Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-5.36472i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.i.337.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.36472i | − 1.89672i | −0.317201 | − | 0.948358i | \(-0.602743\pi\) | ||||
0.317201 | − | 0.948358i | \(-0.397257\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −20.7803 | −2.59753 | ||||||||
\(5\) | 2.69631i | 0.241165i | 0.992703 | + | 0.120583i | \(0.0384763\pi\) | ||||
−0.992703 | + | 0.120583i | \(0.961524\pi\) | |||||||
\(6\) | − 16.0942i | − 1.09507i | ||||||||
\(7\) | − 15.2025i | − 0.820856i | −0.911893 | − | 0.410428i | \(-0.865379\pi\) | ||||
0.911893 | − | 0.410428i | \(-0.134621\pi\) | |||||||
\(8\) | 68.5626i | 3.03007i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 14.4650 | 0.457423 | ||||||||
\(11\) | 66.8848i | 1.83332i | 0.399666 | + | 0.916661i | \(0.369126\pi\) | ||||
−0.399666 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(12\) | −62.3408 | −1.49969 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −81.5570 | −1.55693 | ||||||||
\(15\) | 8.08894i | 0.139237i | ||||||||
\(16\) | 201.577 | 3.14965 | ||||||||
\(17\) | −4.16354 | −0.0594004 | −0.0297002 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0297002 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(18\) | − 48.2825i | − 0.632239i | ||||||||
\(19\) | 26.0850i | 0.314963i | 0.987522 | + | 0.157482i | \(0.0503375\pi\) | ||||
−0.987522 | + | 0.157482i | \(0.949662\pi\) | |||||||
\(20\) | − 56.0301i | − 0.626436i | ||||||||
\(21\) | − 45.6074i | − 0.473921i | ||||||||
\(22\) | 358.819 | 3.47729 | ||||||||
\(23\) | −47.3242 | −0.429034 | −0.214517 | − | 0.976720i | \(-0.568818\pi\) | ||||
−0.214517 | + | 0.976720i | \(0.568818\pi\) | |||||||
\(24\) | 205.688i | 1.74941i | ||||||||
\(25\) | 117.730 | 0.941839 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 315.911i | 2.13220i | ||||||||
\(29\) | 257.007 | 1.64569 | 0.822845 | − | 0.568266i | \(-0.192386\pi\) | ||||
0.822845 | + | 0.568266i | \(0.192386\pi\) | |||||||
\(30\) | 43.3949 | 0.264093 | ||||||||
\(31\) | 206.242i | 1.19491i | 0.801903 | + | 0.597455i | \(0.203821\pi\) | ||||
−0.801903 | + | 0.597455i | \(0.796179\pi\) | |||||||
\(32\) | − 532.906i | − 2.94392i | ||||||||
\(33\) | 200.655i | 1.05847i | ||||||||
\(34\) | 22.3362i | 0.112666i | ||||||||
\(35\) | 40.9906 | 0.197962 | ||||||||
\(36\) | −187.022 | −0.865845 | ||||||||
\(37\) | − 175.686i | − 0.780611i | −0.920685 | − | 0.390305i | \(-0.872369\pi\) | ||||
0.920685 | − | 0.390305i | \(-0.127631\pi\) | |||||||
\(38\) | 139.939 | 0.597396 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −184.866 | −0.730748 | ||||||||
\(41\) | 156.463i | 0.595984i | 0.954568 | + | 0.297992i | \(0.0963169\pi\) | ||||
−0.954568 | + | 0.297992i | \(0.903683\pi\) | |||||||
\(42\) | −244.671 | −0.898895 | ||||||||
\(43\) | −51.9845 | −0.184362 | −0.0921809 | − | 0.995742i | \(-0.529384\pi\) | ||||
−0.0921809 | + | 0.995742i | \(0.529384\pi\) | |||||||
\(44\) | − 1389.88i | − 4.76211i | ||||||||
\(45\) | 24.2668i | 0.0803885i | ||||||||
\(46\) | 253.881i | 0.813755i | ||||||||
\(47\) | 354.222i | 1.09933i | 0.835384 | + | 0.549666i | \(0.185245\pi\) | ||||
−0.835384 | + | 0.549666i | \(0.814755\pi\) | |||||||
\(48\) | 604.732 | 1.81845 | ||||||||
\(49\) | 111.885 | 0.326196 | ||||||||
\(50\) | − 631.588i | − 1.78640i | ||||||||
\(51\) | −12.4906 | −0.0342948 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4723 | −0.0271412 | −0.0135706 | − | 0.999908i | \(-0.504320\pi\) | ||||
−0.0135706 | + | 0.999908i | \(0.504320\pi\) | |||||||
\(54\) | − 144.848i | − 0.365023i | ||||||||
\(55\) | −180.342 | −0.442134 | ||||||||
\(56\) | 1042.32 | 2.48725 | ||||||||
\(57\) | 78.2550i | 0.181844i | ||||||||
\(58\) | − 1378.77i | − 3.12141i | ||||||||
\(59\) | − 445.114i | − 0.982185i | −0.871107 | − | 0.491092i | \(-0.836598\pi\) | ||||
0.871107 | − | 0.491092i | \(-0.163402\pi\) | |||||||
\(60\) | − 168.090i | − 0.361673i | ||||||||
\(61\) | 119.696 | 0.251238 | 0.125619 | − | 0.992079i | \(-0.459908\pi\) | ||||
0.125619 | + | 0.992079i | \(0.459908\pi\) | |||||||
\(62\) | 1106.43 | 2.26640 | ||||||||
\(63\) | − 136.822i | − 0.273619i | ||||||||
\(64\) | −1246.28 | −2.43413 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1076.46 | 2.00761 | ||||||||
\(67\) | − 22.4078i | − 0.0408589i | −0.999791 | − | 0.0204294i | \(-0.993497\pi\) | ||||
0.999791 | − | 0.0204294i | \(-0.00650334\pi\) | |||||||
\(68\) | 86.5195 | 0.154295 | ||||||||
\(69\) | −141.973 | −0.247703 | ||||||||
\(70\) | − 219.903i | − 0.375478i | ||||||||
\(71\) | 285.207i | 0.476731i | 0.971176 | + | 0.238365i | \(0.0766116\pi\) | ||||
−0.971176 | + | 0.238365i | \(0.923388\pi\) | |||||||
\(72\) | 617.064i | 1.01002i | ||||||||
\(73\) | − 740.989i | − 1.18803i | −0.804454 | − | 0.594015i | \(-0.797542\pi\) | ||||
0.804454 | − | 0.594015i | \(-0.202458\pi\) | |||||||
\(74\) | −942.507 | −1.48060 | ||||||||
\(75\) | 353.190 | 0.543771 | ||||||||
\(76\) | − 542.053i | − 0.818128i | ||||||||
\(77\) | 1016.81 | 1.50489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −547.679 | −0.779983 | −0.389992 | − | 0.920818i | \(-0.627522\pi\) | ||||
−0.389992 | + | 0.920818i | \(0.627522\pi\) | |||||||
\(80\) | 543.516i | 0.759586i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 839.378 | 1.13041 | ||||||||
\(83\) | 603.056i | 0.797518i | 0.917056 | + | 0.398759i | \(0.130559\pi\) | ||||
−0.917056 | + | 0.398759i | \(0.869441\pi\) | |||||||
\(84\) | 947.734i | 1.23103i | ||||||||
\(85\) | − 11.2262i | − 0.0143253i | ||||||||
\(86\) | 278.882i | 0.349682i | ||||||||
\(87\) | 771.021 | 0.950139 | ||||||||
\(88\) | −4585.80 | −5.55509 | ||||||||
\(89\) | − 215.668i | − 0.256863i | −0.991718 | − | 0.128431i | \(-0.959006\pi\) | ||||
0.991718 | − | 0.128431i | \(-0.0409942\pi\) | |||||||
\(90\) | 130.185 | 0.152474 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 983.409 | 1.11443 | ||||||||
\(93\) | 618.726i | 0.689881i | ||||||||
\(94\) | 1900.31 | 2.08512 | ||||||||
\(95\) | −70.3333 | −0.0759583 | ||||||||
\(96\) | − 1598.72i | − 1.69967i | ||||||||
\(97\) | 1447.50i | 1.51517i | 0.652735 | + | 0.757586i | \(0.273622\pi\) | ||||
−0.652735 | + | 0.757586i | \(0.726378\pi\) | |||||||
\(98\) | − 600.233i | − 0.618700i | ||||||||
\(99\) | 601.964i | 0.611107i | ||||||||
\(100\) | −2446.46 | −2.44646 | ||||||||
\(101\) | 883.450 | 0.870362 | 0.435181 | − | 0.900343i | \(-0.356684\pi\) | ||||
0.435181 | + | 0.900343i | \(0.356684\pi\) | |||||||
\(102\) | 67.0087i | 0.0650476i | ||||||||
\(103\) | −1251.74 | −1.19745 | −0.598726 | − | 0.800954i | \(-0.704326\pi\) | ||||
−0.598726 | + | 0.800954i | \(0.704326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 122.972 | 0.114293 | ||||||||
\(106\) | 56.1812i | 0.0514792i | ||||||||
\(107\) | −341.614 | −0.308645 | −0.154323 | − | 0.988021i | \(-0.549319\pi\) | ||||
−0.154323 | + | 0.988021i | \(0.549319\pi\) | |||||||
\(108\) | −561.067 | −0.499896 | ||||||||
\(109\) | 775.177i | 0.681179i | 0.940212 | + | 0.340589i | \(0.110627\pi\) | ||||
−0.940212 | + | 0.340589i | \(0.889373\pi\) | |||||||
\(110\) | 967.487i | 0.838603i | ||||||||
\(111\) | − 527.058i | − 0.450686i | ||||||||
\(112\) | − 3064.47i | − 2.58541i | ||||||||
\(113\) | 1279.05 | 1.06480 | 0.532402 | − | 0.846492i | \(-0.321290\pi\) | ||||
0.532402 | + | 0.846492i | \(0.321290\pi\) | |||||||
\(114\) | 419.816 | 0.344907 | ||||||||
\(115\) | − 127.601i | − 0.103468i | ||||||||
\(116\) | −5340.67 | −4.27473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2387.91 | −1.86293 | ||||||||
\(119\) | 63.2961i | 0.0487592i | ||||||||
\(120\) | −554.599 | −0.421898 | ||||||||
\(121\) | −3142.58 | −2.36107 | ||||||||
\(122\) | − 642.137i | − 0.476528i | ||||||||
\(123\) | 469.388i | 0.344091i | ||||||||
\(124\) | − 4285.77i | − 3.10382i | ||||||||
\(125\) | 654.476i | 0.468305i | ||||||||
\(126\) | −734.013 | −0.518977 | ||||||||
\(127\) | 1113.82 | 0.778233 | 0.389117 | − | 0.921188i | \(-0.372780\pi\) | ||||
0.389117 | + | 0.921188i | \(0.372780\pi\) | |||||||
\(128\) | 2422.68i | 1.67294i | ||||||||
\(129\) | −155.953 | −0.106441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2100.12 | 1.40068 | 0.700339 | − | 0.713811i | \(-0.253032\pi\) | ||||
0.700339 | + | 0.713811i | \(0.253032\pi\) | |||||||
\(132\) | − 4169.65i | − 2.74941i | ||||||||
\(133\) | 396.556 | 0.258540 | ||||||||
\(134\) | −120.211 | −0.0774977 | ||||||||
\(135\) | 72.8004i | 0.0464123i | ||||||||
\(136\) | − 285.463i | − 0.179987i | ||||||||
\(137\) | 1205.02i | 0.751471i | 0.926727 | + | 0.375736i | \(0.122610\pi\) | ||||
−0.926727 | + | 0.375736i | \(0.877390\pi\) | |||||||
\(138\) | 761.643i | 0.469822i | ||||||||
\(139\) | 322.890 | 0.197030 | 0.0985149 | − | 0.995136i | \(-0.468591\pi\) | ||||
0.0985149 | + | 0.995136i | \(0.468591\pi\) | |||||||
\(140\) | −851.796 | −0.514213 | ||||||||
\(141\) | 1062.67i | 0.634700i | ||||||||
\(142\) | 1530.06 | 0.904223 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1814.20 | 1.04988 | ||||||||
\(145\) | 692.971i | 0.396884i | ||||||||
\(146\) | −3975.20 | −2.25336 | ||||||||
\(147\) | 335.655 | 0.188329 | ||||||||
\(148\) | 3650.80i | 2.02766i | ||||||||
\(149\) | 1128.86i | 0.620669i | 0.950627 | + | 0.310335i | \(0.100441\pi\) | ||||
−0.950627 | + | 0.310335i | \(0.899559\pi\) | |||||||
\(150\) | − 1894.77i | − 1.03138i | ||||||||
\(151\) | 2940.44i | 1.58470i | 0.610066 | + | 0.792350i | \(0.291143\pi\) | ||||
−0.610066 | + | 0.792350i | \(0.708857\pi\) | |||||||
\(152\) | −1788.46 | −0.954361 | ||||||||
\(153\) | −37.4719 | −0.0198001 | ||||||||
\(154\) | − 5454.93i | − 2.85436i | ||||||||
\(155\) | −556.093 | −0.288171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 629.388 | 0.319940 | 0.159970 | − | 0.987122i | \(-0.448860\pi\) | ||||
0.159970 | + | 0.987122i | \(0.448860\pi\) | |||||||
\(158\) | 2938.15i | 1.47941i | ||||||||
\(159\) | −31.4170 | −0.0156700 | ||||||||
\(160\) | 1436.88 | 0.709972 | ||||||||
\(161\) | 719.444i | 0.352175i | ||||||||
\(162\) | − 434.543i | − 0.210746i | ||||||||
\(163\) | 394.912i | 0.189766i | 0.995488 | + | 0.0948832i | \(0.0302478\pi\) | ||||
−0.995488 | + | 0.0948832i | \(0.969752\pi\) | |||||||
\(164\) | − 3251.33i | − 1.54809i | ||||||||
\(165\) | −541.027 | −0.255266 | ||||||||
\(166\) | 3235.23 | 1.51267 | ||||||||
\(167\) | 151.860i | 0.0703669i | 0.999381 | + | 0.0351834i | \(0.0112015\pi\) | ||||
−0.999381 | + | 0.0351834i | \(0.988798\pi\) | |||||||
\(168\) | 3126.96 | 1.43601 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −60.2255 | −0.0271711 | ||||||||
\(171\) | 234.765i | 0.104988i | ||||||||
\(172\) | 1080.25 | 0.478886 | ||||||||
\(173\) | −538.813 | −0.236793 | −0.118397 | − | 0.992966i | \(-0.537775\pi\) | ||||
−0.118397 | + | 0.992966i | \(0.537775\pi\) | |||||||
\(174\) | − 4136.31i | − 1.80214i | ||||||||
\(175\) | − 1789.78i | − 0.773114i | ||||||||
\(176\) | 13482.5i | 5.77432i | ||||||||
\(177\) | − 1335.34i | − 0.567065i | ||||||||
\(178\) | −1157.00 | −0.487196 | ||||||||
\(179\) | 2220.80 | 0.927319 | 0.463659 | − | 0.886014i | \(-0.346536\pi\) | ||||
0.463659 | + | 0.886014i | \(0.346536\pi\) | |||||||
\(180\) | − 504.271i | − 0.208812i | ||||||||
\(181\) | 3822.78 | 1.56986 | 0.784932 | − | 0.619582i | \(-0.212698\pi\) | ||||
0.784932 | + | 0.619582i | \(0.212698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 359.089 | 0.145052 | ||||||||
\(184\) | − 3244.67i | − 1.30000i | ||||||||
\(185\) | 473.704 | 0.188256 | ||||||||
\(186\) | 3319.30 | 1.30851 | ||||||||
\(187\) | − 278.478i | − 0.108900i | ||||||||
\(188\) | − 7360.84i | − 2.85555i | ||||||||
\(189\) | − 410.467i | − 0.157974i | ||||||||
\(190\) | 377.319i | 0.144071i | ||||||||
\(191\) | 3464.19 | 1.31236 | 0.656178 | − | 0.754606i | \(-0.272172\pi\) | ||||
0.656178 | + | 0.754606i | \(0.272172\pi\) | |||||||
\(192\) | −3738.83 | −1.40535 | ||||||||
\(193\) | − 4697.40i | − 1.75195i | −0.482357 | − | 0.875975i | \(-0.660219\pi\) | ||||
0.482357 | − | 0.875975i | \(-0.339781\pi\) | |||||||
\(194\) | 7765.46 | 2.87385 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2325.00 | −0.847304 | ||||||||
\(197\) | − 2887.89i | − 1.04443i | −0.852813 | − | 0.522217i | \(-0.825105\pi\) | ||||
0.852813 | − | 0.522217i | \(-0.174895\pi\) | |||||||
\(198\) | 3229.37 | 1.15910 | ||||||||
\(199\) | −63.0092 | −0.0224453 | −0.0112226 | − | 0.999937i | \(-0.503572\pi\) | ||||
−0.0112226 | + | 0.999937i | \(0.503572\pi\) | |||||||
\(200\) | 8071.87i | 2.85384i | ||||||||
\(201\) | − 67.2233i | − 0.0235899i | ||||||||
\(202\) | − 4739.47i | − 1.65083i | ||||||||
\(203\) | − 3907.14i | − 1.35087i | ||||||||
\(204\) | 259.558 | 0.0890820 | ||||||||
\(205\) | −421.872 | −0.143731 | ||||||||
\(206\) | 6715.24i | 2.27123i | ||||||||
\(207\) | −425.918 | −0.143011 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1744.69 | −0.577429 | ||||||||
\(210\) | − 659.710i | − 0.216782i | ||||||||
\(211\) | −1049.70 | −0.342484 | −0.171242 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171242 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(212\) | 217.618 | 0.0705002 | ||||||||
\(213\) | 855.622i | 0.275241i | ||||||||
\(214\) | 1832.66i | 0.585412i | ||||||||
\(215\) | − 140.166i | − 0.0444617i | ||||||||
\(216\) | 1851.19i | 0.583137i | ||||||||
\(217\) | 3135.39 | 0.980848 | ||||||||
\(218\) | 4158.61 | 1.29200 | ||||||||
\(219\) | − 2222.97i | − 0.685909i | ||||||||
\(220\) | 3747.56 | 1.14846 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2827.52 | −0.854823 | ||||||||
\(223\) | 2313.49i | 0.694722i | 0.937732 | + | 0.347361i | \(0.112922\pi\) | ||||
−0.937732 | + | 0.347361i | \(0.887078\pi\) | |||||||
\(224\) | −8101.49 | −2.41653 | ||||||||
\(225\) | 1059.57 | 0.313946 | ||||||||
\(226\) | − 6861.74i | − 2.01963i | ||||||||
\(227\) | 3799.46i | 1.11092i | 0.831543 | + | 0.555460i | \(0.187458\pi\) | ||||
−0.831543 | + | 0.555460i | \(0.812542\pi\) | |||||||
\(228\) | − 1626.16i | − 0.472347i | ||||||||
\(229\) | 4321.07i | 1.24692i | 0.781856 | + | 0.623459i | \(0.214273\pi\) | ||||
−0.781856 | + | 0.623459i | \(0.785727\pi\) | |||||||
\(230\) | −684.543 | −0.196250 | ||||||||
\(231\) | 3050.44 | 0.868850 | ||||||||
\(232\) | 17621.1i | 4.98655i | ||||||||
\(233\) | −5279.77 | −1.48450 | −0.742251 | − | 0.670122i | \(-0.766242\pi\) | ||||
−0.742251 | + | 0.670122i | \(0.766242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −955.094 | −0.265121 | ||||||||
\(236\) | 9249.59i | 2.55126i | ||||||||
\(237\) | −1643.04 | −0.450323 | ||||||||
\(238\) | 339.566 | 0.0924823 | ||||||||
\(239\) | 1547.92i | 0.418939i | 0.977815 | + | 0.209469i | \(0.0671737\pi\) | ||||
−0.977815 | + | 0.209469i | \(0.932826\pi\) | |||||||
\(240\) | 1630.55i | 0.438547i | ||||||||
\(241\) | 4918.01i | 1.31451i | 0.753669 | + | 0.657255i | \(0.228282\pi\) | ||||
−0.753669 | + | 0.657255i | \(0.771718\pi\) | |||||||
\(242\) | 16859.1i | 4.47828i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2487.32 | −0.652600 | ||||||||
\(245\) | 301.677i | 0.0786671i | ||||||||
\(246\) | 2518.14 | 0.652644 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −14140.5 | −3.62066 | ||||||||
\(249\) | 1809.17i | 0.460447i | ||||||||
\(250\) | 3511.08 | 0.888241 | ||||||||
\(251\) | −1155.78 | −0.290646 | −0.145323 | − | 0.989384i | \(-0.546422\pi\) | ||||
−0.145323 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(252\) | 2843.20i | 0.710734i | ||||||||
\(253\) | − 3165.27i | − 0.786556i | ||||||||
\(254\) | − 5975.34i | − 1.47609i | ||||||||
\(255\) | − 33.6786i | − 0.00827073i | ||||||||
\(256\) | 3026.80 | 0.738965 | ||||||||
\(257\) | −2351.95 | −0.570859 | −0.285429 | − | 0.958400i | \(-0.592136\pi\) | ||||
−0.285429 | + | 0.958400i | \(0.592136\pi\) | |||||||
\(258\) | 836.647i | 0.201889i | ||||||||
\(259\) | −2670.86 | −0.640769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2313.06 | 0.548563 | ||||||||
\(262\) | − 11266.6i | − 2.65669i | ||||||||
\(263\) | 5521.88 | 1.29465 | 0.647326 | − | 0.762213i | \(-0.275887\pi\) | ||||
0.647326 | + | 0.762213i | \(0.275887\pi\) | |||||||
\(264\) | −13757.4 | −3.20723 | ||||||||
\(265\) | − 28.2367i | − 0.00654553i | ||||||||
\(266\) | − 2127.41i | − 0.490376i | ||||||||
\(267\) | − 647.004i | − 0.148300i | ||||||||
\(268\) | 465.639i | 0.106132i | ||||||||
\(269\) | 3916.95 | 0.887810 | 0.443905 | − | 0.896074i | \(-0.353593\pi\) | ||||
0.443905 | + | 0.896074i | \(0.353593\pi\) | |||||||
\(270\) | 390.554 | 0.0880310 | ||||||||
\(271\) | 2777.53i | 0.622593i | 0.950313 | + | 0.311297i | \(0.100763\pi\) | ||||
−0.950313 | + | 0.311297i | \(0.899237\pi\) | |||||||
\(272\) | −839.276 | −0.187090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6464.58 | 1.42533 | ||||||||
\(275\) | 7874.34i | 1.72669i | ||||||||
\(276\) | 2950.23 | 0.643416 | ||||||||
\(277\) | −6583.08 | −1.42794 | −0.713969 | − | 0.700177i | \(-0.753104\pi\) | ||||
−0.713969 | + | 0.700177i | \(0.753104\pi\) | |||||||
\(278\) | − 1732.21i | − 0.373710i | ||||||||
\(279\) | 1856.18i | 0.398303i | ||||||||
\(280\) | 2810.42i | 0.599839i | ||||||||
\(281\) | − 2871.66i | − 0.609640i | −0.952410 | − | 0.304820i | \(-0.901404\pi\) | ||||
0.952410 | − | 0.304820i | \(-0.0985963\pi\) | |||||||
\(282\) | 5700.92 | 1.20385 | ||||||||
\(283\) | −7518.04 | −1.57916 | −0.789578 | − | 0.613651i | \(-0.789700\pi\) | ||||
−0.789578 | + | 0.613651i | \(0.789700\pi\) | |||||||
\(284\) | − 5926.69i | − 1.23832i | ||||||||
\(285\) | −211.000 | −0.0438546 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2378.62 | 0.489217 | ||||||||
\(288\) | − 4796.16i | − 0.981307i | ||||||||
\(289\) | −4895.66 | −0.996472 | ||||||||
\(290\) | 3717.60 | 0.752776 | ||||||||
\(291\) | 4342.51i | 0.874785i | ||||||||
\(292\) | 15397.9i | 3.08595i | ||||||||
\(293\) | − 4506.57i | − 0.898555i | −0.893392 | − | 0.449278i | \(-0.851681\pi\) | ||||
0.893392 | − | 0.449278i | \(-0.148319\pi\) | |||||||
\(294\) | − 1800.70i | − 0.357207i | ||||||||
\(295\) | 1200.17 | 0.236869 | ||||||||
\(296\) | 12045.5 | 2.36530 | ||||||||
\(297\) | 1805.89i | 0.352823i | ||||||||
\(298\) | 6056.02 | 1.17723 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7339.38 | −1.41246 | ||||||||
\(301\) | 790.292i | 0.151335i | ||||||||
\(302\) | 15774.7 | 3.00573 | ||||||||
\(303\) | 2650.35 | 0.502504 | ||||||||
\(304\) | 5258.15i | 0.992024i | ||||||||
\(305\) | 322.738i | 0.0605900i | ||||||||
\(306\) | 201.026i | 0.0375552i | ||||||||
\(307\) | − 9538.89i | − 1.77333i | −0.462409 | − | 0.886667i | \(-0.653015\pi\) | ||||
0.462409 | − | 0.886667i | \(-0.346985\pi\) | |||||||
\(308\) | −21129.7 | −3.90901 | ||||||||
\(309\) | −3755.22 | −0.691350 | ||||||||
\(310\) | 2983.29i | 0.546578i | ||||||||
\(311\) | 7466.28 | 1.36133 | 0.680666 | − | 0.732594i | \(-0.261691\pi\) | ||||
0.680666 | + | 0.732594i | \(0.261691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1821.65 | −0.328964 | −0.164482 | − | 0.986380i | \(-0.552595\pi\) | ||||
−0.164482 | + | 0.986380i | \(0.552595\pi\) | |||||||
\(314\) | − 3376.49i | − 0.606836i | ||||||||
\(315\) | 368.915 | 0.0659874 | ||||||||
\(316\) | 11380.9 | 2.02603 | ||||||||
\(317\) | 3125.14i | 0.553708i | 0.960912 | + | 0.276854i | \(0.0892918\pi\) | ||||
−0.960912 | + | 0.276854i | \(0.910708\pi\) | |||||||
\(318\) | 168.543i | 0.0297215i | ||||||||
\(319\) | 17189.9i | 3.01708i | ||||||||
\(320\) | − 3360.35i | − 0.587029i | ||||||||
\(321\) | −1024.84 | −0.178196 | ||||||||
\(322\) | 3859.62 | 0.667976 | ||||||||
\(323\) | − 108.606i | − 0.0187090i | ||||||||
\(324\) | −1683.20 | −0.288615 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2118.60 | 0.359933 | ||||||||
\(327\) | 2325.53i | 0.393279i | ||||||||
\(328\) | −10727.5 | −1.80587 | ||||||||
\(329\) | 5385.05 | 0.902394 | ||||||||
\(330\) | 2902.46i | 0.484167i | ||||||||
\(331\) | − 1553.67i | − 0.257999i | −0.991645 | − | 0.128999i | \(-0.958823\pi\) | ||||
0.991645 | − | 0.128999i | \(-0.0411765\pi\) | |||||||
\(332\) | − 12531.7i | − 2.07158i | ||||||||
\(333\) | − 1581.17i | − 0.260204i | ||||||||
\(334\) | 814.686 | 0.133466 | ||||||||
\(335\) | 60.4183 | 0.00985375 | ||||||||
\(336\) | − 9193.42i | − 1.49269i | ||||||||
\(337\) | 3190.43 | 0.515709 | 0.257855 | − | 0.966184i | \(-0.416984\pi\) | ||||
0.257855 | + | 0.966184i | \(0.416984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3837.15 | 0.614764 | ||||||||
\(340\) | 233.283i | 0.0372105i | ||||||||
\(341\) | −13794.5 | −2.19065 | ||||||||
\(342\) | 1259.45 | 0.199132 | ||||||||
\(343\) | − 6915.37i | − 1.08862i | ||||||||
\(344\) | − 3564.19i | − 0.558629i | ||||||||
\(345\) | − 382.802i | − 0.0597373i | ||||||||
\(346\) | 2890.59i | 0.449130i | ||||||||
\(347\) | −5718.68 | −0.884712 | −0.442356 | − | 0.896840i | \(-0.645857\pi\) | ||||
−0.442356 | + | 0.896840i | \(0.645857\pi\) | |||||||
\(348\) | −16022.0 | −2.46802 | ||||||||
\(349\) | 3328.46i | 0.510511i | 0.966874 | + | 0.255256i | \(0.0821596\pi\) | ||||
−0.966874 | + | 0.255256i | \(0.917840\pi\) | |||||||
\(350\) | −9601.70 | −1.46638 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 35643.4 | 5.39715 | ||||||||
\(353\) | − 12306.5i | − 1.85555i | −0.373142 | − | 0.927774i | \(-0.621719\pi\) | ||||
0.373142 | − | 0.927774i | \(-0.378281\pi\) | |||||||
\(354\) | −7163.74 | −1.07556 | ||||||||
\(355\) | −769.008 | −0.114971 | ||||||||
\(356\) | 4481.64i | 0.667210i | ||||||||
\(357\) | 189.888i | 0.0281511i | ||||||||
\(358\) | − 11914.0i | − 1.75886i | ||||||||
\(359\) | − 8539.97i | − 1.25549i | −0.778418 | − | 0.627747i | \(-0.783977\pi\) | ||||
0.778418 | − | 0.627747i | \(-0.216023\pi\) | |||||||
\(360\) | −1663.80 | −0.243583 | ||||||||
\(361\) | 6178.57 | 0.900798 | ||||||||
\(362\) | − 20508.2i | − 2.97759i | ||||||||
\(363\) | −9427.74 | −1.36316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1997.94 | 0.286512 | ||||||||
\(366\) | − 1926.41i | − 0.275123i | ||||||||
\(367\) | 2496.65 | 0.355107 | 0.177553 | − | 0.984111i | \(-0.443182\pi\) | ||||
0.177553 | + | 0.984111i | \(0.443182\pi\) | |||||||
\(368\) | −9539.49 | −1.35130 | ||||||||
\(369\) | 1408.16i | 0.198661i | ||||||||
\(370\) | − 2541.29i | − 0.357069i | ||||||||
\(371\) | 159.205i | 0.0222790i | ||||||||
\(372\) | − 12857.3i | − 1.79199i | ||||||||
\(373\) | −1142.91 | −0.158653 | −0.0793264 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793264 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(374\) | −1493.96 | −0.206552 | ||||||||
\(375\) | 1963.43i | 0.270376i | ||||||||
\(376\) | −24286.4 | −3.33105 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2202.04 | −0.299632 | ||||||||
\(379\) | − 12181.8i | − 1.65102i | −0.564384 | − | 0.825512i | \(-0.690886\pi\) | ||||
0.564384 | − | 0.825512i | \(-0.309114\pi\) | |||||||
\(380\) | 1461.54 | 0.197304 | ||||||||
\(381\) | 3341.46 | 0.449313 | ||||||||
\(382\) | − 18584.4i | − 2.48917i | ||||||||
\(383\) | − 10180.6i | − 1.35824i | −0.734029 | − | 0.679118i | \(-0.762362\pi\) | ||||
0.734029 | − | 0.679118i | \(-0.237638\pi\) | |||||||
\(384\) | 7268.04i | 0.965874i | ||||||||
\(385\) | 2741.65i | 0.362928i | ||||||||
\(386\) | −25200.3 | −3.32295 | ||||||||
\(387\) | −467.860 | −0.0614539 | ||||||||
\(388\) | − 30079.5i | − 3.93571i | ||||||||
\(389\) | −5845.83 | −0.761941 | −0.380971 | − | 0.924587i | \(-0.624410\pi\) | ||||
−0.380971 | + | 0.924587i | \(0.624410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 197.036 | 0.0254848 | ||||||||
\(392\) | 7671.13i | 0.988395i | ||||||||
\(393\) | 6300.37 | 0.808681 | ||||||||
\(394\) | −15492.7 | −1.98100 | ||||||||
\(395\) | − 1476.71i | − 0.188105i | ||||||||
\(396\) | − 12509.0i | − 1.58737i | ||||||||
\(397\) | 2500.92i | 0.316166i | 0.987426 | + | 0.158083i | \(0.0505313\pi\) | ||||
−0.987426 | + | 0.158083i | \(0.949469\pi\) | |||||||
\(398\) | 338.027i | 0.0425723i | ||||||||
\(399\) | 1189.67 | 0.149268 | ||||||||
\(400\) | 23731.7 | 2.96646 | ||||||||
\(401\) | 9189.25i | 1.14436i | 0.820127 | + | 0.572181i | \(0.193902\pi\) | ||||
−0.820127 | + | 0.572181i | \(0.806098\pi\) | |||||||
\(402\) | −360.634 | −0.0447433 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −18358.3 | −2.26080 | ||||||||
\(405\) | 218.401i | 0.0267962i | ||||||||
\(406\) | −20960.7 | −2.56223 | ||||||||
\(407\) | 11750.7 | 1.43111 | ||||||||
\(408\) | − 856.390i | − 0.103916i | ||||||||
\(409\) | 9214.38i | 1.11399i | 0.830516 | + | 0.556995i | \(0.188046\pi\) | ||||
−0.830516 | + | 0.556995i | \(0.811954\pi\) | |||||||
\(410\) | 2263.23i | 0.272617i | ||||||||
\(411\) | 3615.05i | 0.433862i | ||||||||
\(412\) | 26011.5 | 3.11042 | ||||||||
\(413\) | −6766.83 | −0.806232 | ||||||||
\(414\) | 2284.93i | 0.271252i | ||||||||
\(415\) | −1626.03 | −0.192334 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 968.669 | 0.113755 | ||||||||
\(418\) | 9359.78i | 1.09522i | ||||||||
\(419\) | −6494.41 | −0.757214 | −0.378607 | − | 0.925558i | \(-0.623597\pi\) | ||||
−0.378607 | + | 0.925558i | \(0.623597\pi\) | |||||||
\(420\) | −2555.39 | −0.296881 | ||||||||
\(421\) | 3059.56i | 0.354190i | 0.984194 | + | 0.177095i | \(0.0566699\pi\) | ||||
−0.984194 | + | 0.177095i | \(0.943330\pi\) | |||||||
\(422\) | 5631.33i | 0.649595i | ||||||||
\(423\) | 3188.00i | 0.366444i | ||||||||
\(424\) | − 718.010i | − 0.0822398i | ||||||||
\(425\) | −490.173 | −0.0559456 | ||||||||
\(426\) | 4590.18 | 0.522054 | ||||||||
\(427\) | − 1819.68i | − 0.206230i | ||||||||
\(428\) | 7098.82 | 0.801716 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −751.954 | −0.0843313 | ||||||||
\(431\) | 7937.05i | 0.887040i | 0.896264 | + | 0.443520i | \(0.146271\pi\) | ||||
−0.896264 | + | 0.443520i | \(0.853729\pi\) | |||||||
\(432\) | 5442.59 | 0.606150 | ||||||||
\(433\) | −7294.37 | −0.809573 | −0.404786 | − | 0.914411i | \(-0.632654\pi\) | ||||
−0.404786 | + | 0.914411i | \(0.632654\pi\) | |||||||
\(434\) | − 16820.5i | − 1.86039i | ||||||||
\(435\) | 2078.91i | 0.229141i | ||||||||
\(436\) | − 16108.4i | − 1.76938i | ||||||||
\(437\) | − 1234.45i | − 0.135130i | ||||||||
\(438\) | −11925.6 | −1.30098 | ||||||||
\(439\) | −15214.7 | −1.65412 | −0.827059 | − | 0.562115i | \(-0.809988\pi\) | ||||
−0.827059 | + | 0.562115i | \(0.809988\pi\) | |||||||
\(440\) | − 12364.7i | − 1.33970i | ||||||||
\(441\) | 1006.97 | 0.108732 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1517.05 | 0.162703 | 0.0813515 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813515 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(444\) | 10952.4i | 1.17067i | ||||||||
\(445\) | 581.509 | 0.0619464 | ||||||||
\(446\) | 12411.3 | 1.31769 | ||||||||
\(447\) | 3386.58i | 0.358343i | ||||||||
\(448\) | 18946.5i | 1.99807i | ||||||||
\(449\) | 705.247i | 0.0741262i | 0.999313 | + | 0.0370631i | \(0.0118002\pi\) | ||||
−0.999313 | + | 0.0370631i | \(0.988200\pi\) | |||||||
\(450\) | − 5684.30i | − 0.595467i | ||||||||
\(451\) | −10465.0 | −1.09263 | ||||||||
\(452\) | −26579.0 | −2.76586 | ||||||||
\(453\) | 8821.33i | 0.914927i | ||||||||
\(454\) | 20383.1 | 2.10710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5365.37 | −0.551001 | ||||||||
\(457\) | − 7277.73i | − 0.744940i | −0.928044 | − | 0.372470i | \(-0.878511\pi\) | ||||
0.928044 | − | 0.372470i | \(-0.121489\pi\) | |||||||
\(458\) | 23181.4 | 2.36505 | ||||||||
\(459\) | −112.416 | −0.0114316 | ||||||||
\(460\) | 2651.58i | 0.268762i | ||||||||
\(461\) | 1961.88i | 0.198208i | 0.995077 | + | 0.0991041i | \(0.0315977\pi\) | ||||
−0.995077 | + | 0.0991041i | \(0.968402\pi\) | |||||||
\(462\) | − 16364.8i | − 1.64796i | ||||||||
\(463\) | 10374.1i | 1.04131i | 0.853768 | + | 0.520653i | \(0.174311\pi\) | ||||
−0.853768 | + | 0.520653i | \(0.825689\pi\) | |||||||
\(464\) | 51806.8 | 5.18334 | ||||||||
\(465\) | −1668.28 | −0.166376 | ||||||||
\(466\) | 28324.5i | 2.81568i | ||||||||
\(467\) | −8788.92 | −0.870883 | −0.435442 | − | 0.900217i | \(-0.643408\pi\) | ||||
−0.435442 | + | 0.900217i | \(0.643408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −340.653 | −0.0335392 | ||||||||
\(470\) | 5123.82i | 0.502860i | ||||||||
\(471\) | 1888.16 | 0.184718 | ||||||||
\(472\) | 30518.2 | 2.97609 | ||||||||
\(473\) | − 3476.97i | − 0.337995i | ||||||||
\(474\) | 8814.44i | 0.854136i | ||||||||
\(475\) | 3070.98i | 0.296645i | ||||||||
\(476\) | − 1315.31i | − 0.126654i | ||||||||
\(477\) | −94.2510 | −0.00904707 | ||||||||
\(478\) | 8304.14 | 0.794608 | ||||||||
\(479\) | 11141.7i | 1.06279i | 0.847125 | + | 0.531394i | \(0.178332\pi\) | ||||
−0.847125 | + | 0.531394i | \(0.821668\pi\) | |||||||
\(480\) | 4310.65 | 0.409903 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26383.8 | 2.49325 | ||||||||
\(483\) | 2158.33i | 0.203328i | ||||||||
\(484\) | 65303.7 | 6.13295 | ||||||||
\(485\) | −3902.92 | −0.365407 | ||||||||
\(486\) | − 1303.63i | − 0.121674i | ||||||||
\(487\) | − 19640.5i | − 1.82750i | −0.406273 | − | 0.913752i | \(-0.633172\pi\) | ||||
0.406273 | − | 0.913752i | \(-0.366828\pi\) | |||||||
\(488\) | 8206.69i | 0.761269i | ||||||||
\(489\) | 1184.74i | 0.109562i | ||||||||
\(490\) | 1618.41 | 0.149209 | ||||||||
\(491\) | 3410.31 | 0.313453 | 0.156726 | − | 0.987642i | \(-0.449906\pi\) | ||||
0.156726 | + | 0.987642i | \(0.449906\pi\) | |||||||
\(492\) | − 9754.00i | − 0.893789i | ||||||||
\(493\) | −1070.06 | −0.0977546 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1623.08 | −0.147378 | ||||||||
\(496\) | 41573.8i | 3.76354i | ||||||||
\(497\) | 4335.86 | 0.391327 | ||||||||
\(498\) | 9705.68 | 0.873338 | ||||||||
\(499\) | − 5032.44i | − 0.451469i | −0.974189 | − | 0.225735i | \(-0.927522\pi\) | ||||
0.974189 | − | 0.225735i | \(-0.0724782\pi\) | |||||||
\(500\) | − 13600.2i | − 1.21644i | ||||||||
\(501\) | 455.580i | 0.0406263i | ||||||||
\(502\) | 6200.44i | 0.551274i | ||||||||
\(503\) | 17189.4 | 1.52373 | 0.761866 | − | 0.647735i | \(-0.224284\pi\) | ||||
0.761866 | + | 0.647735i | \(0.224284\pi\) | |||||||
\(504\) | 9380.89 | 0.829083 | ||||||||
\(505\) | 2382.06i | 0.209901i | ||||||||
\(506\) | −16980.8 | −1.49187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23145.5 | −2.02149 | ||||||||
\(509\) | − 930.560i | − 0.0810341i | −0.999179 | − | 0.0405170i | \(-0.987099\pi\) | ||||
0.999179 | − | 0.0405170i | \(-0.0129005\pi\) | |||||||
\(510\) | −180.676 | −0.0156872 | ||||||||
\(511\) | −11264.9 | −0.975201 | ||||||||
\(512\) | 3143.50i | 0.271337i | ||||||||
\(513\) | 704.295i | 0.0606148i | ||||||||
\(514\) | 12617.6i | 1.08276i | ||||||||
\(515\) | − 3375.08i | − 0.288784i | ||||||||
\(516\) | 3240.75 | 0.276485 | ||||||||
\(517\) | −23692.1 | −2.01543 | ||||||||
\(518\) | 14328.4i | 1.21536i | ||||||||
\(519\) | −1616.44 | −0.136713 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9869.60 | −0.829933 | −0.414966 | − | 0.909837i | \(-0.636207\pi\) | ||||
−0.414966 | + | 0.909837i | \(0.636207\pi\) | |||||||
\(522\) | − 12408.9i | − 1.04047i | ||||||||
\(523\) | −21420.6 | −1.79093 | −0.895466 | − | 0.445129i | \(-0.853158\pi\) | ||||
−0.895466 | + | 0.445129i | \(0.853158\pi\) | |||||||
\(524\) | −43641.1 | −3.63831 | ||||||||
\(525\) | − 5369.35i | − 0.446358i | ||||||||
\(526\) | − 29623.4i | − 2.45559i | ||||||||
\(527\) | − 858.697i | − 0.0709781i | ||||||||
\(528\) | 40447.4i | 3.33380i | ||||||||
\(529\) | −9927.42 | −0.815930 | ||||||||
\(530\) | −151.482 | −0.0124150 | ||||||||
\(531\) | − 4006.03i | − 0.327395i | ||||||||
\(532\) | −8240.54 | −0.671565 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3471.00 | −0.281283 | ||||||||
\(535\) | − 921.097i | − 0.0744345i | ||||||||
\(536\) | 1536.34 | 0.123805 | ||||||||
\(537\) | 6662.39 | 0.535388 | ||||||||
\(538\) | − 21013.4i | − 1.68392i | ||||||||
\(539\) | 7483.41i | 0.598021i | ||||||||
\(540\) | − 1512.81i | − 0.120558i | ||||||||
\(541\) | − 7771.50i | − 0.617602i | −0.951127 | − | 0.308801i | \(-0.900072\pi\) | ||||
0.951127 | − | 0.308801i | \(-0.0999277\pi\) | |||||||
\(542\) | 14900.7 | 1.18088 | ||||||||
\(543\) | 11468.3 | 0.906361 | ||||||||
\(544\) | 2218.78i | 0.174870i | ||||||||
\(545\) | −2090.12 | −0.164277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15577.5 | −1.21763 | −0.608817 | − | 0.793310i | \(-0.708356\pi\) | ||||
−0.608817 | + | 0.793310i | \(0.708356\pi\) | |||||||
\(548\) | − 25040.6i | − 1.95197i | ||||||||
\(549\) | 1077.27 | 0.0837461 | ||||||||
\(550\) | 42243.7 | 3.27505 | ||||||||
\(551\) | 6704.02i | 0.518332i | ||||||||
\(552\) | − 9734.01i | − 0.750556i | ||||||||
\(553\) | 8326.07i | 0.640254i | ||||||||
\(554\) | 35316.4i | 2.70840i | ||||||||
\(555\) | 1421.11 | 0.108690 | ||||||||
\(556\) | −6709.74 | −0.511792 | ||||||||
\(557\) | 22804.5i | 1.73475i | 0.497652 | + | 0.867377i | \(0.334196\pi\) | ||||
−0.497652 | + | 0.867377i | \(0.665804\pi\) | |||||||
\(558\) | 9957.89 | 0.755468 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8262.78 | 0.623511 | ||||||||
\(561\) | − 835.433i | − 0.0628734i | ||||||||
\(562\) | −15405.7 | −1.15631 | ||||||||
\(563\) | 3517.41 | 0.263306 | 0.131653 | − | 0.991296i | \(-0.457972\pi\) | ||||
0.131653 | + | 0.991296i | \(0.457972\pi\) | |||||||
\(564\) | − 22082.5i | − 1.64865i | ||||||||
\(565\) | 3448.71i | 0.256794i | ||||||||
\(566\) | 40332.2i | 2.99521i | ||||||||
\(567\) | − 1231.40i | − 0.0912062i | ||||||||
\(568\) | −19554.6 | −1.44453 | ||||||||
\(569\) | 6093.44 | 0.448946 | 0.224473 | − | 0.974480i | \(-0.427934\pi\) | ||||
0.224473 | + | 0.974480i | \(0.427934\pi\) | |||||||
\(570\) | 1131.96i | 0.0831797i | ||||||||
\(571\) | −10460.2 | −0.766630 | −0.383315 | − | 0.923618i | \(-0.625218\pi\) | ||||
−0.383315 | + | 0.923618i | \(0.625218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10392.6 | 0.757689 | ||||||||
\(574\) | − 12760.6i | − 0.927906i | ||||||||
\(575\) | −5571.47 | −0.404081 | ||||||||
\(576\) | −11216.5 | −0.811378 | ||||||||
\(577\) | − 9648.19i | − 0.696117i | −0.937473 | − | 0.348058i | \(-0.886841\pi\) | ||||
0.937473 | − | 0.348058i | \(-0.113159\pi\) | |||||||
\(578\) | 26263.9i | 1.89002i | ||||||||
\(579\) | − 14092.2i | − 1.01149i | ||||||||
\(580\) | − 14400.1i | − 1.03092i | ||||||||
\(581\) | 9167.93 | 0.654647 | ||||||||
\(582\) | 23296.4 | 1.65922 | ||||||||
\(583\) | − 700.440i | − 0.0497586i | ||||||||
\(584\) | 50804.1 | 3.59981 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24176.5 | −1.70430 | ||||||||
\(587\) | 2170.73i | 0.152633i | 0.997084 | + | 0.0763166i | \(0.0243160\pi\) | ||||
−0.997084 | + | 0.0763166i | \(0.975684\pi\) | |||||||
\(588\) | −6975.01 | −0.489191 | ||||||||
\(589\) | −5379.82 | −0.376353 | ||||||||
\(590\) | − 6438.56i | − 0.449274i | ||||||||
\(591\) | − 8663.66i | − 0.603004i | ||||||||
\(592\) | − 35414.3i | − 2.45865i | ||||||||
\(593\) | − 22885.9i | − 1.58484i | −0.609975 | − | 0.792421i | \(-0.708820\pi\) | ||||
0.609975 | − | 0.792421i | \(-0.291180\pi\) | |||||||
\(594\) | 9688.11 | 0.669205 | ||||||||
\(595\) | −170.666 | −0.0117590 | ||||||||
\(596\) | − 23458.0i | − 1.61221i | ||||||||
\(597\) | −189.028 | −0.0129588 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23978.7 | −1.63563 | −0.817815 | − | 0.575482i | \(-0.804815\pi\) | ||||
−0.817815 | + | 0.575482i | \(0.804815\pi\) | |||||||
\(600\) | 24215.6i | 1.64766i | ||||||||
\(601\) | 12873.2 | 0.873728 | 0.436864 | − | 0.899528i | \(-0.356089\pi\) | ||||
0.436864 | + | 0.899528i | \(0.356089\pi\) | |||||||
\(602\) | 4239.70 | 0.287039 | ||||||||
\(603\) | − 201.670i | − 0.0136196i | ||||||||
\(604\) | − 61103.2i | − 4.11631i | ||||||||
\(605\) | − 8473.38i | − 0.569408i | ||||||||
\(606\) | − 14218.4i | − 0.953107i | ||||||||
\(607\) | −7117.15 | −0.475908 | −0.237954 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237954 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(608\) | 13900.9 | 0.927227 | ||||||||
\(609\) | − 11721.4i | − 0.779927i | ||||||||
\(610\) | 1731.40 | 0.114922 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 778.675 | 0.0514315 | ||||||||
\(613\) | 173.297i | 0.0114183i | 0.999984 | + | 0.00570913i | \(0.00181728\pi\) | ||||
−0.999984 | + | 0.00570913i | \(0.998183\pi\) | |||||||
\(614\) | −51173.5 | −3.36351 | ||||||||
\(615\) | −1265.62 | −0.0829830 | ||||||||
\(616\) | 69715.5i | 4.55993i | ||||||||
\(617\) | − 6102.75i | − 0.398197i | −0.979979 | − | 0.199099i | \(-0.936199\pi\) | ||||
0.979979 | − | 0.199099i | \(-0.0638014\pi\) | |||||||
\(618\) | 20145.7i | 1.31129i | ||||||||
\(619\) | 14867.8i | 0.965409i | 0.875783 | + | 0.482705i | \(0.160346\pi\) | ||||
−0.875783 | + | 0.482705i | \(0.839654\pi\) | |||||||
\(620\) | 11555.8 | 0.748534 | ||||||||
\(621\) | −1277.75 | −0.0825676 | ||||||||
\(622\) | − 40054.6i | − 2.58206i | ||||||||
\(623\) | −3278.69 | −0.210847 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12951.6 | 0.828900 | ||||||||
\(626\) | 9772.64i | 0.623951i | ||||||||
\(627\) | −5234.07 | −0.333379 | ||||||||
\(628\) | −13078.9 | −0.831056 | ||||||||
\(629\) | 731.475i | 0.0463686i | ||||||||
\(630\) | − 1979.13i | − 0.125159i | ||||||||
\(631\) | 17210.6i | 1.08580i | 0.839796 | + | 0.542902i | \(0.182675\pi\) | ||||
−0.839796 | + | 0.542902i | \(0.817325\pi\) | |||||||
\(632\) | − 37550.3i | − 2.36340i | ||||||||
\(633\) | −3149.09 | −0.197733 | ||||||||
\(634\) | 16765.5 | 1.05023 | ||||||||
\(635\) | 3003.21i | 0.187683i | ||||||||
\(636\) | 652.853 | 0.0407033 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 92218.9 | 5.72254 | ||||||||
\(639\) | 2566.87i | 0.158910i | ||||||||
\(640\) | −6532.30 | −0.403456 | ||||||||
\(641\) | 12636.0 | 0.778616 | 0.389308 | − | 0.921108i | \(-0.372714\pi\) | ||||
0.389308 | + | 0.921108i | \(0.372714\pi\) | |||||||
\(642\) | 5497.99i | 0.337988i | ||||||||
\(643\) | − 9586.37i | − 0.587947i | −0.955814 | − | 0.293973i | \(-0.905022\pi\) | ||||
0.955814 | − | 0.293973i | \(-0.0949777\pi\) | |||||||
\(644\) | − 14950.2i | − 0.914786i | ||||||||
\(645\) | − 420.499i | − 0.0256700i | ||||||||
\(646\) | −582.641 | −0.0354856 | ||||||||
\(647\) | −5244.32 | −0.318664 | −0.159332 | − | 0.987225i | \(-0.550934\pi\) | ||||
−0.159332 | + | 0.987225i | \(0.550934\pi\) | |||||||
\(648\) | 5553.57i | 0.336674i | ||||||||
\(649\) | 29771.4 | 1.80066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9406.17 | 0.566293 | ||||||||
\(652\) | − 8206.39i | − 0.492925i | ||||||||
\(653\) | 18869.0 | 1.13078 | 0.565392 | − | 0.824822i | \(-0.308725\pi\) | ||||
0.565392 | + | 0.824822i | \(0.308725\pi\) | |||||||
\(654\) | 12475.8 | 0.745938 | ||||||||
\(655\) | 5662.59i | 0.337795i | ||||||||
\(656\) | 31539.3i | 1.87714i | ||||||||
\(657\) | − 6668.90i | − 0.396010i | ||||||||
\(658\) | − 28889.3i | − 1.71159i | ||||||||
\(659\) | −24299.8 | −1.43639 | −0.718197 | − | 0.695839i | \(-0.755033\pi\) | ||||
−0.718197 | + | 0.695839i | \(0.755033\pi\) | |||||||
\(660\) | 11242.7 | 0.663062 | ||||||||
\(661\) | − 29915.0i | − 1.76030i | −0.474694 | − | 0.880151i | \(-0.657441\pi\) | ||||
0.474694 | − | 0.880151i | \(-0.342559\pi\) | |||||||
\(662\) | −8335.03 | −0.489350 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41347.1 | −2.41653 | ||||||||
\(665\) | 1069.24i | 0.0623508i | ||||||||
\(666\) | −8482.56 | −0.493532 | ||||||||
\(667\) | −12162.6 | −0.706056 | ||||||||
\(668\) | − 3155.69i | − 0.182780i | ||||||||
\(669\) | 6940.48i | 0.401098i | ||||||||
\(670\) | − 324.128i | − 0.0186898i | ||||||||
\(671\) | 8005.86i | 0.460600i | ||||||||
\(672\) | −24304.5 | −1.39519 | ||||||||
\(673\) | −15493.7 | −0.887426 | −0.443713 | − | 0.896169i | \(-0.646339\pi\) | ||||
−0.443713 | + | 0.896169i | \(0.646339\pi\) | |||||||
\(674\) | − 17115.8i | − 0.978154i | ||||||||
\(675\) | 3178.71 | 0.181257 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11729.7 | 0.665891 | 0.332945 | − | 0.942946i | \(-0.391958\pi\) | ||||
0.332945 | + | 0.942946i | \(0.391958\pi\) | |||||||
\(678\) | − 20585.2i | − 1.16603i | ||||||||
\(679\) | 22005.6 | 1.24374 | ||||||||
\(680\) | 769.698 | 0.0434067 | ||||||||
\(681\) | 11398.4i | 0.641390i | ||||||||
\(682\) | 74003.5i | 4.15505i | ||||||||
\(683\) | 1168.42i | 0.0654587i | 0.999464 | + | 0.0327294i | \(0.0104199\pi\) | ||||
−0.999464 | + | 0.0327294i | \(0.989580\pi\) | |||||||
\(684\) | − 4878.48i | − 0.272709i | ||||||||
\(685\) | −3249.10 | −0.181229 | ||||||||
\(686\) | −37099.1 | −2.06480 | ||||||||
\(687\) | 12963.2i | 0.719909i | ||||||||
\(688\) | −10478.9 | −0.580675 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2053.63 | −0.113305 | ||||||||
\(691\) | 32992.9i | 1.81637i | 0.418574 | + | 0.908183i | \(0.362530\pi\) | ||||
−0.418574 | + | 0.908183i | \(0.637470\pi\) | |||||||
\(692\) | 11196.7 | 0.615078 | ||||||||
\(693\) | 9151.33 | 0.501631 | ||||||||
\(694\) | 30679.2i | 1.67805i | ||||||||
\(695\) | 870.612i | 0.0475168i | ||||||||
\(696\) | 52863.2i | 2.87899i | ||||||||
\(697\) | − 651.438i | − 0.0354017i | ||||||||
\(698\) | 17856.3 | 0.968295 | ||||||||
\(699\) | −15839.3 | −0.857078 | ||||||||
\(700\) | 37192.2i | 2.00819i | ||||||||
\(701\) | 14785.8 | 0.796651 | 0.398326 | − | 0.917244i | \(-0.369591\pi\) | ||||
0.398326 | + | 0.917244i | \(0.369591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4582.77 | 0.245864 | ||||||||
\(704\) | − 83357.0i | − 4.46255i | ||||||||
\(705\) | −2865.28 | −0.153068 | ||||||||
\(706\) | −66021.0 | −3.51945 | ||||||||
\(707\) | − 13430.6i | − 0.714442i | ||||||||
\(708\) | 27748.8i | 1.47297i | ||||||||
\(709\) | − 12634.0i | − 0.669225i | −0.942356 | − | 0.334612i | \(-0.891395\pi\) | ||||
0.942356 | − | 0.334612i | \(-0.108605\pi\) | |||||||
\(710\) | 4125.52i | 0.218067i | ||||||||
\(711\) | −4929.11 | −0.259994 | ||||||||
\(712\) | 14786.8 | 0.778312 | ||||||||
\(713\) | − 9760.24i | − 0.512656i | ||||||||
\(714\) | 1018.70 | 0.0533947 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46148.7 | −2.40874 | ||||||||
\(717\) | 4643.75i | 0.241874i | ||||||||
\(718\) | −45814.6 | −2.38132 | ||||||||
\(719\) | 27296.5 | 1.41584 | 0.707920 | − | 0.706292i | \(-0.249634\pi\) | ||||
0.707920 | + | 0.706292i | \(0.249634\pi\) | |||||||
\(720\) | 4891.64i | 0.253195i | ||||||||
\(721\) | 19029.5i | 0.982936i | ||||||||
\(722\) | − 33146.3i | − 1.70856i | ||||||||
\(723\) | 14754.0i | 0.758932i | ||||||||
\(724\) | −79438.5 | −4.07777 | ||||||||
\(725\) | 30257.4 | 1.54997 | ||||||||
\(726\) | 50577.2i | 2.58553i | ||||||||
\(727\) | −4658.21 | −0.237639 | −0.118819 | − | 0.992916i | \(-0.537911\pi\) | ||||
−0.118819 | + | 0.992916i | \(0.537911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 10718.4i | − 0.543432i | ||||||||
\(731\) | 216.439 | 0.0109512 | ||||||||
\(732\) | −7461.96 | −0.376779 | ||||||||
\(733\) | − 166.474i | − 0.00838864i | −0.999991 | − | 0.00419432i | \(-0.998665\pi\) | ||||
0.999991 | − | 0.00419432i | \(-0.00133510\pi\) | |||||||
\(734\) | − 13393.9i | − 0.673537i | ||||||||
\(735\) | 905.031i | 0.0454185i | ||||||||
\(736\) | 25219.4i | 1.26304i | ||||||||
\(737\) | 1498.74 | 0.0749074 | ||||||||
\(738\) | 7554.41 | 0.376804 | ||||||||
\(739\) | − 12738.1i | − 0.634069i | −0.948414 | − | 0.317035i | \(-0.897313\pi\) | ||||
0.948414 | − | 0.317035i | \(-0.102687\pi\) | |||||||
\(740\) | −9843.70 | −0.489002 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 854.092 | 0.0422570 | ||||||||
\(743\) | − 30724.5i | − 1.51705i | −0.651641 | − | 0.758527i | \(-0.725919\pi\) | ||||
0.651641 | − | 0.758527i | \(-0.274081\pi\) | |||||||
\(744\) | −42421.5 | −2.09039 | ||||||||
\(745\) | −3043.76 | −0.149684 | ||||||||
\(746\) | 6131.38i | 0.300919i | ||||||||
\(747\) | 5427.50i | 0.265839i | ||||||||
\(748\) | 5786.84i | 0.282871i | ||||||||
\(749\) | 5193.37i | 0.253353i | ||||||||
\(750\) | 10533.2 | 0.512826 | ||||||||
\(751\) | 39538.6 | 1.92115 | 0.960575 | − | 0.278021i | \(-0.0896785\pi\) | ||||
0.960575 | + | 0.278021i | \(0.0896785\pi\) | |||||||
\(752\) | 71403.2i | 3.46251i | ||||||||
\(753\) | −3467.34 | −0.167805 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7928.35 | −0.382175 | ||||||||
\(756\) | 8529.61i | 0.410342i | ||||||||
\(757\) | 23035.1 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(758\) | −65352.1 | −3.13153 | ||||||||
\(759\) | − 9495.81i | − 0.454119i | ||||||||
\(760\) | − 4822.23i | − 0.230159i | ||||||||
\(761\) | − 32454.0i | − 1.54594i | −0.634445 | − | 0.772968i | \(-0.718771\pi\) | ||||
0.634445 | − | 0.772968i | \(-0.281229\pi\) | |||||||
\(762\) | − 17926.0i | − 0.852220i | ||||||||
\(763\) | 11784.6 | 0.559150 | ||||||||
\(764\) | −71986.8 | −3.40889 | ||||||||
\(765\) | − 101.036i | − 0.00477511i | ||||||||
\(766\) | −54616.1 | −2.57619 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9080.40 | 0.426641 | ||||||||
\(769\) | − 32216.2i | − 1.51072i | −0.655307 | − | 0.755362i | \(-0.727461\pi\) | ||||
0.655307 | − | 0.755362i | \(-0.272539\pi\) | |||||||
\(770\) | 14708.2 | 0.688372 | ||||||||
\(771\) | −7055.86 | −0.329586 | ||||||||
\(772\) | 97613.2i | 4.55075i | ||||||||
\(773\) | 2924.60i | 0.136081i | 0.997683 | + | 0.0680404i | \(0.0216747\pi\) | ||||
−0.997683 | + | 0.0680404i | \(0.978325\pi\) | |||||||
\(774\) | 2509.94i | 0.116561i | ||||||||
\(775\) | 24280.9i | 1.12541i | ||||||||
\(776\) | −99244.7 | −4.59108 | ||||||||
\(777\) | −8012.58 | −0.369948 | ||||||||
\(778\) | 31361.2i | 1.44519i | ||||||||
\(779\) | −4081.32 | −0.187713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19076.1 | −0.874001 | ||||||||
\(782\) | − 1057.04i | − 0.0483374i | ||||||||
\(783\) | 6939.19 | 0.316713 | ||||||||
\(784\) | 22553.5 | 1.02740 | ||||||||
\(785\) | 1697.03i | 0.0771586i | ||||||||
\(786\) | − 33799.8i | − 1.53384i | ||||||||
\(787\) | − 25507.1i | − 1.15531i | −0.816280 | − | 0.577656i | \(-0.803967\pi\) | ||||
0.816280 | − | 0.577656i | \(-0.196033\pi\) | |||||||
\(788\) | 60011.1i | 2.71295i | ||||||||
\(789\) | 16565.6 | 0.747468 | ||||||||
\(790\) | −7922.16 | −0.356782 | ||||||||
\(791\) | − 19444.7i | − 0.874050i | ||||||||
\(792\) | −41272.2 | −1.85170 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13416.8 | 0.599677 | ||||||||
\(795\) | − 84.7100i | − 0.00377906i | ||||||||
\(796\) | 1309.35 | 0.0583023 | ||||||||
\(797\) | −5448.98 | −0.242174 | −0.121087 | − | 0.992642i | \(-0.538638\pi\) | ||||
−0.121087 | + | 0.992642i | \(0.538638\pi\) | |||||||
\(798\) | − 6382.24i | − 0.283119i | ||||||||
\(799\) | − 1474.82i | − 0.0653008i | ||||||||
\(800\) | − 62739.0i | − 2.77270i | ||||||||
\(801\) | − 1941.01i | − 0.0856209i | ||||||||
\(802\) | 49297.8 | 2.17053 | ||||||||
\(803\) | 49560.9 | 2.17804 | ||||||||
\(804\) | 1396.92i | 0.0612755i | ||||||||
\(805\) | −1939.85 | −0.0849324 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11750.9 | 0.512577 | ||||||||
\(808\) | 60571.7i | 2.63726i | ||||||||
\(809\) | −2453.12 | −0.106610 | −0.0533048 | − | 0.998578i | \(-0.516975\pi\) | ||||
−0.0533048 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(810\) | 1171.66 | 0.0508247 | ||||||||
\(811\) | − 5133.85i | − 0.222286i | −0.993804 | − | 0.111143i | \(-0.964549\pi\) | ||||
0.993804 | − | 0.111143i | \(-0.0354512\pi\) | |||||||
\(812\) | 81191.4i | 3.50894i | ||||||||
\(813\) | 8332.58i | 0.359454i | ||||||||
\(814\) | − 63039.4i | − 2.71441i | ||||||||
\(815\) | −1064.81 | −0.0457651 | ||||||||
\(816\) | −2517.83 | −0.108017 | ||||||||
\(817\) | − 1356.01i | − 0.0580673i | ||||||||
\(818\) | 49432.6 | 2.11292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8766.61 | 0.373345 | ||||||||
\(821\) | − 23854.0i | − 1.01402i | −0.861941 | − | 0.507009i | \(-0.830751\pi\) | ||||
0.861941 | − | 0.507009i | \(-0.169249\pi\) | |||||||
\(822\) | 19393.8 | 0.822913 | ||||||||
\(823\) | −757.156 | −0.0320690 | −0.0160345 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160345 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(824\) | − 85822.6i | − 3.62836i | ||||||||
\(825\) | 23623.0i | 0.996907i | ||||||||
\(826\) | 36302.2i | 1.52919i | ||||||||
\(827\) | − 28621.2i | − 1.20345i | −0.798702 | − | 0.601726i | \(-0.794480\pi\) | ||||
0.798702 | − | 0.601726i | \(-0.205520\pi\) | |||||||
\(828\) | 8850.68 | 0.371476 | ||||||||
\(829\) | −27429.2 | −1.14916 | −0.574582 | − | 0.818447i | \(-0.694835\pi\) | ||||
−0.574582 | + | 0.818447i | \(0.694835\pi\) | |||||||
\(830\) | 8723.19i | 0.364803i | ||||||||
\(831\) | −19749.2 | −0.824421 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −465.838 | −0.0193761 | ||||||||
\(834\) | − 5196.64i | − 0.215761i | ||||||||
\(835\) | −409.462 | −0.0169701 | ||||||||
\(836\) | 36255.1 | 1.49989 | ||||||||
\(837\) | 5568.54i | 0.229960i | ||||||||
\(838\) | 34840.7i | 1.43622i | ||||||||
\(839\) | 4633.62i | 0.190668i | 0.995445 | + | 0.0953339i | \(0.0303919\pi\) | ||||
−0.995445 | + | 0.0953339i | \(0.969608\pi\) | |||||||
\(840\) | 8431.27i | 0.346317i | ||||||||
\(841\) | 41663.6 | 1.70829 | ||||||||
\(842\) | 16413.7 | 0.671798 | ||||||||
\(843\) | − 8614.98i | − 0.351976i | ||||||||
\(844\) | 21813.0 | 0.889614 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17102.7 | 0.695041 | ||||||||
\(847\) | 47775.0i | 1.93810i | ||||||||
\(848\) | −2110.99 | −0.0854853 | ||||||||
\(849\) | −22554.1 | −0.911726 | ||||||||
\(850\) | 2629.64i | 0.106113i | ||||||||
\(851\) | 8314.19i | 0.334908i | ||||||||
\(852\) | − 17780.1i | − 0.714947i | ||||||||
\(853\) | 14854.6i | 0.596261i | 0.954525 | + | 0.298131i | \(0.0963631\pi\) | ||||
−0.954525 | + | 0.298131i | \(0.903637\pi\) | |||||||
\(854\) | −9762.07 | −0.391161 | ||||||||
\(855\) | −632.999 | −0.0253194 | ||||||||
\(856\) | − 23421.9i | − 0.935216i | ||||||||
\(857\) | 42799.5 | 1.70595 | 0.852977 | − | 0.521948i | \(-0.174794\pi\) | ||||
0.852977 | + | 0.521948i | \(0.174794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8246.47 | −0.327551 | −0.163775 | − | 0.986498i | \(-0.552367\pi\) | ||||
−0.163775 | + | 0.986498i | \(0.552367\pi\) | |||||||
\(860\) | 2912.70i | 0.115491i | ||||||||
\(861\) | 7135.85 | 0.282450 | ||||||||
\(862\) | 42580.1 | 1.68246 | ||||||||
\(863\) | 17695.4i | 0.697983i | 0.937126 | + | 0.348991i | \(0.113476\pi\) | ||||
−0.937126 | + | 0.348991i | \(0.886524\pi\) | |||||||
\(864\) | − 14388.5i | − 0.566558i | ||||||||
\(865\) | − 1452.81i | − 0.0571064i | ||||||||
\(866\) | 39132.3i | 1.53553i | ||||||||
\(867\) | −14687.0 | −0.575313 | ||||||||
\(868\) | −65154.2 | −2.54779 | ||||||||
\(869\) | − 36631.4i | − 1.42996i | ||||||||
\(870\) | 11152.8 | 0.434615 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −53148.2 | −2.06402 | ||||||||
\(873\) | 13027.5i | 0.505058i | ||||||||
\(874\) | −6622.49 | −0.256303 | ||||||||
\(875\) | 9949.64 | 0.384411 | ||||||||
\(876\) | 46193.8i | 1.78167i | ||||||||
\(877\) | − 14346.8i | − 0.552401i | −0.961100 | − | 0.276200i | \(-0.910925\pi\) | ||||
0.961100 | − | 0.276200i | \(-0.0890754\pi\) | |||||||
\(878\) | 81622.7i | 3.13739i | ||||||||
\(879\) | − 13519.7i | − 0.518781i | ||||||||
\(880\) | −36353.0 | −1.39257 | ||||||||
\(881\) | 2063.51 | 0.0789121 | 0.0394560 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394560 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(882\) | − 5402.09i | − 0.206233i | ||||||||
\(883\) | 34137.1 | 1.30103 | 0.650513 | − | 0.759495i | \(-0.274554\pi\) | ||||
0.650513 | + | 0.759495i | \(0.274554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3600.50 | 0.136756 | ||||||||
\(886\) | − 8138.58i | − 0.308602i | ||||||||
\(887\) | −22238.5 | −0.841821 | −0.420910 | − | 0.907102i | \(-0.638289\pi\) | ||||
−0.420910 | + | 0.907102i | \(0.638289\pi\) | |||||||
\(888\) | 36136.5 | 1.36561 | ||||||||
\(889\) | − 16932.8i | − 0.638817i | ||||||||
\(890\) | − 3119.63i | − 0.117495i | ||||||||
\(891\) | 5417.67i | 0.203702i | ||||||||
\(892\) | − 48075.0i | − 1.80456i | ||||||||
\(893\) | −9239.89 | −0.346250 | ||||||||
\(894\) | 18168.0 | 0.679676 | ||||||||
\(895\) | 5987.96i | 0.223637i | ||||||||
\(896\) | 36830.7 | 1.37325 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3783.45 | 0.140596 | ||||||||
\(899\) | 53005.7i | 1.96645i | ||||||||
\(900\) | −22018.1 | −0.815486 | ||||||||
\(901\) | 43.6019 | 0.00161220 | ||||||||
\(902\) | 56141.7i | 2.07241i | ||||||||
\(903\) | 2370.88i | 0.0873730i | ||||||||
\(904\) | 87694.9i | 3.22643i | ||||||||
\(905\) | 10307.4i | 0.378597i | ||||||||
\(906\) | 47324.0 | 1.73536 | ||||||||
\(907\) | 44160.3 | 1.61667 | 0.808335 | − | 0.588723i | \(-0.200369\pi\) | ||||
0.808335 | + | 0.588723i | \(0.200369\pi\) | |||||||
\(908\) | − 78953.8i | − 2.88565i | ||||||||
\(909\) | 7951.05 | 0.290121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11916.3 | 0.433376 | 0.216688 | − | 0.976241i | \(-0.430475\pi\) | ||||
0.216688 | + | 0.976241i | \(0.430475\pi\) | |||||||
\(912\) | 15774.4i | 0.572745i | ||||||||
\(913\) | −40335.3 | −1.46211 | ||||||||
\(914\) | −39043.0 | −1.41294 | ||||||||
\(915\) | 968.215i | 0.0349816i | ||||||||
\(916\) | − 89793.0i | − 3.23891i | ||||||||
\(917\) | − 31927.1i | − 1.14975i | ||||||||
\(918\) | 603.078i | 0.0216825i | ||||||||
\(919\) | −20128.9 | −0.722516 | −0.361258 | − | 0.932466i | \(-0.617653\pi\) | ||||
−0.361258 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(920\) | 8748.64 | 0.313515 | ||||||||
\(921\) | − 28616.7i | − 1.02383i | ||||||||
\(922\) | 10525.0 | 0.375945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −63389.0 | −2.25687 | ||||||||
\(925\) | − 20683.5i | − 0.735210i | ||||||||
\(926\) | 55654.1 | 1.97506 | ||||||||
\(927\) | −11265.7 | −0.399151 | ||||||||
\(928\) | − 136961.i | − 4.84478i | ||||||||
\(929\) | − 31428.4i | − 1.10994i | −0.831871 | − | 0.554969i | \(-0.812730\pi\) | ||||
0.831871 | − | 0.554969i | \(-0.187270\pi\) | |||||||
\(930\) | 8949.86i | 0.315567i | ||||||||
\(931\) | 2918.52i | 0.102740i | ||||||||
\(932\) | 109715. | 3.85605 | ||||||||
\(933\) | 22398.9 | 0.785965 | ||||||||
\(934\) | 47150.1i | 1.65182i | ||||||||
\(935\) | 750.863 | 0.0262629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42473.2 | 1.48083 | 0.740416 | − | 0.672149i | \(-0.234629\pi\) | ||||
0.740416 | + | 0.672149i | \(0.234629\pi\) | |||||||
\(938\) | 1827.51i | 0.0636144i | ||||||||
\(939\) | −5464.94 | −0.189927 | ||||||||
\(940\) | 19847.1 | 0.688661 | ||||||||
\(941\) | − 42644.0i | − 1.47732i | −0.674079 | − | 0.738659i | \(-0.735459\pi\) | ||||
0.674079 | − | 0.738659i | \(-0.264541\pi\) | |||||||
\(942\) | − 10129.5i | − 0.350357i | ||||||||
\(943\) | − 7404.46i | − 0.255697i | ||||||||
\(944\) | − 89725.0i | − 3.09354i | ||||||||
\(945\) | 1106.75 | 0.0380978 | ||||||||
\(946\) | −18653.0 | −0.641080 | ||||||||
\(947\) | − 4282.95i | − 0.146966i | −0.997296 | − | 0.0734831i | \(-0.976588\pi\) | ||||
0.997296 | − | 0.0734831i | \(-0.0234115\pi\) | |||||||
\(948\) | 34142.7 | 1.16973 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 16475.0 | 0.562651 | ||||||||
\(951\) | 9375.42i | 0.319683i | ||||||||
\(952\) | −4339.74 | −0.147744 | ||||||||
\(953\) | −40593.9 | −1.37982 | −0.689908 | − | 0.723897i | \(-0.742349\pi\) | ||||
−0.689908 | + | 0.723897i | \(0.742349\pi\) | |||||||
\(954\) | 505.630i | 0.0171597i | ||||||||
\(955\) | 9340.54i | 0.316495i | ||||||||
\(956\) | − 32166.1i | − 1.08821i | ||||||||
\(957\) | 51569.6i | 1.74191i | ||||||||
\(958\) | 59771.9 | 2.01581 | ||||||||
\(959\) | 18319.2 | 0.616850 | ||||||||
\(960\) | − 10081.1i | − 0.338922i | ||||||||
\(961\) | −12744.8 | −0.427808 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3074.52 | −0.102882 | ||||||||
\(964\) | − 102198.i | − 3.41448i | ||||||||
\(965\) | 12665.7 | 0.422510 | ||||||||
\(966\) | 11578.9 | 0.385656 | ||||||||
\(967\) | 17709.4i | 0.588931i | 0.955662 | + | 0.294466i | \(0.0951416\pi\) | ||||
−0.955662 | + | 0.294466i | \(0.904858\pi\) | |||||||
\(968\) | − 215464.i | − 7.15420i | ||||||||
\(969\) | − 325.818i | − 0.0108016i | ||||||||
\(970\) | 20938.1i | 0.693074i | ||||||||
\(971\) | 4038.97 | 0.133488 | 0.0667440 | − | 0.997770i | \(-0.478739\pi\) | ||||
0.0667440 | + | 0.997770i | \(0.478739\pi\) | |||||||
\(972\) | −5049.61 | −0.166632 | ||||||||
\(973\) | − 4908.72i | − 0.161733i | ||||||||
\(974\) | −105366. | −3.46626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24128.1 | 0.791312 | ||||||||
\(977\) | − 2764.30i | − 0.0905197i | −0.998975 | − | 0.0452598i | \(-0.985588\pi\) | ||||
0.998975 | − | 0.0452598i | \(-0.0144116\pi\) | |||||||
\(978\) | 6355.79 | 0.207807 | ||||||||
\(979\) | 14424.9 | 0.470912 | ||||||||
\(980\) | − 6268.93i | − 0.204340i | ||||||||
\(981\) | 6976.59i | 0.227060i | ||||||||
\(982\) | − 18295.4i | − 0.594531i | ||||||||
\(983\) | 17804.5i | 0.577695i | 0.957375 | + | 0.288848i | \(0.0932721\pi\) | ||||
−0.957375 | + | 0.288848i | \(0.906728\pi\) | |||||||
\(984\) | −32182.4 | −1.04262 | ||||||||
\(985\) | 7786.65 | 0.251881 | ||||||||
\(986\) | 5740.57i | 0.185413i | ||||||||
\(987\) | 16155.2 | 0.520997 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2460.12 | 0.0790974 | ||||||||
\(990\) | 8707.39i | 0.279534i | ||||||||
\(991\) | −8129.69 | −0.260593 | −0.130297 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130297 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(992\) | 109908. | 3.51772 | ||||||||
\(993\) | − 4661.02i | − 0.148956i | ||||||||
\(994\) | − 23260.7i | − 0.742237i | ||||||||
\(995\) | − 169.893i | − 0.00541302i | ||||||||
\(996\) | − 37595.0i | − 1.19603i | ||||||||
\(997\) | −29452.9 | −0.935589 | −0.467795 | − | 0.883837i | \(-0.654951\pi\) | ||||
−0.467795 | + | 0.883837i | \(0.654951\pi\) | |||||||
\(998\) | −26997.7 | −0.856309 | ||||||||
\(999\) | − 4743.52i | − 0.150229i |
(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 | 507.4.b.i.337.1 | 10 | ||
13.5 | odd | 4 | 507.4.a.r.1.1 | 10 | |||
13.8 | odd | 4 | 507.4.a.r.1.10 | 10 | |||
13.9 | even | 3 | 39.4.j.c.10.1 | yes | 10 | ||
13.10 | even | 6 | 39.4.j.c.4.1 | ✓ | 10 | ||
13.12 | even | 2 | inner | 507.4.b.i.337.10 | 10 | ||
39.5 | even | 4 | 1521.4.a.bk.1.10 | 10 | |||
39.8 | even | 4 | 1521.4.a.bk.1.1 | 10 | |||
39.23 | odd | 6 | 117.4.q.e.82.5 | 10 | |||
39.35 | odd | 6 | 117.4.q.e.10.5 | 10 | |||
52.23 | odd | 6 | 624.4.bv.h.433.3 | 10 | |||
52.35 | odd | 6 | 624.4.bv.h.49.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.1 | ✓ | 10 | 13.10 | even | 6 | ||
39.4.j.c.10.1 | yes | 10 | 13.9 | even | 3 | ||
117.4.q.e.10.5 | 10 | 39.35 | odd | 6 | |||
117.4.q.e.82.5 | 10 | 39.23 | odd | 6 | |||
507.4.a.r.1.1 | 10 | 13.5 | odd | 4 | |||
507.4.a.r.1.10 | 10 | 13.8 | odd | 4 | |||
507.4.b.i.337.1 | 10 | 1.1 | even | 1 | trivial | ||
507.4.b.i.337.10 | 10 | 13.12 | even | 2 | inner | ||
624.4.bv.h.49.3 | 10 | 52.35 | odd | 6 | |||
624.4.bv.h.433.3 | 10 | 52.23 | odd | 6 | |||
1521.4.a.bk.1.1 | 10 | 39.8 | even | 4 | |||
1521.4.a.bk.1.10 | 10 | 39.5 | even | 4 |