Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 15x + 11 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.03932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.07863 | −1.42811 | −0.714057 | − | 0.700087i | \(-0.753144\pi\) | ||||
−0.714057 | + | 0.700087i | \(0.753144\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 33.2643 | 1.03951 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −72.7077 | −0.824522 | ||||||||
\(7\) | −39.3760 | −0.303730 | −0.151865 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151865 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(8\) | −10.2141 | −0.0564257 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 201.966 | 0.638672 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 299.379 | 0.600162 | ||||||||
\(13\) | −220.765 | −0.362302 | −0.181151 | − | 0.983455i | \(-0.557982\pi\) | ||||
−0.181151 | + | 0.983455i | \(0.557982\pi\) | |||||||
\(14\) | 318.105 | 0.433761 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | −981.943 | −0.958928 | ||||||||
\(17\) | −200.343 | −0.168133 | −0.0840664 | − | 0.996460i | \(-0.526791\pi\) | ||||
−0.0840664 | + | 0.996460i | \(0.526791\pi\) | |||||||
\(18\) | −654.369 | −0.476038 | ||||||||
\(19\) | 350.345 | 0.222645 | 0.111322 | − | 0.993784i | \(-0.464491\pi\) | ||||
0.111322 | + | 0.993784i | \(0.464491\pi\) | |||||||
\(20\) | −831.608 | −0.464883 | ||||||||
\(21\) | −354.384 | −0.175358 | ||||||||
\(22\) | −977.515 | −0.430593 | ||||||||
\(23\) | 1385.09 | 0.545957 | 0.272978 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(24\) | −91.9273 | −0.0325774 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1783.48 | 0.517409 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −1309.82 | −0.315730 | ||||||||
\(29\) | 5506.64 | 1.21588 | 0.607942 | − | 0.793982i | \(-0.291995\pi\) | ||||
0.607942 | + | 0.793982i | \(0.291995\pi\) | |||||||
\(30\) | 1817.69 | 0.368738 | ||||||||
\(31\) | −2450.86 | −0.458051 | −0.229025 | − | 0.973420i | \(-0.573554\pi\) | ||||
−0.229025 | + | 0.973420i | \(0.573554\pi\) | |||||||
\(32\) | 8259.61 | 1.42588 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 1618.50 | 0.240113 | ||||||||
\(35\) | 984.401 | 0.135832 | ||||||||
\(36\) | 2694.41 | 0.346504 | ||||||||
\(37\) | −4060.46 | −0.487609 | −0.243804 | − | 0.969824i | \(-0.578395\pi\) | ||||
−0.243804 | + | 0.969824i | \(0.578395\pi\) | |||||||
\(38\) | −2830.31 | −0.317962 | ||||||||
\(39\) | −1986.88 | −0.209175 | ||||||||
\(40\) | 255.354 | 0.0252343 | ||||||||
\(41\) | 527.283 | 0.0489874 | 0.0244937 | − | 0.999700i | \(-0.492203\pi\) | ||||
0.0244937 | + | 0.999700i | \(0.492203\pi\) | |||||||
\(42\) | 2862.94 | 0.250432 | ||||||||
\(43\) | −12078.9 | −0.996218 | −0.498109 | − | 0.867114i | \(-0.665972\pi\) | ||||
−0.498109 | + | 0.867114i | \(0.665972\pi\) | |||||||
\(44\) | 4024.99 | 0.313424 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −11189.6 | −0.779689 | ||||||||
\(47\) | 563.023 | 0.0371776 | 0.0185888 | − | 0.999827i | \(-0.494083\pi\) | ||||
0.0185888 | + | 0.999827i | \(0.494083\pi\) | |||||||
\(48\) | −8837.48 | −0.553638 | ||||||||
\(49\) | −15256.5 | −0.907748 | ||||||||
\(50\) | −5049.15 | −0.285623 | ||||||||
\(51\) | −1803.09 | −0.0970715 | ||||||||
\(52\) | −7343.59 | −0.376617 | ||||||||
\(53\) | −37203.0 | −1.81923 | −0.909617 | − | 0.415449i | \(-0.863625\pi\) | ||||
−0.909617 | + | 0.415449i | \(0.863625\pi\) | |||||||
\(54\) | −5889.32 | −0.274841 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 402.192 | 0.0171381 | ||||||||
\(57\) | 3153.11 | 0.128544 | ||||||||
\(58\) | −44486.2 | −1.73642 | ||||||||
\(59\) | 2157.64 | 0.0806955 | 0.0403477 | − | 0.999186i | \(-0.487153\pi\) | ||||
0.0403477 | + | 0.999186i | \(0.487153\pi\) | |||||||
\(60\) | −7484.48 | −0.268400 | ||||||||
\(61\) | −39938.0 | −1.37424 | −0.687119 | − | 0.726545i | \(-0.741125\pi\) | ||||
−0.687119 | + | 0.726545i | \(0.741125\pi\) | |||||||
\(62\) | 19799.6 | 0.654149 | ||||||||
\(63\) | −3189.46 | −0.101243 | ||||||||
\(64\) | −35304.2 | −1.07740 | ||||||||
\(65\) | 5519.11 | 0.162026 | ||||||||
\(66\) | −8797.63 | −0.248603 | ||||||||
\(67\) | −38473.2 | −1.04706 | −0.523529 | − | 0.852008i | \(-0.675385\pi\) | ||||
−0.523529 | + | 0.852008i | \(0.675385\pi\) | |||||||
\(68\) | −6664.29 | −0.174776 | ||||||||
\(69\) | 12465.8 | 0.315208 | ||||||||
\(70\) | −7952.62 | −0.193984 | ||||||||
\(71\) | −13725.3 | −0.323129 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(72\) | −827.345 | −0.0188086 | ||||||||
\(73\) | −39736.3 | −0.872731 | −0.436366 | − | 0.899769i | \(-0.643735\pi\) | ||||
−0.436366 | + | 0.899769i | \(0.643735\pi\) | |||||||
\(74\) | 32803.0 | 0.696361 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | 11654.0 | 0.231441 | ||||||||
\(77\) | −4764.50 | −0.0915779 | ||||||||
\(78\) | 16051.3 | 0.298726 | ||||||||
\(79\) | 35672.9 | 0.643088 | 0.321544 | − | 0.946895i | \(-0.395798\pi\) | ||||
0.321544 | + | 0.946895i | \(0.395798\pi\) | |||||||
\(80\) | 24548.6 | 0.428846 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −4259.73 | −0.0699596 | ||||||||
\(83\) | −79999.7 | −1.27466 | −0.637328 | − | 0.770593i | \(-0.719960\pi\) | ||||
−0.637328 | + | 0.770593i | \(0.719960\pi\) | |||||||
\(84\) | −11788.4 | −0.182287 | ||||||||
\(85\) | 5008.58 | 0.0751913 | ||||||||
\(86\) | 97580.6 | 1.42271 | ||||||||
\(87\) | 49559.8 | 0.701991 | ||||||||
\(88\) | −1235.91 | −0.0170130 | ||||||||
\(89\) | −37783.0 | −0.505616 | −0.252808 | − | 0.967516i | \(-0.581354\pi\) | ||||
−0.252808 | + | 0.967516i | \(0.581354\pi\) | |||||||
\(90\) | 16359.2 | 0.212891 | ||||||||
\(91\) | 8692.83 | 0.110042 | ||||||||
\(92\) | 46074.1 | 0.567528 | ||||||||
\(93\) | −22057.7 | −0.264456 | ||||||||
\(94\) | −4548.46 | −0.0530939 | ||||||||
\(95\) | −8758.63 | −0.0995697 | ||||||||
\(96\) | 74336.5 | 0.823235 | ||||||||
\(97\) | −7616.35 | −0.0821897 | −0.0410948 | − | 0.999155i | \(-0.513085\pi\) | ||||
−0.0410948 | + | 0.999155i | \(0.513085\pi\) | |||||||
\(98\) | 123252. | 1.29637 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 20790.2 | 0.207902 | ||||||||
\(101\) | 125963. | 1.22868 | 0.614341 | − | 0.789041i | \(-0.289422\pi\) | ||||
0.614341 | + | 0.789041i | \(0.289422\pi\) | |||||||
\(102\) | 14566.5 | 0.138629 | ||||||||
\(103\) | −165220. | −1.53451 | −0.767257 | − | 0.641340i | \(-0.778379\pi\) | ||||
−0.767257 | + | 0.641340i | \(0.778379\pi\) | |||||||
\(104\) | 2254.92 | 0.0204431 | ||||||||
\(105\) | 8859.61 | 0.0784226 | ||||||||
\(106\) | 300550. | 2.59807 | ||||||||
\(107\) | −13152.3 | −0.111056 | −0.0555279 | − | 0.998457i | \(-0.517684\pi\) | ||||
−0.0555279 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(108\) | 24249.7 | 0.200054 | ||||||||
\(109\) | 37970.9 | 0.306115 | 0.153057 | − | 0.988217i | \(-0.451088\pi\) | ||||
0.153057 | + | 0.988217i | \(0.451088\pi\) | |||||||
\(110\) | 24437.9 | 0.192567 | ||||||||
\(111\) | −36544.2 | −0.281521 | ||||||||
\(112\) | 38665.0 | 0.291255 | ||||||||
\(113\) | −85189.7 | −0.627612 | −0.313806 | − | 0.949487i | \(-0.601604\pi\) | ||||
−0.313806 | + | 0.949487i | \(0.601604\pi\) | |||||||
\(114\) | −25472.8 | −0.183575 | ||||||||
\(115\) | −34627.3 | −0.244159 | ||||||||
\(116\) | 183175. | 1.26392 | ||||||||
\(117\) | −17881.9 | −0.120767 | ||||||||
\(118\) | −17430.8 | −0.115242 | ||||||||
\(119\) | 7888.73 | 0.0510669 | ||||||||
\(120\) | 2298.18 | 0.0145691 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 322645. | 1.96257 | ||||||||
\(123\) | 4745.55 | 0.0282829 | ||||||||
\(124\) | −81526.1 | −0.476148 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 25766.5 | 0.144587 | ||||||||
\(127\) | −141237. | −0.777033 | −0.388517 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388517 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(128\) | 20902.2 | 0.112763 | ||||||||
\(129\) | −108710. | −0.575167 | ||||||||
\(130\) | −44586.9 | −0.231392 | ||||||||
\(131\) | 210469. | 1.07155 | 0.535773 | − | 0.844362i | \(-0.320020\pi\) | ||||
0.535773 | + | 0.844362i | \(0.320020\pi\) | |||||||
\(132\) | 36224.9 | 0.180956 | ||||||||
\(133\) | −13795.2 | −0.0676237 | ||||||||
\(134\) | 310811. | 1.49532 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 2046.33 | 0.00948701 | ||||||||
\(137\) | 19565.1 | 0.0890594 | 0.0445297 | − | 0.999008i | \(-0.485821\pi\) | ||||
0.0445297 | + | 0.999008i | \(0.485821\pi\) | |||||||
\(138\) | −100707. | −0.450154 | ||||||||
\(139\) | 132498. | 0.581663 | 0.290831 | − | 0.956774i | \(-0.406068\pi\) | ||||
0.290831 | + | 0.956774i | \(0.406068\pi\) | |||||||
\(140\) | 32745.5 | 0.141199 | ||||||||
\(141\) | 5067.21 | 0.0214645 | ||||||||
\(142\) | 110882. | 0.461465 | ||||||||
\(143\) | −26712.5 | −0.109238 | ||||||||
\(144\) | −79537.3 | −0.319643 | ||||||||
\(145\) | −137666. | −0.543760 | ||||||||
\(146\) | 321015. | 1.24636 | ||||||||
\(147\) | −137309. | −0.524089 | ||||||||
\(148\) | −135069. | −0.506874 | ||||||||
\(149\) | −153316. | −0.565748 | −0.282874 | − | 0.959157i | \(-0.591288\pi\) | ||||
−0.282874 | + | 0.959157i | \(0.591288\pi\) | |||||||
\(150\) | −45442.3 | −0.164904 | ||||||||
\(151\) | 248151. | 0.885672 | 0.442836 | − | 0.896603i | \(-0.353972\pi\) | ||||
0.442836 | + | 0.896603i | \(0.353972\pi\) | |||||||
\(152\) | −3578.47 | −0.0125629 | ||||||||
\(153\) | −16227.8 | −0.0560443 | ||||||||
\(154\) | 38490.7 | 0.130784 | ||||||||
\(155\) | 61271.4 | 0.204846 | ||||||||
\(156\) | −66092.3 | −0.217440 | ||||||||
\(157\) | −180692. | −0.585047 | −0.292523 | − | 0.956258i | \(-0.594495\pi\) | ||||
−0.292523 | + | 0.956258i | \(0.594495\pi\) | |||||||
\(158\) | −288188. | −0.918403 | ||||||||
\(159\) | −334827. | −1.05033 | ||||||||
\(160\) | −206490. | −0.637675 | ||||||||
\(161\) | −54539.4 | −0.165823 | ||||||||
\(162\) | −53003.9 | −0.158679 | ||||||||
\(163\) | −176045. | −0.518985 | −0.259493 | − | 0.965745i | \(-0.583555\pi\) | ||||
−0.259493 | + | 0.965745i | \(0.583555\pi\) | |||||||
\(164\) | 17539.7 | 0.0509229 | ||||||||
\(165\) | −27225.0 | −0.0778499 | ||||||||
\(166\) | 646288. | 1.82035 | ||||||||
\(167\) | 293818. | 0.815244 | 0.407622 | − | 0.913151i | \(-0.366358\pi\) | ||||
0.407622 | + | 0.913151i | \(0.366358\pi\) | |||||||
\(168\) | 3619.73 | 0.00989471 | ||||||||
\(169\) | −322556. | −0.868737 | ||||||||
\(170\) | −40462.5 | −0.107382 | ||||||||
\(171\) | 28378.0 | 0.0742148 | ||||||||
\(172\) | −401795. | −1.03558 | ||||||||
\(173\) | −20784.9 | −0.0527999 | −0.0263999 | − | 0.999651i | \(-0.508404\pi\) | ||||
−0.0263999 | + | 0.999651i | \(0.508404\pi\) | |||||||
\(174\) | −400375. | −1.00252 | ||||||||
\(175\) | −24610.0 | −0.0607459 | ||||||||
\(176\) | −118815. | −0.289128 | ||||||||
\(177\) | 19418.8 | 0.0465896 | ||||||||
\(178\) | 305235. | 0.722078 | ||||||||
\(179\) | −229326. | −0.534958 | −0.267479 | − | 0.963564i | \(-0.586191\pi\) | ||||
−0.267479 | + | 0.963564i | \(0.586191\pi\) | |||||||
\(180\) | −67360.3 | −0.154961 | ||||||||
\(181\) | −90807.3 | −0.206027 | −0.103014 | − | 0.994680i | \(-0.532849\pi\) | ||||
−0.103014 | + | 0.994680i | \(0.532849\pi\) | |||||||
\(182\) | −70226.2 | −0.157152 | ||||||||
\(183\) | −359442. | −0.793416 | ||||||||
\(184\) | −14147.5 | −0.0308060 | ||||||||
\(185\) | 101512. | 0.218065 | ||||||||
\(186\) | 178196. | 0.377673 | ||||||||
\(187\) | −24241.5 | −0.0506939 | ||||||||
\(188\) | 18728.6 | 0.0386465 | ||||||||
\(189\) | −28705.1 | −0.0584528 | ||||||||
\(190\) | 70757.8 | 0.142197 | ||||||||
\(191\) | −496794. | −0.985356 | −0.492678 | − | 0.870212i | \(-0.663982\pi\) | ||||
−0.492678 | + | 0.870212i | \(0.663982\pi\) | |||||||
\(192\) | −317738. | −0.622036 | ||||||||
\(193\) | 271362. | 0.524391 | 0.262196 | − | 0.965015i | \(-0.415553\pi\) | ||||
0.262196 | + | 0.965015i | \(0.415553\pi\) | |||||||
\(194\) | 61529.7 | 0.117376 | ||||||||
\(195\) | 49672.0 | 0.0935460 | ||||||||
\(196\) | −507498. | −0.943614 | ||||||||
\(197\) | −190972. | −0.350594 | −0.175297 | − | 0.984516i | \(-0.556089\pi\) | ||||
−0.175297 | + | 0.984516i | \(0.556089\pi\) | |||||||
\(198\) | −79178.7 | −0.143531 | ||||||||
\(199\) | 602637. | 1.07876 | 0.539378 | − | 0.842064i | \(-0.318660\pi\) | ||||
0.539378 | + | 0.842064i | \(0.318660\pi\) | |||||||
\(200\) | −6383.84 | −0.0112851 | ||||||||
\(201\) | −346258. | −0.604519 | ||||||||
\(202\) | −1.01761e6 | −1.75470 | ||||||||
\(203\) | −216830. | −0.369300 | ||||||||
\(204\) | −59978.6 | −0.100907 | ||||||||
\(205\) | −13182.1 | −0.0219078 | ||||||||
\(206\) | 1.33476e6 | 2.19146 | ||||||||
\(207\) | 112192. | 0.181986 | ||||||||
\(208\) | 216778. | 0.347422 | ||||||||
\(209\) | 42391.8 | 0.0671299 | ||||||||
\(210\) | −71573.6 | −0.111996 | ||||||||
\(211\) | 918176. | 1.41978 | 0.709888 | − | 0.704315i | \(-0.248746\pi\) | ||||
0.709888 | + | 0.704315i | \(0.248746\pi\) | |||||||
\(212\) | −1.23753e6 | −1.89111 | ||||||||
\(213\) | −123528. | −0.186559 | ||||||||
\(214\) | 106252. | 0.158600 | ||||||||
\(215\) | 301971. | 0.445522 | ||||||||
\(216\) | −7446.11 | −0.0108591 | ||||||||
\(217\) | 96505.0 | 0.139123 | ||||||||
\(218\) | −306753. | −0.437167 | ||||||||
\(219\) | −357627. | −0.503872 | ||||||||
\(220\) | −100625. | −0.140168 | ||||||||
\(221\) | 44228.7 | 0.0609149 | ||||||||
\(222\) | 295227. | 0.402044 | ||||||||
\(223\) | 959605. | 1.29220 | 0.646101 | − | 0.763252i | \(-0.276399\pi\) | ||||
0.646101 | + | 0.763252i | \(0.276399\pi\) | |||||||
\(224\) | −325231. | −0.433083 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 688217. | 0.896301 | ||||||||
\(227\) | −289954. | −0.373477 | −0.186739 | − | 0.982410i | \(-0.559792\pi\) | ||||
−0.186739 | + | 0.982410i | \(0.559792\pi\) | |||||||
\(228\) | 104886. | 0.133623 | ||||||||
\(229\) | 111161. | 0.140076 | 0.0700379 | − | 0.997544i | \(-0.477688\pi\) | ||||
0.0700379 | + | 0.997544i | \(0.477688\pi\) | |||||||
\(230\) | 279741. | 0.348688 | ||||||||
\(231\) | −42880.5 | −0.0528725 | ||||||||
\(232\) | −56245.6 | −0.0686071 | ||||||||
\(233\) | −453216. | −0.546909 | −0.273455 | − | 0.961885i | \(-0.588166\pi\) | ||||
−0.273455 | + | 0.961885i | \(0.588166\pi\) | |||||||
\(234\) | 144462. | 0.172470 | ||||||||
\(235\) | −14075.6 | −0.0166263 | ||||||||
\(236\) | 71772.5 | 0.0838838 | ||||||||
\(237\) | 321056. | 0.371287 | ||||||||
\(238\) | −63730.1 | −0.0729294 | ||||||||
\(239\) | 1.26387e6 | 1.43123 | 0.715614 | − | 0.698496i | \(-0.246147\pi\) | ||||
0.715614 | + | 0.698496i | \(0.246147\pi\) | |||||||
\(240\) | 220937. | 0.247594 | ||||||||
\(241\) | 134350. | 0.149003 | 0.0745013 | − | 0.997221i | \(-0.476264\pi\) | ||||
0.0745013 | + | 0.997221i | \(0.476264\pi\) | |||||||
\(242\) | −118279. | −0.129829 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.32851e6 | −1.42853 | ||||||||
\(245\) | 381413. | 0.405957 | ||||||||
\(246\) | −38337.6 | −0.0403912 | ||||||||
\(247\) | −77343.8 | −0.0806646 | ||||||||
\(248\) | 25033.4 | 0.0258458 | ||||||||
\(249\) | −719997. | −0.735923 | ||||||||
\(250\) | 126229. | 0.127734 | ||||||||
\(251\) | −1.43370e6 | −1.43639 | −0.718197 | − | 0.695840i | \(-0.755032\pi\) | ||||
−0.718197 | + | 0.695840i | \(0.755032\pi\) | |||||||
\(252\) | −106095. | −0.105243 | ||||||||
\(253\) | 167596. | 0.164612 | ||||||||
\(254\) | 1.14100e6 | 1.10969 | ||||||||
\(255\) | 45077.2 | 0.0434117 | ||||||||
\(256\) | 960873. | 0.916360 | ||||||||
\(257\) | −953935. | −0.900920 | −0.450460 | − | 0.892797i | \(-0.648740\pi\) | ||||
−0.450460 | + | 0.892797i | \(0.648740\pi\) | |||||||
\(258\) | 878226. | 0.821404 | ||||||||
\(259\) | 159885. | 0.148101 | ||||||||
\(260\) | 183590. | 0.168428 | ||||||||
\(261\) | 446038. | 0.405294 | ||||||||
\(262\) | −1.70030e6 | −1.53029 | ||||||||
\(263\) | 322280. | 0.287306 | 0.143653 | − | 0.989628i | \(-0.454115\pi\) | ||||
0.143653 | + | 0.989628i | \(0.454115\pi\) | |||||||
\(264\) | −11123.2 | −0.00982245 | ||||||||
\(265\) | 930075. | 0.813586 | ||||||||
\(266\) | 111446. | 0.0965744 | ||||||||
\(267\) | −340047. | −0.291918 | ||||||||
\(268\) | −1.27978e6 | −1.08843 | ||||||||
\(269\) | 808737. | 0.681438 | 0.340719 | − | 0.940165i | \(-0.389329\pi\) | ||||
0.340719 | + | 0.940165i | \(0.389329\pi\) | |||||||
\(270\) | 147233. | 0.122913 | ||||||||
\(271\) | −909303. | −0.752117 | −0.376058 | − | 0.926596i | \(-0.622721\pi\) | ||||
−0.376058 | + | 0.926596i | \(0.622721\pi\) | |||||||
\(272\) | 196726. | 0.161227 | ||||||||
\(273\) | 78235.5 | 0.0635327 | ||||||||
\(274\) | −158059. | −0.127187 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 414667. | 0.327662 | ||||||||
\(277\) | 236933. | 0.185535 | 0.0927675 | − | 0.995688i | \(-0.470429\pi\) | ||||
0.0927675 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(278\) | −1.07040e6 | −0.830681 | ||||||||
\(279\) | −198519. | −0.152684 | ||||||||
\(280\) | −10054.8 | −0.00766441 | ||||||||
\(281\) | −450779. | −0.340563 | −0.170282 | − | 0.985395i | \(-0.554468\pi\) | ||||
−0.170282 | + | 0.985395i | \(0.554468\pi\) | |||||||
\(282\) | −40936.1 | −0.0306538 | ||||||||
\(283\) | 683413. | 0.507245 | 0.253622 | − | 0.967303i | \(-0.418378\pi\) | ||||
0.253622 | + | 0.967303i | \(0.418378\pi\) | |||||||
\(284\) | −456563. | −0.335896 | ||||||||
\(285\) | −78827.6 | −0.0574866 | ||||||||
\(286\) | 215801. | 0.156005 | ||||||||
\(287\) | −20762.3 | −0.0148789 | ||||||||
\(288\) | 669028. | 0.475295 | ||||||||
\(289\) | −1.37972e6 | −0.971731 | ||||||||
\(290\) | 1.11215e6 | 0.776551 | ||||||||
\(291\) | −68547.1 | −0.0474522 | ||||||||
\(292\) | −1.32180e6 | −0.907213 | ||||||||
\(293\) | −1.81068e6 | −1.23218 | −0.616088 | − | 0.787678i | \(-0.711283\pi\) | ||||
−0.616088 | + | 0.787678i | \(0.711283\pi\) | |||||||
\(294\) | 1.10927e6 | 0.748459 | ||||||||
\(295\) | −53941.0 | −0.0360881 | ||||||||
\(296\) | 41474.1 | 0.0275136 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 1.23859e6 | 0.807953 | ||||||||
\(299\) | −305779. | −0.197801 | ||||||||
\(300\) | 187112. | 0.120032 | ||||||||
\(301\) | 475617. | 0.302581 | ||||||||
\(302\) | −2.00472e6 | −1.26484 | ||||||||
\(303\) | 1.13367e6 | 0.709380 | ||||||||
\(304\) | −344019. | −0.213500 | ||||||||
\(305\) | 998450. | 0.614578 | ||||||||
\(306\) | 131099. | 0.0800376 | ||||||||
\(307\) | −3.00860e6 | −1.82187 | −0.910937 | − | 0.412546i | \(-0.864639\pi\) | ||||
−0.910937 | + | 0.412546i | \(0.864639\pi\) | |||||||
\(308\) | −158488. | −0.0951962 | ||||||||
\(309\) | −1.48698e6 | −0.885952 | ||||||||
\(310\) | −494989. | −0.292544 | ||||||||
\(311\) | −2.04083e6 | −1.19648 | −0.598241 | − | 0.801316i | \(-0.704134\pi\) | ||||
−0.598241 | + | 0.801316i | \(0.704134\pi\) | |||||||
\(312\) | 20294.3 | 0.0118029 | ||||||||
\(313\) | −1.73940e6 | −1.00355 | −0.501774 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501774 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(314\) | 1.45975e6 | 0.835513 | ||||||||
\(315\) | 79736.5 | 0.0452773 | ||||||||
\(316\) | 1.18663e6 | 0.668497 | ||||||||
\(317\) | 106704. | 0.0596392 | 0.0298196 | − | 0.999555i | \(-0.490507\pi\) | ||||
0.0298196 | + | 0.999555i | \(0.490507\pi\) | |||||||
\(318\) | 2.70495e6 | 1.50000 | ||||||||
\(319\) | 666304. | 0.366603 | ||||||||
\(320\) | 882605. | 0.481827 | ||||||||
\(321\) | −118370. | −0.0641181 | ||||||||
\(322\) | 440604. | 0.236815 | ||||||||
\(323\) | −70189.3 | −0.0374338 | ||||||||
\(324\) | 218247. | 0.115501 | ||||||||
\(325\) | −137978. | −0.0724604 | ||||||||
\(326\) | 1.42220e6 | 0.741170 | ||||||||
\(327\) | 341738. | 0.176736 | ||||||||
\(328\) | −5385.74 | −0.00276415 | ||||||||
\(329\) | −22169.6 | −0.0112919 | ||||||||
\(330\) | 219941. | 0.111179 | ||||||||
\(331\) | 1.54759e6 | 0.776402 | 0.388201 | − | 0.921575i | \(-0.373097\pi\) | ||||
0.388201 | + | 0.921575i | \(0.373097\pi\) | |||||||
\(332\) | −2.66114e6 | −1.32502 | ||||||||
\(333\) | −328898. | −0.162536 | ||||||||
\(334\) | −2.37365e6 | −1.16426 | ||||||||
\(335\) | 961829. | 0.468259 | ||||||||
\(336\) | 347985. | 0.168156 | ||||||||
\(337\) | 1.22550e6 | 0.587814 | 0.293907 | − | 0.955834i | \(-0.405044\pi\) | ||||
0.293907 | + | 0.955834i | \(0.405044\pi\) | |||||||
\(338\) | 2.60581e6 | 1.24066 | ||||||||
\(339\) | −766708. | −0.362352 | ||||||||
\(340\) | 166607. | 0.0781621 | ||||||||
\(341\) | −296553. | −0.138107 | ||||||||
\(342\) | −229255. | −0.105987 | ||||||||
\(343\) | 1.26253e6 | 0.579440 | ||||||||
\(344\) | 123375. | 0.0562123 | ||||||||
\(345\) | −311645. | −0.140965 | ||||||||
\(346\) | 167914. | 0.0754042 | ||||||||
\(347\) | 3.82684e6 | 1.70615 | 0.853074 | − | 0.521789i | \(-0.174735\pi\) | ||||
0.853074 | + | 0.521789i | \(0.174735\pi\) | |||||||
\(348\) | 1.64857e6 | 0.729727 | ||||||||
\(349\) | 456968. | 0.200827 | 0.100413 | − | 0.994946i | \(-0.467983\pi\) | ||||
0.100413 | + | 0.994946i | \(0.467983\pi\) | |||||||
\(350\) | 198815. | 0.0867521 | ||||||||
\(351\) | −160937. | −0.0697251 | ||||||||
\(352\) | 999413. | 0.429920 | ||||||||
\(353\) | 4.32830e6 | 1.84876 | 0.924380 | − | 0.381474i | \(-0.124583\pi\) | ||||
0.924380 | + | 0.381474i | \(0.124583\pi\) | |||||||
\(354\) | −156877. | −0.0665352 | ||||||||
\(355\) | 343132. | 0.144508 | ||||||||
\(356\) | −1.25683e6 | −0.525594 | ||||||||
\(357\) | 70998.5 | 0.0294835 | ||||||||
\(358\) | 1.85264e6 | 0.763982 | ||||||||
\(359\) | −845380. | −0.346191 | −0.173095 | − | 0.984905i | \(-0.555377\pi\) | ||||
−0.173095 | + | 0.984905i | \(0.555377\pi\) | |||||||
\(360\) | 20683.6 | 0.00841145 | ||||||||
\(361\) | −2.35336e6 | −0.950429 | ||||||||
\(362\) | 733599. | 0.294230 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 289161. | 0.114390 | ||||||||
\(365\) | 993408. | 0.390297 | ||||||||
\(366\) | 2.90380e6 | 1.13309 | ||||||||
\(367\) | 2.96016e6 | 1.14723 | 0.573615 | − | 0.819125i | \(-0.305540\pi\) | ||||
0.573615 | + | 0.819125i | \(0.305540\pi\) | |||||||
\(368\) | −1.36008e6 | −0.523534 | ||||||||
\(369\) | 42709.9 | 0.0163291 | ||||||||
\(370\) | −820075. | −0.311422 | ||||||||
\(371\) | 1.46491e6 | 0.552555 | ||||||||
\(372\) | −733735. | −0.274904 | ||||||||
\(373\) | 1.02299e6 | 0.380713 | 0.190357 | − | 0.981715i | \(-0.439036\pi\) | ||||
0.190357 | + | 0.981715i | \(0.439036\pi\) | |||||||
\(374\) | 195839. | 0.0723968 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −5750.80 | −0.00209777 | ||||||||
\(377\) | −1.21567e6 | −0.440517 | ||||||||
\(378\) | 231898. | 0.0834772 | ||||||||
\(379\) | −4.19402e6 | −1.49980 | −0.749899 | − | 0.661552i | \(-0.769898\pi\) | ||||
−0.749899 | + | 0.661552i | \(0.769898\pi\) | |||||||
\(380\) | −291350. | −0.103504 | ||||||||
\(381\) | −1.27113e6 | −0.448620 | ||||||||
\(382\) | 4.01342e6 | 1.40720 | ||||||||
\(383\) | −1.64287e6 | −0.572276 | −0.286138 | − | 0.958188i | \(-0.592372\pi\) | ||||
−0.286138 | + | 0.958188i | \(0.592372\pi\) | |||||||
\(384\) | 188120. | 0.0651039 | ||||||||
\(385\) | 119113. | 0.0409549 | ||||||||
\(386\) | −2.19223e6 | −0.748891 | ||||||||
\(387\) | −978387. | −0.332073 | ||||||||
\(388\) | −253353. | −0.0854371 | ||||||||
\(389\) | 769820. | 0.257938 | 0.128969 | − | 0.991649i | \(-0.458833\pi\) | ||||
0.128969 | + | 0.991649i | \(0.458833\pi\) | |||||||
\(390\) | −401282. | −0.133594 | ||||||||
\(391\) | −277493. | −0.0917933 | ||||||||
\(392\) | 155832. | 0.0512203 | ||||||||
\(393\) | 1.89422e6 | 0.618657 | ||||||||
\(394\) | 1.54279e6 | 0.500688 | ||||||||
\(395\) | −891822. | −0.287598 | ||||||||
\(396\) | 326024. | 0.104475 | ||||||||
\(397\) | 4.86631e6 | 1.54961 | 0.774806 | − | 0.632199i | \(-0.217847\pi\) | ||||
0.774806 | + | 0.632199i | \(0.217847\pi\) | |||||||
\(398\) | −4.86848e6 | −1.54059 | ||||||||
\(399\) | −124157. | −0.0390426 | ||||||||
\(400\) | −613714. | −0.191786 | ||||||||
\(401\) | 717064. | 0.222688 | 0.111344 | − | 0.993782i | \(-0.464484\pi\) | ||||
0.111344 | + | 0.993782i | \(0.464484\pi\) | |||||||
\(402\) | 2.79730e6 | 0.863323 | ||||||||
\(403\) | 541062. | 0.165953 | ||||||||
\(404\) | 4.19007e6 | 1.27723 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | 1.75169e6 | 0.527402 | ||||||||
\(407\) | −491316. | −0.147019 | ||||||||
\(408\) | 18417.0 | 0.00547733 | ||||||||
\(409\) | −3.80091e6 | −1.12352 | −0.561758 | − | 0.827302i | \(-0.689875\pi\) | ||||
−0.561758 | + | 0.827302i | \(0.689875\pi\) | |||||||
\(410\) | 106493. | 0.0312869 | ||||||||
\(411\) | 176086. | 0.0514185 | ||||||||
\(412\) | −5.49595e6 | −1.59514 | ||||||||
\(413\) | −84959.4 | −0.0245096 | ||||||||
\(414\) | −906361. | −0.259896 | ||||||||
\(415\) | 1.99999e6 | 0.570044 | ||||||||
\(416\) | −1.82343e6 | −0.516601 | ||||||||
\(417\) | 1.19248e6 | 0.335823 | ||||||||
\(418\) | −342468. | −0.0958691 | ||||||||
\(419\) | −1.55888e6 | −0.433787 | −0.216894 | − | 0.976195i | \(-0.569592\pi\) | ||||
−0.216894 | + | 0.976195i | \(0.569592\pi\) | |||||||
\(420\) | 294709. | 0.0815212 | ||||||||
\(421\) | 4.13561e6 | 1.13719 | 0.568596 | − | 0.822617i | \(-0.307487\pi\) | ||||
0.568596 | + | 0.822617i | \(0.307487\pi\) | |||||||
\(422\) | −7.41761e6 | −2.02760 | ||||||||
\(423\) | 45604.9 | 0.0123925 | ||||||||
\(424\) | 379997. | 0.102651 | ||||||||
\(425\) | −125215. | −0.0336266 | ||||||||
\(426\) | 997935. | 0.266427 | ||||||||
\(427\) | 1.57260e6 | 0.417397 | ||||||||
\(428\) | −437502. | −0.115444 | ||||||||
\(429\) | −240413. | −0.0630687 | ||||||||
\(430\) | −2.43952e6 | −0.636257 | ||||||||
\(431\) | −5.25900e6 | −1.36367 | −0.681836 | − | 0.731505i | \(-0.738818\pi\) | ||||
−0.681836 | + | 0.731505i | \(0.738818\pi\) | |||||||
\(432\) | −715836. | −0.184546 | ||||||||
\(433\) | −694549. | −0.178026 | −0.0890130 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890130 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(434\) | −779629. | −0.198684 | ||||||||
\(435\) | −1.23899e6 | −0.313940 | ||||||||
\(436\) | 1.26308e6 | 0.318210 | ||||||||
\(437\) | 485260. | 0.121554 | ||||||||
\(438\) | 2.88914e6 | 0.719586 | ||||||||
\(439\) | −7.80969e6 | −1.93407 | −0.967036 | − | 0.254640i | \(-0.918043\pi\) | ||||
−0.967036 | + | 0.254640i | \(0.918043\pi\) | |||||||
\(440\) | 30897.8 | 0.00760844 | ||||||||
\(441\) | −1.23578e6 | −0.302583 | ||||||||
\(442\) | −357307. | −0.0869934 | ||||||||
\(443\) | −5.43876e6 | −1.31671 | −0.658356 | − | 0.752707i | \(-0.728748\pi\) | ||||
−0.658356 | + | 0.752707i | \(0.728748\pi\) | |||||||
\(444\) | −1.21562e6 | −0.292644 | ||||||||
\(445\) | 944575. | 0.226119 | ||||||||
\(446\) | −7.75229e6 | −1.84541 | ||||||||
\(447\) | −1.37985e6 | −0.326635 | ||||||||
\(448\) | 1.39014e6 | 0.327238 | ||||||||
\(449\) | 5.46277e6 | 1.27878 | 0.639392 | − | 0.768881i | \(-0.279186\pi\) | ||||
0.639392 | + | 0.768881i | \(0.279186\pi\) | |||||||
\(450\) | −408981. | −0.0952076 | ||||||||
\(451\) | 63801.3 | 0.0147703 | ||||||||
\(452\) | −2.83378e6 | −0.652409 | ||||||||
\(453\) | 2.23336e6 | 0.511343 | ||||||||
\(454\) | 2.34243e6 | 0.533368 | ||||||||
\(455\) | −217321. | −0.0492122 | ||||||||
\(456\) | −32206.3 | −0.00725318 | ||||||||
\(457\) | 3.07144e6 | 0.687941 | 0.343970 | − | 0.938980i | \(-0.388228\pi\) | ||||
0.343970 | + | 0.938980i | \(0.388228\pi\) | |||||||
\(458\) | −898028. | −0.200044 | ||||||||
\(459\) | −146050. | −0.0323572 | ||||||||
\(460\) | −1.15185e6 | −0.253806 | ||||||||
\(461\) | 3.85641e6 | 0.845143 | 0.422572 | − | 0.906329i | \(-0.361127\pi\) | ||||
0.422572 | + | 0.906329i | \(0.361127\pi\) | |||||||
\(462\) | 346416. | 0.0755080 | ||||||||
\(463\) | 3.20594e6 | 0.695029 | 0.347514 | − | 0.937675i | \(-0.387026\pi\) | ||||
0.347514 | + | 0.937675i | \(0.387026\pi\) | |||||||
\(464\) | −5.40721e6 | −1.16594 | ||||||||
\(465\) | 551442. | 0.118268 | ||||||||
\(466\) | 3.66136e6 | 0.781049 | ||||||||
\(467\) | −2.43952e6 | −0.517622 | −0.258811 | − | 0.965928i | \(-0.583331\pi\) | ||||
−0.258811 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(468\) | −594830. | −0.125539 | ||||||||
\(469\) | 1.51492e6 | 0.318023 | ||||||||
\(470\) | 113711. | 0.0237443 | ||||||||
\(471\) | −1.62623e6 | −0.337777 | ||||||||
\(472\) | −22038.5 | −0.00455330 | ||||||||
\(473\) | −1.46154e6 | −0.300371 | ||||||||
\(474\) | −2.59369e6 | −0.530240 | ||||||||
\(475\) | 218966. | 0.0445289 | ||||||||
\(476\) | 262413. | 0.0530846 | ||||||||
\(477\) | −3.01344e6 | −0.606411 | ||||||||
\(478\) | −1.02104e7 | −2.04396 | ||||||||
\(479\) | 4.69186e6 | 0.934342 | 0.467171 | − | 0.884167i | \(-0.345273\pi\) | ||||
0.467171 | + | 0.884167i | \(0.345273\pi\) | |||||||
\(480\) | −1.85841e6 | −0.368162 | ||||||||
\(481\) | 896406. | 0.176662 | ||||||||
\(482\) | −1.08536e6 | −0.212793 | ||||||||
\(483\) | −490854. | −0.0957381 | ||||||||
\(484\) | 487023. | 0.0945010 | ||||||||
\(485\) | 190409. | 0.0367564 | ||||||||
\(486\) | −477035. | −0.0916136 | ||||||||
\(487\) | 5.73305e6 | 1.09538 | 0.547688 | − | 0.836683i | \(-0.315508\pi\) | ||||
0.547688 | + | 0.836683i | \(0.315508\pi\) | |||||||
\(488\) | 407932. | 0.0775423 | ||||||||
\(489\) | −1.58441e6 | −0.299636 | ||||||||
\(490\) | −3.08130e6 | −0.579754 | ||||||||
\(491\) | −693872. | −0.129890 | −0.0649449 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649449 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(492\) | 157858. | 0.0294004 | ||||||||
\(493\) | −1.10322e6 | −0.204430 | ||||||||
\(494\) | 624832. | 0.115198 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | 2.40660e6 | 0.439238 | ||||||||
\(497\) | 540448. | 0.0981438 | ||||||||
\(498\) | 5.81659e6 | 1.05098 | ||||||||
\(499\) | 1.23153e6 | 0.221407 | 0.110704 | − | 0.993853i | \(-0.464690\pi\) | ||||
0.110704 | + | 0.993853i | \(0.464690\pi\) | |||||||
\(500\) | −519755. | −0.0929767 | ||||||||
\(501\) | 2.64436e6 | 0.470681 | ||||||||
\(502\) | 1.15823e7 | 2.05133 | ||||||||
\(503\) | −7.61551e6 | −1.34208 | −0.671041 | − | 0.741420i | \(-0.734153\pi\) | ||||
−0.671041 | + | 0.741420i | \(0.734153\pi\) | |||||||
\(504\) | 32577.6 | 0.00571272 | ||||||||
\(505\) | −3.14907e6 | −0.549483 | ||||||||
\(506\) | −1.35395e6 | −0.235085 | ||||||||
\(507\) | −2.90300e6 | −0.501566 | ||||||||
\(508\) | −4.69816e6 | −0.807734 | ||||||||
\(509\) | −1.55496e6 | −0.266026 | −0.133013 | − | 0.991114i | \(-0.542465\pi\) | ||||
−0.133013 | + | 0.991114i | \(0.542465\pi\) | |||||||
\(510\) | −364163. | −0.0619969 | ||||||||
\(511\) | 1.56466e6 | 0.265074 | ||||||||
\(512\) | −8.43141e6 | −1.42143 | ||||||||
\(513\) | 255402. | 0.0428480 | ||||||||
\(514\) | 7.70649e6 | 1.28662 | ||||||||
\(515\) | 4.13051e6 | 0.686255 | ||||||||
\(516\) | −3.61616e6 | −0.597892 | ||||||||
\(517\) | 68125.8 | 0.0112095 | ||||||||
\(518\) | −1.29165e6 | −0.211505 | ||||||||
\(519\) | −187064. | −0.0304840 | ||||||||
\(520\) | −56373.0 | −0.00914245 | ||||||||
\(521\) | −3.26766e6 | −0.527403 | −0.263701 | − | 0.964604i | \(-0.584943\pi\) | ||||
−0.263701 | + | 0.964604i | \(0.584943\pi\) | |||||||
\(522\) | −3.60338e6 | −0.578807 | ||||||||
\(523\) | −8.35303e6 | −1.33533 | −0.667667 | − | 0.744460i | \(-0.732707\pi\) | ||||
−0.667667 | + | 0.744460i | \(0.732707\pi\) | |||||||
\(524\) | 7.00112e6 | 1.11388 | ||||||||
\(525\) | −221490. | −0.0350717 | ||||||||
\(526\) | −2.60358e6 | −0.410305 | ||||||||
\(527\) | 491012. | 0.0770133 | ||||||||
\(528\) | −1.06934e6 | −0.166928 | ||||||||
\(529\) | −4.51787e6 | −0.701931 | ||||||||
\(530\) | −7.51374e6 | −1.16189 | ||||||||
\(531\) | 174769. | 0.0268985 | ||||||||
\(532\) | −458888. | −0.0702956 | ||||||||
\(533\) | −116405. | −0.0177482 | ||||||||
\(534\) | 2.74711e6 | 0.416892 | ||||||||
\(535\) | 328807. | 0.0496657 | ||||||||
\(536\) | 392970. | 0.0590810 | ||||||||
\(537\) | −2.06393e6 | −0.308858 | ||||||||
\(538\) | −6.53349e6 | −0.973172 | ||||||||
\(539\) | −1.84604e6 | −0.273696 | ||||||||
\(540\) | −606243. | −0.0894668 | ||||||||
\(541\) | 4.72814e6 | 0.694540 | 0.347270 | − | 0.937765i | \(-0.387109\pi\) | ||||
0.347270 | + | 0.937765i | \(0.387109\pi\) | |||||||
\(542\) | 7.34593e6 | 1.07411 | ||||||||
\(543\) | −817266. | −0.118950 | ||||||||
\(544\) | −1.65476e6 | −0.239738 | ||||||||
\(545\) | −949272. | −0.136899 | ||||||||
\(546\) | −632036. | −0.0907320 | ||||||||
\(547\) | −3.84639e6 | −0.549648 | −0.274824 | − | 0.961495i | \(-0.588620\pi\) | ||||
−0.274824 | + | 0.961495i | \(0.588620\pi\) | |||||||
\(548\) | 650819. | 0.0925782 | ||||||||
\(549\) | −3.23498e6 | −0.458079 | ||||||||
\(550\) | −610947. | −0.0861185 | ||||||||
\(551\) | 1.92923e6 | 0.270710 | ||||||||
\(552\) | −127328. | −0.0177859 | ||||||||
\(553\) | −1.40466e6 | −0.195325 | ||||||||
\(554\) | −1.91409e6 | −0.264965 | ||||||||
\(555\) | 913604. | 0.125900 | ||||||||
\(556\) | 4.40745e6 | 0.604644 | ||||||||
\(557\) | 1.34095e7 | 1.83137 | 0.915684 | − | 0.401900i | \(-0.131650\pi\) | ||||
0.915684 | + | 0.401900i | \(0.131650\pi\) | |||||||
\(558\) | 1.60376e6 | 0.218050 | ||||||||
\(559\) | 2.66658e6 | 0.360932 | ||||||||
\(560\) | −966625. | −0.130253 | ||||||||
\(561\) | −218174. | −0.0292682 | ||||||||
\(562\) | 3.64168e6 | 0.486363 | ||||||||
\(563\) | 1.51163e6 | 0.200990 | 0.100495 | − | 0.994938i | \(-0.467957\pi\) | ||||
0.100495 | + | 0.994938i | \(0.467957\pi\) | |||||||
\(564\) | 168557. | 0.0223126 | ||||||||
\(565\) | 2.12974e6 | 0.280677 | ||||||||
\(566\) | −5.52105e6 | −0.724403 | ||||||||
\(567\) | −258346. | −0.0337477 | ||||||||
\(568\) | 140192. | 0.0182328 | ||||||||
\(569\) | 1.39221e7 | 1.80271 | 0.901353 | − | 0.433085i | \(-0.142575\pi\) | ||||
0.901353 | + | 0.433085i | \(0.142575\pi\) | |||||||
\(570\) | 636820. | 0.0820974 | ||||||||
\(571\) | −3.44073e6 | −0.441632 | −0.220816 | − | 0.975316i | \(-0.570872\pi\) | ||||
−0.220816 | + | 0.975316i | \(0.570872\pi\) | |||||||
\(572\) | −888574. | −0.113554 | ||||||||
\(573\) | −4.47115e6 | −0.568896 | ||||||||
\(574\) | 167731. | 0.0212488 | ||||||||
\(575\) | 865681. | 0.109191 | ||||||||
\(576\) | −2.85964e6 | −0.359133 | ||||||||
\(577\) | 3.96778e6 | 0.496144 | 0.248072 | − | 0.968742i | \(-0.420203\pi\) | ||||
0.248072 | + | 0.968742i | \(0.420203\pi\) | |||||||
\(578\) | 1.11463e7 | 1.38774 | ||||||||
\(579\) | 2.44226e6 | 0.302758 | ||||||||
\(580\) | −4.57937e6 | −0.565244 | ||||||||
\(581\) | 3.15007e6 | 0.387151 | ||||||||
\(582\) | 553767. | 0.0677672 | ||||||||
\(583\) | −4.50156e6 | −0.548519 | ||||||||
\(584\) | 405872. | 0.0492445 | ||||||||
\(585\) | 447048. | 0.0540088 | ||||||||
\(586\) | 1.46278e7 | 1.75969 | ||||||||
\(587\) | 3.64595e6 | 0.436733 | 0.218366 | − | 0.975867i | \(-0.429927\pi\) | ||||
0.218366 | + | 0.975867i | \(0.429927\pi\) | |||||||
\(588\) | −4.56748e6 | −0.544796 | ||||||||
\(589\) | −858645. | −0.101982 | ||||||||
\(590\) | 435770. | 0.0515380 | ||||||||
\(591\) | −1.71875e6 | −0.202416 | ||||||||
\(592\) | 3.98714e6 | 0.467582 | ||||||||
\(593\) | −486759. | −0.0568431 | −0.0284215 | − | 0.999596i | \(-0.509048\pi\) | ||||
−0.0284215 | + | 0.999596i | \(0.509048\pi\) | |||||||
\(594\) | −712608. | −0.0828676 | ||||||||
\(595\) | −197218. | −0.0228378 | ||||||||
\(596\) | −5.09997e6 | −0.588101 | ||||||||
\(597\) | 5.42373e6 | 0.622820 | ||||||||
\(598\) | 2.47027e6 | 0.282483 | ||||||||
\(599\) | 1.37413e7 | 1.56481 | 0.782404 | − | 0.622771i | \(-0.213993\pi\) | ||||
0.782404 | + | 0.622771i | \(0.213993\pi\) | |||||||
\(600\) | −57454.5 | −0.00651548 | ||||||||
\(601\) | 7.84470e6 | 0.885911 | 0.442955 | − | 0.896544i | \(-0.353930\pi\) | ||||
0.442955 | + | 0.896544i | \(0.353930\pi\) | |||||||
\(602\) | −3.84234e6 | −0.432120 | ||||||||
\(603\) | −3.11633e6 | −0.349019 | ||||||||
\(604\) | 8.25457e6 | 0.920666 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | −9.15848e6 | −1.01308 | ||||||||
\(607\) | −3.41681e6 | −0.376399 | −0.188200 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188200 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(608\) | 2.89371e6 | 0.317465 | ||||||||
\(609\) | −1.95147e6 | −0.213215 | ||||||||
\(610\) | −8.06611e6 | −0.877687 | ||||||||
\(611\) | −124296. | −0.0134695 | ||||||||
\(612\) | −539807. | −0.0582586 | ||||||||
\(613\) | −1.32402e7 | −1.42313 | −0.711564 | − | 0.702621i | \(-0.752013\pi\) | ||||
−0.711564 | + | 0.702621i | \(0.752013\pi\) | |||||||
\(614\) | 2.43054e7 | 2.60184 | ||||||||
\(615\) | −118639. | −0.0126485 | ||||||||
\(616\) | 48665.3 | 0.00516735 | ||||||||
\(617\) | 1.72143e7 | 1.82044 | 0.910220 | − | 0.414126i | \(-0.135913\pi\) | ||||
0.910220 | + | 0.414126i | \(0.135913\pi\) | |||||||
\(618\) | 1.20128e7 | 1.26524 | ||||||||
\(619\) | 1.60142e7 | 1.67988 | 0.839940 | − | 0.542679i | \(-0.182590\pi\) | ||||
0.839940 | + | 0.542679i | \(0.182590\pi\) | |||||||
\(620\) | 2.03815e6 | 0.212940 | ||||||||
\(621\) | 1.00973e6 | 0.105069 | ||||||||
\(622\) | 1.64871e7 | 1.70871 | ||||||||
\(623\) | 1.48774e6 | 0.153571 | ||||||||
\(624\) | 1.95100e6 | 0.200584 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.40520e7 | 1.43318 | ||||||||
\(627\) | 381526. | 0.0387574 | ||||||||
\(628\) | −6.01061e6 | −0.608162 | ||||||||
\(629\) | 813486. | 0.0819830 | ||||||||
\(630\) | −644162. | −0.0646612 | ||||||||
\(631\) | −7.75049e6 | −0.774918 | −0.387459 | − | 0.921887i | \(-0.626647\pi\) | ||||
−0.387459 | + | 0.921887i | \(0.626647\pi\) | |||||||
\(632\) | −364368. | −0.0362867 | ||||||||
\(633\) | 8.26358e6 | 0.819708 | ||||||||
\(634\) | −862021. | −0.0851716 | ||||||||
\(635\) | 3.53093e6 | 0.347500 | ||||||||
\(636\) | −1.11378e7 | −1.09183 | ||||||||
\(637\) | 3.36810e6 | 0.328879 | ||||||||
\(638\) | −5.38282e6 | −0.523550 | ||||||||
\(639\) | −1.11175e6 | −0.107710 | ||||||||
\(640\) | −522556. | −0.0504293 | ||||||||
\(641\) | 8.77648e6 | 0.843675 | 0.421838 | − | 0.906671i | \(-0.361385\pi\) | ||||
0.421838 | + | 0.906671i | \(0.361385\pi\) | |||||||
\(642\) | 956272. | 0.0915680 | ||||||||
\(643\) | −1.51011e7 | −1.44040 | −0.720198 | − | 0.693768i | \(-0.755949\pi\) | ||||
−0.720198 | + | 0.693768i | \(0.755949\pi\) | |||||||
\(644\) | −1.81422e6 | −0.172375 | ||||||||
\(645\) | 2.71774e6 | 0.257222 | ||||||||
\(646\) | 567034. | 0.0534598 | ||||||||
\(647\) | 1.57910e7 | 1.48303 | 0.741516 | − | 0.670936i | \(-0.234107\pi\) | ||||
0.741516 | + | 0.670936i | \(0.234107\pi\) | |||||||
\(648\) | −67015.0 | −0.00626952 | ||||||||
\(649\) | 261075. | 0.0243306 | ||||||||
\(650\) | 1.11467e6 | 0.103482 | ||||||||
\(651\) | 868545. | 0.0803230 | ||||||||
\(652\) | −5.85603e6 | −0.539491 | ||||||||
\(653\) | 1.33260e7 | 1.22297 | 0.611484 | − | 0.791256i | \(-0.290573\pi\) | ||||
0.611484 | + | 0.791256i | \(0.290573\pi\) | |||||||
\(654\) | −2.76078e6 | −0.252399 | ||||||||
\(655\) | −5.26173e6 | −0.479210 | ||||||||
\(656\) | −517762. | −0.0469754 | ||||||||
\(657\) | −3.21864e6 | −0.290910 | ||||||||
\(658\) | 179100. | 0.0161262 | ||||||||
\(659\) | −882213. | −0.0791334 | −0.0395667 | − | 0.999217i | \(-0.512598\pi\) | ||||
−0.0395667 | + | 0.999217i | \(0.512598\pi\) | |||||||
\(660\) | −905622. | −0.0809258 | ||||||||
\(661\) | −5.59700e6 | −0.498255 | −0.249127 | − | 0.968471i | \(-0.580144\pi\) | ||||
−0.249127 | + | 0.968471i | \(0.580144\pi\) | |||||||
\(662\) | −1.25024e7 | −1.10879 | ||||||||
\(663\) | 398058. | 0.0351692 | ||||||||
\(664\) | 817128. | 0.0719234 | ||||||||
\(665\) | 344880. | 0.0302422 | ||||||||
\(666\) | 2.65704e6 | 0.232120 | ||||||||
\(667\) | 7.62720e6 | 0.663820 | ||||||||
\(668\) | 9.77367e6 | 0.847454 | ||||||||
\(669\) | 8.63644e6 | 0.746053 | ||||||||
\(670\) | −7.77027e6 | −0.668727 | ||||||||
\(671\) | −4.83250e6 | −0.414348 | ||||||||
\(672\) | −2.92708e6 | −0.250041 | ||||||||
\(673\) | 1.29320e6 | 0.110060 | 0.0550300 | − | 0.998485i | \(-0.482475\pi\) | ||||
0.0550300 | + | 0.998485i | \(0.482475\pi\) | |||||||
\(674\) | −9.90040e6 | −0.839466 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | −1.07296e7 | −0.903062 | ||||||||
\(677\) | 1.48798e7 | 1.24775 | 0.623873 | − | 0.781526i | \(-0.285558\pi\) | ||||
0.623873 | + | 0.781526i | \(0.285558\pi\) | |||||||
\(678\) | 6.19395e6 | 0.517480 | ||||||||
\(679\) | 299902. | 0.0249634 | ||||||||
\(680\) | −51158.4 | −0.00424272 | ||||||||
\(681\) | −2.60958e6 | −0.215627 | ||||||||
\(682\) | 2.39575e6 | 0.197233 | ||||||||
\(683\) | 8.62925e6 | 0.707817 | 0.353909 | − | 0.935280i | \(-0.384852\pi\) | ||||
0.353909 | + | 0.935280i | \(0.384852\pi\) | |||||||
\(684\) | 943974. | 0.0771471 | ||||||||
\(685\) | −489127. | −0.0398286 | ||||||||
\(686\) | −1.01996e7 | −0.827506 | ||||||||
\(687\) | 1.00045e6 | 0.0808729 | ||||||||
\(688\) | 1.18607e7 | 0.955302 | ||||||||
\(689\) | 8.21310e6 | 0.659112 | ||||||||
\(690\) | 2.51767e6 | 0.201315 | ||||||||
\(691\) | −1.79734e7 | −1.43198 | −0.715988 | − | 0.698113i | \(-0.754023\pi\) | ||||
−0.715988 | + | 0.698113i | \(0.754023\pi\) | |||||||
\(692\) | −691396. | −0.0548860 | ||||||||
\(693\) | −385925. | −0.0305260 | ||||||||
\(694\) | −3.09157e7 | −2.43658 | ||||||||
\(695\) | −3.31244e6 | −0.260127 | ||||||||
\(696\) | −506211. | −0.0396103 | ||||||||
\(697\) | −105638. | −0.00823639 | ||||||||
\(698\) | −3.69167e6 | −0.286804 | ||||||||
\(699\) | −4.07894e6 | −0.315758 | ||||||||
\(700\) | −818636. | −0.0631460 | ||||||||
\(701\) | −2.13485e7 | −1.64086 | −0.820432 | − | 0.571744i | \(-0.806267\pi\) | ||||
−0.820432 | + | 0.571744i | \(0.806267\pi\) | |||||||
\(702\) | 1.30015e6 | 0.0995754 | ||||||||
\(703\) | −1.42256e6 | −0.108563 | ||||||||
\(704\) | −4.27181e6 | −0.324848 | ||||||||
\(705\) | −126680. | −0.00959922 | ||||||||
\(706\) | −3.49667e7 | −2.64024 | ||||||||
\(707\) | −4.95992e6 | −0.373187 | ||||||||
\(708\) | 645953. | 0.0484303 | ||||||||
\(709\) | 6.90604e6 | 0.515957 | 0.257979 | − | 0.966151i | \(-0.416944\pi\) | ||||
0.257979 | + | 0.966151i | \(0.416944\pi\) | |||||||
\(710\) | −2.77204e6 | −0.206373 | ||||||||
\(711\) | 2.88950e6 | 0.214363 | ||||||||
\(712\) | 385921. | 0.0285298 | ||||||||
\(713\) | −3.39466e6 | −0.250076 | ||||||||
\(714\) | −573571. | −0.0421058 | ||||||||
\(715\) | 667813. | 0.0488528 | ||||||||
\(716\) | −7.62837e6 | −0.556095 | ||||||||
\(717\) | 1.13749e7 | 0.826320 | ||||||||
\(718\) | 6.82951e6 | 0.494400 | ||||||||
\(719\) | −1.71863e7 | −1.23983 | −0.619913 | − | 0.784670i | \(-0.712832\pi\) | ||||
−0.619913 | + | 0.784670i | \(0.712832\pi\) | |||||||
\(720\) | 1.98843e6 | 0.142949 | ||||||||
\(721\) | 6.50573e6 | 0.466077 | ||||||||
\(722\) | 1.90119e7 | 1.35732 | ||||||||
\(723\) | 1.20915e6 | 0.0860266 | ||||||||
\(724\) | −3.02065e6 | −0.214167 | ||||||||
\(725\) | 3.44165e6 | 0.243177 | ||||||||
\(726\) | −1.06451e6 | −0.0749566 | ||||||||
\(727\) | −2.43516e7 | −1.70880 | −0.854401 | − | 0.519615i | \(-0.826075\pi\) | ||||
−0.854401 | + | 0.519615i | \(0.826075\pi\) | |||||||
\(728\) | −88789.8 | −0.00620919 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −8.02538e6 | −0.557389 | ||||||||
\(731\) | 2.41992e6 | 0.167497 | ||||||||
\(732\) | −1.19566e7 | −0.824765 | ||||||||
\(733\) | −1.93102e7 | −1.32747 | −0.663737 | − | 0.747966i | \(-0.731031\pi\) | ||||
−0.663737 | + | 0.747966i | \(0.731031\pi\) | |||||||
\(734\) | −2.39141e7 | −1.63838 | ||||||||
\(735\) | 3.43272e6 | 0.234380 | ||||||||
\(736\) | 1.14403e7 | 0.778472 | ||||||||
\(737\) | −4.65525e6 | −0.315700 | ||||||||
\(738\) | −345038. | −0.0233199 | ||||||||
\(739\) | −9.23336e6 | −0.621940 | −0.310970 | − | 0.950420i | \(-0.600654\pi\) | ||||
−0.310970 | + | 0.950420i | \(0.600654\pi\) | |||||||
\(740\) | 3.37672e6 | 0.226681 | ||||||||
\(741\) | −696094. | −0.0465717 | ||||||||
\(742\) | −1.18345e7 | −0.789112 | ||||||||
\(743\) | 8.02302e6 | 0.533170 | 0.266585 | − | 0.963811i | \(-0.414105\pi\) | ||||
0.266585 | + | 0.963811i | \(0.414105\pi\) | |||||||
\(744\) | 225300. | 0.0149221 | ||||||||
\(745\) | 3.83291e6 | 0.253010 | ||||||||
\(746\) | −8.26434e6 | −0.543702 | ||||||||
\(747\) | −6.47998e6 | −0.424885 | ||||||||
\(748\) | −806379. | −0.0526969 | ||||||||
\(749\) | 517885. | 0.0337309 | ||||||||
\(750\) | 1.13606e6 | 0.0737475 | ||||||||
\(751\) | 1.19930e6 | 0.0775938 | 0.0387969 | − | 0.999247i | \(-0.487647\pi\) | ||||
0.0387969 | + | 0.999247i | \(0.487647\pi\) | |||||||
\(752\) | −552856. | −0.0356507 | ||||||||
\(753\) | −1.29033e7 | −0.829302 | ||||||||
\(754\) | 9.82096e6 | 0.629109 | ||||||||
\(755\) | −6.20377e6 | −0.396085 | ||||||||
\(756\) | −954858. | −0.0607623 | ||||||||
\(757\) | −1.40172e7 | −0.889040 | −0.444520 | − | 0.895769i | \(-0.646626\pi\) | ||||
−0.444520 | + | 0.895769i | \(0.646626\pi\) | |||||||
\(758\) | 3.38820e7 | 2.14188 | ||||||||
\(759\) | 1.50836e6 | 0.0950389 | ||||||||
\(760\) | 89461.9 | 0.00561829 | ||||||||
\(761\) | −1.98659e7 | −1.24350 | −0.621750 | − | 0.783215i | \(-0.713578\pi\) | ||||
−0.621750 | + | 0.783215i | \(0.713578\pi\) | |||||||
\(762\) | 1.02690e7 | 0.640681 | ||||||||
\(763\) | −1.49514e6 | −0.0929761 | ||||||||
\(764\) | −1.65255e7 | −1.02429 | ||||||||
\(765\) | 405695. | 0.0250638 | ||||||||
\(766\) | 1.32721e7 | 0.817275 | ||||||||
\(767\) | −476331. | −0.0292361 | ||||||||
\(768\) | 8.64785e6 | 0.529060 | ||||||||
\(769\) | −2.09738e7 | −1.27897 | −0.639486 | − | 0.768803i | \(-0.720853\pi\) | ||||
−0.639486 | + | 0.768803i | \(0.720853\pi\) | |||||||
\(770\) | −962267. | −0.0584883 | ||||||||
\(771\) | −8.58542e6 | −0.520146 | ||||||||
\(772\) | 9.02668e6 | 0.545111 | ||||||||
\(773\) | 7.69041e6 | 0.462914 | 0.231457 | − | 0.972845i | \(-0.425651\pi\) | ||||
0.231457 | + | 0.972845i | \(0.425651\pi\) | |||||||
\(774\) | 7.90403e6 | 0.474238 | ||||||||
\(775\) | −1.53178e6 | −0.0916101 | ||||||||
\(776\) | 77794.4 | 0.00463761 | ||||||||
\(777\) | 1.43896e6 | 0.0855062 | ||||||||
\(778\) | −6.21909e6 | −0.368365 | ||||||||
\(779\) | 184731. | 0.0109068 | ||||||||
\(780\) | 1.65231e6 | 0.0972421 | ||||||||
\(781\) | −1.66076e6 | −0.0974270 | ||||||||
\(782\) | 2.24177e6 | 0.131091 | ||||||||
\(783\) | 4.01434e6 | 0.233997 | ||||||||
\(784\) | 1.49810e7 | 0.870466 | ||||||||
\(785\) | 4.51731e6 | 0.261641 | ||||||||
\(786\) | −1.53027e7 | −0.883513 | ||||||||
\(787\) | −1.39975e6 | −0.0805589 | −0.0402794 | − | 0.999188i | \(-0.512825\pi\) | ||||
−0.0402794 | + | 0.999188i | \(0.512825\pi\) | |||||||
\(788\) | −6.35256e6 | −0.364446 | ||||||||
\(789\) | 2.90052e6 | 0.165876 | ||||||||
\(790\) | 7.20470e6 | 0.410722 | ||||||||
\(791\) | 3.35443e6 | 0.190624 | ||||||||
\(792\) | −100109. | −0.00567100 | ||||||||
\(793\) | 8.81689e6 | 0.497889 | ||||||||
\(794\) | −3.93131e7 | −2.21302 | ||||||||
\(795\) | 8.37068e6 | 0.469724 | ||||||||
\(796\) | 2.00463e7 | 1.12138 | ||||||||
\(797\) | 1.22917e7 | 0.685432 | 0.342716 | − | 0.939439i | \(-0.388653\pi\) | ||||
0.342716 | + | 0.939439i | \(0.388653\pi\) | |||||||
\(798\) | 1.00302e6 | 0.0557573 | ||||||||
\(799\) | −112798. | −0.00625078 | ||||||||
\(800\) | 5.16225e6 | 0.285177 | ||||||||
\(801\) | −3.06042e6 | −0.168539 | ||||||||
\(802\) | −5.79290e6 | −0.318024 | ||||||||
\(803\) | −4.80810e6 | −0.263138 | ||||||||
\(804\) | −1.15181e7 | −0.628404 | ||||||||
\(805\) | 1.36348e6 | 0.0741584 | ||||||||
\(806\) | −4.37104e6 | −0.236999 | ||||||||
\(807\) | 7.27863e6 | 0.393429 | ||||||||
\(808\) | −1.28660e6 | −0.0693292 | ||||||||
\(809\) | −1.19607e7 | −0.642515 | −0.321258 | − | 0.946992i | \(-0.604106\pi\) | ||||
−0.321258 | + | 0.946992i | \(0.604106\pi\) | |||||||
\(810\) | 1.32510e6 | 0.0709636 | ||||||||
\(811\) | −1.15112e7 | −0.614565 | −0.307282 | − | 0.951618i | \(-0.599420\pi\) | ||||
−0.307282 | + | 0.951618i | \(0.599420\pi\) | |||||||
\(812\) | −7.21270e6 | −0.383891 | ||||||||
\(813\) | −8.18373e6 | −0.434235 | ||||||||
\(814\) | 3.96916e6 | 0.209961 | ||||||||
\(815\) | 4.40113e6 | 0.232097 | ||||||||
\(816\) | 1.77053e6 | 0.0930846 | ||||||||
\(817\) | −4.23177e6 | −0.221803 | ||||||||
\(818\) | 3.07062e7 | 1.60451 | ||||||||
\(819\) | 704120. | 0.0366806 | ||||||||
\(820\) | −438493. | −0.0227734 | ||||||||
\(821\) | 2.77684e7 | 1.43778 | 0.718890 | − | 0.695124i | \(-0.244651\pi\) | ||||
0.718890 | + | 0.695124i | \(0.244651\pi\) | |||||||
\(822\) | −1.42253e6 | −0.0734315 | ||||||||
\(823\) | −2.63447e7 | −1.35580 | −0.677898 | − | 0.735156i | \(-0.737109\pi\) | ||||
−0.677898 | + | 0.735156i | \(0.737109\pi\) | |||||||
\(824\) | 1.68758e6 | 0.0865860 | ||||||||
\(825\) | 680625. | 0.0348155 | ||||||||
\(826\) | 686356. | 0.0350025 | ||||||||
\(827\) | −3.32551e7 | −1.69081 | −0.845406 | − | 0.534125i | \(-0.820641\pi\) | ||||
−0.845406 | + | 0.534125i | \(0.820641\pi\) | |||||||
\(828\) | 3.73200e6 | 0.189176 | ||||||||
\(829\) | 2.84581e7 | 1.43820 | 0.719101 | − | 0.694905i | \(-0.244554\pi\) | ||||
0.719101 | + | 0.694905i | \(0.244554\pi\) | |||||||
\(830\) | −1.61572e7 | −0.814087 | ||||||||
\(831\) | 2.13239e6 | 0.107119 | ||||||||
\(832\) | 7.79391e6 | 0.390344 | ||||||||
\(833\) | 3.05654e6 | 0.152622 | ||||||||
\(834\) | −9.63360e6 | −0.479594 | ||||||||
\(835\) | −7.34545e6 | −0.364588 | ||||||||
\(836\) | 1.41013e6 | 0.0697822 | ||||||||
\(837\) | −1.78667e6 | −0.0881519 | ||||||||
\(838\) | 1.25936e7 | 0.619498 | ||||||||
\(839\) | −9.47931e6 | −0.464913 | −0.232457 | − | 0.972607i | \(-0.574676\pi\) | ||||
−0.232457 | + | 0.972607i | \(0.574676\pi\) | |||||||
\(840\) | −90493.3 | −0.00442505 | ||||||||
\(841\) | 9.81196e6 | 0.478372 | ||||||||
\(842\) | −3.34101e7 | −1.62404 | ||||||||
\(843\) | −4.05701e6 | −0.196624 | ||||||||
\(844\) | 3.05425e7 | 1.47587 | ||||||||
\(845\) | 8.06390e6 | 0.388511 | ||||||||
\(846\) | −368425. | −0.0176980 | ||||||||
\(847\) | −576505. | −0.0276118 | ||||||||
\(848\) | 3.65312e7 | 1.74451 | ||||||||
\(849\) | 6.15072e6 | 0.292858 | ||||||||
\(850\) | 1.01156e6 | 0.0480226 | ||||||||
\(851\) | −5.62411e6 | −0.266213 | ||||||||
\(852\) | −4.10907e6 | −0.193930 | ||||||||
\(853\) | 2.13145e7 | 1.00300 | 0.501501 | − | 0.865157i | \(-0.332781\pi\) | ||||
0.501501 | + | 0.865157i | \(0.332781\pi\) | |||||||
\(854\) | −1.27045e7 | −0.596090 | ||||||||
\(855\) | −709449. | −0.0331899 | ||||||||
\(856\) | 134339. | 0.00626640 | ||||||||
\(857\) | 2.21044e7 | 1.02808 | 0.514039 | − | 0.857767i | \(-0.328149\pi\) | ||||
0.514039 | + | 0.857767i | \(0.328149\pi\) | |||||||
\(858\) | 1.94221e6 | 0.0900693 | ||||||||
\(859\) | −7.07193e6 | −0.327006 | −0.163503 | − | 0.986543i | \(-0.552279\pi\) | ||||
−0.163503 | + | 0.986543i | \(0.552279\pi\) | |||||||
\(860\) | 1.00449e7 | 0.463125 | ||||||||
\(861\) | −186861. | −0.00859035 | ||||||||
\(862\) | 4.24855e7 | 1.94748 | ||||||||
\(863\) | −5.45080e6 | −0.249134 | −0.124567 | − | 0.992211i | \(-0.539754\pi\) | ||||
−0.124567 | + | 0.992211i | \(0.539754\pi\) | |||||||
\(864\) | 6.02125e6 | 0.274412 | ||||||||
\(865\) | 519623. | 0.0236128 | ||||||||
\(866\) | 5.61101e6 | 0.254241 | ||||||||
\(867\) | −1.24175e7 | −0.561029 | ||||||||
\(868\) | 3.21017e6 | 0.144620 | ||||||||
\(869\) | 4.31642e6 | 0.193898 | ||||||||
\(870\) | 1.00094e7 | 0.448342 | ||||||||
\(871\) | 8.49351e6 | 0.379351 | ||||||||
\(872\) | −387840. | −0.0172727 | ||||||||
\(873\) | −616924. | −0.0273966 | ||||||||
\(874\) | −3.92023e6 | −0.173593 | ||||||||
\(875\) | 615251. | 0.0271664 | ||||||||
\(876\) | −1.18962e7 | −0.523780 | ||||||||
\(877\) | −2.02823e7 | −0.890467 | −0.445234 | − | 0.895414i | \(-0.646879\pi\) | ||||
−0.445234 | + | 0.895414i | \(0.646879\pi\) | |||||||
\(878\) | 6.30917e7 | 2.76208 | ||||||||
\(879\) | −1.62961e7 | −0.711397 | ||||||||
\(880\) | 2.97038e6 | 0.129302 | ||||||||
\(881\) | −6.58178e6 | −0.285696 | −0.142848 | − | 0.989745i | \(-0.545626\pi\) | ||||
−0.142848 | + | 0.989745i | \(0.545626\pi\) | |||||||
\(882\) | 9.98340e6 | 0.432123 | ||||||||
\(883\) | −1.63860e7 | −0.707247 | −0.353623 | − | 0.935388i | \(-0.615051\pi\) | ||||
−0.353623 | + | 0.935388i | \(0.615051\pi\) | |||||||
\(884\) | 1.47124e6 | 0.0633217 | ||||||||
\(885\) | −485469. | −0.0208355 | ||||||||
\(886\) | 4.39378e7 | 1.88042 | ||||||||
\(887\) | −2.92929e6 | −0.125013 | −0.0625063 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625063 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(888\) | 373267. | 0.0158850 | ||||||||
\(889\) | 5.56136e6 | 0.236008 | ||||||||
\(890\) | −7.63087e6 | −0.322923 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 3.19206e7 | 1.34326 | ||||||||
\(893\) | 197252. | 0.00827739 | ||||||||
\(894\) | 1.11473e7 | 0.466472 | ||||||||
\(895\) | 5.73314e6 | 0.239241 | ||||||||
\(896\) | −823047. | −0.0342495 | ||||||||
\(897\) | −2.75201e6 | −0.114201 | ||||||||
\(898\) | −4.41317e7 | −1.82625 | ||||||||
\(899\) | −1.34960e7 | −0.556936 | ||||||||
\(900\) | 1.68401e6 | 0.0693007 | ||||||||
\(901\) | 7.45337e6 | 0.305873 | ||||||||
\(902\) | −515427. | −0.0210936 | ||||||||
\(903\) | 4.28056e6 | 0.174695 | ||||||||
\(904\) | 870140. | 0.0354134 | ||||||||
\(905\) | 2.27018e6 | 0.0921381 | ||||||||
\(906\) | −1.80425e7 | −0.730256 | ||||||||
\(907\) | −7.88236e6 | −0.318154 | −0.159077 | − | 0.987266i | \(-0.550852\pi\) | ||||
−0.159077 | + | 0.987266i | \(0.550852\pi\) | |||||||
\(908\) | −9.64512e6 | −0.388234 | ||||||||
\(909\) | 1.02030e7 | 0.409561 | ||||||||
\(910\) | 1.75566e6 | 0.0702807 | ||||||||
\(911\) | −2.16713e7 | −0.865146 | −0.432573 | − | 0.901599i | \(-0.642394\pi\) | ||||
−0.432573 | + | 0.901599i | \(0.642394\pi\) | |||||||
\(912\) | −3.09617e6 | −0.123264 | ||||||||
\(913\) | −9.67996e6 | −0.384323 | ||||||||
\(914\) | −2.48130e7 | −0.982458 | ||||||||
\(915\) | 8.98605e6 | 0.354827 | ||||||||
\(916\) | 3.69769e6 | 0.145610 | ||||||||
\(917\) | −8.28745e6 | −0.325460 | ||||||||
\(918\) | 1.17989e6 | 0.0462097 | ||||||||
\(919\) | 4.32037e7 | 1.68746 | 0.843728 | − | 0.536771i | \(-0.180356\pi\) | ||||
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(920\) | 353688. | 0.0137769 | ||||||||
\(921\) | −2.70774e7 | −1.05186 | ||||||||
\(922\) | −3.11545e7 | −1.20696 | ||||||||
\(923\) | 3.03006e6 | 0.117070 | ||||||||
\(924\) | −1.42639e6 | −0.0549616 | ||||||||
\(925\) | −2.53779e6 | −0.0975217 | ||||||||
\(926\) | −2.58996e7 | −0.992580 | ||||||||
\(927\) | −1.33829e7 | −0.511504 | ||||||||
\(928\) | 4.54827e7 | 1.73371 | ||||||||
\(929\) | 3.70288e7 | 1.40767 | 0.703834 | − | 0.710364i | \(-0.251470\pi\) | ||||
0.703834 | + | 0.710364i | \(0.251470\pi\) | |||||||
\(930\) | −4.45490e6 | −0.168900 | ||||||||
\(931\) | −5.34505e6 | −0.202105 | ||||||||
\(932\) | −1.50759e7 | −0.568518 | ||||||||
\(933\) | −1.83675e7 | −0.690790 | ||||||||
\(934\) | 1.97080e7 | 0.739224 | ||||||||
\(935\) | 606038. | 0.0226710 | ||||||||
\(936\) | 182648. | 0.00681438 | ||||||||
\(937\) | 1.22598e7 | 0.456180 | 0.228090 | − | 0.973640i | \(-0.426752\pi\) | ||||
0.228090 | + | 0.973640i | \(0.426752\pi\) | |||||||
\(938\) | −1.22385e7 | −0.454173 | ||||||||
\(939\) | −1.56546e7 | −0.579399 | ||||||||
\(940\) | −468215. | −0.0172833 | ||||||||
\(941\) | −1.25646e7 | −0.462565 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(942\) | 1.31377e7 | 0.482384 | ||||||||
\(943\) | 730335. | 0.0267450 | ||||||||
\(944\) | −2.11868e6 | −0.0773812 | ||||||||
\(945\) | 717628. | 0.0261409 | ||||||||
\(946\) | 1.18073e7 | 0.428964 | ||||||||
\(947\) | 3.16122e7 | 1.14546 | 0.572730 | − | 0.819744i | \(-0.305884\pi\) | ||||
0.572730 | + | 0.819744i | \(0.305884\pi\) | |||||||
\(948\) | 1.06797e7 | 0.385957 | ||||||||
\(949\) | 8.77237e6 | 0.316192 | ||||||||
\(950\) | −1.76894e6 | −0.0635924 | ||||||||
\(951\) | 960334. | 0.0344327 | ||||||||
\(952\) | −80576.6 | −0.00288148 | ||||||||
\(953\) | −2.84509e7 | −1.01476 | −0.507380 | − | 0.861722i | \(-0.669386\pi\) | ||||
−0.507380 | + | 0.861722i | \(0.669386\pi\) | |||||||
\(954\) | 2.43445e7 | 0.866024 | ||||||||
\(955\) | 1.24199e7 | 0.440665 | ||||||||
\(956\) | 4.20419e7 | 1.48778 | ||||||||
\(957\) | 5.99673e6 | 0.211658 | ||||||||
\(958\) | −3.79038e7 | −1.33435 | ||||||||
\(959\) | −770395. | −0.0270500 | ||||||||
\(960\) | 7.94344e6 | 0.278183 | ||||||||
\(961\) | −2.26225e7 | −0.790190 | ||||||||
\(962\) | −7.24174e6 | −0.252293 | ||||||||
\(963\) | −1.06533e6 | −0.0370186 | ||||||||
\(964\) | 4.46905e6 | 0.154890 | ||||||||
\(965\) | −6.78405e6 | −0.234515 | ||||||||
\(966\) | 3.96543e6 | 0.136725 | ||||||||
\(967\) | −4.73439e7 | −1.62816 | −0.814081 | − | 0.580751i | \(-0.802759\pi\) | ||||
−0.814081 | + | 0.580751i | \(0.802759\pi\) | |||||||
\(968\) | −149545. | −0.00512961 | ||||||||
\(969\) | −631704. | −0.0216124 | ||||||||
\(970\) | −1.53824e6 | −0.0524923 | ||||||||
\(971\) | −4.33248e7 | −1.47465 | −0.737324 | − | 0.675539i | \(-0.763911\pi\) | ||||
−0.737324 | + | 0.675539i | \(0.763911\pi\) | |||||||
\(972\) | 1.96423e6 | 0.0666846 | ||||||||
\(973\) | −5.21723e6 | −0.176668 | ||||||||
\(974\) | −4.63152e7 | −1.56432 | ||||||||
\(975\) | −1.24180e6 | −0.0418350 | ||||||||
\(976\) | 3.92168e7 | 1.31780 | ||||||||
\(977\) | −4.64678e7 | −1.55745 | −0.778727 | − | 0.627363i | \(-0.784134\pi\) | ||||
−0.778727 | + | 0.627363i | \(0.784134\pi\) | |||||||
\(978\) | 1.27998e7 | 0.427915 | ||||||||
\(979\) | −4.57174e6 | −0.152449 | ||||||||
\(980\) | 1.26875e7 | 0.421997 | ||||||||
\(981\) | 3.07564e6 | 0.102038 | ||||||||
\(982\) | 5.60553e6 | 0.185498 | ||||||||
\(983\) | −1.02443e7 | −0.338141 | −0.169071 | − | 0.985604i | \(-0.554077\pi\) | ||||
−0.169071 | + | 0.985604i | \(0.554077\pi\) | |||||||
\(984\) | −48471.7 | −0.00159588 | ||||||||
\(985\) | 4.77430e6 | 0.156790 | ||||||||
\(986\) | 8.91250e6 | 0.291949 | ||||||||
\(987\) | −199527. | −0.00651940 | ||||||||
\(988\) | −2.57279e6 | −0.0838517 | ||||||||
\(989\) | −1.67303e7 | −0.543892 | ||||||||
\(990\) | 1.97947e6 | 0.0641890 | ||||||||
\(991\) | −6.52638e6 | −0.211100 | −0.105550 | − | 0.994414i | \(-0.533660\pi\) | ||||
−0.105550 | + | 0.994414i | \(0.533660\pi\) | |||||||
\(992\) | −2.02431e7 | −0.653127 | ||||||||
\(993\) | 1.39283e7 | 0.448256 | ||||||||
\(994\) | −4.36608e6 | −0.140161 | ||||||||
\(995\) | −1.50659e7 | −0.482434 | ||||||||
\(996\) | −2.39502e7 | −0.765000 | ||||||||
\(997\) | 1.08535e7 | 0.345804 | 0.172902 | − | 0.984939i | \(-0.444686\pi\) | ||||
0.172902 | + | 0.984939i | \(0.444686\pi\) | |||||||
\(998\) | −9.94904e6 | −0.316195 | ||||||||
\(999\) | −2.96008e6 | −0.0938403 |
(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 | 165.6.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.d.1.3 | 3 | |||
5.4 | even | 2 | 825.6.a.i.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.d.1.3 | 3 | 3.2 | odd | 2 | |||
825.6.a.i.1.3 | 3 | 5.4 | even | 2 |