Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,8,Mod(1,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.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: | \(31.8632725994\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 102.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −235.000 | −0.840762 | −0.420381 | − | 0.907348i | \(-0.638104\pi\) | ||||
−0.420381 | + | 0.907348i | \(0.638104\pi\) | |||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | −344.000 | −0.379066 | −0.189533 | − | 0.981874i | \(-0.560697\pi\) | ||||
−0.189533 | + | 0.981874i | \(0.560697\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1880.00 | −0.594508 | ||||||||
\(11\) | −4185.00 | −0.948028 | −0.474014 | − | 0.880517i | \(-0.657195\pi\) | ||||
−0.474014 | + | 0.880517i | \(0.657195\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −1833.00 | −0.231399 | −0.115699 | − | 0.993284i | \(-0.536911\pi\) | ||||
−0.115699 | + | 0.993284i | \(0.536911\pi\) | |||||||
\(14\) | −2752.00 | −0.268040 | ||||||||
\(15\) | −6345.00 | −0.485414 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 4913.00 | 0.242536 | ||||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −37829.0 | −1.26528 | −0.632641 | − | 0.774445i | \(-0.718029\pi\) | ||||
−0.632641 | + | 0.774445i | \(0.718029\pi\) | |||||||
\(20\) | −15040.0 | −0.420381 | ||||||||
\(21\) | −9288.00 | −0.218854 | ||||||||
\(22\) | −33480.0 | −0.670357 | ||||||||
\(23\) | −85437.0 | −1.46419 | −0.732097 | − | 0.681201i | \(-0.761458\pi\) | ||||
−0.732097 | + | 0.681201i | \(0.761458\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | −22900.0 | −0.293120 | ||||||||
\(26\) | −14664.0 | −0.163624 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −22016.0 | −0.189533 | ||||||||
\(29\) | 54794.0 | 0.417196 | 0.208598 | − | 0.978001i | \(-0.433110\pi\) | ||||
0.208598 | + | 0.978001i | \(0.433110\pi\) | |||||||
\(30\) | −50760.0 | −0.343239 | ||||||||
\(31\) | −89586.0 | −0.540100 | −0.270050 | − | 0.962846i | \(-0.587040\pi\) | ||||
−0.270050 | + | 0.962846i | \(0.587040\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −112995. | −0.547344 | ||||||||
\(34\) | 39304.0 | 0.171499 | ||||||||
\(35\) | 80840.0 | 0.318704 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 30392.0 | 0.0986400 | 0.0493200 | − | 0.998783i | \(-0.484295\pi\) | ||||
0.0493200 | + | 0.998783i | \(0.484295\pi\) | |||||||
\(38\) | −302632. | −0.894689 | ||||||||
\(39\) | −49491.0 | −0.133598 | ||||||||
\(40\) | −120320. | −0.297254 | ||||||||
\(41\) | 550715. | 1.24791 | 0.623955 | − | 0.781460i | \(-0.285525\pi\) | ||||
0.623955 | + | 0.781460i | \(0.285525\pi\) | |||||||
\(42\) | −74304.0 | −0.154753 | ||||||||
\(43\) | −434107. | −0.832640 | −0.416320 | − | 0.909218i | \(-0.636680\pi\) | ||||
−0.416320 | + | 0.909218i | \(0.636680\pi\) | |||||||
\(44\) | −267840. | −0.474014 | ||||||||
\(45\) | −171315. | −0.280254 | ||||||||
\(46\) | −683496. | −1.03534 | ||||||||
\(47\) | 259378. | 0.364410 | 0.182205 | − | 0.983261i | \(-0.441677\pi\) | ||||
0.182205 | + | 0.983261i | \(0.441677\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | −705207. | −0.856309 | ||||||||
\(50\) | −183200. | −0.207267 | ||||||||
\(51\) | 132651. | 0.140028 | ||||||||
\(52\) | −117312. | −0.115699 | ||||||||
\(53\) | −923366. | −0.851939 | −0.425969 | − | 0.904738i | \(-0.640067\pi\) | ||||
−0.425969 | + | 0.904738i | \(0.640067\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | 983475. | 0.797065 | ||||||||
\(56\) | −176128. | −0.134020 | ||||||||
\(57\) | −1.02138e6 | −0.730511 | ||||||||
\(58\) | 438352. | 0.295002 | ||||||||
\(59\) | −1.32046e6 | −0.837035 | −0.418518 | − | 0.908209i | \(-0.637450\pi\) | ||||
−0.418518 | + | 0.908209i | \(0.637450\pi\) | |||||||
\(60\) | −406080. | −0.242707 | ||||||||
\(61\) | 1.19316e6 | 0.673043 | 0.336521 | − | 0.941676i | \(-0.390750\pi\) | ||||
0.336521 | + | 0.941676i | \(0.390750\pi\) | |||||||
\(62\) | −716688. | −0.381908 | ||||||||
\(63\) | −250776. | −0.126355 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 430755. | 0.194551 | ||||||||
\(66\) | −903960. | −0.387031 | ||||||||
\(67\) | −369324. | −0.150019 | −0.0750094 | − | 0.997183i | \(-0.523899\pi\) | ||||
−0.0750094 | + | 0.997183i | \(0.523899\pi\) | |||||||
\(68\) | 314432. | 0.121268 | ||||||||
\(69\) | −2.30680e6 | −0.845353 | ||||||||
\(70\) | 646720. | 0.225358 | ||||||||
\(71\) | −2.74228e6 | −0.909299 | −0.454650 | − | 0.890670i | \(-0.650236\pi\) | ||||
−0.454650 | + | 0.890670i | \(0.650236\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 1.10217e6 | 0.331602 | 0.165801 | − | 0.986159i | \(-0.446979\pi\) | ||||
0.165801 | + | 0.986159i | \(0.446979\pi\) | |||||||
\(74\) | 243136. | 0.0697490 | ||||||||
\(75\) | −618300. | −0.169233 | ||||||||
\(76\) | −2.42106e6 | −0.632641 | ||||||||
\(77\) | 1.43964e6 | 0.359365 | ||||||||
\(78\) | −395928. | −0.0944681 | ||||||||
\(79\) | 5.53807e6 | 1.26376 | 0.631879 | − | 0.775067i | \(-0.282284\pi\) | ||||
0.631879 | + | 0.775067i | \(0.282284\pi\) | |||||||
\(80\) | −962560. | −0.210190 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 4.40572e6 | 0.882406 | ||||||||
\(83\) | 5.35331e6 | 1.02766 | 0.513830 | − | 0.857892i | \(-0.328226\pi\) | ||||
0.513830 | + | 0.857892i | \(0.328226\pi\) | |||||||
\(84\) | −594432. | −0.109427 | ||||||||
\(85\) | −1.15456e6 | −0.203915 | ||||||||
\(86\) | −3.47286e6 | −0.588765 | ||||||||
\(87\) | 1.47944e6 | 0.240868 | ||||||||
\(88\) | −2.14272e6 | −0.335178 | ||||||||
\(89\) | −4.26979e6 | −0.642009 | −0.321005 | − | 0.947078i | \(-0.604021\pi\) | ||||
−0.321005 | + | 0.947078i | \(0.604021\pi\) | |||||||
\(90\) | −1.37052e6 | −0.198169 | ||||||||
\(91\) | 630552. | 0.0877154 | ||||||||
\(92\) | −5.46797e6 | −0.732097 | ||||||||
\(93\) | −2.41882e6 | −0.311827 | ||||||||
\(94\) | 2.07502e6 | 0.257677 | ||||||||
\(95\) | 8.88982e6 | 1.06380 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | −1.00334e7 | −1.11621 | −0.558105 | − | 0.829771i | \(-0.688471\pi\) | ||||
−0.558105 | + | 0.829771i | \(0.688471\pi\) | |||||||
\(98\) | −5.64166e6 | −0.605502 | ||||||||
\(99\) | −3.05087e6 | −0.316009 | ||||||||
\(100\) | −1.46560e6 | −0.146560 | ||||||||
\(101\) | 927704. | 0.0895952 | 0.0447976 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447976 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(102\) | 1.06121e6 | 0.0990148 | ||||||||
\(103\) | −1.45382e6 | −0.131094 | −0.0655468 | − | 0.997849i | \(-0.520879\pi\) | ||||
−0.0655468 | + | 0.997849i | \(0.520879\pi\) | |||||||
\(104\) | −938496. | −0.0818118 | ||||||||
\(105\) | 2.18268e6 | 0.184004 | ||||||||
\(106\) | −7.38693e6 | −0.602412 | ||||||||
\(107\) | 2.19897e7 | 1.73531 | 0.867654 | − | 0.497169i | \(-0.165627\pi\) | ||||
0.867654 | + | 0.497169i | \(0.165627\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | 1.27832e7 | 0.945471 | 0.472736 | − | 0.881204i | \(-0.343267\pi\) | ||||
0.472736 | + | 0.881204i | \(0.343267\pi\) | |||||||
\(110\) | 7.86780e6 | 0.563610 | ||||||||
\(111\) | 820584. | 0.0569499 | ||||||||
\(112\) | −1.40902e6 | −0.0947666 | ||||||||
\(113\) | 2.54158e7 | 1.65703 | 0.828513 | − | 0.559970i | \(-0.189187\pi\) | ||||
0.828513 | + | 0.559970i | \(0.189187\pi\) | |||||||
\(114\) | −8.17106e6 | −0.516549 | ||||||||
\(115\) | 2.00777e7 | 1.23104 | ||||||||
\(116\) | 3.50682e6 | 0.208598 | ||||||||
\(117\) | −1.33626e6 | −0.0771329 | ||||||||
\(118\) | −1.05637e7 | −0.591873 | ||||||||
\(119\) | −1.69007e6 | −0.0919371 | ||||||||
\(120\) | −3.24864e6 | −0.171620 | ||||||||
\(121\) | −1.97295e6 | −0.101243 | ||||||||
\(122\) | 9.54525e6 | 0.475913 | ||||||||
\(123\) | 1.48693e7 | 0.720481 | ||||||||
\(124\) | −5.73350e6 | −0.270050 | ||||||||
\(125\) | 2.37409e7 | 1.08721 | ||||||||
\(126\) | −2.00621e6 | −0.0893468 | ||||||||
\(127\) | 1.10221e7 | 0.477474 | 0.238737 | − | 0.971084i | \(-0.423267\pi\) | ||||
0.238737 | + | 0.971084i | \(0.423267\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −1.17209e7 | −0.480725 | ||||||||
\(130\) | 3.44604e6 | 0.137568 | ||||||||
\(131\) | 3.83804e7 | 1.49163 | 0.745813 | − | 0.666155i | \(-0.232061\pi\) | ||||
0.745813 | + | 0.666155i | \(0.232061\pi\) | |||||||
\(132\) | −7.23168e6 | −0.273672 | ||||||||
\(133\) | 1.30132e7 | 0.479626 | ||||||||
\(134\) | −2.95459e6 | −0.106079 | ||||||||
\(135\) | −4.62550e6 | −0.161805 | ||||||||
\(136\) | 2.51546e6 | 0.0857493 | ||||||||
\(137\) | −1.53813e7 | −0.511058 | −0.255529 | − | 0.966801i | \(-0.582250\pi\) | ||||
−0.255529 | + | 0.966801i | \(0.582250\pi\) | |||||||
\(138\) | −1.84544e7 | −0.597755 | ||||||||
\(139\) | −1.23072e7 | −0.388694 | −0.194347 | − | 0.980933i | \(-0.562259\pi\) | ||||
−0.194347 | + | 0.980933i | \(0.562259\pi\) | |||||||
\(140\) | 5.17376e6 | 0.159352 | ||||||||
\(141\) | 7.00321e6 | 0.210392 | ||||||||
\(142\) | −2.19382e7 | −0.642972 | ||||||||
\(143\) | 7.67110e6 | 0.219372 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −1.28766e7 | −0.350762 | ||||||||
\(146\) | 8.81733e6 | 0.234478 | ||||||||
\(147\) | −1.90406e7 | −0.494390 | ||||||||
\(148\) | 1.94509e6 | 0.0493200 | ||||||||
\(149\) | 1.72111e7 | 0.426242 | 0.213121 | − | 0.977026i | \(-0.431637\pi\) | ||||
0.213121 | + | 0.977026i | \(0.431637\pi\) | |||||||
\(150\) | −4.94640e6 | −0.119666 | ||||||||
\(151\) | −2.69730e7 | −0.637544 | −0.318772 | − | 0.947831i | \(-0.603270\pi\) | ||||
−0.318772 | + | 0.947831i | \(0.603270\pi\) | |||||||
\(152\) | −1.93684e7 | −0.447345 | ||||||||
\(153\) | 3.58158e6 | 0.0808452 | ||||||||
\(154\) | 1.15171e7 | 0.254110 | ||||||||
\(155\) | 2.10527e7 | 0.454095 | ||||||||
\(156\) | −3.16742e6 | −0.0667990 | ||||||||
\(157\) | −2.24669e7 | −0.463333 | −0.231667 | − | 0.972795i | \(-0.574418\pi\) | ||||
−0.231667 | + | 0.972795i | \(0.574418\pi\) | |||||||
\(158\) | 4.43046e7 | 0.893611 | ||||||||
\(159\) | −2.49309e7 | −0.491867 | ||||||||
\(160\) | −7.70048e6 | −0.148627 | ||||||||
\(161\) | 2.93903e7 | 0.555027 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −7.32660e7 | −1.32509 | −0.662546 | − | 0.749021i | \(-0.730524\pi\) | ||||
−0.662546 | + | 0.749021i | \(0.730524\pi\) | |||||||
\(164\) | 3.52458e7 | 0.623955 | ||||||||
\(165\) | 2.65538e7 | 0.460186 | ||||||||
\(166\) | 4.28265e7 | 0.726665 | ||||||||
\(167\) | −2.23422e7 | −0.371208 | −0.185604 | − | 0.982625i | \(-0.559424\pi\) | ||||
−0.185604 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(168\) | −4.75546e6 | −0.0773766 | ||||||||
\(169\) | −5.93886e7 | −0.946455 | ||||||||
\(170\) | −9.23644e6 | −0.144189 | ||||||||
\(171\) | −2.75773e7 | −0.421761 | ||||||||
\(172\) | −2.77828e7 | −0.416320 | ||||||||
\(173\) | 3.10862e7 | 0.456464 | 0.228232 | − | 0.973607i | \(-0.426705\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426705\pi\) | |||||||
\(174\) | 1.18355e7 | 0.170320 | ||||||||
\(175\) | 7.87760e6 | 0.111112 | ||||||||
\(176\) | −1.71418e7 | −0.237007 | ||||||||
\(177\) | −3.56525e7 | −0.483263 | ||||||||
\(178\) | −3.41583e7 | −0.453969 | ||||||||
\(179\) | −4.13577e7 | −0.538978 | −0.269489 | − | 0.963003i | \(-0.586855\pi\) | ||||
−0.269489 | + | 0.963003i | \(0.586855\pi\) | |||||||
\(180\) | −1.09642e7 | −0.140127 | ||||||||
\(181\) | −1.23423e7 | −0.154711 | −0.0773554 | − | 0.997004i | \(-0.524648\pi\) | ||||
−0.0773554 | + | 0.997004i | \(0.524648\pi\) | |||||||
\(182\) | 5.04442e6 | 0.0620242 | ||||||||
\(183\) | 3.22152e7 | 0.388582 | ||||||||
\(184\) | −4.37437e7 | −0.517671 | ||||||||
\(185\) | −7.14212e6 | −0.0829328 | ||||||||
\(186\) | −1.93506e7 | −0.220495 | ||||||||
\(187\) | −2.05609e7 | −0.229931 | ||||||||
\(188\) | 1.66002e7 | 0.182205 | ||||||||
\(189\) | −6.77095e6 | −0.0729514 | ||||||||
\(190\) | 7.11185e7 | 0.752220 | ||||||||
\(191\) | 4.70786e7 | 0.488885 | 0.244443 | − | 0.969664i | \(-0.421395\pi\) | ||||
0.244443 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −6.59166e7 | −0.660001 | −0.330000 | − | 0.943981i | \(-0.607049\pi\) | ||||
−0.330000 | + | 0.943981i | \(0.607049\pi\) | |||||||
\(194\) | −8.02669e7 | −0.789279 | ||||||||
\(195\) | 1.16304e7 | 0.112324 | ||||||||
\(196\) | −4.51332e7 | −0.428154 | ||||||||
\(197\) | −1.44442e8 | −1.34605 | −0.673025 | − | 0.739620i | \(-0.735005\pi\) | ||||
−0.673025 | + | 0.739620i | \(0.735005\pi\) | |||||||
\(198\) | −2.44069e7 | −0.223452 | ||||||||
\(199\) | −2.13401e8 | −1.91960 | −0.959800 | − | 0.280685i | \(-0.909438\pi\) | ||||
−0.959800 | + | 0.280685i | \(0.909438\pi\) | |||||||
\(200\) | −1.17248e7 | −0.103634 | ||||||||
\(201\) | −9.97175e6 | −0.0866134 | ||||||||
\(202\) | 7.42163e6 | 0.0633534 | ||||||||
\(203\) | −1.88491e7 | −0.158145 | ||||||||
\(204\) | 8.48966e6 | 0.0700140 | ||||||||
\(205\) | −1.29418e8 | −1.04920 | ||||||||
\(206\) | −1.16306e7 | −0.0926971 | ||||||||
\(207\) | −6.22836e7 | −0.488065 | ||||||||
\(208\) | −7.50797e6 | −0.0578497 | ||||||||
\(209\) | 1.58314e8 | 1.19952 | ||||||||
\(210\) | 1.74614e7 | 0.130111 | ||||||||
\(211\) | −1.77492e8 | −1.30074 | −0.650369 | − | 0.759618i | \(-0.725386\pi\) | ||||
−0.650369 | + | 0.759618i | \(0.725386\pi\) | |||||||
\(212\) | −5.90954e7 | −0.425969 | ||||||||
\(213\) | −7.40415e7 | −0.524984 | ||||||||
\(214\) | 1.75918e8 | 1.22705 | ||||||||
\(215\) | 1.02015e8 | 0.700052 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 3.08176e7 | 0.204734 | ||||||||
\(218\) | 1.02266e8 | 0.668549 | ||||||||
\(219\) | 2.97585e7 | 0.191450 | ||||||||
\(220\) | 6.29424e7 | 0.398533 | ||||||||
\(221\) | −9.00553e6 | −0.0561224 | ||||||||
\(222\) | 6.56467e6 | 0.0402696 | ||||||||
\(223\) | −1.84303e8 | −1.11292 | −0.556462 | − | 0.830873i | \(-0.687841\pi\) | ||||
−0.556462 | + | 0.830873i | \(0.687841\pi\) | |||||||
\(224\) | −1.12722e7 | −0.0670101 | ||||||||
\(225\) | −1.66941e7 | −0.0977067 | ||||||||
\(226\) | 2.03326e8 | 1.17169 | ||||||||
\(227\) | 8.22979e6 | 0.0466980 | 0.0233490 | − | 0.999727i | \(-0.492567\pi\) | ||||
0.0233490 | + | 0.999727i | \(0.492567\pi\) | |||||||
\(228\) | −6.53685e7 | −0.365255 | ||||||||
\(229\) | 3.09325e8 | 1.70212 | 0.851062 | − | 0.525065i | \(-0.175959\pi\) | ||||
0.851062 | + | 0.525065i | \(0.175959\pi\) | |||||||
\(230\) | 1.60622e8 | 0.870475 | ||||||||
\(231\) | 3.88703e7 | 0.207480 | ||||||||
\(232\) | 2.80545e7 | 0.147501 | ||||||||
\(233\) | 1.25573e8 | 0.650355 | 0.325177 | − | 0.945653i | \(-0.394576\pi\) | ||||
0.325177 | + | 0.945653i | \(0.394576\pi\) | |||||||
\(234\) | −1.06901e7 | −0.0545412 | ||||||||
\(235\) | −6.09538e7 | −0.306382 | ||||||||
\(236\) | −8.45096e7 | −0.418518 | ||||||||
\(237\) | 1.49528e8 | 0.729631 | ||||||||
\(238\) | −1.35206e7 | −0.0650094 | ||||||||
\(239\) | 3.88888e8 | 1.84260 | 0.921301 | − | 0.388849i | \(-0.127127\pi\) | ||||
0.921301 | + | 0.388849i | \(0.127127\pi\) | |||||||
\(240\) | −2.59891e7 | −0.121353 | ||||||||
\(241\) | −2.00123e8 | −0.920952 | −0.460476 | − | 0.887672i | \(-0.652321\pi\) | ||||
−0.460476 | + | 0.887672i | \(0.652321\pi\) | |||||||
\(242\) | −1.57836e7 | −0.0715898 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 7.63620e7 | 0.336521 | ||||||||
\(245\) | 1.65724e8 | 0.719951 | ||||||||
\(246\) | 1.18954e8 | 0.509457 | ||||||||
\(247\) | 6.93406e7 | 0.292784 | ||||||||
\(248\) | −4.58680e7 | −0.190954 | ||||||||
\(249\) | 1.44539e8 | 0.593320 | ||||||||
\(250\) | 1.89927e8 | 0.768770 | ||||||||
\(251\) | −1.45992e8 | −0.582736 | −0.291368 | − | 0.956611i | \(-0.594110\pi\) | ||||
−0.291368 | + | 0.956611i | \(0.594110\pi\) | |||||||
\(252\) | −1.60497e7 | −0.0631777 | ||||||||
\(253\) | 3.57554e8 | 1.38810 | ||||||||
\(254\) | 8.81766e7 | 0.337625 | ||||||||
\(255\) | −3.11730e7 | −0.117730 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −4.23238e8 | −1.55532 | −0.777658 | − | 0.628688i | \(-0.783592\pi\) | ||||
−0.777658 | + | 0.628688i | \(0.783592\pi\) | |||||||
\(258\) | −9.37671e7 | −0.339924 | ||||||||
\(259\) | −1.04548e7 | −0.0373911 | ||||||||
\(260\) | 2.75683e7 | 0.0972755 | ||||||||
\(261\) | 3.99448e7 | 0.139065 | ||||||||
\(262\) | 3.07043e8 | 1.05474 | ||||||||
\(263\) | 4.67569e7 | 0.158490 | 0.0792448 | − | 0.996855i | \(-0.474749\pi\) | ||||
0.0792448 | + | 0.996855i | \(0.474749\pi\) | |||||||
\(264\) | −5.78534e7 | −0.193515 | ||||||||
\(265\) | 2.16991e8 | 0.716277 | ||||||||
\(266\) | 1.04105e8 | 0.339147 | ||||||||
\(267\) | −1.15284e8 | −0.370664 | ||||||||
\(268\) | −2.36367e7 | −0.0750094 | ||||||||
\(269\) | −2.85453e8 | −0.894132 | −0.447066 | − | 0.894501i | \(-0.647531\pi\) | ||||
−0.447066 | + | 0.894501i | \(0.647531\pi\) | |||||||
\(270\) | −3.70040e7 | −0.114413 | ||||||||
\(271\) | −1.72044e8 | −0.525107 | −0.262554 | − | 0.964917i | \(-0.584565\pi\) | ||||
−0.262554 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(272\) | 2.01236e7 | 0.0606339 | ||||||||
\(273\) | 1.70249e7 | 0.0506425 | ||||||||
\(274\) | −1.23050e8 | −0.361373 | ||||||||
\(275\) | 9.58365e7 | 0.277886 | ||||||||
\(276\) | −1.47635e8 | −0.422676 | ||||||||
\(277\) | 2.88317e8 | 0.815062 | 0.407531 | − | 0.913191i | \(-0.366390\pi\) | ||||
0.407531 | + | 0.913191i | \(0.366390\pi\) | |||||||
\(278\) | −9.84576e7 | −0.274848 | ||||||||
\(279\) | −6.53082e7 | −0.180033 | ||||||||
\(280\) | 4.13901e7 | 0.112679 | ||||||||
\(281\) | 5.53413e7 | 0.148791 | 0.0743956 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743956 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(282\) | 5.60256e7 | 0.148770 | ||||||||
\(283\) | 6.75308e7 | 0.177113 | 0.0885563 | − | 0.996071i | \(-0.471775\pi\) | ||||
0.0885563 | + | 0.996071i | \(0.471775\pi\) | |||||||
\(284\) | −1.75506e8 | −0.454650 | ||||||||
\(285\) | 2.40025e8 | 0.614185 | ||||||||
\(286\) | 6.13688e7 | 0.155120 | ||||||||
\(287\) | −1.89446e8 | −0.473041 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 2.41376e7 | 0.0588235 | ||||||||
\(290\) | −1.03013e8 | −0.248026 | ||||||||
\(291\) | −2.70901e8 | −0.644444 | ||||||||
\(292\) | 7.05386e7 | 0.165801 | ||||||||
\(293\) | −1.54735e8 | −0.359379 | −0.179689 | − | 0.983723i | \(-0.557509\pi\) | ||||
−0.179689 | + | 0.983723i | \(0.557509\pi\) | |||||||
\(294\) | −1.52325e8 | −0.349587 | ||||||||
\(295\) | 3.10309e8 | 0.703747 | ||||||||
\(296\) | 1.55607e7 | 0.0348745 | ||||||||
\(297\) | −8.23734e7 | −0.182448 | ||||||||
\(298\) | 1.37689e8 | 0.301398 | ||||||||
\(299\) | 1.56606e8 | 0.338812 | ||||||||
\(300\) | −3.95712e7 | −0.0846165 | ||||||||
\(301\) | 1.49333e8 | 0.315626 | ||||||||
\(302\) | −2.15784e8 | −0.450812 | ||||||||
\(303\) | 2.50480e7 | 0.0517278 | ||||||||
\(304\) | −1.54948e8 | −0.316320 | ||||||||
\(305\) | −2.80392e8 | −0.565869 | ||||||||
\(306\) | 2.86526e7 | 0.0571662 | ||||||||
\(307\) | −4.94943e8 | −0.976272 | −0.488136 | − | 0.872767i | \(-0.662323\pi\) | ||||
−0.488136 | + | 0.872767i | \(0.662323\pi\) | |||||||
\(308\) | 9.21370e7 | 0.179683 | ||||||||
\(309\) | −3.92532e7 | −0.0756869 | ||||||||
\(310\) | 1.68422e8 | 0.321094 | ||||||||
\(311\) | −6.81862e8 | −1.28539 | −0.642695 | − | 0.766122i | \(-0.722184\pi\) | ||||
−0.642695 | + | 0.766122i | \(0.722184\pi\) | |||||||
\(312\) | −2.53394e7 | −0.0472340 | ||||||||
\(313\) | −2.57050e7 | −0.0473818 | −0.0236909 | − | 0.999719i | \(-0.507542\pi\) | ||||
−0.0236909 | + | 0.999719i | \(0.507542\pi\) | |||||||
\(314\) | −1.79735e8 | −0.327626 | ||||||||
\(315\) | 5.89324e7 | 0.106235 | ||||||||
\(316\) | 3.54436e8 | 0.631879 | ||||||||
\(317\) | 7.39662e8 | 1.30415 | 0.652073 | − | 0.758157i | \(-0.273900\pi\) | ||||
0.652073 | + | 0.758157i | \(0.273900\pi\) | |||||||
\(318\) | −1.99447e8 | −0.347803 | ||||||||
\(319\) | −2.29313e8 | −0.395513 | ||||||||
\(320\) | −6.16038e7 | −0.105095 | ||||||||
\(321\) | 5.93722e8 | 1.00188 | ||||||||
\(322\) | 2.35123e8 | 0.392463 | ||||||||
\(323\) | −1.85854e8 | −0.306876 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 4.19757e7 | 0.0678276 | ||||||||
\(326\) | −5.86128e8 | −0.936981 | ||||||||
\(327\) | 3.45148e8 | 0.545868 | ||||||||
\(328\) | 2.81966e8 | 0.441203 | ||||||||
\(329\) | −8.92260e7 | −0.138136 | ||||||||
\(330\) | 2.12431e8 | 0.325401 | ||||||||
\(331\) | −6.53666e8 | −0.990735 | −0.495368 | − | 0.868683i | \(-0.664967\pi\) | ||||
−0.495368 | + | 0.868683i | \(0.664967\pi\) | |||||||
\(332\) | 3.42612e8 | 0.513830 | ||||||||
\(333\) | 2.21558e7 | 0.0328800 | ||||||||
\(334\) | −1.78737e8 | −0.262484 | ||||||||
\(335\) | 8.67911e7 | 0.126130 | ||||||||
\(336\) | −3.80436e7 | −0.0547135 | ||||||||
\(337\) | −5.68180e8 | −0.808689 | −0.404345 | − | 0.914607i | \(-0.632500\pi\) | ||||
−0.404345 | + | 0.914607i | \(0.632500\pi\) | |||||||
\(338\) | −4.75109e8 | −0.669245 | ||||||||
\(339\) | 6.86227e8 | 0.956684 | ||||||||
\(340\) | −7.38915e7 | −0.101957 | ||||||||
\(341\) | 3.74917e8 | 0.512030 | ||||||||
\(342\) | −2.20619e8 | −0.298230 | ||||||||
\(343\) | 5.25890e8 | 0.703664 | ||||||||
\(344\) | −2.22263e8 | −0.294383 | ||||||||
\(345\) | 5.42098e8 | 0.710740 | ||||||||
\(346\) | 2.48690e8 | 0.322769 | ||||||||
\(347\) | −8.79203e8 | −1.12963 | −0.564815 | − | 0.825218i | \(-0.691052\pi\) | ||||
−0.564815 | + | 0.825218i | \(0.691052\pi\) | |||||||
\(348\) | 9.46840e7 | 0.120434 | ||||||||
\(349\) | −3.28412e8 | −0.413551 | −0.206776 | − | 0.978388i | \(-0.566297\pi\) | ||||
−0.206776 | + | 0.978388i | \(0.566297\pi\) | |||||||
\(350\) | 6.30208e7 | 0.0785680 | ||||||||
\(351\) | −3.60789e7 | −0.0445327 | ||||||||
\(352\) | −1.37134e8 | −0.167589 | ||||||||
\(353\) | −5.34888e8 | −0.647219 | −0.323610 | − | 0.946191i | \(-0.604896\pi\) | ||||
−0.323610 | + | 0.946191i | \(0.604896\pi\) | |||||||
\(354\) | −2.85220e8 | −0.341718 | ||||||||
\(355\) | 6.44435e8 | 0.764504 | ||||||||
\(356\) | −2.73266e8 | −0.321005 | ||||||||
\(357\) | −4.56319e7 | −0.0530799 | ||||||||
\(358\) | −3.30862e8 | −0.381115 | ||||||||
\(359\) | −5.70927e8 | −0.651253 | −0.325627 | − | 0.945498i | \(-0.605575\pi\) | ||||
−0.325627 | + | 0.945498i | \(0.605575\pi\) | |||||||
\(360\) | −8.77133e7 | −0.0990847 | ||||||||
\(361\) | 5.37162e8 | 0.600938 | ||||||||
\(362\) | −9.87383e7 | −0.109397 | ||||||||
\(363\) | −5.32695e7 | −0.0584529 | ||||||||
\(364\) | 4.03553e7 | 0.0438577 | ||||||||
\(365\) | −2.59009e8 | −0.278798 | ||||||||
\(366\) | 2.57722e8 | 0.274769 | ||||||||
\(367\) | 4.94074e8 | 0.521748 | 0.260874 | − | 0.965373i | \(-0.415989\pi\) | ||||
0.260874 | + | 0.965373i | \(0.415989\pi\) | |||||||
\(368\) | −3.49950e8 | −0.366048 | ||||||||
\(369\) | 4.01471e8 | 0.415970 | ||||||||
\(370\) | −5.71370e7 | −0.0586423 | ||||||||
\(371\) | 3.17638e8 | 0.322941 | ||||||||
\(372\) | −1.54805e8 | −0.155913 | ||||||||
\(373\) | −1.58450e8 | −0.158092 | −0.0790461 | − | 0.996871i | \(-0.525187\pi\) | ||||
−0.0790461 | + | 0.996871i | \(0.525187\pi\) | |||||||
\(374\) | −1.64487e8 | −0.162585 | ||||||||
\(375\) | 6.41004e8 | 0.627698 | ||||||||
\(376\) | 1.32802e8 | 0.128838 | ||||||||
\(377\) | −1.00437e8 | −0.0965385 | ||||||||
\(378\) | −5.41676e7 | −0.0515844 | ||||||||
\(379\) | −1.54108e9 | −1.45408 | −0.727038 | − | 0.686597i | \(-0.759104\pi\) | ||||
−0.727038 | + | 0.686597i | \(0.759104\pi\) | |||||||
\(380\) | 5.68948e8 | 0.531900 | ||||||||
\(381\) | 2.97596e8 | 0.275670 | ||||||||
\(382\) | 3.76629e8 | 0.345694 | ||||||||
\(383\) | −1.33583e9 | −1.21495 | −0.607473 | − | 0.794340i | \(-0.707817\pi\) | ||||
−0.607473 | + | 0.794340i | \(0.707817\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | −3.38315e8 | −0.302141 | ||||||||
\(386\) | −5.27333e8 | −0.466691 | ||||||||
\(387\) | −3.16464e8 | −0.277547 | ||||||||
\(388\) | −6.42136e8 | −0.558105 | ||||||||
\(389\) | 1.68908e9 | 1.45488 | 0.727441 | − | 0.686170i | \(-0.240709\pi\) | ||||
0.727441 | + | 0.686170i | \(0.240709\pi\) | |||||||
\(390\) | 9.30431e7 | 0.0794251 | ||||||||
\(391\) | −4.19752e8 | −0.355119 | ||||||||
\(392\) | −3.61066e8 | −0.302751 | ||||||||
\(393\) | 1.03627e9 | 0.861191 | ||||||||
\(394\) | −1.15553e9 | −0.951800 | ||||||||
\(395\) | −1.30145e9 | −1.06252 | ||||||||
\(396\) | −1.95255e8 | −0.158005 | ||||||||
\(397\) | 8.70907e8 | 0.698562 | 0.349281 | − | 0.937018i | \(-0.386426\pi\) | ||||
0.349281 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(398\) | −1.70721e9 | −1.35736 | ||||||||
\(399\) | 3.51356e8 | 0.276912 | ||||||||
\(400\) | −9.37984e7 | −0.0732800 | ||||||||
\(401\) | 1.97489e9 | 1.52946 | 0.764731 | − | 0.644350i | \(-0.222872\pi\) | ||||
0.764731 | + | 0.644350i | \(0.222872\pi\) | |||||||
\(402\) | −7.97740e7 | −0.0612449 | ||||||||
\(403\) | 1.64211e8 | 0.124978 | ||||||||
\(404\) | 5.93731e7 | 0.0447976 | ||||||||
\(405\) | −1.24889e8 | −0.0934180 | ||||||||
\(406\) | −1.50793e8 | −0.111825 | ||||||||
\(407\) | −1.27191e8 | −0.0935135 | ||||||||
\(408\) | 6.79173e7 | 0.0495074 | ||||||||
\(409\) | −7.48222e8 | −0.540753 | −0.270376 | − | 0.962755i | \(-0.587148\pi\) | ||||
−0.270376 | + | 0.962755i | \(0.587148\pi\) | |||||||
\(410\) | −1.03534e9 | −0.741893 | ||||||||
\(411\) | −4.15295e8 | −0.295060 | ||||||||
\(412\) | −9.30447e7 | −0.0655468 | ||||||||
\(413\) | 4.54239e8 | 0.317292 | ||||||||
\(414\) | −4.98269e8 | −0.345114 | ||||||||
\(415\) | −1.25803e9 | −0.864017 | ||||||||
\(416\) | −6.00637e7 | −0.0409059 | ||||||||
\(417\) | −3.32294e8 | −0.224412 | ||||||||
\(418\) | 1.26651e9 | 0.848190 | ||||||||
\(419\) | −7.91638e8 | −0.525748 | −0.262874 | − | 0.964830i | \(-0.584670\pi\) | ||||
−0.262874 | + | 0.964830i | \(0.584670\pi\) | |||||||
\(420\) | 1.39692e8 | 0.0920021 | ||||||||
\(421\) | 1.09245e8 | 0.0713534 | 0.0356767 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356767 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(422\) | −1.41993e9 | −0.919761 | ||||||||
\(423\) | 1.89087e8 | 0.121470 | ||||||||
\(424\) | −4.72763e8 | −0.301206 | ||||||||
\(425\) | −1.12508e8 | −0.0710920 | ||||||||
\(426\) | −5.92332e8 | −0.371220 | ||||||||
\(427\) | −4.10446e8 | −0.255128 | ||||||||
\(428\) | 1.40734e9 | 0.867654 | ||||||||
\(429\) | 2.07120e8 | 0.126655 | ||||||||
\(430\) | 8.16121e8 | 0.495011 | ||||||||
\(431\) | 2.94715e9 | 1.77310 | 0.886548 | − | 0.462636i | \(-0.153096\pi\) | ||||
0.886548 | + | 0.462636i | \(0.153096\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 1.60626e9 | 0.950841 | 0.475420 | − | 0.879759i | \(-0.342296\pi\) | ||||
0.475420 | + | 0.879759i | \(0.342296\pi\) | |||||||
\(434\) | 2.46541e8 | 0.144769 | ||||||||
\(435\) | −3.47668e8 | −0.202513 | ||||||||
\(436\) | 8.18128e8 | 0.472736 | ||||||||
\(437\) | 3.23200e9 | 1.85262 | ||||||||
\(438\) | 2.38068e8 | 0.135376 | ||||||||
\(439\) | −1.11330e9 | −0.628038 | −0.314019 | − | 0.949417i | \(-0.601676\pi\) | ||||
−0.314019 | + | 0.949417i | \(0.601676\pi\) | |||||||
\(440\) | 5.03539e8 | 0.281805 | ||||||||
\(441\) | −5.14096e8 | −0.285436 | ||||||||
\(442\) | −7.20442e7 | −0.0396845 | ||||||||
\(443\) | 7.84768e8 | 0.428873 | 0.214436 | − | 0.976738i | \(-0.431209\pi\) | ||||
0.214436 | + | 0.976738i | \(0.431209\pi\) | |||||||
\(444\) | 5.25174e7 | 0.0284749 | ||||||||
\(445\) | 1.00340e9 | 0.539777 | ||||||||
\(446\) | −1.47442e9 | −0.786956 | ||||||||
\(447\) | 4.64699e8 | 0.246091 | ||||||||
\(448\) | −9.01775e7 | −0.0473833 | ||||||||
\(449\) | −2.36655e9 | −1.23382 | −0.616911 | − | 0.787033i | \(-0.711616\pi\) | ||||
−0.616911 | + | 0.787033i | \(0.711616\pi\) | |||||||
\(450\) | −1.33553e8 | −0.0690890 | ||||||||
\(451\) | −2.30474e9 | −1.18305 | ||||||||
\(452\) | 1.62661e9 | 0.828513 | ||||||||
\(453\) | −7.28272e8 | −0.368086 | ||||||||
\(454\) | 6.58383e7 | 0.0330205 | ||||||||
\(455\) | −1.48180e8 | −0.0737478 | ||||||||
\(456\) | −5.22948e8 | −0.258275 | ||||||||
\(457\) | 1.62527e9 | 0.796558 | 0.398279 | − | 0.917264i | \(-0.369608\pi\) | ||||
0.398279 | + | 0.917264i | \(0.369608\pi\) | |||||||
\(458\) | 2.47460e9 | 1.20358 | ||||||||
\(459\) | 9.67026e7 | 0.0466760 | ||||||||
\(460\) | 1.28497e9 | 0.615519 | ||||||||
\(461\) | −6.34505e8 | −0.301635 | −0.150817 | − | 0.988562i | \(-0.548191\pi\) | ||||
−0.150817 | + | 0.988562i | \(0.548191\pi\) | |||||||
\(462\) | 3.10962e8 | 0.146710 | ||||||||
\(463\) | −2.54209e9 | −1.19030 | −0.595152 | − | 0.803613i | \(-0.702908\pi\) | ||||
−0.595152 | + | 0.803613i | \(0.702908\pi\) | |||||||
\(464\) | 2.24436e8 | 0.104299 | ||||||||
\(465\) | 5.68423e8 | 0.262172 | ||||||||
\(466\) | 1.00458e9 | 0.459870 | ||||||||
\(467\) | −1.92009e8 | −0.0872392 | −0.0436196 | − | 0.999048i | \(-0.513889\pi\) | ||||
−0.0436196 | + | 0.999048i | \(0.513889\pi\) | |||||||
\(468\) | −8.55204e7 | −0.0385664 | ||||||||
\(469\) | 1.27047e8 | 0.0568671 | ||||||||
\(470\) | −4.87631e8 | −0.216645 | ||||||||
\(471\) | −6.06605e8 | −0.267506 | ||||||||
\(472\) | −6.76077e8 | −0.295937 | ||||||||
\(473\) | 1.81674e9 | 0.789366 | ||||||||
\(474\) | 1.19622e9 | 0.515927 | ||||||||
\(475\) | 8.66284e8 | 0.370879 | ||||||||
\(476\) | −1.08165e8 | −0.0459686 | ||||||||
\(477\) | −6.73134e8 | −0.283980 | ||||||||
\(478\) | 3.11110e9 | 1.30292 | ||||||||
\(479\) | −8.56817e8 | −0.356216 | −0.178108 | − | 0.984011i | \(-0.556998\pi\) | ||||
−0.178108 | + | 0.984011i | \(0.556998\pi\) | |||||||
\(480\) | −2.07913e8 | −0.0858099 | ||||||||
\(481\) | −5.57085e7 | −0.0228252 | ||||||||
\(482\) | −1.60098e9 | −0.651212 | ||||||||
\(483\) | 7.93539e8 | 0.320445 | ||||||||
\(484\) | −1.26269e8 | −0.0506217 | ||||||||
\(485\) | 2.35784e9 | 0.938466 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | 4.95013e9 | 1.94207 | 0.971036 | − | 0.238934i | \(-0.0767981\pi\) | ||||
0.971036 | + | 0.238934i | \(0.0767981\pi\) | |||||||
\(488\) | 6.10896e8 | 0.237957 | ||||||||
\(489\) | −1.97818e9 | −0.765042 | ||||||||
\(490\) | 1.32579e9 | 0.509083 | ||||||||
\(491\) | −4.17893e8 | −0.159324 | −0.0796618 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796618 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(492\) | 9.51636e8 | 0.360241 | ||||||||
\(493\) | 2.69203e8 | 0.101185 | ||||||||
\(494\) | 5.54724e8 | 0.207030 | ||||||||
\(495\) | 7.16953e8 | 0.265688 | ||||||||
\(496\) | −3.66944e8 | −0.135025 | ||||||||
\(497\) | 9.43343e8 | 0.344685 | ||||||||
\(498\) | 1.15632e9 | 0.419540 | ||||||||
\(499\) | −1.60682e9 | −0.578917 | −0.289459 | − | 0.957191i | \(-0.593475\pi\) | ||||
−0.289459 | + | 0.957191i | \(0.593475\pi\) | |||||||
\(500\) | 1.51942e9 | 0.543603 | ||||||||
\(501\) | −6.03239e8 | −0.214317 | ||||||||
\(502\) | −1.16794e9 | −0.412057 | ||||||||
\(503\) | −4.37126e8 | −0.153151 | −0.0765754 | − | 0.997064i | \(-0.524399\pi\) | ||||
−0.0765754 | + | 0.997064i | \(0.524399\pi\) | |||||||
\(504\) | −1.28397e8 | −0.0446734 | ||||||||
\(505\) | −2.18010e8 | −0.0753282 | ||||||||
\(506\) | 2.86043e9 | 0.981532 | ||||||||
\(507\) | −1.60349e9 | −0.546436 | ||||||||
\(508\) | 7.05413e8 | 0.238737 | ||||||||
\(509\) | 9.17987e8 | 0.308549 | 0.154275 | − | 0.988028i | \(-0.450696\pi\) | ||||
0.154275 | + | 0.988028i | \(0.450696\pi\) | |||||||
\(510\) | −2.49384e8 | −0.0832478 | ||||||||
\(511\) | −3.79145e8 | −0.125699 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −7.44588e8 | −0.243504 | ||||||||
\(514\) | −3.38590e9 | −1.09977 | ||||||||
\(515\) | 3.41648e8 | 0.110218 | ||||||||
\(516\) | −7.50137e8 | −0.240362 | ||||||||
\(517\) | −1.08550e9 | −0.345471 | ||||||||
\(518\) | −8.36388e7 | −0.0264395 | ||||||||
\(519\) | 8.39328e8 | 0.263540 | ||||||||
\(520\) | 2.20547e8 | 0.0687842 | ||||||||
\(521\) | −1.07807e9 | −0.333975 | −0.166987 | − | 0.985959i | \(-0.553404\pi\) | ||||
−0.166987 | + | 0.985959i | \(0.553404\pi\) | |||||||
\(522\) | 3.19559e8 | 0.0983340 | ||||||||
\(523\) | 2.82939e9 | 0.864841 | 0.432421 | − | 0.901672i | \(-0.357660\pi\) | ||||
0.432421 | + | 0.901672i | \(0.357660\pi\) | |||||||
\(524\) | 2.45635e9 | 0.745813 | ||||||||
\(525\) | 2.12695e8 | 0.0641505 | ||||||||
\(526\) | 3.74056e8 | 0.112069 | ||||||||
\(527\) | −4.40136e8 | −0.130994 | ||||||||
\(528\) | −4.62828e8 | −0.136836 | ||||||||
\(529\) | 3.89466e9 | 1.14386 | ||||||||
\(530\) | 1.73593e9 | 0.506485 | ||||||||
\(531\) | −9.62617e8 | −0.279012 | ||||||||
\(532\) | 8.32843e8 | 0.239813 | ||||||||
\(533\) | −1.00946e9 | −0.288765 | ||||||||
\(534\) | −9.22274e8 | −0.262099 | ||||||||
\(535\) | −5.16758e9 | −1.45898 | ||||||||
\(536\) | −1.89094e8 | −0.0530397 | ||||||||
\(537\) | −1.11666e9 | −0.311179 | ||||||||
\(538\) | −2.28362e9 | −0.632247 | ||||||||
\(539\) | 2.95129e9 | 0.811804 | ||||||||
\(540\) | −2.96032e8 | −0.0809023 | ||||||||
\(541\) | −4.17298e9 | −1.13307 | −0.566534 | − | 0.824038i | \(-0.691716\pi\) | ||||
−0.566534 | + | 0.824038i | \(0.691716\pi\) | |||||||
\(542\) | −1.37635e9 | −0.371307 | ||||||||
\(543\) | −3.33242e8 | −0.0893223 | ||||||||
\(544\) | 1.60989e8 | 0.0428746 | ||||||||
\(545\) | −3.00406e9 | −0.794916 | ||||||||
\(546\) | 1.36199e8 | 0.0358097 | ||||||||
\(547\) | −4.42040e9 | −1.15480 | −0.577399 | − | 0.816462i | \(-0.695932\pi\) | ||||
−0.577399 | + | 0.816462i | \(0.695932\pi\) | |||||||
\(548\) | −9.84402e8 | −0.255529 | ||||||||
\(549\) | 8.69811e8 | 0.224348 | ||||||||
\(550\) | 7.66692e8 | 0.196495 | ||||||||
\(551\) | −2.07280e9 | −0.527870 | ||||||||
\(552\) | −1.18108e9 | −0.298877 | ||||||||
\(553\) | −1.90510e9 | −0.479048 | ||||||||
\(554\) | 2.30654e9 | 0.576336 | ||||||||
\(555\) | −1.92837e8 | −0.0478812 | ||||||||
\(556\) | −7.87661e8 | −0.194347 | ||||||||
\(557\) | 6.40759e9 | 1.57109 | 0.785546 | − | 0.618804i | \(-0.212382\pi\) | ||||
0.785546 | + | 0.618804i | \(0.212382\pi\) | |||||||
\(558\) | −5.22466e8 | −0.127303 | ||||||||
\(559\) | 7.95718e8 | 0.192672 | ||||||||
\(560\) | 3.31121e8 | 0.0796761 | ||||||||
\(561\) | −5.55144e8 | −0.132750 | ||||||||
\(562\) | 4.42730e8 | 0.105211 | ||||||||
\(563\) | −2.40800e9 | −0.568693 | −0.284346 | − | 0.958722i | \(-0.591777\pi\) | ||||
−0.284346 | + | 0.958722i | \(0.591777\pi\) | |||||||
\(564\) | 4.48205e8 | 0.105196 | ||||||||
\(565\) | −5.97271e9 | −1.39316 | ||||||||
\(566\) | 5.40246e8 | 0.125238 | ||||||||
\(567\) | −1.82816e8 | −0.0421185 | ||||||||
\(568\) | −1.40405e9 | −0.321486 | ||||||||
\(569\) | −6.98204e9 | −1.58887 | −0.794437 | − | 0.607346i | \(-0.792234\pi\) | ||||
−0.794437 | + | 0.607346i | \(0.792234\pi\) | |||||||
\(570\) | 1.92020e9 | 0.434295 | ||||||||
\(571\) | 2.32773e9 | 0.523245 | 0.261623 | − | 0.965170i | \(-0.415742\pi\) | ||||
0.261623 | + | 0.965170i | \(0.415742\pi\) | |||||||
\(572\) | 4.90951e8 | 0.109686 | ||||||||
\(573\) | 1.27112e9 | 0.282258 | ||||||||
\(574\) | −1.51557e9 | −0.334490 | ||||||||
\(575\) | 1.95651e9 | 0.429184 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 7.31947e9 | 1.58622 | 0.793111 | − | 0.609077i | \(-0.208460\pi\) | ||||
0.793111 | + | 0.609077i | \(0.208460\pi\) | |||||||
\(578\) | 1.93101e8 | 0.0415945 | ||||||||
\(579\) | −1.77975e9 | −0.381052 | ||||||||
\(580\) | −8.24102e8 | −0.175381 | ||||||||
\(581\) | −1.84154e9 | −0.389551 | ||||||||
\(582\) | −2.16721e9 | −0.455691 | ||||||||
\(583\) | 3.86429e9 | 0.807662 | ||||||||
\(584\) | 5.64309e8 | 0.117239 | ||||||||
\(585\) | 3.14020e8 | 0.0648503 | ||||||||
\(586\) | −1.23788e9 | −0.254119 | ||||||||
\(587\) | −1.98324e9 | −0.404707 | −0.202354 | − | 0.979313i | \(-0.564859\pi\) | ||||
−0.202354 | + | 0.979313i | \(0.564859\pi\) | |||||||
\(588\) | −1.21860e9 | −0.247195 | ||||||||
\(589\) | 3.38895e9 | 0.683379 | ||||||||
\(590\) | 2.48247e9 | 0.497624 | ||||||||
\(591\) | −3.89993e9 | −0.777142 | ||||||||
\(592\) | 1.24486e8 | 0.0246600 | ||||||||
\(593\) | −2.61002e9 | −0.513988 | −0.256994 | − | 0.966413i | \(-0.582732\pi\) | ||||
−0.256994 | + | 0.966413i | \(0.582732\pi\) | |||||||
\(594\) | −6.58987e8 | −0.129010 | ||||||||
\(595\) | 3.97167e8 | 0.0772972 | ||||||||
\(596\) | 1.10151e9 | 0.213121 | ||||||||
\(597\) | −5.76183e9 | −1.10828 | ||||||||
\(598\) | 1.25285e9 | 0.239577 | ||||||||
\(599\) | −3.38989e9 | −0.644453 | −0.322227 | − | 0.946663i | \(-0.604431\pi\) | ||||
−0.322227 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(600\) | −3.16570e8 | −0.0598329 | ||||||||
\(601\) | 2.12243e9 | 0.398816 | 0.199408 | − | 0.979917i | \(-0.436098\pi\) | ||||
0.199408 | + | 0.979917i | \(0.436098\pi\) | |||||||
\(602\) | 1.19466e9 | 0.223181 | ||||||||
\(603\) | −2.69237e8 | −0.0500063 | ||||||||
\(604\) | −1.72627e9 | −0.318772 | ||||||||
\(605\) | 4.63642e8 | 0.0851215 | ||||||||
\(606\) | 2.00384e8 | 0.0365771 | ||||||||
\(607\) | 4.83573e9 | 0.877610 | 0.438805 | − | 0.898582i | \(-0.355402\pi\) | ||||
0.438805 | + | 0.898582i | \(0.355402\pi\) | |||||||
\(608\) | −1.23958e9 | −0.223672 | ||||||||
\(609\) | −5.08927e8 | −0.0913050 | ||||||||
\(610\) | −2.24313e9 | −0.400130 | ||||||||
\(611\) | −4.75440e8 | −0.0843240 | ||||||||
\(612\) | 2.29221e8 | 0.0404226 | ||||||||
\(613\) | −8.79032e9 | −1.54132 | −0.770661 | − | 0.637246i | \(-0.780074\pi\) | ||||
−0.770661 | + | 0.637246i | \(0.780074\pi\) | |||||||
\(614\) | −3.95955e9 | −0.690329 | ||||||||
\(615\) | −3.49429e9 | −0.605753 | ||||||||
\(616\) | 7.37096e8 | 0.127055 | ||||||||
\(617\) | −3.23362e9 | −0.554231 | −0.277116 | − | 0.960837i | \(-0.589379\pi\) | ||||
−0.277116 | + | 0.960837i | \(0.589379\pi\) | |||||||
\(618\) | −3.14026e8 | −0.0535187 | ||||||||
\(619\) | 4.02310e9 | 0.681780 | 0.340890 | − | 0.940103i | \(-0.389272\pi\) | ||||
0.340890 | + | 0.940103i | \(0.389272\pi\) | |||||||
\(620\) | 1.34737e9 | 0.227048 | ||||||||
\(621\) | −1.68166e9 | −0.281784 | ||||||||
\(622\) | −5.45490e9 | −0.908908 | ||||||||
\(623\) | 1.46881e9 | 0.243364 | ||||||||
\(624\) | −2.02715e8 | −0.0333995 | ||||||||
\(625\) | −3.79004e9 | −0.620961 | ||||||||
\(626\) | −2.05640e8 | −0.0335040 | ||||||||
\(627\) | 4.27449e9 | 0.692545 | ||||||||
\(628\) | −1.43788e9 | −0.231667 | ||||||||
\(629\) | 1.49316e8 | 0.0239237 | ||||||||
\(630\) | 4.71459e8 | 0.0751194 | ||||||||
\(631\) | −1.15616e10 | −1.83195 | −0.915977 | − | 0.401231i | \(-0.868582\pi\) | ||||
−0.915977 | + | 0.401231i | \(0.868582\pi\) | |||||||
\(632\) | 2.83549e9 | 0.446806 | ||||||||
\(633\) | −4.79228e9 | −0.750981 | ||||||||
\(634\) | 5.91730e9 | 0.922170 | ||||||||
\(635\) | −2.59019e9 | −0.401442 | ||||||||
\(636\) | −1.59558e9 | −0.245934 | ||||||||
\(637\) | 1.29264e9 | 0.198149 | ||||||||
\(638\) | −1.83450e9 | −0.279670 | ||||||||
\(639\) | −1.99912e9 | −0.303100 | ||||||||
\(640\) | −4.92831e8 | −0.0743135 | ||||||||
\(641\) | 1.28560e10 | 1.92798 | 0.963990 | − | 0.265938i | \(-0.0856818\pi\) | ||||
0.963990 | + | 0.265938i | \(0.0856818\pi\) | |||||||
\(642\) | 4.74978e9 | 0.708436 | ||||||||
\(643\) | −2.59277e9 | −0.384614 | −0.192307 | − | 0.981335i | \(-0.561597\pi\) | ||||
−0.192307 | + | 0.981335i | \(0.561597\pi\) | |||||||
\(644\) | 1.88098e9 | 0.277513 | ||||||||
\(645\) | 2.75441e9 | 0.404175 | ||||||||
\(646\) | −1.48683e9 | −0.216994 | ||||||||
\(647\) | −1.18826e9 | −0.172483 | −0.0862417 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862417 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 5.52613e9 | 0.793533 | ||||||||
\(650\) | 3.35806e8 | 0.0479613 | ||||||||
\(651\) | 8.32075e8 | 0.118203 | ||||||||
\(652\) | −4.68902e9 | −0.662546 | ||||||||
\(653\) | 2.53925e9 | 0.356870 | 0.178435 | − | 0.983952i | \(-0.442897\pi\) | ||||
0.178435 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(654\) | 2.76118e9 | 0.385987 | ||||||||
\(655\) | −9.01940e9 | −1.25410 | ||||||||
\(656\) | 2.25573e9 | 0.311978 | ||||||||
\(657\) | 8.03479e8 | 0.110534 | ||||||||
\(658\) | −7.13808e8 | −0.0976767 | ||||||||
\(659\) | 8.64850e9 | 1.17718 | 0.588588 | − | 0.808433i | \(-0.299684\pi\) | ||||
0.588588 | + | 0.808433i | \(0.299684\pi\) | |||||||
\(660\) | 1.69944e9 | 0.230093 | ||||||||
\(661\) | 7.25099e9 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(662\) | −5.22932e9 | −0.700556 | ||||||||
\(663\) | −2.43149e8 | −0.0324023 | ||||||||
\(664\) | 2.74090e9 | 0.363333 | ||||||||
\(665\) | −3.05810e9 | −0.403251 | ||||||||
\(666\) | 1.77246e8 | 0.0232497 | ||||||||
\(667\) | −4.68143e9 | −0.610856 | ||||||||
\(668\) | −1.42990e9 | −0.185604 | ||||||||
\(669\) | −4.97618e9 | −0.642547 | ||||||||
\(670\) | 6.94329e8 | 0.0891874 | ||||||||
\(671\) | −4.99336e9 | −0.638063 | ||||||||
\(672\) | −3.04349e8 | −0.0386883 | ||||||||
\(673\) | 5.66492e9 | 0.716376 | 0.358188 | − | 0.933650i | \(-0.383395\pi\) | ||||
0.358188 | + | 0.933650i | \(0.383395\pi\) | |||||||
\(674\) | −4.54544e9 | −0.571830 | ||||||||
\(675\) | −4.50741e8 | −0.0564110 | ||||||||
\(676\) | −3.80087e9 | −0.473227 | ||||||||
\(677\) | 9.24182e9 | 1.14471 | 0.572357 | − | 0.820004i | \(-0.306029\pi\) | ||||
0.572357 | + | 0.820004i | \(0.306029\pi\) | |||||||
\(678\) | 5.48981e9 | 0.676478 | ||||||||
\(679\) | 3.45148e9 | 0.423117 | ||||||||
\(680\) | −5.91132e8 | −0.0720947 | ||||||||
\(681\) | 2.22204e8 | 0.0269611 | ||||||||
\(682\) | 2.99934e9 | 0.362060 | ||||||||
\(683\) | 2.38058e9 | 0.285897 | 0.142949 | − | 0.989730i | \(-0.454342\pi\) | ||||
0.142949 | + | 0.989730i | \(0.454342\pi\) | |||||||
\(684\) | −1.76495e9 | −0.210880 | ||||||||
\(685\) | 3.61460e9 | 0.429678 | ||||||||
\(686\) | 4.20712e9 | 0.497566 | ||||||||
\(687\) | 8.35178e9 | 0.982722 | ||||||||
\(688\) | −1.77810e9 | −0.208160 | ||||||||
\(689\) | 1.69253e9 | 0.197137 | ||||||||
\(690\) | 4.33678e9 | 0.502569 | ||||||||
\(691\) | −4.57058e8 | −0.0526985 | −0.0263492 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263492 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(692\) | 1.98952e9 | 0.228232 | ||||||||
\(693\) | 1.04950e9 | 0.119788 | ||||||||
\(694\) | −7.03362e9 | −0.798769 | ||||||||
\(695\) | 2.89219e9 | 0.326799 | ||||||||
\(696\) | 7.57472e8 | 0.0851598 | ||||||||
\(697\) | 2.70566e9 | 0.302663 | ||||||||
\(698\) | −2.62729e9 | −0.292425 | ||||||||
\(699\) | 3.39047e9 | 0.375483 | ||||||||
\(700\) | 5.04166e8 | 0.0555560 | ||||||||
\(701\) | −3.87966e9 | −0.425383 | −0.212692 | − | 0.977119i | \(-0.568223\pi\) | ||||
−0.212692 | + | 0.977119i | \(0.568223\pi\) | |||||||
\(702\) | −2.88632e8 | −0.0314894 | ||||||||
\(703\) | −1.14970e9 | −0.124807 | ||||||||
\(704\) | −1.09707e9 | −0.118503 | ||||||||
\(705\) | −1.64575e9 | −0.176890 | ||||||||
\(706\) | −4.27910e9 | −0.457653 | ||||||||
\(707\) | −3.19130e8 | −0.0339625 | ||||||||
\(708\) | −2.28176e9 | −0.241631 | ||||||||
\(709\) | 1.50551e10 | 1.58643 | 0.793215 | − | 0.608942i | \(-0.208406\pi\) | ||||
0.793215 | + | 0.608942i | \(0.208406\pi\) | |||||||
\(710\) | 5.15548e9 | 0.540586 | ||||||||
\(711\) | 4.03725e9 | 0.421252 | ||||||||
\(712\) | −2.18613e9 | −0.226985 | ||||||||
\(713\) | 7.65396e9 | 0.790811 | ||||||||
\(714\) | −3.65056e8 | −0.0375332 | ||||||||
\(715\) | −1.80271e9 | −0.184440 | ||||||||
\(716\) | −2.64689e9 | −0.269489 | ||||||||
\(717\) | 1.05000e10 | 1.06383 | ||||||||
\(718\) | −4.56741e9 | −0.460505 | ||||||||
\(719\) | 1.19938e10 | 1.20339 | 0.601696 | − | 0.798725i | \(-0.294492\pi\) | ||||
0.601696 | + | 0.798725i | \(0.294492\pi\) | |||||||
\(720\) | −7.01706e8 | −0.0700635 | ||||||||
\(721\) | 5.00115e8 | 0.0496932 | ||||||||
\(722\) | 4.29729e9 | 0.424927 | ||||||||
\(723\) | −5.40332e9 | −0.531712 | ||||||||
\(724\) | −7.89907e8 | −0.0773554 | ||||||||
\(725\) | −1.25478e9 | −0.122288 | ||||||||
\(726\) | −4.26156e8 | −0.0413324 | ||||||||
\(727\) | 1.80966e10 | 1.74674 | 0.873368 | − | 0.487060i | \(-0.161931\pi\) | ||||
0.873368 | + | 0.487060i | \(0.161931\pi\) | |||||||
\(728\) | 3.22843e8 | 0.0310121 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −2.07207e9 | −0.197140 | ||||||||
\(731\) | −2.13277e9 | −0.201945 | ||||||||
\(732\) | 2.06177e9 | 0.194291 | ||||||||
\(733\) | 4.43663e9 | 0.416092 | 0.208046 | − | 0.978119i | \(-0.433290\pi\) | ||||
0.208046 | + | 0.978119i | \(0.433290\pi\) | |||||||
\(734\) | 3.95259e9 | 0.368932 | ||||||||
\(735\) | 4.47454e9 | 0.415664 | ||||||||
\(736\) | −2.79960e9 | −0.258835 | ||||||||
\(737\) | 1.54562e9 | 0.142222 | ||||||||
\(738\) | 3.21177e9 | 0.294135 | ||||||||
\(739\) | −3.90799e9 | −0.356203 | −0.178102 | − | 0.984012i | \(-0.556996\pi\) | ||||
−0.178102 | + | 0.984012i | \(0.556996\pi\) | |||||||
\(740\) | −4.57096e8 | −0.0414664 | ||||||||
\(741\) | 1.87220e9 | 0.169039 | ||||||||
\(742\) | 2.54110e9 | 0.228354 | ||||||||
\(743\) | 4.26083e9 | 0.381095 | 0.190548 | − | 0.981678i | \(-0.438974\pi\) | ||||
0.190548 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(744\) | −1.23844e9 | −0.110247 | ||||||||
\(745\) | −4.04460e9 | −0.358368 | ||||||||
\(746\) | −1.26760e9 | −0.111788 | ||||||||
\(747\) | 3.90257e9 | 0.342553 | ||||||||
\(748\) | −1.31590e9 | −0.114965 | ||||||||
\(749\) | −7.56446e9 | −0.657797 | ||||||||
\(750\) | 5.12803e9 | 0.443850 | ||||||||
\(751\) | 2.18517e10 | 1.88255 | 0.941274 | − | 0.337643i | \(-0.109630\pi\) | ||||
0.941274 | + | 0.337643i | \(0.109630\pi\) | |||||||
\(752\) | 1.06241e9 | 0.0911026 | ||||||||
\(753\) | −3.94179e9 | −0.336443 | ||||||||
\(754\) | −8.03499e8 | −0.0682631 | ||||||||
\(755\) | 6.33866e9 | 0.536023 | ||||||||
\(756\) | −4.33341e8 | −0.0364757 | ||||||||
\(757\) | −3.81516e9 | −0.319652 | −0.159826 | − | 0.987145i | \(-0.551093\pi\) | ||||
−0.159826 | + | 0.987145i | \(0.551093\pi\) | |||||||
\(758\) | −1.23286e10 | −1.02819 | ||||||||
\(759\) | 9.65395e9 | 0.801418 | ||||||||
\(760\) | 4.55159e9 | 0.376110 | ||||||||
\(761\) | −1.45183e10 | −1.19418 | −0.597090 | − | 0.802174i | \(-0.703676\pi\) | ||||
−0.597090 | + | 0.802174i | \(0.703676\pi\) | |||||||
\(762\) | 2.38077e9 | 0.194928 | ||||||||
\(763\) | −4.39744e9 | −0.358396 | ||||||||
\(764\) | 3.01303e9 | 0.244443 | ||||||||
\(765\) | −8.41671e8 | −0.0679715 | ||||||||
\(766\) | −1.06867e10 | −0.859096 | ||||||||
\(767\) | 2.42041e9 | 0.193689 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 1.36277e10 | 1.08064 | 0.540318 | − | 0.841461i | \(-0.318304\pi\) | ||||
0.540318 | + | 0.841461i | \(0.318304\pi\) | |||||||
\(770\) | −2.70652e9 | −0.213646 | ||||||||
\(771\) | −1.14274e10 | −0.897962 | ||||||||
\(772\) | −4.21867e9 | −0.330000 | ||||||||
\(773\) | −2.29018e10 | −1.78337 | −0.891685 | − | 0.452657i | \(-0.850476\pi\) | ||||
−0.891685 | + | 0.452657i | \(0.850476\pi\) | |||||||
\(774\) | −2.53171e9 | −0.196255 | ||||||||
\(775\) | 2.05152e9 | 0.158314 | ||||||||
\(776\) | −5.13708e9 | −0.394640 | ||||||||
\(777\) | −2.82281e8 | −0.0215878 | ||||||||
\(778\) | 1.35127e10 | 1.02876 | ||||||||
\(779\) | −2.08330e10 | −1.57896 | ||||||||
\(780\) | 7.44345e8 | 0.0561621 | ||||||||
\(781\) | 1.14764e10 | 0.862041 | ||||||||
\(782\) | −3.35802e9 | −0.251107 | ||||||||
\(783\) | 1.07851e9 | 0.0802894 | ||||||||
\(784\) | −2.88853e9 | −0.214077 | ||||||||
\(785\) | 5.27971e9 | 0.389553 | ||||||||
\(786\) | 8.29017e9 | 0.608954 | ||||||||
\(787\) | −7.48603e8 | −0.0547444 | −0.0273722 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273722 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(788\) | −9.24427e9 | −0.673025 | ||||||||
\(789\) | 1.26244e9 | 0.0915041 | ||||||||
\(790\) | −1.04116e10 | −0.751314 | ||||||||
\(791\) | −8.74304e9 | −0.628123 | ||||||||
\(792\) | −1.56204e9 | −0.111726 | ||||||||
\(793\) | −2.18705e9 | −0.155741 | ||||||||
\(794\) | 6.96725e9 | 0.493958 | ||||||||
\(795\) | 5.85876e9 | 0.413543 | ||||||||
\(796\) | −1.36577e10 | −0.959800 | ||||||||
\(797\) | −1.65797e10 | −1.16004 | −0.580020 | − | 0.814602i | \(-0.696955\pi\) | ||||
−0.580020 | + | 0.814602i | \(0.696955\pi\) | |||||||
\(798\) | 2.81085e9 | 0.195806 | ||||||||
\(799\) | 1.27432e9 | 0.0883825 | ||||||||
\(800\) | −7.50387e8 | −0.0518168 | ||||||||
\(801\) | −3.11268e9 | −0.214003 | ||||||||
\(802\) | 1.57992e10 | 1.08149 | ||||||||
\(803\) | −4.61256e9 | −0.314368 | ||||||||
\(804\) | −6.38192e8 | −0.0433067 | ||||||||
\(805\) | −6.90673e9 | −0.466645 | ||||||||
\(806\) | 1.31369e9 | 0.0883731 | ||||||||
\(807\) | −7.70723e9 | −0.516227 | ||||||||
\(808\) | 4.74984e8 | 0.0316767 | ||||||||
\(809\) | 1.50355e9 | 0.0998387 | 0.0499194 | − | 0.998753i | \(-0.484104\pi\) | ||||
0.0499194 | + | 0.998753i | \(0.484104\pi\) | |||||||
\(810\) | −9.99109e8 | −0.0660565 | ||||||||
\(811\) | −2.23679e10 | −1.47249 | −0.736243 | − | 0.676717i | \(-0.763402\pi\) | ||||
−0.736243 | + | 0.676717i | \(0.763402\pi\) | |||||||
\(812\) | −1.20634e9 | −0.0790725 | ||||||||
\(813\) | −4.64520e9 | −0.303171 | ||||||||
\(814\) | −1.01752e9 | −0.0661240 | ||||||||
\(815\) | 1.72175e10 | 1.11409 | ||||||||
\(816\) | 5.43338e8 | 0.0350070 | ||||||||
\(817\) | 1.64218e10 | 1.05352 | ||||||||
\(818\) | −5.98577e9 | −0.382370 | ||||||||
\(819\) | 4.59672e8 | 0.0292385 | ||||||||
\(820\) | −8.28275e9 | −0.524598 | ||||||||
\(821\) | −1.53966e10 | −0.971008 | −0.485504 | − | 0.874234i | \(-0.661364\pi\) | ||||
−0.485504 | + | 0.874234i | \(0.661364\pi\) | |||||||
\(822\) | −3.32236e9 | −0.208639 | ||||||||
\(823\) | 1.18952e10 | 0.743829 | 0.371914 | − | 0.928267i | \(-0.378701\pi\) | ||||
0.371914 | + | 0.928267i | \(0.378701\pi\) | |||||||
\(824\) | −7.44357e8 | −0.0463486 | ||||||||
\(825\) | 2.58759e9 | 0.160438 | ||||||||
\(826\) | 3.63391e9 | 0.224359 | ||||||||
\(827\) | 1.84279e10 | 1.13294 | 0.566468 | − | 0.824084i | \(-0.308309\pi\) | ||||
0.566468 | + | 0.824084i | \(0.308309\pi\) | |||||||
\(828\) | −3.98615e9 | −0.244032 | ||||||||
\(829\) | 6.56187e9 | 0.400025 | 0.200012 | − | 0.979793i | \(-0.435902\pi\) | ||||
0.200012 | + | 0.979793i | \(0.435902\pi\) | |||||||
\(830\) | −1.00642e10 | −0.610952 | ||||||||
\(831\) | 7.78456e9 | 0.470577 | ||||||||
\(832\) | −4.80510e8 | −0.0289248 | ||||||||
\(833\) | −3.46468e9 | −0.207685 | ||||||||
\(834\) | −2.65835e9 | −0.158683 | ||||||||
\(835\) | 5.25041e9 | 0.312098 | ||||||||
\(836\) | 1.01321e10 | 0.599761 | ||||||||
\(837\) | −1.76332e9 | −0.103942 | ||||||||
\(838\) | −6.33311e9 | −0.371760 | ||||||||
\(839\) | −2.58040e10 | −1.50841 | −0.754205 | − | 0.656639i | \(-0.771978\pi\) | ||||
−0.754205 | + | 0.656639i | \(0.771978\pi\) | |||||||
\(840\) | 1.11753e9 | 0.0650553 | ||||||||
\(841\) | −1.42475e10 | −0.825948 | ||||||||
\(842\) | 8.73961e8 | 0.0504545 | ||||||||
\(843\) | 1.49422e9 | 0.0859047 | ||||||||
\(844\) | −1.13595e10 | −0.650369 | ||||||||
\(845\) | 1.39563e10 | 0.795743 | ||||||||
\(846\) | 1.51269e9 | 0.0858923 | ||||||||
\(847\) | 6.78693e8 | 0.0383779 | ||||||||
\(848\) | −3.78211e9 | −0.212985 | ||||||||
\(849\) | 1.82333e9 | 0.102256 | ||||||||
\(850\) | −9.00062e8 | −0.0502697 | ||||||||
\(851\) | −2.59660e9 | −0.144428 | ||||||||
\(852\) | −4.73865e9 | −0.262492 | ||||||||
\(853\) | 9.66749e7 | 0.00533325 | 0.00266663 | − | 0.999996i | \(-0.499151\pi\) | ||||
0.00266663 | + | 0.999996i | \(0.499151\pi\) | |||||||
\(854\) | −3.28357e9 | −0.180403 | ||||||||
\(855\) | 6.48068e9 | 0.354600 | ||||||||
\(856\) | 1.12587e10 | 0.613524 | ||||||||
\(857\) | −5.64116e9 | −0.306151 | −0.153075 | − | 0.988215i | \(-0.548918\pi\) | ||||
−0.153075 | + | 0.988215i | \(0.548918\pi\) | |||||||
\(858\) | 1.65696e9 | 0.0895584 | ||||||||
\(859\) | −1.62139e10 | −0.872792 | −0.436396 | − | 0.899755i | \(-0.643745\pi\) | ||||
−0.436396 | + | 0.899755i | \(0.643745\pi\) | |||||||
\(860\) | 6.52897e9 | 0.350026 | ||||||||
\(861\) | −5.11504e9 | −0.273110 | ||||||||
\(862\) | 2.35772e10 | 1.25377 | ||||||||
\(863\) | −2.17887e10 | −1.15397 | −0.576983 | − | 0.816756i | \(-0.695770\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | −7.30526e9 | −0.383778 | ||||||||
\(866\) | 1.28501e10 | 0.672346 | ||||||||
\(867\) | 6.51714e8 | 0.0339618 | ||||||||
\(868\) | 1.97233e9 | 0.102367 | ||||||||
\(869\) | −2.31768e10 | −1.19808 | ||||||||
\(870\) | −2.78134e9 | −0.143198 | ||||||||
\(871\) | 6.76971e8 | 0.0347141 | ||||||||
\(872\) | 6.54502e9 | 0.334275 | ||||||||
\(873\) | −7.31433e9 | −0.372070 | ||||||||
\(874\) | 2.58560e10 | 1.31000 | ||||||||
\(875\) | −8.16686e9 | −0.412123 | ||||||||
\(876\) | 1.90454e9 | 0.0957252 | ||||||||
\(877\) | 1.57947e10 | 0.790700 | 0.395350 | − | 0.918531i | \(-0.370623\pi\) | ||||
0.395350 | + | 0.918531i | \(0.370623\pi\) | |||||||
\(878\) | −8.90640e9 | −0.444090 | ||||||||
\(879\) | −4.17785e9 | −0.207487 | ||||||||
\(880\) | 4.02831e9 | 0.199266 | ||||||||
\(881\) | −3.46306e10 | −1.70626 | −0.853128 | − | 0.521702i | \(-0.825297\pi\) | ||||
−0.853128 | + | 0.521702i | \(0.825297\pi\) | |||||||
\(882\) | −4.11277e9 | −0.201834 | ||||||||
\(883\) | 7.20168e9 | 0.352023 | 0.176012 | − | 0.984388i | \(-0.443680\pi\) | ||||
0.176012 | + | 0.984388i | \(0.443680\pi\) | |||||||
\(884\) | −5.76354e8 | −0.0280612 | ||||||||
\(885\) | 8.37833e9 | 0.406309 | ||||||||
\(886\) | 6.27814e9 | 0.303259 | ||||||||
\(887\) | −7.76600e8 | −0.0373650 | −0.0186825 | − | 0.999825i | \(-0.505947\pi\) | ||||
−0.0186825 | + | 0.999825i | \(0.505947\pi\) | |||||||
\(888\) | 4.20139e8 | 0.0201348 | ||||||||
\(889\) | −3.79159e9 | −0.180995 | ||||||||
\(890\) | 8.02720e9 | 0.381680 | ||||||||
\(891\) | −2.22408e9 | −0.105336 | ||||||||
\(892\) | −1.17954e10 | −0.556462 | ||||||||
\(893\) | −9.81201e9 | −0.461082 | ||||||||
\(894\) | 3.71759e9 | 0.174012 | ||||||||
\(895\) | 9.71906e9 | 0.453152 | ||||||||
\(896\) | −7.21420e8 | −0.0335051 | ||||||||
\(897\) | 4.22836e9 | 0.195613 | ||||||||
\(898\) | −1.89324e10 | −0.872444 | ||||||||
\(899\) | −4.90878e9 | −0.225328 | ||||||||
\(900\) | −1.06842e9 | −0.0488533 | ||||||||
\(901\) | −4.53650e9 | −0.206625 | ||||||||
\(902\) | −1.84379e10 | −0.836545 | ||||||||
\(903\) | 4.03199e9 | 0.182227 | ||||||||
\(904\) | 1.30129e10 | 0.585847 | ||||||||
\(905\) | 2.90044e9 | 0.130075 | ||||||||
\(906\) | −5.82617e9 | −0.260276 | ||||||||
\(907\) | 7.02650e9 | 0.312690 | 0.156345 | − | 0.987703i | \(-0.450029\pi\) | ||||
0.156345 | + | 0.987703i | \(0.450029\pi\) | |||||||
\(908\) | 5.26707e8 | 0.0233490 | ||||||||
\(909\) | 6.76296e8 | 0.0298651 | ||||||||
\(910\) | −1.18544e9 | −0.0521475 | ||||||||
\(911\) | 3.87256e10 | 1.69701 | 0.848503 | − | 0.529190i | \(-0.177504\pi\) | ||||
0.848503 | + | 0.529190i | \(0.177504\pi\) | |||||||
\(912\) | −4.18358e9 | −0.182628 | ||||||||
\(913\) | −2.24036e10 | −0.974250 | ||||||||
\(914\) | 1.30021e10 | 0.563252 | ||||||||
\(915\) | −7.57057e9 | −0.326704 | ||||||||
\(916\) | 1.97968e10 | 0.851062 | ||||||||
\(917\) | −1.32029e10 | −0.565425 | ||||||||
\(918\) | 7.73621e8 | 0.0330049 | ||||||||
\(919\) | 2.34371e10 | 0.996094 | 0.498047 | − | 0.867150i | \(-0.334051\pi\) | ||||
0.498047 | + | 0.867150i | \(0.334051\pi\) | |||||||
\(920\) | 1.02798e10 | 0.435238 | ||||||||
\(921\) | −1.33635e10 | −0.563651 | ||||||||
\(922\) | −5.07604e9 | −0.213288 | ||||||||
\(923\) | 5.02659e9 | 0.210411 | ||||||||
\(924\) | 2.48770e9 | 0.103740 | ||||||||
\(925\) | −6.95977e8 | −0.0289134 | ||||||||
\(926\) | −2.03367e10 | −0.841672 | ||||||||
\(927\) | −1.05984e9 | −0.0436978 | ||||||||
\(928\) | 1.79549e9 | 0.0737505 | ||||||||
\(929\) | 1.70755e10 | 0.698744 | 0.349372 | − | 0.936984i | \(-0.386395\pi\) | ||||
0.349372 | + | 0.936984i | \(0.386395\pi\) | |||||||
\(930\) | 4.54739e9 | 0.185384 | ||||||||
\(931\) | 2.66773e10 | 1.08347 | ||||||||
\(932\) | 8.03667e9 | 0.325177 | ||||||||
\(933\) | −1.84103e10 | −0.742121 | ||||||||
\(934\) | −1.53607e9 | −0.0616874 | ||||||||
\(935\) | 4.83181e9 | 0.193317 | ||||||||
\(936\) | −6.84164e8 | −0.0272706 | ||||||||
\(937\) | −4.17866e10 | −1.65939 | −0.829694 | − | 0.558218i | \(-0.811485\pi\) | ||||
−0.829694 | + | 0.558218i | \(0.811485\pi\) | |||||||
\(938\) | 1.01638e9 | 0.0402111 | ||||||||
\(939\) | −6.94034e8 | −0.0273559 | ||||||||
\(940\) | −3.90105e9 | −0.153191 | ||||||||
\(941\) | −1.20231e10 | −0.470383 | −0.235192 | − | 0.971949i | \(-0.575572\pi\) | ||||
−0.235192 | + | 0.971949i | \(0.575572\pi\) | |||||||
\(942\) | −4.85284e9 | −0.189155 | ||||||||
\(943\) | −4.70514e10 | −1.82718 | ||||||||
\(944\) | −5.40861e9 | −0.209259 | ||||||||
\(945\) | 1.59117e9 | 0.0613347 | ||||||||
\(946\) | 1.45339e10 | 0.558166 | ||||||||
\(947\) | 4.29691e10 | 1.64411 | 0.822056 | − | 0.569407i | \(-0.192827\pi\) | ||||
0.822056 | + | 0.569407i | \(0.192827\pi\) | |||||||
\(948\) | 9.56978e9 | 0.364815 | ||||||||
\(949\) | −2.02027e9 | −0.0767322 | ||||||||
\(950\) | 6.93027e9 | 0.262251 | ||||||||
\(951\) | 1.99709e10 | 0.752949 | ||||||||
\(952\) | −8.65317e8 | −0.0325047 | ||||||||
\(953\) | −3.01447e10 | −1.12820 | −0.564100 | − | 0.825706i | \(-0.690777\pi\) | ||||
−0.564100 | + | 0.825706i | \(0.690777\pi\) | |||||||
\(954\) | −5.38507e9 | −0.200804 | ||||||||
\(955\) | −1.10635e10 | −0.411036 | ||||||||
\(956\) | 2.48888e10 | 0.921301 | ||||||||
\(957\) | −6.19145e9 | −0.228350 | ||||||||
\(958\) | −6.85453e9 | −0.251883 | ||||||||
\(959\) | 5.29116e9 | 0.193725 | ||||||||
\(960\) | −1.66330e9 | −0.0606767 | ||||||||
\(961\) | −1.94870e10 | −0.708292 | ||||||||
\(962\) | −4.45668e8 | −0.0161398 | ||||||||
\(963\) | 1.60305e10 | 0.578436 | ||||||||
\(964\) | −1.28079e10 | −0.460476 | ||||||||
\(965\) | 1.54904e10 | 0.554903 | ||||||||
\(966\) | 6.34831e9 | 0.226589 | ||||||||
\(967\) | −1.06854e10 | −0.380014 | −0.190007 | − | 0.981783i | \(-0.560851\pi\) | ||||
−0.190007 | + | 0.981783i | \(0.560851\pi\) | |||||||
\(968\) | −1.01015e9 | −0.0357949 | ||||||||
\(969\) | −5.01805e9 | −0.177175 | ||||||||
\(970\) | 1.88627e10 | 0.663596 | ||||||||
\(971\) | 5.10197e10 | 1.78842 | 0.894212 | − | 0.447643i | \(-0.147737\pi\) | ||||
0.894212 | + | 0.447643i | \(0.147737\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | 4.23368e9 | 0.147341 | ||||||||
\(974\) | 3.96010e10 | 1.37325 | ||||||||
\(975\) | 1.13334e9 | 0.0391603 | ||||||||
\(976\) | 4.88717e9 | 0.168261 | ||||||||
\(977\) | −5.11414e10 | −1.75445 | −0.877226 | − | 0.480079i | \(-0.840608\pi\) | ||||
−0.877226 | + | 0.480079i | \(0.840608\pi\) | |||||||
\(978\) | −1.58255e10 | −0.540966 | ||||||||
\(979\) | 1.78691e10 | 0.608643 | ||||||||
\(980\) | 1.06063e10 | 0.359976 | ||||||||
\(981\) | 9.31898e9 | 0.315157 | ||||||||
\(982\) | −3.34315e9 | −0.112659 | ||||||||
\(983\) | −5.07243e10 | −1.70325 | −0.851626 | − | 0.524149i | \(-0.824383\pi\) | ||||
−0.851626 | + | 0.524149i | \(0.824383\pi\) | |||||||
\(984\) | 7.61308e9 | 0.254729 | ||||||||
\(985\) | 3.39438e10 | 1.13171 | ||||||||
\(986\) | 2.15362e9 | 0.0715485 | ||||||||
\(987\) | −2.40910e9 | −0.0797527 | ||||||||
\(988\) | 4.43780e9 | 0.146392 | ||||||||
\(989\) | 3.70888e10 | 1.21915 | ||||||||
\(990\) | 5.73563e9 | 0.187870 | ||||||||
\(991\) | −1.71204e10 | −0.558800 | −0.279400 | − | 0.960175i | \(-0.590136\pi\) | ||||
−0.279400 | + | 0.960175i | \(0.590136\pi\) | |||||||
\(992\) | −2.93555e9 | −0.0954771 | ||||||||
\(993\) | −1.76490e10 | −0.572001 | ||||||||
\(994\) | 7.54674e9 | 0.243729 | ||||||||
\(995\) | 5.01492e10 | 1.61393 | ||||||||
\(996\) | 9.25053e9 | 0.296660 | ||||||||
\(997\) | −6.20246e9 | −0.198213 | −0.0991063 | − | 0.995077i | \(-0.531598\pi\) | ||||
−0.0991063 | + | 0.995077i | \(0.531598\pi\) | |||||||
\(998\) | −1.28546e10 | −0.409356 | ||||||||
\(999\) | 5.98206e8 | 0.0189833 |
(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 | 102.8.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 306.8.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.8.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
306.8.a.b.1.1 | 1 | 3.2 | odd | 2 |