Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,4,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.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: | \(92.0429796090\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 76x^{2} + 50x + 1156 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(7.50422\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.9374 | 1.61647 | 0.808235 | − | 0.588860i | \(-0.200423\pi\) | ||||
0.808235 | + | 0.588860i | \(0.200423\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.8448 | −0.845458 | −0.422729 | − | 0.906256i | \(-0.638928\pi\) | ||||
−0.422729 | + | 0.906256i | \(0.638928\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.6366 | 0.365752 | 0.182876 | − | 0.983136i | \(-0.441459\pi\) | ||||
0.182876 | + | 0.983136i | \(0.441459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 106.958 | 1.29146 | 0.645732 | − | 0.763564i | \(-0.276552\pi\) | ||||
0.645732 | + | 0.763564i | \(0.276552\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 89.8123 | 0.933269 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.6366 | 0.286813 | 0.143406 | − | 0.989664i | \(-0.454194\pi\) | ||||
0.143406 | + | 0.989664i | \(0.454194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.43075 | −0.0155648 | −0.00778239 | − | 0.999970i | \(-0.502477\pi\) | ||||
−0.00778239 | + | 0.999970i | \(0.502477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.5272 | −0.269565 | −0.134783 | − | 0.990875i | \(-0.543034\pi\) | ||||
−0.134783 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −92.5343 | −0.488126 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −149.687 | −0.722907 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 45.9326 | 0.204089 | 0.102044 | − | 0.994780i | \(-0.467462\pi\) | ||||
0.102044 | + | 0.994780i | \(0.467462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −281.548 | −1.07245 | −0.536224 | − | 0.844076i | \(-0.680150\pi\) | ||||
−0.536224 | + | 0.844076i | \(0.680150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.2034 | 0.0468254 | 0.0234127 | − | 0.999726i | \(-0.492547\pi\) | ||||
0.0234127 | + | 0.999726i | \(0.492547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −60.9724 | −0.189228 | −0.0946142 | − | 0.995514i | \(-0.530162\pi\) | ||||
−0.0946142 | + | 0.995514i | \(0.530162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 553.250 | 1.61298 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 76.9098 | 0.211167 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 292.614 | 0.758370 | 0.379185 | − | 0.925321i | \(-0.376204\pi\) | ||||
0.379185 | + | 0.925321i | \(0.376204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 154.224 | 0.378101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 320.874 | 0.745628 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 372.847 | 0.822721 | 0.411361 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411361 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 314.934 | 0.661035 | 0.330518 | − | 0.943800i | \(-0.392777\pi\) | ||||
0.330518 | + | 0.943800i | \(0.392777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 269.437 | 0.538823 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −65.0000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25.9113 | −0.0472473 | −0.0236237 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236237 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 94.9098 | 0.165591 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 34.0602 | 0.0569324 | 0.0284662 | − | 0.999595i | \(-0.490938\pi\) | ||||
0.0284662 | + | 0.999595i | \(0.490938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1159.87 | 1.85962 | 0.929812 | − | 0.368034i | \(-0.119969\pi\) | ||||
0.929812 | + | 0.368034i | \(0.119969\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −923.413 | −1.36666 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −544.804 | −0.775889 | −0.387945 | − | 0.921683i | \(-0.626815\pi\) | ||||
−0.387945 | + | 0.921683i | \(0.626815\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −993.993 | −1.31452 | −0.657259 | − | 0.753665i | \(-0.728284\pi\) | ||||
−0.657259 | + | 0.753665i | \(0.728284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −128.183 | −0.163569 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.29224 | −0.00898633 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 528.421 | 0.629354 | 0.314677 | − | 0.949199i | \(-0.398104\pi\) | ||||
0.314677 | + | 0.949199i | \(0.398104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 389.187 | 0.448328 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −139.582 | −0.155634 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −534.790 | −0.577561 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 927.730 | 0.971100 | 0.485550 | − | 0.874209i | \(-0.338619\pi\) | ||||
0.485550 | + | 0.874209i | \(0.338619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −277.603 | −0.281819 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 95.6242 | 0.0942075 | 0.0471038 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471038 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −621.642 | −0.594681 | −0.297341 | − | 0.954771i | \(-0.596100\pi\) | ||||
−0.297341 | + | 0.954771i | \(0.596100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −449.062 | −0.417371 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −218.378 | −0.197303 | −0.0986515 | − | 0.995122i | \(-0.531453\pi\) | ||||
−0.0986515 | + | 0.995122i | \(0.531453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1193.55 | 1.04882 | 0.524412 | − | 0.851465i | \(-0.324285\pi\) | ||||
0.524412 | + | 0.851465i | \(0.324285\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 137.798 | 0.117831 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1154.34 | −0.960983 | −0.480492 | − | 0.876999i | \(-0.659542\pi\) | ||||
−0.480492 | + | 0.876999i | \(0.659542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −158.183 | −0.128266 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 767.494 | 0.591228 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −379.601 | −0.285200 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −844.643 | −0.619178 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −710.316 | −0.496302 | −0.248151 | − | 0.968721i | \(-0.579823\pi\) | ||||
−0.248151 | + | 0.968721i | \(0.579823\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 39.6101 | 0.0270347 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 362.881 | 0.242023 | 0.121012 | − | 0.992651i | \(-0.461386\pi\) | ||||
0.121012 | + | 0.992651i | \(0.461386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3202.05 | 2.08761 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −835.594 | −0.521092 | −0.260546 | − | 0.965461i | \(-0.583903\pi\) | ||||
−0.260546 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2539.45 | 1.54959 | 0.774797 | − | 0.632210i | \(-0.217852\pi\) | ||||
0.774797 | + | 0.632210i | \(0.217852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −182.917 | −0.109251 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −400.982 | −0.234488 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.1537 | 0.00696078 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1659.75 | 0.931252 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2312.03 | 1.27120 | 0.635600 | − | 0.772019i | \(-0.280753\pi\) | ||||
0.635600 | + | 0.772019i | \(0.280753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −292.005 | −0.157371 | −0.0786856 | − | 0.996899i | \(-0.525072\pi\) | ||||
−0.0786856 | + | 0.996899i | \(0.525072\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 230.729 | 0.121917 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 232.636 | 0.120553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1604.54 | −0.815644 | −0.407822 | − | 0.913062i | \(-0.633712\pi\) | ||||
−0.407822 | + | 0.913062i | \(0.633712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 877.841 | 0.437845 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 947.119 | 0.463624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 143.755 | 0.0690785 | 0.0345393 | − | 0.999403i | \(-0.489004\pi\) | ||||
0.0345393 | + | 0.999403i | \(0.489004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 462.671 | 0.218296 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 486.932 | 0.225628 | 0.112814 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112814 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 962.621 | 0.430488 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2697.35 | 1.18541 | 0.592703 | − | 0.805421i | \(-0.298061\pi\) | ||||
0.592703 | + | 0.805421i | \(0.298061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 748.436 | 0.323294 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1118.54 | 0.474998 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2971.14 | 1.24063 | 0.620316 | − | 0.784352i | \(-0.287004\pi\) | ||||
0.620316 | + | 0.784352i | \(0.287004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1247.45 | 0.512276 | 0.256138 | − | 0.966640i | \(-0.417550\pi\) | ||||
0.256138 | + | 0.966640i | \(0.417550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 944.802 | 0.381649 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −229.663 | −0.0912712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −790.755 | −0.309228 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 808.311 | 0.311090 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2222.04 | 0.841785 | 0.420892 | − | 0.907111i | \(-0.361717\pi\) | ||||
0.420892 | + | 0.907111i | \(0.361717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 918.417 | 0.342534 | 0.171267 | − | 0.985225i | \(-0.445214\pi\) | ||||
0.171267 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −195.000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3420.25 | −1.23697 | −0.618485 | − | 0.785797i | \(-0.712253\pi\) | ||||
−0.618485 | + | 0.785797i | \(0.712253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2900.99 | 1.03339 | 0.516697 | − | 0.856168i | \(-0.327161\pi\) | ||||
0.516697 | + | 0.856168i | \(0.327161\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −77.7340 | −0.0272783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −72.7704 | −0.0251600 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1407.74 | 0.479613 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 284.729 | 0.0956042 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3299.09 | −1.09188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4932.98 | 1.60948 | 0.804741 | − | 0.593627i | \(-0.202304\pi\) | ||||
0.804741 | + | 0.593627i | \(0.202304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 102.180 | 0.0328699 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −66.0168 | −0.0209410 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1392.90 | −0.435744 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3479.61 | 1.07365 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 333.276 | 0.101441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1628.76 | −0.489102 | −0.244551 | − | 0.969636i | \(-0.578641\pi\) | ||||
−0.244551 | + | 0.969636i | \(0.578641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3633.27 | 1.06233 | 0.531164 | − | 0.847269i | \(-0.321755\pi\) | ||||
0.531164 | + | 0.847269i | \(0.321755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4430.06 | −1.27837 | −0.639185 | − | 0.769053i | \(-0.720728\pi\) | ||||
−0.639185 | + | 0.769053i | \(0.720728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2770.24 | −0.789040 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1647.65 | −0.463266 | −0.231633 | − | 0.972803i | \(-0.574407\pi\) | ||||
−0.231633 | + | 0.972803i | \(0.574407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 304.862 | 0.0846255 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1634.41 | −0.447960 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1678.88 | −0.454385 | −0.227193 | − | 0.973850i | \(-0.572955\pi\) | ||||
−0.227193 | + | 0.973850i | \(0.572955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3398.22 | 0.908292 | 0.454146 | − | 0.890927i | \(-0.349944\pi\) | ||||
0.454146 | + | 0.890927i | \(0.349944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2766.25 | −0.721344 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1390.45 | 0.358188 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2981.98 | −0.758937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4366.48 | 1.09805 | 0.549023 | − | 0.835807i | \(-0.315000\pi\) | ||||
0.549023 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −975.823 | −0.242488 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −384.549 | −0.0944368 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1403.98 | 0.340770 | 0.170385 | − | 0.985378i | \(-0.445499\pi\) | ||||
0.170385 | + | 0.985378i | \(0.445499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1375.11 | 0.329903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.8767 | −0.00518826 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2903.66 | 0.680788 | 0.340394 | − | 0.940283i | \(-0.389440\pi\) | ||||
0.340394 | + | 0.940283i | \(0.389440\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1463.07 | −0.339153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1585.26 | 0.363358 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1637.84 | 0.371229 | 0.185614 | − | 0.982623i | \(-0.440572\pi\) | ||||
0.185614 | + | 0.982623i | \(0.440572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2030.84 | 0.455221 | 0.227610 | − | 0.973752i | \(-0.426909\pi\) | ||||
0.227610 | + | 0.973752i | \(0.426909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1167.56 | 0.258842 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −771.119 | −0.169092 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1272.98 | −0.276122 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −418.745 | −0.0898551 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4926.47 | −1.04587 | −0.522933 | − | 0.852374i | \(-0.675162\pi\) | ||||
−0.522933 | + | 0.852374i | \(0.675162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3623.18 | 0.761044 | 0.380522 | − | 0.924772i | \(-0.375744\pi\) | ||||
0.380522 | + | 0.924772i | \(0.375744\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1604.37 | −0.333455 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8428.81 | −1.73358 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4255.76 | −0.866225 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2783.19 | 0.560665 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7355.41 | 1.46658 | 0.733290 | − | 0.679916i | \(-0.237984\pi\) | ||||
0.733290 | + | 0.679916i | \(0.237984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1864.24 | −0.367932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −832.808 | −0.162709 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 411.276 | 0.0795475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 395.275 | 0.0756919 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 286.872 | 0.0543907 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1574.67 | −0.295624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3414.14 | −0.634707 | −0.317353 | − | 0.948307i | \(-0.602794\pi\) | ||||
−0.317353 | + | 0.948307i | \(0.602794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1864.92 | −0.343339 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3096.13 | −0.564519 | −0.282259 | − | 0.959338i | \(-0.591084\pi\) | ||||
−0.282259 | + | 0.959338i | \(0.591084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8912.59 | −1.60949 | −0.804743 | − | 0.593623i | \(-0.797697\pi\) | ||||
−0.804743 | + | 0.593623i | \(0.797697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1347.18 | −0.240969 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8748.65 | 1.55007 | 0.775036 | − | 0.631917i | \(-0.217732\pi\) | ||||
0.775036 | + | 0.631917i | \(0.217732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 74.9758 | 0.0131594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −655.135 | −0.113913 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2742.04 | 0.472356 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 325.000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3580.66 | 0.605539 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1825.36 | −0.305882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2029.88 | −0.337077 | −0.168538 | − | 0.985695i | \(-0.553905\pi\) | ||||
−0.168538 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 413.394 | 0.0680296 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 129.557 | 0.0211297 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8400.49 | 1.35787 | 0.678937 | − | 0.734196i | \(-0.262441\pi\) | ||||
0.678937 | + | 0.734196i | \(0.262441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3463.02 | −0.554824 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1435.12 | 0.227906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6294.36 | 0.990856 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −474.549 | −0.0740547 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4996.96 | 0.773057 | 0.386528 | − | 0.922277i | \(-0.373674\pi\) | ||||
0.386528 | + | 0.922277i | \(0.373674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7433.65 | −1.14015 | −0.570077 | − | 0.821591i | \(-0.693087\pi\) | ||||
−0.570077 | + | 0.821591i | \(0.693087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1136.59 | −0.171373 | −0.0856863 | − | 0.996322i | \(-0.527308\pi\) | ||||
−0.0856863 | + | 0.996322i | \(0.527308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −170.301 | −0.0254609 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2302.48 | 0.341345 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2803.47 | 0.412149 | 0.206074 | − | 0.978536i | \(-0.433931\pi\) | ||||
0.206074 | + | 0.978536i | \(0.433931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4581.00 | 0.667881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1138.80 | −0.164660 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5799.35 | −0.831649 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1970.87 | −0.280323 | −0.140161 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140161 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2533.93 | −0.357482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8760.11 | 1.22588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 217.387 | 0.0301766 | 0.0150883 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150883 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.5997 | −0.00431689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5166.63 | 0.700243 | 0.350121 | − | 0.936704i | \(-0.386140\pi\) | ||||
0.350121 | + | 0.936704i | \(0.386140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2130.95 | −0.286540 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11149.3 | −1.48747 | −0.743736 | − | 0.668473i | \(-0.766948\pi\) | ||||
−0.743736 | + | 0.668473i | \(0.766948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4617.07 | 0.611188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 118.830 | 0.0156085 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11092.0 | −1.44573 | −0.722863 | − | 0.690992i | \(-0.757174\pi\) | ||||
−0.722863 | + | 0.690992i | \(0.757174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 811.055 | 0.104902 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1088.64 | 0.139732 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2724.02 | 0.346988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8055.67 | 1.01839 | 0.509197 | − | 0.860650i | \(-0.329942\pi\) | ||||
0.509197 | + | 0.860650i | \(0.329942\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9606.14 | 1.20528 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3318.85 | −0.413305 | −0.206652 | − | 0.978414i | \(-0.566257\pi\) | ||||
−0.206652 | + | 0.978414i | \(0.566257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −604.853 | −0.0747640 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1416.78 | −0.172548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9684.08 | −1.17077 | −0.585387 | − | 0.810754i | \(-0.699058\pi\) | ||||
−0.585387 | + | 0.810754i | \(0.699058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2506.78 | −0.300853 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11162.1 | 1.32990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4969.97 | 0.587870 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7618.36 | 0.894658 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −641.245 | −0.0747658 | −0.0373829 | − | 0.999301i | \(-0.511902\pi\) | ||||
−0.0373829 | + | 0.999301i | \(0.511902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12734.8 | 1.47424 | 0.737120 | − | 0.675762i | \(-0.236185\pi\) | ||||
0.737120 | + | 0.675762i | \(0.236185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −548.751 | −0.0630761 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 640.915 | 0.0731505 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9428.31 | 1.06854 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1202.95 | −0.135382 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 230.903 | 0.0258055 | 0.0129028 | − | 0.999917i | \(-0.495893\pi\) | ||||
0.0129028 | + | 0.999917i | \(0.495893\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4530.51 | 0.502823 | 0.251411 | − | 0.967880i | \(-0.419105\pi\) | ||||
0.251411 | + | 0.967880i | \(0.419105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 36.4612 | 0.00401881 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3383.79 | 0.370408 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4862.75 | −0.528671 | −0.264336 | − | 0.964431i | \(-0.585153\pi\) | ||||
−0.264336 | + | 0.964431i | \(0.585153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4979.25 | 0.537658 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12774.9 | −1.37010 | −0.685048 | − | 0.728498i | \(-0.740219\pi\) | ||||
−0.685048 | + | 0.728498i | \(0.740219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2642.10 | −0.281456 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6936.08 | 0.733927 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8513.83 | 0.894861 | 0.447431 | − | 0.894319i | \(-0.352339\pi\) | ||||
0.447431 | + | 0.894319i | \(0.352339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8684.27 | 0.906710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −876.016 | −0.0908583 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1945.93 | −0.200498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14065.5 | −1.43973 | −0.719865 | − | 0.694114i | \(-0.755796\pi\) | ||||
−0.719865 | + | 0.694114i | \(0.755796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 692.188 | 0.0703891 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2412.53 | 0.243737 | 0.121869 | − | 0.992546i | \(-0.461111\pi\) | ||||
0.121869 | + | 0.992546i | \(0.461111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10195.6 | 1.02339 | 0.511695 | − | 0.859167i | \(-0.329018\pi\) | ||||
0.511695 | + | 0.859167i | \(0.329018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 697.908 | 0.0696015 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2086.70 | −0.206769 | −0.103384 | − | 0.994641i | \(-0.532967\pi\) | ||||
−0.103384 | + | 0.994641i | \(0.532967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −775.719 | −0.0763739 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4813.61 | −0.470912 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −407.254 | −0.0395889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2673.95 | 0.258293 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2633.52 | 0.252790 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10327.2 | 0.985098 | 0.492549 | − | 0.870285i | \(-0.336065\pi\) | ||||
0.492549 | + | 0.870285i | \(0.336065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 597.124 | 0.0566040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2841.36 | 0.267673 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4638.65 | −0.434289 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13131.8 | 1.22188 | 0.610942 | − | 0.791676i | \(-0.290791\pi\) | ||||
0.610942 | + | 0.791676i | \(0.290791\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 431.266 | 0.0398825 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5201.34 | −0.478071 | −0.239036 | − | 0.971011i | \(-0.576831\pi\) | ||||
−0.239036 | + | 0.971011i | \(0.576831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −62.3161 | −0.00569285 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1388.01 | 0.126034 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1019.67 | 0.0920295 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11498.6 | −1.03156 | −0.515781 | − | 0.856721i | \(-0.672498\pi\) | ||||
−0.515781 | + | 0.856721i | \(0.672498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1460.80 | 0.130267 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4117.25 | 0.364969 | 0.182484 | − | 0.983209i | \(-0.441586\pi\) | ||||
0.182484 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −478.121 | −0.0421309 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3110.48 | −0.270864 | −0.135432 | − | 0.990787i | \(-0.543242\pi\) | ||||
−0.135432 | + | 0.990787i | \(0.543242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34723.6 | 3.00603 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2887.86 | 0.248543 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3108.21 | 0.265949 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1880.68 | 0.159985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8092.04 | 0.684395 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18391.6 | −1.54654 | −0.773272 | − | 0.634074i | \(-0.781381\pi\) | ||||
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2462.46 | −0.205881 | −0.102941 | − | 0.994688i | \(-0.532825\pi\) | ||||
−0.102941 | + | 0.994688i | \(0.532825\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2245.31 | 0.186654 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1192.80 | −0.0985942 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11166.1 | −0.917739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3355.62 | 0.274240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3660.12 | −0.297443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1091.89 | 0.0882366 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8913.41 | 0.716280 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17064.9 | −1.36370 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6060.86 | −0.481658 | −0.240829 | − | 0.970568i | \(-0.577419\pi\) | ||||
−0.240829 | + | 0.970568i | \(0.577419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3742.34 | 0.295763 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5967.77 | −0.469048 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8474.72 | −0.662437 | −0.331218 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331218 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2834.40 | 0.220345 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −259.988 | −0.0201014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16310.0 | −1.25420 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −688.990 | −0.0526955 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16771.5 | −1.27582 | −0.637911 | − | 0.770110i | \(-0.720201\pi\) | ||||
−0.637911 | + | 0.770110i | \(0.720201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 171.644 | 0.0129870 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2372.26 | −0.178533 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20461.1 | −1.53167 | −0.765837 | − | 0.643035i | \(-0.777675\pi\) | ||||
−0.765837 | + | 0.643035i | \(0.777675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5771.70 | 0.429765 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2424.93 | 0.179608 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25998.0 | −1.91546 | −0.957728 | − | 0.287675i | \(-0.907118\pi\) | ||||
−0.957728 | + | 0.287675i | \(0.907118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24951.9 | 1.82873 | 0.914366 | − | 0.404889i | \(-0.132690\pi\) | ||||
0.914366 | + | 0.404889i | \(0.132690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6666.11 | 0.486005 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 790.915 | 0.0573625 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11833.9 | −0.853816 | −0.426908 | − | 0.904295i | \(-0.640397\pi\) | ||||
−0.426908 | + | 0.904295i | \(0.640397\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2755.25 | 0.197762 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29757.6 | −2.12488 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9025.60 | −0.641170 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −585.000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −592.026 | −0.0416278 | −0.0208139 | − | 0.999783i | \(-0.506626\pi\) | ||||
−0.0208139 | + | 0.999783i | \(0.506626\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4976.45 | −0.348134 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10260.8 | −0.714165 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1829.53 | 0.126694 | 0.0633472 | − | 0.997992i | \(-0.479822\pi\) | ||||
0.0633472 | + | 0.997992i | \(0.479822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3837.47 | −0.264405 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8702.96 | 0.596631 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28333.7 | −1.93269 | −0.966346 | − | 0.257245i | \(-0.917185\pi\) | ||||
−0.966346 | + | 0.257245i | \(0.917185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24753.2 | −1.68004 | −0.840022 | − | 0.542553i | \(-0.817458\pi\) | ||||
−0.840022 | + | 0.542553i | \(0.817458\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −233.202 | −0.0157491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1898.01 | 0.127545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7302.18 | 0.488280 | 0.244140 | − | 0.969740i | \(-0.421494\pi\) | ||||
0.244140 | + | 0.969740i | \(0.421494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −218.311 | −0.0145261 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −792.641 | −0.0524825 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26820.0 | −1.76713 | −0.883563 | − | 0.468312i | \(-0.844862\pi\) | ||||
−0.883563 | + | 0.468312i | \(0.844862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4223.21 | 0.276905 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5701.67 | −0.372027 | −0.186013 | − | 0.982547i | \(-0.559557\pi\) | ||||
−0.186013 | + | 0.982547i | \(0.559557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9385.86 | −0.609450 | −0.304725 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304725 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 854.188 | 0.0551971 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15819.6 | 1.01733 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9897.27 | −0.630397 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1177.56 | 0.0746459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1551.34 | 0.0978730 | 0.0489365 | − | 0.998802i | \(-0.484417\pi\) | ||||
0.0489365 | + | 0.998802i | \(0.484417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14798.9 | 0.929234 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3551.58 | 0.221953 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7192.26 | 0.447359 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 306.541 | 0.0189775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3746.46 | 0.230852 | 0.115426 | − | 0.993316i | \(-0.463177\pi\) | ||||
0.115426 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9748.79 | −0.597908 | −0.298954 | − | 0.954268i | \(-0.596638\pi\) | ||||
−0.298954 | + | 0.954268i | \(0.596638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −198.050 | −0.0120903 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22052.5 | 1.33999 | 0.669995 | − | 0.742366i | \(-0.266296\pi\) | ||||
0.669995 | + | 0.742366i | \(0.266296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11500.4 | −0.695577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4178.71 | −0.251577 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14505.6 | −0.869293 | −0.434646 | − | 0.900601i | \(-0.643127\pi\) | ||||
−0.434646 | + | 0.900601i | \(0.643127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1814.40 | −0.108236 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10438.8 | 0.619875 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24976.9 | −1.47642 | −0.738210 | − | 0.674571i | \(-0.764329\pi\) | ||||
−0.738210 | + | 0.674571i | \(0.764329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29608.3 | 1.74225 | 0.871126 | − | 0.491059i | \(-0.163390\pi\) | ||||
0.871126 | + | 0.491059i | \(0.163390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 999.828 | 0.0585672 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16010.2 | −0.933609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −76.9006 | −0.00446417 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4886.28 | −0.282383 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9714.06 | −0.558878 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17420.1 | −0.997762 | −0.498881 | − | 0.866671i | \(-0.666256\pi\) | ||||
−0.498881 | + | 0.866671i | \(0.666256\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18655.3 | −1.05906 | −0.529529 | − | 0.848292i | \(-0.677631\pi\) | ||||
−0.529529 | + | 0.848292i | \(0.677631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27773.9 | 1.56975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10899.8 | 0.613336 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29518.2 | −1.65371 | −0.826855 | − | 0.562415i | \(-0.809872\pi\) | ||||
−0.826855 | + | 0.562415i | \(0.809872\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4177.97 | 0.233039 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13290.2 | −0.738067 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3803.98 | 0.210334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6814.27 | 0.375148 | 0.187574 | − | 0.982250i | \(-0.439938\pi\) | ||||
0.187574 | + | 0.982250i | \(0.439938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8310.72 | −0.455553 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12697.3 | −0.692999 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7217.92 | −0.392250 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4942.94 | −0.267467 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13833.0 | −0.745314 | −0.372657 | − | 0.927969i | \(-0.621553\pi\) | ||||
−0.372657 | + | 0.927969i | \(0.621553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4912.86 | 0.263573 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 914.586 | 0.0488586 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2862.74 | 0.152284 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14817.0 | −0.784860 | −0.392430 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392430 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4903.24 | −0.258630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1471.96 | −0.0773147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2004.91 | 0.104866 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5036.65 | −0.262339 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5475.18 | −0.283992 | −0.141996 | − | 0.989867i | \(-0.545352\pi\) | ||||
−0.141996 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18610.4 | −0.961284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10194.7 | 0.524403 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −60.7687 | −0.00311296 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1245.89 | 0.0635593 | 0.0317796 | − | 0.999495i | \(-0.489883\pi\) | ||||
0.0317796 | + | 0.999495i | \(0.489883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 338.489 | 0.0171265 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5575.21 | −0.280935 | −0.140467 | − | 0.990085i | \(-0.544861\pi\) | ||||
−0.140467 | + | 0.990085i | \(0.544861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8298.76 | −0.416468 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 799.228 | 0.0399457 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14543.3 | −0.723930 | −0.361965 | − | 0.932192i | \(-0.617894\pi\) | ||||
−0.361965 | + | 0.932192i | \(0.617894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4171.36 | 0.206800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27422.3 | 1.35400 | 0.677002 | − | 0.735981i | \(-0.263279\pi\) | ||||
0.677002 | + | 0.735981i | \(0.263279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11560.1 | −0.568498 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8945.94 | −0.438172 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6537.69 | −0.318934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22289.4 | 1.08302 | 0.541512 | − | 0.840693i | \(-0.317852\pi\) | ||||
0.541512 | + | 0.840693i | \(0.317852\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13099.4 | 0.633957 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1460.03 | 0.0703785 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23198.2 | −1.11381 | −0.556904 | − | 0.830577i | \(-0.688011\pi\) | ||||
−0.556904 | + | 0.830577i | \(0.688011\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2927.47 | −0.140001 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7255.28 | −0.345603 | −0.172801 | − | 0.984957i | \(-0.555282\pi\) | ||||
−0.172801 | + | 0.984957i | \(0.555282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35732.0 | 1.69539 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1153.65 | −0.0545231 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4847.01 | 0.228182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3230.75 | −0.151500 | −0.0757502 | − | 0.997127i | \(-0.524135\pi\) | ||||
−0.0757502 | + | 0.997127i | \(0.524135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4211.94 | 0.196743 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23646.1 | 1.10025 | 0.550123 | − | 0.835084i | \(-0.314581\pi\) | ||||
0.550123 | + | 0.835084i | \(0.314581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1163.18 | −0.0539131 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4125.32 | 0.190470 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30113.7 | −1.38503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1050.58 | −0.0481339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −65.6302 | −0.00299544 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8022.69 | 0.364767 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4303.98 | 0.194943 | 0.0974717 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974717 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8710.97 | 0.393053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34558.0 | −1.55340 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4094.14 | 0.183338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4389.21 | −0.195810 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14133.4 | −0.628142 | −0.314071 | − | 0.949399i | \(-0.601693\pi\) | ||||
−0.314071 | + | 0.949399i | \(0.601693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1563.12 | −0.0692107 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4755.79 | 0.209785 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35775.9 | −1.57224 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4735.60 | −0.207339 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4913.51 | 0.214329 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8149.34 | −0.354160 | −0.177080 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177080 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −762.204 | −0.0330020 | −0.0165010 | − | 0.999864i | \(-0.505253\pi\) | ||||
−0.0165010 | + | 0.999864i | \(0.505253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6092.53 | 0.262822 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −718.777 | −0.0308929 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1412.20 | 0.0604734 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3502.68 | 0.149443 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15118.9 | −0.642694 | −0.321347 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321347 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46721.1 | 1.97885 | 0.989426 | − | 0.145038i | \(-0.0463303\pi\) | ||||
0.989426 | + | 0.145038i | \(0.0463303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2313.36 | −0.0976251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −667.106 | −0.0280502 | −0.0140251 | − | 0.999902i | \(-0.504464\pi\) | ||||
−0.0140251 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14816.1 | 0.620728 | 0.310364 | − | 0.950618i | \(-0.399549\pi\) | ||||
0.310364 | + | 0.950618i | \(0.399549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3818.93 | −0.159419 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14183.5 | 0.589949 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2434.66 | −0.100904 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1256.23 | −0.0518779 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14951.3 | −0.615226 | −0.307613 | − | 0.951511i | \(-0.599530\pi\) | ||||
−0.307613 | + | 0.951511i | \(0.599530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24383.1 | −0.999758 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14779.4 | −0.603831 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −845.000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11364.3 | −0.461017 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10869.5 | 0.439389 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1453.15 | 0.0585352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38357.3 | 1.53966 | 0.769829 | − | 0.638251i | \(-0.220342\pi\) | ||||
0.769829 | + | 0.638251i | \(0.220342\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4813.11 | −0.192520 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30786.7 | −1.22713 | −0.613566 | − | 0.789643i | \(-0.710266\pi\) | ||||
−0.613566 | + | 0.789643i | \(0.710266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34100.2 | −1.35446 | −0.677231 | − | 0.735770i | \(-0.736820\pi\) | ||||
−0.677231 | + | 0.735770i | \(0.736820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25286.4 | −1.00088 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17823.0 | 0.703014 | 0.351507 | − | 0.936185i | \(-0.385669\pi\) | ||||
0.351507 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13486.7 | −0.530130 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12767.3 | −0.500115 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16804.3 | 0.655982 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −336.847 | −0.0131041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8349.57 | 0.323700 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3742.18 | −0.144581 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43937.2 | 1.69174 | 0.845870 | − | 0.533390i | \(-0.179082\pi\) | ||||
0.845870 | + | 0.533390i | \(0.179082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22066.2 | 0.846730 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21509.0 | 0.822540 | 0.411270 | − | 0.911514i | \(-0.365085\pi\) | ||||
0.411270 | + | 0.911514i | \(0.365085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22046.4 | 0.840228 | 0.420114 | − | 0.907471i | \(-0.361990\pi\) | ||||
0.420114 | + | 0.907471i | \(0.361990\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5592.71 | −0.212426 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9604.36 | −0.363566 | −0.181783 | − | 0.983339i | \(-0.558187\pi\) | ||||
−0.181783 | + | 0.983339i | \(0.558187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21265.0 | −0.802257 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2498.43 | −0.0939398 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6521.48 | −0.244382 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14855.7 | −0.554828 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1233.83 | 0.0459268 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 113.096 | 0.00419572 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7501.62 | 0.277375 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1185.82 | 0.0437007 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6237.23 | −0.229097 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17819.4 | −0.652353 | −0.326177 | − | 0.945309i | \(-0.605760\pi\) | ||||
−0.326177 | + | 0.945309i | \(0.605760\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 860.617 | 0.0314025 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10034.7 | −0.364944 | −0.182472 | − | 0.983211i | \(-0.558410\pi\) | ||||
−0.182472 | + | 0.983211i | \(0.558410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30659.5 | 1.11137 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4724.01 | −0.170679 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10863.7 | 0.391223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54693.5 | −1.96319 | −0.981595 | − | 0.190976i | \(-0.938835\pi\) | ||||
−0.981595 | + | 0.190976i | \(0.938835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10242.4 | −0.366448 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 442.782 | 0.0157902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1148.32 | 0.0408177 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5594.77 | −0.198227 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37434.8 | 1.32206 | 0.661031 | − | 0.750359i | \(-0.270119\pi\) | ||||
0.661031 | + | 0.750359i | \(0.270119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 59174.5 | 2.08310 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9288.38 | −0.325925 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3953.77 | 0.138291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22416.0 | 0.781534 | 0.390767 | − | 0.920490i | \(-0.372210\pi\) | ||||
0.390767 | + | 0.920490i | \(0.372210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26737.8 | −0.929237 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42374.1 | 1.46797 | 0.733983 | − | 0.679168i | \(-0.237659\pi\) | ||||
0.733983 | + | 0.679168i | \(0.237659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8907.21 | −0.307591 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4041.55 | −0.139124 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23229.9 | 0.797117 | 0.398559 | − | 0.917143i | \(-0.369511\pi\) | ||||
0.398559 | + | 0.917143i | \(0.369511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15078.3 | 0.515767 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26245.9 | 0.894935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24063.4 | −0.817933 | −0.408967 | − | 0.912549i | \(-0.634111\pi\) | ||||
−0.408967 | + | 0.912549i | \(0.634111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11110.2 | −0.376458 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 224.927 | 0.00759757 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25015.5 | −0.842330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27626.2 | −0.927335 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1965.40 | −0.0657677 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4592.08 | −0.153186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21899.6 | −0.728276 | −0.364138 | − | 0.931345i | \(-0.618636\pi\) | ||||
−0.364138 | + | 0.931345i | \(0.618636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8226.11 | 0.272715 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5125.99 | 0.169414 | 0.0847070 | − | 0.996406i | \(-0.473005\pi\) | ||||
0.0847070 | + | 0.996406i | \(0.473005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 76024.7 | 2.50487 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 975.000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40536.5 | −1.32741 | −0.663705 | − | 0.747995i | \(-0.731017\pi\) | ||||
−0.663705 | + | 0.747995i | \(0.731017\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16299.0 | −0.532093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10742.0 | 0.349608 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1634.18 | −0.0530235 | −0.0265118 | − | 0.999649i | \(-0.508440\pi\) | ||||
−0.0265118 | + | 0.999649i | \(0.508440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17101.3 | 0.553190 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5476.07 | −0.176601 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 417.709 | 0.0134301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21750.2 | −0.697191 | −0.348596 | − | 0.937273i | \(-0.613341\pi\) | ||||
−0.348596 | + | 0.937273i | \(0.613341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6089.65 | −0.194611 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14504.9 | −0.462148 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2618.14 | −0.0831667 | −0.0415834 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415834 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1240.18 | 0.0392769 |
(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 | 1560.4.a.m.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.4.a.m.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |