Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,4,Mod(337,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(59.8279367458\) |
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: | \( 2 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.337 |
Dual form | 1014.4.b.h.337.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | − 10.0000i | − 0.894427i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||||
0.894427 | − | 0.447214i | \(-0.147584\pi\) | |||||||
\(6\) | 6.00000i | 0.408248i | ||||||||
\(7\) | − 8.00000i | − 0.431959i | −0.976398 | − | 0.215980i | \(-0.930705\pi\) | ||||
0.976398 | − | 0.215980i | \(-0.0692945\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 20.0000 | 0.632456 | ||||||||
\(11\) | 40.0000i | 1.09640i | 0.836346 | + | 0.548202i | \(0.184688\pi\) | ||||
−0.836346 | + | 0.548202i | \(0.815312\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | − 30.0000i | − 0.516398i | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −130.000 | −1.85468 | −0.927342 | − | 0.374215i | \(-0.877912\pi\) | ||||
−0.927342 | + | 0.374215i | \(0.877912\pi\) | |||||||
\(18\) | 18.0000i | 0.235702i | ||||||||
\(19\) | 20.0000i | 0.241490i | 0.992684 | + | 0.120745i | \(0.0385284\pi\) | ||||
−0.992684 | + | 0.120745i | \(0.961472\pi\) | |||||||
\(20\) | 40.0000i | 0.447214i | ||||||||
\(21\) | − 24.0000i | − 0.249392i | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | − 24.0000i | − 0.204124i | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 32.0000i | 0.215980i | ||||||||
\(29\) | −18.0000 | −0.115259 | −0.0576296 | − | 0.998338i | \(-0.518354\pi\) | ||||
−0.0576296 | + | 0.998338i | \(0.518354\pi\) | |||||||
\(30\) | 60.0000 | 0.365148 | ||||||||
\(31\) | 184.000i | 1.06604i | 0.846101 | + | 0.533022i | \(0.178944\pi\) | ||||
−0.846101 | + | 0.533022i | \(0.821056\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 120.000i | 0.633010i | ||||||||
\(34\) | − 260.000i | − 1.31146i | ||||||||
\(35\) | −80.0000 | −0.386356 | ||||||||
\(36\) | −36.0000 | −0.166667 | ||||||||
\(37\) | − 74.0000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | −40.0000 | −0.170759 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −80.0000 | −0.316228 | ||||||||
\(41\) | 362.000i | 1.37890i | 0.724333 | + | 0.689450i | \(0.242148\pi\) | ||||
−0.724333 | + | 0.689450i | \(0.757852\pi\) | |||||||
\(42\) | 48.0000 | 0.176347 | ||||||||
\(43\) | −76.0000 | −0.269532 | −0.134766 | − | 0.990877i | \(-0.543028\pi\) | ||||
−0.134766 | + | 0.990877i | \(0.543028\pi\) | |||||||
\(44\) | − 160.000i | − 0.548202i | ||||||||
\(45\) | − 90.0000i | − 0.298142i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 452.000i | − 1.40279i | −0.712774 | − | 0.701393i | \(-0.752562\pi\) | ||||
0.712774 | − | 0.701393i | \(-0.247438\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 279.000 | 0.813411 | ||||||||
\(50\) | 50.0000i | 0.141421i | ||||||||
\(51\) | −390.000 | −1.07080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 382.000 | 0.990033 | 0.495016 | − | 0.868884i | \(-0.335162\pi\) | ||||
0.495016 | + | 0.868884i | \(0.335162\pi\) | |||||||
\(54\) | 54.0000i | 0.136083i | ||||||||
\(55\) | 400.000 | 0.980654 | ||||||||
\(56\) | −64.0000 | −0.152721 | ||||||||
\(57\) | 60.0000i | 0.139424i | ||||||||
\(58\) | − 36.0000i | − 0.0815005i | ||||||||
\(59\) | 464.000i | 1.02386i | 0.859028 | + | 0.511929i | \(0.171069\pi\) | ||||
−0.859028 | + | 0.511929i | \(0.828931\pi\) | |||||||
\(60\) | 120.000i | 0.258199i | ||||||||
\(61\) | 358.000 | 0.751430 | 0.375715 | − | 0.926735i | \(-0.377397\pi\) | ||||
0.375715 | + | 0.926735i | \(0.377397\pi\) | |||||||
\(62\) | −368.000 | −0.753807 | ||||||||
\(63\) | − 72.0000i | − 0.143986i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −240.000 | −0.447605 | ||||||||
\(67\) | 700.000i | 1.27640i | 0.769872 | + | 0.638199i | \(0.220320\pi\) | ||||
−0.769872 | + | 0.638199i | \(0.779680\pi\) | |||||||
\(68\) | 520.000 | 0.927342 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 160.000i | − 0.273195i | ||||||||
\(71\) | 748.000i | 1.25030i | 0.780505 | + | 0.625150i | \(0.214962\pi\) | ||||
−0.780505 | + | 0.625150i | \(0.785038\pi\) | |||||||
\(72\) | − 72.0000i | − 0.117851i | ||||||||
\(73\) | 1058.00i | 1.69629i | 0.529760 | + | 0.848147i | \(0.322282\pi\) | ||||
−0.529760 | + | 0.848147i | \(0.677718\pi\) | |||||||
\(74\) | 148.000 | 0.232495 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | − 80.0000i | − 0.120745i | ||||||||
\(77\) | 320.000 | 0.473602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −976.000 | −1.38998 | −0.694991 | − | 0.719018i | \(-0.744592\pi\) | ||||
−0.694991 | + | 0.719018i | \(0.744592\pi\) | |||||||
\(80\) | − 160.000i | − 0.223607i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −724.000 | −0.975030 | ||||||||
\(83\) | 1008.00i | 1.33304i | 0.745487 | + | 0.666520i | \(0.232217\pi\) | ||||
−0.745487 | + | 0.666520i | \(0.767783\pi\) | |||||||
\(84\) | 96.0000i | 0.124696i | ||||||||
\(85\) | 1300.00i | 1.65888i | ||||||||
\(86\) | − 152.000i | − 0.190588i | ||||||||
\(87\) | −54.0000 | −0.0665449 | ||||||||
\(88\) | 320.000 | 0.387638 | ||||||||
\(89\) | − 386.000i | − 0.459729i | −0.973223 | − | 0.229865i | \(-0.926172\pi\) | ||||
0.973223 | − | 0.229865i | \(-0.0738284\pi\) | |||||||
\(90\) | 180.000 | 0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 552.000i | 0.615481i | ||||||||
\(94\) | 904.000 | 0.991920 | ||||||||
\(95\) | 200.000 | 0.215995 | ||||||||
\(96\) | 96.0000i | 0.102062i | ||||||||
\(97\) | 614.000i | 0.642704i | 0.946960 | + | 0.321352i | \(0.104137\pi\) | ||||
−0.946960 | + | 0.321352i | \(0.895863\pi\) | |||||||
\(98\) | 558.000i | 0.575168i | ||||||||
\(99\) | 360.000i | 0.365468i | ||||||||
\(100\) | −100.000 | −0.100000 | ||||||||
\(101\) | −518.000 | −0.510326 | −0.255163 | − | 0.966898i | \(-0.582129\pi\) | ||||
−0.255163 | + | 0.966898i | \(0.582129\pi\) | |||||||
\(102\) | − 780.000i | − 0.757172i | ||||||||
\(103\) | −112.000 | −0.107143 | −0.0535713 | − | 0.998564i | \(-0.517060\pi\) | ||||
−0.0535713 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −240.000 | −0.223063 | ||||||||
\(106\) | 764.000i | 0.700059i | ||||||||
\(107\) | −372.000 | −0.336099 | −0.168050 | − | 0.985779i | \(-0.553747\pi\) | ||||
−0.168050 | + | 0.985779i | \(0.553747\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | − 934.000i | − 0.820743i | −0.911918 | − | 0.410371i | \(-0.865399\pi\) | ||||
0.911918 | − | 0.410371i | \(-0.134601\pi\) | |||||||
\(110\) | 800.000i | 0.693427i | ||||||||
\(111\) | − 222.000i | − 0.189832i | ||||||||
\(112\) | − 128.000i | − 0.107990i | ||||||||
\(113\) | 1914.00 | 1.59340 | 0.796699 | − | 0.604376i | \(-0.206578\pi\) | ||||
0.796699 | + | 0.604376i | \(0.206578\pi\) | |||||||
\(114\) | −120.000 | −0.0985880 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 72.0000 | 0.0576296 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −928.000 | −0.723977 | ||||||||
\(119\) | 1040.00i | 0.801148i | ||||||||
\(120\) | −240.000 | −0.182574 | ||||||||
\(121\) | −269.000 | −0.202104 | ||||||||
\(122\) | 716.000i | 0.531341i | ||||||||
\(123\) | 1086.00i | 0.796108i | ||||||||
\(124\) | − 736.000i | − 0.533022i | ||||||||
\(125\) | − 1500.00i | − 1.07331i | ||||||||
\(126\) | 144.000 | 0.101814 | ||||||||
\(127\) | −1296.00 | −0.905523 | −0.452761 | − | 0.891632i | \(-0.649561\pi\) | ||||
−0.452761 | + | 0.891632i | \(0.649561\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | −228.000 | −0.155615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −892.000 | −0.594919 | −0.297460 | − | 0.954734i | \(-0.596139\pi\) | ||||
−0.297460 | + | 0.954734i | \(0.596139\pi\) | |||||||
\(132\) | − 480.000i | − 0.316505i | ||||||||
\(133\) | 160.000 | 0.104314 | ||||||||
\(134\) | −1400.00 | −0.902549 | ||||||||
\(135\) | − 270.000i | − 0.172133i | ||||||||
\(136\) | 1040.00i | 0.655730i | ||||||||
\(137\) | 2326.00i | 1.45054i | 0.688466 | + | 0.725269i | \(0.258284\pi\) | ||||
−0.688466 | + | 0.725269i | \(0.741716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1932.00 | 1.17892 | 0.589461 | − | 0.807797i | \(-0.299340\pi\) | ||||
0.589461 | + | 0.807797i | \(0.299340\pi\) | |||||||
\(140\) | 320.000 | 0.193178 | ||||||||
\(141\) | − 1356.00i | − 0.809899i | ||||||||
\(142\) | −1496.00 | −0.884095 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 180.000i | 0.103091i | ||||||||
\(146\) | −2116.00 | −1.19946 | ||||||||
\(147\) | 837.000 | 0.469623 | ||||||||
\(148\) | 296.000i | 0.164399i | ||||||||
\(149\) | − 882.000i | − 0.484941i | −0.970159 | − | 0.242471i | \(-0.922042\pi\) | ||||
0.970159 | − | 0.242471i | \(-0.0779578\pi\) | |||||||
\(150\) | 150.000i | 0.0816497i | ||||||||
\(151\) | − 1776.00i | − 0.957145i | −0.878048 | − | 0.478572i | \(-0.841154\pi\) | ||||
0.878048 | − | 0.478572i | \(-0.158846\pi\) | |||||||
\(152\) | 160.000 | 0.0853797 | ||||||||
\(153\) | −1170.00 | −0.618228 | ||||||||
\(154\) | 640.000i | 0.334887i | ||||||||
\(155\) | 1840.00 | 0.953499 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2410.00 | −1.22509 | −0.612544 | − | 0.790436i | \(-0.709854\pi\) | ||||
−0.612544 | + | 0.790436i | \(0.709854\pi\) | |||||||
\(158\) | − 1952.00i | − 0.982866i | ||||||||
\(159\) | 1146.00 | 0.571596 | ||||||||
\(160\) | 320.000 | 0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 162.000i | 0.0785674i | ||||||||
\(163\) | 3212.00i | 1.54346i | 0.635953 | + | 0.771728i | \(0.280607\pi\) | ||||
−0.635953 | + | 0.771728i | \(0.719393\pi\) | |||||||
\(164\) | − 1448.00i | − 0.689450i | ||||||||
\(165\) | 1200.00 | 0.566181 | ||||||||
\(166\) | −2016.00 | −0.942602 | ||||||||
\(167\) | 1668.00i | 0.772896i | 0.922311 | + | 0.386448i | \(0.126298\pi\) | ||||
−0.922311 | + | 0.386448i | \(0.873702\pi\) | |||||||
\(168\) | −192.000 | −0.0881733 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2600.00 | −1.17301 | ||||||||
\(171\) | 180.000i | 0.0804967i | ||||||||
\(172\) | 304.000 | 0.134766 | ||||||||
\(173\) | −3598.00 | −1.58122 | −0.790609 | − | 0.612321i | \(-0.790236\pi\) | ||||
−0.790609 | + | 0.612321i | \(0.790236\pi\) | |||||||
\(174\) | − 108.000i | − 0.0470544i | ||||||||
\(175\) | − 200.000i | − 0.0863919i | ||||||||
\(176\) | 640.000i | 0.274101i | ||||||||
\(177\) | 1392.00i | 0.591125i | ||||||||
\(178\) | 772.000 | 0.325078 | ||||||||
\(179\) | −1068.00 | −0.445956 | −0.222978 | − | 0.974824i | \(-0.571578\pi\) | ||||
−0.222978 | + | 0.974824i | \(0.571578\pi\) | |||||||
\(180\) | 360.000i | 0.149071i | ||||||||
\(181\) | 4786.00 | 1.96542 | 0.982709 | − | 0.185158i | \(-0.0592797\pi\) | ||||
0.982709 | + | 0.185158i | \(0.0592797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1074.00 | 0.433838 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −740.000 | −0.294086 | ||||||||
\(186\) | −1104.00 | −0.435211 | ||||||||
\(187\) | − 5200.00i | − 2.03348i | ||||||||
\(188\) | 1808.00i | 0.701393i | ||||||||
\(189\) | − 216.000i | − 0.0831306i | ||||||||
\(190\) | 400.000i | 0.152732i | ||||||||
\(191\) | −1312.00 | −0.497031 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | − 350.000i | − 0.130537i | −0.997868 | − | 0.0652683i | \(-0.979210\pi\) | ||||
0.997868 | − | 0.0652683i | \(-0.0207903\pi\) | |||||||
\(194\) | −1228.00 | −0.454460 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1116.00 | −0.406706 | ||||||||
\(197\) | 342.000i | 0.123688i | 0.998086 | + | 0.0618439i | \(0.0196981\pi\) | ||||
−0.998086 | + | 0.0618439i | \(0.980302\pi\) | |||||||
\(198\) | −720.000 | −0.258425 | ||||||||
\(199\) | 3368.00 | 1.19975 | 0.599877 | − | 0.800092i | \(-0.295216\pi\) | ||||
0.599877 | + | 0.800092i | \(0.295216\pi\) | |||||||
\(200\) | − 200.000i | − 0.0707107i | ||||||||
\(201\) | 2100.00i | 0.736928i | ||||||||
\(202\) | − 1036.00i | − 0.360855i | ||||||||
\(203\) | 144.000i | 0.0497873i | ||||||||
\(204\) | 1560.00 | 0.535401 | ||||||||
\(205\) | 3620.00 | 1.23333 | ||||||||
\(206\) | − 224.000i | − 0.0757613i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −800.000 | −0.264771 | ||||||||
\(210\) | − 480.000i | − 0.157729i | ||||||||
\(211\) | −2004.00 | −0.653844 | −0.326922 | − | 0.945051i | \(-0.606011\pi\) | ||||
−0.326922 | + | 0.945051i | \(0.606011\pi\) | |||||||
\(212\) | −1528.00 | −0.495016 | ||||||||
\(213\) | 2244.00i | 0.721861i | ||||||||
\(214\) | − 744.000i | − 0.237658i | ||||||||
\(215\) | 760.000i | 0.241077i | ||||||||
\(216\) | − 216.000i | − 0.0680414i | ||||||||
\(217\) | 1472.00 | 0.460488 | ||||||||
\(218\) | 1868.00 | 0.580353 | ||||||||
\(219\) | 3174.00i | 0.979356i | ||||||||
\(220\) | −1600.00 | −0.490327 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 444.000 | 0.134231 | ||||||||
\(223\) | 5608.00i | 1.68403i | 0.539451 | + | 0.842017i | \(0.318632\pi\) | ||||
−0.539451 | + | 0.842017i | \(0.681368\pi\) | |||||||
\(224\) | 256.000 | 0.0763604 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 3828.00i | 1.12670i | ||||||||
\(227\) | 1928.00i | 0.563726i | 0.959455 | + | 0.281863i | \(0.0909524\pi\) | ||||
−0.959455 | + | 0.281863i | \(0.909048\pi\) | |||||||
\(228\) | − 240.000i | − 0.0697122i | ||||||||
\(229\) | − 3938.00i | − 1.13638i | −0.822898 | − | 0.568189i | \(-0.807644\pi\) | ||||
0.822898 | − | 0.568189i | \(-0.192356\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 960.000 | 0.273434 | ||||||||
\(232\) | 144.000i | 0.0407503i | ||||||||
\(233\) | −2562.00 | −0.720353 | −0.360176 | − | 0.932884i | \(-0.617283\pi\) | ||||
−0.360176 | + | 0.932884i | \(0.617283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4520.00 | −1.25469 | ||||||||
\(236\) | − 1856.00i | − 0.511929i | ||||||||
\(237\) | −2928.00 | −0.802506 | ||||||||
\(238\) | −2080.00 | −0.566497 | ||||||||
\(239\) | − 7164.00i | − 1.93891i | −0.245260 | − | 0.969457i | \(-0.578873\pi\) | ||||
0.245260 | − | 0.969457i | \(-0.421127\pi\) | |||||||
\(240\) | − 480.000i | − 0.129099i | ||||||||
\(241\) | − 6182.00i | − 1.65236i | −0.563410 | − | 0.826178i | \(-0.690511\pi\) | ||||
0.563410 | − | 0.826178i | \(-0.309489\pi\) | |||||||
\(242\) | − 538.000i | − 0.142909i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1432.00 | −0.375715 | ||||||||
\(245\) | − 2790.00i | − 0.727537i | ||||||||
\(246\) | −2172.00 | −0.562934 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1472.00 | 0.376904 | ||||||||
\(249\) | 3024.00i | 0.769631i | ||||||||
\(250\) | 3000.00 | 0.758947 | ||||||||
\(251\) | 1396.00 | 0.351055 | 0.175527 | − | 0.984475i | \(-0.443837\pi\) | ||||
0.175527 | + | 0.984475i | \(0.443837\pi\) | |||||||
\(252\) | 288.000i | 0.0719932i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 2592.00i | − 0.640301i | ||||||||
\(255\) | 3900.00i | 0.957755i | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6906.00 | −1.67620 | −0.838102 | − | 0.545514i | \(-0.816335\pi\) | ||||
−0.838102 | + | 0.545514i | \(0.816335\pi\) | |||||||
\(258\) | − 456.000i | − 0.110036i | ||||||||
\(259\) | −592.000 | −0.142027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −162.000 | −0.0384197 | ||||||||
\(262\) | − 1784.00i | − 0.420671i | ||||||||
\(263\) | −6848.00 | −1.60557 | −0.802787 | − | 0.596266i | \(-0.796650\pi\) | ||||
−0.802787 | + | 0.596266i | \(0.796650\pi\) | |||||||
\(264\) | 960.000 | 0.223803 | ||||||||
\(265\) | − 3820.00i | − 0.885512i | ||||||||
\(266\) | 320.000i | 0.0737611i | ||||||||
\(267\) | − 1158.00i | − 0.265425i | ||||||||
\(268\) | − 2800.00i | − 0.638199i | ||||||||
\(269\) | −6034.00 | −1.36766 | −0.683828 | − | 0.729643i | \(-0.739686\pi\) | ||||
−0.683828 | + | 0.729643i | \(0.739686\pi\) | |||||||
\(270\) | 540.000 | 0.121716 | ||||||||
\(271\) | 4832.00i | 1.08311i | 0.840665 | + | 0.541556i | \(0.182164\pi\) | ||||
−0.840665 | + | 0.541556i | \(0.817836\pi\) | |||||||
\(272\) | −2080.00 | −0.463671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4652.00 | −1.02568 | ||||||||
\(275\) | 1000.00i | 0.219281i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4082.00 | 0.885428 | 0.442714 | − | 0.896663i | \(-0.354016\pi\) | ||||
0.442714 | + | 0.896663i | \(0.354016\pi\) | |||||||
\(278\) | 3864.00i | 0.833623i | ||||||||
\(279\) | 1656.00i | 0.355348i | ||||||||
\(280\) | 640.000i | 0.136598i | ||||||||
\(281\) | 3350.00i | 0.711189i | 0.934640 | + | 0.355595i | \(0.115722\pi\) | ||||
−0.934640 | + | 0.355595i | \(0.884278\pi\) | |||||||
\(282\) | 2712.00 | 0.572685 | ||||||||
\(283\) | −7796.00 | −1.63754 | −0.818770 | − | 0.574121i | \(-0.805344\pi\) | ||||
−0.818770 | + | 0.574121i | \(0.805344\pi\) | |||||||
\(284\) | − 2992.00i | − 0.625150i | ||||||||
\(285\) | 600.000 | 0.124705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2896.00 | 0.595629 | ||||||||
\(288\) | 288.000i | 0.0589256i | ||||||||
\(289\) | 11987.0 | 2.43985 | ||||||||
\(290\) | −360.000 | −0.0728963 | ||||||||
\(291\) | 1842.00i | 0.371065i | ||||||||
\(292\) | − 4232.00i | − 0.848147i | ||||||||
\(293\) | 3922.00i | 0.781999i | 0.920391 | + | 0.390999i | \(0.127871\pi\) | ||||
−0.920391 | + | 0.390999i | \(0.872129\pi\) | |||||||
\(294\) | 1674.00i | 0.332074i | ||||||||
\(295\) | 4640.00 | 0.915767 | ||||||||
\(296\) | −592.000 | −0.116248 | ||||||||
\(297\) | 1080.00i | 0.211003i | ||||||||
\(298\) | 1764.00 | 0.342905 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −300.000 | −0.0577350 | ||||||||
\(301\) | 608.000i | 0.116427i | ||||||||
\(302\) | 3552.00 | 0.676803 | ||||||||
\(303\) | −1554.00 | −0.294637 | ||||||||
\(304\) | 320.000i | 0.0603726i | ||||||||
\(305\) | − 3580.00i | − 0.672099i | ||||||||
\(306\) | − 2340.00i | − 0.437153i | ||||||||
\(307\) | 5956.00i | 1.10725i | 0.832765 | + | 0.553627i | \(0.186757\pi\) | ||||
−0.832765 | + | 0.553627i | \(0.813243\pi\) | |||||||
\(308\) | −1280.00 | −0.236801 | ||||||||
\(309\) | −336.000 | −0.0618588 | ||||||||
\(310\) | 3680.00i | 0.674226i | ||||||||
\(311\) | −2352.00 | −0.428841 | −0.214421 | − | 0.976741i | \(-0.568786\pi\) | ||||
−0.214421 | + | 0.976741i | \(0.568786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8442.00 | 1.52450 | 0.762252 | − | 0.647280i | \(-0.224093\pi\) | ||||
0.762252 | + | 0.647280i | \(0.224093\pi\) | |||||||
\(314\) | − 4820.00i | − 0.866269i | ||||||||
\(315\) | −720.000 | −0.128785 | ||||||||
\(316\) | 3904.00 | 0.694991 | ||||||||
\(317\) | 5550.00i | 0.983341i | 0.870781 | + | 0.491670i | \(0.163614\pi\) | ||||
−0.870781 | + | 0.491670i | \(0.836386\pi\) | |||||||
\(318\) | 2292.00i | 0.404179i | ||||||||
\(319\) | − 720.000i | − 0.126371i | ||||||||
\(320\) | 640.000i | 0.111803i | ||||||||
\(321\) | −1116.00 | −0.194047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2600.00i | − 0.447888i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6424.00 | −1.09139 | ||||||||
\(327\) | − 2802.00i | − 0.473856i | ||||||||
\(328\) | 2896.00 | 0.487515 | ||||||||
\(329\) | −3616.00 | −0.605947 | ||||||||
\(330\) | 2400.00i | 0.400350i | ||||||||
\(331\) | − 140.000i | − 0.0232480i | −0.999932 | − | 0.0116240i | \(-0.996300\pi\) | ||||
0.999932 | − | 0.0116240i | \(-0.00370012\pi\) | |||||||
\(332\) | − 4032.00i | − 0.666520i | ||||||||
\(333\) | − 666.000i | − 0.109599i | ||||||||
\(334\) | −3336.00 | −0.546520 | ||||||||
\(335\) | 7000.00 | 1.14164 | ||||||||
\(336\) | − 384.000i | − 0.0623480i | ||||||||
\(337\) | 6174.00 | 0.997980 | 0.498990 | − | 0.866608i | \(-0.333704\pi\) | ||||
0.498990 | + | 0.866608i | \(0.333704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5742.00 | 0.919949 | ||||||||
\(340\) | − 5200.00i | − 0.829440i | ||||||||
\(341\) | −7360.00 | −1.16882 | ||||||||
\(342\) | −360.000 | −0.0569198 | ||||||||
\(343\) | − 4976.00i | − 0.783320i | ||||||||
\(344\) | 608.000i | 0.0952941i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 7196.00i | − 1.11809i | ||||||||
\(347\) | −2988.00 | −0.462260 | −0.231130 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231130 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(348\) | 216.000 | 0.0332725 | ||||||||
\(349\) | − 162.000i | − 0.0248472i | −0.999923 | − | 0.0124236i | \(-0.996045\pi\) | ||||
0.999923 | − | 0.0124236i | \(-0.00395465\pi\) | |||||||
\(350\) | 400.000 | 0.0610883 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1280.00 | −0.193819 | ||||||||
\(353\) | 10754.0i | 1.62147i | 0.585416 | + | 0.810733i | \(0.300931\pi\) | ||||
−0.585416 | + | 0.810733i | \(0.699069\pi\) | |||||||
\(354\) | −2784.00 | −0.417989 | ||||||||
\(355\) | 7480.00 | 1.11830 | ||||||||
\(356\) | 1544.00i | 0.229865i | ||||||||
\(357\) | 3120.00i | 0.462543i | ||||||||
\(358\) | − 2136.00i | − 0.315338i | ||||||||
\(359\) | 3588.00i | 0.527486i | 0.964593 | + | 0.263743i | \(0.0849570\pi\) | ||||
−0.964593 | + | 0.263743i | \(0.915043\pi\) | |||||||
\(360\) | −720.000 | −0.105409 | ||||||||
\(361\) | 6459.00 | 0.941682 | ||||||||
\(362\) | 9572.00i | 1.38976i | ||||||||
\(363\) | −807.000 | −0.116685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10580.0 | 1.51721 | ||||||||
\(366\) | 2148.00i | 0.306770i | ||||||||
\(367\) | 11272.0 | 1.60325 | 0.801626 | − | 0.597826i | \(-0.203968\pi\) | ||||
0.801626 | + | 0.597826i | \(0.203968\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3258.00i | 0.459633i | ||||||||
\(370\) | − 1480.00i | − 0.207950i | ||||||||
\(371\) | − 3056.00i | − 0.427654i | ||||||||
\(372\) | − 2208.00i | − 0.307741i | ||||||||
\(373\) | −10914.0 | −1.51503 | −0.757514 | − | 0.652819i | \(-0.773586\pi\) | ||||
−0.757514 | + | 0.652819i | \(0.773586\pi\) | |||||||
\(374\) | 10400.0 | 1.43789 | ||||||||
\(375\) | − 4500.00i | − 0.619677i | ||||||||
\(376\) | −3616.00 | −0.495960 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 432.000 | 0.0587822 | ||||||||
\(379\) | − 8100.00i | − 1.09781i | −0.835886 | − | 0.548904i | \(-0.815045\pi\) | ||||
0.835886 | − | 0.548904i | \(-0.184955\pi\) | |||||||
\(380\) | −800.000 | −0.107998 | ||||||||
\(381\) | −3888.00 | −0.522804 | ||||||||
\(382\) | − 2624.00i | − 0.351454i | ||||||||
\(383\) | − 6180.00i | − 0.824499i | −0.911071 | − | 0.412250i | \(-0.864743\pi\) | ||||
0.911071 | − | 0.412250i | \(-0.135257\pi\) | |||||||
\(384\) | − 384.000i | − 0.0510310i | ||||||||
\(385\) | − 3200.00i | − 0.423603i | ||||||||
\(386\) | 700.000 | 0.0923033 | ||||||||
\(387\) | −684.000 | −0.0898441 | ||||||||
\(388\) | − 2456.00i | − 0.321352i | ||||||||
\(389\) | 7522.00 | 0.980413 | 0.490206 | − | 0.871606i | \(-0.336921\pi\) | ||||
0.490206 | + | 0.871606i | \(0.336921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 2232.00i | − 0.287584i | ||||||||
\(393\) | −2676.00 | −0.343477 | ||||||||
\(394\) | −684.000 | −0.0874605 | ||||||||
\(395\) | 9760.00i | 1.24324i | ||||||||
\(396\) | − 1440.00i | − 0.182734i | ||||||||
\(397\) | 6078.00i | 0.768378i | 0.923254 | + | 0.384189i | \(0.125519\pi\) | ||||
−0.923254 | + | 0.384189i | \(0.874481\pi\) | |||||||
\(398\) | 6736.00i | 0.848355i | ||||||||
\(399\) | 480.000 | 0.0602257 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 1830.00i | 0.227895i | 0.993487 | + | 0.113947i | \(0.0363495\pi\) | ||||
−0.993487 | + | 0.113947i | \(0.963650\pi\) | |||||||
\(402\) | −4200.00 | −0.521087 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2072.00 | 0.255163 | ||||||||
\(405\) | − 810.000i | − 0.0993808i | ||||||||
\(406\) | −288.000 | −0.0352049 | ||||||||
\(407\) | 2960.00 | 0.360496 | ||||||||
\(408\) | 3120.00i | 0.378586i | ||||||||
\(409\) | − 12434.0i | − 1.50323i | −0.659601 | − | 0.751616i | \(-0.729275\pi\) | ||||
0.659601 | − | 0.751616i | \(-0.270725\pi\) | |||||||
\(410\) | 7240.00i | 0.872093i | ||||||||
\(411\) | 6978.00i | 0.837468i | ||||||||
\(412\) | 448.000 | 0.0535713 | ||||||||
\(413\) | 3712.00 | 0.442265 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10080.0 | 1.19231 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5796.00 | 0.680651 | ||||||||
\(418\) | − 1600.00i | − 0.187221i | ||||||||
\(419\) | −14188.0 | −1.65425 | −0.827123 | − | 0.562021i | \(-0.810024\pi\) | ||||
−0.827123 | + | 0.562021i | \(0.810024\pi\) | |||||||
\(420\) | 960.000 | 0.111531 | ||||||||
\(421\) | − 8638.00i | − 0.999977i | −0.866032 | − | 0.499989i | \(-0.833338\pi\) | ||||
0.866032 | − | 0.499989i | \(-0.166662\pi\) | |||||||
\(422\) | − 4008.00i | − 0.462337i | ||||||||
\(423\) | − 4068.00i | − 0.467596i | ||||||||
\(424\) | − 3056.00i | − 0.350029i | ||||||||
\(425\) | −3250.00 | −0.370937 | ||||||||
\(426\) | −4488.00 | −0.510433 | ||||||||
\(427\) | − 2864.00i | − 0.324587i | ||||||||
\(428\) | 1488.00 | 0.168050 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1520.00 | −0.170467 | ||||||||
\(431\) | − 4292.00i | − 0.479671i | −0.970813 | − | 0.239836i | \(-0.922906\pi\) | ||||
0.970813 | − | 0.239836i | \(-0.0770936\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 5982.00 | 0.663918 | 0.331959 | − | 0.943294i | \(-0.392290\pi\) | ||||
0.331959 | + | 0.943294i | \(0.392290\pi\) | |||||||
\(434\) | 2944.00i | 0.325614i | ||||||||
\(435\) | 540.000i | 0.0595196i | ||||||||
\(436\) | 3736.00i | 0.410371i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6348.00 | −0.692510 | ||||||||
\(439\) | −256.000 | −0.0278319 | −0.0139160 | − | 0.999903i | \(-0.504430\pi\) | ||||
−0.0139160 | + | 0.999903i | \(0.504430\pi\) | |||||||
\(440\) | − 3200.00i | − 0.346714i | ||||||||
\(441\) | 2511.00 | 0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12556.0 | 1.34662 | 0.673311 | − | 0.739359i | \(-0.264872\pi\) | ||||
0.673311 | + | 0.739359i | \(0.264872\pi\) | |||||||
\(444\) | 888.000i | 0.0949158i | ||||||||
\(445\) | −3860.00 | −0.411194 | ||||||||
\(446\) | −11216.0 | −1.19079 | ||||||||
\(447\) | − 2646.00i | − 0.279981i | ||||||||
\(448\) | 512.000i | 0.0539949i | ||||||||
\(449\) | 5574.00i | 0.585865i | 0.956133 | + | 0.292932i | \(0.0946311\pi\) | ||||
−0.956133 | + | 0.292932i | \(0.905369\pi\) | |||||||
\(450\) | 450.000i | 0.0471405i | ||||||||
\(451\) | −14480.0 | −1.51183 | ||||||||
\(452\) | −7656.00 | −0.796699 | ||||||||
\(453\) | − 5328.00i | − 0.552608i | ||||||||
\(454\) | −3856.00 | −0.398615 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 480.000 | 0.0492940 | ||||||||
\(457\) | − 1266.00i | − 0.129586i | −0.997899 | − | 0.0647932i | \(-0.979361\pi\) | ||||
0.997899 | − | 0.0647932i | \(-0.0206388\pi\) | |||||||
\(458\) | 7876.00 | 0.803540 | ||||||||
\(459\) | −3510.00 | −0.356934 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7554.00i | − 0.763178i | −0.924332 | − | 0.381589i | \(-0.875377\pi\) | ||||
0.924332 | − | 0.381589i | \(-0.124623\pi\) | |||||||
\(462\) | 1920.00i | 0.193347i | ||||||||
\(463\) | − 6752.00i | − 0.677737i | −0.940834 | − | 0.338868i | \(-0.889956\pi\) | ||||
0.940834 | − | 0.338868i | \(-0.110044\pi\) | |||||||
\(464\) | −288.000 | −0.0288148 | ||||||||
\(465\) | 5520.00 | 0.550503 | ||||||||
\(466\) | − 5124.00i | − 0.509366i | ||||||||
\(467\) | −7924.00 | −0.785180 | −0.392590 | − | 0.919714i | \(-0.628421\pi\) | ||||
−0.392590 | + | 0.919714i | \(0.628421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5600.00 | 0.551352 | ||||||||
\(470\) | − 9040.00i | − 0.887200i | ||||||||
\(471\) | −7230.00 | −0.707305 | ||||||||
\(472\) | 3712.00 | 0.361989 | ||||||||
\(473\) | − 3040.00i | − 0.295517i | ||||||||
\(474\) | − 5856.00i | − 0.567458i | ||||||||
\(475\) | 500.000i | 0.0482980i | ||||||||
\(476\) | − 4160.00i | − 0.400574i | ||||||||
\(477\) | 3438.00 | 0.330011 | ||||||||
\(478\) | 14328.0 | 1.37102 | ||||||||
\(479\) | − 11084.0i | − 1.05729i | −0.848844 | − | 0.528644i | \(-0.822701\pi\) | ||||
0.848844 | − | 0.528644i | \(-0.177299\pi\) | |||||||
\(480\) | 960.000 | 0.0912871 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12364.0 | 1.16839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | 6140.00 | 0.574852 | ||||||||
\(486\) | 486.000i | 0.0453609i | ||||||||
\(487\) | − 4432.00i | − 0.412388i | −0.978511 | − | 0.206194i | \(-0.933892\pi\) | ||||
0.978511 | − | 0.206194i | \(-0.0661078\pi\) | |||||||
\(488\) | − 2864.00i | − 0.265670i | ||||||||
\(489\) | 9636.00i | 0.891114i | ||||||||
\(490\) | 5580.00 | 0.514446 | ||||||||
\(491\) | 1140.00 | 0.104781 | 0.0523905 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523905 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(492\) | − 4344.00i | − 0.398054i | ||||||||
\(493\) | 2340.00 | 0.213769 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3600.00 | 0.326885 | ||||||||
\(496\) | 2944.00i | 0.266511i | ||||||||
\(497\) | 5984.00 | 0.540079 | ||||||||
\(498\) | −6048.00 | −0.544212 | ||||||||
\(499\) | − 1764.00i | − 0.158251i | −0.996865 | − | 0.0791257i | \(-0.974787\pi\) | ||||
0.996865 | − | 0.0791257i | \(-0.0252129\pi\) | |||||||
\(500\) | 6000.00i | 0.536656i | ||||||||
\(501\) | 5004.00i | 0.446232i | ||||||||
\(502\) | 2792.00i | 0.248233i | ||||||||
\(503\) | 16976.0 | 1.50482 | 0.752408 | − | 0.658697i | \(-0.228892\pi\) | ||||
0.752408 | + | 0.658697i | \(0.228892\pi\) | |||||||
\(504\) | −576.000 | −0.0509069 | ||||||||
\(505\) | 5180.00i | 0.456449i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5184.00 | 0.452761 | ||||||||
\(509\) | − 9474.00i | − 0.825005i | −0.910956 | − | 0.412503i | \(-0.864655\pi\) | ||||
0.910956 | − | 0.412503i | \(-0.135345\pi\) | |||||||
\(510\) | −7800.00 | −0.677235 | ||||||||
\(511\) | 8464.00 | 0.732731 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 540.000i | 0.0464748i | ||||||||
\(514\) | − 13812.0i | − 1.18526i | ||||||||
\(515\) | 1120.00i | 0.0958313i | ||||||||
\(516\) | 912.000 | 0.0778073 | ||||||||
\(517\) | 18080.0 | 1.53802 | ||||||||
\(518\) | − 1184.00i | − 0.100429i | ||||||||
\(519\) | −10794.0 | −0.912917 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14114.0 | 1.18684 | 0.593422 | − | 0.804892i | \(-0.297777\pi\) | ||||
0.593422 | + | 0.804892i | \(0.297777\pi\) | |||||||
\(522\) | − 324.000i | − 0.0271668i | ||||||||
\(523\) | 20284.0 | 1.69590 | 0.847952 | − | 0.530074i | \(-0.177836\pi\) | ||||
0.847952 | + | 0.530074i | \(0.177836\pi\) | |||||||
\(524\) | 3568.00 | 0.297460 | ||||||||
\(525\) | − 600.000i | − 0.0498784i | ||||||||
\(526\) | − 13696.0i | − 1.13531i | ||||||||
\(527\) | − 23920.0i | − 1.97718i | ||||||||
\(528\) | 1920.00i | 0.158252i | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 7640.00 | 0.626152 | ||||||||
\(531\) | 4176.00i | 0.341286i | ||||||||
\(532\) | −640.000 | −0.0521570 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2316.00 | 0.187684 | ||||||||
\(535\) | 3720.00i | 0.300616i | ||||||||
\(536\) | 5600.00 | 0.451275 | ||||||||
\(537\) | −3204.00 | −0.257473 | ||||||||
\(538\) | − 12068.0i | − 0.967079i | ||||||||
\(539\) | 11160.0i | 0.891828i | ||||||||
\(540\) | 1080.00i | 0.0860663i | ||||||||
\(541\) | − 14362.0i | − 1.14135i | −0.821176 | − | 0.570675i | \(-0.806682\pi\) | ||||
0.821176 | − | 0.570675i | \(-0.193318\pi\) | |||||||
\(542\) | −9664.00 | −0.765875 | ||||||||
\(543\) | 14358.0 | 1.13473 | ||||||||
\(544\) | − 4160.00i | − 0.327865i | ||||||||
\(545\) | −9340.00 | −0.734095 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20956.0 | −1.63805 | −0.819025 | − | 0.573757i | \(-0.805485\pi\) | ||||
−0.819025 | + | 0.573757i | \(0.805485\pi\) | |||||||
\(548\) | − 9304.00i | − 0.725269i | ||||||||
\(549\) | 3222.00 | 0.250477 | ||||||||
\(550\) | −2000.00 | −0.155055 | ||||||||
\(551\) | − 360.000i | − 0.0278340i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7808.00i | 0.600416i | ||||||||
\(554\) | 8164.00i | 0.626092i | ||||||||
\(555\) | −2220.00 | −0.169791 | ||||||||
\(556\) | −7728.00 | −0.589461 | ||||||||
\(557\) | − 4134.00i | − 0.314476i | −0.987561 | − | 0.157238i | \(-0.949741\pi\) | ||||
0.987561 | − | 0.157238i | \(-0.0502590\pi\) | |||||||
\(558\) | −3312.00 | −0.251269 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1280.00 | −0.0965891 | ||||||||
\(561\) | − 15600.0i | − 1.17403i | ||||||||
\(562\) | −6700.00 | −0.502887 | ||||||||
\(563\) | 16228.0 | 1.21479 | 0.607397 | − | 0.794399i | \(-0.292214\pi\) | ||||
0.607397 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(564\) | 5424.00i | 0.404950i | ||||||||
\(565\) | − 19140.0i | − 1.42518i | ||||||||
\(566\) | − 15592.0i | − 1.15792i | ||||||||
\(567\) | − 648.000i | − 0.0479955i | ||||||||
\(568\) | 5984.00 | 0.442048 | ||||||||
\(569\) | −2514.00 | −0.185224 | −0.0926119 | − | 0.995702i | \(-0.529522\pi\) | ||||
−0.0926119 | + | 0.995702i | \(0.529522\pi\) | |||||||
\(570\) | 1200.00i | 0.0881798i | ||||||||
\(571\) | 11612.0 | 0.851046 | 0.425523 | − | 0.904948i | \(-0.360090\pi\) | ||||
0.425523 | + | 0.904948i | \(0.360090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3936.00 | −0.286961 | ||||||||
\(574\) | 5792.00i | 0.421173i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −576.000 | −0.0416667 | ||||||||
\(577\) | − 6354.00i | − 0.458441i | −0.973375 | − | 0.229221i | \(-0.926382\pi\) | ||||
0.973375 | − | 0.229221i | \(-0.0736177\pi\) | |||||||
\(578\) | 23974.0i | 1.72524i | ||||||||
\(579\) | − 1050.00i | − 0.0753653i | ||||||||
\(580\) | − 720.000i | − 0.0515455i | ||||||||
\(581\) | 8064.00 | 0.575819 | ||||||||
\(582\) | −3684.00 | −0.262383 | ||||||||
\(583\) | 15280.0i | 1.08548i | ||||||||
\(584\) | 8464.00 | 0.599731 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7844.00 | −0.552957 | ||||||||
\(587\) | 13240.0i | 0.930960i | 0.885059 | + | 0.465480i | \(0.154118\pi\) | ||||
−0.885059 | + | 0.465480i | \(0.845882\pi\) | |||||||
\(588\) | −3348.00 | −0.234812 | ||||||||
\(589\) | −3680.00 | −0.257439 | ||||||||
\(590\) | 9280.00i | 0.647545i | ||||||||
\(591\) | 1026.00i | 0.0714112i | ||||||||
\(592\) | − 1184.00i | − 0.0821995i | ||||||||
\(593\) | − 1146.00i | − 0.0793602i | −0.999212 | − | 0.0396801i | \(-0.987366\pi\) | ||||
0.999212 | − | 0.0396801i | \(-0.0126339\pi\) | |||||||
\(594\) | −2160.00 | −0.149202 | ||||||||
\(595\) | 10400.0 | 0.716569 | ||||||||
\(596\) | 3528.00i | 0.242471i | ||||||||
\(597\) | 10104.0 | 0.692679 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10464.0 | 0.713769 | 0.356884 | − | 0.934149i | \(-0.383839\pi\) | ||||
0.356884 | + | 0.934149i | \(0.383839\pi\) | |||||||
\(600\) | − 600.000i | − 0.0408248i | ||||||||
\(601\) | 6650.00 | 0.451346 | 0.225673 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225673 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(602\) | −1216.00 | −0.0823263 | ||||||||
\(603\) | 6300.00i | 0.425466i | ||||||||
\(604\) | 7104.00i | 0.478572i | ||||||||
\(605\) | 2690.00i | 0.180767i | ||||||||
\(606\) | − 3108.00i | − 0.208340i | ||||||||
\(607\) | −6664.00 | −0.445607 | −0.222803 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222803 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(608\) | −640.000 | −0.0426898 | ||||||||
\(609\) | 432.000i | 0.0287447i | ||||||||
\(610\) | 7160.00 | 0.475246 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4680.00 | 0.309114 | ||||||||
\(613\) | − 2134.00i | − 0.140606i | −0.997526 | − | 0.0703030i | \(-0.977603\pi\) | ||||
0.997526 | − | 0.0703030i | \(-0.0223966\pi\) | |||||||
\(614\) | −11912.0 | −0.782947 | ||||||||
\(615\) | 10860.0 | 0.712061 | ||||||||
\(616\) | − 2560.00i | − 0.167444i | ||||||||
\(617\) | 714.000i | 0.0465876i | 0.999729 | + | 0.0232938i | \(0.00741532\pi\) | ||||
−0.999729 | + | 0.0232938i | \(0.992585\pi\) | |||||||
\(618\) | − 672.000i | − 0.0437408i | ||||||||
\(619\) | 29228.0i | 1.89786i | 0.315494 | + | 0.948928i | \(0.397830\pi\) | ||||
−0.315494 | + | 0.948928i | \(0.602170\pi\) | |||||||
\(620\) | −7360.00 | −0.476750 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 4704.00i | − 0.303237i | ||||||||
\(623\) | −3088.00 | −0.198584 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11875.0 | −0.760000 | ||||||||
\(626\) | 16884.0i | 1.07799i | ||||||||
\(627\) | −2400.00 | −0.152866 | ||||||||
\(628\) | 9640.00 | 0.612544 | ||||||||
\(629\) | 9620.00i | 0.609816i | ||||||||
\(630\) | − 1440.00i | − 0.0910650i | ||||||||
\(631\) | − 13536.0i | − 0.853977i | −0.904257 | − | 0.426989i | \(-0.859574\pi\) | ||||
0.904257 | − | 0.426989i | \(-0.140426\pi\) | |||||||
\(632\) | 7808.00i | 0.491433i | ||||||||
\(633\) | −6012.00 | −0.377497 | ||||||||
\(634\) | −11100.0 | −0.695327 | ||||||||
\(635\) | 12960.0i | 0.809924i | ||||||||
\(636\) | −4584.00 | −0.285798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1440.00 | 0.0893576 | ||||||||
\(639\) | 6732.00i | 0.416767i | ||||||||
\(640\) | −1280.00 | −0.0790569 | ||||||||
\(641\) | −17218.0 | −1.06095 | −0.530476 | − | 0.847700i | \(-0.677987\pi\) | ||||
−0.530476 | + | 0.847700i | \(0.677987\pi\) | |||||||
\(642\) | − 2232.00i | − 0.137212i | ||||||||
\(643\) | − 15044.0i | − 0.922671i | −0.887226 | − | 0.461335i | \(-0.847370\pi\) | ||||
0.887226 | − | 0.461335i | \(-0.152630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2280.00i | 0.139186i | ||||||||
\(646\) | 5200.00 | 0.316705 | ||||||||
\(647\) | −25176.0 | −1.52978 | −0.764892 | − | 0.644158i | \(-0.777208\pi\) | ||||
−0.764892 | + | 0.644158i | \(0.777208\pi\) | |||||||
\(648\) | − 648.000i | − 0.0392837i | ||||||||
\(649\) | −18560.0 | −1.12256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4416.00 | 0.265863 | ||||||||
\(652\) | − 12848.0i | − 0.771728i | ||||||||
\(653\) | −16034.0 | −0.960887 | −0.480443 | − | 0.877026i | \(-0.659524\pi\) | ||||
−0.480443 | + | 0.877026i | \(0.659524\pi\) | |||||||
\(654\) | 5604.00 | 0.335067 | ||||||||
\(655\) | 8920.00i | 0.532112i | ||||||||
\(656\) | 5792.00i | 0.344725i | ||||||||
\(657\) | 9522.00i | 0.565432i | ||||||||
\(658\) | − 7232.00i | − 0.428469i | ||||||||
\(659\) | 25356.0 | 1.49883 | 0.749415 | − | 0.662100i | \(-0.230335\pi\) | ||||
0.749415 | + | 0.662100i | \(0.230335\pi\) | |||||||
\(660\) | −4800.00 | −0.283091 | ||||||||
\(661\) | 18310.0i | 1.07742i | 0.842490 | + | 0.538711i | \(0.181089\pi\) | ||||
−0.842490 | + | 0.538711i | \(0.818911\pi\) | |||||||
\(662\) | 280.000 | 0.0164388 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8064.00 | 0.471301 | ||||||||
\(665\) | − 1600.00i | − 0.0933013i | ||||||||
\(666\) | 1332.00 | 0.0774984 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − 6672.00i | − 0.386448i | ||||||||
\(669\) | 16824.0i | 0.972277i | ||||||||
\(670\) | 14000.0i | 0.807264i | ||||||||
\(671\) | 14320.0i | 0.823871i | ||||||||
\(672\) | 768.000 | 0.0440867 | ||||||||
\(673\) | −24802.0 | −1.42057 | −0.710287 | − | 0.703912i | \(-0.751435\pi\) | ||||
−0.710287 | + | 0.703912i | \(0.751435\pi\) | |||||||
\(674\) | 12348.0i | 0.705678i | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22706.0 | −1.28901 | −0.644507 | − | 0.764598i | \(-0.722937\pi\) | ||||
−0.644507 | + | 0.764598i | \(0.722937\pi\) | |||||||
\(678\) | 11484.0i | 0.650502i | ||||||||
\(679\) | 4912.00 | 0.277622 | ||||||||
\(680\) | 10400.0 | 0.586503 | ||||||||
\(681\) | 5784.00i | 0.325467i | ||||||||
\(682\) | − 14720.0i | − 0.826478i | ||||||||
\(683\) | − 14792.0i | − 0.828697i | −0.910118 | − | 0.414349i | \(-0.864009\pi\) | ||||
0.910118 | − | 0.414349i | \(-0.135991\pi\) | |||||||
\(684\) | − 720.000i | − 0.0402484i | ||||||||
\(685\) | 23260.0 | 1.29740 | ||||||||
\(686\) | 9952.00 | 0.553891 | ||||||||
\(687\) | − 11814.0i | − 0.656088i | ||||||||
\(688\) | −1216.00 | −0.0673831 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1148.00i | 0.0632011i | 0.999501 | + | 0.0316006i | \(0.0100604\pi\) | ||||
−0.999501 | + | 0.0316006i | \(0.989940\pi\) | |||||||
\(692\) | 14392.0 | 0.790609 | ||||||||
\(693\) | 2880.00 | 0.157867 | ||||||||
\(694\) | − 5976.00i | − 0.326867i | ||||||||
\(695\) | − 19320.0i | − 1.05446i | ||||||||
\(696\) | 432.000i | 0.0235272i | ||||||||
\(697\) | − 47060.0i | − 2.55742i | ||||||||
\(698\) | 324.000 | 0.0175696 | ||||||||
\(699\) | −7686.00 | −0.415896 | ||||||||
\(700\) | 800.000i | 0.0431959i | ||||||||
\(701\) | −14870.0 | −0.801187 | −0.400594 | − | 0.916256i | \(-0.631196\pi\) | ||||
−0.400594 | + | 0.916256i | \(0.631196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1480.00 | 0.0794015 | ||||||||
\(704\) | − 2560.00i | − 0.137051i | ||||||||
\(705\) | −13560.0 | −0.724396 | ||||||||
\(706\) | −21508.0 | −1.14655 | ||||||||
\(707\) | 4144.00i | 0.220440i | ||||||||
\(708\) | − 5568.00i | − 0.295563i | ||||||||
\(709\) | − 6354.00i | − 0.336572i | −0.985738 | − | 0.168286i | \(-0.946177\pi\) | ||||
0.985738 | − | 0.168286i | \(-0.0538232\pi\) | |||||||
\(710\) | 14960.0i | 0.790759i | ||||||||
\(711\) | −8784.00 | −0.463327 | ||||||||
\(712\) | −3088.00 | −0.162539 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −6240.00 | −0.327067 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4272.00 | 0.222978 | ||||||||
\(717\) | − 21492.0i | − 1.11943i | ||||||||
\(718\) | −7176.00 | −0.372989 | ||||||||
\(719\) | −9288.00 | −0.481758 | −0.240879 | − | 0.970555i | \(-0.577436\pi\) | ||||
−0.240879 | + | 0.970555i | \(0.577436\pi\) | |||||||
\(720\) | − 1440.00i | − 0.0745356i | ||||||||
\(721\) | 896.000i | 0.0462813i | ||||||||
\(722\) | 12918.0i | 0.665870i | ||||||||
\(723\) | − 18546.0i | − 0.953988i | ||||||||
\(724\) | −19144.0 | −0.982709 | ||||||||
\(725\) | −450.000 | −0.0230518 | ||||||||
\(726\) | − 1614.00i | − 0.0825085i | ||||||||
\(727\) | 21544.0 | 1.09907 | 0.549534 | − | 0.835471i | \(-0.314805\pi\) | ||||
0.549534 | + | 0.835471i | \(0.314805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 21160.0i | 1.07283i | ||||||||
\(731\) | 9880.00 | 0.499897 | ||||||||
\(732\) | −4296.00 | −0.216919 | ||||||||
\(733\) | − 19990.0i | − 1.00730i | −0.863909 | − | 0.503648i | \(-0.831991\pi\) | ||||
0.863909 | − | 0.503648i | \(-0.168009\pi\) | |||||||
\(734\) | 22544.0i | 1.13367i | ||||||||
\(735\) | − 8370.00i | − 0.420044i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28000.0 | −1.39945 | ||||||||
\(738\) | −6516.00 | −0.325010 | ||||||||
\(739\) | 532.000i | 0.0264816i | 0.999912 | + | 0.0132408i | \(0.00421481\pi\) | ||||
−0.999912 | + | 0.0132408i | \(0.995785\pi\) | |||||||
\(740\) | 2960.00 | 0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6112.00 | 0.302397 | ||||||||
\(743\) | 25452.0i | 1.25672i | 0.777922 | + | 0.628360i | \(0.216274\pi\) | ||||
−0.777922 | + | 0.628360i | \(0.783726\pi\) | |||||||
\(744\) | 4416.00 | 0.217605 | ||||||||
\(745\) | −8820.00 | −0.433745 | ||||||||
\(746\) | − 21828.0i | − 1.07129i | ||||||||
\(747\) | 9072.00i | 0.444347i | ||||||||
\(748\) | 20800.0i | 1.01674i | ||||||||
\(749\) | 2976.00i | 0.145181i | ||||||||
\(750\) | 9000.00 | 0.438178 | ||||||||
\(751\) | −6440.00 | −0.312915 | −0.156457 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156457 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(752\) | − 7232.00i | − 0.350697i | ||||||||
\(753\) | 4188.00 | 0.202682 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17760.0 | −0.856096 | ||||||||
\(756\) | 864.000i | 0.0415653i | ||||||||
\(757\) | −786.000 | −0.0377380 | −0.0188690 | − | 0.999822i | \(-0.506007\pi\) | ||||
−0.0188690 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(758\) | 16200.0 | 0.776267 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 1600.00i | − 0.0763659i | ||||||||
\(761\) | − 1498.00i | − 0.0713567i | −0.999363 | − | 0.0356784i | \(-0.988641\pi\) | ||||
0.999363 | − | 0.0356784i | \(-0.0113592\pi\) | |||||||
\(762\) | − 7776.00i | − 0.369678i | ||||||||
\(763\) | −7472.00 | −0.354528 | ||||||||
\(764\) | 5248.00 | 0.248516 | ||||||||
\(765\) | 11700.0i | 0.552960i | ||||||||
\(766\) | 12360.0 | 0.583009 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | − 14738.0i | − 0.691113i | −0.938398 | − | 0.345556i | \(-0.887690\pi\) | ||||
0.938398 | − | 0.345556i | \(-0.112310\pi\) | |||||||
\(770\) | 6400.00 | 0.299532 | ||||||||
\(771\) | −20718.0 | −0.967757 | ||||||||
\(772\) | 1400.00i | 0.0652683i | ||||||||
\(773\) | 3822.00i | 0.177837i | 0.996039 | + | 0.0889184i | \(0.0283410\pi\) | ||||
−0.996039 | + | 0.0889184i | \(0.971659\pi\) | |||||||
\(774\) | − 1368.00i | − 0.0635294i | ||||||||
\(775\) | 4600.00i | 0.213209i | ||||||||
\(776\) | 4912.00 | 0.227230 | ||||||||
\(777\) | −1776.00 | −0.0819995 | ||||||||
\(778\) | 15044.0i | 0.693256i | ||||||||
\(779\) | −7240.00 | −0.332991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29920.0 | −1.37083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −486.000 | −0.0221816 | ||||||||
\(784\) | 4464.00 | 0.203353 | ||||||||
\(785\) | 24100.0i | 1.09575i | ||||||||
\(786\) | − 5352.00i | − 0.242875i | ||||||||
\(787\) | − 11900.0i | − 0.538995i | −0.963001 | − | 0.269498i | \(-0.913142\pi\) | ||||
0.963001 | − | 0.269498i | \(-0.0868576\pi\) | |||||||
\(788\) | − 1368.00i | − 0.0618439i | ||||||||
\(789\) | −20544.0 | −0.926978 | ||||||||
\(790\) | −19520.0 | −0.879102 | ||||||||
\(791\) | − 15312.0i | − 0.688283i | ||||||||
\(792\) | 2880.00 | 0.129213 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12156.0 | −0.543325 | ||||||||
\(795\) | − 11460.0i | − 0.511251i | ||||||||
\(796\) | −13472.0 | −0.599877 | ||||||||
\(797\) | 21274.0 | 0.945500 | 0.472750 | − | 0.881197i | \(-0.343261\pi\) | ||||
0.472750 | + | 0.881197i | \(0.343261\pi\) | |||||||
\(798\) | 960.000i | 0.0425860i | ||||||||
\(799\) | 58760.0i | 2.60173i | ||||||||
\(800\) | 800.000i | 0.0353553i | ||||||||
\(801\) | − 3474.00i | − 0.153243i | ||||||||
\(802\) | −3660.00 | −0.161146 | ||||||||
\(803\) | −42320.0 | −1.85983 | ||||||||
\(804\) | − 8400.00i | − 0.368464i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18102.0 | −0.789617 | ||||||||
\(808\) | 4144.00i | 0.180427i | ||||||||
\(809\) | −27566.0 | −1.19798 | −0.598992 | − | 0.800755i | \(-0.704432\pi\) | ||||
−0.598992 | + | 0.800755i | \(0.704432\pi\) | |||||||
\(810\) | 1620.00 | 0.0702728 | ||||||||
\(811\) | 11244.0i | 0.486844i | 0.969921 | + | 0.243422i | \(0.0782699\pi\) | ||||
−0.969921 | + | 0.243422i | \(0.921730\pi\) | |||||||
\(812\) | − 576.000i | − 0.0248936i | ||||||||
\(813\) | 14496.0i | 0.625334i | ||||||||
\(814\) | 5920.00i | 0.254909i | ||||||||
\(815\) | 32120.0 | 1.38051 | ||||||||
\(816\) | −6240.00 | −0.267701 | ||||||||
\(817\) | − 1520.00i | − 0.0650894i | ||||||||
\(818\) | 24868.0 | 1.06295 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14480.0 | −0.616663 | ||||||||
\(821\) | − 13554.0i | − 0.576173i | −0.957604 | − | 0.288086i | \(-0.906981\pi\) | ||||
0.957604 | − | 0.288086i | \(-0.0930190\pi\) | |||||||
\(822\) | −13956.0 | −0.592179 | ||||||||
\(823\) | −14384.0 | −0.609228 | −0.304614 | − | 0.952476i | \(-0.598527\pi\) | ||||
−0.304614 | + | 0.952476i | \(0.598527\pi\) | |||||||
\(824\) | 896.000i | 0.0378806i | ||||||||
\(825\) | 3000.00i | 0.126602i | ||||||||
\(826\) | 7424.00i | 0.312729i | ||||||||
\(827\) | − 2488.00i | − 0.104615i | −0.998631 | − | 0.0523073i | \(-0.983342\pi\) | ||||
0.998631 | − | 0.0523073i | \(-0.0166575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20858.0 | 0.873858 | 0.436929 | − | 0.899496i | \(-0.356066\pi\) | ||||
0.436929 | + | 0.899496i | \(0.356066\pi\) | |||||||
\(830\) | 20160.0i | 0.843089i | ||||||||
\(831\) | 12246.0 | 0.511202 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36270.0 | −1.50862 | ||||||||
\(834\) | 11592.0i | 0.481293i | ||||||||
\(835\) | 16680.0 | 0.691300 | ||||||||
\(836\) | 3200.00 | 0.132386 | ||||||||
\(837\) | 4968.00i | 0.205160i | ||||||||
\(838\) | − 28376.0i | − 1.16973i | ||||||||
\(839\) | 23116.0i | 0.951195i | 0.879663 | + | 0.475598i | \(0.157768\pi\) | ||||
−0.879663 | + | 0.475598i | \(0.842232\pi\) | |||||||
\(840\) | 1920.00i | 0.0788646i | ||||||||
\(841\) | −24065.0 | −0.986715 | ||||||||
\(842\) | 17276.0 | 0.707091 | ||||||||
\(843\) | 10050.0i | 0.410605i | ||||||||
\(844\) | 8016.00 | 0.326922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8136.00 | 0.330640 | ||||||||
\(847\) | 2152.00i | 0.0873006i | ||||||||
\(848\) | 6112.00 | 0.247508 | ||||||||
\(849\) | −23388.0 | −0.945435 | ||||||||
\(850\) | − 6500.00i | − 0.262292i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − 8976.00i | − 0.360930i | ||||||||
\(853\) | 934.000i | 0.0374907i | 0.999824 | + | 0.0187453i | \(0.00596718\pi\) | ||||
−0.999824 | + | 0.0187453i | \(0.994033\pi\) | |||||||
\(854\) | 5728.00 | 0.229518 | ||||||||
\(855\) | 1800.00 | 0.0719985 | ||||||||
\(856\) | 2976.00i | 0.118829i | ||||||||
\(857\) | −12642.0 | −0.503900 | −0.251950 | − | 0.967740i | \(-0.581072\pi\) | ||||
−0.251950 | + | 0.967740i | \(0.581072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22796.0 | −0.905459 | −0.452730 | − | 0.891648i | \(-0.649550\pi\) | ||||
−0.452730 | + | 0.891648i | \(0.649550\pi\) | |||||||
\(860\) | − 3040.00i | − 0.120539i | ||||||||
\(861\) | 8688.00 | 0.343886 | ||||||||
\(862\) | 8584.00 | 0.339179 | ||||||||
\(863\) | 76.0000i | 0.00299776i | 0.999999 | + | 0.00149888i | \(0.000477109\pi\) | ||||
−0.999999 | + | 0.00149888i | \(0.999523\pi\) | |||||||
\(864\) | 864.000i | 0.0340207i | ||||||||
\(865\) | 35980.0i | 1.41429i | ||||||||
\(866\) | 11964.0i | 0.469461i | ||||||||
\(867\) | 35961.0 | 1.40865 | ||||||||
\(868\) | −5888.00 | −0.230244 | ||||||||
\(869\) | − 39040.0i | − 1.52398i | ||||||||
\(870\) | −1080.00 | −0.0420867 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7472.00 | −0.290176 | ||||||||
\(873\) | 5526.00i | 0.214235i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12000.0 | −0.463627 | ||||||||
\(876\) | − 12696.0i | − 0.489678i | ||||||||
\(877\) | 46130.0i | 1.77617i | 0.459681 | + | 0.888084i | \(0.347964\pi\) | ||||
−0.459681 | + | 0.888084i | \(0.652036\pi\) | |||||||
\(878\) | − 512.000i | − 0.0196801i | ||||||||
\(879\) | 11766.0i | 0.451487i | ||||||||
\(880\) | 6400.00 | 0.245164 | ||||||||
\(881\) | −6682.00 | −0.255530 | −0.127765 | − | 0.991804i | \(-0.540780\pi\) | ||||
−0.127765 | + | 0.991804i | \(0.540780\pi\) | |||||||
\(882\) | 5022.00i | 0.191723i | ||||||||
\(883\) | −47404.0 | −1.80665 | −0.903325 | − | 0.428957i | \(-0.858881\pi\) | ||||
−0.903325 | + | 0.428957i | \(0.858881\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13920.0 | 0.528718 | ||||||||
\(886\) | 25112.0i | 0.952206i | ||||||||
\(887\) | 33672.0 | 1.27463 | 0.637314 | − | 0.770604i | \(-0.280045\pi\) | ||||
0.637314 | + | 0.770604i | \(0.280045\pi\) | |||||||
\(888\) | −1776.00 | −0.0671156 | ||||||||
\(889\) | 10368.0i | 0.391149i | ||||||||
\(890\) | − 7720.00i | − 0.290758i | ||||||||
\(891\) | 3240.00i | 0.121823i | ||||||||
\(892\) | − 22432.0i | − 0.842017i | ||||||||
\(893\) | 9040.00 | 0.338759 | ||||||||
\(894\) | 5292.00 | 0.197976 | ||||||||
\(895\) | 10680.0i | 0.398875i | ||||||||
\(896\) | −1024.00 | −0.0381802 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11148.0 | −0.414269 | ||||||||
\(899\) | − 3312.00i | − 0.122871i | ||||||||
\(900\) | −900.000 | −0.0333333 | ||||||||
\(901\) | −49660.0 | −1.83620 | ||||||||
\(902\) | − 28960.0i | − 1.06903i | ||||||||
\(903\) | 1824.00i | 0.0672192i | ||||||||
\(904\) | − 15312.0i | − 0.563351i | ||||||||
\(905\) | − 47860.0i | − 1.75792i | ||||||||
\(906\) | 10656.0 | 0.390753 | ||||||||
\(907\) | 14540.0 | 0.532296 | 0.266148 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266148 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(908\) | − 7712.00i | − 0.281863i | ||||||||
\(909\) | −4662.00 | −0.170109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7840.00 | −0.285127 | −0.142564 | − | 0.989786i | \(-0.545535\pi\) | ||||
−0.142564 | + | 0.989786i | \(0.545535\pi\) | |||||||
\(912\) | 960.000i | 0.0348561i | ||||||||
\(913\) | −40320.0 | −1.46155 | ||||||||
\(914\) | 2532.00 | 0.0916314 | ||||||||
\(915\) | − 10740.0i | − 0.388037i | ||||||||
\(916\) | 15752.0i | 0.568189i | ||||||||
\(917\) | 7136.00i | 0.256981i | ||||||||
\(918\) | − 7020.00i | − 0.252391i | ||||||||
\(919\) | 47720.0 | 1.71288 | 0.856440 | − | 0.516246i | \(-0.172671\pi\) | ||||
0.856440 | + | 0.516246i | \(0.172671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17868.0i | 0.639273i | ||||||||
\(922\) | 15108.0 | 0.539648 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3840.00 | −0.136717 | ||||||||
\(925\) | − 1850.00i | − 0.0657596i | ||||||||
\(926\) | 13504.0 | 0.479232 | ||||||||
\(927\) | −1008.00 | −0.0357142 | ||||||||
\(928\) | − 576.000i | − 0.0203751i | ||||||||
\(929\) | − 7502.00i | − 0.264944i | −0.991187 | − | 0.132472i | \(-0.957709\pi\) | ||||
0.991187 | − | 0.132472i | \(-0.0422914\pi\) | |||||||
\(930\) | 11040.0i | 0.389264i | ||||||||
\(931\) | 5580.00i | 0.196431i | ||||||||
\(932\) | 10248.0 | 0.360176 | ||||||||
\(933\) | −7056.00 | −0.247592 | ||||||||
\(934\) | − 15848.0i | − 0.555206i | ||||||||
\(935\) | −52000.0 | −1.81880 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22058.0 | 0.769054 | 0.384527 | − | 0.923114i | \(-0.374365\pi\) | ||||
0.384527 | + | 0.923114i | \(0.374365\pi\) | |||||||
\(938\) | 11200.0i | 0.389865i | ||||||||
\(939\) | 25326.0 | 0.880173 | ||||||||
\(940\) | 18080.0 | 0.627345 | ||||||||
\(941\) | − 23338.0i | − 0.808498i | −0.914649 | − | 0.404249i | \(-0.867533\pi\) | ||||
0.914649 | − | 0.404249i | \(-0.132467\pi\) | |||||||
\(942\) | − 14460.0i | − 0.500140i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 7424.00i | 0.255965i | ||||||||
\(945\) | −2160.00 | −0.0743543 | ||||||||
\(946\) | 6080.00 | 0.208962 | ||||||||
\(947\) | − 30488.0i | − 1.04617i | −0.852279 | − | 0.523087i | \(-0.824780\pi\) | ||||
0.852279 | − | 0.523087i | \(-0.175220\pi\) | |||||||
\(948\) | 11712.0 | 0.401253 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1000.00 | −0.0341519 | ||||||||
\(951\) | 16650.0i | 0.567732i | ||||||||
\(952\) | 8320.00 | 0.283249 | ||||||||
\(953\) | −9522.00 | −0.323660 | −0.161830 | − | 0.986819i | \(-0.551740\pi\) | ||||
−0.161830 | + | 0.986819i | \(0.551740\pi\) | |||||||
\(954\) | 6876.00i | 0.233353i | ||||||||
\(955\) | 13120.0i | 0.444558i | ||||||||
\(956\) | 28656.0i | 0.969457i | ||||||||
\(957\) | − 2160.00i | − 0.0729602i | ||||||||
\(958\) | 22168.0 | 0.747615 | ||||||||
\(959\) | 18608.0 | 0.626573 | ||||||||
\(960\) | 1920.00i | 0.0645497i | ||||||||
\(961\) | −4065.00 | −0.136451 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3348.00 | −0.112033 | ||||||||
\(964\) | 24728.0i | 0.826178i | ||||||||
\(965\) | −3500.00 | −0.116755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7616.00i | 0.253272i | 0.991949 | + | 0.126636i | \(0.0404180\pi\) | ||||
−0.991949 | + | 0.126636i | \(0.959582\pi\) | |||||||
\(968\) | 2152.00i | 0.0714544i | ||||||||
\(969\) | − 7800.00i | − 0.258588i | ||||||||
\(970\) | 12280.0i | 0.406481i | ||||||||
\(971\) | 51316.0 | 1.69599 | 0.847996 | − | 0.530002i | \(-0.177809\pi\) | ||||
0.847996 | + | 0.530002i | \(0.177809\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | − 15456.0i | − 0.509246i | ||||||||
\(974\) | 8864.00 | 0.291603 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5728.00 | 0.187857 | ||||||||
\(977\) | 48666.0i | 1.59362i | 0.604232 | + | 0.796808i | \(0.293480\pi\) | ||||
−0.604232 | + | 0.796808i | \(0.706520\pi\) | |||||||
\(978\) | −19272.0 | −0.630113 | ||||||||
\(979\) | 15440.0 | 0.504050 | ||||||||
\(980\) | 11160.0i | 0.363768i | ||||||||
\(981\) | − 8406.00i | − 0.273581i | ||||||||
\(982\) | 2280.00i | 0.0740914i | ||||||||
\(983\) | 17388.0i | 0.564182i | 0.959388 | + | 0.282091i | \(0.0910280\pi\) | ||||
−0.959388 | + | 0.282091i | \(0.908972\pi\) | |||||||
\(984\) | 8688.00 | 0.281467 | ||||||||
\(985\) | 3420.00 | 0.110630 | ||||||||
\(986\) | 4680.00i | 0.151158i | ||||||||
\(987\) | −10848.0 | −0.349844 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 7200.00i | 0.231142i | ||||||||
\(991\) | 11496.0 | 0.368499 | 0.184249 | − | 0.982880i | \(-0.441015\pi\) | ||||
0.184249 | + | 0.982880i | \(0.441015\pi\) | |||||||
\(992\) | −5888.00 | −0.188452 | ||||||||
\(993\) | − 420.000i | − 0.0134223i | ||||||||
\(994\) | 11968.0i | 0.381893i | ||||||||
\(995\) | − 33680.0i | − 1.07309i | ||||||||
\(996\) | − 12096.0i | − 0.384816i | ||||||||
\(997\) | 48862.0 | 1.55213 | 0.776066 | − | 0.630652i | \(-0.217212\pi\) | ||||
0.776066 | + | 0.630652i | \(0.217212\pi\) | |||||||
\(998\) | 3528.00 | 0.111901 | ||||||||
\(999\) | − 1998.00i | − 0.0632772i |
(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 | 1014.4.b.h.337.2 | 2 | ||
13.5 | odd | 4 | 1014.4.a.j.1.1 | 1 | |||
13.8 | odd | 4 | 78.4.a.c.1.1 | ✓ | 1 | ||
13.12 | even | 2 | inner | 1014.4.b.h.337.1 | 2 | ||
39.8 | even | 4 | 234.4.a.h.1.1 | 1 | |||
52.47 | even | 4 | 624.4.a.d.1.1 | 1 | |||
65.34 | odd | 4 | 1950.4.a.l.1.1 | 1 | |||
104.21 | odd | 4 | 2496.4.a.a.1.1 | 1 | |||
104.99 | even | 4 | 2496.4.a.j.1.1 | 1 | |||
156.47 | odd | 4 | 1872.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.4.a.c.1.1 | ✓ | 1 | 13.8 | odd | 4 | ||
234.4.a.h.1.1 | 1 | 39.8 | even | 4 | |||
624.4.a.d.1.1 | 1 | 52.47 | even | 4 | |||
1014.4.a.j.1.1 | 1 | 13.5 | odd | 4 | |||
1014.4.b.h.337.1 | 2 | 13.12 | even | 2 | inner | ||
1014.4.b.h.337.2 | 2 | 1.1 | even | 1 | trivial | ||
1872.4.a.d.1.1 | 1 | 156.47 | odd | 4 | |||
1950.4.a.l.1.1 | 1 | 65.34 | odd | 4 | |||
2496.4.a.a.1.1 | 1 | 104.21 | odd | 4 | |||
2496.4.a.j.1.1 | 1 | 104.99 | even | 4 |