12492.0 | 0.105481 | 0.0527403 | − | 0.998608i | \(-0.483204\pi\) | ||||
0.0527403 | + | 0.998608i | \(0.483204\pi\) | |||||||
\(108\) | −22599.0 | −0.186436 | ||||||||
\(109\) | −198748. | −1.60227 | −0.801137 | − | 0.598482i | \(-0.795771\pi\) | ||||
−0.801137 | + | 0.598482i | \(0.795771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −91746.0 | −0.706773 | ||||||||
\(112\) | 24154.0 | 0.181947 | ||||||||
\(113\) | 166554. | 1.22704 | 0.613520 | − | 0.789679i | \(-0.289753\pi\) | ||||
0.613520 | + | 0.789679i | \(0.289753\pi\) | |||||||
\(114\) | 19440.0 | 0.140099 | ||||||||
\(115\) | 145544. | 1.02624 | ||||||||
\(116\) | −171306. | −1.18203 | ||||||||
\(117\) | 56052.0 | 0.378553 | ||||||||
\(118\) | −6416.00 | −0.0424189 | ||||||||
\(119\) | 37492.0 | 0.242701 | ||||||||
\(120\) | −52164.0 | −0.330687 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 42096.0 | 0.256060 | ||||||||
\(123\) | 95598.0 | 0.569752 | ||||||||
\(124\) | −148552. | −0.867609 | ||||||||
\(125\) | −203688. | −1.16598 | ||||||||
\(126\) | −2106.00 | −0.0118177 | ||||||||
\(127\) | −304226. | −1.67374 | −0.836868 | − | 0.547405i | \(-0.815616\pi\) | ||||
−0.836868 | + | 0.547405i | \(0.815616\pi\) | |||||||
\(128\) | 121023. | 0.652894 | ||||||||
\(129\) | −77220.0 | −0.408560 | ||||||||
\(130\) | 63664.0 | 0.330397 | ||||||||
\(131\) | −274428. | −1.39717 | −0.698586 | − | 0.715526i | \(-0.746187\pi\) | ||||
−0.698586 | + | 0.715526i | \(0.746187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56160.0 | −0.275295 | ||||||||
\(134\) | 28444.0 | 0.136845 | ||||||||
\(135\) | −67068.0 | −0.316724 | ||||||||
\(136\) | 90846.0 | 0.421171 | ||||||||
\(137\) | −245458. | −1.11732 | −0.558658 | − | 0.829398i | \(-0.688683\pi\) | ||||
−0.558658 | + | 0.829398i | \(0.688683\pi\) | |||||||
\(138\) | 14238.0 | 0.0636431 | ||||||||
\(139\) | 59888.0 | 0.262907 | 0.131454 | − | 0.991322i | \(-0.458036\pi\) | ||||
0.131454 | + | 0.991322i | \(0.458036\pi\) | |||||||
\(140\) | 74152.0 | 0.319744 | ||||||||
\(141\) | −21258.0 | −0.0900481 | ||||||||
\(142\) | −45690.0 | −0.190152 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 75249.0 | 0.302409 | ||||||||
\(145\) | −508392. | −2.00807 | ||||||||
\(146\) | −18374.0 | −0.0713381 | ||||||||
\(147\) | −145179. | −0.554128 | ||||||||
\(148\) | 316014. | 1.18591 | ||||||||
\(149\) | −72038.0 | −0.265825 | −0.132913 | − | 0.991128i | \(-0.542433\pi\) | ||||
−0.132913 | + | 0.991128i | \(0.542433\pi\) | |||||||
\(150\) | −48051.0 | −0.174371 | ||||||||
\(151\) | 323110. | 1.15321 | 0.576605 | − | 0.817023i | \(-0.304377\pi\) | ||||
0.576605 | + | 0.817023i | \(0.304377\pi\) | |||||||
\(152\) | −136080. | −0.477733 | ||||||||
\(153\) | 116802. | 0.403387 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −440864. | −1.47393 | ||||||||
\(156\) | −193068. | −0.635183 | ||||||||
\(157\) | −318766. | −1.03210 | −0.516051 | − | 0.856558i | \(-0.672599\pi\) | ||||
−0.516051 | + | 0.856558i | \(0.672599\pi\) | |||||||
\(158\) | −105214. | −0.335298 | ||||||||
\(159\) | −277236. | −0.869675 | ||||||||
\(160\) | 270940. | 0.836707 | ||||||||
\(161\) | −41132.0 | −0.125059 | ||||||||
\(162\) | −6561.00 | −0.0196419 | ||||||||
\(163\) | −431996. | −1.27353 | −0.636767 | − | 0.771056i | \(-0.719729\pi\) | ||||
−0.636767 | + | 0.771056i | \(0.719729\pi\) | |||||||
\(164\) | −329282. | −0.956001 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62292.0 | 0.175454 | ||||||||
\(167\) | 251580. | 0.698047 | 0.349024 | − | 0.937114i | \(-0.386513\pi\) | ||||
0.349024 | + | 0.937114i | \(0.386513\pi\) | |||||||
\(168\) | 14742.0 | 0.0402980 | ||||||||
\(169\) | 107571. | 0.289720 | ||||||||
\(170\) | 132664. | 0.352071 | ||||||||
\(171\) | −174960. | −0.457560 | ||||||||
\(172\) | 265980. | 0.685532 | ||||||||
\(173\) | −476634. | −1.21079 | −0.605396 | − | 0.795924i | \(-0.706985\pi\) | ||||
−0.605396 | + | 0.795924i | \(0.706985\pi\) | |||||||
\(174\) | −49734.0 | −0.124532 | ||||||||
\(175\) | 138814. | 0.342640 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 57744.0 | 0.138540 | ||||||||
\(178\) | 72246.0 | 0.170909 | ||||||||
\(179\) | 90192.0 | 0.210395 | 0.105198 | − | 0.994451i | \(-0.466453\pi\) | ||||
0.105198 | + | 0.994451i | \(0.466453\pi\) | |||||||
\(180\) | 231012. | 0.531439 | ||||||||
\(181\) | 248002. | 0.562676 | 0.281338 | − | 0.959609i | \(-0.409222\pi\) | ||||
0.281338 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(182\) | −17992.0 | −0.0402625 | ||||||||
\(183\) | −378864. | −0.836288 | ||||||||
\(184\) | −99666.0 | −0.217021 | ||||||||
\(185\) | 937848. | 2.01467 | ||||||||
\(186\) | −43128.0 | −0.0914065 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 73222.0 | 0.151094 | ||||||||
\(189\) | 18954.0 | 0.0385964 | ||||||||
\(190\) | −198720. | −0.399354 | ||||||||
\(191\) | −156802. | −0.311006 | −0.155503 | − | 0.987835i | \(-0.549700\pi\) | ||||
−0.155503 | + | 0.987835i | \(0.549700\pi\) | |||||||
\(192\) | −241047. | −0.471899 | ||||||||
\(193\) | 431234. | 0.833335 | 0.416668 | − | 0.909059i | \(-0.363198\pi\) | ||||
0.416668 | + | 0.909059i | \(0.363198\pi\) | |||||||
\(194\) | −79262.0 | −0.151203 | ||||||||
\(195\) | −572976. | −1.07907 | ||||||||
\(196\) | 500061. | 0.929786 | ||||||||
\(197\) | 864974. | 1.58795 | 0.793976 | − | 0.607949i | \(-0.208007\pi\) | ||||
0.793976 | + | 0.607949i | \(0.208007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −480060. | −0.859336 | −0.429668 | − | 0.902987i | \(-0.641369\pi\) | ||||
−0.429668 | + | 0.902987i | \(0.641369\pi\) | |||||||
\(200\) | 336357. | 0.594601 | ||||||||
\(201\) | −255996. | −0.446934 | ||||||||
\(202\) | −24958.0 | −0.0430359 | ||||||||
\(203\) | 143676. | 0.244706 | ||||||||
\(204\) | −402318. | −0.676853 | ||||||||
\(205\) | −977224. | −1.62409 | ||||||||
\(206\) | 56812.0 | 0.0932765 | ||||||||
\(207\) | −128142. | −0.207857 | ||||||||
\(208\) | 642868. | 1.03030 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 21528.0 | 0.0336865 | ||||||||
\(211\) | −525900. | −0.813199 | −0.406600 | − | 0.913606i | \(-0.633286\pi\) | ||||
−0.406600 | + | 0.913606i | \(0.633286\pi\) | |||||||
\(212\) | 954924. | 1.45925 | ||||||||
\(213\) | 411210. | 0.621033 | ||||||||
\(214\) | −12492.0 | −0.0186465 | ||||||||
\(215\) | 789360. | 1.16461 | ||||||||
\(216\) | 45927.0 | 0.0669782 | ||||||||
\(217\) | 124592. | 0.179614 | ||||||||
\(218\) | 198748. | 0.283245 | ||||||||
\(219\) | 165366. | 0.232989 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 997864. | 1.37433 | ||||||||
\(222\) | 91746.0 | 0.124941 | ||||||||
\(223\) | −245264. | −0.330272 | −0.165136 | − | 0.986271i | \(-0.552806\pi\) | ||||
−0.165136 | + | 0.986271i | \(0.552806\pi\) | |||||||
\(224\) | −76570.0 | −0.101962 | ||||||||
\(225\) | 432459. | 0.569493 | ||||||||
\(226\) | −166554. | −0.216912 | ||||||||
\(227\) | 799308. | 1.02955 | 0.514777 | − | 0.857324i | \(-0.327875\pi\) | ||||
0.514777 | + | 0.857324i | \(0.327875\pi\) | |||||||
\(228\) | 602640. | 0.767752 | ||||||||
\(229\) | −1.53989e6 | −1.94045 | −0.970224 | − | 0.242208i | \(-0.922128\pi\) | ||||
−0.970224 | + | 0.242208i | \(0.922128\pi\) | |||||||
\(230\) | −145544. | −0.181416 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 348138. | 0.424650 | ||||||||
\(233\) | 721830. | 0.871054 | 0.435527 | − | 0.900176i | \(-0.356562\pi\) | ||||
0.435527 | + | 0.900176i | \(0.356562\pi\) | |||||||
\(234\) | −56052.0 | −0.0669193 | ||||||||
\(235\) | 217304. | 0.256684 | ||||||||
\(236\) | −198896. | −0.232459 | ||||||||
\(237\) | 946926. | 1.09508 | ||||||||
\(238\) | −37492.0 | −0.0429038 | ||||||||
\(239\) | 638436. | 0.722974 | 0.361487 | − | 0.932377i | \(-0.382269\pi\) | ||||
0.361487 | + | 0.932377i | \(0.382269\pi\) | |||||||
\(240\) | −769212. | −0.862021 | ||||||||
\(241\) | −220990. | −0.245092 | −0.122546 | − | 0.992463i | \(-0.539106\pi\) | ||||
−0.122546 | + | 0.992463i | \(0.539106\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 1.30498e6 | 1.40323 | ||||||||
\(245\) | 1.48405e6 | 1.57955 | ||||||||
\(246\) | −95598.0 | −0.100719 | ||||||||
\(247\) | −1.49472e6 | −1.55890 | ||||||||
\(248\) | 301896. | 0.311694 | ||||||||
\(249\) | −560628. | −0.573029 | ||||||||
\(250\) | 203688. | 0.206118 | ||||||||
\(251\) | 627304. | 0.628483 | 0.314242 | − | 0.949343i | \(-0.398250\pi\) | ||||
0.314242 | + | 0.949343i | \(0.398250\pi\) | |||||||
\(252\) | −65286.0 | −0.0647618 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 304226. | 0.295878 | ||||||||
\(255\) | −1.19398e6 | −1.14986 | ||||||||
\(256\) | 736033. | 0.701936 | ||||||||
\(257\) | −468014. | −0.442004 | −0.221002 | − | 0.975273i | \(-0.570933\pi\) | ||||
−0.221002 | + | 0.975273i | \(0.570933\pi\) | |||||||
\(258\) | 77220.0 | 0.0722238 | ||||||||
\(259\) | −265044. | −0.245510 | ||||||||
\(260\) | 1.97358e6 | 1.81060 | ||||||||
\(261\) | 447606. | 0.406719 | ||||||||
\(262\) | 274428. | 0.246988 | ||||||||
\(263\) | −1.54510e6 | −1.37743 | −0.688713 | − | 0.725034i | \(-0.741824\pi\) | ||||
−0.688713 | + | 0.725034i | \(0.741824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.83397e6 | 2.47902 | ||||||||
\(266\) | 56160.0 | 0.0486657 | ||||||||
\(267\) | −650214. | −0.558185 | ||||||||
\(268\) | 881764. | 0.749921 | ||||||||
\(269\) | −1.07457e6 | −0.905430 | −0.452715 | − | 0.891655i | \(-0.649544\pi\) | ||||
−0.452715 | + | 0.891655i | \(0.649544\pi\) | |||||||
\(270\) | 67068.0 | 0.0559894 | ||||||||
\(271\) | −1.58723e6 | −1.31285 | −0.656427 | − | 0.754389i | \(-0.727933\pi\) | ||||
−0.656427 | + | 0.754389i | \(0.727933\pi\) | |||||||
\(272\) | 1.33962e6 | 1.09789 | ||||||||
\(273\) | 161928. | 0.131497 | ||||||||
\(274\) | 245458. | 0.197515 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 441378. | 0.348769 | ||||||||
\(277\) | −692704. | −0.542436 | −0.271218 | − | 0.962518i | \(-0.587426\pi\) | ||||
−0.271218 | + | 0.962518i | \(0.587426\pi\) | |||||||
\(278\) | −59888.0 | −0.0464759 | ||||||||
\(279\) | 388152. | 0.298532 | ||||||||
\(280\) | −150696. | −0.114870 | ||||||||
\(281\) | 567018. | 0.428382 | 0.214191 | − | 0.976792i | \(-0.431289\pi\) | ||||
0.214191 | + | 0.976792i | \(0.431289\pi\) | |||||||
\(282\) | 21258.0 | 0.0159184 | ||||||||
\(283\) | −714916. | −0.530626 | −0.265313 | − | 0.964162i | \(-0.585475\pi\) | ||||
−0.265313 | + | 0.964162i | \(0.585475\pi\) | |||||||
\(284\) | −1.41639e6 | −1.04205 | ||||||||
\(285\) | 1.78848e6 | 1.30428 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 276172. | 0.197913 | ||||||||
\(288\) | −238545. | −0.169469 | ||||||||
\(289\) | 659507. | 0.464488 | ||||||||
\(290\) | 508392. | 0.354980 | ||||||||
\(291\) | 713358. | 0.493827 | ||||||||
\(292\) | −569594. | −0.390938 | ||||||||
\(293\) | −2.14409e6 | −1.45907 | −0.729533 | − | 0.683946i | \(-0.760262\pi\) | ||||
−0.729533 | + | 0.683946i | \(0.760262\pi\) | |||||||
\(294\) | 145179. | 0.0979570 | ||||||||
\(295\) | −590272. | −0.394909 | ||||||||
\(296\) | −642222. | −0.426045 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 72038.0 | 0.0469917 | ||||||||
\(299\) | −1.09474e6 | −0.708165 | ||||||||
\(300\) | −1.48958e6 | −0.955567 | ||||||||
\(301\) | −223080. | −0.141920 | ||||||||
\(302\) | −323110. | −0.203860 | ||||||||
\(303\) | 224622. | 0.140555 | ||||||||
\(304\) | −2.00664e6 | −1.24533 | ||||||||
\(305\) | 3.87283e6 | 2.38385 | ||||||||
\(306\) | −116802. | −0.0713094 | ||||||||
\(307\) | 588808. | 0.356556 | 0.178278 | − | 0.983980i | \(-0.442947\pi\) | ||||
0.178278 | + | 0.983980i | \(0.442947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −511308. | −0.304640 | ||||||||
\(310\) | 440864. | 0.260556 | ||||||||
\(311\) | 2.51827e6 | 1.47639 | 0.738194 | − | 0.674588i | \(-0.235679\pi\) | ||||
0.738194 | + | 0.674588i | \(0.235679\pi\) | |||||||
\(312\) | 392364. | 0.228193 | ||||||||
\(313\) | −2.23562e6 | −1.28985 | −0.644923 | − | 0.764248i | \(-0.723110\pi\) | ||||
−0.644923 | + | 0.764248i | \(0.723110\pi\) | |||||||
\(314\) | 318766. | 0.182452 | ||||||||
\(315\) | −193752. | −0.110020 | ||||||||
\(316\) | −3.26163e6 | −1.83746 | ||||||||
\(317\) | 1.06079e6 | 0.592901 | 0.296450 | − | 0.955048i | \(-0.404197\pi\) | ||||
0.296450 | + | 0.955048i | \(0.404197\pi\) | |||||||
\(318\) | 277236. | 0.153738 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.46404e6 | 1.34515 | ||||||||
\(321\) | 112428. | 0.0608992 | ||||||||
\(322\) | 41132.0 | 0.0221075 | ||||||||
\(323\) | −3.11472e6 | −1.66116 | ||||||||
\(324\) | −203391. | −0.107639 | ||||||||
\(325\) | 3.69459e6 | 1.94025 | ||||||||
\(326\) | 431996. | 0.225131 | ||||||||
\(327\) | −1.78873e6 | −0.925073 | ||||||||
\(328\) | 669186. | 0.343449 | ||||||||
\(329\) | −61412.0 | −0.0312798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.34566e6 | −1.17678 | −0.588390 | − | 0.808577i | \(-0.700238\pi\) | ||||
−0.588390 | + | 0.808577i | \(0.700238\pi\) | |||||||
\(332\) | 1.93105e6 | 0.961499 | ||||||||
\(333\) | −825714. | −0.408055 | ||||||||
\(334\) | −251580. | −0.123399 | ||||||||
\(335\) | 2.61685e6 | 1.27399 | ||||||||
\(336\) | 217386. | 0.105047 | ||||||||
\(337\) | −839978. | −0.402896 | −0.201448 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201448 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(338\) | −107571. | −0.0512157 | ||||||||
\(339\) | 1.49899e6 | 0.708432 | ||||||||
\(340\) | 4.11258e6 | 1.92938 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 174960. | 0.0808860 | ||||||||
\(343\) | −856388. | −0.393039 | ||||||||
\(344\) | −540540. | −0.246281 | ||||||||
\(345\) | 1.30990e6 | 0.592501 | ||||||||
\(346\) | 476634. | 0.214040 | ||||||||
\(347\) | 2.02560e6 | 0.903086 | 0.451543 | − | 0.892249i | \(-0.350874\pi\) | ||||
0.451543 | + | 0.892249i | \(0.350874\pi\) | |||||||
\(348\) | −1.54175e6 | −0.682444 | ||||||||
\(349\) | 378924. | 0.166528 | 0.0832642 | − | 0.996528i | \(-0.473465\pi\) | ||||
0.0832642 | + | 0.996528i | \(0.473465\pi\) | |||||||
\(350\) | −138814. | −0.0605708 | ||||||||
\(351\) | 504468. | 0.218558 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.98730e6 | −0.848842 | −0.424421 | − | 0.905465i | \(-0.639522\pi\) | ||||
−0.424421 | + | 0.905465i | \(0.639522\pi\) | |||||||
\(354\) | −57744.0 | −0.0244906 | ||||||||
\(355\) | −4.20348e6 | −1.77026 | ||||||||
\(356\) | 2.23963e6 | 0.936592 | ||||||||
\(357\) | 337428. | 0.140123 | ||||||||
\(358\) | −90192.0 | −0.0371929 | ||||||||
\(359\) | 3.43975e6 | 1.40861 | 0.704305 | − | 0.709898i | \(-0.251259\pi\) | ||||
0.704305 | + | 0.709898i | \(0.251259\pi\) | |||||||
\(360\) | −469476. | −0.190923 | ||||||||
\(361\) | 2.18950e6 | 0.884254 | ||||||||
\(362\) | −248002. | −0.0994681 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −557752. | −0.220642 | ||||||||
\(365\) | −1.69041e6 | −0.664140 | ||||||||
\(366\) | 378864. | 0.147836 | ||||||||
\(367\) | −1.79679e6 | −0.696358 | −0.348179 | − | 0.937428i | \(-0.613200\pi\) | ||||
−0.348179 | + | 0.937428i | \(0.613200\pi\) | |||||||
\(368\) | −1.46968e6 | −0.565721 | ||||||||
\(369\) | 860382. | 0.328947 | ||||||||
\(370\) | −937848. | −0.356146 | ||||||||
\(371\) | −800904. | −0.302096 | ||||||||
\(372\) | −1.33697e6 | −0.500915 | ||||||||
\(373\) | 1.43541e6 | 0.534201 | 0.267100 | − | 0.963669i | \(-0.413934\pi\) | ||||
0.267100 | + | 0.963669i | \(0.413934\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.83319e6 | −0.673178 | ||||||||
\(376\) | −148806. | −0.0542814 | ||||||||
\(377\) | 3.82399e6 | 1.38568 | ||||||||
\(378\) | −18954.0 | −0.00682294 | ||||||||
\(379\) | 2.66235e6 | 0.952065 | 0.476033 | − | 0.879428i | \(-0.342074\pi\) | ||||
0.476033 | + | 0.879428i | \(0.342074\pi\) | |||||||
\(380\) | −6.16032e6 | −2.18849 | ||||||||
\(381\) | −2.73803e6 | −0.966332 | ||||||||
\(382\) | 156802. | 0.0549785 | ||||||||
\(383\) | 2.04091e6 | 0.710932 | 0.355466 | − | 0.934689i | \(-0.384322\pi\) | ||||
0.355466 | + | 0.934689i | \(0.384322\pi\) | |||||||
\(384\) | 1.08921e6 | 0.376949 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −431234. | −0.147314 | ||||||||
\(387\) | −694980. | −0.235882 | ||||||||
\(388\) | −2.45712e6 | −0.828605 | ||||||||
\(389\) | −4.29947e6 | −1.44059 | −0.720296 | − | 0.693667i | \(-0.755994\pi\) | ||||
−0.720296 | + | 0.693667i | \(0.755994\pi\) | |||||||
\(390\) | 572976. | 0.190755 | ||||||||
\(391\) | −2.28124e6 | −0.754623 | ||||||||
\(392\) | −1.01625e6 | −0.334031 | ||||||||
\(393\) | −2.46985e6 | −0.806658 | ||||||||
\(394\) | −864974. | −0.280713 | ||||||||
\(395\) | −9.67969e6 | −3.12154 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 728818. | 0.232083 | 0.116041 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116041 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(398\) | 480060. | 0.151911 | ||||||||
\(399\) | −505440. | −0.158942 | ||||||||
\(400\) | 4.95993e6 | 1.54998 | ||||||||
\(401\) | −5.92515e6 | −1.84009 | −0.920044 | − | 0.391814i | \(-0.871848\pi\) | ||||
−0.920044 | + | 0.391814i | \(0.871848\pi\) | |||||||
\(402\) | 255996. | 0.0790075 | ||||||||
\(403\) | 3.31606e6 | 1.01709 | ||||||||
\(404\) | −773698. | −0.235840 | ||||||||
\(405\) | −603612. | −0.182861 | ||||||||
\(406\) | −143676. | −0.0432583 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 817614. | 0.243163 | ||||||||
\(409\) | −1.38212e6 | −0.408542 | −0.204271 | − | 0.978914i | \(-0.565482\pi\) | ||||
−0.204271 | + | 0.978914i | \(0.565482\pi\) | |||||||
\(410\) | 977224. | 0.287101 | ||||||||
\(411\) | −2.20912e6 | −0.645082 | ||||||||
\(412\) | 1.76117e6 | 0.511162 | ||||||||
\(413\) | 166816. | 0.0481241 | ||||||||
\(414\) | 128142. | 0.0367444 | ||||||||
\(415\) | 5.73086e6 | 1.63343 | ||||||||
\(416\) | −2.03794e6 | −0.577375 | ||||||||
\(417\) | 538992. | 0.151790 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.47794e6 | 1.52434 | 0.762170 | − | 0.647377i | \(-0.224134\pi\) | ||||
0.762170 | + | 0.647377i | \(0.224134\pi\) | |||||||
\(420\) | 667368. | 0.184604 | ||||||||
\(421\) | 1.02873e6 | 0.282877 | 0.141439 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141439 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(422\) | 525900. | 0.143755 | ||||||||
\(423\) | −191322. | −0.0519893 | ||||||||
\(424\) | −1.94065e6 | −0.524243 | ||||||||
\(425\) | 7.69884e6 | 2.06753 | ||||||||
\(426\) | −411210. | −0.109784 | ||||||||
\(427\) | −1.09450e6 | −0.290499 | ||||||||
\(428\) | −387252. | −0.102184 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −789360. | −0.205875 | ||||||||
\(431\) | 5.14310e6 | 1.33362 | 0.666810 | − | 0.745228i | \(-0.267659\pi\) | ||||
0.666810 | + | 0.745228i | \(0.267659\pi\) | |||||||
\(432\) | 677241. | 0.174596 | ||||||||
\(433\) | 412954. | 0.105848 | 0.0529239 | − | 0.998599i | \(-0.483146\pi\) | ||||
0.0529239 | + | 0.998599i | \(0.483146\pi\) | |||||||
\(434\) | −124592. | −0.0317516 | ||||||||
\(435\) | −4.57553e6 | −1.15936 | ||||||||
\(436\) | 6.16119e6 | 1.55220 | ||||||||
\(437\) | 3.41712e6 | 0.855966 | ||||||||
\(438\) | −165366. | −0.0411871 | ||||||||
\(439\) | −5.96365e6 | −1.47690 | −0.738450 | − | 0.674309i | \(-0.764442\pi\) | ||||
−0.738450 | + | 0.674309i | \(0.764442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.30661e6 | −0.319926 | ||||||||
\(442\) | −997864. | −0.242949 | ||||||||
\(443\) | 2.18433e6 | 0.528821 | 0.264410 | − | 0.964410i | \(-0.414823\pi\) | ||||
0.264410 | + | 0.964410i | \(0.414823\pi\) | |||||||
\(444\) | 2.84413e6 | 0.684686 | ||||||||
\(445\) | 6.64663e6 | 1.59112 | ||||||||
\(446\) | 245264. | 0.0583844 | ||||||||
\(447\) | −648342. | −0.153474 | ||||||||
\(448\) | −696358. | −0.163922 | ||||||||
\(449\) | −7858.00 | −0.00183948 | −0.000919742 | − | 1.00000i | \(-0.500293\pi\) | ||||
−0.000919742 | 1.00000i | \(0.500293\pi\) | ||||||||
\(450\) | −432459. | −0.100673 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.16317e6 | −1.18870 | ||||||||
\(453\) | 2.90799e6 | 0.665806 | ||||||||
\(454\) | −799308. | −0.182001 | ||||||||
\(455\) | −1.65526e6 | −0.374834 | ||||||||
\(456\) | −1.22472e6 | −0.275819 | ||||||||
\(457\) | 899922. | 0.201565 | 0.100782 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100782 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(458\) | 1.53989e6 | 0.343026 | ||||||||
\(459\) | 1.05122e6 | 0.232895 | ||||||||
\(460\) | −4.51186e6 | −0.994172 | ||||||||
\(461\) | −1.13619e6 | −0.249000 | −0.124500 | − | 0.992220i | \(-0.539733\pi\) | ||||
−0.124500 | + | 0.992220i | \(0.539733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.38964e6 | −1.60203 | −0.801016 | − | 0.598643i | \(-0.795707\pi\) | ||||
−0.801016 | + | 0.598643i | \(0.795707\pi\) | |||||||
\(464\) | 5.13365e6 | 1.10696 | ||||||||
\(465\) | −3.96778e6 | −0.850971 | ||||||||
\(466\) | −721830. | −0.153982 | ||||||||
\(467\) | 4.20851e6 | 0.892968 | 0.446484 | − | 0.894792i | \(-0.352676\pi\) | ||||
0.446484 | + | 0.894792i | \(0.352676\pi\) | |||||||
\(468\) | −1.73761e6 | −0.366723 | ||||||||
\(469\) | −739544. | −0.155250 | ||||||||
\(470\) | −217304. | −0.0453757 | ||||||||
\(471\) | −2.86889e6 | −0.595885 | ||||||||
\(472\) | 404208. | 0.0835122 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −946926. | −0.193584 | ||||||||
\(475\) | −1.15322e7 | −2.34520 | ||||||||
\(476\) | −1.16225e6 | −0.235116 | ||||||||
\(477\) | −2.49512e6 | −0.502107 | ||||||||
\(478\) | −638436. | −0.127805 | ||||||||
\(479\) | −7.39441e6 | −1.47253 | −0.736266 | − | 0.676692i | \(-0.763413\pi\) | ||||
−0.736266 | + | 0.676692i | \(0.763413\pi\) | |||||||
\(480\) | 2.43846e6 | 0.483073 | ||||||||
\(481\) | −7.05425e6 | −1.39023 | ||||||||
\(482\) | 220990. | 0.0433266 | ||||||||
\(483\) | −370188. | −0.0722029 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.29210e6 | −1.40766 | ||||||||
\(486\) | −59049.0 | −0.0113402 | ||||||||
\(487\) | −3.81644e6 | −0.729181 | −0.364591 | − | 0.931168i | \(-0.618791\pi\) | ||||
−0.364591 | + | 0.931168i | \(0.618791\pi\) | |||||||
\(488\) | −2.65205e6 | −0.504118 | ||||||||
\(489\) | −3.88796e6 | −0.735275 | ||||||||
\(490\) | −1.48405e6 | −0.279228 | ||||||||
\(491\) | −1.69716e6 | −0.317702 | −0.158851 | − | 0.987303i | \(-0.550779\pi\) | ||||
−0.158851 | + | 0.987303i | \(0.550779\pi\) | |||||||
\(492\) | −2.96354e6 | −0.551947 | ||||||||
\(493\) | 7.96849e6 | 1.47659 | ||||||||
\(494\) | 1.49472e6 | 0.275577 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.45177e6 | 0.812509 | ||||||||
\(497\) | 1.18794e6 | 0.215727 | ||||||||
\(498\) | 560628. | 0.101298 | ||||||||
\(499\) | 6.95160e6 | 1.24978 | 0.624889 | − | 0.780713i | \(-0.285144\pi\) | ||||
0.624889 | + | 0.780713i | \(0.285144\pi\) | |||||||
\(500\) | 6.31433e6 | 1.12954 | ||||||||
\(501\) | 2.26422e6 | 0.403018 | ||||||||
\(502\) | −627304. | −0.111101 | ||||||||
\(503\) | −6.01023e6 | −1.05918 | −0.529591 | − | 0.848253i | \(-0.677655\pi\) | ||||
−0.529591 | + | 0.848253i | \(0.677655\pi\) | |||||||
\(504\) | 132678. | 0.0232660 | ||||||||
\(505\) | −2.29614e6 | −0.400654 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 968139. | 0.167270 | ||||||||
\(508\) | 9.43101e6 | 1.62143 | ||||||||
\(509\) | 624660. | 0.106868 | 0.0534342 | − | 0.998571i | \(-0.482983\pi\) | ||||
0.0534342 | + | 0.998571i | \(0.482983\pi\) | |||||||
\(510\) | 1.19398e6 | 0.203269 | ||||||||
\(511\) | 477724. | 0.0809328 | ||||||||
\(512\) | −4.60877e6 | −0.776980 | ||||||||
\(513\) | −1.57464e6 | −0.264173 | ||||||||
\(514\) | 468014. | 0.0781360 | ||||||||
\(515\) | 5.22670e6 | 0.868380 | ||||||||
\(516\) | 2.39382e6 | 0.395792 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 265044. | 0.0434004 | ||||||||
\(519\) | −4.28971e6 | −0.699051 | ||||||||
\(520\) | −4.01083e6 | −0.650468 | ||||||||
\(521\) | −647490. | −0.104505 | −0.0522527 | − | 0.998634i | \(-0.516640\pi\) | ||||
−0.0522527 | + | 0.998634i | \(0.516640\pi\) | |||||||
\(522\) | −447606. | −0.0718985 | ||||||||
\(523\) | 114676. | 0.0183324 | 0.00916618 | − | 0.999958i | \(-0.497082\pi\) | ||||
0.00916618 | + | 0.999958i | \(0.497082\pi\) | |||||||
\(524\) | 8.50727e6 | 1.35351 | ||||||||
\(525\) | 1.24933e6 | 0.197823 | ||||||||
\(526\) | 1.54510e6 | 0.243497 | ||||||||
\(527\) | 6.91006e6 | 1.08382 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.93362e6 | −0.611157 | ||||||||
\(530\) | −2.83397e6 | −0.438233 | ||||||||
\(531\) | 519696. | 0.0799858 | ||||||||
\(532\) | 1.74096e6 | 0.266692 | ||||||||
\(533\) | 7.35042e6 | 1.12071 | ||||||||
\(534\) | 650214. | 0.0986741 | ||||||||
\(535\) | −1.14926e6 | −0.173594 | ||||||||
\(536\) | −1.79197e6 | −0.269413 | ||||||||
\(537\) | 811728. | 0.121472 | ||||||||
\(538\) | 1.07457e6 | 0.160059 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.07911e6 | 0.306826 | ||||||||
\(541\) | 2.12404e6 | 0.312011 | 0.156006 | − | 0.987756i | \(-0.450138\pi\) | ||||
0.156006 | + | 0.987756i | \(0.450138\pi\) | |||||||
\(542\) | 1.58723e6 | 0.232082 | ||||||||
\(543\) | 2.23202e6 | 0.324861 | ||||||||
\(544\) | −4.24669e6 | −0.615252 | ||||||||
\(545\) | 1.82848e7 | 2.63693 | ||||||||
\(546\) | −161928. | −0.0232456 | ||||||||
\(547\) | −1.22672e7 | −1.75299 | −0.876494 | − | 0.481413i | \(-0.840124\pi\) | ||||
−0.876494 | + | 0.481413i | \(0.840124\pi\) | |||||||
\(548\) | 7.60920e6 | 1.08240 | ||||||||
\(549\) | −3.40978e6 | −0.482831 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.19362e7 | −1.67489 | ||||||||
\(552\) | −896994. | −0.125297 | ||||||||
\(553\) | 2.73556e6 | 0.380394 | ||||||||
\(554\) | 692704. | 0.0958900 | ||||||||
\(555\) | 8.44063e6 | 1.16317 | ||||||||
\(556\) | −1.85653e6 | −0.254692 | ||||||||
\(557\) | −1.10980e7 | −1.51568 | −0.757839 | − | 0.652442i | \(-0.773745\pi\) | ||||
−0.757839 | + | 0.652442i | \(0.773745\pi\) | |||||||
\(558\) | −388152. | −0.0527736 | ||||||||
\(559\) | −5.93736e6 | −0.803644 | ||||||||
\(560\) | −2.22217e6 | −0.299438 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −567018. | −0.0757279 | ||||||||
\(563\) | −4.61984e6 | −0.614265 | −0.307132 | − | 0.951667i | \(-0.599369\pi\) | ||||
−0.307132 | + | 0.951667i | \(0.599369\pi\) | |||||||
\(564\) | 658998. | 0.0872341 | ||||||||
\(565\) | −1.53230e7 | −2.01940 | ||||||||
\(566\) | 714916. | 0.0938024 | ||||||||
\(567\) | 170586. | 0.0222836 | ||||||||
\(568\) | 2.87847e6 | 0.374361 | ||||||||
\(569\) | −1.01716e7 | −1.31707 | −0.658537 | − | 0.752548i | \(-0.728824\pi\) | ||||
−0.658537 | + | 0.752548i | \(0.728824\pi\) | |||||||
\(570\) | −1.78848e6 | −0.230567 | ||||||||
\(571\) | 9.36866e6 | 1.20251 | 0.601253 | − | 0.799059i | \(-0.294669\pi\) | ||||
0.601253 | + | 0.799059i | \(0.294669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.41122e6 | −0.179559 | ||||||||
\(574\) | −276172. | −0.0349865 | ||||||||
\(575\) | −8.44630e6 | −1.06536 | ||||||||
\(576\) | −2.16942e6 | −0.272451 | ||||||||
\(577\) | −6.14973e6 | −0.768983 | −0.384491 | − | 0.923129i | \(-0.625623\pi\) | ||||
−0.384491 | + | 0.923129i | \(0.625623\pi\) | |||||||
\(578\) | −659507. | −0.0821107 | ||||||||
\(579\) | 3.88111e6 | 0.481126 | ||||||||
\(580\) | 1.57602e7 | 1.94532 | ||||||||
\(581\) | −1.61959e6 | −0.199051 | ||||||||
\(582\) | −713358. | −0.0872972 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.15756e6 | 0.140447 | ||||||||
\(585\) | −5.15678e6 | −0.623002 | ||||||||
\(586\) | 2.14409e6 | 0.257929 | ||||||||
\(587\) | 1.04649e6 | 0.125354 | 0.0626771 | − | 0.998034i | \(-0.480036\pi\) | ||||
0.0626771 | + | 0.998034i | \(0.480036\pi\) | |||||||
\(588\) | 4.50055e6 | 0.536812 | ||||||||
\(589\) | −1.03507e7 | −1.22937 | ||||||||
\(590\) | 590272. | 0.0698107 | ||||||||
\(591\) | 7.78477e6 | 0.916805 | ||||||||
\(592\) | −9.47023e6 | −1.11060 | ||||||||
\(593\) | 3.31784e6 | 0.387453 | 0.193726 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193726 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.44926e6 | −0.399424 | ||||||||
\(596\) | 2.23318e6 | 0.257518 | ||||||||
\(597\) | −4.32054e6 | −0.496138 | ||||||||
\(598\) | 1.09474e6 | 0.125187 | ||||||||
\(599\) | −1.73991e7 | −1.98134 | −0.990670 | − | 0.136280i | \(-0.956485\pi\) | ||||
−0.990670 | + | 0.136280i | \(0.956485\pi\) | |||||||
\(600\) | 3.02721e6 | 0.343293 | ||||||||
\(601\) | −7.13163e6 | −0.805383 | −0.402691 | − | 0.915336i | \(-0.631925\pi\) | ||||
−0.402691 | + | 0.915336i | \(0.631925\pi\) | |||||||
\(602\) | 223080. | 0.0250882 | ||||||||
\(603\) | −2.30396e6 | −0.258037 | ||||||||
\(604\) | −1.00164e7 | −1.11717 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −224622. | −0.0248468 | ||||||||
\(607\) | 9.64617e6 | 1.06263 | 0.531317 | − | 0.847173i | \(-0.321697\pi\) | ||||
0.531317 | + | 0.847173i | \(0.321697\pi\) | |||||||
\(608\) | 6.36120e6 | 0.697879 | ||||||||
\(609\) | 1.29308e6 | 0.141281 | ||||||||
\(610\) | −3.87283e6 | −0.421409 | ||||||||
\(611\) | −1.63450e6 | −0.177126 | ||||||||
\(612\) | −3.62086e6 | −0.390781 | ||||||||
\(613\) | −3.68170e6 | −0.395729 | −0.197864 | − | 0.980229i | \(-0.563401\pi\) | ||||
−0.197864 | + | 0.980229i | \(0.563401\pi\) | |||||||
\(614\) | −588808. | −0.0630308 | ||||||||
\(615\) | −8.79502e6 | −0.937667 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.83190e7 | 1.93727 | 0.968635 | − | 0.248489i | \(-0.0799340\pi\) | ||||
0.968635 | + | 0.248489i | \(0.0799340\pi\) | |||||||
\(618\) | 511308. | 0.0538532 | ||||||||
\(619\) | 1.09660e6 | 0.115033 | 0.0575166 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575166 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(620\) | 1.36668e7 | 1.42786 | ||||||||
\(621\) | −1.15328e6 | −0.120007 | ||||||||
\(622\) | −2.51827e6 | −0.260991 | ||||||||
\(623\) | −1.87840e6 | −0.193895 | ||||||||
\(624\) | 5.78581e6 | 0.594844 | ||||||||
\(625\) | 2.05492e6 | 0.210424 | ||||||||
\(626\) | 2.23562e6 | 0.228015 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.88175e6 | 0.999849 | ||||||||
\(629\) | −1.46997e7 | −1.48144 | ||||||||
\(630\) | 193752. | 0.0194489 | ||||||||
\(631\) | −9.58030e6 | −0.957869 | −0.478934 | − | 0.877851i | \(-0.658977\pi\) | ||||
−0.478934 | + | 0.877851i | \(0.658977\pi\) | |||||||
\(632\) | 6.62848e6 | 0.660118 | ||||||||
\(633\) | −4.73310e6 | −0.469501 | ||||||||
\(634\) | −1.06079e6 | −0.104811 | ||||||||
\(635\) | 2.79888e7 | 2.75454 | ||||||||
\(636\) | 8.59432e6 | 0.842497 | ||||||||
\(637\) | −1.11627e7 | −1.08998 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.70089e6 | 0.358554 | ||||||||
\(640\) | −1.11341e7 | −1.07450 | ||||||||
\(641\) | −1.18062e7 | −1.13492 | −0.567462 | − | 0.823400i | \(-0.692075\pi\) | ||||
−0.567462 | + | 0.823400i | \(0.692075\pi\) | |||||||
\(642\) | −112428. | −0.0107656 | ||||||||
\(643\) | −5.88298e6 | −0.561138 | −0.280569 | − | 0.959834i | \(-0.590523\pi\) | ||||
−0.280569 | + | 0.959834i | \(0.590523\pi\) | |||||||
\(644\) | 1.27509e6 | 0.121151 | ||||||||
\(645\) | 7.10424e6 | 0.672385 | ||||||||
\(646\) | 3.11472e6 | 0.293655 | ||||||||
\(647\) | −3.62822e6 | −0.340748 | −0.170374 | − | 0.985379i | \(-0.554498\pi\) | ||||
−0.170374 | + | 0.985379i | \(0.554498\pi\) | |||||||
\(648\) | 413343. | 0.0386699 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.69459e6 | −0.342991 | ||||||||
\(651\) | 1.12133e6 | 0.103700 | ||||||||
\(652\) | 1.33919e7 | 1.23374 | ||||||||
\(653\) | −5.70795e6 | −0.523838 | −0.261919 | − | 0.965090i | \(-0.584355\pi\) | ||||
−0.261919 | + | 0.965090i | \(0.584355\pi\) | |||||||
\(654\) | 1.78873e6 | 0.163531 | ||||||||
\(655\) | 2.52474e7 | 2.29939 | ||||||||
\(656\) | 9.86784e6 | 0.895287 | ||||||||
\(657\) | 1.48829e6 | 0.134516 | ||||||||
\(658\) | 61412.0 | 0.00552953 | ||||||||
\(659\) | −1.08205e7 | −0.970588 | −0.485294 | − | 0.874351i | \(-0.661287\pi\) | ||||
−0.485294 | + | 0.874351i | \(0.661287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.14311e7 | 1.01762 | 0.508809 | − | 0.860879i | \(-0.330086\pi\) | ||||
0.508809 | + | 0.860879i | \(0.330086\pi\) | |||||||
\(662\) | 2.34566e6 | 0.208027 | ||||||||
\(663\) | 8.98078e6 | 0.793469 | ||||||||
\(664\) | −3.92440e6 | −0.345424 | ||||||||
\(665\) | 5.16672e6 | 0.453065 | ||||||||
\(666\) | 825714. | 0.0721347 | ||||||||
\(667\) | −8.74213e6 | −0.760857 | ||||||||
\(668\) | −7.79898e6 | −0.676233 | ||||||||
\(669\) | −2.20738e6 | −0.190683 | ||||||||
\(670\) | −2.61685e6 | −0.225212 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −689130. | −0.0588678 | ||||||||
\(673\) | 2.03858e7 | 1.73496 | 0.867482 | − | 0.497468i | \(-0.165737\pi\) | ||||
0.867482 | + | 0.497468i | \(0.165737\pi\) | |||||||
\(674\) | 839978. | 0.0712227 | ||||||||
\(675\) | 3.89213e6 | 0.328797 | ||||||||
\(676\) | −3.33470e6 | −0.280666 | ||||||||
\(677\) | −6.09278e6 | −0.510909 | −0.255455 | − | 0.966821i | \(-0.582225\pi\) | ||||
−0.255455 | + | 0.966821i | \(0.582225\pi\) | |||||||
\(678\) | −1.49899e6 | −0.125234 | ||||||||
\(679\) | 2.06081e6 | 0.171539 | ||||||||
\(680\) | −8.35783e6 | −0.693141 | ||||||||
\(681\) | 7.19377e6 | 0.594414 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.44978e7 | 1.18918 | 0.594592 | − | 0.804027i | \(-0.297314\pi\) | ||||
0.594592 | + | 0.804027i | \(0.297314\pi\) | |||||||
\(684\) | 5.42376e6 | 0.443262 | ||||||||
\(685\) | 2.25821e7 | 1.83882 | ||||||||
\(686\) | 856388. | 0.0694801 | ||||||||
\(687\) | −1.38590e7 | −1.12032 | ||||||||
\(688\) | −7.97082e6 | −0.641995 | ||||||||
\(689\) | −2.13164e7 | −1.71067 | ||||||||
\(690\) | −1.30990e6 | −0.104740 | ||||||||
\(691\) | 9.87069e6 | 0.786416 | 0.393208 | − | 0.919449i | \(-0.371365\pi\) | ||||
0.393208 | + | 0.919449i | \(0.371365\pi\) | |||||||
\(692\) | 1.47757e7 | 1.17296 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.02560e6 | −0.159645 | ||||||||
\(695\) | −5.50970e6 | −0.432679 | ||||||||
\(696\) | 3.13324e6 | 0.245172 | ||||||||
\(697\) | 1.53169e7 | 1.19423 | ||||||||
\(698\) | −378924. | −0.0294384 | ||||||||
\(699\) | 6.49647e6 | 0.502903 | ||||||||
\(700\) | −4.30323e6 | −0.331933 | ||||||||
\(701\) | −6.35411e6 | −0.488382 | −0.244191 | − | 0.969727i | \(-0.578522\pi\) | ||||
−0.244191 | + | 0.969727i | \(0.578522\pi\) | |||||||
\(702\) | −504468. | −0.0386359 | ||||||||
\(703\) | 2.20190e7 | 1.68039 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.95574e6 | 0.148196 | ||||||||
\(706\) | 1.98730e6 | 0.150056 | ||||||||
\(707\) | 648908. | 0.0488241 | ||||||||
\(708\) | −1.79006e6 | −0.134210 | ||||||||
\(709\) | −411382. | −0.0307348 | −0.0153674 | − | 0.999882i | \(-0.504892\pi\) | ||||
−0.0153674 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(710\) | 4.20348e6 | 0.312941 | ||||||||
\(711\) | 8.52233e6 | 0.632244 | ||||||||
\(712\) | −4.55150e6 | −0.336476 | ||||||||
\(713\) | −7.58094e6 | −0.558470 | ||||||||
\(714\) | −337428. | −0.0247705 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.79595e6 | −0.203820 | ||||||||
\(717\) | 5.74592e6 | 0.417409 | ||||||||
\(718\) | −3.43975e6 | −0.249009 | ||||||||
\(719\) | 6.29795e6 | 0.454336 | 0.227168 | − | 0.973856i | \(-0.427053\pi\) | ||||
0.227168 | + | 0.973856i | \(0.427053\pi\) | |||||||
\(720\) | −6.92291e6 | −0.497688 | ||||||||
\(721\) | −1.47711e6 | −0.105822 | ||||||||
\(722\) | −2.18950e6 | −0.156316 | ||||||||
\(723\) | −1.98891e6 | −0.141504 | ||||||||
\(724\) | −7.68806e6 | −0.545093 | ||||||||
\(725\) | 2.95033e7 | 2.08461 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.14699e7 | 0.804866 | 0.402433 | − | 0.915449i | \(-0.368165\pi\) | ||||
0.402433 | + | 0.915449i | \(0.368165\pi\) | |||||||
\(728\) | 1.13350e6 | 0.0792668 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.69041e6 | 0.117404 | ||||||||
\(731\) | −1.23724e7 | −0.856365 | ||||||||
\(732\) | 1.17448e7 | 0.810154 | ||||||||
\(733\) | 1.87547e7 | 1.28929 | 0.644646 | − | 0.764481i | \(-0.277005\pi\) | ||||
0.644646 | + | 0.764481i | \(0.277005\pi\) | |||||||
\(734\) | 1.79679e6 | 0.123100 | ||||||||
\(735\) | 1.33565e7 | 0.911955 | ||||||||
\(736\) | 4.65899e6 | 0.317028 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −860382. | −0.0581501 | ||||||||
\(739\) | −2.79727e6 | −0.188418 | −0.0942091 | − | 0.995552i | \(-0.530032\pi\) | ||||
−0.0942091 | + | 0.995552i | \(0.530032\pi\) | |||||||
\(740\) | −2.90733e7 | −1.95171 | ||||||||
\(741\) | −1.34525e7 | −0.900030 | ||||||||
\(742\) | 800904. | 0.0534036 | ||||||||
\(743\) | 2.25651e7 | 1.49956 | 0.749781 | − | 0.661686i | \(-0.230159\pi\) | ||||
0.749781 | + | 0.661686i | \(0.230159\pi\) | |||||||
\(744\) | 2.71706e6 | 0.179956 | ||||||||
\(745\) | 6.62750e6 | 0.437481 | ||||||||
\(746\) | −1.43541e6 | −0.0944342 | ||||||||
\(747\) | −5.04565e6 | −0.330838 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 324792. | 0.0211544 | ||||||||
\(750\) | 1.83319e6 | 0.119002 | ||||||||
\(751\) | −7.49233e6 | −0.484749 | −0.242375 | − | 0.970183i | \(-0.577926\pi\) | ||||
−0.242375 | + | 0.970183i | \(0.577926\pi\) | |||||||
\(752\) | −2.19430e6 | −0.141498 | ||||||||
\(753\) | 5.64574e6 | 0.362855 | ||||||||
\(754\) | −3.82399e6 | −0.244956 | ||||||||
\(755\) | −2.97261e7 | −1.89789 | ||||||||
\(756\) | −587574. | −0.0373902 | ||||||||
\(757\) | 2.88492e7 | 1.82976 | 0.914880 | − | 0.403727i | \(-0.132285\pi\) | ||||
0.914880 | + | 0.403727i | \(0.132285\pi\) | |||||||
\(758\) | −2.66235e6 | −0.168303 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.25194e7 | 0.786227 | ||||||||
\(761\) | 9.56279e6 | 0.598581 | 0.299291 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299291 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(762\) | 2.73803e6 | 0.170825 | ||||||||
\(763\) | −5.16745e6 | −0.321340 | ||||||||
\(764\) | 4.86086e6 | 0.301287 | ||||||||
\(765\) | −1.07458e7 | −0.663872 | ||||||||
\(766\) | −2.04091e6 | −0.125676 | ||||||||
\(767\) | 4.43987e6 | 0.272510 | ||||||||
\(768\) | 6.62430e6 | 0.405263 | ||||||||
\(769\) | 744898. | 0.0454235 | 0.0227118 | − | 0.999742i | \(-0.492770\pi\) | ||||
0.0227118 | + | 0.999742i | \(0.492770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.21213e6 | −0.255191 | ||||||||
\(772\) | −1.33683e7 | −0.807293 | ||||||||
\(773\) | 6.07336e6 | 0.365578 | 0.182789 | − | 0.983152i | \(-0.441487\pi\) | ||||
0.182789 | + | 0.983152i | \(0.441487\pi\) | |||||||
\(774\) | 694980. | 0.0416984 | ||||||||
\(775\) | 2.55845e7 | 1.53011 | ||||||||
\(776\) | 4.99351e6 | 0.297681 | ||||||||
\(777\) | −2.38540e6 | −0.141745 | ||||||||
\(778\) | 4.29947e6 | 0.254663 | ||||||||
\(779\) | −2.29435e7 | −1.35462 | ||||||||
\(780\) | 1.77623e7 | 1.04535 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.28124e6 | 0.133400 | ||||||||
\(783\) | 4.02845e6 | 0.234819 | ||||||||
\(784\) | −1.49857e7 | −0.870737 | ||||||||
\(785\) | 2.93265e7 | 1.69858 | ||||||||
\(786\) | 2.46985e6 | 0.142598 | ||||||||
\(787\) | 1.47512e7 | 0.848966 | 0.424483 | − | 0.905436i | \(-0.360456\pi\) | ||||
0.424483 | + | 0.905436i | \(0.360456\pi\) | |||||||
\(788\) | −2.68142e7 | −1.53833 | ||||||||
\(789\) | −1.39059e7 | −0.795257 | ||||||||
\(790\) | 9.67969e6 | 0.551815 | ||||||||
\(791\) | 4.33040e6 | 0.246086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.91304e7 | −1.64499 | ||||||||
\(794\) | −728818. | −0.0410268 | ||||||||
\(795\) | 2.55057e7 | 1.43126 | ||||||||
\(796\) | 1.48819e7 | 0.832481 | ||||||||
\(797\) | −2.78359e7 | −1.55224 | −0.776121 | − | 0.630584i | \(-0.782815\pi\) | ||||
−0.776121 | + | 0.630584i | \(0.782815\pi\) | |||||||
\(798\) | 505440. | 0.0280972 | ||||||||
\(799\) | −3.40600e6 | −0.188746 | ||||||||
\(800\) | −1.57234e7 | −0.868601 | ||||||||
\(801\) | −5.85193e6 | −0.322268 | ||||||||
\(802\) | 5.92515e6 | 0.325285 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.93588e6 | 0.432967 | ||||||||
\(805\) | 3.78414e6 | 0.205815 | ||||||||
\(806\) | −3.31606e6 | −0.179798 | ||||||||
\(807\) | −9.67115e6 | −0.522750 | ||||||||
\(808\) | 1.57235e6 | 0.0847270 | ||||||||
\(809\) | −2.54767e7 | −1.36859 | −0.684293 | − | 0.729207i | \(-0.739889\pi\) | ||||
−0.684293 | + | 0.729207i | \(0.739889\pi\) | |||||||
\(810\) | 603612. | 0.0323255 | ||||||||
\(811\) | 1.91915e7 | 1.02460 | 0.512302 | − | 0.858805i | \(-0.328793\pi\) | ||||
0.512302 | + | 0.858805i | \(0.328793\pi\) | |||||||
\(812\) | −4.45396e6 | −0.237059 | ||||||||
\(813\) | −1.42851e7 | −0.757977 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.97436e7 | 2.09591 | ||||||||
\(816\) | 1.20566e7 | 0.633867 | ||||||||
\(817\) | 1.85328e7 | 0.971373 | ||||||||
\(818\) | 1.38212e6 | 0.0722207 | ||||||||
\(819\) | 1.45735e6 | 0.0759197 | ||||||||
\(820\) | 3.02939e7 | 1.57333 | ||||||||
\(821\) | −3.27107e6 | −0.169368 | −0.0846840 | − | 0.996408i | \(-0.526988\pi\) | ||||
−0.0846840 | + | 0.996408i | \(0.526988\pi\) | |||||||
\(822\) | 2.20912e6 | 0.114036 | ||||||||
\(823\) | −3.19195e7 | −1.64269 | −0.821347 | − | 0.570430i | \(-0.806777\pi\) | ||||
−0.821347 | + | 0.570430i | \(0.806777\pi\) | |||||||
\(824\) | −3.57916e6 | −0.183638 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −166816. | −0.00850722 | ||||||||
\(827\) | −2.45556e7 | −1.24850 | −0.624248 | − | 0.781226i | \(-0.714595\pi\) | ||||
−0.624248 | + | 0.781226i | \(0.714595\pi\) | |||||||
\(828\) | 3.97240e6 | 0.201362 | ||||||||
\(829\) | −1.40969e7 | −0.712421 | −0.356211 | − | 0.934406i | \(-0.615931\pi\) | ||||
−0.356211 | + | 0.934406i | \(0.615931\pi\) | |||||||
\(830\) | −5.73086e6 | −0.288752 | ||||||||
\(831\) | −6.23434e6 | −0.313175 | ||||||||
\(832\) | −1.85338e7 | −0.928233 | ||||||||
\(833\) | −2.32609e7 | −1.16149 | ||||||||
\(834\) | −538992. | −0.0268329 | ||||||||
\(835\) | −2.31454e7 | −1.14881 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.49337e6 | 0.172358 | ||||||||
\(838\) | −5.47794e6 | −0.269468 | ||||||||
\(839\) | −3.01443e6 | −0.147843 | −0.0739213 | − | 0.997264i | \(-0.523551\pi\) | ||||
−0.0739213 | + | 0.997264i | \(0.523551\pi\) | |||||||
\(840\) | −1.35626e6 | −0.0663202 | ||||||||
\(841\) | 1.00255e7 | 0.488784 | ||||||||
\(842\) | −1.02873e6 | −0.0500061 | ||||||||
\(843\) | 5.10316e6 | 0.247326 | ||||||||
\(844\) | 1.63029e7 | 0.787787 | ||||||||
\(845\) | −9.89653e6 | −0.476806 | ||||||||
\(846\) | 191322. | 0.00919050 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.86169e7 | −1.36657 | ||||||||
\(849\) | −6.43424e6 | −0.306357 | ||||||||
\(850\) | −7.69884e6 | −0.365492 | ||||||||
\(851\) | 1.61269e7 | 0.763356 | ||||||||
\(852\) | −1.27475e7 | −0.601626 | ||||||||
\(853\) | 1.67201e7 | 0.786806 | 0.393403 | − | 0.919366i | \(-0.371298\pi\) | ||||
0.393403 | + | 0.919366i | \(0.371298\pi\) | |||||||
\(854\) | 1.09450e6 | 0.0513534 | ||||||||
\(855\) | 1.60963e7 | 0.753028 | ||||||||
\(856\) | 786996. | 0.0367103 | ||||||||
\(857\) | 9.15871e6 | 0.425973 | 0.212987 | − | 0.977055i | \(-0.431681\pi\) | ||||
0.212987 | + | 0.977055i | \(0.431681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.51068e7 | 0.698536 | 0.349268 | − | 0.937023i | \(-0.386430\pi\) | ||||
0.349268 | + | 0.937023i | \(0.386430\pi\) | |||||||
\(860\) | −2.44702e7 | −1.12821 | ||||||||
\(861\) | 2.48555e6 | 0.114265 | ||||||||
\(862\) | −5.14310e6 | −0.235753 | ||||||||
\(863\) | 5.11568e6 | 0.233817 | 0.116909 | − | 0.993143i | \(-0.462702\pi\) | ||||
0.116909 | + | 0.993143i | \(0.462702\pi\) | |||||||
\(864\) | −2.14690e6 | −0.0978427 | ||||||||
\(865\) | 4.38503e7 | 1.99266 | ||||||||
\(866\) | −412954. | −0.0187114 | ||||||||
\(867\) | 5.93556e6 | 0.268172 | ||||||||
\(868\) | −3.86235e6 | −0.174001 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.57553e6 | 0.204948 | ||||||||
\(871\) | −1.96832e7 | −0.879127 | ||||||||
\(872\) | −1.25211e7 | −0.557638 | ||||||||
\(873\) | 6.42022e6 | 0.285111 | ||||||||
\(874\) | −3.41712e6 | −0.151315 | ||||||||
\(875\) | −5.29589e6 | −0.233840 | ||||||||
\(876\) | −5.12635e6 | −0.225708 | ||||||||
\(877\) | 1.26998e7 | 0.557568 | 0.278784 | − | 0.960354i | \(-0.410069\pi\) | ||||
0.278784 | + | 0.960354i | \(0.410069\pi\) | |||||||
\(878\) | 5.96365e6 | 0.261081 | ||||||||
\(879\) | −1.92968e7 | −0.842392 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.38173e6 | −0.363826 | −0.181913 | − | 0.983315i | \(-0.558229\pi\) | ||||
−0.181913 | + | 0.983315i | \(0.558229\pi\) | |||||||
\(882\) | 1.30661e6 | 0.0565555 | ||||||||
\(883\) | −1.69529e7 | −0.731715 | −0.365858 | − | 0.930671i | \(-0.619224\pi\) | ||||
−0.365858 | + | 0.930671i | \(0.619224\pi\) | |||||||
\(884\) | −3.09338e7 | −1.33138 | ||||||||
\(885\) | −5.31245e6 | −0.228001 | ||||||||
\(886\) | −2.18433e6 | −0.0934832 | ||||||||
\(887\) | 1.05143e7 | 0.448717 | 0.224359 | − | 0.974507i | \(-0.427971\pi\) | ||||
0.224359 | + | 0.974507i | \(0.427971\pi\) | |||||||
\(888\) | −5.78000e6 | −0.245977 | ||||||||
\(889\) | −7.90988e6 | −0.335672 | ||||||||
\(890\) | −6.64663e6 | −0.281272 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.60318e6 | 0.319951 | ||||||||
\(893\) | 5.10192e6 | 0.214094 | ||||||||
\(894\) | 648342. | 0.0271307 | ||||||||
\(895\) | −8.29766e6 | −0.346257 | ||||||||
\(896\) | 3.14660e6 | 0.130940 | ||||||||
\(897\) | −9.85270e6 | −0.408859 | ||||||||
\(898\) | 7858.00 | 0.000325178 0 | ||||||||
\(899\) | 2.64806e7 | 1.09277 | ||||||||
\(900\) | −1.34062e7 | −0.551697 | ||||||||
\(901\) | −4.44194e7 | −1.82289 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.00772e6 | −0.0819377 | ||||||||
\(904\) | 1.04929e7 | 0.427046 | ||||||||
\(905\) | −2.28162e7 | −0.926023 | ||||||||
\(906\) | −2.90799e6 | −0.117699 | ||||||||
\(907\) | −1.53747e7 | −0.620569 | −0.310284 | − | 0.950644i | \(-0.600424\pi\) | ||||
−0.310284 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(908\) | −2.47785e7 | −0.997381 | ||||||||
\(909\) | 2.02160e6 | 0.0811494 | ||||||||
\(910\) | 1.65526e6 | 0.0662619 | ||||||||
\(911\) | 1.25424e7 | 0.500708 | 0.250354 | − | 0.968154i | \(-0.419453\pi\) | ||||
0.250354 | + | 0.968154i | \(0.419453\pi\) | |||||||
\(912\) | −1.80598e7 | −0.718993 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −899922. | −0.0356319 | ||||||||
\(915\) | 3.48555e7 | 1.37632 | ||||||||
\(916\) | 4.77367e7 | 1.87981 | ||||||||
\(917\) | −7.13513e6 | −0.280207 | ||||||||
\(918\) | −1.05122e6 | −0.0411705 | ||||||||
\(919\) | −3.31432e7 | −1.29451 | −0.647256 | − | 0.762273i | \(-0.724084\pi\) | ||||
−0.647256 | + | 0.762273i | \(0.724084\pi\) | |||||||
\(920\) | 9.16927e6 | 0.357162 | ||||||||
\(921\) | 5.29927e6 | 0.205858 | ||||||||
\(922\) | 1.13619e6 | 0.0440173 | ||||||||
\(923\) | 3.16175e7 | 1.22158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.44258e7 | −2.09146 | ||||||||
\(926\) | 7.38964e6 | 0.283202 | ||||||||
\(927\) | −4.60177e6 | −0.175884 | ||||||||
\(928\) | −1.62741e7 | −0.620335 | ||||||||
\(929\) | 3.10442e7 | 1.18016 | 0.590080 | − | 0.807345i | \(-0.299096\pi\) | ||||
0.590080 | + | 0.807345i | \(0.299096\pi\) | |||||||
\(930\) | 3.96778e6 | 0.150432 | ||||||||
\(931\) | 3.48430e7 | 1.31747 | ||||||||
\(932\) | −2.23767e7 | −0.843834 | ||||||||
\(933\) | 2.26644e7 | 0.852393 | ||||||||
\(934\) | −4.20851e6 | −0.157856 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.53128e6 | 0.131747 | ||||||||
\(937\) | 3.10737e7 | 1.15623 | 0.578115 | − | 0.815955i | \(-0.303788\pi\) | ||||
0.578115 | + | 0.815955i | \(0.303788\pi\) | |||||||
\(938\) | 739544. | 0.0274446 | ||||||||
\(939\) | −2.01206e7 | −0.744692 | ||||||||
\(940\) | −6.73642e6 | −0.248662 | ||||||||
\(941\) | 2.50349e7 | 0.921664 | 0.460832 | − | 0.887488i | \(-0.347551\pi\) | ||||
0.460832 | + | 0.887488i | \(0.347551\pi\) | |||||||
\(942\) | 2.86889e6 | 0.105339 | ||||||||
\(943\) | −1.68040e7 | −0.615366 | ||||||||
\(944\) | 5.96046e6 | 0.217696 | ||||||||
\(945\) | −1.74377e6 | −0.0635198 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.37383e6 | −0.194719 | −0.0973596 | − | 0.995249i | \(-0.531040\pi\) | ||||
−0.0973596 | + | 0.995249i | \(0.531040\pi\) | |||||||
\(948\) | −2.93547e7 | −1.06086 | ||||||||
\(949\) | 1.27148e7 | 0.458294 | ||||||||
\(950\) | 1.15322e7 | 0.414576 | ||||||||
\(951\) | 9.54713e6 | 0.342311 | ||||||||
\(952\) | 2.36200e6 | 0.0844669 | ||||||||
\(953\) | −7.26908e6 | −0.259267 | −0.129634 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129634 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(954\) | 2.49512e6 | 0.0887608 | ||||||||
\(955\) | 1.44258e7 | 0.511836 | ||||||||
\(956\) | −1.97915e7 | −0.700381 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.39441e6 | 0.260309 | ||||||||
\(959\) | −6.38191e6 | −0.224080 | ||||||||
\(960\) | 2.21763e7 | 0.776625 | ||||||||
\(961\) | −5.66589e6 | −0.197906 | ||||||||
\(962\) | 7.05425e6 | 0.245761 | ||||||||
\(963\) | 1.01185e6 | 0.0351602 | ||||||||
\(964\) | 6.85069e6 | 0.237433 | ||||||||
\(965\) | −3.96735e7 | −1.37146 | ||||||||
\(966\) | 370188. | 0.0127638 | ||||||||
\(967\) | 2.54428e7 | 0.874983 | 0.437491 | − | 0.899223i | \(-0.355867\pi\) | ||||
0.437491 | + | 0.899223i | \(0.355867\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.80325e7 | −0.959074 | ||||||||
\(970\) | 7.29210e6 | 0.248842 | ||||||||
\(971\) | 9.88213e6 | 0.336358 | 0.168179 | − | 0.985756i | \(-0.446211\pi\) | ||||
0.168179 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(972\) | −1.83052e6 | −0.0621453 | ||||||||
\(973\) | 1.55709e6 | 0.0527268 | ||||||||
\(974\) | 3.81644e6 | 0.128902 | ||||||||
\(975\) | 3.32513e7 | 1.12020 | ||||||||
\(976\) | −3.91072e7 | −1.31411 | ||||||||
\(977\) | 2.22197e6 | 0.0744736 | 0.0372368 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372368 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(978\) | 3.88796e6 | 0.129980 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.60056e7 | −1.53019 | ||||||||
\(981\) | −1.60986e7 | −0.534091 | ||||||||
\(982\) | 1.69716e6 | 0.0561623 | ||||||||
\(983\) | 2.53706e7 | 0.837428 | 0.418714 | − | 0.908118i | \(-0.362481\pi\) | ||||
0.418714 | + | 0.908118i | \(0.362481\pi\) | |||||||
\(984\) | 6.02267e6 | 0.198290 | ||||||||
\(985\) | −7.95776e7 | −2.61337 | ||||||||
\(986\) | −7.96849e6 | −0.261026 | ||||||||
\(987\) | −552708. | −0.0180594 | ||||||||
\(988\) | 4.63363e7 | 1.51018 | ||||||||
\(989\) | 1.35736e7 | 0.441269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.24132e7 | 1.04843 | 0.524214 | − | 0.851587i | \(-0.324359\pi\) | ||||
0.524214 | + | 0.851587i | \(0.324359\pi\) | |||||||
\(992\) | −1.41124e7 | −0.455327 | ||||||||
\(993\) | −2.11109e7 | −0.679414 | ||||||||
\(994\) | −1.18794e6 | −0.0381354 | ||||||||
\(995\) | 4.41655e7 | 1.41425 | ||||||||
\(996\) | 1.73795e7 | 0.555122 | ||||||||
\(997\) | 1.55048e6 | 0.0494000 | 0.0247000 | − | 0.999695i | \(-0.492137\pi\) | ||||
0.0247000 | + | 0.999695i | \(0.492137\pi\) | |||||||
\(998\) | −6.95160e6 | −0.220932 | ||||||||
\(999\) | −7.43143e6 | −0.235591 |
(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 | 363.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 1089.6.a.h.1.1 | 1 | |||
11.10 | odd | 2 | 33.6.a.b.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 99.6.a.a.1.1 | 1 | |||
44.43 | even | 2 | 528.6.a.a.1.1 | 1 | |||
55.54 | odd | 2 | 825.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.b.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
99.6.a.a.1.1 | 1 | 33.32 | even | 2 | |||
363.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
528.6.a.a.1.1 | 1 | 44.43 | even | 2 | |||
825.6.a.a.1.1 | 1 | 55.54 | odd | 2 | |||
1089.6.a.h.1.1 | 1 | 3.2 | odd | 2 |