Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.12909 | −1.08348 | −0.541740 | − | 0.840546i | \(-0.682234\pi\) | ||||
−0.541740 | + | 0.840546i | \(0.682234\pi\) | |||||||
\(3\) | −3.52111 | −0.225880 | −0.112940 | − | 0.993602i | \(-0.536027\pi\) | ||||
−0.112940 | + | 0.993602i | \(0.536027\pi\) | |||||||
\(4\) | 5.56569 | 0.173928 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 21.5812 | 0.244736 | ||||||||
\(7\) | 66.3590 | 0.511864 | 0.255932 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255932 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(8\) | 162.018 | 0.895032 | ||||||||
\(9\) | −230.602 | −0.948978 | ||||||||
\(10\) | 153.227 | 0.484547 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −19.5974 | −0.0392867 | ||||||||
\(13\) | −258.929 | −0.424935 | −0.212467 | − | 0.977168i | \(-0.568150\pi\) | ||||
−0.212467 | + | 0.977168i | \(0.568150\pi\) | |||||||
\(14\) | −406.720 | −0.554594 | ||||||||
\(15\) | 88.0279 | 0.101016 | ||||||||
\(16\) | −1171.13 | −1.14368 | ||||||||
\(17\) | −79.1073 | −0.0663887 | −0.0331943 | − | 0.999449i | \(-0.510568\pi\) | ||||
−0.0331943 | + | 0.999449i | \(0.510568\pi\) | |||||||
\(18\) | 1413.38 | 1.02820 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −139.142 | −0.0777828 | ||||||||
\(21\) | −233.658 | −0.115620 | ||||||||
\(22\) | −741.619 | −0.326681 | ||||||||
\(23\) | −300.025 | −0.118260 | −0.0591299 | − | 0.998250i | \(-0.518833\pi\) | ||||
−0.0591299 | + | 0.998250i | \(0.518833\pi\) | |||||||
\(24\) | −570.485 | −0.202170 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1587.00 | 0.460408 | ||||||||
\(27\) | 1667.61 | 0.440234 | ||||||||
\(28\) | 369.333 | 0.0890273 | ||||||||
\(29\) | 4039.24 | 0.891876 | 0.445938 | − | 0.895064i | \(-0.352870\pi\) | ||||
0.445938 | + | 0.895064i | \(0.352870\pi\) | |||||||
\(30\) | −539.530 | −0.109449 | ||||||||
\(31\) | 1467.71 | 0.274306 | 0.137153 | − | 0.990550i | \(-0.456205\pi\) | ||||
0.137153 | + | 0.990550i | \(0.456205\pi\) | |||||||
\(32\) | 1993.34 | 0.344118 | ||||||||
\(33\) | −426.055 | −0.0681053 | ||||||||
\(34\) | 484.855 | 0.0719308 | ||||||||
\(35\) | −1658.97 | −0.228913 | ||||||||
\(36\) | −1283.46 | −0.165054 | ||||||||
\(37\) | −4621.83 | −0.555022 | −0.277511 | − | 0.960722i | \(-0.589509\pi\) | ||||
−0.277511 | + | 0.960722i | \(0.589509\pi\) | |||||||
\(38\) | −2212.60 | −0.248567 | ||||||||
\(39\) | 911.718 | 0.0959840 | ||||||||
\(40\) | −4050.45 | −0.400271 | ||||||||
\(41\) | −10855.9 | −1.00857 | −0.504283 | − | 0.863538i | \(-0.668243\pi\) | ||||
−0.504283 | + | 0.863538i | \(0.668243\pi\) | |||||||
\(42\) | 1432.11 | 0.125272 | ||||||||
\(43\) | −11329.9 | −0.934449 | −0.467225 | − | 0.884139i | \(-0.654746\pi\) | ||||
−0.467225 | + | 0.884139i | \(0.654746\pi\) | |||||||
\(44\) | 673.448 | 0.0524412 | ||||||||
\(45\) | 5765.04 | 0.424396 | ||||||||
\(46\) | 1838.88 | 0.128132 | ||||||||
\(47\) | 13598.3 | 0.897928 | 0.448964 | − | 0.893550i | \(-0.351793\pi\) | ||||
0.448964 | + | 0.893550i | \(0.351793\pi\) | |||||||
\(48\) | 4123.67 | 0.258333 | ||||||||
\(49\) | −12403.5 | −0.737995 | ||||||||
\(50\) | −3830.68 | −0.216696 | ||||||||
\(51\) | 278.546 | 0.0149959 | ||||||||
\(52\) | −1441.12 | −0.0739079 | ||||||||
\(53\) | 3881.38 | 0.189800 | 0.0949002 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0949002 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(54\) | −10220.9 | −0.476985 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 10751.4 | 0.458135 | ||||||||
\(57\) | −1271.12 | −0.0518203 | ||||||||
\(58\) | −24756.8 | −0.966329 | ||||||||
\(59\) | −7937.40 | −0.296858 | −0.148429 | − | 0.988923i | \(-0.547422\pi\) | ||||
−0.148429 | + | 0.988923i | \(0.547422\pi\) | |||||||
\(60\) | 489.935 | 0.0175696 | ||||||||
\(61\) | −803.334 | −0.0276421 | −0.0138211 | − | 0.999904i | \(-0.504400\pi\) | ||||
−0.0138211 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(62\) | −8995.71 | −0.297205 | ||||||||
\(63\) | −15302.5 | −0.485748 | ||||||||
\(64\) | 25258.6 | 0.770832 | ||||||||
\(65\) | 6473.22 | 0.190037 | ||||||||
\(66\) | 2611.33 | 0.0737907 | ||||||||
\(67\) | −35178.6 | −0.957395 | −0.478697 | − | 0.877980i | \(-0.658891\pi\) | ||||
−0.478697 | + | 0.877980i | \(0.658891\pi\) | |||||||
\(68\) | −440.286 | −0.0115468 | ||||||||
\(69\) | 1056.42 | 0.0267125 | ||||||||
\(70\) | 10168.0 | 0.248022 | ||||||||
\(71\) | 35845.4 | 0.843892 | 0.421946 | − | 0.906621i | \(-0.361347\pi\) | ||||
0.421946 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(72\) | −37361.7 | −0.849366 | ||||||||
\(73\) | 34264.9 | 0.752562 | 0.376281 | − | 0.926506i | \(-0.377203\pi\) | ||||
0.376281 | + | 0.926506i | \(0.377203\pi\) | |||||||
\(74\) | 28327.6 | 0.601355 | ||||||||
\(75\) | −2200.70 | −0.0451759 | ||||||||
\(76\) | 2009.21 | 0.0399017 | ||||||||
\(77\) | 8029.44 | 0.154333 | ||||||||
\(78\) | −5588.00 | −0.103997 | ||||||||
\(79\) | 81499.1 | 1.46921 | 0.734607 | − | 0.678493i | \(-0.237367\pi\) | ||||
0.734607 | + | 0.678493i | \(0.237367\pi\) | |||||||
\(80\) | 29278.1 | 0.511468 | ||||||||
\(81\) | 50164.4 | 0.849538 | ||||||||
\(82\) | 66536.5 | 1.09276 | ||||||||
\(83\) | 15608.2 | 0.248690 | 0.124345 | − | 0.992239i | \(-0.460317\pi\) | ||||
0.124345 | + | 0.992239i | \(0.460317\pi\) | |||||||
\(84\) | −1300.46 | −0.0201095 | ||||||||
\(85\) | 1977.68 | 0.0296899 | ||||||||
\(86\) | 69442.0 | 1.01246 | ||||||||
\(87\) | −14222.6 | −0.201457 | ||||||||
\(88\) | 19604.2 | 0.269862 | ||||||||
\(89\) | −80771.0 | −1.08089 | −0.540444 | − | 0.841380i | \(-0.681744\pi\) | ||||
−0.540444 | + | 0.841380i | \(0.681744\pi\) | |||||||
\(90\) | −35334.4 | −0.459824 | ||||||||
\(91\) | −17182.3 | −0.217509 | ||||||||
\(92\) | −1669.84 | −0.0205687 | ||||||||
\(93\) | −5167.97 | −0.0619602 | ||||||||
\(94\) | −83345.4 | −0.972886 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −7018.79 | −0.0777292 | ||||||||
\(97\) | −23793.8 | −0.256764 | −0.128382 | − | 0.991725i | \(-0.540978\pi\) | ||||
−0.128382 | + | 0.991725i | \(0.540978\pi\) | |||||||
\(98\) | 76022.0 | 0.799603 | ||||||||
\(99\) | −27902.8 | −0.286128 | ||||||||
\(100\) | 3478.55 | 0.0347855 | ||||||||
\(101\) | 1699.50 | 0.0165775 | 0.00828873 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828873 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(102\) | −1707.23 | −0.0162477 | ||||||||
\(103\) | −38712.2 | −0.359546 | −0.179773 | − | 0.983708i | \(-0.557536\pi\) | ||||
−0.179773 | + | 0.983708i | \(0.557536\pi\) | |||||||
\(104\) | −41951.2 | −0.380330 | ||||||||
\(105\) | 5841.44 | 0.0517067 | ||||||||
\(106\) | −23789.3 | −0.205645 | ||||||||
\(107\) | 113177. | 0.955648 | 0.477824 | − | 0.878456i | \(-0.341426\pi\) | ||||
0.477824 | + | 0.878456i | \(0.341426\pi\) | |||||||
\(108\) | 9281.37 | 0.0765690 | ||||||||
\(109\) | 172897. | 1.39386 | 0.696932 | − | 0.717137i | \(-0.254548\pi\) | ||||
0.696932 | + | 0.717137i | \(0.254548\pi\) | |||||||
\(110\) | 18540.5 | 0.146096 | ||||||||
\(111\) | 16274.0 | 0.125368 | ||||||||
\(112\) | −77714.7 | −0.585407 | ||||||||
\(113\) | 200084. | 1.47407 | 0.737033 | − | 0.675857i | \(-0.236226\pi\) | ||||
0.737033 | + | 0.675857i | \(0.236226\pi\) | |||||||
\(114\) | 7790.82 | 0.0561463 | ||||||||
\(115\) | 7500.61 | 0.0528874 | ||||||||
\(116\) | 22481.1 | 0.155122 | ||||||||
\(117\) | 59709.4 | 0.403254 | ||||||||
\(118\) | 48649.0 | 0.321639 | ||||||||
\(119\) | −5249.48 | −0.0339820 | ||||||||
\(120\) | 14262.1 | 0.0904130 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 4923.70 | 0.0299497 | ||||||||
\(123\) | 38224.7 | 0.227814 | ||||||||
\(124\) | 8168.80 | 0.0477094 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 93790.3 | 0.526298 | ||||||||
\(127\) | −89177.5 | −0.490621 | −0.245311 | − | 0.969445i | \(-0.578890\pi\) | ||||
−0.245311 | + | 0.969445i | \(0.578890\pi\) | |||||||
\(128\) | −218599. | −1.17930 | ||||||||
\(129\) | 39893.9 | 0.211073 | ||||||||
\(130\) | −39674.9 | −0.205901 | ||||||||
\(131\) | 361081. | 1.83834 | 0.919171 | − | 0.393859i | \(-0.128860\pi\) | ||||
0.919171 | + | 0.393859i | \(0.128860\pi\) | |||||||
\(132\) | −2371.29 | −0.0118454 | ||||||||
\(133\) | 23955.6 | 0.117430 | ||||||||
\(134\) | 215612. | 1.03732 | ||||||||
\(135\) | −41690.2 | −0.196879 | ||||||||
\(136\) | −12816.8 | −0.0594200 | ||||||||
\(137\) | −389149. | −1.77139 | −0.885697 | − | 0.464265i | \(-0.846319\pi\) | ||||
−0.885697 | + | 0.464265i | \(0.846319\pi\) | |||||||
\(138\) | −6474.89 | −0.0289424 | ||||||||
\(139\) | 243135. | 1.06736 | 0.533678 | − | 0.845688i | \(-0.320809\pi\) | ||||
0.533678 | + | 0.845688i | \(0.320809\pi\) | |||||||
\(140\) | −9233.33 | −0.0398142 | ||||||||
\(141\) | −47881.3 | −0.202824 | ||||||||
\(142\) | −219699. | −0.914340 | ||||||||
\(143\) | −31330.4 | −0.128123 | ||||||||
\(144\) | 270063. | 1.08532 | ||||||||
\(145\) | −100981. | −0.398859 | ||||||||
\(146\) | −210012. | −0.815385 | ||||||||
\(147\) | 43674.1 | 0.166698 | ||||||||
\(148\) | −25723.7 | −0.0965336 | ||||||||
\(149\) | 144484. | 0.533158 | 0.266579 | − | 0.963813i | \(-0.414107\pi\) | ||||
0.266579 | + | 0.963813i | \(0.414107\pi\) | |||||||
\(150\) | 13488.3 | 0.0489472 | ||||||||
\(151\) | 271861. | 0.970297 | 0.485149 | − | 0.874432i | \(-0.338765\pi\) | ||||
0.485149 | + | 0.874432i | \(0.338765\pi\) | |||||||
\(152\) | 58488.6 | 0.205335 | ||||||||
\(153\) | 18242.3 | 0.0630014 | ||||||||
\(154\) | −49213.1 | −0.167216 | ||||||||
\(155\) | −36692.7 | −0.122673 | ||||||||
\(156\) | 5074.34 | 0.0166943 | ||||||||
\(157\) | 72078.9 | 0.233377 | 0.116689 | − | 0.993169i | \(-0.462772\pi\) | ||||
0.116689 | + | 0.993169i | \(0.462772\pi\) | |||||||
\(158\) | −499515. | −1.59186 | ||||||||
\(159\) | −13666.8 | −0.0428720 | ||||||||
\(160\) | −49833.6 | −0.153894 | ||||||||
\(161\) | −19909.3 | −0.0605329 | ||||||||
\(162\) | −307462. | −0.920457 | ||||||||
\(163\) | 271978. | 0.801798 | 0.400899 | − | 0.916122i | \(-0.368698\pi\) | ||||
0.400899 | + | 0.916122i | \(0.368698\pi\) | |||||||
\(164\) | −60420.3 | −0.175418 | ||||||||
\(165\) | 10651.4 | 0.0304576 | ||||||||
\(166\) | −95664.2 | −0.269451 | ||||||||
\(167\) | −63921.7 | −0.177361 | −0.0886803 | − | 0.996060i | \(-0.528265\pi\) | ||||
−0.0886803 | + | 0.996060i | \(0.528265\pi\) | |||||||
\(168\) | −37856.8 | −0.103483 | ||||||||
\(169\) | −304249. | −0.819431 | ||||||||
\(170\) | −12121.4 | −0.0321684 | ||||||||
\(171\) | −83247.2 | −0.217711 | ||||||||
\(172\) | −63058.8 | −0.162527 | ||||||||
\(173\) | −332899. | −0.845662 | −0.422831 | − | 0.906209i | \(-0.638964\pi\) | ||||
−0.422831 | + | 0.906209i | \(0.638964\pi\) | |||||||
\(174\) | 87171.6 | 0.218274 | ||||||||
\(175\) | 41474.4 | 0.102373 | ||||||||
\(176\) | −141706. | −0.344832 | ||||||||
\(177\) | 27948.5 | 0.0670541 | ||||||||
\(178\) | 495052. | 1.17112 | ||||||||
\(179\) | 123748. | 0.288673 | 0.144337 | − | 0.989529i | \(-0.453895\pi\) | ||||
0.144337 | + | 0.989529i | \(0.453895\pi\) | |||||||
\(180\) | 32086.4 | 0.0738142 | ||||||||
\(181\) | −530556. | −1.20375 | −0.601873 | − | 0.798592i | \(-0.705579\pi\) | ||||
−0.601873 | + | 0.798592i | \(0.705579\pi\) | |||||||
\(182\) | 105312. | 0.235666 | ||||||||
\(183\) | 2828.63 | 0.00624379 | ||||||||
\(184\) | −48609.4 | −0.105846 | ||||||||
\(185\) | 115546. | 0.248213 | ||||||||
\(186\) | 31674.9 | 0.0671326 | ||||||||
\(187\) | −9571.98 | −0.0200169 | ||||||||
\(188\) | 75684.1 | 0.156174 | ||||||||
\(189\) | 110661. | 0.225340 | ||||||||
\(190\) | 55315.0 | 0.111163 | ||||||||
\(191\) | −8344.74 | −0.0165512 | −0.00827560 | − | 0.999966i | \(-0.502634\pi\) | ||||
−0.00827560 | + | 0.999966i | \(0.502634\pi\) | |||||||
\(192\) | −88938.5 | −0.174115 | ||||||||
\(193\) | 354967. | 0.685953 | 0.342976 | − | 0.939344i | \(-0.388565\pi\) | ||||
0.342976 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(194\) | 145834. | 0.278199 | ||||||||
\(195\) | −22793.0 | −0.0429254 | ||||||||
\(196\) | −69033.9 | −0.128358 | ||||||||
\(197\) | 415434. | 0.762670 | 0.381335 | − | 0.924437i | \(-0.375464\pi\) | ||||
0.381335 | + | 0.924437i | \(0.375464\pi\) | |||||||
\(198\) | 171019. | 0.310014 | ||||||||
\(199\) | −634264. | −1.13537 | −0.567685 | − | 0.823246i | \(-0.692161\pi\) | ||||
−0.567685 | + | 0.823246i | \(0.692161\pi\) | |||||||
\(200\) | 101261. | 0.179006 | ||||||||
\(201\) | 123868. | 0.216256 | ||||||||
\(202\) | −10416.4 | −0.0179613 | ||||||||
\(203\) | 268040. | 0.456519 | ||||||||
\(204\) | 1550.30 | 0.00260819 | ||||||||
\(205\) | 271396. | 0.451044 | ||||||||
\(206\) | 237270. | 0.389561 | ||||||||
\(207\) | 69186.2 | 0.112226 | ||||||||
\(208\) | 303238. | 0.485988 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | −35802.7 | −0.0560231 | ||||||||
\(211\) | 557857. | 0.862614 | 0.431307 | − | 0.902205i | \(-0.358053\pi\) | ||||
0.431307 | + | 0.902205i | \(0.358053\pi\) | |||||||
\(212\) | 21602.6 | 0.0330115 | ||||||||
\(213\) | −126216. | −0.190618 | ||||||||
\(214\) | −693670. | −1.03542 | ||||||||
\(215\) | 283248. | 0.417898 | ||||||||
\(216\) | 270182. | 0.394024 | ||||||||
\(217\) | 97395.6 | 0.140407 | ||||||||
\(218\) | −1.05970e6 | −1.51022 | ||||||||
\(219\) | −120651. | −0.169988 | ||||||||
\(220\) | −16836.2 | −0.0234524 | ||||||||
\(221\) | 20483.2 | 0.0282109 | ||||||||
\(222\) | −99744.8 | −0.135834 | ||||||||
\(223\) | −258512. | −0.348112 | −0.174056 | − | 0.984736i | \(-0.555687\pi\) | ||||
−0.174056 | + | 0.984736i | \(0.555687\pi\) | |||||||
\(224\) | 132276. | 0.176142 | ||||||||
\(225\) | −144126. | −0.189796 | ||||||||
\(226\) | −1.22633e6 | −1.59712 | ||||||||
\(227\) | −934603. | −1.20382 | −0.601911 | − | 0.798563i | \(-0.705594\pi\) | ||||
−0.601911 | + | 0.798563i | \(0.705594\pi\) | |||||||
\(228\) | −7074.67 | −0.00901299 | ||||||||
\(229\) | 642630. | 0.809789 | 0.404895 | − | 0.914363i | \(-0.367308\pi\) | ||||
0.404895 | + | 0.914363i | \(0.367308\pi\) | |||||||
\(230\) | −45971.9 | −0.0573024 | ||||||||
\(231\) | −28272.6 | −0.0348606 | ||||||||
\(232\) | 654430. | 0.798258 | ||||||||
\(233\) | 1.30470e6 | 1.57442 | 0.787212 | − | 0.616682i | \(-0.211524\pi\) | ||||
0.787212 | + | 0.616682i | \(0.211524\pi\) | |||||||
\(234\) | −365964. | −0.436917 | ||||||||
\(235\) | −339959. | −0.401565 | ||||||||
\(236\) | −44177.1 | −0.0516318 | ||||||||
\(237\) | −286968. | −0.331865 | ||||||||
\(238\) | 32174.5 | 0.0368188 | ||||||||
\(239\) | 95610.5 | 0.108271 | 0.0541353 | − | 0.998534i | \(-0.482760\pi\) | ||||
0.0541353 | + | 0.998534i | \(0.482760\pi\) | |||||||
\(240\) | −103092. | −0.115530 | ||||||||
\(241\) | −757816. | −0.840468 | −0.420234 | − | 0.907416i | \(-0.638052\pi\) | ||||
−0.420234 | + | 0.907416i | \(0.638052\pi\) | |||||||
\(242\) | −89735.9 | −0.0984981 | ||||||||
\(243\) | −581863. | −0.632128 | ||||||||
\(244\) | −4471.10 | −0.00480773 | ||||||||
\(245\) | 310087. | 0.330041 | ||||||||
\(246\) | −234282. | −0.246832 | ||||||||
\(247\) | −93473.3 | −0.0974867 | ||||||||
\(248\) | 237795. | 0.245513 | ||||||||
\(249\) | −54958.4 | −0.0561740 | ||||||||
\(250\) | 95767.0 | 0.0969093 | ||||||||
\(251\) | −156846. | −0.157140 | −0.0785702 | − | 0.996909i | \(-0.525035\pi\) | ||||
−0.0785702 | + | 0.996909i | \(0.525035\pi\) | |||||||
\(252\) | −85168.9 | −0.0844850 | ||||||||
\(253\) | −36303.0 | −0.0356567 | ||||||||
\(254\) | 546577. | 0.531578 | ||||||||
\(255\) | −6963.64 | −0.00670635 | ||||||||
\(256\) | 531538. | 0.506914 | ||||||||
\(257\) | 31470.6 | 0.0297216 | 0.0148608 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148608 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(258\) | −244513. | −0.228693 | ||||||||
\(259\) | −306700. | −0.284096 | ||||||||
\(260\) | 36027.9 | 0.0330526 | ||||||||
\(261\) | −931455. | −0.846371 | ||||||||
\(262\) | −2.21310e6 | −1.99181 | ||||||||
\(263\) | 1.25606e6 | 1.11975 | 0.559877 | − | 0.828576i | \(-0.310848\pi\) | ||||
0.559877 | + | 0.828576i | \(0.310848\pi\) | |||||||
\(264\) | −69028.6 | −0.0609564 | ||||||||
\(265\) | −97034.6 | −0.0848813 | ||||||||
\(266\) | −146826. | −0.127233 | ||||||||
\(267\) | 284404. | 0.244150 | ||||||||
\(268\) | −195793. | −0.166517 | ||||||||
\(269\) | −2.21915e6 | −1.86985 | −0.934925 | − | 0.354846i | \(-0.884533\pi\) | ||||
−0.934925 | + | 0.354846i | \(0.884533\pi\) | |||||||
\(270\) | 255522. | 0.213314 | ||||||||
\(271\) | −720989. | −0.596355 | −0.298178 | − | 0.954510i | \(-0.596379\pi\) | ||||
−0.298178 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(272\) | 92644.5 | 0.0759272 | ||||||||
\(273\) | 60500.7 | 0.0491308 | ||||||||
\(274\) | 2.38513e6 | 1.91927 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 5879.71 | 0.00464604 | ||||||||
\(277\) | −1.50482e6 | −1.17838 | −0.589192 | − | 0.807993i | \(-0.700554\pi\) | ||||
−0.589192 | + | 0.807993i | \(0.700554\pi\) | |||||||
\(278\) | −1.49019e6 | −1.15646 | ||||||||
\(279\) | −338456. | −0.260311 | ||||||||
\(280\) | −268784. | −0.204884 | ||||||||
\(281\) | −260752. | −0.196998 | −0.0984989 | − | 0.995137i | \(-0.531404\pi\) | ||||
−0.0984989 | + | 0.995137i | \(0.531404\pi\) | |||||||
\(282\) | 293469. | 0.219755 | ||||||||
\(283\) | 2.19492e6 | 1.62912 | 0.814558 | − | 0.580082i | \(-0.196980\pi\) | ||||
0.814558 | + | 0.580082i | \(0.196980\pi\) | |||||||
\(284\) | 199504. | 0.146776 | ||||||||
\(285\) | 31778.1 | 0.0231748 | ||||||||
\(286\) | 192027. | 0.138818 | ||||||||
\(287\) | −720383. | −0.516249 | ||||||||
\(288\) | −459669. | −0.326560 | ||||||||
\(289\) | −1.41360e6 | −0.995593 | ||||||||
\(290\) | 618921. | 0.432155 | ||||||||
\(291\) | 83780.7 | 0.0579978 | ||||||||
\(292\) | 190708. | 0.130891 | ||||||||
\(293\) | −1.44787e6 | −0.985279 | −0.492639 | − | 0.870234i | \(-0.663968\pi\) | ||||
−0.492639 | + | 0.870234i | \(0.663968\pi\) | |||||||
\(294\) | −267682. | −0.180614 | ||||||||
\(295\) | 198435. | 0.132759 | ||||||||
\(296\) | −748821. | −0.496762 | ||||||||
\(297\) | 201780. | 0.132736 | ||||||||
\(298\) | −885558. | −0.577665 | ||||||||
\(299\) | 77685.0 | 0.0502527 | ||||||||
\(300\) | −12248.4 | −0.00785734 | ||||||||
\(301\) | −751842. | −0.478311 | ||||||||
\(302\) | −1.66626e6 | −1.05130 | ||||||||
\(303\) | −5984.13 | −0.00374451 | ||||||||
\(304\) | −422776. | −0.262377 | ||||||||
\(305\) | 20083.3 | 0.0123619 | ||||||||
\(306\) | −111808. | −0.0682608 | ||||||||
\(307\) | 1.00421e6 | 0.608105 | 0.304053 | − | 0.952655i | \(-0.401660\pi\) | ||||
0.304053 | + | 0.952655i | \(0.401660\pi\) | |||||||
\(308\) | 44689.3 | 0.0268427 | ||||||||
\(309\) | 136310. | 0.0812141 | ||||||||
\(310\) | 224893. | 0.132914 | ||||||||
\(311\) | 1.34266e6 | 0.787165 | 0.393582 | − | 0.919289i | \(-0.371236\pi\) | ||||
0.393582 | + | 0.919289i | \(0.371236\pi\) | |||||||
\(312\) | 147715. | 0.0859088 | ||||||||
\(313\) | 126408. | 0.0729311 | 0.0364655 | − | 0.999335i | \(-0.488390\pi\) | ||||
0.0364655 | + | 0.999335i | \(0.488390\pi\) | |||||||
\(314\) | −441778. | −0.252860 | ||||||||
\(315\) | 382562. | 0.217233 | ||||||||
\(316\) | 453598. | 0.255537 | ||||||||
\(317\) | −64785.4 | −0.0362101 | −0.0181050 | − | 0.999836i | \(-0.505763\pi\) | ||||
−0.0181050 | + | 0.999836i | \(0.505763\pi\) | |||||||
\(318\) | 83765.0 | 0.0464509 | ||||||||
\(319\) | 488748. | 0.268911 | ||||||||
\(320\) | −631466. | −0.344727 | ||||||||
\(321\) | −398508. | −0.215861 | ||||||||
\(322\) | 122026. | 0.0655862 | ||||||||
\(323\) | −28557.7 | −0.0152306 | ||||||||
\(324\) | 279199. | 0.147758 | ||||||||
\(325\) | −161831. | −0.0849869 | ||||||||
\(326\) | −1.66698e6 | −0.868732 | ||||||||
\(327\) | −608789. | −0.314845 | ||||||||
\(328\) | −1.75885e6 | −0.902699 | ||||||||
\(329\) | 902372. | 0.459617 | ||||||||
\(330\) | −65283.2 | −0.0330002 | ||||||||
\(331\) | 631201. | 0.316663 | 0.158332 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158332 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(332\) | 86870.5 | 0.0432541 | ||||||||
\(333\) | 1.06580e6 | 0.526704 | ||||||||
\(334\) | 391782. | 0.192167 | ||||||||
\(335\) | 879464. | 0.428160 | ||||||||
\(336\) | 273642. | 0.132232 | ||||||||
\(337\) | 2.94849e6 | 1.41425 | 0.707123 | − | 0.707091i | \(-0.249993\pi\) | ||||
0.707123 | + | 0.707091i | \(0.249993\pi\) | |||||||
\(338\) | 1.86477e6 | 0.887836 | ||||||||
\(339\) | −704520. | −0.332961 | ||||||||
\(340\) | 11007.2 | 0.00516390 | ||||||||
\(341\) | 177593. | 0.0827064 | ||||||||
\(342\) | 510229. | 0.235885 | ||||||||
\(343\) | −1.93838e6 | −0.889617 | ||||||||
\(344\) | −1.83565e6 | −0.836362 | ||||||||
\(345\) | −26410.5 | −0.0119462 | ||||||||
\(346\) | 2.04036e6 | 0.916257 | ||||||||
\(347\) | −4.29871e6 | −1.91653 | −0.958263 | − | 0.285888i | \(-0.907711\pi\) | ||||
−0.958263 | + | 0.285888i | \(0.907711\pi\) | |||||||
\(348\) | −79158.6 | −0.0350389 | ||||||||
\(349\) | −3.85898e6 | −1.69594 | −0.847968 | − | 0.530048i | \(-0.822174\pi\) | ||||
−0.847968 | + | 0.530048i | \(0.822174\pi\) | |||||||
\(350\) | −254200. | −0.110919 | ||||||||
\(351\) | −431791. | −0.187071 | ||||||||
\(352\) | 241195. | 0.103755 | ||||||||
\(353\) | −560930. | −0.239592 | −0.119796 | − | 0.992799i | \(-0.538224\pi\) | ||||
−0.119796 | + | 0.992799i | \(0.538224\pi\) | |||||||
\(354\) | −171299. | −0.0726517 | ||||||||
\(355\) | −896134. | −0.377400 | ||||||||
\(356\) | −449546. | −0.187996 | ||||||||
\(357\) | 18484.0 | 0.00767584 | ||||||||
\(358\) | −758464. | −0.312772 | ||||||||
\(359\) | −3.63173e6 | −1.48723 | −0.743614 | − | 0.668609i | \(-0.766890\pi\) | ||||
−0.743614 | + | 0.668609i | \(0.766890\pi\) | |||||||
\(360\) | 934042. | 0.379848 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 3.25182e6 | 1.30423 | ||||||||
\(363\) | −51552.6 | −0.0205345 | ||||||||
\(364\) | −95631.0 | −0.0378308 | ||||||||
\(365\) | −856622. | −0.336556 | ||||||||
\(366\) | −17336.9 | −0.00676502 | ||||||||
\(367\) | 1.28554e6 | 0.498218 | 0.249109 | − | 0.968475i | \(-0.419862\pi\) | ||||
0.249109 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(368\) | 351366. | 0.135251 | ||||||||
\(369\) | 2.50338e6 | 0.957107 | ||||||||
\(370\) | −708190. | −0.268934 | ||||||||
\(371\) | 257565. | 0.0971520 | ||||||||
\(372\) | −28763.3 | −0.0107766 | ||||||||
\(373\) | −4.39605e6 | −1.63603 | −0.818013 | − | 0.575199i | \(-0.804925\pi\) | ||||
−0.818013 | + | 0.575199i | \(0.804925\pi\) | |||||||
\(374\) | 58667.5 | 0.0216879 | ||||||||
\(375\) | 55017.4 | 0.0202033 | ||||||||
\(376\) | 2.20318e6 | 0.803674 | ||||||||
\(377\) | −1.04587e6 | −0.378989 | ||||||||
\(378\) | −678249. | −0.244151 | ||||||||
\(379\) | −4.80435e6 | −1.71805 | −0.859026 | − | 0.511932i | \(-0.828930\pi\) | ||||
−0.859026 | + | 0.511932i | \(0.828930\pi\) | |||||||
\(380\) | −50230.3 | −0.0178446 | ||||||||
\(381\) | 314004. | 0.110821 | ||||||||
\(382\) | 51145.6 | 0.0179329 | ||||||||
\(383\) | −2.15034e6 | −0.749047 | −0.374524 | − | 0.927217i | \(-0.622194\pi\) | ||||
−0.374524 | + | 0.927217i | \(0.622194\pi\) | |||||||
\(384\) | 769713. | 0.266380 | ||||||||
\(385\) | −200736. | −0.0690197 | ||||||||
\(386\) | −2.17562e6 | −0.743216 | ||||||||
\(387\) | 2.61270e6 | 0.886772 | ||||||||
\(388\) | −132429. | −0.0446584 | ||||||||
\(389\) | −4.17313e6 | −1.39826 | −0.699131 | − | 0.714994i | \(-0.746429\pi\) | ||||
−0.699131 | + | 0.714994i | \(0.746429\pi\) | |||||||
\(390\) | 139700. | 0.0465088 | ||||||||
\(391\) | 23734.1 | 0.00785111 | ||||||||
\(392\) | −2.00959e6 | −0.660530 | ||||||||
\(393\) | −1.27141e6 | −0.415244 | ||||||||
\(394\) | −2.54623e6 | −0.826338 | ||||||||
\(395\) | −2.03748e6 | −0.657052 | ||||||||
\(396\) | −155298. | −0.0497655 | ||||||||
\(397\) | 865597. | 0.275638 | 0.137819 | − | 0.990457i | \(-0.455991\pi\) | ||||
0.137819 | + | 0.990457i | \(0.455991\pi\) | |||||||
\(398\) | 3.88746e6 | 1.23015 | ||||||||
\(399\) | −84350.4 | −0.0265250 | ||||||||
\(400\) | −731953. | −0.228735 | ||||||||
\(401\) | −2.70235e6 | −0.839230 | −0.419615 | − | 0.907702i | \(-0.637835\pi\) | ||||
−0.419615 | + | 0.907702i | \(0.637835\pi\) | |||||||
\(402\) | −759196. | −0.234309 | ||||||||
\(403\) | −380032. | −0.116562 | ||||||||
\(404\) | 9458.88 | 0.00288328 | ||||||||
\(405\) | −1.25411e6 | −0.379925 | ||||||||
\(406\) | −1.64284e6 | −0.494629 | ||||||||
\(407\) | −559242. | −0.167345 | ||||||||
\(408\) | 45129.5 | 0.0134218 | ||||||||
\(409\) | −4.70657e6 | −1.39122 | −0.695610 | − | 0.718419i | \(-0.744866\pi\) | ||||
−0.695610 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(410\) | −1.66341e6 | −0.488697 | ||||||||
\(411\) | 1.37024e6 | 0.400122 | ||||||||
\(412\) | −215460. | −0.0625350 | ||||||||
\(413\) | −526718. | −0.151951 | ||||||||
\(414\) | −424048. | −0.121595 | ||||||||
\(415\) | −390206. | −0.111218 | ||||||||
\(416\) | −516134. | −0.146228 | ||||||||
\(417\) | −856104. | −0.241094 | ||||||||
\(418\) | −267725. | −0.0749458 | ||||||||
\(419\) | −2.18241e6 | −0.607296 | −0.303648 | − | 0.952784i | \(-0.598205\pi\) | ||||
−0.303648 | + | 0.952784i | \(0.598205\pi\) | |||||||
\(420\) | 32511.6 | 0.00899322 | ||||||||
\(421\) | −6.78164e6 | −1.86479 | −0.932393 | − | 0.361445i | \(-0.882284\pi\) | ||||
−0.932393 | + | 0.361445i | \(0.882284\pi\) | |||||||
\(422\) | −3.41915e6 | −0.934625 | ||||||||
\(423\) | −3.13580e6 | −0.852114 | ||||||||
\(424\) | 628855. | 0.169877 | ||||||||
\(425\) | −49442.0 | −0.0132777 | ||||||||
\(426\) | 773586. | 0.206531 | ||||||||
\(427\) | −53308.4 | −0.0141490 | ||||||||
\(428\) | 629906. | 0.166214 | ||||||||
\(429\) | 110318. | 0.0289403 | ||||||||
\(430\) | −1.73605e6 | −0.452784 | ||||||||
\(431\) | −2.80849e6 | −0.728249 | −0.364125 | − | 0.931350i | \(-0.618632\pi\) | ||||
−0.364125 | + | 0.931350i | \(0.618632\pi\) | |||||||
\(432\) | −1.95298e6 | −0.503486 | ||||||||
\(433\) | −1.55510e6 | −0.398601 | −0.199301 | − | 0.979938i | \(-0.563867\pi\) | ||||
−0.199301 | + | 0.979938i | \(0.563867\pi\) | |||||||
\(434\) | −596946. | −0.152129 | ||||||||
\(435\) | 355565. | 0.0900941 | ||||||||
\(436\) | 962289. | 0.242432 | ||||||||
\(437\) | −108309. | −0.0271307 | ||||||||
\(438\) | 739478. | 0.184179 | ||||||||
\(439\) | 4.09040e6 | 1.01299 | 0.506494 | − | 0.862243i | \(-0.330941\pi\) | ||||
0.506494 | + | 0.862243i | \(0.330941\pi\) | |||||||
\(440\) | −490105. | −0.120686 | ||||||||
\(441\) | 2.86027e6 | 0.700341 | ||||||||
\(442\) | −125543. | −0.0305659 | ||||||||
\(443\) | 4.01440e6 | 0.971876 | 0.485938 | − | 0.873993i | \(-0.338478\pi\) | ||||
0.485938 | + | 0.873993i | \(0.338478\pi\) | |||||||
\(444\) | 90576.0 | 0.0218050 | ||||||||
\(445\) | 2.01928e6 | 0.483388 | ||||||||
\(446\) | 1.58444e6 | 0.377172 | ||||||||
\(447\) | −508746. | −0.120429 | ||||||||
\(448\) | 1.67614e6 | 0.394561 | ||||||||
\(449\) | −2.58697e6 | −0.605586 | −0.302793 | − | 0.953056i | \(-0.597919\pi\) | ||||
−0.302793 | + | 0.953056i | \(0.597919\pi\) | |||||||
\(450\) | 883361. | 0.205640 | ||||||||
\(451\) | −1.31356e6 | −0.304094 | ||||||||
\(452\) | 1.11361e6 | 0.256381 | ||||||||
\(453\) | −957254. | −0.219170 | ||||||||
\(454\) | 5.72826e6 | 1.30432 | ||||||||
\(455\) | 429556. | 0.0972729 | ||||||||
\(456\) | −205945. | −0.0463809 | ||||||||
\(457\) | 3.30693e6 | 0.740687 | 0.370344 | − | 0.928895i | \(-0.379240\pi\) | ||||
0.370344 | + | 0.928895i | \(0.379240\pi\) | |||||||
\(458\) | −3.93873e6 | −0.877390 | ||||||||
\(459\) | −131920. | −0.0292266 | ||||||||
\(460\) | 41746.1 | 0.00919858 | ||||||||
\(461\) | −4.93804e6 | −1.08219 | −0.541093 | − | 0.840963i | \(-0.681989\pi\) | ||||
−0.541093 | + | 0.840963i | \(0.681989\pi\) | |||||||
\(462\) | 173285. | 0.0377708 | ||||||||
\(463\) | 4.05661e6 | 0.879450 | 0.439725 | − | 0.898132i | \(-0.355076\pi\) | ||||
0.439725 | + | 0.898132i | \(0.355076\pi\) | |||||||
\(464\) | −4.73045e6 | −1.02002 | ||||||||
\(465\) | 129199. | 0.0277094 | ||||||||
\(466\) | −7.99663e6 | −1.70586 | ||||||||
\(467\) | −433114. | −0.0918988 | −0.0459494 | − | 0.998944i | \(-0.514631\pi\) | ||||
−0.0459494 | + | 0.998944i | \(0.514631\pi\) | |||||||
\(468\) | 332324. | 0.0701370 | ||||||||
\(469\) | −2.33441e6 | −0.490056 | ||||||||
\(470\) | 2.08363e6 | 0.435088 | ||||||||
\(471\) | −253798. | −0.0527152 | ||||||||
\(472\) | −1.28600e6 | −0.265697 | ||||||||
\(473\) | −1.37092e6 | −0.281747 | ||||||||
\(474\) | 1.75885e6 | 0.359569 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −29216.9 | −0.00591041 | ||||||||
\(477\) | −895054. | −0.180116 | ||||||||
\(478\) | −586005. | −0.117309 | ||||||||
\(479\) | −848551. | −0.168982 | −0.0844908 | − | 0.996424i | \(-0.526926\pi\) | ||||
−0.0844908 | + | 0.996424i | \(0.526926\pi\) | |||||||
\(480\) | 175470. | 0.0347616 | ||||||||
\(481\) | 1.19673e6 | 0.235848 | ||||||||
\(482\) | 4.64472e6 | 0.910630 | ||||||||
\(483\) | 70103.0 | 0.0136732 | ||||||||
\(484\) | 81487.2 | 0.0158116 | ||||||||
\(485\) | 594845. | 0.114828 | ||||||||
\(486\) | 3.56629e6 | 0.684898 | ||||||||
\(487\) | 166891. | 0.0318868 | 0.0159434 | − | 0.999873i | \(-0.494925\pi\) | ||||
0.0159434 | + | 0.999873i | \(0.494925\pi\) | |||||||
\(488\) | −130155. | −0.0247406 | ||||||||
\(489\) | −957666. | −0.181110 | ||||||||
\(490\) | −1.90055e6 | −0.357593 | ||||||||
\(491\) | 7.95201e6 | 1.48858 | 0.744292 | − | 0.667854i | \(-0.232787\pi\) | ||||
0.744292 | + | 0.667854i | \(0.232787\pi\) | |||||||
\(492\) | 212747. | 0.0396232 | ||||||||
\(493\) | −319533. | −0.0592105 | ||||||||
\(494\) | 572906. | 0.105625 | ||||||||
\(495\) | 697570. | 0.127960 | ||||||||
\(496\) | −1.71887e6 | −0.313718 | ||||||||
\(497\) | 2.37866e6 | 0.431958 | ||||||||
\(498\) | 336845. | 0.0608634 | ||||||||
\(499\) | −2.46610e6 | −0.443363 | −0.221681 | − | 0.975119i | \(-0.571154\pi\) | ||||
−0.221681 | + | 0.975119i | \(0.571154\pi\) | |||||||
\(500\) | −86963.8 | −0.0155566 | ||||||||
\(501\) | 225076. | 0.0400622 | ||||||||
\(502\) | 961320. | 0.170258 | ||||||||
\(503\) | −7.62765e6 | −1.34422 | −0.672110 | − | 0.740451i | \(-0.734612\pi\) | ||||
−0.672110 | + | 0.740451i | \(0.734612\pi\) | |||||||
\(504\) | −2.47928e6 | −0.434760 | ||||||||
\(505\) | −42487.5 | −0.00741366 | ||||||||
\(506\) | 222504. | 0.0386333 | ||||||||
\(507\) | 1.07130e6 | 0.185093 | ||||||||
\(508\) | −496334. | −0.0853326 | ||||||||
\(509\) | −1.57613e6 | −0.269648 | −0.134824 | − | 0.990870i | \(-0.543047\pi\) | ||||
−0.134824 | + | 0.990870i | \(0.543047\pi\) | |||||||
\(510\) | 42680.8 | 0.00726619 | ||||||||
\(511\) | 2.27378e6 | 0.385209 | ||||||||
\(512\) | 3.73734e6 | 0.630068 | ||||||||
\(513\) | 602006. | 0.100997 | ||||||||
\(514\) | −192886. | −0.0322027 | ||||||||
\(515\) | 967804. | 0.160794 | ||||||||
\(516\) | 222037. | 0.0367114 | ||||||||
\(517\) | 1.64540e6 | 0.270735 | ||||||||
\(518\) | 1.87979e6 | 0.307812 | ||||||||
\(519\) | 1.17217e6 | 0.191018 | ||||||||
\(520\) | 1.04878e6 | 0.170089 | ||||||||
\(521\) | 2.02209e6 | 0.326366 | 0.163183 | − | 0.986596i | \(-0.447824\pi\) | ||||
0.163183 | + | 0.986596i | \(0.447824\pi\) | |||||||
\(522\) | 5.70897e6 | 0.917025 | ||||||||
\(523\) | 7.30394e6 | 1.16762 | 0.583812 | − | 0.811889i | \(-0.301560\pi\) | ||||
0.583812 | + | 0.811889i | \(0.301560\pi\) | |||||||
\(524\) | 2.00966e6 | 0.319738 | ||||||||
\(525\) | −146036. | −0.0231239 | ||||||||
\(526\) | −7.69852e6 | −1.21323 | ||||||||
\(527\) | −116106. | −0.0182108 | ||||||||
\(528\) | 498964. | 0.0778904 | ||||||||
\(529\) | −6.34633e6 | −0.986015 | ||||||||
\(530\) | 594733. | 0.0919671 | ||||||||
\(531\) | 1.83038e6 | 0.281712 | ||||||||
\(532\) | 133329. | 0.0204243 | ||||||||
\(533\) | 2.81089e6 | 0.428575 | ||||||||
\(534\) | −1.74314e6 | −0.264532 | ||||||||
\(535\) | −2.82942e6 | −0.427379 | ||||||||
\(536\) | −5.69956e6 | −0.856899 | ||||||||
\(537\) | −435732. | −0.0652054 | ||||||||
\(538\) | 1.36014e7 | 2.02594 | ||||||||
\(539\) | −1.50082e6 | −0.222514 | ||||||||
\(540\) | −232034. | −0.0342427 | ||||||||
\(541\) | −2.47936e6 | −0.364205 | −0.182103 | − | 0.983280i | \(-0.558290\pi\) | ||||
−0.182103 | + | 0.983280i | \(0.558290\pi\) | |||||||
\(542\) | 4.41900e6 | 0.646139 | ||||||||
\(543\) | 1.86815e6 | 0.271902 | ||||||||
\(544\) | −157688. | −0.0228455 | ||||||||
\(545\) | −4.32242e6 | −0.623355 | ||||||||
\(546\) | −370814. | −0.0532322 | ||||||||
\(547\) | 9.79661e6 | 1.39993 | 0.699967 | − | 0.714175i | \(-0.253198\pi\) | ||||
0.699967 | + | 0.714175i | \(0.253198\pi\) | |||||||
\(548\) | −2.16588e6 | −0.308094 | ||||||||
\(549\) | 185250. | 0.0262318 | ||||||||
\(550\) | −463512. | −0.0653363 | ||||||||
\(551\) | 1.45816e6 | 0.204610 | ||||||||
\(552\) | 171159. | 0.0239085 | ||||||||
\(553\) | 5.40819e6 | 0.752038 | ||||||||
\(554\) | 9.22320e6 | 1.27675 | ||||||||
\(555\) | −406850. | −0.0560663 | ||||||||
\(556\) | 1.35321e6 | 0.185643 | ||||||||
\(557\) | −1.03889e7 | −1.41884 | −0.709420 | − | 0.704786i | \(-0.751043\pi\) | ||||
−0.709420 | + | 0.704786i | \(0.751043\pi\) | |||||||
\(558\) | 2.07443e6 | 0.282041 | ||||||||
\(559\) | 2.93364e6 | 0.397080 | ||||||||
\(560\) | 1.94287e6 | 0.261802 | ||||||||
\(561\) | 33704.0 | 0.00452142 | ||||||||
\(562\) | 1.59817e6 | 0.213443 | ||||||||
\(563\) | 7.00356e6 | 0.931210 | 0.465605 | − | 0.884993i | \(-0.345837\pi\) | ||||
0.465605 | + | 0.884993i | \(0.345837\pi\) | |||||||
\(564\) | −266492. | −0.0352766 | ||||||||
\(565\) | −5.00211e6 | −0.659222 | ||||||||
\(566\) | −1.34528e7 | −1.76511 | ||||||||
\(567\) | 3.32886e6 | 0.434848 | ||||||||
\(568\) | 5.80760e6 | 0.755311 | ||||||||
\(569\) | −1.60867e6 | −0.208299 | −0.104149 | − | 0.994562i | \(-0.533212\pi\) | ||||
−0.104149 | + | 0.994562i | \(0.533212\pi\) | |||||||
\(570\) | −194770. | −0.0251094 | ||||||||
\(571\) | 7.74529e6 | 0.994140 | 0.497070 | − | 0.867711i | \(-0.334409\pi\) | ||||
0.497070 | + | 0.867711i | \(0.334409\pi\) | |||||||
\(572\) | −174375. | −0.0222841 | ||||||||
\(573\) | 29382.8 | 0.00373858 | ||||||||
\(574\) | 4.41529e6 | 0.559345 | ||||||||
\(575\) | −187515. | −0.0236520 | ||||||||
\(576\) | −5.82468e6 | −0.731503 | ||||||||
\(577\) | −7.94489e6 | −0.993455 | −0.496728 | − | 0.867906i | \(-0.665465\pi\) | ||||
−0.496728 | + | 0.867906i | \(0.665465\pi\) | |||||||
\(578\) | 8.66407e6 | 1.07870 | ||||||||
\(579\) | −1.24988e6 | −0.154943 | ||||||||
\(580\) | −562028. | −0.0693726 | ||||||||
\(581\) | 1.03575e6 | 0.127296 | ||||||||
\(582\) | −513499. | −0.0628394 | ||||||||
\(583\) | 469647. | 0.0572269 | ||||||||
\(584\) | 5.55153e6 | 0.673567 | ||||||||
\(585\) | −1.49274e6 | −0.180341 | ||||||||
\(586\) | 8.87409e6 | 1.06753 | ||||||||
\(587\) | −9.21609e6 | −1.10396 | −0.551978 | − | 0.833859i | \(-0.686127\pi\) | ||||
−0.551978 | + | 0.833859i | \(0.686127\pi\) | |||||||
\(588\) | 243076. | 0.0289934 | ||||||||
\(589\) | 529843. | 0.0629301 | ||||||||
\(590\) | −1.21623e6 | −0.143841 | ||||||||
\(591\) | −1.46279e6 | −0.172272 | ||||||||
\(592\) | 5.41275e6 | 0.634766 | ||||||||
\(593\) | −4.22598e6 | −0.493504 | −0.246752 | − | 0.969079i | \(-0.579363\pi\) | ||||
−0.246752 | + | 0.969079i | \(0.579363\pi\) | |||||||
\(594\) | −1.23673e6 | −0.143816 | ||||||||
\(595\) | 131237. | 0.0151972 | ||||||||
\(596\) | 804155. | 0.0927308 | ||||||||
\(597\) | 2.23332e6 | 0.256457 | ||||||||
\(598\) | −476138. | −0.0544477 | ||||||||
\(599\) | 4.30342e6 | 0.490057 | 0.245028 | − | 0.969516i | \(-0.421203\pi\) | ||||
0.245028 | + | 0.969516i | \(0.421203\pi\) | |||||||
\(600\) | −356553. | −0.0404339 | ||||||||
\(601\) | −2.40661e6 | −0.271782 | −0.135891 | − | 0.990724i | \(-0.543390\pi\) | ||||
−0.135891 | + | 0.990724i | \(0.543390\pi\) | |||||||
\(602\) | 4.60810e6 | 0.518240 | ||||||||
\(603\) | 8.11224e6 | 0.908547 | ||||||||
\(604\) | 1.51309e6 | 0.168762 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 36677.3 | 0.00405710 | ||||||||
\(607\) | 9.89092e6 | 1.08960 | 0.544798 | − | 0.838568i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838568i | \(0.316606\pi\) | |||||||
\(608\) | 719597. | 0.0789461 | ||||||||
\(609\) | −943798. | −0.103118 | ||||||||
\(610\) | −123093. | −0.0133939 | ||||||||
\(611\) | −3.52100e6 | −0.381560 | ||||||||
\(612\) | 101531. | 0.0109577 | ||||||||
\(613\) | 8.57915e6 | 0.922132 | 0.461066 | − | 0.887366i | \(-0.347467\pi\) | ||||
0.461066 | + | 0.887366i | \(0.347467\pi\) | |||||||
\(614\) | −6.15489e6 | −0.658870 | ||||||||
\(615\) | −955618. | −0.101882 | ||||||||
\(616\) | 1.30091e6 | 0.138133 | ||||||||
\(617\) | 5.76038e6 | 0.609170 | 0.304585 | − | 0.952485i | \(-0.401482\pi\) | ||||
0.304585 | + | 0.952485i | \(0.401482\pi\) | |||||||
\(618\) | −835455. | −0.0879938 | ||||||||
\(619\) | −5.46621e6 | −0.573402 | −0.286701 | − | 0.958020i | \(-0.592559\pi\) | ||||
−0.286701 | + | 0.958020i | \(0.592559\pi\) | |||||||
\(620\) | −204220. | −0.0213363 | ||||||||
\(621\) | −500323. | −0.0520620 | ||||||||
\(622\) | −8.22929e6 | −0.852877 | ||||||||
\(623\) | −5.35988e6 | −0.553268 | ||||||||
\(624\) | −1.06774e6 | −0.109775 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −774764. | −0.0790193 | ||||||||
\(627\) | −153806. | −0.0156244 | ||||||||
\(628\) | 401168. | 0.0405908 | ||||||||
\(629\) | 365621. | 0.0368472 | ||||||||
\(630\) | −2.34476e6 | −0.235368 | ||||||||
\(631\) | 1.16461e7 | 1.16441 | 0.582207 | − | 0.813041i | \(-0.302189\pi\) | ||||
0.582207 | + | 0.813041i | \(0.302189\pi\) | |||||||
\(632\) | 1.32043e7 | 1.31499 | ||||||||
\(633\) | −1.96428e6 | −0.194847 | ||||||||
\(634\) | 397076. | 0.0392329 | ||||||||
\(635\) | 2.22944e6 | 0.219412 | ||||||||
\(636\) | −76065.1 | −0.00745663 | ||||||||
\(637\) | 3.21162e6 | 0.313600 | ||||||||
\(638\) | −2.99558e6 | −0.291359 | ||||||||
\(639\) | −8.26600e6 | −0.800836 | ||||||||
\(640\) | 5.46498e6 | 0.527398 | ||||||||
\(641\) | −1.79189e7 | −1.72252 | −0.861262 | − | 0.508161i | \(-0.830326\pi\) | ||||
−0.861262 | + | 0.508161i | \(0.830326\pi\) | |||||||
\(642\) | 2.44249e6 | 0.233881 | ||||||||
\(643\) | 6.34522e6 | 0.605228 | 0.302614 | − | 0.953113i | \(-0.402141\pi\) | ||||
0.302614 | + | 0.953113i | \(0.402141\pi\) | |||||||
\(644\) | −110809. | −0.0105284 | ||||||||
\(645\) | −997349. | −0.0943947 | ||||||||
\(646\) | 175033. | 0.0165021 | ||||||||
\(647\) | 1.44082e7 | 1.35316 | 0.676581 | − | 0.736368i | \(-0.263461\pi\) | ||||
0.676581 | + | 0.736368i | \(0.263461\pi\) | |||||||
\(648\) | 8.12754e6 | 0.760364 | ||||||||
\(649\) | −960426. | −0.0895060 | ||||||||
\(650\) | 991873. | 0.0920816 | ||||||||
\(651\) | −342941. | −0.0317152 | ||||||||
\(652\) | 1.51375e6 | 0.139455 | ||||||||
\(653\) | 1.71783e7 | 1.57652 | 0.788258 | − | 0.615345i | \(-0.210983\pi\) | ||||
0.788258 | + | 0.615345i | \(0.210983\pi\) | |||||||
\(654\) | 3.73132e6 | 0.341129 | ||||||||
\(655\) | −9.02702e6 | −0.822131 | ||||||||
\(656\) | 1.27136e7 | 1.15347 | ||||||||
\(657\) | −7.90154e6 | −0.714165 | ||||||||
\(658\) | −5.53072e6 | −0.497985 | ||||||||
\(659\) | −2.55642e6 | −0.229308 | −0.114654 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114654 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(660\) | 59282.2 | 0.00529742 | ||||||||
\(661\) | 3.95119e6 | 0.351742 | 0.175871 | − | 0.984413i | \(-0.443726\pi\) | ||||
0.175871 | + | 0.984413i | \(0.443726\pi\) | |||||||
\(662\) | −3.86869e6 | −0.343098 | ||||||||
\(663\) | −72123.5 | −0.00637226 | ||||||||
\(664\) | 2.52882e6 | 0.222586 | ||||||||
\(665\) | −598890. | −0.0525161 | ||||||||
\(666\) | −6.53240e6 | −0.570673 | ||||||||
\(667\) | −1.21187e6 | −0.105473 | ||||||||
\(668\) | −355768. | −0.0308479 | ||||||||
\(669\) | 910251. | 0.0786314 | ||||||||
\(670\) | −5.39031e6 | −0.463902 | ||||||||
\(671\) | −97203.4 | −0.00833442 | ||||||||
\(672\) | −465760. | −0.0397868 | ||||||||
\(673\) | 7.32719e6 | 0.623591 | 0.311796 | − | 0.950149i | \(-0.399070\pi\) | ||||
0.311796 | + | 0.950149i | \(0.399070\pi\) | |||||||
\(674\) | −1.80715e7 | −1.53231 | ||||||||
\(675\) | 1.04225e6 | 0.0880469 | ||||||||
\(676\) | −1.69335e6 | −0.142522 | ||||||||
\(677\) | 5.81850e6 | 0.487910 | 0.243955 | − | 0.969787i | \(-0.421555\pi\) | ||||
0.243955 | + | 0.969787i | \(0.421555\pi\) | |||||||
\(678\) | 4.31806e6 | 0.360757 | ||||||||
\(679\) | −1.57893e6 | −0.131428 | ||||||||
\(680\) | 320420. | 0.0265734 | ||||||||
\(681\) | 3.29084e6 | 0.271919 | ||||||||
\(682\) | −1.08848e6 | −0.0896107 | ||||||||
\(683\) | 2.77439e6 | 0.227571 | 0.113785 | − | 0.993505i | \(-0.463702\pi\) | ||||
0.113785 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(684\) | −463328. | −0.0378659 | ||||||||
\(685\) | 9.72873e6 | 0.792191 | ||||||||
\(686\) | 1.18805e7 | 0.963882 | ||||||||
\(687\) | −2.26277e6 | −0.182915 | ||||||||
\(688\) | 1.32688e7 | 1.06871 | ||||||||
\(689\) | −1.00500e6 | −0.0806527 | ||||||||
\(690\) | 161872. | 0.0129434 | ||||||||
\(691\) | 6.99799e6 | 0.557543 | 0.278771 | − | 0.960357i | \(-0.410073\pi\) | ||||
0.278771 | + | 0.960357i | \(0.410073\pi\) | |||||||
\(692\) | −1.85281e6 | −0.147084 | ||||||||
\(693\) | −1.85160e6 | −0.146459 | ||||||||
\(694\) | 2.63472e7 | 2.07652 | ||||||||
\(695\) | −6.07836e6 | −0.477336 | ||||||||
\(696\) | −2.30432e6 | −0.180310 | ||||||||
\(697\) | 858777. | 0.0669574 | ||||||||
\(698\) | 2.36520e7 | 1.83751 | ||||||||
\(699\) | −4.59401e6 | −0.355630 | ||||||||
\(700\) | 230833. | 0.0178055 | ||||||||
\(701\) | 2.57702e6 | 0.198072 | 0.0990360 | − | 0.995084i | \(-0.468424\pi\) | ||||
0.0990360 | + | 0.995084i | \(0.468424\pi\) | |||||||
\(702\) | 2.64649e6 | 0.202687 | ||||||||
\(703\) | −1.66848e6 | −0.127331 | ||||||||
\(704\) | 3.05629e6 | 0.232415 | ||||||||
\(705\) | 1.19703e6 | 0.0907054 | ||||||||
\(706\) | 3.43799e6 | 0.259593 | ||||||||
\(707\) | 112777. | 0.00848540 | ||||||||
\(708\) | 155553. | 0.0116626 | ||||||||
\(709\) | −6.24043e6 | −0.466229 | −0.233114 | − | 0.972449i | \(-0.574892\pi\) | ||||
−0.233114 | + | 0.972449i | \(0.574892\pi\) | |||||||
\(710\) | 5.49248e6 | 0.408905 | ||||||||
\(711\) | −1.87938e7 | −1.39425 | ||||||||
\(712\) | −1.30864e7 | −0.967429 | ||||||||
\(713\) | −440349. | −0.0324394 | ||||||||
\(714\) | −113290. | −0.00831661 | ||||||||
\(715\) | 783260. | 0.0572982 | ||||||||
\(716\) | 688744. | 0.0502083 | ||||||||
\(717\) | −336656. | −0.0244561 | ||||||||
\(718\) | 2.22592e7 | 1.61138 | ||||||||
\(719\) | −1.91821e7 | −1.38380 | −0.691900 | − | 0.721994i | \(-0.743226\pi\) | ||||
−0.691900 | + | 0.721994i | \(0.743226\pi\) | |||||||
\(720\) | −6.75159e6 | −0.485372 | ||||||||
\(721\) | −2.56890e6 | −0.184039 | ||||||||
\(722\) | −798749. | −0.0570252 | ||||||||
\(723\) | 2.66836e6 | 0.189845 | ||||||||
\(724\) | −2.95291e6 | −0.209365 | ||||||||
\(725\) | 2.52452e6 | 0.178375 | ||||||||
\(726\) | 315971. | 0.0222487 | ||||||||
\(727\) | −8.02243e6 | −0.562950 | −0.281475 | − | 0.959568i | \(-0.590824\pi\) | ||||
−0.281475 | + | 0.959568i | \(0.590824\pi\) | |||||||
\(728\) | −2.78384e6 | −0.194677 | ||||||||
\(729\) | −1.01411e7 | −0.706754 | ||||||||
\(730\) | 5.25031e6 | 0.364651 | ||||||||
\(731\) | 896279. | 0.0620369 | ||||||||
\(732\) | 15743.3 | 0.00108597 | ||||||||
\(733\) | 7.56459e6 | 0.520027 | 0.260013 | − | 0.965605i | \(-0.416273\pi\) | ||||
0.260013 | + | 0.965605i | \(0.416273\pi\) | |||||||
\(734\) | −7.87916e6 | −0.539809 | ||||||||
\(735\) | −1.09185e6 | −0.0745496 | ||||||||
\(736\) | −598052. | −0.0406953 | ||||||||
\(737\) | −4.25660e6 | −0.288665 | ||||||||
\(738\) | −1.53434e7 | −1.03701 | ||||||||
\(739\) | −1.22451e6 | −0.0824805 | −0.0412402 | − | 0.999149i | \(-0.513131\pi\) | ||||
−0.0412402 | + | 0.999149i | \(0.513131\pi\) | |||||||
\(740\) | 643092. | 0.0431712 | ||||||||
\(741\) | 329130. | 0.0220203 | ||||||||
\(742\) | −1.57864e6 | −0.105262 | ||||||||
\(743\) | −2.01415e7 | −1.33850 | −0.669251 | − | 0.743037i | \(-0.733385\pi\) | ||||
−0.669251 | + | 0.743037i | \(0.733385\pi\) | |||||||
\(744\) | −837305. | −0.0554564 | ||||||||
\(745\) | −3.61211e6 | −0.238435 | ||||||||
\(746\) | 2.69438e7 | 1.77260 | ||||||||
\(747\) | −3.59929e6 | −0.236002 | ||||||||
\(748\) | −53274.6 | −0.00348150 | ||||||||
\(749\) | 7.51030e6 | 0.489162 | ||||||||
\(750\) | −337206. | −0.0218898 | ||||||||
\(751\) | 8.63154e6 | 0.558455 | 0.279228 | − | 0.960225i | \(-0.409922\pi\) | ||||
0.279228 | + | 0.960225i | \(0.409922\pi\) | |||||||
\(752\) | −1.59254e7 | −1.02694 | ||||||||
\(753\) | 552271. | 0.0354948 | ||||||||
\(754\) | 6.41026e6 | 0.410627 | ||||||||
\(755\) | −6.79653e6 | −0.433930 | ||||||||
\(756\) | 615902. | 0.0391929 | ||||||||
\(757\) | −1.86237e7 | −1.18121 | −0.590604 | − | 0.806961i | \(-0.701111\pi\) | ||||
−0.590604 | + | 0.806961i | \(0.701111\pi\) | |||||||
\(758\) | 2.94462e7 | 1.86147 | ||||||||
\(759\) | 127827. | 0.00805412 | ||||||||
\(760\) | −1.46221e6 | −0.0918284 | ||||||||
\(761\) | 6.00562e6 | 0.375921 | 0.187960 | − | 0.982177i | \(-0.439812\pi\) | ||||
0.187960 | + | 0.982177i | \(0.439812\pi\) | |||||||
\(762\) | −1.92456e6 | −0.120073 | ||||||||
\(763\) | 1.14733e7 | 0.713469 | ||||||||
\(764\) | −46444.2 | −0.00287871 | ||||||||
\(765\) | −456057. | −0.0281751 | ||||||||
\(766\) | 1.31796e7 | 0.811577 | ||||||||
\(767\) | 2.05522e6 | 0.126145 | ||||||||
\(768\) | −1.87160e6 | −0.114501 | ||||||||
\(769\) | 1.48691e7 | 0.906712 | 0.453356 | − | 0.891330i | \(-0.350227\pi\) | ||||
0.453356 | + | 0.891330i | \(0.350227\pi\) | |||||||
\(770\) | 1.23033e6 | 0.0747815 | ||||||||
\(771\) | −110811. | −0.00671350 | ||||||||
\(772\) | 1.97563e6 | 0.119306 | ||||||||
\(773\) | −1.75443e7 | −1.05606 | −0.528028 | − | 0.849227i | \(-0.677068\pi\) | ||||
−0.528028 | + | 0.849227i | \(0.677068\pi\) | |||||||
\(774\) | −1.60135e7 | −0.960799 | ||||||||
\(775\) | 917318. | 0.0548612 | ||||||||
\(776\) | −3.85503e6 | −0.229812 | ||||||||
\(777\) | 1.07993e6 | 0.0641714 | ||||||||
\(778\) | 2.55775e7 | 1.51499 | ||||||||
\(779\) | −3.91896e6 | −0.231381 | ||||||||
\(780\) | −126858. | −0.00746591 | ||||||||
\(781\) | 4.33729e6 | 0.254443 | ||||||||
\(782\) | −145468. | −0.00850652 | ||||||||
\(783\) | 6.73586e6 | 0.392634 | ||||||||
\(784\) | 1.45260e7 | 0.844028 | ||||||||
\(785\) | −1.80197e6 | −0.104370 | ||||||||
\(786\) | 7.79256e6 | 0.449908 | ||||||||
\(787\) | −5.55400e6 | −0.319646 | −0.159823 | − | 0.987146i | \(-0.551092\pi\) | ||||
−0.159823 | + | 0.987146i | \(0.551092\pi\) | |||||||
\(788\) | 2.31218e6 | 0.132649 | ||||||||
\(789\) | −4.42275e6 | −0.252929 | ||||||||
\(790\) | 1.24879e7 | 0.711902 | ||||||||
\(791\) | 1.32774e7 | 0.754521 | ||||||||
\(792\) | −4.52076e6 | −0.256094 | ||||||||
\(793\) | 208006. | 0.0117461 | ||||||||
\(794\) | −5.30532e6 | −0.298648 | ||||||||
\(795\) | 341670. | 0.0191729 | ||||||||
\(796\) | −3.53011e6 | −0.197472 | ||||||||
\(797\) | −3.60622e6 | −0.201097 | −0.100549 | − | 0.994932i | \(-0.532060\pi\) | ||||
−0.100549 | + | 0.994932i | \(0.532060\pi\) | |||||||
\(798\) | 516991. | 0.0287393 | ||||||||
\(799\) | −1.07573e6 | −0.0596122 | ||||||||
\(800\) | 1.24584e6 | 0.0688236 | ||||||||
\(801\) | 1.86259e7 | 1.02574 | ||||||||
\(802\) | 1.65629e7 | 0.909288 | ||||||||
\(803\) | 4.14605e6 | 0.226906 | ||||||||
\(804\) | 689409. | 0.0376129 | ||||||||
\(805\) | 497733. | 0.0270712 | ||||||||
\(806\) | 2.32925e6 | 0.126293 | ||||||||
\(807\) | 7.81389e6 | 0.422361 | ||||||||
\(808\) | 275350. | 0.0148374 | ||||||||
\(809\) | −8.69499e6 | −0.467087 | −0.233543 | − | 0.972346i | \(-0.575032\pi\) | ||||
−0.233543 | + | 0.972346i | \(0.575032\pi\) | |||||||
\(810\) | 7.68655e6 | 0.411641 | ||||||||
\(811\) | 6.45171e6 | 0.344447 | 0.172224 | − | 0.985058i | \(-0.444905\pi\) | ||||
0.172224 | + | 0.985058i | \(0.444905\pi\) | |||||||
\(812\) | 1.49182e6 | 0.0794013 | ||||||||
\(813\) | 2.53868e6 | 0.134705 | ||||||||
\(814\) | 3.42764e6 | 0.181315 | ||||||||
\(815\) | −6.79946e6 | −0.358575 | ||||||||
\(816\) | −326212. | −0.0171504 | ||||||||
\(817\) | −4.09010e6 | −0.214377 | ||||||||
\(818\) | 2.88469e7 | 1.50736 | ||||||||
\(819\) | 3.96226e6 | 0.206411 | ||||||||
\(820\) | 1.51051e6 | 0.0784491 | ||||||||
\(821\) | −9.35989e6 | −0.484633 | −0.242316 | − | 0.970197i | \(-0.577907\pi\) | ||||
−0.242316 | + | 0.970197i | \(0.577907\pi\) | |||||||
\(822\) | −8.39832e6 | −0.433523 | ||||||||
\(823\) | −1.75646e7 | −0.903940 | −0.451970 | − | 0.892033i | \(-0.649279\pi\) | ||||
−0.451970 | + | 0.892033i | \(0.649279\pi\) | |||||||
\(824\) | −6.27207e6 | −0.321805 | ||||||||
\(825\) | −266284. | −0.0136211 | ||||||||
\(826\) | 3.22830e6 | 0.164636 | ||||||||
\(827\) | −1.21583e6 | −0.0618169 | −0.0309085 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309085 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(828\) | 385068. | 0.0195192 | ||||||||
\(829\) | 1.44716e7 | 0.731360 | 0.365680 | − | 0.930741i | \(-0.380836\pi\) | ||||
0.365680 | + | 0.930741i | \(0.380836\pi\) | |||||||
\(830\) | 2.39160e6 | 0.120502 | ||||||||
\(831\) | 5.29866e6 | 0.266173 | ||||||||
\(832\) | −6.54019e6 | −0.327553 | ||||||||
\(833\) | 981206. | 0.0489945 | ||||||||
\(834\) | 5.24714e6 | 0.261221 | ||||||||
\(835\) | 1.59804e6 | 0.0793181 | ||||||||
\(836\) | 243115. | 0.0120308 | ||||||||
\(837\) | 2.44756e6 | 0.120759 | ||||||||
\(838\) | 1.33761e7 | 0.657993 | ||||||||
\(839\) | 483536. | 0.0237151 | 0.0118575 | − | 0.999930i | \(-0.496226\pi\) | ||||
0.0118575 | + | 0.999930i | \(0.496226\pi\) | |||||||
\(840\) | 946419. | 0.0462792 | ||||||||
\(841\) | −4.19572e6 | −0.204558 | ||||||||
\(842\) | 4.15652e7 | 2.02046 | ||||||||
\(843\) | 918137. | 0.0444978 | ||||||||
\(844\) | 3.10486e6 | 0.150032 | ||||||||
\(845\) | 7.60622e6 | 0.366461 | ||||||||
\(846\) | 1.92196e7 | 0.923248 | ||||||||
\(847\) | 971562. | 0.0465331 | ||||||||
\(848\) | −4.54559e6 | −0.217070 | ||||||||
\(849\) | −7.72855e6 | −0.367984 | ||||||||
\(850\) | 303035. | 0.0143862 | ||||||||
\(851\) | 1.38666e6 | 0.0656368 | ||||||||
\(852\) | −702476. | −0.0331538 | ||||||||
\(853\) | −2.49242e7 | −1.17287 | −0.586433 | − | 0.809998i | \(-0.699468\pi\) | ||||
−0.586433 | + | 0.809998i | \(0.699468\pi\) | |||||||
\(854\) | 326732. | 0.0153302 | ||||||||
\(855\) | 2.08118e6 | 0.0973631 | ||||||||
\(856\) | 1.83367e7 | 0.855336 | ||||||||
\(857\) | −2.26913e7 | −1.05538 | −0.527688 | − | 0.849438i | \(-0.676941\pi\) | ||||
−0.527688 | + | 0.849438i | \(0.676941\pi\) | |||||||
\(858\) | −676148. | −0.0313562 | ||||||||
\(859\) | −4.02087e7 | −1.85925 | −0.929624 | − | 0.368510i | \(-0.879868\pi\) | ||||
−0.929624 | + | 0.368510i | \(0.879868\pi\) | |||||||
\(860\) | 1.57647e6 | 0.0726841 | ||||||||
\(861\) | 2.53655e6 | 0.116610 | ||||||||
\(862\) | 1.72135e7 | 0.789043 | ||||||||
\(863\) | −2.30864e6 | −0.105518 | −0.0527592 | − | 0.998607i | \(-0.516802\pi\) | ||||
−0.0527592 | + | 0.998607i | \(0.516802\pi\) | |||||||
\(864\) | 3.32411e6 | 0.151493 | ||||||||
\(865\) | 8.32246e6 | 0.378191 | ||||||||
\(866\) | 9.53134e6 | 0.431876 | ||||||||
\(867\) | 4.97744e6 | 0.224884 | ||||||||
\(868\) | 542074. | 0.0244207 | ||||||||
\(869\) | 9.86139e6 | 0.442984 | ||||||||
\(870\) | −2.17929e6 | −0.0976151 | ||||||||
\(871\) | 9.10874e6 | 0.406830 | ||||||||
\(872\) | 2.80124e7 | 1.24755 | ||||||||
\(873\) | 5.48689e6 | 0.243664 | ||||||||
\(874\) | 663834. | 0.0293955 | ||||||||
\(875\) | −1.03686e6 | −0.0457825 | ||||||||
\(876\) | −671503. | −0.0295657 | ||||||||
\(877\) | −1.65067e7 | −0.724705 | −0.362353 | − | 0.932041i | \(-0.618026\pi\) | ||||
−0.362353 | + | 0.932041i | \(0.618026\pi\) | |||||||
\(878\) | −2.50704e7 | −1.09755 | ||||||||
\(879\) | 5.09810e6 | 0.222554 | ||||||||
\(880\) | 3.54265e6 | 0.154213 | ||||||||
\(881\) | −3.31242e7 | −1.43782 | −0.718912 | − | 0.695101i | \(-0.755360\pi\) | ||||
−0.718912 | + | 0.695101i | \(0.755360\pi\) | |||||||
\(882\) | −1.75308e7 | −0.758806 | ||||||||
\(883\) | 4.43697e7 | 1.91507 | 0.957535 | − | 0.288317i | \(-0.0930958\pi\) | ||||
0.957535 | + | 0.288317i | \(0.0930958\pi\) | |||||||
\(884\) | 114003. | 0.00490665 | ||||||||
\(885\) | −698713. | −0.0299875 | ||||||||
\(886\) | −2.46046e7 | −1.05301 | ||||||||
\(887\) | 1.25234e7 | 0.534456 | 0.267228 | − | 0.963633i | \(-0.413892\pi\) | ||||
0.267228 | + | 0.963633i | \(0.413892\pi\) | |||||||
\(888\) | 2.63668e6 | 0.112209 | ||||||||
\(889\) | −5.91773e6 | −0.251131 | ||||||||
\(890\) | −1.23763e7 | −0.523741 | ||||||||
\(891\) | 6.06989e6 | 0.256145 | ||||||||
\(892\) | −1.43880e6 | −0.0605463 | ||||||||
\(893\) | 4.90900e6 | 0.205999 | ||||||||
\(894\) | 3.11815e6 | 0.130483 | ||||||||
\(895\) | −3.09371e6 | −0.129099 | ||||||||
\(896\) | −1.45060e7 | −0.603641 | ||||||||
\(897\) | −273538. | −0.0113511 | ||||||||
\(898\) | 1.58558e7 | 0.656140 | ||||||||
\(899\) | 5.92842e6 | 0.244647 | ||||||||
\(900\) | −802160. | −0.0330107 | ||||||||
\(901\) | −307046. | −0.0126006 | ||||||||
\(902\) | 8.05091e6 | 0.329480 | ||||||||
\(903\) | 2.64732e6 | 0.108041 | ||||||||
\(904\) | 3.24173e7 | 1.31934 | ||||||||
\(905\) | 1.32639e7 | 0.538332 | ||||||||
\(906\) | 5.86709e6 | 0.237467 | ||||||||
\(907\) | −3.99966e7 | −1.61437 | −0.807187 | − | 0.590295i | \(-0.799011\pi\) | ||||
−0.807187 | + | 0.590295i | \(0.799011\pi\) | |||||||
\(908\) | −5.20170e6 | −0.209378 | ||||||||
\(909\) | −391908. | −0.0157316 | ||||||||
\(910\) | −2.63279e6 | −0.105393 | ||||||||
\(911\) | 2.53678e6 | 0.101272 | 0.0506358 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506358 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(912\) | 1.48864e6 | 0.0592657 | ||||||||
\(913\) | 1.88860e6 | 0.0749829 | ||||||||
\(914\) | −2.02685e7 | −0.802519 | ||||||||
\(915\) | −70715.8 | −0.00279231 | ||||||||
\(916\) | 3.57667e6 | 0.140845 | ||||||||
\(917\) | 2.39610e7 | 0.940981 | ||||||||
\(918\) | 808548. | 0.0316664 | ||||||||
\(919\) | 1.96621e7 | 0.767963 | 0.383981 | − | 0.923341i | \(-0.374553\pi\) | ||||
0.383981 | + | 0.923341i | \(0.374553\pi\) | |||||||
\(920\) | 1.21524e6 | 0.0473359 | ||||||||
\(921\) | −3.53594e6 | −0.137359 | ||||||||
\(922\) | 3.02657e7 | 1.17253 | ||||||||
\(923\) | −9.28140e6 | −0.358599 | ||||||||
\(924\) | −157356. | −0.00606323 | ||||||||
\(925\) | −2.88865e6 | −0.111004 | ||||||||
\(926\) | −2.48633e7 | −0.952866 | ||||||||
\(927\) | 8.92709e6 | 0.341201 | ||||||||
\(928\) | 8.05159e6 | 0.306910 | ||||||||
\(929\) | 2.75281e6 | 0.104650 | 0.0523248 | − | 0.998630i | \(-0.483337\pi\) | ||||
0.0523248 | + | 0.998630i | \(0.483337\pi\) | |||||||
\(930\) | −791873. | −0.0300226 | ||||||||
\(931\) | −4.47766e6 | −0.169308 | ||||||||
\(932\) | 7.26156e6 | 0.273836 | ||||||||
\(933\) | −4.72766e6 | −0.177804 | ||||||||
\(934\) | 2.65459e6 | 0.0995705 | ||||||||
\(935\) | 239300. | 0.00895185 | ||||||||
\(936\) | 9.67401e6 | 0.360925 | ||||||||
\(937\) | 6.87582e6 | 0.255844 | 0.127922 | − | 0.991784i | \(-0.459169\pi\) | ||||
0.127922 | + | 0.991784i | \(0.459169\pi\) | |||||||
\(938\) | 1.43078e7 | 0.530966 | ||||||||
\(939\) | −445096. | −0.0164736 | ||||||||
\(940\) | −1.89210e6 | −0.0698433 | ||||||||
\(941\) | 2.30189e7 | 0.847444 | 0.423722 | − | 0.905792i | \(-0.360723\pi\) | ||||
0.423722 | + | 0.905792i | \(0.360723\pi\) | |||||||
\(942\) | 1.55555e6 | 0.0571158 | ||||||||
\(943\) | 3.25702e6 | 0.119273 | ||||||||
\(944\) | 9.29569e6 | 0.339509 | ||||||||
\(945\) | −2.76652e6 | −0.100775 | ||||||||
\(946\) | 8.40249e6 | 0.305267 | ||||||||
\(947\) | −2.03916e7 | −0.738883 | −0.369441 | − | 0.929254i | \(-0.620451\pi\) | ||||
−0.369441 | + | 0.929254i | \(0.620451\pi\) | |||||||
\(948\) | −1.59717e6 | −0.0577206 | ||||||||
\(949\) | −8.87217e6 | −0.319790 | ||||||||
\(950\) | −1.38287e6 | −0.0497134 | ||||||||
\(951\) | 228117. | 0.00817912 | ||||||||
\(952\) | −850511. | −0.0304150 | ||||||||
\(953\) | −7.84956e6 | −0.279971 | −0.139985 | − | 0.990154i | \(-0.544706\pi\) | ||||
−0.139985 | + | 0.990154i | \(0.544706\pi\) | |||||||
\(954\) | 5.48586e6 | 0.195152 | ||||||||
\(955\) | 208618. | 0.00740192 | ||||||||
\(956\) | 532138. | 0.0188313 | ||||||||
\(957\) | −1.72094e6 | −0.0607414 | ||||||||
\(958\) | 5.20084e6 | 0.183088 | ||||||||
\(959\) | −2.58236e7 | −0.906713 | ||||||||
\(960\) | 2.22346e6 | 0.0778667 | ||||||||
\(961\) | −2.64750e7 | −0.924756 | ||||||||
\(962\) | −7.33484e6 | −0.255536 | ||||||||
\(963\) | −2.60988e7 | −0.906889 | ||||||||
\(964\) | −4.21777e6 | −0.146181 | ||||||||
\(965\) | −8.87417e6 | −0.306767 | ||||||||
\(966\) | −429667. | −0.0148146 | ||||||||
\(967\) | 1.61301e7 | 0.554716 | 0.277358 | − | 0.960767i | \(-0.410541\pi\) | ||||
0.277358 | + | 0.960767i | \(0.410541\pi\) | |||||||
\(968\) | 2.37211e6 | 0.0813666 | ||||||||
\(969\) | 100555. | 0.00344028 | ||||||||
\(970\) | −3.64586e6 | −0.124414 | ||||||||
\(971\) | 3.77106e7 | 1.28356 | 0.641779 | − | 0.766890i | \(-0.278197\pi\) | ||||
0.641779 | + | 0.766890i | \(0.278197\pi\) | |||||||
\(972\) | −3.23847e6 | −0.109945 | ||||||||
\(973\) | 1.61342e7 | 0.546342 | ||||||||
\(974\) | −1.02289e6 | −0.0345487 | ||||||||
\(975\) | 569824. | 0.0191968 | ||||||||
\(976\) | 940805. | 0.0316137 | ||||||||
\(977\) | −2.52479e7 | −0.846232 | −0.423116 | − | 0.906076i | \(-0.639064\pi\) | ||||
−0.423116 | + | 0.906076i | \(0.639064\pi\) | |||||||
\(978\) | 5.86962e6 | 0.196229 | ||||||||
\(979\) | −9.77329e6 | −0.325900 | ||||||||
\(980\) | 1.72585e6 | 0.0574033 | ||||||||
\(981\) | −3.98703e7 | −1.32275 | ||||||||
\(982\) | −4.87386e7 | −1.61285 | ||||||||
\(983\) | −460177. | −0.0151894 | −0.00759471 | − | 0.999971i | \(-0.502417\pi\) | ||||
−0.00759471 | + | 0.999971i | \(0.502417\pi\) | |||||||
\(984\) | 6.19310e6 | 0.203901 | ||||||||
\(985\) | −1.03859e7 | −0.341077 | ||||||||
\(986\) | 1.95845e6 | 0.0641533 | ||||||||
\(987\) | −3.17736e6 | −0.103818 | ||||||||
\(988\) | −520243. | −0.0169556 | ||||||||
\(989\) | 3.39925e6 | 0.110508 | ||||||||
\(990\) | −4.27547e6 | −0.138642 | ||||||||
\(991\) | 1.33944e7 | 0.433252 | 0.216626 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216626 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(992\) | 2.92565e6 | 0.0943937 | ||||||||
\(993\) | −2.22253e6 | −0.0715278 | ||||||||
\(994\) | −1.45790e7 | −0.468018 | ||||||||
\(995\) | 1.58566e7 | 0.507753 | ||||||||
\(996\) | −305881. | −0.00977022 | ||||||||
\(997\) | −5.74306e7 | −1.82981 | −0.914904 | − | 0.403672i | \(-0.867734\pi\) | ||||
−0.914904 | + | 0.403672i | \(0.867734\pi\) | |||||||
\(998\) | 1.51149e7 | 0.480374 | ||||||||
\(999\) | −7.70740e6 | −0.244340 |
(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 | 1045.6.a.a.1.10 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.a.1.10 | ✓ | 35 | 1.1 | even | 1 | trivial |