Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,6,Mod(1,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, 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("575.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.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: | \(92.2206963925\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.13410 | 0.554036 | 0.277018 | − | 0.960865i | \(-0.410654\pi\) | ||||
0.277018 | + | 0.960865i | \(0.410654\pi\) | |||||||
\(3\) | −27.5349 | −1.76637 | −0.883183 | − | 0.469028i | \(-0.844604\pi\) | ||||
−0.883183 | + | 0.469028i | \(0.844604\pi\) | |||||||
\(4\) | −22.1774 | −0.693044 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −86.2973 | −0.978631 | ||||||||
\(7\) | −98.9863 | −0.763537 | −0.381768 | − | 0.924258i | \(-0.624685\pi\) | ||||
−0.381768 | + | 0.924258i | \(0.624685\pi\) | |||||||
\(8\) | −169.798 | −0.938008 | ||||||||
\(9\) | 515.172 | 2.12005 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −172.976 | −0.431027 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(12\) | 610.653 | 1.22417 | ||||||||
\(13\) | −499.623 | −0.819944 | −0.409972 | − | 0.912098i | \(-0.634462\pi\) | ||||
−0.409972 | + | 0.912098i | \(0.634462\pi\) | |||||||
\(14\) | −310.233 | −0.423027 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 177.514 | 0.173353 | ||||||||
\(17\) | −185.294 | −0.155503 | −0.0777516 | − | 0.996973i | \(-0.524774\pi\) | ||||
−0.0777516 | + | 0.996973i | \(0.524774\pi\) | |||||||
\(18\) | 1614.60 | 1.17458 | ||||||||
\(19\) | −457.866 | −0.290974 | −0.145487 | − | 0.989360i | \(-0.546475\pi\) | ||||
−0.145487 | + | 0.989360i | \(0.546475\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2725.58 | 1.34869 | ||||||||
\(22\) | −542.125 | −0.238805 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 4675.36 | 1.65687 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1565.87 | −0.454279 | ||||||||
\(27\) | −7494.24 | −1.97842 | ||||||||
\(28\) | 2195.26 | 0.529164 | ||||||||
\(29\) | 4657.20 | 1.02832 | 0.514161 | − | 0.857693i | \(-0.328103\pi\) | ||||
0.514161 | + | 0.857693i | \(0.328103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9047.26 | 1.69088 | 0.845440 | − | 0.534070i | \(-0.179338\pi\) | ||||
0.845440 | + | 0.534070i | \(0.179338\pi\) | |||||||
\(32\) | 5989.87 | 1.03405 | ||||||||
\(33\) | 4762.89 | 0.761352 | ||||||||
\(34\) | −580.731 | −0.0861545 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11425.2 | −1.46929 | ||||||||
\(37\) | −5379.45 | −0.646002 | −0.323001 | − | 0.946399i | \(-0.604692\pi\) | ||||
−0.323001 | + | 0.946399i | \(0.604692\pi\) | |||||||
\(38\) | −1435.00 | −0.161210 | ||||||||
\(39\) | 13757.1 | 1.44832 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 957.099 | 0.0889195 | 0.0444598 | − | 0.999011i | \(-0.485843\pi\) | ||||
0.0444598 | + | 0.999011i | \(0.485843\pi\) | |||||||
\(42\) | 8542.25 | 0.747221 | ||||||||
\(43\) | 19714.5 | 1.62598 | 0.812989 | − | 0.582279i | \(-0.197839\pi\) | ||||
0.812989 | + | 0.582279i | \(0.197839\pi\) | |||||||
\(44\) | 3836.16 | 0.298721 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1657.94 | 0.115525 | ||||||||
\(47\) | 22583.7 | 1.49125 | 0.745623 | − | 0.666368i | \(-0.232152\pi\) | ||||
0.745623 | + | 0.666368i | \(0.232152\pi\) | |||||||
\(48\) | −4887.83 | −0.306206 | ||||||||
\(49\) | −7008.71 | −0.417012 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5102.06 | 0.274676 | ||||||||
\(52\) | 11080.3 | 0.568257 | ||||||||
\(53\) | −15608.8 | −0.763271 | −0.381635 | − | 0.924313i | \(-0.624639\pi\) | ||||
−0.381635 | + | 0.924313i | \(0.624639\pi\) | |||||||
\(54\) | −23487.7 | −1.09612 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16807.6 | 0.716203 | ||||||||
\(57\) | 12607.3 | 0.513967 | ||||||||
\(58\) | 14596.1 | 0.569728 | ||||||||
\(59\) | 506.470 | 0.0189419 | 0.00947096 | − | 0.999955i | \(-0.496985\pi\) | ||||
0.00947096 | + | 0.999955i | \(0.496985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31327.9 | 1.07797 | 0.538985 | − | 0.842316i | \(-0.318808\pi\) | ||||
0.538985 | + | 0.842316i | \(0.318808\pi\) | |||||||
\(62\) | 28355.1 | 0.936809 | ||||||||
\(63\) | −50995.0 | −1.61874 | ||||||||
\(64\) | 13092.4 | 0.399549 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 14927.4 | 0.421817 | ||||||||
\(67\) | −43689.5 | −1.18902 | −0.594511 | − | 0.804087i | \(-0.702654\pi\) | ||||
−0.594511 | + | 0.804087i | \(0.702654\pi\) | |||||||
\(68\) | 4109.34 | 0.107771 | ||||||||
\(69\) | −14566.0 | −0.368313 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18754.4 | −0.441526 | −0.220763 | − | 0.975327i | \(-0.570855\pi\) | ||||
−0.220763 | + | 0.975327i | \(0.570855\pi\) | |||||||
\(72\) | −87475.0 | −1.98862 | ||||||||
\(73\) | −39706.2 | −0.872070 | −0.436035 | − | 0.899930i | \(-0.643618\pi\) | ||||
−0.436035 | + | 0.899930i | \(0.643618\pi\) | |||||||
\(74\) | −16859.8 | −0.357909 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10154.3 | 0.201658 | ||||||||
\(77\) | 17122.3 | 0.329105 | ||||||||
\(78\) | 43116.1 | 0.802423 | ||||||||
\(79\) | −21075.0 | −0.379927 | −0.189964 | − | 0.981791i | \(-0.560837\pi\) | ||||
−0.189964 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81166.6 | 1.37456 | ||||||||
\(82\) | 2999.65 | 0.0492646 | ||||||||
\(83\) | −59205.2 | −0.943333 | −0.471666 | − | 0.881777i | \(-0.656347\pi\) | ||||
−0.471666 | + | 0.881777i | \(0.656347\pi\) | |||||||
\(84\) | −60446.3 | −0.934698 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 61787.3 | 0.900851 | ||||||||
\(87\) | −128236. | −1.81639 | ||||||||
\(88\) | 29370.9 | 0.404307 | ||||||||
\(89\) | −74791.3 | −1.00087 | −0.500433 | − | 0.865775i | \(-0.666826\pi\) | ||||
−0.500433 | + | 0.865775i | \(0.666826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49455.8 | 0.626057 | ||||||||
\(92\) | −11731.8 | −0.144510 | ||||||||
\(93\) | −249116. | −2.98672 | ||||||||
\(94\) | 70779.5 | 0.826205 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −164931. | −1.82651 | ||||||||
\(97\) | 46828.3 | 0.505335 | 0.252668 | − | 0.967553i | \(-0.418692\pi\) | ||||
0.252668 | + | 0.967553i | \(0.418692\pi\) | |||||||
\(98\) | −21966.0 | −0.231040 | ||||||||
\(99\) | −89112.5 | −0.913799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 124353. | 1.21297 | 0.606487 | − | 0.795094i | \(-0.292578\pi\) | ||||
0.606487 | + | 0.795094i | \(0.292578\pi\) | |||||||
\(102\) | 15990.4 | 0.152180 | ||||||||
\(103\) | −165230. | −1.53460 | −0.767299 | − | 0.641290i | \(-0.778400\pi\) | ||||
−0.767299 | + | 0.641290i | \(0.778400\pi\) | |||||||
\(104\) | 84834.8 | 0.769114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48919.5 | −0.422880 | ||||||||
\(107\) | 136352. | 1.15133 | 0.575667 | − | 0.817684i | \(-0.304743\pi\) | ||||
0.575667 | + | 0.817684i | \(0.304743\pi\) | |||||||
\(108\) | 166203. | 1.37113 | ||||||||
\(109\) | 223278. | 1.80003 | 0.900016 | − | 0.435858i | \(-0.143555\pi\) | ||||
0.900016 | + | 0.435858i | \(0.143555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 148123. | 1.14108 | ||||||||
\(112\) | −17571.4 | −0.132362 | ||||||||
\(113\) | 106206. | 0.782443 | 0.391222 | − | 0.920297i | \(-0.372053\pi\) | ||||
0.391222 | + | 0.920297i | \(0.372053\pi\) | |||||||
\(114\) | 39512.6 | 0.284756 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −103284. | −0.712673 | ||||||||
\(117\) | −257392. | −1.73832 | ||||||||
\(118\) | 1587.33 | 0.0104945 | ||||||||
\(119\) | 18341.6 | 0.118732 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −131130. | −0.814216 | ||||||||
\(122\) | 98184.8 | 0.597234 | ||||||||
\(123\) | −26353.6 | −0.157064 | ||||||||
\(124\) | −200645. | −1.17185 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −159824. | −0.896839 | ||||||||
\(127\) | 295410. | 1.62524 | 0.812618 | − | 0.582797i | \(-0.198042\pi\) | ||||
0.812618 | + | 0.582797i | \(0.198042\pi\) | |||||||
\(128\) | −150643. | −0.812687 | ||||||||
\(129\) | −542838. | −2.87207 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −75570.6 | −0.384746 | −0.192373 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192373 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(132\) | −105628. | −0.527650 | ||||||||
\(133\) | 45322.5 | 0.222170 | ||||||||
\(134\) | −136927. | −0.658762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31462.5 | 0.145863 | ||||||||
\(137\) | −400299. | −1.82215 | −0.911073 | − | 0.412245i | \(-0.864745\pi\) | ||||
−0.911073 | + | 0.412245i | \(0.864745\pi\) | |||||||
\(138\) | −45651.3 | −0.204059 | ||||||||
\(139\) | 66371.9 | 0.291371 | 0.145686 | − | 0.989331i | \(-0.453461\pi\) | ||||
0.145686 | + | 0.989331i | \(0.453461\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −621839. | −2.63409 | ||||||||
\(142\) | −58778.1 | −0.244622 | ||||||||
\(143\) | 86422.9 | 0.353418 | ||||||||
\(144\) | 91450.2 | 0.367518 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −124443. | −0.483158 | ||||||||
\(147\) | 192984. | 0.736595 | ||||||||
\(148\) | 119302. | 0.447708 | ||||||||
\(149\) | 181608. | 0.670147 | 0.335073 | − | 0.942192i | \(-0.391239\pi\) | ||||
0.335073 | + | 0.942192i | \(0.391239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −179415. | −0.640350 | −0.320175 | − | 0.947358i | \(-0.603742\pi\) | ||||
−0.320175 | + | 0.947358i | \(0.603742\pi\) | |||||||
\(152\) | 77744.5 | 0.272936 | ||||||||
\(153\) | −95458.4 | −0.329675 | ||||||||
\(154\) | 53663.0 | 0.182336 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −305096. | −1.00375 | ||||||||
\(157\) | −574225. | −1.85923 | −0.929615 | − | 0.368531i | \(-0.879861\pi\) | ||||
−0.929615 | + | 0.368531i | \(0.879861\pi\) | |||||||
\(158\) | −66051.3 | −0.210494 | ||||||||
\(159\) | 429786. | 1.34822 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −52363.8 | −0.159208 | ||||||||
\(162\) | 254384. | 0.761558 | ||||||||
\(163\) | 157294. | 0.463705 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(164\) | −21226.0 | −0.0616251 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −185555. | −0.522640 | ||||||||
\(167\) | 150221. | 0.416811 | 0.208406 | − | 0.978042i | \(-0.433173\pi\) | ||||
0.208406 | + | 0.978042i | \(0.433173\pi\) | |||||||
\(168\) | −462797. | −1.26508 | ||||||||
\(169\) | −121670. | −0.327692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −235880. | −0.616880 | ||||||||
\(172\) | −437217. | −1.12687 | ||||||||
\(173\) | −408467. | −1.03763 | −0.518813 | − | 0.854887i | \(-0.673626\pi\) | ||||
−0.518813 | + | 0.854887i | \(0.673626\pi\) | |||||||
\(174\) | −401903. | −1.00635 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −30705.7 | −0.0747200 | ||||||||
\(177\) | −13945.6 | −0.0334584 | ||||||||
\(178\) | −234404. | −0.554517 | ||||||||
\(179\) | 83182.2 | 0.194043 | 0.0970214 | − | 0.995282i | \(-0.469068\pi\) | ||||
0.0970214 | + | 0.995282i | \(0.469068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 383086. | 0.869160 | 0.434580 | − | 0.900633i | \(-0.356897\pi\) | ||||
0.434580 | + | 0.900633i | \(0.356897\pi\) | |||||||
\(182\) | 155000. | 0.346859 | ||||||||
\(183\) | −862611. | −1.90409 | ||||||||
\(184\) | −89822.9 | −0.195588 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −780754. | −1.65475 | ||||||||
\(187\) | 32051.5 | 0.0670261 | ||||||||
\(188\) | −500847. | −1.03350 | ||||||||
\(189\) | 741827. | 1.51060 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 906396. | 1.79777 | 0.898886 | − | 0.438182i | \(-0.144377\pi\) | ||||
0.898886 | + | 0.438182i | \(0.144377\pi\) | |||||||
\(192\) | −360499. | −0.705750 | ||||||||
\(193\) | −609358. | −1.17755 | −0.588775 | − | 0.808297i | \(-0.700390\pi\) | ||||
−0.588775 | + | 0.808297i | \(0.700390\pi\) | |||||||
\(194\) | 146765. | 0.279974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 155435. | 0.289007 | ||||||||
\(197\) | −690338. | −1.26735 | −0.633675 | − | 0.773600i | \(-0.718454\pi\) | ||||
−0.633675 | + | 0.773600i | \(0.718454\pi\) | |||||||
\(198\) | −279288. | −0.506278 | ||||||||
\(199\) | −118685. | −0.212452 | −0.106226 | − | 0.994342i | \(-0.533877\pi\) | ||||
−0.106226 | + | 0.994342i | \(0.533877\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.20299e6 | 2.10025 | ||||||||
\(202\) | 389734. | 0.672031 | ||||||||
\(203\) | −460999. | −0.785162 | ||||||||
\(204\) | −113150. | −0.190362 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −517846. | −0.850223 | ||||||||
\(207\) | 272526. | 0.442061 | ||||||||
\(208\) | −88690.0 | −0.142140 | ||||||||
\(209\) | 79199.9 | 0.125418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.18355e6 | 1.83012 | 0.915062 | − | 0.403314i | \(-0.132142\pi\) | ||||
0.915062 | + | 0.403314i | \(0.132142\pi\) | |||||||
\(212\) | 346162. | 0.528980 | ||||||||
\(213\) | 516400. | 0.779897 | ||||||||
\(214\) | 427340. | 0.637881 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.27250e6 | 1.85577 | ||||||||
\(217\) | −895555. | −1.29105 | ||||||||
\(218\) | 699777. | 0.997283 | ||||||||
\(219\) | 1.09331e6 | 1.54039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 92577.3 | 0.127504 | ||||||||
\(222\) | 464232. | 0.632198 | ||||||||
\(223\) | 1.37756e6 | 1.85501 | 0.927507 | − | 0.373806i | \(-0.121948\pi\) | ||||
0.927507 | + | 0.373806i | \(0.121948\pi\) | |||||||
\(224\) | −592915. | −0.789537 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 332860. | 0.433502 | ||||||||
\(227\) | 1.14830e6 | 1.47908 | 0.739539 | − | 0.673114i | \(-0.235043\pi\) | ||||
0.739539 | + | 0.673114i | \(0.235043\pi\) | |||||||
\(228\) | −279597. | −0.356202 | ||||||||
\(229\) | 171814. | 0.216506 | 0.108253 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108253 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −471461. | −0.581320 | ||||||||
\(232\) | −790780. | −0.964575 | ||||||||
\(233\) | 651670. | 0.786390 | 0.393195 | − | 0.919455i | \(-0.371370\pi\) | ||||
0.393195 | + | 0.919455i | \(0.371370\pi\) | |||||||
\(234\) | −806693. | −0.963094 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11232.2 | −0.0131276 | ||||||||
\(237\) | 580300. | 0.671091 | ||||||||
\(238\) | 57484.4 | 0.0657821 | ||||||||
\(239\) | −1.53723e6 | −1.74078 | −0.870389 | − | 0.492365i | \(-0.836133\pi\) | ||||
−0.870389 | + | 0.492365i | \(0.836133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 913293. | 1.01290 | 0.506451 | − | 0.862269i | \(-0.330957\pi\) | ||||
0.506451 | + | 0.862269i | \(0.330957\pi\) | |||||||
\(242\) | −410976. | −0.451105 | ||||||||
\(243\) | −413814. | −0.449562 | ||||||||
\(244\) | −694771. | −0.747080 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −82595.0 | −0.0870194 | ||||||||
\(247\) | 228760. | 0.238583 | ||||||||
\(248\) | −1.53620e6 | −1.58606 | ||||||||
\(249\) | 1.63021e6 | 1.66627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 432806. | 0.433620 | 0.216810 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216810 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(252\) | 1.13094e6 | 1.12186 | ||||||||
\(253\) | −91504.4 | −0.0898754 | ||||||||
\(254\) | 925846. | 0.900440 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −891087. | −0.849807 | ||||||||
\(257\) | −1.43836e6 | −1.35842 | −0.679210 | − | 0.733944i | \(-0.737677\pi\) | ||||
−0.679210 | + | 0.733944i | \(0.737677\pi\) | |||||||
\(258\) | −1.70131e6 | −1.59123 | ||||||||
\(259\) | 532492. | 0.493246 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.39926e6 | 2.18010 | ||||||||
\(262\) | −236846. | −0.213163 | ||||||||
\(263\) | −172554. | −0.153828 | −0.0769142 | − | 0.997038i | \(-0.524507\pi\) | ||||
−0.0769142 | + | 0.997038i | \(0.524507\pi\) | |||||||
\(264\) | −808727. | −0.714154 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 142045. | 0.123090 | ||||||||
\(267\) | 2.05937e6 | 1.76790 | ||||||||
\(268\) | 968920. | 0.824045 | ||||||||
\(269\) | −243007. | −0.204757 | −0.102378 | − | 0.994746i | \(-0.532645\pi\) | ||||
−0.102378 | + | 0.994746i | \(0.532645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.16968e6 | −1.79462 | −0.897310 | − | 0.441400i | \(-0.854482\pi\) | ||||
−0.897310 | + | 0.441400i | \(0.854482\pi\) | |||||||
\(272\) | −32892.3 | −0.0269570 | ||||||||
\(273\) | −1.36176e6 | −1.10585 | ||||||||
\(274\) | −1.25458e6 | −1.00954 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 323035. | 0.255257 | ||||||||
\(277\) | −858654. | −0.672386 | −0.336193 | − | 0.941793i | \(-0.609140\pi\) | ||||
−0.336193 | + | 0.941793i | \(0.609140\pi\) | |||||||
\(278\) | 208016. | 0.161430 | ||||||||
\(279\) | 4.66090e6 | 3.58475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.29812e6 | 1.73623 | 0.868115 | − | 0.496363i | \(-0.165331\pi\) | ||||
0.868115 | + | 0.496363i | \(0.165331\pi\) | |||||||
\(282\) | −1.94891e6 | −1.45938 | ||||||||
\(283\) | −382115. | −0.283614 | −0.141807 | − | 0.989894i | \(-0.545291\pi\) | ||||
−0.141807 | + | 0.989894i | \(0.545291\pi\) | |||||||
\(284\) | 415923. | 0.305997 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 270858. | 0.195807 | ||||||||
\(287\) | −94739.6 | −0.0678933 | ||||||||
\(288\) | 3.08581e6 | 2.19224 | ||||||||
\(289\) | −1.38552e6 | −0.975819 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.28942e6 | −0.892607 | ||||||||
\(292\) | 880580. | 0.604382 | ||||||||
\(293\) | 4228.48 | 0.00287750 | 0.00143875 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00143875 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(294\) | 604833. | 0.408100 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 913418. | 0.605955 | ||||||||
\(297\) | 1.29633e6 | 0.852752 | ||||||||
\(298\) | 569179. | 0.371286 | ||||||||
\(299\) | −264301. | −0.170970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.95147e6 | −1.24149 | ||||||||
\(302\) | −562306. | −0.354777 | ||||||||
\(303\) | −3.42404e6 | −2.14255 | ||||||||
\(304\) | −81277.6 | −0.0504414 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −299176. | −0.182652 | ||||||||
\(307\) | 454799. | 0.275406 | 0.137703 | − | 0.990474i | \(-0.456028\pi\) | ||||
0.137703 | + | 0.990474i | \(0.456028\pi\) | |||||||
\(308\) | −379728. | −0.228084 | ||||||||
\(309\) | 4.54958e6 | 2.71066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.90140e6 | −1.70101 | −0.850506 | − | 0.525966i | \(-0.823704\pi\) | ||||
−0.850506 | + | 0.525966i | \(0.823704\pi\) | |||||||
\(312\) | −2.33592e6 | −1.35854 | ||||||||
\(313\) | 2.58180e6 | 1.48957 | 0.744785 | − | 0.667304i | \(-0.232552\pi\) | ||||
0.744785 | + | 0.667304i | \(0.232552\pi\) | |||||||
\(314\) | −1.79968e6 | −1.03008 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 467389. | 0.263306 | ||||||||
\(317\) | −2.07352e6 | −1.15894 | −0.579468 | − | 0.814995i | \(-0.696740\pi\) | ||||
−0.579468 | + | 0.814995i | \(0.696740\pi\) | |||||||
\(318\) | 1.34699e6 | 0.746961 | ||||||||
\(319\) | −805584. | −0.443235 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.75443e6 | −2.03368 | ||||||||
\(322\) | −164113. | −0.0882073 | ||||||||
\(323\) | 84839.9 | 0.0452474 | ||||||||
\(324\) | −1.80006e6 | −0.952632 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 492974. | 0.256909 | ||||||||
\(327\) | −6.14795e6 | −3.17951 | ||||||||
\(328\) | −162513. | −0.0834072 | ||||||||
\(329\) | −2.23547e6 | −1.13862 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.30721e6 | 1.65917 | 0.829587 | − | 0.558377i | \(-0.188576\pi\) | ||||
0.829587 | + | 0.558377i | \(0.188576\pi\) | |||||||
\(332\) | 1.31302e6 | 0.653771 | ||||||||
\(333\) | −2.77134e6 | −1.36956 | ||||||||
\(334\) | 470808. | 0.230929 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 483828. | 0.233799 | ||||||||
\(337\) | 1.83038e6 | 0.877945 | 0.438973 | − | 0.898500i | \(-0.355342\pi\) | ||||
0.438973 | + | 0.898500i | \(0.355342\pi\) | |||||||
\(338\) | −381325. | −0.181553 | ||||||||
\(339\) | −2.92437e6 | −1.38208 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56496e6 | −0.728816 | ||||||||
\(342\) | −739272. | −0.341774 | ||||||||
\(343\) | 2.35743e6 | 1.08194 | ||||||||
\(344\) | −3.34747e6 | −1.52518 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.28018e6 | −0.574883 | ||||||||
\(347\) | 1.81015e6 | 0.807030 | 0.403515 | − | 0.914973i | \(-0.367788\pi\) | ||||
0.403515 | + | 0.914973i | \(0.367788\pi\) | |||||||
\(348\) | 2.84393e6 | 1.25884 | ||||||||
\(349\) | 1.63329e6 | 0.717793 | 0.358896 | − | 0.933377i | \(-0.383153\pi\) | ||||
0.358896 | + | 0.933377i | \(0.383153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.74430e6 | 1.62219 | ||||||||
\(352\) | −1.03610e6 | −0.445704 | ||||||||
\(353\) | 833243. | 0.355906 | 0.177953 | − | 0.984039i | \(-0.443053\pi\) | ||||
0.177953 | + | 0.984039i | \(0.443053\pi\) | |||||||
\(354\) | −43707.0 | −0.0185371 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.65868e6 | 0.693644 | ||||||||
\(357\) | −505034. | −0.209725 | ||||||||
\(358\) | 260701. | 0.107507 | ||||||||
\(359\) | −636036. | −0.260463 | −0.130231 | − | 0.991484i | \(-0.541572\pi\) | ||||
−0.130231 | + | 0.991484i | \(0.541572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26646e6 | −0.915334 | ||||||||
\(362\) | 1.20063e6 | 0.481546 | ||||||||
\(363\) | 3.61066e6 | 1.43820 | ||||||||
\(364\) | −1.09680e6 | −0.433885 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.70351e6 | −1.05493 | ||||||||
\(367\) | −372220. | −0.144256 | −0.0721282 | − | 0.997395i | \(-0.522979\pi\) | ||||
−0.0721282 | + | 0.997395i | \(0.522979\pi\) | |||||||
\(368\) | 93904.8 | 0.0361467 | ||||||||
\(369\) | 493071. | 0.188514 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.54505e6 | 0.582785 | ||||||||
\(372\) | 5.52474e6 | 2.06992 | ||||||||
\(373\) | 18520.2 | 0.00689245 | 0.00344622 | − | 0.999994i | \(-0.498903\pi\) | ||||
0.00344622 | + | 0.999994i | \(0.498903\pi\) | |||||||
\(374\) | 100453. | 0.0371349 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.83465e6 | −1.39880 | ||||||||
\(377\) | −2.32684e6 | −0.843167 | ||||||||
\(378\) | 2.32496e6 | 0.836925 | ||||||||
\(379\) | 4.32941e6 | 1.54821 | 0.774106 | − | 0.633056i | \(-0.218200\pi\) | ||||
0.774106 | + | 0.633056i | \(0.218200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.13410e6 | −2.87076 | ||||||||
\(382\) | 2.84074e6 | 0.996031 | ||||||||
\(383\) | −3.16493e6 | −1.10247 | −0.551235 | − | 0.834350i | \(-0.685843\pi\) | ||||
−0.551235 | + | 0.834350i | \(0.685843\pi\) | |||||||
\(384\) | 4.14794e6 | 1.43550 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.90979e6 | −0.652406 | ||||||||
\(387\) | 1.01564e7 | 3.44716 | ||||||||
\(388\) | −1.03853e6 | −0.350219 | ||||||||
\(389\) | −2.47737e6 | −0.830074 | −0.415037 | − | 0.909804i | \(-0.636231\pi\) | ||||
−0.415037 | + | 0.909804i | \(0.636231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −98020.6 | −0.0324247 | ||||||||
\(392\) | 1.19006e6 | 0.391160 | ||||||||
\(393\) | 2.08083e6 | 0.679603 | ||||||||
\(394\) | −2.16359e6 | −0.702158 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.97628e6 | 0.633303 | ||||||||
\(397\) | −1.98642e6 | −0.632550 | −0.316275 | − | 0.948667i | \(-0.602432\pi\) | ||||
−0.316275 | + | 0.948667i | \(0.602432\pi\) | |||||||
\(398\) | −371970. | −0.117706 | ||||||||
\(399\) | −1.24795e6 | −0.392433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.05157e6 | −0.947681 | −0.473840 | − | 0.880611i | \(-0.657133\pi\) | ||||
−0.473840 | + | 0.880611i | \(0.657133\pi\) | |||||||
\(402\) | 3.77029e6 | 1.16361 | ||||||||
\(403\) | −4.52022e6 | −1.38643 | ||||||||
\(404\) | −2.75782e6 | −0.840643 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.44482e6 | −0.435008 | ||||||||
\(407\) | 930517. | 0.278444 | ||||||||
\(408\) | −866318. | −0.257648 | ||||||||
\(409\) | −1.54349e6 | −0.456243 | −0.228122 | − | 0.973633i | \(-0.573258\pi\) | ||||
−0.228122 | + | 0.973633i | \(0.573258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10222e7 | 3.21858 | ||||||||
\(412\) | 3.66436e6 | 1.06354 | ||||||||
\(413\) | −50133.6 | −0.0144628 | ||||||||
\(414\) | 854125. | 0.244918 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.99268e6 | −0.847865 | ||||||||
\(417\) | −1.82754e6 | −0.514669 | ||||||||
\(418\) | 248221. | 0.0694860 | ||||||||
\(419\) | 782997. | 0.217884 | 0.108942 | − | 0.994048i | \(-0.465254\pi\) | ||||
0.108942 | + | 0.994048i | \(0.465254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.89001e6 | −0.519707 | −0.259854 | − | 0.965648i | \(-0.583674\pi\) | ||||
−0.259854 | + | 0.965648i | \(0.583674\pi\) | |||||||
\(422\) | 3.70937e6 | 1.01395 | ||||||||
\(423\) | 1.16345e7 | 3.16152 | ||||||||
\(424\) | 2.65033e6 | 0.715954 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.61845e6 | 0.432091 | ||||||||
\(427\) | −3.10103e6 | −0.823069 | ||||||||
\(428\) | −3.02393e6 | −0.797925 | ||||||||
\(429\) | −2.37965e6 | −0.624266 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.47121e6 | 0.381489 | 0.190745 | − | 0.981640i | \(-0.438910\pi\) | ||||
0.190745 | + | 0.981640i | \(0.438910\pi\) | |||||||
\(432\) | −1.33033e6 | −0.342966 | ||||||||
\(433\) | −1638.32 | −0.000419931 0 | −0.000209966 | − | 1.00000i | \(-0.500067\pi\) | ||||
−0.000209966 | 1.00000i | \(0.500067\pi\) | ||||||||
\(434\) | −2.80676e6 | −0.715289 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.95173e6 | −1.24750 | ||||||||
\(437\) | −242211. | −0.0606723 | ||||||||
\(438\) | 3.42654e6 | 0.853435 | ||||||||
\(439\) | −6.97689e6 | −1.72783 | −0.863914 | − | 0.503640i | \(-0.831994\pi\) | ||||
−0.863914 | + | 0.503640i | \(0.831994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.61069e6 | −0.884085 | ||||||||
\(442\) | 290147. | 0.0706418 | ||||||||
\(443\) | 3.49744e6 | 0.846723 | 0.423361 | − | 0.905961i | \(-0.360850\pi\) | ||||
0.423361 | + | 0.905961i | \(0.360850\pi\) | |||||||
\(444\) | −3.28498e6 | −0.790816 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.31740e6 | 1.02774 | ||||||||
\(447\) | −5.00057e6 | −1.18372 | ||||||||
\(448\) | −1.29597e6 | −0.305070 | ||||||||
\(449\) | −4.00137e6 | −0.936684 | −0.468342 | − | 0.883547i | \(-0.655149\pi\) | ||||
−0.468342 | + | 0.883547i | \(0.655149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −165555. | −0.0383267 | ||||||||
\(452\) | −2.35537e6 | −0.542267 | ||||||||
\(453\) | 4.94019e6 | 1.13109 | ||||||||
\(454\) | 3.59889e6 | 0.819463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.14069e6 | −0.482105 | ||||||||
\(457\) | 4.37124e6 | 0.979072 | 0.489536 | − | 0.871983i | \(-0.337166\pi\) | ||||
0.489536 | + | 0.871983i | \(0.337166\pi\) | |||||||
\(458\) | 538482. | 0.119952 | ||||||||
\(459\) | 1.38864e6 | 0.307651 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.70022e6 | 0.372610 | 0.186305 | − | 0.982492i | \(-0.440349\pi\) | ||||
0.186305 | + | 0.982492i | \(0.440349\pi\) | |||||||
\(462\) | −1.47761e6 | −0.322073 | ||||||||
\(463\) | 5.77097e6 | 1.25111 | 0.625557 | − | 0.780179i | \(-0.284872\pi\) | ||||
0.625557 | + | 0.780179i | \(0.284872\pi\) | |||||||
\(464\) | 826717. | 0.178263 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.04240e6 | 0.435689 | ||||||||
\(467\) | −3.25780e6 | −0.691246 | −0.345623 | − | 0.938373i | \(-0.612332\pi\) | ||||
−0.345623 | + | 0.938373i | \(0.612332\pi\) | |||||||
\(468\) | 5.70828e6 | 1.20473 | ||||||||
\(469\) | 4.32466e6 | 0.907863 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.58113e7 | 3.28408 | ||||||||
\(472\) | −85997.4 | −0.0177677 | ||||||||
\(473\) | −3.41014e6 | −0.700841 | ||||||||
\(474\) | 1.81872e6 | 0.371809 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −406769. | −0.0822868 | ||||||||
\(477\) | −8.04120e6 | −1.61817 | ||||||||
\(478\) | −4.81783e6 | −0.964454 | ||||||||
\(479\) | −5.35349e6 | −1.06610 | −0.533051 | − | 0.846083i | \(-0.678955\pi\) | ||||
−0.533051 | + | 0.846083i | \(0.678955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.68770e6 | 0.529685 | ||||||||
\(482\) | 2.86236e6 | 0.561185 | ||||||||
\(483\) | 1.44183e6 | 0.281220 | ||||||||
\(484\) | 2.90813e6 | 0.564287 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.29694e6 | −0.249074 | ||||||||
\(487\) | −3.94606e6 | −0.753948 | −0.376974 | − | 0.926224i | \(-0.623035\pi\) | ||||
−0.376974 | + | 0.926224i | \(0.623035\pi\) | |||||||
\(488\) | −5.31940e6 | −1.01114 | ||||||||
\(489\) | −4.33107e6 | −0.819073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.46612e6 | −0.836038 | −0.418019 | − | 0.908438i | \(-0.637276\pi\) | ||||
−0.418019 | + | 0.908438i | \(0.637276\pi\) | |||||||
\(492\) | 584455. | 0.108853 | ||||||||
\(493\) | −862951. | −0.159908 | ||||||||
\(494\) | 716959. | 0.132183 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.60601e6 | 0.293120 | ||||||||
\(497\) | 1.85642e6 | 0.337121 | ||||||||
\(498\) | 5.10925e6 | 0.923175 | ||||||||
\(499\) | 421495. | 0.0757777 | 0.0378889 | − | 0.999282i | \(-0.487937\pi\) | ||||
0.0378889 | + | 0.999282i | \(0.487937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.13633e6 | −0.736242 | ||||||||
\(502\) | 1.35646e6 | 0.240241 | ||||||||
\(503\) | 165744. | 0.0292090 | 0.0146045 | − | 0.999893i | \(-0.495351\pi\) | ||||
0.0146045 | + | 0.999893i | \(0.495351\pi\) | |||||||
\(504\) | 8.65882e6 | 1.51839 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −286784. | −0.0497942 | ||||||||
\(507\) | 3.35017e6 | 0.578824 | ||||||||
\(508\) | −6.55143e6 | −1.12636 | ||||||||
\(509\) | −2.54136e6 | −0.434782 | −0.217391 | − | 0.976085i | \(-0.569755\pi\) | ||||
−0.217391 | + | 0.976085i | \(0.569755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.93037e6 | 0.665857 | ||||||||
\(512\) | 2.02781e6 | 0.341863 | ||||||||
\(513\) | 3.43136e6 | 0.575669 | ||||||||
\(514\) | −4.50796e6 | −0.752614 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.20387e7 | 1.99047 | ||||||||
\(517\) | −3.90643e6 | −0.642768 | ||||||||
\(518\) | 1.66889e6 | 0.273276 | ||||||||
\(519\) | 1.12471e7 | 1.83283 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.00488e7 | −1.62189 | −0.810944 | − | 0.585124i | \(-0.801046\pi\) | ||||
−0.810944 | + | 0.585124i | \(0.801046\pi\) | |||||||
\(522\) | 7.51952e6 | 1.20785 | ||||||||
\(523\) | 5.25311e6 | 0.839774 | 0.419887 | − | 0.907576i | \(-0.362070\pi\) | ||||
0.419887 | + | 0.907576i | \(0.362070\pi\) | |||||||
\(524\) | 1.67596e6 | 0.266646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −540803. | −0.0852265 | ||||||||
\(527\) | −1.67641e6 | −0.262937 | ||||||||
\(528\) | 845479. | 0.131983 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 260919. | 0.0401578 | ||||||||
\(532\) | −1.00513e6 | −0.153973 | ||||||||
\(533\) | −478189. | −0.0729090 | ||||||||
\(534\) | 6.45429e6 | 0.979479 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.41837e6 | 1.11531 | ||||||||
\(537\) | −2.29042e6 | −0.342751 | ||||||||
\(538\) | −761609. | −0.113443 | ||||||||
\(539\) | 1.21234e6 | 0.179743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.45549e6 | 0.654489 | 0.327244 | − | 0.944940i | \(-0.393880\pi\) | ||||
0.327244 | + | 0.944940i | \(0.393880\pi\) | |||||||
\(542\) | −6.80000e6 | −0.994285 | ||||||||
\(543\) | −1.05482e7 | −1.53526 | ||||||||
\(544\) | −1.10989e6 | −0.160798 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.26791e6 | −0.612679 | ||||||||
\(547\) | 2.77840e6 | 0.397033 | 0.198516 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198516 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(548\) | 8.87759e6 | 1.26283 | ||||||||
\(549\) | 1.61393e7 | 2.28535 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.13237e6 | −0.299215 | ||||||||
\(552\) | 2.47327e6 | 0.345480 | ||||||||
\(553\) | 2.08614e6 | 0.290089 | ||||||||
\(554\) | −2.69111e6 | −0.372527 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.47196e6 | −0.201933 | ||||||||
\(557\) | 1.26464e7 | 1.72715 | 0.863575 | − | 0.504220i | \(-0.168220\pi\) | ||||
0.863575 | + | 0.504220i | \(0.168220\pi\) | |||||||
\(558\) | 1.46077e7 | 1.98608 | ||||||||
\(559\) | −9.84982e6 | −1.33321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −882535. | −0.118393 | ||||||||
\(562\) | 7.20255e6 | 0.961935 | ||||||||
\(563\) | 3.99645e6 | 0.531377 | 0.265689 | − | 0.964059i | \(-0.414401\pi\) | ||||
0.265689 | + | 0.964059i | \(0.414401\pi\) | |||||||
\(564\) | 1.37908e7 | 1.82554 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.19759e6 | −0.157132 | ||||||||
\(567\) | −8.03438e6 | −1.04953 | ||||||||
\(568\) | 3.18444e6 | 0.414155 | ||||||||
\(569\) | −1.09077e6 | −0.141238 | −0.0706191 | − | 0.997503i | \(-0.522497\pi\) | ||||
−0.0706191 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 226191. | 0.0290325 | 0.0145162 | − | 0.999895i | \(-0.495379\pi\) | ||||
0.0145162 | + | 0.999895i | \(0.495379\pi\) | |||||||
\(572\) | −1.91664e6 | −0.244934 | ||||||||
\(573\) | −2.49576e7 | −3.17553 | ||||||||
\(574\) | −296924. | −0.0376154 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.74485e6 | 0.847064 | ||||||||
\(577\) | −3.28573e6 | −0.410858 | −0.205429 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205429 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(578\) | −4.34237e6 | −0.540639 | ||||||||
\(579\) | 1.67786e7 | 2.07999 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.86051e6 | 0.720269 | ||||||||
\(582\) | −4.04116e6 | −0.494537 | ||||||||
\(583\) | 2.69994e6 | 0.328991 | ||||||||
\(584\) | 6.74202e6 | 0.818008 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13252.5 | 0.00159424 | ||||||||
\(587\) | 7.43016e6 | 0.890027 | 0.445013 | − | 0.895524i | \(-0.353199\pi\) | ||||
0.445013 | + | 0.895524i | \(0.353199\pi\) | |||||||
\(588\) | −4.27989e6 | −0.510493 | ||||||||
\(589\) | −4.14244e6 | −0.492003 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.90084e7 | 2.23860 | ||||||||
\(592\) | −954928. | −0.111987 | ||||||||
\(593\) | 8.97683e6 | 1.04830 | 0.524151 | − | 0.851626i | \(-0.324383\pi\) | ||||
0.524151 | + | 0.851626i | \(0.324383\pi\) | |||||||
\(594\) | 4.06282e6 | 0.472456 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.02760e6 | −0.464441 | ||||||||
\(597\) | 3.26797e6 | 0.375269 | ||||||||
\(598\) | −828345. | −0.0947237 | ||||||||
\(599\) | −1.40377e7 | −1.59856 | −0.799280 | − | 0.600959i | \(-0.794785\pi\) | ||||
−0.799280 | + | 0.600959i | \(0.794785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.15574e6 | 1.03397 | 0.516984 | − | 0.855995i | \(-0.327055\pi\) | ||||
0.516984 | + | 0.855995i | \(0.327055\pi\) | |||||||
\(602\) | −6.11610e6 | −0.687833 | ||||||||
\(603\) | −2.25076e7 | −2.52079 | ||||||||
\(604\) | 3.97897e6 | 0.443790 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.07313e7 | −1.18705 | ||||||||
\(607\) | −7.53570e6 | −0.830141 | −0.415070 | − | 0.909789i | \(-0.636243\pi\) | ||||
−0.415070 | + | 0.909789i | \(0.636243\pi\) | |||||||
\(608\) | −2.74256e6 | −0.300882 | ||||||||
\(609\) | 1.26936e7 | 1.38688 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.12833e7 | −1.22274 | ||||||||
\(612\) | 2.11702e6 | 0.228479 | ||||||||
\(613\) | 9.98554e6 | 1.07330 | 0.536649 | − | 0.843805i | \(-0.319690\pi\) | ||||
0.536649 | + | 0.843805i | \(0.319690\pi\) | |||||||
\(614\) | 1.42539e6 | 0.152585 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.90732e6 | −0.308703 | ||||||||
\(617\) | −6.82945e6 | −0.722226 | −0.361113 | − | 0.932522i | \(-0.617603\pi\) | ||||
−0.361113 | + | 0.932522i | \(0.617603\pi\) | |||||||
\(618\) | 1.42589e7 | 1.50181 | ||||||||
\(619\) | −9.08935e6 | −0.953468 | −0.476734 | − | 0.879047i | \(-0.658180\pi\) | ||||
−0.476734 | + | 0.879047i | \(0.658180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.96445e6 | −0.412529 | ||||||||
\(622\) | −9.09330e6 | −0.942422 | ||||||||
\(623\) | 7.40332e6 | 0.764199 | ||||||||
\(624\) | 2.44207e6 | 0.251071 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.09161e6 | 0.825276 | ||||||||
\(627\) | −2.18076e6 | −0.221534 | ||||||||
\(628\) | 1.27348e7 | 1.28853 | ||||||||
\(629\) | 996781. | 0.100455 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.93201e6 | 0.593100 | 0.296550 | − | 0.955017i | \(-0.404164\pi\) | ||||
0.296550 | + | 0.955017i | \(0.404164\pi\) | |||||||
\(632\) | 3.57849e6 | 0.356375 | ||||||||
\(633\) | −3.25890e7 | −3.23267 | ||||||||
\(634\) | −6.49862e6 | −0.642093 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.53154e6 | −0.934373 | ||||||||
\(637\) | 3.50172e6 | 0.341926 | ||||||||
\(638\) | −2.52478e6 | −0.245568 | ||||||||
\(639\) | −9.66173e6 | −0.936058 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.20892e7 | −1.16212 | −0.581062 | − | 0.813859i | \(-0.697363\pi\) | ||||
−0.581062 | + | 0.813859i | \(0.697363\pi\) | |||||||
\(642\) | −1.17668e7 | −1.12673 | ||||||||
\(643\) | −1.09118e7 | −1.04081 | −0.520404 | − | 0.853920i | \(-0.674219\pi\) | ||||
−0.520404 | + | 0.853920i | \(0.674219\pi\) | |||||||
\(644\) | 1.16129e6 | 0.110338 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 265897. | 0.0250687 | ||||||||
\(647\) | 8.06391e6 | 0.757330 | 0.378665 | − | 0.925534i | \(-0.376383\pi\) | ||||
0.378665 | + | 0.925534i | \(0.376383\pi\) | |||||||
\(648\) | −1.37819e7 | −1.28935 | ||||||||
\(649\) | −87607.3 | −0.00816448 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.46590e7 | 2.28047 | ||||||||
\(652\) | −3.48836e6 | −0.321368 | ||||||||
\(653\) | −897296. | −0.0823479 | −0.0411740 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411740 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(654\) | −1.92683e7 | −1.76157 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 169898. | 0.0154145 | ||||||||
\(657\) | −2.04555e7 | −1.84883 | ||||||||
\(658\) | −7.00620e6 | −0.630838 | ||||||||
\(659\) | 1.32258e6 | 0.118634 | 0.0593168 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593168 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.38914e7 | −1.23663 | −0.618317 | − | 0.785929i | \(-0.712185\pi\) | ||||
−0.618317 | + | 0.785929i | \(0.712185\pi\) | |||||||
\(662\) | 1.03651e7 | 0.919243 | ||||||||
\(663\) | −2.54911e6 | −0.225219 | ||||||||
\(664\) | 1.00529e7 | 0.884853 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.68568e6 | −0.758784 | ||||||||
\(667\) | 2.46366e6 | 0.214420 | ||||||||
\(668\) | −3.33151e6 | −0.288869 | ||||||||
\(669\) | −3.79309e7 | −3.27663 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.41898e6 | −0.464634 | ||||||||
\(672\) | 1.63259e7 | 1.39461 | ||||||||
\(673\) | 1.38217e7 | 1.17632 | 0.588159 | − | 0.808745i | \(-0.299853\pi\) | ||||
0.588159 | + | 0.808745i | \(0.299853\pi\) | |||||||
\(674\) | 5.73661e6 | 0.486414 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.69832e6 | 0.227105 | ||||||||
\(677\) | −4.26668e6 | −0.357782 | −0.178891 | − | 0.983869i | \(-0.557251\pi\) | ||||
−0.178891 | + | 0.983869i | \(0.557251\pi\) | |||||||
\(678\) | −9.16529e6 | −0.765723 | ||||||||
\(679\) | −4.63536e6 | −0.385842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.16184e7 | −2.61259 | ||||||||
\(682\) | −4.90475e6 | −0.403790 | ||||||||
\(683\) | 1.34750e6 | 0.110529 | 0.0552646 | − | 0.998472i | \(-0.482400\pi\) | ||||
0.0552646 | + | 0.998472i | \(0.482400\pi\) | |||||||
\(684\) | 5.23120e6 | 0.427525 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.38843e6 | 0.599434 | ||||||||
\(687\) | −4.73088e6 | −0.382429 | ||||||||
\(688\) | 3.49960e6 | 0.281869 | ||||||||
\(689\) | 7.79850e6 | 0.625839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.29881e7 | −1.03478 | −0.517392 | − | 0.855748i | \(-0.673097\pi\) | ||||
−0.517392 | + | 0.855748i | \(0.673097\pi\) | |||||||
\(692\) | 9.05873e6 | 0.719121 | ||||||||
\(693\) | 8.82092e6 | 0.697719 | ||||||||
\(694\) | 5.67318e6 | 0.447124 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.17741e7 | 1.70379 | ||||||||
\(697\) | −177345. | −0.0138273 | ||||||||
\(698\) | 5.11889e6 | 0.397683 | ||||||||
\(699\) | −1.79437e7 | −1.38905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.78237e7 | −1.36994 | −0.684970 | − | 0.728571i | \(-0.740185\pi\) | ||||
−0.684970 | + | 0.728571i | \(0.740185\pi\) | |||||||
\(702\) | 1.17350e7 | 0.898754 | ||||||||
\(703\) | 2.46307e6 | 0.187970 | ||||||||
\(704\) | −2.26468e6 | −0.172216 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.61147e6 | 0.197185 | ||||||||
\(707\) | −1.23092e7 | −0.926150 | ||||||||
\(708\) | 309278. | 0.0231881 | ||||||||
\(709\) | −1.38491e7 | −1.03468 | −0.517341 | − | 0.855779i | \(-0.673078\pi\) | ||||
−0.517341 | + | 0.855779i | \(0.673078\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.08573e7 | −0.805465 | ||||||||
\(712\) | 1.26994e7 | 0.938821 | ||||||||
\(713\) | 4.78600e6 | 0.352573 | ||||||||
\(714\) | −1.58283e6 | −0.116195 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.84476e6 | −0.134480 | ||||||||
\(717\) | 4.23274e7 | 3.07485 | ||||||||
\(718\) | −1.99340e6 | −0.144306 | ||||||||
\(719\) | −6.39208e6 | −0.461126 | −0.230563 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230563 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.63555e7 | 1.17172 | ||||||||
\(722\) | −7.10331e6 | −0.507128 | ||||||||
\(723\) | −2.51475e7 | −1.78916 | ||||||||
\(724\) | −8.49585e6 | −0.602366 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.13162e7 | 0.796817 | ||||||||
\(727\) | −9.15468e6 | −0.642403 | −0.321201 | − | 0.947011i | \(-0.604087\pi\) | ||||
−0.321201 | + | 0.947011i | \(0.604087\pi\) | |||||||
\(728\) | −8.39748e6 | −0.587247 | ||||||||
\(729\) | −8.32912e6 | −0.580471 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.65298e6 | −0.252845 | ||||||||
\(732\) | 1.91305e7 | 1.31962 | ||||||||
\(733\) | 1.29905e7 | 0.893028 | 0.446514 | − | 0.894777i | \(-0.352665\pi\) | ||||
0.446514 | + | 0.894777i | \(0.352665\pi\) | |||||||
\(734\) | −1.16658e6 | −0.0799232 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.16864e6 | 0.215615 | ||||||||
\(737\) | 7.55725e6 | 0.512501 | ||||||||
\(738\) | 1.54533e6 | 0.104444 | ||||||||
\(739\) | −3.98014e6 | −0.268094 | −0.134047 | − | 0.990975i | \(-0.542797\pi\) | ||||
−0.134047 | + | 0.990975i | \(0.542797\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.29890e6 | −0.421424 | ||||||||
\(742\) | 4.84236e6 | 0.322884 | ||||||||
\(743\) | 1.96581e6 | 0.130638 | 0.0653192 | − | 0.997864i | \(-0.479193\pi\) | ||||
0.0653192 | + | 0.997864i | \(0.479193\pi\) | |||||||
\(744\) | 4.22992e7 | 2.80156 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 58044.2 | 0.00381867 | ||||||||
\(747\) | −3.05009e7 | −1.99991 | ||||||||
\(748\) | −710819. | −0.0464520 | ||||||||
\(749\) | −1.34970e7 | −0.879086 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.00617e6 | 0.194497 | 0.0972487 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972487 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(752\) | 4.00891e6 | 0.258513 | ||||||||
\(753\) | −1.19173e7 | −0.765931 | ||||||||
\(754\) | −7.29256e6 | −0.467145 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.64518e7 | −1.04691 | ||||||||
\(757\) | −8.54036e6 | −0.541672 | −0.270836 | − | 0.962626i | \(-0.587300\pi\) | ||||
−0.270836 | + | 0.962626i | \(0.587300\pi\) | |||||||
\(758\) | 1.35688e7 | 0.857766 | ||||||||
\(759\) | 2.51957e6 | 0.158753 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00401e6 | −0.250630 | −0.125315 | − | 0.992117i | \(-0.539994\pi\) | ||||
−0.125315 | + | 0.992117i | \(0.539994\pi\) | |||||||
\(762\) | −2.54931e7 | −1.59051 | ||||||||
\(763\) | −2.21015e7 | −1.37439 | ||||||||
\(764\) | −2.01015e7 | −1.24594 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.91921e6 | −0.610809 | ||||||||
\(767\) | −253044. | −0.0155313 | ||||||||
\(768\) | 2.45360e7 | 1.50107 | ||||||||
\(769\) | −3.19689e6 | −0.194945 | −0.0974725 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974725 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.96051e7 | 2.39947 | ||||||||
\(772\) | 1.35140e7 | 0.816094 | ||||||||
\(773\) | −1.56246e7 | −0.940503 | −0.470251 | − | 0.882532i | \(-0.655837\pi\) | ||||
−0.470251 | + | 0.882532i | \(0.655837\pi\) | |||||||
\(774\) | 3.18311e7 | 1.90985 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.95134e6 | −0.474008 | ||||||||
\(777\) | −1.46621e7 | −0.871254 | ||||||||
\(778\) | −7.76433e6 | −0.459891 | ||||||||
\(779\) | −438223. | −0.0258733 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.24406e6 | 0.190310 | ||||||||
\(782\) | −307207. | −0.0179644 | ||||||||
\(783\) | −3.49021e7 | −2.03445 | ||||||||
\(784\) | −1.24414e6 | −0.0722904 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.52154e6 | 0.376525 | ||||||||
\(787\) | −2.27061e7 | −1.30679 | −0.653395 | − | 0.757018i | \(-0.726656\pi\) | ||||
−0.653395 | + | 0.757018i | \(0.726656\pi\) | |||||||
\(788\) | 1.53099e7 | 0.878329 | ||||||||
\(789\) | 4.75127e6 | 0.271717 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.05129e7 | −0.597424 | ||||||||
\(792\) | 1.51311e7 | 0.857151 | ||||||||
\(793\) | −1.56521e7 | −0.883874 | ||||||||
\(794\) | −6.22565e6 | −0.350456 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.63212e6 | 0.147239 | ||||||||
\(797\) | −2.22676e7 | −1.24173 | −0.620866 | − | 0.783916i | \(-0.713219\pi\) | ||||
−0.620866 | + | 0.783916i | \(0.713219\pi\) | |||||||
\(798\) | −3.91121e6 | −0.217422 | ||||||||
\(799\) | −4.18462e6 | −0.231894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.85304e7 | −2.12189 | ||||||||
\(802\) | −9.56393e6 | −0.525050 | ||||||||
\(803\) | 6.86823e6 | 0.375886 | ||||||||
\(804\) | −2.66791e7 | −1.45557 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.41668e7 | −0.768131 | ||||||||
\(807\) | 6.69118e6 | 0.361676 | ||||||||
\(808\) | −2.11148e7 | −1.13778 | ||||||||
\(809\) | 3.12578e7 | 1.67914 | 0.839570 | − | 0.543251i | \(-0.182807\pi\) | ||||
0.839570 | + | 0.543251i | \(0.182807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.17398e6 | −0.276231 | −0.138116 | − | 0.990416i | \(-0.544105\pi\) | ||||
−0.138116 | + | 0.990416i | \(0.544105\pi\) | |||||||
\(812\) | 1.02237e7 | 0.544152 | ||||||||
\(813\) | 5.97420e7 | 3.16996 | ||||||||
\(814\) | 2.91634e6 | 0.154268 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 905687. | 0.0476160 | ||||||||
\(817\) | −9.02660e6 | −0.473118 | ||||||||
\(818\) | −4.83747e6 | −0.252775 | ||||||||
\(819\) | 2.54783e7 | 1.32727 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.51567e7 | −1.30255 | −0.651277 | − | 0.758840i | \(-0.725766\pi\) | ||||
−0.651277 | + | 0.758840i | \(0.725766\pi\) | |||||||
\(822\) | 3.45447e7 | 1.78321 | ||||||||
\(823\) | −2.17605e7 | −1.11988 | −0.559938 | − | 0.828535i | \(-0.689175\pi\) | ||||
−0.559938 | + | 0.828535i | \(0.689175\pi\) | |||||||
\(824\) | 2.80556e7 | 1.43946 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −157124. | −0.00801294 | ||||||||
\(827\) | 2.25721e7 | 1.14765 | 0.573823 | − | 0.818979i | \(-0.305460\pi\) | ||||
0.573823 | + | 0.818979i | \(0.305460\pi\) | |||||||
\(828\) | −6.04392e6 | −0.306368 | ||||||||
\(829\) | 1.17900e6 | 0.0595836 | 0.0297918 | − | 0.999556i | \(-0.490516\pi\) | ||||
0.0297918 | + | 0.999556i | \(0.490516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.36430e7 | 1.18768 | ||||||||
\(832\) | −6.54127e6 | −0.327608 | ||||||||
\(833\) | 1.29867e6 | 0.0648467 | ||||||||
\(834\) | −5.72771e6 | −0.285145 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.75645e6 | −0.0869200 | ||||||||
\(837\) | −6.78024e7 | −3.34527 | ||||||||
\(838\) | 2.45399e6 | 0.120716 | ||||||||
\(839\) | 5.57632e6 | 0.273491 | 0.136746 | − | 0.990606i | \(-0.456336\pi\) | ||||
0.136746 | + | 0.990606i | \(0.456336\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17832e6 | 0.0574477 | ||||||||
\(842\) | −5.92349e6 | −0.287937 | ||||||||
\(843\) | −6.32786e7 | −3.06682 | ||||||||
\(844\) | −2.62481e7 | −1.26836 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.64636e7 | 1.75160 | ||||||||
\(847\) | 1.29801e7 | 0.621684 | ||||||||
\(848\) | −2.77077e6 | −0.132316 | ||||||||
\(849\) | 1.05215e7 | 0.500966 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.84573e6 | −0.134701 | ||||||||
\(852\) | −1.14524e7 | −0.540503 | ||||||||
\(853\) | −2.78507e7 | −1.31058 | −0.655289 | − | 0.755378i | \(-0.727453\pi\) | ||||
−0.655289 | + | 0.755378i | \(0.727453\pi\) | |||||||
\(854\) | −9.71895e6 | −0.456010 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.31522e7 | −1.07996 | ||||||||
\(857\) | −7.89202e6 | −0.367059 | −0.183530 | − | 0.983014i | \(-0.558752\pi\) | ||||
−0.183530 | + | 0.983014i | \(0.558752\pi\) | |||||||
\(858\) | −7.45806e6 | −0.345866 | ||||||||
\(859\) | 1.81190e7 | 0.837823 | 0.418911 | − | 0.908027i | \(-0.362412\pi\) | ||||
0.418911 | + | 0.908027i | \(0.362412\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.60865e6 | 0.119924 | ||||||||
\(862\) | 4.61093e6 | 0.211359 | ||||||||
\(863\) | 272254. | 0.0124437 | 0.00622183 | − | 0.999981i | \(-0.498020\pi\) | ||||
0.00622183 | + | 0.999981i | \(0.498020\pi\) | |||||||
\(864\) | −4.48895e7 | −2.04579 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5134.65 | −0.000232657 0 | ||||||||
\(867\) | 3.81503e7 | 1.72365 | ||||||||
\(868\) | 1.98611e7 | 0.894754 | ||||||||
\(869\) | 3.64548e6 | 0.163759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.18283e7 | 0.974932 | ||||||||
\(872\) | −3.79121e7 | −1.68844 | ||||||||
\(873\) | 2.41247e7 | 1.07134 | ||||||||
\(874\) | −759115. | −0.0336147 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.42467e7 | −1.06756 | ||||||||
\(877\) | −8.51694e6 | −0.373925 | −0.186962 | − | 0.982367i | \(-0.559864\pi\) | ||||
−0.186962 | + | 0.982367i | \(0.559864\pi\) | |||||||
\(878\) | −2.18663e7 | −0.957279 | ||||||||
\(879\) | −116431. | −0.00508272 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −475215. | −0.0206277 | −0.0103138 | − | 0.999947i | \(-0.503283\pi\) | ||||
−0.0103138 | + | 0.999947i | \(0.503283\pi\) | |||||||
\(882\) | −1.13163e7 | −0.489815 | ||||||||
\(883\) | −2.40143e7 | −1.03650 | −0.518249 | − | 0.855230i | \(-0.673416\pi\) | ||||
−0.518249 | + | 0.855230i | \(0.673416\pi\) | |||||||
\(884\) | −2.05312e6 | −0.0883658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.09613e7 | 0.469115 | ||||||||
\(887\) | −840273. | −0.0358601 | −0.0179300 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179300 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(888\) | −2.51509e7 | −1.07034 | ||||||||
\(889\) | −2.92416e7 | −1.24093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.40399e7 | −0.592474 | ||||||||
\(892\) | −3.05506e7 | −1.28561 | ||||||||
\(893\) | −1.03403e7 | −0.433914 | ||||||||
\(894\) | −1.56723e7 | −0.655826 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.49116e7 | 0.620517 | ||||||||
\(897\) | 7.27750e6 | 0.301996 | ||||||||
\(898\) | −1.25407e7 | −0.518957 | ||||||||
\(899\) | 4.21349e7 | 1.73877 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.89221e6 | 0.118691 | ||||||||
\(902\) | −518867. | −0.0212344 | ||||||||
\(903\) | 5.37335e7 | 2.19293 | ||||||||
\(904\) | −1.80335e7 | −0.733938 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.54831e7 | 0.626666 | ||||||||
\(907\) | −2.64919e7 | −1.06929 | −0.534643 | − | 0.845078i | \(-0.679554\pi\) | ||||
−0.534643 | + | 0.845078i | \(0.679554\pi\) | |||||||
\(908\) | −2.54663e7 | −1.02507 | ||||||||
\(909\) | 6.40630e7 | 2.57156 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.82537e7 | −0.728709 | −0.364355 | − | 0.931260i | \(-0.618710\pi\) | ||||
−0.364355 | + | 0.931260i | \(0.618710\pi\) | |||||||
\(912\) | 2.23797e6 | 0.0890979 | ||||||||
\(913\) | 1.02411e7 | 0.406602 | ||||||||
\(914\) | 1.36999e7 | 0.542441 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.81038e6 | −0.150048 | ||||||||
\(917\) | 7.48045e6 | 0.293768 | ||||||||
\(918\) | 4.35214e6 | 0.170450 | ||||||||
\(919\) | 3.48435e7 | 1.36092 | 0.680461 | − | 0.732784i | \(-0.261780\pi\) | ||||
0.680461 | + | 0.732784i | \(0.261780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.25228e7 | −0.486468 | ||||||||
\(922\) | 5.32868e6 | 0.206439 | ||||||||
\(923\) | 9.37011e6 | 0.362027 | ||||||||
\(924\) | 1.04558e7 | 0.402880 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.80868e7 | 0.693162 | ||||||||
\(927\) | −8.51217e7 | −3.25342 | ||||||||
\(928\) | 2.78960e7 | 1.06334 | ||||||||
\(929\) | −4.36870e6 | −0.166078 | −0.0830391 | − | 0.996546i | \(-0.526463\pi\) | ||||
−0.0830391 | + | 0.996546i | \(0.526463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.20905e6 | 0.121340 | ||||||||
\(932\) | −1.44523e7 | −0.545003 | ||||||||
\(933\) | 7.98899e7 | 3.00461 | ||||||||
\(934\) | −1.02103e7 | −0.382975 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.37045e7 | 1.63056 | ||||||||
\(937\) | 1.90567e7 | 0.709087 | 0.354543 | − | 0.935040i | \(-0.384636\pi\) | ||||
0.354543 | + | 0.935040i | \(0.384636\pi\) | |||||||
\(938\) | 1.35539e7 | 0.502989 | ||||||||
\(939\) | −7.10895e7 | −2.63113 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.86363e6 | −0.252685 | −0.126343 | − | 0.991987i | \(-0.540324\pi\) | ||||
−0.126343 | + | 0.991987i | \(0.540324\pi\) | |||||||
\(942\) | 4.95541e7 | 1.81950 | ||||||||
\(943\) | 506305. | 0.0185410 | ||||||||
\(944\) | 89905.5 | 0.00328364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.06877e7 | −0.388291 | ||||||||
\(947\) | 2.04942e7 | 0.742602 | 0.371301 | − | 0.928513i | \(-0.378912\pi\) | ||||
0.371301 | + | 0.928513i | \(0.378912\pi\) | |||||||
\(948\) | −1.28695e7 | −0.465095 | ||||||||
\(949\) | 1.98381e7 | 0.715048 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.70942e7 | 2.04711 | ||||||||
\(952\) | −3.11436e6 | −0.111372 | ||||||||
\(953\) | 2.36728e6 | 0.0844341 | 0.0422170 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422170 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(954\) | −2.52019e7 | −0.896526 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.40917e7 | 1.20644 | ||||||||
\(957\) | 2.21817e7 | 0.782916 | ||||||||
\(958\) | −1.67784e7 | −0.590659 | ||||||||
\(959\) | 3.96241e7 | 1.39128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.32238e7 | 1.85908 | ||||||||
\(962\) | 8.42353e6 | 0.293465 | ||||||||
\(963\) | 7.02446e7 | 2.44089 | ||||||||
\(964\) | −2.02545e7 | −0.701986 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.51885e6 | 0.155806 | ||||||||
\(967\) | 193505. | 0.00665465 | 0.00332732 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332732 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(968\) | 2.22656e7 | 0.763740 | ||||||||
\(969\) | −2.33606e6 | −0.0799236 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.18283e7 | 0.402602 | 0.201301 | − | 0.979529i | \(-0.435483\pi\) | ||||
0.201301 | + | 0.979529i | \(0.435483\pi\) | |||||||
\(972\) | 9.17733e6 | 0.311566 | ||||||||
\(973\) | −6.56990e6 | −0.222473 | ||||||||
\(974\) | −1.23674e7 | −0.417715 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.56113e6 | 0.186870 | ||||||||
\(977\) | 1.27220e7 | 0.426400 | 0.213200 | − | 0.977009i | \(-0.431611\pi\) | ||||
0.213200 | + | 0.977009i | \(0.431611\pi\) | |||||||
\(978\) | −1.35740e7 | −0.453796 | ||||||||
\(979\) | 1.29371e7 | 0.431401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.15027e8 | 3.81616 | ||||||||
\(982\) | −1.39973e7 | −0.463196 | ||||||||
\(983\) | 2.62540e7 | 0.866588 | 0.433294 | − | 0.901253i | \(-0.357351\pi\) | ||||
0.433294 | + | 0.901253i | \(0.357351\pi\) | |||||||
\(984\) | 4.47478e6 | 0.147328 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.70458e6 | −0.0885946 | ||||||||
\(987\) | 6.15536e7 | 2.01122 | ||||||||
\(988\) | −5.07331e6 | −0.165348 | ||||||||
\(989\) | 1.04290e7 | 0.339040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.49258e7 | 1.77661 | 0.888306 | − | 0.459253i | \(-0.151883\pi\) | ||||
0.888306 | + | 0.459253i | \(0.151883\pi\) | |||||||
\(992\) | 5.41919e7 | 1.74846 | ||||||||
\(993\) | −9.10638e7 | −2.93071 | ||||||||
\(994\) | 5.81823e6 | 0.186778 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.61539e7 | −1.15480 | ||||||||
\(997\) | 3.45837e7 | 1.10188 | 0.550939 | − | 0.834545i | \(-0.314270\pi\) | ||||
0.550939 | + | 0.834545i | \(0.314270\pi\) | |||||||
\(998\) | 1.32101e6 | 0.0419836 | ||||||||
\(999\) | 4.03149e7 | 1.27806 |
(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 | 575.6.a.l.1.19 | 27 | ||
5.2 | odd | 4 | 115.6.b.a.24.36 | yes | 54 | ||
5.3 | odd | 4 | 115.6.b.a.24.19 | ✓ | 54 | ||
5.4 | even | 2 | 575.6.a.m.1.9 | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.6.b.a.24.19 | ✓ | 54 | 5.3 | odd | 4 | ||
115.6.b.a.24.36 | yes | 54 | 5.2 | odd | 4 | ||
575.6.a.l.1.19 | 27 | 1.1 | even | 1 | trivial | ||
575.6.a.m.1.9 | 27 | 5.4 | even | 2 |