Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 26355x^{2} - 7203x + 128450070 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-80.8568\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 94.6269 | 0.729910 | 0.364955 | − | 0.931025i | \(-0.381084\pi\) | ||||
0.364955 | + | 0.931025i | \(0.381084\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −613.114 | −1.52778 | −0.763888 | − | 0.645349i | \(-0.776712\pi\) | ||||
−0.763888 | + | 0.645349i | \(0.776712\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −983.389 | −1.61386 | −0.806932 | − | 0.590645i | \(-0.798873\pi\) | ||||
−0.806932 | + | 0.590645i | \(0.798873\pi\) | |||||||
\(14\) | −378.507 | −0.516124 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1418.72 | −1.19063 | −0.595313 | − | 0.803494i | \(-0.702972\pi\) | ||||
−0.595313 | + | 0.803494i | \(0.702972\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 851.642 | 0.421414 | ||||||||
\(22\) | 2452.46 | 1.08030 | ||||||||
\(23\) | 517.954 | 0.204161 | 0.102080 | − | 0.994776i | \(-0.467450\pi\) | ||||
0.102080 | + | 0.994776i | \(0.467450\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 3933.55 | 1.14117 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 1514.03 | 0.364955 | ||||||||
\(29\) | 3308.73 | 0.730577 | 0.365288 | − | 0.930894i | \(-0.380970\pi\) | ||||
0.365288 | + | 0.930894i | \(0.380970\pi\) | |||||||
\(30\) | 900.000 | 0.182574 | ||||||||
\(31\) | 1286.62 | 0.240462 | 0.120231 | − | 0.992746i | \(-0.461637\pi\) | ||||
0.120231 | + | 0.992746i | \(0.461637\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −5518.03 | −0.882062 | ||||||||
\(34\) | 5674.90 | 0.841900 | ||||||||
\(35\) | −2365.67 | −0.326426 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 5560.25 | 0.667713 | 0.333856 | − | 0.942624i | \(-0.391650\pi\) | ||||
0.333856 | + | 0.942624i | \(0.391650\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | −8850.50 | −0.931764 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 8443.04 | 0.784403 | 0.392202 | − | 0.919879i | \(-0.371714\pi\) | ||||
0.392202 | + | 0.919879i | \(0.371714\pi\) | |||||||
\(42\) | −3406.57 | −0.297985 | ||||||||
\(43\) | 23850.1 | 1.96707 | 0.983535 | − | 0.180716i | \(-0.0578416\pi\) | ||||
0.983535 | + | 0.180716i | \(0.0578416\pi\) | |||||||
\(44\) | −9809.83 | −0.763888 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −2071.82 | −0.144363 | ||||||||
\(47\) | −14363.8 | −0.948475 | −0.474238 | − | 0.880397i | \(-0.657276\pi\) | ||||
−0.474238 | + | 0.880397i | \(0.657276\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | −7852.76 | −0.467231 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −12768.5 | −0.687409 | ||||||||
\(52\) | −15734.2 | −0.806932 | ||||||||
\(53\) | −16913.3 | −0.827063 | −0.413531 | − | 0.910490i | \(-0.635705\pi\) | ||||
−0.413531 | + | 0.910490i | \(0.635705\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 15327.9 | 0.683242 | ||||||||
\(56\) | −6056.12 | −0.258062 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | −13234.9 | −0.516596 | ||||||||
\(59\) | 14310.4 | 0.535209 | 0.267604 | − | 0.963529i | \(-0.413768\pi\) | ||||
0.267604 | + | 0.963529i | \(0.413768\pi\) | |||||||
\(60\) | −3600.00 | −0.129099 | ||||||||
\(61\) | 42281.9 | 1.45489 | 0.727445 | − | 0.686166i | \(-0.240708\pi\) | ||||
0.727445 | + | 0.686166i | \(0.240708\pi\) | |||||||
\(62\) | −5146.48 | −0.170032 | ||||||||
\(63\) | 7664.78 | 0.243303 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 24584.7 | 0.721742 | ||||||||
\(66\) | 22072.1 | 0.623712 | ||||||||
\(67\) | 20705.8 | 0.563514 | 0.281757 | − | 0.959486i | \(-0.409083\pi\) | ||||
0.281757 | + | 0.959486i | \(0.409083\pi\) | |||||||
\(68\) | −22699.6 | −0.595313 | ||||||||
\(69\) | 4661.59 | 0.117872 | ||||||||
\(70\) | 9462.69 | 0.230818 | ||||||||
\(71\) | 37.7768 | 0.000889362 0 | 0.000444681 | − | 1.00000i | \(-0.499858\pi\) | ||||
0.000444681 | 1.00000i | \(0.499858\pi\) | ||||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 30975.2 | 0.680310 | 0.340155 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340155 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(74\) | −22241.0 | −0.472144 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | −58017.1 | −1.11514 | ||||||||
\(78\) | 35402.0 | 0.658857 | ||||||||
\(79\) | −64612.5 | −1.16479 | −0.582396 | − | 0.812905i | \(-0.697885\pi\) | ||||
−0.582396 | + | 0.812905i | \(0.697885\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −33772.2 | −0.554657 | ||||||||
\(83\) | 100570. | 1.60241 | 0.801204 | − | 0.598391i | \(-0.204193\pi\) | ||||
0.801204 | + | 0.598391i | \(0.204193\pi\) | |||||||
\(84\) | 13626.3 | 0.210707 | ||||||||
\(85\) | 35468.1 | 0.532464 | ||||||||
\(86\) | −95400.6 | −1.39093 | ||||||||
\(87\) | 29778.5 | 0.421799 | ||||||||
\(88\) | 39239.3 | 0.540150 | ||||||||
\(89\) | 48895.8 | 0.654329 | 0.327165 | − | 0.944967i | \(-0.393907\pi\) | ||||
0.327165 | + | 0.944967i | \(0.393907\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | −93055.0 | −1.17798 | ||||||||
\(92\) | 8287.27 | 0.102080 | ||||||||
\(93\) | 11579.6 | 0.138831 | ||||||||
\(94\) | 57455.4 | 0.670673 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 92291.9 | 0.995943 | 0.497971 | − | 0.867193i | \(-0.334078\pi\) | ||||
0.497971 | + | 0.867193i | \(0.334078\pi\) | |||||||
\(98\) | 31411.0 | 0.330382 | ||||||||
\(99\) | −49662.3 | −0.509259 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −16865.5 | −0.164511 | −0.0822556 | − | 0.996611i | \(-0.526212\pi\) | ||||
−0.0822556 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(102\) | 51074.1 | 0.486071 | ||||||||
\(103\) | 80870.7 | 0.751101 | 0.375550 | − | 0.926802i | \(-0.377454\pi\) | ||||
0.375550 | + | 0.926802i | \(0.377454\pi\) | |||||||
\(104\) | 62936.9 | 0.570587 | ||||||||
\(105\) | −21291.0 | −0.188462 | ||||||||
\(106\) | 67653.2 | 0.584822 | ||||||||
\(107\) | −200516. | −1.69313 | −0.846566 | − | 0.532284i | \(-0.821334\pi\) | ||||
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −115645. | −0.932310 | −0.466155 | − | 0.884703i | \(-0.654361\pi\) | ||||
−0.466155 | + | 0.884703i | \(0.654361\pi\) | |||||||
\(110\) | −61311.4 | −0.483125 | ||||||||
\(111\) | 50042.2 | 0.385504 | ||||||||
\(112\) | 24224.5 | 0.182478 | ||||||||
\(113\) | −24053.7 | −0.177209 | −0.0886046 | − | 0.996067i | \(-0.528241\pi\) | ||||
−0.0886046 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(114\) | 12996.0 | 0.0936586 | ||||||||
\(115\) | −12948.9 | −0.0913034 | ||||||||
\(116\) | 52939.6 | 0.365288 | ||||||||
\(117\) | −79654.5 | −0.537954 | ||||||||
\(118\) | −57241.8 | −0.378450 | ||||||||
\(119\) | −134249. | −0.869050 | ||||||||
\(120\) | 14400.0 | 0.0912871 | ||||||||
\(121\) | 214858. | 1.33410 | ||||||||
\(122\) | −169128. | −1.02876 | ||||||||
\(123\) | 75987.4 | 0.452875 | ||||||||
\(124\) | 20585.9 | 0.120231 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −30659.1 | −0.172041 | ||||||||
\(127\) | 15990.8 | 0.0879756 | 0.0439878 | − | 0.999032i | \(-0.485994\pi\) | ||||
0.0439878 | + | 0.999032i | \(0.485994\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 214651. | 1.13569 | ||||||||
\(130\) | −98338.9 | −0.510348 | ||||||||
\(131\) | −17110.3 | −0.0871121 | −0.0435560 | − | 0.999051i | \(-0.513869\pi\) | ||||
−0.0435560 | + | 0.999051i | \(0.513869\pi\) | |||||||
\(132\) | −88288.5 | −0.441031 | ||||||||
\(133\) | −34160.3 | −0.167453 | ||||||||
\(134\) | −82823.1 | −0.398465 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 90798.3 | 0.420950 | ||||||||
\(137\) | −123786. | −0.563471 | −0.281735 | − | 0.959492i | \(-0.590910\pi\) | ||||
−0.281735 | + | 0.959492i | \(0.590910\pi\) | |||||||
\(138\) | −18646.4 | −0.0833482 | ||||||||
\(139\) | −86142.9 | −0.378166 | −0.189083 | − | 0.981961i | \(-0.560552\pi\) | ||||
−0.189083 | + | 0.981961i | \(0.560552\pi\) | |||||||
\(140\) | −37850.7 | −0.163213 | ||||||||
\(141\) | −129275. | −0.547602 | ||||||||
\(142\) | −151.107 | −0.000628874 0 | ||||||||
\(143\) | 602930. | 2.46562 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −82718.1 | −0.326724 | ||||||||
\(146\) | −123901. | −0.481052 | ||||||||
\(147\) | −70674.8 | −0.269756 | ||||||||
\(148\) | 88964.0 | 0.333856 | ||||||||
\(149\) | −15526.0 | −0.0572919 | −0.0286459 | − | 0.999590i | \(-0.509120\pi\) | ||||
−0.0286459 | + | 0.999590i | \(0.509120\pi\) | |||||||
\(150\) | −22500.0 | −0.0816497 | ||||||||
\(151\) | 2995.97 | 0.0106929 | 0.00534645 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534645 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | −114917. | −0.396876 | ||||||||
\(154\) | 232068. | 0.788523 | ||||||||
\(155\) | −32165.5 | −0.107538 | ||||||||
\(156\) | −141608. | −0.465882 | ||||||||
\(157\) | 365967. | 1.18493 | 0.592466 | − | 0.805596i | \(-0.298155\pi\) | ||||
0.592466 | + | 0.805596i | \(0.298155\pi\) | |||||||
\(158\) | 258450. | 0.823633 | ||||||||
\(159\) | −152220. | −0.477505 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 49012.4 | 0.149019 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −436835. | −1.28780 | −0.643901 | − | 0.765109i | \(-0.722685\pi\) | ||||
−0.643901 | + | 0.765109i | \(0.722685\pi\) | |||||||
\(164\) | 135089. | 0.392202 | ||||||||
\(165\) | 137951. | 0.394470 | ||||||||
\(166\) | −402280. | −1.13307 | ||||||||
\(167\) | 313346. | 0.869428 | 0.434714 | − | 0.900569i | \(-0.356849\pi\) | ||||
0.434714 | + | 0.900569i | \(0.356849\pi\) | |||||||
\(168\) | −54505.1 | −0.148992 | ||||||||
\(169\) | 595760. | 1.60456 | ||||||||
\(170\) | −141872. | −0.376509 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 381602. | 0.983535 | ||||||||
\(173\) | 86867.9 | 0.220670 | 0.110335 | − | 0.993894i | \(-0.464808\pi\) | ||||
0.110335 | + | 0.993894i | \(0.464808\pi\) | |||||||
\(174\) | −119114. | −0.298257 | ||||||||
\(175\) | 59141.8 | 0.145982 | ||||||||
\(176\) | −156957. | −0.381944 | ||||||||
\(177\) | 128794. | 0.309003 | ||||||||
\(178\) | −195583. | −0.462680 | ||||||||
\(179\) | 577947. | 1.34820 | 0.674101 | − | 0.738639i | \(-0.264531\pi\) | ||||
0.674101 | + | 0.738639i | \(0.264531\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | 570827. | 1.29512 | 0.647558 | − | 0.762017i | \(-0.275791\pi\) | ||||
0.647558 | + | 0.762017i | \(0.275791\pi\) | |||||||
\(182\) | 372220. | 0.832954 | ||||||||
\(183\) | 380537. | 0.839981 | ||||||||
\(184\) | −33149.1 | −0.0721817 | ||||||||
\(185\) | −139006. | −0.298610 | ||||||||
\(186\) | −46318.3 | −0.0981681 | ||||||||
\(187\) | 869840. | 1.81901 | ||||||||
\(188\) | −229821. | −0.474238 | ||||||||
\(189\) | 68983.0 | 0.140471 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | 210943. | 0.418390 | 0.209195 | − | 0.977874i | \(-0.432916\pi\) | ||||
0.209195 | + | 0.977874i | \(0.432916\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −418042. | −0.807842 | −0.403921 | − | 0.914794i | \(-0.632353\pi\) | ||||
−0.403921 | + | 0.914794i | \(0.632353\pi\) | |||||||
\(194\) | −369168. | −0.704238 | ||||||||
\(195\) | 221262. | 0.416698 | ||||||||
\(196\) | −125644. | −0.233616 | ||||||||
\(197\) | 921835. | 1.69234 | 0.846170 | − | 0.532913i | \(-0.178903\pi\) | ||||
0.846170 | + | 0.532913i | \(0.178903\pi\) | |||||||
\(198\) | 198649. | 0.360100 | ||||||||
\(199\) | 720466. | 1.28968 | 0.644838 | − | 0.764319i | \(-0.276925\pi\) | ||||
0.644838 | + | 0.764319i | \(0.276925\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 186352. | 0.325345 | ||||||||
\(202\) | 67462.0 | 0.116327 | ||||||||
\(203\) | 313094. | 0.533255 | ||||||||
\(204\) | −204296. | −0.343704 | ||||||||
\(205\) | −211076. | −0.350796 | ||||||||
\(206\) | −323483. | −0.531108 | ||||||||
\(207\) | 41954.3 | 0.0680535 | ||||||||
\(208\) | −251747. | −0.403466 | ||||||||
\(209\) | 221334. | 0.350496 | ||||||||
\(210\) | 85164.2 | 0.133263 | ||||||||
\(211\) | 561945. | 0.868936 | 0.434468 | − | 0.900687i | \(-0.356936\pi\) | ||||
0.434468 | + | 0.900687i | \(0.356936\pi\) | |||||||
\(212\) | −270613. | −0.413531 | ||||||||
\(213\) | 339.991 | 0.000513474 0 | ||||||||
\(214\) | 802066. | 1.19722 | ||||||||
\(215\) | −596254. | −0.879701 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 121749. | 0.175515 | ||||||||
\(218\) | 462580. | 0.659242 | ||||||||
\(219\) | 278777. | 0.392777 | ||||||||
\(220\) | 245246. | 0.341621 | ||||||||
\(221\) | 1.39516e6 | 1.92151 | ||||||||
\(222\) | −200169. | −0.272593 | ||||||||
\(223\) | 121273. | 0.163305 | 0.0816527 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816527 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(224\) | −96897.9 | −0.129031 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 96214.9 | 0.125306 | ||||||||
\(227\) | −678530. | −0.873985 | −0.436993 | − | 0.899465i | \(-0.643956\pi\) | ||||
−0.436993 | + | 0.899465i | \(0.643956\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | 212100. | 0.267271 | 0.133635 | − | 0.991031i | \(-0.457335\pi\) | ||||
0.133635 | + | 0.991031i | \(0.457335\pi\) | |||||||
\(230\) | 51795.4 | 0.0645613 | ||||||||
\(231\) | −522154. | −0.643826 | ||||||||
\(232\) | −211758. | −0.258298 | ||||||||
\(233\) | −719902. | −0.868728 | −0.434364 | − | 0.900738i | \(-0.643027\pi\) | ||||
−0.434364 | + | 0.900738i | \(0.643027\pi\) | |||||||
\(234\) | 318618. | 0.380391 | ||||||||
\(235\) | 359096. | 0.424171 | ||||||||
\(236\) | 228967. | 0.267604 | ||||||||
\(237\) | −581512. | −0.672493 | ||||||||
\(238\) | 536998. | 0.614511 | ||||||||
\(239\) | 239724. | 0.271466 | 0.135733 | − | 0.990745i | \(-0.456661\pi\) | ||||
0.135733 | + | 0.990745i | \(0.456661\pi\) | |||||||
\(240\) | −57600.0 | −0.0645497 | ||||||||
\(241\) | 1.13435e6 | 1.25807 | 0.629036 | − | 0.777376i | \(-0.283450\pi\) | ||||
0.629036 | + | 0.777376i | \(0.283450\pi\) | |||||||
\(242\) | −859433. | −0.943351 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 676511. | 0.727445 | ||||||||
\(245\) | 196319. | 0.208952 | ||||||||
\(246\) | −303950. | −0.320231 | ||||||||
\(247\) | 355003. | 0.370246 | ||||||||
\(248\) | −82343.6 | −0.0850160 | ||||||||
\(249\) | 905130. | 0.925151 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | −1.52013e6 | −1.52299 | −0.761493 | − | 0.648173i | \(-0.775533\pi\) | ||||
−0.761493 | + | 0.648173i | \(0.775533\pi\) | |||||||
\(252\) | 122636. | 0.121652 | ||||||||
\(253\) | −317565. | −0.311912 | ||||||||
\(254\) | −63963.4 | −0.0622081 | ||||||||
\(255\) | 319213. | 0.307418 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 642217. | 0.606526 | 0.303263 | − | 0.952907i | \(-0.401924\pi\) | ||||
0.303263 | + | 0.952907i | \(0.401924\pi\) | |||||||
\(258\) | −858605. | −0.803053 | ||||||||
\(259\) | 526149. | 0.487370 | ||||||||
\(260\) | 393355. | 0.360871 | ||||||||
\(261\) | 268007. | 0.243526 | ||||||||
\(262\) | 68441.0 | 0.0615975 | ||||||||
\(263\) | −229857. | −0.204912 | −0.102456 | − | 0.994738i | \(-0.532670\pi\) | ||||
−0.102456 | + | 0.994738i | \(0.532670\pi\) | |||||||
\(264\) | 353154. | 0.311856 | ||||||||
\(265\) | 422832. | 0.369874 | ||||||||
\(266\) | 136641. | 0.118407 | ||||||||
\(267\) | 440062. | 0.377777 | ||||||||
\(268\) | 331293. | 0.281757 | ||||||||
\(269\) | 783628. | 0.660282 | 0.330141 | − | 0.943932i | \(-0.392904\pi\) | ||||
0.330141 | + | 0.943932i | \(0.392904\pi\) | |||||||
\(270\) | 72900.0 | 0.0608581 | ||||||||
\(271\) | 966852. | 0.799718 | 0.399859 | − | 0.916577i | \(-0.369059\pi\) | ||||
0.399859 | + | 0.916577i | \(0.369059\pi\) | |||||||
\(272\) | −363193. | −0.297657 | ||||||||
\(273\) | −837495. | −0.680104 | ||||||||
\(274\) | 495146. | 0.398434 | ||||||||
\(275\) | −383196. | −0.305555 | ||||||||
\(276\) | 74585.4 | 0.0589361 | ||||||||
\(277\) | 121779. | 0.0953617 | 0.0476808 | − | 0.998863i | \(-0.484817\pi\) | ||||
0.0476808 | + | 0.998863i | \(0.484817\pi\) | |||||||
\(278\) | 344572. | 0.267404 | ||||||||
\(279\) | 104216. | 0.0801539 | ||||||||
\(280\) | 151403. | 0.115409 | ||||||||
\(281\) | −1.47565e6 | −1.11486 | −0.557428 | − | 0.830226i | \(-0.688212\pi\) | ||||
−0.557428 | + | 0.830226i | \(0.688212\pi\) | |||||||
\(282\) | 517098. | 0.387213 | ||||||||
\(283\) | −744205. | −0.552365 | −0.276183 | − | 0.961105i | \(-0.589069\pi\) | ||||
−0.276183 | + | 0.961105i | \(0.589069\pi\) | |||||||
\(284\) | 604.428 | 0.000444681 0 | ||||||||
\(285\) | 81225.0 | 0.0592349 | ||||||||
\(286\) | −2.41172e6 | −1.74346 | ||||||||
\(287\) | 798939. | 0.572544 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 592921. | 0.417592 | ||||||||
\(290\) | 330873. | 0.231029 | ||||||||
\(291\) | 830627. | 0.575008 | ||||||||
\(292\) | 495603. | 0.340155 | ||||||||
\(293\) | 122599. | 0.0834289 | 0.0417145 | − | 0.999130i | \(-0.486718\pi\) | ||||
0.0417145 | + | 0.999130i | \(0.486718\pi\) | |||||||
\(294\) | 282699. | 0.190746 | ||||||||
\(295\) | −357761. | −0.239353 | ||||||||
\(296\) | −355856. | −0.236072 | ||||||||
\(297\) | −446960. | −0.294021 | ||||||||
\(298\) | 62103.9 | 0.0405115 | ||||||||
\(299\) | −509351. | −0.329487 | ||||||||
\(300\) | 90000.0 | 0.0577350 | ||||||||
\(301\) | 2.25686e6 | 1.43578 | ||||||||
\(302\) | −11983.9 | −0.00756102 | ||||||||
\(303\) | −151789. | −0.0949806 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | −1.05705e6 | −0.650646 | ||||||||
\(306\) | 459667. | 0.280633 | ||||||||
\(307\) | −2.36136e6 | −1.42994 | −0.714968 | − | 0.699157i | \(-0.753559\pi\) | ||||
−0.714968 | + | 0.699157i | \(0.753559\pi\) | |||||||
\(308\) | −928273. | −0.557570 | ||||||||
\(309\) | 727836. | 0.433648 | ||||||||
\(310\) | 128662. | 0.0760407 | ||||||||
\(311\) | −2.31762e6 | −1.35875 | −0.679377 | − | 0.733789i | \(-0.737750\pi\) | ||||
−0.679377 | + | 0.733789i | \(0.737750\pi\) | |||||||
\(312\) | 566432. | 0.329428 | ||||||||
\(313\) | −558773. | −0.322385 | −0.161192 | − | 0.986923i | \(-0.551534\pi\) | ||||
−0.161192 | + | 0.986923i | \(0.551534\pi\) | |||||||
\(314\) | −1.46387e6 | −0.837873 | ||||||||
\(315\) | −191619. | −0.108809 | ||||||||
\(316\) | −1.03380e6 | −0.582396 | ||||||||
\(317\) | −1.36549e6 | −0.763201 | −0.381601 | − | 0.924327i | \(-0.624627\pi\) | ||||
−0.381601 | + | 0.924327i | \(0.624627\pi\) | |||||||
\(318\) | 608879. | 0.337647 | ||||||||
\(319\) | −2.02863e6 | −1.11616 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −1.80465e6 | −0.977530 | ||||||||
\(322\) | −196050. | −0.105372 | ||||||||
\(323\) | 512159. | 0.273148 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −614618. | −0.322773 | ||||||||
\(326\) | 1.74734e6 | 0.910613 | ||||||||
\(327\) | −1.04080e6 | −0.538269 | ||||||||
\(328\) | −540355. | −0.277328 | ||||||||
\(329\) | −1.35921e6 | −0.692302 | ||||||||
\(330\) | −551803. | −0.278933 | ||||||||
\(331\) | −2.09707e6 | −1.05207 | −0.526033 | − | 0.850464i | \(-0.676321\pi\) | ||||
−0.526033 | + | 0.850464i | \(0.676321\pi\) | |||||||
\(332\) | 1.60912e6 | 0.801204 | ||||||||
\(333\) | 450380. | 0.222571 | ||||||||
\(334\) | −1.25339e6 | −0.614778 | ||||||||
\(335\) | −517645. | −0.252011 | ||||||||
\(336\) | 218020. | 0.105353 | ||||||||
\(337\) | 1.99343e6 | 0.956152 | 0.478076 | − | 0.878319i | \(-0.341334\pi\) | ||||
0.478076 | + | 0.878319i | \(0.341334\pi\) | |||||||
\(338\) | −2.38304e6 | −1.13459 | ||||||||
\(339\) | −216484. | −0.102312 | ||||||||
\(340\) | 567490. | 0.266232 | ||||||||
\(341\) | −788845. | −0.367372 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | −2.33348e6 | −1.07095 | ||||||||
\(344\) | −1.52641e6 | −0.695464 | ||||||||
\(345\) | −116540. | −0.0527140 | ||||||||
\(346\) | −347472. | −0.156038 | ||||||||
\(347\) | 2.46044e6 | 1.09695 | 0.548477 | − | 0.836166i | \(-0.315208\pi\) | ||||
0.548477 | + | 0.836166i | \(0.315208\pi\) | |||||||
\(348\) | 476456. | 0.210899 | ||||||||
\(349\) | 4.02725e6 | 1.76989 | 0.884943 | − | 0.465699i | \(-0.154197\pi\) | ||||
0.884943 | + | 0.465699i | \(0.154197\pi\) | |||||||
\(350\) | −236567. | −0.103225 | ||||||||
\(351\) | −716890. | −0.310588 | ||||||||
\(352\) | 627829. | 0.270075 | ||||||||
\(353\) | −624915. | −0.266922 | −0.133461 | − | 0.991054i | \(-0.542609\pi\) | ||||
−0.133461 | + | 0.991054i | \(0.542609\pi\) | |||||||
\(354\) | −515176. | −0.218498 | ||||||||
\(355\) | −944.419 | −0.000397735 0 | ||||||||
\(356\) | 782332. | 0.327165 | ||||||||
\(357\) | −1.20824e6 | −0.501746 | ||||||||
\(358\) | −2.31179e6 | −0.953323 | ||||||||
\(359\) | 3.80986e6 | 1.56017 | 0.780087 | − | 0.625671i | \(-0.215175\pi\) | ||||
0.780087 | + | 0.625671i | \(0.215175\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −2.28331e6 | −0.915785 | ||||||||
\(363\) | 1.93372e6 | 0.770243 | ||||||||
\(364\) | −1.48888e6 | −0.588988 | ||||||||
\(365\) | −774380. | −0.304244 | ||||||||
\(366\) | −1.52215e6 | −0.593956 | ||||||||
\(367\) | 1.24404e6 | 0.482137 | 0.241068 | − | 0.970508i | \(-0.422502\pi\) | ||||
0.241068 | + | 0.970508i | \(0.422502\pi\) | |||||||
\(368\) | 132596. | 0.0510402 | ||||||||
\(369\) | 683886. | 0.261468 | ||||||||
\(370\) | 556025. | 0.211149 | ||||||||
\(371\) | −1.60045e6 | −0.603682 | ||||||||
\(372\) | 185273. | 0.0694153 | ||||||||
\(373\) | 3.30542e6 | 1.23014 | 0.615069 | − | 0.788473i | \(-0.289128\pi\) | ||||
0.615069 | + | 0.788473i | \(0.289128\pi\) | |||||||
\(374\) | −3.47936e6 | −1.28624 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | 919286. | 0.335337 | ||||||||
\(377\) | −3.25376e6 | −1.17905 | ||||||||
\(378\) | −275932. | −0.0993282 | ||||||||
\(379\) | 166417. | 0.0595114 | 0.0297557 | − | 0.999557i | \(-0.490527\pi\) | ||||
0.0297557 | + | 0.999557i | \(0.490527\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | 143918. | 0.0507927 | ||||||||
\(382\) | −843770. | −0.295846 | ||||||||
\(383\) | −3.24313e6 | −1.12971 | −0.564855 | − | 0.825190i | \(-0.691068\pi\) | ||||
−0.564855 | + | 0.825190i | \(0.691068\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 1.45043e6 | 0.498705 | ||||||||
\(386\) | 1.67217e6 | 0.571231 | ||||||||
\(387\) | 1.93186e6 | 0.655690 | ||||||||
\(388\) | 1.47667e6 | 0.497971 | ||||||||
\(389\) | 2.36343e6 | 0.791898 | 0.395949 | − | 0.918272i | \(-0.370416\pi\) | ||||
0.395949 | + | 0.918272i | \(0.370416\pi\) | |||||||
\(390\) | −885050. | −0.294650 | ||||||||
\(391\) | −734834. | −0.243079 | ||||||||
\(392\) | 502576. | 0.165191 | ||||||||
\(393\) | −153992. | −0.0502942 | ||||||||
\(394\) | −3.68734e6 | −1.19667 | ||||||||
\(395\) | 1.61531e6 | 0.520911 | ||||||||
\(396\) | −794596. | −0.254629 | ||||||||
\(397\) | −4.68658e6 | −1.49238 | −0.746190 | − | 0.665733i | \(-0.768119\pi\) | ||||
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(398\) | −2.88186e6 | −0.911939 | ||||||||
\(399\) | −307443. | −0.0966789 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −1.51865e6 | −0.471626 | −0.235813 | − | 0.971799i | \(-0.575775\pi\) | ||||
−0.235813 | + | 0.971799i | \(0.575775\pi\) | |||||||
\(402\) | −745408. | −0.230054 | ||||||||
\(403\) | −1.26525e6 | −0.388072 | ||||||||
\(404\) | −269848. | −0.0822556 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −1.25238e6 | −0.377068 | ||||||||
\(407\) | −3.40907e6 | −1.02012 | ||||||||
\(408\) | 817185. | 0.243036 | ||||||||
\(409\) | 5.38381e6 | 1.59141 | 0.795704 | − | 0.605686i | \(-0.207101\pi\) | ||||
0.795704 | + | 0.605686i | \(0.207101\pi\) | |||||||
\(410\) | 844304. | 0.248050 | ||||||||
\(411\) | −1.11408e6 | −0.325320 | ||||||||
\(412\) | 1.29393e6 | 0.375550 | ||||||||
\(413\) | 1.35415e6 | 0.390654 | ||||||||
\(414\) | −167817. | −0.0481211 | ||||||||
\(415\) | −2.51425e6 | −0.716619 | ||||||||
\(416\) | 1.00699e6 | 0.285293 | ||||||||
\(417\) | −775287. | −0.218334 | ||||||||
\(418\) | −885337. | −0.247838 | ||||||||
\(419\) | −3.99972e6 | −1.11300 | −0.556499 | − | 0.830849i | \(-0.687856\pi\) | ||||
−0.556499 | + | 0.830849i | \(0.687856\pi\) | |||||||
\(420\) | −340657. | −0.0942310 | ||||||||
\(421\) | 4.80526e6 | 1.32133 | 0.660666 | − | 0.750680i | \(-0.270274\pi\) | ||||
0.660666 | + | 0.750680i | \(0.270274\pi\) | |||||||
\(422\) | −2.24778e6 | −0.614431 | ||||||||
\(423\) | −1.16347e6 | −0.316158 | ||||||||
\(424\) | 1.08245e6 | 0.292411 | ||||||||
\(425\) | −886702. | −0.238125 | ||||||||
\(426\) | −1359.96 | −0.000363081 0 | ||||||||
\(427\) | 4.00100e6 | 1.06194 | ||||||||
\(428\) | −3.20826e6 | −0.846566 | ||||||||
\(429\) | 5.42637e6 | 1.42353 | ||||||||
\(430\) | 2.38501e6 | 0.622042 | ||||||||
\(431\) | −2.77677e6 | −0.720023 | −0.360012 | − | 0.932948i | \(-0.617227\pi\) | ||||
−0.360012 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −1.83502e6 | −0.470349 | −0.235174 | − | 0.971953i | \(-0.575566\pi\) | ||||
−0.235174 | + | 0.971953i | \(0.575566\pi\) | |||||||
\(434\) | −486995. | −0.124108 | ||||||||
\(435\) | −744463. | −0.188634 | ||||||||
\(436\) | −1.85032e6 | −0.466155 | ||||||||
\(437\) | −186982. | −0.0468377 | ||||||||
\(438\) | −1.11511e6 | −0.277735 | ||||||||
\(439\) | −1.23249e6 | −0.305227 | −0.152614 | − | 0.988286i | \(-0.548769\pi\) | ||||
−0.152614 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(440\) | −980983. | −0.241563 | ||||||||
\(441\) | −636073. | −0.155744 | ||||||||
\(442\) | −5.58063e6 | −1.35871 | ||||||||
\(443\) | −1.44347e6 | −0.349461 | −0.174730 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174730 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(444\) | 800676. | 0.192752 | ||||||||
\(445\) | −1.22239e6 | −0.292625 | ||||||||
\(446\) | −485090. | −0.115474 | ||||||||
\(447\) | −139734. | −0.0330775 | ||||||||
\(448\) | 387592. | 0.0912388 | ||||||||
\(449\) | 6.78670e6 | 1.58870 | 0.794352 | − | 0.607458i | \(-0.207811\pi\) | ||||
0.794352 | + | 0.607458i | \(0.207811\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | −5.17655e6 | −1.19839 | ||||||||
\(452\) | −384860. | −0.0886046 | ||||||||
\(453\) | 26963.8 | 0.00617355 | ||||||||
\(454\) | 2.71412e6 | 0.618001 | ||||||||
\(455\) | 2.32637e6 | 0.526806 | ||||||||
\(456\) | 207936. | 0.0468293 | ||||||||
\(457\) | 5.70240e6 | 1.27723 | 0.638613 | − | 0.769528i | \(-0.279509\pi\) | ||||
0.638613 | + | 0.769528i | \(0.279509\pi\) | |||||||
\(458\) | −848399. | −0.188989 | ||||||||
\(459\) | −1.03425e6 | −0.229136 | ||||||||
\(460\) | −207182. | −0.0456517 | ||||||||
\(461\) | −3.10351e6 | −0.680143 | −0.340072 | − | 0.940400i | \(-0.610451\pi\) | ||||
−0.340072 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(462\) | 2.08862e6 | 0.455254 | ||||||||
\(463\) | −2.39485e6 | −0.519189 | −0.259594 | − | 0.965718i | \(-0.583589\pi\) | ||||
−0.259594 | + | 0.965718i | \(0.583589\pi\) | |||||||
\(464\) | 847034. | 0.182644 | ||||||||
\(465\) | −289489. | −0.0620869 | ||||||||
\(466\) | 2.87961e6 | 0.614283 | ||||||||
\(467\) | 7.82454e6 | 1.66022 | 0.830112 | − | 0.557597i | \(-0.188276\pi\) | ||||
0.830112 | + | 0.557597i | \(0.188276\pi\) | |||||||
\(468\) | −1.27447e6 | −0.268977 | ||||||||
\(469\) | 1.95932e6 | 0.411315 | ||||||||
\(470\) | −1.43638e6 | −0.299934 | ||||||||
\(471\) | 3.29371e6 | 0.684120 | ||||||||
\(472\) | −915868. | −0.189225 | ||||||||
\(473\) | −1.46229e7 | −3.00524 | ||||||||
\(474\) | 2.32605e6 | 0.475524 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −2.14799e6 | −0.434525 | ||||||||
\(477\) | −1.36998e6 | −0.275688 | ||||||||
\(478\) | −958894. | −0.191956 | ||||||||
\(479\) | 317612. | 0.0632496 | 0.0316248 | − | 0.999500i | \(-0.489932\pi\) | ||||
0.0316248 | + | 0.999500i | \(0.489932\pi\) | |||||||
\(480\) | 230400. | 0.0456435 | ||||||||
\(481\) | −5.46788e6 | −1.07760 | ||||||||
\(482\) | −4.53741e6 | −0.889592 | ||||||||
\(483\) | 441112. | 0.0860361 | ||||||||
\(484\) | 3.43773e6 | 0.667050 | ||||||||
\(485\) | −2.30730e6 | −0.445399 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 2.12267e6 | 0.405565 | 0.202783 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202783 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(488\) | −2.70604e6 | −0.514381 | ||||||||
\(489\) | −3.93152e6 | −0.743513 | ||||||||
\(490\) | −785276. | −0.147752 | ||||||||
\(491\) | 7.61911e6 | 1.42627 | 0.713133 | − | 0.701029i | \(-0.247276\pi\) | ||||
0.713133 | + | 0.701029i | \(0.247276\pi\) | |||||||
\(492\) | 1.21580e6 | 0.226438 | ||||||||
\(493\) | −4.69417e6 | −0.869844 | ||||||||
\(494\) | −1.42001e6 | −0.261803 | ||||||||
\(495\) | 1.24156e6 | 0.227747 | ||||||||
\(496\) | 329375. | 0.0601154 | ||||||||
\(497\) | 3574.70 | 0.000649154 0 | ||||||||
\(498\) | −3.62052e6 | −0.654180 | ||||||||
\(499\) | −1.11962e6 | −0.201289 | −0.100644 | − | 0.994922i | \(-0.532090\pi\) | ||||
−0.100644 | + | 0.994922i | \(0.532090\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | 2.82012e6 | 0.501964 | ||||||||
\(502\) | 6.08051e6 | 1.07691 | ||||||||
\(503\) | −9.34148e6 | −1.64625 | −0.823125 | − | 0.567860i | \(-0.807771\pi\) | ||||
−0.823125 | + | 0.567860i | \(0.807771\pi\) | |||||||
\(504\) | −490546. | −0.0860207 | ||||||||
\(505\) | 421637. | 0.0735717 | ||||||||
\(506\) | 1.27026e6 | 0.220555 | ||||||||
\(507\) | 5.36184e6 | 0.926390 | ||||||||
\(508\) | 255853. | 0.0439878 | ||||||||
\(509\) | 3.60261e6 | 0.616343 | 0.308172 | − | 0.951331i | \(-0.400283\pi\) | ||||
0.308172 | + | 0.951331i | \(0.400283\pi\) | |||||||
\(510\) | −1.27685e6 | −0.217378 | ||||||||
\(511\) | 2.93109e6 | 0.496565 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | −2.56887e6 | −0.428878 | ||||||||
\(515\) | −2.02177e6 | −0.335902 | ||||||||
\(516\) | 3.43442e6 | 0.567844 | ||||||||
\(517\) | 8.80668e6 | 1.44906 | ||||||||
\(518\) | −2.10459e6 | −0.344623 | ||||||||
\(519\) | 781811. | 0.127404 | ||||||||
\(520\) | −1.57342e6 | −0.255174 | ||||||||
\(521\) | −7.78592e6 | −1.25665 | −0.628327 | − | 0.777950i | \(-0.716260\pi\) | ||||
−0.628327 | + | 0.777950i | \(0.716260\pi\) | |||||||
\(522\) | −1.07203e6 | −0.172199 | ||||||||
\(523\) | 1.13511e7 | 1.81461 | 0.907304 | − | 0.420475i | \(-0.138137\pi\) | ||||
0.907304 | + | 0.420475i | \(0.138137\pi\) | |||||||
\(524\) | −273764. | −0.0435560 | ||||||||
\(525\) | 532276. | 0.0842828 | ||||||||
\(526\) | 919428. | 0.144895 | ||||||||
\(527\) | −1.82536e6 | −0.286300 | ||||||||
\(528\) | −1.41262e6 | −0.220516 | ||||||||
\(529\) | −6.16807e6 | −0.958318 | ||||||||
\(530\) | −1.69133e6 | −0.261540 | ||||||||
\(531\) | 1.15915e6 | 0.178403 | ||||||||
\(532\) | −546565. | −0.0837264 | ||||||||
\(533\) | −8.30279e6 | −1.26592 | ||||||||
\(534\) | −1.76025e6 | −0.267129 | ||||||||
\(535\) | 5.01291e6 | 0.757191 | ||||||||
\(536\) | −1.32517e6 | −0.199232 | ||||||||
\(537\) | 5.20152e6 | 0.778385 | ||||||||
\(538\) | −3.13451e6 | −0.466890 | ||||||||
\(539\) | 4.81464e6 | 0.713825 | ||||||||
\(540\) | −291600. | −0.0430331 | ||||||||
\(541\) | 6.97868e6 | 1.02513 | 0.512566 | − | 0.858648i | \(-0.328695\pi\) | ||||
0.512566 | + | 0.858648i | \(0.328695\pi\) | |||||||
\(542\) | −3.86741e6 | −0.565486 | ||||||||
\(543\) | 5.13745e6 | 0.747735 | ||||||||
\(544\) | 1.45277e6 | 0.210475 | ||||||||
\(545\) | 2.89112e6 | 0.416942 | ||||||||
\(546\) | 3.34998e6 | 0.480906 | ||||||||
\(547\) | −6.40187e6 | −0.914826 | −0.457413 | − | 0.889254i | \(-0.651224\pi\) | ||||
−0.457413 | + | 0.889254i | \(0.651224\pi\) | |||||||
\(548\) | −1.98058e6 | −0.281735 | ||||||||
\(549\) | 3.42483e6 | 0.484963 | ||||||||
\(550\) | 1.53279e6 | 0.216060 | ||||||||
\(551\) | −1.19445e6 | −0.167606 | ||||||||
\(552\) | −298342. | −0.0416741 | ||||||||
\(553\) | −6.11407e6 | −0.850194 | ||||||||
\(554\) | −487117. | −0.0674309 | ||||||||
\(555\) | −1.25106e6 | −0.172403 | ||||||||
\(556\) | −1.37829e6 | −0.189083 | ||||||||
\(557\) | −1.37919e7 | −1.88358 | −0.941791 | − | 0.336199i | \(-0.890859\pi\) | ||||
−0.941791 | + | 0.336199i | \(0.890859\pi\) | |||||||
\(558\) | −416865. | −0.0566774 | ||||||||
\(559\) | −2.34540e7 | −3.17458 | ||||||||
\(560\) | −605612. | −0.0816064 | ||||||||
\(561\) | 7.82856e6 | 1.05021 | ||||||||
\(562\) | 5.90261e6 | 0.788322 | ||||||||
\(563\) | 1.05556e6 | 0.140350 | 0.0701749 | − | 0.997535i | \(-0.477644\pi\) | ||||
0.0701749 | + | 0.997535i | \(0.477644\pi\) | |||||||
\(564\) | −2.06839e6 | −0.273801 | ||||||||
\(565\) | 601343. | 0.0792503 | ||||||||
\(566\) | 2.97682e6 | 0.390581 | ||||||||
\(567\) | 620847. | 0.0811011 | ||||||||
\(568\) | −2417.71 | −0.000314437 0 | ||||||||
\(569\) | −1.24916e6 | −0.161747 | −0.0808736 | − | 0.996724i | \(-0.525771\pi\) | ||||
−0.0808736 | + | 0.996724i | \(0.525771\pi\) | |||||||
\(570\) | −324900. | −0.0418854 | ||||||||
\(571\) | 1.16283e7 | 1.49255 | 0.746273 | − | 0.665640i | \(-0.231841\pi\) | ||||
0.746273 | + | 0.665640i | \(0.231841\pi\) | |||||||
\(572\) | 9.64687e6 | 1.23281 | ||||||||
\(573\) | 1.89848e6 | 0.241557 | ||||||||
\(574\) | −3.19575e6 | −0.404850 | ||||||||
\(575\) | 323722. | 0.0408321 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −6.27747e6 | −0.784956 | −0.392478 | − | 0.919761i | \(-0.628382\pi\) | ||||
−0.392478 | + | 0.919761i | \(0.628382\pi\) | |||||||
\(578\) | −2.37168e6 | −0.295282 | ||||||||
\(579\) | −3.76238e6 | −0.466408 | ||||||||
\(580\) | −1.32349e6 | −0.163362 | ||||||||
\(581\) | 9.51662e6 | 1.16961 | ||||||||
\(582\) | −3.32251e6 | −0.406592 | ||||||||
\(583\) | 1.03698e7 | 1.26357 | ||||||||
\(584\) | −1.98241e6 | −0.240526 | ||||||||
\(585\) | 1.99136e6 | 0.240581 | ||||||||
\(586\) | −490395. | −0.0589932 | ||||||||
\(587\) | 7.88932e6 | 0.945027 | 0.472513 | − | 0.881323i | \(-0.343347\pi\) | ||||
0.472513 | + | 0.881323i | \(0.343347\pi\) | |||||||
\(588\) | −1.13080e6 | −0.134878 | ||||||||
\(589\) | −464470. | −0.0551657 | ||||||||
\(590\) | 1.43104e6 | 0.169248 | ||||||||
\(591\) | 8.29651e6 | 0.977073 | ||||||||
\(592\) | 1.42342e6 | 0.166928 | ||||||||
\(593\) | 8.29668e6 | 0.968874 | 0.484437 | − | 0.874826i | \(-0.339024\pi\) | ||||
0.484437 | + | 0.874826i | \(0.339024\pi\) | |||||||
\(594\) | 1.78784e6 | 0.207904 | ||||||||
\(595\) | 3.35623e6 | 0.388651 | ||||||||
\(596\) | −248415. | −0.0286459 | ||||||||
\(597\) | 6.48419e6 | 0.744595 | ||||||||
\(598\) | 2.03740e6 | 0.232983 | ||||||||
\(599\) | 1.16906e7 | 1.33128 | 0.665638 | − | 0.746274i | \(-0.268159\pi\) | ||||
0.665638 | + | 0.746274i | \(0.268159\pi\) | |||||||
\(600\) | −360000. | −0.0408248 | ||||||||
\(601\) | −8.58241e6 | −0.969221 | −0.484611 | − | 0.874730i | \(-0.661039\pi\) | ||||
−0.484611 | + | 0.874730i | \(0.661039\pi\) | |||||||
\(602\) | −9.02746e6 | −1.01525 | ||||||||
\(603\) | 1.67717e6 | 0.187838 | ||||||||
\(604\) | 47935.6 | 0.00534645 | ||||||||
\(605\) | −5.37146e6 | −0.596628 | ||||||||
\(606\) | 607158. | 0.0671615 | ||||||||
\(607\) | −5.59550e6 | −0.616406 | −0.308203 | − | 0.951321i | \(-0.599728\pi\) | ||||
−0.308203 | + | 0.951321i | \(0.599728\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | 2.81785e6 | 0.307875 | ||||||||
\(610\) | 4.22819e6 | 0.460076 | ||||||||
\(611\) | 1.41252e7 | 1.53071 | ||||||||
\(612\) | −1.83867e6 | −0.198438 | ||||||||
\(613\) | −1.22426e7 | −1.31589 | −0.657947 | − | 0.753064i | \(-0.728575\pi\) | ||||
−0.657947 | + | 0.753064i | \(0.728575\pi\) | |||||||
\(614\) | 9.44545e6 | 1.01112 | ||||||||
\(615\) | −1.89968e6 | −0.202532 | ||||||||
\(616\) | 3.71309e6 | 0.394261 | ||||||||
\(617\) | 6.16362e6 | 0.651813 | 0.325907 | − | 0.945402i | \(-0.394331\pi\) | ||||
0.325907 | + | 0.945402i | \(0.394331\pi\) | |||||||
\(618\) | −2.91135e6 | −0.306636 | ||||||||
\(619\) | 1.03768e6 | 0.108852 | 0.0544260 | − | 0.998518i | \(-0.482667\pi\) | ||||
0.0544260 | + | 0.998518i | \(0.482667\pi\) | |||||||
\(620\) | −514648. | −0.0537689 | ||||||||
\(621\) | 377589. | 0.0392907 | ||||||||
\(622\) | 9.27047e6 | 0.960784 | ||||||||
\(623\) | 4.62685e6 | 0.477601 | ||||||||
\(624\) | −2.26573e6 | −0.232941 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.23509e6 | 0.227961 | ||||||||
\(627\) | 1.99201e6 | 0.202359 | ||||||||
\(628\) | 5.85548e6 | 0.592466 | ||||||||
\(629\) | −7.88846e6 | −0.794997 | ||||||||
\(630\) | 766478. | 0.0769393 | ||||||||
\(631\) | 1.02819e7 | 1.02802 | 0.514008 | − | 0.857785i | \(-0.328160\pi\) | ||||
0.514008 | + | 0.857785i | \(0.328160\pi\) | |||||||
\(632\) | 4.13520e6 | 0.411816 | ||||||||
\(633\) | 5.05751e6 | 0.501680 | ||||||||
\(634\) | 5.46194e6 | 0.539665 | ||||||||
\(635\) | −399771. | −0.0393439 | ||||||||
\(636\) | −2.43551e6 | −0.238753 | ||||||||
\(637\) | 7.72231e6 | 0.754048 | ||||||||
\(638\) | 8.11451e6 | 0.789243 | ||||||||
\(639\) | 3059.92 | 0.000296454 0 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | 4.63984e6 | 0.446023 | 0.223012 | − | 0.974816i | \(-0.428411\pi\) | ||||
0.223012 | + | 0.974816i | \(0.428411\pi\) | |||||||
\(642\) | 7.21859e6 | 0.691218 | ||||||||
\(643\) | −1.41813e7 | −1.35266 | −0.676332 | − | 0.736597i | \(-0.736431\pi\) | ||||
−0.676332 | + | 0.736597i | \(0.736431\pi\) | |||||||
\(644\) | 784198. | 0.0745094 | ||||||||
\(645\) | −5.36628e6 | −0.507895 | ||||||||
\(646\) | −2.04864e6 | −0.193145 | ||||||||
\(647\) | −7.60555e6 | −0.714282 | −0.357141 | − | 0.934050i | \(-0.616248\pi\) | ||||
−0.357141 | + | 0.934050i | \(0.616248\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −8.77394e6 | −0.817679 | ||||||||
\(650\) | 2.45847e6 | 0.228235 | ||||||||
\(651\) | 1.09574e6 | 0.101334 | ||||||||
\(652\) | −6.98937e6 | −0.643901 | ||||||||
\(653\) | −1.93820e7 | −1.77875 | −0.889376 | − | 0.457177i | \(-0.848861\pi\) | ||||
−0.889376 | + | 0.457177i | \(0.848861\pi\) | |||||||
\(654\) | 4.16322e6 | 0.380614 | ||||||||
\(655\) | 427756. | 0.0389577 | ||||||||
\(656\) | 2.16142e6 | 0.196101 | ||||||||
\(657\) | 2.50899e6 | 0.226770 | ||||||||
\(658\) | 5.43682e6 | 0.489531 | ||||||||
\(659\) | −1.52426e6 | −0.136725 | −0.0683623 | − | 0.997661i | \(-0.521777\pi\) | ||||
−0.0683623 | + | 0.997661i | \(0.521777\pi\) | |||||||
\(660\) | 2.20721e6 | 0.197235 | ||||||||
\(661\) | 4.95206e6 | 0.440841 | 0.220421 | − | 0.975405i | \(-0.429257\pi\) | ||||
0.220421 | + | 0.975405i | \(0.429257\pi\) | |||||||
\(662\) | 8.38828e6 | 0.743923 | ||||||||
\(663\) | 1.25564e7 | 1.10938 | ||||||||
\(664\) | −6.43648e6 | −0.566537 | ||||||||
\(665\) | 854007. | 0.0748872 | ||||||||
\(666\) | −1.80152e6 | −0.157381 | ||||||||
\(667\) | 1.71377e6 | 0.149155 | ||||||||
\(668\) | 5.01354e6 | 0.434714 | ||||||||
\(669\) | 1.09145e6 | 0.0942844 | ||||||||
\(670\) | 2.07058e6 | 0.178199 | ||||||||
\(671\) | −2.59236e7 | −2.22275 | ||||||||
\(672\) | −872081. | −0.0744961 | ||||||||
\(673\) | −1.19068e7 | −1.01335 | −0.506674 | − | 0.862138i | \(-0.669125\pi\) | ||||
−0.506674 | + | 0.862138i | \(0.669125\pi\) | |||||||
\(674\) | −7.97373e6 | −0.676101 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | 9.53216e6 | 0.802278 | ||||||||
\(677\) | −1.09393e7 | −0.917316 | −0.458658 | − | 0.888613i | \(-0.651670\pi\) | ||||
−0.458658 | + | 0.888613i | \(0.651670\pi\) | |||||||
\(678\) | 865934. | 0.0723453 | ||||||||
\(679\) | 8.73330e6 | 0.726949 | ||||||||
\(680\) | −2.26996e6 | −0.188255 | ||||||||
\(681\) | −6.10677e6 | −0.504596 | ||||||||
\(682\) | 3.15538e6 | 0.259771 | ||||||||
\(683\) | 2.25582e7 | 1.85035 | 0.925173 | − | 0.379546i | \(-0.123920\pi\) | ||||
0.925173 | + | 0.379546i | \(0.123920\pi\) | |||||||
\(684\) | −467856. | −0.0382360 | ||||||||
\(685\) | 3.09466e6 | 0.251992 | ||||||||
\(686\) | 9.33390e6 | 0.757274 | ||||||||
\(687\) | 1.90890e6 | 0.154309 | ||||||||
\(688\) | 6.10564e6 | 0.491768 | ||||||||
\(689\) | 1.66323e7 | 1.33477 | ||||||||
\(690\) | 466159. | 0.0372745 | ||||||||
\(691\) | 1.92705e7 | 1.53531 | 0.767657 | − | 0.640861i | \(-0.221423\pi\) | ||||
0.767657 | + | 0.640861i | \(0.221423\pi\) | |||||||
\(692\) | 1.38989e6 | 0.110335 | ||||||||
\(693\) | −4.69938e6 | −0.371713 | ||||||||
\(694\) | −9.84175e6 | −0.775664 | ||||||||
\(695\) | 2.15357e6 | 0.169121 | ||||||||
\(696\) | −1.90583e6 | −0.149128 | ||||||||
\(697\) | −1.19783e7 | −0.933931 | ||||||||
\(698\) | −1.61090e7 | −1.25150 | ||||||||
\(699\) | −6.47912e6 | −0.501560 | ||||||||
\(700\) | 946269. | 0.0729910 | ||||||||
\(701\) | 3.93645e6 | 0.302559 | 0.151280 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151280 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(702\) | 2.86756e6 | 0.219619 | ||||||||
\(703\) | −2.00725e6 | −0.153184 | ||||||||
\(704\) | −2.51132e6 | −0.190972 | ||||||||
\(705\) | 3.23186e6 | 0.244895 | ||||||||
\(706\) | 2.49966e6 | 0.188742 | ||||||||
\(707\) | −1.59593e6 | −0.120078 | ||||||||
\(708\) | 2.06070e6 | 0.154501 | ||||||||
\(709\) | 1.86732e7 | 1.39509 | 0.697546 | − | 0.716540i | \(-0.254275\pi\) | ||||
0.697546 | + | 0.716540i | \(0.254275\pi\) | |||||||
\(710\) | 3777.68 | 0.000281241 0 | ||||||||
\(711\) | −5.23361e6 | −0.388264 | ||||||||
\(712\) | −3.12933e6 | −0.231340 | ||||||||
\(713\) | 666410. | 0.0490928 | ||||||||
\(714\) | 4.83298e6 | 0.354788 | ||||||||
\(715\) | −1.50732e7 | −1.10266 | ||||||||
\(716\) | 9.24715e6 | 0.674101 | ||||||||
\(717\) | 2.15751e6 | 0.156731 | ||||||||
\(718\) | −1.52395e7 | −1.10321 | ||||||||
\(719\) | −1.00226e7 | −0.723034 | −0.361517 | − | 0.932366i | \(-0.617741\pi\) | ||||
−0.361517 | + | 0.932366i | \(0.617741\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | 7.65254e6 | 0.548236 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | 1.02092e7 | 0.726348 | ||||||||
\(724\) | 9.13324e6 | 0.647558 | ||||||||
\(725\) | 2.06795e6 | 0.146115 | ||||||||
\(726\) | −7.73490e6 | −0.544644 | ||||||||
\(727\) | −1.12364e7 | −0.788479 | −0.394239 | − | 0.919008i | \(-0.628992\pi\) | ||||
−0.394239 | + | 0.919008i | \(0.628992\pi\) | |||||||
\(728\) | 5.95552e6 | 0.416477 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.09752e6 | 0.215133 | ||||||||
\(731\) | −3.38368e7 | −2.34205 | ||||||||
\(732\) | 6.08860e6 | 0.419990 | ||||||||
\(733\) | −1.41728e7 | −0.974309 | −0.487155 | − | 0.873316i | \(-0.661965\pi\) | ||||
−0.487155 | + | 0.873316i | \(0.661965\pi\) | |||||||
\(734\) | −4.97617e6 | −0.340922 | ||||||||
\(735\) | 1.76687e6 | 0.120639 | ||||||||
\(736\) | −530385. | −0.0360908 | ||||||||
\(737\) | −1.26950e7 | −0.860923 | ||||||||
\(738\) | −2.73555e6 | −0.184886 | ||||||||
\(739\) | 1.54330e7 | 1.03953 | 0.519767 | − | 0.854308i | \(-0.326019\pi\) | ||||
0.519767 | + | 0.854308i | \(0.326019\pi\) | |||||||
\(740\) | −2.22410e6 | −0.149305 | ||||||||
\(741\) | 3.19503e6 | 0.213761 | ||||||||
\(742\) | 6.40181e6 | 0.426867 | ||||||||
\(743\) | −2.07933e6 | −0.138182 | −0.0690908 | − | 0.997610i | \(-0.522010\pi\) | ||||
−0.0690908 | + | 0.997610i | \(0.522010\pi\) | |||||||
\(744\) | −741093. | −0.0490840 | ||||||||
\(745\) | 388149. | 0.0256217 | ||||||||
\(746\) | −1.32217e7 | −0.869840 | ||||||||
\(747\) | 8.14617e6 | 0.534136 | ||||||||
\(748\) | 1.39174e7 | 0.909506 | ||||||||
\(749\) | −1.89742e7 | −1.23583 | ||||||||
\(750\) | 562500. | 0.0365148 | ||||||||
\(751\) | −1.90164e7 | −1.23035 | −0.615175 | − | 0.788391i | \(-0.710915\pi\) | ||||
−0.615175 | + | 0.788391i | \(0.710915\pi\) | |||||||
\(752\) | −3.67714e6 | −0.237119 | ||||||||
\(753\) | −1.36812e7 | −0.879297 | ||||||||
\(754\) | 1.30151e7 | 0.833715 | ||||||||
\(755\) | −74899.3 | −0.00478201 | ||||||||
\(756\) | 1.10373e6 | 0.0702356 | ||||||||
\(757\) | −1.37514e6 | −0.0872182 | −0.0436091 | − | 0.999049i | \(-0.513886\pi\) | ||||
−0.0436091 | + | 0.999049i | \(0.513886\pi\) | |||||||
\(758\) | −665669. | −0.0420809 | ||||||||
\(759\) | −2.85809e6 | −0.180082 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | 1.05023e7 | 0.657390 | 0.328695 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328695 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(762\) | −575670. | −0.0359159 | ||||||||
\(763\) | −1.09431e7 | −0.680502 | ||||||||
\(764\) | 3.37508e6 | 0.209195 | ||||||||
\(765\) | 2.87292e6 | 0.177488 | ||||||||
\(766\) | 1.29725e7 | 0.798826 | ||||||||
\(767\) | −1.40727e7 | −0.863753 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | −4.99693e6 | −0.304711 | −0.152355 | − | 0.988326i | \(-0.548686\pi\) | ||||
−0.152355 | + | 0.988326i | \(0.548686\pi\) | |||||||
\(770\) | −5.80171e6 | −0.352638 | ||||||||
\(771\) | 5.77996e6 | 0.350178 | ||||||||
\(772\) | −6.68867e6 | −0.403921 | ||||||||
\(773\) | −3.43234e6 | −0.206606 | −0.103303 | − | 0.994650i | \(-0.532941\pi\) | ||||
−0.103303 | + | 0.994650i | \(0.532941\pi\) | |||||||
\(774\) | −7.72745e6 | −0.463643 | ||||||||
\(775\) | 804137. | 0.0480923 | ||||||||
\(776\) | −5.90668e6 | −0.352119 | ||||||||
\(777\) | 4.73534e6 | 0.281383 | ||||||||
\(778\) | −9.45374e6 | −0.559957 | ||||||||
\(779\) | −3.04794e6 | −0.179954 | ||||||||
\(780\) | 3.54020e6 | 0.208349 | ||||||||
\(781\) | −23161.5 | −0.00135875 | ||||||||
\(782\) | 2.93934e6 | 0.171883 | ||||||||
\(783\) | 2.41206e6 | 0.140600 | ||||||||
\(784\) | −2.01031e6 | −0.116808 | ||||||||
\(785\) | −9.14918e6 | −0.529917 | ||||||||
\(786\) | 615969. | 0.0355633 | ||||||||
\(787\) | 1.76794e7 | 1.01749 | 0.508746 | − | 0.860917i | \(-0.330109\pi\) | ||||
0.508746 | + | 0.860917i | \(0.330109\pi\) | |||||||
\(788\) | 1.47494e7 | 0.846170 | ||||||||
\(789\) | −2.06871e6 | −0.118306 | ||||||||
\(790\) | −6.46125e6 | −0.368340 | ||||||||
\(791\) | −2.27613e6 | −0.129347 | ||||||||
\(792\) | 3.17838e6 | 0.180050 | ||||||||
\(793\) | −4.15796e7 | −2.34799 | ||||||||
\(794\) | 1.87463e7 | 1.05527 | ||||||||
\(795\) | 3.80549e6 | 0.213547 | ||||||||
\(796\) | 1.15275e7 | 0.644838 | ||||||||
\(797\) | 2.92233e7 | 1.62961 | 0.814804 | − | 0.579737i | \(-0.196845\pi\) | ||||
0.814804 | + | 0.579737i | \(0.196845\pi\) | |||||||
\(798\) | 1.22977e6 | 0.0683623 | ||||||||
\(799\) | 2.03783e7 | 1.12928 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 3.96056e6 | 0.218110 | ||||||||
\(802\) | 6.07461e6 | 0.333490 | ||||||||
\(803\) | −1.89913e7 | −1.03936 | ||||||||
\(804\) | 2.98163e6 | 0.162672 | ||||||||
\(805\) | −1.22531e6 | −0.0666433 | ||||||||
\(806\) | 5.06099e6 | 0.274409 | ||||||||
\(807\) | 7.05265e6 | 0.381214 | ||||||||
\(808\) | 1.07939e6 | 0.0581635 | ||||||||
\(809\) | 2.33358e7 | 1.25358 | 0.626789 | − | 0.779189i | \(-0.284369\pi\) | ||||
0.626789 | + | 0.779189i | \(0.284369\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | 2.56264e7 | 1.36815 | 0.684077 | − | 0.729409i | \(-0.260205\pi\) | ||||
0.684077 | + | 0.729409i | \(0.260205\pi\) | |||||||
\(812\) | 5.00951e6 | 0.266628 | ||||||||
\(813\) | 8.70167e6 | 0.461717 | ||||||||
\(814\) | 1.36363e7 | 0.721331 | ||||||||
\(815\) | 1.09209e7 | 0.575922 | ||||||||
\(816\) | −3.26874e6 | −0.171852 | ||||||||
\(817\) | −8.60990e6 | −0.451277 | ||||||||
\(818\) | −2.15352e7 | −1.12530 | ||||||||
\(819\) | −7.53745e6 | −0.392658 | ||||||||
\(820\) | −3.37722e6 | −0.175398 | ||||||||
\(821\) | 3.39526e7 | 1.75799 | 0.878993 | − | 0.476834i | \(-0.158216\pi\) | ||||
0.878993 | + | 0.476834i | \(0.158216\pi\) | |||||||
\(822\) | 4.45631e6 | 0.230036 | ||||||||
\(823\) | −3.55156e6 | −0.182776 | −0.0913882 | − | 0.995815i | \(-0.529130\pi\) | ||||
−0.0913882 | + | 0.995815i | \(0.529130\pi\) | |||||||
\(824\) | −5.17572e6 | −0.265554 | ||||||||
\(825\) | −3.44877e6 | −0.176412 | ||||||||
\(826\) | −5.41661e6 | −0.276234 | ||||||||
\(827\) | −6.74117e6 | −0.342745 | −0.171373 | − | 0.985206i | \(-0.554820\pi\) | ||||
−0.171373 | + | 0.985206i | \(0.554820\pi\) | |||||||
\(828\) | 671269. | 0.0340268 | ||||||||
\(829\) | 1.21627e7 | 0.614674 | 0.307337 | − | 0.951601i | \(-0.400562\pi\) | ||||
0.307337 | + | 0.951601i | \(0.400562\pi\) | |||||||
\(830\) | 1.00570e7 | 0.506726 | ||||||||
\(831\) | 1.09601e6 | 0.0550571 | ||||||||
\(832\) | −4.02796e6 | −0.201733 | ||||||||
\(833\) | 1.11409e7 | 0.556298 | ||||||||
\(834\) | 3.10115e6 | 0.154386 | ||||||||
\(835\) | −7.83366e6 | −0.388820 | ||||||||
\(836\) | 3.54135e6 | 0.175248 | ||||||||
\(837\) | 937946. | 0.0462769 | ||||||||
\(838\) | 1.59989e7 | 0.787008 | ||||||||
\(839\) | 2.04276e7 | 1.00187 | 0.500935 | − | 0.865485i | \(-0.332989\pi\) | ||||
0.500935 | + | 0.865485i | \(0.332989\pi\) | |||||||
\(840\) | 1.36263e6 | 0.0666314 | ||||||||
\(841\) | −9.56349e6 | −0.466258 | ||||||||
\(842\) | −1.92211e7 | −0.934323 | ||||||||
\(843\) | −1.32809e7 | −0.643662 | ||||||||
\(844\) | 8.99112e6 | 0.434468 | ||||||||
\(845\) | −1.48940e7 | −0.717579 | ||||||||
\(846\) | 4.65389e6 | 0.223558 | ||||||||
\(847\) | 2.03314e7 | 0.973773 | ||||||||
\(848\) | −4.32980e6 | −0.206766 | ||||||||
\(849\) | −6.69784e6 | −0.318908 | ||||||||
\(850\) | 3.54681e6 | 0.168380 | ||||||||
\(851\) | 2.87995e6 | 0.136321 | ||||||||
\(852\) | 5439.85 | 0.000256737 0 | ||||||||
\(853\) | 3.21514e7 | 1.51296 | 0.756479 | − | 0.654018i | \(-0.226918\pi\) | ||||
0.756479 | + | 0.654018i | \(0.226918\pi\) | |||||||
\(854\) | −1.60040e7 | −0.750904 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | 1.28331e7 | 0.598612 | ||||||||
\(857\) | −2.63220e7 | −1.22424 | −0.612121 | − | 0.790764i | \(-0.709683\pi\) | ||||
−0.612121 | + | 0.790764i | \(0.709683\pi\) | |||||||
\(858\) | −2.17055e7 | −1.00659 | ||||||||
\(859\) | 1.21188e6 | 0.0560374 | 0.0280187 | − | 0.999607i | \(-0.491080\pi\) | ||||
0.0280187 | + | 0.999607i | \(0.491080\pi\) | |||||||
\(860\) | −9.54006e6 | −0.439850 | ||||||||
\(861\) | 7.19045e6 | 0.330558 | ||||||||
\(862\) | 1.11071e7 | 0.509133 | ||||||||
\(863\) | −5.47409e6 | −0.250199 | −0.125099 | − | 0.992144i | \(-0.539925\pi\) | ||||
−0.125099 | + | 0.992144i | \(0.539925\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −2.17170e6 | −0.0986868 | ||||||||
\(866\) | 7.34007e6 | 0.332587 | ||||||||
\(867\) | 5.33628e6 | 0.241097 | ||||||||
\(868\) | 1.94798e6 | 0.0877577 | ||||||||
\(869\) | 3.96148e7 | 1.77954 | ||||||||
\(870\) | 2.97785e6 | 0.133384 | ||||||||
\(871\) | −2.03618e7 | −0.909435 | ||||||||
\(872\) | 7.40127e6 | 0.329621 | ||||||||
\(873\) | 7.47565e6 | 0.331981 | ||||||||
\(874\) | 747926. | 0.0331192 | ||||||||
\(875\) | −1.47854e6 | −0.0652851 | ||||||||
\(876\) | 4.46043e6 | 0.196389 | ||||||||
\(877\) | −2.98986e7 | −1.31266 | −0.656330 | − | 0.754474i | \(-0.727892\pi\) | ||||
−0.656330 | + | 0.754474i | \(0.727892\pi\) | |||||||
\(878\) | 4.92998e6 | 0.215828 | ||||||||
\(879\) | 1.10339e6 | 0.0481677 | ||||||||
\(880\) | 3.92393e6 | 0.170811 | ||||||||
\(881\) | 892818. | 0.0387546 | 0.0193773 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193773 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(882\) | 2.54429e6 | 0.110127 | ||||||||
\(883\) | −9.71539e6 | −0.419332 | −0.209666 | − | 0.977773i | \(-0.567238\pi\) | ||||
−0.209666 | + | 0.977773i | \(0.567238\pi\) | |||||||
\(884\) | 2.23225e7 | 0.960754 | ||||||||
\(885\) | −3.21985e6 | −0.138190 | ||||||||
\(886\) | 5.77388e6 | 0.247106 | ||||||||
\(887\) | 3.82580e7 | 1.63273 | 0.816364 | − | 0.577538i | \(-0.195987\pi\) | ||||
0.816364 | + | 0.577538i | \(0.195987\pi\) | |||||||
\(888\) | −3.20270e6 | −0.136296 | ||||||||
\(889\) | 1.51316e6 | 0.0642142 | ||||||||
\(890\) | 4.88958e6 | 0.206917 | ||||||||
\(891\) | −4.02264e6 | −0.169753 | ||||||||
\(892\) | 1.94036e6 | 0.0816527 | ||||||||
\(893\) | 5.18535e6 | 0.217595 | ||||||||
\(894\) | 558935. | 0.0233893 | ||||||||
\(895\) | −1.44487e7 | −0.602934 | ||||||||
\(896\) | −1.55037e6 | −0.0645155 | ||||||||
\(897\) | −4.58415e6 | −0.190230 | ||||||||
\(898\) | −2.71468e7 | −1.12338 | ||||||||
\(899\) | 4.25707e6 | 0.175676 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 2.39953e7 | 0.984723 | ||||||||
\(902\) | 2.07062e7 | 0.847392 | ||||||||
\(903\) | 2.03118e7 | 0.828951 | ||||||||
\(904\) | 1.53944e6 | 0.0626529 | ||||||||
\(905\) | −1.42707e7 | −0.579193 | ||||||||
\(906\) | −107855. | −0.00436536 | ||||||||
\(907\) | −3.97217e7 | −1.60328 | −0.801641 | − | 0.597806i | \(-0.796039\pi\) | ||||
−0.801641 | + | 0.597806i | \(0.796039\pi\) | |||||||
\(908\) | −1.08565e7 | −0.436993 | ||||||||
\(909\) | −1.36611e6 | −0.0548371 | ||||||||
\(910\) | −9.30550e6 | −0.372508 | ||||||||
\(911\) | 9.37882e6 | 0.374414 | 0.187207 | − | 0.982320i | \(-0.440056\pi\) | ||||
0.187207 | + | 0.982320i | \(0.440056\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | −6.16609e7 | −2.44812 | ||||||||
\(914\) | −2.28096e7 | −0.903135 | ||||||||
\(915\) | −9.51343e6 | −0.375651 | ||||||||
\(916\) | 3.39360e6 | 0.133635 | ||||||||
\(917\) | −1.61909e6 | −0.0635840 | ||||||||
\(918\) | 4.13700e6 | 0.162024 | ||||||||
\(919\) | −3.04741e7 | −1.19026 | −0.595131 | − | 0.803629i | \(-0.702900\pi\) | ||||
−0.595131 | + | 0.803629i | \(0.702900\pi\) | |||||||
\(920\) | 828727. | 0.0322806 | ||||||||
\(921\) | −2.12523e7 | −0.825574 | ||||||||
\(922\) | 1.24140e7 | 0.480934 | ||||||||
\(923\) | −37149.2 | −0.00143531 | ||||||||
\(924\) | −8.35446e6 | −0.321913 | ||||||||
\(925\) | 3.47515e6 | 0.133543 | ||||||||
\(926\) | 9.57939e6 | 0.367122 | ||||||||
\(927\) | 6.55053e6 | 0.250367 | ||||||||
\(928\) | −3.38813e6 | −0.129149 | ||||||||
\(929\) | −2.66683e7 | −1.01381 | −0.506905 | − | 0.862002i | \(-0.669211\pi\) | ||||
−0.506905 | + | 0.862002i | \(0.669211\pi\) | |||||||
\(930\) | 1.15796e6 | 0.0439021 | ||||||||
\(931\) | 2.83485e6 | 0.107190 | ||||||||
\(932\) | −1.15184e7 | −0.434364 | ||||||||
\(933\) | −2.08586e7 | −0.784477 | ||||||||
\(934\) | −3.12982e7 | −1.17396 | ||||||||
\(935\) | −2.17460e7 | −0.813487 | ||||||||
\(936\) | 5.09789e6 | 0.190196 | ||||||||
\(937\) | −1.31362e7 | −0.488788 | −0.244394 | − | 0.969676i | \(-0.578589\pi\) | ||||
−0.244394 | + | 0.969676i | \(0.578589\pi\) | |||||||
\(938\) | −7.83729e6 | −0.290843 | ||||||||
\(939\) | −5.02896e6 | −0.186129 | ||||||||
\(940\) | 5.74554e6 | 0.212086 | ||||||||
\(941\) | −2.01910e6 | −0.0743333 | −0.0371666 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371666 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(942\) | −1.31748e7 | −0.483746 | ||||||||
\(943\) | 4.37311e6 | 0.160144 | ||||||||
\(944\) | 3.66347e6 | 0.133802 | ||||||||
\(945\) | −1.72457e6 | −0.0628207 | ||||||||
\(946\) | 5.84915e7 | 2.12503 | ||||||||
\(947\) | 3.06998e7 | 1.11240 | 0.556200 | − | 0.831048i | \(-0.312259\pi\) | ||||
0.556200 | + | 0.831048i | \(0.312259\pi\) | |||||||
\(948\) | −9.30419e6 | −0.336247 | ||||||||
\(949\) | −3.04607e7 | −1.09793 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | −1.22894e7 | −0.440634 | ||||||||
\(952\) | 8.59196e6 | 0.307256 | ||||||||
\(953\) | 4.06107e7 | 1.44847 | 0.724233 | − | 0.689556i | \(-0.242194\pi\) | ||||
0.724233 | + | 0.689556i | \(0.242194\pi\) | |||||||
\(954\) | 5.47991e6 | 0.194941 | ||||||||
\(955\) | −5.27356e6 | −0.187109 | ||||||||
\(956\) | 3.83558e6 | 0.135733 | ||||||||
\(957\) | −1.82576e7 | −0.644414 | ||||||||
\(958\) | −1.27045e6 | −0.0447242 | ||||||||
\(959\) | −1.17135e7 | −0.411283 | ||||||||
\(960\) | −921600. | −0.0322749 | ||||||||
\(961\) | −2.69738e7 | −0.942178 | ||||||||
\(962\) | 2.18715e7 | 0.761976 | ||||||||
\(963\) | −1.62418e7 | −0.564377 | ||||||||
\(964\) | 1.81496e7 | 0.629036 | ||||||||
\(965\) | 1.04511e7 | 0.361278 | ||||||||
\(966\) | −1.76445e6 | −0.0608367 | ||||||||
\(967\) | −2.25532e7 | −0.775608 | −0.387804 | − | 0.921742i | \(-0.626766\pi\) | ||||
−0.387804 | + | 0.921742i | \(0.626766\pi\) | |||||||
\(968\) | −1.37509e7 | −0.471676 | ||||||||
\(969\) | 4.60943e6 | 0.157702 | ||||||||
\(970\) | 9.22919e6 | 0.314945 | ||||||||
\(971\) | 4.45749e7 | 1.51720 | 0.758598 | − | 0.651559i | \(-0.225885\pi\) | ||||
0.758598 | + | 0.651559i | \(0.225885\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | −8.15144e6 | −0.276027 | ||||||||
\(974\) | −8.49069e6 | −0.286778 | ||||||||
\(975\) | −5.53156e6 | −0.186353 | ||||||||
\(976\) | 1.08242e7 | 0.363722 | ||||||||
\(977\) | 4.21455e7 | 1.41259 | 0.706293 | − | 0.707920i | \(-0.250366\pi\) | ||||
0.706293 | + | 0.707920i | \(0.250366\pi\) | |||||||
\(978\) | 1.57261e7 | 0.525743 | ||||||||
\(979\) | −2.99787e7 | −0.999668 | ||||||||
\(980\) | 3.14110e6 | 0.104476 | ||||||||
\(981\) | −9.36724e6 | −0.310770 | ||||||||
\(982\) | −3.04764e7 | −1.00852 | ||||||||
\(983\) | −7.47617e6 | −0.246772 | −0.123386 | − | 0.992359i | \(-0.539375\pi\) | ||||
−0.123386 | + | 0.992359i | \(0.539375\pi\) | |||||||
\(984\) | −4.86319e6 | −0.160116 | ||||||||
\(985\) | −2.30459e7 | −0.756837 | ||||||||
\(986\) | 1.87767e7 | 0.615073 | ||||||||
\(987\) | −1.22328e7 | −0.399701 | ||||||||
\(988\) | 5.68005e6 | 0.185123 | ||||||||
\(989\) | 1.23533e7 | 0.401598 | ||||||||
\(990\) | −4.96623e6 | −0.161042 | ||||||||
\(991\) | 5.19925e7 | 1.68173 | 0.840865 | − | 0.541245i | \(-0.182047\pi\) | ||||
0.840865 | + | 0.541245i | \(0.182047\pi\) | |||||||
\(992\) | −1.31750e6 | −0.0425080 | ||||||||
\(993\) | −1.88736e7 | −0.607411 | ||||||||
\(994\) | −14298.8 | −0.000459022 0 | ||||||||
\(995\) | −1.80116e7 | −0.576761 | ||||||||
\(996\) | 1.44821e7 | 0.462575 | ||||||||
\(997\) | 5.14642e7 | 1.63971 | 0.819856 | − | 0.572570i | \(-0.194054\pi\) | ||||
0.819856 | + | 0.572570i | \(0.194054\pi\) | |||||||
\(998\) | 4.47848e6 | 0.142333 | ||||||||
\(999\) | 4.05342e6 | 0.128501 |
(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 | 570.6.a.k.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.k.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |