Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,4,Mod(27,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.d (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: | \(1.65205348016\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 27.8 | ||
Root | \(4.98105 + 1.39897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.27 |
Dual form | 28.4.d.b.27.6 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | + | 2.79793i | 0.146447 | + | 0.989219i | ||||
\(3\) | 7.54788 | 1.45259 | 0.726296 | − | 0.687383i | \(-0.241240\pi\) | ||||
0.726296 | + | 0.687383i | \(0.241240\pi\) | |||||||
\(4\) | −7.65685 | + | 2.31788i | −0.957107 | + | 0.289735i | ||||
\(5\) | − | 8.74756i | − | 0.782405i | −0.920305 | − | 0.391203i | \(-0.872059\pi\) | ||
0.920305 | − | 0.391203i | \(-0.127941\pi\) | |||||||
\(6\) | 3.12644 | + | 21.1185i | 0.212727 | + | 1.43693i | ||||
\(7\) | −13.8008 | + | 12.3507i | −0.745171 | + | 0.666874i | ||||
\(8\) | −9.65685 | − | 20.4633i | −0.426777 | − | 0.904357i | ||||
\(9\) | 29.9706 | 1.11002 | ||||||||
\(10\) | 24.4751 | − | 3.62336i | 0.773970 | − | 0.114581i | ||||
\(11\) | 0.397686i | 0.0109006i | 0.999985 | + | 0.00545031i | \(0.00173490\pi\) | ||||
−0.999985 | + | 0.00545031i | \(0.998265\pi\) | |||||||
\(12\) | −57.7931 | + | 17.4951i | −1.39028 | + | 0.420867i | ||||
\(13\) | − | 75.7263i | − | 1.61559i | −0.589462 | − | 0.807796i | \(-0.700660\pi\) | ||
0.589462 | − | 0.807796i | \(-0.299340\pi\) | |||||||
\(14\) | −40.2728 | − | 33.4978i | −0.768812 | − | 0.639475i | ||||
\(15\) | − | 66.0256i | − | 1.13652i | ||||||
\(16\) | 53.2548 | − | 35.4954i | 0.832107 | − | 0.554615i | ||||
\(17\) | 84.4739i | 1.20517i | 0.798054 | + | 0.602586i | \(0.205863\pi\) | ||||
−0.798054 | + | 0.602586i | \(0.794137\pi\) | |||||||
\(18\) | 12.4142 | + | 83.8556i | 0.162559 | + | 1.09805i | ||||
\(19\) | 20.0536 | 0.242138 | 0.121069 | − | 0.992644i | \(-0.461368\pi\) | ||||
0.121069 | + | 0.992644i | \(0.461368\pi\) | |||||||
\(20\) | 20.2758 | + | 66.9788i | 0.226691 | + | 0.748845i | ||||
\(21\) | −104.167 | + | 93.2214i | −1.08243 | + | 0.968695i | ||||
\(22\) | −1.11270 | + | 0.164727i | −0.0107831 | + | 0.00159636i | ||||
\(23\) | 122.382i | 1.10950i | 0.832019 | + | 0.554748i | \(0.187185\pi\) | ||||
−0.832019 | + | 0.554748i | \(0.812815\pi\) | |||||||
\(24\) | −72.8888 | − | 154.454i | −0.619932 | − | 1.31366i | ||||
\(25\) | 48.4802 | 0.387842 | ||||||||
\(26\) | 211.877 | − | 31.3669i | 1.59817 | − | 0.236598i | ||||
\(27\) | 22.4215 | 0.159815 | ||||||||
\(28\) | 77.0430 | − | 126.556i | 0.519991 | − | 0.854172i | ||||
\(29\) | −175.823 | −1.12585 | −0.562924 | − | 0.826509i | \(-0.690324\pi\) | ||||
−0.562924 | + | 0.826509i | \(0.690324\pi\) | |||||||
\(30\) | 184.735 | − | 27.3487i | 1.12426 | − | 0.166439i | ||||
\(31\) | −128.092 | −0.742128 | −0.371064 | − | 0.928607i | \(-0.621007\pi\) | ||||
−0.371064 | + | 0.928607i | \(0.621007\pi\) | |||||||
\(32\) | 121.373 | + | 134.301i | 0.670495 | + | 0.741914i | ||||
\(33\) | 3.00169i | 0.0158341i | ||||||||
\(34\) | −236.352 | + | 34.9902i | −1.19218 | + | 0.176493i | ||||
\(35\) | 108.038 | + | 120.723i | 0.521765 | + | 0.583026i | ||||
\(36\) | −229.480 | + | 69.4683i | −1.06241 | + | 0.321612i | ||||
\(37\) | 253.196 | 1.12500 | 0.562502 | − | 0.826796i | \(-0.309839\pi\) | ||||
0.562502 | + | 0.826796i | \(0.309839\pi\) | |||||||
\(38\) | 8.30649 | + | 56.1087i | 0.0354603 | + | 0.239527i | ||||
\(39\) | − | 571.574i | − | 2.34680i | ||||||
\(40\) | −179.004 | + | 84.4739i | −0.707574 | + | 0.333912i | ||||
\(41\) | 81.4722i | 0.310337i | 0.987888 | + | 0.155169i | \(0.0495921\pi\) | ||||
−0.987888 | + | 0.155169i | \(0.950408\pi\) | |||||||
\(42\) | −303.975 | − | 252.837i | −1.11677 | − | 0.928896i | ||||
\(43\) | 69.1388i | 0.245199i | 0.992456 | + | 0.122600i | \(0.0391231\pi\) | ||||
−0.992456 | + | 0.122600i | \(0.960877\pi\) | |||||||
\(44\) | −0.921790 | − | 3.04502i | −0.00315830 | − | 0.0104331i | ||||
\(45\) | − | 262.169i | − | 0.868486i | ||||||
\(46\) | −342.416 | + | 50.6922i | −1.09753 | + | 0.162482i | ||||
\(47\) | −147.923 | −0.459081 | −0.229541 | − | 0.973299i | \(-0.573722\pi\) | ||||
−0.229541 | + | 0.973299i | \(0.573722\pi\) | |||||||
\(48\) | 401.961 | − | 267.915i | 1.20871 | − | 0.805629i | ||||
\(49\) | 37.9218 | − | 340.897i | 0.110559 | − | 0.993870i | ||||
\(50\) | 20.0812 | + | 135.644i | 0.0567981 | + | 0.383660i | ||||
\(51\) | 637.599i | 1.75062i | ||||||||
\(52\) | 175.525 | + | 579.826i | 0.468094 | + | 1.54629i | ||||
\(53\) | 283.921 | 0.735840 | 0.367920 | − | 0.929857i | \(-0.380070\pi\) | ||||
0.367920 | + | 0.929857i | \(0.380070\pi\) | |||||||
\(54\) | 9.28727 | + | 62.7337i | 0.0234044 | + | 0.158092i | ||||
\(55\) | 3.47878 | 0.00852870 | ||||||||
\(56\) | 386.007 | + | 163.140i | 0.921113 | + | 0.389294i | ||||
\(57\) | 151.362 | 0.351727 | ||||||||
\(58\) | −72.8284 | − | 491.942i | −0.164877 | − | 1.11371i | ||||
\(59\) | 632.911 | 1.39658 | 0.698288 | − | 0.715816i | \(-0.253945\pi\) | ||||
0.698288 | + | 0.715816i | \(0.253945\pi\) | |||||||
\(60\) | 153.040 | + | 505.548i | 0.329289 | + | 1.08777i | ||||
\(61\) | − | 3.25919i | − | 0.00684093i | −0.999994 | − | 0.00342046i | \(-0.998911\pi\) | ||
0.999994 | − | 0.00342046i | \(-0.00108877\pi\) | |||||||
\(62\) | −53.0574 | − | 358.392i | −0.108682 | − | 0.734127i | ||||
\(63\) | −413.616 | + | 370.157i | −0.827155 | + | 0.740244i | ||||
\(64\) | −325.490 | + | 395.222i | −0.635723 | + | 0.771917i | ||||
\(65\) | −662.420 | −1.26405 | ||||||||
\(66\) | −8.39852 | + | 1.24334i | −0.0156634 | + | 0.00231886i | ||||
\(67\) | − | 551.508i | − | 1.00563i | −0.864393 | − | 0.502817i | \(-0.832297\pi\) | ||
0.864393 | − | 0.502817i | \(-0.167703\pi\) | |||||||
\(68\) | −195.801 | − | 646.804i | −0.349181 | − | 1.15348i | ||||
\(69\) | 923.724i | 1.61164i | ||||||||
\(70\) | −293.024 | + | 352.289i | −0.500329 | + | 0.601522i | ||||
\(71\) | − | 486.278i | − | 0.812825i | −0.913690 | − | 0.406412i | \(-0.866780\pi\) | ||
0.913690 | − | 0.406412i | \(-0.133220\pi\) | |||||||
\(72\) | −289.421 | − | 613.296i | −0.473731 | − | 1.00386i | ||||
\(73\) | − | 165.946i | − | 0.266062i | −0.991112 | − | 0.133031i | \(-0.957529\pi\) | ||
0.991112 | − | 0.133031i | \(-0.0424710\pi\) | |||||||
\(74\) | 104.877 | + | 708.425i | 0.164753 | + | 1.11288i | ||||
\(75\) | 365.923 | 0.563376 | ||||||||
\(76\) | −153.548 | + | 46.4820i | −0.231752 | + | 0.0701559i | ||||
\(77\) | −4.91169 | − | 5.48837i | −0.00726934 | − | 0.00812282i | ||||
\(78\) | 1599.22 | − | 236.754i | 2.32149 | − | 0.343680i | ||||
\(79\) | − | 279.010i | − | 0.397355i | −0.980065 | − | 0.198677i | \(-0.936335\pi\) | ||
0.980065 | − | 0.198677i | \(-0.0636646\pi\) | |||||||
\(80\) | −310.498 | − | 465.850i | −0.433934 | − | 0.651045i | ||||
\(81\) | −639.971 | −0.877875 | ||||||||
\(82\) | −227.954 | + | 33.7469i | −0.306991 | + | 0.0454478i | ||||
\(83\) | −622.183 | −0.822813 | −0.411406 | − | 0.911452i | \(-0.634962\pi\) | ||||
−0.411406 | + | 0.911452i | \(0.634962\pi\) | |||||||
\(84\) | 581.511 | − | 955.229i | 0.755335 | − | 1.24076i | ||||
\(85\) | 738.940 | 0.942933 | ||||||||
\(86\) | −193.446 | + | 28.6382i | −0.242556 | + | 0.0359086i | ||||
\(87\) | −1327.09 | −1.63540 | ||||||||
\(88\) | 8.13795 | − | 3.84039i | 0.00985805 | − | 0.00465213i | ||||
\(89\) | 696.803i | 0.829898i | 0.909845 | + | 0.414949i | \(0.136201\pi\) | ||||
−0.909845 | + | 0.414949i | \(0.863799\pi\) | |||||||
\(90\) | 733.532 | − | 108.594i | 0.859123 | − | 0.127187i | ||||
\(91\) | 935.271 | + | 1045.08i | 1.07740 | + | 1.20389i | ||||
\(92\) | −283.667 | − | 937.060i | −0.321460 | − | 1.06191i | ||||
\(93\) | −966.823 | −1.07801 | ||||||||
\(94\) | −61.2718 | − | 413.879i | −0.0672309 | − | 0.454132i | ||||
\(95\) | − | 175.420i | − | 0.189450i | ||||||
\(96\) | 916.106 | + | 1013.69i | 0.973955 | + | 1.07770i | ||||
\(97\) | − | 1623.01i | − | 1.69889i | −0.527679 | − | 0.849444i | \(-0.676938\pi\) | ||
0.527679 | − | 0.849444i | \(-0.323062\pi\) | |||||||
\(98\) | 969.515 | − | 35.1017i | 0.999345 | − | 0.0361817i | ||||
\(99\) | 11.9189i | 0.0120999i | ||||||||
\(100\) | −371.206 | + | 112.372i | −0.371206 | + | 0.112372i | ||||
\(101\) | 774.501i | 0.763027i | 0.924363 | + | 0.381513i | \(0.124597\pi\) | ||||
−0.924363 | + | 0.381513i | \(0.875403\pi\) | |||||||
\(102\) | −1783.96 | + | 264.102i | −1.73175 | + | 0.256373i | ||||
\(103\) | −28.8584 | −0.0276068 | −0.0138034 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138034 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(104\) | −1549.61 | + | 731.278i | −1.46107 | + | 0.689497i | ||||
\(105\) | 815.460 | + | 911.203i | 0.757912 | + | 0.846898i | ||||
\(106\) | 117.604 | + | 794.392i | 0.107761 | + | 0.727907i | ||||
\(107\) | 51.9136i | 0.0469035i | 0.999725 | + | 0.0234517i | \(0.00746561\pi\) | ||||
−0.999725 | + | 0.0234517i | \(0.992534\pi\) | |||||||
\(108\) | −171.678 | + | 51.9703i | −0.152960 | + | 0.0463042i | ||||
\(109\) | 132.197 | 0.116167 | 0.0580833 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580833 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(110\) | 1.44096 | + | 9.73339i | 0.00124900 | + | 0.00843675i | ||||
\(111\) | 1911.09 | 1.63417 | ||||||||
\(112\) | −296.565 | + | 1147.60i | −0.250203 | + | 0.968193i | ||||
\(113\) | 318.049 | 0.264774 | 0.132387 | − | 0.991198i | \(-0.457736\pi\) | ||||
0.132387 | + | 0.991198i | \(0.457736\pi\) | |||||||
\(114\) | 62.6964 | + | 423.502i | 0.0515093 | + | 0.347935i | ||||
\(115\) | 1070.54 | 0.868075 | ||||||||
\(116\) | 1346.25 | − | 407.538i | 1.07756 | − | 0.326198i | ||||
\(117\) | − | 2269.56i | − | 1.79334i | ||||||
\(118\) | 262.160 | + | 1770.84i | 0.204524 | + | 1.38152i | ||||
\(119\) | −1043.31 | − | 1165.80i | −0.803698 | − | 0.898059i | ||||
\(120\) | −1351.10 | + | 637.599i | −1.02782 | + | 0.485038i | ||||
\(121\) | 1330.84 | 0.999881 | ||||||||
\(122\) | 9.11900 | − | 1.35000i | 0.00676717 | − | 0.00100183i | ||||
\(123\) | 614.943i | 0.450793i | ||||||||
\(124\) | 980.781 | − | 296.902i | 0.710296 | − | 0.215021i | ||||
\(125\) | − | 1517.53i | − | 1.08585i | ||||||
\(126\) | −1207.00 | − | 1003.95i | −0.853397 | − | 0.709831i | ||||
\(127\) | 845.289i | 0.590608i | 0.955403 | + | 0.295304i | \(0.0954209\pi\) | ||||
−0.955403 | + | 0.295304i | \(0.904579\pi\) | |||||||
\(128\) | −1240.63 | − | 746.994i | −0.856694 | − | 0.515825i | ||||
\(129\) | 521.852i | 0.356174i | ||||||||
\(130\) | −274.384 | − | 1853.41i | −0.185116 | − | 1.25042i | ||||
\(131\) | −1464.88 | −0.977001 | −0.488501 | − | 0.872564i | \(-0.662456\pi\) | ||||
−0.488501 | + | 0.872564i | \(0.662456\pi\) | |||||||
\(132\) | −6.95756 | − | 22.9835i | −0.00458771 | − | 0.0151550i | ||||
\(133\) | −276.755 | + | 247.676i | −0.180434 | + | 0.161475i | ||||
\(134\) | 1543.08 | − | 228.442i | 0.994791 | − | 0.147272i | ||||
\(135\) | − | 196.133i | − | 0.125040i | ||||||
\(136\) | 1728.61 | − | 815.752i | 1.08991 | − | 0.514339i | ||||
\(137\) | 747.803 | 0.466344 | 0.233172 | − | 0.972436i | \(-0.425089\pi\) | ||||
0.233172 | + | 0.972436i | \(0.425089\pi\) | |||||||
\(138\) | −2584.52 | + | 382.619i | −1.59427 | + | 0.236020i | ||||
\(139\) | −2129.17 | −1.29924 | −0.649618 | − | 0.760261i | \(-0.725071\pi\) | ||||
−0.649618 | + | 0.760261i | \(0.725071\pi\) | |||||||
\(140\) | −1107.05 | − | 673.938i | −0.668308 | − | 0.406844i | ||||
\(141\) | −1116.51 | −0.666858 | ||||||||
\(142\) | 1360.57 | − | 201.423i | 0.804061 | − | 0.119035i | ||||
\(143\) | 30.1153 | 0.0176110 | ||||||||
\(144\) | 1596.08 | − | 1063.82i | 0.923656 | − | 0.615635i | ||||
\(145\) | 1538.03i | 0.880869i | ||||||||
\(146\) | 464.306 | − | 68.7371i | 0.263193 | − | 0.0389639i | ||||
\(147\) | 286.229 | − | 2573.05i | 0.160597 | − | 1.44369i | ||||
\(148\) | −1938.68 | + | 586.879i | −1.07675 | + | 0.325954i | ||||
\(149\) | −843.177 | −0.463596 | −0.231798 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231798 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(150\) | 151.570 | + | 1023.83i | 0.0825044 | + | 0.557302i | ||||
\(151\) | 2088.40i | 1.12551i | 0.826625 | + | 0.562753i | \(0.190258\pi\) | ||||
−0.826625 | + | 0.562753i | \(0.809742\pi\) | |||||||
\(152\) | −193.655 | − | 410.363i | −0.103339 | − | 0.218979i | ||||
\(153\) | 2531.73i | 1.33777i | ||||||||
\(154\) | 13.3216 | − | 16.0159i | 0.00697068 | − | 0.00838052i | ||||
\(155\) | 1120.49i | 0.580645i | ||||||||
\(156\) | 1324.84 | + | 4376.46i | 0.679950 | + | 2.24613i | ||||
\(157\) | − | 168.690i | − | 0.0857513i | −0.999080 | − | 0.0428756i | \(-0.986348\pi\) | ||
0.999080 | − | 0.0428756i | \(-0.0136519\pi\) | |||||||
\(158\) | 780.650 | − | 115.570i | 0.393071 | − | 0.0581913i | ||||
\(159\) | 2143.00 | 1.06888 | ||||||||
\(160\) | 1174.80 | − | 1061.71i | 0.580477 | − | 0.524599i | ||||
\(161\) | −1511.50 | − | 1688.96i | −0.739893 | − | 0.826763i | ||||
\(162\) | −265.084 | − | 1790.59i | −0.128562 | − | 0.868410i | ||||
\(163\) | − | 2882.96i | − | 1.38534i | −0.721254 | − | 0.692670i | \(-0.756434\pi\) | ||
0.721254 | − | 0.692670i | \(-0.243566\pi\) | |||||||
\(164\) | −188.843 | − | 623.821i | −0.0899156 | − | 0.297026i | ||||
\(165\) | 26.2574 | 0.0123887 | ||||||||
\(166\) | −257.717 | − | 1740.83i | −0.120498 | − | 0.813942i | ||||
\(167\) | 1988.79 | 0.921542 | 0.460771 | − | 0.887519i | \(-0.347573\pi\) | ||||
0.460771 | + | 0.887519i | \(0.347573\pi\) | |||||||
\(168\) | 2913.54 | + | 1231.36i | 1.33800 | + | 0.565486i | ||||
\(169\) | −3537.48 | −1.61014 | ||||||||
\(170\) | 306.079 | + | 2067.51i | 0.138089 | + | 0.932767i | ||||
\(171\) | 601.019 | 0.268778 | ||||||||
\(172\) | −160.256 | − | 529.386i | −0.0710429 | − | 0.234682i | ||||
\(173\) | 2516.46i | 1.10591i | 0.833210 | + | 0.552957i | \(0.186501\pi\) | ||||
−0.833210 | + | 0.552957i | \(0.813499\pi\) | |||||||
\(174\) | −549.701 | − | 3713.12i | −0.239498 | − | 1.61776i | ||||
\(175\) | −669.064 | + | 598.763i | −0.289008 | + | 0.258641i | ||||
\(176\) | 14.1160 | + | 21.1787i | 0.00604565 | + | 0.00907048i | ||||
\(177\) | 4777.14 | 2.02866 | ||||||||
\(178\) | −1949.61 | + | 288.625i | −0.820951 | + | 0.121536i | ||||
\(179\) | 2602.74i | 1.08681i | 0.839472 | + | 0.543403i | \(0.182864\pi\) | ||||
−0.839472 | + | 0.543403i | \(0.817136\pi\) | |||||||
\(180\) | 607.678 | + | 2007.39i | 0.251631 | + | 0.831234i | ||||
\(181\) | 2374.53i | 0.975125i | 0.873088 | + | 0.487562i | \(0.162114\pi\) | ||||
−0.873088 | + | 0.487562i | \(0.837886\pi\) | |||||||
\(182\) | −2536.66 | + | 3049.71i | −1.03313 | + | 1.24209i | ||||
\(183\) | − | 24.6000i | − | 0.00993707i | ||||||
\(184\) | 2504.33 | − | 1181.82i | 1.00338 | − | 0.473507i | ||||
\(185\) | − | 2214.85i | − | 0.880209i | ||||||
\(186\) | −400.471 | − | 2705.10i | −0.157871 | − | 1.06639i | ||||
\(187\) | −33.5941 | −0.0131371 | ||||||||
\(188\) | 1132.63 | − | 342.869i | 0.439390 | − | 0.133012i | ||||
\(189\) | −309.433 | + | 276.920i | −0.119090 | + | 0.106577i | ||||
\(190\) | 490.814 | − | 72.6615i | 0.187407 | − | 0.0277443i | ||||
\(191\) | 322.049i | 0.122004i | 0.998138 | + | 0.0610018i | \(0.0194295\pi\) | ||||
−0.998138 | + | 0.0610018i | \(0.980570\pi\) | |||||||
\(192\) | −2456.76 | + | 2983.09i | −0.923446 | + | 1.12128i | ||||
\(193\) | −3949.91 | −1.47316 | −0.736582 | − | 0.676349i | \(-0.763561\pi\) | ||||
−0.736582 | + | 0.676349i | \(0.763561\pi\) | |||||||
\(194\) | 4541.08 | − | 672.274i | 1.68057 | − | 0.248796i | ||||
\(195\) | −4999.87 | −1.83615 | ||||||||
\(196\) | 499.798 | + | 2698.10i | 0.182142 | + | 0.983272i | ||||
\(197\) | 2712.37 | 0.980957 | 0.490478 | − | 0.871453i | \(-0.336822\pi\) | ||||
0.490478 | + | 0.871453i | \(0.336822\pi\) | |||||||
\(198\) | −33.3482 | + | 4.93696i | −0.0119695 | + | 0.00177199i | ||||
\(199\) | −2828.98 | −1.00774 | −0.503872 | − | 0.863779i | \(-0.668092\pi\) | ||||
−0.503872 | + | 0.863779i | \(0.668092\pi\) | |||||||
\(200\) | −468.167 | − | 992.064i | −0.165522 | − | 0.350748i | ||||
\(201\) | − | 4162.72i | − | 1.46077i | ||||||
\(202\) | −2167.00 | + | 320.809i | −0.754800 | + | 0.111743i | ||||
\(203\) | 2426.50 | − | 2171.54i | 0.838949 | − | 0.750798i | ||||
\(204\) | −1477.88 | − | 4882.00i | −0.507217 | − | 1.67553i | ||||
\(205\) | 712.683 | 0.242809 | ||||||||
\(206\) | −11.9535 | − | 80.7439i | −0.00404293 | − | 0.0273092i | ||||
\(207\) | 3667.85i | 1.23156i | ||||||||
\(208\) | −2687.94 | − | 4032.79i | −0.896033 | − | 1.34435i | ||||
\(209\) | 7.97505i | 0.00263945i | ||||||||
\(210\) | −2211.71 | + | 2659.03i | −0.726773 | + | 0.873766i | ||||
\(211\) | − | 4950.07i | − | 1.61506i | −0.589828 | − | 0.807529i | \(-0.700804\pi\) | ||
0.589828 | − | 0.807529i | \(-0.299196\pi\) | |||||||
\(212\) | −2173.94 | + | 658.096i | −0.704278 | + | 0.213199i | ||||
\(213\) | − | 3670.37i | − | 1.18070i | ||||||
\(214\) | −145.251 | + | 21.5033i | −0.0463978 | + | 0.00686886i | ||||
\(215\) | 604.796 | 0.191845 | ||||||||
\(216\) | −216.521 | − | 458.816i | −0.0682054 | − | 0.144530i | ||||
\(217\) | 1767.76 | − | 1582.02i | 0.553012 | − | 0.494906i | ||||
\(218\) | 54.7577 | + | 369.878i | 0.0170122 | + | 0.114914i | ||||
\(219\) | − | 1252.54i | − | 0.386479i | ||||||
\(220\) | −26.6365 | + | 8.06341i | −0.00816288 | + | 0.00247107i | ||||
\(221\) | 6396.90 | 1.94707 | ||||||||
\(222\) | 791.601 | + | 5347.11i | 0.239319 | + | 1.61655i | ||||
\(223\) | 5958.68 | 1.78934 | 0.894669 | − | 0.446729i | \(-0.147411\pi\) | ||||
0.894669 | + | 0.446729i | \(0.147411\pi\) | |||||||
\(224\) | −3333.74 | − | 354.419i | −0.994396 | − | 0.105717i | ||||
\(225\) | 1452.98 | 0.430513 | ||||||||
\(226\) | 131.740 | + | 889.879i | 0.0387753 | + | 0.261920i | ||||
\(227\) | 817.324 | 0.238977 | 0.119488 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119488 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(228\) | −1158.96 | + | 350.841i | −0.336640 | + | 0.101908i | ||||
\(229\) | 3095.86i | 0.893364i | 0.894693 | + | 0.446682i | \(0.147394\pi\) | ||||
−0.894693 | + | 0.446682i | \(0.852606\pi\) | |||||||
\(230\) | 443.433 | + | 2995.31i | 0.127127 | + | 0.858716i | ||||
\(231\) | −37.0729 | − | 41.4256i | −0.0105594 | − | 0.0117991i | ||||
\(232\) | 1697.90 | + | 3597.92i | 0.480486 | + | 1.01817i | ||||
\(233\) | −2649.92 | −0.745072 | −0.372536 | − | 0.928018i | \(-0.621512\pi\) | ||||
−0.372536 | + | 0.928018i | \(0.621512\pi\) | |||||||
\(234\) | 6350.08 | − | 940.083i | 1.77401 | − | 0.262629i | ||||
\(235\) | 1293.97i | 0.359188i | ||||||||
\(236\) | −4846.11 | + | 1467.01i | −1.33667 | + | 0.404638i | ||||
\(237\) | − | 2105.93i | − | 0.577194i | ||||||
\(238\) | 2829.69 | − | 3402.00i | 0.770678 | − | 0.926550i | ||||
\(239\) | 4292.34i | 1.16171i | 0.814007 | + | 0.580855i | \(0.197282\pi\) | ||||
−0.814007 | + | 0.580855i | \(0.802718\pi\) | |||||||
\(240\) | −2343.60 | − | 3516.18i | −0.630329 | − | 0.945702i | ||||
\(241\) | 5048.97i | 1.34951i | 0.738041 | + | 0.674756i | \(0.235751\pi\) | ||||
−0.738041 | + | 0.674756i | \(0.764249\pi\) | |||||||
\(242\) | 551.253 | + | 3723.61i | 0.146429 | + | 0.989101i | ||||
\(243\) | −5435.80 | −1.43501 | ||||||||
\(244\) | 7.55443 | + | 24.9552i | 0.00198206 | + | 0.00654750i | ||||
\(245\) | −2982.02 | − | 331.723i | −0.777609 | − | 0.0865021i | ||||
\(246\) | −1720.57 | + | 254.718i | −0.445933 | + | 0.0660171i | ||||
\(247\) | − | 1518.59i | − | 0.391196i | ||||||
\(248\) | 1236.96 | + | 2621.18i | 0.316723 | + | 0.671149i | ||||
\(249\) | −4696.17 | −1.19521 | ||||||||
\(250\) | 4245.94 | − | 628.581i | 1.07415 | − | 0.159020i | ||||
\(251\) | 478.767 | 0.120396 | 0.0601982 | − | 0.998186i | \(-0.480827\pi\) | ||||
0.0601982 | + | 0.998186i | \(0.480827\pi\) | |||||||
\(252\) | 2309.02 | − | 3792.95i | 0.577201 | − | 0.948148i | ||||
\(253\) | −48.6696 | −0.0120942 | ||||||||
\(254\) | −2365.06 | + | 350.130i | −0.584241 | + | 0.0864926i | ||||
\(255\) | 5577.44 | 1.36970 | ||||||||
\(256\) | 1576.15 | − | 3780.60i | 0.384803 | − | 0.922999i | ||||
\(257\) | − | 2082.43i | − | 0.505442i | −0.967539 | − | 0.252721i | \(-0.918674\pi\) | ||
0.967539 | − | 0.252721i | \(-0.0813255\pi\) | |||||||
\(258\) | −1460.11 | + | 216.158i | −0.352334 | + | 0.0521605i | ||||
\(259\) | −3494.30 | + | 3127.14i | −0.838320 | + | 0.750236i | ||||
\(260\) | 5072.06 | − | 1535.41i | 1.20983 | − | 0.366240i | ||||
\(261\) | −5269.53 | −1.24971 | ||||||||
\(262\) | −606.773 | − | 4098.64i | −0.143079 | − | 0.966468i | ||||
\(263\) | − | 4105.49i | − | 0.962568i | −0.876565 | − | 0.481284i | \(-0.840171\pi\) | ||
0.876565 | − | 0.481284i | \(-0.159829\pi\) | |||||||
\(264\) | 61.4243 | − | 28.9869i | 0.0143197 | − | 0.00675764i | ||||
\(265\) | − | 2483.61i | − | 0.575725i | ||||||
\(266\) | −807.616 | − | 671.752i | −0.186158 | − | 0.154841i | ||||
\(267\) | 5259.39i | 1.20550i | ||||||||
\(268\) | 1278.33 | + | 4222.82i | 0.291368 | + | 0.962498i | ||||
\(269\) | 6020.46i | 1.36459i | 0.731078 | + | 0.682294i | \(0.239017\pi\) | ||||
−0.731078 | + | 0.682294i | \(0.760983\pi\) | |||||||
\(270\) | 548.767 | − | 81.2410i | 0.123692 | − | 0.0183117i | ||||
\(271\) | 108.476 | 0.0243153 | 0.0121577 | − | 0.999926i | \(-0.496130\pi\) | ||||
0.0121577 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(272\) | 2998.43 | + | 4498.64i | 0.668407 | + | 1.00283i | ||||
\(273\) | 7059.32 | + | 7888.15i | 1.56502 | + | 1.74876i | ||||
\(274\) | 309.750 | + | 2092.30i | 0.0682945 | + | 0.461316i | ||||
\(275\) | 19.2799i | 0.00422772i | ||||||||
\(276\) | −2141.09 | − | 7072.82i | −0.466950 | − | 1.54251i | ||||
\(277\) | −1079.19 | −0.234088 | −0.117044 | − | 0.993127i | \(-0.537342\pi\) | ||||
−0.117044 | + | 0.993127i | \(0.537342\pi\) | |||||||
\(278\) | −881.931 | − | 5957.27i | −0.190269 | − | 1.28523i | ||||
\(279\) | −3838.98 | −0.823778 | ||||||||
\(280\) | 1427.08 | − | 3376.62i | 0.304586 | − | 0.720684i | ||||
\(281\) | 482.626 | 0.102459 | 0.0512296 | − | 0.998687i | \(-0.483686\pi\) | ||||
0.0512296 | + | 0.998687i | \(0.483686\pi\) | |||||||
\(282\) | −462.473 | − | 3123.91i | −0.0976590 | − | 0.659668i | ||||
\(283\) | −2476.45 | −0.520175 | −0.260088 | − | 0.965585i | \(-0.583751\pi\) | ||||
−0.260088 | + | 0.965585i | \(0.583751\pi\) | |||||||
\(284\) | 1127.14 | + | 3723.36i | 0.235504 | + | 0.777960i | ||||
\(285\) | − | 1324.05i | − | 0.275193i | ||||||
\(286\) | 12.4742 | + | 84.2606i | 0.00257907 | + | 0.0174211i | ||||
\(287\) | −1006.24 | − | 1124.38i | −0.206956 | − | 0.231254i | ||||
\(288\) | 3637.60 | + | 4025.07i | 0.744264 | + | 0.823540i | ||||
\(289\) | −2222.84 | −0.452440 | ||||||||
\(290\) | −4303.29 | + | 637.071i | −0.871372 | + | 0.129000i | ||||
\(291\) | − | 12250.3i | − | 2.46779i | ||||||
\(292\) | 384.644 | + | 1270.63i | 0.0770876 | + | 0.254650i | ||||
\(293\) | − | 4641.77i | − | 0.925513i | −0.886485 | − | 0.462757i | \(-0.846860\pi\) | ||
0.886485 | − | 0.462757i | \(-0.153140\pi\) | |||||||
\(294\) | 7317.79 | − | 264.943i | 1.45164 | − | 0.0525572i | ||||
\(295\) | − | 5536.43i | − | 1.09269i | ||||||
\(296\) | −2445.08 | − | 5181.22i | −0.480126 | − | 1.01741i | ||||
\(297\) | 8.91670i | 0.00174209i | ||||||||
\(298\) | −349.256 | − | 2359.15i | −0.0678921 | − | 0.458598i | ||||
\(299\) | 9267.53 | 1.79249 | ||||||||
\(300\) | −2801.82 | + | 848.167i | −0.539211 | + | 0.163230i | ||||
\(301\) | −853.911 | − | 954.168i | −0.163517 | − | 0.182715i | ||||
\(302\) | −5843.20 | + | 865.043i | −1.11337 | + | 0.164827i | ||||
\(303\) | 5845.84i | 1.10837i | ||||||||
\(304\) | 1067.95 | − | 711.811i | 0.201485 | − | 0.134293i | ||||
\(305\) | −28.5100 | −0.00535238 | ||||||||
\(306\) | −7083.61 | + | 1048.68i | −1.32334 | + | 0.195911i | ||||
\(307\) | 1544.80 | 0.287187 | 0.143594 | − | 0.989637i | \(-0.454134\pi\) | ||||
0.143594 | + | 0.989637i | \(0.454134\pi\) | |||||||
\(308\) | 50.3295 | + | 30.6389i | 0.00931100 | + | 0.00566823i | ||||
\(309\) | −217.820 | −0.0401014 | ||||||||
\(310\) | −3135.06 | + | 464.123i | −0.574385 | + | 0.0850335i | ||||
\(311\) | −8897.39 | −1.62227 | −0.811133 | − | 0.584862i | \(-0.801149\pi\) | ||||
−0.811133 | + | 0.584862i | \(0.801149\pi\) | |||||||
\(312\) | −11696.3 | + | 5519.60i | −2.12234 | + | 1.00156i | ||||
\(313\) | 1960.82i | 0.354096i | 0.984202 | + | 0.177048i | \(0.0566548\pi\) | ||||
−0.984202 | + | 0.177048i | \(0.943345\pi\) | |||||||
\(314\) | 471.984 | − | 69.8738i | 0.0848268 | − | 0.0125580i | ||||
\(315\) | 3237.97 | + | 3618.13i | 0.579171 | + | 0.647171i | ||||
\(316\) | 646.712 | + | 2136.34i | 0.115128 | + | 0.380311i | ||||
\(317\) | −4234.84 | −0.750322 | −0.375161 | − | 0.926960i | \(-0.622413\pi\) | ||||
−0.375161 | + | 0.926960i | \(0.622413\pi\) | |||||||
\(318\) | 887.661 | + | 5995.98i | 0.156533 | + | 1.05735i | ||||
\(319\) | − | 69.9225i | − | 0.0122724i | ||||||
\(320\) | 3457.22 | + | 2847.25i | 0.603952 | + | 0.497393i | ||||
\(321\) | 391.838i | 0.0681316i | ||||||||
\(322\) | 4099.52 | − | 4928.66i | 0.709495 | − | 0.852993i | ||||
\(323\) | 1694.01i | 0.291818i | ||||||||
\(324\) | 4900.16 | − | 1483.38i | 0.840220 | − | 0.254351i | ||||
\(325\) | − | 3671.23i | − | 0.626594i | ||||||
\(326\) | 8066.32 | − | 1194.16i | 1.37040 | − | 0.202878i | ||||
\(327\) | 997.806 | 0.168743 | ||||||||
\(328\) | 1667.19 | − | 786.765i | 0.280656 | − | 0.132445i | ||||
\(329\) | 2041.45 | − | 1826.95i | 0.342094 | − | 0.306149i | ||||
\(330\) | 10.8762 | + | 73.4665i | 0.00181429 | + | 0.0122551i | ||||
\(331\) | 9859.53i | 1.63725i | 0.574330 | + | 0.818624i | \(0.305262\pi\) | ||||
−0.574330 | + | 0.818624i | \(0.694738\pi\) | |||||||
\(332\) | 4763.97 | − | 1442.15i | 0.787520 | − | 0.238398i | ||||
\(333\) | 7588.43 | 1.24878 | ||||||||
\(334\) | 823.786 | + | 5564.51i | 0.134957 | + | 0.911607i | ||||
\(335\) | −4824.35 | −0.786813 | ||||||||
\(336\) | −2238.44 | + | 8661.92i | −0.363443 | + | 1.40639i | ||||
\(337\) | 6869.41 | 1.11039 | 0.555194 | − | 0.831721i | \(-0.312644\pi\) | ||||
0.555194 | + | 0.831721i | \(0.312644\pi\) | |||||||
\(338\) | −1465.27 | − | 9897.62i | −0.235800 | − | 1.59278i | ||||
\(339\) | 2400.60 | 0.384609 | ||||||||
\(340\) | −5657.96 | + | 1712.78i | −0.902488 | + | 0.273201i | ||||
\(341\) | − | 50.9403i | − | 0.00808966i | ||||||
\(342\) | 248.950 | + | 1681.61i | 0.0393616 | + | 0.265880i | ||||
\(343\) | 3686.96 | + | 5173.00i | 0.580400 | + | 0.814332i | ||||
\(344\) | 1414.81 | − | 667.663i | 0.221748 | − | 0.104645i | ||||
\(345\) | 8080.33 | 1.26096 | ||||||||
\(346\) | −7040.90 | + | 1042.35i | −1.09399 | + | 0.161957i | ||||
\(347\) | 257.299i | 0.0398055i | 0.999802 | + | 0.0199028i | \(0.00633567\pi\) | ||||
−0.999802 | + | 0.0199028i | \(0.993664\pi\) | |||||||
\(348\) | 10161.4 | − | 3076.05i | 1.56525 | − | 0.473832i | ||||
\(349\) | 2840.72i | 0.435703i | 0.975982 | + | 0.217851i | \(0.0699048\pi\) | ||||
−0.975982 | + | 0.217851i | \(0.930095\pi\) | |||||||
\(350\) | −1952.44 | − | 1623.98i | −0.298177 | − | 0.248015i | ||||
\(351\) | − | 1697.90i | − | 0.258196i | ||||||
\(352\) | −53.4095 | + | 48.2682i | −0.00808732 | + | 0.00730881i | ||||
\(353\) | − | 11322.4i | − | 1.70717i | −0.520953 | − | 0.853585i | \(-0.674423\pi\) | ||
0.520953 | − | 0.853585i | \(-0.325577\pi\) | |||||||
\(354\) | 1978.76 | + | 13366.1i | 0.297090 | + | 2.00678i | ||||
\(355\) | −4253.74 | −0.635959 | ||||||||
\(356\) | −1615.11 | − | 5335.32i | −0.240451 | − | 0.794301i | ||||
\(357\) | −7874.78 | − | 8799.35i | −1.16744 | − | 1.30451i | ||||
\(358\) | −7282.30 | + | 1078.09i | −1.07509 | + | 0.159159i | ||||
\(359\) | − | 5421.36i | − | 0.797014i | −0.917165 | − | 0.398507i | \(-0.869528\pi\) | ||
0.917165 | − | 0.398507i | \(-0.130472\pi\) | |||||||
\(360\) | −5364.84 | + | 2531.73i | −0.785422 | + | 0.370650i | ||||
\(361\) | −6456.85 | −0.941369 | ||||||||
\(362\) | −6643.78 | + | 983.563i | −0.964611 | + | 0.142804i | ||||
\(363\) | 10045.0 | 1.45242 | ||||||||
\(364\) | −9583.61 | − | 5834.18i | −1.37999 | − | 0.840094i | ||||
\(365\) | −1451.62 | −0.208168 | ||||||||
\(366\) | 68.8291 | − | 10.1897i | 0.00982994 | − | 0.00145525i | ||||
\(367\) | 10941.3 | 1.55622 | 0.778109 | − | 0.628129i | \(-0.216179\pi\) | ||||
0.778109 | + | 0.628129i | \(0.216179\pi\) | |||||||
\(368\) | 4343.99 | + | 6517.43i | 0.615343 | + | 0.923218i | ||||
\(369\) | 2441.77i | 0.344481i | ||||||||
\(370\) | 6196.99 | − | 917.419i | 0.870719 | − | 0.128904i | ||||
\(371\) | −3918.32 | + | 3506.61i | −0.548327 | + | 0.490713i | ||||
\(372\) | 7402.82 | − | 2240.98i | 1.03177 | − | 0.312337i | ||||
\(373\) | 389.936 | 0.0541290 | 0.0270645 | − | 0.999634i | \(-0.491384\pi\) | ||||
0.0270645 | + | 0.999634i | \(0.491384\pi\) | |||||||
\(374\) | −13.9151 | − | 93.9940i | −0.00192389 | − | 0.0129955i | ||||
\(375\) | − | 11454.1i | − | 1.57730i | ||||||
\(376\) | 1428.47 | + | 3026.99i | 0.195925 | + | 0.415174i | ||||
\(377\) | 13314.5i | 1.81891i | ||||||||
\(378\) | −902.975 | − | 751.069i | −0.122868 | − | 0.102198i | ||||
\(379\) | − | 12927.3i | − | 1.75207i | −0.482252 | − | 0.876033i | \(-0.660181\pi\) | ||
0.482252 | − | 0.876033i | \(-0.339819\pi\) | |||||||
\(380\) | 406.604 | + | 1343.17i | 0.0548903 | + | 0.181324i | ||||
\(381\) | 6380.14i | 0.857912i | ||||||||
\(382\) | −901.072 | + | 133.397i | −0.120688 | + | 0.0178670i | ||||
\(383\) | −12981.5 | −1.73192 | −0.865960 | − | 0.500113i | \(-0.833292\pi\) | ||||
−0.865960 | + | 0.500113i | \(0.833292\pi\) | |||||||
\(384\) | −9364.10 | − | 5638.22i | −1.24443 | − | 0.749282i | ||||
\(385\) | −48.0098 | + | 42.9653i | −0.00635534 | + | 0.00568757i | ||||
\(386\) | −1636.11 | − | 11051.6i | −0.215740 | − | 1.45728i | ||||
\(387\) | 2072.13i | 0.272176i | ||||||||
\(388\) | 3761.96 | + | 12427.2i | 0.492228 | + | 1.62602i | ||||
\(389\) | 12562.9 | 1.63745 | 0.818723 | − | 0.574188i | \(-0.194682\pi\) | ||||
0.818723 | + | 0.574188i | \(0.194682\pi\) | |||||||
\(390\) | −2071.02 | − | 13989.3i | −0.268897 | − | 1.81635i | ||||
\(391\) | −10338.1 | −1.33713 | ||||||||
\(392\) | −7342.08 | + | 2515.99i | −0.945997 | + | 0.324175i | ||||
\(393\) | −11056.7 | −1.41918 | ||||||||
\(394\) | 1123.50 | + | 7589.03i | 0.143658 | + | 0.970381i | ||||
\(395\) | −2440.65 | −0.310893 | ||||||||
\(396\) | −27.6266 | − | 91.2611i | −0.00350577 | − | 0.0115809i | ||||
\(397\) | − | 5874.41i | − | 0.742640i | −0.928505 | − | 0.371320i | \(-0.878905\pi\) | ||
0.928505 | − | 0.371320i | \(-0.121095\pi\) | |||||||
\(398\) | −1171.80 | − | 7915.29i | −0.147581 | − | 0.996878i | ||||
\(399\) | −2088.92 | + | 1869.43i | −0.262097 | + | 0.234558i | ||||
\(400\) | 2581.81 | − | 1720.82i | 0.322726 | − | 0.215103i | ||||
\(401\) | 4771.54 | 0.594213 | 0.297106 | − | 0.954844i | \(-0.403978\pi\) | ||||
0.297106 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(402\) | 11647.0 | − | 1724.25i | 1.44502 | − | 0.213925i | ||||
\(403\) | 9699.93i | 1.19898i | ||||||||
\(404\) | −1795.20 | − | 5930.24i | −0.221076 | − | 0.730298i | ||||
\(405\) | 5598.18i | 0.686854i | ||||||||
\(406\) | 7080.90 | + | 5889.69i | 0.865565 | + | 0.719952i | ||||
\(407\) | 100.692i | 0.0122632i | ||||||||
\(408\) | 13047.4 | − | 6157.20i | 1.58319 | − | 0.747125i | ||||
\(409\) | − | 2248.81i | − | 0.271874i | −0.990718 | − | 0.135937i | \(-0.956596\pi\) | ||
0.990718 | − | 0.135937i | \(-0.0434044\pi\) | |||||||
\(410\) | 295.203 | + | 1994.04i | 0.0355586 | + | 0.240192i | ||||
\(411\) | 5644.33 | 0.677407 | ||||||||
\(412\) | 220.965 | − | 66.8904i | 0.0264227 | − | 0.00799868i | ||||
\(413\) | −8734.66 | + | 7816.88i | −1.04069 | + | 0.931340i | ||||
\(414\) | −10262.4 | + | 1519.28i | −1.21828 | + | 0.180358i | ||||
\(415\) | 5442.58i | 0.643773i | ||||||||
\(416\) | 10170.1 | − | 9191.10i | 1.19863 | − | 1.08325i | ||||
\(417\) | −16070.7 | −1.88726 | ||||||||
\(418\) | −22.3136 | + | 3.30337i | −0.00261099 | + | 0.000386539i | ||||
\(419\) | 10323.4 | 1.20366 | 0.601829 | − | 0.798625i | \(-0.294439\pi\) | ||||
0.601829 | + | 0.798625i | \(0.294439\pi\) | |||||||
\(420\) | −8355.92 | − | 5086.80i | −0.970779 | − | 0.590978i | ||||
\(421\) | 3245.09 | 0.375668 | 0.187834 | − | 0.982201i | \(-0.439853\pi\) | ||||
0.187834 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(422\) | 13850.0 | − | 2050.39i | 1.59765 | − | 0.236520i | ||||
\(423\) | −4433.34 | −0.509590 | ||||||||
\(424\) | −2741.78 | − | 5809.95i | −0.314040 | − | 0.665462i | ||||
\(425\) | 4095.31i | 0.467416i | ||||||||
\(426\) | 10269.4 | − | 1520.32i | 1.16797 | − | 0.172910i | ||||
\(427\) | 40.2532 | + | 44.9793i | 0.00456204 | + | 0.00509766i | ||||
\(428\) | −120.330 | − | 397.495i | −0.0135896 | − | 0.0448916i | ||||
\(429\) | 227.307 | 0.0255815 | ||||||||
\(430\) | 250.515 | + | 1692.18i | 0.0280951 | + | 0.189777i | ||||
\(431\) | − | 9556.09i | − | 1.06798i | −0.845490 | − | 0.533992i | \(-0.820691\pi\) | ||
0.845490 | − | 0.533992i | \(-0.179309\pi\) | |||||||
\(432\) | 1194.05 | − | 795.859i | 0.132983 | − | 0.0886360i | ||||
\(433\) | − | 5658.90i | − | 0.628058i | −0.949413 | − | 0.314029i | \(-0.898321\pi\) | ||
0.949413 | − | 0.314029i | \(-0.101679\pi\) | |||||||
\(434\) | 5158.62 | + | 4290.79i | 0.570557 | + | 0.474573i | ||||
\(435\) | 11608.8i | 1.27954i | ||||||||
\(436\) | −1012.21 | + | 306.417i | −0.111184 | + | 0.0336576i | ||||
\(437\) | 2454.20i | 0.268651i | ||||||||
\(438\) | 3504.53 | − | 518.820i | 0.382312 | − | 0.0565986i | ||||
\(439\) | 3329.73 | 0.362003 | 0.181001 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181001 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(440\) | −33.5941 | − | 71.1872i | −0.00363985 | − | 0.00771299i | ||||
\(441\) | 1136.54 | − | 10216.9i | 0.122723 | − | 1.10322i | ||||
\(442\) | 2649.68 | + | 17898.1i | 0.285141 | + | 1.92608i | ||||
\(443\) | 6566.55i | 0.704257i | 0.935952 | + | 0.352129i | \(0.114542\pi\) | ||||
−0.935952 | + | 0.352129i | \(0.885458\pi\) | |||||||
\(444\) | −14633.0 | + | 4429.69i | −1.56408 | + | 0.473477i | ||||
\(445\) | 6095.32 | 0.649317 | ||||||||
\(446\) | 2468.16 | + | 16672.0i | 0.262043 | + | 1.77005i | ||||
\(447\) | −6364.21 | −0.673415 | ||||||||
\(448\) | −389.238 | − | 9474.38i | −0.0410486 | − | 0.999157i | ||||
\(449\) | −15156.4 | −1.59304 | −0.796518 | − | 0.604615i | \(-0.793327\pi\) | ||||
−0.796518 | + | 0.604615i | \(0.793327\pi\) | |||||||
\(450\) | 601.844 | + | 4065.34i | 0.0630471 | + | 0.425871i | ||||
\(451\) | −32.4003 | −0.00338287 | ||||||||
\(452\) | −2435.25 | + | 737.200i | −0.253417 | + | 0.0767145i | ||||
\(453\) | 15763.0i | 1.63490i | ||||||||
\(454\) | 338.547 | + | 2286.82i | 0.0349973 | + | 0.236400i | ||||
\(455\) | 9141.90 | − | 8181.34i | 0.941932 | − | 0.842961i | ||||
\(456\) | −1461.69 | − | 3097.37i | −0.150109 | − | 0.318087i | ||||
\(457\) | 16572.9 | 1.69638 | 0.848191 | − | 0.529690i | \(-0.177692\pi\) | ||||
0.848191 | + | 0.529690i | \(0.177692\pi\) | |||||||
\(458\) | −8662.02 | + | 1282.35i | −0.883732 | + | 0.130830i | ||||
\(459\) | 1894.03i | 0.192605i | ||||||||
\(460\) | −8196.99 | + | 2481.39i | −0.830840 | + | 0.251512i | ||||
\(461\) | − | 5823.47i | − | 0.588343i | −0.955753 | − | 0.294171i | \(-0.904956\pi\) | ||
0.955753 | − | 0.294171i | \(-0.0950436\pi\) | |||||||
\(462\) | 100.550 | − | 120.886i | 0.0101255 | − | 0.0121735i | ||||
\(463\) | − | 12952.0i | − | 1.30007i | −0.759906 | − | 0.650033i | \(-0.774755\pi\) | ||
0.759906 | − | 0.650033i | \(-0.225245\pi\) | |||||||
\(464\) | −9363.44 | + | 6240.92i | −0.936825 | + | 0.624412i | ||||
\(465\) | 8457.34i | 0.843440i | ||||||||
\(466\) | −1097.63 | − | 7414.29i | −0.109113 | − | 0.737039i | ||||
\(467\) | 7199.70 | 0.713410 | 0.356705 | − | 0.934217i | \(-0.383900\pi\) | ||||
0.356705 | + | 0.934217i | \(0.383900\pi\) | |||||||
\(468\) | 5260.58 | + | 17377.7i | 0.519595 | + | 1.71642i | ||||
\(469\) | 6811.50 | + | 7611.23i | 0.670630 | + | 0.749369i | ||||
\(470\) | −3620.43 | + | 535.979i | −0.355315 | + | 0.0526018i | ||||
\(471\) | − | 1273.25i | − | 0.124562i | ||||||
\(472\) | −6111.93 | − | 12951.4i | −0.596027 | − | 1.26300i | ||||
\(473\) | −27.4955 | −0.00267282 | ||||||||
\(474\) | 5892.26 | − | 872.306i | 0.570971 | − | 0.0845281i | ||||
\(475\) | 972.205 | 0.0939112 | ||||||||
\(476\) | 10690.7 | + | 6508.12i | 1.02942 | + | 0.626679i | ||||
\(477\) | 8509.27 | 0.816798 | ||||||||
\(478\) | −12009.7 | + | 1777.95i | −1.14918 | + | 0.170128i | ||||
\(479\) | 10505.0 | 1.00205 | 0.501027 | − | 0.865431i | \(-0.332956\pi\) | ||||
0.501027 | + | 0.865431i | \(0.332956\pi\) | |||||||
\(480\) | 8867.28 | − | 8013.69i | 0.843196 | − | 0.762028i | ||||
\(481\) | − | 19173.6i | − | 1.81755i | ||||||
\(482\) | −14126.7 | + | 2091.35i | −1.33496 | + | 0.197632i | ||||
\(483\) | −11408.6 | − | 12748.1i | −1.07476 | − | 1.20095i | ||||
\(484\) | −10190.1 | + | 3084.74i | −0.956993 | + | 0.289701i | ||||
\(485\) | −14197.4 | −1.32922 | ||||||||
\(486\) | −2251.58 | − | 15209.0i | −0.210152 | − | 1.41954i | ||||
\(487\) | 14612.5i | 1.35966i | 0.733369 | + | 0.679831i | \(0.237947\pi\) | ||||
−0.733369 | + | 0.679831i | \(0.762053\pi\) | |||||||
\(488\) | −66.6937 | + | 31.4735i | −0.00618664 | + | 0.00291955i | ||||
\(489\) | − | 21760.2i | − | 2.01233i | ||||||
\(490\) | −307.054 | − | 8480.89i | −0.0283087 | − | 0.781893i | ||||
\(491\) | 16952.7i | 1.55818i | 0.626913 | + | 0.779089i | \(0.284318\pi\) | ||||
−0.626913 | + | 0.779089i | \(0.715682\pi\) | |||||||
\(492\) | −1425.37 | − | 4708.53i | −0.130611 | − | 0.431457i | ||||
\(493\) | − | 14852.5i | − | 1.35684i | ||||||
\(494\) | 4248.91 | − | 629.020i | 0.386978 | − | 0.0572893i | ||||
\(495\) | 104.261 | 0.00946704 | ||||||||
\(496\) | −6821.51 | + | 4546.67i | −0.617530 | + | 0.411596i | ||||
\(497\) | 6005.86 | + | 6711.00i | 0.542051 | + | 0.605693i | ||||
\(498\) | −1945.22 | − | 13139.6i | −0.175035 | − | 1.18232i | ||||
\(499\) | − | 17687.3i | − | 1.58676i | −0.608727 | − | 0.793379i | \(-0.708320\pi\) | ||
0.608727 | − | 0.793379i | \(-0.291680\pi\) | |||||||
\(500\) | 3517.45 | + | 11619.5i | 0.314611 | + | 1.03928i | ||||
\(501\) | 15011.2 | 1.33862 | ||||||||
\(502\) | 198.312 | + | 1339.56i | 0.0176316 | + | 0.119098i | ||||
\(503\) | −14327.9 | −1.27008 | −0.635038 | − | 0.772481i | \(-0.719016\pi\) | ||||
−0.635038 | + | 0.772481i | \(0.719016\pi\) | |||||||
\(504\) | 11568.8 | + | 4889.39i | 1.02246 | + | 0.432125i | ||||
\(505\) | 6774.99 | 0.596996 | ||||||||
\(506\) | −20.1596 | − | 136.174i | −0.00177115 | − | 0.0119638i | ||||
\(507\) | −26700.5 | −2.33888 | ||||||||
\(508\) | −1959.28 | − | 6472.25i | −0.171120 | − | 0.565275i | ||||
\(509\) | − | 16759.3i | − | 1.45941i | −0.683759 | − | 0.729707i | \(-0.739656\pi\) | ||
0.683759 | − | 0.729707i | \(-0.260344\pi\) | |||||||
\(510\) | 2310.25 | + | 15605.3i | 0.200587 | + | 1.35493i | ||||
\(511\) | 2049.55 | + | 2290.18i | 0.177430 | + | 0.198262i | ||||
\(512\) | 11230.7 | + | 2844.00i | 0.969400 | + | 0.245485i | ||||
\(513\) | 449.632 | 0.0386973 | ||||||||
\(514\) | 5826.51 | − | 862.572i | 0.499993 | − | 0.0740203i | ||||
\(515\) | 252.441i | 0.0215997i | ||||||||
\(516\) | −1209.59 | − | 3995.74i | −0.103196 | − | 0.340897i | ||||
\(517\) | − | 58.8270i | − | 0.00500427i | ||||||
\(518\) | −10196.9 | − | 8481.50i | −0.864916 | − | 0.719413i | ||||
\(519\) | 18994.0i | 1.60644i | ||||||||
\(520\) | 6396.90 | + | 13555.3i | 0.539466 | + | 1.14315i | ||||
\(521\) | 18219.8i | 1.53210i | 0.642783 | + | 0.766049i | \(0.277780\pi\) | ||||
−0.642783 | + | 0.766049i | \(0.722220\pi\) | |||||||
\(522\) | −2182.71 | − | 14743.8i | −0.183016 | − | 1.23624i | ||||
\(523\) | 8500.33 | 0.710695 | 0.355348 | − | 0.934734i | \(-0.384362\pi\) | ||||
0.355348 | + | 0.934734i | \(0.384362\pi\) | |||||||
\(524\) | 11216.4 | − | 3395.42i | 0.935094 | − | 0.283072i | ||||
\(525\) | −5050.02 | + | 4519.40i | −0.419811 | + | 0.375700i | ||||
\(526\) | 11486.9 | − | 1700.55i | 0.952190 | − | 0.140965i | ||||
\(527\) | − | 10820.4i | − | 0.894392i | ||||||
\(528\) | 106.546 | + | 159.854i | 0.00878186 | + | 0.0131757i | ||||
\(529\) | −2810.33 | −0.230980 | ||||||||
\(530\) | 6948.99 | − | 1028.75i | 0.569518 | − | 0.0843130i | ||||
\(531\) | 18968.7 | 1.55023 | ||||||||
\(532\) | 1544.99 | − | 2537.90i | 0.125910 | − | 0.206827i | ||||
\(533\) | 6169.59 | 0.501378 | ||||||||
\(534\) | −14715.4 | + | 2178.51i | −1.19251 | + | 0.176542i | ||||
\(535\) | 454.117 | 0.0366975 | ||||||||
\(536\) | −11285.7 | + | 5325.83i | −0.909452 | + | 0.429181i | ||||
\(537\) | 19645.2i | 1.57868i | ||||||||
\(538\) | −16844.8 | + | 2493.76i | −1.34988 | + | 0.199839i | ||||
\(539\) | 135.570 | + | 15.0810i | 0.0108338 | + | 0.00120516i | ||||
\(540\) | 454.614 | + | 1501.76i | 0.0362286 | + | 0.119677i | ||||
\(541\) | −18444.5 | −1.46579 | −0.732895 | − | 0.680342i | \(-0.761831\pi\) | ||||
−0.732895 | + | 0.680342i | \(0.761831\pi\) | |||||||
\(542\) | 44.9323 | + | 303.509i | 0.00356090 | + | 0.0240532i | ||||
\(543\) | 17922.7i | 1.41646i | ||||||||
\(544\) | −11344.9 | + | 10252.8i | −0.894134 | + | 0.808062i | ||||
\(545\) | − | 1156.40i | − | 0.0908894i | ||||||
\(546\) | −19146.4 | + | 23018.9i | −1.50072 | + | 1.80424i | ||||
\(547\) | − | 16381.3i | − | 1.28046i | −0.768182 | − | 0.640232i | \(-0.778838\pi\) | ||
0.768182 | − | 0.640232i | \(-0.221162\pi\) | |||||||
\(548\) | −5725.82 | + | 1733.32i | −0.446341 | + | 0.135116i | ||||
\(549\) | − | 97.6798i | − | 0.00759357i | ||||||
\(550\) | −53.9439 | + | 7.98600i | −0.00418214 | + | 0.000619135i | ||||
\(551\) | −3525.90 | −0.272610 | ||||||||
\(552\) | 18902.4 | − | 8920.27i | 1.45750 | − | 0.687812i | ||||
\(553\) | 3445.96 | + | 3850.54i | 0.264985 | + | 0.296097i | ||||
\(554\) | −447.015 | − | 3019.50i | −0.0342813 | − | 0.231564i | ||||
\(555\) | − | 16717.4i | − | 1.27858i | ||||||
\(556\) | 16302.7 | − | 4935.17i | 1.24351 | − | 0.376435i | ||||
\(557\) | −22097.0 | −1.68094 | −0.840468 | − | 0.541862i | \(-0.817720\pi\) | ||||
−0.840468 | + | 0.541862i | \(0.817720\pi\) | |||||||
\(558\) | −1590.16 | − | 10741.2i | −0.120639 | − | 0.814896i | ||||
\(559\) | 5235.63 | 0.396142 | ||||||||
\(560\) | 10038.7 | + | 2594.22i | 0.757520 | + | 0.195760i | ||||
\(561\) | −253.564 | −0.0190829 | ||||||||
\(562\) | 199.910 | + | 1350.35i | 0.0150048 | + | 0.101355i | ||||
\(563\) | 22890.4 | 1.71353 | 0.856764 | − | 0.515709i | \(-0.172472\pi\) | ||||
0.856764 | + | 0.515709i | \(0.172472\pi\) | |||||||
\(564\) | 8548.94 | − | 2587.94i | 0.638254 | − | 0.193212i | ||||
\(565\) | − | 2782.15i | − | 0.207161i | ||||||
\(566\) | −1025.78 | − | 6928.94i | −0.0761779 | − | 0.514567i | ||||
\(567\) | 8832.08 | − | 7904.07i | 0.654167 | − | 0.585431i | ||||
\(568\) | −9950.83 | + | 4695.91i | −0.735084 | + | 0.346895i | ||||
\(569\) | 11664.1 | 0.859375 | 0.429688 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429688 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(570\) | 3704.61 | − | 548.440i | 0.272226 | − | 0.0403011i | ||||
\(571\) | 11808.4i | 0.865439i | 0.901529 | + | 0.432720i | \(0.142446\pi\) | ||||
−0.901529 | + | 0.432720i | \(0.857554\pi\) | |||||||
\(572\) | −230.588 | + | 69.8037i | −0.0168556 | + | 0.00510252i | ||||
\(573\) | 2430.79i | 0.177221i | ||||||||
\(574\) | 2729.14 | − | 3281.11i | 0.198453 | − | 0.238591i | ||||
\(575\) | 5933.10i | 0.430309i | ||||||||
\(576\) | −9755.13 | + | 11845.0i | −0.705666 | + | 0.856844i | ||||
\(577\) | 14572.9i | 1.05144i | 0.850659 | + | 0.525718i | \(0.176203\pi\) | ||||
−0.850659 | + | 0.525718i | \(0.823797\pi\) | |||||||
\(578\) | −920.730 | − | 6219.35i | −0.0662583 | − | 0.447562i | ||||
\(579\) | −29813.4 | −2.13990 | ||||||||
\(580\) | −3564.96 | − | 11776.4i | −0.255219 | − | 0.843086i | ||||
\(581\) | 8586.60 | − | 7684.38i | 0.613136 | − | 0.548712i | ||||
\(582\) | 34275.6 | − | 5074.25i | 2.44118 | − | 0.361399i | ||||
\(583\) | 112.911i | 0.00802112i | ||||||||
\(584\) | −3395.80 | + | 1602.52i | −0.240615 | + | 0.113549i | ||||
\(585\) | −19853.1 | −1.40312 | ||||||||
\(586\) | 12987.4 | − | 1922.69i | 0.915535 | − | 0.135538i | ||||
\(587\) | −5506.03 | −0.387152 | −0.193576 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193576 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(588\) | 3772.42 | + | 20364.9i | 0.264578 | + | 1.42829i | ||||
\(589\) | −2568.71 | −0.179697 | ||||||||
\(590\) | 15490.6 | − | 2293.26i | 1.08091 | − | 0.160021i | ||||
\(591\) | 20472.7 | 1.42493 | ||||||||
\(592\) | 13483.9 | − | 8987.29i | 0.936124 | − | 0.623945i | ||||
\(593\) | 7223.08i | 0.500197i | 0.968220 | + | 0.250098i | \(0.0804629\pi\) | ||||
−0.968220 | + | 0.250098i | \(0.919537\pi\) | |||||||
\(594\) | −24.9483 | + | 3.69342i | −0.00172330 | + | 0.000255123i | ||||
\(595\) | −10197.9 | + | 9126.41i | −0.702646 | + | 0.628817i | ||||
\(596\) | 6456.09 | − | 1954.39i | 0.443711 | − | 0.134320i | ||||
\(597\) | −21352.8 | −1.46384 | ||||||||
\(598\) | 3838.74 | + | 25929.9i | 0.262504 | + | 1.77317i | ||||
\(599\) | 11260.6i | 0.768107i | 0.923311 | + | 0.384054i | \(0.125472\pi\) | ||||
−0.923311 | + | 0.384054i | \(0.874528\pi\) | |||||||
\(600\) | −3533.67 | − | 7487.98i | −0.240436 | − | 0.509493i | ||||
\(601\) | 25380.2i | 1.72259i | 0.508103 | + | 0.861296i | \(0.330347\pi\) | ||||
−0.508103 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(602\) | 2316.00 | − | 2784.41i | 0.156799 | − | 0.188512i | ||||
\(603\) | − | 16529.0i | − | 1.11627i | ||||||
\(604\) | −4840.67 | − | 15990.6i | −0.326099 | − | 1.07723i | ||||
\(605\) | − | 11641.6i | − | 0.782312i | ||||||
\(606\) | −16356.3 | + | 2421.43i | −1.09642 | + | 0.162316i | ||||
\(607\) | −9071.99 | −0.606624 | −0.303312 | − | 0.952891i | \(-0.598092\pi\) | ||||
−0.303312 | + | 0.952891i | \(0.598092\pi\) | |||||||
\(608\) | 2433.96 | + | 2693.22i | 0.162352 | + | 0.179645i | ||||
\(609\) | 18314.9 | − | 16390.5i | 1.21865 | − | 1.09060i | ||||
\(610\) | −11.8092 | − | 79.7690i | −0.000783838 | − | 0.00529467i | ||||
\(611\) | 11201.7i | 0.741689i | ||||||||
\(612\) | −5868.25 | − | 19385.1i | −0.387598 | − | 1.28039i | ||||
\(613\) | 10393.9 | 0.684837 | 0.342419 | − | 0.939547i | \(-0.388754\pi\) | ||||
0.342419 | + | 0.939547i | \(0.388754\pi\) | |||||||
\(614\) | 639.878 | + | 4322.25i | 0.0420576 | + | 0.284091i | ||||
\(615\) | 5379.25 | 0.352703 | ||||||||
\(616\) | −64.8784 | + | 153.510i | −0.00424355 | + | 0.0100407i | ||||
\(617\) | 16600.4 | 1.08316 | 0.541578 | − | 0.840651i | \(-0.317827\pi\) | ||||
0.541578 | + | 0.840651i | \(0.317827\pi\) | |||||||
\(618\) | −90.2240 | − | 609.445i | −0.00587272 | − | 0.0396691i | ||||
\(619\) | −25628.2 | −1.66411 | −0.832054 | − | 0.554695i | \(-0.812835\pi\) | ||||
−0.832054 | + | 0.554695i | \(0.812835\pi\) | |||||||
\(620\) | −2597.17 | − | 8579.44i | −0.168233 | − | 0.555739i | ||||
\(621\) | 2743.98i | 0.177314i | ||||||||
\(622\) | −3685.42 | − | 24894.3i | −0.237575 | − | 1.60478i | ||||
\(623\) | −8605.98 | − | 9616.41i | −0.553437 | − | 0.618416i | ||||
\(624\) | −20288.2 | − | 30439.1i | −1.30157 | − | 1.95278i | ||||
\(625\) | −7214.64 | −0.461737 | ||||||||
\(626\) | −5486.25 | + | 812.199i | −0.350279 | + | 0.0518562i | ||||
\(627\) | 60.1947i | 0.00383404i | ||||||||
\(628\) | 391.004 | + | 1291.64i | 0.0248452 | + | 0.0820731i | ||||
\(629\) | 21388.4i | 1.35582i | ||||||||
\(630\) | −8782.09 | + | 10558.3i | −0.555376 | + | 0.667702i | ||||
\(631\) | − | 6093.01i | − | 0.384404i | −0.981355 | − | 0.192202i | \(-0.938437\pi\) | ||
0.981355 | − | 0.192202i | \(-0.0615628\pi\) | |||||||
\(632\) | −5709.45 | + | 2694.36i | −0.359351 | + | 0.169582i | ||||
\(633\) | − | 37362.6i | − | 2.34602i | ||||||
\(634\) | −1754.13 | − | 11848.8i | −0.109882 | − | 0.742233i | ||||
\(635\) | 7394.21 | 0.462095 | ||||||||
\(636\) | −16408.7 | + | 4967.23i | −1.02303 | + | 0.309691i | ||||
\(637\) | −25814.9 | − | 2871.68i | −1.60569 | − | 0.178619i | ||||
\(638\) | 195.638 | − | 28.9628i | 0.0121401 | − | 0.00179726i | ||||
\(639\) | − | 14574.0i | − | 0.902253i | ||||||
\(640\) | −6534.37 | + | 10852.4i | −0.403584 | + | 0.670282i | ||||
\(641\) | −9793.98 | −0.603493 | −0.301747 | − | 0.953388i | \(-0.597570\pi\) | ||||
−0.301747 | + | 0.953388i | \(0.597570\pi\) | |||||||
\(642\) | −1096.34 | + | 162.304i | −0.0673970 | + | 0.00997764i | ||||
\(643\) | −15275.5 | −0.936868 | −0.468434 | − | 0.883499i | \(-0.655182\pi\) | ||||
−0.468434 | + | 0.883499i | \(0.655182\pi\) | |||||||
\(644\) | 15488.1 | + | 9428.66i | 0.947699 | + | 0.576928i | ||||
\(645\) | 4564.93 | 0.278673 | ||||||||
\(646\) | −4739.72 | + | 701.681i | −0.288672 | + | 0.0427357i | ||||
\(647\) | −10058.4 | −0.611184 | −0.305592 | − | 0.952163i | \(-0.598854\pi\) | ||||
−0.305592 | + | 0.952163i | \(0.598854\pi\) | |||||||
\(648\) | 6180.10 | + | 13095.9i | 0.374656 | + | 0.793912i | ||||
\(649\) | 251.700i | 0.0152236i | ||||||||
\(650\) | 10271.9 | − | 1520.67i | 0.619839 | − | 0.0917626i | ||||
\(651\) | 13342.9 | − | 11940.9i | 0.803301 | − | 0.718896i | ||||
\(652\) | 6682.35 | + | 22074.4i | 0.401382 | + | 1.32592i | ||||
\(653\) | 24996.0 | 1.49796 | 0.748981 | − | 0.662592i | \(-0.230544\pi\) | ||||
0.748981 | + | 0.662592i | \(0.230544\pi\) | |||||||
\(654\) | 413.305 | + | 2791.80i | 0.0247118 | + | 0.166923i | ||||
\(655\) | 12814.1i | 0.764411i | ||||||||
\(656\) | 2891.89 | + | 4338.79i | 0.172118 | + | 0.258234i | ||||
\(657\) | − | 4973.50i | − | 0.295334i | ||||||
\(658\) | 5957.29 | + | 4955.10i | 0.352947 | + | 0.293571i | ||||
\(659\) | 15031.5i | 0.888532i | 0.895895 | + | 0.444266i | \(0.146536\pi\) | ||||
−0.895895 | + | 0.444266i | \(0.853464\pi\) | |||||||
\(660\) | −201.049 | + | 60.8617i | −0.0118573 | + | 0.00358945i | ||||
\(661\) | 6084.60i | 0.358039i | 0.983846 | + | 0.179019i | \(0.0572924\pi\) | ||||
−0.983846 | + | 0.179019i | \(0.942708\pi\) | |||||||
\(662\) | −27586.3 | + | 4083.95i | −1.61960 | + | 0.239769i | ||||
\(663\) | 48283.0 | 2.82829 | ||||||||
\(664\) | 6008.33 | + | 12731.9i | 0.351157 | + | 0.744117i | ||||
\(665\) | 2166.56 | + | 2420.93i | 0.126339 | + | 0.141173i | ||||
\(666\) | 3143.23 | + | 21231.9i | 0.182879 | + | 1.23531i | ||||
\(667\) | − | 21517.6i | − | 1.24912i | ||||||
\(668\) | −15227.9 | + | 4609.79i | −0.882014 | + | 0.267003i | ||||
\(669\) | 44975.4 | 2.59918 | ||||||||
\(670\) | −1998.31 | − | 13498.2i | −0.115226 | − | 0.778330i | ||||
\(671\) | 1.29613 | 7.45704e−5 | ||||||||
\(672\) | −25162.7 | − | 2675.12i | −1.44445 | − | 0.153564i | ||||
\(673\) | −9507.60 | −0.544563 | −0.272282 | − | 0.962218i | \(-0.587778\pi\) | ||||
−0.272282 | + | 0.962218i | \(0.587778\pi\) | |||||||
\(674\) | 2845.40 | + | 19220.1i | 0.162612 | + | 1.09842i | ||||
\(675\) | 1087.00 | 0.0619831 | ||||||||
\(676\) | 27086.0 | − | 8199.46i | 1.54108 | − | 0.466515i | ||||
\(677\) | − | 19963.6i | − | 1.13333i | −0.823948 | − | 0.566665i | \(-0.808233\pi\) | ||
0.823948 | − | 0.566665i | \(-0.191767\pi\) | |||||||
\(678\) | 994.359 | + | 6716.70i | 0.0563247 | + | 0.380462i | ||||
\(679\) | 20045.3 | + | 22398.8i | 1.13294 | + | 1.26596i | ||||
\(680\) | −7135.84 | − | 15121.1i | −0.402422 | − | 0.852748i | ||||
\(681\) | 6169.07 | 0.347135 | ||||||||
\(682\) | 142.528 | − | 21.1002i | 0.00800244 | − | 0.00118470i | ||||
\(683\) | − | 21589.2i | − | 1.20950i | −0.796415 | − | 0.604751i | \(-0.793273\pi\) | ||
0.796415 | − | 0.604751i | \(-0.206727\pi\) | |||||||
\(684\) | −4601.91 | + | 1393.09i | −0.257249 | + | 0.0778745i | ||||
\(685\) | − | 6541.45i | − | 0.364870i | ||||||
\(686\) | −12946.5 | + | 12458.6i | −0.720554 | + | 0.693398i | ||||
\(687\) | 23367.2i | 1.29769i | ||||||||
\(688\) | 2454.11 | + | 3681.98i | 0.135991 | + | 0.204032i | ||||
\(689\) | − | 21500.3i | − | 1.18882i | ||||||
\(690\) | 3346.98 | + | 22608.2i | 0.184663 | + | 1.24736i | ||||
\(691\) | 8948.20 | 0.492628 | 0.246314 | − | 0.969190i | \(-0.420781\pi\) | ||||
0.246314 | + | 0.969190i | \(0.420781\pi\) | |||||||
\(692\) | −5832.87 | − | 19268.2i | −0.320423 | − | 1.05848i | ||||
\(693\) | −147.206 | − | 164.489i | −0.00806911 | − | 0.00901650i | ||||
\(694\) | −719.905 | + | 106.577i | −0.0393764 | + | 0.00582939i | ||||
\(695\) | 18625.0i | 1.01653i | ||||||||
\(696\) | 12815.6 | + | 27156.7i | 0.697949 | + | 1.47898i | ||||
\(697\) | −6882.27 | −0.374010 | ||||||||
\(698\) | −7948.14 | + | 1176.66i | −0.431005 | + | 0.0638072i | ||||
\(699\) | −20001.3 | −1.08228 | ||||||||
\(700\) | 3735.06 | − | 6135.46i | 0.201674 | − | 0.331284i | ||||
\(701\) | −8280.23 | −0.446134 | −0.223067 | − | 0.974803i | \(-0.571607\pi\) | ||||
−0.223067 | + | 0.974803i | \(0.571607\pi\) | |||||||
\(702\) | 4750.60 | − | 703.291i | 0.255413 | − | 0.0378120i | ||||
\(703\) | 5077.50 | 0.272406 | ||||||||
\(704\) | −157.174 | − | 129.443i | −0.00841437 | − | 0.00692978i | ||||
\(705\) | 9766.72i | 0.521753i | ||||||||
\(706\) | 31679.4 | − | 4689.90i | 1.68877 | − | 0.250009i | ||||
\(707\) | −9565.61 | − | 10688.7i | −0.508843 | − | 0.568585i | ||||
\(708\) | −36577.9 | + | 11072.9i | −1.94164 | + | 0.587773i | ||||
\(709\) | 4270.33 | 0.226200 | 0.113100 | − | 0.993584i | \(-0.463922\pi\) | ||||
0.113100 | + | 0.993584i | \(0.463922\pi\) | |||||||
\(710\) | −1761.96 | − | 11901.7i | −0.0931340 | − | 0.629102i | ||||
\(711\) | − | 8362.07i | − | 0.441072i | ||||||
\(712\) | 14258.9 | − | 6728.92i | 0.750525 | − | 0.354181i | ||||
\(713\) | − | 15676.1i | − | 0.823388i | ||||||
\(714\) | 21358.2 | − | 25677.9i | 1.11948 | − | 1.34590i | ||||
\(715\) | − | 263.435i | − | 0.0137789i | ||||||
\(716\) | −6032.85 | − | 19928.8i | −0.314886 | − | 1.04019i | ||||
\(717\) | 32398.1i | 1.68749i | ||||||||
\(718\) | 15168.6 | − | 2245.60i | 0.788422 | − | 0.116720i | ||||
\(719\) | −24383.1 | −1.26472 | −0.632362 | − | 0.774673i | \(-0.717915\pi\) | ||||
−0.632362 | + | 0.774673i | \(0.717915\pi\) | |||||||
\(720\) | −9305.80 | − | 13961.8i | −0.481676 | − | 0.722673i | ||||
\(721\) | 398.268 | − | 356.421i | 0.0205718 | − | 0.0184103i | ||||
\(722\) | −2674.52 | − | 18065.8i | −0.137860 | − | 0.931220i | ||||
\(723\) | 38109.0i | 1.96029i | ||||||||
\(724\) | −5503.89 | − | 18181.4i | −0.282528 | − | 0.933298i | ||||
\(725\) | −8523.96 | −0.436651 | ||||||||
\(726\) | 4160.79 | + | 28105.3i | 0.212702 | + | 1.43676i | ||||
\(727\) | 19046.5 | 0.971660 | 0.485830 | − | 0.874053i | \(-0.338517\pi\) | ||||
0.485830 | + | 0.874053i | \(0.338517\pi\) | |||||||
\(728\) | 12354.0 | − | 29230.9i | 0.628941 | − | 1.48814i | ||||
\(729\) | −23749.6 | −1.20661 | ||||||||
\(730\) | −601.282 | − | 4061.54i | −0.0304855 | − | 0.205924i | ||||
\(731\) | −5840.42 | −0.295507 | ||||||||
\(732\) | 57.0199 | + | 188.359i | 0.00287912 | + | 0.00951084i | ||||
\(733\) | 29493.0i | 1.48615i | 0.669208 | + | 0.743075i | \(0.266633\pi\) | ||||
−0.669208 | + | 0.743075i | \(0.733367\pi\) | |||||||
\(734\) | 4532.04 | + | 30613.1i | 0.227903 | + | 1.53944i | ||||
\(735\) | −22507.9 | − | 2503.81i | −1.12955 | − | 0.125652i | ||||
\(736\) | −16436.0 | + | 14853.8i | −0.823150 | + | 0.743911i | ||||
\(737\) | 219.327 | 0.0109620 | ||||||||
\(738\) | −6831.90 | + | 1011.41i | −0.340767 | + | 0.0504480i | ||||
\(739\) | − | 4813.56i | − | 0.239607i | −0.992798 | − | 0.119804i | \(-0.961773\pi\) | ||
0.992798 | − | 0.119804i | \(-0.0382265\pi\) | |||||||
\(740\) | 5133.76 | + | 16958.8i | 0.255028 | + | 0.842454i | ||||
\(741\) | − | 11462.1i | − | 0.568248i | ||||||
\(742\) | −11434.3 | − | 9510.72i | −0.565723 | − | 0.470552i | ||||
\(743\) | − | 17606.1i | − | 0.869318i | −0.900595 | − | 0.434659i | \(-0.856869\pi\) | ||
0.900595 | − | 0.434659i | \(-0.143131\pi\) | |||||||
\(744\) | 9336.46 | + | 19784.3i | 0.460069 | + | 0.974905i | ||||
\(745\) | 7375.74i | 0.362720i | ||||||||
\(746\) | 161.517 | + | 1091.01i | 0.00792701 | + | 0.0535454i | ||||
\(747\) | −18647.2 | −0.913339 | ||||||||
\(748\) | 257.225 | − | 77.8671i | 0.0125736 | − | 0.00380629i | ||||
\(749\) | −641.167 | − | 716.446i | −0.0312787 | − | 0.0349511i | ||||
\(750\) | 32047.9 | − | 4744.46i | 1.56030 | − | 0.230991i | ||||
\(751\) | 6572.41i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(752\) | −7877.63 | + | 5250.59i | −0.382005 | + | 0.254614i | ||||
\(753\) | 3613.68 | 0.174887 | ||||||||
\(754\) | −37253.0 | + | 5515.03i | −1.79930 | + | 0.266373i | ||||
\(755\) | 18268.4 | 0.880602 | ||||||||
\(756\) | 1727.42 | − | 2837.57i | 0.0831025 | − | 0.136510i | ||||
\(757\) | −10562.7 | −0.507146 | −0.253573 | − | 0.967316i | \(-0.581606\pi\) | ||||
−0.253573 | + | 0.967316i | \(0.581606\pi\) | |||||||
\(758\) | 36169.8 | − | 5354.68i | 1.73318 | − | 0.256584i | ||||
\(759\) | −367.352 | −0.0175679 | ||||||||
\(760\) | −3589.67 | + | 1694.01i | −0.171330 | + | 0.0808528i | ||||
\(761\) | − | 15844.6i | − | 0.754750i | −0.926061 | − | 0.377375i | \(-0.876827\pi\) | ||
0.926061 | − | 0.377375i | \(-0.123173\pi\) | |||||||
\(762\) | −17851.2 | + | 2642.74i | −0.848663 | + | 0.125638i | ||||
\(763\) | −1824.42 | + | 1632.72i | −0.0865640 | + | 0.0774684i | ||||
\(764\) | −746.473 | − | 2465.88i | −0.0353487 | − | 0.116770i | ||||
\(765\) | 22146.5 | 1.04668 | ||||||||
\(766\) | −5377.13 | − | 36321.5i | −0.253634 | − | 1.71325i | ||||
\(767\) | − | 47928.1i | − | 2.25630i | ||||||
\(768\) | 11896.6 | − | 28535.5i | 0.558962 | − | 1.34074i | ||||
\(769\) | 6030.08i | 0.282770i | 0.989955 | + | 0.141385i | \(0.0451555\pi\) | ||||
−0.989955 | + | 0.141385i | \(0.954844\pi\) | |||||||
\(770\) | −140.100 | − | 116.531i | −0.00655697 | − | 0.00545390i | ||||
\(771\) | − | 15718.0i | − | 0.734201i | ||||||
\(772\) | 30243.9 | − | 9155.42i | 1.40997 | − | 0.426828i | ||||
\(773\) | 16990.3i | 0.790556i | 0.918562 | + | 0.395278i | \(0.129352\pi\) | ||||
−0.918562 | + | 0.395278i | \(0.870648\pi\) | |||||||
\(774\) | −5797.68 | + | 858.304i | −0.269242 | + | 0.0398593i | ||||
\(775\) | −6209.92 | −0.287828 | ||||||||
\(776\) | −33212.2 | + | 15673.2i | −1.53640 | + | 0.725046i | ||||
\(777\) | −26374.5 | + | 23603.3i | −1.21774 | + | 1.08979i | ||||
\(778\) | 5203.74 | + | 35150.3i | 0.239799 | + | 1.61979i | ||||
\(779\) | 1633.81i | 0.0751443i | ||||||||
\(780\) | 38283.3 | − | 11589.1i | 1.75739 | − | 0.531996i | ||||
\(781\) | 193.386 | 0.00886029 | ||||||||
\(782\) | −4282.17 | − | 28925.2i | −0.195819 | − | 1.32272i | ||||
\(783\) | −3942.22 | −0.179928 | ||||||||
\(784\) | −10080.8 | − | 19500.5i | −0.459218 | − | 0.888323i | ||||
\(785\) | −1475.63 | −0.0670923 | ||||||||
\(786\) | −4579.85 | − | 30936.0i | −0.207835 | − | 1.40388i | ||||
\(787\) | 41103.6 | 1.86173 | 0.930867 | − | 0.365357i | \(-0.119053\pi\) | ||||
0.930867 | + | 0.365357i | \(0.119053\pi\) | |||||||
\(788\) | −20768.2 | + | 6286.96i | −0.938880 | + | 0.284218i | ||||
\(789\) | − | 30987.8i | − | 1.39822i | ||||||
\(790\) | −1010.95 | − | 6828.78i | −0.0455292 | − | 0.307541i | ||||
\(791\) | −4389.31 | + | 3928.12i | −0.197302 | + | 0.176571i | ||||
\(792\) | 243.899 | − | 115.099i | 0.0109426 | − | 0.00516396i | ||||
\(793\) | −246.807 | −0.0110522 | ||||||||
\(794\) | 16436.2 | − | 2433.26i | 0.734633 | − | 0.108757i | ||||
\(795\) | − | 18746.0i | − | 0.836294i | ||||||
\(796\) | 21661.1 | − | 6557.24i | 0.964518 | − | 0.291979i | ||||
\(797\) | − | 6489.74i | − | 0.288430i | −0.989546 | − | 0.144215i | \(-0.953934\pi\) | ||
0.989546 | − | 0.144215i | \(-0.0460656\pi\) | |||||||
\(798\) | −6095.79 | − | 5070.31i | −0.270412 | − | 0.224921i | ||||
\(799\) | − | 12495.7i | − | 0.553272i | ||||||
\(800\) | 5884.17 | + | 6510.93i | 0.260046 | + | 0.287745i | ||||
\(801\) | 20883.6i | 0.921205i | ||||||||
\(802\) | 1976.44 | + | 13350.4i | 0.0870204 | + | 0.587806i | ||||
\(803\) | 65.9944 | 0.00290024 | ||||||||
\(804\) | 9648.70 | + | 31873.3i | 0.423238 | + | 1.39812i | ||||
\(805\) | −14774.3 | + | 13221.9i | −0.646864 | + | 0.578896i | ||||
\(806\) | −27139.7 | + | 4017.84i | −1.18605 | + | 0.175586i | ||||
\(807\) | 45441.7i | 1.98219i | ||||||||
\(808\) | 15848.8 | − | 7479.24i | 0.690049 | − | 0.325642i | ||||
\(809\) | −2747.19 | −0.119390 | −0.0596948 | − | 0.998217i | \(-0.519013\pi\) | ||||
−0.0596948 | + | 0.998217i | \(0.519013\pi\) | |||||||
\(810\) | −15663.3 | + | 2318.84i | −0.679449 | + | 0.100587i | ||||
\(811\) | −17346.1 | −0.751053 | −0.375526 | − | 0.926812i | \(-0.622538\pi\) | ||||
−0.375526 | + | 0.926812i | \(0.622538\pi\) | |||||||
\(812\) | −13546.0 | + | 22251.5i | −0.585431 | + | 0.961667i | ||||
\(813\) | 818.765 | 0.0353202 | ||||||||
\(814\) | −281.731 | + | 41.7082i | −0.0121310 | + | 0.00179591i | ||||
\(815\) | −25218.8 | −1.08390 | ||||||||
\(816\) | 22631.8 | + | 33955.2i | 0.970922 | + | 1.45670i | ||||
\(817\) | 1386.48i | 0.0593720i | ||||||||
\(818\) | 6292.01 | − | 931.486i | 0.268942 | − | 0.0398150i | ||||
\(819\) | 28030.6 | + | 31321.7i | 1.19593 | + | 1.33635i | ||||
\(820\) | −5456.91 | + | 1651.92i | −0.232395 | + | 0.0703505i | ||||
\(821\) | −1049.07 | −0.0445956 | −0.0222978 | − | 0.999751i | \(-0.507098\pi\) | ||||
−0.0222978 | + | 0.999751i | \(0.507098\pi\) | |||||||
\(822\) | 2337.96 | + | 15792.5i | 0.0992040 | + | 0.670104i | ||||
\(823\) | 4120.54i | 0.174524i | 0.996185 | + | 0.0872618i | \(0.0278117\pi\) | ||||
−0.996185 | + | 0.0872618i | \(0.972188\pi\) | |||||||
\(824\) | 278.681 | + | 590.537i | 0.0117820 | + | 0.0249664i | ||||
\(825\) | 145.522i | 0.00614114i | ||||||||
\(826\) | −25489.1 | − | 21201.1i | −1.07370 | − | 0.893077i | ||||
\(827\) | − | 493.902i | − | 0.0207674i | −0.999946 | − | 0.0103837i | \(-0.996695\pi\) | ||
0.999946 | − | 0.0103837i | \(-0.00330530\pi\) | |||||||
\(828\) | −8501.66 | − | 28084.2i | −0.356827 | − | 1.17874i | ||||
\(829\) | − | 7903.16i | − | 0.331108i | −0.986201 | − | 0.165554i | \(-0.947059\pi\) | ||
0.986201 | − | 0.165554i | \(-0.0529412\pi\) | |||||||
\(830\) | −15228.0 | + | 2254.39i | −0.636832 | + | 0.0942784i | ||||
\(831\) | −8145.61 | −0.340034 | ||||||||
\(832\) | 29928.7 | + | 24648.2i | 1.24710 | + | 1.02707i | ||||
\(833\) | 28796.9 | + | 3203.40i | 1.19778 | + | 0.133243i | ||||
\(834\) | −6656.71 | − | 44964.8i | −0.276383 | − | 1.86691i | ||||
\(835\) | − | 17397.1i | − | 0.721020i | ||||||
\(836\) | −18.4852 | − | 61.0638i | −0.000764743 | − | 0.00252624i | ||||
\(837\) | −2872.01 | −0.118603 | ||||||||
\(838\) | 4276.10 | + | 28884.3i | 0.176272 | + | 1.19068i | ||||
\(839\) | 35079.5 | 1.44348 | 0.721739 | − | 0.692166i | \(-0.243343\pi\) | ||||
0.721739 | + | 0.692166i | \(0.243343\pi\) | |||||||
\(840\) | 10771.4 | − | 25486.3i | 0.442439 | − | 1.04686i | ||||
\(841\) | 6524.86 | 0.267533 | ||||||||
\(842\) | 1344.16 | + | 9079.55i | 0.0550153 | + | 0.371617i | ||||
\(843\) | 3642.80 | 0.148831 | ||||||||
\(844\) | 11473.7 | + | 37902.0i | 0.467939 | + | 1.54578i | ||||
\(845\) | 30944.3i | 1.25978i | ||||||||
\(846\) | −1836.35 | − | 12404.2i | −0.0746277 | − | 0.504096i | ||||
\(847\) | −18366.6 | + | 16436.8i | −0.745082 | + | 0.666794i | ||||
\(848\) | 15120.2 | − | 10077.9i | 0.612298 | − | 0.408108i | ||||
\(849\) | −18692.0 | −0.755602 | ||||||||
\(850\) | −11458.4 | + | 1696.33i | −0.462377 | + | 0.0684515i | ||||
\(851\) | 30986.6i | 1.24819i | ||||||||
\(852\) | 8507.49 | + | 28103.5i | 0.342091 | + | 1.13006i | ||||
\(853\) | − | 34167.2i | − | 1.37147i | −0.727852 | − | 0.685734i | \(-0.759481\pi\) | ||
0.727852 | − | 0.685734i | \(-0.240519\pi\) | |||||||
\(854\) | −109.176 | + | 131.257i | −0.00437461 | + | 0.00525939i | ||||
\(855\) | − | 5257.44i | − | 0.210293i | ||||||
\(856\) | 1062.32 | − | 501.322i | 0.0424175 | − | 0.0200173i | ||||
\(857\) | 9678.21i | 0.385766i | 0.981222 | + | 0.192883i | \(0.0617838\pi\) | ||||
−0.981222 | + | 0.192883i | \(0.938216\pi\) | |||||||
\(858\) | 94.1535 | + | 635.989i | 0.00374633 | + | 0.0253057i | ||||
\(859\) | 7458.37 | 0.296247 | 0.148124 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148124 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(860\) | −4630.83 | + | 1401.85i | −0.183616 | + | 0.0555844i | ||||
\(861\) | −7594.96 | − | 8486.68i | −0.300622 | − | 0.335918i | ||||
\(862\) | 26737.3 | − | 3958.26i | 1.05647 | − | 0.156403i | ||||
\(863\) | 2106.36i | 0.0830839i | 0.999137 | + | 0.0415420i | \(0.0132270\pi\) | ||||
−0.999137 | + | 0.0415420i | \(0.986773\pi\) | |||||||
\(864\) | 2721.35 | + | 3011.22i | 0.107155 | + | 0.118569i | ||||
\(865\) | 22012.9 | 0.865274 | ||||||||
\(866\) | 15833.2 | − | 2343.99i | 0.621287 | − | 0.0919770i | ||||
\(867\) | −16777.7 | −0.657211 | ||||||||
\(868\) | −9868.58 | + | 16210.8i | −0.385900 | + | 0.633905i | ||||
\(869\) | 110.958 | 0.00433141 | ||||||||
\(870\) | −32480.7 | + | 4808.54i | −1.26575 | + | 0.187385i | ||||
\(871\) | −41763.7 | −1.62469 | ||||||||
\(872\) | −1276.61 | − | 2705.18i | −0.0495772 | − | 0.105056i | ||||
\(873\) | − | 48642.6i | − | 1.88580i | ||||||
\(874\) | −6866.69 | + | 1016.56i | −0.265754 | + | 0.0393430i | ||||
\(875\) | 18742.5 | + | 20943.0i | 0.724128 | + | 0.809147i | ||||
\(876\) | 2903.25 | + | 9590.53i | 0.111977 | + | 0.369902i | ||||
\(877\) | 1942.72 | 0.0748015 | 0.0374007 | − | 0.999300i | \(-0.488092\pi\) | ||||
0.0374007 | + | 0.999300i | \(0.488092\pi\) | |||||||
\(878\) | 1379.22 | + | 9316.35i | 0.0530141 | + | 0.358100i | ||||
\(879\) | − | 35035.6i | − | 1.34439i | ||||||
\(880\) | 185.262 | − | 123.481i | 0.00709679 | − | 0.00473015i | ||||
\(881\) | − | 11938.8i | − | 0.456561i | −0.973595 | − | 0.228280i | \(-0.926690\pi\) | ||
0.973595 | − | 0.228280i | \(-0.0733103\pi\) | |||||||
\(882\) | 29056.9 | − | 1052.02i | 1.10929 | − | 0.0401624i | ||||
\(883\) | 6631.93i | 0.252754i | 0.991982 | + | 0.126377i | \(0.0403350\pi\) | ||||
−0.991982 | + | 0.126377i | \(0.959665\pi\) | |||||||
\(884\) | −48980.1 | + | 14827.3i | −1.86355 | + | 0.564134i | ||||
\(885\) | − | 41788.3i | − | 1.58723i | ||||||
\(886\) | −18372.8 | + | 2719.95i | −0.696664 | + | 0.103136i | ||||
\(887\) | 26193.4 | 0.991530 | 0.495765 | − | 0.868457i | \(-0.334888\pi\) | ||||
0.495765 | + | 0.868457i | \(0.334888\pi\) | |||||||
\(888\) | −18455.2 | − | 39107.2i | −0.697426 | − | 1.47787i | ||||
\(889\) | −10439.9 | − | 11665.6i | −0.393861 | − | 0.440104i | ||||
\(890\) | 2524.77 | + | 17054.3i | 0.0950903 | + | 0.642316i | ||||
\(891\) | − | 254.507i | − | 0.00956938i | ||||||
\(892\) | −45624.7 | + | 13811.5i | −1.71259 | + | 0.518435i | ||||
\(893\) | −2966.40 | −0.111161 | ||||||||
\(894\) | −2636.14 | − | 17806.6i | −0.0986194 | − | 0.666155i | ||||
\(895\) | 22767.6 | 0.850322 | ||||||||
\(896\) | 26347.5 | − | 5013.48i | 0.982373 | − | 0.186929i | ||||
\(897\) | 69950.3 | 2.60376 | ||||||||
\(898\) | −6277.97 | − | 42406.5i | −0.233295 | − | 1.57586i | ||||
\(899\) | 22521.5 | 0.835523 | ||||||||
\(900\) | −11125.3 | + | 3367.84i | −0.412046 | + | 0.124735i | ||||
\(901\) | 23983.9i | 0.886814i | ||||||||
\(902\) | −13.4207 | − | 90.6540i | −0.000495409 | − | 0.00334639i | ||||
\(903\) | −6445.22 | − | 7201.95i | −0.237523 | − | 0.265411i | ||||
\(904\) | −3071.35 | − | 6508.32i | −0.113000 | − | 0.239451i | ||||
\(905\) | 20771.4 | 0.762943 | ||||||||
\(906\) | −44103.8 | + | 6529.25i | −1.61727 | + | 0.239426i | ||||
\(907\) | − | 19976.6i | − | 0.731324i | −0.930748 | − | 0.365662i | \(-0.880843\pi\) | ||
0.930748 | − | 0.365662i | \(-0.119157\pi\) | |||||||
\(908\) | −6258.13 | + | 1894.46i | −0.228726 | + | 0.0692400i | ||||
\(909\) | 23212.2i | 0.846976i | ||||||||
\(910\) | 26677.5 | + | 22189.6i | 0.971815 | + | 0.808328i | ||||
\(911\) | − | 33720.7i | − | 1.22636i | −0.789942 | − | 0.613182i | \(-0.789889\pi\) | ||
0.789942 | − | 0.613182i | \(-0.210111\pi\) | |||||||
\(912\) | 8060.78 | − | 5372.67i | 0.292675 | − | 0.195073i | ||||
\(913\) | − | 247.433i | − | 0.00896917i | ||||||
\(914\) | 6864.71 | + | 46369.8i | 0.248429 | + | 1.67809i | ||||
\(915\) | −215.190 | −0.00777482 | ||||||||
\(916\) | −7175.85 | − | 23704.6i | −0.258839 | − | 0.855045i | ||||
\(917\) | 20216.5 | − | 18092.3i | 0.728033 | − | 0.651536i | ||||
\(918\) | −5299.36 | + | 784.532i | −0.190528 | + | 0.0282063i | ||||
\(919\) | − | 39693.8i | − | 1.42479i | −0.701780 | − | 0.712393i | \(-0.747611\pi\) | ||
0.701780 | − | 0.712393i | \(-0.252389\pi\) | |||||||
\(920\) | −10338.1 | − | 21906.8i | −0.370474 | − | 0.785050i | ||||
\(921\) | 11660.0 | 0.417166 | ||||||||
\(922\) | 16293.7 | − | 2412.16i | 0.581999 | − | 0.0861608i | ||||
\(923\) | −36824.0 | −1.31319 | ||||||||
\(924\) | 379.881 | + | 231.259i | 0.0135251 | + | 0.00823361i | ||||
\(925\) | 12275.0 | 0.436324 | ||||||||
\(926\) | 36238.8 | − | 5364.89i | 1.28605 | − | 0.190390i | ||||
\(927\) | −864.903 | −0.0306442 | ||||||||
\(928\) | −21340.1 | − | 23613.2i | −0.754875 | − | 0.835282i | ||||
\(929\) | 32215.1i | 1.13772i | 0.822434 | + | 0.568860i | \(0.192615\pi\) | ||||
−0.822434 | + | 0.568860i | \(0.807385\pi\) | |||||||
\(930\) | −23663.1 | + | 3503.14i | −0.834346 | + | 0.123519i | ||||
\(931\) | 760.470 | − | 6836.23i | 0.0267705 | − | 0.240653i | ||||
\(932\) | 20290.0 | − | 6142.20i | 0.713113 | − | 0.215874i | ||||
\(933\) | −67156.5 | −2.35649 | ||||||||
\(934\) | 2982.21 | + | 20144.3i | 0.104476 | + | 0.705718i | ||||
\(935\) | 293.866i | 0.0102786i | ||||||||
\(936\) | −46442.6 | + | 21916.8i | −1.62182 | + | 0.765356i | ||||
\(937\) | 28308.4i | 0.986973i | 0.869753 | + | 0.493487i | \(0.164278\pi\) | ||||
−0.869753 | + | 0.493487i | \(0.835722\pi\) | |||||||
\(938\) | −18474.3 | + | 22210.8i | −0.643078 | + | 0.773142i | ||||
\(939\) | 14800.1i | 0.514357i | ||||||||
\(940\) | −2999.27 | − | 9907.72i | −0.104069 | − | 0.343781i | ||||
\(941\) | − | 35128.7i | − | 1.21696i | −0.793568 | − | 0.608482i | \(-0.791779\pi\) | ||
0.793568 | − | 0.608482i | \(-0.208221\pi\) | |||||||
\(942\) | 3562.48 | − | 527.399i | 0.123219 | − | 0.0182416i | ||||
\(943\) | −9970.72 | −0.344318 | ||||||||
\(944\) | 33705.6 | − | 22465.4i | 1.16210 | − | 0.774563i | ||||
\(945\) | 2422.38 | + | 2706.78i | 0.0833861 | + | 0.0931764i | ||||
\(946\) | −11.3890 | − | 76.9306i | −0.000391426 | − | 0.00264401i | ||||
\(947\) | 49095.2i | 1.68467i | 0.538957 | + | 0.842333i | \(0.318819\pi\) | ||||
−0.538957 | + | 0.842333i | \(0.681181\pi\) | |||||||
\(948\) | 4881.31 | + | 16124.8i | 0.167234 | + | 0.552436i | ||||
\(949\) | −12566.5 | −0.429848 | ||||||||
\(950\) | 402.700 | + | 2720.16i | 0.0137530 | + | 0.0928987i | ||||
\(951\) | −31964.1 | −1.08991 | ||||||||
\(952\) | −13781.1 | + | 32607.5i | −0.469167 | + | 1.11010i | ||||
\(953\) | −49122.8 | −1.66972 | −0.834860 | − | 0.550463i | \(-0.814451\pi\) | ||||
−0.834860 | + | 0.550463i | \(0.814451\pi\) | |||||||
\(954\) | 3524.65 | + | 23808.4i | 0.119617 | + | 0.807992i | ||||
\(955\) | 2817.15 | 0.0954562 | ||||||||
\(956\) | −9949.15 | − | 32865.8i | −0.336588 | − | 1.11188i | ||||
\(957\) | − | 527.767i | − | 0.0178268i | ||||||
\(958\) | 4351.30 | + | 29392.2i | 0.146748 | + | 0.991251i | ||||
\(959\) | −10320.2 | + | 9235.87i | −0.347506 | + | 0.310993i | ||||
\(960\) | 26094.7 | + | 21490.7i | 0.877295 | + | 0.722509i | ||||
\(961\) | −13383.5 | −0.449246 | ||||||||
\(962\) | 53646.4 | − | 7941.97i | 1.79795 | − | 0.266174i | ||||
\(963\) | 1555.88i | 0.0520639i | ||||||||
\(964\) | −11702.9 | − | 38659.2i | −0.391002 | − | 1.29163i | ||||
\(965\) | 34552.0i | 1.15261i | ||||||||
\(966\) | 30942.7 | − | 37201.0i | 1.03061 | − | 1.23905i | ||||
\(967\) | 25958.2i | 0.863247i | 0.902054 | + | 0.431624i | \(0.142059\pi\) | ||||
−0.902054 | + | 0.431624i | \(0.857941\pi\) | |||||||
\(968\) | −12851.7 | − | 27233.4i | −0.426726 | − | 0.904250i | ||||
\(969\) | 12786.2i | 0.423892i | ||||||||
\(970\) | −5880.76 | − | 39723.4i | −0.194660 | − | 1.31489i | ||||
\(971\) | 29381.4 | 0.971055 | 0.485528 | − | 0.874221i | \(-0.338627\pi\) | ||||
0.485528 | + | 0.874221i | \(0.338627\pi\) | |||||||
\(972\) | 41621.2 | − | 12599.6i | 1.37346 | − | 0.415773i | ||||
\(973\) | 29384.2 | − | 26296.7i | 0.968153 | − | 0.866426i | ||||
\(974\) | −40884.8 | + | 6052.70i | −1.34500 | + | 0.199118i | ||||
\(975\) | − | 27710.0i | − | 0.910186i | ||||||
\(976\) | −115.686 | − | 173.568i | −0.00379409 | − | 0.00569238i | ||||
\(977\) | −31221.5 | −1.02238 | −0.511189 | − | 0.859468i | \(-0.670795\pi\) | ||||
−0.511189 | + | 0.859468i | \(0.670795\pi\) | |||||||
\(978\) | 60883.6 | − | 9013.38i | 1.99064 | − | 0.294699i | ||||
\(979\) | −277.109 | −0.00904641 | ||||||||
\(980\) | 23601.8 | − | 4372.02i | 0.769317 | − | 0.142509i | ||||
\(981\) | 3962.01 | 0.128947 | ||||||||
\(982\) | −47432.6 | + | 7022.05i | −1.54138 | + | 0.228190i | ||||
\(983\) | −19941.1 | −0.647021 | −0.323511 | − | 0.946225i | \(-0.604863\pi\) | ||||
−0.323511 | + | 0.946225i | \(0.604863\pi\) | |||||||
\(984\) | 12583.7 | − | 5938.41i | 0.407678 | − | 0.192388i | ||||
\(985\) | − | 23726.6i | − | 0.767506i | ||||||
\(986\) | 41556.3 | − | 6152.10i | 1.34221 | − | 0.198705i | ||||
\(987\) | 15408.7 | − | 13789.6i | 0.496923 | − | 0.444710i | ||||
\(988\) | 3519.91 | + | 11627.6i | 0.113343 | + | 0.374416i | ||||
\(989\) | −8461.34 | −0.272047 | ||||||||
\(990\) | 43.1863 | + | 291.715i | 0.00138642 | + | 0.00936497i | ||||
\(991\) | 12092.8i | 0.387629i | 0.981038 | + | 0.193815i | \(0.0620861\pi\) | ||||
−0.981038 | + | 0.193815i | \(0.937914\pi\) | |||||||
\(992\) | −15546.8 | − | 17202.8i | −0.497593 | − | 0.550595i | ||||
\(993\) | 74418.6i | 2.37825i | ||||||||
\(994\) | −16289.2 | + | 19583.8i | −0.519782 | + | 0.624909i | ||||
\(995\) | 24746.6i | 0.788464i | ||||||||
\(996\) | 35957.9 | − | 10885.2i | 1.14394 | − | 0.346295i | ||||
\(997\) | − | 13741.5i | − | 0.436509i | −0.975892 | − | 0.218254i | \(-0.929964\pi\) | ||
0.975892 | − | 0.218254i | \(-0.0700362\pi\) | |||||||
\(998\) | 49487.9 | − | 7326.32i | 1.56965 | − | 0.232375i | ||||
\(999\) | 5677.02 | 0.179793 |
(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 | 28.4.d.b.27.8 | yes | 8 | |
3.2 | odd | 2 | 252.4.b.d.55.2 | 8 | |||
4.3 | odd | 2 | inner | 28.4.d.b.27.5 | ✓ | 8 | |
7.2 | even | 3 | 196.4.f.c.31.5 | 16 | |||
7.3 | odd | 6 | 196.4.f.c.19.2 | 16 | |||
7.4 | even | 3 | 196.4.f.c.19.1 | 16 | |||
7.5 | odd | 6 | 196.4.f.c.31.6 | 16 | |||
7.6 | odd | 2 | inner | 28.4.d.b.27.7 | yes | 8 | |
8.3 | odd | 2 | 448.4.f.d.447.8 | 8 | |||
8.5 | even | 2 | 448.4.f.d.447.2 | 8 | |||
12.11 | even | 2 | 252.4.b.d.55.4 | 8 | |||
21.20 | even | 2 | 252.4.b.d.55.1 | 8 | |||
28.3 | even | 6 | 196.4.f.c.19.5 | 16 | |||
28.11 | odd | 6 | 196.4.f.c.19.6 | 16 | |||
28.19 | even | 6 | 196.4.f.c.31.1 | 16 | |||
28.23 | odd | 6 | 196.4.f.c.31.2 | 16 | |||
28.27 | even | 2 | inner | 28.4.d.b.27.6 | yes | 8 | |
56.13 | odd | 2 | 448.4.f.d.447.7 | 8 | |||
56.27 | even | 2 | 448.4.f.d.447.1 | 8 | |||
84.83 | odd | 2 | 252.4.b.d.55.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.d.b.27.5 | ✓ | 8 | 4.3 | odd | 2 | inner | |
28.4.d.b.27.6 | yes | 8 | 28.27 | even | 2 | inner | |
28.4.d.b.27.7 | yes | 8 | 7.6 | odd | 2 | inner | |
28.4.d.b.27.8 | yes | 8 | 1.1 | even | 1 | trivial | |
196.4.f.c.19.1 | 16 | 7.4 | even | 3 | |||
196.4.f.c.19.2 | 16 | 7.3 | odd | 6 | |||
196.4.f.c.19.5 | 16 | 28.3 | even | 6 | |||
196.4.f.c.19.6 | 16 | 28.11 | odd | 6 | |||
196.4.f.c.31.1 | 16 | 28.19 | even | 6 | |||
196.4.f.c.31.2 | 16 | 28.23 | odd | 6 | |||
196.4.f.c.31.5 | 16 | 7.2 | even | 3 | |||
196.4.f.c.31.6 | 16 | 7.5 | odd | 6 | |||
252.4.b.d.55.1 | 8 | 21.20 | even | 2 | |||
252.4.b.d.55.2 | 8 | 3.2 | odd | 2 | |||
252.4.b.d.55.3 | 8 | 84.83 | odd | 2 | |||
252.4.b.d.55.4 | 8 | 12.11 | even | 2 | |||
448.4.f.d.447.1 | 8 | 56.27 | even | 2 | |||
448.4.f.d.447.2 | 8 | 8.5 | even | 2 | |||
448.4.f.d.447.7 | 8 | 56.13 | odd | 2 | |||
448.4.f.d.447.8 | 8 | 8.3 | odd | 2 |