Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + 7443872 x^{2} - 12856224 x - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(3.16483\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.16483 | 0.559469 | 0.279734 | − | 0.960077i | \(-0.409754\pi\) | ||||
0.279734 | + | 0.960077i | \(0.409754\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −21.9838 | −0.686995 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −28.4835 | −0.323009 | ||||||||
\(7\) | 223.585 | 1.72464 | 0.862318 | − | 0.506366i | \(-0.169012\pi\) | ||||
0.862318 | + | 0.506366i | \(0.169012\pi\) | |||||||
\(8\) | −170.850 | −0.943821 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 197.855 | 0.396637 | ||||||||
\(13\) | 999.193 | 1.63980 | 0.819900 | − | 0.572507i | \(-0.194029\pi\) | ||||
0.819900 | + | 0.572507i | \(0.194029\pi\) | |||||||
\(14\) | 707.609 | 0.964880 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 162.772 | 0.158957 | ||||||||
\(17\) | 2010.59 | 1.68734 | 0.843668 | − | 0.536865i | \(-0.180392\pi\) | ||||
0.843668 | + | 0.536865i | \(0.180392\pi\) | |||||||
\(18\) | 256.351 | 0.186490 | ||||||||
\(19\) | −856.966 | −0.544602 | −0.272301 | − | 0.962212i | \(-0.587785\pi\) | ||||
−0.272301 | + | 0.962212i | \(0.587785\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2012.27 | −0.995720 | ||||||||
\(22\) | 382.945 | 0.168686 | ||||||||
\(23\) | 2374.78 | 0.936059 | 0.468030 | − | 0.883713i | \(-0.344964\pi\) | ||||
0.468030 | + | 0.883713i | \(0.344964\pi\) | |||||||
\(24\) | 1537.65 | 0.544915 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3162.28 | 0.917416 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −4915.26 | −1.18482 | ||||||||
\(29\) | 4716.76 | 1.04147 | 0.520737 | − | 0.853717i | \(-0.325657\pi\) | ||||
0.520737 | + | 0.853717i | \(0.325657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9118.77 | −1.70425 | −0.852123 | − | 0.523342i | \(-0.824685\pi\) | ||||
−0.852123 | + | 0.523342i | \(0.824685\pi\) | |||||||
\(32\) | 5982.34 | 1.03275 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 6363.19 | 0.944012 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1780.69 | −0.228998 | ||||||||
\(37\) | −3138.40 | −0.376881 | −0.188440 | − | 0.982085i | \(-0.560343\pi\) | ||||
−0.188440 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(38\) | −2712.15 | −0.304688 | ||||||||
\(39\) | −8992.73 | −0.946739 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11989.9 | −1.11392 | −0.556961 | − | 0.830539i | \(-0.688033\pi\) | ||||
−0.556961 | + | 0.830539i | \(0.688033\pi\) | |||||||
\(42\) | −6368.48 | −0.557074 | ||||||||
\(43\) | −8608.69 | −0.710012 | −0.355006 | − | 0.934864i | \(-0.615521\pi\) | ||||
−0.355006 | + | 0.934864i | \(0.615521\pi\) | |||||||
\(44\) | −2660.04 | −0.207137 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7515.77 | 0.523696 | ||||||||
\(47\) | 18196.2 | 1.20153 | 0.600767 | − | 0.799424i | \(-0.294862\pi\) | ||||
0.600767 | + | 0.799424i | \(0.294862\pi\) | |||||||
\(48\) | −1464.95 | −0.0917738 | ||||||||
\(49\) | 33183.3 | 1.97437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18095.3 | −0.974184 | ||||||||
\(52\) | −21966.1 | −1.12653 | ||||||||
\(53\) | 10919.2 | 0.533952 | 0.266976 | − | 0.963703i | \(-0.413976\pi\) | ||||
0.266976 | + | 0.963703i | \(0.413976\pi\) | |||||||
\(54\) | −2307.16 | −0.107670 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −38199.5 | −1.62775 | ||||||||
\(57\) | 7712.69 | 0.314426 | ||||||||
\(58\) | 14927.7 | 0.582672 | ||||||||
\(59\) | −38947.0 | −1.45661 | −0.728305 | − | 0.685253i | \(-0.759692\pi\) | ||||
−0.728305 | + | 0.685253i | \(0.759692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36320.3 | −1.24976 | −0.624878 | − | 0.780722i | \(-0.714851\pi\) | ||||
−0.624878 | + | 0.780722i | \(0.714851\pi\) | |||||||
\(62\) | −28859.4 | −0.953472 | ||||||||
\(63\) | 18110.4 | 0.574879 | ||||||||
\(64\) | 13724.4 | 0.418835 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3446.50 | −0.0973910 | ||||||||
\(67\) | 53109.7 | 1.44540 | 0.722698 | − | 0.691164i | \(-0.242902\pi\) | ||||
0.722698 | + | 0.691164i | \(0.242902\pi\) | |||||||
\(68\) | −44200.5 | −1.15919 | ||||||||
\(69\) | −21373.0 | −0.540434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52703.0 | 1.24077 | 0.620383 | − | 0.784299i | \(-0.286977\pi\) | ||||
0.620383 | + | 0.784299i | \(0.286977\pi\) | |||||||
\(72\) | −13838.8 | −0.314607 | ||||||||
\(73\) | 55220.6 | 1.21281 | 0.606406 | − | 0.795155i | \(-0.292610\pi\) | ||||
0.606406 | + | 0.795155i | \(0.292610\pi\) | |||||||
\(74\) | −9932.51 | −0.210853 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18839.4 | 0.374139 | ||||||||
\(77\) | 27053.8 | 0.519998 | ||||||||
\(78\) | −28460.5 | −0.529671 | ||||||||
\(79\) | 71829.6 | 1.29490 | 0.647450 | − | 0.762108i | \(-0.275836\pi\) | ||||
0.647450 | + | 0.762108i | \(0.275836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −37945.9 | −0.623204 | ||||||||
\(83\) | 17356.7 | 0.276548 | 0.138274 | − | 0.990394i | \(-0.455845\pi\) | ||||
0.138274 | + | 0.990394i | \(0.455845\pi\) | |||||||
\(84\) | 44237.3 | 0.684054 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −27245.0 | −0.397229 | ||||||||
\(87\) | −42450.8 | −0.601295 | ||||||||
\(88\) | −20672.8 | −0.284573 | ||||||||
\(89\) | −44666.7 | −0.597736 | −0.298868 | − | 0.954294i | \(-0.596609\pi\) | ||||
−0.298868 | + | 0.954294i | \(0.596609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 223405. | 2.82806 | ||||||||
\(92\) | −52206.7 | −0.643068 | ||||||||
\(93\) | 82068.9 | 0.983946 | ||||||||
\(94\) | 57587.9 | 0.672221 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −53841.0 | −0.596260 | ||||||||
\(97\) | −136962. | −1.47799 | −0.738993 | − | 0.673713i | \(-0.764698\pi\) | ||||
−0.738993 | + | 0.673713i | \(0.764698\pi\) | |||||||
\(98\) | 105019. | 1.10460 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −159090. | −1.55182 | −0.775909 | − | 0.630845i | \(-0.782708\pi\) | ||||
−0.775909 | + | 0.630845i | \(0.782708\pi\) | |||||||
\(102\) | −57268.7 | −0.545025 | ||||||||
\(103\) | −153555. | −1.42616 | −0.713082 | − | 0.701080i | \(-0.752701\pi\) | ||||
−0.713082 | + | 0.701080i | \(0.752701\pi\) | |||||||
\(104\) | −170712. | −1.54768 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 34557.5 | 0.298729 | ||||||||
\(107\) | 52408.5 | 0.442529 | 0.221265 | − | 0.975214i | \(-0.428982\pi\) | ||||
0.221265 | + | 0.975214i | \(0.428982\pi\) | |||||||
\(108\) | 16026.2 | 0.132212 | ||||||||
\(109\) | −90098.5 | −0.726359 | −0.363180 | − | 0.931719i | \(-0.618309\pi\) | ||||
−0.363180 | + | 0.931719i | \(0.618309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28245.6 | 0.217592 | ||||||||
\(112\) | 36393.3 | 0.274143 | ||||||||
\(113\) | 50729.4 | 0.373735 | 0.186867 | − | 0.982385i | \(-0.440167\pi\) | ||||
0.186867 | + | 0.982385i | \(0.440167\pi\) | |||||||
\(114\) | 24409.4 | 0.175912 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −103692. | −0.715487 | ||||||||
\(117\) | 80934.6 | 0.546600 | ||||||||
\(118\) | −123261. | −0.814928 | ||||||||
\(119\) | 449538. | 2.91004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −114948. | −0.699199 | ||||||||
\(123\) | 107909. | 0.643123 | ||||||||
\(124\) | 200466. | 1.17081 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 57316.3 | 0.321627 | ||||||||
\(127\) | 338912. | 1.86456 | 0.932282 | − | 0.361733i | \(-0.117815\pi\) | ||||
0.932282 | + | 0.361733i | \(0.117815\pi\) | |||||||
\(128\) | −147999. | −0.798427 | ||||||||
\(129\) | 77478.2 | 0.409926 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −214136. | −1.09021 | −0.545106 | − | 0.838367i | \(-0.683511\pi\) | ||||
−0.545106 | + | 0.838367i | \(0.683511\pi\) | |||||||
\(132\) | 23940.4 | 0.119590 | ||||||||
\(133\) | −191605. | −0.939241 | ||||||||
\(134\) | 168083. | 0.808653 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −343509. | −1.59254 | ||||||||
\(137\) | −61579.4 | −0.280307 | −0.140153 | − | 0.990130i | \(-0.544760\pi\) | ||||
−0.140153 | + | 0.990130i | \(0.544760\pi\) | |||||||
\(138\) | −67641.9 | −0.302356 | ||||||||
\(139\) | 241459. | 1.06000 | 0.530000 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.530000 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −163766. | −0.693706 | ||||||||
\(142\) | 166796. | 0.694169 | ||||||||
\(143\) | 120902. | 0.494418 | ||||||||
\(144\) | 13184.5 | 0.0529856 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 174764. | 0.678531 | ||||||||
\(147\) | −298649. | −1.13990 | ||||||||
\(148\) | 68994.1 | 0.258915 | ||||||||
\(149\) | 209027. | 0.771325 | 0.385662 | − | 0.922640i | \(-0.373973\pi\) | ||||
0.385662 | + | 0.922640i | \(0.373973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 128993. | 0.460389 | 0.230195 | − | 0.973145i | \(-0.426064\pi\) | ||||
0.230195 | + | 0.973145i | \(0.426064\pi\) | |||||||
\(152\) | 146412. | 0.514007 | ||||||||
\(153\) | 162858. | 0.562445 | ||||||||
\(154\) | 85620.7 | 0.290922 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 197695. | 0.650405 | ||||||||
\(157\) | 192991. | 0.624866 | 0.312433 | − | 0.949940i | \(-0.398856\pi\) | ||||
0.312433 | + | 0.949940i | \(0.398856\pi\) | |||||||
\(158\) | 227329. | 0.724456 | ||||||||
\(159\) | −98273.1 | −0.308277 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 530965. | 1.61436 | ||||||||
\(162\) | 20764.5 | 0.0621632 | ||||||||
\(163\) | 98844.2 | 0.291395 | 0.145698 | − | 0.989329i | \(-0.453457\pi\) | ||||
0.145698 | + | 0.989329i | \(0.453457\pi\) | |||||||
\(164\) | 263583. | 0.765258 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 54930.9 | 0.154720 | ||||||||
\(167\) | −12212.4 | −0.0338851 | −0.0169425 | − | 0.999856i | \(-0.505393\pi\) | ||||
−0.0169425 | + | 0.999856i | \(0.505393\pi\) | |||||||
\(168\) | 343795. | 0.939781 | ||||||||
\(169\) | 627093. | 1.68894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −69414.2 | −0.181534 | ||||||||
\(172\) | 189252. | 0.487775 | ||||||||
\(173\) | 209579. | 0.532393 | 0.266197 | − | 0.963919i | \(-0.414233\pi\) | ||||
0.266197 | + | 0.963919i | \(0.414233\pi\) | |||||||
\(174\) | −134350. | −0.336406 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19695.4 | 0.0479273 | ||||||||
\(177\) | 350523. | 0.840975 | ||||||||
\(178\) | −141363. | −0.334414 | ||||||||
\(179\) | −245093. | −0.571740 | −0.285870 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285870 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 420637. | 0.954356 | 0.477178 | − | 0.878807i | \(-0.341660\pi\) | ||||
0.477178 | + | 0.878807i | \(0.341660\pi\) | |||||||
\(182\) | 707038. | 1.58221 | ||||||||
\(183\) | 326883. | 0.721547 | ||||||||
\(184\) | −405730. | −0.883472 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 259734. | 0.550487 | ||||||||
\(187\) | 243282. | 0.508751 | ||||||||
\(188\) | −400022. | −0.825448 | ||||||||
\(189\) | −162993. | −0.331907 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 838901. | 1.66390 | 0.831950 | − | 0.554851i | \(-0.187225\pi\) | ||||
0.831950 | + | 0.554851i | \(0.187225\pi\) | |||||||
\(192\) | −123520. | −0.241815 | ||||||||
\(193\) | 847703. | 1.63814 | 0.819069 | − | 0.573696i | \(-0.194491\pi\) | ||||
0.819069 | + | 0.573696i | \(0.194491\pi\) | |||||||
\(194\) | −433461. | −0.826886 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −729496. | −1.35638 | ||||||||
\(197\) | −877903. | −1.61169 | −0.805844 | − | 0.592128i | \(-0.798288\pi\) | ||||
−0.805844 | + | 0.592128i | \(0.798288\pi\) | |||||||
\(198\) | 31018.5 | 0.0562287 | ||||||||
\(199\) | 132070. | 0.236413 | 0.118207 | − | 0.992989i | \(-0.462286\pi\) | ||||
0.118207 | + | 0.992989i | \(0.462286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −477987. | −0.834499 | ||||||||
\(202\) | −503495. | −0.868193 | ||||||||
\(203\) | 1.05460e6 | 1.79616 | ||||||||
\(204\) | 397805. | 0.669260 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −485975. | −0.797894 | ||||||||
\(207\) | 192357. | 0.312020 | ||||||||
\(208\) | 162640. | 0.260657 | ||||||||
\(209\) | −103693. | −0.164204 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −638957. | −0.988020 | −0.494010 | − | 0.869456i | \(-0.664469\pi\) | ||||
−0.494010 | + | 0.869456i | \(0.664469\pi\) | |||||||
\(212\) | −240047. | −0.366822 | ||||||||
\(213\) | −474327. | −0.716356 | ||||||||
\(214\) | 165864. | 0.247581 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 124549. | 0.181638 | ||||||||
\(217\) | −2.03882e6 | −2.93920 | ||||||||
\(218\) | −285147. | −0.406375 | ||||||||
\(219\) | −496985. | −0.700218 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00897e6 | 2.76689 | ||||||||
\(222\) | 89392.6 | 0.121736 | ||||||||
\(223\) | 75080.5 | 0.101103 | 0.0505516 | − | 0.998721i | \(-0.483902\pi\) | ||||
0.0505516 | + | 0.998721i | \(0.483902\pi\) | |||||||
\(224\) | 1.33756e6 | 1.78112 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 160550. | 0.209093 | ||||||||
\(227\) | 480604. | 0.619046 | 0.309523 | − | 0.950892i | \(-0.399831\pi\) | ||||
0.309523 | + | 0.950892i | \(0.399831\pi\) | |||||||
\(228\) | −169555. | −0.216009 | ||||||||
\(229\) | 331611. | 0.417870 | 0.208935 | − | 0.977930i | \(-0.433000\pi\) | ||||
0.208935 | + | 0.977930i | \(0.433000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −243484. | −0.300221 | ||||||||
\(232\) | −805857. | −0.982965 | ||||||||
\(233\) | −69038.0 | −0.0833102 | −0.0416551 | − | 0.999132i | \(-0.513263\pi\) | ||||
−0.0416551 | + | 0.999132i | \(0.513263\pi\) | |||||||
\(234\) | 256144. | 0.305805 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 856203. | 1.00068 | ||||||||
\(237\) | −646467. | −0.747610 | ||||||||
\(238\) | 1.42271e6 | 1.62808 | ||||||||
\(239\) | 735334. | 0.832703 | 0.416351 | − | 0.909204i | \(-0.363309\pi\) | ||||
0.416351 | + | 0.909204i | \(0.363309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −70515.7 | −0.0782065 | −0.0391033 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391033 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(242\) | 46336.3 | 0.0508608 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 798460. | 0.858576 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 341513. | 0.359807 | ||||||||
\(247\) | −856274. | −0.893038 | ||||||||
\(248\) | 1.55794e6 | 1.60850 | ||||||||
\(249\) | −156210. | −0.159665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 451414. | 0.452262 | 0.226131 | − | 0.974097i | \(-0.427392\pi\) | ||||
0.226131 | + | 0.974097i | \(0.427392\pi\) | |||||||
\(252\) | −398136. | −0.394939 | ||||||||
\(253\) | 287348. | 0.282232 | ||||||||
\(254\) | 1.07260e6 | 1.04316 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −907574. | −0.865530 | ||||||||
\(257\) | −794147. | −0.750012 | −0.375006 | − | 0.927022i | \(-0.622359\pi\) | ||||
−0.375006 | + | 0.927022i | \(0.622359\pi\) | |||||||
\(258\) | 245205. | 0.229341 | ||||||||
\(259\) | −701699. | −0.649982 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 382057. | 0.347158 | ||||||||
\(262\) | −677703. | −0.609939 | ||||||||
\(263\) | −889131. | −0.792641 | −0.396320 | − | 0.918112i | \(-0.629713\pi\) | ||||
−0.396320 | + | 0.918112i | \(0.629713\pi\) | |||||||
\(264\) | 186055. | 0.164298 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −606397. | −0.525476 | ||||||||
\(267\) | 402001. | 0.345103 | ||||||||
\(268\) | −1.16755e6 | −0.992979 | ||||||||
\(269\) | −1.74480e6 | −1.47016 | −0.735082 | − | 0.677978i | \(-0.762856\pi\) | ||||
−0.735082 | + | 0.677978i | \(0.762856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 806384. | 0.666989 | 0.333495 | − | 0.942752i | \(-0.391772\pi\) | ||||
0.333495 | + | 0.942752i | \(0.391772\pi\) | |||||||
\(272\) | 327268. | 0.268214 | ||||||||
\(273\) | −2.01064e6 | −1.63278 | ||||||||
\(274\) | −194888. | −0.156823 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 469860. | 0.371275 | ||||||||
\(277\) | 1.76740e6 | 1.38400 | 0.692000 | − | 0.721897i | \(-0.256730\pi\) | ||||
0.692000 | + | 0.721897i | \(0.256730\pi\) | |||||||
\(278\) | 764176. | 0.593037 | ||||||||
\(279\) | −738620. | −0.568082 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 79693.3 | 0.0602082 | 0.0301041 | − | 0.999547i | \(-0.490416\pi\) | ||||
0.0301041 | + | 0.999547i | \(0.490416\pi\) | |||||||
\(282\) | −518291. | −0.388107 | ||||||||
\(283\) | −763339. | −0.566567 | −0.283283 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(284\) | −1.15861e6 | −0.852400 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 382636. | 0.276611 | ||||||||
\(287\) | −2.68075e6 | −1.92111 | ||||||||
\(288\) | 484569. | 0.344251 | ||||||||
\(289\) | 2.62262e6 | 1.84710 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.23266e6 | 0.853315 | ||||||||
\(292\) | −1.21396e6 | −0.833196 | ||||||||
\(293\) | 402977. | 0.274228 | 0.137114 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137114 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(294\) | −945175. | −0.637741 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 536195. | 0.355708 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 661536. | 0.431532 | ||||||||
\(299\) | 2.37286e6 | 1.53495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.92477e6 | −1.22451 | ||||||||
\(302\) | 408243. | 0.257573 | ||||||||
\(303\) | 1.43181e6 | 0.895943 | ||||||||
\(304\) | −139490. | −0.0865682 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 515418. | 0.314671 | ||||||||
\(307\) | −2.24468e6 | −1.35928 | −0.679639 | − | 0.733546i | \(-0.737864\pi\) | ||||
−0.679639 | + | 0.733546i | \(0.737864\pi\) | |||||||
\(308\) | −594746. | −0.357236 | ||||||||
\(309\) | 1.38199e6 | 0.823397 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −378005. | −0.221614 | −0.110807 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110807 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(312\) | 1.53641e6 | 0.893552 | ||||||||
\(313\) | 2.25734e6 | 1.30237 | 0.651187 | − | 0.758917i | \(-0.274271\pi\) | ||||
0.651187 | + | 0.758917i | \(0.274271\pi\) | |||||||
\(314\) | 610783. | 0.349593 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.57909e6 | −0.889589 | ||||||||
\(317\) | −3.00613e6 | −1.68019 | −0.840097 | − | 0.542436i | \(-0.817502\pi\) | ||||
−0.840097 | + | 0.542436i | \(0.817502\pi\) | |||||||
\(318\) | −311018. | −0.172472 | ||||||||
\(319\) | 570727. | 0.314016 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −471676. | −0.255494 | ||||||||
\(322\) | 1.68041e6 | 0.903185 | ||||||||
\(323\) | −1.72301e6 | −0.918927 | ||||||||
\(324\) | −144236. | −0.0763328 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 312825. | 0.163026 | ||||||||
\(327\) | 810887. | 0.419364 | ||||||||
\(328\) | 2.04847e6 | 1.05134 | ||||||||
\(329\) | 4.06840e6 | 2.07221 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −289324. | −0.145149 | −0.0725746 | − | 0.997363i | \(-0.523122\pi\) | ||||
−0.0725746 | + | 0.997363i | \(0.523122\pi\) | |||||||
\(332\) | −381566. | −0.189987 | ||||||||
\(333\) | −254210. | −0.125627 | ||||||||
\(334\) | −38650.1 | −0.0189576 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −327540. | −0.158276 | ||||||||
\(337\) | −290901. | −0.139531 | −0.0697655 | − | 0.997563i | \(-0.522225\pi\) | ||||
−0.0697655 | + | 0.997563i | \(0.522225\pi\) | |||||||
\(338\) | 1.98464e6 | 0.944911 | ||||||||
\(339\) | −456564. | −0.215776 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.10337e6 | −0.513849 | ||||||||
\(342\) | −219684. | −0.101563 | ||||||||
\(343\) | 3.66149e6 | 1.68044 | ||||||||
\(344\) | 1.47079e6 | 0.670124 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 663282. | 0.297857 | ||||||||
\(347\) | 3.62678e6 | 1.61695 | 0.808476 | − | 0.588529i | \(-0.200293\pi\) | ||||
0.808476 | + | 0.588529i | \(0.200293\pi\) | |||||||
\(348\) | 933231. | 0.413087 | ||||||||
\(349\) | 3.99131e6 | 1.75409 | 0.877046 | − | 0.480407i | \(-0.159511\pi\) | ||||
0.877046 | + | 0.480407i | \(0.159511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −728411. | −0.315580 | ||||||||
\(352\) | 723863. | 0.311386 | ||||||||
\(353\) | −3.83884e6 | −1.63969 | −0.819847 | − | 0.572582i | \(-0.805942\pi\) | ||||
−0.819847 | + | 0.572582i | \(0.805942\pi\) | |||||||
\(354\) | 1.10935e6 | 0.470499 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 981946. | 0.410641 | ||||||||
\(357\) | −4.04584e6 | −1.68011 | ||||||||
\(358\) | −775678. | −0.319870 | ||||||||
\(359\) | −3.98280e6 | −1.63099 | −0.815496 | − | 0.578762i | \(-0.803536\pi\) | ||||
−0.815496 | + | 0.578762i | \(0.803536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.74171e6 | −0.703408 | ||||||||
\(362\) | 1.33124e6 | 0.533932 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −4.91129e6 | −1.94286 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.03453e6 | 0.403683 | ||||||||
\(367\) | 1.13099e6 | 0.438323 | 0.219162 | − | 0.975689i | \(-0.429668\pi\) | ||||
0.219162 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(368\) | 386547. | 0.148793 | ||||||||
\(369\) | −971179. | −0.371307 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.44138e6 | 0.920874 | ||||||||
\(372\) | −1.80419e6 | −0.675966 | ||||||||
\(373\) | −2.59821e6 | −0.966945 | −0.483472 | − | 0.875360i | \(-0.660625\pi\) | ||||
−0.483472 | + | 0.875360i | \(0.660625\pi\) | |||||||
\(374\) | 769946. | 0.284630 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.10882e6 | −1.13403 | ||||||||
\(377\) | 4.71295e6 | 1.70781 | ||||||||
\(378\) | −515847. | −0.185691 | ||||||||
\(379\) | 2.07353e6 | 0.741500 | 0.370750 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370750 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.05020e6 | −1.07651 | ||||||||
\(382\) | 2.65498e6 | 0.930899 | ||||||||
\(383\) | −2.26397e6 | −0.788632 | −0.394316 | − | 0.918975i | \(-0.629018\pi\) | ||||
−0.394316 | + | 0.918975i | \(0.629018\pi\) | |||||||
\(384\) | 1.33199e6 | 0.460972 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.68284e6 | 0.916486 | ||||||||
\(387\) | −697304. | −0.236671 | ||||||||
\(388\) | 3.01095e6 | 1.01537 | ||||||||
\(389\) | 989122. | 0.331418 | 0.165709 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165709 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.77471e6 | 1.57945 | ||||||||
\(392\) | −5.66935e6 | −1.86345 | ||||||||
\(393\) | 1.92722e6 | 0.629434 | ||||||||
\(394\) | −2.77842e6 | −0.901689 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −215464. | −0.0690456 | ||||||||
\(397\) | −1.93874e6 | −0.617368 | −0.308684 | − | 0.951165i | \(-0.599889\pi\) | ||||
−0.308684 | + | 0.951165i | \(0.599889\pi\) | |||||||
\(398\) | 417979. | 0.132266 | ||||||||
\(399\) | 1.72444e6 | 0.542271 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.89960e6 | −1.21104 | −0.605520 | − | 0.795830i | \(-0.707035\pi\) | ||||
−0.605520 | + | 0.795830i | \(0.707035\pi\) | |||||||
\(402\) | −1.51275e6 | −0.466876 | ||||||||
\(403\) | −9.11141e6 | −2.79462 | ||||||||
\(404\) | 3.49742e6 | 1.06609 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.33762e6 | 1.00490 | ||||||||
\(407\) | −379746. | −0.113634 | ||||||||
\(408\) | 3.09158e6 | 0.919455 | ||||||||
\(409\) | 1.63513e6 | 0.483331 | 0.241665 | − | 0.970360i | \(-0.422306\pi\) | ||||
0.241665 | + | 0.970360i | \(0.422306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 554214. | 0.161835 | ||||||||
\(412\) | 3.37572e6 | 0.979768 | ||||||||
\(413\) | −8.70796e6 | −2.51212 | ||||||||
\(414\) | 608777. | 0.174565 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.97751e6 | 1.69351 | ||||||||
\(417\) | −2.17313e6 | −0.611991 | ||||||||
\(418\) | −328170. | −0.0918668 | ||||||||
\(419\) | −3.50652e6 | −0.975755 | −0.487878 | − | 0.872912i | \(-0.662229\pi\) | ||||
−0.487878 | + | 0.872912i | \(0.662229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 233311. | 0.0641549 | 0.0320774 | − | 0.999485i | \(-0.489788\pi\) | ||||
0.0320774 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(422\) | −2.02219e6 | −0.552766 | ||||||||
\(423\) | 1.47389e6 | 0.400511 | ||||||||
\(424\) | −1.86555e6 | −0.503955 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.50117e6 | −0.400779 | ||||||||
\(427\) | −8.12068e6 | −2.15538 | ||||||||
\(428\) | −1.15214e6 | −0.304015 | ||||||||
\(429\) | −1.08812e6 | −0.285452 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.88958e6 | 1.52718 | 0.763591 | − | 0.645700i | \(-0.223434\pi\) | ||||
0.763591 | + | 0.645700i | \(0.223434\pi\) | |||||||
\(432\) | −118661. | −0.0305913 | ||||||||
\(433\) | −1.07678e6 | −0.276000 | −0.138000 | − | 0.990432i | \(-0.544067\pi\) | ||||
−0.138000 | + | 0.990432i | \(0.544067\pi\) | |||||||
\(434\) | −6.45253e6 | −1.64439 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.98071e6 | 0.499005 | ||||||||
\(437\) | −2.03510e6 | −0.509780 | ||||||||
\(438\) | −1.57287e6 | −0.391750 | ||||||||
\(439\) | −3.45853e6 | −0.856505 | −0.428253 | − | 0.903659i | \(-0.640871\pi\) | ||||
−0.428253 | + | 0.903659i | \(0.640871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.68784e6 | 0.658124 | ||||||||
\(442\) | 6.35805e6 | 1.54799 | ||||||||
\(443\) | 3.46996e6 | 0.840070 | 0.420035 | − | 0.907508i | \(-0.362018\pi\) | ||||
0.420035 | + | 0.907508i | \(0.362018\pi\) | |||||||
\(444\) | −620947. | −0.149485 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 237617. | 0.0565640 | ||||||||
\(447\) | −1.88125e6 | −0.445325 | ||||||||
\(448\) | 3.06857e6 | 0.722339 | ||||||||
\(449\) | −2.98659e6 | −0.699133 | −0.349566 | − | 0.936912i | \(-0.613671\pi\) | ||||
−0.349566 | + | 0.936912i | \(0.613671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.45077e6 | −0.335860 | ||||||||
\(452\) | −1.11523e6 | −0.256754 | ||||||||
\(453\) | −1.16094e6 | −0.265806 | ||||||||
\(454\) | 1.52103e6 | 0.346337 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.31771e6 | −0.296762 | ||||||||
\(457\) | 8.27627e6 | 1.85372 | 0.926860 | − | 0.375408i | \(-0.122498\pi\) | ||||
0.926860 | + | 0.375408i | \(0.122498\pi\) | |||||||
\(458\) | 1.04949e6 | 0.233785 | ||||||||
\(459\) | −1.46572e6 | −0.324728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.25876e6 | 1.15247 | 0.576237 | − | 0.817283i | \(-0.304521\pi\) | ||||
0.576237 | + | 0.817283i | \(0.304521\pi\) | |||||||
\(462\) | −770586. | −0.167964 | ||||||||
\(463\) | 2.91066e6 | 0.631013 | 0.315507 | − | 0.948923i | \(-0.397826\pi\) | ||||
0.315507 | + | 0.948923i | \(0.397826\pi\) | |||||||
\(464\) | 767755. | 0.165549 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −218494. | −0.0466095 | ||||||||
\(467\) | 905276. | 0.192083 | 0.0960415 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960415 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(468\) | −1.77925e6 | −0.375511 | ||||||||
\(469\) | 1.18745e7 | 2.49278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.73692e6 | −0.360767 | ||||||||
\(472\) | 6.65408e6 | 1.37478 | ||||||||
\(473\) | −1.04165e6 | −0.214077 | ||||||||
\(474\) | −2.04596e6 | −0.418265 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.88258e6 | −1.99918 | ||||||||
\(477\) | 884458. | 0.177984 | ||||||||
\(478\) | 2.32721e6 | 0.465871 | ||||||||
\(479\) | −1.83868e6 | −0.366158 | −0.183079 | − | 0.983098i | \(-0.558606\pi\) | ||||
−0.183079 | + | 0.983098i | \(0.558606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.13587e6 | −0.618009 | ||||||||
\(482\) | −223170. | −0.0437541 | ||||||||
\(483\) | −4.77868e6 | −0.932052 | ||||||||
\(484\) | −321865. | −0.0624541 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −186880. | −0.0358899 | ||||||||
\(487\) | 2.81488e6 | 0.537821 | 0.268911 | − | 0.963165i | \(-0.413336\pi\) | ||||
0.268911 | + | 0.963165i | \(0.413336\pi\) | |||||||
\(488\) | 6.20532e6 | 1.17955 | ||||||||
\(489\) | −889598. | −0.168237 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.61534e6 | −1.23836 | −0.619182 | − | 0.785247i | \(-0.712536\pi\) | ||||
−0.619182 | + | 0.785247i | \(0.712536\pi\) | |||||||
\(492\) | −2.37225e6 | −0.441822 | ||||||||
\(493\) | 9.48347e6 | 1.75732 | ||||||||
\(494\) | −2.70996e6 | −0.499627 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.48428e6 | −0.270901 | ||||||||
\(497\) | 1.17836e7 | 2.13987 | ||||||||
\(498\) | −494378. | −0.0893276 | ||||||||
\(499\) | 2.83864e6 | 0.510339 | 0.255170 | − | 0.966896i | \(-0.417869\pi\) | ||||
0.255170 | + | 0.966896i | \(0.417869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 109911. | 0.0195636 | ||||||||
\(502\) | 1.42865e6 | 0.253026 | ||||||||
\(503\) | −906183. | −0.159697 | −0.0798483 | − | 0.996807i | \(-0.525444\pi\) | ||||
−0.0798483 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(504\) | −3.09416e6 | −0.542583 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 909408. | 0.157900 | ||||||||
\(507\) | −5.64383e6 | −0.975112 | ||||||||
\(508\) | −7.45058e6 | −1.28095 | ||||||||
\(509\) | −3.13716e6 | −0.536714 | −0.268357 | − | 0.963320i | \(-0.586481\pi\) | ||||
−0.268357 | + | 0.963320i | \(0.586481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23465e7 | 2.09166 | ||||||||
\(512\) | 1.86366e6 | 0.314190 | ||||||||
\(513\) | 624728. | 0.104809 | ||||||||
\(514\) | −2.51334e6 | −0.419608 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.70327e6 | −0.281617 | ||||||||
\(517\) | 2.20174e6 | 0.362276 | ||||||||
\(518\) | −2.22076e6 | −0.363645 | ||||||||
\(519\) | −1.88621e6 | −0.307377 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.29715e6 | −0.209362 | −0.104681 | − | 0.994506i | \(-0.533382\pi\) | ||||
−0.104681 | + | 0.994506i | \(0.533382\pi\) | |||||||
\(522\) | 1.20915e6 | 0.194224 | ||||||||
\(523\) | 7.45988e6 | 1.19255 | 0.596276 | − | 0.802779i | \(-0.296646\pi\) | ||||
0.596276 | + | 0.802779i | \(0.296646\pi\) | |||||||
\(524\) | 4.70752e6 | 0.748970 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.81395e6 | −0.443458 | ||||||||
\(527\) | −1.83341e7 | −2.87564 | ||||||||
\(528\) | −177259. | −0.0276708 | ||||||||
\(529\) | −796777. | −0.123793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.15470e6 | −0.485537 | ||||||||
\(532\) | 4.21221e6 | 0.645254 | ||||||||
\(533\) | −1.19802e7 | −1.82661 | ||||||||
\(534\) | 1.27226e6 | 0.193074 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.07378e6 | −1.36419 | ||||||||
\(537\) | 2.20584e6 | 0.330094 | ||||||||
\(538\) | −5.52201e6 | −0.822511 | ||||||||
\(539\) | 4.01518e6 | 0.595296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.01922e7 | −1.49718 | −0.748591 | − | 0.663032i | \(-0.769270\pi\) | ||||
−0.748591 | + | 0.663032i | \(0.769270\pi\) | |||||||
\(542\) | 2.55207e6 | 0.373159 | ||||||||
\(543\) | −3.78573e6 | −0.550998 | ||||||||
\(544\) | 1.20280e7 | 1.74260 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.36334e6 | −0.913489 | ||||||||
\(547\) | 8.45753e6 | 1.20858 | 0.604289 | − | 0.796765i | \(-0.293457\pi\) | ||||
0.604289 | + | 0.796765i | \(0.293457\pi\) | |||||||
\(548\) | 1.35375e6 | 0.192569 | ||||||||
\(549\) | −2.94195e6 | −0.416585 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.04210e6 | −0.567189 | ||||||||
\(552\) | 3.65157e6 | 0.510073 | ||||||||
\(553\) | 1.60600e7 | 2.23323 | ||||||||
\(554\) | 5.59354e6 | 0.774305 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.30819e6 | −0.728215 | ||||||||
\(557\) | 1.27511e7 | 1.74144 | 0.870720 | − | 0.491778i | \(-0.163653\pi\) | ||||
0.870720 | + | 0.491778i | \(0.163653\pi\) | |||||||
\(558\) | −2.33761e6 | −0.317824 | ||||||||
\(559\) | −8.60173e6 | −1.16428 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.18953e6 | −0.293728 | ||||||||
\(562\) | 252216. | 0.0336846 | ||||||||
\(563\) | 6.44710e6 | 0.857223 | 0.428611 | − | 0.903489i | \(-0.359003\pi\) | ||||
0.428611 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(564\) | 3.60020e6 | 0.476573 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.41584e6 | −0.316976 | ||||||||
\(567\) | 1.46694e6 | 0.191626 | ||||||||
\(568\) | −9.00430e6 | −1.17106 | ||||||||
\(569\) | −7.05536e6 | −0.913563 | −0.456782 | − | 0.889579i | \(-0.650998\pi\) | ||||
−0.456782 | + | 0.889579i | \(0.650998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 393546. | 0.0505132 | 0.0252566 | − | 0.999681i | \(-0.491960\pi\) | ||||
0.0252566 | + | 0.999681i | \(0.491960\pi\) | |||||||
\(572\) | −2.65790e6 | −0.339663 | ||||||||
\(573\) | −7.55010e6 | −0.960653 | ||||||||
\(574\) | −8.48414e6 | −1.07480 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.11168e6 | 0.139612 | ||||||||
\(577\) | 2.27712e6 | 0.284738 | 0.142369 | − | 0.989814i | \(-0.454528\pi\) | ||||
0.142369 | + | 0.989814i | \(0.454528\pi\) | |||||||
\(578\) | 8.30016e6 | 1.03340 | ||||||||
\(579\) | −7.62932e6 | −0.945779 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.88069e6 | 0.476945 | ||||||||
\(582\) | 3.90115e6 | 0.477403 | ||||||||
\(583\) | 1.32123e6 | 0.160993 | ||||||||
\(584\) | −9.43442e6 | −1.14468 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.27536e6 | 0.153422 | ||||||||
\(587\) | 1.39306e6 | 0.166868 | 0.0834341 | − | 0.996513i | \(-0.473411\pi\) | ||||
0.0834341 | + | 0.996513i | \(0.473411\pi\) | |||||||
\(588\) | 6.56546e6 | 0.783108 | ||||||||
\(589\) | 7.81447e6 | 0.928136 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.90113e6 | 0.930508 | ||||||||
\(592\) | −510843. | −0.0599078 | ||||||||
\(593\) | 4.53743e6 | 0.529874 | 0.264937 | − | 0.964266i | \(-0.414649\pi\) | ||||
0.264937 | + | 0.964266i | \(0.414649\pi\) | |||||||
\(594\) | −279167. | −0.0324637 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.59522e6 | −0.529896 | ||||||||
\(597\) | −1.18863e6 | −0.136493 | ||||||||
\(598\) | 7.50970e6 | 0.858756 | ||||||||
\(599\) | −4.08022e6 | −0.464640 | −0.232320 | − | 0.972639i | \(-0.574632\pi\) | ||||
−0.232320 | + | 0.972639i | \(0.574632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33295e7 | −1.50532 | −0.752660 | − | 0.658409i | \(-0.771230\pi\) | ||||
−0.752660 | + | 0.658409i | \(0.771230\pi\) | |||||||
\(602\) | −6.09158e6 | −0.685076 | ||||||||
\(603\) | 4.30188e6 | 0.481798 | ||||||||
\(604\) | −2.83577e6 | −0.316285 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.53145e6 | 0.501252 | ||||||||
\(607\) | 5.04375e6 | 0.555625 | 0.277812 | − | 0.960635i | \(-0.410391\pi\) | ||||
0.277812 | + | 0.960635i | \(0.410391\pi\) | |||||||
\(608\) | −5.12666e6 | −0.562439 | ||||||||
\(609\) | −9.49136e6 | −1.03702 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.81815e7 | 1.97028 | ||||||||
\(612\) | −3.58024e6 | −0.386397 | ||||||||
\(613\) | −4.29244e6 | −0.461374 | −0.230687 | − | 0.973028i | \(-0.574097\pi\) | ||||
−0.230687 | + | 0.973028i | \(0.574097\pi\) | |||||||
\(614\) | −7.10404e6 | −0.760474 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.62213e6 | −0.490784 | ||||||||
\(617\) | 6.86553e6 | 0.726041 | 0.363020 | − | 0.931781i | \(-0.381746\pi\) | ||||
0.363020 | + | 0.931781i | \(0.381746\pi\) | |||||||
\(618\) | 4.37377e6 | 0.460665 | ||||||||
\(619\) | 1.81177e6 | 0.190054 | 0.0950269 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950269 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.73121e6 | −0.180145 | ||||||||
\(622\) | −1.19632e6 | −0.123986 | ||||||||
\(623\) | −9.98682e6 | −1.03088 | ||||||||
\(624\) | −1.46376e6 | −0.150491 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.14410e6 | 0.728638 | ||||||||
\(627\) | 933235. | 0.0948031 | ||||||||
\(628\) | −4.24267e6 | −0.429280 | ||||||||
\(629\) | −6.31004e6 | −0.635925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.04264e6 | −0.804129 | −0.402064 | − | 0.915611i | \(-0.631707\pi\) | ||||
−0.402064 | + | 0.915611i | \(0.631707\pi\) | |||||||
\(632\) | −1.22721e7 | −1.22215 | ||||||||
\(633\) | 5.75062e6 | 0.570434 | ||||||||
\(634\) | −9.51389e6 | −0.940016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.16042e6 | 0.211785 | ||||||||
\(637\) | 3.31565e7 | 3.23757 | ||||||||
\(638\) | 1.80626e6 | 0.175682 | ||||||||
\(639\) | 4.26895e6 | 0.413589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.75102e6 | 0.360583 | 0.180291 | − | 0.983613i | \(-0.442296\pi\) | ||||
0.180291 | + | 0.983613i | \(0.442296\pi\) | |||||||
\(642\) | −1.49278e6 | −0.142941 | ||||||||
\(643\) | −1.92270e7 | −1.83393 | −0.916966 | − | 0.398964i | \(-0.869370\pi\) | ||||
−0.916966 | + | 0.398964i | \(0.869370\pi\) | |||||||
\(644\) | −1.16726e7 | −1.10906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.45303e6 | −0.514111 | ||||||||
\(647\) | 1.65974e7 | 1.55876 | 0.779382 | − | 0.626549i | \(-0.215533\pi\) | ||||
0.779382 | + | 0.626549i | \(0.215533\pi\) | |||||||
\(648\) | −1.12095e6 | −0.104869 | ||||||||
\(649\) | −4.71258e6 | −0.439185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.83494e7 | 1.69695 | ||||||||
\(652\) | −2.17297e6 | −0.200187 | ||||||||
\(653\) | 5.30043e6 | 0.486439 | 0.243219 | − | 0.969971i | \(-0.421797\pi\) | ||||
0.243219 | + | 0.969971i | \(0.421797\pi\) | |||||||
\(654\) | 2.56632e6 | 0.234621 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.95161e6 | −0.177065 | ||||||||
\(657\) | 4.47287e6 | 0.404271 | ||||||||
\(658\) | 1.28758e7 | 1.15934 | ||||||||
\(659\) | 1.22198e7 | 1.09610 | 0.548051 | − | 0.836445i | \(-0.315370\pi\) | ||||
0.548051 | + | 0.836445i | \(0.315370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.92583e6 | 0.527528 | 0.263764 | − | 0.964587i | \(-0.415036\pi\) | ||||
0.263764 | + | 0.964587i | \(0.415036\pi\) | |||||||
\(662\) | −915662. | −0.0812064 | ||||||||
\(663\) | −1.80807e7 | −1.59747 | ||||||||
\(664\) | −2.96538e6 | −0.261012 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −804533. | −0.0702843 | ||||||||
\(667\) | 1.12012e7 | 0.974881 | ||||||||
\(668\) | 268474. | 0.0232789 | ||||||||
\(669\) | −675724. | −0.0583719 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.39476e6 | −0.376816 | ||||||||
\(672\) | −1.20381e7 | −1.02833 | ||||||||
\(673\) | 1.44387e7 | 1.22882 | 0.614412 | − | 0.788986i | \(-0.289393\pi\) | ||||
0.614412 | + | 0.788986i | \(0.289393\pi\) | |||||||
\(674\) | −920653. | −0.0780632 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.37859e7 | −1.16030 | ||||||||
\(677\) | 2.08078e7 | 1.74483 | 0.872417 | − | 0.488763i | \(-0.162552\pi\) | ||||
0.872417 | + | 0.488763i | \(0.162552\pi\) | |||||||
\(678\) | −1.44495e6 | −0.120720 | ||||||||
\(679\) | −3.06226e7 | −2.54899 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.32543e6 | −0.357406 | ||||||||
\(682\) | −3.49199e6 | −0.287483 | ||||||||
\(683\) | −1.34086e7 | −1.09985 | −0.549923 | − | 0.835215i | \(-0.685343\pi\) | ||||
−0.549923 | + | 0.835215i | \(0.685343\pi\) | |||||||
\(684\) | 1.52599e6 | 0.124713 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.15880e7 | 0.940152 | ||||||||
\(687\) | −2.98450e6 | −0.241257 | ||||||||
\(688\) | −1.40125e6 | −0.112861 | ||||||||
\(689\) | 1.09104e7 | 0.875575 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.76242e7 | −1.40415 | −0.702076 | − | 0.712102i | \(-0.747743\pi\) | ||||
−0.702076 | + | 0.712102i | \(0.747743\pi\) | |||||||
\(692\) | −4.60735e6 | −0.365751 | ||||||||
\(693\) | 2.19136e6 | 0.173333 | ||||||||
\(694\) | 1.14781e7 | 0.904634 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.25271e6 | 0.567515 | ||||||||
\(697\) | −2.41067e7 | −1.87956 | ||||||||
\(698\) | 1.26318e7 | 0.981359 | ||||||||
\(699\) | 621342. | 0.0480992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.59651e6 | 0.199570 | 0.0997850 | − | 0.995009i | \(-0.468184\pi\) | ||||
0.0997850 | + | 0.995009i | \(0.468184\pi\) | |||||||
\(702\) | −2.30530e6 | −0.176557 | ||||||||
\(703\) | 2.68950e6 | 0.205250 | ||||||||
\(704\) | 1.66065e6 | 0.126284 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.21493e7 | −0.917358 | ||||||||
\(707\) | −3.55703e7 | −2.67632 | ||||||||
\(708\) | −7.70583e6 | −0.577745 | ||||||||
\(709\) | −1.04437e7 | −0.780259 | −0.390129 | − | 0.920760i | \(-0.627570\pi\) | ||||
−0.390129 | + | 0.920760i | \(0.627570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.81820e6 | 0.431633 | ||||||||
\(712\) | 7.63130e6 | 0.564155 | ||||||||
\(713\) | −2.16550e7 | −1.59527 | ||||||||
\(714\) | −1.28044e7 | −0.939971 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.38809e6 | 0.392782 | ||||||||
\(717\) | −6.61801e6 | −0.480761 | ||||||||
\(718\) | −1.26049e7 | −0.912489 | ||||||||
\(719\) | −1.16530e7 | −0.840650 | −0.420325 | − | 0.907374i | \(-0.638084\pi\) | ||||
−0.420325 | + | 0.907374i | \(0.638084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.43325e7 | −2.45962 | ||||||||
\(722\) | −5.51222e6 | −0.393535 | ||||||||
\(723\) | 634641. | 0.0451526 | ||||||||
\(724\) | −9.24721e6 | −0.655638 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −417027. | −0.0293645 | ||||||||
\(727\) | 9.42203e6 | 0.661163 | 0.330581 | − | 0.943777i | \(-0.392755\pi\) | ||||
0.330581 | + | 0.943777i | \(0.392755\pi\) | |||||||
\(728\) | −3.81686e7 | −2.66918 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.73086e7 | −1.19803 | ||||||||
\(732\) | −7.18614e6 | −0.495699 | ||||||||
\(733\) | 6.06936e6 | 0.417237 | 0.208619 | − | 0.977997i | \(-0.433103\pi\) | ||||
0.208619 | + | 0.977997i | \(0.433103\pi\) | |||||||
\(734\) | 3.57940e6 | 0.245228 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.42067e7 | 0.966717 | ||||||||
\(737\) | 6.42627e6 | 0.435803 | ||||||||
\(738\) | −3.07362e6 | −0.207735 | ||||||||
\(739\) | 1.54739e7 | 1.04229 | 0.521144 | − | 0.853469i | \(-0.325505\pi\) | ||||
0.521144 | + | 0.853469i | \(0.325505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.70646e6 | 0.515596 | ||||||||
\(742\) | 7.72655e6 | 0.515200 | ||||||||
\(743\) | −1.84749e7 | −1.22775 | −0.613876 | − | 0.789402i | \(-0.710391\pi\) | ||||
−0.613876 | + | 0.789402i | \(0.710391\pi\) | |||||||
\(744\) | −1.40215e7 | −0.928669 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.22289e6 | −0.540975 | ||||||||
\(747\) | 1.40589e6 | 0.0921827 | ||||||||
\(748\) | −5.34826e6 | −0.349509 | ||||||||
\(749\) | 1.17177e7 | 0.763202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.07376e7 | 1.34171 | 0.670856 | − | 0.741588i | \(-0.265927\pi\) | ||||
0.670856 | + | 0.741588i | \(0.265927\pi\) | |||||||
\(752\) | 2.96183e6 | 0.190992 | ||||||||
\(753\) | −4.06272e6 | −0.261114 | ||||||||
\(754\) | 1.49157e7 | 0.955465 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.58322e6 | 0.228018 | ||||||||
\(757\) | −1.55685e6 | −0.0987432 | −0.0493716 | − | 0.998780i | \(-0.515722\pi\) | ||||
−0.0493716 | + | 0.998780i | \(0.515722\pi\) | |||||||
\(758\) | 6.56236e6 | 0.414846 | ||||||||
\(759\) | −2.58613e6 | −0.162947 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.49641e7 | 1.56262 | 0.781312 | − | 0.624140i | \(-0.214551\pi\) | ||||
0.781312 | + | 0.624140i | \(0.214551\pi\) | |||||||
\(762\) | −9.65339e6 | −0.602271 | ||||||||
\(763\) | −2.01447e7 | −1.25271 | ||||||||
\(764\) | −1.84423e7 | −1.14309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.16510e6 | −0.441215 | ||||||||
\(767\) | −3.89155e7 | −2.38855 | ||||||||
\(768\) | 8.16817e6 | 0.499714 | ||||||||
\(769\) | 3.71595e6 | 0.226597 | 0.113298 | − | 0.993561i | \(-0.463858\pi\) | ||||
0.113298 | + | 0.993561i | \(0.463858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.14733e6 | 0.433020 | ||||||||
\(772\) | −1.86358e7 | −1.12539 | ||||||||
\(773\) | −3.04530e7 | −1.83308 | −0.916539 | − | 0.399946i | \(-0.869029\pi\) | ||||
−0.916539 | + | 0.399946i | \(0.869029\pi\) | |||||||
\(774\) | −2.20685e6 | −0.132410 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.33999e7 | 1.39495 | ||||||||
\(777\) | 6.31529e6 | 0.375267 | ||||||||
\(778\) | 3.13041e6 | 0.185418 | ||||||||
\(779\) | 1.02749e7 | 0.606644 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.37707e6 | 0.374105 | ||||||||
\(782\) | 1.51112e7 | 0.883651 | ||||||||
\(783\) | −3.43851e6 | −0.200432 | ||||||||
\(784\) | 5.40130e6 | 0.313840 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.09933e6 | 0.352149 | ||||||||
\(787\) | 2.23713e7 | 1.28752 | 0.643760 | − | 0.765228i | \(-0.277374\pi\) | ||||
0.643760 | + | 0.765228i | \(0.277374\pi\) | |||||||
\(788\) | 1.92997e7 | 1.10722 | ||||||||
\(789\) | 8.00218e6 | 0.457631 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13423e7 | 0.644557 | ||||||||
\(792\) | −1.67450e6 | −0.0948575 | ||||||||
\(793\) | −3.62910e7 | −2.04935 | ||||||||
\(794\) | −6.13580e6 | −0.345398 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.90341e6 | −0.162415 | ||||||||
\(797\) | 4.96966e6 | 0.277128 | 0.138564 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138564 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(798\) | 5.45757e6 | 0.303384 | ||||||||
\(799\) | 3.65851e7 | 2.02739 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.61801e6 | −0.199245 | ||||||||
\(802\) | −1.23416e7 | −0.677539 | ||||||||
\(803\) | 6.68169e6 | 0.365677 | ||||||||
\(804\) | 1.05080e7 | 0.573297 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.88361e7 | −1.56350 | ||||||||
\(807\) | 1.57032e7 | 0.848800 | ||||||||
\(808\) | 2.71806e7 | 1.46464 | ||||||||
\(809\) | −2.69703e7 | −1.44882 | −0.724410 | − | 0.689369i | \(-0.757888\pi\) | ||||
−0.724410 | + | 0.689369i | \(0.757888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.73142e7 | −0.924378 | −0.462189 | − | 0.886782i | \(-0.652936\pi\) | ||||
−0.462189 | + | 0.886782i | \(0.652936\pi\) | |||||||
\(812\) | −2.31841e7 | −1.23396 | ||||||||
\(813\) | −7.25746e6 | −0.385086 | ||||||||
\(814\) | −1.20183e6 | −0.0635746 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.94541e6 | −0.154853 | ||||||||
\(817\) | 7.37735e6 | 0.386674 | ||||||||
\(818\) | 5.17492e6 | 0.270408 | ||||||||
\(819\) | 1.80958e7 | 0.942686 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.77928e7 | 0.921269 | 0.460634 | − | 0.887590i | \(-0.347622\pi\) | ||||
0.460634 | + | 0.887590i | \(0.347622\pi\) | |||||||
\(822\) | 1.75399e6 | 0.0905417 | ||||||||
\(823\) | −1.50458e7 | −0.774314 | −0.387157 | − | 0.922014i | \(-0.626543\pi\) | ||||
−0.387157 | + | 0.922014i | \(0.626543\pi\) | |||||||
\(824\) | 2.62348e7 | 1.34604 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.75592e7 | −1.40545 | ||||||||
\(827\) | −1.07676e7 | −0.547461 | −0.273731 | − | 0.961806i | \(-0.588258\pi\) | ||||
−0.273731 | + | 0.961806i | \(0.588258\pi\) | |||||||
\(828\) | −4.22874e6 | −0.214356 | ||||||||
\(829\) | −2.87834e6 | −0.145464 | −0.0727322 | − | 0.997352i | \(-0.523172\pi\) | ||||
−0.0727322 | + | 0.997352i | \(0.523172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.59066e7 | −0.799053 | ||||||||
\(832\) | 1.37133e7 | 0.686806 | ||||||||
\(833\) | 6.67180e7 | 3.33143 | ||||||||
\(834\) | −6.87759e6 | −0.342390 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.27957e6 | 0.112807 | ||||||||
\(837\) | 6.64758e6 | 0.327982 | ||||||||
\(838\) | −1.10975e7 | −0.545905 | ||||||||
\(839\) | −3.26365e7 | −1.60066 | −0.800330 | − | 0.599560i | \(-0.795342\pi\) | ||||
−0.800330 | + | 0.599560i | \(0.795342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.73663e6 | 0.0846678 | ||||||||
\(842\) | 738390. | 0.0358926 | ||||||||
\(843\) | −717239. | −0.0347612 | ||||||||
\(844\) | 1.40467e7 | 0.678765 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.66462e6 | 0.224074 | ||||||||
\(847\) | 3.27351e6 | 0.156785 | ||||||||
\(848\) | 1.77734e6 | 0.0848754 | ||||||||
\(849\) | 6.87005e6 | 0.327108 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.45300e6 | −0.352783 | ||||||||
\(852\) | 1.04275e7 | 0.492133 | ||||||||
\(853\) | 1.64332e7 | 0.773305 | 0.386652 | − | 0.922226i | \(-0.373631\pi\) | ||||
0.386652 | + | 0.922226i | \(0.373631\pi\) | |||||||
\(854\) | −2.57006e7 | −1.20586 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.95398e6 | −0.417668 | ||||||||
\(857\) | 1.27204e7 | 0.591628 | 0.295814 | − | 0.955246i | \(-0.404409\pi\) | ||||
0.295814 | + | 0.955246i | \(0.404409\pi\) | |||||||
\(858\) | −3.44372e6 | −0.159702 | ||||||||
\(859\) | 1.60847e7 | 0.743755 | 0.371878 | − | 0.928282i | \(-0.378714\pi\) | ||||
0.371878 | + | 0.928282i | \(0.378714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.41268e7 | 1.10915 | ||||||||
\(862\) | 1.86395e7 | 0.854410 | ||||||||
\(863\) | 1.66292e7 | 0.760056 | 0.380028 | − | 0.924975i | \(-0.375914\pi\) | ||||
0.380028 | + | 0.924975i | \(0.375914\pi\) | |||||||
\(864\) | −4.36113e6 | −0.198753 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.40784e6 | −0.154413 | ||||||||
\(867\) | −2.36036e7 | −1.06643 | ||||||||
\(868\) | 4.48211e7 | 2.01922 | ||||||||
\(869\) | 8.69139e6 | 0.390427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.30668e7 | 2.37016 | ||||||||
\(872\) | 1.53933e7 | 0.685553 | ||||||||
\(873\) | −1.10939e7 | −0.492662 | ||||||||
\(874\) | −6.44076e6 | −0.285206 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.09256e7 | 0.481046 | ||||||||
\(877\) | 2.13465e7 | 0.937191 | 0.468595 | − | 0.883413i | \(-0.344760\pi\) | ||||
0.468595 | + | 0.883413i | \(0.344760\pi\) | |||||||
\(878\) | −1.09457e7 | −0.479188 | ||||||||
\(879\) | −3.62679e6 | −0.158325 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.40726e7 | −1.47899 | −0.739495 | − | 0.673162i | \(-0.764935\pi\) | ||||
−0.739495 | + | 0.673162i | \(0.764935\pi\) | |||||||
\(882\) | 8.50658e6 | 0.368200 | ||||||||
\(883\) | −7.87284e6 | −0.339805 | −0.169902 | − | 0.985461i | \(-0.554345\pi\) | ||||
−0.169902 | + | 0.985461i | \(0.554345\pi\) | |||||||
\(884\) | −4.41648e7 | −1.90084 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.09819e7 | 0.469993 | ||||||||
\(887\) | 2.57330e7 | 1.09820 | 0.549100 | − | 0.835757i | \(-0.314971\pi\) | ||||
0.549100 | + | 0.835757i | \(0.314971\pi\) | |||||||
\(888\) | −4.82575e6 | −0.205368 | ||||||||
\(889\) | 7.57756e7 | 3.21569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −1.65056e6 | −0.0694574 | ||||||||
\(893\) | −1.55935e7 | −0.654358 | ||||||||
\(894\) | −5.95383e6 | −0.249145 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.30905e7 | −1.37700 | ||||||||
\(897\) | −2.13557e7 | −0.886203 | ||||||||
\(898\) | −9.45205e6 | −0.391143 | ||||||||
\(899\) | −4.30110e7 | −1.77493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.19541e7 | 0.900957 | ||||||||
\(902\) | −4.59145e6 | −0.187903 | ||||||||
\(903\) | 1.73230e7 | 0.706973 | ||||||||
\(904\) | −8.66710e6 | −0.352738 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.67418e6 | −0.148710 | ||||||||
\(907\) | 2.93343e7 | 1.18402 | 0.592008 | − | 0.805932i | \(-0.298335\pi\) | ||||
0.592008 | + | 0.805932i | \(0.298335\pi\) | |||||||
\(908\) | −1.05655e7 | −0.425281 | ||||||||
\(909\) | −1.28863e7 | −0.517273 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.38249e6 | 0.254797 | 0.127399 | − | 0.991852i | \(-0.459337\pi\) | ||||
0.127399 | + | 0.991852i | \(0.459337\pi\) | |||||||
\(912\) | 1.25541e6 | 0.0499802 | ||||||||
\(913\) | 2.10015e6 | 0.0833824 | ||||||||
\(914\) | 2.61930e7 | 1.03710 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.29009e6 | −0.287074 | ||||||||
\(917\) | −4.78775e7 | −1.88022 | ||||||||
\(918\) | −4.63876e6 | −0.181675 | ||||||||
\(919\) | −4.36179e6 | −0.170363 | −0.0851817 | − | 0.996365i | \(-0.527147\pi\) | ||||
−0.0851817 | + | 0.996365i | \(0.527147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.02021e7 | 0.784780 | ||||||||
\(922\) | 1.66431e7 | 0.644772 | ||||||||
\(923\) | 5.26605e7 | 2.03461 | ||||||||
\(924\) | 5.35271e6 | 0.206250 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.21174e6 | 0.353032 | ||||||||
\(927\) | −1.24379e7 | −0.475388 | ||||||||
\(928\) | 2.82172e7 | 1.07558 | ||||||||
\(929\) | 1.47406e7 | 0.560371 | 0.280186 | − | 0.959946i | \(-0.409604\pi\) | ||||
0.280186 | + | 0.959946i | \(0.409604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.84369e7 | −1.07525 | ||||||||
\(932\) | 1.51772e6 | 0.0572337 | ||||||||
\(933\) | 3.40205e6 | 0.127949 | ||||||||
\(934\) | 2.86505e6 | 0.107464 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.38277e7 | −0.515892 | ||||||||
\(937\) | −2.20101e7 | −0.818978 | −0.409489 | − | 0.912315i | \(-0.634293\pi\) | ||||
−0.409489 | + | 0.912315i | \(0.634293\pi\) | |||||||
\(938\) | 3.75809e7 | 1.39463 | ||||||||
\(939\) | −2.03161e7 | −0.751927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.04925e7 | 0.386282 | 0.193141 | − | 0.981171i | \(-0.438132\pi\) | ||||
0.193141 | + | 0.981171i | \(0.438132\pi\) | |||||||
\(942\) | −5.49705e6 | −0.201838 | ||||||||
\(943\) | −2.84732e7 | −1.04270 | ||||||||
\(944\) | −6.33947e6 | −0.231538 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.29665e6 | −0.119769 | ||||||||
\(947\) | −2.19095e7 | −0.793885 | −0.396943 | − | 0.917843i | \(-0.629929\pi\) | ||||
−0.396943 | + | 0.917843i | \(0.629929\pi\) | |||||||
\(948\) | 1.42118e7 | 0.513605 | ||||||||
\(949\) | 5.51760e7 | 1.98877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.70552e7 | 0.970060 | ||||||||
\(952\) | −7.68035e7 | −2.74656 | ||||||||
\(953\) | −2.07187e7 | −0.738974 | −0.369487 | − | 0.929236i | \(-0.620467\pi\) | ||||
−0.369487 | + | 0.929236i | \(0.620467\pi\) | |||||||
\(954\) | 2.79916e6 | 0.0995765 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.61655e7 | −0.572063 | ||||||||
\(957\) | −5.13655e6 | −0.181297 | ||||||||
\(958\) | −5.81912e6 | −0.204854 | ||||||||
\(959\) | −1.37682e7 | −0.483428 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.45228e7 | 1.90445 | ||||||||
\(962\) | −9.92449e6 | −0.345757 | ||||||||
\(963\) | 4.24509e6 | 0.147510 | ||||||||
\(964\) | 1.55021e6 | 0.0537275 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.51237e7 | −0.521454 | ||||||||
\(967\) | 4.84470e7 | 1.66610 | 0.833050 | − | 0.553197i | \(-0.186593\pi\) | ||||
0.833050 | + | 0.553197i | \(0.186593\pi\) | |||||||
\(968\) | −2.50141e6 | −0.0858019 | ||||||||
\(969\) | 1.55071e7 | 0.530543 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.80579e7 | −0.955007 | −0.477503 | − | 0.878630i | \(-0.658458\pi\) | ||||
−0.477503 | + | 0.878630i | \(0.658458\pi\) | |||||||
\(972\) | 1.29812e6 | 0.0440707 | ||||||||
\(973\) | 5.39866e7 | 1.82811 | ||||||||
\(974\) | 8.90864e6 | 0.300894 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.91193e6 | −0.198657 | ||||||||
\(977\) | −1.41314e7 | −0.473640 | −0.236820 | − | 0.971554i | \(-0.576105\pi\) | ||||
−0.236820 | + | 0.971554i | \(0.576105\pi\) | |||||||
\(978\) | −2.81543e6 | −0.0941233 | ||||||||
\(979\) | −5.40468e6 | −0.180224 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.29798e6 | −0.242120 | ||||||||
\(982\) | −2.09364e7 | −0.692826 | ||||||||
\(983\) | −3.18529e7 | −1.05139 | −0.525697 | − | 0.850672i | \(-0.676195\pi\) | ||||
−0.525697 | + | 0.850672i | \(0.676195\pi\) | |||||||
\(984\) | −1.84362e7 | −0.606993 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.00136e7 | 0.983164 | ||||||||
\(987\) | −3.66156e7 | −1.19639 | ||||||||
\(988\) | 1.88242e7 | 0.613513 | ||||||||
\(989\) | −2.04437e7 | −0.664613 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.56789e6 | 0.309480 | 0.154740 | − | 0.987955i | \(-0.450546\pi\) | ||||
0.154740 | + | 0.987955i | \(0.450546\pi\) | |||||||
\(992\) | −5.45516e7 | −1.76006 | ||||||||
\(993\) | 2.60392e6 | 0.0838019 | ||||||||
\(994\) | 3.72932e7 | 1.19719 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.43409e6 | 0.109689 | ||||||||
\(997\) | −954420. | −0.0304090 | −0.0152045 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152045 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(998\) | 8.98382e6 | 0.285519 | ||||||||
\(999\) | 2.28789e6 | 0.0725307 |
(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 | 825.6.a.u.1.7 | yes | 10 | |
5.4 | even | 2 | 825.6.a.t.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.4 | ✓ | 10 | 5.4 | even | 2 | ||
825.6.a.u.1.7 | yes | 10 | 1.1 | even | 1 | trivial |