Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(23,143)]
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, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.j (of order \(6\), 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: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.18 | ||
Character | \(\chi\) | \(=\) | 143.23 |
Dual form | 143.4.j.a.56.18 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.575952 | + | 0.332526i | −0.203630 | + | 0.117566i | −0.598347 | − | 0.801237i | \(-0.704176\pi\) |
0.394718 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(3\) | 1.60738 | + | 2.78407i | 0.309341 | + | 0.535795i | 0.978218 | − | 0.207578i | \(-0.0665581\pi\) |
−0.668877 | + | 0.743373i | \(0.733225\pi\) | |||||||
\(4\) | −3.77885 | + | 6.54517i | −0.472357 | + | 0.818146i | ||||
\(5\) | 10.5229i | 0.941200i | 0.882347 | + | 0.470600i | \(0.155963\pi\) | ||||
−0.882347 | + | 0.470600i | \(0.844037\pi\) | |||||||
\(6\) | −1.85155 | − | 1.06899i | −0.125982 | − | 0.0727358i | ||||
\(7\) | 25.1101 | + | 14.4973i | 1.35582 | + | 0.782780i | 0.989057 | − | 0.147536i | \(-0.0471342\pi\) |
0.366759 | + | 0.930316i | \(0.380467\pi\) | |||||||
\(8\) | − | 10.3467i | − | 0.457263i | ||||||
\(9\) | 8.33263 | − | 14.4325i | 0.308616 | − | 0.534538i | ||||
\(10\) | −3.49915 | − | 6.06070i | −0.110653 | − | 0.191656i | ||||
\(11\) | −9.52628 | + | 5.50000i | −0.261116 | + | 0.150756i | ||||
\(12\) | −24.2963 | −0.584478 | ||||||||
\(13\) | −42.0756 | + | 20.6553i | −0.897668 | + | 0.440673i | ||||
\(14\) | −19.2829 | −0.368112 | ||||||||
\(15\) | −29.2966 | + | 16.9144i | −0.504290 | + | 0.291152i | ||||
\(16\) | −26.7903 | − | 46.4021i | −0.418598 | − | 0.725033i | ||||
\(17\) | −19.0169 | + | 32.9382i | −0.271310 | + | 0.469923i | −0.969198 | − | 0.246284i | \(-0.920790\pi\) |
0.697887 | + | 0.716208i | \(0.254124\pi\) | |||||||
\(18\) | 11.0833i | 0.145131i | ||||||||
\(19\) | −61.1353 | − | 35.2965i | −0.738179 | − | 0.426188i | 0.0832278 | − | 0.996531i | \(-0.473477\pi\) |
−0.821407 | + | 0.570343i | \(0.806810\pi\) | |||||||
\(20\) | −68.8744 | − | 39.7646i | −0.770039 | − | 0.444582i | ||||
\(21\) | 93.2109i | 0.968585i | ||||||||
\(22\) | 3.65779 | − | 6.33547i | 0.0354474 | − | 0.0613967i | ||||
\(23\) | 96.2881 | + | 166.776i | 0.872933 | + | 1.51196i | 0.858948 | + | 0.512063i | \(0.171118\pi\) |
0.0139852 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(24\) | 28.8059 | − | 16.6311i | 0.244999 | − | 0.141450i | ||||
\(25\) | 14.2678 | 0.114142 | ||||||||
\(26\) | 17.3651 | − | 25.8877i | 0.130984 | − | 0.195269i | ||||
\(27\) | 140.374 | 1.00055 | ||||||||
\(28\) | −189.774 | + | 109.566i | −1.28086 | + | 0.739503i | ||||
\(29\) | −85.5932 | − | 148.252i | −0.548078 | − | 0.949298i | −0.998406 | − | 0.0564355i | \(-0.982026\pi\) |
0.450329 | − | 0.892863i | \(-0.351307\pi\) | |||||||
\(30\) | 11.2490 | − | 19.4838i | 0.0684590 | − | 0.118574i | ||||
\(31\) | − | 168.441i | − | 0.975900i | −0.872872 | − | 0.487950i | \(-0.837745\pi\) | ||
0.872872 | − | 0.487950i | \(-0.162255\pi\) | |||||||
\(32\) | 102.544 | + | 59.2037i | 0.566479 | + | 0.327057i | ||||
\(33\) | −30.6248 | − | 17.6812i | −0.161548 | − | 0.0932699i | ||||
\(34\) | − | 25.2944i | − | 0.127587i | ||||||
\(35\) | −152.554 | + | 264.231i | −0.736753 | + | 1.27609i | ||||
\(36\) | 62.9756 | + | 109.077i | 0.291554 | + | 0.504986i | ||||
\(37\) | −212.993 | + | 122.971i | −0.946373 | + | 0.546389i | −0.891952 | − | 0.452129i | \(-0.850664\pi\) |
−0.0544206 | + | 0.998518i | \(0.517331\pi\) | |||||||
\(38\) | 46.9480 | 0.200420 | ||||||||
\(39\) | −125.138 | − | 83.9406i | −0.513796 | − | 0.344648i | ||||
\(40\) | 108.877 | 0.430376 | ||||||||
\(41\) | 54.9558 | − | 31.7287i | 0.209333 | − | 0.120858i | −0.391668 | − | 0.920106i | \(-0.628102\pi\) |
0.601001 | + | 0.799248i | \(0.294769\pi\) | |||||||
\(42\) | −30.9950 | − | 53.6850i | −0.113872 | − | 0.197233i | ||||
\(43\) | 42.5257 | − | 73.6567i | 0.150817 | − | 0.261222i | −0.780711 | − | 0.624892i | \(-0.785143\pi\) |
0.931528 | + | 0.363670i | \(0.118476\pi\) | |||||||
\(44\) | − | 83.1348i | − | 0.284842i | ||||||
\(45\) | 151.873 | + | 87.6837i | 0.503108 | + | 0.290469i | ||||
\(46\) | −110.915 | − | 64.0366i | −0.355510 | − | 0.205254i | ||||
\(47\) | 61.8204i | 0.191860i | 0.995388 | + | 0.0959301i | \(0.0305825\pi\) | ||||
−0.995388 | + | 0.0959301i | \(0.969417\pi\) | |||||||
\(48\) | 86.1246 | − | 149.172i | 0.258979 | − | 0.448566i | ||||
\(49\) | 248.843 | + | 431.009i | 0.725490 | + | 1.25659i | ||||
\(50\) | −8.21757 | + | 4.74442i | −0.0232428 | + | 0.0134192i | ||||
\(51\) | −122.270 | −0.335710 | ||||||||
\(52\) | 23.8054 | − | 353.445i | 0.0634850 | − | 0.942578i | ||||
\(53\) | −216.218 | −0.560373 | −0.280187 | − | 0.959946i | \(-0.590396\pi\) | ||||
−0.280187 | + | 0.959946i | \(0.590396\pi\) | |||||||
\(54\) | −80.8485 | + | 46.6779i | −0.203742 | + | 0.117631i | ||||
\(55\) | −57.8761 | − | 100.244i | −0.141891 | − | 0.245763i | ||||
\(56\) | 149.999 | − | 259.806i | 0.357936 | − | 0.619964i | ||||
\(57\) | − | 226.940i | − | 0.527350i | ||||||
\(58\) | 98.5951 | + | 56.9239i | 0.223210 | + | 0.128870i | ||||
\(59\) | 563.238 | + | 325.185i | 1.24284 | + | 0.717551i | 0.969671 | − | 0.244416i | \(-0.0785962\pi\) |
0.273165 | + | 0.961967i | \(0.411930\pi\) | |||||||
\(60\) | − | 255.668i | − | 0.550110i | ||||||
\(61\) | 190.028 | − | 329.139i | 0.398863 | − | 0.690851i | −0.594723 | − | 0.803931i | \(-0.702738\pi\) |
0.993586 | + | 0.113080i | \(0.0360716\pi\) | |||||||
\(62\) | 56.0110 | + | 97.0139i | 0.114732 | + | 0.198722i | ||||
\(63\) | 418.466 | − | 241.601i | 0.836852 | − | 0.483157i | ||||
\(64\) | 349.898 | 0.683394 | ||||||||
\(65\) | −217.354 | − | 442.759i | −0.414761 | − | 0.844885i | ||||
\(66\) | 23.5179 | 0.0438614 | ||||||||
\(67\) | 409.382 | − | 236.357i | 0.746478 | − | 0.430979i | −0.0779421 | − | 0.996958i | \(-0.524835\pi\) |
0.824420 | + | 0.565979i | \(0.191502\pi\) | |||||||
\(68\) | −143.724 | − | 248.937i | −0.256310 | − | 0.443943i | ||||
\(69\) | −309.544 | + | 536.146i | −0.540069 | + | 0.935426i | ||||
\(70\) | − | 202.913i | − | 0.346467i | ||||||
\(71\) | 298.613 | + | 172.404i | 0.499138 | + | 0.288177i | 0.728357 | − | 0.685197i | \(-0.240284\pi\) |
−0.229220 | + | 0.973375i | \(0.573617\pi\) | |||||||
\(72\) | −149.329 | − | 86.2151i | −0.244425 | − | 0.141119i | ||||
\(73\) | 784.161i | 1.25725i | 0.777709 | + | 0.628624i | \(0.216382\pi\) | ||||
−0.777709 | + | 0.628624i | \(0.783618\pi\) | |||||||
\(74\) | 81.7824 | − | 141.651i | 0.128473 | − | 0.222522i | ||||
\(75\) | 22.9339 | + | 39.7226i | 0.0353090 | + | 0.0611570i | ||||
\(76\) | 462.043 | − | 266.760i | 0.697368 | − | 0.402625i | ||||
\(77\) | −318.940 | −0.472034 | ||||||||
\(78\) | 99.9856 | + | 6.73428i | 0.145143 | + | 0.00977574i | ||||
\(79\) | 408.156 | 0.581280 | 0.290640 | − | 0.956832i | \(-0.406132\pi\) | ||||
0.290640 | + | 0.956832i | \(0.406132\pi\) | |||||||
\(80\) | 488.287 | − | 281.912i | 0.682401 | − | 0.393985i | ||||
\(81\) | 0.653583 | + | 1.13204i | 0.000896548 | + | 0.00155287i | ||||
\(82\) | −21.1013 | + | 36.5484i | −0.0284176 | + | 0.0492207i | ||||
\(83\) | 1091.09i | 1.44292i | 0.692456 | + | 0.721460i | \(0.256529\pi\) | ||||
−0.692456 | + | 0.721460i | \(0.743471\pi\) | |||||||
\(84\) | −610.081 | − | 352.230i | −0.792444 | − | 0.457518i | ||||
\(85\) | −346.607 | − | 200.114i | −0.442292 | − | 0.255357i | ||||
\(86\) | 56.5636i | 0.0709234i | ||||||||
\(87\) | 275.162 | − | 476.595i | 0.339086 | − | 0.587314i | ||||
\(88\) | 56.9067 | + | 98.5654i | 0.0689350 | + | 0.119399i | ||||
\(89\) | 573.719 | − | 331.237i | 0.683305 | − | 0.394506i | −0.117794 | − | 0.993038i | \(-0.537582\pi\) |
0.801099 | + | 0.598532i | \(0.204249\pi\) | |||||||
\(90\) | −116.628 | −0.136597 | ||||||||
\(91\) | −1355.97 | − | 91.3278i | −1.56202 | − | 0.105206i | ||||
\(92\) | −1455.43 | −1.64934 | ||||||||
\(93\) | 468.952 | − | 270.750i | 0.522882 | − | 0.301886i | ||||
\(94\) | −20.5569 | − | 35.6056i | −0.0225562 | − | 0.0390685i | ||||
\(95\) | 371.423 | − | 643.323i | 0.401128 | − | 0.694774i | ||||
\(96\) | 380.652i | 0.404689i | ||||||||
\(97\) | 1520.76 | + | 878.012i | 1.59186 | + | 0.919058i | 0.992989 | + | 0.118209i | \(0.0377154\pi\) |
0.598867 | + | 0.800849i | \(0.295618\pi\) | |||||||
\(98\) | −286.643 | − | 165.494i | −0.295463 | − | 0.170585i | ||||
\(99\) | 183.318i | 0.186102i | ||||||||
\(100\) | −53.9160 | + | 93.3852i | −0.0539160 | + | 0.0933852i | ||||
\(101\) | 24.9954 | + | 43.2933i | 0.0246251 | + | 0.0426519i | 0.878075 | − | 0.478522i | \(-0.158827\pi\) |
−0.853450 | + | 0.521174i | \(0.825494\pi\) | |||||||
\(102\) | 70.4215 | − | 40.6579i | 0.0683605 | − | 0.0394680i | ||||
\(103\) | −1388.01 | −1.32782 | −0.663908 | − | 0.747814i | \(-0.731103\pi\) | ||||
−0.663908 | + | 0.747814i | \(0.731103\pi\) | |||||||
\(104\) | 213.714 | + | 435.343i | 0.201503 | + | 0.410470i | ||||
\(105\) | −980.853 | −0.911632 | ||||||||
\(106\) | 124.531 | − | 71.8980i | 0.114109 | − | 0.0658807i | ||||
\(107\) | 649.042 | + | 1124.17i | 0.586404 | + | 1.01568i | 0.994699 | + | 0.102832i | \(0.0327903\pi\) |
−0.408294 | + | 0.912850i | \(0.633876\pi\) | |||||||
\(108\) | −530.452 | + | 918.769i | −0.472618 | + | 0.818598i | ||||
\(109\) | − | 1113.79i | − | 0.978731i | −0.872079 | − | 0.489365i | \(-0.837228\pi\) | ||
0.872079 | − | 0.489365i | \(-0.162772\pi\) | |||||||
\(110\) | 66.6677 | + | 38.4906i | 0.0577865 | + | 0.0333631i | ||||
\(111\) | −684.723 | − | 395.325i | −0.585504 | − | 0.338041i | ||||
\(112\) | − | 1553.55i | − | 1.31068i | ||||||
\(113\) | −185.925 | + | 322.031i | −0.154782 | + | 0.268090i | −0.932980 | − | 0.359929i | \(-0.882801\pi\) |
0.778198 | + | 0.628019i | \(0.216134\pi\) | |||||||
\(114\) | 75.4635 | + | 130.707i | 0.0619983 | + | 0.107384i | ||||
\(115\) | −1754.97 | + | 1013.23i | −1.42306 | + | 0.821605i | ||||
\(116\) | 1293.78 | 1.03555 | ||||||||
\(117\) | −52.4926 | + | 779.371i | −0.0414782 | + | 0.615837i | ||||
\(118\) | −432.530 | −0.337438 | ||||||||
\(119\) | −955.030 | + | 551.387i | −0.735693 | + | 0.424753i | ||||
\(120\) | 175.008 | + | 303.123i | 0.133133 | + | 0.230593i | ||||
\(121\) | 60.5000 | − | 104.789i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 252.757i | 0.187570i | ||||||||
\(123\) | 176.670 | + | 102.001i | 0.129511 | + | 0.0747730i | ||||
\(124\) | 1102.47 | + | 636.514i | 0.798429 | + | 0.460973i | ||||
\(125\) | 1465.51i | 1.04863i | ||||||||
\(126\) | −160.677 | + | 278.301i | −0.113605 | + | 0.196770i | ||||
\(127\) | −7.95328 | − | 13.7755i | −0.00555701 | − | 0.00962502i | 0.863234 | − | 0.504805i | \(-0.168436\pi\) |
−0.868791 | + | 0.495180i | \(0.835102\pi\) | |||||||
\(128\) | −1021.87 | + | 589.979i | −0.705639 | + | 0.407401i | ||||
\(129\) | 273.421 | 0.186615 | ||||||||
\(130\) | 272.414 | + | 182.732i | 0.183787 | + | 0.123282i | ||||
\(131\) | −1358.53 | −0.906073 | −0.453037 | − | 0.891492i | \(-0.649659\pi\) | ||||
−0.453037 | + | 0.891492i | \(0.649659\pi\) | |||||||
\(132\) | 231.453 | − | 133.630i | 0.152617 | − | 0.0881133i | ||||
\(133\) | −1023.41 | − | 1772.59i | −0.667223 | − | 1.15566i | ||||
\(134\) | −157.190 | + | 272.260i | −0.101337 | + | 0.175520i | ||||
\(135\) | 1477.14i | 0.941721i | ||||||||
\(136\) | 340.801 | + | 196.762i | 0.214878 | + | 0.124060i | ||||
\(137\) | 606.241 | + | 350.013i | 0.378063 | + | 0.218275i | 0.676975 | − | 0.736006i | \(-0.263290\pi\) |
−0.298912 | + | 0.954281i | \(0.596624\pi\) | |||||||
\(138\) | − | 411.726i | − | 0.253974i | ||||||
\(139\) | 1101.43 | − | 1907.74i | 0.672103 | − | 1.16412i | −0.305204 | − | 0.952287i | \(-0.598725\pi\) |
0.977307 | − | 0.211829i | \(-0.0679420\pi\) | |||||||
\(140\) | −1152.96 | − | 1996.98i | −0.696020 | − | 1.20554i | ||||
\(141\) | −172.112 | + | 99.3692i | −0.102798 | + | 0.0593503i | ||||
\(142\) | −229.315 | −0.135519 | ||||||||
\(143\) | 287.220 | − | 428.184i | 0.167962 | − | 0.250395i | ||||
\(144\) | −892.934 | −0.516744 | ||||||||
\(145\) | 1560.04 | − | 900.692i | 0.893480 | − | 0.515851i | ||||
\(146\) | −260.754 | − | 451.639i | −0.147809 | − | 0.256013i | ||||
\(147\) | −799.973 | + | 1385.59i | −0.448848 | + | 0.777428i | ||||
\(148\) | − | 1858.76i | − | 1.03236i | ||||||
\(149\) | 1465.06 | + | 845.851i | 0.805518 | + | 0.465066i | 0.845397 | − | 0.534138i | \(-0.179364\pi\) |
−0.0398790 | + | 0.999205i | \(0.512697\pi\) | |||||||
\(150\) | −26.4176 | − | 15.2522i | −0.0143799 | − | 0.00830225i | ||||
\(151\) | − | 2987.30i | − | 1.60996i | −0.593305 | − | 0.804978i | \(-0.702177\pi\) | ||
0.593305 | − | 0.804978i | \(-0.297823\pi\) | |||||||
\(152\) | −365.201 | + | 632.548i | −0.194880 | + | 0.337542i | ||||
\(153\) | 316.921 | + | 548.924i | 0.167461 | + | 0.290051i | ||||
\(154\) | 183.694 | − | 106.056i | 0.0961202 | − | 0.0554950i | ||||
\(155\) | 1772.49 | 0.918517 | ||||||||
\(156\) | 1022.28 | − | 501.846i | 0.524667 | − | 0.257563i | ||||
\(157\) | −2277.76 | −1.15787 | −0.578934 | − | 0.815374i | \(-0.696531\pi\) | ||||
−0.578934 | + | 0.815374i | \(0.696531\pi\) | |||||||
\(158\) | −235.078 | + | 135.722i | −0.118366 | + | 0.0683386i | ||||
\(159\) | −347.545 | − | 601.966i | −0.173347 | − | 0.300245i | ||||
\(160\) | −622.996 | + | 1079.06i | −0.307826 | + | 0.533170i | ||||
\(161\) | 5583.67i | 2.73326i | ||||||||
\(162\) | −0.752865 | − | 0.434667i | −0.000365128 | − | 0.000210806i | ||||
\(163\) | −591.552 | − | 341.533i | −0.284257 | − | 0.164116i | 0.351092 | − | 0.936341i | \(-0.385810\pi\) |
−0.635349 | + | 0.772225i | \(0.719144\pi\) | |||||||
\(164\) | 479.593i | 0.228353i | ||||||||
\(165\) | 186.058 | − | 322.263i | 0.0877856 | − | 0.152049i | ||||
\(166\) | −362.815 | − | 628.414i | −0.169638 | − | 0.293822i | ||||
\(167\) | 141.856 | − | 81.9005i | 0.0657313 | − | 0.0379500i | −0.466774 | − | 0.884377i | \(-0.654584\pi\) |
0.532505 | + | 0.846427i | \(0.321251\pi\) | |||||||
\(168\) | 964.424 | 0.442898 | ||||||||
\(169\) | 1343.72 | − | 1738.17i | 0.611615 | − | 0.791155i | ||||
\(170\) | 266.172 | 0.120085 | ||||||||
\(171\) | −1018.84 | + | 588.225i | −0.455628 | + | 0.263057i | ||||
\(172\) | 321.397 | + | 556.676i | 0.142478 | + | 0.246780i | ||||
\(173\) | 1050.79 | − | 1820.02i | 0.461792 | − | 0.799847i | −0.537258 | − | 0.843418i | \(-0.680540\pi\) |
0.999050 | + | 0.0435704i | \(0.0138733\pi\) | |||||||
\(174\) | 365.994i | 0.159460i | ||||||||
\(175\) | 358.266 | + | 206.845i | 0.154756 | + | 0.0893485i | ||||
\(176\) | 510.423 | + | 294.693i | 0.218606 | + | 0.126212i | ||||
\(177\) | 2090.79i | 0.887873i | ||||||||
\(178\) | −220.290 | + | 381.553i | −0.0927608 | + | 0.160666i | ||||
\(179\) | −74.2953 | − | 128.683i | −0.0310228 | − | 0.0537332i | 0.850097 | − | 0.526626i | \(-0.176543\pi\) |
−0.881120 | + | 0.472893i | \(0.843210\pi\) | |||||||
\(180\) | −1147.81 | + | 662.688i | −0.475292 | + | 0.274410i | ||||
\(181\) | −2458.73 | −1.00970 | −0.504851 | − | 0.863206i | \(-0.668453\pi\) | ||||
−0.504851 | + | 0.863206i | \(0.668453\pi\) | |||||||
\(182\) | 811.341 | − | 398.294i | 0.330443 | − | 0.162217i | ||||
\(183\) | 1221.79 | 0.493539 | ||||||||
\(184\) | 1725.58 | − | 996.263i | 0.691366 | − | 0.399160i | ||||
\(185\) | −1294.02 | − | 2241.31i | −0.514261 | − | 0.890726i | ||||
\(186\) | −180.062 | + | 311.877i | −0.0709829 | + | 0.122946i | ||||
\(187\) | − | 418.372i | − | 0.163606i | ||||||
\(188\) | −404.625 | − | 233.610i | −0.156970 | − | 0.0906265i | ||||
\(189\) | 3524.79 | + | 2035.04i | 1.35657 | + | 0.783213i | ||||
\(190\) | 494.031i | 0.188636i | ||||||||
\(191\) | −2258.35 | + | 3911.57i | −0.855541 | + | 1.48184i | 0.0206014 | + | 0.999788i | \(0.493442\pi\) |
−0.876142 | + | 0.482053i | \(0.839891\pi\) | |||||||
\(192\) | 562.420 | + | 974.140i | 0.211402 | + | 0.366159i | ||||
\(193\) | 1043.17 | − | 602.276i | 0.389064 | − | 0.224626i | −0.292691 | − | 0.956207i | \(-0.594551\pi\) |
0.681754 | + | 0.731581i | \(0.261217\pi\) | |||||||
\(194\) | −1167.85 | −0.432199 | ||||||||
\(195\) | 883.302 | − | 1316.81i | 0.324382 | − | 0.483585i | ||||
\(196\) | −3761.37 | −1.37076 | ||||||||
\(197\) | −280.818 | + | 162.130i | −0.101561 | + | 0.0586360i | −0.549920 | − | 0.835217i | \(-0.685342\pi\) |
0.448359 | + | 0.893853i | \(0.352008\pi\) | |||||||
\(198\) | −60.9579 | − | 105.582i | −0.0218793 | − | 0.0378960i | ||||
\(199\) | 2175.27 | − | 3767.68i | 0.774880 | − | 1.34213i | −0.159982 | − | 0.987120i | \(-0.551144\pi\) |
0.934862 | − | 0.355011i | \(-0.115523\pi\) | |||||||
\(200\) | − | 147.625i | − | 0.0521931i | ||||||
\(201\) | 1316.07 | + | 759.833i | 0.461833 | + | 0.266639i | ||||
\(202\) | −28.7923 | − | 16.6232i | −0.0100288 | − | 0.00579013i | ||||
\(203\) | − | 4963.48i | − | 1.71610i | ||||||
\(204\) | 462.040 | − | 800.276i | 0.158575 | − | 0.274660i | ||||
\(205\) | 333.880 | + | 578.296i | 0.113752 | + | 0.197024i | ||||
\(206\) | 799.429 | − | 461.551i | 0.270383 | − | 0.156106i | ||||
\(207\) | 3209.33 | 1.07760 | ||||||||
\(208\) | 2085.67 | + | 1399.04i | 0.695264 | + | 0.466374i | ||||
\(209\) | 776.523 | 0.257001 | ||||||||
\(210\) | 564.924 | − | 326.159i | 0.185635 | − | 0.107177i | ||||
\(211\) | −1990.02 | − | 3446.81i | −0.649281 | − | 1.12459i | −0.983295 | − | 0.182020i | \(-0.941736\pi\) |
0.334013 | − | 0.942568i | \(-0.391597\pi\) | |||||||
\(212\) | 817.055 | − | 1415.18i | 0.264696 | − | 0.458467i | ||||
\(213\) | 1108.48i | 0.356581i | ||||||||
\(214\) | −747.634 | − | 431.647i | −0.238819 | − | 0.137882i | ||||
\(215\) | 775.085 | + | 447.496i | 0.245862 | + | 0.141949i | ||||
\(216\) | − | 1452.40i | − | 0.457516i | ||||||
\(217\) | 2441.94 | − | 4229.56i | 0.763915 | − | 1.32314i | ||||
\(218\) | 370.364 | + | 641.489i | 0.115065 | + | 0.199299i | ||||
\(219\) | −2183.16 | + | 1260.45i | −0.673627 | + | 0.388919i | ||||
\(220\) | 874.822 | 0.268093 | ||||||||
\(221\) | 119.800 | − | 1778.70i | 0.0364643 | − | 0.541394i | ||||
\(222\) | 525.823 | 0.158968 | ||||||||
\(223\) | 1586.39 | − | 915.903i | 0.476379 | − | 0.275038i | −0.242527 | − | 0.970145i | \(-0.577976\pi\) |
0.718906 | + | 0.695107i | \(0.244643\pi\) | |||||||
\(224\) | 1716.59 | + | 2973.21i | 0.512028 | + | 0.886858i | ||||
\(225\) | 118.888 | − | 205.921i | 0.0352262 | − | 0.0610136i | ||||
\(226\) | − | 247.299i | − | 0.0727881i | ||||||
\(227\) | −3077.89 | − | 1777.02i | −0.899943 | − | 0.519582i | −0.0227610 | − | 0.999741i | \(-0.507246\pi\) |
−0.877182 | + | 0.480159i | \(0.840579\pi\) | |||||||
\(228\) | 1485.36 | + | 857.573i | 0.431449 | + | 0.249097i | ||||
\(229\) | 525.734i | 0.151709i | 0.997119 | + | 0.0758547i | \(0.0241685\pi\) | ||||
−0.997119 | + | 0.0758547i | \(0.975831\pi\) | |||||||
\(230\) | 673.853 | − | 1167.15i | 0.193185 | − | 0.334606i | ||||
\(231\) | −512.660 | − | 887.953i | −0.146020 | − | 0.252914i | ||||
\(232\) | −1533.91 | + | 885.605i | −0.434079 | + | 0.250616i | ||||
\(233\) | −45.3279 | −0.0127448 | −0.00637238 | − | 0.999980i | \(-0.502028\pi\) | ||||
−0.00637238 | + | 0.999980i | \(0.502028\pi\) | |||||||
\(234\) | −228.928 | − | 466.335i | −0.0639550 | − | 0.130279i | ||||
\(235\) | −650.532 | −0.180579 | ||||||||
\(236\) | −4256.78 | + | 2457.66i | −1.17412 | + | 0.677880i | ||||
\(237\) | 656.064 | + | 1136.34i | 0.179814 | + | 0.311447i | ||||
\(238\) | 366.701 | − | 635.145i | 0.0998727 | − | 0.172985i | ||||
\(239\) | − | 2128.63i | − | 0.576107i | −0.957614 | − | 0.288053i | \(-0.906992\pi\) | ||
0.957614 | − | 0.288053i | \(-0.0930081\pi\) | |||||||
\(240\) | 1569.73 | + | 906.284i | 0.422190 | + | 0.243751i | ||||
\(241\) | 4404.66 | + | 2543.03i | 1.17730 | + | 0.679713i | 0.955388 | − | 0.295354i | \(-0.0954375\pi\) |
0.221910 | + | 0.975067i | \(0.428771\pi\) | |||||||
\(242\) | 80.4713i | 0.0213756i | ||||||||
\(243\) | 1892.94 | − | 3278.68i | 0.499722 | − | 0.865544i | ||||
\(244\) | 1436.18 | + | 2487.53i | 0.376811 | + | 0.652656i | ||||
\(245\) | −4535.48 | + | 2618.56i | −1.18270 | + | 0.682831i | ||||
\(246\) | −135.671 | −0.0351630 | ||||||||
\(247\) | 3301.37 | + | 222.355i | 0.850449 | + | 0.0572799i | ||||
\(248\) | −1742.81 | −0.446243 | ||||||||
\(249\) | −3037.67 | + | 1753.80i | −0.773110 | + | 0.446355i | ||||
\(250\) | −487.319 | − | 844.061i | −0.123283 | − | 0.213532i | ||||
\(251\) | −706.046 | + | 1222.91i | −0.177551 | + | 0.307527i | −0.941041 | − | 0.338292i | \(-0.890151\pi\) |
0.763490 | + | 0.645819i | \(0.223484\pi\) | |||||||
\(252\) | 3651.90i | 0.912890i | ||||||||
\(253\) | −1834.54 | − | 1059.17i | −0.455875 | − | 0.263199i | ||||
\(254\) | 9.16141 | + | 5.28934i | 0.00226314 | + | 0.00130663i | ||||
\(255\) | − | 1286.64i | − | 0.315970i | ||||||
\(256\) | −1007.22 | + | 1744.56i | −0.245904 | + | 0.425919i | ||||
\(257\) | 3517.46 | + | 6092.43i | 0.853749 | + | 1.47874i | 0.877801 | + | 0.479025i | \(0.159010\pi\) |
−0.0240525 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(258\) | −157.477 | + | 90.9195i | −0.0380004 | + | 0.0219395i | ||||
\(259\) | −7131.01 | −1.71081 | ||||||||
\(260\) | 3719.28 | + | 250.503i | 0.887154 | + | 0.0597521i | ||||
\(261\) | −2852.86 | −0.676582 | ||||||||
\(262\) | 782.450 | − | 451.747i | 0.184503 | − | 0.106523i | ||||
\(263\) | −3259.44 | − | 5645.51i | −0.764204 | − | 1.32364i | −0.940667 | − | 0.339332i | \(-0.889799\pi\) |
0.176463 | − | 0.984307i | \(-0.443534\pi\) | |||||||
\(264\) | −182.942 | + | 316.865i | −0.0426489 | + | 0.0738700i | ||||
\(265\) | − | 2275.25i | − | 0.527423i | ||||||
\(266\) | 1178.87 | + | 680.619i | 0.271733 | + | 0.156885i | ||||
\(267\) | 1844.38 | + | 1064.85i | 0.422749 | + | 0.244074i | ||||
\(268\) | 3572.63i | 0.814303i | ||||||||
\(269\) | 2933.22 | − | 5080.49i | 0.664839 | − | 1.15153i | −0.314490 | − | 0.949261i | \(-0.601834\pi\) |
0.979329 | − | 0.202274i | \(-0.0648332\pi\) | |||||||
\(270\) | −491.189 | − | 850.764i | −0.110714 | − | 0.191762i | ||||
\(271\) | −6256.02 | + | 3611.92i | −1.40231 | + | 0.809624i | −0.994629 | − | 0.103500i | \(-0.966996\pi\) |
−0.407681 | + | 0.913124i | \(0.633663\pi\) | |||||||
\(272\) | 2037.87 | 0.454280 | ||||||||
\(273\) | −1925.30 | − | 3921.91i | −0.426829 | − | 0.869468i | ||||
\(274\) | −465.554 | −0.102647 | ||||||||
\(275\) | −135.919 | + | 78.4730i | −0.0298045 | + | 0.0172076i | ||||
\(276\) | −2339.44 | − | 4052.04i | −0.510210 | − | 0.883710i | ||||
\(277\) | 2787.06 | − | 4827.33i | 0.604542 | − | 1.04710i | −0.387582 | − | 0.921835i | \(-0.626689\pi\) |
0.992124 | − | 0.125262i | \(-0.0399772\pi\) | |||||||
\(278\) | 1465.02i | 0.316065i | ||||||||
\(279\) | −2431.03 | − | 1403.56i | −0.521656 | − | 0.301178i | ||||
\(280\) | 2733.92 | + | 1578.43i | 0.583510 | + | 0.336890i | ||||
\(281\) | − | 83.0572i | − | 0.0176326i | −0.999961 | − | 0.00881632i | \(-0.997194\pi\) | ||
0.999961 | − | 0.00881632i | \(-0.00280636\pi\) | |||||||
\(282\) | 66.0856 | − | 114.464i | 0.0139551 | − | 0.0241710i | ||||
\(283\) | 2225.48 | + | 3854.65i | 0.467460 | + | 0.809664i | 0.999309 | − | 0.0371751i | \(-0.0118359\pi\) |
−0.531849 | + | 0.846839i | \(0.678503\pi\) | |||||||
\(284\) | −2256.83 | + | 1302.98i | −0.471542 | + | 0.272245i | ||||
\(285\) | 2388.08 | 0.496342 | ||||||||
\(286\) | −23.0428 | + | 342.122i | −0.00476415 | + | 0.0707345i | ||||
\(287\) | 1839.92 | 0.378422 | ||||||||
\(288\) | 1708.92 | − | 986.644i | 0.349649 | − | 0.201870i | ||||
\(289\) | 1733.22 | + | 3002.02i | 0.352782 | + | 0.611035i | ||||
\(290\) | −599.007 | + | 1037.51i | −0.121293 | + | 0.210085i | ||||
\(291\) | 5645.21i | 1.13721i | ||||||||
\(292\) | −5132.46 | − | 2963.23i | −1.02861 | − | 0.593870i | ||||
\(293\) | −648.797 | − | 374.583i | −0.129362 | − | 0.0746872i | 0.433922 | − | 0.900950i | \(-0.357129\pi\) |
−0.563285 | + | 0.826263i | \(0.690463\pi\) | |||||||
\(294\) | − | 1064.05i | − | 0.211077i | ||||||
\(295\) | −3421.91 | + | 5926.91i | −0.675359 | + | 1.16976i | ||||
\(296\) | 1272.35 | + | 2203.77i | 0.249843 | + | 0.432741i | ||||
\(297\) | −1337.24 | + | 772.056i | −0.261261 | + | 0.150839i | ||||
\(298\) | −1125.07 | −0.218703 | ||||||||
\(299\) | −7496.19 | − | 5028.35i | −1.44989 | − | 0.972565i | ||||
\(300\) | −346.655 | −0.0667137 | ||||||||
\(301\) | 2135.65 | − | 1233.02i | 0.408959 | − | 0.236113i | ||||
\(302\) | 993.356 | + | 1720.54i | 0.189276 | + | 0.327835i | ||||
\(303\) | −80.3545 | + | 139.178i | −0.0152351 | + | 0.0263880i | ||||
\(304\) | 3782.41i | 0.713606i | ||||||||
\(305\) | 3463.51 | + | 1999.66i | 0.650229 | + | 0.375410i | ||||
\(306\) | −365.063 | − | 210.769i | −0.0682002 | − | 0.0393754i | ||||
\(307\) | − | 6250.03i | − | 1.16192i | −0.813934 | − | 0.580958i | \(-0.802678\pi\) | ||
0.813934 | − | 0.580958i | \(-0.197322\pi\) | |||||||
\(308\) | 1205.23 | − | 2087.52i | 0.222969 | − | 0.386193i | ||||
\(309\) | −2231.07 | − | 3864.33i | −0.410748 | − | 0.711437i | ||||
\(310\) | −1020.87 | + | 589.400i | −0.187037 | + | 0.107986i | ||||
\(311\) | −4650.16 | −0.847866 | −0.423933 | − | 0.905694i | \(-0.639351\pi\) | ||||
−0.423933 | + | 0.905694i | \(0.639351\pi\) | |||||||
\(312\) | −868.507 | + | 1294.76i | −0.157595 | + | 0.234940i | ||||
\(313\) | −2500.00 | −0.451465 | −0.225732 | − | 0.974189i | \(-0.572477\pi\) | ||||
−0.225732 | + | 0.974189i | \(0.572477\pi\) | |||||||
\(314\) | 1311.88 | − | 757.415i | 0.235776 | − | 0.136126i | ||||
\(315\) | 2542.35 | + | 4403.49i | 0.454747 | + | 0.787645i | ||||
\(316\) | −1542.36 | + | 2671.45i | −0.274572 | + | 0.475572i | ||||
\(317\) | 9258.35i | 1.64038i | 0.572091 | + | 0.820190i | \(0.306132\pi\) | ||||
−0.572091 | + | 0.820190i | \(0.693868\pi\) | |||||||
\(318\) | 400.338 | + | 231.135i | 0.0705970 | + | 0.0407592i | ||||
\(319\) | 1630.77 | + | 941.525i | 0.286224 | + | 0.165252i | ||||
\(320\) | 3681.95i | 0.643210i | ||||||||
\(321\) | −2086.52 | + | 3613.96i | −0.362798 | + | 0.628385i | ||||
\(322\) | −1856.72 | − | 3215.92i | −0.321338 | − | 0.556573i | ||||
\(323\) | 2325.21 | − | 1342.46i | 0.400551 | − | 0.231258i | ||||
\(324\) | −9.87918 | −0.00169396 | ||||||||
\(325\) | −600.327 | + | 294.706i | −0.102462 | + | 0.0502995i | ||||
\(326\) | 454.274 | 0.0771776 | ||||||||
\(327\) | 3100.87 | − | 1790.29i | 0.524399 | − | 0.302762i | ||||
\(328\) | −328.287 | − | 568.610i | −0.0552641 | − | 0.0957202i | ||||
\(329\) | −896.229 | + | 1552.31i | −0.150184 | + | 0.260127i | ||||
\(330\) | 247.477i | 0.0412823i | ||||||||
\(331\) | 4797.36 | + | 2769.76i | 0.796636 | + | 0.459938i | 0.842294 | − | 0.539019i | \(-0.181205\pi\) |
−0.0456573 | + | 0.998957i | \(0.514538\pi\) | |||||||
\(332\) | −7141.35 | − | 4123.06i | −1.18052 | − | 0.681573i | ||||
\(333\) | 4098.70i | 0.674497i | ||||||||
\(334\) | −54.4681 | + | 94.3415i | −0.00892323 | + | 0.0154555i | ||||
\(335\) | 2487.17 | + | 4307.90i | 0.405638 | + | 0.702585i | ||||
\(336\) | 4325.19 | − | 2497.15i | 0.702257 | − | 0.405448i | ||||
\(337\) | −8246.13 | −1.33292 | −0.666462 | − | 0.745539i | \(-0.732192\pi\) | ||||
−0.666462 | + | 0.745539i | \(0.732192\pi\) | |||||||
\(338\) | −195.931 | + | 1447.92i | −0.0315303 | + | 0.233008i | ||||
\(339\) | −1195.41 | −0.191522 | ||||||||
\(340\) | 2619.55 | − | 1512.40i | 0.417839 | − | 0.241239i | ||||
\(341\) | 926.426 | + | 1604.62i | 0.147122 | + | 0.254824i | ||||
\(342\) | 391.200 | − | 677.579i | 0.0618529 | − | 0.107132i | ||||
\(343\) | 4485.06i | 0.706037i | ||||||||
\(344\) | −762.103 | − | 440.000i | −0.119447 | − | 0.0689629i | ||||
\(345\) | −5641.83 | − | 3257.31i | −0.880423 | − | 0.508313i | ||||
\(346\) | 1397.66i | 0.217164i | ||||||||
\(347\) | 3347.54 | − | 5798.12i | 0.517883 | − | 0.897000i | −0.481901 | − | 0.876226i | \(-0.660053\pi\) |
0.999784 | − | 0.0207747i | \(-0.00661326\pi\) | |||||||
\(348\) | 2079.60 | + | 3601.97i | 0.320339 | + | 0.554844i | ||||
\(349\) | 4222.44 | − | 2437.82i | 0.647627 | − | 0.373908i | −0.139919 | − | 0.990163i | \(-0.544684\pi\) |
0.787546 | + | 0.616255i | \(0.211351\pi\) | |||||||
\(350\) | −275.125 | −0.0420173 | ||||||||
\(351\) | −5906.31 | + | 2899.46i | −0.898165 | + | 0.440916i | ||||
\(352\) | −1302.48 | −0.197223 | ||||||||
\(353\) | 10663.7 | − | 6156.67i | 1.60784 | − | 0.928290i | 0.617993 | − | 0.786183i | \(-0.287946\pi\) |
0.989851 | − | 0.142106i | \(-0.0453875\pi\) | |||||||
\(354\) | −695.242 | − | 1204.20i | −0.104383 | − | 0.180797i | ||||
\(355\) | −1814.20 | + | 3142.28i | −0.271233 | + | 0.469789i | ||||
\(356\) | 5006.79i | 0.745391i | ||||||||
\(357\) | −3070.20 | − | 1772.58i | −0.455161 | − | 0.262787i | ||||
\(358\) | 85.5810 | + | 49.4102i | 0.0126343 | + | 0.00729444i | ||||
\(359\) | − | 12095.7i | − | 1.77824i | −0.457678 | − | 0.889118i | \(-0.651319\pi\) | ||
0.457678 | − | 0.889118i | \(-0.348681\pi\) | |||||||
\(360\) | 907.236 | − | 1571.38i | 0.132821 | − | 0.230052i | ||||
\(361\) | −937.816 | − | 1624.34i | −0.136728 | − | 0.236819i | ||||
\(362\) | 1416.11 | − | 817.592i | 0.205605 | − | 0.118706i | ||||
\(363\) | 388.987 | 0.0562439 | ||||||||
\(364\) | 5721.76 | − | 8529.91i | 0.823905 | − | 1.22827i | ||||
\(365\) | −8251.68 | −1.18332 | ||||||||
\(366\) | −703.695 | + | 406.278i | −0.100499 | + | 0.0580233i | ||||
\(367\) | −4318.51 | − | 7479.88i | −0.614236 | − | 1.06389i | −0.990518 | − | 0.137383i | \(-0.956131\pi\) |
0.376282 | − | 0.926505i | \(-0.377202\pi\) | |||||||
\(368\) | 5159.17 | − | 8935.95i | 0.730817 | − | 1.26581i | ||||
\(369\) | − | 1057.54i | − | 0.149195i | ||||||
\(370\) | 1490.59 | + | 860.591i | 0.209438 | + | 0.120919i | ||||
\(371\) | −5429.24 | − | 3134.57i | −0.759763 | − | 0.438649i | ||||
\(372\) | 4092.49i | 0.570392i | ||||||||
\(373\) | 6914.12 | − | 11975.6i | 0.959784 | − | 1.66239i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.723020 | − | 0.690827i | \(-0.242753\pi\) | |||||||
\(374\) | 139.119 | + | 240.962i | 0.0192345 | + | 0.0333151i | ||||
\(375\) | −4080.07 | + | 2355.63i | −0.561851 | + | 0.324385i | ||||
\(376\) | 639.636 | 0.0877306 | ||||||||
\(377\) | 6663.57 | + | 4469.84i | 0.910322 | + | 0.610632i | ||||
\(378\) | −2706.81 | −0.368316 | ||||||||
\(379\) | −9623.53 | + | 5556.15i | −1.30429 | + | 0.753035i | −0.981138 | − | 0.193310i | \(-0.938078\pi\) |
−0.323157 | + | 0.946345i | \(0.604744\pi\) | |||||||
\(380\) | 2807.10 | + | 4862.05i | 0.378951 | + | 0.656362i | ||||
\(381\) | 25.5680 | − | 44.2850i | 0.00343802 | − | 0.00595483i | ||||
\(382\) | − | 3003.84i | − | 0.402329i | ||||||
\(383\) | 10575.7 | + | 6105.88i | 1.41095 | + | 0.814611i | 0.995478 | − | 0.0949964i | \(-0.0302839\pi\) |
0.415470 | + | 0.909607i | \(0.363617\pi\) | |||||||
\(384\) | −3285.09 | − | 1896.65i | −0.436566 | − | 0.252052i | ||||
\(385\) | − | 3356.19i | − | 0.444279i | ||||||
\(386\) | −400.545 | + | 693.764i | −0.0528166 | + | 0.0914810i | ||||
\(387\) | −708.702 | − | 1227.51i | −0.0930888 | − | 0.161235i | ||||
\(388\) | −11493.5 | + | 6635.76i | −1.50385 | + | 0.868246i | ||||
\(389\) | 6803.65 | 0.886783 | 0.443392 | − | 0.896328i | \(-0.353775\pi\) | ||||
0.443392 | + | 0.896328i | \(0.353775\pi\) | |||||||
\(390\) | −70.8644 | + | 1052.14i | −0.00920092 | + | 0.136608i | ||||
\(391\) | −7324.41 | −0.947343 | ||||||||
\(392\) | 4459.51 | − | 2574.70i | 0.574590 | − | 0.331740i | ||||
\(393\) | −2183.69 | − | 3782.25i | −0.280286 | − | 0.485469i | ||||
\(394\) | 107.825 | − | 186.758i | 0.0137872 | − | 0.0238801i | ||||
\(395\) | 4295.00i | 0.547101i | ||||||||
\(396\) | −1199.85 | − | 692.731i | −0.152259 | − | 0.0879067i | ||||
\(397\) | 2446.94 | + | 1412.74i | 0.309341 | + | 0.178598i | 0.646631 | − | 0.762803i | \(-0.276177\pi\) |
−0.337291 | + | 0.941401i | \(0.609511\pi\) | |||||||
\(398\) | 2893.34i | 0.364397i | ||||||||
\(399\) | 3290.02 | − | 5698.48i | 0.412799 | − | 0.714989i | ||||
\(400\) | −382.239 | − | 662.057i | −0.0477798 | − | 0.0827571i | ||||
\(401\) | 11999.5 | − | 6927.92i | 1.49433 | − | 0.862752i | 0.494352 | − | 0.869262i | \(-0.335406\pi\) |
0.999979 | + | 0.00650991i | \(0.00207218\pi\) | |||||||
\(402\) | −1010.66 | −0.125390 | ||||||||
\(403\) | 3479.20 | + | 7087.26i | 0.430052 | + | 0.876034i | ||||
\(404\) | −377.816 | −0.0465273 | ||||||||
\(405\) | −11.9124 | + | 6.87762i | −0.00146156 | + | 0.000843831i | ||||
\(406\) | 1650.49 | + | 2858.72i | 0.201754 | + | 0.349448i | ||||
\(407\) | 1352.69 | − | 2342.92i | 0.164742 | − | 0.285342i | ||||
\(408\) | 1265.09i | 0.153508i | ||||||||
\(409\) | 7714.62 | + | 4454.04i | 0.932673 | + | 0.538479i | 0.887656 | − | 0.460507i | \(-0.152332\pi\) |
0.0450171 | + | 0.998986i | \(0.485666\pi\) | |||||||
\(410\) | −384.597 | − | 222.047i | −0.0463266 | − | 0.0267467i | ||||
\(411\) | 2250.42i | 0.270086i | ||||||||
\(412\) | 5245.10 | − | 9084.78i | 0.627203 | − | 1.08635i | ||||
\(413\) | 9428.62 | + | 16330.8i | 1.12337 | + | 1.94573i | ||||
\(414\) | −1848.42 | + | 1067.19i | −0.219432 | + | 0.126689i | ||||
\(415\) | −11481.4 | −1.35808 | ||||||||
\(416\) | −5537.46 | − | 372.962i | −0.652635 | − | 0.0439567i | ||||
\(417\) | 7081.70 | 0.831637 | ||||||||
\(418\) | −447.240 | + | 258.214i | −0.0523330 | + | 0.0302145i | ||||
\(419\) | −104.511 | − | 181.018i | −0.0121854 | − | 0.0211058i | 0.859868 | − | 0.510516i | \(-0.170546\pi\) |
−0.872054 | + | 0.489410i | \(0.837212\pi\) | |||||||
\(420\) | 3706.50 | − | 6419.84i | 0.430616 | − | 0.745848i | ||||
\(421\) | − | 6752.89i | − | 0.781747i | −0.920444 | − | 0.390874i | \(-0.872173\pi\) | ||
0.920444 | − | 0.390874i | \(-0.127827\pi\) | |||||||
\(422\) | 2292.31 | + | 1323.46i | 0.264426 | + | 0.152666i | ||||
\(423\) | 892.225 | + | 515.127i | 0.102557 | + | 0.0592111i | ||||
\(424\) | 2237.14i | 0.256238i | ||||||||
\(425\) | −271.329 | + | 469.956i | −0.0309680 | + | 0.0536382i | ||||
\(426\) | −368.598 | − | 638.430i | −0.0419216 | − | 0.0726104i | ||||
\(427\) | 9543.24 | − | 5509.79i | 1.08157 | − | 0.624444i | ||||
\(428\) | −9810.54 | −1.10797 | ||||||||
\(429\) | 1653.77 | + | 111.385i | 0.186118 | + | 0.0125355i | ||||
\(430\) | −595.216 | −0.0667531 | ||||||||
\(431\) | −589.167 | + | 340.156i | −0.0658450 | + | 0.0380156i | −0.532561 | − | 0.846392i | \(-0.678770\pi\) |
0.466716 | + | 0.884407i | \(0.345437\pi\) | |||||||
\(432\) | −3760.65 | − | 6513.64i | −0.418830 | − | 0.725434i | ||||
\(433\) | −5641.40 | + | 9771.19i | −0.626116 | + | 1.08447i | 0.362208 | + | 0.932097i | \(0.382023\pi\) |
−0.988324 | + | 0.152368i | \(0.951310\pi\) | |||||||
\(434\) | 3248.03i | 0.359241i | ||||||||
\(435\) | 5015.18 | + | 2895.52i | 0.552780 | + | 0.319148i | ||||
\(436\) | 7289.93 | + | 4208.85i | 0.800744 | + | 0.462310i | ||||
\(437\) | − | 13594.5i | − | 1.48813i | ||||||
\(438\) | 838.264 | − | 1451.92i | 0.0914470 | − | 0.158391i | ||||
\(439\) | 2365.18 | + | 4096.61i | 0.257139 | + | 0.445377i | 0.965474 | − | 0.260499i | \(-0.0838869\pi\) |
−0.708335 | + | 0.705876i | \(0.750554\pi\) | |||||||
\(440\) | −1037.20 | + | 598.826i | −0.112378 | + | 0.0648816i | ||||
\(441\) | 8294.07 | 0.895591 | ||||||||
\(442\) | 522.464 | + | 1064.28i | 0.0562241 | + | 0.114531i | ||||
\(443\) | −669.977 | −0.0718546 | −0.0359273 | − | 0.999354i | \(-0.511438\pi\) | ||||
−0.0359273 | + | 0.999354i | \(0.511438\pi\) | |||||||
\(444\) | 5174.93 | − | 2987.75i | 0.553134 | − | 0.319352i | ||||
\(445\) | 3485.59 | + | 6037.21i | 0.371309 | + | 0.643127i | ||||
\(446\) | −609.123 | + | 1055.03i | −0.0646700 | + | 0.112012i | ||||
\(447\) | 5438.43i | 0.575457i | ||||||||
\(448\) | 8785.95 | + | 5072.57i | 0.926556 | + | 0.534947i | ||||
\(449\) | 1411.20 | + | 814.754i | 0.148326 | + | 0.0856361i | 0.572326 | − | 0.820026i | \(-0.306041\pi\) |
−0.424000 | + | 0.905662i | \(0.639374\pi\) | |||||||
\(450\) | 158.134i | 0.0165656i | ||||||||
\(451\) | −349.016 | + | 604.514i | −0.0364402 | + | 0.0631163i | ||||
\(452\) | −1405.17 | − | 2433.82i | −0.146224 | − | 0.253268i | ||||
\(453\) | 8316.87 | − | 4801.75i | 0.862606 | − | 0.498026i | ||||
\(454\) | 2363.62 | 0.244340 | ||||||||
\(455\) | 961.037 | − | 14268.8i | 0.0990200 | − | 1.47017i | ||||
\(456\) | −2348.08 | −0.241138 | ||||||||
\(457\) | 9977.27 | − | 5760.38i | 1.02126 | − | 0.589626i | 0.106793 | − | 0.994281i | \(-0.465942\pi\) |
0.914469 | + | 0.404655i | \(0.132608\pi\) | |||||||
\(458\) | −174.820 | − | 302.797i | −0.0178358 | − | 0.0308925i | ||||
\(459\) | −2669.47 | + | 4623.66i | −0.271460 | + | 0.470183i | ||||
\(460\) | − | 15315.4i | − | 1.55236i | ||||||
\(461\) | −7157.57 | − | 4132.42i | −0.723126 | − | 0.417497i | 0.0927762 | − | 0.995687i | \(-0.470426\pi\) |
−0.815902 | + | 0.578190i | \(0.803759\pi\) | |||||||
\(462\) | 590.535 | + | 340.945i | 0.0594679 | + | 0.0343338i | ||||
\(463\) | 8472.07i | 0.850390i | 0.905102 | + | 0.425195i | \(0.139794\pi\) | ||||
−0.905102 | + | 0.425195i | \(0.860206\pi\) | |||||||
\(464\) | −4586.13 | + | 7943.41i | −0.458849 | + | 0.794749i | ||||
\(465\) | 2849.08 | + | 4934.75i | 0.284135 | + | 0.492137i | ||||
\(466\) | 26.1067 | − | 15.0727i | 0.00259521 | − | 0.00149835i | ||||
\(467\) | −6897.41 | −0.683456 | −0.341728 | − | 0.939799i | \(-0.611012\pi\) | ||||
−0.341728 | + | 0.939799i | \(0.611012\pi\) | |||||||
\(468\) | −4902.75 | − | 3288.70i | −0.484252 | − | 0.324830i | ||||
\(469\) | 13706.1 | 1.34945 | ||||||||
\(470\) | 374.675 | − | 216.319i | 0.0367712 | − | 0.0212299i | ||||
\(471\) | −3661.24 | − | 6341.46i | −0.358176 | − | 0.620380i | ||||
\(472\) | 3364.59 | − | 5827.64i | 0.328110 | − | 0.568303i | ||||
\(473\) | 935.566i | 0.0909458i | ||||||||
\(474\) | −755.722 | − | 436.316i | −0.0732309 | − | 0.0422799i | ||||
\(475\) | −872.267 | − | 503.604i | −0.0842576 | − | 0.0486461i | ||||
\(476\) | − | 8334.44i | − | 0.802539i | ||||||
\(477\) | −1801.66 | + | 3120.57i | −0.172940 | + | 0.299541i | ||||
\(478\) | 707.824 | + | 1225.99i | 0.0677304 | + | 0.117312i | ||||
\(479\) | −8393.77 | + | 4846.14i | −0.800670 | + | 0.462267i | −0.843705 | − | 0.536806i | \(-0.819631\pi\) |
0.0430354 | + | 0.999074i | \(0.486297\pi\) | |||||||
\(480\) | −4005.58 | −0.380893 | ||||||||
\(481\) | 6421.80 | − | 9573.53i | 0.608750 | − | 0.907516i | ||||
\(482\) | −3382.49 | −0.319644 | ||||||||
\(483\) | −15545.3 | + | 8975.11i | −1.46447 | + | 0.845510i | ||||
\(484\) | 457.241 | + | 791.965i | 0.0429415 | + | 0.0743769i | ||||
\(485\) | −9239.27 | + | 16002.9i | −0.865018 | + | 1.49825i | ||||
\(486\) | 2517.81i | 0.235001i | ||||||||
\(487\) | 3531.16 | + | 2038.72i | 0.328567 | + | 0.189698i | 0.655205 | − | 0.755451i | \(-0.272582\pi\) |
−0.326638 | + | 0.945150i | \(0.605916\pi\) | |||||||
\(488\) | −3405.49 | − | 1966.16i | −0.315901 | − | 0.182385i | ||||
\(489\) | − | 2195.90i | − | 0.203071i | ||||||
\(490\) | 1741.48 | − | 3016.33i | 0.160555 | − | 0.278089i | ||||
\(491\) | −10238.5 | − | 17733.6i | −0.941054 | − | 1.62995i | −0.763466 | − | 0.645848i | \(-0.776504\pi\) |
−0.177588 | − | 0.984105i | \(-0.556830\pi\) | |||||||
\(492\) | −1335.22 | + | 770.890i | −0.122350 | + | 0.0706391i | ||||
\(493\) | 6510.87 | 0.594796 | ||||||||
\(494\) | −1975.37 | + | 969.724i | −0.179911 | + | 0.0883197i | ||||
\(495\) | −1929.04 | −0.175160 | ||||||||
\(496\) | −7816.02 | + | 4512.58i | −0.707560 | + | 0.408510i | ||||
\(497\) | 4998.78 | + | 8658.15i | 0.451159 | + | 0.781431i | ||||
\(498\) | 1166.37 | − | 2020.21i | 0.104952 | − | 0.181782i | ||||
\(499\) | − | 11763.9i | − | 1.05536i | −0.849444 | − | 0.527679i | \(-0.823062\pi\) | ||
0.849444 | − | 0.527679i | \(-0.176938\pi\) | |||||||
\(500\) | −9591.98 | − | 5537.93i | −0.857933 | − | 0.495328i | ||||
\(501\) | 456.034 | + | 263.291i | 0.0406668 | + | 0.0234790i | ||||
\(502\) | − | 939.115i | − | 0.0834955i | ||||||
\(503\) | −11241.8 | + | 19471.4i | −0.996515 | + | 1.72601i | −0.426021 | + | 0.904713i | \(0.640085\pi\) |
−0.570494 | + | 0.821301i | \(0.693248\pi\) | |||||||
\(504\) | −2499.77 | − | 4329.73i | −0.220930 | − | 0.382662i | ||||
\(505\) | −455.573 | + | 263.025i | −0.0401440 | + | 0.0231772i | ||||
\(506\) | 1408.81 | 0.123773 | ||||||||
\(507\) | 6999.06 | + | 947.105i | 0.613095 | + | 0.0829633i | ||||
\(508\) | 120.217 | 0.0104996 | ||||||||
\(509\) | −4041.33 | + | 2333.26i | −0.351923 | + | 0.203183i | −0.665532 | − | 0.746370i | \(-0.731795\pi\) |
0.313609 | + | 0.949552i | \(0.398462\pi\) | |||||||
\(510\) | 427.840 | + | 741.041i | 0.0371472 | + | 0.0643409i | ||||
\(511\) | −11368.2 | + | 19690.3i | −0.984149 | + | 1.70460i | ||||
\(512\) | − | 10779.4i | − | 0.930441i | ||||||
\(513\) | −8581.79 | − | 4954.70i | −0.738587 | − | 0.426424i | ||||
\(514\) | −4051.78 | − | 2339.30i | −0.347697 | − | 0.200743i | ||||
\(515\) | − | 14606.0i | − | 1.24974i | ||||||
\(516\) | −1033.22 | + | 1789.58i | −0.0881489 | + | 0.152678i | ||||
\(517\) | −340.012 | − | 588.918i | −0.0289240 | − | 0.0500979i | ||||
\(518\) | 4107.12 | − | 2371.25i | 0.348372 | − | 0.201132i | ||||
\(519\) | 6756.09 | 0.571405 | ||||||||
\(520\) | −4581.09 | + | 2248.89i | −0.386335 | + | 0.189655i | ||||
\(521\) | −18591.4 | −1.56335 | −0.781674 | − | 0.623687i | \(-0.785634\pi\) | ||||
−0.781674 | + | 0.623687i | \(0.785634\pi\) | |||||||
\(522\) | 1643.11 | − | 948.651i | 0.137772 | − | 0.0795428i | ||||
\(523\) | 2981.38 | + | 5163.90i | 0.249267 | + | 0.431743i | 0.963323 | − | 0.268346i | \(-0.0864771\pi\) |
−0.714056 | + | 0.700089i | \(0.753144\pi\) | |||||||
\(524\) | 5133.70 | − | 8891.82i | 0.427990 | − | 0.741300i | ||||
\(525\) | 1329.92i | 0.110557i | ||||||||
\(526\) | 3754.56 | + | 2167.69i | 0.311229 | + | 0.179688i | ||||
\(527\) | 5548.15 | + | 3203.23i | 0.458598 | + | 0.264772i | ||||
\(528\) | 1894.74i | 0.156170i | ||||||||
\(529\) | −12459.3 | + | 21580.2i | −1.02403 | + | 1.77366i | ||||
\(530\) | 756.578 | + | 1310.43i | 0.0620069 | + | 0.107399i | ||||
\(531\) | 9386.50 | − | 5419.30i | 0.767118 | − | 0.442896i | ||||
\(532\) | 15469.2 | 1.26067 | ||||||||
\(533\) | −1656.93 | + | 2470.13i | −0.134652 | + | 0.200738i | ||||
\(534\) | −1416.36 | −0.114779 | ||||||||
\(535\) | −11829.6 | + | 6829.83i | −0.955960 | + | 0.551924i | ||||
\(536\) | −2445.51 | − | 4235.75i | −0.197071 | − | 0.341337i | ||||
\(537\) | 238.842 | − | 413.687i | 0.0191933 | − | 0.0332438i | ||||
\(538\) | 3901.49i | 0.312649i | ||||||||
\(539\) | −4741.10 | − | 2737.27i | −0.378875 | − | 0.218744i | ||||
\(540\) | −9668.15 | − | 5581.91i | −0.770465 | − | 0.444828i | ||||
\(541\) | 10281.4i | 0.817068i | 0.912743 | + | 0.408534i | \(0.133960\pi\) | ||||
−0.912743 | + | 0.408534i | \(0.866040\pi\) | |||||||
\(542\) | 2402.11 | − | 4160.58i | 0.190368 | − | 0.329727i | ||||
\(543\) | −3952.13 | − | 6845.29i | −0.312343 | − | 0.540993i | ||||
\(544\) | −3900.13 | + | 2251.74i | −0.307383 | + | 0.177468i | ||||
\(545\) | 11720.3 | 0.921181 | ||||||||
\(546\) | 2413.01 | + | 1618.62i | 0.189135 | + | 0.126869i | ||||
\(547\) | −2031.38 | −0.158785 | −0.0793926 | − | 0.996843i | \(-0.525298\pi\) | ||||
−0.0793926 | + | 0.996843i | \(0.525298\pi\) | |||||||
\(548\) | −4581.79 | + | 2645.30i | −0.357161 | + | 0.206207i | ||||
\(549\) | −3166.87 | − | 5485.18i | −0.246191 | − | 0.426415i | ||||
\(550\) | 52.1886 | − | 90.3933i | 0.00404605 | − | 0.00700797i | ||||
\(551\) | 12084.6i | 0.934336i | ||||||||
\(552\) | 5547.33 | + | 3202.75i | 0.427736 | + | 0.246953i | ||||
\(553\) | 10248.8 | + | 5917.16i | 0.788109 | + | 0.455015i | ||||
\(554\) | 3707.08i | 0.284294i | ||||||||
\(555\) | 4159.98 | − | 7205.29i | 0.318164 | − | 0.551077i | ||||
\(556\) | 8324.30 | + | 14418.1i | 0.634944 | + | 1.09976i | ||||
\(557\) | −8868.27 | + | 5120.10i | −0.674615 | + | 0.389489i | −0.797823 | − | 0.602892i | \(-0.794015\pi\) |
0.123208 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(558\) | 1866.88 | 0.141633 | ||||||||
\(559\) | −267.897 | + | 3977.54i | −0.0202698 | + | 0.300951i | ||||
\(560\) | 16347.9 | 1.23361 | ||||||||
\(561\) | 1164.78 | − | 672.484i | 0.0876594 | − | 0.0506102i | ||||
\(562\) | 27.6187 | + | 47.8369i | 0.00207299 | + | 0.00359053i | ||||
\(563\) | 9525.14 | − | 16498.0i | 0.713031 | − | 1.23501i | −0.250683 | − | 0.968069i | \(-0.580655\pi\) |
0.963714 | − | 0.266937i | \(-0.0860116\pi\) | |||||||
\(564\) | − | 1502.01i | − | 0.112138i | ||||||
\(565\) | −3388.72 | − | 1956.48i | −0.252326 | − | 0.145681i | ||||
\(566\) | −2563.54 | − | 1480.06i | −0.190377 | − | 0.109914i | ||||
\(567\) | 37.9008i | 0.00280720i | ||||||||
\(568\) | 1783.81 | − | 3089.65i | 0.131773 | − | 0.228237i | ||||
\(569\) | 3442.50 | + | 5962.59i | 0.253633 | + | 0.439305i | 0.964523 | − | 0.263998i | \(-0.0850411\pi\) |
−0.710890 | + | 0.703303i | \(0.751708\pi\) | |||||||
\(570\) | −1375.42 | + | 794.097i | −0.101070 | + | 0.0583528i | ||||
\(571\) | −26902.4 | −1.97168 | −0.985839 | − | 0.167692i | \(-0.946369\pi\) | ||||
−0.985839 | + | 0.167692i | \(0.946369\pi\) | |||||||
\(572\) | 1717.17 | + | 3497.95i | 0.125522 | + | 0.255693i | ||||
\(573\) | −14520.1 | −1.05862 | ||||||||
\(574\) | −1059.71 | + | 611.822i | −0.0770581 | + | 0.0444895i | ||||
\(575\) | 1373.82 | + | 2379.53i | 0.0996388 | + | 0.172579i | ||||
\(576\) | 2915.57 | − | 5049.91i | 0.210906 | − | 0.365300i | ||||
\(577\) | 2399.20i | 0.173102i | 0.996247 | + | 0.0865512i | \(0.0275846\pi\) | ||||
−0.996247 | + | 0.0865512i | \(0.972415\pi\) | |||||||
\(578\) | −1996.50 | − | 1152.68i | −0.143674 | − | 0.0829500i | ||||
\(579\) | 3353.56 | + | 1936.18i | 0.240707 | + | 0.138972i | ||||
\(580\) | 13614.3i | 0.974662i | ||||||||
\(581\) | −15817.8 | + | 27397.3i | −1.12949 | + | 1.95633i | ||||
\(582\) | −1877.18 | − | 3251.37i | −0.133697 | − | 0.231570i | ||||
\(583\) | 2059.75 | − | 1189.20i | 0.146323 | − | 0.0844795i | ||||
\(584\) | 8113.47 | 0.574893 | ||||||||
\(585\) | −8201.27 | − | 552.376i | −0.579625 | − | 0.0390392i | ||||
\(586\) | 498.234 | 0.0351226 | ||||||||
\(587\) | 13742.7 | − | 7934.34i | 0.966305 | − | 0.557897i | 0.0681974 | − | 0.997672i | \(-0.478275\pi\) |
0.898108 | + | 0.439775i | \(0.144942\pi\) | |||||||
\(588\) | −6045.96 | − | 10471.9i | −0.424033 | − | 0.734446i | ||||
\(589\) | −5945.38 | + | 10297.7i | −0.415917 | + | 0.720389i | ||||
\(590\) | − | 4551.49i | − | 0.317596i | ||||||
\(591\) | −902.764 | − | 521.211i | −0.0628338 | − | 0.0362771i | ||||
\(592\) | 11412.3 | + | 6588.88i | 0.792300 | + | 0.457435i | ||||
\(593\) | 795.575i | 0.0550933i | 0.999621 | + | 0.0275467i | \(0.00876949\pi\) | ||||
−0.999621 | + | 0.0275467i | \(0.991231\pi\) | |||||||
\(594\) | 513.457 | − | 889.333i | 0.0354670 | − | 0.0614306i | ||||
\(595\) | −5802.21 | − | 10049.7i | −0.399777 | − | 0.692434i | ||||
\(596\) | −11072.5 | + | 6392.70i | −0.760984 | + | 0.439354i | ||||
\(597\) | 13986.0 | 0.958809 | ||||||||
\(598\) | 5989.50 | + | 403.408i | 0.409580 | + | 0.0275863i | ||||
\(599\) | 11565.7 | 0.788917 | 0.394458 | − | 0.918914i | \(-0.370932\pi\) | ||||
0.394458 | + | 0.918914i | \(0.370932\pi\) | |||||||
\(600\) | 410.997 | − | 237.289i | 0.0279648 | − | 0.0161455i | ||||
\(601\) | −560.946 | − | 971.587i | −0.0380723 | − | 0.0659432i | 0.846361 | − | 0.532609i | \(-0.178788\pi\) |
−0.884434 | + | 0.466666i | \(0.845455\pi\) | |||||||
\(602\) | −820.020 | + | 1420.32i | −0.0555175 | + | 0.0961591i | ||||
\(603\) | − | 7877.90i | − | 0.532028i | ||||||
\(604\) | 19552.4 | + | 11288.6i | 1.31718 | + | 0.760473i | ||||
\(605\) | 1102.69 | + | 636.638i | 0.0741003 | + | 0.0427818i | ||||
\(606\) | − | 106.880i | − | 0.00716451i | ||||||
\(607\) | −9491.63 | + | 16440.0i | −0.634684 | + | 1.09931i | 0.351898 | + | 0.936039i | \(0.385537\pi\) |
−0.986582 | + | 0.163267i | \(0.947797\pi\) | |||||||
\(608\) | −4179.36 | − | 7238.87i | −0.278776 | − | 0.482853i | ||||
\(609\) | 13818.7 | − | 7978.22i | 0.919476 | − | 0.530860i | ||||
\(610\) | −2659.75 | −0.176541 | ||||||||
\(611\) | −1276.92 | − | 2601.13i | −0.0845476 | − | 0.172227i | ||||
\(612\) | −4790.40 | −0.316406 | ||||||||
\(613\) | −16635.1 | + | 9604.29i | −1.09606 | + | 0.632812i | −0.935184 | − | 0.354162i | \(-0.884766\pi\) |
−0.160878 | + | 0.986974i | \(0.551433\pi\) | |||||||
\(614\) | 2078.30 | + | 3599.72i | 0.136601 | + | 0.236601i | ||||
\(615\) | −1073.35 | + | 1859.09i | −0.0703764 | + | 0.121895i | ||||
\(616\) | 3299.98i | 0.215844i | ||||||||
\(617\) | −23127.9 | − | 13352.9i | −1.50907 | − | 0.871261i | −0.999944 | − | 0.0105688i | \(-0.996636\pi\) |
−0.509125 | − | 0.860693i | \(-0.670031\pi\) | |||||||
\(618\) | 2569.98 | + | 1483.78i | 0.167281 | + | 0.0965798i | ||||
\(619\) | − | 4297.92i | − | 0.279076i | −0.990217 | − | 0.139538i | \(-0.955438\pi\) | ||
0.990217 | − | 0.139538i | \(-0.0445618\pi\) | |||||||
\(620\) | −6698.00 | + | 11601.3i | −0.433868 | + | 0.751481i | ||||
\(621\) | 13516.3 | + | 23411.0i | 0.873416 | + | 1.51280i | ||||
\(622\) | 2678.27 | − | 1546.30i | 0.172651 | − | 0.0996799i | ||||
\(623\) | 19208.2 | 1.23525 | ||||||||
\(624\) | −542.554 | + | 8055.44i | −0.0348070 | + | 0.516788i | ||||
\(625\) | −13638.0 | −0.872829 | ||||||||
\(626\) | 1439.88 | − | 831.315i | 0.0919316 | − | 0.0530767i | ||||
\(627\) | 1248.17 | + | 2161.90i | 0.0795010 | + | 0.137700i | ||||
\(628\) | 8607.33 | − | 14908.3i | 0.546927 | − | 0.947305i | ||||
\(629\) | − | 9354.14i | − | 0.592963i | ||||||
\(630\) | −2928.55 | − | 1690.80i | −0.185200 | − | 0.106925i | ||||
\(631\) | 6979.35 | + | 4029.53i | 0.440322 | + | 0.254220i | 0.703734 | − | 0.710463i | \(-0.251515\pi\) |
−0.263412 | + | 0.964683i | \(0.584848\pi\) | |||||||
\(632\) | − | 4223.06i | − | 0.265798i | ||||||
\(633\) | 6397.44 | − | 11080.7i | 0.401699 | − | 0.695763i | ||||
\(634\) | −3078.64 | − | 5332.36i | −0.192852 | − | 0.334030i | ||||
\(635\) | 144.959 | − | 83.6919i | 0.00905906 | − | 0.00523025i | ||||
\(636\) | 5253.29 | 0.327526 | ||||||||
\(637\) | −19372.8 | − | 12995.1i | −1.20499 | − | 0.808293i | ||||
\(638\) | −1252.33 | −0.0777117 | ||||||||
\(639\) | 4976.46 | − | 2873.16i | 0.308084 | − | 0.177872i | ||||
\(640\) | −6208.31 | − | 10753.1i | −0.383446 | − | 0.664147i | ||||
\(641\) | 2919.34 | − | 5056.44i | 0.179886 | − | 0.311571i | −0.761955 | − | 0.647629i | \(-0.775760\pi\) |
0.941841 | + | 0.336058i | \(0.109094\pi\) | |||||||
\(642\) | − | 2775.29i | − | 0.170610i | ||||||
\(643\) | −5961.21 | − | 3441.70i | −0.365610 | − | 0.211085i | 0.305929 | − | 0.952054i | \(-0.401033\pi\) |
−0.671539 | + | 0.740969i | \(0.734366\pi\) | |||||||
\(644\) | −36546.0 | − | 21099.9i | −2.23620 | − | 1.29107i | ||||
\(645\) | 2877.19i | 0.175642i | ||||||||
\(646\) | −892.805 | + | 1546.38i | −0.0543761 | + | 0.0941821i | ||||
\(647\) | −8582.42 | − | 14865.2i | −0.521499 | − | 0.903262i | −0.999687 | − | 0.0250052i | \(-0.992040\pi\) |
0.478189 | − | 0.878257i | \(-0.341294\pi\) | |||||||
\(648\) | 11.7129 | − | 6.76242i | 0.000710068 | − | 0.000409958i | ||||
\(649\) | −7154.08 | −0.432700 | ||||||||
\(650\) | 247.762 | − | 369.361i | 0.0149508 | − | 0.0222885i | ||||
\(651\) | 15700.5 | 0.945242 | ||||||||
\(652\) | 4470.78 | − | 2581.20i | 0.268542 | − | 0.155043i | ||||
\(653\) | −8188.61 | − | 14183.1i | −0.490727 | − | 0.849965i | 0.509216 | − | 0.860639i | \(-0.329936\pi\) |
−0.999943 | + | 0.0106743i | \(0.996602\pi\) | |||||||
\(654\) | −1190.63 | + | 2062.24i | −0.0711888 | + | 0.123303i | ||||
\(655\) | − | 14295.8i | − | 0.852796i | ||||||
\(656\) | −2944.56 | − | 1700.04i | −0.175253 | − | 0.101182i | ||||
\(657\) | 11317.4 | + | 6534.12i | 0.672048 | + | 0.388007i | ||||
\(658\) | − | 1192.08i | − | 0.0706261i | ||||||
\(659\) | 10249.1 | − | 17752.0i | 0.605839 | − | 1.04934i | −0.386079 | − | 0.922466i | \(-0.626171\pi\) |
0.991918 | − | 0.126878i | \(-0.0404958\pi\) | |||||||
\(660\) | 1406.18 | + | 2435.57i | 0.0829323 | + | 0.143643i | ||||
\(661\) | −12701.5 | + | 7333.19i | −0.747397 | + | 0.431510i | −0.824753 | − | 0.565494i | \(-0.808686\pi\) |
0.0773555 | + | 0.997004i | \(0.475352\pi\) | |||||||
\(662\) | −3684.06 | −0.216292 | ||||||||
\(663\) | 5144.58 | − | 2525.52i | 0.301356 | − | 0.147938i | ||||
\(664\) | 11289.1 | 0.659794 | ||||||||
\(665\) | 18652.9 | − | 10769.2i | 1.08771 | − | 0.627990i | ||||
\(666\) | −1362.92 | − | 2360.65i | −0.0792977 | − | 0.137348i | ||||
\(667\) | 16483.2 | − | 28549.8i | 0.956871 | − | 1.65735i | ||||
\(668\) | 1237.96i | 0.0717037i | ||||||||
\(669\) | 5099.88 | + | 2944.42i | 0.294728 | + | 0.170161i | ||||
\(670\) | −2864.98 | − | 1654.10i | −0.165200 | − | 0.0953781i | ||||
\(671\) | 4180.62i | 0.240523i | ||||||||
\(672\) | −5518.43 | + | 9558.20i | −0.316783 | + | 0.548684i | ||||
\(673\) | −12614.6 | − | 21849.1i | −0.722520 | − | 1.25144i | −0.959987 | − | 0.280045i | \(-0.909651\pi\) |
0.237467 | − | 0.971396i | \(-0.423683\pi\) | |||||||
\(674\) | 4749.37 | − | 2742.05i | 0.271423 | − | 0.156706i | ||||
\(675\) | 2002.83 | 0.114206 | ||||||||
\(676\) | 6298.88 | + | 15363.1i | 0.358380 | + | 0.874098i | ||||
\(677\) | 25265.0 | 1.43429 | 0.717143 | − | 0.696926i | \(-0.245449\pi\) | ||||
0.717143 | + | 0.696926i | \(0.245449\pi\) | |||||||
\(678\) | 688.499 | − | 397.505i | 0.0389995 | − | 0.0225164i | ||||
\(679\) | 25457.6 | + | 44093.9i | 1.43884 | + | 2.49215i | ||||
\(680\) | −2070.51 | + | 3586.23i | −0.116765 | + | 0.202244i | ||||
\(681\) | − | 11425.4i | − | 0.642913i | ||||||
\(682\) | −1067.15 | − | 616.121i | −0.0599170 | − | 0.0345931i | ||||
\(683\) | 13195.9 | + | 7618.66i | 0.739279 | + | 0.426823i | 0.821807 | − | 0.569766i | \(-0.192966\pi\) |
−0.0825281 | + | 0.996589i | \(0.526299\pi\) | |||||||
\(684\) | − | 8891.26i | − | 0.497026i | ||||||
\(685\) | −3683.17 | + | 6379.43i | −0.205440 | + | 0.355833i | ||||
\(686\) | −1491.40 | − | 2583.18i | −0.0830057 | − | 0.143770i | ||||
\(687\) | −1463.68 | + | 845.056i | −0.0812851 | + | 0.0469300i | ||||
\(688\) | −4557.11 | −0.252526 | ||||||||
\(689\) | 9097.50 | − | 4466.04i | 0.503029 | − | 0.246941i | ||||
\(690\) | 4332.56 | 0.239040 | ||||||||
\(691\) | 2853.52 | − | 1647.48i | 0.157096 | − | 0.0906992i | −0.419391 | − | 0.907806i | \(-0.637756\pi\) |
0.576487 | + | 0.817106i | \(0.304423\pi\) | |||||||
\(692\) | 7941.56 | + | 13755.2i | 0.436261 | + | 0.755626i | ||||
\(693\) | −2657.61 | + | 4603.12i | −0.145677 | + | 0.252320i | ||||
\(694\) | 4452.58i | 0.243541i | ||||||||
\(695\) | 20075.0 | + | 11590.3i | 1.09567 | + | 0.632583i | ||||
\(696\) | −4931.18 | − | 2847.02i | −0.268557 | − | 0.155052i | ||||
\(697\) | 2413.53i | 0.131161i | ||||||||
\(698\) | −1621.28 | + | 2808.14i | −0.0879174 | + | 0.152277i | ||||
\(699\) | −72.8593 | − | 126.196i | −0.00394248 | − | 0.00682857i | ||||
\(700\) | −2707.67 | + | 1563.27i | −0.146200 | + | 0.0844087i | ||||
\(701\) | −747.881 | −0.0402954 | −0.0201477 | − | 0.999797i | \(-0.506414\pi\) | ||||
−0.0201477 | + | 0.999797i | \(0.506414\pi\) | |||||||
\(702\) | 2437.61 | − | 3633.95i | 0.131056 | − | 0.195377i | ||||
\(703\) | 17361.8 | 0.931457 | ||||||||
\(704\) | −3333.22 | + | 1924.44i | −0.178445 | + | 0.103025i | ||||
\(705\) | −1045.66 | − | 1811.13i | −0.0558605 | − | 0.0967532i | ||||
\(706\) | −4094.50 | + | 7091.88i | −0.218270 | + | 0.378055i | ||||
\(707\) | 1449.46i | 0.0771042i | ||||||||
\(708\) | −13684.6 | − | 7900.80i | −0.726410 | − | 0.419393i | ||||
\(709\) | −5166.07 | − | 2982.63i | −0.273647 | − | 0.157990i | 0.356897 | − | 0.934144i | \(-0.383835\pi\) |
−0.630544 | + | 0.776154i | \(0.717168\pi\) | |||||||
\(710\) | − | 2413.07i | − | 0.127551i | ||||||
\(711\) | 3401.01 | − | 5890.73i | 0.179392 | − | 0.310717i | ||||
\(712\) | −3427.20 | − | 5936.09i | −0.180393 | − | 0.312450i | ||||
\(713\) | 28091.9 | − | 16218.9i | 1.47553 | − | 0.851896i | ||||
\(714\) | 2357.72 | 0.123579 | ||||||||
\(715\) | 4505.75 | + | 3022.40i | 0.235672 | + | 0.158086i | ||||
\(716\) | 1123.00 | 0.0586154 | ||||||||
\(717\) | 5926.25 | − | 3421.52i | 0.308675 | − | 0.178214i | ||||
\(718\) | 4022.13 | + | 6966.54i | 0.209059 | + | 0.362102i | ||||
\(719\) | −6847.41 | + | 11860.1i | −0.355167 | + | 0.615167i | −0.987147 | − | 0.159818i | \(-0.948909\pi\) |
0.631979 | + | 0.774985i | \(0.282243\pi\) | |||||||
\(720\) | − | 9396.29i | − | 0.486360i | ||||||
\(721\) | −34853.1 | − | 20122.4i | −1.80027 | − | 1.03939i | ||||
\(722\) | 1080.27 | + | 623.696i | 0.0556837 | + | 0.0321490i | ||||
\(723\) | 16350.5i | 0.841054i | ||||||||
\(724\) | 9291.19 | − | 16092.8i | 0.476940 | − | 0.826084i | ||||
\(725\) | −1221.23 | − | 2115.23i | −0.0625590 | − | 0.108355i | ||||
\(726\) | −224.038 | + | 129.348i | −0.0114529 | + | 0.00661235i | ||||
\(727\) | 11312.0 | 0.577081 | 0.288541 | − | 0.957468i | \(-0.406830\pi\) | ||||
0.288541 | + | 0.957468i | \(0.406830\pi\) | |||||||
\(728\) | −944.940 | + | 14029.8i | −0.0481069 | + | 0.714255i | ||||
\(729\) | 12206.1 | 0.620132 | ||||||||
\(730\) | 4752.57 | − | 2743.90i | 0.240960 | − | 0.139118i | ||||
\(731\) | 1617.41 | + | 2801.44i | 0.0818362 | + | 0.141744i | ||||
\(732\) | −4616.98 | + | 7996.85i | −0.233126 | + | 0.403787i | ||||
\(733\) | 19038.0i | 0.959326i | 0.877453 | + | 0.479663i | \(0.159241\pi\) | ||||
−0.877453 | + | 0.479663i | \(0.840759\pi\) | |||||||
\(734\) | 4974.51 | + | 2872.04i | 0.250153 | + | 0.144426i | ||||
\(735\) | −14580.5 | − | 8418.07i | −0.731715 | − | 0.422456i | ||||
\(736\) | 22802.4i | 1.14200i | ||||||||
\(737\) | −2599.93 | + | 4503.20i | −0.129945 | + | 0.225071i | ||||
\(738\) | 351.658 | + | 609.089i | 0.0175403 | + | 0.0303806i | ||||
\(739\) | 5694.85 | − | 3287.92i | 0.283476 | − | 0.163665i | −0.351520 | − | 0.936180i | \(-0.614335\pi\) |
0.634996 | + | 0.772516i | \(0.281002\pi\) | |||||||
\(740\) | 19559.7 | 0.971658 | ||||||||
\(741\) | 4687.51 | + | 9548.65i | 0.232389 | + | 0.473385i | ||||
\(742\) | 4169.31 | 0.206280 | ||||||||
\(743\) | −11618.4 | + | 6707.90i | −0.573672 | + | 0.331210i | −0.758615 | − | 0.651540i | \(-0.774123\pi\) |
0.184942 | + | 0.982749i | \(0.440790\pi\) | |||||||
\(744\) | −2801.36 | − | 4852.10i | −0.138041 | − | 0.239095i | ||||
\(745\) | −8900.84 | + | 15416.7i | −0.437720 | + | 0.758154i | ||||
\(746\) | 9196.49i | 0.451350i | ||||||||
\(747\) | 15747.2 | + | 9091.63i | 0.771297 | + | 0.445308i | ||||
\(748\) | 2738.31 | + | 1580.96i | 0.133854 | + | 0.0772805i | ||||
\(749\) | 37637.4i | 1.83610i | ||||||||
\(750\) | 1566.62 | − | 2713.46i | 0.0762730 | − | 0.132109i | ||||
\(751\) | −10868.7 | − | 18825.2i | −0.528104 | − | 0.914703i | −0.999463 | − | 0.0327615i | \(-0.989570\pi\) |
0.471359 | − | 0.881941i | \(-0.343763\pi\) | |||||||
\(752\) | 2868.60 | − | 1656.19i | 0.139105 | − | 0.0803124i | ||||
\(753\) | −4539.55 | −0.219695 | ||||||||
\(754\) | −5324.23 | − | 358.600i | −0.257158 | − | 0.0173202i | ||||
\(755\) | 31435.2 | 1.51529 | ||||||||
\(756\) | −26639.3 | + | 15380.2i | −1.28157 | + | 0.739912i | ||||
\(757\) | −11241.0 | − | 19470.0i | −0.539712 | − | 0.934808i | −0.998919 | − | 0.0464789i | \(-0.985200\pi\) |
0.459208 | − | 0.888329i | \(-0.348133\pi\) | |||||||
\(758\) | 3695.13 | − | 6400.15i | 0.177062 | − | 0.306681i | ||||
\(759\) | − | 6809.97i | − | 0.325674i | ||||||
\(760\) | −6656.26 | − | 3842.99i | −0.317695 | − | 0.183421i | ||||
\(761\) | 7691.00 | + | 4440.40i | 0.366358 | + | 0.211517i | 0.671866 | − | 0.740673i | \(-0.265493\pi\) |
−0.305508 | + | 0.952189i | \(0.598826\pi\) | |||||||
\(762\) | 34.0080i | 0.00161677i | ||||||||
\(763\) | 16146.9 | − | 27967.3i | 0.766131 | − | 1.32698i | ||||
\(764\) | −17067.9 | − | 29562.5i | −0.808241 | − | 1.39991i | ||||
\(765\) | −5776.29 | + | 3334.94i | −0.272996 | + | 0.157615i | ||||
\(766\) | −8121.45 | −0.383081 | ||||||||
\(767\) | −30415.4 | − | 2048.55i | −1.43186 | − | 0.0964393i | ||||
\(768\) | −6475.98 | −0.304273 | ||||||||
\(769\) | 8104.38 | − | 4679.06i | 0.380041 | − | 0.219417i | −0.297795 | − | 0.954630i | \(-0.596251\pi\) |
0.677836 | + | 0.735213i | \(0.262918\pi\) | |||||||
\(770\) | 1116.02 | + | 1933.00i | 0.0522319 | + | 0.0904683i | ||||
\(771\) | −11307.8 | + | 19585.7i | −0.528199 | + | 0.914868i | ||||
\(772\) | 9103.66i | 0.424414i | ||||||||
\(773\) | −17249.5 | − | 9959.00i | −0.802615 | − | 0.463390i | 0.0417698 | − | 0.999127i | \(-0.486700\pi\) |
−0.844385 | + | 0.535737i | \(0.820034\pi\) | |||||||
\(774\) | 816.357 | + | 471.324i | 0.0379113 | + | 0.0218881i | ||||
\(775\) | − | 2403.29i | − | 0.111392i | ||||||
\(776\) | 9084.51 | − | 15734.8i | 0.420251 | − | 0.727897i | ||||
\(777\) | −11462.3 | − | 19853.3i | −0.529224 | − | 0.916643i | ||||
\(778\) | −3918.57 | + | 2262.39i | −0.180575 | + | 0.104255i | ||||
\(779\) | −4479.65 | −0.206034 | ||||||||
\(780\) | 5280.90 | + | 10757.4i | 0.242419 | + | 0.493816i | ||||
\(781\) | −3792.89 | −0.173778 | ||||||||
\(782\) | 4218.50 | − | 2435.55i | 0.192907 | − | 0.111375i | ||||
\(783\) | −12015.0 | − | 20810.6i | −0.548381 | − | 0.949824i | ||||
\(784\) | 13333.2 | − | 23093.7i | 0.607378 | − | 1.05201i | ||||
\(785\) | − | 23968.8i | − | 1.08979i | ||||||
\(786\) | 2515.39 | + | 1452.26i | 0.114149 | + | 0.0659040i | ||||
\(787\) | 2175.43 | + | 1255.99i | 0.0985334 | + | 0.0568883i | 0.548457 | − | 0.836179i | \(-0.315215\pi\) |
−0.449924 | + | 0.893067i | \(0.648549\pi\) | |||||||
\(788\) | − | 2450.66i | − | 0.110788i | ||||||
\(789\) | 10478.3 | − | 18149.0i | 0.472799 | − | 0.818913i | ||||
\(790\) | −1428.20 | − | 2473.71i | −0.0643203 | − | 0.111406i | ||||
\(791\) | −9337.17 | + | 5390.82i | −0.419711 | + | 0.242320i | ||||
\(792\) | 1896.73 | 0.0850977 | ||||||||
\(793\) | −1197.11 | + | 17773.8i | −0.0536074 | + | 0.795923i | ||||
\(794\) | −1879.09 | −0.0839880 | ||||||||
\(795\) | 6334.45 | − | 3657.19i | 0.282591 | − | 0.163154i | ||||
\(796\) | 16440.1 | + | 28475.1i | 0.732039 | + | 1.26793i | ||||
\(797\) | 6322.89 | − | 10951.6i | 0.281014 | − | 0.486731i | −0.690621 | − | 0.723217i | \(-0.742663\pi\) |
0.971635 | + | 0.236486i | \(0.0759958\pi\) | |||||||
\(798\) | 4376.06i | 0.194124i | ||||||||
\(799\) | −2036.25 | − | 1175.63i | −0.0901596 | − | 0.0520537i | ||||
\(800\) | 1463.07 | + | 844.707i | 0.0646594 | + | 0.0373311i | ||||
\(801\) | − | 11040.3i | − | 0.487004i | ||||||
\(802\) | −4607.42 | + | 7980.29i | −0.202860 | + | 0.351364i | ||||
\(803\) | −4312.89 | − | 7470.14i | −0.189537 | − | 0.328288i | ||||
\(804\) | −9946.47 | + | 5742.59i | −0.436300 | + | 0.251898i | ||||
\(805\) | −58756.6 | −2.57254 | ||||||||
\(806\) | −4360.55 | − | 2925.00i | −0.190563 | − | 0.127827i | ||||
\(807\) | 18859.3 | 0.822649 | ||||||||
\(808\) | 447.942 | − | 258.619i | 0.0195032 | − | 0.0112602i | ||||
\(809\) | 7067.04 | + | 12240.5i | 0.307125 | + | 0.531956i | 0.977732 | − | 0.209857i | \(-0.0672997\pi\) |
−0.670607 | + | 0.741813i | \(0.733966\pi\) | |||||||
\(810\) | 4.57397 | − | 7.92235i | 0.000198411 | − | 0.000343658i | ||||
\(811\) | 250.820i | 0.0108600i | 0.999985 | + | 0.00543002i | \(0.00172844\pi\) | ||||
−0.999985 | + | 0.00543002i | \(0.998272\pi\) | |||||||
\(812\) | 32486.8 | + | 18756.3i | 1.40402 | + | 0.810610i | ||||
\(813\) | −20111.7 | − | 11611.5i | −0.867585 | − | 0.500901i | ||||
\(814\) | 1799.21i | 0.0774722i | ||||||||
\(815\) | 3593.93 | − | 6224.87i | 0.154466 | − | 0.267543i | ||||
\(816\) | 3275.64 | + | 5673.58i | 0.140528 | + | 0.243401i | ||||
\(817\) | −5199.65 | + | 3002.02i | −0.222659 | + | 0.128552i | ||||
\(818\) | −5924.33 | −0.253227 | ||||||||
\(819\) | −12616.9 | + | 18809.0i | −0.538301 | + | 0.802492i | ||||
\(820\) | −5046.73 | −0.214926 | ||||||||
\(821\) | 11469.5 | − | 6621.90i | 0.487560 | − | 0.281493i | −0.236002 | − | 0.971753i | \(-0.575837\pi\) |
0.723562 | + | 0.690260i | \(0.242504\pi\) | |||||||
\(822\) | −748.324 | − | 1296.14i | −0.0317528 | − | 0.0549975i | ||||
\(823\) | 12138.6 | − | 21024.7i | 0.514127 | − | 0.890494i | −0.485739 | − | 0.874104i | \(-0.661449\pi\) |
0.999866 | − | 0.0163900i | \(-0.00521734\pi\) | |||||||
\(824\) | 14361.3i | 0.607161i | ||||||||
\(825\) | −436.949 | − | 252.272i | −0.0184395 | − | 0.0106461i | ||||
\(826\) | −10860.9 | − | 6270.52i | −0.457503 | − | 0.264140i | ||||
\(827\) | 34821.6i | 1.46417i | 0.681215 | + | 0.732083i | \(0.261452\pi\) | ||||
−0.681215 | + | 0.732083i | \(0.738548\pi\) | |||||||
\(828\) | −12127.6 | + | 21005.6i | −0.509014 | + | 0.881637i | ||||
\(829\) | 3350.63 | + | 5803.46i | 0.140377 | + | 0.243139i | 0.927638 | − | 0.373479i | \(-0.121835\pi\) |
−0.787262 | + | 0.616619i | \(0.788502\pi\) | |||||||
\(830\) | 6612.76 | − | 3817.88i | 0.276545 | − | 0.159663i | ||||
\(831\) | 17919.5 | 0.748039 | ||||||||
\(832\) | −14722.2 | + | 7227.23i | −0.613461 | + | 0.301153i | ||||
\(833\) | −18928.9 | −0.787332 | ||||||||
\(834\) | −4078.72 | + | 2354.85i | −0.169346 | + | 0.0977719i | ||||
\(835\) | 861.834 | + | 1492.74i | 0.0357185 | + | 0.0618663i | ||||
\(836\) | −2934.37 | + | 5082.47i | −0.121396 | + | 0.210264i | ||||
\(837\) | − | 23644.7i | − | 0.976440i | ||||||
\(838\) | 120.386 | + | 69.5051i | 0.00496263 | + | 0.00286517i | ||||
\(839\) | −32308.5 | − | 18653.3i | −1.32946 | − | 0.767562i | −0.344240 | − | 0.938882i | \(-0.611863\pi\) |
−0.985215 | + | 0.171320i | \(0.945197\pi\) | |||||||
\(840\) | 10148.6i | 0.416856i | ||||||||
\(841\) | −2457.88 | + | 4257.18i | −0.100778 | + | 0.174553i | ||||
\(842\) | 2245.51 | + | 3889.34i | 0.0919066 | + | 0.159187i | ||||
\(843\) | 231.237 | − | 133.505i | 0.00944748 | − | 0.00545451i | ||||
\(844\) | 30079.9 | 1.22677 | ||||||||
\(845\) | 18290.6 | + | 14139.9i | 0.744635 | + | 0.575652i | ||||
\(846\) | −685.172 | −0.0278448 | ||||||||
\(847\) | 3038.32 | − | 1754.17i | 0.123256 | − | 0.0711618i | ||||
\(848\) | 5792.53 | + | 10033.0i | 0.234571 | + | 0.406289i | ||||
\(849\) | −7154.41 | + | 12391.8i | −0.289209 | + | 0.500925i | ||||
\(850\) | − | 360.896i | − | 0.0145631i | ||||||
\(851\) | −41017.4 | − | 23681.4i | −1.65224 | − | 0.953922i | ||||
\(852\) | −7255.17 | − | 4188.78i | −0.291735 | − | 0.168433i | ||||
\(853\) | 36525.1i | 1.46611i | 0.680167 | + | 0.733057i | \(0.261907\pi\) | ||||
−0.680167 | + | 0.733057i | \(0.738093\pi\) | |||||||
\(854\) | −3664.30 | + | 6346.75i | −0.146826 | + | 0.254311i | ||||
\(855\) | −6189.86 | − | 10721.1i | −0.247589 | − | 0.428837i | ||||
\(856\) | 11631.5 | − | 6715.43i | 0.464434 | − | 0.268141i | ||||
\(857\) | 5408.05 | 0.215561 | 0.107780 | − | 0.994175i | \(-0.465626\pi\) | ||||
0.107780 | + | 0.994175i | \(0.465626\pi\) | |||||||
\(858\) | −989.529 | + | 485.768i | −0.0393729 | + | 0.0193285i | ||||
\(859\) | 38851.4 | 1.54318 | 0.771591 | − | 0.636119i | \(-0.219461\pi\) | ||||
0.771591 | + | 0.636119i | \(0.219461\pi\) | |||||||
\(860\) | −5857.87 | + | 3382.04i | −0.232269 | + | 0.134101i | ||||
\(861\) | 2957.46 | + | 5122.48i | 0.117062 | + | 0.202757i | ||||
\(862\) | 226.221 | − | 391.827i | 0.00893866 | − | 0.0154822i | ||||
\(863\) | − | 35630.7i | − | 1.40543i | −0.711474 | − | 0.702713i | \(-0.751972\pi\) | ||
0.711474 | − | 0.702713i | \(-0.248028\pi\) | |||||||
\(864\) | 14394.4 | + | 8310.64i | 0.566793 | + | 0.327238i | ||||
\(865\) | 19152.0 | + | 11057.4i | 0.752816 | + | 0.434639i | ||||
\(866\) | − | 7503.65i | − | 0.294439i | ||||||
\(867\) | −5571.89 | + | 9650.79i | −0.218260 | + | 0.378037i | ||||
\(868\) | 18455.5 | + | 31965.8i | 0.721681 | + | 1.24999i | ||||
\(869\) | −3888.21 | + | 2244.86i | −0.151782 | + | 0.0876313i | ||||
\(870\) | −3851.34 | −0.150083 | ||||||||
\(871\) | −12343.0 | + | 18400.8i | −0.480168 | + | 0.715828i | ||||
\(872\) | −11524.0 | −0.447537 | ||||||||
\(873\) | 25343.9 | − | 14632.3i | 0.982544 | − | 0.567272i | ||||
\(874\) | 4520.53 | + | 7829.80i | 0.174954 | + | 0.303028i | ||||
\(875\) | −21245.9 | + | 36798.9i | −0.820848 | + | 1.42175i | ||||
\(876\) | − | 19052.2i | − | 0.734834i | ||||||
\(877\) | −20414.1 | − | 11786.1i | −0.786015 | − | 0.453806i | 0.0525425 | − | 0.998619i | \(-0.483268\pi\) |
−0.838558 | + | 0.544812i | \(0.816601\pi\) | |||||||
\(878\) | −2724.46 | − | 1572.97i | −0.104722 | − | 0.0604614i | ||||
\(879\) | − | 2408.39i | − | 0.0924154i | ||||||
\(880\) | −3101.04 | + | 5371.15i | −0.118791 | + | 0.205752i | ||||
\(881\) | 753.555 | + | 1305.19i | 0.0288171 | + | 0.0499127i | 0.880074 | − | 0.474836i | \(-0.157493\pi\) |
−0.851257 | + | 0.524749i | \(0.824159\pi\) | |||||||
\(882\) | −4776.98 | + | 2757.99i | −0.182369 | + | 0.105291i | ||||
\(883\) | −12632.0 | −0.481428 | −0.240714 | − | 0.970596i | \(-0.577382\pi\) | ||||
−0.240714 | + | 0.970596i | \(0.577382\pi\) | |||||||
\(884\) | 11189.2 | + | 7505.54i | 0.425715 | + | 0.285564i | ||||
\(885\) | −22001.3 | −0.835666 | ||||||||
\(886\) | 385.875 | − | 222.785i | 0.0146317 | − | 0.00844763i | ||||
\(887\) | −1660.05 | − | 2875.29i | −0.0628399 | − | 0.108842i | 0.832894 | − | 0.553433i | \(-0.186682\pi\) |
−0.895734 | + | 0.444591i | \(0.853349\pi\) | |||||||
\(888\) | −4090.30 | + | 7084.61i | −0.154574 | + | 0.267730i | ||||
\(889\) | − | 461.204i | − | 0.0173997i | ||||||
\(890\) | −4015.06 | − | 2318.10i | −0.151219 | − | 0.0873065i | ||||
\(891\) | −12.4524 | − | 7.18942i | −0.000468207 | − | 0.000270319i | ||||
\(892\) | 13844.3i | 0.519664i | ||||||||
\(893\) | 2182.04 | − | 3779.41i | 0.0817685 | − | 0.141627i | ||||
\(894\) | −1808.42 | − | 3132.28i | −0.0676539 | − | 0.117180i | ||||
\(895\) | 1354.13 | − | 781.805i | 0.0505736 | − | 0.0291987i | ||||
\(896\) | −34212.4 | −1.27562 | ||||||||
\(897\) | 1950.02 | − | 28952.4i | 0.0725855 | − | 1.07770i | ||||
\(898\) | −1083.71 | −0.0402715 | ||||||||
\(899\) | −24971.7 | + | 14417.4i | −0.926421 | + | 0.534869i | ||||
\(900\) | 898.524 | + | 1556.29i | 0.0332786 | + | 0.0576403i | ||||
\(901\) | 4111.79 | − | 7121.83i | 0.152035 | − | 0.263332i | ||||
\(902\) | − | 464.228i | − | 0.0171365i | ||||||
\(903\) | 6865.61 | + | 3963.86i | 0.253016 | + | 0.146079i | ||||
\(904\) | 3331.96 | + | 1923.71i | 0.122588 | + | 0.0707760i | ||||
\(905\) | − | 25873.1i | − | 0.950332i | ||||||
\(906\) | −3193.41 | + | 5531.15i | −0.117102 | + | 0.202826i | ||||
\(907\) | 10285.1 | + | 17814.3i | 0.376527 | + | 0.652164i | 0.990554 | − | 0.137121i | \(-0.0437849\pi\) |
−0.614027 | + | 0.789285i | \(0.710452\pi\) | |||||||
\(908\) | 23261.8 | − | 13430.2i | 0.850188 | − | 0.490856i | ||||
\(909\) | 833.110 | 0.0303988 | ||||||||
\(910\) | 4191.22 | + | 8537.68i | 0.152679 | + | 0.311013i | ||||
\(911\) | 51427.6 | 1.87033 | 0.935165 | − | 0.354211i | \(-0.115251\pi\) | ||||
0.935165 | + | 0.354211i | \(0.115251\pi\) | |||||||
\(912\) | −10530.5 | + | 6079.79i | −0.382346 | + | 0.220748i | ||||
\(913\) | −6000.98 | − | 10394.0i | −0.217529 | − | 0.376770i | ||||
\(914\) | −3830.95 | + | 6635.40i | −0.138640 | + | 0.240131i | ||||
\(915\) | 12856.9i | 0.464519i | ||||||||
\(916\) | −3441.01 | − | 1986.67i | −0.124120 | − | 0.0716609i | ||||
\(917\) | −34112.8 | − | 19695.1i | −1.22847 | − | 0.709256i | ||||
\(918\) | − | 3550.67i | − | 0.127658i | ||||||
\(919\) | 4715.43 | − | 8167.37i | 0.169258 | − | 0.293163i | −0.768901 | − | 0.639367i | \(-0.779196\pi\) |
0.938159 | + | 0.346204i | \(0.112530\pi\) | |||||||
\(920\) | 10483.6 | + | 18158.1i | 0.375690 | + | 0.650713i | ||||
\(921\) | 17400.5 | − | 10046.2i | 0.622549 | − | 0.359429i | ||||
\(922\) | 5496.55 | 0.196333 | ||||||||
\(923\) | −16125.4 | − | 1086.08i | −0.575052 | − | 0.0387312i | ||||
\(924\) | 7749.07 | 0.275894 | ||||||||
\(925\) | −3038.94 | + | 1754.53i | −0.108021 | + | 0.0623662i | ||||
\(926\) | −2817.18 | − | 4879.50i | −0.0999766 | − | 0.173165i | ||||
\(927\) | −11565.8 | + | 20032.6i | −0.409785 | + | 0.709769i | ||||
\(928\) | − | 20269.7i | − | 0.717011i | ||||||
\(929\) | 19629.5 | + | 11333.1i | 0.693242 | + | 0.400244i | 0.804826 | − | 0.593511i | \(-0.202259\pi\) |
−0.111583 | + | 0.993755i | \(0.535592\pi\) | |||||||
\(930\) | −3281.87 | − | 1894.79i | −0.115717 | − | 0.0668091i | ||||
\(931\) | − | 35133.2i | − | 1.23678i | ||||||
\(932\) | 171.287 | − | 296.678i | 0.00602007 | − | 0.0104271i | ||||
\(933\) | −7474.59 | − | 12946.4i | −0.262280 | − | 0.454282i | ||||
\(934\) | 3972.57 | − | 2293.57i | 0.139172 | − | 0.0803510i | ||||
\(935\) | 4402.50 | 0.153986 | ||||||||
\(936\) | 8063.90 | + | 543.124i | 0.281599 | + | 0.0189664i | ||||
\(937\) | 39917.7 | 1.39173 | 0.695867 | − | 0.718171i | \(-0.255020\pi\) | ||||
0.695867 | + | 0.718171i | \(0.255020\pi\) | |||||||
\(938\) | −7894.08 | + | 4557.65i | −0.274788 | + | 0.158649i | ||||
\(939\) | −4018.46 | − | 6960.18i | −0.139657 | − | 0.241892i | ||||
\(940\) | 2458.27 | − | 4257.84i | 0.0852976 | − | 0.147740i | ||||
\(941\) | 3426.69i | 0.118711i | 0.998237 | + | 0.0593554i | \(0.0189045\pi\) | ||||
−0.998237 | + | 0.0593554i | \(0.981095\pi\) | |||||||
\(942\) | 4217.40 | + | 2434.92i | 0.145871 | + | 0.0842185i | ||||
\(943\) | 10583.2 | + | 6110.20i | 0.365467 | + | 0.211003i | ||||
\(944\) | − | 34847.2i | − | 1.20146i | ||||||
\(945\) | −21414.6 | + | 37091.2i | −0.737160 | + | 1.27680i | ||||
\(946\) | −311.100 | − | 538.841i | −0.0106921 | − | 0.0185193i | ||||
\(947\) | −23636.7 | + | 13646.6i | −0.811075 | + | 0.468275i | −0.847329 | − | 0.531068i | \(-0.821791\pi\) |
0.0362538 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(948\) | −9916.67 | −0.339745 | ||||||||
\(949\) | −16197.1 | − | 32994.1i | −0.554035 | − | 1.12859i | ||||
\(950\) | 669.845 | 0.0228765 | ||||||||
\(951\) | −25775.9 | + | 14881.7i | −0.878907 | + | 0.507437i | ||||
\(952\) | 5705.03 | + | 9881.39i | 0.194224 | + | 0.336405i | ||||
\(953\) | −16703.7 | + | 28931.6i | −0.567770 | + | 0.983406i | 0.429016 | + | 0.903297i | \(0.358860\pi\) |
−0.996786 | + | 0.0801094i | \(0.974473\pi\) | |||||||
\(954\) | − | 2396.40i | − | 0.0813273i | ||||||
\(955\) | −41161.2 | − | 23764.4i | −1.39471 | − | 0.805235i | ||||
\(956\) | 13932.2 | + | 8043.77i | 0.471339 | + | 0.272128i | ||||
\(957\) | 6053.57i | 0.204477i | ||||||||
\(958\) | 3222.94 | − | 5582.29i | 0.108693 | − | 0.188263i | ||||
\(959\) | 10148.5 | + | 17577.7i | 0.341723 | + | 0.591881i | ||||
\(960\) | −10250.8 | + | 5918.31i | −0.344629 | + | 0.198971i | ||||
\(961\) | 1418.61 | 0.0476189 | ||||||||
\(962\) | −515.200 | + | 7649.30i | −0.0172669 | + | 0.256365i | ||||
\(963\) | 21632.9 | 0.723895 | ||||||||
\(964\) | −33289.1 | + | 19219.5i | −1.11221 | + | 0.642134i | ||||
\(965\) | 6337.72 | + | 10977.2i | 0.211418 | + | 0.366187i | ||||
\(966\) | 5968.91 | − | 10338.5i | 0.198806 | − | 0.344342i | ||||
\(967\) | − | 17254.6i | − | 0.573807i | −0.957959 | − | 0.286904i | \(-0.907374\pi\) | ||
0.957959 | − | 0.286904i | \(-0.0926259\pi\) | |||||||
\(968\) | −1084.22 | − | 625.974i | −0.0360001 | − | 0.0207847i | ||||
\(969\) | 7475.00 | + | 4315.70i | 0.247814 | + | 0.143075i | ||||
\(970\) | − | 12289.2i | − | 0.406785i | ||||||
\(971\) | −5488.49 | + | 9506.34i | −0.181394 | + | 0.314184i | −0.942356 | − | 0.334613i | \(-0.891394\pi\) |
0.760961 | + | 0.648797i | \(0.224728\pi\) | |||||||
\(972\) | 14306.3 | + | 24779.3i | 0.472094 | + | 0.817691i | ||||
\(973\) | 55314.0 | − | 31935.6i | 1.82249 | − | 1.05222i | ||||
\(974\) | −2711.70 | −0.0892080 | ||||||||
\(975\) | −1785.44 | − | 1197.65i | −0.0586459 | − | 0.0393389i | ||||
\(976\) | −20363.7 | −0.667853 | ||||||||
\(977\) | −21386.1 | + | 12347.3i | −0.700310 | + | 0.404324i | −0.807463 | − | 0.589918i | \(-0.799160\pi\) |
0.107153 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(978\) | 730.193 | + | 1264.73i | 0.0238742 | + | 0.0413514i | ||||
\(979\) | −3643.61 | + | 6310.91i | −0.118948 | + | 0.206024i | ||||
\(980\) | − | 39580.6i | − | 1.29016i | ||||||
\(981\) | −16074.8 | − | 9280.79i | −0.523169 | − | 0.302052i | ||||
\(982\) | 11793.8 | + | 6809.14i | 0.383253 | + | 0.221271i | ||||
\(983\) | − | 4763.40i | − | 0.154556i | −0.997010 | − | 0.0772782i | \(-0.975377\pi\) | ||
0.997010 | − | 0.0772782i | \(-0.0246230\pi\) | |||||||
\(984\) | 1055.37 | − | 1827.95i | 0.0341909 | − | 0.0592204i | ||||
\(985\) | −1706.09 | − | 2955.03i | −0.0551882 | − | 0.0955888i | ||||
\(986\) | −3749.94 | + | 2165.03i | −0.121118 | + | 0.0699276i | ||||
\(987\) | −5762.34 | −0.185833 | ||||||||
\(988\) | −13930.7 | + | 20767.7i | −0.448579 | + | 0.668735i | ||||
\(989\) | 16378.9 | 0.526611 | ||||||||
\(990\) | 1111.04 | − | 641.456i | 0.0356677 | − | 0.0205928i | ||||
\(991\) | 13846.1 | + | 23982.1i | 0.443830 | + | 0.768736i | 0.997970 | − | 0.0636877i | \(-0.0202862\pi\) |
−0.554140 | + | 0.832423i | \(0.686953\pi\) | |||||||
\(992\) | 9972.32 | − | 17272.6i | 0.319175 | − | 0.552827i | ||||
\(993\) | 17808.3i | 0.569112i | ||||||||
\(994\) | −5758.12 | − | 3324.45i | −0.183739 | − | 0.106082i | ||||
\(995\) | 39647.1 | + | 22890.3i | 1.26321 | + | 0.729317i | ||||
\(996\) | − | 26509.4i | − | 0.843355i | ||||||
\(997\) | 1668.22 | − | 2889.44i | 0.0529920 | − | 0.0917848i | −0.838313 | − | 0.545190i | \(-0.816458\pi\) |
0.891305 | + | 0.453405i | \(0.149791\pi\) | |||||||
\(998\) | 3911.79 | + | 6775.43i | 0.124074 | + | 0.214902i | ||||
\(999\) | −29898.6 | + | 17262.0i | −0.946896 | + | 0.546691i |
(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.j.a.23.18 | ✓ | 72 | |
13.2 | odd | 12 | 1859.4.a.m.1.18 | 36 | |||
13.4 | even | 6 | inner | 143.4.j.a.56.18 | yes | 72 | |
13.11 | odd | 12 | 1859.4.a.l.1.19 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.j.a.23.18 | ✓ | 72 | 1.1 | even | 1 | trivial | |
143.4.j.a.56.18 | yes | 72 | 13.4 | even | 6 | inner | |
1859.4.a.l.1.19 | 36 | 13.11 | odd | 12 | |||
1859.4.a.m.1.18 | 36 | 13.2 | odd | 12 |