Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.896575 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.517638 | −0.231495 | −0.115747 | − | 0.993279i | \(-0.536926\pi\) | ||||
−0.115747 | + | 0.993279i | \(0.536926\pi\) | |||||||
\(6\) | 0.896575 | 0.366025 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.19615 | −0.732051 | ||||||||
\(10\) | 0.517638 | 0.163692 | ||||||||
\(11\) | 0.464102 | 0.139932 | 0.0699660 | − | 0.997549i | \(-0.477711\pi\) | ||||
0.0699660 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(12\) | −0.896575 | −0.258819 | ||||||||
\(13\) | −5.79555 | −1.60740 | −0.803699 | − | 0.595036i | \(-0.797138\pi\) | ||||
−0.803699 | + | 0.595036i | \(0.797138\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.464102 | 0.119831 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.65685 | 1.37199 | 0.685994 | − | 0.727607i | \(-0.259367\pi\) | ||||
0.685994 | + | 0.727607i | \(0.259367\pi\) | |||||||
\(18\) | 2.19615 | 0.517638 | ||||||||
\(19\) | 5.27792 | 1.21084 | 0.605419 | − | 0.795907i | \(-0.293006\pi\) | ||||
0.605419 | + | 0.795907i | \(0.293006\pi\) | |||||||
\(20\) | −0.517638 | −0.115747 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.464102 | −0.0989468 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0.896575 | 0.183013 | ||||||||
\(25\) | −4.73205 | −0.946410 | ||||||||
\(26\) | 5.79555 | 1.13660 | ||||||||
\(27\) | 4.65874 | 0.896575 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.464102 | −0.0847330 | ||||||||
\(31\) | 8.24504 | 1.48085 | 0.740427 | − | 0.672137i | \(-0.234623\pi\) | ||||
0.740427 | + | 0.672137i | \(0.234623\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.416102 | −0.0724341 | ||||||||
\(34\) | −5.65685 | −0.970143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.19615 | −0.366025 | ||||||||
\(37\) | 4.92820 | 0.810192 | 0.405096 | − | 0.914274i | \(-0.367238\pi\) | ||||
0.405096 | + | 0.914274i | \(0.367238\pi\) | |||||||
\(38\) | −5.27792 | −0.856191 | ||||||||
\(39\) | 5.19615 | 0.832050 | ||||||||
\(40\) | 0.517638 | 0.0818458 | ||||||||
\(41\) | −7.72741 | −1.20682 | −0.603409 | − | 0.797432i | \(-0.706191\pi\) | ||||
−0.603409 | + | 0.797432i | \(0.706191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73205 | −0.569132 | −0.284566 | − | 0.958656i | \(-0.591850\pi\) | ||||
−0.284566 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(44\) | 0.464102 | 0.0699660 | ||||||||
\(45\) | 1.13681 | 0.169466 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 8.24504 | 1.20266 | 0.601332 | − | 0.799000i | \(-0.294637\pi\) | ||||
0.601332 | + | 0.799000i | \(0.294637\pi\) | |||||||
\(48\) | −0.896575 | −0.129410 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.73205 | 0.669213 | ||||||||
\(51\) | −5.07180 | −0.710194 | ||||||||
\(52\) | −5.79555 | −0.803699 | ||||||||
\(53\) | −14.4641 | −1.98680 | −0.993399 | − | 0.114714i | \(-0.963405\pi\) | ||||
−0.993399 | + | 0.114714i | \(0.963405\pi\) | |||||||
\(54\) | −4.65874 | −0.633975 | ||||||||
\(55\) | −0.240237 | −0.0323935 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.73205 | −0.626775 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 0.757875 | 0.0986669 | 0.0493334 | − | 0.998782i | \(-0.484290\pi\) | ||||
0.0493334 | + | 0.998782i | \(0.484290\pi\) | |||||||
\(60\) | 0.464102 | 0.0599153 | ||||||||
\(61\) | −3.10583 | −0.397661 | −0.198830 | − | 0.980034i | \(-0.563714\pi\) | ||||
−0.198830 | + | 0.980034i | \(0.563714\pi\) | |||||||
\(62\) | −8.24504 | −1.04712 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | 0.416102 | 0.0512186 | ||||||||
\(67\) | 11.4641 | 1.40056 | 0.700281 | − | 0.713867i | \(-0.253058\pi\) | ||||
0.700281 | + | 0.713867i | \(0.253058\pi\) | |||||||
\(68\) | 5.65685 | 0.685994 | ||||||||
\(69\) | −1.79315 | −0.215870 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 2.19615 | 0.258819 | ||||||||
\(73\) | −12.6264 | −1.47781 | −0.738903 | − | 0.673811i | \(-0.764656\pi\) | ||||
−0.738903 | + | 0.673811i | \(0.764656\pi\) | |||||||
\(74\) | −4.92820 | −0.572892 | ||||||||
\(75\) | 4.24264 | 0.489898 | ||||||||
\(76\) | 5.27792 | 0.605419 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.19615 | −0.588348 | ||||||||
\(79\) | −15.5885 | −1.75384 | −0.876919 | − | 0.480638i | \(-0.840405\pi\) | ||||
−0.876919 | + | 0.480638i | \(0.840405\pi\) | |||||||
\(80\) | −0.517638 | −0.0578737 | ||||||||
\(81\) | 2.41154 | 0.267949 | ||||||||
\(82\) | 7.72741 | 0.853349 | ||||||||
\(83\) | −15.4548 | −1.69639 | −0.848193 | − | 0.529687i | \(-0.822309\pi\) | ||||
−0.848193 | + | 0.529687i | \(0.822309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.92820 | −0.317608 | ||||||||
\(86\) | 3.73205 | 0.402437 | ||||||||
\(87\) | 0.896575 | 0.0961230 | ||||||||
\(88\) | −0.464102 | −0.0494734 | ||||||||
\(89\) | 13.6617 | 1.44813 | 0.724067 | − | 0.689730i | \(-0.242271\pi\) | ||||
0.724067 | + | 0.689730i | \(0.242271\pi\) | |||||||
\(90\) | −1.13681 | −0.119831 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | −7.39230 | −0.766546 | ||||||||
\(94\) | −8.24504 | −0.850411 | ||||||||
\(95\) | −2.73205 | −0.280302 | ||||||||
\(96\) | 0.896575 | 0.0915064 | ||||||||
\(97\) | 12.6264 | 1.28202 | 0.641008 | − | 0.767535i | \(-0.278517\pi\) | ||||
0.641008 | + | 0.767535i | \(0.278517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.01924 | −0.102437 | ||||||||
\(100\) | −4.73205 | −0.473205 | ||||||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | 5.07180 | 0.502183 | ||||||||
\(103\) | −4.89898 | −0.482711 | −0.241355 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241355 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(104\) | 5.79555 | 0.568301 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.4641 | 1.40488 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 4.65874 | 0.448288 | ||||||||
\(109\) | 3.39230 | 0.324924 | 0.162462 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162462 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(110\) | 0.240237 | 0.0229057 | ||||||||
\(111\) | −4.41851 | −0.419386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | 4.73205 | 0.443197 | ||||||||
\(115\) | −1.03528 | −0.0965400 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 12.7279 | 1.17670 | ||||||||
\(118\) | −0.757875 | −0.0697680 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.464102 | −0.0423665 | ||||||||
\(121\) | −10.7846 | −0.980419 | ||||||||
\(122\) | 3.10583 | 0.281189 | ||||||||
\(123\) | 6.92820 | 0.624695 | ||||||||
\(124\) | 8.24504 | 0.740427 | ||||||||
\(125\) | 5.03768 | 0.450584 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3205 | −1.18200 | −0.591002 | − | 0.806670i | \(-0.701267\pi\) | ||||
−0.591002 | + | 0.806670i | \(0.701267\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.34607 | 0.294605 | ||||||||
\(130\) | −3.00000 | −0.263117 | ||||||||
\(131\) | −3.20736 | −0.280229 | −0.140114 | − | 0.990135i | \(-0.544747\pi\) | ||||
−0.140114 | + | 0.990135i | \(0.544747\pi\) | |||||||
\(132\) | −0.416102 | −0.0362170 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.4641 | −0.990348 | ||||||||
\(135\) | −2.41154 | −0.207553 | ||||||||
\(136\) | −5.65685 | −0.485071 | ||||||||
\(137\) | 7.85641 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(138\) | 1.79315 | 0.152643 | ||||||||
\(139\) | −10.8332 | −0.918863 | −0.459432 | − | 0.888213i | \(-0.651947\pi\) | ||||
−0.459432 | + | 0.888213i | \(0.651947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.39230 | −0.622544 | ||||||||
\(142\) | 4.00000 | 0.335673 | ||||||||
\(143\) | −2.68973 | −0.224926 | ||||||||
\(144\) | −2.19615 | −0.183013 | ||||||||
\(145\) | 0.517638 | 0.0429875 | ||||||||
\(146\) | 12.6264 | 1.04497 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.92820 | 0.405096 | ||||||||
\(149\) | 11.1962 | 0.917225 | 0.458612 | − | 0.888636i | \(-0.348347\pi\) | ||||
0.458612 | + | 0.888636i | \(0.348347\pi\) | |||||||
\(150\) | −4.24264 | −0.346410 | ||||||||
\(151\) | 11.4641 | 0.932935 | 0.466468 | − | 0.884538i | \(-0.345526\pi\) | ||||
0.466468 | + | 0.884538i | \(0.345526\pi\) | |||||||
\(152\) | −5.27792 | −0.428096 | ||||||||
\(153\) | −12.4233 | −1.00437 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.26795 | −0.342810 | ||||||||
\(156\) | 5.19615 | 0.416025 | ||||||||
\(157\) | −6.41473 | −0.511951 | −0.255976 | − | 0.966683i | \(-0.582397\pi\) | ||||
−0.255976 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(158\) | 15.5885 | 1.24015 | ||||||||
\(159\) | 12.9682 | 1.02844 | ||||||||
\(160\) | 0.517638 | 0.0409229 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41154 | −0.189469 | ||||||||
\(163\) | 20.3205 | 1.59163 | 0.795813 | − | 0.605543i | \(-0.207044\pi\) | ||||
0.795813 | + | 0.605543i | \(0.207044\pi\) | |||||||
\(164\) | −7.72741 | −0.603409 | ||||||||
\(165\) | 0.215390 | 0.0167681 | ||||||||
\(166\) | 15.4548 | 1.19953 | ||||||||
\(167\) | −12.6264 | −0.977059 | −0.488530 | − | 0.872547i | \(-0.662467\pi\) | ||||
−0.488530 | + | 0.872547i | \(0.662467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.5885 | 1.58373 | ||||||||
\(170\) | 2.92820 | 0.224583 | ||||||||
\(171\) | −11.5911 | −0.886394 | ||||||||
\(172\) | −3.73205 | −0.284566 | ||||||||
\(173\) | −5.00052 | −0.380182 | −0.190091 | − | 0.981766i | \(-0.560878\pi\) | ||||
−0.190091 | + | 0.981766i | \(0.560878\pi\) | |||||||
\(174\) | −0.896575 | −0.0679692 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.464102 | 0.0349830 | ||||||||
\(177\) | −0.679492 | −0.0510737 | ||||||||
\(178\) | −13.6617 | −1.02398 | ||||||||
\(179\) | −25.8564 | −1.93260 | −0.966299 | − | 0.257421i | \(-0.917127\pi\) | ||||
−0.966299 | + | 0.257421i | \(0.917127\pi\) | |||||||
\(180\) | 1.13681 | 0.0847330 | ||||||||
\(181\) | −15.4176 | −1.14598 | −0.572992 | − | 0.819561i | \(-0.694218\pi\) | ||||
−0.572992 | + | 0.819561i | \(0.694218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.78461 | 0.205844 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | −2.55103 | −0.187555 | ||||||||
\(186\) | 7.39230 | 0.542030 | ||||||||
\(187\) | 2.62536 | 0.191985 | ||||||||
\(188\) | 8.24504 | 0.601332 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.73205 | 0.198204 | ||||||||
\(191\) | −10.3923 | −0.751961 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(192\) | −0.896575 | −0.0647048 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | −12.6264 | −0.906522 | ||||||||
\(195\) | −2.68973 | −0.192615 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.9282 | −1.34858 | −0.674289 | − | 0.738467i | \(-0.735550\pi\) | ||||
−0.674289 | + | 0.738467i | \(0.735550\pi\) | |||||||
\(198\) | 1.01924 | 0.0724341 | ||||||||
\(199\) | 14.6969 | 1.04184 | 0.520919 | − | 0.853606i | \(-0.325589\pi\) | ||||
0.520919 | + | 0.853606i | \(0.325589\pi\) | |||||||
\(200\) | 4.73205 | 0.334607 | ||||||||
\(201\) | −10.2784 | −0.724985 | ||||||||
\(202\) | −11.3137 | −0.796030 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.07180 | −0.355097 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 4.89898 | 0.341328 | ||||||||
\(207\) | −4.39230 | −0.305286 | ||||||||
\(208\) | −5.79555 | −0.401849 | ||||||||
\(209\) | 2.44949 | 0.169435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3923 | −0.921964 | −0.460982 | − | 0.887409i | \(-0.652503\pi\) | ||||
−0.460982 | + | 0.887409i | \(0.652503\pi\) | |||||||
\(212\) | −14.4641 | −0.993399 | ||||||||
\(213\) | 3.58630 | 0.245729 | ||||||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | 1.93185 | 0.131751 | ||||||||
\(216\) | −4.65874 | −0.316987 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.39230 | −0.229756 | ||||||||
\(219\) | 11.3205 | 0.764969 | ||||||||
\(220\) | −0.240237 | −0.0161968 | ||||||||
\(221\) | −32.7846 | −2.20533 | ||||||||
\(222\) | 4.41851 | 0.296551 | ||||||||
\(223\) | 19.5959 | 1.31224 | 0.656120 | − | 0.754657i | \(-0.272197\pi\) | ||||
0.656120 | + | 0.754657i | \(0.272197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.3923 | 0.692820 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | −11.0363 | −0.732505 | −0.366253 | − | 0.930515i | \(-0.619359\pi\) | ||||
−0.366253 | + | 0.930515i | \(0.619359\pi\) | |||||||
\(228\) | −4.73205 | −0.313388 | ||||||||
\(229\) | −10.0754 | −0.665799 | −0.332899 | − | 0.942962i | \(-0.608027\pi\) | ||||
−0.332899 | + | 0.942962i | \(0.608027\pi\) | |||||||
\(230\) | 1.03528 | 0.0682641 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −24.1244 | −1.58044 | −0.790220 | − | 0.612824i | \(-0.790034\pi\) | ||||
−0.790220 | + | 0.612824i | \(0.790034\pi\) | |||||||
\(234\) | −12.7279 | −0.832050 | ||||||||
\(235\) | −4.26795 | −0.278410 | ||||||||
\(236\) | 0.757875 | 0.0493334 | ||||||||
\(237\) | 13.9762 | 0.907854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.9282 | −0.965625 | −0.482813 | − | 0.875724i | \(-0.660385\pi\) | ||||
−0.482813 | + | 0.875724i | \(0.660385\pi\) | |||||||
\(240\) | 0.464102 | 0.0299576 | ||||||||
\(241\) | 10.6945 | 0.688896 | 0.344448 | − | 0.938805i | \(-0.388066\pi\) | ||||
0.344448 | + | 0.938805i | \(0.388066\pi\) | |||||||
\(242\) | 10.7846 | 0.693261 | ||||||||
\(243\) | −16.1384 | −1.03528 | ||||||||
\(244\) | −3.10583 | −0.198830 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.92820 | −0.441726 | ||||||||
\(247\) | −30.5885 | −1.94630 | ||||||||
\(248\) | −8.24504 | −0.523561 | ||||||||
\(249\) | 13.8564 | 0.878114 | ||||||||
\(250\) | −5.03768 | −0.318611 | ||||||||
\(251\) | 2.31079 | 0.145856 | 0.0729279 | − | 0.997337i | \(-0.476766\pi\) | ||||
0.0729279 | + | 0.997337i | \(0.476766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.928203 | 0.0583556 | ||||||||
\(254\) | 13.3205 | 0.835803 | ||||||||
\(255\) | 2.62536 | 0.164406 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.83083 | −0.426096 | −0.213048 | − | 0.977042i | \(-0.568339\pi\) | ||||
−0.213048 | + | 0.977042i | \(0.568339\pi\) | |||||||
\(258\) | −3.34607 | −0.208317 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.00000 | 0.186052 | ||||||||
\(261\) | 2.19615 | 0.135938 | ||||||||
\(262\) | 3.20736 | 0.198152 | ||||||||
\(263\) | 1.19615 | 0.0737579 | 0.0368790 | − | 0.999320i | \(-0.488258\pi\) | ||||
0.0368790 | + | 0.999320i | \(0.488258\pi\) | |||||||
\(264\) | 0.416102 | 0.0256093 | ||||||||
\(265\) | 7.48717 | 0.459933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2487 | −0.749609 | ||||||||
\(268\) | 11.4641 | 0.700281 | ||||||||
\(269\) | −2.82843 | −0.172452 | −0.0862261 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862261 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(270\) | 2.41154 | 0.146762 | ||||||||
\(271\) | 17.3867 | 1.05616 | 0.528082 | − | 0.849193i | \(-0.322911\pi\) | ||||
0.528082 | + | 0.849193i | \(0.322911\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.85641 | −0.474623 | ||||||||
\(275\) | −2.19615 | −0.132433 | ||||||||
\(276\) | −1.79315 | −0.107935 | ||||||||
\(277\) | 18.9282 | 1.13729 | 0.568643 | − | 0.822585i | \(-0.307469\pi\) | ||||
0.568643 | + | 0.822585i | \(0.307469\pi\) | |||||||
\(278\) | 10.8332 | 0.649734 | ||||||||
\(279\) | −18.1074 | −1.08406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.85641 | −0.528329 | −0.264164 | − | 0.964478i | \(-0.585096\pi\) | ||||
−0.264164 | + | 0.964478i | \(0.585096\pi\) | |||||||
\(282\) | 7.39230 | 0.440205 | ||||||||
\(283\) | −27.0459 | −1.60771 | −0.803857 | − | 0.594823i | \(-0.797222\pi\) | ||||
−0.803857 | + | 0.594823i | \(0.797222\pi\) | |||||||
\(284\) | −4.00000 | −0.237356 | ||||||||
\(285\) | 2.44949 | 0.145095 | ||||||||
\(286\) | 2.68973 | 0.159047 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.19615 | 0.129410 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | −0.517638 | −0.0303968 | ||||||||
\(291\) | −11.3205 | −0.663620 | ||||||||
\(292\) | −12.6264 | −0.738903 | ||||||||
\(293\) | −8.20788 | −0.479509 | −0.239755 | − | 0.970833i | \(-0.577067\pi\) | ||||
−0.239755 | + | 0.970833i | \(0.577067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.392305 | −0.0228409 | ||||||||
\(296\) | −4.92820 | −0.286446 | ||||||||
\(297\) | 2.16213 | 0.125460 | ||||||||
\(298\) | −11.1962 | −0.648576 | ||||||||
\(299\) | −11.5911 | −0.670331 | ||||||||
\(300\) | 4.24264 | 0.244949 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.4641 | −0.659685 | ||||||||
\(303\) | −10.1436 | −0.582734 | ||||||||
\(304\) | 5.27792 | 0.302709 | ||||||||
\(305\) | 1.60770 | 0.0920564 | ||||||||
\(306\) | 12.4233 | 0.710194 | ||||||||
\(307\) | 6.27603 | 0.358192 | 0.179096 | − | 0.983832i | \(-0.442683\pi\) | ||||
0.179096 | + | 0.983832i | \(0.442683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.39230 | 0.249869 | ||||||||
\(310\) | 4.26795 | 0.242403 | ||||||||
\(311\) | 6.59059 | 0.373718 | 0.186859 | − | 0.982387i | \(-0.440169\pi\) | ||||
0.186859 | + | 0.982387i | \(0.440169\pi\) | |||||||
\(312\) | −5.19615 | −0.294174 | ||||||||
\(313\) | −27.0088 | −1.52663 | −0.763313 | − | 0.646029i | \(-0.776428\pi\) | ||||
−0.763313 | + | 0.646029i | \(0.776428\pi\) | |||||||
\(314\) | 6.41473 | 0.362004 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5885 | −0.876919 | ||||||||
\(317\) | −26.3923 | −1.48234 | −0.741170 | − | 0.671318i | \(-0.765729\pi\) | ||||
−0.741170 | + | 0.671318i | \(0.765729\pi\) | |||||||
\(318\) | −12.9682 | −0.727218 | ||||||||
\(319\) | −0.464102 | −0.0259847 | ||||||||
\(320\) | −0.517638 | −0.0289368 | ||||||||
\(321\) | 16.1384 | 0.900755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.8564 | 1.66125 | ||||||||
\(324\) | 2.41154 | 0.133975 | ||||||||
\(325\) | 27.4249 | 1.52126 | ||||||||
\(326\) | −20.3205 | −1.12545 | ||||||||
\(327\) | −3.04146 | −0.168193 | ||||||||
\(328\) | 7.72741 | 0.426675 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.215390 | −0.0118568 | ||||||||
\(331\) | 7.19615 | 0.395536 | 0.197768 | − | 0.980249i | \(-0.436631\pi\) | ||||
0.197768 | + | 0.980249i | \(0.436631\pi\) | |||||||
\(332\) | −15.4548 | −0.848193 | ||||||||
\(333\) | −10.8231 | −0.593101 | ||||||||
\(334\) | 12.6264 | 0.690885 | ||||||||
\(335\) | −5.93426 | −0.324223 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.92820 | 0.268456 | 0.134228 | − | 0.990950i | \(-0.457144\pi\) | ||||
0.134228 | + | 0.990950i | \(0.457144\pi\) | |||||||
\(338\) | −20.5885 | −1.11986 | ||||||||
\(339\) | 3.58630 | 0.194781 | ||||||||
\(340\) | −2.92820 | −0.158804 | ||||||||
\(341\) | 3.82654 | 0.207219 | ||||||||
\(342\) | 11.5911 | 0.626775 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.73205 | 0.201219 | ||||||||
\(345\) | 0.928203 | 0.0499728 | ||||||||
\(346\) | 5.00052 | 0.268829 | ||||||||
\(347\) | −11.0718 | −0.594365 | −0.297183 | − | 0.954821i | \(-0.596047\pi\) | ||||
−0.297183 | + | 0.954821i | \(0.596047\pi\) | |||||||
\(348\) | 0.896575 | 0.0480615 | ||||||||
\(349\) | 26.2509 | 1.40518 | 0.702589 | − | 0.711596i | \(-0.252027\pi\) | ||||
0.702589 | + | 0.711596i | \(0.252027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | −1.44115 | ||||||||
\(352\) | −0.464102 | −0.0247367 | ||||||||
\(353\) | 2.17209 | 0.115609 | 0.0578043 | − | 0.998328i | \(-0.481590\pi\) | ||||
0.0578043 | + | 0.998328i | \(0.481590\pi\) | |||||||
\(354\) | 0.679492 | 0.0361146 | ||||||||
\(355\) | 2.07055 | 0.109894 | ||||||||
\(356\) | 13.6617 | 0.724067 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.8564 | 1.36655 | ||||||||
\(359\) | −3.87564 | −0.204549 | −0.102274 | − | 0.994756i | \(-0.532612\pi\) | ||||
−0.102274 | + | 0.994756i | \(0.532612\pi\) | |||||||
\(360\) | −1.13681 | −0.0599153 | ||||||||
\(361\) | 8.85641 | 0.466127 | ||||||||
\(362\) | 15.4176 | 0.810334 | ||||||||
\(363\) | 9.66922 | 0.507502 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.53590 | 0.342105 | ||||||||
\(366\) | −2.78461 | −0.145554 | ||||||||
\(367\) | 32.0464 | 1.67281 | 0.836405 | − | 0.548112i | \(-0.184653\pi\) | ||||
0.836405 | + | 0.548112i | \(0.184653\pi\) | |||||||
\(368\) | 2.00000 | 0.104257 | ||||||||
\(369\) | 16.9706 | 0.883452 | ||||||||
\(370\) | 2.55103 | 0.132622 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.39230 | −0.383273 | ||||||||
\(373\) | 22.6603 | 1.17330 | 0.586652 | − | 0.809839i | \(-0.300446\pi\) | ||||
0.586652 | + | 0.809839i | \(0.300446\pi\) | |||||||
\(374\) | −2.62536 | −0.135754 | ||||||||
\(375\) | −4.51666 | −0.233239 | ||||||||
\(376\) | −8.24504 | −0.425206 | ||||||||
\(377\) | 5.79555 | 0.298486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.60770 | −0.288048 | −0.144024 | − | 0.989574i | \(-0.546004\pi\) | ||||
−0.144024 | + | 0.989574i | \(0.546004\pi\) | |||||||
\(380\) | −2.73205 | −0.140151 | ||||||||
\(381\) | 11.9428 | 0.611850 | ||||||||
\(382\) | 10.3923 | 0.531717 | ||||||||
\(383\) | −8.20788 | −0.419403 | −0.209702 | − | 0.977765i | \(-0.567249\pi\) | ||||
−0.209702 | + | 0.977765i | \(0.567249\pi\) | |||||||
\(384\) | 0.896575 | 0.0457532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | 8.19615 | 0.416634 | ||||||||
\(388\) | 12.6264 | 0.641008 | ||||||||
\(389\) | 11.3205 | 0.573973 | 0.286986 | − | 0.957935i | \(-0.407347\pi\) | ||||
0.286986 | + | 0.957935i | \(0.407347\pi\) | |||||||
\(390\) | 2.68973 | 0.136200 | ||||||||
\(391\) | 11.3137 | 0.572159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.87564 | 0.145057 | ||||||||
\(394\) | 18.9282 | 0.953589 | ||||||||
\(395\) | 8.06918 | 0.406004 | ||||||||
\(396\) | −1.01924 | −0.0512186 | ||||||||
\(397\) | −7.58871 | −0.380866 | −0.190433 | − | 0.981700i | \(-0.560989\pi\) | ||||
−0.190433 | + | 0.981700i | \(0.560989\pi\) | |||||||
\(398\) | −14.6969 | −0.736691 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.73205 | −0.236603 | ||||||||
\(401\) | −3.14359 | −0.156984 | −0.0784918 | − | 0.996915i | \(-0.525010\pi\) | ||||
−0.0784918 | + | 0.996915i | \(0.525010\pi\) | |||||||
\(402\) | 10.2784 | 0.512642 | ||||||||
\(403\) | −47.7846 | −2.38032 | ||||||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | −1.24831 | −0.0620288 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.28719 | 0.113372 | ||||||||
\(408\) | 5.07180 | 0.251091 | ||||||||
\(409\) | −22.6274 | −1.11885 | −0.559427 | − | 0.828880i | \(-0.688979\pi\) | ||||
−0.559427 | + | 0.828880i | \(0.688979\pi\) | |||||||
\(410\) | −4.00000 | −0.197546 | ||||||||
\(411\) | −7.04386 | −0.347448 | ||||||||
\(412\) | −4.89898 | −0.241355 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.39230 | 0.215870 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 5.79555 | 0.284150 | ||||||||
\(417\) | 9.71281 | 0.475638 | ||||||||
\(418\) | −2.44949 | −0.119808 | ||||||||
\(419\) | −19.7990 | −0.967244 | −0.483622 | − | 0.875277i | \(-0.660679\pi\) | ||||
−0.483622 | + | 0.875277i | \(0.660679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4641 | 0.948622 | 0.474311 | − | 0.880357i | \(-0.342697\pi\) | ||||
0.474311 | + | 0.880357i | \(0.342697\pi\) | |||||||
\(422\) | 13.3923 | 0.651927 | ||||||||
\(423\) | −18.1074 | −0.880411 | ||||||||
\(424\) | 14.4641 | 0.702439 | ||||||||
\(425\) | −26.7685 | −1.29846 | ||||||||
\(426\) | −3.58630 | −0.173757 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 2.41154 | 0.116430 | ||||||||
\(430\) | −1.93185 | −0.0931622 | ||||||||
\(431\) | −4.39230 | −0.211570 | −0.105785 | − | 0.994389i | \(-0.533736\pi\) | ||||
−0.105785 | + | 0.994389i | \(0.533736\pi\) | |||||||
\(432\) | 4.65874 | 0.224144 | ||||||||
\(433\) | 8.96575 | 0.430867 | 0.215433 | − | 0.976519i | \(-0.430884\pi\) | ||||
0.215433 | + | 0.976519i | \(0.430884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.464102 | −0.0222520 | ||||||||
\(436\) | 3.39230 | 0.162462 | ||||||||
\(437\) | 10.5558 | 0.504954 | ||||||||
\(438\) | −11.3205 | −0.540915 | ||||||||
\(439\) | 20.8343 | 0.994365 | 0.497183 | − | 0.867646i | \(-0.334368\pi\) | ||||
0.497183 | + | 0.867646i | \(0.334368\pi\) | |||||||
\(440\) | 0.240237 | 0.0114528 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.7846 | 1.55940 | ||||||||
\(443\) | −40.2487 | −1.91227 | −0.956137 | − | 0.292920i | \(-0.905373\pi\) | ||||
−0.956137 | + | 0.292920i | \(0.905373\pi\) | |||||||
\(444\) | −4.41851 | −0.209693 | ||||||||
\(445\) | −7.07180 | −0.335235 | ||||||||
\(446\) | −19.5959 | −0.927894 | ||||||||
\(447\) | −10.0382 | −0.474790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.07180 | 0.239353 | 0.119676 | − | 0.992813i | \(-0.461814\pi\) | ||||
0.119676 | + | 0.992813i | \(0.461814\pi\) | |||||||
\(450\) | −10.3923 | −0.489898 | ||||||||
\(451\) | −3.58630 | −0.168872 | ||||||||
\(452\) | −4.00000 | −0.188144 | ||||||||
\(453\) | −10.2784 | −0.482923 | ||||||||
\(454\) | 11.0363 | 0.517960 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.73205 | 0.221599 | ||||||||
\(457\) | −32.9282 | −1.54032 | −0.770158 | − | 0.637853i | \(-0.779823\pi\) | ||||
−0.770158 | + | 0.637853i | \(0.779823\pi\) | |||||||
\(458\) | 10.0754 | 0.470791 | ||||||||
\(459\) | 26.3538 | 1.23009 | ||||||||
\(460\) | −1.03528 | −0.0482700 | ||||||||
\(461\) | −14.6969 | −0.684505 | −0.342252 | − | 0.939608i | \(-0.611190\pi\) | ||||
−0.342252 | + | 0.939608i | \(0.611190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8564 | −0.643962 | −0.321981 | − | 0.946746i | \(-0.604349\pi\) | ||||
−0.321981 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 3.82654 | 0.177451 | ||||||||
\(466\) | 24.1244 | 1.11754 | ||||||||
\(467\) | −32.6656 | −1.51158 | −0.755792 | − | 0.654812i | \(-0.772748\pi\) | ||||
−0.755792 | + | 0.654812i | \(0.772748\pi\) | |||||||
\(468\) | 12.7279 | 0.588348 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.26795 | 0.196866 | ||||||||
\(471\) | 5.75129 | 0.265005 | ||||||||
\(472\) | −0.757875 | −0.0348840 | ||||||||
\(473\) | −1.73205 | −0.0796398 | ||||||||
\(474\) | −13.9762 | −0.641949 | ||||||||
\(475\) | −24.9754 | −1.14595 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.7654 | 1.45444 | ||||||||
\(478\) | 14.9282 | 0.682800 | ||||||||
\(479\) | 0.138701 | 0.00633740 | 0.00316870 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316870 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(480\) | −0.464102 | −0.0211832 | ||||||||
\(481\) | −28.5617 | −1.30230 | ||||||||
\(482\) | −10.6945 | −0.487123 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7846 | −0.490210 | ||||||||
\(485\) | −6.53590 | −0.296780 | ||||||||
\(486\) | 16.1384 | 0.732051 | ||||||||
\(487\) | −7.32051 | −0.331724 | −0.165862 | − | 0.986149i | \(-0.553041\pi\) | ||||
−0.165862 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(488\) | 3.10583 | 0.140594 | ||||||||
\(489\) | −18.2189 | −0.823886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3205 | 1.00731 | 0.503655 | − | 0.863905i | \(-0.331988\pi\) | ||||
0.503655 | + | 0.863905i | \(0.331988\pi\) | |||||||
\(492\) | 6.92820 | 0.312348 | ||||||||
\(493\) | −5.65685 | −0.254772 | ||||||||
\(494\) | 30.5885 | 1.37624 | ||||||||
\(495\) | 0.527596 | 0.0237137 | ||||||||
\(496\) | 8.24504 | 0.370213 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.8564 | −0.620920 | ||||||||
\(499\) | 20.9282 | 0.936875 | 0.468438 | − | 0.883497i | \(-0.344817\pi\) | ||||
0.468438 | + | 0.883497i | \(0.344817\pi\) | |||||||
\(500\) | 5.03768 | 0.225292 | ||||||||
\(501\) | 11.3205 | 0.505763 | ||||||||
\(502\) | −2.31079 | −0.103136 | ||||||||
\(503\) | 1.37705 | 0.0613996 | 0.0306998 | − | 0.999529i | \(-0.490226\pi\) | ||||
0.0306998 | + | 0.999529i | \(0.490226\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.85641 | −0.260607 | ||||||||
\(506\) | −0.928203 | −0.0412637 | ||||||||
\(507\) | −18.4591 | −0.819798 | ||||||||
\(508\) | −13.3205 | −0.591002 | ||||||||
\(509\) | −35.4940 | −1.57325 | −0.786623 | − | 0.617434i | \(-0.788172\pi\) | ||||
−0.786623 | + | 0.617434i | \(0.788172\pi\) | |||||||
\(510\) | −2.62536 | −0.116253 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 24.5885 | 1.08561 | ||||||||
\(514\) | 6.83083 | 0.301295 | ||||||||
\(515\) | 2.53590 | 0.111745 | ||||||||
\(516\) | 3.34607 | 0.147302 | ||||||||
\(517\) | 3.82654 | 0.168291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.48334 | 0.196797 | ||||||||
\(520\) | −3.00000 | −0.131559 | ||||||||
\(521\) | 29.7356 | 1.30274 | 0.651371 | − | 0.758759i | \(-0.274194\pi\) | ||||
0.651371 | + | 0.758759i | \(0.274194\pi\) | |||||||
\(522\) | −2.19615 | −0.0961230 | ||||||||
\(523\) | 14.4195 | 0.630522 | 0.315261 | − | 0.949005i | \(-0.397908\pi\) | ||||
0.315261 | + | 0.949005i | \(0.397908\pi\) | |||||||
\(524\) | −3.20736 | −0.140114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.19615 | −0.0521547 | ||||||||
\(527\) | 46.6410 | 2.03171 | ||||||||
\(528\) | −0.416102 | −0.0181085 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −7.48717 | −0.325222 | ||||||||
\(531\) | −1.66441 | −0.0722292 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.7846 | 1.93984 | ||||||||
\(534\) | 12.2487 | 0.530054 | ||||||||
\(535\) | 9.31749 | 0.402830 | ||||||||
\(536\) | −11.4641 | −0.495174 | ||||||||
\(537\) | 23.1822 | 1.00039 | ||||||||
\(538\) | 2.82843 | 0.121942 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.41154 | −0.103776 | ||||||||
\(541\) | 26.9282 | 1.15773 | 0.578867 | − | 0.815422i | \(-0.303495\pi\) | ||||
0.578867 | + | 0.815422i | \(0.303495\pi\) | |||||||
\(542\) | −17.3867 | −0.746821 | ||||||||
\(543\) | 13.8231 | 0.593205 | ||||||||
\(544\) | −5.65685 | −0.242536 | ||||||||
\(545\) | −1.75599 | −0.0752182 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2487 | 1.37886 | 0.689428 | − | 0.724355i | \(-0.257862\pi\) | ||||
0.689428 | + | 0.724355i | \(0.257862\pi\) | |||||||
\(548\) | 7.85641 | 0.335609 | ||||||||
\(549\) | 6.82087 | 0.291108 | ||||||||
\(550\) | 2.19615 | 0.0936443 | ||||||||
\(551\) | −5.27792 | −0.224847 | ||||||||
\(552\) | 1.79315 | 0.0763216 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.9282 | −0.804182 | ||||||||
\(555\) | 2.28719 | 0.0970857 | ||||||||
\(556\) | −10.8332 | −0.459432 | ||||||||
\(557\) | −36.9282 | −1.56470 | −0.782349 | − | 0.622840i | \(-0.785979\pi\) | ||||
−0.782349 | + | 0.622840i | \(0.785979\pi\) | |||||||
\(558\) | 18.1074 | 0.766546 | ||||||||
\(559\) | 21.6293 | 0.914822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.35383 | −0.0993787 | ||||||||
\(562\) | 8.85641 | 0.373585 | ||||||||
\(563\) | −16.3514 | −0.689129 | −0.344564 | − | 0.938763i | \(-0.611973\pi\) | ||||
−0.344564 | + | 0.938763i | \(0.611973\pi\) | |||||||
\(564\) | −7.39230 | −0.311272 | ||||||||
\(565\) | 2.07055 | 0.0871088 | ||||||||
\(566\) | 27.0459 | 1.13682 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.00000 | 0.167836 | ||||||||
\(569\) | 0.535898 | 0.0224660 | 0.0112330 | − | 0.999937i | \(-0.496424\pi\) | ||||
0.0112330 | + | 0.999937i | \(0.496424\pi\) | |||||||
\(570\) | −2.44949 | −0.102598 | ||||||||
\(571\) | 11.4641 | 0.479758 | 0.239879 | − | 0.970803i | \(-0.422892\pi\) | ||||
0.239879 | + | 0.970803i | \(0.422892\pi\) | |||||||
\(572\) | −2.68973 | −0.112463 | ||||||||
\(573\) | 9.31749 | 0.389244 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.46410 | −0.394680 | ||||||||
\(576\) | −2.19615 | −0.0915064 | ||||||||
\(577\) | −6.69213 | −0.278597 | −0.139299 | − | 0.990250i | \(-0.544485\pi\) | ||||
−0.139299 | + | 0.990250i | \(0.544485\pi\) | |||||||
\(578\) | −15.0000 | −0.623918 | ||||||||
\(579\) | 14.3452 | 0.596166 | ||||||||
\(580\) | 0.517638 | 0.0214938 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.3205 | 0.469250 | ||||||||
\(583\) | −6.71281 | −0.278016 | ||||||||
\(584\) | 12.6264 | 0.522484 | ||||||||
\(585\) | −6.58846 | −0.272399 | ||||||||
\(586\) | 8.20788 | 0.339064 | ||||||||
\(587\) | 22.7017 | 0.937001 | 0.468501 | − | 0.883463i | \(-0.344794\pi\) | ||||
0.468501 | + | 0.883463i | \(0.344794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.5167 | 1.79307 | ||||||||
\(590\) | 0.392305 | 0.0161509 | ||||||||
\(591\) | 16.9706 | 0.698076 | ||||||||
\(592\) | 4.92820 | 0.202548 | ||||||||
\(593\) | 26.1493 | 1.07383 | 0.536913 | − | 0.843638i | \(-0.319591\pi\) | ||||
0.536913 | + | 0.843638i | \(0.319591\pi\) | |||||||
\(594\) | −2.16213 | −0.0887133 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1962 | 0.458612 | ||||||||
\(597\) | −13.1769 | −0.539295 | ||||||||
\(598\) | 11.5911 | 0.473996 | ||||||||
\(599\) | 22.5167 | 0.920006 | 0.460003 | − | 0.887917i | \(-0.347848\pi\) | ||||
0.460003 | + | 0.887917i | \(0.347848\pi\) | |||||||
\(600\) | −4.24264 | −0.173205 | ||||||||
\(601\) | −2.82843 | −0.115374 | −0.0576870 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576870 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.1769 | −1.02528 | ||||||||
\(604\) | 11.4641 | 0.466468 | ||||||||
\(605\) | 5.58252 | 0.226962 | ||||||||
\(606\) | 10.1436 | 0.412055 | ||||||||
\(607\) | −27.1846 | −1.10339 | −0.551695 | − | 0.834046i | \(-0.686019\pi\) | ||||
−0.551695 | + | 0.834046i | \(0.686019\pi\) | |||||||
\(608\) | −5.27792 | −0.214048 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.60770 | −0.0650937 | ||||||||
\(611\) | −47.7846 | −1.93316 | ||||||||
\(612\) | −12.4233 | −0.502183 | ||||||||
\(613\) | 22.9090 | 0.925284 | 0.462642 | − | 0.886545i | \(-0.346901\pi\) | ||||
0.462642 | + | 0.886545i | \(0.346901\pi\) | |||||||
\(614\) | −6.27603 | −0.253280 | ||||||||
\(615\) | −3.58630 | −0.144614 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.392305 | 0.0157936 | 0.00789680 | − | 0.999969i | \(-0.497486\pi\) | ||||
0.00789680 | + | 0.999969i | \(0.497486\pi\) | |||||||
\(618\) | −4.39230 | −0.176684 | ||||||||
\(619\) | −5.41662 | −0.217712 | −0.108856 | − | 0.994058i | \(-0.534719\pi\) | ||||
−0.108856 | + | 0.994058i | \(0.534719\pi\) | |||||||
\(620\) | −4.26795 | −0.171405 | ||||||||
\(621\) | 9.31749 | 0.373898 | ||||||||
\(622\) | −6.59059 | −0.264259 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.19615 | 0.208013 | ||||||||
\(625\) | 21.0526 | 0.842102 | ||||||||
\(626\) | 27.0088 | 1.07949 | ||||||||
\(627\) | −2.19615 | −0.0877059 | ||||||||
\(628\) | −6.41473 | −0.255976 | ||||||||
\(629\) | 27.8781 | 1.11157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.3923 | 0.811805 | 0.405902 | − | 0.913916i | \(-0.366957\pi\) | ||||
0.405902 | + | 0.913916i | \(0.366957\pi\) | |||||||
\(632\) | 15.5885 | 0.620076 | ||||||||
\(633\) | 12.0072 | 0.477244 | ||||||||
\(634\) | 26.3923 | 1.04817 | ||||||||
\(635\) | 6.89520 | 0.273628 | ||||||||
\(636\) | 12.9682 | 0.514221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.464102 | 0.0183740 | ||||||||
\(639\) | 8.78461 | 0.347514 | ||||||||
\(640\) | 0.517638 | 0.0204614 | ||||||||
\(641\) | 28.7846 | 1.13692 | 0.568462 | − | 0.822710i | \(-0.307539\pi\) | ||||
0.568462 | + | 0.822710i | \(0.307539\pi\) | |||||||
\(642\) | −16.1384 | −0.636930 | ||||||||
\(643\) | 6.96953 | 0.274852 | 0.137426 | − | 0.990512i | \(-0.456117\pi\) | ||||
0.137426 | + | 0.990512i | \(0.456117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.73205 | −0.0681994 | ||||||||
\(646\) | −29.8564 | −1.17468 | ||||||||
\(647\) | 6.96953 | 0.274001 | 0.137000 | − | 0.990571i | \(-0.456254\pi\) | ||||
0.137000 | + | 0.990571i | \(0.456254\pi\) | |||||||
\(648\) | −2.41154 | −0.0947343 | ||||||||
\(649\) | 0.351731 | 0.0138066 | ||||||||
\(650\) | −27.4249 | −1.07569 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.3205 | 0.795813 | ||||||||
\(653\) | 39.7128 | 1.55408 | 0.777041 | − | 0.629450i | \(-0.216720\pi\) | ||||
0.777041 | + | 0.629450i | \(0.216720\pi\) | |||||||
\(654\) | 3.04146 | 0.118930 | ||||||||
\(655\) | 1.66025 | 0.0648715 | ||||||||
\(656\) | −7.72741 | −0.301705 | ||||||||
\(657\) | 27.7295 | 1.08183 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.3923 | −1.61242 | −0.806208 | − | 0.591633i | \(-0.798484\pi\) | ||||
−0.806208 | + | 0.591633i | \(0.798484\pi\) | |||||||
\(660\) | 0.215390 | 0.00838406 | ||||||||
\(661\) | −36.6680 | −1.42622 | −0.713110 | − | 0.701052i | \(-0.752714\pi\) | ||||
−0.713110 | + | 0.701052i | \(0.752714\pi\) | |||||||
\(662\) | −7.19615 | −0.279686 | ||||||||
\(663\) | 29.3939 | 1.14156 | ||||||||
\(664\) | 15.4548 | 0.599763 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.8231 | 0.419386 | ||||||||
\(667\) | −2.00000 | −0.0774403 | ||||||||
\(668\) | −12.6264 | −0.488530 | ||||||||
\(669\) | −17.5692 | −0.679265 | ||||||||
\(670\) | 5.93426 | 0.229260 | ||||||||
\(671\) | −1.44142 | −0.0556454 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.0000 | 1.42625 | 0.713123 | − | 0.701039i | \(-0.247280\pi\) | ||||
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | −4.92820 | −0.189827 | ||||||||
\(675\) | −22.0454 | −0.848528 | ||||||||
\(676\) | 20.5885 | 0.791864 | ||||||||
\(677\) | 3.58630 | 0.137833 | 0.0689164 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689164 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(678\) | −3.58630 | −0.137731 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.92820 | 0.112291 | ||||||||
\(681\) | 9.89488 | 0.379173 | ||||||||
\(682\) | −3.82654 | −0.146526 | ||||||||
\(683\) | 24.3923 | 0.933346 | 0.466673 | − | 0.884430i | \(-0.345453\pi\) | ||||
0.466673 | + | 0.884430i | \(0.345453\pi\) | |||||||
\(684\) | −11.5911 | −0.443197 | ||||||||
\(685\) | −4.06678 | −0.155383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.03332 | 0.344643 | ||||||||
\(688\) | −3.73205 | −0.142283 | ||||||||
\(689\) | 83.8275 | 3.19357 | ||||||||
\(690\) | −0.928203 | −0.0353361 | ||||||||
\(691\) | −29.3939 | −1.11820 | −0.559098 | − | 0.829102i | \(-0.688852\pi\) | ||||
−0.559098 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(692\) | −5.00052 | −0.190091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0718 | 0.420280 | ||||||||
\(695\) | 5.60770 | 0.212712 | ||||||||
\(696\) | −0.896575 | −0.0339846 | ||||||||
\(697\) | −43.7128 | −1.65574 | ||||||||
\(698\) | −26.2509 | −0.993611 | ||||||||
\(699\) | 21.6293 | 0.818095 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8038 | 0.785750 | 0.392875 | − | 0.919592i | \(-0.371480\pi\) | ||||
0.392875 | + | 0.919592i | \(0.371480\pi\) | |||||||
\(702\) | 27.0000 | 1.01905 | ||||||||
\(703\) | 26.0106 | 0.981010 | ||||||||
\(704\) | 0.464102 | 0.0174915 | ||||||||
\(705\) | 3.82654 | 0.144116 | ||||||||
\(706\) | −2.17209 | −0.0817476 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.679492 | −0.0255369 | ||||||||
\(709\) | 7.67949 | 0.288409 | 0.144205 | − | 0.989548i | \(-0.453938\pi\) | ||||
0.144205 | + | 0.989548i | \(0.453938\pi\) | |||||||
\(710\) | −2.07055 | −0.0777064 | ||||||||
\(711\) | 34.2346 | 1.28390 | ||||||||
\(712\) | −13.6617 | −0.511992 | ||||||||
\(713\) | 16.4901 | 0.617559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.39230 | 0.0520692 | ||||||||
\(716\) | −25.8564 | −0.966299 | ||||||||
\(717\) | 13.3843 | 0.499844 | ||||||||
\(718\) | 3.87564 | 0.144638 | ||||||||
\(719\) | 17.2480 | 0.643241 | 0.321620 | − | 0.946869i | \(-0.395773\pi\) | ||||
0.321620 | + | 0.946869i | \(0.395773\pi\) | |||||||
\(720\) | 1.13681 | 0.0423665 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.85641 | −0.329601 | ||||||||
\(723\) | −9.58846 | −0.356599 | ||||||||
\(724\) | −15.4176 | −0.572992 | ||||||||
\(725\) | 4.73205 | 0.175744 | ||||||||
\(726\) | −9.66922 | −0.358858 | ||||||||
\(727\) | −29.2180 | −1.08364 | −0.541818 | − | 0.840496i | \(-0.682264\pi\) | ||||
−0.541818 | + | 0.840496i | \(0.682264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.23463 | 0.267949 | ||||||||
\(730\) | −6.53590 | −0.241904 | ||||||||
\(731\) | −21.1117 | −0.780843 | ||||||||
\(732\) | 2.78461 | 0.102922 | ||||||||
\(733\) | 8.55961 | 0.316156 | 0.158078 | − | 0.987427i | \(-0.449470\pi\) | ||||
0.158078 | + | 0.987427i | \(0.449470\pi\) | |||||||
\(734\) | −32.0464 | −1.18286 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 5.32051 | 0.195983 | ||||||||
\(738\) | −16.9706 | −0.624695 | ||||||||
\(739\) | 24.2679 | 0.892711 | 0.446355 | − | 0.894856i | \(-0.352722\pi\) | ||||
0.446355 | + | 0.894856i | \(0.352722\pi\) | |||||||
\(740\) | −2.55103 | −0.0937776 | ||||||||
\(741\) | 27.4249 | 1.00748 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.0000 | −1.61420 | −0.807102 | − | 0.590412i | \(-0.798965\pi\) | ||||
−0.807102 | + | 0.590412i | \(0.798965\pi\) | |||||||
\(744\) | 7.39230 | 0.271015 | ||||||||
\(745\) | −5.79555 | −0.212333 | ||||||||
\(746\) | −22.6603 | −0.829651 | ||||||||
\(747\) | 33.9411 | 1.24184 | ||||||||
\(748\) | 2.62536 | 0.0959925 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.51666 | 0.164925 | ||||||||
\(751\) | 22.6410 | 0.826182 | 0.413091 | − | 0.910690i | \(-0.364449\pi\) | ||||
0.413091 | + | 0.910690i | \(0.364449\pi\) | |||||||
\(752\) | 8.24504 | 0.300666 | ||||||||
\(753\) | −2.07180 | −0.0755005 | ||||||||
\(754\) | −5.79555 | −0.211062 | ||||||||
\(755\) | −5.93426 | −0.215970 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.60770 | 0.131124 | 0.0655620 | − | 0.997849i | \(-0.479116\pi\) | ||||
0.0655620 | + | 0.997849i | \(0.479116\pi\) | |||||||
\(758\) | 5.60770 | 0.203681 | ||||||||
\(759\) | −0.832204 | −0.0302071 | ||||||||
\(760\) | 2.73205 | 0.0991019 | ||||||||
\(761\) | −22.3228 | −0.809201 | −0.404601 | − | 0.914493i | \(-0.632589\pi\) | ||||
−0.404601 | + | 0.914493i | \(0.632589\pi\) | |||||||
\(762\) | −11.9428 | −0.432643 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3923 | −0.375980 | ||||||||
\(765\) | 6.43078 | 0.232505 | ||||||||
\(766\) | 8.20788 | 0.296563 | ||||||||
\(767\) | −4.39230 | −0.158597 | ||||||||
\(768\) | −0.896575 | −0.0323524 | ||||||||
\(769\) | −39.1918 | −1.41329 | −0.706647 | − | 0.707566i | \(-0.749793\pi\) | ||||
−0.706647 | + | 0.707566i | \(0.749793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.12436 | 0.220563 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | 7.93048 | 0.285239 | 0.142620 | − | 0.989778i | \(-0.454447\pi\) | ||||
0.142620 | + | 0.989778i | \(0.454447\pi\) | |||||||
\(774\) | −8.19615 | −0.294605 | ||||||||
\(775\) | −39.0160 | −1.40150 | ||||||||
\(776\) | −12.6264 | −0.453261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.3205 | −0.405860 | ||||||||
\(779\) | −40.7846 | −1.46126 | ||||||||
\(780\) | −2.68973 | −0.0963077 | ||||||||
\(781\) | −1.85641 | −0.0664274 | ||||||||
\(782\) | −11.3137 | −0.404577 | ||||||||
\(783\) | −4.65874 | −0.166490 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.32051 | 0.118514 | ||||||||
\(786\) | −2.87564 | −0.102571 | ||||||||
\(787\) | 20.5569 | 0.732773 | 0.366387 | − | 0.930463i | \(-0.380595\pi\) | ||||
0.366387 | + | 0.930463i | \(0.380595\pi\) | |||||||
\(788\) | −18.9282 | −0.674289 | ||||||||
\(789\) | −1.07244 | −0.0381799 | ||||||||
\(790\) | −8.06918 | −0.287089 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.01924 | 0.0362170 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 7.58871 | 0.269313 | ||||||||
\(795\) | −6.71281 | −0.238079 | ||||||||
\(796\) | 14.6969 | 0.520919 | ||||||||
\(797\) | −48.6381 | −1.72285 | −0.861424 | − | 0.507886i | \(-0.830427\pi\) | ||||
−0.861424 | + | 0.507886i | \(0.830427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.6410 | 1.65004 | ||||||||
\(800\) | 4.73205 | 0.167303 | ||||||||
\(801\) | −30.0031 | −1.06011 | ||||||||
\(802\) | 3.14359 | 0.111004 | ||||||||
\(803\) | −5.85993 | −0.206792 | ||||||||
\(804\) | −10.2784 | −0.362492 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47.7846 | 1.68314 | ||||||||
\(807\) | 2.53590 | 0.0892679 | ||||||||
\(808\) | −11.3137 | −0.398015 | ||||||||
\(809\) | 39.0718 | 1.37369 | 0.686846 | − | 0.726803i | \(-0.258995\pi\) | ||||
0.686846 | + | 0.726803i | \(0.258995\pi\) | |||||||
\(810\) | 1.24831 | 0.0438610 | ||||||||
\(811\) | 6.69213 | 0.234992 | 0.117496 | − | 0.993073i | \(-0.462513\pi\) | ||||
0.117496 | + | 0.993073i | \(0.462513\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.5885 | −0.546711 | ||||||||
\(814\) | −2.28719 | −0.0801659 | ||||||||
\(815\) | −10.5187 | −0.368453 | ||||||||
\(816\) | −5.07180 | −0.177548 | ||||||||
\(817\) | −19.6975 | −0.689127 | ||||||||
\(818\) | 22.6274 | 0.791149 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 45.2487 | 1.57919 | 0.789595 | − | 0.613628i | \(-0.210290\pi\) | ||||
0.789595 | + | 0.613628i | \(0.210290\pi\) | |||||||
\(822\) | 7.04386 | 0.245683 | ||||||||
\(823\) | −13.8564 | −0.483004 | −0.241502 | − | 0.970400i | \(-0.577640\pi\) | ||||
−0.241502 | + | 0.970400i | \(0.577640\pi\) | |||||||
\(824\) | 4.89898 | 0.170664 | ||||||||
\(825\) | 1.96902 | 0.0685524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.5167 | −1.96528 | −0.982638 | − | 0.185531i | \(-0.940600\pi\) | ||||
−0.982638 | + | 0.185531i | \(0.940600\pi\) | |||||||
\(828\) | −4.39230 | −0.152643 | ||||||||
\(829\) | −26.7685 | −0.929709 | −0.464855 | − | 0.885387i | \(-0.653893\pi\) | ||||
−0.464855 | + | 0.885387i | \(0.653893\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −16.9706 | −0.588702 | ||||||||
\(832\) | −5.79555 | −0.200925 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.71281 | −0.336327 | ||||||||
\(835\) | 6.53590 | 0.226184 | ||||||||
\(836\) | 2.44949 | 0.0847174 | ||||||||
\(837\) | 38.4115 | 1.32770 | ||||||||
\(838\) | 19.7990 | 0.683945 | ||||||||
\(839\) | −22.4887 | −0.776397 | −0.388198 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388198 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −19.4641 | −0.670777 | ||||||||
\(843\) | 7.94044 | 0.273483 | ||||||||
\(844\) | −13.3923 | −0.460982 | ||||||||
\(845\) | −10.6574 | −0.366625 | ||||||||
\(846\) | 18.1074 | 0.622544 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.4641 | −0.496699 | ||||||||
\(849\) | 24.2487 | 0.832214 | ||||||||
\(850\) | 26.7685 | 0.918153 | ||||||||
\(851\) | 9.85641 | 0.337873 | ||||||||
\(852\) | 3.58630 | 0.122865 | ||||||||
\(853\) | 6.13733 | 0.210138 | 0.105069 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105069 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 18.4219 | 0.629282 | 0.314641 | − | 0.949211i | \(-0.398116\pi\) | ||||
0.314641 | + | 0.949211i | \(0.398116\pi\) | |||||||
\(858\) | −2.41154 | −0.0823287 | ||||||||
\(859\) | 11.9329 | 0.407145 | 0.203572 | − | 0.979060i | \(-0.434745\pi\) | ||||
0.203572 | + | 0.979060i | \(0.434745\pi\) | |||||||
\(860\) | 1.93185 | 0.0658756 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.39230 | 0.149602 | ||||||||
\(863\) | 17.3205 | 0.589597 | 0.294798 | − | 0.955559i | \(-0.404747\pi\) | ||||
0.294798 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(864\) | −4.65874 | −0.158494 | ||||||||
\(865\) | 2.58846 | 0.0880102 | ||||||||
\(866\) | −8.96575 | −0.304669 | ||||||||
\(867\) | −13.4486 | −0.456739 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.23463 | −0.245418 | ||||||||
\(870\) | 0.464102 | 0.0157345 | ||||||||
\(871\) | −66.4408 | −2.25126 | ||||||||
\(872\) | −3.39230 | −0.114878 | ||||||||
\(873\) | −27.7295 | −0.938500 | ||||||||
\(874\) | −10.5558 | −0.357056 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.3205 | 0.382485 | ||||||||
\(877\) | 1.33975 | 0.0452400 | 0.0226200 | − | 0.999744i | \(-0.492799\pi\) | ||||
0.0226200 | + | 0.999744i | \(0.492799\pi\) | |||||||
\(878\) | −20.8343 | −0.703122 | ||||||||
\(879\) | 7.35898 | 0.248212 | ||||||||
\(880\) | −0.240237 | −0.00809838 | ||||||||
\(881\) | −2.34795 | −0.0791046 | −0.0395523 | − | 0.999218i | \(-0.512593\pi\) | ||||
−0.0395523 | + | 0.999218i | \(0.512593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.7128 | −1.26914 | −0.634569 | − | 0.772867i | \(-0.718822\pi\) | ||||
−0.634569 | + | 0.772867i | \(0.718822\pi\) | |||||||
\(884\) | −32.7846 | −1.10267 | ||||||||
\(885\) | 0.351731 | 0.0118233 | ||||||||
\(886\) | 40.2487 | 1.35218 | ||||||||
\(887\) | 17.4882 | 0.587196 | 0.293598 | − | 0.955929i | \(-0.405147\pi\) | ||||
0.293598 | + | 0.955929i | \(0.405147\pi\) | |||||||
\(888\) | 4.41851 | 0.148275 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.07180 | 0.237047 | ||||||||
\(891\) | 1.11920 | 0.0374946 | ||||||||
\(892\) | 19.5959 | 0.656120 | ||||||||
\(893\) | 43.5167 | 1.45623 | ||||||||
\(894\) | 10.0382 | 0.335727 | ||||||||
\(895\) | 13.3843 | 0.447386 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.3923 | 0.346989 | ||||||||
\(898\) | −5.07180 | −0.169248 | ||||||||
\(899\) | −8.24504 | −0.274988 | ||||||||
\(900\) | 10.3923 | 0.346410 | ||||||||
\(901\) | −81.8213 | −2.72586 | ||||||||
\(902\) | 3.58630 | 0.119411 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.00000 | 0.133038 | ||||||||
\(905\) | 7.98076 | 0.265290 | ||||||||
\(906\) | 10.2784 | 0.341478 | ||||||||
\(907\) | −42.3923 | −1.40761 | −0.703807 | − | 0.710392i | \(-0.748518\pi\) | ||||
−0.703807 | + | 0.710392i | \(0.748518\pi\) | |||||||
\(908\) | −11.0363 | −0.366253 | ||||||||
\(909\) | −24.8466 | −0.824111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.6603 | 0.551979 | 0.275989 | − | 0.961161i | \(-0.410995\pi\) | ||||
0.275989 | + | 0.961161i | \(0.410995\pi\) | |||||||
\(912\) | −4.73205 | −0.156694 | ||||||||
\(913\) | −7.17260 | −0.237379 | ||||||||
\(914\) | 32.9282 | 1.08917 | ||||||||
\(915\) | −1.44142 | −0.0476519 | ||||||||
\(916\) | −10.0754 | −0.332899 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −26.3538 | −0.869806 | ||||||||
\(919\) | −49.3205 | −1.62693 | −0.813467 | − | 0.581611i | \(-0.802422\pi\) | ||||
−0.813467 | + | 0.581611i | \(0.802422\pi\) | |||||||
\(920\) | 1.03528 | 0.0341320 | ||||||||
\(921\) | −5.62693 | −0.185414 | ||||||||
\(922\) | 14.6969 | 0.484018 | ||||||||
\(923\) | 23.1822 | 0.763052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.3205 | −0.766774 | ||||||||
\(926\) | 13.8564 | 0.455350 | ||||||||
\(927\) | 10.7589 | 0.353369 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 27.9797 | 0.917983 | 0.458991 | − | 0.888441i | \(-0.348211\pi\) | ||||
0.458991 | + | 0.888441i | \(0.348211\pi\) | |||||||
\(930\) | −3.82654 | −0.125477 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.1244 | −0.790220 | ||||||||
\(933\) | −5.90897 | −0.193451 | ||||||||
\(934\) | 32.6656 | 1.06885 | ||||||||
\(935\) | −1.35898 | −0.0444435 | ||||||||
\(936\) | −12.7279 | −0.416025 | ||||||||
\(937\) | 47.5756 | 1.55423 | 0.777113 | − | 0.629361i | \(-0.216683\pi\) | ||||
0.777113 | + | 0.629361i | \(0.216683\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2154 | 0.790239 | ||||||||
\(940\) | −4.26795 | −0.139205 | ||||||||
\(941\) | 9.10446 | 0.296797 | 0.148398 | − | 0.988928i | \(-0.452588\pi\) | ||||
0.148398 | + | 0.988928i | \(0.452588\pi\) | |||||||
\(942\) | −5.75129 | −0.187387 | ||||||||
\(943\) | −15.4548 | −0.503278 | ||||||||
\(944\) | 0.757875 | 0.0246667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.73205 | 0.0563138 | ||||||||
\(947\) | 14.6603 | 0.476394 | 0.238197 | − | 0.971217i | \(-0.423444\pi\) | ||||
0.238197 | + | 0.971217i | \(0.423444\pi\) | |||||||
\(948\) | 13.9762 | 0.453927 | ||||||||
\(949\) | 73.1769 | 2.37542 | ||||||||
\(950\) | 24.9754 | 0.810308 | ||||||||
\(951\) | 23.6627 | 0.767315 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.3397 | 0.626476 | 0.313238 | − | 0.949675i | \(-0.398586\pi\) | ||||
0.313238 | + | 0.949675i | \(0.398586\pi\) | |||||||
\(954\) | −31.7654 | −1.02844 | ||||||||
\(955\) | 5.37945 | 0.174075 | ||||||||
\(956\) | −14.9282 | −0.482813 | ||||||||
\(957\) | 0.416102 | 0.0134507 | ||||||||
\(958\) | −0.138701 | −0.00448122 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.464102 | 0.0149788 | ||||||||
\(961\) | 36.9808 | 1.19293 | ||||||||
\(962\) | 28.5617 | 0.920865 | ||||||||
\(963\) | 39.5307 | 1.27386 | ||||||||
\(964\) | 10.6945 | 0.344448 | ||||||||
\(965\) | 8.28221 | 0.266614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.07180 | 0.195256 | 0.0976279 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976279 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(968\) | 10.7846 | 0.346630 | ||||||||
\(969\) | −26.7685 | −0.859929 | ||||||||
\(970\) | 6.53590 | 0.209855 | ||||||||
\(971\) | 22.6002 | 0.725275 | 0.362638 | − | 0.931930i | \(-0.381876\pi\) | ||||
0.362638 | + | 0.931930i | \(0.381876\pi\) | |||||||
\(972\) | −16.1384 | −0.517638 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.32051 | 0.234564 | ||||||||
\(975\) | −24.5885 | −0.787461 | ||||||||
\(976\) | −3.10583 | −0.0994151 | ||||||||
\(977\) | −38.7128 | −1.23853 | −0.619266 | − | 0.785181i | \(-0.712570\pi\) | ||||
−0.619266 | + | 0.785181i | \(0.712570\pi\) | |||||||
\(978\) | 18.2189 | 0.582575 | ||||||||
\(979\) | 6.34040 | 0.202640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.45002 | −0.237861 | ||||||||
\(982\) | −22.3205 | −0.712276 | ||||||||
\(983\) | 47.0579 | 1.50092 | 0.750458 | − | 0.660919i | \(-0.229833\pi\) | ||||
0.750458 | + | 0.660919i | \(0.229833\pi\) | |||||||
\(984\) | −6.92820 | −0.220863 | ||||||||
\(985\) | 9.79796 | 0.312189 | ||||||||
\(986\) | 5.65685 | 0.180151 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.5885 | −0.973148 | ||||||||
\(989\) | −7.46410 | −0.237345 | ||||||||
\(990\) | −0.527596 | −0.0167681 | ||||||||
\(991\) | 22.0000 | 0.698853 | 0.349427 | − | 0.936964i | \(-0.386376\pi\) | ||||
0.349427 | + | 0.936964i | \(0.386376\pi\) | |||||||
\(992\) | −8.24504 | −0.261780 | ||||||||
\(993\) | −6.45189 | −0.204745 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.60770 | −0.241180 | ||||||||
\(996\) | 13.8564 | 0.439057 | ||||||||
\(997\) | −11.0363 | −0.349523 | −0.174762 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174762 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(998\) | −20.9282 | −0.662471 | ||||||||
\(999\) | 22.9592 | 0.726398 |
(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 | 2842.2.a.q.1.2 | ✓ | 4 | |
7.6 | odd | 2 | inner | 2842.2.a.q.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.q.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2842.2.a.q.1.3 | yes | 4 | 7.6 | odd | 2 | inner |