Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
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: | \( x^{4} - x^{3} - 43x^{2} - 11x + 222 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 308) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.25471\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 | ||||||||
\(3\) | 6.25471 | 1.20372 | 0.601859 | − | 0.798602i | \(-0.294427\pi\) | ||||
0.601859 | + | 0.798602i | \(0.294427\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.1213 | 1.53138 | 0.765690 | − | 0.643210i | \(-0.222398\pi\) | ||||
0.765690 | + | 0.643210i | \(0.222398\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.1213 | 0.448939 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.7778 | 1.10466 | 0.552330 | − | 0.833626i | \(-0.313739\pi\) | ||||
0.552330 | + | 0.833626i | \(0.313739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 107.089 | 1.84335 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −104.255 | −1.48738 | −0.743691 | − | 0.668523i | \(-0.766927\pi\) | ||||
−0.743691 | + | 0.668523i | \(0.766927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.6685 | −0.128816 | −0.0644082 | − | 0.997924i | \(-0.520516\pi\) | ||||
−0.0644082 | + | 0.997924i | \(0.520516\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 43.7829 | 0.454963 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.26667 | 0.0840102 | 0.0420051 | − | 0.999117i | \(-0.486625\pi\) | ||||
0.0420051 | + | 0.999117i | \(0.486625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 168.140 | 1.34512 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −93.0616 | −0.663323 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 223.275 | 1.42969 | 0.714847 | − | 0.699281i | \(-0.246496\pi\) | ||||
0.714847 | + | 0.699281i | \(0.246496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 237.641 | 1.37682 | 0.688412 | − | 0.725320i | \(-0.258308\pi\) | ||||
0.688412 | + | 0.725320i | \(0.258308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −68.8018 | −0.362935 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 119.849 | 0.578807 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 361.973 | 1.60832 | 0.804161 | − | 0.594411i | \(-0.202615\pi\) | ||||
0.804161 | + | 0.594411i | \(0.202615\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 323.855 | 1.32970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 273.492 | 1.04176 | 0.520881 | − | 0.853629i | \(-0.325603\pi\) | ||||
0.520881 | + | 0.853629i | \(0.325603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −149.666 | −0.530789 | −0.265394 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265394 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 207.534 | 0.687495 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −531.944 | −1.65089 | −0.825447 | − | 0.564480i | \(-0.809077\pi\) | ||||
−0.825447 | + | 0.564480i | \(0.809077\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −652.083 | −1.79039 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 408.170 | 1.05786 | 0.528928 | − | 0.848667i | \(-0.322594\pi\) | ||||
0.528928 | + | 0.848667i | \(0.322594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −188.335 | −0.461728 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −66.7280 | −0.155059 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −416.905 | −0.919938 | −0.459969 | − | 0.887935i | \(-0.652140\pi\) | ||||
−0.459969 | + | 0.887935i | \(0.652140\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 393.132 | 0.825170 | 0.412585 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412585 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 84.8494 | 0.169683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 886.505 | 1.69165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1042.79 | 1.90145 | 0.950723 | − | 0.310043i | \(-0.100343\pi\) | ||||
0.950723 | + | 0.310043i | \(0.100343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 57.9603 | 0.101125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 552.909 | 0.924200 | 0.462100 | − | 0.886828i | \(-0.347096\pi\) | ||||
0.462100 | + | 0.886828i | \(0.347096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 724.799 | 1.16207 | 0.581036 | − | 0.813878i | \(-0.302647\pi\) | ||||
0.581036 | + | 0.813878i | \(0.302647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1051.67 | 1.61915 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −77.0000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 516.261 | 0.735239 | 0.367620 | − | 0.929976i | \(-0.380173\pi\) | ||||
0.367620 | + | 0.929976i | \(0.380173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −909.349 | −1.24739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1396.82 | −1.84724 | −0.923621 | − | 0.383306i | \(-0.874785\pi\) | ||||
−0.923621 | + | 0.383306i | \(0.874785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1784.98 | −2.27775 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1396.52 | 1.72095 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −329.372 | −0.392285 | −0.196142 | − | 0.980575i | \(-0.562841\pi\) | ||||
−0.196142 | + | 0.980575i | \(0.562841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 362.444 | 0.417522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1486.37 | 1.65731 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −182.658 | −0.197267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6082 | −0.0111042 | −0.00555208 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555208 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −133.335 | −0.135360 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1303.55 | −1.28424 | −0.642118 | − | 0.766606i | \(-0.721944\pi\) | ||||
−0.642118 | + | 0.766606i | \(0.721944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −27.0841 | −0.0259095 | −0.0129547 | − | 0.999916i | \(-0.504124\pi\) | ||||
−0.0129547 | + | 0.999916i | \(0.504124\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 749.623 | 0.696721 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 284.914 | 0.257417 | 0.128709 | − | 0.991682i | \(-0.458917\pi\) | ||||
0.128709 | + | 0.991682i | \(0.458917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −357.655 | −0.314286 | −0.157143 | − | 0.987576i | \(-0.550228\pi\) | ||||
−0.157143 | + | 0.987576i | \(0.550228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2264.03 | 1.93597 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1354.20 | −1.12737 | −0.563685 | − | 0.825990i | \(-0.690617\pi\) | ||||
−0.563685 | + | 0.825990i | \(0.690617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 158.658 | 0.128651 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 627.616 | 0.495924 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −729.783 | −0.562178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1710.61 | 1.25399 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 738.620 | 0.528513 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1253.58 | −0.875886 | −0.437943 | − | 0.899003i | \(-0.644293\pi\) | ||||
−0.437943 | + | 0.899003i | \(0.644293\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −936.120 | −0.638921 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1998.97 | −1.33321 | −0.666605 | − | 0.745411i | \(-0.732253\pi\) | ||||
−0.666605 | + | 0.745411i | \(0.732253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −74.6792 | −0.0486880 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1593.34 | −1.01580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1885.33 | 1.17573 | 0.587863 | − | 0.808960i | \(-0.299969\pi\) | ||||
0.587863 | + | 0.808960i | \(0.299969\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2008.67 | −1.22571 | −0.612853 | − | 0.790197i | \(-0.709978\pi\) | ||||
−0.612853 | + | 0.790197i | \(0.709978\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3327.15 | −1.98721 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −569.555 | −0.333067 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3822.77 | 2.18940 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 306.481 | 0.171960 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2222.24 | −1.22183 | −0.610916 | − | 0.791695i | \(-0.709199\pi\) | ||||
−0.610916 | + | 0.791695i | \(0.709199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1174.25 | −0.632840 | −0.316420 | − | 0.948619i | \(-0.602481\pi\) | ||||
−0.316420 | + | 0.948619i | \(0.602481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1263.71 | −0.667743 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4068.73 | 2.10844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2737.25 | 1.39144 | 0.695720 | − | 0.718313i | \(-0.255085\pi\) | ||||
0.695720 | + | 0.718313i | \(0.255085\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2552.98 | 1.27336 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 64.8667 | 0.0317529 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 310.189 | 0.149055 | 0.0745273 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745273 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1177.98 | −0.555791 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2151.91 | 0.997124 | 0.498562 | − | 0.866854i | \(-0.333862\pi\) | ||||
0.498562 | + | 0.866854i | \(0.333862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 483.938 | 0.220272 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −129.316 | −0.0578306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2368.70 | −1.04098 | −0.520489 | − | 0.853869i | \(-0.674250\pi\) | ||||
−0.520489 | + | 0.853869i | \(0.674250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1176.98 | 0.508408 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2607.62 | −1.10735 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1269.04 | −0.529901 | −0.264950 | − | 0.964262i | \(-0.585356\pi\) | ||||
−0.264950 | + | 0.964262i | \(0.585356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −357.969 | −0.147003 | −0.0735017 | − | 0.997295i | \(-0.523417\pi\) | ||||
−0.0735017 | + | 0.997295i | \(0.523417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2458.92 | 0.993273 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6197.46 | 2.46295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1146.80 | 0.448463 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −651.431 | −0.250713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2230.57 | 0.845016 | 0.422508 | − | 0.906359i | \(-0.361150\pi\) | ||||
0.422508 | + | 0.906359i | \(0.361150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4323.07 | −1.61234 | −0.806169 | − | 0.591685i | \(-0.798463\pi\) | ||||
−0.806169 | + | 0.591685i | \(0.798463\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5544.83 | 2.03627 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −553.415 | −0.200148 | −0.100074 | − | 0.994980i | \(-0.531908\pi\) | ||||
−0.100074 | + | 0.994980i | \(0.531908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1669.85 | −0.594836 | −0.297418 | − | 0.954747i | \(-0.596126\pi\) | ||||
−0.297418 | + | 0.954747i | \(0.596126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6522.33 | 2.28881 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1562.93 | 0.540374 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4682.55 | 1.59533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 112.324 | 0.0377154 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 117.353 | 0.0388396 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3562.75 | −1.16242 | −0.581208 | − | 0.813755i | \(-0.697420\pi\) | ||||
−0.581208 | + | 0.813755i | \(0.697420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3458.28 | 1.11248 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2562.49 | −0.812839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1663.49 | 0.520390 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4533.40 | 1.39881 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5398.08 | −1.64305 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1334.49 | 0.400735 | 0.200368 | − | 0.979721i | \(-0.435786\pi\) | ||||
0.200368 | + | 0.979721i | \(0.435786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2038.09 | 0.603877 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2334.36 | −0.682541 | −0.341271 | − | 0.939965i | \(-0.610857\pi\) | ||||
−0.341271 | + | 0.939965i | \(0.610857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4512.13 | −1.30205 | −0.651026 | − | 0.759055i | \(-0.725661\pi\) | ||||
−0.651026 | + | 0.759055i | \(0.725661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −481.612 | −0.137176 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −173.678 | −0.0488327 | −0.0244164 | − | 0.999702i | \(-0.507773\pi\) | ||||
−0.0244164 | + | 0.999702i | \(0.507773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9107.59 | −2.52814 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3229.06 | 0.885021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4781.56 | 1.29411 | 0.647057 | − | 0.762442i | \(-0.276000\pi\) | ||||
0.647057 | + | 0.762442i | \(0.276000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1574.30 | 0.420787 | 0.210394 | − | 0.977617i | \(-0.432525\pi\) | ||||
0.210394 | + | 0.977617i | \(0.432525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3175.05 | −0.838187 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 838.946 | 0.218768 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −552.389 | −0.142298 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8736.71 | −2.22356 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3835.27 | 0.964462 | 0.482231 | − | 0.876044i | \(-0.339827\pi\) | ||||
0.482231 | + | 0.876044i | \(0.339827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −101.933 | −0.0253300 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11164.5 | −2.74177 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6643.79 | 1.61256 | 0.806281 | − | 0.591533i | \(-0.201477\pi\) | ||||
0.806281 | + | 0.591533i | \(0.201477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2533.81 | 0.607889 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2706.39 | 0.641845 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4597.37 | 1.07789 | 0.538947 | − | 0.842340i | \(-0.318822\pi\) | ||||
0.538947 | + | 0.842340i | \(0.318822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6988.41 | 1.61998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2060.12 | −0.472201 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1944.55 | −0.440749 | −0.220375 | − | 0.975415i | \(-0.570728\pi\) | ||||
−0.220375 | + | 0.975415i | \(0.570728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1524.87 | 0.341806 | 0.170903 | − | 0.985288i | \(-0.445332\pi\) | ||||
0.170903 | + | 0.985288i | \(0.445332\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2266.98 | 0.502579 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1849.54 | −0.405570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2785.41 | 0.604184 | 0.302092 | − | 0.953279i | \(-0.402315\pi\) | ||||
0.302092 | + | 0.953279i | \(0.402315\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2880.52 | 0.618109 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1731.31 | −0.367549 | −0.183775 | − | 0.982968i | \(-0.558832\pi\) | ||||
−0.183775 | + | 0.982968i | \(0.558832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2587.78 | −0.543561 | −0.271780 | − | 0.962359i | \(-0.587612\pi\) | ||||
−0.271780 | + | 0.962359i | \(0.587612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1142.47 | −0.237454 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1914.44 | 0.393749 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5956.06 | 1.21231 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −66.3515 | −0.0133663 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2948.77 | −0.587949 | −0.293974 | − | 0.955813i | \(-0.594978\pi\) | ||||
−0.293974 | + | 0.955813i | \(0.594978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7137.97 | −1.40877 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1023.68 | 0.199999 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 479.808 | 0.0928026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1047.67 | −0.200619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8153.31 | −1.54586 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6730.95 | 1.26365 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −674.370 | −0.125369 | −0.0626846 | − | 0.998033i | \(-0.519966\pi\) | ||||
−0.0626846 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −169.403 | −0.0311877 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6705.01 | 1.22253 | 0.611264 | − | 0.791426i | \(-0.290661\pi\) | ||||
0.611264 | + | 0.791426i | \(0.290661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9621.90 | −1.73758 | −0.868789 | − | 0.495182i | \(-0.835101\pi\) | ||||
−0.868789 | + | 0.495182i | \(0.835101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1452.74 | 0.259849 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4107.58 | 0.727774 | 0.363887 | − | 0.931443i | \(-0.381449\pi\) | ||||
0.363887 | + | 0.931443i | \(0.381449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2456.03 | −0.431069 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1782.05 | 0.309858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1112.24 | 0.191599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8705.93 | 1.48590 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2237.03 | −0.378312 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3723.61 | −0.623979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8663.71 | 1.43867 | 0.719336 | − | 0.694662i | \(-0.244446\pi\) | ||||
0.719336 | + | 0.694662i | \(0.244446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4387.59 | 0.722038 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17853.9 | 2.91183 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1631.87 | 0.263780 | 0.131890 | − | 0.991264i | \(-0.457895\pi\) | ||||
0.131890 | + | 0.991264i | \(0.457895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8470.15 | −1.35704 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2614.05 | −0.415128 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 992.358 | 0.154860 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4472.09 | −0.691858 | −0.345929 | − | 0.938261i | \(-0.612436\pi\) | ||||
−0.345929 | + | 0.938261i | \(0.612436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3460.47 | 0.530758 | 0.265379 | − | 0.964144i | \(-0.414503\pi\) | ||||
0.265379 | + | 0.964144i | \(0.414503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4818.52 | −0.732746 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1926.77 | −0.290514 | −0.145257 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145257 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9466.54 | 1.41530 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4564.58 | −0.676704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1256.66 | −0.184747 | −0.0923733 | − | 0.995724i | \(-0.529445\pi\) | ||||
−0.0923733 | + | 0.995724i | \(0.529445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6745.18 | −0.983406 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 756.819 | 0.109429 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12409.5 | 1.77957 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6976.14 | −0.992238 | −0.496119 | − | 0.868254i | \(-0.665242\pi\) | ||||
−0.496119 | + | 0.868254i | \(0.665242\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3315.09 | 0.467687 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2857.19 | 0.399832 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1727.72 | −0.239834 | −0.119917 | − | 0.992784i | \(-0.538263\pi\) | ||||
−0.119917 | + | 0.992784i | \(0.538263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4619.85 | 0.636181 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11560.7 | 1.57933 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 439.486 | 0.0595643 | 0.0297822 | − | 0.999556i | \(-0.490519\pi\) | ||||
0.0297822 | + | 0.999556i | \(0.490519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7840.79 | −1.05432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5054.81 | −0.674382 | −0.337191 | − | 0.941436i | \(-0.609477\pi\) | ||||
−0.337191 | + | 0.941436i | \(0.609477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1318.34 | −0.174517 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1814.16 | −0.238292 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8651.92 | −1.12769 | −0.563843 | − | 0.825882i | \(-0.690678\pi\) | ||||
−0.563843 | + | 0.825882i | \(0.690678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −966.095 | −0.124955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12502.9 | −1.60481 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8839.08 | 1.12593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5525.88 | −0.698579 | −0.349290 | − | 0.937015i | \(-0.613577\pi\) | ||||
−0.349290 | + | 0.937015i | \(0.613577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −467.096 | −0.0586067 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4581.53 | 0.570551 | 0.285275 | − | 0.958446i | \(-0.407915\pi\) | ||||
0.285275 | + | 0.958446i | \(0.407915\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12304.5 | 1.52092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15569.3 | −1.91023 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3981.70 | −0.484928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15452.5 | 1.86816 | 0.934079 | − | 0.357067i | \(-0.116223\pi\) | ||||
0.934079 | + | 0.357067i | \(0.116223\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11792.2 | 1.41524 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2918.33 | −0.347704 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23915.5 | −2.82883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12563.6 | −1.47540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12626.7 | 1.47221 | 0.736105 | − | 0.676867i | \(-0.236663\pi\) | ||||
0.736105 | + | 0.676867i | \(0.236663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7718.68 | −0.893553 | −0.446776 | − | 0.894646i | \(-0.647428\pi\) | ||||
−0.446776 | + | 0.894646i | \(0.647428\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6447.87 | −0.741150 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17529.4 | −2.00071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2751.92 | 0.311885 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3562.40 | −0.400919 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7452.18 | −0.832852 | −0.416426 | − | 0.909170i | \(-0.636717\pi\) | ||||
−0.416426 | + | 0.909170i | \(0.636717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6247.78 | −0.693416 | −0.346708 | − | 0.937973i | \(-0.612700\pi\) | ||||
−0.346708 | + | 0.937973i | \(0.612700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23910.3 | 2.63543 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −98.8611 | −0.0108219 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15177.2 | −1.65004 | −0.825020 | − | 0.565104i | \(-0.808836\pi\) | ||||
−0.825020 | + | 0.565104i | \(0.808836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 593.946 | 0.0641341 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6242.85 | −0.669541 | −0.334770 | − | 0.942300i | \(-0.608659\pi\) | ||||
−0.334770 | + | 0.942300i | \(0.608659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5639.29 | −0.600737 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13899.5 | −1.47074 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15058.3 | −1.58273 | −0.791366 | − | 0.611343i | \(-0.790630\pi\) | ||||
−0.791366 | + | 0.611343i | \(0.790630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3008.41 | −0.314103 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7344.57 | −0.761762 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6205.53 | 0.639384 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2560.84 | 0.262125 | 0.131063 | − | 0.991374i | \(-0.458161\pi\) | ||||
0.131063 | + | 0.991374i | \(0.458161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9702.12 | 0.986615 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9820.30 | −0.992141 | −0.496071 | − | 0.868282i | \(-0.665224\pi\) | ||||
−0.496071 | + | 0.868282i | \(0.665224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14118.1 | −1.41711 | −0.708557 | − | 0.705653i | \(-0.750654\pi\) | ||||
−0.708557 | + | 0.705653i | \(0.750654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25448.7 | 2.53797 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2199.62 | −0.217958 | −0.108979 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108979 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7299.52 | 0.718679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17120.7 | 1.67490 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1646.33 | 0.160039 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1793.80 | −0.173274 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4947.56 | 0.474913 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10629.7 | 1.01395 | 0.506977 | − | 0.861960i | \(-0.330763\pi\) | ||||
0.506977 | + | 0.861960i | \(0.330763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18742.1 | 1.77665 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 405.722 | 0.0382215 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −181.627 | −0.0170047 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13822.7 | 1.28617 | 0.643086 | − | 0.765794i | \(-0.277654\pi\) | ||||
0.643086 | + | 0.765794i | \(0.277654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1940.14 | 0.179420 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4112.53 | 0.377996 | 0.188998 | − | 0.981977i | \(-0.439476\pi\) | ||||
0.188998 | + | 0.981977i | \(0.439476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23277.5 | −2.12650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2282.87 | −0.207288 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3870.36 | 0.349315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14392.5 | 1.29117 | 0.645587 | − | 0.763687i | \(-0.276613\pi\) | ||||
0.645587 | + | 0.763687i | \(0.276613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13459.6 | 1.20026 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18788.3 | −1.66546 | −0.832732 | − | 0.553676i | \(-0.813225\pi\) | ||||
−0.832732 | + | 0.553676i | \(0.813225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22318.5 | −1.96665 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3026.89 | 0.265145 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15738.9 | 1.37056 | 0.685278 | − | 0.728282i | \(-0.259681\pi\) | ||||
0.685278 | + | 0.728282i | \(0.259681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5073.59 | 0.439222 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 992.824 | 0.0854469 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −463.716 | −0.0396772 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5851.38 | 0.497763 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14815.5 | −1.25304 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3426.41 | −0.288126 | −0.144063 | − | 0.989569i | \(-0.546017\pi\) | ||||
−0.144063 | + | 0.989569i | \(0.546017\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17110.3 | −1.43056 | −0.715279 | − | 0.698839i | \(-0.753700\pi\) | ||||
−0.715279 | + | 0.698839i | \(0.753700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7361.68 | 0.611981 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24775.2 | −2.04786 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12081.1 | −0.992942 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5053.44 | −0.412996 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14160.8 | 1.15079 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4878.10 | 0.394203 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7937.45 | −0.637851 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4624.29 | 0.367493 | 0.183746 | − | 0.982974i | \(-0.441177\pi\) | ||||
0.183746 | + | 0.982974i | \(0.441177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2238.99 | −0.176951 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6123.53 | −0.481291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2710.72 | 0.211887 | 0.105943 | − | 0.994372i | \(-0.466214\pi\) | ||||
0.105943 | + | 0.994372i | \(0.466214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4765.29 | 0.370451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2382.00 | −0.184168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3613.83 | 0.277894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38763.3 | 2.96470 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11574.4 | 0.880476 | 0.440238 | − | 0.897881i | \(-0.354894\pi\) | ||||
0.440238 | + | 0.897881i | \(0.354894\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7749.40 | −0.586341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7172.91 | 0.539823 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3321.46 | 0.248637 | 0.124319 | − | 0.992242i | \(-0.460326\pi\) | ||||
0.124319 | + | 0.992242i | \(0.460326\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23185.8 | −1.72643 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6365.45 | −0.471470 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11684.6 | −0.860889 | −0.430444 | − | 0.902617i | \(-0.641643\pi\) | ||||
−0.430444 | + | 0.902617i | \(0.641643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16714.8 | −1.22503 | −0.612517 | − | 0.790458i | \(-0.709843\pi\) | ||||
−0.612517 | + | 0.790458i | \(0.709843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13951.5 | 1.01716 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1558.10 | 0.113004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26798.6 | 1.93352 | 0.966759 | − | 0.255690i | \(-0.0823025\pi\) | ||||
0.966759 | + | 0.255690i | \(0.0823025\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27039.5 | −1.94080 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9777.75 | −0.698192 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4489.86 | −0.318956 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10745.6 | 0.759448 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10893.3 | −0.765955 | −0.382978 | − | 0.923758i | \(-0.625101\pi\) | ||||
−0.382978 | + | 0.923758i | \(0.625101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2535.26 | −0.177357 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3461.45 | −0.240922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27442.2 | −1.90037 | −0.950183 | − | 0.311693i | \(-0.899104\pi\) | ||||
−0.950183 | + | 0.311693i | \(0.899104\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12494.9 | −0.860907 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10444.4 | −0.716016 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14171.3 | −0.966650 | −0.483325 | − | 0.875441i | \(-0.660571\pi\) | ||||
−0.483325 | + | 0.875441i | \(0.660571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7536.43 | −0.511510 | −0.255755 | − | 0.966742i | \(-0.582324\pi\) | ||||
−0.255755 | + | 0.966742i | \(0.582324\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12640.0 | 0.853632 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2071.68 | 0.139216 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18503.3 | −1.23727 | −0.618637 | − | 0.785677i | \(-0.712315\pi\) | ||||
−0.618637 | + | 0.785677i | \(0.712315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9775.64 | 0.650458 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27542.9 | −1.82367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6228.56 | −0.410390 | −0.205195 | − | 0.978721i | \(-0.565783\pi\) | ||||
−0.205195 | + | 0.978721i | \(0.565783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29288.0 | 1.92033 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25238.3 | −1.64677 | −0.823383 | − | 0.567487i | \(-0.807916\pi\) | ||||
−0.823383 | + | 0.567487i | \(0.807916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12499.1 | 0.811601 | 0.405801 | − | 0.913962i | \(-0.366993\pi\) | ||||
0.405801 | + | 0.913962i | \(0.366993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −862.371 | −0.0557259 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2305.60 | −0.148270 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8371.38 | −0.535768 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 734.008 | 0.0467520 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37737.4 | −2.39219 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16328.7 | 1.03017 | 0.515083 | − | 0.857140i | \(-0.327761\pi\) | ||||
0.515083 | + | 0.857140i | \(0.327761\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22283.9 | −1.39922 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21463.0 | −1.34131 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2537.11 | 0.157808 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6702.00 | 0.414909 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20978.0 | −1.29264 | −0.646320 | − | 0.763067i | \(-0.723693\pi\) | ||||
−0.646320 | + | 0.763067i | \(0.723693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15007.0 | 0.920401 | 0.460200 | − | 0.887815i | \(-0.347778\pi\) | ||||
0.460200 | + | 0.887815i | \(0.347778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16027.6 | −0.978430 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22590.1 | 1.37266 | 0.686330 | − | 0.727291i | \(-0.259221\pi\) | ||||
0.686330 | + | 0.727291i | \(0.259221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4585.95 | 0.277372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10404.6 | 0.626404 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2700.87 | 0.161858 | 0.0809289 | − | 0.996720i | \(-0.474211\pi\) | ||||
0.0809289 | + | 0.996720i | \(0.474211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34225.0 | −2.04165 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8785.53 | 0.521699 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1350.92 | 0.0798548 | 0.0399274 | − | 0.999203i | \(-0.487287\pi\) | ||||
0.0399274 | + | 0.999203i | \(0.487287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18705.0 | 1.10066 | 0.550332 | − | 0.834946i | \(-0.314501\pi\) | ||||
0.550332 | + | 0.834946i | \(0.314501\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33763.4 | −1.97777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1278.61 | −0.0745598 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2069.02 | 0.120109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8346.83 | 0.482372 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4324.45 | −0.248798 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20297.5 | 1.16257 | 0.581287 | − | 0.813699i | \(-0.302549\pi\) | ||||
0.581287 | + | 0.813699i | \(0.302549\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15647.4 | −0.892251 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27278.3 | 1.54858 | 0.774292 | − | 0.632828i | \(-0.218106\pi\) | ||||
0.774292 | + | 0.632828i | \(0.218106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −74.2577 | −0.00419698 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14600.7 | −0.821587 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24957.7 | 1.39821 | 0.699107 | − | 0.715017i | \(-0.253581\pi\) | ||||
0.699107 | + | 0.715017i | \(0.253581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32279.4 | 1.80048 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28222.0 | −1.56730 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21134.1 | 1.16857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21736.3 | −1.19665 | −0.598327 | − | 0.801252i | \(-0.704168\pi\) | ||||
−0.598327 | + | 0.801252i | \(0.704168\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −933.343 | −0.0511613 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34391.1 | −1.87702 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28512.8 | −1.54950 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1086.30 | −0.0587809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31392.4 | −1.69141 | −0.845703 | − | 0.533654i | \(-0.820819\pi\) | ||||
−0.845703 | + | 0.533654i | \(0.820819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3861.69 | −0.207178 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −56965.3 | −3.04317 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9124.84 | −0.485396 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18502.6 | 0.980087 | 0.490043 | − | 0.871698i | \(-0.336981\pi\) | ||||
0.490043 | + | 0.871698i | \(0.336981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6257.77 | 0.330077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2202.14 | 0.115667 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9751.55 | −0.510052 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29907.2 | 1.55775 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7460.88 | 0.386987 | 0.193494 | − | 0.981102i | \(-0.438018\pi\) | ||||
0.193494 | + | 0.981102i | \(0.438018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −189.589 | −0.00979286 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9846.79 | 0.506509 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37541.5 | 1.92311 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29929.1 | −1.52684 | −0.763418 | − | 0.645905i | \(-0.776480\pi\) | ||||
−0.763418 | + | 0.645905i | \(0.776480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4693.44 | 0.238452 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15603.4 | 0.789486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14889.8 | 0.750297 | 0.375148 | − | 0.926965i | \(-0.377592\pi\) | ||||
0.375148 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5247.36 | 0.263336 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11470.7 | −0.573307 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27119.4 | −1.34994 | −0.674969 | − | 0.737846i | \(-0.735843\pi\) | ||||
−0.674969 | + | 0.737846i | \(0.735843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3455.03 | −0.171287 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19717.6 | 0.973580 | 0.486790 | − | 0.873519i | \(-0.338168\pi\) | ||||
0.486790 | + | 0.873519i | \(0.338168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38047.7 | −1.87109 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16931.4 | −0.829298 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1994.40 | 0.0972946 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −986.613 | −0.0479388 | −0.0239694 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239694 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23988.5 | 1.16094 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20104.7 | −0.969118 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34780.1 | 1.66989 | 0.834944 | − | 0.550335i | \(-0.185500\pi\) | ||||
0.834944 | + | 0.550335i | \(0.185500\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −637.563 | −0.0304902 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39587.1 | −1.88572 | −0.942858 | − | 0.333195i | \(-0.891873\pi\) | ||||
−0.942858 | + | 0.333195i | \(0.891873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2503.59 | −0.118789 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21636.4 | −1.02257 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21586.4 | −1.01622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30842.8 | 1.44632 | 0.723160 | − | 0.690681i | \(-0.242689\pi\) | ||||
0.723160 | + | 0.690681i | \(0.242689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41555.0 | 1.94107 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17396.5 | −0.809455 | −0.404728 | − | 0.914437i | \(-0.632634\pi\) | ||||
−0.404728 | + | 0.914437i | \(0.632634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39957.0 | 1.85200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15848.2 | 0.731727 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2917.74 | −0.134196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6082.00 | −0.278657 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20778.3 | −0.948349 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46865.4 | 2.13082 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17731.1 | 0.803106 | 0.401553 | − | 0.915836i | \(-0.368471\pi\) | ||||
0.401553 | + | 0.915836i | \(0.368471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28755.2 | 1.29748 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9479.43 | −0.426106 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20355.5 | 0.911532 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 43710.4 | 1.95000 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17460.0 | −0.775992 | −0.387996 | − | 0.921661i | \(-0.626833\pi\) | ||||
−0.387996 | + | 0.921661i | \(0.626833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55457.7 | 2.45551 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3992.43 | −0.176112 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7972.79 | −0.350378 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1110.60 | 0.0486257 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12162.6 | −0.530538 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30027.9 | 1.30498 | 0.652488 | − | 0.757799i | \(-0.273725\pi\) | ||||
0.652488 | + | 0.757799i | \(0.273725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25186.5 | −1.09053 | −0.545263 | − | 0.838265i | \(-0.683570\pi\) | ||||
−0.545263 | + | 0.838265i | \(0.683570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9537.62 | 0.411438 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5310.86 | 0.228259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1596.71 | 0.0683743 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4393.31 | 0.187442 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 614.667 | 0.0261291 | 0.0130646 | − | 0.999915i | \(-0.495841\pi\) | ||||
0.0130646 | + | 0.999915i | \(0.495841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29936.2 | 1.26794 | 0.633968 | − | 0.773359i | \(-0.281425\pi\) | ||||
0.633968 | + | 0.773359i | \(0.281425\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11568.3 | −0.488192 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25253.2 | −1.06184 | −0.530918 | − | 0.847423i | \(-0.678153\pi\) | ||||
−0.530918 | + | 0.847423i | \(0.678153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19136.9 | −0.801751 | −0.400876 | − | 0.916132i | \(-0.631294\pi\) | ||||
−0.400876 | + | 0.916132i | \(0.631294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17421.9 | 0.727267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5108.48 | −0.212483 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36843.6 | 1.52698 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22115.2 | −0.913279 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20495.3 | −0.843359 | −0.421679 | − | 0.906745i | \(-0.638559\pi\) | ||||
−0.421679 | + | 0.906745i | \(0.638559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25462.8 | 1.04403 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10828.8 | −0.442426 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8285.66 | 0.337320 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16185.8 | −0.654294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3354.28 | 0.135115 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18030.4 | −0.723739 | −0.361870 | − | 0.932229i | \(-0.617861\pi\) | ||||
−0.361870 | + | 0.932229i | \(0.617861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2214.06 | −0.0885606 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48876.2 | −1.94817 | −0.974083 | − | 0.226192i | \(-0.927372\pi\) | ||||
−0.974083 | + | 0.226192i | \(0.927372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31747.6 | 1.26102 | 0.630508 | − | 0.776182i | \(-0.282846\pi\) | ||||
0.630508 | + | 0.776182i | \(0.282846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11974.3 | 0.473963 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36175.9 | 1.42693 | 0.713466 | − | 0.700689i | \(-0.247124\pi\) | ||||
0.713466 | + | 0.700689i | \(0.247124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40555.3 | −1.59413 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37253.4 | 1.45928 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5678.87 | −0.221683 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53993.2 | 2.10045 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −128.586 | −0.00498509 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5170.34 | 0.199759 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22724.7 | 0.874980 | 0.437490 | − | 0.899223i | \(-0.355868\pi\) | ||||
0.437490 | + | 0.899223i | \(0.355868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18443.7 | −0.707725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6148.28 | −0.235120 | −0.117560 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117560 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34001.7 | −1.29586 | −0.647932 | − | 0.761698i | \(-0.724366\pi\) | ||||
−0.647932 | + | 0.761698i | \(0.724366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −44645.9 | −1.69577 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38642.9 | 1.46280 | 0.731398 | − | 0.681950i | \(-0.238868\pi\) | ||||
0.731398 | + | 0.681950i | \(0.238868\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8775.08 | −0.331054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10002.8 | 0.376103 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5675.02 | 0.212662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21727.6 | −0.811479 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3001.05 | 0.111708 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53059.3 | 1.96844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42553.6 | −1.57344 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6552.84 | −0.241489 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6128.91 | −0.225118 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5093.73 | −0.186477 | −0.0932385 | − | 0.995644i | \(-0.529722\pi\) | ||||
−0.0932385 | + | 0.995644i | \(0.529722\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15800.8 | −0.576543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19515.5 | −0.709744 | −0.354872 | − | 0.934915i | \(-0.615476\pi\) | ||||
−0.354872 | + | 0.934915i | \(0.615476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15365.0 | 0.556965 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 42100.1 | 1.52108 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13992.8 | −0.503906 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3173.14 | −0.113898 | −0.0569490 | − | 0.998377i | \(-0.518137\pi\) | ||||
−0.0569490 | + | 0.998377i | \(0.518137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4217.99 | −0.150909 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28628.4 | 1.02093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60862.2 | 2.16339 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −328.296 | −0.0116318 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2919.60 | −0.103110 | −0.0515548 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515548 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −522.754 | −0.0184023 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41937.9 | 1.47158 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19634.8 | 0.686766 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36268.3 | 1.26450 | 0.632248 | − | 0.774766i | \(-0.282132\pi\) | ||||
0.632248 | + | 0.774766i | \(0.282132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60182.2 | −2.09156 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3009.02 | −0.104242 | −0.0521208 | − | 0.998641i | \(-0.516598\pi\) | ||||
−0.0521208 | + | 0.998641i | \(0.516598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2534.36 | 0.0875187 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11153.4 | −0.383936 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6520.30 | −0.223739 | −0.111870 | − | 0.993723i | \(-0.535684\pi\) | ||||
−0.111870 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37528.5 | 1.28369 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25691.7 | 0.876036 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56034.5 | 1.90465 | 0.952326 | − | 0.305081i | \(-0.0986835\pi\) | ||||
0.952326 | + | 0.305081i | \(0.0986835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38190.3 | 1.29404 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15361.7 | −0.518886 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13197.3 | 0.444383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26682.1 | 0.895644 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3453.54 | 0.115565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −74016.7 | −2.46910 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18669.7 | 0.620865 | 0.310433 | − | 0.950595i | \(-0.399526\pi\) | ||||
0.310433 | + | 0.950595i | \(0.399526\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6956.72 | 0.230632 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5467.04 | −0.180686 | −0.0903428 | − | 0.995911i | \(-0.528796\pi\) | ||||
−0.0903428 | + | 0.995911i | \(0.528796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14060.7 | −0.463273 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 54453.0 | 1.78861 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46112.2 | 1.50999 | 0.754996 | − | 0.655730i | \(-0.227639\pi\) | ||||
0.754996 | + | 0.655730i | \(0.227639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3623.09 | 0.118278 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4335.26 | −0.141095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28357.6 | −0.920109 | −0.460055 | − | 0.887891i | \(-0.652170\pi\) | ||||
−0.460055 | + | 0.887891i | \(0.652170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9475.20 | −0.306503 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23290.1 | −0.751095 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1386.91 | −0.0445917 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34281.1 | 1.09886 | 0.549432 | − | 0.835539i | \(-0.314844\pi\) | ||||
0.549432 | + | 0.835539i | \(0.314844\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54189.0 | 1.73176 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28590.0 | −0.910920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20833.1 | 0.661775 | 0.330888 | − | 0.943670i | \(-0.392652\pi\) | ||||
0.330888 | + | 0.943670i | \(0.392652\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33685.8 | −1.06684 |
(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 | 1232.4.a.v.1.4 | 4 | ||
4.3 | odd | 2 | 308.4.a.d.1.1 | ✓ | 4 | ||
28.27 | even | 2 | 2156.4.a.f.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.4.a.d.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
1232.4.a.v.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2156.4.a.f.1.4 | 4 | 28.27 | even | 2 |