Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.100");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.e (of order \(3\), degree \(2\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.7 | ||
Character | \(\chi\) | \(=\) | 143.100 |
Dual form | 143.4.e.b.133.7 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.706890 | + | 1.22437i | −0.249923 | + | 0.432880i | −0.963504 | − | 0.267693i | \(-0.913739\pi\) |
0.713581 | + | 0.700573i | \(0.247072\pi\) | |||||||
\(3\) | −2.88255 | + | 4.99273i | −0.554748 | + | 0.960851i | 0.443175 | + | 0.896435i | \(0.353852\pi\) |
−0.997923 | + | 0.0644163i | \(0.979481\pi\) | |||||||
\(4\) | 3.00061 | + | 5.19721i | 0.375077 | + | 0.649652i | ||||
\(5\) | −4.58681 | −0.410257 | −0.205128 | − | 0.978735i | \(-0.565761\pi\) | ||||
−0.205128 | + | 0.978735i | \(0.565761\pi\) | |||||||
\(6\) | −4.07530 | − | 7.05862i | −0.277289 | − | 0.480278i | ||||
\(7\) | −18.2120 | − | 31.5441i | −0.983354 | − | 1.70322i | −0.649033 | − | 0.760760i | \(-0.724826\pi\) |
−0.334321 | − | 0.942459i | \(-0.608507\pi\) | |||||||
\(8\) | −19.7947 | −0.874808 | ||||||||
\(9\) | −3.11823 | − | 5.40093i | −0.115490 | − | 0.200034i | ||||
\(10\) | 3.24237 | − | 5.61595i | 0.102533 | − | 0.177592i | ||||
\(11\) | −5.50000 | + | 9.52628i | −0.150756 | + | 0.261116i | ||||
\(12\) | −34.5977 | −0.832292 | ||||||||
\(13\) | 23.5611 | − | 40.5201i | 0.502667 | − | 0.864480i | ||||
\(14\) | 51.4954 | 0.983053 | ||||||||
\(15\) | 13.2217 | − | 22.9007i | 0.227589 | − | 0.394196i | ||||
\(16\) | −10.0123 | + | 17.3418i | −0.156442 | + | 0.270965i | ||||
\(17\) | 33.3510 | + | 57.7657i | 0.475812 | + | 0.824131i | 0.999616 | − | 0.0277079i | \(-0.00882081\pi\) |
−0.523804 | + | 0.851839i | \(0.675487\pi\) | |||||||
\(18\) | 8.81698 | 0.115455 | ||||||||
\(19\) | −9.57122 | − | 16.5778i | −0.115568 | − | 0.200169i | 0.802439 | − | 0.596734i | \(-0.203535\pi\) |
−0.918007 | + | 0.396565i | \(0.870202\pi\) | |||||||
\(20\) | −13.7632 | − | 23.8386i | −0.153878 | − | 0.266524i | ||||
\(21\) | 209.988 | 2.18205 | ||||||||
\(22\) | −7.77579 | − | 13.4681i | −0.0753547 | − | 0.130518i | ||||
\(23\) | 73.9592 | − | 128.101i | 0.670502 | − | 1.16134i | −0.307259 | − | 0.951626i | \(-0.599412\pi\) |
0.977762 | − | 0.209719i | \(-0.0672548\pi\) | |||||||
\(24\) | 57.0591 | − | 98.8293i | 0.485298 | − | 0.840561i | ||||
\(25\) | −103.961 | −0.831689 | ||||||||
\(26\) | 32.9564 | + | 57.4907i | 0.248588 | + | 0.433648i | ||||
\(27\) | −119.704 | −0.853224 | ||||||||
\(28\) | 109.294 | − | 189.303i | 0.737666 | − | 1.27768i | ||||
\(29\) | 8.97156 | − | 15.5392i | 0.0574475 | − | 0.0995020i | −0.835871 | − | 0.548925i | \(-0.815037\pi\) |
0.893319 | + | 0.449423i | \(0.148370\pi\) | |||||||
\(30\) | 18.6926 | + | 32.3765i | 0.113760 | + | 0.197037i | ||||
\(31\) | −272.137 | −1.57668 | −0.788341 | − | 0.615238i | \(-0.789060\pi\) | ||||
−0.788341 | + | 0.615238i | \(0.789060\pi\) | |||||||
\(32\) | −93.3337 | − | 161.659i | −0.515601 | − | 0.893047i | ||||
\(33\) | −31.7081 | − | 54.9200i | −0.167263 | − | 0.289708i | ||||
\(34\) | −94.3020 | −0.475666 | ||||||||
\(35\) | 83.5348 | + | 144.687i | 0.403428 | + | 0.698757i | ||||
\(36\) | 18.7132 | − | 32.4122i | 0.0866352 | − | 0.150057i | ||||
\(37\) | 122.434 | − | 212.061i | 0.543999 | − | 0.942234i | −0.454670 | − | 0.890660i | \(-0.650243\pi\) |
0.998669 | − | 0.0515739i | \(-0.0164238\pi\) | |||||||
\(38\) | 27.0632 | 0.115532 | ||||||||
\(39\) | 134.390 | + | 234.435i | 0.551784 | + | 0.962556i | ||||
\(40\) | 90.7943 | 0.358896 | ||||||||
\(41\) | 22.3085 | − | 38.6395i | 0.0849758 | − | 0.147182i | −0.820405 | − | 0.571783i | \(-0.806252\pi\) |
0.905381 | + | 0.424600i | \(0.139585\pi\) | |||||||
\(42\) | −148.438 | + | 257.103i | −0.545346 | + | 0.944567i | ||||
\(43\) | −15.5306 | − | 26.8998i | −0.0550790 | − | 0.0953997i | 0.837171 | − | 0.546941i | \(-0.184208\pi\) |
−0.892250 | + | 0.451541i | \(0.850874\pi\) | |||||||
\(44\) | −66.0135 | −0.226180 | ||||||||
\(45\) | 14.3027 | + | 24.7730i | 0.0473805 | + | 0.0820655i | ||||
\(46\) | 104.562 | + | 181.107i | 0.335148 | + | 0.580494i | ||||
\(47\) | 285.729 | 0.886761 | 0.443381 | − | 0.896333i | \(-0.353779\pi\) | ||||
0.443381 | + | 0.896333i | \(0.353779\pi\) | |||||||
\(48\) | −57.7218 | − | 99.9771i | −0.173571 | − | 0.300634i | ||||
\(49\) | −491.852 | + | 851.913i | −1.43397 | + | 2.48371i | ||||
\(50\) | 73.4891 | − | 127.287i | 0.207859 | − | 0.360022i | ||||
\(51\) | −384.544 | −1.05582 | ||||||||
\(52\) | 281.289 | + | 0.866972i | 0.750150 | + | 0.00231206i | ||||
\(53\) | −436.642 | −1.13165 | −0.565825 | − | 0.824526i | \(-0.691442\pi\) | ||||
−0.565825 | + | 0.824526i | \(0.691442\pi\) | |||||||
\(54\) | 84.6176 | − | 146.562i | 0.213241 | − | 0.369344i | ||||
\(55\) | 25.2274 | − | 43.6952i | 0.0618485 | − | 0.107125i | ||||
\(56\) | 360.500 | + | 624.404i | 0.860246 | + | 1.48999i | ||||
\(57\) | 110.358 | 0.256444 | ||||||||
\(58\) | 12.6838 | + | 21.9690i | 0.0287149 | + | 0.0497357i | ||||
\(59\) | −434.200 | − | 752.056i | −0.958102 | − | 1.65948i | −0.727104 | − | 0.686527i | \(-0.759134\pi\) |
−0.230998 | − | 0.972954i | \(-0.574199\pi\) | |||||||
\(60\) | 158.693 | 0.341453 | ||||||||
\(61\) | −93.2896 | − | 161.582i | −0.195812 | − | 0.339156i | 0.751355 | − | 0.659899i | \(-0.229401\pi\) |
−0.947166 | + | 0.320743i | \(0.896067\pi\) | |||||||
\(62\) | 192.371 | − | 333.196i | 0.394050 | − | 0.682514i | ||||
\(63\) | −113.578 | + | 196.723i | −0.227135 | + | 0.393409i | ||||
\(64\) | 103.710 | 0.202559 | ||||||||
\(65\) | −108.070 | + | 185.858i | −0.206222 | + | 0.354659i | ||||
\(66\) | 89.6565 | 0.167211 | ||||||||
\(67\) | −344.196 | + | 596.165i | −0.627615 | + | 1.08706i | 0.360414 | + | 0.932793i | \(0.382636\pi\) |
−0.988029 | + | 0.154269i | \(0.950698\pi\) | |||||||
\(68\) | −200.147 | + | 346.665i | −0.356932 | + | 0.618225i | ||||
\(69\) | 426.383 | + | 738.516i | 0.743919 | + | 1.28851i | ||||
\(70\) | −236.200 | −0.403304 | ||||||||
\(71\) | 59.5232 | + | 103.097i | 0.0994944 | + | 0.172329i | 0.911475 | − | 0.411354i | \(-0.134944\pi\) |
−0.811981 | + | 0.583684i | \(0.801611\pi\) | |||||||
\(72\) | 61.7242 | + | 106.910i | 0.101032 | + | 0.174992i | ||||
\(73\) | −786.334 | −1.26073 | −0.630366 | − | 0.776298i | \(-0.717095\pi\) | ||||
−0.630366 | + | 0.776298i | \(0.717095\pi\) | |||||||
\(74\) | 173.094 | + | 299.808i | 0.271916 | + | 0.470972i | ||||
\(75\) | 299.674 | − | 519.050i | 0.461378 | − | 0.799130i | ||||
\(76\) | 57.4391 | − | 99.4874i | 0.0866936 | − | 0.150158i | ||||
\(77\) | 400.663 | 0.592985 | ||||||||
\(78\) | −382.034 | − | 1.17748i | −0.554575 | − | 0.00170928i | ||||
\(79\) | 254.973 | 0.363123 | 0.181562 | − | 0.983380i | \(-0.441885\pi\) | ||||
0.181562 | + | 0.983380i | \(0.441885\pi\) | |||||||
\(80\) | 45.9244 | − | 79.5433i | 0.0641812 | − | 0.111165i | ||||
\(81\) | 429.245 | − | 743.475i | 0.588814 | − | 1.01986i | ||||
\(82\) | 31.5393 | + | 54.6277i | 0.0424748 | + | 0.0735686i | ||||
\(83\) | −768.286 | −1.01603 | −0.508014 | − | 0.861349i | \(-0.669620\pi\) | ||||
−0.508014 | + | 0.861349i | \(0.669620\pi\) | |||||||
\(84\) | 630.093 | + | 1091.35i | 0.818437 | + | 1.41758i | ||||
\(85\) | −152.975 | − | 264.960i | −0.195205 | − | 0.338105i | ||||
\(86\) | 43.9138 | 0.0550621 | ||||||||
\(87\) | 51.7220 | + | 89.5851i | 0.0637377 | + | 0.110397i | ||||
\(88\) | 108.871 | − | 188.569i | 0.131882 | − | 0.228427i | ||||
\(89\) | 63.1485 | − | 109.376i | 0.0752104 | − | 0.130268i | −0.825967 | − | 0.563718i | \(-0.809371\pi\) |
0.901178 | + | 0.433450i | \(0.142704\pi\) | |||||||
\(90\) | −40.4418 | −0.0473660 | ||||||||
\(91\) | −1707.26 | − | 5.26201i | −1.96670 | − | 0.00606164i | ||||
\(92\) | 887.692 | 1.00596 | ||||||||
\(93\) | 784.448 | − | 1358.70i | 0.874661 | − | 1.51496i | ||||
\(94\) | −201.979 | + | 349.837i | −0.221622 | + | 0.383861i | ||||
\(95\) | 43.9014 | + | 76.0394i | 0.0474125 | + | 0.0821208i | ||||
\(96\) | 1076.16 | 1.14411 | ||||||||
\(97\) | 679.714 | + | 1177.30i | 0.711489 | + | 1.23234i | 0.964298 | + | 0.264819i | \(0.0853123\pi\) |
−0.252809 | + | 0.967516i | \(0.581354\pi\) | |||||||
\(98\) | −695.370 | − | 1204.42i | −0.716765 | − | 1.24147i | ||||
\(99\) | 68.6010 | 0.0696431 | ||||||||
\(100\) | −311.947 | − | 540.309i | −0.311947 | − | 0.540309i | ||||
\(101\) | −575.437 | + | 996.685i | −0.566912 | + | 0.981920i | 0.429957 | + | 0.902849i | \(0.358529\pi\) |
−0.996869 | + | 0.0790705i | \(0.974805\pi\) | |||||||
\(102\) | 271.831 | − | 470.824i | 0.263875 | − | 0.457045i | ||||
\(103\) | −861.231 | −0.823879 | −0.411940 | − | 0.911211i | \(-0.635149\pi\) | ||||
−0.411940 | + | 0.911211i | \(0.635149\pi\) | |||||||
\(104\) | −466.383 | + | 802.080i | −0.439737 | + | 0.756254i | ||||
\(105\) | −963.175 | −0.895202 | ||||||||
\(106\) | 308.658 | − | 534.611i | 0.282826 | − | 0.489868i | ||||
\(107\) | 448.126 | − | 776.177i | 0.404878 | − | 0.701270i | −0.589429 | − | 0.807820i | \(-0.700647\pi\) |
0.994307 | + | 0.106550i | \(0.0339805\pi\) | |||||||
\(108\) | −359.186 | − | 622.128i | −0.320024 | − | 0.554299i | ||||
\(109\) | −1332.10 | −1.17057 | −0.585283 | − | 0.810829i | \(-0.699017\pi\) | ||||
−0.585283 | + | 0.810829i | \(0.699017\pi\) | |||||||
\(110\) | 35.6661 | + | 61.7754i | 0.0309148 | + | 0.0535460i | ||||
\(111\) | 705.843 | + | 1222.56i | 0.603564 | + | 1.04540i | ||||
\(112\) | 729.373 | 0.615350 | ||||||||
\(113\) | 326.924 | + | 566.250i | 0.272163 | + | 0.471401i | 0.969416 | − | 0.245425i | \(-0.0789275\pi\) |
−0.697252 | + | 0.716826i | \(0.745594\pi\) | |||||||
\(114\) | −78.0111 | + | 135.119i | −0.0640913 | + | 0.111009i | ||||
\(115\) | −339.237 | + | 587.575i | −0.275078 | + | 0.476449i | ||||
\(116\) | 107.681 | 0.0861888 | ||||||||
\(117\) | −292.315 | − | 0.900955i | −0.230979 | − | 0.000711908i | ||||
\(118\) | 1227.73 | 0.957808 | ||||||||
\(119\) | 1214.78 | − | 2104.05i | 0.935784 | − | 1.62083i | ||||
\(120\) | −261.719 | + | 453.311i | −0.199097 | + | 0.344846i | ||||
\(121\) | −60.5000 | − | 104.789i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 263.782 | 0.195751 | ||||||||
\(123\) | 128.611 | + | 222.761i | 0.0942802 | + | 0.163298i | ||||
\(124\) | −816.577 | − | 1414.35i | −0.591377 | − | 1.02429i | ||||
\(125\) | 1050.20 | 0.751463 | ||||||||
\(126\) | −160.575 | − | 278.123i | −0.113533 | − | 0.196644i | ||||
\(127\) | 1108.17 | − | 1919.41i | 0.774285 | − | 1.34110i | −0.160910 | − | 0.986969i | \(-0.551443\pi\) |
0.935195 | − | 0.354133i | \(-0.115224\pi\) | |||||||
\(128\) | 673.358 | − | 1166.29i | 0.464977 | − | 0.805363i | ||||
\(129\) | 179.071 | 0.122220 | ||||||||
\(130\) | −151.165 | − | 263.699i | −0.101985 | − | 0.177907i | ||||
\(131\) | 1946.18 | 1.29801 | 0.649003 | − | 0.760786i | \(-0.275186\pi\) | ||||
0.649003 | + | 0.760786i | \(0.275186\pi\) | |||||||
\(132\) | 190.287 | − | 329.587i | 0.125473 | − | 0.217325i | ||||
\(133\) | −348.622 | + | 603.830i | −0.227288 | + | 0.393675i | ||||
\(134\) | −486.617 | − | 842.846i | −0.313711 | − | 0.543364i | ||||
\(135\) | 549.060 | 0.350041 | ||||||||
\(136\) | −660.172 | − | 1143.45i | −0.416245 | − | 0.720957i | ||||
\(137\) | 366.431 | + | 634.677i | 0.228513 | + | 0.395797i | 0.957368 | − | 0.288872i | \(-0.0932802\pi\) |
−0.728854 | + | 0.684669i | \(0.759947\pi\) | |||||||
\(138\) | −1205.62 | −0.743691 | ||||||||
\(139\) | −525.977 | − | 911.018i | −0.320955 | − | 0.555910i | 0.659730 | − | 0.751502i | \(-0.270670\pi\) |
−0.980685 | + | 0.195592i | \(0.937337\pi\) | |||||||
\(140\) | −501.312 | + | 868.297i | −0.302633 | + | 0.524175i | ||||
\(141\) | −823.628 | + | 1426.57i | −0.491929 | + | 0.852046i | ||||
\(142\) | −168.305 | −0.0994639 | ||||||||
\(143\) | 256.419 | + | 447.310i | 0.149950 | + | 0.261580i | ||||
\(144\) | 124.882 | 0.0722698 | ||||||||
\(145\) | −41.1508 | + | 71.2753i | −0.0235682 | + | 0.0408213i | ||||
\(146\) | 555.852 | − | 962.764i | 0.315086 | − | 0.545746i | ||||
\(147\) | −2835.58 | − | 4911.37i | −1.59098 | − | 2.75566i | ||||
\(148\) | 1469.50 | 0.816165 | ||||||||
\(149\) | 1396.83 | + | 2419.38i | 0.768004 | + | 1.33022i | 0.938643 | + | 0.344889i | \(0.112083\pi\) |
−0.170639 | + | 0.985334i | \(0.554583\pi\) | |||||||
\(150\) | 423.673 | + | 733.822i | 0.230618 | + | 0.399442i | ||||
\(151\) | −1089.88 | −0.587374 | −0.293687 | − | 0.955902i | \(-0.594882\pi\) | ||||
−0.293687 | + | 0.955902i | \(0.594882\pi\) | |||||||
\(152\) | 189.459 | + | 328.153i | 0.101100 | + | 0.175110i | ||||
\(153\) | 207.992 | − | 360.253i | 0.109903 | − | 0.190358i | ||||
\(154\) | −283.225 | + | 490.560i | −0.148201 | + | 0.256691i | ||||
\(155\) | 1248.24 | 0.646845 | ||||||||
\(156\) | −815.160 | + | 1401.90i | −0.418365 | + | 0.719500i | ||||
\(157\) | 2.99728 | 0.00152362 | 0.000761812 | − | 1.00000i | \(-0.499758\pi\) | ||||
0.000761812 | 1.00000i | \(0.499758\pi\) | ||||||||
\(158\) | −180.238 | + | 312.182i | −0.0907530 | + | 0.157189i | ||||
\(159\) | 1258.64 | − | 2180.04i | 0.627780 | − | 1.08735i | ||||
\(160\) | 428.104 | + | 741.498i | 0.211529 | + | 0.366379i | ||||
\(161\) | −5387.77 | −2.63737 | ||||||||
\(162\) | 606.859 | + | 1051.11i | 0.294317 | + | 0.509772i | ||||
\(163\) | 207.984 | + | 360.239i | 0.0999421 | + | 0.173105i | 0.911660 | − | 0.410944i | \(-0.134801\pi\) |
−0.811718 | + | 0.584049i | \(0.801468\pi\) | |||||||
\(164\) | 267.757 | 0.127490 | ||||||||
\(165\) | 145.439 | + | 251.908i | 0.0686206 | + | 0.118854i | ||||
\(166\) | 543.093 | − | 940.665i | 0.253929 | − | 0.439818i | ||||
\(167\) | 38.4111 | − | 66.5299i | 0.0177984 | − | 0.0308278i | −0.856989 | − | 0.515335i | \(-0.827668\pi\) |
0.874787 | + | 0.484507i | \(0.161001\pi\) | |||||||
\(168\) | −4156.64 | −1.90888 | ||||||||
\(169\) | −1086.75 | − | 1909.39i | −0.494652 | − | 0.869091i | ||||
\(170\) | 432.545 | 0.195145 | ||||||||
\(171\) | −59.6905 | + | 103.387i | −0.0266938 | + | 0.0462351i | ||||
\(172\) | 93.2028 | − | 161.432i | 0.0413177 | − | 0.0715644i | ||||
\(173\) | 1475.69 | + | 2555.96i | 0.648522 | + | 1.12327i | 0.983476 | + | 0.181039i | \(0.0579461\pi\) |
−0.334953 | + | 0.942235i | \(0.608721\pi\) | |||||||
\(174\) | −146.247 | −0.0637182 | ||||||||
\(175\) | 1893.34 | + | 3279.36i | 0.817845 | + | 1.41655i | ||||
\(176\) | −110.135 | − | 190.759i | −0.0471689 | − | 0.0816990i | ||||
\(177\) | 5006.42 | 2.12602 | ||||||||
\(178\) | 89.2780 | + | 154.634i | 0.0375937 | + | 0.0651141i | ||||
\(179\) | −1300.50 | + | 2252.54i | −0.543040 | + | 0.940572i | 0.455688 | + | 0.890140i | \(0.349393\pi\) |
−0.998727 | + | 0.0504326i | \(0.983940\pi\) | |||||||
\(180\) | −85.8339 | + | 148.669i | −0.0355427 | + | 0.0615617i | ||||
\(181\) | −3064.17 | −1.25833 | −0.629166 | − | 0.777271i | \(-0.716604\pi\) | ||||
−0.629166 | + | 0.777271i | \(0.716604\pi\) | |||||||
\(182\) | 1213.29 | − | 2086.60i | 0.494148 | − | 0.849829i | ||||
\(183\) | 1075.65 | 0.434504 | ||||||||
\(184\) | −1464.00 | + | 2535.72i | −0.586561 | + | 1.01595i | ||||
\(185\) | −561.579 | + | 972.684i | −0.223179 | + | 0.386558i | ||||
\(186\) | 1109.04 | + | 1920.91i | 0.437196 | + | 0.757246i | ||||
\(187\) | −733.722 | −0.286926 | ||||||||
\(188\) | 857.361 | + | 1484.99i | 0.332604 | + | 0.576086i | ||||
\(189\) | 2180.05 | + | 3775.95i | 0.839022 | + | 1.45323i | ||||
\(190\) | −124.134 | −0.0473979 | ||||||||
\(191\) | 1624.95 | + | 2814.50i | 0.615588 | + | 1.06623i | 0.990281 | + | 0.139081i | \(0.0444148\pi\) |
−0.374693 | + | 0.927149i | \(0.622252\pi\) | |||||||
\(192\) | −298.951 | + | 517.798i | −0.112369 | + | 0.194630i | ||||
\(193\) | 1382.67 | − | 2394.85i | 0.515683 | − | 0.893189i | −0.484152 | − | 0.874984i | \(-0.660872\pi\) |
0.999834 | − | 0.0182045i | \(-0.00579501\pi\) | |||||||
\(194\) | −1921.93 | −0.711271 | ||||||||
\(195\) | −616.419 | − | 1075.31i | −0.226373 | − | 0.394895i | ||||
\(196\) | −5903.43 | −2.15140 | ||||||||
\(197\) | −576.466 | + | 998.468i | −0.208485 | + | 0.361106i | −0.951237 | − | 0.308460i | \(-0.900187\pi\) |
0.742753 | + | 0.669566i | \(0.233520\pi\) | |||||||
\(198\) | −48.4934 | + | 83.9930i | −0.0174054 | + | 0.0301471i | ||||
\(199\) | −867.222 | − | 1502.07i | −0.308923 | − | 0.535071i | 0.669204 | − | 0.743079i | \(-0.266635\pi\) |
−0.978127 | + | 0.208008i | \(0.933302\pi\) | |||||||
\(200\) | 2057.88 | 0.727569 | ||||||||
\(201\) | −1984.33 | − | 3436.95i | −0.696336 | − | 1.20609i | ||||
\(202\) | −813.541 | − | 1409.09i | −0.283369 | − | 0.490809i | ||||
\(203\) | −653.559 | −0.225965 | ||||||||
\(204\) | −1153.87 | − | 1998.56i | −0.396015 | − | 0.685917i | ||||
\(205\) | −102.325 | + | 177.232i | −0.0348619 | + | 0.0603825i | ||||
\(206\) | 608.795 | − | 1054.46i | 0.205907 | − | 0.356641i | ||||
\(207\) | −922.487 | −0.309745 | ||||||||
\(208\) | 466.789 | + | 814.288i | 0.155606 | + | 0.271446i | ||||
\(209\) | 210.567 | 0.0696900 | ||||||||
\(210\) | 680.858 | − | 1179.28i | 0.223732 | − | 0.387515i | ||||
\(211\) | −348.235 | + | 603.160i | −0.113618 | + | 0.196793i | −0.917227 | − | 0.398366i | \(-0.869577\pi\) |
0.803608 | + | 0.595159i | \(0.202911\pi\) | |||||||
\(212\) | −1310.19 | − | 2269.32i | −0.424455 | − | 0.735178i | ||||
\(213\) | −686.315 | −0.220777 | ||||||||
\(214\) | 633.552 | + | 1097.34i | 0.202377 | + | 0.350527i | ||||
\(215\) | 71.2360 | + | 123.384i | 0.0225965 | + | 0.0391384i | ||||
\(216\) | 2369.50 | 0.746408 | ||||||||
\(217\) | 4956.14 | + | 8584.29i | 1.55044 | + | 2.68544i | ||||
\(218\) | 941.646 | − | 1630.98i | 0.292552 | − | 0.506715i | ||||
\(219\) | 2266.65 | − | 3925.95i | 0.699388 | − | 1.21138i | ||||
\(220\) | 302.791 | 0.0927917 | ||||||||
\(221\) | 3126.45 | + | 9.63616i | 0.951620 | + | 0.00293302i | ||||
\(222\) | −1995.81 | −0.603379 | ||||||||
\(223\) | 487.058 | − | 843.610i | 0.146259 | − | 0.253329i | −0.783583 | − | 0.621287i | \(-0.786610\pi\) |
0.929842 | + | 0.367959i | \(0.119943\pi\) | |||||||
\(224\) | −3399.58 | + | 5888.25i | −1.01404 | + | 1.75636i | ||||
\(225\) | 324.175 | + | 561.487i | 0.0960518 | + | 0.166367i | ||||
\(226\) | −924.398 | −0.272080 | ||||||||
\(227\) | −1423.18 | − | 2465.03i | −0.416124 | − | 0.720747i | 0.579422 | − | 0.815028i | \(-0.303278\pi\) |
−0.995546 | + | 0.0942803i | \(0.969945\pi\) | |||||||
\(228\) | 331.142 | + | 573.555i | 0.0961861 | + | 0.166599i | ||||
\(229\) | −1336.07 | −0.385545 | −0.192773 | − | 0.981243i | \(-0.561748\pi\) | ||||
−0.192773 | + | 0.981243i | \(0.561748\pi\) | |||||||
\(230\) | −479.606 | − | 830.702i | −0.137497 | − | 0.238152i | ||||
\(231\) | −1154.93 | + | 2000.40i | −0.328957 | + | 0.569770i | ||||
\(232\) | −177.589 | + | 307.593i | −0.0502555 | + | 0.0870451i | ||||
\(233\) | 667.227 | 0.187603 | 0.0938015 | − | 0.995591i | \(-0.470098\pi\) | ||||
0.0938015 | + | 0.995591i | \(0.470098\pi\) | |||||||
\(234\) | 207.738 | − | 357.264i | 0.0580352 | − | 0.0998082i | ||||
\(235\) | −1310.58 | −0.363800 | ||||||||
\(236\) | 2605.73 | − | 4513.26i | 0.718723 | − | 1.24487i | ||||
\(237\) | −734.975 | + | 1273.01i | −0.201442 | + | 0.348908i | ||||
\(238\) | 1717.43 | + | 2974.67i | 0.467749 | + | 0.810164i | ||||
\(239\) | 1121.96 | 0.303655 | 0.151827 | − | 0.988407i | \(-0.451484\pi\) | ||||
0.151827 | + | 0.988407i | \(0.451484\pi\) | |||||||
\(240\) | 264.759 | + | 458.576i | 0.0712088 | + | 0.123337i | ||||
\(241\) | 2213.08 | + | 3833.17i | 0.591524 | + | 1.02455i | 0.994027 | + | 0.109131i | \(0.0348068\pi\) |
−0.402504 | + | 0.915418i | \(0.631860\pi\) | |||||||
\(242\) | 171.067 | 0.0454406 | ||||||||
\(243\) | 858.641 | + | 1487.21i | 0.226674 | + | 0.392612i | ||||
\(244\) | 559.852 | − | 969.692i | 0.146889 | − | 0.254419i | ||||
\(245\) | 2256.03 | − | 3907.56i | 0.588296 | − | 1.01896i | ||||
\(246\) | −363.655 | −0.0942513 | ||||||||
\(247\) | −897.244 | − | 2.76543i | −0.231135 | − | 0.000712388i | ||||
\(248\) | 5386.85 | 1.37930 | ||||||||
\(249\) | 2214.62 | − | 3835.84i | 0.563639 | − | 0.976251i | ||||
\(250\) | −742.377 | + | 1285.83i | −0.187808 | + | 0.325293i | ||||
\(251\) | −3405.04 | − | 5897.70i | −0.856271 | − | 1.48311i | −0.875460 | − | 0.483290i | \(-0.839442\pi\) |
0.0191889 | − | 0.999816i | \(-0.493892\pi\) | |||||||
\(252\) | −1363.22 | −0.340772 | ||||||||
\(253\) | 813.551 | + | 1409.11i | 0.202164 | + | 0.350158i | ||||
\(254\) | 1566.71 | + | 2713.62i | 0.387024 | + | 0.670345i | ||||
\(255\) | 1763.83 | 0.433158 | ||||||||
\(256\) | 1366.82 | + | 2367.40i | 0.333697 | + | 0.577980i | ||||
\(257\) | 399.940 | − | 692.716i | 0.0970723 | − | 0.168134i | −0.813399 | − | 0.581706i | \(-0.802386\pi\) |
0.910472 | + | 0.413572i | \(0.135719\pi\) | |||||||
\(258\) | −126.584 | + | 219.250i | −0.0305456 | + | 0.0529065i | ||||
\(259\) | −8919.03 | −2.13977 | ||||||||
\(260\) | −1290.22 | − | 3.97663i | −0.307754 | − | 0.000948540i | ||||
\(261\) | −111.902 | −0.0265384 | ||||||||
\(262\) | −1375.74 | + | 2382.85i | −0.324402 | + | 0.561881i | ||||
\(263\) | −1233.14 | + | 2135.87i | −0.289122 | + | 0.500773i | −0.973600 | − | 0.228260i | \(-0.926696\pi\) |
0.684479 | + | 0.729033i | \(0.260030\pi\) | |||||||
\(264\) | 627.651 | + | 1087.12i | 0.146323 | + | 0.253439i | ||||
\(265\) | 2002.79 | 0.464267 | ||||||||
\(266\) | −492.874 | − | 853.683i | −0.113609 | − | 0.196777i | ||||
\(267\) | 364.058 | + | 630.566i | 0.0834456 | + | 0.144532i | ||||
\(268\) | −4131.20 | −0.941615 | ||||||||
\(269\) | −808.181 | − | 1399.81i | −0.183181 | − | 0.317279i | 0.759781 | − | 0.650179i | \(-0.225306\pi\) |
−0.942962 | + | 0.332900i | \(0.891973\pi\) | |||||||
\(270\) | −388.125 | + | 672.252i | −0.0874834 | + | 0.151526i | ||||
\(271\) | −739.554 | + | 1280.94i | −0.165774 | + | 0.287129i | −0.936930 | − | 0.349518i | \(-0.886345\pi\) |
0.771156 | + | 0.636646i | \(0.219679\pi\) | |||||||
\(272\) | −1335.68 | −0.297748 | ||||||||
\(273\) | 4947.54 | − | 8508.72i | 1.09685 | − | 1.88634i | ||||
\(274\) | −1036.11 | −0.228443 | ||||||||
\(275\) | 571.787 | − | 990.363i | 0.125382 | − | 0.217168i | ||||
\(276\) | −2558.82 | + | 4432.00i | −0.558054 | + | 0.966577i | ||||
\(277\) | −2006.73 | − | 3475.76i | −0.435281 | − | 0.753928i | 0.562038 | − | 0.827111i | \(-0.310017\pi\) |
−0.997318 | + | 0.0731835i | \(0.976684\pi\) | |||||||
\(278\) | 1487.23 | 0.320857 | ||||||||
\(279\) | 848.584 | + | 1469.79i | 0.182091 | + | 0.315391i | ||||
\(280\) | −1653.54 | − | 2864.02i | −0.352922 | − | 0.611278i | ||||
\(281\) | 5857.68 | 1.24356 | 0.621779 | − | 0.783193i | \(-0.286410\pi\) | ||||
0.621779 | + | 0.783193i | \(0.286410\pi\) | |||||||
\(282\) | −1164.43 | − | 2016.85i | −0.245889 | − | 0.425892i | ||||
\(283\) | 456.155 | − | 790.083i | 0.0958148 | − | 0.165956i | −0.814134 | − | 0.580678i | \(-0.802788\pi\) |
0.909948 | + | 0.414722i | \(0.136121\pi\) | |||||||
\(284\) | −357.212 | + | 618.709i | −0.0746360 | + | 0.129273i | ||||
\(285\) | −506.192 | −0.105208 | ||||||||
\(286\) | −728.933 | − | 2.24667i | −0.150709 | − | 0.000464505i | ||||
\(287\) | −1625.13 | −0.334245 | ||||||||
\(288\) | −582.072 | + | 1008.18i | −0.119093 | + | 0.206276i | ||||
\(289\) | 231.919 | − | 401.696i | 0.0472053 | − | 0.0817619i | ||||
\(290\) | −58.1782 | − | 100.768i | −0.0117805 | − | 0.0204044i | ||||
\(291\) | −7837.24 | −1.57879 | ||||||||
\(292\) | −2359.49 | − | 4086.75i | −0.472871 | − | 0.819037i | ||||
\(293\) | −2748.51 | − | 4760.56i | −0.548020 | − | 0.949198i | −0.998410 | − | 0.0563663i | \(-0.982049\pi\) |
0.450390 | − | 0.892832i | \(-0.351285\pi\) | |||||||
\(294\) | 8017.77 | 1.59050 | ||||||||
\(295\) | 1991.59 | + | 3449.54i | 0.393068 | + | 0.680813i | ||||
\(296\) | −2423.53 | + | 4197.68i | −0.475895 | + | 0.824274i | ||||
\(297\) | 658.372 | − | 1140.33i | 0.128628 | − | 0.222791i | ||||
\(298\) | −3949.62 | −0.767769 | ||||||||
\(299\) | −3448.10 | − | 6015.03i | −0.666920 | − | 1.16341i | ||||
\(300\) | 3596.82 | 0.692208 | ||||||||
\(301\) | −565.687 | + | 979.798i | −0.108324 | + | 0.187623i | ||||
\(302\) | 770.427 | − | 1334.42i | 0.146798 | − | 0.254262i | ||||
\(303\) | −3317.45 | − | 5746.00i | −0.628986 | − | 1.08944i | ||||
\(304\) | 383.319 | 0.0723185 | ||||||||
\(305\) | 427.901 | + | 741.147i | 0.0803330 | + | 0.139141i | ||||
\(306\) | 294.055 | + | 509.318i | 0.0549347 | + | 0.0951497i | ||||
\(307\) | −6790.79 | −1.26245 | −0.631223 | − | 0.775602i | \(-0.717447\pi\) | ||||
−0.631223 | + | 0.775602i | \(0.717447\pi\) | |||||||
\(308\) | 1202.24 | + | 2082.33i | 0.222415 | + | 0.385234i | ||||
\(309\) | 2482.54 | − | 4299.89i | 0.457045 | − | 0.791626i | ||||
\(310\) | −882.367 | + | 1528.30i | −0.161662 | + | 0.280006i | ||||
\(311\) | −4402.30 | −0.802673 | −0.401337 | − | 0.915931i | \(-0.631454\pi\) | ||||
−0.401337 | + | 0.915931i | \(0.631454\pi\) | |||||||
\(312\) | −2660.20 | − | 4640.57i | −0.482705 | − | 0.842052i | ||||
\(313\) | 8325.85 | 1.50353 | 0.751765 | − | 0.659431i | \(-0.229203\pi\) | ||||
0.751765 | + | 0.659431i | \(0.229203\pi\) | |||||||
\(314\) | −2.11875 | + | 3.66977i | −0.000380789 | + | 0.000659546i | ||||
\(315\) | 520.961 | − | 902.332i | 0.0931837 | − | 0.161399i | ||||
\(316\) | 765.077 | + | 1325.15i | 0.136199 | + | 0.235904i | ||||
\(317\) | 6896.82 | 1.22197 | 0.610984 | − | 0.791643i | \(-0.290774\pi\) | ||||
0.610984 | + | 0.791643i | \(0.290774\pi\) | |||||||
\(318\) | 1779.45 | + | 3082.09i | 0.313794 | + | 0.543507i | ||||
\(319\) | 98.6872 | + | 170.931i | 0.0173211 | + | 0.0300010i | ||||
\(320\) | −475.700 | −0.0831014 | ||||||||
\(321\) | 2583.49 | + | 4474.74i | 0.449211 | + | 0.778056i | ||||
\(322\) | 3808.56 | − | 6596.62i | 0.659139 | − | 1.14166i | ||||
\(323\) | 638.420 | − | 1105.78i | 0.109977 | − | 0.190486i | ||||
\(324\) | 5152.00 | 0.883402 | ||||||||
\(325\) | −2449.44 | + | 4212.51i | −0.418063 | + | 0.718979i | ||||
\(326\) | −588.087 | −0.0999115 | ||||||||
\(327\) | 3839.84 | − | 6650.80i | 0.649369 | − | 1.12474i | ||||
\(328\) | −441.589 | + | 764.855i | −0.0743375 | + | 0.128756i | ||||
\(329\) | −5203.68 | − | 9013.04i | −0.872001 | − | 1.51035i | ||||
\(330\) | −411.237 | −0.0685996 | ||||||||
\(331\) | 5285.30 | + | 9154.41i | 0.877663 | + | 1.52016i | 0.853898 | + | 0.520440i | \(0.174232\pi\) |
0.0237651 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(332\) | −2305.33 | − | 3992.95i | −0.381088 | − | 0.660064i | ||||
\(333\) | −1527.10 | −0.251306 | ||||||||
\(334\) | 54.3048 | + | 94.0587i | 0.00889649 | + | 0.0154092i | ||||
\(335\) | 1578.76 | − | 2734.49i | 0.257483 | − | 0.445974i | ||||
\(336\) | −2102.46 | + | 3641.56i | −0.341364 | + | 0.591260i | ||||
\(337\) | 106.696 | 0.0172465 | 0.00862326 | − | 0.999963i | \(-0.497255\pi\) | ||||
0.00862326 | + | 0.999963i | \(0.497255\pi\) | |||||||
\(338\) | 3106.02 | + | 19.1465i | 0.499837 | + | 0.00308116i | ||||
\(339\) | −3769.51 | −0.603928 | ||||||||
\(340\) | 918.036 | − | 1590.09i | 0.146434 | − | 0.253631i | ||||
\(341\) | 1496.75 | − | 2592.45i | 0.237694 | − | 0.411698i | ||||
\(342\) | −84.3892 | − | 146.166i | −0.0133428 | − | 0.0231105i | ||||
\(343\) | 23337.0 | 3.67370 | ||||||||
\(344\) | 307.423 | + | 532.473i | 0.0481836 | + | 0.0834564i | ||||
\(345\) | −1955.74 | − | 3387.43i | −0.305198 | − | 0.528618i | ||||
\(346\) | −4172.59 | −0.648324 | ||||||||
\(347\) | 671.562 | + | 1163.18i | 0.103894 | + | 0.179950i | 0.913286 | − | 0.407319i | \(-0.133536\pi\) |
−0.809392 | + | 0.587269i | \(0.800203\pi\) | |||||||
\(348\) | −310.395 | + | 537.621i | −0.0478131 | + | 0.0828146i | ||||
\(349\) | 2150.41 | − | 3724.61i | 0.329824 | − | 0.571272i | −0.652653 | − | 0.757657i | \(-0.726344\pi\) |
0.982477 | + | 0.186385i | \(0.0596772\pi\) | |||||||
\(350\) | −5353.53 | −0.817594 | ||||||||
\(351\) | −2820.36 | + | 4850.42i | −0.428888 | + | 0.737595i | ||||
\(352\) | 2053.34 | 0.310919 | ||||||||
\(353\) | −3343.20 | + | 5790.60i | −0.504081 | + | 0.873095i | 0.495907 | + | 0.868375i | \(0.334836\pi\) |
−0.999989 | + | 0.00471927i | \(0.998498\pi\) | |||||||
\(354\) | −3538.99 | + | 6129.70i | −0.531342 | + | 0.920311i | ||||
\(355\) | −273.021 | − | 472.887i | −0.0408182 | − | 0.0706992i | ||||
\(356\) | 757.936 | 0.112839 | ||||||||
\(357\) | 7003.31 | + | 12130.1i | 1.03825 | + | 1.79830i | ||||
\(358\) | −1838.62 | − | 3184.59i | −0.271437 | − | 0.470142i | ||||
\(359\) | −10285.4 | −1.51209 | −0.756046 | − | 0.654519i | \(-0.772871\pi\) | ||||
−0.756046 | + | 0.654519i | \(0.772871\pi\) | |||||||
\(360\) | −283.117 | − | 490.374i | −0.0414489 | − | 0.0717915i | ||||
\(361\) | 3246.28 | − | 5622.73i | 0.473288 | − | 0.819759i | ||||
\(362\) | 2166.03 | − | 3751.68i | 0.314487 | − | 0.544707i | ||||
\(363\) | 697.578 | 0.100863 | ||||||||
\(364\) | −5095.48 | − | 8888.79i | −0.733725 | − | 1.27994i | ||||
\(365\) | 3606.77 | 0.517224 | ||||||||
\(366\) | −760.365 | + | 1316.99i | −0.108593 | + | 0.188088i | ||||
\(367\) | −1029.49 | + | 1783.13i | −0.146428 | + | 0.253620i | −0.929905 | − | 0.367801i | \(-0.880111\pi\) |
0.783477 | + | 0.621421i | \(0.213444\pi\) | |||||||
\(368\) | 1481.00 | + | 2565.16i | 0.209789 | + | 0.363365i | ||||
\(369\) | −278.252 | −0.0392554 | ||||||||
\(370\) | −793.950 | − | 1375.16i | −0.111555 | − | 0.193220i | ||||
\(371\) | 7952.12 | + | 13773.5i | 1.11281 | + | 1.92745i | ||||
\(372\) | 9415.30 | 1.31226 | ||||||||
\(373\) | −4396.59 | − | 7615.12i | −0.610314 | − | 1.05709i | −0.991187 | − | 0.132467i | \(-0.957710\pi\) |
0.380874 | − | 0.924627i | \(-0.375623\pi\) | |||||||
\(374\) | 518.661 | − | 898.347i | 0.0717094 | − | 0.124204i | ||||
\(375\) | −3027.26 | + | 5243.37i | −0.416872 | + | 0.722044i | ||||
\(376\) | −5655.90 | −0.775746 | ||||||||
\(377\) | −418.270 | − | 729.649i | −0.0571405 | − | 0.0996785i | ||||
\(378\) | −6164.21 | −0.838764 | ||||||||
\(379\) | 2423.59 | − | 4197.79i | 0.328474 | − | 0.568934i | −0.653735 | − | 0.756723i | \(-0.726799\pi\) |
0.982209 | + | 0.187790i | \(0.0601323\pi\) | |||||||
\(380\) | −263.462 | + | 456.330i | −0.0355666 | + | 0.0616032i | ||||
\(381\) | 6388.72 | + | 11065.6i | 0.859066 | + | 1.48795i | ||||
\(382\) | −4594.65 | −0.615399 | ||||||||
\(383\) | −6794.74 | − | 11768.8i | −0.906515 | − | 1.57013i | −0.818871 | − | 0.573977i | \(-0.805400\pi\) |
−0.0876434 | − | 0.996152i | \(-0.527934\pi\) | |||||||
\(384\) | 3881.98 | + | 6723.79i | 0.515889 | + | 0.893547i | ||||
\(385\) | −1837.77 | −0.243276 | ||||||||
\(386\) | 1954.79 | + | 3385.80i | 0.257762 | + | 0.446457i | ||||
\(387\) | −96.8561 | + | 167.760i | −0.0127221 | + | 0.0220354i | ||||
\(388\) | −4079.12 | + | 7065.24i | −0.533726 | + | 0.924441i | ||||
\(389\) | 11891.3 | 1.54991 | 0.774955 | − | 0.632017i | \(-0.217773\pi\) | ||||
0.774955 | + | 0.632017i | \(0.217773\pi\) | |||||||
\(390\) | 1752.32 | + | 5.40088i | 0.227518 | + | 0.000701242i | ||||
\(391\) | 9866.46 | 1.27613 | ||||||||
\(392\) | 9736.04 | − | 16863.3i | 1.25445 | − | 2.17277i | ||||
\(393\) | −5609.98 | + | 9716.77i | −0.720066 | + | 1.24719i | ||||
\(394\) | −814.996 | − | 1411.61i | −0.104210 | − | 0.180498i | ||||
\(395\) | −1169.51 | −0.148974 | ||||||||
\(396\) | 205.845 | + | 356.534i | 0.0261215 | + | 0.0452437i | ||||
\(397\) | −4558.45 | − | 7895.48i | −0.576278 | − | 0.998142i | −0.995902 | − | 0.0904443i | \(-0.971171\pi\) |
0.419624 | − | 0.907698i | \(-0.362162\pi\) | |||||||
\(398\) | 2452.12 | 0.308829 | ||||||||
\(399\) | −2009.84 | − | 3481.15i | −0.252175 | − | 0.436780i | ||||
\(400\) | 1040.89 | − | 1802.87i | 0.130111 | − | 0.225359i | ||||
\(401\) | −7363.38 | + | 12753.8i | −0.916982 | + | 1.58826i | −0.113009 | + | 0.993594i | \(0.536049\pi\) |
−0.803973 | + | 0.594666i | \(0.797284\pi\) | |||||||
\(402\) | 5610.80 | 0.696123 | ||||||||
\(403\) | −6411.83 | + | 11027.0i | −0.792546 | + | 1.36301i | ||||
\(404\) | −6906.65 | −0.850541 | ||||||||
\(405\) | −1968.87 | + | 3410.18i | −0.241565 | + | 0.418403i | ||||
\(406\) | 461.994 | − | 800.198i | 0.0564739 | − | 0.0978157i | ||||
\(407\) | 1346.77 | + | 2332.67i | 0.164022 | + | 0.284094i | ||||
\(408\) | 7611.92 | 0.923643 | ||||||||
\(409\) | −252.867 | − | 437.978i | −0.0305708 | − | 0.0529502i | 0.850335 | − | 0.526241i | \(-0.176399\pi\) |
−0.880906 | + | 0.473291i | \(0.843066\pi\) | |||||||
\(410\) | −144.665 | − | 250.567i | −0.0174256 | − | 0.0301820i | ||||
\(411\) | −4225.03 | −0.507069 | ||||||||
\(412\) | −2584.22 | − | 4476.00i | −0.309018 | − | 0.535235i | ||||
\(413\) | −15815.3 | + | 27392.9i | −1.88431 | + | 3.26372i | ||||
\(414\) | 652.096 | − | 1129.46i | 0.0774125 | − | 0.134082i | ||||
\(415\) | 3523.98 | 0.416832 | ||||||||
\(416\) | −8749.47 | − | 26.9671i | −1.03120 | − | 0.00317829i | ||||
\(417\) | 6064.62 | 0.712196 | ||||||||
\(418\) | −148.848 | + | 257.812i | −0.0174172 | + | 0.0301674i | ||||
\(419\) | −8274.89 | + | 14332.5i | −0.964809 | + | 1.67110i | −0.254681 | + | 0.967025i | \(0.581970\pi\) |
−0.710128 | + | 0.704073i | \(0.751363\pi\) | |||||||
\(420\) | −2890.11 | − | 5005.83i | −0.335769 | − | 0.581570i | ||||
\(421\) | −6756.16 | −0.782126 | −0.391063 | − | 0.920364i | \(-0.627893\pi\) | ||||
−0.391063 | + | 0.920364i | \(0.627893\pi\) | |||||||
\(422\) | −492.327 | − | 852.736i | −0.0567917 | − | 0.0983662i | ||||
\(423\) | −890.967 | − | 1543.20i | −0.102412 | − | 0.177383i | ||||
\(424\) | 8643.18 | 0.989976 | ||||||||
\(425\) | −3467.21 | − | 6005.39i | −0.395728 | − | 0.685421i | ||||
\(426\) | 485.149 | − | 840.303i | 0.0551773 | − | 0.0955700i | ||||
\(427\) | −3397.97 | + | 5885.46i | −0.385104 | + | 0.667020i | ||||
\(428\) | 5378.61 | 0.607442 | ||||||||
\(429\) | −2972.44 | − | 9.16147i | −0.334524 | − | 0.00103105i | ||||
\(430\) | −201.424 | −0.0225896 | ||||||||
\(431\) | 819.536 | − | 1419.48i | 0.0915909 | − | 0.158640i | −0.816590 | − | 0.577218i | \(-0.804138\pi\) |
0.908181 | + | 0.418578i | \(0.137471\pi\) | |||||||
\(432\) | 1198.51 | − | 2075.88i | 0.133480 | − | 0.231194i | ||||
\(433\) | −4913.07 | − | 8509.69i | −0.545282 | − | 0.944456i | −0.998589 | − | 0.0531016i | \(-0.983089\pi\) |
0.453307 | − | 0.891354i | \(-0.350244\pi\) | |||||||
\(434\) | −14013.8 | −1.54996 | ||||||||
\(435\) | −237.239 | − | 410.910i | −0.0261488 | − | 0.0452911i | ||||
\(436\) | −3997.11 | − | 6923.20i | −0.439052 | − | 0.760461i | ||||
\(437\) | −2831.52 | −0.309954 | ||||||||
\(438\) | 3204.55 | + | 5550.43i | 0.349587 | + | 0.605502i | ||||
\(439\) | 6332.64 | − | 10968.5i | 0.688475 | − | 1.19247i | −0.283856 | − | 0.958867i | \(-0.591614\pi\) |
0.972331 | − | 0.233607i | \(-0.0750528\pi\) | |||||||
\(440\) | −499.369 | + | 864.932i | −0.0541056 | + | 0.0937136i | ||||
\(441\) | 6134.83 | 0.662437 | ||||||||
\(442\) | −2221.86 | + | 3821.12i | −0.239102 | + | 0.411204i | ||||
\(443\) | −8179.44 | −0.877239 | −0.438619 | − | 0.898673i | \(-0.644532\pi\) | ||||
−0.438619 | + | 0.898673i | \(0.644532\pi\) | |||||||
\(444\) | −4235.92 | + | 7336.83i | −0.452766 | + | 0.784213i | ||||
\(445\) | −289.650 | + | 501.688i | −0.0308556 | + | 0.0534434i | ||||
\(446\) | 688.593 | + | 1192.68i | 0.0731073 | + | 0.126626i | ||||
\(447\) | −16105.7 | −1.70419 | ||||||||
\(448\) | −1888.77 | − | 3271.45i | −0.199188 | − | 0.345003i | ||||
\(449\) | 8209.81 | + | 14219.8i | 0.862906 | + | 1.49460i | 0.869111 | + | 0.494616i | \(0.164691\pi\) |
−0.00620552 | + | 0.999981i | \(0.501975\pi\) | |||||||
\(450\) | −916.623 | −0.0960223 | ||||||||
\(451\) | 245.394 | + | 425.034i | 0.0256212 | + | 0.0443771i | ||||
\(452\) | −1961.95 | + | 3398.19i | −0.204164 | + | 0.353623i | ||||
\(453\) | 3141.65 | − | 5441.49i | 0.325844 | − | 0.564379i | ||||
\(454\) | 4024.14 | 0.415996 | ||||||||
\(455\) | 7830.88 | + | 24.1358i | 0.806851 | + | 0.00248683i | ||||
\(456\) | −2184.50 | −0.224339 | ||||||||
\(457\) | −3405.48 | + | 5898.47i | −0.348581 | + | 0.603761i | −0.985998 | − | 0.166759i | \(-0.946670\pi\) |
0.637416 | + | 0.770520i | \(0.280003\pi\) | |||||||
\(458\) | 944.453 | − | 1635.84i | 0.0963567 | − | 0.166895i | ||||
\(459\) | −3992.25 | − | 6914.78i | −0.405975 | − | 0.703169i | ||||
\(460\) | −4071.67 | −0.412702 | ||||||||
\(461\) | 1227.58 | + | 2126.22i | 0.124021 | + | 0.214811i | 0.921350 | − | 0.388734i | \(-0.127088\pi\) |
−0.797329 | + | 0.603545i | \(0.793754\pi\) | |||||||
\(462\) | −1632.82 | − | 2828.13i | −0.164428 | − | 0.284798i | ||||
\(463\) | 244.604 | 0.0245523 | 0.0122761 | − | 0.999925i | \(-0.496092\pi\) | ||||
0.0122761 | + | 0.999925i | \(0.496092\pi\) | |||||||
\(464\) | 179.651 | + | 311.165i | 0.0179744 | + | 0.0311325i | ||||
\(465\) | −3598.11 | + | 6232.12i | −0.358836 | + | 0.621521i | ||||
\(466\) | −471.656 | + | 816.932i | −0.0468864 | + | 0.0812095i | ||||
\(467\) | −8341.80 | −0.826579 | −0.413289 | − | 0.910600i | \(-0.635620\pi\) | ||||
−0.413289 | + | 0.910600i | \(0.635620\pi\) | |||||||
\(468\) | −872.441 | − | 1521.93i | −0.0861723 | − | 0.150323i | ||||
\(469\) | 25074.0 | 2.46867 | ||||||||
\(470\) | 926.437 | − | 1604.64i | 0.0909221 | − | 0.157482i | ||||
\(471\) | −8.63981 | + | 14.9646i | −0.000845226 | + | 0.00146397i | ||||
\(472\) | 8594.84 | + | 14886.7i | 0.838156 | + | 1.45173i | ||||
\(473\) | 341.674 | 0.0332139 | ||||||||
\(474\) | −1039.09 | − | 1799.76i | −0.100690 | − | 0.174400i | ||||
\(475\) | 995.036 | + | 1723.45i | 0.0961165 | + | 0.166479i | ||||
\(476\) | 14580.3 | 1.40396 | ||||||||
\(477\) | 1361.55 | + | 2358.27i | 0.130694 | + | 0.226369i | ||||
\(478\) | −793.101 | + | 1373.69i | −0.0758904 | + | 0.131446i | ||||
\(479\) | 6949.98 | − | 12037.7i | 0.662949 | − | 1.14826i | −0.316888 | − | 0.948463i | \(-0.602638\pi\) |
0.979837 | − | 0.199799i | \(-0.0640288\pi\) | |||||||
\(480\) | −4936.13 | −0.469380 | ||||||||
\(481\) | −5708.07 | − | 9957.41i | −0.541092 | − | 0.943906i | ||||
\(482\) | −6257.63 | −0.591342 | ||||||||
\(483\) | 15530.5 | − | 26899.7i | 1.46307 | − | 2.53412i | ||||
\(484\) | 363.074 | − | 628.863i | 0.0340979 | − | 0.0590593i | ||||
\(485\) | −3117.72 | − | 5400.04i | −0.291893 | − | 0.505574i | ||||
\(486\) | −2427.86 | −0.226605 | ||||||||
\(487\) | 2814.79 | + | 4875.36i | 0.261910 | + | 0.453642i | 0.966750 | − | 0.255725i | \(-0.0823142\pi\) |
−0.704839 | + | 0.709367i | \(0.748981\pi\) | |||||||
\(488\) | 1846.63 | + | 3198.46i | 0.171298 | + | 0.296696i | ||||
\(489\) | −2398.10 | −0.221771 | ||||||||
\(490\) | 3189.53 | + | 5524.43i | 0.294058 | + | 0.509323i | ||||
\(491\) | −2275.54 | + | 3941.35i | −0.209152 | + | 0.362262i | −0.951448 | − | 0.307811i | \(-0.900404\pi\) |
0.742296 | + | 0.670073i | \(0.233737\pi\) | |||||||
\(492\) | −771.824 | + | 1336.84i | −0.0707246 | + | 0.122499i | ||||
\(493\) | 1196.84 | 0.109337 | ||||||||
\(494\) | 637.638 | − | 1096.60i | 0.0580743 | − | 0.0998755i | ||||
\(495\) | −314.660 | −0.0285715 | ||||||||
\(496\) | 2724.70 | − | 4719.33i | 0.246659 | − | 0.427226i | ||||
\(497\) | 2168.07 | − | 3755.21i | 0.195676 | − | 0.338922i | ||||
\(498\) | 3130.99 | + | 5423.04i | 0.281733 | + | 0.487976i | ||||
\(499\) | 10244.4 | 0.919046 | 0.459523 | − | 0.888166i | \(-0.348020\pi\) | ||||
0.459523 | + | 0.888166i | \(0.348020\pi\) | |||||||
\(500\) | 3151.25 | + | 5458.12i | 0.281856 | + | 0.488189i | ||||
\(501\) | 221.444 | + | 383.552i | 0.0197473 | + | 0.0342033i | ||||
\(502\) | 9627.95 | 0.856009 | ||||||||
\(503\) | −5672.06 | − | 9824.30i | −0.502793 | − | 0.870862i | −0.999995 | − | 0.00322754i | \(-0.998973\pi\) |
0.497202 | − | 0.867635i | \(-0.334361\pi\) | |||||||
\(504\) | 2248.24 | − | 3894.07i | 0.198700 | − | 0.344158i | ||||
\(505\) | 2639.42 | − | 4571.60i | 0.232579 | − | 0.402839i | ||||
\(506\) | −2300.36 | −0.202102 | ||||||||
\(507\) | 12665.7 | + | 78.0756i | 1.10947 | + | 0.00683917i | ||||
\(508\) | 13300.8 | 1.16167 | ||||||||
\(509\) | −540.233 | + | 935.712i | −0.0470441 | + | 0.0814827i | −0.888589 | − | 0.458705i | \(-0.848313\pi\) |
0.841545 | + | 0.540188i | \(0.181647\pi\) | |||||||
\(510\) | −1246.83 | + | 2159.58i | −0.108256 | + | 0.187506i | ||||
\(511\) | 14320.7 | + | 24804.2i | 1.23975 | + | 2.14730i | ||||
\(512\) | 6908.96 | 0.596359 | ||||||||
\(513\) | 1145.71 | + | 1984.43i | 0.0986053 | + | 0.170789i | ||||
\(514\) | 565.427 | + | 979.349i | 0.0485212 | + | 0.0840413i | ||||
\(515\) | 3950.30 | 0.338002 | ||||||||
\(516\) | 537.324 | + | 930.673i | 0.0458418 | + | 0.0794004i | ||||
\(517\) | −1571.51 | + | 2721.93i | −0.133684 | + | 0.231548i | ||||
\(518\) | 6304.77 | − | 10920.2i | 0.534779 | − | 0.926265i | ||||
\(519\) | −17015.0 | −1.43907 | ||||||||
\(520\) | 2139.21 | − | 3678.99i | 0.180405 | − | 0.310258i | ||||
\(521\) | 364.476 | 0.0306488 | 0.0153244 | − | 0.999883i | \(-0.495122\pi\) | ||||
0.0153244 | + | 0.999883i | \(0.495122\pi\) | |||||||
\(522\) | 79.1020 | − | 137.009i | 0.00663257 | − | 0.0114880i | ||||
\(523\) | 3706.38 | − | 6419.64i | 0.309883 | − | 0.536733i | −0.668454 | − | 0.743754i | \(-0.733044\pi\) |
0.978336 | + | 0.207021i | \(0.0663769\pi\) | |||||||
\(524\) | 5839.74 | + | 10114.7i | 0.486852 | + | 0.843252i | ||||
\(525\) | −21830.6 | −1.81479 | ||||||||
\(526\) | −1743.40 | − | 3019.65i | −0.144516 | − | 0.250310i | ||||
\(527\) | −9076.03 | − | 15720.1i | −0.750205 | − | 1.29939i | ||||
\(528\) | 1269.88 | 0.104667 | ||||||||
\(529\) | −4856.42 | − | 8411.57i | −0.399147 | − | 0.691343i | ||||
\(530\) | −1415.76 | + | 2452.16i | −0.116031 | + | 0.200972i | ||||
\(531\) | −2707.87 | + | 4690.17i | −0.221302 | + | 0.383307i | ||||
\(532\) | −4184.32 | −0.341002 | ||||||||
\(533\) | −1040.06 | − | 1814.33i | −0.0845217 | − | 0.147444i | ||||
\(534\) | −1029.39 | −0.0834200 | ||||||||
\(535\) | −2055.47 | + | 3560.18i | −0.166104 | + | 0.287701i | ||||
\(536\) | 6813.24 | − | 11800.9i | 0.549043 | − | 0.950971i | ||||
\(537\) | −7497.53 | − | 12986.1i | −0.602500 | − | 1.04356i | ||||
\(538\) | 2285.18 | 0.183125 | ||||||||
\(539\) | −5410.37 | − | 9371.04i | −0.432358 | − | 0.748867i | ||||
\(540\) | 1647.52 | + | 2853.58i | 0.131292 | + | 0.227405i | ||||
\(541\) | −15557.0 | −1.23632 | −0.618160 | − | 0.786052i | \(-0.712122\pi\) | ||||
−0.618160 | + | 0.786052i | \(0.712122\pi\) | |||||||
\(542\) | −1045.57 | − | 1810.97i | −0.0828614 | − | 0.143520i | ||||
\(543\) | 8832.65 | − | 15298.6i | 0.698057 | − | 1.20907i | ||||
\(544\) | 6225.55 | − | 10783.0i | 0.490659 | − | 0.849846i | ||||
\(545\) | 6110.08 | 0.480233 | ||||||||
\(546\) | 6920.45 | + | 12072.4i | 0.542432 | + | 0.946243i | ||||
\(547\) | 9260.17 | 0.723833 | 0.361916 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361916 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(548\) | −2199.04 | + | 3808.84i | −0.171420 | + | 0.296908i | ||||
\(549\) | −581.796 | + | 1007.70i | −0.0452285 | + | 0.0783381i | ||||
\(550\) | 808.380 | + | 1400.16i | 0.0626717 | + | 0.108551i | ||||
\(551\) | −343.475 | −0.0265563 | ||||||||
\(552\) | −8440.10 | − | 14618.7i | −0.650787 | − | 1.12720i | ||||
\(553\) | −4643.57 | − | 8042.90i | −0.357079 | − | 0.618479i | ||||
\(554\) | 5674.15 | 0.435147 | ||||||||
\(555\) | −3237.57 | − | 5607.63i | −0.247616 | − | 0.428884i | ||||
\(556\) | 3156.50 | − | 5467.23i | 0.240765 | − | 0.417018i | ||||
\(557\) | 4868.47 | − | 8432.44i | 0.370348 | − | 0.641462i | −0.619271 | − | 0.785177i | \(-0.712572\pi\) |
0.989619 | + | 0.143716i | \(0.0459051\pi\) | |||||||
\(558\) | −2399.42 | −0.182035 | ||||||||
\(559\) | −1455.90 | − | 4.48729i | −0.110158 | − | 0.000339521i | ||||
\(560\) | −3345.49 | −0.252452 | ||||||||
\(561\) | 2114.99 | − | 3663.28i | 0.159171 | − | 0.275693i | ||||
\(562\) | −4140.73 | + | 7171.96i | −0.310794 | + | 0.538311i | ||||
\(563\) | 4454.36 | + | 7715.17i | 0.333444 | + | 0.577541i | 0.983185 | − | 0.182614i | \(-0.0584560\pi\) |
−0.649741 | + | 0.760156i | \(0.725123\pi\) | |||||||
\(564\) | −9885.55 | −0.738044 | ||||||||
\(565\) | −1499.54 | − | 2597.28i | −0.111657 | − | 0.193395i | ||||
\(566\) | 644.903 | + | 1117.00i | 0.0478927 | + | 0.0829526i | ||||
\(567\) | −31269.6 | −2.31605 | ||||||||
\(568\) | −1178.24 | − | 2040.77i | −0.0870385 | − | 0.150755i | ||||
\(569\) | 4900.68 | − | 8488.22i | 0.361067 | − | 0.625386i | −0.627070 | − | 0.778963i | \(-0.715746\pi\) |
0.988137 | + | 0.153577i | \(0.0490793\pi\) | |||||||
\(570\) | 357.822 | − | 619.766i | 0.0262939 | − | 0.0455424i | ||||
\(571\) | −22452.5 | −1.64555 | −0.822774 | − | 0.568369i | \(-0.807575\pi\) | ||||
−0.822774 | + | 0.568369i | \(0.807575\pi\) | |||||||
\(572\) | −1555.35 | + | 2674.87i | −0.113693 | + | 0.195528i | ||||
\(573\) | −18736.0 | −1.36598 | ||||||||
\(574\) | 1148.79 | − | 1989.76i | 0.0835356 | − | 0.144688i | ||||
\(575\) | −7688.88 | + | 13317.5i | −0.557650 | + | 0.965878i | ||||
\(576\) | −323.393 | − | 560.133i | −0.0233936 | − | 0.0405189i | ||||
\(577\) | −14182.5 | −1.02326 | −0.511632 | − | 0.859205i | \(-0.670959\pi\) | ||||
−0.511632 | + | 0.859205i | \(0.670959\pi\) | |||||||
\(578\) | 327.883 | + | 567.910i | 0.0235954 | + | 0.0408684i | ||||
\(579\) | 7971.24 | + | 13806.6i | 0.572148 | + | 0.990989i | ||||
\(580\) | −493.911 | −0.0353595 | ||||||||
\(581\) | 13992.0 | + | 24234.9i | 0.999115 | + | 1.73052i | ||||
\(582\) | 5540.07 | − | 9595.68i | 0.394576 | − | 0.683426i | ||||
\(583\) | 2401.53 | − | 4159.58i | 0.170603 | − | 0.295492i | ||||
\(584\) | 15565.2 | 1.10290 | ||||||||
\(585\) | 1340.79 | + | 4.13251i | 0.0947606 | + | 0.000292065i | ||||
\(586\) | 7771.58 | 0.547852 | ||||||||
\(587\) | −2624.64 | + | 4546.01i | −0.184549 | + | 0.319649i | −0.943425 | − | 0.331587i | \(-0.892416\pi\) |
0.758875 | + | 0.651236i | \(0.225749\pi\) | |||||||
\(588\) | 17017.0 | − | 29474.2i | 1.19348 | − | 2.06717i | ||||
\(589\) | 2604.68 | + | 4511.44i | 0.182214 | + | 0.315604i | ||||
\(590\) | −5631.35 | −0.392947 | ||||||||
\(591\) | −3323.39 | − | 5756.28i | −0.231313 | − | 0.400646i | ||||
\(592\) | 2451.68 | + | 4246.43i | 0.170208 | + | 0.294809i | ||||
\(593\) | −19570.7 | −1.35526 | −0.677632 | − | 0.735401i | \(-0.736994\pi\) | ||||
−0.677632 | + | 0.735401i | \(0.736994\pi\) | |||||||
\(594\) | 930.793 | + | 1612.18i | 0.0642945 | + | 0.111361i | ||||
\(595\) | −5571.94 | + | 9650.89i | −0.383912 | + | 0.664954i | ||||
\(596\) | −8382.68 | + | 14519.2i | −0.576121 | + | 0.997871i | ||||
\(597\) | 9999.26 | 0.685498 | ||||||||
\(598\) | 9802.05 | + | 30.2113i | 0.670294 | + | 0.00206594i | ||||
\(599\) | 11276.0 | 0.769159 | 0.384579 | − | 0.923092i | \(-0.374346\pi\) | ||||
0.384579 | + | 0.923092i | \(0.374346\pi\) | |||||||
\(600\) | −5931.94 | + | 10274.4i | −0.403617 | + | 0.699085i | ||||
\(601\) | 9794.15 | − | 16964.0i | 0.664745 | − | 1.15137i | −0.314610 | − | 0.949221i | \(-0.601874\pi\) |
0.979354 | − | 0.202151i | \(-0.0647931\pi\) | |||||||
\(602\) | −799.756 | − | 1385.22i | −0.0541456 | − | 0.0937829i | ||||
\(603\) | 4293.13 | 0.289933 | ||||||||
\(604\) | −3270.32 | − | 5664.35i | −0.220310 | − | 0.381588i | ||||
\(605\) | 277.502 | + | 480.647i | 0.0186480 | + | 0.0322993i | ||||
\(606\) | 9380.30 | 0.628793 | ||||||||
\(607\) | 445.557 | + | 771.727i | 0.0297934 | + | 0.0516037i | 0.880538 | − | 0.473976i | \(-0.157182\pi\) |
−0.850744 | + | 0.525580i | \(0.823848\pi\) | |||||||
\(608\) | −1786.64 | + | 3094.54i | −0.119174 | + | 0.206415i | ||||
\(609\) | 1883.92 | − | 3263.04i | 0.125353 | − | 0.217119i | ||||
\(610\) | −1209.92 | −0.0803084 | ||||||||
\(611\) | 6732.07 | − | 11577.7i | 0.445746 | − | 0.766588i | ||||
\(612\) | 2496.42 | 0.164888 | ||||||||
\(613\) | −5463.49 | + | 9463.05i | −0.359981 | + | 0.623506i | −0.987957 | − | 0.154727i | \(-0.950550\pi\) |
0.627976 | + | 0.778233i | \(0.283884\pi\) | |||||||
\(614\) | 4800.34 | − | 8314.43i | 0.315515 | − | 0.546487i | ||||
\(615\) | −589.914 | − | 1021.76i | −0.0386791 | − | 0.0669941i | ||||
\(616\) | −7930.99 | −0.518748 | ||||||||
\(617\) | −3916.56 | − | 6783.68i | −0.255550 | − | 0.442626i | 0.709494 | − | 0.704711i | \(-0.248923\pi\) |
−0.965045 | + | 0.262085i | \(0.915590\pi\) | |||||||
\(618\) | 3509.77 | + | 6079.10i | 0.228453 | + | 0.395691i | ||||
\(619\) | 14887.3 | 0.966673 | 0.483337 | − | 0.875435i | \(-0.339425\pi\) | ||||
0.483337 | + | 0.875435i | \(0.339425\pi\) | |||||||
\(620\) | 3745.48 | + | 6487.36i | 0.242616 | + | 0.420224i | ||||
\(621\) | −8853.21 | + | 15334.2i | −0.572089 | + | 0.990887i | ||||
\(622\) | 3111.94 | − | 5390.04i | 0.200607 | − | 0.347461i | ||||
\(623\) | −4600.23 | −0.295834 | ||||||||
\(624\) | −5411.07 | − | 16.6776i | −0.347141 | − | 0.00106994i | ||||
\(625\) | 8178.08 | 0.523397 | ||||||||
\(626\) | −5885.46 | + | 10193.9i | −0.375767 | + | 0.650848i | ||||
\(627\) | −606.970 | + | 1051.30i | −0.0386604 | + | 0.0669617i | ||||
\(628\) | 8.99367 | + | 15.5775i | 0.000571475 | + | 0.000989825i | ||||
\(629\) | 16333.1 | 1.03537 | ||||||||
\(630\) | 736.525 | + | 1275.70i | 0.0465775 | + | 0.0806747i | ||||
\(631\) | −1038.34 | − | 1798.46i | −0.0655084 | − | 0.113464i | 0.831411 | − | 0.555658i | \(-0.187534\pi\) |
−0.896919 | + | 0.442194i | \(0.854200\pi\) | |||||||
\(632\) | −5047.11 | −0.317663 | ||||||||
\(633\) | −2007.61 | − | 3477.28i | −0.126059 | − | 0.218341i | ||||
\(634\) | −4875.29 | + | 8444.26i | −0.305398 | + | 0.528966i | ||||
\(635\) | −5082.97 | + | 8803.96i | −0.317656 | + | 0.550196i | ||||
\(636\) | 15106.8 | 0.941862 | ||||||||
\(637\) | 22931.0 | + | 40001.9i | 1.42631 | + | 2.48812i | ||||
\(638\) | −279.044 | −0.0173158 | ||||||||
\(639\) | 371.214 | − | 642.961i | 0.0229812 | − | 0.0398046i | ||||
\(640\) | −3088.56 | + | 5349.55i | −0.190760 | + | 0.330406i | ||||
\(641\) | 5440.21 | + | 9422.72i | 0.335219 | + | 0.580616i | 0.983527 | − | 0.180762i | \(-0.0578564\pi\) |
−0.648308 | + | 0.761378i | \(0.724523\pi\) | |||||||
\(642\) | −7304.98 | −0.449073 | ||||||||
\(643\) | −5984.10 | − | 10364.8i | −0.367014 | − | 0.635686i | 0.622083 | − | 0.782951i | \(-0.286286\pi\) |
−0.989097 | + | 0.147265i | \(0.952953\pi\) | |||||||
\(644\) | −16166.6 | − | 28001.4i | −0.989214 | − | 1.71337i | ||||
\(645\) | −821.366 | −0.0501415 | ||||||||
\(646\) | 902.585 | + | 1563.32i | 0.0549717 | + | 0.0952138i | ||||
\(647\) | 12262.0 | − | 21238.4i | 0.745085 | − | 1.29052i | −0.205071 | − | 0.978747i | \(-0.565742\pi\) |
0.950155 | − | 0.311777i | \(-0.100924\pi\) | |||||||
\(648\) | −8496.76 | + | 14716.8i | −0.515099 | + | 0.892178i | ||||
\(649\) | 9552.40 | 0.577757 | ||||||||
\(650\) | −3426.19 | − | 5976.80i | −0.206748 | − | 0.360661i | ||||
\(651\) | −57145.4 | −3.44041 | ||||||||
\(652\) | −1248.16 | + | 2161.88i | −0.0749719 | + | 0.129855i | ||||
\(653\) | −3417.97 | + | 5920.09i | −0.204832 | + | 0.354780i | −0.950079 | − | 0.312009i | \(-0.898998\pi\) |
0.745247 | + | 0.666788i | \(0.232331\pi\) | |||||||
\(654\) | 5428.69 | + | 9402.77i | 0.324585 | + | 0.562198i | ||||
\(655\) | −8926.77 | −0.532516 | ||||||||
\(656\) | 446.718 | + | 773.738i | 0.0265875 | + | 0.0460509i | ||||
\(657\) | 2451.97 | + | 4246.94i | 0.145602 | + | 0.252190i | ||||
\(658\) | 14713.7 | 0.871733 | ||||||||
\(659\) | 4212.31 | + | 7295.94i | 0.248996 | + | 0.431274i | 0.963248 | − | 0.268615i | \(-0.0865660\pi\) |
−0.714251 | + | 0.699889i | \(0.753233\pi\) | |||||||
\(660\) | −872.812 | + | 1511.75i | −0.0514760 | + | 0.0891591i | ||||
\(661\) | 3082.72 | − | 5339.42i | 0.181398 | − | 0.314190i | −0.760959 | − | 0.648800i | \(-0.775271\pi\) |
0.942357 | + | 0.334610i | \(0.108605\pi\) | |||||||
\(662\) | −14944.5 | −0.877394 | ||||||||
\(663\) | −9060.28 | + | 15581.8i | −0.530727 | + | 0.912738i | ||||
\(664\) | 15207.9 | 0.888830 | ||||||||
\(665\) | 1599.06 | − | 2769.65i | 0.0932465 | − | 0.161508i | ||||
\(666\) | 1079.49 | − | 1869.74i | 0.0628071 | − | 0.108785i | ||||
\(667\) | −1327.06 | − | 2298.53i | −0.0770374 | − | 0.133433i | ||||
\(668\) | 461.027 | 0.0267031 | ||||||||
\(669\) | 2807.94 | + | 4863.50i | 0.162274 | + | 0.281067i | ||||
\(670\) | 2232.02 | + | 3865.97i | 0.128702 | + | 0.222919i | ||||
\(671\) | 2052.37 | 0.118079 | ||||||||
\(672\) | −19599.0 | − | 33946.4i | −1.12507 | − | 1.94868i | ||||
\(673\) | −2992.00 | + | 5182.29i | −0.171372 | + | 0.296824i | −0.938900 | − | 0.344191i | \(-0.888153\pi\) |
0.767528 | + | 0.641015i | \(0.221487\pi\) | |||||||
\(674\) | −75.4220 | + | 130.635i | −0.00431031 | + | 0.00746567i | ||||
\(675\) | 12444.6 | 0.709618 | ||||||||
\(676\) | 6662.61 | − | 11377.4i | 0.379074 | − | 0.647327i | ||||
\(677\) | 2571.50 | 0.145983 | 0.0729917 | − | 0.997333i | \(-0.476745\pi\) | ||||
0.0729917 | + | 0.997333i | \(0.476745\pi\) | |||||||
\(678\) | 2664.63 | − | 4615.27i | 0.150936 | − | 0.261428i | ||||
\(679\) | 24757.9 | − | 42881.9i | 1.39929 | − | 2.42364i | ||||
\(680\) | 3028.08 | + | 5244.79i | 0.170767 | + | 0.295777i | ||||
\(681\) | 16409.6 | 0.923375 | ||||||||
\(682\) | 2116.08 | + | 3665.15i | 0.118810 | + | 0.205786i | ||||
\(683\) | −8865.40 | − | 15355.3i | −0.496669 | − | 0.860256i | 0.503323 | − | 0.864098i | \(-0.332110\pi\) |
−0.999993 | + | 0.00384174i | \(0.998777\pi\) | |||||||
\(684\) | −716.433 | −0.0400490 | ||||||||
\(685\) | −1680.75 | − | 2911.14i | −0.0937491 | − | 0.162378i | ||||
\(686\) | −16496.7 | + | 28573.1i | −0.918142 | + | 1.59027i | ||||
\(687\) | 3851.29 | − | 6670.62i | 0.213880 | − | 0.370451i | ||||
\(688\) | 621.987 | 0.0344666 | ||||||||
\(689\) | −10287.8 | + | 17692.8i | −0.568843 | + | 0.978289i | ||||
\(690\) | 5529.96 | 0.305104 | ||||||||
\(691\) | −8967.96 | + | 15533.0i | −0.493715 | + | 0.855140i | −0.999974 | − | 0.00724164i | \(-0.997695\pi\) |
0.506258 | + | 0.862382i | \(0.331028\pi\) | |||||||
\(692\) | −8855.93 | + | 15338.9i | −0.486491 | + | 0.842628i | ||||
\(693\) | −1249.36 | − | 2163.96i | −0.0684838 | − | 0.118617i | ||||
\(694\) | −1898.88 | −0.103862 | ||||||||
\(695\) | 2412.55 | + | 4178.67i | 0.131674 | + | 0.228066i | ||||
\(696\) | −1023.82 | − | 1773.31i | −0.0557583 | − | 0.0965762i | ||||
\(697\) | 2976.05 | 0.161730 | ||||||||
\(698\) | 3040.20 | + | 5265.78i | 0.164862 | + | 0.285549i | ||||
\(699\) | −1923.32 | + | 3331.28i | −0.104072 | + | 0.180259i | ||||
\(700\) | −11362.4 | + | 19680.2i | −0.613509 | + | 1.06263i | ||||
\(701\) | 17474.8 | 0.941530 | 0.470765 | − | 0.882259i | \(-0.343978\pi\) | ||||
0.470765 | + | 0.882259i | \(0.343978\pi\) | |||||||
\(702\) | −3945.02 | − | 6881.87i | −0.212101 | − | 0.369999i | ||||
\(703\) | −4687.36 | −0.251475 | ||||||||
\(704\) | −570.408 | + | 987.975i | −0.0305370 | + | 0.0528916i | ||||
\(705\) | 3777.82 | − | 6543.38i | 0.201817 | − | 0.349557i | ||||
\(706\) | −4726.55 | − | 8186.63i | −0.251963 | − | 0.436413i | ||||
\(707\) | 41919.3 | 2.22990 | ||||||||
\(708\) | 15022.3 | + | 26019.4i | 0.797420 | + | 1.38117i | ||||
\(709\) | −1399.18 | − | 2423.46i | −0.0741149 | − | 0.128371i | 0.826586 | − | 0.562810i | \(-0.190280\pi\) |
−0.900701 | + | 0.434439i | \(0.856946\pi\) | |||||||
\(710\) | 771.984 | 0.0408057 | ||||||||
\(711\) | −795.065 | − | 1377.09i | −0.0419371 | − | 0.0726372i | ||||
\(712\) | −1250.00 | + | 2165.07i | −0.0657947 | + | 0.113960i | ||||
\(713\) | −20127.0 | + | 34861.0i | −1.05717 | + | 1.83107i | ||||
\(714\) | −19802.3 | −1.03793 | ||||||||
\(715\) | −1176.15 | − | 2051.72i | −0.0615181 | − | 0.107315i | ||||
\(716\) | −15609.2 | −0.814726 | ||||||||
\(717\) | −3234.10 | + | 5601.63i | −0.168452 | + | 0.291767i | ||||
\(718\) | 7270.62 | − | 12593.1i | 0.377907 | − | 0.654554i | ||||
\(719\) | −1365.29 | − | 2364.76i | −0.0708163 | − | 0.122657i | 0.828443 | − | 0.560073i | \(-0.189227\pi\) |
−0.899259 | + | 0.437416i | \(0.855894\pi\) | |||||||
\(720\) | −572.811 | −0.0296492 | ||||||||
\(721\) | 15684.7 | + | 27166.7i | 0.810165 | + | 1.40325i | ||||
\(722\) | 4589.53 | + | 7949.30i | 0.236571 | + | 0.409754i | ||||
\(723\) | −25517.3 | −1.31259 | ||||||||
\(724\) | −9194.40 | − | 15925.2i | −0.471971 | − | 0.817478i | ||||
\(725\) | −932.694 | + | 1615.47i | −0.0477785 | + | 0.0827547i | ||||
\(726\) | −493.111 | + | 854.093i | −0.0252081 | + | 0.0436617i | ||||
\(727\) | −7661.76 | −0.390865 | −0.195433 | − | 0.980717i | \(-0.562611\pi\) | ||||
−0.195433 | + | 0.980717i | \(0.562611\pi\) | |||||||
\(728\) | 33794.6 | + | 104.160i | 1.72048 | + | 0.00530277i | ||||
\(729\) | 13278.9 | 0.674640 | ||||||||
\(730\) | −2549.59 | + | 4416.01i | −0.129266 | + | 0.223896i | ||||
\(731\) | 1035.92 | − | 1794.27i | 0.0524146 | − | 0.0907847i | ||||
\(732\) | 3227.61 | + | 5590.38i | 0.162972 | + | 0.282276i | ||||
\(733\) | 5686.26 | 0.286530 | 0.143265 | − | 0.989684i | \(-0.454240\pi\) | ||||
0.143265 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(734\) | −1455.47 | − | 2520.95i | −0.0731914 | − | 0.126771i | ||||
\(735\) | 13006.3 | + | 22527.5i | 0.652712 | + | 1.13053i | ||||
\(736\) | −27611.6 | −1.38285 | ||||||||
\(737\) | −3786.16 | − | 6557.81i | −0.189233 | − | 0.327761i | ||||
\(738\) | 196.694 | − | 340.684i | 0.00981084 | − | 0.0169929i | ||||
\(739\) | 15013.7 | − | 26004.5i | 0.747344 | − | 1.29444i | −0.201747 | − | 0.979438i | \(-0.564662\pi\) |
0.949091 | − | 0.315001i | \(-0.102005\pi\) | |||||||
\(740\) | −6740.33 | −0.334837 | ||||||||
\(741\) | 2600.16 | − | 4471.72i | 0.128906 | − | 0.221691i | ||||
\(742\) | −22485.1 | −1.11247 | ||||||||
\(743\) | 9076.93 | − | 15721.7i | 0.448183 | − | 0.776276i | −0.550084 | − | 0.835109i | \(-0.685405\pi\) |
0.998268 | + | 0.0588327i | \(0.0187378\pi\) | |||||||
\(744\) | −15527.9 | + | 26895.1i | −0.765161 | + | 1.32530i | ||||
\(745\) | −6406.99 | − | 11097.2i | −0.315079 | − | 0.545733i | ||||
\(746\) | 12431.6 | 0.610126 | ||||||||
\(747\) | 2395.69 | + | 4149.46i | 0.117341 | + | 0.203241i | ||||
\(748\) | −2201.62 | − | 3813.31i | −0.107619 | − | 0.186402i | ||||
\(749\) | −32645.0 | −1.59256 | ||||||||
\(750\) | −4279.88 | − | 7412.97i | −0.208372 | − | 0.360911i | ||||
\(751\) | −482.822 | + | 836.272i | −0.0234600 | + | 0.0406338i | −0.877517 | − | 0.479545i | \(-0.840802\pi\) |
0.854057 | + | 0.520179i | \(0.174135\pi\) | |||||||
\(752\) | −2860.79 | + | 4955.03i | −0.138726 | + | 0.240281i | ||||
\(753\) | 39260.8 | 1.90006 | ||||||||
\(754\) | 1189.03 | + | 3.66475i | 0.0574296 | + | 0.000177006i | ||||
\(755\) | 4999.08 | 0.240974 | ||||||||
\(756\) | −13083.0 | + | 22660.3i | −0.629395 | + | 1.09014i | ||||
\(757\) | 6152.91 | − | 10657.2i | 0.295418 | − | 0.511679i | −0.679664 | − | 0.733524i | \(-0.737874\pi\) |
0.975082 | + | 0.221845i | \(0.0712077\pi\) | |||||||
\(758\) | 3426.43 | + | 5934.75i | 0.164187 | + | 0.284380i | ||||
\(759\) | −9380.42 | −0.448600 | ||||||||
\(760\) | −869.012 | − | 1505.17i | −0.0414768 | − | 0.0718400i | ||||
\(761\) | −7481.71 | − | 12958.7i | −0.356389 | − | 0.617284i | 0.630966 | − | 0.775811i | \(-0.282659\pi\) |
−0.987355 | + | 0.158527i | \(0.949325\pi\) | |||||||
\(762\) | −18064.5 | −0.858803 | ||||||||
\(763\) | 24260.1 | + | 42019.8i | 1.15108 | + | 1.99373i | ||||
\(764\) | −9751.70 | + | 16890.4i | −0.461785 | + | 0.799836i | ||||
\(765\) | −954.020 | + | 1652.41i | −0.0450885 | + | 0.0780955i | ||||
\(766\) | 19212.5 | 0.906237 | ||||||||
\(767\) | −40703.6 | − | 125.454i | −1.91619 | − | 0.00590598i | ||||
\(768\) | −15759.7 | −0.740470 | ||||||||
\(769\) | −10146.2 | + | 17573.8i | −0.475789 | + | 0.824091i | −0.999615 | − | 0.0277344i | \(-0.991171\pi\) |
0.523826 | + | 0.851825i | \(0.324504\pi\) | |||||||
\(770\) | 1299.10 | − | 2250.10i | 0.0608003 | − | 0.105309i | ||||
\(771\) | 2305.70 | + | 3993.58i | 0.107701 | + | 0.186544i | ||||
\(772\) | 16595.4 | 0.773682 | ||||||||
\(773\) | −2504.36 | − | 4337.67i | −0.116527 | − | 0.201831i | 0.801862 | − | 0.597509i | \(-0.203843\pi\) |
−0.918389 | + | 0.395678i | \(0.870510\pi\) | |||||||
\(774\) | −136.933 | − | 237.175i | −0.00635912 | − | 0.0110143i | ||||
\(775\) | 28291.6 | 1.31131 | ||||||||
\(776\) | −13454.7 | − | 23304.2i | −0.622417 | − | 1.07806i | ||||
\(777\) | 25709.6 | − | 44530.3i | 1.18703 | − | 2.05600i | ||||
\(778\) | −8405.87 | + | 14559.4i | −0.387359 | + | 0.670925i | ||||
\(779\) | −854.079 | −0.0392819 | ||||||||
\(780\) | 3738.98 | − | 6430.25i | 0.171637 | − | 0.295180i | ||||
\(781\) | −1309.51 | −0.0599974 | ||||||||
\(782\) | −6974.50 | + | 12080.2i | −0.318935 | + | 0.552412i | ||||
\(783\) | −1073.93 | + | 1860.10i | −0.0490156 | + | 0.0848975i | ||||
\(784\) | −9849.11 | − | 17059.2i | −0.448666 | − | 0.777112i | ||||
\(785\) | −13.7479 | −0.000625076 | ||||||||
\(786\) | −7931.27 | − | 13737.4i | −0.359923 | − | 0.623404i | ||||
\(787\) | 12325.6 | + | 21348.5i | 0.558272 | + | 0.966955i | 0.997641 | + | 0.0686482i | \(0.0218686\pi\) |
−0.439369 | + | 0.898306i | \(0.644798\pi\) | |||||||
\(788\) | −6919.01 | −0.312791 | ||||||||
\(789\) | −7109.21 | − | 12313.5i | −0.320779 | − | 0.555605i | ||||
\(790\) | 826.718 | − | 1431.92i | 0.0372320 | − | 0.0644878i | ||||
\(791\) | 11907.9 | − | 20625.1i | 0.535266 | − | 0.927108i | ||||
\(792\) | −1357.93 | −0.0609243 | ||||||||
\(793\) | −8745.33 | − | 26.9543i | −0.391621 | − | 0.00120703i | ||||
\(794\) | 12889.3 | 0.576101 | ||||||||
\(795\) | −5773.16 | + | 9999.41i | −0.257551 | + | 0.446091i | ||||
\(796\) | 5204.40 | − | 9014.28i | 0.231740 | − | 0.401385i | ||||
\(797\) | −18671.9 | − | 32340.7i | −0.829854 | − | 1.43735i | −0.898152 | − | 0.439684i | \(-0.855090\pi\) |
0.0682985 | − | 0.997665i | \(-0.478243\pi\) | |||||||
\(798\) | 5682.95 | 0.252098 | ||||||||
\(799\) | 9529.34 | + | 16505.3i | 0.421932 | + | 0.730808i | ||||
\(800\) | 9703.09 | + | 16806.2i | 0.428820 | + | 0.742738i | ||||
\(801\) | −787.645 | −0.0347442 | ||||||||
\(802\) | −10410.2 | − | 18031.0i | −0.458350 | − | 0.793886i | ||||
\(803\) | 4324.84 | − | 7490.84i | 0.190063 | − | 0.329198i | ||||
\(804\) | 11908.4 | − | 20625.9i | 0.522359 | − | 0.904752i | ||||
\(805\) | 24712.7 | 1.08200 | ||||||||
\(806\) | −8968.65 | − | 15645.3i | −0.391944 | − | 0.683726i | ||||
\(807\) | 9318.50 | 0.406477 | ||||||||
\(808\) | 11390.6 | − | 19729.0i | 0.495939 | − | 0.858991i | ||||
\(809\) | 3491.80 | − | 6047.98i | 0.151749 | − | 0.262837i | −0.780121 | − | 0.625628i | \(-0.784843\pi\) |
0.931871 | + | 0.362791i | \(0.118176\pi\) | |||||||
\(810\) | −2783.54 | − | 4821.24i | −0.120745 | − | 0.209137i | ||||
\(811\) | 8267.04 | 0.357947 | 0.178973 | − | 0.983854i | \(-0.442722\pi\) | ||||
0.178973 | + | 0.983854i | \(0.442722\pi\) | |||||||
\(812\) | −1961.08 | − | 3396.69i | −0.0847542 | − | 0.146798i | ||||
\(813\) | −4263.61 | − | 7384.78i | −0.183925 | − | 0.318568i | ||||
\(814\) | −3808.07 | −0.163972 | ||||||||
\(815\) | −953.983 | − | 1652.35i | −0.0410019 | − | 0.0710174i | ||||
\(816\) | 3850.16 | − | 6668.67i | 0.165175 | − | 0.286091i | ||||
\(817\) | −297.294 | + | 514.929i | −0.0127307 | + | 0.0220503i | ||||
\(818\) | 714.996 | 0.0305614 | ||||||||
\(819\) | 5295.21 | + | 9237.21i | 0.225921 | + | 0.394108i | ||||
\(820\) | −1228.15 | −0.0523035 | ||||||||
\(821\) | −12587.4 | + | 21802.0i | −0.535083 | + | 0.926791i | 0.464076 | + | 0.885795i | \(0.346386\pi\) |
−0.999159 | + | 0.0409955i | \(0.986947\pi\) | |||||||
\(822\) | 2986.63 | − | 5173.00i | 0.126728 | − | 0.219500i | ||||
\(823\) | −213.267 | − | 369.389i | −0.00903283 | − | 0.0156453i | 0.861474 | − | 0.507802i | \(-0.169542\pi\) |
−0.870506 | + | 0.492157i | \(0.836209\pi\) | |||||||
\(824\) | 17047.8 | 0.720737 | ||||||||
\(825\) | 3296.41 | + | 5709.55i | 0.139111 | + | 0.240947i | ||||
\(826\) | −22359.3 | − | 38727.5i | −0.941865 | − | 1.63136i | ||||
\(827\) | 4450.31 | 0.187125 | 0.0935626 | − | 0.995613i | \(-0.470174\pi\) | ||||
0.0935626 | + | 0.995613i | \(0.470174\pi\) | |||||||
\(828\) | −2768.03 | − | 4794.36i | −0.116178 | − | 0.201227i | ||||
\(829\) | −2052.74 | + | 3555.46i | −0.0860009 | + | 0.148958i | −0.905817 | − | 0.423669i | \(-0.860742\pi\) |
0.819816 | + | 0.572627i | \(0.194075\pi\) | |||||||
\(830\) | −2491.07 | + | 4314.65i | −0.104176 | + | 0.180438i | ||||
\(831\) | 23138.0 | 0.965883 | ||||||||
\(832\) | 2443.53 | − | 4202.35i | 0.101820 | − | 0.175109i | ||||
\(833\) | −65615.1 | −2.72920 | ||||||||
\(834\) | −4287.02 | + | 7425.34i | −0.177994 | + | 0.308295i | ||||
\(835\) | −176.184 | + | 305.160i | −0.00730193 | + | 0.0126473i | ||||
\(836\) | 631.830 | + | 1094.36i | 0.0261391 | + | 0.0452743i | ||||
\(837\) | 32575.8 | 1.34526 | ||||||||
\(838\) | −11698.9 | − | 20263.0i | −0.482256 | − | 0.835293i | ||||
\(839\) | 17780.3 | + | 30796.4i | 0.731639 | + | 1.26724i | 0.956182 | + | 0.292772i | \(0.0945776\pi\) |
−0.224544 | + | 0.974464i | \(0.572089\pi\) | |||||||
\(840\) | 19065.7 | 0.783130 | ||||||||
\(841\) | 12033.5 | + | 20842.7i | 0.493400 | + | 0.854593i | ||||
\(842\) | 4775.86 | − | 8272.04i | 0.195472 | − | 0.338567i | ||||
\(843\) | −16885.1 | + | 29245.8i | −0.689861 | + | 1.19487i | ||||
\(844\) | −4179.67 | −0.170462 | ||||||||
\(845\) | 4984.72 | + | 8758.02i | 0.202934 | + | 0.356550i | ||||
\(846\) | 2519.26 | 0.102381 | ||||||||
\(847\) | −2203.65 | + | 3816.83i | −0.0893958 | + | 0.154838i | ||||
\(848\) | 4371.78 | − | 7572.14i | 0.177037 | − | 0.306637i | ||||
\(849\) | 2629.78 | + | 4554.92i | 0.106306 | + | 0.184128i | ||||
\(850\) | 9803.75 | 0.395607 | ||||||||
\(851\) | −18110.2 | − | 31367.7i | −0.729505 | − | 1.26354i | ||||
\(852\) | −2059.37 | − | 3566.93i | −0.0828083 | − | 0.143428i | ||||
\(853\) | 5551.18 | 0.222824 | 0.111412 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111412 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(854\) | −4803.99 | − | 8320.75i | −0.192493 | − | 0.333408i | ||||
\(855\) | 273.789 | − | 474.216i | 0.0109513 | − | 0.0189683i | ||||
\(856\) | −8870.50 | + | 15364.2i | −0.354191 | + | 0.613477i | ||||
\(857\) | 40685.8 | 1.62170 | 0.810851 | − | 0.585252i | \(-0.199005\pi\) | ||||
0.810851 | + | 0.585252i | \(0.199005\pi\) | |||||||
\(858\) | 2112.40 | − | 3632.89i | 0.0840516 | − | 0.144551i | ||||
\(859\) | 7789.22 | 0.309389 | 0.154694 | − | 0.987962i | \(-0.450561\pi\) | ||||
0.154694 | + | 0.987962i | \(0.450561\pi\) | |||||||
\(860\) | −427.503 | + | 740.458i | −0.0169509 | + | 0.0293598i | ||||
\(861\) | 4684.52 | − | 8113.83i | 0.185422 | − | 0.321160i | ||||
\(862\) | 1158.64 | + | 2006.83i | 0.0457814 | + | 0.0792957i | ||||
\(863\) | −2318.11 | −0.0914360 | −0.0457180 | − | 0.998954i | \(-0.514558\pi\) | ||||
−0.0457180 | + | 0.998954i | \(0.514558\pi\) | |||||||
\(864\) | 11172.4 | + | 19351.2i | 0.439923 | + | 0.761969i | ||||
\(865\) | −6768.69 | − | 11723.7i | −0.266061 | − | 0.460831i | ||||
\(866\) | 13892.0 | 0.545115 | ||||||||
\(867\) | 1337.04 | + | 2315.82i | 0.0523740 | + | 0.0907145i | ||||
\(868\) | −29742.9 | + | 51516.3i | −1.16307 | + | 2.01449i | ||||
\(869\) | −1402.35 | + | 2428.95i | −0.0547429 | + | 0.0948175i | ||||
\(870\) | 670.807 | 0.0261408 | ||||||||
\(871\) | 16047.0 | + | 27993.1i | 0.624262 | + | 1.08899i | ||||
\(872\) | 26368.4 | 1.02402 | ||||||||
\(873\) | 4239.01 | − | 7342.17i | 0.164340 | − | 0.284645i | ||||
\(874\) | 2001.57 | − | 3466.82i | 0.0774647 | − | 0.134173i | ||||
\(875\) | −19126.2 | − | 33127.6i | −0.738954 | − | 1.27991i | ||||
\(876\) | 27205.4 | 1.04930 | ||||||||
\(877\) | −21547.6 | − | 37321.5i | −0.829659 | − | 1.43701i | −0.898306 | − | 0.439370i | \(-0.855202\pi\) |
0.0686476 | − | 0.997641i | \(-0.478132\pi\) | |||||||
\(878\) | 8952.96 | + | 15507.0i | 0.344132 | + | 0.596054i | ||||
\(879\) | 31690.9 | 1.21605 | ||||||||
\(880\) | 505.168 | + | 874.976i | 0.0193514 | + | 0.0335176i | ||||
\(881\) | 2495.28 | − | 4321.95i | 0.0954235 | − | 0.165278i | −0.814362 | − | 0.580358i | \(-0.802913\pi\) |
0.909785 | + | 0.415079i | \(0.136246\pi\) | |||||||
\(882\) | −4336.65 | + | 7511.29i | −0.165558 | + | 0.286756i | ||||
\(883\) | 14086.4 | 0.536859 | 0.268429 | − | 0.963299i | \(-0.413495\pi\) | ||||
0.268429 | + | 0.963299i | \(0.413495\pi\) | |||||||
\(884\) | 9331.20 | + | 16277.8i | 0.355025 | + | 0.619322i | ||||
\(885\) | −22963.5 | −0.872214 | ||||||||
\(886\) | 5781.96 | − | 10014.6i | 0.219242 | − | 0.379739i | ||||
\(887\) | 9054.08 | − | 15682.1i | 0.342735 | − | 0.593635i | −0.642204 | − | 0.766534i | \(-0.721980\pi\) |
0.984940 | + | 0.172898i | \(0.0553132\pi\) | |||||||
\(888\) | −13971.9 | − | 24200.1i | −0.528003 | − | 0.914528i | ||||
\(889\) | −80727.9 | −3.04559 | ||||||||
\(890\) | −409.501 | − | 709.277i | −0.0154230 | − | 0.0267135i | ||||
\(891\) | 4721.70 | + | 8178.22i | 0.177534 | + | 0.307498i | ||||
\(892\) | 5845.90 | 0.219434 | ||||||||
\(893\) | −2734.77 | − | 4736.76i | −0.102481 | − | 0.177502i | ||||
\(894\) | 11385.0 | − | 19719.4i | 0.425918 | − | 0.737712i | ||||
\(895\) | 5965.16 | − | 10332.0i | 0.222786 | − | 0.385876i | ||||
\(896\) | −49052.7 | −1.82895 | ||||||||
\(897\) | 39970.8 | + | 123.195i | 1.48783 | + | 0.00458570i | ||||
\(898\) | −23213.7 | −0.862641 | ||||||||
\(899\) | −2441.49 | + | 4228.78i | −0.0905765 | + | 0.156883i | ||||
\(900\) | −1945.45 | + | 3369.61i | −0.0720536 | + | 0.124800i | ||||
\(901\) | −14562.5 | − | 25222.9i | −0.538453 | − | 0.932628i | ||||
\(902\) | −693.865 | −0.0256133 | ||||||||
\(903\) | −3261.24 | − | 5648.64i | −0.120185 | − | 0.208167i | ||||
\(904\) | −6471.36 | − | 11208.7i | −0.238091 | − | 0.412385i | ||||
\(905\) | 14054.8 | 0.516239 | ||||||||
\(906\) | 4441.59 | + | 7693.07i | 0.162872 | + | 0.282103i | ||||
\(907\) | 1129.60 | − | 1956.52i | 0.0413535 | − | 0.0716264i | −0.844608 | − | 0.535385i | \(-0.820166\pi\) |
0.885961 | + | 0.463759i | \(0.153500\pi\) | |||||||
\(908\) | 8540.85 | − | 14793.2i | 0.312157 | − | 0.540671i | ||||
\(909\) | 7177.37 | 0.261890 | ||||||||
\(910\) | −5565.12 | + | 9570.83i | −0.202727 | + | 0.348648i | ||||
\(911\) | −6484.37 | −0.235825 | −0.117913 | − | 0.993024i | \(-0.537620\pi\) | ||||
−0.117913 | + | 0.993024i | \(0.537620\pi\) | |||||||
\(912\) | −1104.94 | + | 1913.81i | −0.0401185 | + | 0.0694873i | ||||
\(913\) | 4225.57 | − | 7318.90i | 0.153172 | − | 0.265302i | ||||
\(914\) | −4814.60 | − | 8339.14i | −0.174237 | − | 0.301788i | ||||
\(915\) | −4933.79 | −0.178258 | ||||||||
\(916\) | −4009.02 | − | 6943.83i | −0.144609 | − | 0.250470i | ||||
\(917\) | −35443.8 | − | 61390.5i | −1.27640 | − | 2.21079i | ||||
\(918\) | 11288.3 | 0.405850 | ||||||||
\(919\) | −14677.6 | − | 25422.4i | −0.526845 | − | 0.912522i | −0.999511 | − | 0.0312802i | \(-0.990042\pi\) |
0.472666 | − | 0.881242i | \(-0.343292\pi\) | |||||||
\(920\) | 6715.07 | − | 11630.8i | 0.240641 | − | 0.416802i | ||||
\(921\) | 19574.8 | − | 33904.6i | 0.700339 | − | 1.21302i | ||||
\(922\) | −3471.04 | −0.123983 | ||||||||
\(923\) | 5579.93 | + | 17.1981i | 0.198988 | + | 0.000613308i | ||||
\(924\) | −13862.0 | −0.493536 | ||||||||
\(925\) | −12728.3 | + | 22046.1i | −0.452438 | + | 0.783646i | ||||
\(926\) | −172.908 | + | 299.486i | −0.00613619 | + | 0.0106282i | ||||
\(927\) | 2685.51 | + | 4651.45i | 0.0951498 | + | 0.164804i | ||||
\(928\) | −3349.40 | −0.118480 | ||||||||
\(929\) | −18403.7 | − | 31876.1i | −0.649952 | − | 1.12575i | −0.983134 | − | 0.182887i | \(-0.941456\pi\) |
0.333182 | − | 0.942862i | \(-0.391878\pi\) | |||||||
\(930\) | −5086.94 | − | 8810.84i | −0.179363 | − | 0.310665i | ||||
\(931\) | 18830.5 | 0.662884 | ||||||||
\(932\) | 2002.09 | + | 3467.72i | 0.0703655 | + | 0.121877i | ||||
\(933\) | 12689.9 | − | 21979.5i | 0.445281 | − | 0.771250i | ||||
\(934\) | 5896.73 | − | 10213.4i | 0.206581 | − | 0.357809i | ||||
\(935\) | 3365.44 | 0.117713 | ||||||||
\(936\) | 5786.27 | + | 17.8341i | 0.202062 | + | 0.000622783i | ||||
\(937\) | −42007.8 | −1.46460 | −0.732302 | − | 0.680979i | \(-0.761554\pi\) | ||||
−0.732302 | + | 0.680979i | \(0.761554\pi\) | |||||||
\(938\) | −17724.5 | + | 30699.8i | −0.616979 | + | 1.06864i | ||||
\(939\) | −23999.7 | + | 41568.7i | −0.834080 | + | 1.44467i | ||||
\(940\) | −3932.55 | − | 6811.38i | −0.136453 | − | 0.236343i | ||||
\(941\) | 6635.64 | 0.229879 | 0.114939 | − | 0.993373i | \(-0.463333\pi\) | ||||
0.114939 | + | 0.993373i | \(0.463333\pi\) | |||||||
\(942\) | −12.2148 | − | 21.1566i | −0.000422484 | − | 0.000731763i | ||||
\(943\) | −3299.84 | − | 5715.49i | −0.113953 | − | 0.197372i | ||||
\(944\) | 17389.3 | 0.599548 | ||||||||
\(945\) | −9999.46 | − | 17319.6i | −0.344214 | − | 0.596196i | ||||
\(946\) | −241.526 | + | 418.335i | −0.00830093 | + | 0.0143776i | ||||
\(947\) | 4800.78 | − | 8315.20i | 0.164736 | − | 0.285330i | −0.771826 | − | 0.635834i | \(-0.780656\pi\) |
0.936561 | + | 0.350504i | \(0.113990\pi\) | |||||||
\(948\) | −8821.50 | −0.302225 | ||||||||
\(949\) | −18526.9 | + | 31862.3i | −0.633728 | + | 1.08988i | ||||
\(950\) | −2813.52 | −0.0960871 | ||||||||
\(951\) | −19880.5 | + | 34434.0i | −0.677884 | + | 1.17413i | ||||
\(952\) | −24046.1 | + | 41649.0i | −0.818632 | + | 1.41791i | ||||
\(953\) | 12897.3 | + | 22338.9i | 0.438390 | + | 0.759314i | 0.997566 | − | 0.0697352i | \(-0.0222154\pi\) |
−0.559175 | + | 0.829049i | \(0.688882\pi\) | |||||||
\(954\) | −3849.86 | −0.130654 | ||||||||
\(955\) | −7453.34 | − | 12909.6i | −0.252549 | − | 0.437428i | ||||
\(956\) | 3366.56 | + | 5831.06i | 0.113894 | + | 0.197270i | ||||
\(957\) | −1137.88 | −0.0384353 | ||||||||
\(958\) | 9825.74 | + | 17018.7i | 0.331373 | + | 0.573955i | ||||
\(959\) | 13346.9 | − | 23117.5i | 0.449419 | − | 0.778416i | ||||
\(960\) | 1371.23 | − | 2375.04i | 0.0461003 | − | 0.0798481i | ||||
\(961\) | 44267.3 | 1.48593 | ||||||||
\(962\) | 16226.5 | + | 50.0124i | 0.543829 | + | 0.00167616i | ||||
\(963\) | −5589.44 | −0.187038 | ||||||||
\(964\) | −13281.2 | + | 23003.7i | −0.443734 | + | 0.768569i | ||||
\(965\) | −6342.04 | + | 10984.7i | −0.211562 | + | 0.366437i | ||||
\(966\) | 21956.8 | + | 38030.2i | 0.731312 | + | 1.26667i | ||||
\(967\) | 33439.2 | 1.11203 | 0.556015 | − | 0.831172i | \(-0.312330\pi\) | ||||
0.556015 | + | 0.831172i | \(0.312330\pi\) | |||||||
\(968\) | 1197.58 | + | 2074.26i | 0.0397640 | + | 0.0688733i | ||||
\(969\) | 3680.56 | + | 6374.92i | 0.122019 | + | 0.211343i | ||||
\(970\) | 8815.53 | 0.291804 | ||||||||
\(971\) | 14665.1 | + | 25400.7i | 0.484681 | + | 0.839492i | 0.999845 | − | 0.0175996i | \(-0.00560242\pi\) |
−0.515164 | + | 0.857091i | \(0.672269\pi\) | |||||||
\(972\) | −5152.90 | + | 8925.09i | −0.170041 | + | 0.294519i | ||||
\(973\) | −19158.1 | + | 33182.9i | −0.631225 | + | 1.09331i | ||||
\(974\) | −7958.99 | −0.261830 | ||||||||
\(975\) | −13971.3 | − | 24372.2i | −0.458913 | − | 0.800548i | ||||
\(976\) | 3736.16 | 0.122532 | ||||||||
\(977\) | 17391.9 | − | 30123.6i | 0.569515 | − | 0.986428i | −0.427099 | − | 0.904205i | \(-0.640464\pi\) |
0.996614 | − | 0.0822237i | \(-0.0262022\pi\) | |||||||
\(978\) | 1695.19 | − | 2936.16i | 0.0554257 | − | 0.0960000i | ||||
\(979\) | 694.633 | + | 1203.14i | 0.0226768 | + | 0.0392773i | ||||
\(980\) | 27077.9 | 0.882624 | ||||||||
\(981\) | 4153.78 | + | 7194.56i | 0.135189 | + | 0.234154i | ||||
\(982\) | −3217.11 | − | 5572.20i | −0.104544 | − | 0.181075i | ||||
\(983\) | −8853.18 | −0.287256 | −0.143628 | − | 0.989632i | \(-0.545877\pi\) | ||||
−0.143628 | + | 0.989632i | \(0.545877\pi\) | |||||||
\(984\) | −2545.81 | − | 4409.47i | −0.0824771 | − | 0.142855i | ||||
\(985\) | 2644.14 | − | 4579.78i | 0.0855323 | − | 0.148146i | ||||
\(986\) | −846.036 | + | 1465.38i | −0.0273258 | + | 0.0473297i | ||||
\(987\) | 59999.5 | 1.93496 | ||||||||
\(988\) | −2677.91 | − | 4671.47i | −0.0862304 | − | 0.150424i | ||||
\(989\) | −4594.53 | −0.147723 | ||||||||
\(990\) | 222.430 | − | 385.260i | 0.00714069 | − | 0.0123680i | ||||
\(991\) | −18296.5 | + | 31690.5i | −0.586487 | + | 1.01582i | 0.408202 | + | 0.912892i | \(0.366156\pi\) |
−0.994688 | + | 0.102933i | \(0.967177\pi\) | |||||||
\(992\) | 25399.5 | + | 43993.3i | 0.812939 | + | 1.40805i | ||||
\(993\) | −60940.7 | −1.94753 | ||||||||
\(994\) | 3065.17 | + | 5309.03i | 0.0978082 | + | 0.169409i | ||||
\(995\) | 3977.78 | + | 6889.72i | 0.126738 | + | 0.219516i | ||||
\(996\) | 26580.9 | 0.845631 | ||||||||
\(997\) | 4832.12 | + | 8369.48i | 0.153495 | + | 0.265862i | 0.932510 | − | 0.361144i | \(-0.117614\pi\) |
−0.779015 | + | 0.627005i | \(0.784280\pi\) | |||||||
\(998\) | −7241.69 | + | 12543.0i | −0.229691 | + | 0.397837i | ||||
\(999\) | −14655.8 | + | 25384.6i | −0.464153 | + | 0.803937i |
(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 | 143.4.e.b.100.7 | ✓ | 34 | |
13.3 | even | 3 | inner | 143.4.e.b.133.7 | yes | 34 | |
13.4 | even | 6 | 1859.4.a.h.1.7 | 17 | |||
13.9 | even | 3 | 1859.4.a.g.1.11 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.e.b.100.7 | ✓ | 34 | 1.1 | even | 1 | trivial | |
143.4.e.b.133.7 | yes | 34 | 13.3 | even | 3 | inner | |
1859.4.a.g.1.11 | 17 | 13.9 | even | 3 | |||
1859.4.a.h.1.7 | 17 | 13.4 | even | 6 |