Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,6,Mod(2,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.2");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.c (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(1.12268673869\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(-1.27069 + 2.20090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.2 |
Dual form | 7.6.c.a.4.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54138 | − | 4.40180i | 0.449257 | − | 0.778136i | −0.549081 | − | 0.835769i | \(-0.685022\pi\) |
0.998338 | + | 0.0576333i | \(0.0183554\pi\) | |||||||
\(3\) | −1.04138 | − | 1.80373i | −0.0668046 | − | 0.115709i | 0.830688 | − | 0.556738i | \(-0.187947\pi\) |
−0.897493 | + | 0.441029i | \(0.854614\pi\) | |||||||
\(4\) | 3.08276 | + | 5.33950i | 0.0963363 | + | 0.166859i | ||||
\(5\) | −20.9138 | + | 36.2238i | −0.374118 | + | 0.647991i | −0.990195 | − | 0.139695i | \(-0.955388\pi\) |
0.616077 | + | 0.787686i | \(0.288721\pi\) | |||||||
\(6\) | −10.5862 | −0.120050 | ||||||||
\(7\) | −127.159 | − | 25.2522i | −0.980846 | − | 0.194784i | ||||
\(8\) | 193.986 | 1.07163 | ||||||||
\(9\) | 119.331 | − | 206.687i | 0.491074 | − | 0.850566i | ||||
\(10\) | 106.300 | + | 184.117i | 0.336150 | + | 0.582229i | ||||
\(11\) | −36.0482 | − | 62.4374i | −0.0898260 | − | 0.155583i | 0.817611 | − | 0.575770i | \(-0.195298\pi\) |
−0.907437 | + | 0.420187i | \(0.861964\pi\) | |||||||
\(12\) | 6.42066 | − | 11.1209i | 0.0128714 | − | 0.0222940i | ||||
\(13\) | −632.317 | −1.03771 | −0.518856 | − | 0.854862i | \(-0.673642\pi\) | ||||
−0.518856 | + | 0.854862i | \(0.673642\pi\) | |||||||
\(14\) | −434.314 | + | 495.552i | −0.592220 | + | 0.675724i | ||||
\(15\) | 87.1170 | 0.0999712 | ||||||||
\(16\) | 394.345 | − | 683.025i | 0.385102 | − | 0.667017i | ||||
\(17\) | 987.962 | + | 1711.20i | 0.829121 | + | 1.43608i | 0.898728 | + | 0.438506i | \(0.144492\pi\) |
−0.0696071 | + | 0.997574i | \(0.522175\pi\) | |||||||
\(18\) | −606.531 | − | 1050.54i | −0.441237 | − | 0.764245i | ||||
\(19\) | 932.463 | − | 1615.07i | 0.592581 | − | 1.02638i | −0.401303 | − | 0.915945i | \(-0.631443\pi\) |
0.993883 | − | 0.110434i | \(-0.0352242\pi\) | |||||||
\(20\) | −257.889 | −0.144164 | ||||||||
\(21\) | 86.8727 | + | 255.656i | 0.0429868 | + | 0.126505i | ||||
\(22\) | −366.449 | −0.161420 | ||||||||
\(23\) | −206.855 | + | 358.284i | −0.0815356 | + | 0.141224i | −0.903910 | − | 0.427723i | \(-0.859316\pi\) |
0.822374 | + | 0.568947i | \(0.192649\pi\) | |||||||
\(24\) | −202.014 | − | 349.898i | −0.0715901 | − | 0.123998i | ||||
\(25\) | 687.725 | + | 1191.17i | 0.220072 | + | 0.381176i | ||||
\(26\) | −1606.96 | + | 2783.34i | −0.466199 | + | 0.807481i | ||||
\(27\) | −1003.19 | −0.264833 | ||||||||
\(28\) | −257.166 | − | 756.810i | −0.0619896 | − | 0.182428i | ||||
\(29\) | 731.934 | 0.161613 | 0.0808066 | − | 0.996730i | \(-0.474250\pi\) | ||||
0.0808066 | + | 0.996730i | \(0.474250\pi\) | |||||||
\(30\) | 221.398 | − | 383.472i | 0.0449128 | − | 0.0777912i | ||||
\(31\) | −3061.59 | − | 5302.83i | −0.572193 | − | 0.991067i | −0.996340 | − | 0.0854740i | \(-0.972760\pi\) |
0.424148 | − | 0.905593i | \(-0.360574\pi\) | |||||||
\(32\) | 1099.42 | + | 1904.25i | 0.189797 | + | 0.328738i | ||||
\(33\) | −75.0799 | + | 130.042i | −0.0120016 | + | 0.0207874i | ||||
\(34\) | 10043.2 | 1.48995 | ||||||||
\(35\) | 3574.10 | − | 4078.05i | 0.493170 | − | 0.562707i | ||||
\(36\) | 1471.48 | 0.189233 | ||||||||
\(37\) | −5175.19 | + | 8963.69i | −0.621473 | + | 1.07642i | 0.367739 | + | 0.929929i | \(0.380132\pi\) |
−0.989212 | + | 0.146493i | \(0.953201\pi\) | |||||||
\(38\) | −4739.49 | − | 8209.03i | −0.532442 | − | 0.922216i | ||||
\(39\) | 658.483 | + | 1140.53i | 0.0693240 | + | 0.120073i | ||||
\(40\) | −4056.99 | + | 7026.92i | −0.400917 | + | 0.694408i | ||||
\(41\) | −3529.84 | −0.327941 | −0.163970 | − | 0.986465i | \(-0.552430\pi\) | ||||
−0.163970 | + | 0.986465i | \(0.552430\pi\) | |||||||
\(42\) | 1346.13 | + | 267.324i | 0.117750 | + | 0.0233838i | ||||
\(43\) | −14515.2 | −1.19716 | −0.598581 | − | 0.801062i | \(-0.704269\pi\) | ||||
−0.598581 | + | 0.801062i | \(0.704269\pi\) | |||||||
\(44\) | 222.256 | − | 384.959i | 0.0173070 | − | 0.0299766i | ||||
\(45\) | 4991.33 | + | 8645.24i | 0.367439 | + | 0.636423i | ||||
\(46\) | 1051.40 | + | 1821.07i | 0.0732608 | + | 0.126892i | ||||
\(47\) | 10711.7 | − | 18553.1i | 0.707314 | − | 1.22510i | −0.258536 | − | 0.966002i | \(-0.583240\pi\) |
0.965850 | − | 0.259102i | \(-0.0834265\pi\) | |||||||
\(48\) | −1642.65 | −0.102906 | ||||||||
\(49\) | 15531.7 | + | 6422.06i | 0.924118 | + | 0.382106i | ||||
\(50\) | 6991.08 | 0.395475 | ||||||||
\(51\) | 2057.69 | − | 3564.03i | 0.110778 | − | 0.191874i | ||||
\(52\) | −1949.28 | − | 3376.26i | −0.0999693 | − | 0.173152i | ||||
\(53\) | −6289.73 | − | 10894.1i | −0.307569 | − | 0.532725i | 0.670261 | − | 0.742125i | \(-0.266182\pi\) |
−0.977830 | + | 0.209400i | \(0.932849\pi\) | |||||||
\(54\) | −2549.48 | + | 4415.83i | −0.118978 | + | 0.206076i | ||||
\(55\) | 3015.62 | 0.134422 | ||||||||
\(56\) | −24667.0 | − | 4898.57i | −1.05111 | − | 0.208737i | ||||
\(57\) | −3884.20 | −0.158349 | ||||||||
\(58\) | 1860.12 | − | 3221.83i | 0.0726059 | − | 0.125757i | ||||
\(59\) | 18067.0 | + | 31292.9i | 0.675702 | + | 1.17035i | 0.976263 | + | 0.216588i | \(0.0694928\pi\) |
−0.300561 | + | 0.953763i | \(0.597174\pi\) | |||||||
\(60\) | 268.561 | + | 465.161i | 0.00963086 | + | 0.0166811i | ||||
\(61\) | −2012.40 | + | 3485.58i | −0.0692451 | + | 0.119936i | −0.898569 | − | 0.438832i | \(-0.855392\pi\) |
0.829324 | + | 0.558768i | \(0.188726\pi\) | |||||||
\(62\) | −31122.6 | −1.02825 | ||||||||
\(63\) | −20393.3 | + | 23268.7i | −0.647345 | + | 0.738621i | ||||
\(64\) | 36414.2 | 1.11127 | ||||||||
\(65\) | 13224.2 | − | 22904.9i | 0.388226 | − | 0.672428i | ||||
\(66\) | 381.613 | + | 660.974i | 0.0107836 | + | 0.0186777i | ||||
\(67\) | −7782.97 | − | 13480.5i | −0.211816 | − | 0.366876i | 0.740467 | − | 0.672093i | \(-0.234604\pi\) |
−0.952283 | + | 0.305217i | \(0.901271\pi\) | |||||||
\(68\) | −6091.31 | + | 10550.5i | −0.159749 | + | 0.276693i | ||||
\(69\) | 861.661 | 0.0217878 | ||||||||
\(70\) | −8867.61 | − | 26096.4i | −0.216303 | − | 0.636553i | ||||
\(71\) | 12180.8 | 0.286766 | 0.143383 | − | 0.989667i | \(-0.454202\pi\) | ||||
0.143383 | + | 0.989667i | \(0.454202\pi\) | |||||||
\(72\) | 23148.6 | − | 40094.5i | 0.526251 | − | 0.911494i | ||||
\(73\) | −9794.56 | − | 16964.7i | −0.215119 | − | 0.372596i | 0.738191 | − | 0.674592i | \(-0.235680\pi\) |
−0.953309 | + | 0.301996i | \(0.902347\pi\) | |||||||
\(74\) | 26304.3 | + | 45560.3i | 0.558402 | + | 0.967181i | ||||
\(75\) | 1432.37 | − | 2480.93i | 0.0294037 | − | 0.0509286i | ||||
\(76\) | 11498.2 | 0.228348 | ||||||||
\(77\) | 3007.17 | + | 8849.75i | 0.0578004 | + | 0.170100i | ||||
\(78\) | 6693.83 | 0.124577 | ||||||||
\(79\) | −18044.9 | + | 31254.7i | −0.325302 | + | 0.563439i | −0.981573 | − | 0.191085i | \(-0.938799\pi\) |
0.656272 | + | 0.754525i | \(0.272133\pi\) | |||||||
\(80\) | 16494.5 | + | 28569.3i | 0.288147 | + | 0.499085i | ||||
\(81\) | −27952.7 | − | 48415.6i | −0.473382 | − | 0.819922i | ||||
\(82\) | −8970.66 | + | 15537.6i | −0.147330 | + | 0.255182i | ||||
\(83\) | −24572.6 | −0.391522 | −0.195761 | − | 0.980652i | \(-0.562718\pi\) | ||||
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(84\) | −1097.27 | + | 1251.99i | −0.0169674 | + | 0.0193598i | ||||
\(85\) | −82648.2 | −1.24076 | ||||||||
\(86\) | −36888.7 | + | 63893.2i | −0.537833 | + | 0.931555i | ||||
\(87\) | −762.222 | − | 1320.21i | −0.0107965 | − | 0.0187001i | ||||
\(88\) | −6992.86 | − | 12112.0i | −0.0962605 | − | 0.166728i | ||||
\(89\) | 35121.7 | − | 60832.5i | 0.470002 | − | 0.814068i | −0.529409 | − | 0.848367i | \(-0.677586\pi\) |
0.999412 | + | 0.0342986i | \(0.0109197\pi\) | |||||||
\(90\) | 50739.5 | 0.660298 | ||||||||
\(91\) | 80404.6 | + | 15967.4i | 1.01784 | + | 0.202130i | ||||
\(92\) | −2550.74 | −0.0314193 | ||||||||
\(93\) | −6376.56 | + | 11044.5i | −0.0764503 | + | 0.132416i | ||||
\(94\) | −54444.8 | − | 94301.2i | −0.635531 | − | 1.10077i | ||||
\(95\) | 39002.7 | + | 67554.7i | 0.443390 | + | 0.767974i | ||||
\(96\) | 2289.83 | − | 3966.10i | 0.0253586 | − | 0.0439224i | ||||
\(97\) | 105758. | 1.14126 | 0.570630 | − | 0.821207i | \(-0.306699\pi\) | ||||
0.570630 | + | 0.821207i | \(0.306699\pi\) | |||||||
\(98\) | 67740.5 | − | 52046.4i | 0.712497 | − | 0.547426i | ||||
\(99\) | −17206.7 | −0.176445 | ||||||||
\(100\) | −4240.18 | + | 7344.22i | −0.0424018 | + | 0.0734422i | ||||
\(101\) | −18230.9 | − | 31576.8i | −0.177830 | − | 0.308010i | 0.763307 | − | 0.646036i | \(-0.223574\pi\) |
−0.941137 | + | 0.338025i | \(0.890241\pi\) | |||||||
\(102\) | −10458.8 | − | 18115.1i | −0.0995359 | − | 0.172401i | ||||
\(103\) | −32260.0 | + | 55876.0i | −0.299621 | + | 0.518958i | −0.976049 | − | 0.217550i | \(-0.930193\pi\) |
0.676428 | + | 0.736508i | \(0.263527\pi\) | |||||||
\(104\) | −122661. | −1.11205 | ||||||||
\(105\) | −11077.7 | − | 2199.89i | −0.0980563 | − | 0.0194728i | ||||
\(106\) | −63938.4 | −0.552710 | ||||||||
\(107\) | −33022.8 | + | 57197.2i | −0.278840 | + | 0.482964i | −0.971097 | − | 0.238687i | \(-0.923283\pi\) |
0.692257 | + | 0.721651i | \(0.256616\pi\) | |||||||
\(108\) | −3092.59 | − | 5356.52i | −0.0255131 | − | 0.0441900i | ||||
\(109\) | 18969.0 | + | 32855.3i | 0.152925 | + | 0.264874i | 0.932302 | − | 0.361682i | \(-0.117797\pi\) |
−0.779377 | + | 0.626556i | \(0.784464\pi\) | |||||||
\(110\) | 7663.85 | − | 13274.2i | 0.0603900 | − | 0.104599i | ||||
\(111\) | 21557.4 | 0.166069 | ||||||||
\(112\) | −67392.2 | + | 76894.5i | −0.507650 | + | 0.579229i | ||||
\(113\) | 123802. | 0.912080 | 0.456040 | − | 0.889959i | \(-0.349267\pi\) | ||||
0.456040 | + | 0.889959i | \(0.349267\pi\) | |||||||
\(114\) | −9871.22 | + | 17097.5i | −0.0711392 | + | 0.123217i | ||||
\(115\) | −8652.27 | − | 14986.2i | −0.0610078 | − | 0.105669i | ||||
\(116\) | 2256.38 | + | 3908.16i | 0.0155692 | + | 0.0269667i | ||||
\(117\) | −75455.1 | + | 130692.i | −0.509594 | + | 0.882642i | ||||
\(118\) | 183660. | 1.21426 | ||||||||
\(119\) | −82416.5 | − | 242542.i | −0.533515 | − | 1.57007i | ||||
\(120\) | 16899.5 | 0.107132 | ||||||||
\(121\) | 77926.6 | − | 134973.i | 0.483863 | − | 0.838075i | ||||
\(122\) | 10228.5 | + | 17716.4i | 0.0622177 | + | 0.107764i | ||||
\(123\) | 3675.91 | + | 6366.86i | 0.0219079 | + | 0.0379457i | ||||
\(124\) | 18876.3 | − | 32694.7i | 0.110246 | − | 0.190952i | ||||
\(125\) | −188243. | −1.07757 | ||||||||
\(126\) | 50597.3 | + | 148902.i | 0.283923 | + | 0.835553i | ||||
\(127\) | 128724. | 0.708189 | 0.354095 | − | 0.935210i | \(-0.384789\pi\) | ||||
0.354095 | + | 0.935210i | \(0.384789\pi\) | |||||||
\(128\) | 57361.0 | − | 99352.2i | 0.309451 | − | 0.535985i | ||||
\(129\) | 15115.9 | + | 26181.5i | 0.0799760 | + | 0.138522i | ||||
\(130\) | −67215.3 | − | 116420.i | −0.348827 | − | 0.604186i | ||||
\(131\) | 73951.1 | − | 128087.i | 0.376501 | − | 0.652120i | −0.614049 | − | 0.789268i | \(-0.710460\pi\) |
0.990551 | + | 0.137148i | \(0.0437936\pi\) | |||||||
\(132\) | −925.814 | −0.00462476 | ||||||||
\(133\) | −159355. | + | 181824.i | −0.781153 | + | 0.891295i | ||||
\(134\) | −79118.0 | −0.380639 | ||||||||
\(135\) | 20980.5 | − | 36339.3i | 0.0990789 | − | 0.171610i | ||||
\(136\) | 191651. | + | 331950.i | 0.888514 | + | 1.53895i | ||||
\(137\) | 45578.7 | + | 78944.6i | 0.207472 | + | 0.359353i | 0.950918 | − | 0.309444i | \(-0.100143\pi\) |
−0.743445 | + | 0.668797i | \(0.766810\pi\) | |||||||
\(138\) | 2189.81 | − | 3792.86i | 0.00978833 | − | 0.0169539i | ||||
\(139\) | −334657. | −1.46914 | −0.734570 | − | 0.678533i | \(-0.762616\pi\) | ||||
−0.734570 | + | 0.678533i | \(0.762616\pi\) | |||||||
\(140\) | 32792.9 | + | 6512.26i | 0.141403 | + | 0.0280809i | ||||
\(141\) | −44619.7 | −0.189007 | ||||||||
\(142\) | 30955.9 | − | 53617.3i | 0.128832 | − | 0.223143i | ||||
\(143\) | 22793.9 | + | 39480.2i | 0.0932135 | + | 0.161451i | ||||
\(144\) | −94115.1 | − | 163012.i | −0.378228 | − | 0.655110i | ||||
\(145\) | −15307.5 | + | 26513.4i | −0.0604623 | + | 0.104724i | ||||
\(146\) | −99566.9 | −0.386574 | ||||||||
\(147\) | −4590.74 | − | 34702.7i | −0.0175222 | − | 0.132455i | ||||
\(148\) | −63815.5 | −0.239482 | ||||||||
\(149\) | −69135.7 | + | 119746.i | −0.255115 | + | 0.441873i | −0.964927 | − | 0.262519i | \(-0.915447\pi\) |
0.709812 | + | 0.704392i | \(0.248780\pi\) | |||||||
\(150\) | −7280.38 | − | 12610.0i | −0.0264196 | − | 0.0457601i | ||||
\(151\) | −55584.6 | − | 96275.4i | −0.198386 | − | 0.343615i | 0.749619 | − | 0.661870i | \(-0.230237\pi\) |
−0.948005 | + | 0.318254i | \(0.896903\pi\) | |||||||
\(152\) | 180885. | − | 313302.i | 0.635029 | − | 1.09990i | ||||
\(153\) | 471578. | 1.62864 | ||||||||
\(154\) | 46597.2 | + | 9253.63i | 0.158328 | + | 0.0314420i | ||||
\(155\) | 256118. | 0.856270 | ||||||||
\(156\) | −4059.90 | + | 7031.95i | −0.0133568 | + | 0.0231347i | ||||
\(157\) | 19074.3 | + | 33037.6i | 0.0617587 | + | 0.106969i | 0.895252 | − | 0.445561i | \(-0.146996\pi\) |
−0.833493 | + | 0.552530i | \(0.813662\pi\) | |||||||
\(158\) | 91717.9 | + | 158860.i | 0.292288 | + | 0.506258i | ||||
\(159\) | −13100.0 | + | 22689.9i | −0.0410941 | + | 0.0711770i | ||||
\(160\) | −91972.3 | −0.284025 | ||||||||
\(161\) | 35350.9 | − | 40335.4i | 0.107482 | − | 0.122637i | ||||
\(162\) | −284154. | −0.850681 | ||||||||
\(163\) | 106452. | − | 184381.i | 0.313824 | − | 0.543559i | −0.665363 | − | 0.746520i | \(-0.731723\pi\) |
0.979187 | + | 0.202961i | \(0.0650565\pi\) | |||||||
\(164\) | −10881.7 | − | 18847.6i | −0.0315926 | − | 0.0547200i | ||||
\(165\) | −3140.41 | − | 5439.36i | −0.00898001 | − | 0.0155538i | ||||
\(166\) | −62448.3 | + | 108164.i | −0.175894 | + | 0.304657i | ||||
\(167\) | −120396. | −0.334057 | −0.167028 | − | 0.985952i | \(-0.553417\pi\) | ||||
−0.167028 | + | 0.985952i | \(0.553417\pi\) | |||||||
\(168\) | 16852.1 | + | 49593.8i | 0.0460661 | + | 0.135567i | ||||
\(169\) | 28532.2 | 0.0768456 | ||||||||
\(170\) | −210041. | + | 363801.i | −0.557418 | + | 0.965477i | ||||
\(171\) | −222543. | − | 385457.i | −0.582002 | − | 1.00806i | ||||
\(172\) | −44747.0 | − | 77504.1i | −0.115330 | − | 0.199758i | ||||
\(173\) | −356457. | + | 617402.i | −0.905507 | + | 1.56838i | −0.0852723 | + | 0.996358i | \(0.527176\pi\) |
−0.820235 | + | 0.572027i | \(0.806157\pi\) | |||||||
\(174\) | −7748.39 | −0.0194016 | ||||||||
\(175\) | −57370.5 | − | 168835.i | −0.141610 | − | 0.416741i | ||||
\(176\) | −56861.7 | −0.138369 | ||||||||
\(177\) | 37629.2 | − | 65175.7i | 0.0902801 | − | 0.156370i | ||||
\(178\) | −178515. | − | 309197.i | −0.422304 | − | 0.731451i | ||||
\(179\) | 374869. | + | 649292.i | 0.874474 | + | 1.51463i | 0.857322 | + | 0.514780i | \(0.172127\pi\) |
0.0171519 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(180\) | −30774.2 | + | 53302.5i | −0.0707955 | + | 0.122621i | ||||
\(181\) | 623718. | 1.41511 | 0.707557 | − | 0.706656i | \(-0.249797\pi\) | ||||
0.707557 | + | 0.706656i | \(0.249797\pi\) | |||||||
\(182\) | 274624. | − | 313346.i | 0.614554 | − | 0.701206i | ||||
\(183\) | 8382.69 | 0.0185036 | ||||||||
\(184\) | −40127.1 | + | 69502.2i | −0.0873762 | + | 0.151340i | ||||
\(185\) | −216466. | − | 374930.i | −0.465008 | − | 0.805417i | ||||
\(186\) | 32410.5 | + | 56136.7i | 0.0686916 | + | 0.118977i | ||||
\(187\) | 71228.6 | − | 123372.i | 0.148953 | − | 0.257995i | ||||
\(188\) | 132086. | 0.272560 | ||||||||
\(189\) | 127564. | + | 25332.7i | 0.259761 | + | 0.0515853i | ||||
\(190\) | 396483. | 0.796784 | ||||||||
\(191\) | −208863. | + | 361761.i | −0.414265 | + | 0.717528i | −0.995351 | − | 0.0963141i | \(-0.969295\pi\) |
0.581086 | + | 0.813842i | \(0.302628\pi\) | |||||||
\(192\) | −37921.1 | − | 65681.3i | −0.0742383 | − | 0.128585i | ||||
\(193\) | −385350. | − | 667446.i | −0.744667 | − | 1.28980i | −0.950350 | − | 0.311183i | \(-0.899275\pi\) |
0.205683 | − | 0.978619i | \(-0.434058\pi\) | |||||||
\(194\) | 268772. | − | 465527.i | 0.512719 | − | 0.888056i | ||||
\(195\) | −55085.6 | −0.103741 | ||||||||
\(196\) | 13589.8 | + | 102729.i | 0.0252681 | + | 0.191009i | ||||
\(197\) | −479193. | −0.879721 | −0.439861 | − | 0.898066i | \(-0.644972\pi\) | ||||
−0.439861 | + | 0.898066i | \(0.644972\pi\) | |||||||
\(198\) | −43728.8 | + | 75740.4i | −0.0792692 | + | 0.137298i | ||||
\(199\) | 214343. | + | 371253.i | 0.383687 | + | 0.664565i | 0.991586 | − | 0.129449i | \(-0.0413210\pi\) |
−0.607899 | + | 0.794014i | \(0.707988\pi\) | |||||||
\(200\) | 133409. | + | 231072.i | 0.235836 | + | 0.408481i | ||||
\(201\) | −16210.1 | + | 28076.7i | −0.0283006 | + | 0.0490180i | ||||
\(202\) | −185327. | −0.319565 | ||||||||
\(203\) | −93071.7 | − | 18482.9i | −0.158518 | − | 0.0314797i | ||||
\(204\) | 25373.5 | 0.0426879 | ||||||||
\(205\) | 73822.4 | − | 127864.i | 0.122688 | − | 0.212502i | ||||
\(206\) | 163970. | + | 284005.i | 0.269213 | + | 0.466291i | ||||
\(207\) | 49368.5 | + | 85508.8i | 0.0800800 | + | 0.138703i | ||||
\(208\) | −249351. | + | 431889.i | −0.399625 | + | 0.692171i | ||||
\(209\) | −134455. | −0.212917 | ||||||||
\(210\) | −37836.1 | + | 43171.0i | −0.0592050 | + | 0.0675529i | ||||
\(211\) | −588544. | −0.910066 | −0.455033 | − | 0.890475i | \(-0.650373\pi\) | ||||
−0.455033 | + | 0.890475i | \(0.650373\pi\) | |||||||
\(212\) | 38779.5 | − | 67168.1i | 0.0592601 | − | 0.102642i | ||||
\(213\) | −12684.8 | − | 21970.7i | −0.0191573 | − | 0.0331815i | ||||
\(214\) | 167847. | + | 290720.i | 0.250541 | + | 0.433950i | ||||
\(215\) | 303569. | − | 525797.i | 0.447879 | − | 0.775750i | ||||
\(216\) | −194605. | −0.283804 | ||||||||
\(217\) | 255400. | + | 751612.i | 0.368189 | + | 1.08354i | ||||
\(218\) | 192830. | 0.274811 | ||||||||
\(219\) | −20399.7 | + | 35333.4i | −0.0287418 | + | 0.0497823i | ||||
\(220\) | 9296.45 | + | 16101.9i | 0.0129497 | + | 0.0224296i | ||||
\(221\) | −624706. | − | 1.08202e6i | −0.860389 | − | 1.49024i | ||||
\(222\) | 54785.5 | − | 94891.3i | 0.0746077 | − | 0.129224i | ||||
\(223\) | −363249. | −0.489151 | −0.244575 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244575 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(224\) | −91714.4 | − | 269905.i | −0.122129 | − | 0.359410i | ||||
\(225\) | 328268. | 0.432287 | ||||||||
\(226\) | 314629. | − | 544954.i | 0.409758 | − | 0.709722i | ||||
\(227\) | 421521. | + | 730095.i | 0.542943 | + | 0.940405i | 0.998733 | + | 0.0503177i | \(0.0160234\pi\) |
−0.455790 | + | 0.890087i | \(0.650643\pi\) | |||||||
\(228\) | −11974.1 | − | 20739.7i | −0.0152547 | − | 0.0264219i | ||||
\(229\) | 284333. | − | 492479.i | 0.358293 | − | 0.620582i | −0.629382 | − | 0.777096i | \(-0.716692\pi\) |
0.987676 | + | 0.156513i | \(0.0500254\pi\) | |||||||
\(230\) | −87954.8 | −0.109633 | ||||||||
\(231\) | 12830.9 | − | 14640.1i | 0.0158208 | − | 0.0180515i | ||||
\(232\) | 141985. | 0.173190 | ||||||||
\(233\) | 528255. | − | 914965.i | 0.637461 | − | 1.10412i | −0.348526 | − | 0.937299i | \(-0.613318\pi\) |
0.985988 | − | 0.166817i | \(-0.0533488\pi\) | |||||||
\(234\) | 383520. | + | 664277.i | 0.457877 | + | 0.793066i | ||||
\(235\) | 448043. | + | 776034.i | 0.529237 | + | 0.916666i | ||||
\(236\) | −111392. | + | 192937.i | −0.130189 | + | 0.225495i | ||||
\(237\) | 75166.5 | 0.0869267 | ||||||||
\(238\) | −1.27707e6 | − | 253611.i | −1.46142 | − | 0.290219i | ||||
\(239\) | 853715. | 0.966759 | 0.483379 | − | 0.875411i | \(-0.339409\pi\) | ||||
0.483379 | + | 0.875411i | \(0.339409\pi\) | |||||||
\(240\) | 34354.1 | − | 59503.1i | 0.0384991 | − | 0.0666825i | ||||
\(241\) | 194444. | + | 336787.i | 0.215651 | + | 0.373519i | 0.953474 | − | 0.301476i | \(-0.0974792\pi\) |
−0.737823 | + | 0.674995i | \(0.764146\pi\) | |||||||
\(242\) | −396082. | − | 686034.i | −0.434757 | − | 0.753022i | ||||
\(243\) | −180106. | + | 311953.i | −0.195665 | + | 0.338902i | ||||
\(244\) | −24815.0 | −0.0266833 | ||||||||
\(245\) | −557458. | + | 428306.i | −0.593330 | + | 0.455867i | ||||
\(246\) | 37367.5 | 0.0393692 | ||||||||
\(247\) | −589612. | + | 1.02124e6i | −0.614928 | + | 1.06509i | ||||
\(248\) | −593906. | − | 1.02868e6i | −0.613181 | − | 1.06206i | ||||
\(249\) | 25589.4 | + | 44322.2i | 0.0261555 | + | 0.0453026i | ||||
\(250\) | −478398. | + | 828609.i | −0.484104 | + | 0.838493i | ||||
\(251\) | −839328. | −0.840906 | −0.420453 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420453 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(252\) | −187111. | − | 37158.0i | −0.185609 | − | 0.0368596i | ||||
\(253\) | 29827.1 | 0.0292961 | ||||||||
\(254\) | 327136. | − | 566616.i | 0.318159 | − | 0.551067i | ||||
\(255\) | 86068.3 | + | 149075.i | 0.0828882 | + | 0.143567i | ||||
\(256\) | 291075. | + | 504157.i | 0.277591 | + | 0.480802i | ||||
\(257\) | −145993. | + | 252867.i | −0.137879 | + | 0.238814i | −0.926694 | − | 0.375817i | \(-0.877362\pi\) |
0.788814 | + | 0.614632i | \(0.210695\pi\) | |||||||
\(258\) | 153661. | 0.143719 | ||||||||
\(259\) | 884423. | − | 1.00913e6i | 0.819239 | − | 0.934752i | ||||
\(260\) | 163068. | 0.149601 | ||||||||
\(261\) | 87342.4 | − | 151282.i | 0.0793641 | − | 0.137463i | ||||
\(262\) | −375876. | − | 651037.i | −0.338292 | − | 0.585939i | ||||
\(263\) | 144248. | + | 249844.i | 0.128594 | + | 0.222731i | 0.923132 | − | 0.384483i | \(-0.125620\pi\) |
−0.794538 | + | 0.607214i | \(0.792287\pi\) | |||||||
\(264\) | −14564.5 | + | 25226.4i | −0.0128613 | + | 0.0222764i | ||||
\(265\) | 526169. | 0.460268 | ||||||||
\(266\) | 395371. | + | 1.16353e6i | 0.342611 | + | 1.00826i | ||||
\(267\) | −146300. | −0.125593 | ||||||||
\(268\) | 47986.1 | − | 83114.4i | 0.0408111 | − | 0.0706869i | ||||
\(269\) | 129685. | + | 224621.i | 0.109272 | + | 0.189265i | 0.915476 | − | 0.402374i | \(-0.131815\pi\) |
−0.806204 | + | 0.591638i | \(0.798481\pi\) | |||||||
\(270\) | −106639. | − | 184704.i | −0.0890237 | − | 0.154194i | ||||
\(271\) | 1.09776e6 | − | 1.90137e6i | 0.907994 | − | 1.57269i | 0.0911464 | − | 0.995838i | \(-0.470947\pi\) |
0.816847 | − | 0.576854i | \(-0.195720\pi\) | |||||||
\(272\) | 1.55839e6 | 1.27719 | ||||||||
\(273\) | −54931.1 | − | 161656.i | −0.0446079 | − | 0.131276i | ||||
\(274\) | 463331. | 0.372834 | ||||||||
\(275\) | 49582.5 | − | 85879.5i | 0.0395364 | − | 0.0684790i | ||||
\(276\) | 2656.30 | + | 4600.84i | 0.00209896 | + | 0.00363550i | ||||
\(277\) | −63495.3 | − | 109977.i | −0.0497213 | − | 0.0861198i | 0.840094 | − | 0.542441i | \(-0.182500\pi\) |
−0.889815 | + | 0.456322i | \(0.849167\pi\) | |||||||
\(278\) | −850491. | + | 1.47309e6i | −0.660021 | + | 1.14319i | ||||
\(279\) | −1.46137e6 | −1.12396 | ||||||||
\(280\) | 693327. | − | 791086.i | 0.528497 | − | 0.603016i | ||||
\(281\) | −2.22759e6 | −1.68294 | −0.841472 | − | 0.540301i | \(-0.818310\pi\) | ||||
−0.841472 | + | 0.540301i | \(0.818310\pi\) | |||||||
\(282\) | −113396. | + | 196407.i | −0.0849129 | + | 0.147073i | ||||
\(283\) | −594473. | − | 1.02966e6i | −0.441231 | − | 0.764235i | 0.556550 | − | 0.830814i | \(-0.312125\pi\) |
−0.997781 | + | 0.0665792i | \(0.978792\pi\) | |||||||
\(284\) | 37550.4 | + | 65039.1i | 0.0276260 | + | 0.0478497i | ||||
\(285\) | 81233.4 | − | 140700.i | 0.0592410 | − | 0.102608i | ||||
\(286\) | 231712. | 0.167507 | ||||||||
\(287\) | 448850. | + | 89136.0i | 0.321659 | + | 0.0638776i | ||||
\(288\) | 524780. | 0.372817 | ||||||||
\(289\) | −1.24221e6 | + | 2.15157e6i | −0.874884 | + | 1.51534i | ||||
\(290\) | 77804.5 | + | 134761.i | 0.0543263 | + | 0.0940958i | ||||
\(291\) | −110135. | − | 190759.i | −0.0762415 | − | 0.132054i | ||||
\(292\) | 60388.6 | − | 104596.i | 0.0414475 | − | 0.0717891i | ||||
\(293\) | 1.83223e6 | 1.24684 | 0.623421 | − | 0.781886i | \(-0.285742\pi\) | ||||
0.623421 | + | 0.781886i | \(0.285742\pi\) | |||||||
\(294\) | −164421. | − | 67985.1i | −0.110940 | − | 0.0458718i | ||||
\(295\) | −1.51140e6 | −1.01117 | ||||||||
\(296\) | −1.00392e6 | + | 1.73883e6i | −0.665991 | + | 1.15353i | ||||
\(297\) | 36163.1 | + | 62636.4i | 0.0237889 | + | 0.0412037i | ||||
\(298\) | 351400. | + | 608643.i | 0.229225 | + | 0.397029i | ||||
\(299\) | 130798. | − | 226549.i | 0.0846104 | − | 0.146550i | ||||
\(300\) | 17662.6 | 0.0113306 | ||||||||
\(301\) | 1.84574e6 | + | 366541.i | 1.17423 | + | 0.233188i | ||||
\(302\) | −565047. | −0.356506 | ||||||||
\(303\) | −37970.6 | + | 65767.1i | −0.0237597 | + | 0.0411530i | ||||
\(304\) | −735423. | − | 1.27379e6i | −0.456408 | − | 0.790522i | ||||
\(305\) | −84173.8 | − | 145793.i | −0.0518117 | − | 0.0897404i | ||||
\(306\) | 1.19846e6 | − | 2.07579e6i | 0.731678 | − | 1.26730i | ||||
\(307\) | −717638. | −0.434569 | −0.217285 | − | 0.976108i | \(-0.569720\pi\) | ||||
−0.217285 | + | 0.976108i | \(0.569720\pi\) | |||||||
\(308\) | −37982.9 | + | 43338.4i | −0.0228145 | + | 0.0260313i | ||||
\(309\) | 134380. | 0.0800642 | ||||||||
\(310\) | 650893. | − | 1.12738e6i | 0.384685 | − | 0.666294i | ||||
\(311\) | 428446. | + | 742090.i | 0.251186 | + | 0.435067i | 0.963853 | − | 0.266436i | \(-0.0858462\pi\) |
−0.712667 | + | 0.701503i | \(0.752513\pi\) | |||||||
\(312\) | 127737. | + | 221247.i | 0.0742898 | + | 0.128674i | ||||
\(313\) | −808495. | + | 1.40035e6i | −0.466462 | + | 0.807936i | −0.999266 | − | 0.0383025i | \(-0.987805\pi\) |
0.532804 | + | 0.846239i | \(0.321138\pi\) | |||||||
\(314\) | 193900. | 0.110982 | ||||||||
\(315\) | −416380. | − | 1.22536e6i | −0.236436 | − | 0.695805i | ||||
\(316\) | −222512. | −0.125354 | ||||||||
\(317\) | 1.13280e6 | − | 1.96206e6i | 0.633145 | − | 1.09664i | −0.353760 | − | 0.935336i | \(-0.615097\pi\) |
0.986905 | − | 0.161303i | \(-0.0515698\pi\) | |||||||
\(318\) | 66584.3 | + | 115327.i | 0.0369236 | + | 0.0639535i | ||||
\(319\) | −26384.9 | − | 45700.0i | −0.0145171 | − | 0.0251443i | ||||
\(320\) | −761561. | + | 1.31906e6i | −0.415747 | + | 0.720096i | ||||
\(321\) | 137557. | 0.0745111 | ||||||||
\(322\) | −87708.2 | − | 258115.i | −0.0471412 | − | 0.138731i | ||||
\(323\) | 3.68495e6 | 1.96528 | ||||||||
\(324\) | 172343. | − | 298507.i | 0.0912078 | − | 0.157977i | ||||
\(325\) | −434860. | − | 753200.i | −0.228371 | − | 0.395551i | ||||
\(326\) | −541072. | − | 937163.i | −0.281975 | − | 0.488395i | ||||
\(327\) | 39508.0 | − | 68429.8i | 0.0204322 | − | 0.0353896i | ||||
\(328\) | −684740. | −0.351432 | ||||||||
\(329\) | −1.83059e6 | + | 2.08870e6i | −0.932396 | + | 1.06386i | ||||
\(330\) | −31924.0 | −0.0161373 | ||||||||
\(331\) | −354825. | + | 614575.i | −0.178010 | + | 0.308322i | −0.941199 | − | 0.337853i | \(-0.890299\pi\) |
0.763189 | + | 0.646175i | \(0.223633\pi\) | |||||||
\(332\) | −75751.5 | − | 131205.i | −0.0377178 | − | 0.0653291i | ||||
\(333\) | 1.23512e6 | + | 2.13929e6i | 0.610379 | + | 1.05721i | ||||
\(334\) | −305972. | + | 529958.i | −0.150077 | + | 0.259941i | ||||
\(335\) | 651086. | 0.316976 | ||||||||
\(336\) | 208878. | + | 41480.5i | 0.100935 | + | 0.0200445i | ||||
\(337\) | 603572. | 0.289504 | 0.144752 | − | 0.989468i | \(-0.453762\pi\) | ||||
0.144752 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(338\) | 72511.3 | − | 125593.i | 0.0345234 | − | 0.0597963i | ||||
\(339\) | −128925. | − | 223305.i | −0.0609312 | − | 0.105536i | ||||
\(340\) | −254785. | − | 441300.i | −0.119530 | − | 0.207032i | ||||
\(341\) | −220730. | + | 382315.i | −0.102796 | + | 0.178047i | ||||
\(342\) | −2.26227e6 | −1.04587 | ||||||||
\(343\) | −1.81281e6 | − | 1.20883e6i | −0.831990 | − | 0.554791i | ||||
\(344\) | −2.81576e6 | −1.28292 | ||||||||
\(345\) | −18020.6 | + | 31212.6i | −0.00815121 | + | 0.0141183i | ||||
\(346\) | 1.81179e6 | + | 3.13811e6i | 0.813611 | + | 1.40922i | ||||
\(347\) | −878655. | − | 1.52188e6i | −0.391737 | − | 0.678509i | 0.600942 | − | 0.799293i | \(-0.294792\pi\) |
−0.992679 | + | 0.120784i | \(0.961459\pi\) | |||||||
\(348\) | 4699.50 | − | 8139.77i | 0.00208019 | − | 0.00360300i | ||||
\(349\) | 391875. | 0.172220 | 0.0861102 | − | 0.996286i | \(-0.472556\pi\) | ||||
0.0861102 | + | 0.996286i | \(0.472556\pi\) | |||||||
\(350\) | −888977. | − | 176540.i | −0.387901 | − | 0.0770323i | ||||
\(351\) | 634333. | 0.274821 | ||||||||
\(352\) | 79264.3 | − | 137290.i | 0.0340974 | − | 0.0590584i | ||||
\(353\) | −246204. | − | 426437.i | −0.105162 | − | 0.182145i | 0.808643 | − | 0.588300i | \(-0.200203\pi\) |
−0.913804 | + | 0.406155i | \(0.866869\pi\) | |||||||
\(354\) | −191260. | − | 331273.i | −0.0811179 | − | 0.140500i | ||||
\(355\) | −254746. | + | 441233.i | −0.107284 | + | 0.185822i | ||||
\(356\) | 433087. | 0.181113 | ||||||||
\(357\) | −351653. | + | 401236.i | −0.146030 | + | 0.166621i | ||||
\(358\) | 3.81074e6 | 1.57145 | ||||||||
\(359\) | 1.88516e6 | − | 3.26519e6i | 0.771991 | − | 1.33713i | −0.164480 | − | 0.986380i | \(-0.552594\pi\) |
0.936470 | − | 0.350747i | \(-0.114072\pi\) | |||||||
\(360\) | 968251. | + | 1.67706e6i | 0.393760 | + | 0.682012i | ||||
\(361\) | −500924. | − | 867625.i | −0.202304 | − | 0.350400i | ||||
\(362\) | 1.58510e6 | − | 2.74548e6i | 0.635750 | − | 1.10115i | ||||
\(363\) | −324605. | −0.129297 | ||||||||
\(364\) | 162611. | + | 478544.i | 0.0643273 | + | 0.189308i | ||||
\(365\) | 819367. | 0.321919 | ||||||||
\(366\) | 21303.6 | − | 36899.0i | 0.00831286 | − | 0.0143983i | ||||
\(367\) | 1.09884e6 | + | 1.90325e6i | 0.425863 | + | 0.737617i | 0.996501 | − | 0.0835854i | \(-0.0266371\pi\) |
−0.570637 | + | 0.821202i | \(0.693304\pi\) | |||||||
\(368\) | 163145. | + | 282575.i | 0.0627991 | + | 0.108771i | ||||
\(369\) | −421219. | + | 729573.i | −0.161043 | + | 0.278935i | ||||
\(370\) | −2.20049e6 | −0.835632 | ||||||||
\(371\) | 524694. | + | 1.54411e6i | 0.197911 | + | 0.582431i | ||||
\(372\) | −78629.7 | −0.0294598 | ||||||||
\(373\) | 828178. | − | 1.43445e6i | 0.308213 | − | 0.533841i | −0.669758 | − | 0.742579i | \(-0.733602\pi\) |
0.977972 | + | 0.208738i | \(0.0669356\pi\) | |||||||
\(374\) | −362038. | − | 627068.i | −0.133837 | − | 0.231812i | ||||
\(375\) | 196033. | + | 339539.i | 0.0719864 | + | 0.124684i | ||||
\(376\) | 2.07791e6 | − | 3.59905e6i | 0.757981 | − | 1.31286i | ||||
\(377\) | −462814. | −0.167708 | ||||||||
\(378\) | 435698. | − | 497132.i | 0.156840 | − | 0.178954i | ||||
\(379\) | −2.82050e6 | −1.00862 | −0.504310 | − | 0.863523i | \(-0.668253\pi\) | ||||
−0.504310 | + | 0.863523i | \(0.668253\pi\) | |||||||
\(380\) | −240472. | + | 416510.i | −0.0854291 | + | 0.147968i | ||||
\(381\) | −134050. | − | 232182.i | −0.0473103 | − | 0.0819439i | ||||
\(382\) | 1.06160e6 | + | 1.83875e6i | 0.372223 | + | 0.644709i | ||||
\(383\) | −1.62422e6 | + | 2.81324e6i | −0.565781 | + | 0.979962i | 0.431195 | + | 0.902259i | \(0.358092\pi\) |
−0.996977 | + | 0.0777034i | \(0.975241\pi\) | |||||||
\(384\) | −238939. | −0.0826911 | ||||||||
\(385\) | −383463. | − | 76151.0i | −0.131847 | − | 0.0261833i | ||||
\(386\) | −3.91729e6 | −1.33819 | ||||||||
\(387\) | −1.73212e6 | + | 3.00012e6i | −0.587895 | + | 1.01826i | ||||
\(388\) | 326027. | + | 564696.i | 0.109945 | + | 0.190430i | ||||
\(389\) | −2.32674e6 | − | 4.03003e6i | −0.779604 | − | 1.35031i | −0.932170 | − | 0.362021i | \(-0.882087\pi\) |
0.152566 | − | 0.988293i | \(-0.451246\pi\) | |||||||
\(390\) | −139994. | + | 242476.i | −0.0466065 | + | 0.0807248i | ||||
\(391\) | −817461. | −0.270411 | ||||||||
\(392\) | 3.01293e6 | + | 1.24579e6i | 0.990316 | + | 0.409478i | ||||
\(393\) | −308045. | −0.100608 | ||||||||
\(394\) | −1.21781e6 | + | 2.10931e6i | −0.395221 | + | 0.684543i | ||||
\(395\) | −754775. | − | 1.30731e6i | −0.243402 | − | 0.421585i | ||||
\(396\) | −53044.1 | − | 91875.2i | −0.0169981 | − | 0.0294415i | ||||
\(397\) | 581804. | − | 1.00771e6i | 0.185268 | − | 0.320894i | −0.758399 | − | 0.651791i | \(-0.774018\pi\) |
0.943667 | + | 0.330897i | \(0.107351\pi\) | |||||||
\(398\) | 2.17891e6 | 0.689495 | ||||||||
\(399\) | 493909. | + | 98084.3i | 0.155316 | + | 0.0308438i | ||||
\(400\) | 1.08480e6 | 0.339001 | ||||||||
\(401\) | −161190. | + | 279189.i | −0.0500584 | + | 0.0867037i | −0.889969 | − | 0.456021i | \(-0.849274\pi\) |
0.839910 | + | 0.542725i | \(0.182607\pi\) | |||||||
\(402\) | 82392.0 | + | 142707.i | 0.0254284 | + | 0.0440434i | ||||
\(403\) | 1.93589e6 | + | 3.35307e6i | 0.593771 | + | 1.02844i | ||||
\(404\) | 112403. | − | 194688.i | 0.0342630 | − | 0.0593452i | ||||
\(405\) | 2.33839e6 | 0.708403 | ||||||||
\(406\) | −317889. | + | 362711.i | −0.0957106 | + | 0.109206i | ||||
\(407\) | 746226. | 0.223298 | ||||||||
\(408\) | 399164. | − | 691372.i | 0.118714 | − | 0.205618i | ||||
\(409\) | −693451. | − | 1.20109e6i | −0.204978 | − | 0.355033i | 0.745148 | − | 0.666900i | \(-0.232379\pi\) |
−0.950126 | + | 0.311867i | \(0.899046\pi\) | |||||||
\(410\) | −375222. | − | 649903.i | −0.110237 | − | 0.190936i | ||||
\(411\) | 94929.6 | − | 164423.i | 0.0277202 | − | 0.0480129i | ||||
\(412\) | −397800. | −0.115457 | ||||||||
\(413\) | −1.50716e6 | − | 4.43540e6i | −0.434794 | − | 1.27955i | ||||
\(414\) | 501857. | 0.143906 | ||||||||
\(415\) | 513907. | − | 890112.i | 0.146475 | − | 0.253702i | ||||
\(416\) | −695182. | − | 1.20409e6i | −0.196954 | − | 0.341135i | ||||
\(417\) | 348506. | + | 603630.i | 0.0981454 | + | 0.169993i | ||||
\(418\) | −341700. | + | 591842.i | −0.0956543 | + | 0.165678i | ||||
\(419\) | 4.90871e6 | 1.36594 | 0.682971 | − | 0.730446i | \(-0.260688\pi\) | ||||
0.682971 | + | 0.730446i | \(0.260688\pi\) | |||||||
\(420\) | −22403.5 | − | 65931.1i | −0.00619717 | − | 0.0182376i | ||||
\(421\) | 2.43924e6 | 0.670733 | 0.335367 | − | 0.942088i | \(-0.391140\pi\) | ||||
0.335367 | + | 0.942088i | \(0.391140\pi\) | |||||||
\(422\) | −1.49572e6 | + | 2.59065e6i | −0.408854 | + | 0.708155i | ||||
\(423\) | −2.55647e6 | − | 4.42793e6i | −0.694687 | − | 1.20323i | ||||
\(424\) | −1.22012e6 | − | 2.11331e6i | −0.329601 | − | 0.570886i | ||||
\(425\) | −1.35889e6 | + | 2.35367e6i | −0.364933 | + | 0.632082i | ||||
\(426\) | −128948. | −0.0344263 | ||||||||
\(427\) | 343912. | − | 392404.i | 0.0912805 | − | 0.104151i | ||||
\(428\) | −407206. | −0.107450 | ||||||||
\(429\) | 47474.3 | − | 82227.9i | 0.0124542 | − | 0.0215713i | ||||
\(430\) | −1.54297e6 | − | 2.67250e6i | −0.402426 | − | 0.697022i | ||||
\(431\) | 2.61376e6 | + | 4.52717e6i | 0.677755 | + | 1.17391i | 0.975655 | + | 0.219309i | \(0.0703803\pi\) |
−0.297900 | + | 0.954597i | \(0.596286\pi\) | |||||||
\(432\) | −395602. | + | 685202.i | −0.101988 | + | 0.176648i | ||||
\(433\) | −2.63022e6 | −0.674174 | −0.337087 | − | 0.941473i | \(-0.609442\pi\) | ||||
−0.337087 | + | 0.941473i | \(0.609442\pi\) | |||||||
\(434\) | 3.95751e6 | + | 785914.i | 1.00855 | + | 0.200286i | ||||
\(435\) | 63763.9 | 0.0161567 | ||||||||
\(436\) | −116954. | + | 202570.i | −0.0294645 | + | 0.0510340i | ||||
\(437\) | 385770. | + | 668173.i | 0.0966328 | + | 0.167373i | ||||
\(438\) | 103687. | + | 179591.i | 0.0258249 | + | 0.0447301i | ||||
\(439\) | −1.27706e6 | + | 2.21193e6i | −0.316264 | + | 0.547785i | −0.979705 | − | 0.200443i | \(-0.935762\pi\) |
0.663442 | + | 0.748228i | \(0.269095\pi\) | |||||||
\(440\) | 584990. | 0.144051 | ||||||||
\(441\) | 3.18077e6 | − | 2.44385e6i | 0.778817 | − | 0.598381i | ||||
\(442\) | −6.35046e6 | −1.54614 | ||||||||
\(443\) | −1.91950e6 | + | 3.32467e6i | −0.464707 | + | 0.804896i | −0.999188 | − | 0.0402844i | \(-0.987174\pi\) |
0.534481 | + | 0.845180i | \(0.320507\pi\) | |||||||
\(444\) | 66456.3 | + | 115106.i | 0.0159985 | + | 0.0277102i | ||||
\(445\) | 1.46906e6 | + | 2.54448e6i | 0.351672 | + | 0.609114i | ||||
\(446\) | −923155. | + | 1.59895e6i | −0.219754 | + | 0.380626i | ||||
\(447\) | 287986. | 0.0681715 | ||||||||
\(448\) | −4.63039e6 | − | 919538.i | −1.08999 | − | 0.216459i | ||||
\(449\) | 1.49369e6 | 0.349658 | 0.174829 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174829 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(450\) | 834253. | − | 1.44497e6i | 0.194208 | − | 0.336378i | ||||
\(451\) | 127244. | + | 220394.i | 0.0294576 | + | 0.0510221i | ||||
\(452\) | 381653. | + | 661043.i | 0.0878664 | + | 0.152189i | ||||
\(453\) | −115770. | + | 200519.i | −0.0265063 | + | 0.0459102i | ||||
\(454\) | 4.28498e6 | 0.975684 | ||||||||
\(455\) | −2.25997e6 | + | 2.57862e6i | −0.511768 | + | 0.583928i | ||||
\(456\) | −753481. | −0.169692 | ||||||||
\(457\) | 1.08111e6 | − | 1.87253e6i | 0.242146 | − | 0.419410i | −0.719179 | − | 0.694825i | \(-0.755482\pi\) |
0.961325 | + | 0.275415i | \(0.0888153\pi\) | |||||||
\(458\) | −1.44520e6 | − | 2.50316e6i | −0.321932 | − | 0.557602i | ||||
\(459\) | −991112. | − | 1.71666e6i | −0.219579 | − | 0.380322i | ||||
\(460\) | 53345.8 | − | 92397.6i | 0.0117545 | − | 0.0203594i | ||||
\(461\) | −6.11949e6 | −1.34111 | −0.670553 | − | 0.741862i | \(-0.733943\pi\) | ||||
−0.670553 | + | 0.741862i | \(0.733943\pi\) | |||||||
\(462\) | −31834.4 | − | 93685.1i | −0.00693893 | − | 0.0204205i | ||||
\(463\) | 3.93615e6 | 0.853335 | 0.426667 | − | 0.904409i | \(-0.359687\pi\) | ||||
0.426667 | + | 0.904409i | \(0.359687\pi\) | |||||||
\(464\) | 288634. | − | 499929.i | 0.0622376 | − | 0.107799i | ||||
\(465\) | −266716. | − | 461966.i | −0.0572028 | − | 0.0990782i | ||||
\(466\) | −2.68500e6 | − | 4.65055e6i | −0.572768 | − | 0.992063i | ||||
\(467\) | 2.73522e6 | − | 4.73754e6i | 0.580363 | − | 1.00522i | −0.415073 | − | 0.909788i | \(-0.636244\pi\) |
0.995436 | − | 0.0954306i | \(-0.0304228\pi\) | |||||||
\(468\) | −930441. | −0.196369 | ||||||||
\(469\) | 649261. | + | 1.91070e6i | 0.136297 | + | 0.401107i | ||||
\(470\) | 4.55459e6 | 0.951054 | ||||||||
\(471\) | 39727.1 | − | 68809.4i | 0.00825154 | − | 0.0142921i | ||||
\(472\) | 3.50475e6 | + | 6.07040e6i | 0.724105 | + | 1.25419i | ||||
\(473\) | 523248. | + | 906293.i | 0.107536 | + | 0.186258i | ||||
\(474\) | 191027. | − | 330868.i | 0.0390524 | − | 0.0676408i | ||||
\(475\) | 2.56511e6 | 0.521641 | ||||||||
\(476\) | 1.04098e6 | − | 1.18776e6i | 0.210585 | − | 0.240277i | ||||
\(477\) | −3.00224e6 | −0.604157 | ||||||||
\(478\) | 2.16962e6 | − | 3.75788e6i | 0.434323 | − | 0.752270i | ||||
\(479\) | 3.33145e6 | + | 5.77023e6i | 0.663428 | + | 1.14909i | 0.979709 | + | 0.200426i | \(0.0642326\pi\) |
−0.316280 | + | 0.948666i | \(0.602434\pi\) | |||||||
\(480\) | 95778.2 | + | 165893.i | 0.0189742 | + | 0.0328643i | ||||
\(481\) | 3.27236e6 | − | 5.66790e6i | 0.644910 | − | 1.11702i | ||||
\(482\) | 1.97663e6 | 0.387531 | ||||||||
\(483\) | −109568. | − | 21758.8i | −0.0213705 | − | 0.00424392i | ||||
\(484\) | 960916. | 0.186454 | ||||||||
\(485\) | −2.21181e6 | + | 3.83096e6i | −0.426966 | + | 0.739526i | ||||
\(486\) | 915437. | + | 1.58558e6i | 0.175808 | + | 0.304508i | ||||
\(487\) | −4.76846e6 | − | 8.25922e6i | −0.911079 | − | 1.57804i | −0.812543 | − | 0.582902i | \(-0.801917\pi\) |
−0.0985363 | − | 0.995133i | \(-0.531416\pi\) | |||||||
\(488\) | −390378. | + | 676154.i | −0.0742054 | + | 0.128527i | ||||
\(489\) | −443430. | −0.0838595 | ||||||||
\(490\) | 468604. | + | 3.54231e6i | 0.0881690 | + | 0.666493i | ||||
\(491\) | −8.19294e6 | −1.53369 | −0.766843 | − | 0.641835i | \(-0.778173\pi\) | ||||
−0.766843 | + | 0.641835i | \(0.778173\pi\) | |||||||
\(492\) | −22663.9 | + | 39255.0i | −0.00422106 | + | 0.00731110i | ||||
\(493\) | 723123. | + | 1.25249e6i | 0.133997 | + | 0.232090i | ||||
\(494\) | 2.99686e6 | + | 5.19071e6i | 0.552521 | + | 0.956995i | ||||
\(495\) | 359858. | − | 623292.i | 0.0660112 | − | 0.114335i | ||||
\(496\) | −4.82928e6 | −0.881411 | ||||||||
\(497\) | −1.54889e6 | − | 307590.i | −0.281274 | − | 0.0558575i | ||||
\(498\) | 260130. | 0.0470021 | ||||||||
\(499\) | 2.15718e6 | − | 3.73635e6i | 0.387825 | − | 0.671733i | −0.604332 | − | 0.796733i | \(-0.706560\pi\) |
0.992157 | + | 0.125000i | \(0.0398931\pi\) | |||||||
\(500\) | −580309. | − | 1.00512e6i | −0.103809 | − | 0.179802i | ||||
\(501\) | 125378. | + | 217161.i | 0.0223165 | + | 0.0386534i | ||||
\(502\) | −2.13305e6 | + | 3.69455e6i | −0.377783 | + | 0.654339i | ||||
\(503\) | −1.04015e7 | −1.83306 | −0.916529 | − | 0.399968i | \(-0.869021\pi\) | ||||
−0.916529 | + | 0.399968i | \(0.869021\pi\) | |||||||
\(504\) | −3.95602e6 | + | 4.51382e6i | −0.693716 | + | 0.791530i | ||||
\(505\) | 1.52511e6 | 0.266117 | ||||||||
\(506\) | 75802.0 | − | 131293.i | 0.0131615 | − | 0.0227963i | ||||
\(507\) | −29712.9 | − | 51464.3i | −0.00513364 | − | 0.00889173i | ||||
\(508\) | 396825. | + | 687320.i | 0.0682243 | + | 0.118168i | ||||
\(509\) | 1.54698e6 | − | 2.67945e6i | 0.264661 | − | 0.458406i | −0.702814 | − | 0.711374i | \(-0.748073\pi\) |
0.967475 | + | 0.252968i | \(0.0814066\pi\) | |||||||
\(510\) | 874930. | 0.148952 | ||||||||
\(511\) | 817069. | + | 2.40454e6i | 0.138422 | + | 0.407361i | ||||
\(512\) | 6.63004e6 | 1.11774 | ||||||||
\(513\) | −935435. | + | 1.62022e6i | −0.156935 | + | 0.271820i | ||||
\(514\) | 742048. | + | 1.28527e6i | 0.123887 | + | 0.214578i | ||||
\(515\) | −1.34936e6 | − | 2.33716e6i | −0.224187 | − | 0.388303i | ||||
\(516\) | −93197.4 | + | 161423.i | −0.0154092 | + | 0.0266895i | ||||
\(517\) | −1.54455e6 | −0.254141 | ||||||||
\(518\) | −2.19432e6 | − | 6.45763e6i | −0.359315 | − | 1.05742i | ||||
\(519\) | 1.48483e6 | 0.241968 | ||||||||
\(520\) | 2.56531e6 | − | 4.44324e6i | 0.416036 | − | 0.720596i | ||||
\(521\) | 3.80087e6 | + | 6.58331e6i | 0.613464 | + | 1.06255i | 0.990652 | + | 0.136414i | \(0.0435578\pi\) |
−0.377188 | + | 0.926137i | \(0.623109\pi\) | |||||||
\(522\) | −443941. | − | 768928.i | −0.0713097 | − | 0.123512i | ||||
\(523\) | −2.37835e6 | + | 4.11942e6i | −0.380208 | + | 0.658539i | −0.991092 | − | 0.133181i | \(-0.957481\pi\) |
0.610884 | + | 0.791720i | \(0.290814\pi\) | |||||||
\(524\) | 911895. | 0.145083 | ||||||||
\(525\) | −244787. | + | 279302.i | −0.0387605 | + | 0.0442258i | ||||
\(526\) | 1.46635e6 | 0.231086 | ||||||||
\(527\) | 6.04947e6 | − | 1.04780e7i | 0.948835 | − | 1.64343i | ||||
\(528\) | 59214.7 | + | 102563.i | 0.00924368 | + | 0.0160105i | ||||
\(529\) | 3.13259e6 | + | 5.42581e6i | 0.486704 | + | 0.842996i | ||||
\(530\) | 1.33720e6 | − | 2.31609e6i | 0.206779 | − | 0.358151i | ||||
\(531\) | 8.62380e6 | 1.32728 | ||||||||
\(532\) | −1.46210e6 | − | 290355.i | −0.223974 | − | 0.0444786i | ||||
\(533\) | 2.23198e6 | 0.340308 | ||||||||
\(534\) | −371805. | + | 643984.i | −0.0564237 | + | 0.0977287i | ||||
\(535\) | −1.38127e6 | − | 2.39242e6i | −0.208638 | − | 0.361371i | ||||
\(536\) | −1.50979e6 | − | 2.61503e6i | −0.226989 | − | 0.393156i | ||||
\(537\) | 780763. | − | 1.35232e6i | 0.116838 | − | 0.202369i | ||||
\(538\) | 1.31832e6 | 0.196365 | ||||||||
\(539\) | −158912. | − | 1.20126e6i | −0.0235605 | − | 0.178100i | ||||
\(540\) | 258711. | 0.0381796 | ||||||||
\(541\) | −5.50261e6 | + | 9.53079e6i | −0.808305 | + | 1.40003i | 0.105732 | + | 0.994395i | \(0.466281\pi\) |
−0.914037 | + | 0.405631i | \(0.867052\pi\) | |||||||
\(542\) | −5.57964e6 | − | 9.66421e6i | −0.815845 | − | 1.41309i | ||||
\(543\) | −649528. | − | 1.12502e6i | −0.0945362 | − | 0.163742i | ||||
\(544\) | −2.17237e6 | + | 3.76266e6i | −0.314729 | + | 0.545127i | ||||
\(545\) | −1.58686e6 | −0.228848 | ||||||||
\(546\) | −851179. | − | 169034.i | −0.122191 | − | 0.0242656i | ||||
\(547\) | −4.46311e6 | −0.637778 | −0.318889 | − | 0.947792i | \(-0.603310\pi\) | ||||
−0.318889 | + | 0.947792i | \(0.603310\pi\) | |||||||
\(548\) | −281017. | + | 486735.i | −0.0399743 | + | 0.0692375i | ||||
\(549\) | 480283. | + | 831875.i | 0.0680090 | + | 0.117795i | ||||
\(550\) | −252016. | − | 436505.i | −0.0355240 | − | 0.0615294i | ||||
\(551\) | 682501. | − | 1.18213e6i | 0.0957688 | − | 0.165876i | ||||
\(552\) | 167150. | 0.0233485 | ||||||||
\(553\) | 3.08381e6 | − | 3.51863e6i | 0.428820 | − | 0.489284i | ||||
\(554\) | −645463. | −0.0893505 | ||||||||
\(555\) | −450847. | + | 780890.i | −0.0621294 | + | 0.107611i | ||||
\(556\) | −1.03167e6 | − | 1.78690e6i | −0.141532 | − | 0.245140i | ||||
\(557\) | 3.22611e6 | + | 5.58779e6i | 0.440597 | + | 0.763136i | 0.997734 | − | 0.0672845i | \(-0.0214335\pi\) |
−0.557137 | + | 0.830421i | \(0.688100\pi\) | |||||||
\(558\) | −3.71390e6 | + | 6.43266e6i | −0.504945 | + | 0.874591i | ||||
\(559\) | 9.17823e6 | 1.24231 | ||||||||
\(560\) | −1.37598e6 | − | 4.04936e6i | −0.185414 | − | 0.545653i | ||||
\(561\) | −296704. | −0.0398031 | ||||||||
\(562\) | −5.66116e6 | + | 9.80541e6i | −0.756074 | + | 1.30956i | ||||
\(563\) | −873740. | − | 1.51336e6i | −0.116175 | − | 0.201220i | 0.802074 | − | 0.597225i | \(-0.203730\pi\) |
−0.918249 | + | 0.396004i | \(0.870397\pi\) | |||||||
\(564\) | −137552. | − | 238247.i | −0.0182083 | − | 0.0315377i | ||||
\(565\) | −2.58918e6 | + | 4.48459e6i | −0.341225 | + | 0.591019i | ||||
\(566\) | −6.04313e6 | −0.792905 | ||||||||
\(567\) | 2.33184e6 | + | 6.86233e6i | 0.304607 | + | 0.896425i | ||||
\(568\) | 2.36290e6 | 0.307308 | ||||||||
\(569\) | −256394. | + | 444088.i | −0.0331992 | + | 0.0575027i | −0.882148 | − | 0.470973i | \(-0.843903\pi\) |
0.848948 | + | 0.528476i | \(0.177236\pi\) | |||||||
\(570\) | −412890. | − | 715146.i | −0.0532288 | − | 0.0921951i | ||||
\(571\) | −2.61182e6 | − | 4.52380e6i | −0.335238 | − | 0.580649i | 0.648293 | − | 0.761391i | \(-0.275483\pi\) |
−0.983530 | + | 0.180742i | \(0.942150\pi\) | |||||||
\(572\) | −140536. | + | 243416.i | −0.0179597 | + | 0.0311071i | ||||
\(573\) | 870024. | 0.110699 | ||||||||
\(574\) | 1.53306e6 | − | 1.74922e6i | 0.194213 | − | 0.221597i | ||||
\(575\) | −569038. | −0.0717748 | ||||||||
\(576\) | 4.34535e6 | − | 7.52637e6i | 0.545718 | − | 0.945212i | ||||
\(577\) | −3.31987e6 | − | 5.75018e6i | −0.415127 | − | 0.719021i | 0.580315 | − | 0.814392i | \(-0.302930\pi\) |
−0.995442 | + | 0.0953713i | \(0.969596\pi\) | |||||||
\(578\) | 6.31386e6 | + | 1.09359e7i | 0.786096 | + | 1.36156i | ||||
\(579\) | −802593. | + | 1.39013e6i | −0.0994945 | + | 0.172329i | ||||
\(580\) | −188758. | −0.0232989 | ||||||||
\(581\) | 3.12462e6 | + | 620511.i | 0.384022 | + | 0.0762621i | ||||
\(582\) | −1.11958e6 | −0.137008 | ||||||||
\(583\) | −453467. | + | 785429.i | −0.0552554 | + | 0.0957051i | ||||
\(584\) | −1.90001e6 | − | 3.29092e6i | −0.230528 | − | 0.399286i | ||||
\(585\) | −3.15611e6 | − | 5.46654e6i | −0.381296 | − | 0.660424i | ||||
\(586\) | 4.65640e6 | − | 8.06512e6i | 0.560152 | − | 0.970212i | ||||
\(587\) | 774096. | 0.0927256 | 0.0463628 | − | 0.998925i | \(-0.485237\pi\) | ||||
0.0463628 | + | 0.998925i | \(0.485237\pi\) | |||||||
\(588\) | 171143. | − | 131492.i | 0.0204134 | − | 0.0156840i | ||||
\(589\) | −1.14193e7 | −1.35628 | ||||||||
\(590\) | −3.84104e6 | + | 6.65287e6i | −0.454275 | + | 0.786827i | ||||
\(591\) | 499023. | + | 864333.i | 0.0587695 | + | 0.101792i | ||||
\(592\) | 4.08162e6 | + | 7.06957e6i | 0.478661 | + | 0.829065i | ||||
\(593\) | 7.18778e6 | − | 1.24496e7i | 0.839379 | − | 1.45385i | −0.0510354 | − | 0.998697i | \(-0.516252\pi\) |
0.890415 | − | 0.455150i | \(-0.150415\pi\) | |||||||
\(594\) | 367617. | 0.0427494 | ||||||||
\(595\) | 1.05094e7 | + | 2.08705e6i | 1.21699 | + | 0.241679i | ||||
\(596\) | −852515. | −0.0983075 | ||||||||
\(597\) | 446426. | − | 773232.i | 0.0512641 | − | 0.0887920i | ||||
\(598\) | −664816. | − | 1.15150e6i | −0.0760236 | − | 0.131677i | ||||
\(599\) | −6.04174e6 | − | 1.04646e7i | −0.688010 | − | 1.19167i | −0.972481 | − | 0.232984i | \(-0.925151\pi\) |
0.284471 | − | 0.958685i | \(-0.408182\pi\) | |||||||
\(600\) | 277860. | − | 481267.i | 0.0315099 | − | 0.0545768i | ||||
\(601\) | 5.75607e6 | 0.650040 | 0.325020 | − | 0.945707i | \(-0.394629\pi\) | ||||
0.325020 | + | 0.945707i | \(0.394629\pi\) | |||||||
\(602\) | 6.30416e6 | − | 7.19305e6i | 0.708984 | − | 0.808950i | ||||
\(603\) | −3.71500e6 | −0.416069 | ||||||||
\(604\) | 342708. | − | 593588.i | 0.0382237 | − | 0.0662053i | ||||
\(605\) | 3.25948e6 | + | 5.64559e6i | 0.362043 | + | 0.627077i | ||||
\(606\) | 192996. | + | 334278.i | 0.0213484 | + | 0.0369766i | ||||
\(607\) | −2.10060e6 | + | 3.63835e6i | −0.231405 | + | 0.400805i | −0.958222 | − | 0.286026i | \(-0.907666\pi\) |
0.726817 | + | 0.686831i | \(0.240999\pi\) | |||||||
\(608\) | 4.10067e6 | 0.449879 | ||||||||
\(609\) | 63585.1 | + | 187124.i | 0.00694723 | + | 0.0204449i | ||||
\(610\) | −855671. | −0.0931070 | ||||||||
\(611\) | −6.77317e6 | + | 1.17315e7i | −0.733988 | + | 1.27130i | ||||
\(612\) | 1.45376e6 | + | 2.51799e6i | 0.156897 | + | 0.271754i | ||||
\(613\) | 1.32271e6 | + | 2.29101e6i | 0.142172 | + | 0.246249i | 0.928314 | − | 0.371796i | \(-0.121258\pi\) |
−0.786142 | + | 0.618046i | \(0.787925\pi\) | |||||||
\(614\) | −1.82379e6 | + | 3.15890e6i | −0.195233 | + | 0.338154i | ||||
\(615\) | −307509. | −0.0327846 | ||||||||
\(616\) | 583349. | + | 1.71673e6i | 0.0619408 | + | 0.182285i | ||||
\(617\) | 6.43533e6 | 0.680546 | 0.340273 | − | 0.940327i | \(-0.389480\pi\) | ||||
0.340273 | + | 0.940327i | \(0.389480\pi\) | |||||||
\(618\) | 341511. | − | 591514.i | 0.0359694 | − | 0.0623009i | ||||
\(619\) | −7.05885e6 | − | 1.22263e7i | −0.740469 | − | 1.28253i | −0.952282 | − | 0.305220i | \(-0.901270\pi\) |
0.211812 | − | 0.977310i | \(-0.432063\pi\) | |||||||
\(620\) | 789551. | + | 1.36754e6i | 0.0824899 | + | 0.142877i | ||||
\(621\) | 207515. | − | 359426.i | 0.0215933 | − | 0.0374008i | ||||
\(622\) | 4.35538e6 | 0.451388 | ||||||||
\(623\) | −6.00218e6 | + | 6.84848e6i | −0.619567 | + | 0.706927i | ||||
\(624\) | 1.03868e6 | 0.106787 | ||||||||
\(625\) | 1.78774e6 | − | 3.09646e6i | 0.183065 | − | 0.317077i | ||||
\(626\) | 4.10939e6 | + | 7.11767e6i | 0.419123 | + | 0.725942i | ||||
\(627\) | 140018. | + | 242519.i | 0.0142238 | + | 0.0246364i | ||||
\(628\) | −117603. | + | 203694.i | −0.0118992 | + | 0.0206101i | ||||
\(629\) | −2.04516e7 | −2.06111 | ||||||||
\(630\) | −6.45197e6 | − | 1.28128e6i | −0.647651 | − | 0.128616i | ||||
\(631\) | −4.70856e6 | −0.470777 | −0.235388 | − | 0.971901i | \(-0.575636\pi\) | ||||
−0.235388 | + | 0.971901i | \(0.575636\pi\) | |||||||
\(632\) | −3.50046e6 | + | 6.06298e6i | −0.348604 | + | 0.603800i | ||||
\(633\) | 612899. | + | 1.06157e6i | 0.0607966 | + | 0.105303i | ||||
\(634\) | −5.75773e6 | − | 9.97268e6i | −0.568890 | − | 0.985346i | ||||
\(635\) | −2.69210e6 | + | 4.66286e6i | −0.264946 | + | 0.458900i | ||||
\(636\) | −161537. | −0.0158354 | ||||||||
\(637\) | −9.82094e6 | − | 4.06078e6i | −0.958968 | − | 0.396516i | ||||
\(638\) | −268217. | −0.0260876 | ||||||||
\(639\) | 1.45354e6 | − | 2.51761e6i | 0.140824 | − | 0.243914i | ||||
\(640\) | 2.39928e6 | + | 4.15567e6i | 0.231542 | + | 0.401043i | ||||
\(641\) | 5.20870e6 | + | 9.02173e6i | 0.500707 | + | 0.867251i | 1.00000 | 0.000816994i | \(0.000260057\pi\) | |
−0.499292 | + | 0.866434i | \(0.666407\pi\) | |||||||
\(642\) | 349586. | − | 605500.i | 0.0334746 | − | 0.0579798i | ||||
\(643\) | 1.27284e7 | 1.21407 | 0.607037 | − | 0.794674i | \(-0.292358\pi\) | ||||
0.607037 | + | 0.794674i | \(0.292358\pi\) | |||||||
\(644\) | 324349. | + | 64411.8i | 0.0308175 | + | 0.00611999i | ||||
\(645\) | −1.26452e6 | −0.119682 | ||||||||
\(646\) | 9.36487e6 | − | 1.62204e7i | 0.882918 | − | 1.52926i | ||||
\(647\) | 8.06740e6 | + | 1.39731e7i | 0.757657 | + | 1.31230i | 0.944042 | + | 0.329824i | \(0.106989\pi\) |
−0.186385 | + | 0.982477i | \(0.559677\pi\) | |||||||
\(648\) | −5.42245e6 | − | 9.39196e6i | −0.507292 | − | 0.878655i | ||||
\(649\) | 1.30256e6 | − | 2.25611e6i | 0.121391 | − | 0.210256i | ||||
\(650\) | −4.42058e6 | −0.410390 | ||||||||
\(651\) | 1.08973e6 | − | 1.24339e6i | 0.100778 | − | 0.114988i | ||||
\(652\) | 1.31267e6 | 0.120931 | ||||||||
\(653\) | 7.51475e6 | − | 1.30159e7i | 0.689654 | − | 1.19452i | −0.282296 | − | 0.959327i | \(-0.591096\pi\) |
0.971950 | − | 0.235189i | \(-0.0755708\pi\) | |||||||
\(654\) | −200810. | − | 347812.i | −0.0183586 | − | 0.0317981i | ||||
\(655\) | 3.09320e6 | + | 5.35758e6i | 0.281712 | + | 0.487939i | ||||
\(656\) | −1.39197e6 | + | 2.41097e6i | −0.126291 | + | 0.218742i | ||||
\(657\) | −4.67518e6 | −0.422557 | ||||||||
\(658\) | 4.54182e6 | + | 1.33661e7i | 0.408945 | + | 1.20348i | ||||
\(659\) | 1.67927e7 | 1.50628 | 0.753140 | − | 0.657860i | \(-0.228538\pi\) | ||||
0.753140 | + | 0.657860i | \(0.228538\pi\) | |||||||
\(660\) | 19362.3 | − | 33536.5i | 0.00173020 | − | 0.00299680i | ||||
\(661\) | −5.42702e6 | − | 9.39987e6i | −0.483123 | − | 0.836794i | 0.516689 | − | 0.856173i | \(-0.327164\pi\) |
−0.999812 | + | 0.0193794i | \(0.993831\pi\) | |||||||
\(662\) | 1.80349e6 | + | 3.12374e6i | 0.159944 | + | 0.277032i | ||||
\(663\) | −1.30111e6 | + | 2.25359e6i | −0.114956 | + | 0.199110i | ||||
\(664\) | −4.76675e6 | −0.419567 | ||||||||
\(665\) | −3.25363e6 | − | 9.57506e6i | −0.285308 | − | 0.839629i | ||||
\(666\) | 1.25557e7 | 1.09687 | ||||||||
\(667\) | −151404. | + | 262240.i | −0.0131772 | + | 0.0228236i | ||||
\(668\) | −371152. | − | 642853.i | −0.0321818 | − | 0.0557405i | ||||
\(669\) | 378281. | + | 655202.i | 0.0326775 | + | 0.0565992i | ||||
\(670\) | 1.65466e6 | − | 2.86595e6i | 0.142404 | − | 0.246651i | ||||
\(671\) | 290174. | 0.0248801 | ||||||||
\(672\) | −391325. | + | 446501.i | −0.0334283 | + | 0.0381417i | ||||
\(673\) | 1.23697e7 | 1.05274 | 0.526371 | − | 0.850255i | \(-0.323552\pi\) | ||||
0.526371 | + | 0.850255i | \(0.323552\pi\) | |||||||
\(674\) | 1.53391e6 | − | 2.65680e6i | 0.130062 | − | 0.225273i | ||||
\(675\) | −689917. | − | 1.19497e6i | −0.0582824 | − | 0.100948i | ||||
\(676\) | 87958.1 | + | 152348.i | 0.00740302 | + | 0.0128224i | ||||
\(677\) | 502503. | − | 870361.i | 0.0421373 | − | 0.0729840i | −0.844188 | − | 0.536048i | \(-0.819917\pi\) |
0.886325 | + | 0.463064i | \(0.153250\pi\) | |||||||
\(678\) | −1.31060e6 | −0.109495 | ||||||||
\(679\) | −1.34481e7 | − | 2.67062e6i | −1.11940 | − | 0.222299i | ||||
\(680\) | −1.60326e7 | −1.32963 | ||||||||
\(681\) | 877928. | − | 1.52062e6i | 0.0725422 | − | 0.125647i | ||||
\(682\) | 1.12192e6 | + | 1.94322e6i | 0.0923633 | + | 0.159978i | ||||
\(683\) | −935093. | − | 1.61963e6i | −0.0767014 | − | 0.132851i | 0.825123 | − | 0.564952i | \(-0.191105\pi\) |
−0.901825 | + | 0.432102i | \(0.857772\pi\) | |||||||
\(684\) | 1.37210e6 | − | 2.37654e6i | 0.112136 | − | 0.194225i | ||||
\(685\) | −3.81290e6 | −0.310476 | ||||||||
\(686\) | −9.92808e6 | + | 4.90755e6i | −0.805480 | + | 0.398157i | ||||
\(687\) | −1.18440e6 | −0.0957426 | ||||||||
\(688\) | −5.72401e6 | + | 9.91427e6i | −0.461030 | + | 0.798527i | ||||
\(689\) | 3.97711e6 | + | 6.88855e6i | 0.319168 | + | 0.552815i | ||||
\(690\) | 91594.5 | + | 158646.i | 0.00732397 | + | 0.0126855i | ||||
\(691\) | −9.69333e6 | + | 1.67893e7i | −0.772286 | + | 1.33764i | 0.164022 | + | 0.986457i | \(0.447553\pi\) |
−0.936307 | + | 0.351181i | \(0.885780\pi\) | |||||||
\(692\) | −4.39549e6 | −0.348933 | ||||||||
\(693\) | 2.18798e6 | + | 434506.i | 0.173065 | + | 0.0343687i | ||||
\(694\) | −8.93199e6 | −0.703963 | ||||||||
\(695\) | 6.99896e6 | − | 1.21226e7i | 0.549631 | − | 0.951989i | ||||
\(696\) | −147861. | − | 256102.i | −0.0115699 | − | 0.0200397i | ||||
\(697\) | −3.48735e6 | − | 6.04026e6i | −0.271902 | − | 0.470949i | ||||
\(698\) | 995905. | − | 1.72496e6i | 0.0773712 | − | 0.134011i | ||||
\(699\) | −2.20046e6 | −0.170342 | ||||||||
\(700\) | 724634. | − | 826807.i | 0.0558951 | − | 0.0637763i | ||||
\(701\) | 1.17488e7 | 0.903024 | 0.451512 | − | 0.892265i | \(-0.350885\pi\) | ||||
0.451512 | + | 0.892265i | \(0.350885\pi\) | |||||||
\(702\) | 1.61208e6 | − | 2.79221e6i | 0.123465 | − | 0.213848i | ||||
\(703\) | 9.65134e6 | + | 1.67166e7i | 0.736545 | + | 1.27573i | ||||
\(704\) | −1.31267e6 | − | 2.27361e6i | −0.0998214 | − | 0.172896i | ||||
\(705\) | 933168. | − | 1.61629e6i | 0.0707110 | − | 0.122475i | ||||
\(706\) | −2.50279e6 | −0.188978 | ||||||||
\(707\) | 1.52083e6 | + | 4.47564e6i | 0.114428 | + | 0.336749i | ||||
\(708\) | 464008. | 0.0347890 | ||||||||
\(709\) | −8.39738e6 | + | 1.45447e7i | −0.627377 | + | 1.08665i | 0.360699 | + | 0.932682i | \(0.382538\pi\) |
−0.988076 | + | 0.153966i | \(0.950795\pi\) | |||||||
\(710\) | 1.29481e6 | + | 2.24268e6i | 0.0963965 | + | 0.166964i | ||||
\(711\) | 4.30663e6 | + | 7.45931e6i | 0.319495 | + | 0.553381i | ||||
\(712\) | 6.81312e6 | − | 1.18007e7i | 0.503670 | − | 0.872382i | ||||
\(713\) | 2.53322e6 | 0.186616 | ||||||||
\(714\) | 872476. | + | 2.56760e6i | 0.0640484 | + | 0.188487i | ||||
\(715\) | −1.90683e6 | −0.139491 | ||||||||
\(716\) | −2.31126e6 | + | 4.00323e6i | −0.168487 | + | 0.291828i | ||||
\(717\) | −889043. | − | 1.53987e6i | −0.0645840 | − | 0.111863i | ||||
\(718\) | −9.58182e6 | − | 1.65962e7i | −0.693644 | − | 1.20143i | ||||
\(719\) | 8.25652e6 | − | 1.43007e7i | 0.595628 | − | 1.03166i | −0.397830 | − | 0.917459i | \(-0.630237\pi\) |
0.993458 | − | 0.114199i | \(-0.0364300\pi\) | |||||||
\(720\) | 7.87323e6 | 0.566007 | ||||||||
\(721\) | 5.51314e6 | − | 6.29049e6i | 0.394967 | − | 0.450657i | ||||
\(722\) | −5.09215e6 | −0.363545 | ||||||||
\(723\) | 404981. | − | 701447.i | 0.0288130 | − | 0.0499056i | ||||
\(724\) | 1.92277e6 | + | 3.33034e6i | 0.136327 | + | 0.236125i | ||||
\(725\) | 503369. | + | 871861.i | 0.0355665 | + | 0.0616030i | ||||
\(726\) | −824945. | + | 1.42885e6i | −0.0580876 | + | 0.100611i | ||||
\(727\) | −1.25756e6 | −0.0882453 | −0.0441227 | − | 0.999026i | \(-0.514049\pi\) | ||||
−0.0441227 | + | 0.999026i | \(0.514049\pi\) | |||||||
\(728\) | 1.55974e7 | + | 3.09745e6i | 1.09075 | + | 0.216609i | ||||
\(729\) | −1.28348e7 | −0.894479 | ||||||||
\(730\) | 2.08232e6 | − | 3.60669e6i | 0.144624 | − | 0.250496i | ||||
\(731\) | −1.43405e7 | − | 2.48385e7i | −0.992592 | − | 1.71922i | ||||
\(732\) | 25841.9 | + | 44759.4i | 0.00178257 | + | 0.00308750i | ||||
\(733\) | 991661. | − | 1.71761e6i | 0.0681716 | − | 0.118077i | −0.829925 | − | 0.557875i | \(-0.811617\pi\) |
0.898096 | + | 0.439798i | \(0.144950\pi\) | |||||||
\(734\) | 1.11703e7 | 0.765288 | ||||||||
\(735\) | 1.35307e6 | + | 559471.i | 0.0923852 | + | 0.0381996i | ||||
\(736\) | −909684. | −0.0619007 | ||||||||
\(737\) | −561125. | + | 971896.i | −0.0380532 | + | 0.0659100i | ||||
\(738\) | 2.14096e6 | + | 3.70825e6i | 0.144700 | + | 0.250627i | ||||
\(739\) | 1.19404e7 | + | 2.06813e7i | 0.804278 | + | 1.39305i | 0.916777 | + | 0.399399i | \(0.130781\pi\) |
−0.112499 | + | 0.993652i | \(0.535885\pi\) | |||||||
\(740\) | 1.33463e6 | − | 2.31164e6i | 0.0895943 | − | 0.155182i | ||||
\(741\) | 2.45604e6 | 0.164320 | ||||||||
\(742\) | 8.13032e6 | + | 1.61458e6i | 0.542123 | + | 0.107659i | ||||
\(743\) | −1.90819e7 | −1.26809 | −0.634043 | − | 0.773298i | \(-0.718606\pi\) | ||||
−0.634043 | + | 0.773298i | \(0.718606\pi\) | |||||||
\(744\) | −1.23697e6 | + | 2.14249e6i | −0.0819266 | + | 0.141901i | ||||
\(745\) | −2.89178e6 | − | 5.00871e6i | −0.190886 | − | 0.330625i | ||||
\(746\) | −4.20943e6 | − | 7.29095e6i | −0.276934 | − | 0.479664i | ||||
\(747\) | −2.93227e6 | + | 5.07885e6i | −0.192266 | + | 0.333015i | ||||
\(748\) | 878323. | 0.0573985 | ||||||||
\(749\) | 5.64349e6 | − | 6.43922e6i | 0.367573 | − | 0.419400i | ||||
\(750\) | 1.99278e6 | 0.129362 | ||||||||
\(751\) | 1.87903e6 | − | 3.25457e6i | 0.121572 | − | 0.210569i | −0.798816 | − | 0.601576i | \(-0.794540\pi\) |
0.920388 | + | 0.391007i | \(0.127873\pi\) | |||||||
\(752\) | −8.44817e6 | − | 1.46327e7i | −0.544776 | − | 0.943580i | ||||
\(753\) | 874060. | + | 1.51392e6i | 0.0561764 | + | 0.0973004i | ||||
\(754\) | −1.17619e6 | + | 2.03722e6i | −0.0753439 | + | 0.130500i | ||||
\(755\) | 4.64994e6 | 0.296880 | ||||||||
\(756\) | 257986. | + | 759223.i | 0.0164169 | + | 0.0483131i | ||||
\(757\) | 1.69904e7 | 1.07761 | 0.538807 | − | 0.842429i | \(-0.318875\pi\) | ||||
0.538807 | + | 0.842429i | \(0.318875\pi\) | |||||||
\(758\) | −7.16795e6 | + | 1.24153e7i | −0.453129 | + | 0.784843i | ||||
\(759\) | −31061.4 | − | 53799.8i | −0.00195711 | − | 0.00338982i | ||||
\(760\) | 7.56599e6 | + | 1.31047e7i | 0.475151 | + | 0.822986i | ||||
\(761\) | −1.11999e7 | + | 1.93988e7i | −0.701056 | + | 1.21426i | 0.267040 | + | 0.963685i | \(0.413954\pi\) |
−0.968096 | + | 0.250579i | \(0.919379\pi\) | |||||||
\(762\) | −1.36269e6 | −0.0850180 | ||||||||
\(763\) | −1.58241e6 | − | 4.65685e6i | −0.0984027 | − | 0.289588i | ||||
\(764\) | −2.57550e6 | −0.159635 | ||||||||
\(765\) | −9.86250e6 | + | 1.70824e7i | −0.609303 | + | 1.05534i | ||||
\(766\) | 8.25554e6 | + | 1.42990e7i | 0.508362 | + | 0.880510i | ||||
\(767\) | −1.14241e7 | − | 1.97871e7i | −0.701184 | − | 1.21449i | ||||
\(768\) | 606241. | − | 1.05004e6i | 0.0370888 | − | 0.0642396i | ||||
\(769\) | −1.87866e7 | −1.14560 | −0.572799 | − | 0.819696i | \(-0.694142\pi\) | ||||
−0.572799 | + | 0.819696i | \(0.694142\pi\) | |||||||
\(770\) | −1.30973e6 | + | 1.49440e6i | −0.0796075 | + | 0.0908321i | ||||
\(771\) | 608138. | 0.0368439 | ||||||||
\(772\) | 2.37589e6 | − | 4.11516e6i | 0.143477 | − | 0.248509i | ||||
\(773\) | −4.65419e6 | − | 8.06129e6i | −0.280153 | − | 0.485239i | 0.691269 | − | 0.722597i | \(-0.257052\pi\) |
−0.971422 | + | 0.237358i | \(0.923719\pi\) | |||||||
\(774\) | 8.80394e6 | + | 1.52489e7i | 0.528232 | + | 0.914925i | ||||
\(775\) | 4.21106e6 | − | 7.29377e6i | 0.251847 | − | 0.436212i | ||||
\(776\) | 2.05156e7 | 1.22301 | ||||||||
\(777\) | −2.74121e6 | − | 544370.i | −0.162888 | − | 0.0323476i | ||||
\(778\) | −2.36525e7 | −1.40097 | ||||||||
\(779\) | −3.29144e6 | + | 5.70094e6i | −0.194331 | + | 0.336592i | ||||
\(780\) | −169816. | − | 294130.i | −0.00999405 | − | 0.0173102i | ||||
\(781\) | −439095. | − | 760534.i | −0.0257591 | − | 0.0446161i | ||||
\(782\) | −2.07748e6 | + | 3.59830e6i | −0.121484 | + | 0.210417i | ||||
\(783\) | −734267. | −0.0428006 | ||||||||
\(784\) | 1.05113e7 | − | 8.07601e6i | 0.610751 | − | 0.469252i | ||||
\(785\) | −1.59566e6 | −0.0924201 | ||||||||
\(786\) | −782861. | + | 1.35595e6i | −0.0451989 | + | 0.0782868i | ||||
\(787\) | −8.67133e6 | − | 1.50192e7i | −0.499056 | − | 0.864390i | 0.500944 | − | 0.865480i | \(-0.332986\pi\) |
−0.999999 | + | 0.00109025i | \(0.999653\pi\) | |||||||
\(788\) | −1.47724e6 | − | 2.55865e6i | −0.0847491 | − | 0.146790i | ||||
\(789\) | 300434. | − | 520366.i | 0.0171813 | − | 0.0297589i | ||||
\(790\) | −7.67268e6 | −0.437401 | ||||||||
\(791\) | −1.57425e7 | − | 3.12628e6i | −0.894610 | − | 0.177659i | ||||
\(792\) | −3.33786e6 | −0.189084 | ||||||||
\(793\) | 1.27247e6 | − | 2.20399e6i | 0.0718565 | − | 0.124459i | ||||
\(794\) | −2.95717e6 | − | 5.12197e6i | −0.166466 | − | 0.288327i | ||||
\(795\) | −547943. | − | 949064.i | −0.0307480 | − | 0.0532571i | ||||
\(796\) | −1.32154e6 | + | 2.28897e6i | −0.0739259 | + | 0.128043i | ||||
\(797\) | 3.10445e7 | 1.73117 | 0.865584 | − | 0.500764i | \(-0.166948\pi\) | ||||
0.865584 | + | 0.500764i | \(0.166948\pi\) | |||||||
\(798\) | 1.68696e6 | − | 1.92482e6i | 0.0937772 | − | 0.107000i | ||||
\(799\) | 4.23309e7 | 2.34580 | ||||||||
\(800\) | −1.51220e6 | + | 2.61920e6i | −0.0835379 | + | 0.144692i | ||||
\(801\) | −8.38221e6 | − | 1.45184e7i | −0.461612 | − | 0.799536i | ||||
\(802\) | 819290. | + | 1.41905e6i | 0.0449782 | + | 0.0779045i | ||||
\(803\) | −706153. | + | 1.22309e6i | −0.0386465 | + | 0.0669377i | ||||
\(804\) | −199887. | −0.0109055 | ||||||||
\(805\) | 721778. | + | 2.12411e6i | 0.0392567 | + | 0.115528i | ||||
\(806\) | 1.96794e7 | 1.06702 | ||||||||
\(807\) | 270103. | − | 467832.i | 0.0145997 | − | 0.0252875i | ||||
\(808\) | −3.53655e6 | − | 6.12548e6i | −0.190568 | − | 0.330074i | ||||
\(809\) | 1.23519e7 | + | 2.13941e7i | 0.663533 | + | 1.14927i | 0.979681 | + | 0.200563i | \(0.0642772\pi\) |
−0.316147 | + | 0.948710i | \(0.602389\pi\) | |||||||
\(810\) | 5.94275e6 | − | 1.02931e7i | 0.318255 | − | 0.551233i | ||||
\(811\) | 8.42005e6 | 0.449534 | 0.224767 | − | 0.974413i | \(-0.427838\pi\) | ||||
0.224767 | + | 0.974413i | \(0.427838\pi\) | |||||||
\(812\) | −188229. | − | 553935.i | −0.0100183 | − | 0.0294828i | ||||
\(813\) | −4.57273e6 | −0.242633 | ||||||||
\(814\) | 1.89644e6 | − | 3.28474e6i | 0.100318 | − | 0.173756i | ||||
\(815\) | 4.45265e6 | + | 7.71221e6i | 0.234814 | + | 0.406710i | ||||
\(816\) | −1.62288e6 | − | 2.81091e6i | −0.0853220 | − | 0.147782i | ||||
\(817\) | −1.35349e7 | + | 2.34432e7i | −0.709415 | + | 1.22874i | ||||
\(818\) | −7.04930e6 | −0.368352 | ||||||||
\(819\) | 1.28950e7 | − | 1.47132e7i | 0.671757 | − | 0.766475i | ||||
\(820\) | 910307. | 0.0472774 | ||||||||
\(821\) | 1.29413e7 | − | 2.24150e7i | 0.670071 | − | 1.16060i | −0.307812 | − | 0.951447i | \(-0.599597\pi\) |
0.977883 | − | 0.209150i | \(-0.0670698\pi\) | |||||||
\(822\) | −482505. | − | 835723.i | −0.0249070 | − | 0.0431402i | ||||
\(823\) | −8.60020e6 | − | 1.48960e7i | −0.442597 | − | 0.766601i | 0.555284 | − | 0.831661i | \(-0.312610\pi\) |
−0.997881 | + | 0.0650597i | \(0.979276\pi\) | |||||||
\(824\) | −6.25801e6 | + | 1.08392e7i | −0.321084 | + | 0.556133i | ||||
\(825\) | −206537. | −0.0105649 | ||||||||
\(826\) | −2.33540e7 | − | 4.63782e6i | −1.19100 | − | 0.236518i | ||||
\(827\) | −2.40337e7 | −1.22196 | −0.610979 | − | 0.791647i | \(-0.709224\pi\) | ||||
−0.610979 | + | 0.791647i | \(0.709224\pi\) | |||||||
\(828\) | −304383. | + | 527207.i | −0.0154292 | + | 0.0267242i | ||||
\(829\) | 1.62368e7 | + | 2.81230e7i | 0.820567 | + | 1.42126i | 0.905261 | + | 0.424857i | \(0.139676\pi\) |
−0.0846934 | + | 0.996407i | \(0.526991\pi\) | |||||||
\(830\) | −2.61206e6 | − | 4.52423e6i | −0.131610 | − | 0.227955i | ||||
\(831\) | −132246. | + | 229056.i | −0.00664323 | + | 0.0115064i | ||||
\(832\) | −2.30254e7 | −1.15318 | ||||||||
\(833\) | 4.35526e6 | + | 3.29225e7i | 0.217471 | + | 1.64392i | ||||
\(834\) | 3.54274e6 | 0.176370 | ||||||||
\(835\) | 2.51793e6 | − | 4.36119e6i | 0.124976 | − | 0.216466i | ||||
\(836\) | −414491. | − | 717920.i | −0.0205116 | − | 0.0355272i | ||||
\(837\) | 3.07135e6 | + | 5.31973e6i | 0.151536 | + | 0.262468i | ||||
\(838\) | 1.24749e7 | − | 2.16072e7i | 0.613659 | − | 1.06289i | ||||
\(839\) | −1.24404e7 | −0.610139 | −0.305069 | − | 0.952330i | \(-0.598680\pi\) | ||||
−0.305069 | + | 0.952330i | \(0.598680\pi\) | |||||||
\(840\) | −2.14892e6 | − | 426749.i | −0.105080 | − | 0.0208677i | ||||
\(841\) | −1.99754e7 | −0.973881 | ||||||||
\(842\) | 6.19905e6 | − | 1.07371e7i | 0.301332 | − | 0.521922i | ||||
\(843\) | 2.31977e6 | + | 4.01796e6i | 0.112428 | + | 0.194732i | ||||
\(844\) | −1.81434e6 | − | 3.14253e6i | −0.0876724 | − | 0.151853i | ||||
\(845\) | −596718. | + | 1.03355e6i | −0.0287493 | + | 0.0497952i | ||||
\(846\) | −2.59878e7 | −1.24837 | ||||||||
\(847\) | −1.33174e7 | + | 1.51951e7i | −0.637838 | + | 0.727774i | ||||
\(848\) | −9.92129e6 | −0.473782 | ||||||||
\(849\) | −1.23815e6 | + | 2.14453e6i | −0.0589526 | + | 0.102109i | ||||
\(850\) | 6.90693e6 | + | 1.19632e7i | 0.327897 | + | 0.567934i | ||||
\(851\) | −2.14103e6 | − | 3.70838e6i | −0.101344 | − | 0.175533i | ||||
\(852\) | 78208.5 | − | 135461.i | 0.00369109 | − | 0.00639316i | ||||
\(853\) | −999355. | −0.0470270 | −0.0235135 | − | 0.999724i | \(-0.507485\pi\) | ||||
−0.0235135 | + | 0.999724i | \(0.507485\pi\) | |||||||
\(854\) | −853272. | − | 2.51108e6i | −0.0400353 | − | 0.117819i | ||||
\(855\) | 1.86169e7 | 0.870949 | ||||||||
\(856\) | −6.40597e6 | + | 1.10955e7i | −0.298814 | + | 0.517561i | ||||
\(857\) | 1.32233e7 | + | 2.29034e7i | 0.615016 | + | 1.06524i | 0.990382 | + | 0.138363i | \(0.0441840\pi\) |
−0.375365 | + | 0.926877i | \(0.622483\pi\) | |||||||
\(858\) | −241301. | − | 417945.i | −0.0111903 | − | 0.0193821i | ||||
\(859\) | 1.43358e7 | − | 2.48304e7i | 0.662887 | − | 1.14815i | −0.316967 | − | 0.948437i | \(-0.602664\pi\) |
0.979854 | − | 0.199717i | \(-0.0640024\pi\) | |||||||
\(860\) | 3.74332e6 | 0.172588 | ||||||||
\(861\) | −306647. | − | 902426.i | −0.0140971 | − | 0.0414862i | ||||
\(862\) | 2.65703e7 | 1.21794 | ||||||||
\(863\) | −2.04087e6 | + | 3.53488e6i | −0.0932798 | + | 0.161565i | −0.908889 | − | 0.417037i | \(-0.863068\pi\) |
0.815610 | + | 0.578603i | \(0.196402\pi\) | |||||||
\(864\) | −1.10292e6 | − | 1.91032e6i | −0.0502645 | − | 0.0870607i | ||||
\(865\) | −1.49098e7 | − | 2.58244e7i | −0.677532 | − | 1.17352i | ||||
\(866\) | −6.68439e6 | + | 1.15777e7i | −0.302878 | + | 0.524599i | ||||
\(867\) | 5.17446e6 | 0.233785 | ||||||||
\(868\) | −3.22590e6 | + | 3.68075e6i | −0.145329 | + | 0.165820i | ||||
\(869\) | 2.60195e6 | 0.116882 | ||||||||
\(870\) | 162048. | − | 280676.i | 0.00725849 | − | 0.0125721i | ||||
\(871\) | 4.92131e6 | + | 8.52395e6i | 0.219804 | + | 0.380711i | ||||
\(872\) | 3.67973e6 | + | 6.37348e6i | 0.163880 | + | 0.283848i | ||||
\(873\) | 1.26202e7 | − | 2.18589e7i | 0.560444 | − | 0.970717i | ||||
\(874\) | 3.92155e6 | 0.173652 | ||||||||
\(875\) | 2.39367e7 | + | 4.75354e6i | 1.05693 | + | 0.209893i | ||||
\(876\) | −251550. | −0.0110755 | ||||||||
\(877\) | 1.41202e7 | − | 2.44570e7i | 0.619931 | − | 1.07375i | −0.369567 | − | 0.929204i | \(-0.620494\pi\) |
0.989498 | − | 0.144547i | \(-0.0461726\pi\) | |||||||
\(878\) | 6.49098e6 | + | 1.12427e7i | 0.284167 | + | 0.492192i | ||||
\(879\) | −1.90805e6 | − | 3.30484e6i | −0.0832948 | − | 0.144271i | ||||
\(880\) | 1.18920e6 | − | 2.05975e6i | 0.0517662 | − | 0.0896617i | ||||
\(881\) | 1.61480e7 | 0.700936 | 0.350468 | − | 0.936575i | \(-0.386022\pi\) | ||||
0.350468 | + | 0.936575i | \(0.386022\pi\) | |||||||
\(882\) | −2.67379e6 | − | 2.02119e7i | −0.115732 | − | 0.874852i | ||||
\(883\) | −3.86021e7 | −1.66613 | −0.833065 | − | 0.553174i | \(-0.813416\pi\) | ||||
−0.833065 | + | 0.553174i | \(0.813416\pi\) | |||||||
\(884\) | 3.85164e6 | − | 6.67123e6i | 0.165773 | − | 0.287128i | ||||
\(885\) | 1.57394e6 | + | 2.72615e6i | 0.0675508 | + | 0.117001i | ||||
\(886\) | 9.75637e6 | + | 1.68985e7i | 0.417546 | + | 0.723210i | ||||
\(887\) | −3.64544e6 | + | 6.31408e6i | −0.155575 | + | 0.269464i | −0.933268 | − | 0.359180i | \(-0.883056\pi\) |
0.777693 | + | 0.628644i | \(0.216390\pi\) | |||||||
\(888\) | 4.18184e6 | 0.177965 | ||||||||
\(889\) | −1.63683e7 | − | 3.25055e6i | −0.694625 | − | 0.137944i | ||||
\(890\) | 1.49337e7 | 0.631965 | ||||||||
\(891\) | −2.01529e6 | + | 3.49059e6i | −0.0850441 | + | 0.147301i | ||||
\(892\) | −1.11981e6 | − | 1.93957e6i | −0.0471230 | − | 0.0816194i | ||||
\(893\) | −1.99764e7 | − | 3.46002e7i | −0.838281 | − | 1.45194i | ||||
\(894\) | 731883. | − | 1.26766e6i | 0.0306265 | − | 0.0530467i | ||||
\(895\) | −3.13598e7 | −1.30862 | ||||||||
\(896\) | −9.80281e6 | + | 1.11850e7i | −0.407925 | + | 0.465443i | ||||
\(897\) | −544843. | −0.0226095 | ||||||||
\(898\) | 3.79603e6 | − | 6.57491e6i | 0.157086 | − | 0.272082i | ||||
\(899\) | −2.24088e6 | − | 3.88132e6i | −0.0924739 | − | 0.160170i | ||||
\(900\) | 1.01197e6 | + | 1.75279e6i | 0.0416449 | + | 0.0721311i | ||||
\(901\) | 1.24280e7 | − | 2.15260e7i | 0.510024 | − | 0.883387i | ||||
\(902\) | 1.29351e6 | 0.0529361 | ||||||||
\(903\) | −1.26098e6 | − | 3.71091e6i | −0.0514622 | − | 0.151447i | ||||
\(904\) | 2.40160e7 | 0.977415 | ||||||||
\(905\) | −1.30443e7 | + | 2.25934e7i | −0.529419 | + | 0.916981i | ||||
\(906\) | 588429. | + | 1.01919e6i | 0.0238163 | + | 0.0412510i | ||||
\(907\) | 1.86667e7 | + | 3.23317e7i | 0.753443 | + | 1.30500i | 0.946145 | + | 0.323744i | \(0.104942\pi\) |
−0.192702 | + | 0.981257i | \(0.561725\pi\) | |||||||
\(908\) | −2.59890e6 | + | 4.50142e6i | −0.104610 | + | 0.181190i | ||||
\(909\) | −8.70205e6 | −0.349311 | ||||||||
\(910\) | 5.60714e6 | + | 1.65012e7i | 0.224460 | + | 0.660559i | ||||
\(911\) | −2475.17 | −9.88120e−5 | −4.94060e−5 | − | 1.00000i | \(-0.500016\pi\) | ||||
−4.94060e−5 | 1.00000i | \(0.500016\pi\) | ||||||||
\(912\) | −1.53171e6 | + | 2.65300e6i | −0.0609804 | + | 0.105621i | ||||
\(913\) | 885798. | + | 1.53425e6i | 0.0351688 | + | 0.0609142i | ||||
\(914\) | −5.49501e6 | − | 9.51763e6i | −0.217572 | − | 0.376846i | ||||
\(915\) | −175314. | + | 303653.i | −0.00692252 | + | 0.0119902i | ||||
\(916\) | 3.50613e6 | 0.138067 | ||||||||
\(917\) | −1.26380e7 | + | 1.44200e7i | −0.496313 | + | 0.566293i | ||||
\(918\) | −1.00752e7 | −0.394590 | ||||||||
\(919\) | 2.24119e6 | − | 3.88185e6i | 0.0875366 | − | 0.151618i | −0.818933 | − | 0.573890i | \(-0.805434\pi\) |
0.906469 | + | 0.422272i | \(0.138767\pi\) | |||||||
\(920\) | −1.67842e6 | − | 2.90711e6i | −0.0653780 | − | 0.113238i | ||||
\(921\) | 747334. | + | 1.29442e6i | 0.0290313 | + | 0.0502836i | ||||
\(922\) | −1.55520e7 | + | 2.69368e7i | −0.602501 | + | 1.04356i | ||||
\(923\) | −7.70210e6 | −0.297581 | ||||||||
\(924\) | 117725. | + | 23378.8i | 0.00453618 | + | 0.000900829i | ||||
\(925\) | −1.42364e7 | −0.547075 | ||||||||
\(926\) | 1.00033e7 | − | 1.73262e7i | 0.383367 | − | 0.664011i | ||||
\(927\) | 7.69925e6 | + | 1.33355e7i | 0.294272 | + | 0.509694i | ||||
\(928\) | 804703. | + | 1.39379e6i | 0.0306737 | + | 0.0531283i | ||||
\(929\) | −1.06429e7 | + | 1.84341e7i | −0.404596 | + | 0.700781i | −0.994274 | − | 0.106857i | \(-0.965921\pi\) |
0.589678 | + | 0.807638i | \(0.299255\pi\) | |||||||
\(930\) | −2.71131e6 | −0.102795 | ||||||||
\(931\) | 2.48548e7 | − | 1.90964e7i | 0.939801 | − | 0.722068i | ||||
\(932\) | 6.51394e6 | 0.245643 | ||||||||
\(933\) | 892351. | − | 1.54560e6i | 0.0335608 | − | 0.0581289i | ||||
\(934\) | −1.39025e7 | − | 2.40798e7i | −0.521465 | − | 0.903203i | ||||
\(935\) | 2.97932e6 | + | 5.16034e6i | 0.111452 | + | 0.193041i | ||||
\(936\) | −1.46373e7 | + | 2.53525e7i | −0.546097 | + | 0.945868i | ||||
\(937\) | 6.79757e6 | 0.252932 | 0.126466 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126466 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(938\) | 1.00605e7 | + | 1.99790e6i | 0.373348 | + | 0.0741424i | ||||
\(939\) | 3.36781e6 | 0.124647 | ||||||||
\(940\) | −2.76242e6 | + | 4.78465e6i | −0.101970 | + | 0.176616i | ||||
\(941\) | −2.45441e7 | − | 4.25117e7i | −0.903595 | − | 1.56507i | −0.822792 | − | 0.568342i | \(-0.807585\pi\) |
−0.0808027 | − | 0.996730i | \(-0.525748\pi\) | |||||||
\(942\) | −201924. | − | 349742.i | −0.00741413 | − | 0.0128416i | ||||
\(943\) | 730166. | − | 1.26468e6i | 0.0267388 | − | 0.0463130i | ||||
\(944\) | 2.84985e7 | 1.04086 | ||||||||
\(945\) | −3.58549e6 | + | 4.09105e6i | −0.130608 | + | 0.149024i | ||||
\(946\) | 5.31910e6 | 0.193246 | ||||||||
\(947\) | −1.22742e7 | + | 2.12596e7i | −0.444753 | + | 0.770334i | −0.998035 | − | 0.0626595i | \(-0.980042\pi\) |
0.553282 | + | 0.832994i | \(0.313375\pi\) | |||||||
\(948\) | 231720. | + | 401351.i | 0.00837420 | + | 0.0145045i | ||||
\(949\) | 6.19327e6 | + | 1.07271e7i | 0.223231 | + | 0.386648i | ||||
\(950\) | 6.51892e6 | − | 1.12911e7i | 0.234351 | − | 0.405908i | ||||
\(951\) | −4.71869e6 | −0.169188 | ||||||||
\(952\) | −1.59877e7 | − | 4.70499e7i | −0.571732 | − | 1.68254i | ||||
\(953\) | −513120. | −0.0183015 | −0.00915075 | − | 0.999958i | \(-0.502913\pi\) | ||||
−0.00915075 | + | 0.999958i | \(0.502913\pi\) | |||||||
\(954\) | −7.62984e6 | + | 1.32153e7i | −0.271422 | + | 0.470116i | ||||
\(955\) | −8.73625e6 | − | 1.51316e7i | −0.309968 | − | 0.536880i | ||||
\(956\) | 2.63180e6 | + | 4.55841e6i | 0.0931340 | + | 0.161313i | ||||
\(957\) | −54953.5 | + | 95182.3i | −0.00193962 | + | 0.00335951i | ||||
\(958\) | 3.38659e7 | 1.19220 | ||||||||
\(959\) | −3.80221e6 | − | 1.11895e7i | −0.133502 | − | 0.392882i | ||||
\(960\) | 3.17230e6 | 0.111095 | ||||||||
\(961\) | −4.43206e6 | + | 7.67656e6i | −0.154809 | + | 0.268138i | ||||
\(962\) | −1.66326e7 | − | 2.88086e7i | −0.579460 | − | 1.00365i | ||||
\(963\) | 7.88129e6 | + | 1.36508e7i | 0.273862 | + | 0.474343i | ||||
\(964\) | −1.19885e6 | + | 2.07647e6i | −0.0415501 | + | 0.0719669i | ||||
\(965\) | 3.22366e7 | 1.11437 | ||||||||
\(966\) | −374231. | + | 426998.i | −0.0129032 | + | 0.0147225i | ||||
\(967\) | 3.34818e7 | 1.15144 | 0.575722 | − | 0.817645i | \(-0.304721\pi\) | ||||
0.575722 | + | 0.817645i | \(0.304721\pi\) | |||||||
\(968\) | 1.51167e7 | − | 2.61829e7i | 0.518523 | − | 0.898108i | ||||
\(969\) | −3.83744e6 | − | 6.64664e6i | −0.131290 | − | 0.227401i | ||||
\(970\) | 1.12421e7 | + | 1.94719e7i | 0.383635 | + | 0.664475i | ||||
\(971\) | −2.38018e6 | + | 4.12259e6i | −0.0810143 | + | 0.140321i | −0.903686 | − | 0.428196i | \(-0.859149\pi\) |
0.822672 | + | 0.568517i | \(0.192483\pi\) | |||||||
\(972\) | −2.22090e6 | −0.0753986 | ||||||||
\(973\) | 4.25546e7 | + | 8.45081e6i | 1.44100 | + | 0.286165i | ||||
\(974\) | −4.84739e7 | −1.63723 | ||||||||
\(975\) | −905711. | + | 1.56874e6i | −0.0305125 | + | 0.0528492i | ||||
\(976\) | 1.58716e6 | + | 2.74904e6i | 0.0533329 | + | 0.0923753i | ||||
\(977\) | −1.43669e7 | − | 2.48842e7i | −0.481534 | − | 0.834041i | 0.518242 | − | 0.855234i | \(-0.326587\pi\) |
−0.999775 | + | 0.0211935i | \(0.993253\pi\) | |||||||
\(978\) | −1.12692e6 | + | 1.95189e6i | −0.0376745 | + | 0.0652541i | ||||
\(979\) | −5.06430e6 | −0.168874 | ||||||||
\(980\) | −4.00545e6 | − | 1.65618e6i | −0.133225 | − | 0.0550862i | ||||
\(981\) | 9.05437e6 | 0.300390 | ||||||||
\(982\) | −2.08214e7 | + | 3.60637e7i | −0.689019 | + | 1.19342i | ||||
\(983\) | 2.48536e7 | + | 4.30477e7i | 0.820362 | + | 1.42091i | 0.905413 | + | 0.424532i | \(0.139561\pi\) |
−0.0850509 | + | 0.996377i | \(0.527105\pi\) | |||||||
\(984\) | 713076. | + | 1.23508e6i | 0.0234773 | + | 0.0406638i | ||||
\(985\) | 1.00218e7 | − | 1.73582e7i | 0.329119 | − | 0.570051i | ||||
\(986\) | 7.35092e6 | 0.240796 | ||||||||
\(987\) | 5.67378e6 | + | 1.12674e6i | 0.185387 | + | 0.0368156i | ||||
\(988\) | −7.27054e6 | −0.236960 | ||||||||
\(989\) | 3.00255e6 | − | 5.20057e6i | 0.0976113 | − | 0.169068i | ||||
\(990\) | −1.82907e6 | − | 3.16804e6i | −0.0593120 | − | 0.102731i | ||||
\(991\) | 1.45533e6 | + | 2.52070e6i | 0.0470736 | + | 0.0815338i | 0.888602 | − | 0.458679i | \(-0.151677\pi\) |
−0.841529 | + | 0.540213i | \(0.818344\pi\) | |||||||
\(992\) | 6.73194e6 | − | 1.16601e7i | 0.217201 | − | 0.376203i | ||||
\(993\) | 1.47803e6 | 0.0475676 | ||||||||
\(994\) | −5.29027e6 | + | 6.03620e6i | −0.169829 | + | 0.193775i | ||||
\(995\) | −1.79309e7 | −0.574176 | ||||||||
\(996\) | −157772. | + | 273270.i | −0.00503944 | + | 0.00872857i | ||||
\(997\) | −7.16765e6 | − | 1.24147e7i | −0.228370 | − | 0.395548i | 0.728955 | − | 0.684561i | \(-0.240006\pi\) |
−0.957325 | + | 0.289013i | \(0.906673\pi\) | |||||||
\(998\) | −1.09645e7 | − | 1.89910e7i | −0.348466 | − | 0.603561i | ||||
\(999\) | 5.19169e6 | − | 8.99227e6i | 0.164587 | − | 0.285073i |
(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 | 7.6.c.a.2.2 | ✓ | 4 | |
3.2 | odd | 2 | 63.6.e.d.37.1 | 4 | |||
4.3 | odd | 2 | 112.6.i.c.65.2 | 4 | |||
7.2 | even | 3 | 49.6.a.d.1.1 | 2 | |||
7.3 | odd | 6 | 49.6.c.f.18.2 | 4 | |||
7.4 | even | 3 | inner | 7.6.c.a.4.2 | yes | 4 | |
7.5 | odd | 6 | 49.6.a.e.1.1 | 2 | |||
7.6 | odd | 2 | 49.6.c.f.30.2 | 4 | |||
21.2 | odd | 6 | 441.6.a.n.1.2 | 2 | |||
21.5 | even | 6 | 441.6.a.m.1.2 | 2 | |||
21.11 | odd | 6 | 63.6.e.d.46.1 | 4 | |||
28.11 | odd | 6 | 112.6.i.c.81.2 | 4 | |||
28.19 | even | 6 | 784.6.a.t.1.2 | 2 | |||
28.23 | odd | 6 | 784.6.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.c.a.2.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7.6.c.a.4.2 | yes | 4 | 7.4 | even | 3 | inner | |
49.6.a.d.1.1 | 2 | 7.2 | even | 3 | |||
49.6.a.e.1.1 | 2 | 7.5 | odd | 6 | |||
49.6.c.f.18.2 | 4 | 7.3 | odd | 6 | |||
49.6.c.f.30.2 | 4 | 7.6 | odd | 2 | |||
63.6.e.d.37.1 | 4 | 3.2 | odd | 2 | |||
63.6.e.d.46.1 | 4 | 21.11 | odd | 6 | |||
112.6.i.c.65.2 | 4 | 4.3 | odd | 2 | |||
112.6.i.c.81.2 | 4 | 28.11 | odd | 6 | |||
441.6.a.m.1.2 | 2 | 21.5 | even | 6 | |||
441.6.a.n.1.2 | 2 | 21.2 | odd | 6 | |||
784.6.a.t.1.2 | 2 | 28.19 | even | 6 | |||
784.6.a.ba.1.1 | 2 | 28.23 | odd | 6 |