Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,6,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (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: | \(84.2015054018\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.6.d.d.274.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.176777i | −0.996086 | − | 0.0883883i | \(-0.971828\pi\) | ||||
0.996086 | − | 0.0883883i | \(-0.0281716\pi\) | |||||||
\(3\) | − 9.00000i | − 0.577350i | ||||||||
\(4\) | 31.0000 | 0.968750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −9.00000 | −0.102062 | ||||||||
\(7\) | 49.0000i | 0.377964i | ||||||||
\(8\) | − 63.0000i | − 0.348029i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −340.000 | −0.847222 | −0.423611 | − | 0.905844i | \(-0.639238\pi\) | ||||
−0.423611 | + | 0.905844i | \(0.639238\pi\) | |||||||
\(12\) | − 279.000i | − 0.559308i | ||||||||
\(13\) | 454.000i | 0.745071i | 0.928018 | + | 0.372535i | \(0.121511\pi\) | ||||
−0.928018 | + | 0.372535i | \(0.878489\pi\) | |||||||
\(14\) | 49.0000 | 0.0668153 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 929.000 | 0.907227 | ||||||||
\(17\) | 798.000i | 0.669700i | 0.942271 | + | 0.334850i | \(0.108686\pi\) | ||||
−0.942271 | + | 0.334850i | \(0.891314\pi\) | |||||||
\(18\) | 81.0000i | 0.0589256i | ||||||||
\(19\) | −892.000 | −0.566867 | −0.283433 | − | 0.958992i | \(-0.591473\pi\) | ||||
−0.283433 | + | 0.958992i | \(0.591473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 340.000i | 0.149769i | ||||||||
\(23\) | − 3192.00i | − 1.25818i | −0.777332 | − | 0.629091i | \(-0.783427\pi\) | ||||
0.777332 | − | 0.629091i | \(-0.216573\pi\) | |||||||
\(24\) | −567.000 | −0.200935 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 454.000 | 0.131711 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 1519.00i | 0.366153i | ||||||||
\(29\) | 8242.00 | 1.81986 | 0.909929 | − | 0.414764i | \(-0.136136\pi\) | ||||
0.909929 | + | 0.414764i | \(0.136136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2496.00 | −0.466488 | −0.233244 | − | 0.972418i | \(-0.574934\pi\) | ||||
−0.233244 | + | 0.972418i | \(0.574934\pi\) | |||||||
\(32\) | − 2945.00i | − 0.508406i | ||||||||
\(33\) | 3060.00i | 0.489144i | ||||||||
\(34\) | 798.000 | 0.118387 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2511.00 | −0.322917 | ||||||||
\(37\) | − 9798.00i | − 1.17661i | −0.808639 | − | 0.588306i | \(-0.799795\pi\) | ||||
0.808639 | − | 0.588306i | \(-0.200205\pi\) | |||||||
\(38\) | 892.000i | 0.100209i | ||||||||
\(39\) | 4086.00 | 0.430167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19834.0 | 1.84268 | 0.921342 | − | 0.388754i | \(-0.127094\pi\) | ||||
0.921342 | + | 0.388754i | \(0.127094\pi\) | |||||||
\(42\) | − 441.000i | − 0.0385758i | ||||||||
\(43\) | − 17236.0i | − 1.42156i | −0.703414 | − | 0.710780i | \(-0.748342\pi\) | ||||
0.703414 | − | 0.710780i | \(-0.251658\pi\) | |||||||
\(44\) | −10540.0 | −0.820746 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3192.00 | −0.222417 | ||||||||
\(47\) | − 8928.00i | − 0.589535i | −0.955569 | − | 0.294767i | \(-0.904758\pi\) | ||||
0.955569 | − | 0.294767i | \(-0.0952422\pi\) | |||||||
\(48\) | − 8361.00i | − 0.523788i | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7182.00 | 0.386652 | ||||||||
\(52\) | 14074.0i | 0.721787i | ||||||||
\(53\) | 150.000i | 0.00733502i | 0.999993 | + | 0.00366751i | \(0.00116741\pi\) | ||||
−0.999993 | + | 0.00366751i | \(0.998833\pi\) | |||||||
\(54\) | 729.000 | 0.0340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3087.00 | 0.131543 | ||||||||
\(57\) | 8028.00i | 0.327281i | ||||||||
\(58\) | − 8242.00i | − 0.321709i | ||||||||
\(59\) | 42396.0 | 1.58560 | 0.792802 | − | 0.609479i | \(-0.208621\pi\) | ||||
0.792802 | + | 0.609479i | \(0.208621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14758.0 | 0.507812 | 0.253906 | − | 0.967229i | \(-0.418285\pi\) | ||||
0.253906 | + | 0.967229i | \(0.418285\pi\) | |||||||
\(62\) | 2496.00i | 0.0824642i | ||||||||
\(63\) | − 3969.00i | − 0.125988i | ||||||||
\(64\) | 26783.0 | 0.817352 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3060.00 | 0.0864692 | ||||||||
\(67\) | 1676.00i | 0.0456128i | 0.999740 | + | 0.0228064i | \(0.00726014\pi\) | ||||
−0.999740 | + | 0.0228064i | \(0.992740\pi\) | |||||||
\(68\) | 24738.0i | 0.648772i | ||||||||
\(69\) | −28728.0 | −0.726411 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14568.0 | 0.342968 | 0.171484 | − | 0.985187i | \(-0.445144\pi\) | ||||
0.171484 | + | 0.985187i | \(0.445144\pi\) | |||||||
\(72\) | 5103.00i | 0.116010i | ||||||||
\(73\) | 78378.0i | 1.72142i | 0.509095 | + | 0.860710i | \(0.329980\pi\) | ||||
−0.509095 | + | 0.860710i | \(0.670020\pi\) | |||||||
\(74\) | −9798.00 | −0.207998 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27652.0 | −0.549152 | ||||||||
\(77\) | − 16660.0i | − 0.320220i | ||||||||
\(78\) | − 4086.00i | − 0.0760435i | ||||||||
\(79\) | 2272.00 | 0.0409582 | 0.0204791 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204791 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − 19834.0i | − 0.325743i | ||||||||
\(83\) | − 37764.0i | − 0.601704i | −0.953671 | − | 0.300852i | \(-0.902729\pi\) | ||||
0.953671 | − | 0.300852i | \(-0.0972710\pi\) | |||||||
\(84\) | 13671.0 | 0.211399 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17236.0 | −0.251299 | ||||||||
\(87\) | − 74178.0i | − 1.05070i | ||||||||
\(88\) | 21420.0i | 0.294858i | ||||||||
\(89\) | 117286. | 1.56954 | 0.784768 | − | 0.619790i | \(-0.212782\pi\) | ||||
0.784768 | + | 0.619790i | \(0.212782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22246.0 | −0.281610 | ||||||||
\(92\) | − 98952.0i | − 1.21886i | ||||||||
\(93\) | 22464.0i | 0.269327i | ||||||||
\(94\) | −8928.00 | −0.104216 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −26505.0 | −0.293528 | ||||||||
\(97\) | − 10002.0i | − 0.107934i | −0.998543 | − | 0.0539669i | \(-0.982813\pi\) | ||||
0.998543 | − | 0.0539669i | \(-0.0171865\pi\) | |||||||
\(98\) | 2401.00i | 0.0252538i | ||||||||
\(99\) | 27540.0 | 0.282407 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −108770. | −1.06098 | −0.530488 | − | 0.847692i | \(-0.677991\pi\) | ||||
−0.530488 | + | 0.847692i | \(0.677991\pi\) | |||||||
\(102\) | − 7182.00i | − 0.0683510i | ||||||||
\(103\) | − 199192.i | − 1.85003i | −0.379930 | − | 0.925015i | \(-0.624052\pi\) | ||||
0.379930 | − | 0.925015i | \(-0.375948\pi\) | |||||||
\(104\) | 28602.0 | 0.259306 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 150.000 | 0.00129666 | ||||||||
\(107\) | 79972.0i | 0.675272i | 0.941277 | + | 0.337636i | \(0.109627\pi\) | ||||
−0.941277 | + | 0.337636i | \(0.890373\pi\) | |||||||
\(108\) | 22599.0i | 0.186436i | ||||||||
\(109\) | 46098.0 | 0.371634 | 0.185817 | − | 0.982584i | \(-0.440507\pi\) | ||||
0.185817 | + | 0.982584i | \(0.440507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −88182.0 | −0.679317 | ||||||||
\(112\) | 45521.0i | 0.342899i | ||||||||
\(113\) | 262706.i | 1.93541i | 0.252078 | + | 0.967707i | \(0.418886\pi\) | ||||
−0.252078 | + | 0.967707i | \(0.581114\pi\) | |||||||
\(114\) | 8028.00 | 0.0578556 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 255502. | 1.76299 | ||||||||
\(117\) | − 36774.0i | − 0.248357i | ||||||||
\(118\) | − 42396.0i | − 0.280298i | ||||||||
\(119\) | −39102.0 | −0.253123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −45451.0 | −0.282215 | ||||||||
\(122\) | − 14758.0i | − 0.0897693i | ||||||||
\(123\) | − 178506.i | − 1.06387i | ||||||||
\(124\) | −77376.0 | −0.451910 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3969.00 | −0.0222718 | ||||||||
\(127\) | − 196608.i | − 1.08166i | −0.841131 | − | 0.540831i | \(-0.818110\pi\) | ||||
0.841131 | − | 0.540831i | \(-0.181890\pi\) | |||||||
\(128\) | − 121023.i | − 0.652894i | ||||||||
\(129\) | −155124. | −0.820738 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77140.0 | −0.392737 | −0.196368 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196368 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(132\) | 94860.0i | 0.473858i | ||||||||
\(133\) | − 43708.0i | − 0.214255i | ||||||||
\(134\) | 1676.00 | 0.00806329 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 50274.0 | 0.233075 | ||||||||
\(137\) | − 208170.i | − 0.947582i | −0.880637 | − | 0.473791i | \(-0.842885\pi\) | ||||
0.880637 | − | 0.473791i | \(-0.157115\pi\) | |||||||
\(138\) | 28728.0i | 0.128413i | ||||||||
\(139\) | 275580. | 1.20979 | 0.604896 | − | 0.796304i | \(-0.293215\pi\) | ||||
0.604896 | + | 0.796304i | \(0.293215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −80352.0 | −0.340368 | ||||||||
\(142\) | − 14568.0i | − 0.0606288i | ||||||||
\(143\) | − 154360.i | − 0.631240i | ||||||||
\(144\) | −75249.0 | −0.302409 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 78378.0 | 0.304307 | ||||||||
\(147\) | 21609.0i | 0.0824786i | ||||||||
\(148\) | − 303738.i | − 1.13984i | ||||||||
\(149\) | 296106. | 1.09265 | 0.546326 | − | 0.837573i | \(-0.316026\pi\) | ||||
0.546326 | + | 0.837573i | \(0.316026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −426472. | −1.52212 | −0.761059 | − | 0.648683i | \(-0.775320\pi\) | ||||
−0.761059 | + | 0.648683i | \(0.775320\pi\) | |||||||
\(152\) | 56196.0i | 0.197286i | ||||||||
\(153\) | − 64638.0i | − 0.223233i | ||||||||
\(154\) | −16660.0 | −0.0566074 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 126666. | 0.416724 | ||||||||
\(157\) | − 178486.i | − 0.577903i | −0.957344 | − | 0.288952i | \(-0.906693\pi\) | ||||
0.957344 | − | 0.288952i | \(-0.0933067\pi\) | |||||||
\(158\) | − 2272.00i | − 0.00724045i | ||||||||
\(159\) | 1350.00 | 0.00423488 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 156408. | 0.475548 | ||||||||
\(162\) | − 6561.00i | − 0.0196419i | ||||||||
\(163\) | 252772.i | 0.745178i | 0.927996 | + | 0.372589i | \(0.121530\pi\) | ||||
−0.927996 | + | 0.372589i | \(0.878470\pi\) | |||||||
\(164\) | 614854. | 1.78510 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37764.0 | −0.106367 | ||||||||
\(167\) | − 508088.i | − 1.40977i | −0.709322 | − | 0.704884i | \(-0.750999\pi\) | ||||
0.709322 | − | 0.704884i | \(-0.249001\pi\) | |||||||
\(168\) | − 27783.0i | − 0.0759462i | ||||||||
\(169\) | 165177. | 0.444870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 72252.0 | 0.188956 | ||||||||
\(172\) | − 534316.i | − 1.37714i | ||||||||
\(173\) | − 221834.i | − 0.563525i | −0.959484 | − | 0.281762i | \(-0.909081\pi\) | ||||
0.959484 | − | 0.281762i | \(-0.0909190\pi\) | |||||||
\(174\) | −74178.0 | −0.185739 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −315860. | −0.768622 | ||||||||
\(177\) | − 381564.i | − 0.915449i | ||||||||
\(178\) | − 117286.i | − 0.277457i | ||||||||
\(179\) | 113564. | 0.264916 | 0.132458 | − | 0.991189i | \(-0.457713\pi\) | ||||
0.132458 | + | 0.991189i | \(0.457713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 663118. | 1.50451 | 0.752254 | − | 0.658873i | \(-0.228967\pi\) | ||||
0.752254 | + | 0.658873i | \(0.228967\pi\) | |||||||
\(182\) | 22246.0i | 0.0497821i | ||||||||
\(183\) | − 132822.i | − 0.293185i | ||||||||
\(184\) | −201096. | −0.437884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 22464.0 | 0.0476107 | ||||||||
\(187\) | − 271320.i | − 0.567385i | ||||||||
\(188\) | − 276768.i | − 0.571112i | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 505664. | 1.00295 | 0.501474 | − | 0.865173i | \(-0.332791\pi\) | ||||
0.501474 | + | 0.865173i | \(0.332791\pi\) | |||||||
\(192\) | − 241047.i | − 0.471899i | ||||||||
\(193\) | − 432382.i | − 0.835554i | −0.908550 | − | 0.417777i | \(-0.862809\pi\) | ||||
0.908550 | − | 0.417777i | \(-0.137191\pi\) | |||||||
\(194\) | −10002.0 | −0.0190802 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −74431.0 | −0.138393 | ||||||||
\(197\) | 131962.i | 0.242261i | 0.992637 | + | 0.121130i | \(0.0386519\pi\) | ||||
−0.992637 | + | 0.121130i | \(0.961348\pi\) | |||||||
\(198\) | − 27540.0i | − 0.0499230i | ||||||||
\(199\) | −298536. | −0.534397 | −0.267199 | − | 0.963642i | \(-0.586098\pi\) | ||||
−0.267199 | + | 0.963642i | \(0.586098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15084.0 | 0.0263346 | ||||||||
\(202\) | 108770.i | 0.187556i | ||||||||
\(203\) | 403858.i | 0.687842i | ||||||||
\(204\) | 222642. | 0.374569 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −199192. | −0.327042 | ||||||||
\(207\) | 258552.i | 0.419394i | ||||||||
\(208\) | 421766.i | 0.675948i | ||||||||
\(209\) | 303280. | 0.480262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17062e6 | −1.81013 | −0.905065 | − | 0.425273i | \(-0.860178\pi\) | ||||
−0.905065 | + | 0.425273i | \(0.860178\pi\) | |||||||
\(212\) | 4650.00i | 0.00710581i | ||||||||
\(213\) | − 131112.i | − 0.198013i | ||||||||
\(214\) | 79972.0 | 0.119372 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 45927.0 | 0.0669782 | ||||||||
\(217\) | − 122304.i | − 0.176316i | ||||||||
\(218\) | − 46098.0i | − 0.0656963i | ||||||||
\(219\) | 705402. | 0.993863 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −362292. | −0.498974 | ||||||||
\(222\) | 88182.0i | 0.120087i | ||||||||
\(223\) | 399376.i | 0.537799i | 0.963168 | + | 0.268899i | \(0.0866599\pi\) | ||||
−0.963168 | + | 0.268899i | \(0.913340\pi\) | |||||||
\(224\) | 144305. | 0.192159 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 262706. | 0.342136 | ||||||||
\(227\) | − 707916.i | − 0.911837i | −0.890022 | − | 0.455918i | \(-0.849311\pi\) | ||||
0.890022 | − | 0.455918i | \(-0.150689\pi\) | |||||||
\(228\) | 248868.i | 0.317053i | ||||||||
\(229\) | 735778. | 0.927167 | 0.463584 | − | 0.886053i | \(-0.346563\pi\) | ||||
0.463584 | + | 0.886053i | \(0.346563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −149940. | −0.184879 | ||||||||
\(232\) | − 519246.i | − 0.633364i | ||||||||
\(233\) | − 208758.i | − 0.251915i | −0.992036 | − | 0.125957i | \(-0.959800\pi\) | ||||
0.992036 | − | 0.125957i | \(-0.0402002\pi\) | |||||||
\(234\) | −36774.0 | −0.0439037 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.31428e6 | 1.53605 | ||||||||
\(237\) | − 20448.0i | − 0.0236472i | ||||||||
\(238\) | 39102.0i | 0.0447462i | ||||||||
\(239\) | −713376. | −0.807837 | −0.403919 | − | 0.914795i | \(-0.632352\pi\) | ||||
−0.403919 | + | 0.914795i | \(0.632352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −505246. | −0.560351 | −0.280176 | − | 0.959949i | \(-0.590393\pi\) | ||||
−0.280176 | + | 0.959949i | \(0.590393\pi\) | |||||||
\(242\) | 45451.0i | 0.0498890i | ||||||||
\(243\) | − 59049.0i | − 0.0641500i | ||||||||
\(244\) | 457498. | 0.491943 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −178506. | −0.188068 | ||||||||
\(247\) | − 404968.i | − 0.422356i | ||||||||
\(248\) | 157248.i | 0.162351i | ||||||||
\(249\) | −339876. | −0.347394 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 317108. | 0.317704 | 0.158852 | − | 0.987302i | \(-0.449221\pi\) | ||||
0.158852 | + | 0.987302i | \(0.449221\pi\) | |||||||
\(252\) | − 123039.i | − 0.122051i | ||||||||
\(253\) | 1.08528e6i | 1.06596i | ||||||||
\(254\) | −196608. | −0.191213 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 736033. | 0.701936 | ||||||||
\(257\) | 1.44285e6i | 1.36266i | 0.731977 | + | 0.681329i | \(0.238598\pi\) | ||||
−0.731977 | + | 0.681329i | \(0.761402\pi\) | |||||||
\(258\) | 155124.i | 0.145087i | ||||||||
\(259\) | 480102. | 0.444717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −667602. | −0.606619 | ||||||||
\(262\) | 77140.0i | 0.0694267i | ||||||||
\(263\) | 271496.i | 0.242033i | 0.992651 | + | 0.121016i | \(0.0386153\pi\) | ||||
−0.992651 | + | 0.121016i | \(0.961385\pi\) | |||||||
\(264\) | 192780. | 0.170236 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −43708.0 | −0.0378754 | ||||||||
\(267\) | − 1.05557e6i | − 0.906172i | ||||||||
\(268\) | 51956.0i | 0.0441874i | ||||||||
\(269\) | −850614. | −0.716724 | −0.358362 | − | 0.933583i | \(-0.616665\pi\) | ||||
−0.358362 | + | 0.933583i | \(0.616665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −540128. | −0.446759 | −0.223380 | − | 0.974732i | \(-0.571709\pi\) | ||||
−0.223380 | + | 0.974732i | \(0.571709\pi\) | |||||||
\(272\) | 741342.i | 0.607570i | ||||||||
\(273\) | 200214.i | 0.162588i | ||||||||
\(274\) | −208170. | −0.167510 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −890568. | −0.703711 | ||||||||
\(277\) | − 513574.i | − 0.402164i | −0.979574 | − | 0.201082i | \(-0.935554\pi\) | ||||
0.979574 | − | 0.201082i | \(-0.0644458\pi\) | |||||||
\(278\) | − 275580.i | − 0.213863i | ||||||||
\(279\) | 202176. | 0.155496 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.35642e6 | −1.02478 | −0.512388 | − | 0.858754i | \(-0.671239\pi\) | ||||
−0.512388 | + | 0.858754i | \(0.671239\pi\) | |||||||
\(282\) | 80352.0i | 0.0601692i | ||||||||
\(283\) | 286756.i | 0.212837i | 0.994321 | + | 0.106418i | \(0.0339383\pi\) | ||||
−0.994321 | + | 0.106418i | \(0.966062\pi\) | |||||||
\(284\) | 451608. | 0.332251 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −154360. | −0.111589 | ||||||||
\(287\) | 971866.i | 0.696469i | ||||||||
\(288\) | 238545.i | 0.169469i | ||||||||
\(289\) | 783053. | 0.551501 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −90018.0 | −0.0623156 | ||||||||
\(292\) | 2.42972e6i | 1.66763i | ||||||||
\(293\) | − 1.70727e6i | − 1.16180i | −0.813974 | − | 0.580901i | \(-0.802700\pi\) | ||||
0.813974 | − | 0.580901i | \(-0.197300\pi\) | |||||||
\(294\) | 21609.0 | 0.0145803 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −617274. | −0.409495 | ||||||||
\(297\) | − 247860.i | − 0.163048i | ||||||||
\(298\) | − 296106.i | − 0.193155i | ||||||||
\(299\) | 1.44917e6 | 0.937434 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 844564. | 0.537299 | ||||||||
\(302\) | 426472.i | 0.269075i | ||||||||
\(303\) | 978930.i | 0.612555i | ||||||||
\(304\) | −828668. | −0.514276 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −64638.0 | −0.0394625 | ||||||||
\(307\) | 546788.i | 0.331111i | 0.986201 | + | 0.165555i | \(0.0529416\pi\) | ||||
−0.986201 | + | 0.165555i | \(0.947058\pi\) | |||||||
\(308\) | − 516460.i | − 0.310213i | ||||||||
\(309\) | −1.79273e6 | −1.06812 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.23426e6 | 1.89616 | 0.948079 | − | 0.318035i | \(-0.103023\pi\) | ||||
0.948079 | + | 0.318035i | \(0.103023\pi\) | |||||||
\(312\) | − 257418.i | − 0.149711i | ||||||||
\(313\) | 1.81313e6i | 1.04609i | 0.852306 | + | 0.523044i | \(0.175204\pi\) | ||||
−0.852306 | + | 0.523044i | \(0.824796\pi\) | |||||||
\(314\) | −178486. | −0.102160 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 70432.0 | 0.0396782 | ||||||||
\(317\) | 1.27658e6i | 0.713509i | 0.934198 | + | 0.356754i | \(0.116117\pi\) | ||||
−0.934198 | + | 0.356754i | \(0.883883\pi\) | |||||||
\(318\) | − 1350.00i | 0 0.000748628i | ||||||||
\(319\) | −2.80228e6 | −1.54182 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 719748. | 0.389868 | ||||||||
\(322\) | − 156408.i | − 0.0840658i | ||||||||
\(323\) | − 711816.i | − 0.379631i | ||||||||
\(324\) | 203391. | 0.107639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 252772. | 0.131730 | ||||||||
\(327\) | − 414882.i | − 0.214563i | ||||||||
\(328\) | − 1.24954e6i | − 0.641307i | ||||||||
\(329\) | 437472. | 0.222823 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.73621e6 | −0.871029 | −0.435515 | − | 0.900182i | \(-0.643434\pi\) | ||||
−0.435515 | + | 0.900182i | \(0.643434\pi\) | |||||||
\(332\) | − 1.17068e6i | − 0.582901i | ||||||||
\(333\) | 793638.i | 0.392204i | ||||||||
\(334\) | −508088. | −0.249214 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 409689. | 0.197973 | ||||||||
\(337\) | − 2.07215e6i | − 0.993907i | −0.867777 | − | 0.496953i | \(-0.834452\pi\) | ||||
0.867777 | − | 0.496953i | \(-0.165548\pi\) | |||||||
\(338\) | − 165177.i | − 0.0786426i | ||||||||
\(339\) | 2.36435e6 | 1.11741 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 848640. | 0.395219 | ||||||||
\(342\) | − 72252.0i | − 0.0334029i | ||||||||
\(343\) | − 117649.i | − 0.0539949i | ||||||||
\(344\) | −1.08587e6 | −0.494744 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −221834. | −0.0996180 | ||||||||
\(347\) | 1.65146e6i | 0.736282i | 0.929770 | + | 0.368141i | \(0.120006\pi\) | ||||
−0.929770 | + | 0.368141i | \(0.879994\pi\) | |||||||
\(348\) | − 2.29952e6i | − 1.01786i | ||||||||
\(349\) | −1.26645e6 | −0.556578 | −0.278289 | − | 0.960497i | \(-0.589767\pi\) | ||||
−0.278289 | + | 0.960497i | \(0.589767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −330966. | −0.143389 | ||||||||
\(352\) | 1.00130e6i | 0.430732i | ||||||||
\(353\) | 573218.i | 0.244840i | 0.992478 | + | 0.122420i | \(0.0390656\pi\) | ||||
−0.992478 | + | 0.122420i | \(0.960934\pi\) | |||||||
\(354\) | −381564. | −0.161830 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.63587e6 | 1.52049 | ||||||||
\(357\) | 351918.i | 0.146141i | ||||||||
\(358\) | − 113564.i | − 0.0468310i | ||||||||
\(359\) | −4.46322e6 | −1.82773 | −0.913866 | − | 0.406016i | \(-0.866918\pi\) | ||||
−0.913866 | + | 0.406016i | \(0.866918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.68044e6 | −0.678662 | ||||||||
\(362\) | − 663118.i | − 0.265962i | ||||||||
\(363\) | 409059.i | 0.162937i | ||||||||
\(364\) | −689626. | −0.272810 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −132822. | −0.0518283 | ||||||||
\(367\) | 4.50797e6i | 1.74709i | 0.486742 | + | 0.873546i | \(0.338185\pi\) | ||||
−0.486742 | + | 0.873546i | \(0.661815\pi\) | |||||||
\(368\) | − 2.96537e6i | − 1.14146i | ||||||||
\(369\) | −1.60655e6 | −0.614228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7350.00 | −0.00277238 | ||||||||
\(372\) | 696384.i | 0.260910i | ||||||||
\(373\) | 1.66535e6i | 0.619774i | 0.950773 | + | 0.309887i | \(0.100291\pi\) | ||||
−0.950773 | + | 0.309887i | \(0.899709\pi\) | |||||||
\(374\) | −271320. | −0.100300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −562464. | −0.205175 | ||||||||
\(377\) | 3.74187e6i | 1.35592i | ||||||||
\(378\) | 35721.0i | 0.0128586i | ||||||||
\(379\) | 2.53232e6 | 0.905568 | 0.452784 | − | 0.891620i | \(-0.350431\pi\) | ||||
0.452784 | + | 0.891620i | \(0.350431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.76947e6 | −0.624498 | ||||||||
\(382\) | − 505664.i | − 0.177298i | ||||||||
\(383\) | 796368.i | 0.277407i | 0.990334 | + | 0.138703i | \(0.0442934\pi\) | ||||
−0.990334 | + | 0.138703i | \(0.955707\pi\) | |||||||
\(384\) | −1.08921e6 | −0.376949 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −432382. | −0.147706 | ||||||||
\(387\) | 1.39612e6i | 0.473853i | ||||||||
\(388\) | − 310062.i | − 0.104561i | ||||||||
\(389\) | −1.94799e6 | −0.652699 | −0.326349 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326349 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.54722e6 | 0.842605 | ||||||||
\(392\) | 151263.i | 0.0497184i | ||||||||
\(393\) | 694260.i | 0.226747i | ||||||||
\(394\) | 131962. | 0.0428261 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 853740. | 0.273582 | ||||||||
\(397\) | − 1.08116e6i | − 0.344281i | −0.985072 | − | 0.172140i | \(-0.944932\pi\) | ||||
0.985072 | − | 0.172140i | \(-0.0550683\pi\) | |||||||
\(398\) | 298536.i | 0.0944689i | ||||||||
\(399\) | −393372. | −0.123700 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.76770e6 | 0.859524 | 0.429762 | − | 0.902942i | \(-0.358598\pi\) | ||||
0.429762 | + | 0.902942i | \(0.358598\pi\) | |||||||
\(402\) | − 15084.0i | − 0.00465534i | ||||||||
\(403\) | − 1.13318e6i | − 0.347566i | ||||||||
\(404\) | −3.37187e6 | −1.02782 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 403858. | 0.121594 | ||||||||
\(407\) | 3.33132e6i | 0.996851i | ||||||||
\(408\) | − 452466.i | − 0.134566i | ||||||||
\(409\) | −2.36350e6 | −0.698630 | −0.349315 | − | 0.937005i | \(-0.613586\pi\) | ||||
−0.349315 | + | 0.937005i | \(0.613586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.87353e6 | −0.547087 | ||||||||
\(412\) | − 6.17495e6i | − 1.79222i | ||||||||
\(413\) | 2.07740e6i | 0.599302i | ||||||||
\(414\) | 258552. | 0.0741391 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.33703e6 | 0.378798 | ||||||||
\(417\) | − 2.48022e6i | − 0.698474i | ||||||||
\(418\) | − 303280.i | − 0.0848991i | ||||||||
\(419\) | 2.98669e6 | 0.831104 | 0.415552 | − | 0.909569i | \(-0.363588\pi\) | ||||
0.415552 | + | 0.909569i | \(0.363588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.46331e6 | −0.952326 | −0.476163 | − | 0.879357i | \(-0.657973\pi\) | ||||
−0.476163 | + | 0.879357i | \(0.657973\pi\) | |||||||
\(422\) | 1.17062e6i | 0.319989i | ||||||||
\(423\) | 723168.i | 0.196512i | ||||||||
\(424\) | 9450.00 | 0.00255280 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −131112. | −0.0350041 | ||||||||
\(427\) | 723142.i | 0.191935i | ||||||||
\(428\) | 2.47913e6i | 0.654169i | ||||||||
\(429\) | −1.38924e6 | −0.364447 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.33693e6 | 0.605971 | 0.302986 | − | 0.952995i | \(-0.402017\pi\) | ||||
0.302986 | + | 0.952995i | \(0.402017\pi\) | |||||||
\(432\) | 677241.i | 0.174596i | ||||||||
\(433\) | − 3.50838e6i | − 0.899264i | −0.893214 | − | 0.449632i | \(-0.851555\pi\) | ||||
0.893214 | − | 0.449632i | \(-0.148445\pi\) | |||||||
\(434\) | −122304. | −0.0311685 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.42904e6 | 0.360021 | ||||||||
\(437\) | 2.84726e6i | 0.713221i | ||||||||
\(438\) | − 705402.i | − 0.175692i | ||||||||
\(439\) | −3.54833e6 | −0.878744 | −0.439372 | − | 0.898305i | \(-0.644799\pi\) | ||||
−0.439372 | + | 0.898305i | \(0.644799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 362292.i | 0.0882070i | ||||||||
\(443\) | 1.76833e6i | 0.428109i | 0.976822 | + | 0.214055i | \(0.0686670\pi\) | ||||
−0.976822 | + | 0.214055i | \(0.931333\pi\) | |||||||
\(444\) | −2.73364e6 | −0.658088 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 399376. | 0.0950703 | ||||||||
\(447\) | − 2.66495e6i | − 0.630842i | ||||||||
\(448\) | 1.31237e6i | 0.308930i | ||||||||
\(449\) | 5.52579e6 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.74356e6 | −1.56116 | ||||||||
\(452\) | 8.14389e6i | 1.87493i | ||||||||
\(453\) | 3.83825e6i | 0.878795i | ||||||||
\(454\) | −707916. | −0.161191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 505764. | 0.113903 | ||||||||
\(457\) | 2.96226e6i | 0.663488i | 0.943369 | + | 0.331744i | \(0.107637\pi\) | ||||
−0.943369 | + | 0.331744i | \(0.892363\pi\) | |||||||
\(458\) | − 735778.i | − 0.163902i | ||||||||
\(459\) | −581742. | −0.128884 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.11884e6 | 0.464350 | 0.232175 | − | 0.972674i | \(-0.425416\pi\) | ||||
0.232175 | + | 0.972674i | \(0.425416\pi\) | |||||||
\(462\) | 149940.i | 0.0326823i | ||||||||
\(463\) | 3.19226e6i | 0.692062i | 0.938223 | + | 0.346031i | \(0.112471\pi\) | ||||
−0.938223 | + | 0.346031i | \(0.887529\pi\) | |||||||
\(464\) | 7.65682e6 | 1.65102 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −208758. | −0.0445326 | ||||||||
\(467\) | 7.42621e6i | 1.57571i | 0.615863 | + | 0.787853i | \(0.288807\pi\) | ||||
−0.615863 | + | 0.787853i | \(0.711193\pi\) | |||||||
\(468\) | − 1.13999e6i | − 0.240596i | ||||||||
\(469\) | −82124.0 | −0.0172400 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.60637e6 | −0.333653 | ||||||||
\(472\) | − 2.67095e6i | − 0.551837i | ||||||||
\(473\) | 5.86024e6i | 1.20438i | ||||||||
\(474\) | −20448.0 | −0.00418028 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.21216e6 | −0.245213 | ||||||||
\(477\) | − 12150.0i | − 0.00244501i | ||||||||
\(478\) | 713376.i | 0.142807i | ||||||||
\(479\) | 3.39685e6 | 0.676453 | 0.338226 | − | 0.941065i | \(-0.390173\pi\) | ||||
0.338226 | + | 0.941065i | \(0.390173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.44829e6 | 0.876659 | ||||||||
\(482\) | 505246.i | 0.0990570i | ||||||||
\(483\) | − 1.40767e6i | − 0.274558i | ||||||||
\(484\) | −1.40898e6 | −0.273396 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −59049.0 | −0.0113402 | ||||||||
\(487\) | 3.71382e6i | 0.709574i | 0.934947 | + | 0.354787i | \(0.115447\pi\) | ||||
−0.934947 | + | 0.354787i | \(0.884553\pi\) | |||||||
\(488\) | − 929754.i | − 0.176733i | ||||||||
\(489\) | 2.27495e6 | 0.430229 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.57494e6 | 1.04361 | 0.521803 | − | 0.853066i | \(-0.325260\pi\) | ||||
0.521803 | + | 0.853066i | \(0.325260\pi\) | |||||||
\(492\) | − 5.53369e6i | − 1.03063i | ||||||||
\(493\) | 6.57712e6i | 1.21876i | ||||||||
\(494\) | −404968. | −0.0746626 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.31878e6 | −0.423210 | ||||||||
\(497\) | 713832.i | 0.129630i | ||||||||
\(498\) | 339876.i | 0.0614111i | ||||||||
\(499\) | −3.92698e6 | −0.706004 | −0.353002 | − | 0.935623i | \(-0.614839\pi\) | ||||
−0.353002 | + | 0.935623i | \(0.614839\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.57279e6 | −0.813930 | ||||||||
\(502\) | − 317108.i | − 0.0561627i | ||||||||
\(503\) | 6.42079e6i | 1.13154i | 0.824564 | + | 0.565768i | \(0.191420\pi\) | ||||
−0.824564 | + | 0.565768i | \(0.808580\pi\) | |||||||
\(504\) | −250047. | −0.0438475 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.08528e6 | 0.188437 | ||||||||
\(507\) | − 1.48659e6i | − 0.256846i | ||||||||
\(508\) | − 6.09485e6i | − 1.04786i | ||||||||
\(509\) | −146278. | −0.0250256 | −0.0125128 | − | 0.999922i | \(-0.503983\pi\) | ||||
−0.0125128 | + | 0.999922i | \(0.503983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.84052e6 | −0.650636 | ||||||||
\(512\) | − 4.60877e6i | − 0.776980i | ||||||||
\(513\) | − 650268.i | − 0.109094i | ||||||||
\(514\) | 1.44285e6 | 0.240886 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.80884e6 | −0.795090 | ||||||||
\(517\) | 3.03552e6i | 0.499467i | ||||||||
\(518\) | − 480102.i | − 0.0786157i | ||||||||
\(519\) | −1.99651e6 | −0.325351 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.70937e6 | 1.24430 | 0.622149 | − | 0.782899i | \(-0.286260\pi\) | ||||
0.622149 | + | 0.782899i | \(0.286260\pi\) | |||||||
\(522\) | 667602.i | 0.107236i | ||||||||
\(523\) | − 569420.i | − 0.0910287i | −0.998964 | − | 0.0455144i | \(-0.985507\pi\) | ||||
0.998964 | − | 0.0455144i | \(-0.0144927\pi\) | |||||||
\(524\) | −2.39134e6 | −0.380464 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 271496. | 0.0427857 | ||||||||
\(527\) | − 1.99181e6i | − 0.312407i | ||||||||
\(528\) | 2.84274e6i | 0.443764i | ||||||||
\(529\) | −3.75252e6 | −0.583021 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.43408e6 | −0.528535 | ||||||||
\(532\) | − 1.35495e6i | − 0.207560i | ||||||||
\(533\) | 9.00464e6i | 1.37293i | ||||||||
\(534\) | −1.05557e6 | −0.160190 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 105588. | 0.0158746 | ||||||||
\(537\) | − 1.02208e6i | − 0.152949i | ||||||||
\(538\) | 850614.i | 0.126700i | ||||||||
\(539\) | 816340. | 0.121032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.44802e6 | −1.38787 | −0.693933 | − | 0.720040i | \(-0.744124\pi\) | ||||
−0.693933 | + | 0.720040i | \(0.744124\pi\) | |||||||
\(542\) | 540128.i | 0.0789766i | ||||||||
\(543\) | − 5.96806e6i | − 0.868628i | ||||||||
\(544\) | 2.35011e6 | 0.340479 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 200214. | 0.0287417 | ||||||||
\(547\) | 1.35321e6i | 0.193374i | 0.995315 | + | 0.0966869i | \(0.0308245\pi\) | ||||
−0.995315 | + | 0.0966869i | \(0.969175\pi\) | |||||||
\(548\) | − 6.45327e6i | − 0.917970i | ||||||||
\(549\) | −1.19540e6 | −0.169271 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.35186e6 | −1.03162 | ||||||||
\(552\) | 1.80986e6i | 0.252812i | ||||||||
\(553\) | 111328.i | 0.0154807i | ||||||||
\(554\) | −513574. | −0.0710933 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.54298e6 | 1.17199 | ||||||||
\(557\) | − 8.19390e6i | − 1.11906i | −0.828811 | − | 0.559529i | \(-0.810982\pi\) | ||||
0.828811 | − | 0.559529i | \(-0.189018\pi\) | |||||||
\(558\) | − 202176.i | − 0.0274881i | ||||||||
\(559\) | 7.82514e6 | 1.05916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.44188e6 | −0.327580 | ||||||||
\(562\) | 1.35642e6i | 0.181157i | ||||||||
\(563\) | − 1.05796e7i | − 1.40669i | −0.710847 | − | 0.703347i | \(-0.751688\pi\) | ||||
0.710847 | − | 0.703347i | \(-0.248312\pi\) | |||||||
\(564\) | −2.49091e6 | −0.329732 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 286756. | 0.0376246 | ||||||||
\(567\) | 321489.i | 0.0419961i | ||||||||
\(568\) | − 917784.i | − 0.119363i | ||||||||
\(569\) | 1.20205e7 | 1.55648 | 0.778238 | − | 0.627969i | \(-0.216114\pi\) | ||||
0.778238 | + | 0.627969i | \(0.216114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.48948e6 | −0.319534 | −0.159767 | − | 0.987155i | \(-0.551074\pi\) | ||||
−0.159767 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(572\) | − 4.78516e6i | − 0.611514i | ||||||||
\(573\) | − 4.55098e6i | − 0.579053i | ||||||||
\(574\) | 971866. | 0.123119 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.16942e6 | −0.272451 | ||||||||
\(577\) | − 8.21322e6i | − 1.02701i | −0.858087 | − | 0.513504i | \(-0.828347\pi\) | ||||
0.858087 | − | 0.513504i | \(-0.171653\pi\) | |||||||
\(578\) | − 783053.i | − 0.0974926i | ||||||||
\(579\) | −3.89144e6 | −0.482407 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85044e6 | 0.227423 | ||||||||
\(582\) | 90018.0i | 0.0110159i | ||||||||
\(583\) | − 51000.0i | − 0.00621439i | ||||||||
\(584\) | 4.93781e6 | 0.599105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.70727e6 | −0.205380 | ||||||||
\(587\) | 1.21827e6i | 0.145931i | 0.997334 | + | 0.0729655i | \(0.0232463\pi\) | ||||
−0.997334 | + | 0.0729655i | \(0.976754\pi\) | |||||||
\(588\) | 669879.i | 0.0799012i | ||||||||
\(589\) | 2.22643e6 | 0.264436 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.18766e6 | 0.139869 | ||||||||
\(592\) | − 9.10234e6i | − 1.06745i | ||||||||
\(593\) | − 8.42379e6i | − 0.983718i | −0.870675 | − | 0.491859i | \(-0.836317\pi\) | ||||
0.870675 | − | 0.491859i | \(-0.163683\pi\) | |||||||
\(594\) | −247860. | −0.0288231 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.17929e6 | 1.05851 | ||||||||
\(597\) | 2.68682e6i | 0.308534i | ||||||||
\(598\) | − 1.44917e6i | − 0.165717i | ||||||||
\(599\) | −8.21254e6 | −0.935212 | −0.467606 | − | 0.883937i | \(-0.654883\pi\) | ||||
−0.467606 | + | 0.883937i | \(0.654883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.25478e6 | 0.367566 | 0.183783 | − | 0.982967i | \(-0.441166\pi\) | ||||
0.183783 | + | 0.982967i | \(0.441166\pi\) | |||||||
\(602\) | − 844564.i | − 0.0949820i | ||||||||
\(603\) | − 135756.i | − 0.0152043i | ||||||||
\(604\) | −1.32206e7 | −1.47455 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 978930. | 0.108285 | ||||||||
\(607\) | − 7.82101e6i | − 0.861571i | −0.902454 | − | 0.430785i | \(-0.858237\pi\) | ||||
0.902454 | − | 0.430785i | \(-0.141763\pi\) | |||||||
\(608\) | 2.62694e6i | 0.288198i | ||||||||
\(609\) | 3.63472e6 | 0.397126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.05331e6 | 0.439245 | ||||||||
\(612\) | − 2.00378e6i | − 0.216257i | ||||||||
\(613\) | − 9.51670e6i | − 1.02290i | −0.859312 | − | 0.511452i | \(-0.829108\pi\) | ||||
0.859312 | − | 0.511452i | \(-0.170892\pi\) | |||||||
\(614\) | 546788. | 0.0585326 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.04958e6 | −0.111446 | ||||||||
\(617\) | 7.04895e6i | 0.745438i | 0.927944 | + | 0.372719i | \(0.121574\pi\) | ||||
−0.927944 | + | 0.372719i | \(0.878426\pi\) | |||||||
\(618\) | 1.79273e6i | 0.188818i | ||||||||
\(619\) | 6.32174e6 | 0.663147 | 0.331574 | − | 0.943429i | \(-0.392420\pi\) | ||||
0.331574 | + | 0.943429i | \(0.392420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.32697e6 | 0.242137 | ||||||||
\(622\) | − 3.23426e6i | − 0.335197i | ||||||||
\(623\) | 5.74701e6i | 0.593229i | ||||||||
\(624\) | 3.79589e6 | 0.390259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.81313e6 | 0.184924 | ||||||||
\(627\) | − 2.72952e6i | − 0.277279i | ||||||||
\(628\) | − 5.53307e6i | − 0.559844i | ||||||||
\(629\) | 7.81880e6 | 0.787977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.61236e6 | 0.861090 | 0.430545 | − | 0.902569i | \(-0.358321\pi\) | ||||
0.430545 | + | 0.902569i | \(0.358321\pi\) | |||||||
\(632\) | − 143136.i | − 0.0142546i | ||||||||
\(633\) | 1.05356e7i | 1.04508i | ||||||||
\(634\) | 1.27658e6 | 0.126132 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 41850.0 | 0.00410254 | ||||||||
\(637\) | − 1.09005e6i | − 0.106439i | ||||||||
\(638\) | 2.80228e6i | 0.272559i | ||||||||
\(639\) | −1.18001e6 | −0.114323 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.22829e6 | −0.502590 | −0.251295 | − | 0.967910i | \(-0.580857\pi\) | ||||
−0.251295 | + | 0.967910i | \(0.580857\pi\) | |||||||
\(642\) | − 719748.i | − 0.0689196i | ||||||||
\(643\) | 1.61373e7i | 1.53923i | 0.638508 | + | 0.769615i | \(0.279552\pi\) | ||||
−0.638508 | + | 0.769615i | \(0.720448\pi\) | |||||||
\(644\) | 4.84865e6 | 0.460687 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −711816. | −0.0671099 | ||||||||
\(647\) | 1.58749e7i | 1.49090i | 0.666560 | + | 0.745451i | \(0.267766\pi\) | ||||
−0.666560 | + | 0.745451i | \(0.732234\pi\) | |||||||
\(648\) | − 413343.i | − 0.0386699i | ||||||||
\(649\) | −1.44146e7 | −1.34336 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.10074e6 | −0.101796 | ||||||||
\(652\) | 7.83593e6i | 0.721891i | ||||||||
\(653\) | − 5.94112e6i | − 0.545237i | −0.962122 | − | 0.272619i | \(-0.912110\pi\) | ||||
0.962122 | − | 0.272619i | \(-0.0878897\pi\) | |||||||
\(654\) | −414882. | −0.0379298 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.84258e7 | 1.67173 | ||||||||
\(657\) | − 6.34862e6i | − 0.573807i | ||||||||
\(658\) | − 437472.i | − 0.0393900i | ||||||||
\(659\) | 7.64430e6 | 0.685684 | 0.342842 | − | 0.939393i | \(-0.388610\pi\) | ||||
0.342842 | + | 0.939393i | \(0.388610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.58688e6 | −0.675398 | −0.337699 | − | 0.941254i | \(-0.609649\pi\) | ||||
−0.337699 | + | 0.941254i | \(0.609649\pi\) | |||||||
\(662\) | 1.73621e6i | 0.153978i | ||||||||
\(663\) | 3.26063e6i | 0.288083i | ||||||||
\(664\) | −2.37913e6 | −0.209410 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 793638. | 0.0693325 | ||||||||
\(667\) | − 2.63085e7i | − 2.28971i | ||||||||
\(668\) | − 1.57507e7i | − 1.36571i | ||||||||
\(669\) | 3.59438e6 | 0.310498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.01772e6 | −0.430229 | ||||||||
\(672\) | − 1.29874e6i | − 0.110943i | ||||||||
\(673\) | − 2.06681e7i | − 1.75899i | −0.475910 | − | 0.879494i | \(-0.657881\pi\) | ||||
0.475910 | − | 0.879494i | \(-0.342119\pi\) | |||||||
\(674\) | −2.07215e6 | −0.175700 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.12049e6 | 0.430968 | ||||||||
\(677\) | − 7.89541e6i | − 0.662068i | −0.943619 | − | 0.331034i | \(-0.892602\pi\) | ||||
0.943619 | − | 0.331034i | \(-0.107398\pi\) | |||||||
\(678\) | − 2.36435e6i | − 0.197532i | ||||||||
\(679\) | 490098. | 0.0407951 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.37124e6 | −0.526449 | ||||||||
\(682\) | − 848640.i | − 0.0698655i | ||||||||
\(683\) | − 1.96015e7i | − 1.60782i | −0.594750 | − | 0.803911i | \(-0.702749\pi\) | ||||
0.594750 | − | 0.803911i | \(-0.297251\pi\) | |||||||
\(684\) | 2.23981e6 | 0.183051 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −117649. | −0.00954504 | ||||||||
\(687\) | − 6.62200e6i | − 0.535300i | ||||||||
\(688\) | − 1.60122e7i | − 1.28968i | ||||||||
\(689\) | −68100.0 | −0.00546511 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.72710e7 | −1.37601 | −0.688005 | − | 0.725706i | \(-0.741513\pi\) | ||||
−0.688005 | + | 0.725706i | \(0.741513\pi\) | |||||||
\(692\) | − 6.87685e6i | − 0.545914i | ||||||||
\(693\) | 1.34946e6i | 0.106740i | ||||||||
\(694\) | 1.65146e6 | 0.130158 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.67321e6 | −0.365673 | ||||||||
\(697\) | 1.58275e7i | 1.23405i | ||||||||
\(698\) | 1.26645e6i | 0.0983900i | ||||||||
\(699\) | −1.87882e6 | −0.145443 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.36344e6 | −0.412238 | −0.206119 | − | 0.978527i | \(-0.566083\pi\) | ||||
−0.206119 | + | 0.978527i | \(0.566083\pi\) | |||||||
\(702\) | 330966.i | 0.0253478i | ||||||||
\(703\) | 8.73982e6i | 0.666982i | ||||||||
\(704\) | −9.10622e6 | −0.692479 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 573218. | 0.0432821 | ||||||||
\(707\) | − 5.32973e6i | − 0.401011i | ||||||||
\(708\) | − 1.18285e7i | − 0.886841i | ||||||||
\(709\) | 1.73733e7 | 1.29798 | 0.648988 | − | 0.760798i | \(-0.275192\pi\) | ||||
0.648988 | + | 0.760798i | \(0.275192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −184032. | −0.0136527 | ||||||||
\(712\) | − 7.38902e6i | − 0.546244i | ||||||||
\(713\) | 7.96723e6i | 0.586926i | ||||||||
\(714\) | 351918. | 0.0258343 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.52048e6 | 0.256637 | ||||||||
\(717\) | 6.42038e6i | 0.466405i | ||||||||
\(718\) | 4.46322e6i | 0.323100i | ||||||||
\(719\) | −424608. | −0.0306313 | −0.0153157 | − | 0.999883i | \(-0.504875\pi\) | ||||
−0.0153157 | + | 0.999883i | \(0.504875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.76041e6 | 0.699246 | ||||||||
\(722\) | 1.68044e6i | 0.119972i | ||||||||
\(723\) | 4.54721e6i | 0.323519i | ||||||||
\(724\) | 2.05567e7 | 1.45749 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 409059. | 0.0288034 | ||||||||
\(727\) | − 2.18290e7i | − 1.53179i | −0.642968 | − | 0.765893i | \(-0.722297\pi\) | ||||
0.642968 | − | 0.765893i | \(-0.277703\pi\) | |||||||
\(728\) | 1.40150e6i | 0.0980086i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.37543e7 | 0.952020 | ||||||||
\(732\) | − 4.11748e6i | − 0.284023i | ||||||||
\(733\) | 2.17675e7i | 1.49640i | 0.663470 | + | 0.748202i | \(0.269083\pi\) | ||||
−0.663470 | + | 0.748202i | \(0.730917\pi\) | |||||||
\(734\) | 4.50797e6 | 0.308845 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.40044e6 | −0.639667 | ||||||||
\(737\) | − 569840.i | − 0.0386442i | ||||||||
\(738\) | 1.60655e6i | 0.108581i | ||||||||
\(739\) | −6.21786e6 | −0.418822 | −0.209411 | − | 0.977828i | \(-0.567155\pi\) | ||||
−0.209411 | + | 0.977828i | \(0.567155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.64471e6 | −0.243847 | ||||||||
\(742\) | 7350.00i | 0 0.000490092i | ||||||||
\(743\) | 3.77647e6i | 0.250966i | 0.992096 | + | 0.125483i | \(0.0400480\pi\) | ||||
−0.992096 | + | 0.125483i | \(0.959952\pi\) | |||||||
\(744\) | 1.41523e6 | 0.0937336 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.66535e6 | 0.109562 | ||||||||
\(747\) | 3.05888e6i | 0.200568i | ||||||||
\(748\) | − 8.41092e6i | − 0.549654i | ||||||||
\(749\) | −3.91863e6 | −0.255229 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.88795e6 | −0.186849 | −0.0934244 | − | 0.995626i | \(-0.529781\pi\) | ||||
−0.0934244 | + | 0.995626i | \(0.529781\pi\) | |||||||
\(752\) | − 8.29411e6i | − 0.534842i | ||||||||
\(753\) | − 2.85397e6i | − 0.183427i | ||||||||
\(754\) | 3.74187e6 | 0.239696 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.10735e6 | −0.0704662 | ||||||||
\(757\) | − 1.25519e6i | − 0.0796104i | −0.999207 | − | 0.0398052i | \(-0.987326\pi\) | ||||
0.999207 | − | 0.0398052i | \(-0.0126737\pi\) | |||||||
\(758\) | − 2.53232e6i | − 0.160083i | ||||||||
\(759\) | 9.76752e6 | 0.615432 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.42623e7 | −0.892746 | −0.446373 | − | 0.894847i | \(-0.647284\pi\) | ||||
−0.446373 | + | 0.894847i | \(0.647284\pi\) | |||||||
\(762\) | 1.76947e6i | 0.110397i | ||||||||
\(763\) | 2.25880e6i | 0.140465i | ||||||||
\(764\) | 1.56756e7 | 0.971606 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 796368. | 0.0490390 | ||||||||
\(767\) | 1.92478e7i | 1.18139i | ||||||||
\(768\) | − 6.62430e6i | − 0.405263i | ||||||||
\(769\) | 2.02261e7 | 1.23338 | 0.616689 | − | 0.787207i | \(-0.288474\pi\) | ||||
0.616689 | + | 0.787207i | \(0.288474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29856e7 | 0.786732 | ||||||||
\(772\) | − 1.34038e7i | − 0.809443i | ||||||||
\(773\) | 2.62288e7i | 1.57881i | 0.613872 | + | 0.789406i | \(0.289611\pi\) | ||||
−0.613872 | + | 0.789406i | \(0.710389\pi\) | |||||||
\(774\) | 1.39612e6 | 0.0837663 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −630126. | −0.0375641 | ||||||||
\(777\) | − 4.32092e6i | − 0.256758i | ||||||||
\(778\) | 1.94799e6i | 0.115382i | ||||||||
\(779\) | −1.76919e7 | −1.04456 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.95312e6 | −0.290570 | ||||||||
\(782\) | − 2.54722e6i | − 0.148953i | ||||||||
\(783\) | 6.00842e6i | 0.350232i | ||||||||
\(784\) | −2.23053e6 | −0.129604 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 694260. | 0.0400835 | ||||||||
\(787\) | 9.92829e6i | 0.571397i | 0.958320 | + | 0.285698i | \(0.0922255\pi\) | ||||
−0.958320 | + | 0.285698i | \(0.907774\pi\) | |||||||
\(788\) | 4.09082e6i | 0.234690i | ||||||||
\(789\) | 2.44346e6 | 0.139738 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.28726e7 | −0.731518 | ||||||||
\(792\) | − 1.73502e6i | − 0.0982860i | ||||||||
\(793\) | 6.70013e6i | 0.378356i | ||||||||
\(794\) | −1.08116e6 | −0.0608608 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.25462e6 | −0.517697 | ||||||||
\(797\) | − 1.09033e7i | − 0.608014i | −0.952670 | − | 0.304007i | \(-0.901675\pi\) | ||||
0.952670 | − | 0.304007i | \(-0.0983246\pi\) | |||||||
\(798\) | 393372.i | 0.0218674i | ||||||||
\(799\) | 7.12454e6 | 0.394812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.50017e6 | −0.523179 | ||||||||
\(802\) | − 2.76770e6i | − 0.151944i | ||||||||
\(803\) | − 2.66485e7i | − 1.45843i | ||||||||
\(804\) | 467604. | 0.0255116 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.13318e6 | −0.0614416 | ||||||||
\(807\) | 7.65553e6i | 0.413801i | ||||||||
\(808\) | 6.85251e6i | 0.369251i | ||||||||
\(809\) | −6.06398e6 | −0.325751 | −0.162876 | − | 0.986647i | \(-0.552077\pi\) | ||||
−0.162876 | + | 0.986647i | \(0.552077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.59438e6 | −0.458841 | −0.229421 | − | 0.973327i | \(-0.573683\pi\) | ||||
−0.229421 | + | 0.973327i | \(0.573683\pi\) | |||||||
\(812\) | 1.25196e7i | 0.666347i | ||||||||
\(813\) | 4.86115e6i | 0.257937i | ||||||||
\(814\) | 3.33132e6 | 0.176220 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.67208e6 | 0.350781 | ||||||||
\(817\) | 1.53745e7i | 0.805835i | ||||||||
\(818\) | 2.36350e6i | 0.123501i | ||||||||
\(819\) | 1.80193e6 | 0.0938701 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.01396e6 | −0.104278 | −0.0521391 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521391 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(822\) | 1.87353e6i | 0.0967122i | ||||||||
\(823\) | − 2.64679e7i | − 1.36213i | −0.732221 | − | 0.681067i | \(-0.761516\pi\) | ||||
0.732221 | − | 0.681067i | \(-0.238484\pi\) | |||||||
\(824\) | −1.25491e7 | −0.643864 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.07740e6 | 0.105943 | ||||||||
\(827\) | 3.90229e6i | 0.198407i | 0.995067 | + | 0.0992033i | \(0.0316294\pi\) | ||||
−0.995067 | + | 0.0992033i | \(0.968371\pi\) | |||||||
\(828\) | 8.01511e6i | 0.406288i | ||||||||
\(829\) | 1.95595e7 | 0.988487 | 0.494244 | − | 0.869323i | \(-0.335445\pi\) | ||||
0.494244 | + | 0.869323i | \(0.335445\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.62217e6 | −0.232190 | ||||||||
\(832\) | 1.21595e7i | 0.608985i | ||||||||
\(833\) | − 1.91600e6i | − 0.0956715i | ||||||||
\(834\) | −2.48022e6 | −0.123474 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.40168e6 | 0.465254 | ||||||||
\(837\) | − 1.81958e6i | − 0.0897756i | ||||||||
\(838\) | − 2.98669e6i | − 0.146920i | ||||||||
\(839\) | 2.45448e7 | 1.20380 | 0.601901 | − | 0.798570i | \(-0.294410\pi\) | ||||
0.601901 | + | 0.798570i | \(0.294410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.74194e7 | 2.31188 | ||||||||
\(842\) | 3.46331e6i | 0.168349i | ||||||||
\(843\) | 1.22078e7i | 0.591655i | ||||||||
\(844\) | −3.62892e7 | −1.75356 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 723168. | 0.0347387 | ||||||||
\(847\) | − 2.22710e6i | − 0.106667i | ||||||||
\(848\) | 139350.i | 0.00665453i | ||||||||
\(849\) | 2.58080e6 | 0.122881 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.12752e7 | −1.48039 | ||||||||
\(852\) | − 4.06447e6i | − 0.191825i | ||||||||
\(853\) | 3.38305e7i | 1.59197i | 0.605314 | + | 0.795987i | \(0.293048\pi\) | ||||
−0.605314 | + | 0.795987i | \(0.706952\pi\) | |||||||
\(854\) | 723142. | 0.0339296 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.03824e6 | 0.235014 | ||||||||
\(857\) | − 3.18009e7i | − 1.47907i | −0.673120 | − | 0.739534i | \(-0.735046\pi\) | ||||
0.673120 | − | 0.739534i | \(-0.264954\pi\) | |||||||
\(858\) | 1.38924e6i | 0.0644257i | ||||||||
\(859\) | −638420. | −0.0295205 | −0.0147602 | − | 0.999891i | \(-0.504699\pi\) | ||||
−0.0147602 | + | 0.999891i | \(0.504699\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.74679e6 | 0.402106 | ||||||||
\(862\) | − 2.33693e6i | − 0.107122i | ||||||||
\(863\) | − 4.22256e6i | − 0.192996i | −0.995333 | − | 0.0964981i | \(-0.969236\pi\) | ||||
0.995333 | − | 0.0964981i | \(-0.0307642\pi\) | |||||||
\(864\) | 2.14690e6 | 0.0978427 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.50838e6 | −0.158969 | ||||||||
\(867\) | − 7.04748e6i | − 0.318409i | ||||||||
\(868\) | − 3.79142e6i | − 0.170806i | ||||||||
\(869\) | −772480. | −0.0347007 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −760904. | −0.0339848 | ||||||||
\(872\) | − 2.90417e6i | − 0.129340i | ||||||||
\(873\) | 810162.i | 0.0359779i | ||||||||
\(874\) | 2.84726e6 | 0.126081 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.18675e7 | 0.962805 | ||||||||
\(877\) | 2.45043e7i | 1.07583i | 0.842999 | + | 0.537915i | \(0.180788\pi\) | ||||
−0.842999 | + | 0.537915i | \(0.819212\pi\) | |||||||
\(878\) | 3.54833e6i | 0.155341i | ||||||||
\(879\) | −1.53654e7 | −0.670767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.77630e7 | −1.20511 | −0.602555 | − | 0.798078i | \(-0.705850\pi\) | ||||
−0.602555 | + | 0.798078i | \(0.705850\pi\) | |||||||
\(882\) | − 194481.i | − 0.00841794i | ||||||||
\(883\) | 3.30170e7i | 1.42507i | 0.701638 | + | 0.712534i | \(0.252452\pi\) | ||||
−0.701638 | + | 0.712534i | \(0.747548\pi\) | |||||||
\(884\) | −1.12311e7 | −0.483381 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.76833e6 | 0.0756797 | ||||||||
\(887\) | − 4.34462e6i | − 0.185414i | −0.995693 | − | 0.0927070i | \(-0.970448\pi\) | ||||
0.995693 | − | 0.0927070i | \(-0.0295520\pi\) | |||||||
\(888\) | 5.55547e6i | 0.236422i | ||||||||
\(889\) | 9.63379e6 | 0.408830 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23074e6 | −0.0941358 | ||||||||
\(892\) | 1.23807e7i | 0.520993i | ||||||||
\(893\) | 7.96378e6i | 0.334188i | ||||||||
\(894\) | −2.66495e6 | −0.111518 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.93013e6 | 0.246771 | ||||||||
\(897\) | − 1.30425e7i | − 0.541228i | ||||||||
\(898\) | − 5.52579e6i | − 0.228667i | ||||||||
\(899\) | −2.05720e7 | −0.848942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −119700. | −0.00491227 | ||||||||
\(902\) | 6.74356e6i | 0.275977i | ||||||||
\(903\) | − 7.60108e6i | − 0.310210i | ||||||||
\(904\) | 1.65505e7 | 0.673580 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.83825e6 | 0.155350 | ||||||||
\(907\) | − 1.96499e7i | − 0.793128i | −0.918007 | − | 0.396564i | \(-0.870203\pi\) | ||||
0.918007 | − | 0.396564i | \(-0.129797\pi\) | |||||||
\(908\) | − 2.19454e7i | − 0.883342i | ||||||||
\(909\) | 8.81037e6 | 0.353659 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.26518e6 | −0.290035 | −0.145018 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145018 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(912\) | 7.45801e6i | 0.296918i | ||||||||
\(913\) | 1.28398e7i | 0.509777i | ||||||||
\(914\) | 2.96226e6 | 0.117289 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.28091e7 | 0.898193 | ||||||||
\(917\) | − 3.77986e6i | − 0.148440i | ||||||||
\(918\) | 581742.i | 0.0227837i | ||||||||
\(919\) | −9.82532e6 | −0.383758 | −0.191879 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191879 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.92109e6 | 0.191167 | ||||||||
\(922\) | − 2.11884e6i | − 0.0820863i | ||||||||
\(923\) | 6.61387e6i | 0.255536i | ||||||||
\(924\) | −4.64814e6 | −0.179102 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.19226e6 | 0.122340 | ||||||||
\(927\) | 1.61346e7i | 0.616677i | ||||||||
\(928\) | − 2.42727e7i | − 0.925226i | ||||||||
\(929\) | −2.71152e7 | −1.03080 | −0.515399 | − | 0.856951i | \(-0.672356\pi\) | ||||
−0.515399 | + | 0.856951i | \(0.672356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.14169e6 | 0.0809809 | ||||||||
\(932\) | − 6.47150e6i | − 0.244042i | ||||||||
\(933\) | − 2.91084e7i | − 1.09475i | ||||||||
\(934\) | 7.42621e6 | 0.278548 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.31676e6 | −0.0864354 | ||||||||
\(937\) | 4.53522e7i | 1.68752i | 0.536720 | + | 0.843761i | \(0.319663\pi\) | ||||
−0.536720 | + | 0.843761i | \(0.680337\pi\) | |||||||
\(938\) | 82124.0i | 0.00304764i | ||||||||
\(939\) | 1.63182e7 | 0.603959 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.65780e7 | 1.71477 | 0.857387 | − | 0.514672i | \(-0.172086\pi\) | ||||
0.857387 | + | 0.514672i | \(0.172086\pi\) | |||||||
\(942\) | 1.60637e6i | 0.0589820i | ||||||||
\(943\) | − 6.33101e7i | − 2.31843i | ||||||||
\(944\) | 3.93859e7 | 1.43850 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.86024e6 | 0.212906 | ||||||||
\(947\) | − 2.53799e7i | − 0.919632i | −0.888014 | − | 0.459816i | \(-0.847915\pi\) | ||||
0.888014 | − | 0.459816i | \(-0.152085\pi\) | |||||||
\(948\) | − 633888.i | − 0.0229082i | ||||||||
\(949\) | −3.55836e7 | −1.28258 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14892e7 | 0.411944 | ||||||||
\(952\) | 2.46343e6i | 0.0880942i | ||||||||
\(953\) | 1.52948e7i | 0.545520i | 0.962082 | + | 0.272760i | \(0.0879365\pi\) | ||||
−0.962082 | + | 0.272760i | \(0.912063\pi\) | |||||||
\(954\) | −12150.0 | −0.000432220 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.21147e7 | −0.782592 | ||||||||
\(957\) | 2.52205e7i | 0.890173i | ||||||||
\(958\) | − 3.39685e6i | − 0.119581i | ||||||||
\(959\) | 1.02003e7 | 0.358152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.23991e7 | −0.782389 | ||||||||
\(962\) | − 4.44829e6i | − 0.154973i | ||||||||
\(963\) | − 6.47773e6i | − 0.225091i | ||||||||
\(964\) | −1.56626e7 | −0.542840 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.40767e6 | −0.0485354 | ||||||||
\(967\) | 5.71465e6i | 0.196527i | 0.995160 | + | 0.0982637i | \(0.0313289\pi\) | ||||
−0.995160 | + | 0.0982637i | \(0.968671\pi\) | |||||||
\(968\) | 2.86341e6i | 0.0982190i | ||||||||
\(969\) | −6.40634e6 | −0.219180 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.30250e7 | 0.443332 | 0.221666 | − | 0.975123i | \(-0.428851\pi\) | ||||
0.221666 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(972\) | − 1.83052e6i | − 0.0621453i | ||||||||
\(973\) | 1.35034e7i | 0.457258i | ||||||||
\(974\) | 3.71382e6 | 0.125436 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.37102e7 | 0.460700 | ||||||||
\(977\) | 1.70360e7i | 0.570992i | 0.958380 | + | 0.285496i | \(0.0921583\pi\) | ||||
−0.958380 | + | 0.285496i | \(0.907842\pi\) | |||||||
\(978\) | − 2.27495e6i | − 0.0760544i | ||||||||
\(979\) | −3.98772e7 | −1.32974 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.73394e6 | −0.123878 | ||||||||
\(982\) | − 5.57494e6i | − 0.184485i | ||||||||
\(983\) | − 1.36985e7i | − 0.452156i | −0.974109 | − | 0.226078i | \(-0.927410\pi\) | ||||
0.974109 | − | 0.226078i | \(-0.0725903\pi\) | |||||||
\(984\) | −1.12459e7 | −0.370259 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.57712e6 | 0.215448 | ||||||||
\(987\) | − 3.93725e6i | − 0.128647i | ||||||||
\(988\) | − 1.25540e7i | − 0.409157i | ||||||||
\(989\) | −5.50173e7 | −1.78858 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.49088e7 | −1.12915 | −0.564574 | − | 0.825383i | \(-0.690959\pi\) | ||||
−0.564574 | + | 0.825383i | \(0.690959\pi\) | |||||||
\(992\) | 7.35072e6i | 0.237165i | ||||||||
\(993\) | 1.56259e7i | 0.502889i | ||||||||
\(994\) | 713832. | 0.0229155 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.05362e7 | −0.336538 | ||||||||
\(997\) | − 875662.i | − 0.0278996i | −0.999903 | − | 0.0139498i | \(-0.995559\pi\) | ||||
0.999903 | − | 0.0139498i | \(-0.00444051\pi\) | |||||||
\(998\) | 3.92698e6i | 0.124805i | ||||||||
\(999\) | 7.14274e6 | 0.226439 |
(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 | 525.6.d.d.274.1 | 2 | ||
5.2 | odd | 4 | 21.6.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 525.6.a.c.1.1 | 1 | |||
5.4 | even | 2 | inner | 525.6.d.d.274.2 | 2 | ||
15.2 | even | 4 | 63.6.a.c.1.1 | 1 | |||
20.7 | even | 4 | 336.6.a.l.1.1 | 1 | |||
35.2 | odd | 12 | 147.6.e.f.67.1 | 2 | |||
35.12 | even | 12 | 147.6.e.e.67.1 | 2 | |||
35.17 | even | 12 | 147.6.e.e.79.1 | 2 | |||
35.27 | even | 4 | 147.6.a.e.1.1 | 1 | |||
35.32 | odd | 12 | 147.6.e.f.79.1 | 2 | |||
60.47 | odd | 4 | 1008.6.a.t.1.1 | 1 | |||
105.62 | odd | 4 | 441.6.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
63.6.a.c.1.1 | 1 | 15.2 | even | 4 | |||
147.6.a.e.1.1 | 1 | 35.27 | even | 4 | |||
147.6.e.e.67.1 | 2 | 35.12 | even | 12 | |||
147.6.e.e.79.1 | 2 | 35.17 | even | 12 | |||
147.6.e.f.67.1 | 2 | 35.2 | odd | 12 | |||
147.6.e.f.79.1 | 2 | 35.32 | odd | 12 | |||
336.6.a.l.1.1 | 1 | 20.7 | even | 4 | |||
441.6.a.d.1.1 | 1 | 105.62 | odd | 4 | |||
525.6.a.c.1.1 | 1 | 5.3 | odd | 4 | |||
525.6.d.d.274.1 | 2 | 1.1 | even | 1 | trivial | ||
525.6.d.d.274.2 | 2 | 5.4 | even | 2 | inner | ||
1008.6.a.t.1.1 | 1 | 60.47 | odd | 4 |