Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(71,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.71");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.e (of order \(2\), degree \(1\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.25 | ||
Character | \(\chi\) | \(=\) | 252.71 |
Dual form | 252.4.e.a.71.26 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42938 | − | 2.44067i | 0.505360 | − | 0.862908i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.91377 | − | 6.97728i | −0.489222 | − | 0.872159i | ||||
\(5\) | − | 15.7775i | − | 1.41118i | −0.708619 | − | 0.705591i | \(-0.750682\pi\) | ||
0.708619 | − | 0.705591i | \(-0.249318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | −22.6235 | − | 0.420902i | −0.999827 | − | 0.0186014i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −38.5077 | − | 22.5520i | −1.21772 | − | 0.713156i | ||||
\(11\) | 23.5125 | 0.644480 | 0.322240 | − | 0.946658i | \(-0.395564\pi\) | ||||
0.322240 | + | 0.946658i | \(0.395564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.7320 | −0.804999 | −0.402499 | − | 0.915420i | \(-0.631858\pi\) | ||||
−0.402499 | + | 0.915420i | \(0.631858\pi\) | |||||||
\(14\) | −17.0847 | − | 10.0056i | −0.326149 | − | 0.191008i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −33.3648 | + | 54.6150i | −0.521324 | + | 0.853359i | ||||
\(17\) | − | 31.9239i | − | 0.455452i | −0.973725 | − | 0.227726i | \(-0.926871\pi\) | ||
0.973725 | − | 0.227726i | \(-0.0731291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.8804i | 0.348717i | 0.984682 | + | 0.174359i | \(0.0557852\pi\) | ||||
−0.984682 | + | 0.174359i | \(0.944215\pi\) | |||||||
\(20\) | −110.084 | + | 61.7495i | −1.23078 | + | 0.690381i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 33.6082 | − | 57.3863i | 0.325695 | − | 0.556127i | ||||
\(23\) | 50.8589 | 0.461079 | 0.230539 | − | 0.973063i | \(-0.425951\pi\) | ||||
0.230539 | + | 0.973063i | \(0.425951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.929 | −0.991435 | ||||||||
\(26\) | −53.9332 | + | 92.0916i | −0.406814 | + | 0.694640i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −48.8409 | + | 27.3964i | −0.329645 | + | 0.184908i | ||||
\(29\) | 205.159i | 1.31369i | 0.754024 | + | 0.656847i | \(0.228110\pi\) | ||||
−0.754024 | + | 0.656847i | \(0.771890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 176.645i | − | 1.02343i | −0.859156 | − | 0.511714i | \(-0.829011\pi\) | ||
0.859156 | − | 0.511714i | \(-0.170989\pi\) | |||||||
\(32\) | 85.6065 | + | 159.498i | 0.472914 | + | 0.881109i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −77.9159 | − | 45.6313i | −0.393014 | − | 0.230168i | ||||
\(35\) | −110.442 | −0.533377 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −338.457 | −1.50384 | −0.751920 | − | 0.659255i | \(-0.770872\pi\) | ||||
−0.751920 | + | 0.659255i | \(0.770872\pi\) | |||||||
\(38\) | 70.4877 | + | 41.2810i | 0.300911 | + | 0.176228i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.64077 | + | 356.942i | −0.0262500 | + | 1.41094i | ||||
\(41\) | 77.7879i | 0.296303i | 0.988965 | + | 0.148152i | \(0.0473323\pi\) | ||||
−0.988965 | + | 0.148152i | \(0.952668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 463.054i | − | 1.64221i | −0.570775 | − | 0.821106i | \(-0.693357\pi\) | ||
0.570775 | − | 0.821106i | \(-0.306643\pi\) | |||||||
\(44\) | −92.0225 | − | 164.053i | −0.315294 | − | 0.562089i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 72.6965 | − | 124.130i | 0.233011 | − | 0.397869i | ||||
\(47\) | −352.149 | −1.09290 | −0.546450 | − | 0.837492i | \(-0.684021\pi\) | ||||
−0.546450 | + | 0.837492i | \(0.684021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −177.142 | + | 302.471i | −0.501032 | + | 0.855517i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 147.675 | + | 263.267i | 0.393823 | + | 0.702087i | ||||
\(53\) | − | 155.551i | − | 0.403142i | −0.979474 | − | 0.201571i | \(-0.935395\pi\) | ||
0.979474 | − | 0.201571i | \(-0.0646048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 370.968i | − | 0.909479i | ||||||
\(56\) | −2.94631 | + | 158.365i | −0.00703067 | + | 0.377899i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 500.727 | + | 293.250i | 1.13360 | + | 0.663889i | ||||
\(59\) | 761.398 | 1.68010 | 0.840048 | − | 0.542513i | \(-0.182527\pi\) | ||||
0.840048 | + | 0.542513i | \(0.182527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.2208 | −0.0844221 | −0.0422110 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422110 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(62\) | −431.132 | − | 252.491i | −0.883125 | − | 0.517200i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 511.646 | + | 19.0445i | 0.999308 | + | 0.0371964i | ||||
\(65\) | 595.317i | 1.13600i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 838.691i | − | 1.52929i | −0.644451 | − | 0.764645i | \(-0.722914\pi\) | ||
0.644451 | − | 0.764645i | \(-0.277086\pi\) | |||||||
\(68\) | −222.742 | + | 124.943i | −0.397227 | + | 0.222817i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −157.864 | + | 269.554i | −0.269547 | + | 0.460255i | ||||
\(71\) | −70.1497 | −0.117257 | −0.0586285 | − | 0.998280i | \(-0.518673\pi\) | ||||
−0.0586285 | + | 0.998280i | \(0.518673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 726.789 | 1.16526 | 0.582632 | − | 0.812736i | \(-0.302023\pi\) | ||||
0.582632 | + | 0.812736i | \(0.302023\pi\) | |||||||
\(74\) | −483.783 | + | 826.064i | −0.759981 | + | 1.29768i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 201.507 | − | 113.031i | 0.304137 | − | 0.170600i | ||||
\(77\) | − | 164.587i | − | 0.243591i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 992.308i | 1.41321i | 0.707610 | + | 0.706604i | \(0.249774\pi\) | ||||
−0.707610 | + | 0.706604i | \(0.750226\pi\) | |||||||
\(80\) | 861.687 | + | 526.412i | 1.20424 | + | 0.735683i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 189.855 | + | 111.188i | 0.255682 | + | 0.149740i | ||||
\(83\) | 1116.85 | 1.47700 | 0.738498 | − | 0.674256i | \(-0.235536\pi\) | ||||
0.738498 | + | 0.674256i | \(0.235536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −503.680 | −0.642726 | ||||||||
\(86\) | −1130.16 | − | 661.878i | −1.41708 | − | 0.829909i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −531.935 | − | 9.89644i | −0.644368 | − | 0.0119882i | ||||
\(89\) | − | 1592.19i | − | 1.89631i | −0.317810 | − | 0.948155i | \(-0.602947\pi\) | ||
0.317810 | − | 0.948155i | \(-0.397053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 264.124i | 0.304261i | ||||||||
\(92\) | −199.050 | − | 354.857i | −0.225570 | − | 0.402134i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −503.353 | + | 859.481i | −0.552308 | + | 0.943072i | ||||
\(95\) | 455.661 | 0.492103 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1263.10 | −1.32215 | −0.661075 | − | 0.750320i | \(-0.729899\pi\) | ||||
−0.661075 | + | 0.750320i | \(0.729899\pi\) | |||||||
\(98\) | −70.0394 | + | 119.593i | −0.0721943 | + | 0.123273i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 485.031 | + | 864.689i | 0.485031 | + | 0.864689i | ||||
\(101\) | − | 1484.69i | − | 1.46269i | −0.682006 | − | 0.731347i | \(-0.738892\pi\) | ||
0.682006 | − | 0.731347i | \(-0.261108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1244.15i | − | 1.19019i | −0.803655 | − | 0.595095i | \(-0.797114\pi\) | ||
0.803655 | − | 0.595095i | \(-0.202886\pi\) | |||||||
\(104\) | 853.631 | + | 15.8815i | 0.804859 | + | 0.0149741i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −379.649 | − | 222.341i | −0.347875 | − | 0.203732i | ||||
\(107\) | 1825.93 | 1.64972 | 0.824858 | − | 0.565340i | \(-0.191255\pi\) | ||||
0.824858 | + | 0.565340i | \(0.191255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 209.445 | 0.184048 | 0.0920238 | − | 0.995757i | \(-0.470666\pi\) | ||||
0.0920238 | + | 0.995757i | \(0.470666\pi\) | |||||||
\(110\) | −905.412 | − | 530.252i | −0.784797 | − | 0.459614i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 382.305 | + | 233.553i | 0.322539 | + | 0.197042i | ||||
\(113\) | − | 1021.23i | − | 0.850169i | −0.905154 | − | 0.425084i | \(-0.860244\pi\) | ||
0.905154 | − | 0.425084i | \(-0.139756\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 802.426i | − | 0.650666i | ||||||
\(116\) | 1431.45 | − | 802.948i | 1.14575 | − | 0.642688i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1088.32 | − | 1858.32i | 0.849054 | − | 1.44977i | ||||
\(119\) | −223.467 | −0.172145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −778.163 | −0.584646 | ||||||||
\(122\) | −57.4906 | + | 98.1659i | −0.0426636 | + | 0.0728485i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1232.50 | + | 691.347i | −0.892593 | + | 0.500684i | ||||
\(125\) | − | 16.8921i | − | 0.0120870i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2003.37i | 1.39976i | 0.714258 | + | 0.699882i | \(0.246764\pi\) | ||||
−0.714258 | + | 0.699882i | \(0.753236\pi\) | |||||||
\(128\) | 777.815 | − | 1221.54i | 0.537108 | − | 0.843514i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1452.97 | + | 850.931i | 0.980264 | + | 0.574089i | ||||
\(131\) | −1168.94 | −0.779624 | −0.389812 | − | 0.920894i | \(-0.627460\pi\) | ||||
−0.389812 | + | 0.920894i | \(0.627460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 202.163 | 0.131803 | ||||||||
\(134\) | −2046.97 | − | 1198.80i | −1.31964 | − | 0.772843i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.4368 | + | 722.231i | −0.00847205 | + | 0.455373i | ||||
\(137\) | − | 472.985i | − | 0.294962i | −0.989065 | − | 0.147481i | \(-0.952883\pi\) | ||
0.989065 | − | 0.147481i | \(-0.0471166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2857.76i | − | 1.74382i | −0.489662 | − | 0.871912i | \(-0.662880\pi\) | ||
0.489662 | − | 0.871912i | \(-0.337120\pi\) | |||||||
\(140\) | 432.247 | + | 770.588i | 0.260939 | + | 0.465190i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −100.270 | + | 171.213i | −0.0592570 | + | 0.101182i | ||||
\(143\) | −887.174 | −0.518805 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3236.90 | 1.85386 | ||||||||
\(146\) | 1038.85 | − | 1773.85i | 0.588878 | − | 1.00552i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1324.65 | + | 2361.51i | 0.735711 | + | 1.31159i | ||||
\(149\) | 3076.95i | 1.69177i | 0.533368 | + | 0.845883i | \(0.320926\pi\) | ||||
−0.533368 | + | 0.845883i | \(0.679074\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1309.38i | 0.705668i | 0.935686 | + | 0.352834i | \(0.114782\pi\) | ||||
−0.935686 | + | 0.352834i | \(0.885218\pi\) | |||||||
\(152\) | 12.1558 | − | 653.376i | 0.00648662 | − | 0.348657i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −401.704 | − | 235.257i | −0.210196 | − | 0.123101i | ||||
\(155\) | −2787.01 | −1.44424 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 48.9931 | 0.0249049 | 0.0124525 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124525 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(158\) | 2421.90 | + | 1418.38i | 1.21947 | + | 0.714179i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2516.47 | − | 1350.66i | 1.24340 | − | 0.667367i | ||||
\(161\) | − | 356.012i | − | 0.174271i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1861.23i | 0.894371i | 0.894441 | + | 0.447186i | \(0.147574\pi\) | ||||
−0.894441 | + | 0.447186i | \(0.852426\pi\) | |||||||
\(164\) | 542.748 | − | 304.444i | 0.258424 | − | 0.144958i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1596.40 | − | 2725.87i | 0.746415 | − | 1.27451i | ||||
\(167\) | −276.319 | −0.128037 | −0.0640186 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640186 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −773.294 | −0.351977 | ||||||||
\(170\) | −719.947 | + | 1229.32i | −0.324808 | + | 0.554614i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3230.86 | + | 1812.29i | −1.43227 | + | 0.803406i | ||||
\(173\) | 304.273i | 0.133719i | 0.997762 | + | 0.0668597i | \(0.0212980\pi\) | ||||
−0.997762 | + | 0.0668597i | \(0.978702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 867.505i | 0.374727i | ||||||||
\(176\) | −784.488 | + | 1284.13i | −0.335983 | + | 0.549973i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3886.01 | − | 2275.83i | −1.63634 | − | 0.958320i | ||||
\(179\) | 2828.65 | 1.18113 | 0.590567 | − | 0.806988i | \(-0.298904\pi\) | ||||
0.590567 | + | 0.806988i | \(0.298904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2289.94 | 0.940386 | 0.470193 | − | 0.882564i | \(-0.344184\pi\) | ||||
0.470193 | + | 0.882564i | \(0.344184\pi\) | |||||||
\(182\) | 644.641 | + | 377.533i | 0.262549 | + | 0.153761i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1150.61 | − | 21.4066i | −0.460999 | − | 0.00857671i | ||||
\(185\) | 5340.01i | 2.12219i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 750.611i | − | 0.293530i | ||||||
\(188\) | 1378.23 | + | 2457.04i | 0.534670 | + | 0.953182i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 651.310 | − | 1112.12i | 0.248689 | − | 0.424640i | ||||
\(191\) | −314.085 | −0.118986 | −0.0594932 | − | 0.998229i | \(-0.518948\pi\) | ||||
−0.0594932 | + | 0.998229i | \(0.518948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2133.16 | −0.795587 | −0.397793 | − | 0.917475i | \(-0.630224\pi\) | ||||
−0.397793 | + | 0.917475i | \(0.630224\pi\) | |||||||
\(194\) | −1805.45 | + | 3082.82i | −0.668162 | + | 1.14089i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 191.775 | + | 341.887i | 0.0698888 | + | 0.124594i | ||||
\(197\) | − | 1510.64i | − | 0.546339i | −0.961966 | − | 0.273170i | \(-0.911928\pi\) | ||
0.961966 | − | 0.273170i | \(-0.0880720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 328.162i | − | 0.116898i | −0.998290 | − | 0.0584492i | \(-0.981384\pi\) | ||
0.998290 | − | 0.0584492i | \(-0.0186156\pi\) | |||||||
\(200\) | 2803.72 | + | 52.1621i | 0.991263 | + | 0.0184421i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3623.64 | − | 2122.18i | −1.26217 | − | 0.739187i | ||||
\(203\) | 1436.12 | 0.496530 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1227.30 | 0.418138 | ||||||||
\(206\) | −3036.56 | − | 1778.36i | −1.02703 | − | 0.601475i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1258.92 | − | 2060.73i | 0.419665 | − | 0.686953i | ||||
\(209\) | 679.050i | 0.224741i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4199.04i | 1.37002i | 0.728535 | + | 0.685009i | \(0.240202\pi\) | ||||
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(212\) | −1085.32 | + | 608.791i | −0.351605 | + | 0.197226i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2609.94 | − | 4456.50i | 0.833701 | − | 1.42355i | ||||
\(215\) | −7305.84 | −2.31746 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1236.51 | −0.386820 | ||||||||
\(218\) | 299.375 | − | 511.187i | 0.0930104 | − | 0.158816i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2588.35 | + | 1451.88i | −0.793210 | + | 0.444937i | ||||
\(221\) | 1204.55i | 0.366638i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1522.53i | 0.457202i | 0.973520 | + | 0.228601i | \(0.0734152\pi\) | ||||
−0.973520 | + | 0.228601i | \(0.926585\pi\) | |||||||
\(224\) | 1116.48 | − | 599.246i | 0.333028 | − | 0.178745i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2492.48 | − | 1459.72i | −0.733618 | − | 0.429642i | ||||
\(227\) | 1831.97 | 0.535649 | 0.267825 | − | 0.963468i | \(-0.413695\pi\) | ||||
0.267825 | + | 0.963468i | \(0.413695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 417.356 | 0.120435 | 0.0602176 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602176 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(230\) | −1958.46 | − | 1146.97i | −0.561465 | − | 0.328821i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 86.3519 | − | 4641.42i | 0.0244366 | − | 1.31347i | ||||
\(233\) | − | 431.598i | − | 0.121352i | −0.998158 | − | 0.0606759i | \(-0.980674\pi\) | ||
0.998158 | − | 0.0606759i | \(-0.0193256\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5556.03i | 1.54228i | ||||||||
\(236\) | −2979.94 | − | 5312.49i | −0.821939 | − | 1.46531i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −319.419 | + | 545.411i | −0.0869952 | + | 0.148545i | ||||
\(239\) | −3365.90 | −0.910971 | −0.455485 | − | 0.890243i | \(-0.650534\pi\) | ||||
−0.455485 | + | 0.890243i | \(0.650534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4055.66 | 1.08402 | 0.542008 | − | 0.840373i | \(-0.317664\pi\) | ||||
0.542008 | + | 0.840373i | \(0.317664\pi\) | |||||||
\(242\) | −1112.29 | + | 1899.24i | −0.295457 | + | 0.504496i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 157.415 | + | 280.632i | 0.0413011 | + | 0.0736295i | ||||
\(245\) | 773.097i | 0.201597i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1089.72i | − | 0.280717i | ||||||
\(248\) | −74.3500 | + | 3996.32i | −0.0190372 | + | 1.02325i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −41.2280 | − | 24.1451i | −0.0104300 | − | 0.00610828i | ||||
\(251\) | −1222.93 | −0.307531 | −0.153766 | − | 0.988107i | \(-0.549140\pi\) | ||||
−0.153766 | + | 0.988107i | \(0.549140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1195.82 | 0.297156 | ||||||||
\(254\) | 4889.57 | + | 2863.56i | 1.20787 | + | 0.707386i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1869.59 | − | 3644.43i | −0.456442 | − | 0.889753i | ||||
\(257\) | 933.046i | 0.226466i | 0.993568 | + | 0.113233i | \(0.0361207\pi\) | ||||
−0.993568 | + | 0.113233i | \(0.963879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2369.20i | 0.568398i | ||||||||
\(260\) | 4153.69 | − | 2329.94i | 0.990773 | − | 0.555756i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1670.85 | + | 2853.00i | −0.393991 | + | 0.672744i | ||||
\(263\) | −2725.50 | −0.639018 | −0.319509 | − | 0.947583i | \(-0.603518\pi\) | ||||
−0.319509 | + | 0.947583i | \(0.603518\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2454.20 | −0.568907 | ||||||||
\(266\) | 288.967 | − | 493.414i | 0.0666078 | − | 0.113734i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5851.78 | + | 3282.45i | −1.33379 | + | 0.748162i | ||||
\(269\) | 6736.86i | 1.52697i | 0.645828 | + | 0.763483i | \(0.276512\pi\) | ||||
−0.645828 | + | 0.763483i | \(0.723488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4267.63i | − | 0.956606i | −0.878195 | − | 0.478303i | \(-0.841252\pi\) | ||
0.878195 | − | 0.478303i | \(-0.158748\pi\) | |||||||
\(272\) | 1743.52 | + | 1065.13i | 0.388664 | + | 0.237438i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1154.40 | − | 676.073i | −0.254526 | − | 0.149062i | ||||
\(275\) | −2913.89 | −0.638960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7464.54 | −1.61914 | −0.809568 | − | 0.587026i | \(-0.800299\pi\) | ||||
−0.809568 | + | 0.587026i | \(0.800299\pi\) | |||||||
\(278\) | −6974.85 | − | 4084.80i | −1.50476 | − | 0.881260i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2498.60 | + | 46.4854i | 0.533284 | + | 0.00992155i | ||||
\(281\) | − | 1541.92i | − | 0.327343i | −0.986515 | − | 0.163671i | \(-0.947666\pi\) | ||
0.986515 | − | 0.163671i | \(-0.0523337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.84660i | 0.00122807i | 1.00000 | 0.000614036i | \(0.000195454\pi\) | |||||
−1.00000 | 0.000614036i | \(0.999805\pi\) | ||||||||
\(284\) | 274.550 | + | 489.454i | 0.0573646 | + | 0.102267i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1268.10 | + | 2165.30i | −0.262184 | + | 0.447682i | ||||
\(287\) | 544.515 | 0.111992 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3893.86 | 0.792563 | ||||||||
\(290\) | 4626.75 | − | 7900.22i | 0.936869 | − | 1.59971i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2844.49 | − | 5071.01i | −0.570072 | − | 1.01630i | ||||
\(293\) | − | 8241.62i | − | 1.64328i | −0.570008 | − | 0.821639i | \(-0.693060\pi\) | ||
0.570008 | − | 0.821639i | \(-0.306940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 12013.0i | − | 2.37092i | ||||||
\(296\) | 7657.09 | + | 142.457i | 1.50358 | + | 0.0279735i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7509.82 | + | 4398.11i | 1.45984 | + | 0.854952i | ||||
\(299\) | −1919.01 | −0.371168 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3241.38 | −0.620698 | ||||||||
\(302\) | 3195.77 | + | 1871.59i | 0.608927 | + | 0.356617i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1577.30 | − | 963.588i | −0.297581 | − | 0.181795i | ||||
\(305\) | 634.584i | 0.119135i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9164.01i | 1.70364i | 0.523833 | + | 0.851821i | \(0.324501\pi\) | ||||
−0.523833 | + | 0.851821i | \(0.675499\pi\) | |||||||
\(308\) | −1148.37 | + | 644.158i | −0.212450 | + | 0.119170i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3983.68 | + | 6802.18i | −0.729864 | + | 1.24625i | ||||
\(311\) | 8767.25 | 1.59854 | 0.799269 | − | 0.600974i | \(-0.205221\pi\) | ||||
0.799269 | + | 0.600974i | \(0.205221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1440.96 | −0.260216 | −0.130108 | − | 0.991500i | \(-0.541532\pi\) | ||||
−0.130108 | + | 0.991500i | \(0.541532\pi\) | |||||||
\(314\) | 70.0295 | − | 119.576i | 0.0125860 | − | 0.0214907i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6923.61 | − | 3883.67i | 1.23254 | − | 0.691372i | ||||
\(317\) | 1454.49i | 0.257705i | 0.991664 | + | 0.128852i | \(0.0411294\pi\) | ||||
−0.991664 | + | 0.128852i | \(0.958871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4823.81i | 0.846650i | ||||||||
\(320\) | 300.475 | − | 8072.49i | 0.0524908 | − | 1.41021i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −868.910 | − | 508.875i | −0.150380 | − | 0.0880699i | ||||
\(323\) | 921.976 | 0.158824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4676.11 | 0.798104 | ||||||||
\(326\) | 4542.65 | + | 2660.39i | 0.771760 | + | 0.451980i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 32.7410 | − | 1759.83i | 0.00551165 | − | 0.296252i | ||||
\(329\) | 2465.05i | 0.413077i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 240.686i | − | 0.0399677i | −0.999800 | − | 0.0199839i | \(-0.993639\pi\) | ||
0.999800 | − | 0.0199839i | \(-0.00636149\pi\) | |||||||
\(332\) | −4371.11 | − | 7792.59i | −0.722578 | − | 1.28818i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −394.964 | + | 674.405i | −0.0647050 | + | 0.110484i | ||||
\(335\) | −13232.5 | −2.15811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1392.47 | −0.225083 | −0.112541 | − | 0.993647i | \(-0.535899\pi\) | ||||
−0.112541 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(338\) | −1105.33 | + | 1887.36i | −0.177875 | + | 0.303724i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1971.29 | + | 3514.31i | 0.314436 | + | 0.560560i | ||||
\(341\) | − | 4153.35i | − | 0.659579i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −194.900 | + | 10475.9i | −0.0305474 | + | 1.64193i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 742.631 | + | 434.920i | 0.115388 | + | 0.0675765i | ||||
\(347\) | 8230.21 | 1.27326 | 0.636629 | − | 0.771170i | \(-0.280328\pi\) | ||||
0.636629 | + | 0.771170i | \(0.280328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2298.41 | 0.352524 | 0.176262 | − | 0.984343i | \(-0.443599\pi\) | ||||
0.176262 | + | 0.984343i | \(0.443599\pi\) | |||||||
\(350\) | 2117.30 | + | 1239.99i | 0.323355 | + | 0.189372i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2012.82 | + | 3750.19i | 0.304783 | + | 0.567857i | ||||
\(353\) | 6796.30i | 1.02473i | 0.858767 | + | 0.512366i | \(0.171231\pi\) | ||||
−0.858767 | + | 0.512366i | \(0.828769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1106.79i | 0.165471i | ||||||||
\(356\) | −11109.1 | + | 6231.46i | −1.65388 | + | 0.927716i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4043.20 | − | 6903.81i | 0.596899 | − | 1.01921i | ||||
\(359\) | 11252.7 | 1.65430 | 0.827150 | − | 0.561981i | \(-0.189960\pi\) | ||||
0.827150 | + | 0.561981i | \(0.189960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6024.92 | 0.878396 | ||||||||
\(362\) | 3273.18 | − | 5589.00i | 0.475234 | − | 0.811467i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1842.87 | − | 1033.72i | 0.265364 | − | 0.148851i | ||||
\(365\) | − | 11466.9i | − | 1.64440i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2173.56i | − | 0.309152i | −0.987981 | − | 0.154576i | \(-0.950599\pi\) | ||
0.987981 | − | 0.154576i | \(-0.0494011\pi\) | |||||||
\(368\) | −1696.89 | + | 2777.66i | −0.240372 | + | 0.393466i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13033.2 | + | 7632.88i | 1.83126 | + | 1.07247i | ||||
\(371\) | −1088.86 | −0.152374 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13792.9 | 1.91466 | 0.957330 | − | 0.288997i | \(-0.0933217\pi\) | ||||
0.957330 | + | 0.288997i | \(0.0933217\pi\) | |||||||
\(374\) | −1832.00 | − | 1072.90i | −0.253289 | − | 0.148338i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7966.85 | + | 148.220i | 1.09271 | + | 0.0203294i | ||||
\(377\) | − | 7741.08i | − | 1.05752i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 404.932i | − | 0.0548812i | −0.999623 | − | 0.0274406i | \(-0.991264\pi\) | ||
0.999623 | − | 0.0274406i | \(-0.00873571\pi\) | |||||||
\(380\) | −1783.35 | − | 3179.27i | −0.240748 | − | 0.429192i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −448.946 | + | 766.579i | −0.0601310 | + | 0.102674i | ||||
\(383\) | 9664.87 | 1.28943 | 0.644715 | − | 0.764423i | \(-0.276976\pi\) | ||||
0.644715 | + | 0.764423i | \(0.276976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2596.78 | −0.343751 | ||||||||
\(386\) | −3049.09 | + | 5206.35i | −0.402058 | + | 0.686518i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4943.49 | + | 8813.00i | 0.646824 | + | 1.15313i | ||||
\(389\) | 3344.96i | 0.435980i | 0.975951 | + | 0.217990i | \(0.0699500\pi\) | ||||
−0.975951 | + | 0.217990i | \(0.930050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1623.62i | − | 0.209999i | ||||||
\(392\) | 1108.55 | + | 20.6242i | 0.142832 | + | 0.00265734i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3686.98 | − | 2159.27i | −0.471441 | − | 0.276098i | ||||
\(395\) | 15656.1 | 1.99429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5442.74 | 0.688069 | 0.344035 | − | 0.938957i | \(-0.388206\pi\) | ||||
0.344035 | + | 0.938957i | \(0.388206\pi\) | |||||||
\(398\) | −800.937 | − | 469.067i | −0.100873 | − | 0.0590759i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4134.87 | − | 6768.40i | 0.516859 | − | 0.846050i | ||||
\(401\) | − | 14165.2i | − | 1.76403i | −0.471218 | − | 0.882017i | \(-0.656186\pi\) | ||
0.471218 | − | 0.882017i | \(-0.343814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6665.16i | 0.823859i | ||||||||
\(404\) | −10359.1 | + | 5810.73i | −1.27570 | + | 0.715581i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2052.75 | − | 3505.09i | 0.250927 | − | 0.428460i | ||||
\(407\) | −7957.97 | −0.969194 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9568.46 | 1.15680 | 0.578399 | − | 0.815754i | \(-0.303678\pi\) | ||||
0.578399 | + | 0.815754i | \(0.303678\pi\) | |||||||
\(410\) | 1754.27 | − | 2995.43i | 0.211310 | − | 0.360814i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8680.77 | + | 4869.32i | −1.03804 | + | 0.582267i | ||||
\(413\) | − | 5329.79i | − | 0.635016i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 17621.1i | − | 2.08431i | ||||||
\(416\) | −3230.11 | − | 6018.17i | −0.380695 | − | 0.709291i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1657.34 | + | 970.618i | 0.193931 | + | 0.113575i | ||||
\(419\) | −3341.64 | −0.389618 | −0.194809 | − | 0.980841i | \(-0.562409\pi\) | ||||
−0.194809 | + | 0.980841i | \(0.562409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10585.4 | −1.22542 | −0.612708 | − | 0.790309i | \(-0.709920\pi\) | ||||
−0.612708 | + | 0.790309i | \(0.709920\pi\) | |||||||
\(422\) | 10248.5 | + | 6002.00i | 1.18220 | + | 0.692353i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −65.4716 | + | 3519.10i | −0.00749901 | + | 0.403073i | ||||
\(425\) | 3956.31i | 0.451551i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 281.546i | 0.0319085i | ||||||||
\(428\) | −7146.29 | − | 12740.0i | −0.807077 | − | 1.43881i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10442.8 | + | 17831.2i | −1.17115 | + | 1.99976i | ||||
\(431\) | −4326.10 | −0.483482 | −0.241741 | − | 0.970341i | \(-0.577719\pi\) | ||||
−0.241741 | + | 0.970341i | \(0.577719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11443.7 | −1.27009 | −0.635046 | − | 0.772474i | \(-0.719019\pi\) | ||||
−0.635046 | + | 0.772474i | \(0.719019\pi\) | |||||||
\(434\) | −1767.44 | + | 3017.92i | −0.195483 | + | 0.333790i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −819.720 | − | 1461.36i | −0.0900401 | − | 0.160519i | ||||
\(437\) | 1468.83i | 0.160786i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16418.3i | − | 1.78497i | −0.451075 | − | 0.892486i | \(-0.648959\pi\) | ||
0.451075 | − | 0.892486i | \(-0.351041\pi\) | |||||||
\(440\) | −156.141 | + | 8392.60i | −0.0169176 | + | 0.909321i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2939.92 | + | 1721.76i | 0.316375 | + | 0.185285i | ||||
\(443\) | 13807.7 | 1.48087 | 0.740433 | − | 0.672130i | \(-0.234620\pi\) | ||||
0.740433 | + | 0.672130i | \(0.234620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25120.7 | −2.67604 | ||||||||
\(446\) | 3716.00 | + | 2176.27i | 0.394524 | + | 0.231052i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 133.312 | − | 3581.52i | 0.0140589 | − | 0.377703i | ||||
\(449\) | − | 934.788i | − | 0.0982525i | −0.998793 | − | 0.0491263i | \(-0.984356\pi\) | ||
0.998793 | − | 0.0491263i | \(-0.0156437\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1828.99i | 0.190961i | ||||||||
\(452\) | −7125.39 | + | 3996.86i | −0.741483 | + | 0.415921i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2618.58 | − | 4471.25i | 0.270696 | − | 0.462216i | ||||
\(455\) | 4167.22 | 0.429368 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11772.2 | −1.20499 | −0.602493 | − | 0.798124i | \(-0.705826\pi\) | ||||
−0.602493 | + | 0.798124i | \(0.705826\pi\) | |||||||
\(458\) | 596.558 | − | 1018.63i | 0.0608632 | − | 0.103925i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5598.75 | + | 3140.51i | −0.567485 | + | 0.318320i | ||||
\(461\) | 8920.56i | 0.901240i | 0.892716 | + | 0.450620i | \(0.148797\pi\) | ||||
−0.892716 | + | 0.450620i | \(0.851203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4574.14i | 0.459132i | 0.973293 | + | 0.229566i | \(0.0737307\pi\) | ||||
−0.973293 | + | 0.229566i | \(0.926269\pi\) | |||||||
\(464\) | −11204.8 | − | 6845.09i | −1.12105 | − | 0.684861i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1053.39 | − | 616.916i | −0.104715 | − | 0.0613264i | ||||
\(467\) | 137.173 | 0.0135923 | 0.00679614 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679614 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5870.84 | −0.578018 | ||||||||
\(470\) | 13560.5 | + | 7941.66i | 1.33085 | + | 0.779407i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17225.5 | − | 320.474i | −1.67980 | − | 0.0312521i | ||||
\(473\) | − | 10887.6i | − | 1.05837i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3579.13i | − | 0.345730i | ||||||
\(476\) | 874.601 | + | 1559.19i | 0.0842170 | + | 0.150138i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4811.14 | + | 8215.07i | −0.460369 | + | 0.786084i | ||||
\(479\) | −10928.1 | −1.04242 | −0.521210 | − | 0.853428i | \(-0.674519\pi\) | ||||
−0.521210 | + | 0.853428i | \(0.674519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12770.7 | 1.21059 | ||||||||
\(482\) | 5797.06 | − | 9898.53i | 0.547819 | − | 0.935406i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3045.55 | + | 5429.46i | 0.286021 | + | 0.509904i | ||||
\(485\) | 19928.6i | 1.86579i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9011.53i | − | 0.838504i | −0.907870 | − | 0.419252i | \(-0.862292\pi\) | ||
0.907870 | − | 0.419252i | \(-0.137708\pi\) | |||||||
\(488\) | 909.936 | + | 16.9290i | 0.0844075 | + | 0.00157037i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1886.88 | + | 1105.05i | 0.173960 | + | 0.101879i | ||||
\(491\) | 6797.47 | 0.624777 | 0.312388 | − | 0.949954i | \(-0.398871\pi\) | ||||
0.312388 | + | 0.949954i | \(0.398871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6549.49 | 0.598325 | ||||||||
\(494\) | −2659.64 | − | 1557.61i | −0.242233 | − | 0.141863i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9647.43 | + | 5893.70i | 0.873352 | + | 0.533538i | ||||
\(497\) | 491.048i | 0.0443189i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 709.640i | − | 0.0636630i | −0.999493 | − | 0.0318315i | \(-0.989866\pi\) | ||
0.999493 | − | 0.0318315i | \(-0.0101340\pi\) | |||||||
\(500\) | −117.861 | + | 66.1117i | −0.0105418 | + | 0.00591321i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1748.02 | + | 2984.76i | −0.155414 | + | 0.265371i | ||||
\(503\) | −1150.21 | −0.101959 | −0.0509795 | − | 0.998700i | \(-0.516234\pi\) | ||||
−0.0509795 | + | 0.998700i | \(0.516234\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23424.7 | −2.06413 | ||||||||
\(506\) | 1709.27 | − | 2918.60i | 0.150171 | − | 0.256418i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13978.0 | − | 7840.73i | 1.22082 | − | 0.684795i | ||||
\(509\) | 3194.56i | 0.278186i | 0.990279 | + | 0.139093i | \(0.0444186\pi\) | ||||
−0.990279 | + | 0.139093i | \(0.955581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5087.52i | − | 0.440428i | ||||||
\(512\) | −11567.2 | − | 646.207i | −0.998443 | − | 0.0557784i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2277.26 | + | 1333.67i | 0.195420 | + | 0.114447i | ||||
\(515\) | −19629.6 | −1.67958 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8279.90 | −0.704352 | ||||||||
\(518\) | 5782.45 | + | 3386.48i | 0.490475 | + | 0.287246i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 250.570 | − | 13468.2i | 0.0211312 | − | 1.13580i | ||||
\(521\) | 6422.65i | 0.540079i | 0.962849 | + | 0.270040i | \(0.0870368\pi\) | ||||
−0.962849 | + | 0.270040i | \(0.912963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8840.42i | − | 0.739129i | −0.929205 | − | 0.369565i | \(-0.879507\pi\) | ||
0.929205 | − | 0.369565i | \(-0.120493\pi\) | |||||||
\(524\) | 4574.97 | + | 8156.02i | 0.381409 | + | 0.679957i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3895.77 | + | 6652.07i | −0.322934 | + | 0.551414i | ||||
\(527\) | −5639.19 | −0.466123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9580.37 | −0.787406 | ||||||||
\(530\) | −3507.98 | + | 5989.91i | −0.287503 | + | 0.490915i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −791.220 | − | 1410.55i | −0.0644807 | − | 0.114953i | ||||
\(533\) | − | 2935.10i | − | 0.238524i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 28808.6i | − | 2.32805i | ||||||
\(536\) | −353.007 | + | 18974.1i | −0.0284469 | + | 1.52903i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16442.5 | + | 9629.51i | 1.31763 | + | 0.771668i | ||||
\(539\) | −1152.11 | −0.0920686 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13395.6 | 1.06455 | 0.532275 | − | 0.846571i | \(-0.321337\pi\) | ||||
0.532275 | + | 0.846571i | \(0.321337\pi\) | |||||||
\(542\) | −10415.9 | − | 6100.05i | −0.825463 | − | 0.483431i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5091.79 | − | 2732.90i | 0.401303 | − | 0.215390i | ||||
\(545\) | − | 3304.52i | − | 0.259725i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16033.9i | 1.25331i | 0.779297 | + | 0.626655i | \(0.215577\pi\) | ||||
−0.779297 | + | 0.626655i | \(0.784423\pi\) | |||||||
\(548\) | −3300.15 | + | 1851.16i | −0.257254 | + | 0.144302i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4165.04 | + | 7111.85i | −0.322905 | + | 0.551364i | ||||
\(551\) | −5925.09 | −0.458108 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6946.15 | 0.534142 | ||||||||
\(554\) | −10669.6 | + | 18218.5i | −0.818247 | + | 1.39717i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19939.3 | + | 11184.6i | −1.52089 | + | 0.853117i | ||||
\(557\) | − | 19550.5i | − | 1.48722i | −0.668613 | − | 0.743610i | \(-0.733112\pi\) | ||
0.668613 | − | 0.743610i | \(-0.266888\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17472.0i | 1.32198i | ||||||||
\(560\) | 3684.89 | − | 6031.81i | 0.278062 | − | 0.455162i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3763.33 | − | 2203.98i | −0.282467 | − | 0.165426i | ||||
\(563\) | 5558.55 | 0.416101 | 0.208051 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208051 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16112.4 | −1.19974 | ||||||||
\(566\) | 14.2696 | + | 8.35698i | 0.00105971 | + | 0.000620619i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1587.03 | + | 29.5261i | 0.117237 | + | 0.00218114i | ||||
\(569\) | 24053.5i | 1.77219i | 0.463502 | + | 0.886096i | \(0.346593\pi\) | ||||
−0.463502 | + | 0.886096i | \(0.653407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7034.11i | 0.515531i | 0.966207 | + | 0.257766i | \(0.0829862\pi\) | ||||
−0.966207 | + | 0.257766i | \(0.917014\pi\) | |||||||
\(572\) | 3472.20 | + | 6190.06i | 0.253811 | + | 0.452481i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 778.317 | − | 1328.98i | 0.0565964 | − | 0.0966389i | ||||
\(575\) | −6302.91 | −0.457130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21687.4 | 1.56475 | 0.782373 | − | 0.622810i | \(-0.214009\pi\) | ||||
0.782373 | + | 0.622810i | \(0.214009\pi\) | |||||||
\(578\) | 5565.79 | − | 9503.65i | 0.400530 | − | 0.683909i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12668.5 | − | 22584.8i | −0.906950 | − | 1.61686i | ||||
\(581\) | − | 7817.97i | − | 0.558252i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3657.39i | − | 0.259817i | ||||||
\(584\) | −16442.5 | − | 305.907i | −1.16506 | − | 0.0216755i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20115.1 | − | 11780.4i | −1.41800 | − | 0.830448i | ||||
\(587\) | 19803.0 | 1.39243 | 0.696215 | − | 0.717833i | \(-0.254866\pi\) | ||||
0.696215 | + | 0.717833i | \(0.254866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5101.57 | 0.356887 | ||||||||
\(590\) | −29319.7 | − | 17171.0i | −2.04589 | − | 1.19817i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11292.5 | − | 18484.8i | 0.783988 | − | 1.28331i | ||||
\(593\) | 2320.01i | 0.160660i | 0.996768 | + | 0.0803301i | \(0.0255974\pi\) | ||||
−0.996768 | + | 0.0803301i | \(0.974403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3525.76i | 0.242928i | ||||||||
\(596\) | 21468.7 | − | 12042.5i | 1.47549 | − | 0.827649i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2742.98 | + | 4683.68i | −0.187574 | + | 0.320284i | ||||
\(599\) | −9216.77 | −0.628693 | −0.314346 | − | 0.949308i | \(-0.601785\pi\) | ||||
−0.314346 | + | 0.949308i | \(0.601785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3122.88 | 0.211955 | 0.105977 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105977 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(602\) | −4633.15 | + | 7911.15i | −0.313676 | + | 0.535605i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9135.90 | − | 5124.62i | 0.615455 | − | 0.345228i | ||||
\(605\) | 12277.5i | 0.825041i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13819.8i | 0.924099i | 0.886854 | + | 0.462049i | \(0.152886\pi\) | ||||
−0.886854 | + | 0.462049i | \(0.847114\pi\) | |||||||
\(608\) | −4606.36 | + | 2472.35i | −0.307258 | + | 0.164913i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1548.81 | + | 907.058i | 0.102803 | + | 0.0602061i | ||||
\(611\) | 13287.3 | 0.879782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21961.3 | 1.44700 | 0.723498 | − | 0.690327i | \(-0.242533\pi\) | ||||
0.723498 | + | 0.690327i | \(0.242533\pi\) | |||||||
\(614\) | 22366.4 | + | 13098.8i | 1.47009 | + | 0.860953i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −69.2751 | + | 3723.54i | −0.00453112 | + | 0.243548i | ||||
\(617\) | − | 8350.99i | − | 0.544892i | −0.962171 | − | 0.272446i | \(-0.912167\pi\) | ||
0.962171 | − | 0.272446i | \(-0.0878326\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9479.90i | − | 0.615556i | −0.951458 | − | 0.307778i | \(-0.900415\pi\) | ||
0.951458 | − | 0.307778i | \(-0.0995854\pi\) | |||||||
\(620\) | 10907.7 | + | 19445.7i | 0.706556 | + | 1.25961i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12531.7 | − | 21398.0i | 0.807837 | − | 1.37939i | ||||
\(623\) | −11145.3 | −0.716737 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15757.7 | −1.00849 | ||||||||
\(626\) | −2059.67 | + | 3516.90i | −0.131503 | + | 0.224543i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −191.748 | − | 341.838i | −0.0121840 | − | 0.0217211i | ||||
\(629\) | 10804.9i | 0.684927i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12675.6i | 0.799693i | 0.916582 | + | 0.399846i | \(0.130937\pi\) | ||||
−0.916582 | + | 0.399846i | \(0.869063\pi\) | |||||||
\(632\) | 417.664 | − | 22449.5i | 0.0262876 | − | 1.41296i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3549.94 | + | 2079.02i | 0.222376 | + | 0.130234i | ||||
\(635\) | 31608.1 | 1.97532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1848.87 | 0.115000 | ||||||||
\(638\) | 11773.3 | + | 6895.03i | 0.730581 | + | 0.427863i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19272.8 | − | 12272.0i | −1.19035 | − | 0.757957i | ||||
\(641\) | 415.766i | 0.0256190i | 0.999918 | + | 0.0128095i | \(0.00407750\pi\) | ||||
−0.999918 | + | 0.0128095i | \(0.995922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1748.72i | − | 0.107252i | −0.998561 | − | 0.0536258i | \(-0.982922\pi\) | ||
0.998561 | − | 0.0536258i | \(-0.0170778\pi\) | |||||||
\(644\) | −2484.00 | + | 1393.35i | −0.151992 | + | 0.0852574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1317.85 | − | 2250.24i | 0.0802633 | − | 0.137051i | ||||
\(647\) | −17144.4 | −1.04175 | −0.520877 | − | 0.853632i | \(-0.674395\pi\) | ||||
−0.520877 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17902.4 | 1.08279 | ||||||||
\(650\) | 6683.91 | − | 11412.8i | 0.403330 | − | 0.688690i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12986.3 | − | 7284.42i | 0.780034 | − | 0.437546i | ||||
\(653\) | 13708.4i | 0.821520i | 0.911743 | + | 0.410760i | \(0.134737\pi\) | ||||
−0.911743 | + | 0.410760i | \(0.865263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18442.9i | 1.10019i | ||||||||
\(656\) | −4248.38 | − | 2595.37i | −0.252853 | − | 0.154470i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6016.37 | + | 3523.47i | 0.356448 | + | 0.208753i | ||||
\(659\) | 3117.98 | 0.184308 | 0.0921542 | − | 0.995745i | \(-0.470625\pi\) | ||||
0.0921542 | + | 0.995745i | \(0.470625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21138.9 | 1.24389 | 0.621944 | − | 0.783062i | \(-0.286343\pi\) | ||||
0.621944 | + | 0.783062i | \(0.286343\pi\) | |||||||
\(662\) | −587.437 | − | 344.031i | −0.0344885 | − | 0.0201981i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25267.1 | − | 470.085i | −1.47674 | − | 0.0274742i | ||||
\(665\) | − | 3189.62i | − | 0.185998i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10434.2i | 0.605717i | ||||||||
\(668\) | 1081.45 | + | 1927.96i | 0.0626386 | + | 0.111669i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18914.1 | + | 32296.1i | −1.09062 | + | 1.86225i | ||||
\(671\) | −945.691 | −0.0544083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2307.32 | −0.132156 | −0.0660778 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660778 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(674\) | −1990.37 | + | 3398.58i | −0.113748 | + | 0.194226i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3026.50 | + | 5395.48i | 0.172195 | + | 0.306980i | ||||
\(677\) | − | 3314.25i | − | 0.188149i | −0.995565 | − | 0.0940746i | \(-0.970011\pi\) | ||
0.995565 | − | 0.0940746i | \(-0.0299892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8841.71i | 0.499725i | ||||||||
\(680\) | 11395.0 | + | 212.000i | 0.642615 | + | 0.0119556i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10137.0 | − | 5936.70i | −0.569157 | − | 0.333325i | ||||
\(683\) | 24300.2 | 1.36138 | 0.680690 | − | 0.732571i | \(-0.261680\pi\) | ||||
0.680690 | + | 0.732571i | \(0.261680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7462.52 | −0.416246 | ||||||||
\(686\) | 837.151 | + | 490.276i | 0.0465927 | + | 0.0272869i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25289.7 | + | 15449.7i | 1.40140 | + | 0.856125i | ||||
\(689\) | 5869.25i | 0.324529i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24627.2i | 1.35580i | 0.735152 | + | 0.677902i | \(0.237111\pi\) | ||||
−0.735152 | + | 0.677902i | \(0.762889\pi\) | |||||||
\(692\) | 2123.00 | − | 1190.86i | 0.116625 | − | 0.0654184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11764.1 | − | 20087.3i | 0.643455 | − | 1.09871i | ||||
\(695\) | −45088.2 | −2.46085 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2483.29 | 0.134952 | ||||||||
\(698\) | 3285.28 | − | 5609.66i | 0.178152 | − | 0.304196i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6052.83 | − | 3395.22i | 0.326822 | − | 0.183325i | ||||
\(701\) | 11630.1i | 0.626625i | 0.949650 | + | 0.313313i | \(0.101439\pi\) | ||||
−0.949650 | + | 0.313313i | \(0.898561\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9774.79i | − | 0.524414i | ||||||
\(704\) | 12030.1 | + | 447.784i | 0.644034 | + | 0.0239723i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16587.6 | + | 9714.47i | 0.884251 | + | 0.517859i | ||||
\(707\) | −10392.8 | −0.552846 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22039.3 | 1.16742 | 0.583711 | − | 0.811961i | \(-0.301600\pi\) | ||||
0.583711 | + | 0.811961i | \(0.301600\pi\) | |||||||
\(710\) | 2701.31 | + | 1582.01i | 0.142786 | + | 0.0836224i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −670.154 | + | 36020.8i | −0.0352740 | + | 1.89598i | ||||
\(713\) | − | 8983.95i | − | 0.471881i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13997.4i | 0.732129i | ||||||||
\(716\) | −11070.7 | − | 19736.3i | −0.577837 | − | 1.03014i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16084.3 | − | 27464.1i | 0.836018 | − | 1.42751i | ||||
\(719\) | −30873.4 | −1.60137 | −0.800684 | − | 0.599087i | \(-0.795530\pi\) | ||||
−0.800684 | + | 0.599087i | \(0.795530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8709.04 | −0.449850 | ||||||||
\(722\) | 8611.87 | − | 14704.9i | 0.443907 | − | 0.757976i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8962.31 | − | 15977.5i | −0.460057 | − | 0.820167i | ||||
\(725\) | − | 25425.3i | − | 1.30244i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4726.44i | − | 0.241120i | −0.992706 | − | 0.120560i | \(-0.961531\pi\) | ||
0.992706 | − | 0.120560i | \(-0.0384690\pi\) | |||||||
\(728\) | 111.170 | − | 5975.41i | 0.00565968 | − | 0.304208i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27987.0 | − | 16390.5i | −1.41897 | − | 0.831014i | ||||
\(731\) | −14782.5 | −0.747949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13188.7 | −0.664580 | −0.332290 | − | 0.943177i | \(-0.607821\pi\) | ||||
−0.332290 | + | 0.943177i | \(0.607821\pi\) | |||||||
\(734\) | −5304.94 | − | 3106.83i | −0.266770 | − | 0.156233i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4353.85 | + | 8111.88i | 0.218051 | + | 0.406261i | ||||
\(737\) | − | 19719.7i | − | 0.985597i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16007.0i | − | 0.796786i | −0.917215 | − | 0.398393i | \(-0.869568\pi\) | ||
0.917215 | − | 0.398393i | \(-0.130432\pi\) | |||||||
\(740\) | 37258.7 | − | 20899.6i | 1.85089 | − | 1.03822i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1556.38 | + | 2657.54i | −0.0770036 | + | 0.131484i | ||||
\(743\) | 8589.38 | 0.424110 | 0.212055 | − | 0.977258i | \(-0.431984\pi\) | ||||
0.212055 | + | 0.977258i | \(0.431984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48546.5 | 2.38739 | ||||||||
\(746\) | 19715.2 | − | 33663.9i | 0.967593 | − | 1.65218i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5237.22 | + | 2937.72i | −0.256005 | + | 0.143601i | ||||
\(749\) | − | 12781.5i | − | 0.623534i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15818.0i | 0.768585i | 0.923211 | + | 0.384292i | \(0.125555\pi\) | ||||
−0.923211 | + | 0.384292i | \(0.874445\pi\) | |||||||
\(752\) | 11749.4 | − | 19232.6i | 0.569755 | − | 0.932635i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18893.5 | − | 11064.9i | −0.912545 | − | 0.534430i | ||||
\(755\) | 20658.7 | 0.995826 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10993.9 | −0.527846 | −0.263923 | − | 0.964544i | \(-0.585016\pi\) | ||||
−0.263923 | + | 0.964544i | \(0.585016\pi\) | |||||||
\(758\) | −988.307 | − | 578.800i | −0.0473574 | − | 0.0277348i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10308.6 | − | 191.788i | −0.492018 | − | 0.00915381i | ||||
\(761\) | 15944.5i | 0.759508i | 0.925087 | + | 0.379754i | \(0.123991\pi\) | ||||
−0.925087 | + | 0.379754i | \(0.876009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1466.12i | − | 0.0695635i | ||||||
\(764\) | 1229.26 | + | 2191.46i | 0.0582107 | + | 0.103775i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13814.7 | − | 23588.8i | 0.651627 | − | 1.11266i | ||||
\(767\) | −28729.1 | −1.35247 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21870.6 | −1.02558 | −0.512792 | − | 0.858513i | \(-0.671389\pi\) | ||||
−0.512792 | + | 0.858513i | \(0.671389\pi\) | |||||||
\(770\) | −3711.77 | + | 6337.88i | −0.173718 | + | 0.296625i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8348.70 | + | 14883.6i | 0.389218 | + | 0.693878i | ||||
\(773\) | − | 19936.1i | − | 0.927620i | −0.885935 | − | 0.463810i | \(-0.846482\pi\) | ||
0.885935 | − | 0.463810i | \(-0.153518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21891.4i | 1.01466i | ||||||||
\(776\) | 28575.8 | + | 531.641i | 1.32192 | + | 0.0245938i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8163.95 | + | 4781.20i | 0.376211 | + | 0.220327i | ||||
\(779\) | −2246.55 | −0.103326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1649.39 | −0.0755697 | ||||||||
\(782\) | −3962.72 | − | 2320.76i | −0.181210 | − | 0.106125i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1634.87 | − | 2676.13i | 0.0744749 | − | 0.121908i | ||||
\(785\) | − | 772.988i | − | 0.0351454i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 27000.3i | − | 1.22294i | −0.791266 | − | 0.611472i | \(-0.790578\pi\) | ||
0.791266 | − | 0.611472i | \(-0.209422\pi\) | |||||||
\(788\) | −10540.2 | + | 5912.31i | −0.476495 | + | 0.267281i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22378.5 | − | 38211.5i | 1.00784 | − | 1.72089i | ||||
\(791\) | −7148.60 | −0.321334 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1517.61 | 0.0679597 | ||||||||
\(794\) | 7779.72 | − | 13284.0i | 0.347723 | − | 0.593741i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2289.68 | + | 1284.35i | −0.101954 | + | 0.0571893i | ||||
\(797\) | − | 16938.8i | − | 0.752826i | −0.926452 | − | 0.376413i | \(-0.877157\pi\) | ||
0.926452 | − | 0.376413i | \(-0.122843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11242.0i | 0.497763i | ||||||||
\(800\) | −10609.2 | − | 19766.5i | −0.468863 | − | 0.873562i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −34572.7 | − | 20247.4i | −1.52220 | − | 0.891473i | ||||
\(803\) | 17088.6 | 0.750989 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5616.98 | −0.245929 | ||||||||
\(806\) | 16267.5 | + | 9527.01i | 0.710915 | + | 0.416346i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −624.908 | + | 33588.9i | −0.0272081 | + | 1.46244i | ||||
\(809\) | 9479.48i | 0.411966i | 0.978556 | + | 0.205983i | \(0.0660392\pi\) | ||||
−0.978556 | + | 0.205983i | \(0.933961\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32925.6i | 1.42562i | 0.701359 | + | 0.712808i | \(0.252577\pi\) | ||||
−0.701359 | + | 0.712808i | \(0.747423\pi\) | |||||||
\(812\) | −5620.63 | − | 10020.2i | −0.242913 | − | 0.433053i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11374.9 | + | 19422.8i | −0.489792 | + | 0.836326i | ||||
\(815\) | 29365.5 | 1.26212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13373.2 | 0.572667 | ||||||||
\(818\) | 13676.9 | − | 23353.5i | 0.584599 | − | 0.998210i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4803.37 | − | 8563.20i | −0.204562 | − | 0.364683i | ||||
\(821\) | 9381.63i | 0.398808i | 0.979917 | + | 0.199404i | \(0.0639006\pi\) | ||||
−0.979917 | + | 0.199404i | \(0.936099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35540.1i | − | 1.50529i | −0.658428 | − | 0.752644i | \(-0.728778\pi\) | ||
0.658428 | − | 0.752644i | \(-0.271222\pi\) | |||||||
\(824\) | −523.664 | + | 28147.0i | −0.0221392 | + | 1.18999i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13008.3 | − | 7618.27i | −0.547961 | − | 0.320912i | ||||
\(827\) | 1743.92 | 0.0733278 | 0.0366639 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366639 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43358.5 | −1.81653 | −0.908264 | − | 0.418398i | \(-0.862592\pi\) | ||||
−0.908264 | + | 0.418398i | \(0.862592\pi\) | |||||||
\(830\) | −43007.5 | − | 25187.2i | −1.79857 | − | 1.05333i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19305.4 | − | 718.589i | −0.804442 | − | 0.0299430i | ||||
\(833\) | 1564.27i | 0.0650646i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4359.62i | 0.180684i | ||||||||
\(836\) | 4737.92 | − | 2657.65i | 0.196010 | − | 0.109948i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4776.46 | + | 8155.86i | −0.196898 | + | 0.336205i | ||||
\(839\) | −13882.5 | −0.571248 | −0.285624 | − | 0.958342i | \(-0.592201\pi\) | ||||
−0.285624 | + | 0.958342i | \(0.592201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17701.4 | −0.725794 | ||||||||
\(842\) | −15130.5 | + | 25835.5i | −0.619277 | + | 1.05742i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29297.9 | − | 16434.1i | 1.19487 | − | 0.670242i | ||||
\(845\) | 12200.6i | 0.496704i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5447.14i | 0.220975i | ||||||||
\(848\) | 8495.40 | + | 5189.92i | 0.344025 | + | 0.210168i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9656.06 | + | 5655.05i | 0.389647 | + | 0.228196i | ||||
\(851\) | −17213.6 | −0.693388 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26331.9 | 1.05696 | 0.528480 | − | 0.848946i | \(-0.322762\pi\) | ||||
0.528480 | + | 0.848946i | \(0.322762\pi\) | |||||||
\(854\) | 687.161 | + | 402.434i | 0.0275342 | + | 0.0161253i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41309.0 | − | 768.538i | −1.64943 | − | 0.0306870i | ||||
\(857\) | 23177.4i | 0.923832i | 0.886924 | + | 0.461916i | \(0.152838\pi\) | ||||
−0.886924 | + | 0.461916i | \(0.847162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27339.6i | 1.08593i | 0.839755 | + | 0.542965i | \(0.182698\pi\) | ||||
−0.839755 | + | 0.542965i | \(0.817302\pi\) | |||||||
\(860\) | 28593.4 | + | 50974.9i | 1.13375 | + | 2.02120i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6183.62 | + | 10558.6i | −0.244333 | + | 0.417201i | ||||
\(863\) | 10007.4 | 0.394736 | 0.197368 | − | 0.980330i | \(-0.436761\pi\) | ||||
0.197368 | + | 0.980330i | \(0.436761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4800.67 | 0.188702 | ||||||||
\(866\) | −16357.4 | + | 27930.4i | −0.641854 | + | 1.09597i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4839.43 | + | 8627.48i | 0.189241 | + | 0.337368i | ||||
\(869\) | 23331.6i | 0.910784i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31645.5i | 1.23108i | ||||||||
\(872\) | −4738.38 | − | 88.1557i | −0.184016 | − | 0.00342354i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3584.93 | + | 2099.50i | 0.138744 | + | 0.0812549i | ||||
\(875\) | −118.244 | −0.00456845 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33763.4 | 1.30001 | 0.650005 | − | 0.759930i | \(-0.274767\pi\) | ||||
0.650005 | + | 0.759930i | \(0.274767\pi\) | |||||||
\(878\) | −40071.7 | − | 23467.9i | −1.54027 | − | 0.902054i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20260.4 | + | 12377.3i | 0.776111 | + | 0.474133i | ||||
\(881\) | 2440.72i | 0.0933372i | 0.998910 | + | 0.0466686i | \(0.0148605\pi\) | ||||
−0.998910 | + | 0.0466686i | \(0.985140\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11198.0i | 0.426777i | 0.976967 | + | 0.213388i | \(0.0684499\pi\) | ||||
−0.976967 | + | 0.213388i | \(0.931550\pi\) | |||||||
\(884\) | 8404.51 | − | 4714.35i | 0.319767 | − | 0.179367i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19736.4 | − | 33700.1i | 0.748371 | − | 1.27785i | ||||
\(887\) | 40801.1 | 1.54449 | 0.772247 | − | 0.635322i | \(-0.219133\pi\) | ||||
0.772247 | + | 0.635322i | \(0.219133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14023.6 | 0.529061 | ||||||||
\(890\) | −35906.9 | + | 61311.5i | −1.35236 | + | 2.30917i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10623.1 | − | 5958.83i | 0.398753 | − | 0.223673i | ||||
\(893\) | − | 10170.2i | − | 0.381112i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 44629.0i | − | 1.66680i | ||||||
\(896\) | −8550.77 | − | 5444.71i | −0.318818 | − | 0.203008i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2281.51 | − | 1336.16i | −0.0847829 | − | 0.0496529i | ||||
\(899\) | 36240.3 | 1.34447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4965.79 | −0.183612 | ||||||||
\(902\) | 4463.96 | + | 2614.31i | 0.164782 | + | 0.0965043i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −429.837 | + | 23103.8i | −0.0158143 | + | 0.850022i | ||||
\(905\) | − | 36129.5i | − | 1.32706i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13257.2i | − | 0.485334i | −0.970110 | − | 0.242667i | \(-0.921978\pi\) | ||
0.970110 | − | 0.242667i | \(-0.0780222\pi\) | |||||||
\(908\) | −7169.93 | − | 12782.2i | −0.262051 | − | 0.467172i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5956.52 | − | 10170.8i | 0.216985 | − | 0.370505i | ||||
\(911\) | −10748.9 | −0.390919 | −0.195460 | − | 0.980712i | \(-0.562620\pi\) | ||||
−0.195460 | + | 0.980712i | \(0.562620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26260.0 | 0.951894 | ||||||||
\(914\) | −16826.8 | + | 28732.0i | −0.608953 | + | 1.03979i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1633.44 | − | 2912.01i | −0.0589195 | − | 0.105039i | ||||
\(917\) | 8182.58i | 0.294670i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36773.1i | − | 1.31995i | −0.751289 | − | 0.659973i | \(-0.770568\pi\) | ||
0.751289 | − | 0.659973i | \(-0.229432\pi\) | |||||||
\(920\) | −337.742 | + | 18153.7i | −0.0121033 | + | 0.650554i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21772.2 | + | 12750.8i | 0.777688 | + | 0.455451i | ||||
\(923\) | 2646.89 | 0.0943917 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41944.8 | 1.49096 | ||||||||
\(926\) | 11164.0 | + | 6538.16i | 0.396189 | + | 0.232027i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32722.5 | + | 17563.0i | −1.15751 | + | 0.621264i | ||||
\(929\) | 48989.7i | 1.73014i | 0.501651 | + | 0.865070i | \(0.332726\pi\) | ||||
−0.501651 | + | 0.865070i | \(0.667274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1415.14i | − | 0.0498167i | ||||||
\(932\) | −3011.38 | + | 1689.18i | −0.105838 | + | 0.0593679i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 196.071 | − | 334.794i | 0.00686900 | − | 0.0117289i | ||||
\(935\) | −11842.8 | −0.414224 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36515.8 | −1.27313 | −0.636564 | − | 0.771224i | \(-0.719645\pi\) | ||||
−0.636564 | + | 0.771224i | \(0.719645\pi\) | |||||||
\(938\) | −8391.63 | + | 14328.8i | −0.292107 | + | 0.498776i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 38766.0 | − | 21745.1i | 1.34511 | − | 0.754517i | ||||
\(941\) | 5560.99i | 0.192650i | 0.995350 | + | 0.0963248i | \(0.0307087\pi\) | ||||
−0.995350 | + | 0.0963248i | \(0.969291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3956.21i | 0.136619i | ||||||||
\(944\) | −25403.9 | + | 41583.7i | −0.875874 | + | 1.43372i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26573.0 | − | 15562.4i | −0.913279 | − | 0.534860i | ||||
\(947\) | −42010.7 | −1.44157 | −0.720783 | − | 0.693160i | \(-0.756218\pi\) | ||||
−0.720783 | + | 0.693160i | \(0.756218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27423.2 | −0.938035 | ||||||||
\(950\) | −8735.49 | − | 5115.92i | −0.298333 | − | 0.174718i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5055.62 | + | 94.0578i | 0.172115 | + | 0.00320213i | ||||
\(953\) | − | 34345.1i | − | 1.16742i | −0.811964 | − | 0.583708i | \(-0.801601\pi\) | ||
0.811964 | − | 0.583708i | \(-0.198399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4955.48i | 0.167911i | ||||||||
\(956\) | 13173.4 | + | 23484.8i | 0.445667 | + | 0.794512i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15620.4 | + | 26672.0i | −0.526798 | + | 0.899513i | ||||
\(959\) | −3310.90 | −0.111485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1412.29 | −0.0474064 | ||||||||
\(962\) | 18254.1 | − | 31169.1i | 0.611783 | − | 1.04463i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15872.9 | − | 28297.4i | −0.530324 | − | 0.945435i | ||||
\(965\) | 33655.9i | 1.12272i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10449.5i | 0.347499i | 0.984790 | + | 0.173750i | \(0.0555884\pi\) | ||||
−0.984790 | + | 0.173750i | \(0.944412\pi\) | |||||||
\(968\) | 17604.8 | + | 327.530i | 0.584544 | + | 0.0108752i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48639.1 | + | 28485.4i | 1.61001 | + | 0.942898i | ||||
\(971\) | 17540.5 | 0.579713 | 0.289857 | − | 0.957070i | \(-0.406392\pi\) | ||||
0.289857 | + | 0.957070i | \(0.406392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20004.3 | −0.659104 | ||||||||
\(974\) | −21994.2 | − | 12880.9i | −0.723552 | − | 0.423747i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1341.96 | − | 2196.66i | 0.0440113 | − | 0.0720423i | ||||
\(977\) | 42272.5i | 1.38425i | 0.721776 | + | 0.692127i | \(0.243326\pi\) | ||||
−0.721776 | + | 0.692127i | \(0.756674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 37436.3i | − | 1.22213i | ||||||
\(980\) | 5394.11 | − | 3025.73i | 0.175825 | − | 0.0986258i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9716.13 | − | 16590.4i | 0.315737 | − | 0.539125i | ||||
\(983\) | −20775.1 | −0.674084 | −0.337042 | − | 0.941490i | \(-0.609426\pi\) | ||||
−0.337042 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23834.1 | −0.770984 | ||||||||
\(986\) | 9361.68 | − | 15985.2i | 0.302370 | − | 0.516300i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7603.26 | + | 4264.91i | −0.244830 | + | 0.137333i | ||||
\(989\) | − | 23550.4i | − | 0.757190i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12344.0i | − | 0.395683i | −0.980234 | − | 0.197841i | \(-0.936607\pi\) | ||
0.980234 | − | 0.197841i | \(-0.0633931\pi\) | |||||||
\(992\) | 28174.4 | − | 15121.9i | 0.901752 | − | 0.483993i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1198.49 | + | 701.892i | 0.0382432 | + | 0.0223970i | ||||
\(995\) | −5177.58 | −0.164965 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50011.2 | −1.58864 | −0.794319 | − | 0.607501i | \(-0.792172\pi\) | ||||
−0.794319 | + | 0.607501i | \(0.792172\pi\) | |||||||
\(998\) | −1732.00 | − | 1014.34i | −0.0549354 | − | 0.0321728i | ||||
\(999\) | 0 | 0 |
(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 | 252.4.e.a.71.25 | yes | 36 | |
3.2 | odd | 2 | inner | 252.4.e.a.71.12 | yes | 36 | |
4.3 | odd | 2 | inner | 252.4.e.a.71.11 | ✓ | 36 | |
12.11 | even | 2 | inner | 252.4.e.a.71.26 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.e.a.71.11 | ✓ | 36 | 4.3 | odd | 2 | inner | |
252.4.e.a.71.12 | yes | 36 | 3.2 | odd | 2 | inner | |
252.4.e.a.71.25 | yes | 36 | 1.1 | even | 1 | trivial | |
252.4.e.a.71.26 | yes | 36 | 12.11 | even | 2 | inner |