Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 71.6 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.4.h.b.35.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.664105 | + | 2.74936i | −0.234797 | + | 0.972044i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.11793 | − | 3.65173i | −0.889741 | − | 0.456466i | ||||
\(5\) | 14.2911 | + | 8.25096i | 1.27823 | + | 0.737988i | 0.976523 | − | 0.215411i | \(-0.0691093\pi\) |
0.301710 | + | 0.953400i | \(0.402443\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.2620 | − | 11.1209i | 1.04005 | − | 0.600473i | 0.120203 | − | 0.992749i | \(-0.461645\pi\) |
0.919848 | + | 0.392276i | \(0.128312\pi\) | |||||||
\(8\) | 14.7670 | − | 17.1446i | 0.652613 | − | 0.757691i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −32.1756 | + | 33.8118i | −1.01748 | + | 1.06922i | ||||
\(11\) | 6.37655 | + | 11.0445i | 0.174782 | + | 0.302732i | 0.940086 | − | 0.340938i | \(-0.110745\pi\) |
−0.765304 | + | 0.643669i | \(0.777411\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.1766 | + | 19.3584i | −0.238449 | + | 0.413005i | −0.960269 | − | 0.279075i | \(-0.909972\pi\) |
0.721821 | + | 0.692080i | \(0.243306\pi\) | |||||||
\(14\) | 17.7834 | + | 60.3436i | 0.339486 | + | 1.15196i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 37.3298 | + | 51.9854i | 0.583278 | + | 0.812273i | ||||
\(17\) | 117.295i | 1.67343i | 0.547639 | + | 0.836715i | \(0.315527\pi\) | ||||
−0.547639 | + | 0.836715i | \(0.684473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 27.7307i | − | 0.334835i | −0.985886 | − | 0.167417i | \(-0.946457\pi\) | ||
0.985886 | − | 0.167417i | \(-0.0535427\pi\) | |||||||
\(20\) | −71.5926 | − | 110.917i | −0.800430 | − | 1.24009i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −34.6000 | + | 10.1967i | −0.335307 | + | 0.0988156i | ||||
\(23\) | 17.5836 | − | 30.4556i | 0.159410 | − | 0.276106i | −0.775246 | − | 0.631659i | \(-0.782374\pi\) |
0.934656 | + | 0.355553i | \(0.115708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 73.6567 | + | 127.577i | 0.589254 | + | 1.02062i | ||||
\(26\) | −45.8008 | − | 43.5845i | −0.345472 | − | 0.328755i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −177.716 | + | 8.81837i | −1.19947 | + | 0.0595184i | ||||
\(29\) | −1.01189 | + | 0.584217i | −0.00647945 | + | 0.00374091i | −0.503236 | − | 0.864149i | \(-0.667857\pi\) |
0.496757 | + | 0.867890i | \(0.334524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −119.361 | − | 68.9130i | −0.691543 | − | 0.399263i | 0.112647 | − | 0.993635i | \(-0.464067\pi\) |
−0.804190 | + | 0.594373i | \(0.797400\pi\) | |||||||
\(32\) | −167.717 | + | 68.1091i | −0.926517 | + | 0.376253i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −322.487 | − | 77.8965i | −1.62665 | − | 0.392916i | ||||
\(35\) | 367.033 | 1.77257 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 233.596 | 1.03792 | 0.518959 | − | 0.854799i | \(-0.326320\pi\) | ||||
0.518959 | + | 0.854799i | \(0.326320\pi\) | |||||||
\(38\) | 76.2416 | + | 18.4161i | 0.325474 | + | 0.0786180i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 352.495 | − | 123.173i | 1.39336 | − | 0.486885i | ||||
\(41\) | −13.2561 | − | 7.65340i | −0.0504940 | − | 0.0291527i | 0.474541 | − | 0.880234i | \(-0.342614\pi\) |
−0.525034 | + | 0.851081i | \(0.675948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 361.460 | − | 208.689i | 1.28191 | − | 0.740112i | 0.304714 | − | 0.952444i | \(-0.401439\pi\) |
0.977198 | + | 0.212332i | \(0.0681059\pi\) | |||||||
\(44\) | −5.05631 | − | 101.900i | −0.0173243 | − | 0.349135i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 72.0561 | + | 68.5693i | 0.230958 | + | 0.219782i | ||||
\(47\) | −116.494 | − | 201.773i | −0.361539 | − | 0.626204i | 0.626675 | − | 0.779281i | \(-0.284415\pi\) |
−0.988214 | + | 0.153076i | \(0.951082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 75.8499 | − | 131.376i | 0.221137 | − | 0.383020i | ||||
\(50\) | −399.671 | + | 117.784i | −1.13044 | + | 0.333143i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 150.246 | − | 96.9781i | 0.400680 | − | 0.258624i | ||||
\(53\) | − | 180.951i | − | 0.468972i | −0.972120 | − | 0.234486i | \(-0.924659\pi\) | ||
0.972120 | − | 0.234486i | \(-0.0753407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 210.451i | 0.515949i | ||||||||
\(56\) | 93.7774 | − | 494.461i | 0.223777 | − | 1.17991i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.934217 | − | 3.17004i | −0.00211498 | − | 0.00717666i | ||||
\(59\) | −313.716 | + | 543.373i | −0.692244 | + | 1.19900i | 0.278857 | + | 0.960333i | \(0.410045\pi\) |
−0.971101 | + | 0.238669i | \(0.923289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −382.110 | − | 661.834i | −0.802035 | − | 1.38917i | −0.918274 | − | 0.395945i | \(-0.870417\pi\) |
0.116239 | − | 0.993221i | \(-0.462916\pi\) | |||||||
\(62\) | 268.735 | − | 282.400i | 0.550473 | − | 0.578465i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −75.8742 | − | 506.347i | −0.148192 | − | 0.988959i | ||||
\(65\) | −319.452 | + | 184.435i | −0.609586 | + | 0.351945i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −113.463 | − | 65.5077i | −0.206891 | − | 0.119448i | 0.392975 | − | 0.919549i | \(-0.371446\pi\) |
−0.599866 | + | 0.800101i | \(0.704779\pi\) | |||||||
\(68\) | 428.330 | − | 834.900i | 0.763863 | − | 1.48892i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −243.749 | + | 1009.11i | −0.416194 | + | 1.72302i | ||||
\(71\) | 22.6910 | 0.0379285 | 0.0189643 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189643 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 387.864 | 0.621863 | 0.310932 | − | 0.950432i | \(-0.399359\pi\) | ||||
0.310932 | + | 0.950432i | \(0.399359\pi\) | |||||||
\(74\) | −155.133 | + | 642.240i | −0.243700 | + | 1.00890i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −101.265 | + | 197.385i | −0.152840 | + | 0.297916i | ||||
\(77\) | 245.650 | + | 141.826i | 0.363565 | + | 0.209904i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −486.411 | + | 280.830i | −0.692729 | + | 0.399947i | −0.804633 | − | 0.593772i | \(-0.797638\pi\) |
0.111905 | + | 0.993719i | \(0.464305\pi\) | |||||||
\(80\) | 104.553 | + | 1050.93i | 0.146118 | + | 1.46873i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 29.8454 | − | 31.3630i | 0.0401935 | − | 0.0422374i | ||||
\(83\) | −342.111 | − | 592.554i | −0.452429 | − | 0.783629i | 0.546108 | − | 0.837715i | \(-0.316109\pi\) |
−0.998536 | + | 0.0540856i | \(0.982776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −967.799 | + | 1676.28i | −1.23497 | + | 2.13903i | ||||
\(86\) | 333.713 | + | 1132.38i | 0.418433 | + | 1.41985i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 283.516 | + | 53.7704i | 0.343442 | + | 0.0651357i | ||||
\(89\) | − | 278.003i | − | 0.331103i | −0.986201 | − | 0.165552i | \(-0.947060\pi\) | ||
0.986201 | − | 0.165552i | \(-0.0529405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 497.177i | 0.572728i | ||||||||
\(92\) | −236.374 | + | 152.571i | −0.267866 | + | 0.172898i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 632.110 | − | 186.284i | 0.693587 | − | 0.204402i | ||||
\(95\) | 228.805 | − | 396.302i | 0.247104 | − | 0.427997i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −264.443 | − | 458.028i | −0.276805 | − | 0.479440i | 0.693784 | − | 0.720183i | \(-0.255942\pi\) |
−0.970589 | + | 0.240743i | \(0.922609\pi\) | |||||||
\(98\) | 310.827 | + | 295.786i | 0.320390 | + | 0.304887i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −58.4063 | − | 1177.06i | −0.0584063 | − | 1.17706i | ||||
\(101\) | 1241.84 | − | 716.977i | 1.22344 | − | 0.706355i | 0.257793 | − | 0.966200i | \(-0.417005\pi\) |
0.965650 | + | 0.259845i | \(0.0836714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −199.095 | − | 114.948i | −0.190460 | − | 0.109962i | 0.401738 | − | 0.915755i | \(-0.368406\pi\) |
−0.592198 | + | 0.805792i | \(0.701740\pi\) | |||||||
\(104\) | 166.848 | + | 477.484i | 0.157316 | + | 0.450203i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 497.498 | + | 120.170i | 0.455862 | + | 0.110113i | ||||
\(107\) | −1676.13 | −1.51437 | −0.757184 | − | 0.653201i | \(-0.773426\pi\) | ||||
−0.757184 | + | 0.653201i | \(0.773426\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −540.666 | −0.475104 | −0.237552 | − | 0.971375i | \(-0.576345\pi\) | ||||
−0.237552 | + | 0.971375i | \(0.576345\pi\) | |||||||
\(110\) | −578.604 | − | 139.762i | −0.501525 | − | 0.121143i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1297.17 | + | 586.202i | 1.09439 | + | 0.494562i | ||||
\(113\) | −1110.83 | − | 641.340i | −0.924764 | − | 0.533913i | −0.0396123 | − | 0.999215i | \(-0.512612\pi\) |
−0.885152 | + | 0.465302i | \(0.845946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 502.576 | − | 290.163i | 0.407526 | − | 0.235285i | ||||
\(116\) | 9.33599 | − | 0.463257i | 0.00747263 | − | 0.000370796i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1285.59 | − | 1223.38i | −1.00295 | − | 0.954414i | ||||
\(119\) | 1304.43 | + | 2259.34i | 1.00485 | + | 1.74045i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 584.179 | − | 1011.83i | 0.438902 | − | 0.760201i | ||||
\(122\) | 2073.38 | − | 611.029i | 1.53865 | − | 0.453442i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 597.950 | + | 926.391i | 0.433044 | + | 0.670906i | ||||
\(125\) | 368.214i | 0.263472i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2674.79i | 1.86889i | 0.356109 | + | 0.934444i | \(0.384103\pi\) | ||||
−0.356109 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(128\) | 1442.52 | + | 127.662i | 0.996107 | + | 0.0881552i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −294.929 | − | 1000.77i | −0.198977 | − | 0.675180i | ||||
\(131\) | 413.401 | − | 716.031i | 0.275717 | − | 0.477557i | −0.694598 | − | 0.719398i | \(-0.744418\pi\) |
0.970316 | + | 0.241841i | \(0.0777513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −308.391 | − | 534.149i | −0.201059 | − | 0.348245i | ||||
\(134\) | 255.455 | − | 268.446i | 0.164686 | − | 0.173061i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2010.98 | + | 1732.09i | 1.26794 | + | 1.09210i | ||||
\(137\) | −560.929 | + | 323.852i | −0.349806 | + | 0.201960i | −0.664600 | − | 0.747200i | \(-0.731398\pi\) |
0.314794 | + | 0.949160i | \(0.398065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2312.71 | − | 1335.24i | −1.41124 | − | 0.814777i | −0.415730 | − | 0.909488i | \(-0.636474\pi\) |
−0.995505 | + | 0.0947110i | \(0.969807\pi\) | |||||||
\(140\) | −2612.52 | − | 1340.30i | −1.57713 | − | 0.809117i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.0692 | + | 62.3857i | −0.00890550 | + | 0.0368682i | ||||
\(143\) | −285.073 | −0.166706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.2814 | −0.0110430 | ||||||||
\(146\) | −257.583 | + | 1066.38i | −0.146012 | + | 0.604479i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1662.72 | − | 853.030i | −0.923479 | − | 0.473774i | ||||
\(149\) | 90.2485 | + | 52.1050i | 0.0496204 | + | 0.0286484i | 0.524605 | − | 0.851346i | \(-0.324213\pi\) |
−0.474985 | + | 0.879994i | \(0.657546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2382.77 | − | 1375.69i | 1.28415 | − | 0.741407i | 0.306549 | − | 0.951855i | \(-0.400826\pi\) |
0.977605 | + | 0.210448i | \(0.0674924\pi\) | |||||||
\(152\) | −475.431 | − | 409.498i | −0.253701 | − | 0.218517i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −553.069 | + | 581.193i | −0.289400 | + | 0.304116i | ||||
\(155\) | −1137.20 | − | 1969.68i | −0.589302 | − | 1.02070i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 581.545 | − | 1007.27i | 0.295620 | − | 0.512029i | −0.679509 | − | 0.733667i | \(-0.737807\pi\) |
0.975129 | + | 0.221638i | \(0.0711404\pi\) | |||||||
\(158\) | −449.073 | − | 1523.82i | −0.226116 | − | 0.767269i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2958.83 | − | 410.477i | −1.46198 | − | 0.202819i | ||||
\(161\) | − | 782.182i | − | 0.382886i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2930.45i | − | 1.40816i | −0.710120 | − | 0.704081i | \(-0.751359\pi\) | ||
0.710120 | − | 0.704081i | \(-0.248641\pi\) | |||||||
\(164\) | 66.4077 | + | 102.884i | 0.0316193 | + | 0.0489871i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1856.34 | − | 547.067i | 0.867951 | − | 0.255787i | ||||
\(167\) | 435.960 | − | 755.105i | 0.202010 | − | 0.349891i | −0.747166 | − | 0.664637i | \(-0.768586\pi\) |
0.949176 | + | 0.314746i | \(0.101919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 848.667 | + | 1469.93i | 0.386284 | + | 0.669064i | ||||
\(170\) | −3965.96 | − | 3774.05i | −1.78927 | − | 1.70268i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3334.92 | + | 165.481i | −1.47840 | + | 0.0733592i | ||||
\(173\) | −2020.19 | + | 1166.36i | −0.887816 | + | 0.512581i | −0.873227 | − | 0.487313i | \(-0.837977\pi\) |
−0.0145882 | + | 0.999894i | \(0.504644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2837.55 | + | 1638.26i | 1.22571 | + | 0.707662i | ||||
\(176\) | −336.119 | + | 743.778i | −0.143954 | + | 0.318547i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 764.328 | + | 184.623i | 0.321847 | + | 0.0777420i | ||||
\(179\) | 638.773 | 0.266727 | 0.133364 | − | 0.991067i | \(-0.457422\pi\) | ||||
0.133364 | + | 0.991067i | \(0.457422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4031.01 | 1.65537 | 0.827686 | − | 0.561192i | \(-0.189657\pi\) | ||||
0.827686 | + | 0.561192i | \(0.189657\pi\) | |||||||
\(182\) | −1366.92 | − | 330.178i | −0.556717 | − | 0.134475i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −262.494 | − | 751.200i | −0.105170 | − | 0.300974i | ||||
\(185\) | 3338.34 | + | 1927.39i | 1.32670 | + | 0.765972i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1295.47 | + | 747.940i | −0.506600 | + | 0.292486i | ||||
\(188\) | 92.3740 | + | 1861.61i | 0.0358355 | + | 0.722190i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 937.624 | + | 892.252i | 0.358013 | + | 0.340688i | ||||
\(191\) | 1831.72 | + | 3172.63i | 0.693918 | + | 1.20190i | 0.970544 | + | 0.240924i | \(0.0774505\pi\) |
−0.276626 | + | 0.960978i | \(0.589216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −708.828 | + | 1227.73i | −0.264366 | + | 0.457895i | −0.967397 | − | 0.253264i | \(-0.918496\pi\) |
0.703032 | + | 0.711159i | \(0.251829\pi\) | |||||||
\(194\) | 1434.90 | − | 422.868i | 0.531030 | − | 0.156496i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1019.64 | + | 658.141i | −0.371590 | + | 0.239847i | ||||
\(197\) | 876.917i | 0.317146i | 0.987347 | + | 0.158573i | \(0.0506893\pi\) | ||||
−0.987347 | + | 0.158573i | \(0.949311\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1485.45i | − | 0.529149i | −0.964365 | − | 0.264574i | \(-0.914769\pi\) | ||
0.964365 | − | 0.264574i | \(-0.0852315\pi\) | |||||||
\(200\) | 3274.94 | + | 621.111i | 1.15787 | + | 0.219596i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1146.51 | + | 3890.41i | 0.399348 | + | 1.35509i | ||||
\(203\) | −12.9941 | + | 22.5064i | −0.00449263 | + | 0.00778147i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −126.296 | − | 218.751i | −0.0430287 | − | 0.0745279i | ||||
\(206\) | 448.252 | − | 471.046i | 0.151608 | − | 0.159317i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1423.58 | + | 141.626i | −0.474555 | + | 0.0472116i | ||||
\(209\) | 306.272 | − | 176.826i | 0.101365 | − | 0.0585231i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −266.434 | − | 153.826i | −0.0869294 | − | 0.0501887i | 0.455905 | − | 0.890028i | \(-0.349316\pi\) |
−0.542835 | + | 0.839840i | \(0.682649\pi\) | |||||||
\(212\) | −660.783 | + | 1288.00i | −0.214070 | + | 0.417264i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1113.13 | − | 4608.28i | 0.355569 | − | 1.47203i | ||||
\(215\) | 6887.55 | 2.18478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3065.50 | −0.958986 | ||||||||
\(218\) | 359.059 | − | 1486.48i | 0.111553 | − | 0.461823i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 768.509 | − | 1497.97i | 0.235513 | − | 0.459061i | ||||
\(221\) | −2270.66 | − | 1310.96i | −0.691135 | − | 0.399027i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3380.52 | + | 1951.74i | −1.01514 | + | 0.586091i | −0.912692 | − | 0.408647i | \(-0.866001\pi\) |
−0.102447 | + | 0.994738i | \(0.532667\pi\) | |||||||
\(224\) | −2473.14 | + | 3177.09i | −0.737694 | + | 0.947671i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2500.98 | − | 2628.16i | 0.736119 | − | 0.773551i | ||||
\(227\) | −964.382 | − | 1670.36i | −0.281975 | − | 0.488394i | 0.689896 | − | 0.723908i | \(-0.257656\pi\) |
−0.971871 | + | 0.235514i | \(0.924323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1148.71 | + | 1989.62i | −0.331479 | + | 0.574139i | −0.982802 | − | 0.184662i | \(-0.940881\pi\) |
0.651323 | + | 0.758801i | \(0.274214\pi\) | |||||||
\(230\) | 463.997 | + | 1574.46i | 0.133022 | + | 0.451378i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.92642 | + | 25.9756i | −0.00139412 | + | 0.00735079i | ||||
\(233\) | 3366.60i | 0.946580i | 0.880907 | + | 0.473290i | \(0.156934\pi\) | ||||
−0.880907 | + | 0.473290i | \(0.843066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3844.74i | − | 1.06725i | ||||||
\(236\) | 4217.26 | − | 2722.08i | 1.16322 | − | 0.750816i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7078.02 | + | 2085.91i | −1.92773 | + | 0.568106i | ||||
\(239\) | −307.571 | + | 532.729i | −0.0832432 | + | 0.144182i | −0.904641 | − | 0.426174i | \(-0.859861\pi\) |
0.821398 | + | 0.570355i | \(0.193195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2195.78 | + | 3803.20i | 0.586898 | + | 1.01654i | 0.994636 | + | 0.103438i | \(0.0329844\pi\) |
−0.407738 | + | 0.913099i | \(0.633682\pi\) | |||||||
\(242\) | 2393.92 | + | 2278.08i | 0.635897 | + | 0.605125i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 302.995 | + | 6106.25i | 0.0794971 | + | 1.60210i | ||||
\(245\) | 2167.95 | − | 1251.67i | 0.565329 | − | 0.326393i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 536.823 | + | 309.935i | 0.138288 | + | 0.0798408i | ||||
\(248\) | −2944.08 | + | 1028.76i | −0.753828 | + | 0.263412i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1012.35 | − | 244.533i | −0.256107 | − | 0.0618624i | ||||
\(251\) | −7726.08 | −1.94289 | −0.971446 | − | 0.237259i | \(-0.923751\pi\) | ||||
−0.971446 | + | 0.237259i | \(0.923751\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 448.490 | 0.111448 | ||||||||
\(254\) | −7353.94 | − | 1776.34i | −1.81664 | − | 0.438809i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1308.97 | + | 3881.21i | −0.319573 | + | 0.947562i | ||||
\(257\) | 2222.83 | + | 1283.35i | 0.539518 | + | 0.311491i | 0.744884 | − | 0.667194i | \(-0.232505\pi\) |
−0.205365 | + | 0.978685i | \(0.565838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4499.53 | − | 2597.81i | 1.07949 | − | 0.623243i | ||||
\(260\) | 2947.34 | − | 146.249i | 0.703024 | − | 0.0348844i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1694.08 | + | 1612.11i | 0.399469 | + | 0.380138i | ||||
\(263\) | −2003.92 | − | 3470.89i | −0.469837 | − | 0.813781i | 0.529569 | − | 0.848267i | \(-0.322354\pi\) |
−0.999405 | + | 0.0344862i | \(0.989021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1493.02 | − | 2585.98i | 0.346096 | − | 0.599456i | ||||
\(266\) | 1673.37 | − | 493.146i | 0.385717 | − | 0.113672i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 568.403 | + | 880.614i | 0.129555 | + | 0.200717i | ||||
\(269\) | 2242.21i | 0.508214i | 0.967176 | + | 0.254107i | \(0.0817816\pi\) | ||||
−0.967176 | + | 0.254107i | \(0.918218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6324.08i | 1.41757i | 0.705426 | + | 0.708784i | \(0.250756\pi\) | ||||
−0.705426 | + | 0.708784i | \(0.749244\pi\) | |||||||
\(272\) | −6097.65 | + | 4378.61i | −1.35928 | + | 0.976075i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −517.870 | − | 1757.27i | −0.114181 | − | 0.387446i | ||||
\(275\) | −939.352 | + | 1627.01i | −0.205982 | + | 0.356771i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −625.852 | − | 1084.01i | −0.135754 | − | 0.235132i | 0.790131 | − | 0.612938i | \(-0.210012\pi\) |
−0.925885 | + | 0.377805i | \(0.876679\pi\) | |||||||
\(278\) | 5206.95 | − | 5471.73i | 1.12335 | − | 1.18048i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5419.96 | − | 6292.64i | 1.15680 | − | 1.34306i | ||||
\(281\) | 1190.34 | − | 687.240i | 0.252703 | − | 0.145898i | −0.368298 | − | 0.929708i | \(-0.620060\pi\) |
0.621001 | + | 0.783810i | \(0.286726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4006.16 | + | 2312.96i | 0.841490 | + | 0.485835i | 0.857771 | − | 0.514033i | \(-0.171849\pi\) |
−0.0162801 | + | 0.999867i | \(0.505182\pi\) | |||||||
\(284\) | −161.513 | − | 82.8613i | −0.0337466 | − | 0.0173131i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 189.318 | − | 783.767i | 0.0391421 | − | 0.162046i | ||||
\(287\) | −340.452 | −0.0700217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8845.19 | −1.80037 | ||||||||
\(290\) | 12.8049 | − | 53.0115i | 0.00259286 | − | 0.0107343i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2760.79 | − | 1416.37i | −0.553297 | − | 0.283859i | ||||
\(293\) | −5522.68 | − | 3188.52i | −1.10116 | − | 0.635752i | −0.164631 | − | 0.986355i | \(-0.552643\pi\) |
−0.936524 | + | 0.350603i | \(0.885977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8966.70 | + | 5176.92i | −1.76970 | + | 1.02174i | ||||
\(296\) | 3449.51 | − | 4004.91i | 0.677360 | − | 0.786422i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −203.190 | + | 213.522i | −0.0394982 | + | 0.0415067i | ||||
\(299\) | 393.049 | + | 680.781i | 0.0760221 | + | 0.131674i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4641.63 | − | 8039.54i | 0.888835 | − | 1.53951i | ||||
\(302\) | 2199.86 | + | 7464.70i | 0.419165 | + | 1.42233i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1441.59 | − | 1035.18i | 0.271977 | − | 0.195302i | ||||
\(305\) | − | 12611.1i | − | 2.36757i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6609.36i | − | 1.22872i | −0.789027 | − | 0.614359i | \(-0.789415\pi\) | ||
0.789027 | − | 0.614359i | \(-0.210585\pi\) | |||||||
\(308\) | −1230.61 | − | 1906.56i | −0.227664 | − | 0.352715i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6170.58 | − | 1818.48i | 1.13053 | − | 0.333171i | ||||
\(311\) | −2568.35 | + | 4448.51i | −0.468288 | + | 0.811098i | −0.999343 | − | 0.0362387i | \(-0.988462\pi\) |
0.531055 | + | 0.847337i | \(0.321796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3101.42 | − | 5371.82i | −0.560072 | − | 0.970074i | −0.997489 | − | 0.0708150i | \(-0.977440\pi\) |
0.437417 | − | 0.899259i | \(-0.355893\pi\) | |||||||
\(314\) | 2383.13 | + | 2267.81i | 0.428305 | + | 0.407579i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4487.75 | − | 222.685i | 0.798911 | − | 0.0396424i | ||||
\(317\) | −1580.62 | + | 912.574i | −0.280053 | + | 0.161689i | −0.633447 | − | 0.773786i | \(-0.718361\pi\) |
0.353395 | + | 0.935474i | \(0.385027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.9048 | − | 7.45058i | −0.00226498 | − | 0.00130769i | ||||
\(320\) | 3093.52 | − | 7862.28i | 0.540416 | − | 1.37348i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2150.50 | + | 519.451i | 0.372182 | + | 0.0899003i | ||||
\(323\) | 3252.68 | 0.560322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3292.93 | −0.562027 | ||||||||
\(326\) | 8056.84 | + | 1946.13i | 1.36880 | + | 0.330632i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −326.966 | + | 114.253i | −0.0550418 | + | 0.0192334i | ||||
\(329\) | −4487.80 | − | 2591.03i | −0.752038 | − | 0.434189i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3444.37 | + | 1988.61i | −0.571963 | + | 0.330223i | −0.757933 | − | 0.652332i | \(-0.773791\pi\) |
0.185970 | + | 0.982555i | \(0.440457\pi\) | |||||||
\(332\) | 271.278 | + | 5467.05i | 0.0448443 | + | 0.903745i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1786.53 | + | 1700.08i | 0.292678 | + | 0.278516i | ||||
\(335\) | −1081.00 | − | 1872.35i | −0.176303 | − | 0.305366i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 578.847 | − | 1002.59i | 0.0935662 | − | 0.162061i | −0.815443 | − | 0.578837i | \(-0.803507\pi\) |
0.909009 | + | 0.416776i | \(0.136840\pi\) | |||||||
\(338\) | −4604.98 | + | 1357.10i | −0.741059 | + | 0.218392i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13010.0 | − | 8397.48i | 2.07520 | − | 1.33946i | ||||
\(341\) | − | 1757.71i | − | 0.279136i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4254.87i | 0.669800i | ||||||||
\(344\) | 1759.78 | − | 9278.79i | 0.275816 | − | 1.45430i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1865.11 | − | 6328.80i | −0.289795 | − | 0.983348i | ||||
\(347\) | −1241.63 | + | 2150.56i | −0.192086 | + | 0.332703i | −0.945941 | − | 0.324337i | \(-0.894859\pi\) |
0.753855 | + | 0.657041i | \(0.228192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2986.90 | + | 5173.47i | 0.458124 | + | 0.793494i | 0.998862 | − | 0.0476973i | \(-0.0151883\pi\) |
−0.540738 | + | 0.841191i | \(0.681855\pi\) | |||||||
\(350\) | −6388.60 | + | 6713.46i | −0.975671 | + | 1.02528i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1821.69 | − | 1418.06i | −0.275842 | − | 0.214724i | ||||
\(353\) | 893.160 | − | 515.666i | 0.134669 | − | 0.0777511i | −0.431152 | − | 0.902279i | \(-0.641893\pi\) |
0.565821 | + | 0.824528i | \(0.308559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 324.279 | + | 187.223i | 0.0484815 | + | 0.0279908i | ||||
\(356\) | −1015.19 | + | 1978.80i | −0.151137 | + | 0.294596i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −424.213 | + | 1756.22i | −0.0626267 | + | 0.259271i | ||||
\(359\) | 4218.99 | 0.620249 | 0.310125 | − | 0.950696i | \(-0.399629\pi\) | ||||
0.310125 | + | 0.950696i | \(0.399629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6090.01 | 0.887886 | ||||||||
\(362\) | −2677.01 | + | 11082.7i | −0.388676 | + | 1.60909i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1815.55 | − | 3538.87i | 0.261431 | − | 0.509580i | ||||
\(365\) | 5542.99 | + | 3200.25i | 0.794887 | + | 0.458928i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2632.91 | − | 1520.11i | 0.374487 | − | 0.216210i | −0.300930 | − | 0.953646i | \(-0.597297\pi\) |
0.675417 | + | 0.737436i | \(0.263964\pi\) | |||||||
\(368\) | 2239.64 | − | 222.813i | 0.317254 | − | 0.0315623i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7516.11 | + | 7898.31i | −1.05606 | + | 1.10977i | ||||
\(371\) | −2012.34 | − | 3485.48i | −0.281605 | − | 0.487754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2558.92 | + | 4432.17i | −0.355216 | + | 0.615253i | −0.987155 | − | 0.159766i | \(-0.948926\pi\) |
0.631939 | + | 0.775018i | \(0.282259\pi\) | |||||||
\(374\) | −1196.03 | − | 4058.42i | −0.165361 | − | 0.561112i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5179.57 | − | 982.335i | −0.710415 | − | 0.134734i | ||||
\(377\) | − | 26.1183i | − | 0.00356806i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2840.61i | 0.384993i | 0.981298 | + | 0.192497i | \(0.0616585\pi\) | ||||
−0.981298 | + | 0.192497i | \(0.938342\pi\) | |||||||
\(380\) | −3075.80 | + | 1985.31i | −0.415224 | + | 0.268012i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9939.14 | + | 2929.09i | −1.33123 | + | 0.392317i | ||||
\(383\) | 2814.33 | − | 4874.56i | 0.375472 | − | 0.650336i | −0.614926 | − | 0.788585i | \(-0.710814\pi\) |
0.990397 | + | 0.138249i | \(0.0441474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2340.41 | + | 4053.70i | 0.309814 | + | 0.536613i | ||||
\(386\) | −2904.72 | − | 2764.16i | −0.383022 | − | 0.364487i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 209.691 | + | 4225.88i | 0.0274367 | + | 0.552930i | ||||
\(389\) | 3084.76 | − | 1780.99i | 0.402065 | − | 0.232132i | −0.285309 | − | 0.958435i | \(-0.592096\pi\) |
0.687375 | + | 0.726303i | \(0.258763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3572.30 | + | 2062.47i | 0.462044 | + | 0.266761i | ||||
\(392\) | −1132.31 | − | 3240.44i | −0.145894 | − | 0.417517i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2410.96 | − | 582.365i | −0.308280 | − | 0.0744648i | ||||
\(395\) | −9268.46 | −1.18062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9427.52 | −1.19182 | −0.595911 | − | 0.803050i | \(-0.703209\pi\) | ||||
−0.595911 | + | 0.803050i | \(0.703209\pi\) | |||||||
\(398\) | 4084.03 | + | 986.494i | 0.514356 | + | 0.124242i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3882.56 | + | 8591.50i | −0.485321 | + | 1.07394i | ||||
\(401\) | 7475.17 | + | 4315.79i | 0.930903 | + | 0.537457i | 0.887097 | − | 0.461583i | \(-0.152718\pi\) |
0.0438059 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2668.10 | − | 1540.43i | 0.329795 | − | 0.190407i | ||||
\(404\) | −11457.5 | + | 568.529i | −1.41097 | + | 0.0700133i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −53.2487 | − | 50.6719i | −0.00650908 | − | 0.00619410i | ||||
\(407\) | 1489.54 | + | 2579.96i | 0.181410 | + | 0.314211i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2932.40 | + | 5079.07i | −0.354518 | + | 0.614044i | −0.987035 | − | 0.160503i | \(-0.948688\pi\) |
0.632517 | + | 0.774546i | \(0.282022\pi\) | |||||||
\(410\) | 685.298 | − | 201.959i | 0.0825474 | − | 0.0243269i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 997.387 | + | 1545.23i | 0.119266 | + | 0.184777i | ||||
\(413\) | 13955.3i | 1.66270i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11291.0i | − | 1.33555i | ||||||
\(416\) | 556.025 | − | 4007.98i | 0.0655321 | − | 0.472373i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 282.762 | + | 959.482i | 0.0330869 | + | 0.112272i | ||||
\(419\) | 3477.85 | − | 6023.82i | 0.405500 | − | 0.702346i | −0.588880 | − | 0.808221i | \(-0.700431\pi\) |
0.994379 | + | 0.105875i | \(0.0337642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4697.89 | + | 8136.99i | 0.543851 | + | 0.941978i | 0.998678 | + | 0.0513981i | \(0.0163677\pi\) |
−0.454827 | + | 0.890580i | \(0.650299\pi\) | |||||||
\(422\) | 599.863 | − | 630.366i | 0.0691964 | − | 0.0727151i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3102.33 | − | 2672.09i | −0.355336 | − | 0.306057i | ||||
\(425\) | −14964.2 | + | 8639.59i | −1.70793 | + | 0.986074i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14720.4 | − | 8498.83i | −1.66831 | − | 0.963202i | ||||
\(428\) | 11930.6 | + | 6120.76i | 1.34740 | + | 0.691258i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4574.06 | + | 18936.3i | −0.512978 | + | 2.12370i | ||||
\(431\) | 7346.03 | 0.820988 | 0.410494 | − | 0.911863i | \(-0.365356\pi\) | ||||
0.410494 | + | 0.911863i | \(0.365356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13673.0 | 1.51751 | 0.758755 | − | 0.651376i | \(-0.225808\pi\) | ||||
0.758755 | + | 0.651376i | \(0.225808\pi\) | |||||||
\(434\) | 2035.82 | − | 8428.17i | 0.225167 | − | 0.932177i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3848.42 | + | 1974.36i | 0.422720 | + | 0.216869i | ||||
\(437\) | −844.556 | − | 487.604i | −0.0924498 | − | 0.0533759i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4995.87 | − | 2884.37i | 0.543144 | − | 0.313584i | −0.203208 | − | 0.979135i | \(-0.565137\pi\) |
0.746352 | + | 0.665551i | \(0.231804\pi\) | |||||||
\(440\) | 3608.09 | + | 3107.72i | 0.390930 | + | 0.336715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5112.26 | − | 5372.22i | 0.550148 | − | 0.578124i | ||||
\(443\) | 4826.45 | + | 8359.66i | 0.517634 | + | 0.896568i | 0.999790 | + | 0.0204826i | \(0.00652029\pi\) |
−0.482157 | + | 0.876085i | \(0.660146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2293.79 | − | 3972.96i | 0.244351 | − | 0.423228i | ||||
\(446\) | −3121.02 | − | 10590.4i | −0.331355 | − | 1.12437i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7092.53 | − | 8909.46i | −0.747970 | − | 0.939582i | ||||
\(449\) | 11492.2i | 1.20791i | 0.797018 | + | 0.603955i | \(0.206410\pi\) | ||||
−0.797018 | + | 0.603955i | \(0.793590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 195.209i | − | 0.0203815i | ||||||
\(452\) | 5564.83 | + | 8621.46i | 0.579088 | + | 0.897167i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5232.86 | − | 1542.14i | 0.540948 | − | 0.159419i | ||||
\(455\) | −4102.19 | + | 7105.19i | −0.422667 | + | 0.732080i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8821.06 | − | 15278.5i | −0.902914 | − | 1.56389i | −0.823693 | − | 0.567036i | \(-0.808090\pi\) |
−0.0792214 | − | 0.996857i | \(-0.525243\pi\) | |||||||
\(458\) | −4707.31 | − | 4479.53i | −0.480258 | − | 0.457018i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4636.90 | + | 230.085i | −0.469992 | + | 0.0233213i | ||||
\(461\) | 11142.2 | − | 6432.95i | 1.12569 | − | 0.649918i | 0.182843 | − | 0.983142i | \(-0.441470\pi\) |
0.942848 | + | 0.333224i | \(0.108137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11984.7 | + | 6919.34i | 1.20297 | + | 0.694534i | 0.961214 | − | 0.275804i | \(-0.0889440\pi\) |
0.241754 | + | 0.970338i | \(0.422277\pi\) | |||||||
\(464\) | −68.1446 | − | 30.7950i | −0.00681796 | − | 0.00308109i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9255.98 | − | 2235.78i | −0.920118 | − | 0.222254i | ||||
\(467\) | −81.1441 | −0.00804047 | −0.00402024 | − | 0.999992i | \(-0.501280\pi\) | ||||
−0.00402024 | + | 0.999992i | \(0.501280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2914.03 | −0.286902 | ||||||||
\(470\) | 10570.6 | + | 2553.31i | 1.03741 | + | 0.250586i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4683.27 | + | 13402.5i | 0.456706 | + | 1.30699i | ||||
\(473\) | 4609.74 | + | 2661.44i | 0.448110 | + | 0.258717i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3537.80 | − | 2042.55i | 0.341738 | − | 0.197302i | ||||
\(476\) | −1034.35 | − | 20845.3i | −0.0995998 | − | 2.00723i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1260.40 | − | 1199.41i | −0.120606 | − | 0.114769i | ||||
\(479\) | 7472.06 | + | 12942.0i | 0.712750 | + | 1.23452i | 0.963821 | + | 0.266550i | \(0.0858838\pi\) |
−0.251071 | + | 0.967969i | \(0.580783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2610.81 | + | 4522.06i | −0.247490 | + | 0.428666i | ||||
\(482\) | −11914.6 | + | 3511.25i | −1.12592 | + | 0.331811i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7853.06 | + | 5068.86i | −0.737515 | + | 0.476038i | ||||
\(485\) | − | 8727.63i | − | 0.817116i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5934.04i | 0.552150i | 0.961136 | + | 0.276075i | \(0.0890338\pi\) | ||||
−0.961136 | + | 0.276075i | \(0.910966\pi\) | |||||||
\(488\) | −16989.5 | − | 3222.15i | −1.57598 | − | 0.298893i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2001.53 | + | 6791.72i | 0.184531 | + | 0.626160i | ||||
\(491\) | 10032.4 | − | 17376.6i | 0.922110 | − | 1.59714i | 0.125965 | − | 0.992035i | \(-0.459797\pi\) |
0.796145 | − | 0.605106i | \(-0.206869\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −68.5259 | − | 118.690i | −0.00626015 | − | 0.0108429i | ||||
\(494\) | −1208.63 | + | 1270.09i | −0.110079 | + | 0.115676i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −873.242 | − | 8777.53i | −0.0790519 | − | 0.794602i | ||||
\(497\) | 437.074 | − | 252.345i | 0.0394476 | − | 0.0227751i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8148.09 | + | 4704.30i | 0.730979 | + | 0.422031i | 0.818780 | − | 0.574107i | \(-0.194651\pi\) |
−0.0878012 | + | 0.996138i | \(0.527984\pi\) | |||||||
\(500\) | 1344.62 | − | 2620.92i | 0.120266 | − | 0.234422i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5130.93 | − | 21241.8i | 0.456185 | − | 1.88858i | ||||
\(503\) | −12736.4 | −1.12900 | −0.564501 | − | 0.825432i | \(-0.690931\pi\) | ||||
−0.564501 | + | 0.825432i | \(0.690931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23663.0 | 2.08513 | ||||||||
\(506\) | −297.845 | + | 1233.06i | −0.0261676 | + | 0.108332i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9767.58 | − | 19038.9i | 0.853084 | − | 1.66283i | ||||
\(509\) | −7921.59 | − | 4573.53i | −0.689820 | − | 0.398268i | 0.113724 | − | 0.993512i | \(-0.463722\pi\) |
−0.803545 | + | 0.595244i | \(0.797055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7471.04 | − | 4313.40i | 0.646769 | − | 0.373412i | ||||
\(512\) | −9801.54 | − | 6176.37i | −0.846037 | − | 0.533124i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5004.58 | + | 5259.07i | −0.429460 | + | 0.451299i | ||||
\(515\) | −1896.86 | − | 3285.45i | −0.162302 | − | 0.281115i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1485.66 | − | 2573.23i | 0.126381 | − | 0.218899i | ||||
\(518\) | 4154.13 | + | 14096.0i | 0.352359 | + | 1.19565i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1555.26 | + | 8200.42i | −0.131159 | + | 0.691562i | ||||
\(521\) | − | 7691.78i | − | 0.646801i | −0.946262 | − | 0.323400i | \(-0.895174\pi\) | ||
0.946262 | − | 0.323400i | \(-0.104826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9967.82i | − | 0.833389i | −0.909047 | − | 0.416694i | \(-0.863189\pi\) | ||
0.909047 | − | 0.416694i | \(-0.136811\pi\) | |||||||
\(524\) | −5557.30 | + | 3587.03i | −0.463305 | + | 0.299046i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10873.5 | − | 3204.45i | 0.901347 | − | 0.265629i | ||||
\(527\) | 8083.17 | − | 14000.5i | 0.668138 | − | 1.15725i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5465.14 | + | 9465.89i | 0.449177 | + | 0.777997i | ||||
\(530\) | 6118.27 | + | 5822.21i | 0.501435 | + | 0.477171i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 244.539 | + | 4928.19i | 0.0199288 | + | 0.401624i | ||||
\(533\) | 296.316 | − | 171.078i | 0.0240804 | − | 0.0139028i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23953.7 | − | 13829.7i | −1.93572 | − | 1.11759i | ||||
\(536\) | −2798.60 | + | 977.923i | −0.225525 | + | 0.0788057i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6164.62 | − | 1489.06i | −0.494007 | − | 0.119327i | ||||
\(539\) | 1934.64 | 0.154603 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6050.08 | 0.480801 | 0.240400 | − | 0.970674i | \(-0.422721\pi\) | ||||
0.240400 | + | 0.970674i | \(0.422721\pi\) | |||||||
\(542\) | −17387.2 | − | 4199.86i | −1.37794 | − | 0.332840i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7988.88 | − | 19672.5i | −0.629633 | − | 1.55046i | ||||
\(545\) | −7726.70 | − | 4461.01i | −0.607294 | − | 0.350622i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11232.1 | + | 6484.87i | −0.877972 | + | 0.506898i | −0.869989 | − | 0.493071i | \(-0.835874\pi\) |
−0.00798299 | + | 0.999968i | \(0.502541\pi\) | |||||||
\(548\) | 5175.27 | − | 256.800i | 0.403425 | − | 0.0200181i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3849.39 | − | 3663.12i | −0.298434 | − | 0.283992i | ||||
\(551\) | 16.2007 | + | 28.0605i | 0.00125259 | + | 0.00216954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6246.17 | + | 10818.7i | −0.480315 | + | 0.831930i | ||||
\(554\) | 3395.95 | − | 1000.80i | 0.260434 | − | 0.0767504i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11585.8 | + | 17949.6i | 0.883716 | + | 1.36912i | ||||
\(557\) | 2223.88i | 0.169172i | 0.996416 | + | 0.0845859i | \(0.0269567\pi\) | ||||
−0.996416 | + | 0.0845859i | \(0.973043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9329.75i | 0.705915i | ||||||||
\(560\) | 13701.3 | + | 19080.4i | 1.03390 | + | 1.43981i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1098.96 | + | 3729.06i | 0.0824855 | + | 0.279895i | ||||
\(563\) | −8913.79 | + | 15439.1i | −0.667267 | + | 1.15574i | 0.311398 | + | 0.950280i | \(0.399203\pi\) |
−0.978665 | + | 0.205461i | \(0.934131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10583.3 | − | 18330.9i | −0.788043 | − | 1.36493i | ||||
\(566\) | −9019.67 | + | 9478.33i | −0.669832 | + | 0.703894i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 335.077 | − | 389.028i | 0.0247527 | − | 0.0287381i | ||||
\(569\) | −9765.76 | + | 5638.26i | −0.719511 | + | 0.415410i | −0.814573 | − | 0.580061i | \(-0.803029\pi\) |
0.0950615 | + | 0.995471i | \(0.469695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6527.00 | − | 3768.37i | −0.478365 | − | 0.276184i | 0.241370 | − | 0.970433i | \(-0.422403\pi\) |
−0.719735 | + | 0.694249i | \(0.755737\pi\) | |||||||
\(572\) | 2029.13 | + | 1041.01i | 0.148325 | + | 0.0760957i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 226.096 | − | 936.023i | 0.0164409 | − | 0.0680642i | ||||
\(575\) | 5180.59 | 0.375731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16888.0 | −1.21847 | −0.609233 | − | 0.792991i | \(-0.708523\pi\) | ||||
−0.609233 | + | 0.792991i | \(0.708523\pi\) | |||||||
\(578\) | 5874.14 | − | 24318.6i | 0.422720 | − | 1.75004i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 137.244 | + | 70.4104i | 0.00982540 | + | 0.00504075i | ||||
\(581\) | −13179.5 | − | 7609.18i | −0.941097 | − | 0.543343i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1998.51 | − | 1153.84i | 0.141973 | − | 0.0819679i | ||||
\(584\) | 5727.57 | − | 6649.77i | 0.405836 | − | 0.471180i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12434.0 | − | 13066.3i | 0.876527 | − | 0.921099i | ||||
\(587\) | −8103.83 | − | 14036.3i | −0.569814 | − | 0.986947i | −0.996584 | − | 0.0825870i | \(-0.973682\pi\) |
0.426770 | − | 0.904360i | \(-0.359652\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1911.00 | + | 3309.96i | −0.133687 | + | 0.231552i | ||||
\(590\) | −8278.38 | − | 28090.7i | −0.577654 | − | 1.96013i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8720.10 | + | 12143.6i | 0.605395 | + | 0.843073i | ||||
\(593\) | − | 22320.8i | − | 1.54571i | −0.634583 | − | 0.772855i | \(-0.718828\pi\) | ||
0.634583 | − | 0.772855i | \(-0.281172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 43051.3i | 2.96627i | ||||||||
\(596\) | −452.109 | − | 700.442i | −0.0310723 | − | 0.0481397i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2132.74 | + | 628.522i | −0.145843 | + | 0.0429802i | ||||
\(599\) | −4883.72 | + | 8458.84i | −0.333127 | + | 0.576993i | −0.983123 | − | 0.182944i | \(-0.941437\pi\) |
0.649996 | + | 0.759938i | \(0.274771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9316.81 | − | 16137.2i | −0.632347 | − | 1.09526i | −0.987071 | − | 0.160286i | \(-0.948758\pi\) |
0.354724 | − | 0.934971i | \(-0.384575\pi\) | |||||||
\(602\) | 19021.0 | + | 18100.6i | 1.28777 | + | 1.22546i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21984.1 | + | 1090.86i | −1.48099 | + | 0.0734876i | ||||
\(605\) | 16697.1 | − | 9640.08i | 1.12204 | − | 0.647810i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −371.545 | − | 214.512i | −0.0248444 | − | 0.0143439i | 0.487526 | − | 0.873108i | \(-0.337899\pi\) |
−0.512371 | + | 0.858764i | \(0.671233\pi\) | |||||||
\(608\) | 1888.71 | + | 4650.92i | 0.125983 | + | 0.310230i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34672.4 | + | 8375.10i | 2.30138 | + | 0.555898i | ||||
\(611\) | 5208.01 | 0.344834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4211.54 | −0.277492 | −0.138746 | − | 0.990328i | \(-0.544307\pi\) | ||||
−0.138746 | + | 0.990328i | \(0.544307\pi\) | |||||||
\(614\) | 18171.5 | + | 4389.31i | 1.19437 | + | 0.288499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6059.06 | − | 2117.23i | 0.396309 | − | 0.138483i | ||||
\(617\) | 23419.6 | + | 13521.3i | 1.52810 | + | 0.882248i | 0.999442 | + | 0.0334113i | \(0.0106371\pi\) |
0.528656 | + | 0.848836i | \(0.322696\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8368.15 | − | 4831.35i | 0.543367 | − | 0.313713i | −0.203075 | − | 0.979163i | \(-0.565094\pi\) |
0.746442 | + | 0.665450i | \(0.231760\pi\) | |||||||
\(620\) | 901.744 | + | 18172.8i | 0.0584111 | + | 1.17716i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10524.9 | − | 10015.6i | −0.678471 | − | 0.645640i | ||||
\(623\) | −3091.65 | − | 5354.89i | −0.198819 | − | 0.344364i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6168.97 | − | 10685.0i | 0.394814 | − | 0.683838i | ||||
\(626\) | 16828.7 | − | 4959.46i | 1.07446 | − | 0.316645i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7817.66 | + | 5046.00i | −0.496749 | + | 0.320633i | ||||
\(629\) | 27399.8i | 1.73688i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10846.5i | − | 0.684297i | −0.939646 | − | 0.342149i | \(-0.888845\pi\) | ||
0.939646 | − | 0.342149i | \(-0.111155\pi\) | |||||||
\(632\) | −2368.10 | + | 12486.3i | −0.149048 | + | 0.785885i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1459.29 | − | 4951.75i | −0.0914130 | − | 0.310188i | ||||
\(635\) | −22069.6 | + | 38225.6i | −1.37922 | + | 2.38888i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1695.49 | + | 2936.67i | 0.105459 | + | 0.182661i | ||||
\(638\) | 29.0545 | − | 30.5319i | 0.00180294 | − | 0.00189462i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19561.8 | + | 13726.6i | 1.20820 | + | 0.847798i | ||||
\(641\) | −12772.5 | + | 7374.18i | −0.787023 | + | 0.454388i | −0.838914 | − | 0.544265i | \(-0.816809\pi\) |
0.0518903 | + | 0.998653i | \(0.483475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12787.4 | + | 7382.82i | 0.784271 | + | 0.452799i | 0.837942 | − | 0.545759i | \(-0.183759\pi\) |
−0.0536706 | + | 0.998559i | \(0.517092\pi\) | |||||||
\(644\) | −2856.31 | + | 5567.52i | −0.174774 | + | 0.340669i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2160.12 | + | 8942.78i | −0.131562 | + | 0.544658i | ||||
\(647\) | −27157.4 | −1.65018 | −0.825090 | − | 0.565002i | \(-0.808875\pi\) | ||||
−0.825090 | + | 0.565002i | \(0.808875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8001.72 | −0.483968 | ||||||||
\(650\) | 2186.85 | − | 9053.43i | 0.131962 | − | 0.546315i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10701.2 | + | 20858.7i | −0.642777 | + | 1.25290i | ||||
\(653\) | 2658.60 | + | 1534.94i | 0.159325 | + | 0.0919861i | 0.577542 | − | 0.816361i | \(-0.304012\pi\) |
−0.418218 | + | 0.908347i | \(0.637345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11815.9 | − | 6821.90i | 0.704862 | − | 0.406952i | ||||
\(656\) | −96.9813 | − | 974.823i | −0.00577208 | − | 0.0580190i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10104.1 | − | 10617.9i | 0.598628 | − | 0.629068i | ||||
\(659\) | −579.767 | − | 1004.19i | −0.0342709 | − | 0.0593589i | 0.848381 | − | 0.529386i | \(-0.177578\pi\) |
−0.882652 | + | 0.470027i | \(0.844244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8919.74 | + | 15449.4i | −0.524868 | + | 0.909097i | 0.474713 | + | 0.880141i | \(0.342552\pi\) |
−0.999581 | + | 0.0289568i | \(0.990781\pi\) | |||||||
\(662\) | −3179.97 | − | 10790.5i | −0.186697 | − | 0.633509i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15211.0 | − | 2884.86i | −0.889010 | − | 0.168606i | ||||
\(665\) | − | 10178.1i | − | 0.593517i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.0905i | 0.00238535i | ||||||||
\(668\) | −5860.57 | + | 3782.78i | −0.339449 | + | 0.219102i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5865.67 | − | 1728.62i | 0.338225 | − | 0.0996755i | ||||
\(671\) | 4873.09 | − | 8440.44i | 0.280363 | − | 0.485603i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6058.30 | + | 10493.3i | 0.346999 | + | 0.601020i | 0.985715 | − | 0.168423i | \(-0.0538673\pi\) |
−0.638716 | + | 0.769443i | \(0.720534\pi\) | |||||||
\(674\) | 2372.07 | + | 2257.28i | 0.135562 | + | 0.129002i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −672.953 | − | 13562.0i | −0.0382882 | − | 0.771620i | ||||
\(677\) | 18626.5 | − | 10754.0i | 1.05742 | − | 0.610504i | 0.132705 | − | 0.991156i | \(-0.457634\pi\) |
0.924718 | + | 0.380652i | \(0.124300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10187.4 | − | 5881.70i | −0.575783 | − | 0.332428i | ||||
\(680\) | 14447.6 | + | 41346.0i | 0.814768 | + | 2.33169i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4832.57 | + | 1167.30i | 0.271332 | + | 0.0655402i | ||||
\(683\) | 33849.4 | 1.89636 | 0.948179 | − | 0.317738i | \(-0.102923\pi\) | ||||
0.948179 | + | 0.317738i | \(0.102923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10688.4 | −0.596178 | ||||||||
\(686\) | −11698.2 | − | 2825.68i | −0.651075 | − | 0.157267i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24342.0 | + | 11000.3i | 1.34888 | + | 0.609570i | ||||
\(689\) | 3502.93 | + | 2022.42i | 0.193688 | + | 0.111826i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1786.94 | − | 1031.69i | 0.0983771 | − | 0.0567980i | −0.450004 | − | 0.893026i | \(-0.648578\pi\) |
0.548381 | + | 0.836228i | \(0.315244\pi\) | |||||||
\(692\) | 18638.8 | − | 924.866i | 1.02390 | − | 0.0508065i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5088.08 | − | 4841.87i | −0.278301 | − | 0.264834i | ||||
\(695\) | −22034.1 | − | 38164.2i | −1.20259 | − | 2.08295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 897.708 | − | 1554.88i | 0.0487850 | − | 0.0844981i | ||||
\(698\) | −16207.3 | + | 4776.33i | −0.878877 | + | 0.259007i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14215.0 | − | 22023.0i | −0.767538 | − | 1.18913i | ||||
\(701\) | − | 19641.7i | − | 1.05828i | −0.848534 | − | 0.529141i | \(-0.822514\pi\) | ||
0.848534 | − | 0.529141i | \(-0.177486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6477.79i | − | 0.347531i | ||||||
\(704\) | 5108.54 | − | 4066.74i | 0.273488 | − | 0.217715i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 824.598 | + | 2798.07i | 0.0439577 | + | 0.149160i | ||||
\(707\) | 15946.9 | − | 27620.8i | 0.848295 | − | 1.46929i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2685.98 | + | 4652.26i | 0.142277 | + | 0.246431i | 0.928354 | − | 0.371698i | \(-0.121224\pi\) |
−0.786077 | + | 0.618129i | \(0.787891\pi\) | |||||||
\(710\) | −730.097 | + | 767.223i | −0.0385916 | + | 0.0405540i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4766.24 | − | 4105.25i | −0.250874 | − | 0.216083i | ||||
\(713\) | −4197.58 | + | 2423.47i | −0.220478 | + | 0.127293i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4074.00 | − | 2352.13i | −0.213090 | − | 0.123027i | ||||
\(716\) | −4546.74 | − | 2332.63i | −0.237318 | − | 0.121752i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2801.85 | + | 11599.5i | −0.145633 | + | 0.602910i | ||||
\(719\) | −12836.0 | −0.665788 | −0.332894 | − | 0.942964i | \(-0.608025\pi\) | ||||
−0.332894 | + | 0.942964i | \(0.608025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5113.29 | −0.264118 | ||||||||
\(722\) | −4044.41 | + | 16743.6i | −0.208473 | + | 0.863065i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28692.4 | − | 14720.1i | −1.47285 | − | 0.755620i | ||||
\(725\) | −149.065 | − | 86.0630i | −0.00763607 | − | 0.00440869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29745.3 | + | 17173.5i | −1.51746 | + | 0.876106i | −0.517670 | + | 0.855580i | \(0.673200\pi\) |
−0.999789 | + | 0.0205251i | \(0.993466\pi\) | |||||||
\(728\) | 8523.89 | + | 7341.78i | 0.433951 | + | 0.373770i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12479.8 | + | 13114.4i | −0.632735 | + | 0.664910i | ||||
\(731\) | 24478.3 | + | 42397.6i | 1.23852 | + | 2.14519i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4537.51 | + | 7859.19i | −0.228645 | + | 0.396024i | −0.957407 | − | 0.288743i | \(-0.906763\pi\) |
0.728762 | + | 0.684767i | \(0.240096\pi\) | |||||||
\(734\) | 2430.80 | + | 8248.33i | 0.122238 | + | 0.414784i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −874.765 | + | 6305.54i | −0.0438101 | + | 0.315795i | ||||
\(737\) | − | 1670.85i | − | 0.0835098i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16863.2i | 0.839410i | 0.907661 | + | 0.419705i | \(0.137866\pi\) | ||||
−0.907661 | + | 0.419705i | \(0.862134\pi\) | |||||||
\(740\) | −16723.8 | − | 25909.8i | −0.830781 | − | 1.28711i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10919.2 | − | 3217.92i | 0.540239 | − | 0.159210i | ||||
\(743\) | −15021.9 | + | 26018.6i | −0.741721 | + | 1.28470i | 0.209990 | + | 0.977704i | \(0.432657\pi\) |
−0.951711 | + | 0.306995i | \(0.900677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 859.832 | + | 1489.27i | 0.0422843 | + | 0.0732386i | ||||
\(746\) | −10486.2 | − | 9978.81i | −0.514649 | − | 0.489745i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11952.3 | − | 593.081i | 0.584252 | − | 0.0289909i | ||||
\(749\) | −32285.6 | + | 18640.1i | −1.57502 | + | 0.909338i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7313.00 | − | 4222.17i | −0.355333 | − | 0.205152i | 0.311698 | − | 0.950181i | \(-0.399102\pi\) |
−0.667032 | + | 0.745029i | \(0.732435\pi\) | |||||||
\(752\) | 6140.57 | − | 13588.1i | 0.297771 | − | 0.658920i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 71.8084 | + | 17.3453i | 0.00346831 | + | 0.000837769i | ||||
\(755\) | 45403.2 | 2.18860 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35193.1 | 1.68971 | 0.844857 | − | 0.534992i | \(-0.179685\pi\) | ||||
0.844857 | + | 0.534992i | \(0.179685\pi\) | |||||||
\(758\) | −7809.86 | − | 1886.47i | −0.374231 | − | 0.0903952i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3415.68 | − | 9774.93i | −0.163026 | − | 0.466545i | ||||
\(761\) | −13659.8 | − | 7886.50i | −0.650681 | − | 0.375671i | 0.138036 | − | 0.990427i | \(-0.455921\pi\) |
−0.788717 | + | 0.614756i | \(0.789254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10414.3 | + | 6012.70i | −0.494133 | + | 0.285288i | ||||
\(764\) | −1452.47 | − | 29271.5i | −0.0687806 | − | 1.38613i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11532.9 | + | 10974.8i | 0.543996 | + | 0.517672i | ||||
\(767\) | −7012.57 | − | 12146.1i | −0.330129 | − | 0.571801i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10370.9 | − | 17962.9i | 0.486325 | − | 0.842340i | −0.513551 | − | 0.858059i | \(-0.671670\pi\) |
0.999876 | + | 0.0157189i | \(0.00500369\pi\) | |||||||
\(770\) | −12699.4 | + | 3742.53i | −0.594355 | + | 0.175158i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9528.70 | − | 6150.42i | 0.444230 | − | 0.286734i | ||||
\(773\) | 35223.1i | 1.63892i | 0.573133 | + | 0.819462i | \(0.305728\pi\) | ||||
−0.573133 | + | 0.819462i | \(0.694272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20303.6i | − | 0.941067i | ||||||
\(776\) | −11757.7 | − | 2229.92i | −0.543915 | − | 0.103156i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2847.96 | + | 9663.86i | 0.131239 | + | 0.445329i | ||||
\(779\) | −212.234 | + | 367.600i | −0.00976133 | + | 0.0169071i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 144.690 | + | 250.611i | 0.00662923 | + | 0.0114822i | ||||
\(782\) | −8042.85 | + | 8451.84i | −0.367790 | + | 0.386493i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9661.09 | − | 961.144i | 0.440101 | − | 0.0437839i | ||||
\(785\) | 16621.8 | − | 9596.62i | 0.755743 | − | 0.436329i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19651.8 | + | 11346.0i | 0.890102 | + | 0.513901i | 0.873976 | − | 0.485969i | \(-0.161533\pi\) |
0.0161261 | + | 0.999870i | \(0.494867\pi\) | |||||||
\(788\) | 3202.26 | − | 6241.83i | 0.144766 | − | 0.282178i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6155.23 | − | 25482.3i | 0.277207 | − | 1.14762i | ||||
\(791\) | −28529.2 | −1.28240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17082.8 | 0.764977 | ||||||||
\(794\) | 6260.87 | − | 25919.6i | 0.279836 | − | 1.15850i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5424.45 | + | 10573.3i | −0.241538 | + | 0.470805i | ||||
\(797\) | −27480.8 | − | 15866.1i | −1.22136 | − | 0.705150i | −0.256149 | − | 0.966637i | \(-0.582454\pi\) |
−0.965207 | + | 0.261488i | \(0.915787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23667.0 | − | 13664.2i | 1.04791 | − | 0.605010i | ||||
\(800\) | −21042.7 | − | 16380.2i | −0.929964 | − | 0.723910i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16829.9 | + | 17685.8i | −0.741005 | + | 0.778686i | ||||
\(803\) | 2473.24 | + | 4283.77i | 0.108691 | + | 0.188258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6453.75 | − | 11178.2i | 0.282565 | − | 0.489417i | ||||
\(806\) | 2463.28 | + | 8358.56i | 0.107650 | + | 0.365282i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6045.92 | − | 31878.4i | 0.263236 | − | 1.38797i | ||||
\(809\) | − | 18376.4i | − | 0.798613i | −0.916817 | − | 0.399307i | \(-0.869251\pi\) | ||
0.916817 | − | 0.399307i | \(-0.130749\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28834.7i | − | 1.24849i | −0.781229 | − | 0.624244i | \(-0.785407\pi\) | ||
0.781229 | − | 0.624244i | \(-0.214593\pi\) | |||||||
\(812\) | 174.678 | − | 112.748i | 0.00754926 | − | 0.00487276i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8082.44 | + | 2381.91i | −0.348021 | + | 0.102563i | ||||
\(815\) | 24179.0 | − | 41879.2i | 1.03921 | − | 1.79996i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5787.09 | − | 10023.5i | −0.247815 | − | 0.429228i | ||||
\(818\) | −12016.8 | − | 11435.3i | −0.513638 | − | 0.488783i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 100.147 | + | 2018.25i | 0.00426497 | + | 0.0859517i | ||||
\(821\) | 14471.4 | − | 8355.08i | 0.615172 | − | 0.355170i | −0.159815 | − | 0.987147i | \(-0.551090\pi\) |
0.774987 | + | 0.631977i | \(0.217756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −453.509 | − | 261.833i | −0.0192082 | − | 0.0110898i | 0.490365 | − | 0.871517i | \(-0.336863\pi\) |
−0.509573 | + | 0.860427i | \(0.670197\pi\) | |||||||
\(824\) | −4910.76 | + | 1715.98i | −0.207615 | + | 0.0725473i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38368.0 | − | 9267.77i | −1.61622 | − | 0.390396i | ||||
\(827\) | −28676.4 | −1.20577 | −0.602887 | − | 0.797826i | \(-0.705983\pi\) | ||||
−0.602887 | + | 0.797826i | \(0.705983\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14521.0 | 0.608365 | 0.304183 | − | 0.952614i | \(-0.401617\pi\) | ||||
0.304183 | + | 0.952614i | \(0.401617\pi\) | |||||||
\(830\) | 31042.9 | + | 7498.40i | 1.29821 | + | 0.313582i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10650.1 | + | 4190.43i | 0.443781 | + | 0.174612i | ||||
\(833\) | 15409.8 | + | 8896.84i | 0.640957 | + | 0.370057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12460.7 | − | 7194.18i | 0.516431 | − | 0.298161i | ||||
\(836\) | −2825.74 | + | 140.215i | −0.116902 | + | 0.00580076i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14252.0 | + | 13562.3i | 0.587501 | + | 0.559072i | ||||
\(839\) | 15594.8 | + | 27010.9i | 0.641706 | + | 1.11147i | 0.985052 | + | 0.172258i | \(0.0551064\pi\) |
−0.343346 | + | 0.939209i | \(0.611560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12193.8 | + | 21120.3i | −0.499972 | + | 0.865977i | ||||
\(842\) | −25491.4 | + | 7512.37i | −1.04334 | + | 0.307474i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1334.73 | + | 2067.87i | 0.0544352 | + | 0.0843352i | ||||
\(845\) | 28009.3i | 1.14029i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25986.4i | − | 1.05420i | ||||||
\(848\) | 9406.81 | − | 6754.86i | 0.380933 | − | 0.273541i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13815.5 | − | 46879.5i | −0.557491 | − | 1.89171i | ||||
\(851\) | 4107.46 | − | 7114.32i | 0.165455 | − | 0.286576i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6544.93 | − | 11336.2i | −0.262713 | − | 0.455032i | 0.704249 | − | 0.709953i | \(-0.251284\pi\) |
−0.966962 | + | 0.254921i | \(0.917951\pi\) | |||||||
\(854\) | 33142.2 | − | 34827.5i | 1.32799 | − | 1.39552i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24751.3 | + | 28736.5i | −0.988297 | + | 1.14742i | ||||
\(857\) | 15414.8 | − | 8899.73i | 0.614421 | − | 0.354736i | −0.160273 | − | 0.987073i | \(-0.551237\pi\) |
0.774694 | + | 0.632337i | \(0.217904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36673.2 | + | 21173.3i | 1.45666 | + | 0.841004i | 0.998845 | − | 0.0480428i | \(-0.0152984\pi\) |
0.457816 | + | 0.889047i | \(0.348632\pi\) | |||||||
\(860\) | −49025.1 | − | 25151.4i | −1.94388 | − | 0.997275i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4878.54 | + | 20196.9i | −0.192765 | + | 0.798037i | ||||
\(863\) | 41963.9 | 1.65524 | 0.827618 | − | 0.561291i | \(-0.189695\pi\) | ||||
0.827618 | + | 0.561291i | \(0.189695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38494.2 | −1.51311 | ||||||||
\(866\) | −9080.31 | + | 37591.9i | −0.356306 | + | 1.47509i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21820.0 | + | 11194.4i | 0.853249 | + | 0.437744i | ||||
\(869\) | −6203.26 | − | 3581.45i | −0.242153 | − | 0.139807i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2536.26 | − | 1464.31i | 0.0986656 | − | 0.0569646i | ||||
\(872\) | −7983.99 | + | 9269.50i | −0.310060 | + | 0.359982i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1901.47 | − | 1998.16i | 0.0735907 | − | 0.0773328i | ||||
\(875\) | 4094.88 | + | 7092.54i | 0.158208 | + | 0.274025i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21665.7 | − | 37526.1i | 0.834206 | − | 1.44489i | −0.0604689 | − | 0.998170i | \(-0.519260\pi\) |
0.894675 | − | 0.446717i | \(-0.147407\pi\) | |||||||
\(878\) | 4612.37 | + | 15651.0i | 0.177289 | + | 0.601588i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10940.4 | + | 7856.09i | −0.419091 | + | 0.300942i | ||||
\(881\) | 38532.4i | 1.47354i | 0.676142 | + | 0.736771i | \(0.263651\pi\) | ||||
−0.676142 | + | 0.736771i | \(0.736349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7198.92i | − | 0.274364i | −0.990546 | − | 0.137182i | \(-0.956196\pi\) | ||
0.990546 | − | 0.137182i | \(-0.0438045\pi\) | |||||||
\(884\) | 11375.1 | + | 17623.2i | 0.432789 | + | 0.670510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26189.0 | + | 7717.94i | −0.993042 | + | 0.292652i | ||||
\(887\) | −7110.04 | + | 12315.0i | −0.269145 | + | 0.466173i | −0.968641 | − | 0.248463i | \(-0.920075\pi\) |
0.699496 | + | 0.714636i | \(0.253408\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29746.1 | + | 51521.7i | 1.12222 | + | 1.94374i | ||||
\(890\) | 9399.76 | + | 8944.90i | 0.354023 | + | 0.336892i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31189.5 | − | 1547.64i | 1.17074 | − | 0.0580928i | ||||
\(893\) | −5595.30 | + | 3230.45i | −0.209675 | + | 0.121056i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9128.76 | + | 5270.49i | 0.340940 | + | 0.196842i | ||||
\(896\) | 29205.5 | − | 13583.1i | 1.08894 | − | 0.506450i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31596.3 | − | 7632.05i | −1.17414 | − | 0.283614i | ||||
\(899\) | 161.041 | 0.00597442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21224.7 | 0.784791 | ||||||||
\(902\) | 536.700 | + | 129.640i | 0.0198117 | + | 0.00478551i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27399.1 | + | 9574.14i | −1.00805 | + | 0.352247i | ||||
\(905\) | 57607.4 | + | 33259.7i | 2.11595 | + | 1.22164i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43283.2 | + | 24989.6i | −1.58456 | + | 0.914845i | −0.590377 | + | 0.807127i | \(0.701021\pi\) |
−0.994181 | + | 0.107718i | \(0.965646\pi\) | |||||||
\(908\) | 764.709 | + | 15411.1i | 0.0279491 | + | 0.563256i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16810.4 | − | 15997.0i | −0.612374 | − | 0.582741i | ||||
\(911\) | −7306.31 | − | 12654.9i | −0.265718 | − | 0.460237i | 0.702034 | − | 0.712144i | \(-0.252276\pi\) |
−0.967751 | + | 0.251907i | \(0.918942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4362.98 | − | 7556.90i | 0.158153 | − | 0.273929i | ||||
\(914\) | 47864.2 | − | 14105.7i | 1.73218 | − | 0.510476i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15442.0 | − | 9967.21i | 0.557005 | − | 0.359526i | ||||
\(917\) | − | 18389.6i | − | 0.662244i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 45594.4i | − | 1.63658i | −0.574804 | − | 0.818291i | \(-0.694922\pi\) | ||
0.574804 | − | 0.818291i | \(-0.305078\pi\) | |||||||
\(920\) | 2446.80 | − | 12901.3i | 0.0876833 | − | 0.462329i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10286.9 | + | 34906.0i | 0.367441 | + | 1.24682i | ||||
\(923\) | −253.608 | + | 439.263i | −0.00904401 | + | 0.0156647i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17205.9 | + | 29801.5i | 0.611597 | + | 1.05932i | ||||
\(926\) | −26982.8 | + | 28354.9i | −0.957571 | + | 1.00626i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 129.922 | − | 166.903i | 0.00459579 | − | 0.00590393i | ||||
\(929\) | −44791.1 | + | 25860.1i | −1.58186 | + | 0.913287i | −0.587272 | + | 0.809390i | \(0.699798\pi\) |
−0.994588 | + | 0.103897i | \(0.966869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3643.14 | − | 2103.37i | −0.128248 | − | 0.0740442i | ||||
\(932\) | 12293.9 | − | 23963.2i | 0.432081 | − | 0.842211i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 53.8882 | − | 223.094i | 0.00188788 | − | 0.00781570i | ||||
\(935\) | −24684.9 | −0.863404 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42197.0 | −1.47120 | −0.735601 | − | 0.677415i | \(-0.763100\pi\) | ||||
−0.735601 | + | 0.677415i | \(0.763100\pi\) | |||||||
\(938\) | 1935.22 | − | 8011.70i | 0.0673638 | − | 0.278882i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14039.9 | + | 27366.6i | −0.487162 | + | 0.949574i | ||||
\(941\) | 9360.06 | + | 5404.03i | 0.324261 | + | 0.187212i | 0.653290 | − | 0.757108i | \(-0.273388\pi\) |
−0.329029 | + | 0.944320i | \(0.606722\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −466.178 | + | 269.148i | −0.0160985 | + | 0.00929446i | ||||
\(944\) | −39958.5 | + | 3975.31i | −1.37769 | + | 0.137061i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10378.6 | + | 10906.4i | −0.356699 | + | 0.374837i | ||||
\(947\) | 372.832 | + | 645.764i | 0.0127935 | + | 0.0221589i | 0.872351 | − | 0.488880i | \(-0.162594\pi\) |
−0.859558 | + | 0.511039i | \(0.829261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4335.00 | + | 7508.44i | −0.148283 | + | 0.256833i | ||||
\(950\) | 3266.23 | + | 11083.1i | 0.111548 | + | 0.378510i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 57998.0 | + | 10999.7i | 1.97450 | + | 0.374476i | ||||
\(953\) | − | 49163.3i | − | 1.67110i | −0.549417 | − | 0.835548i | \(-0.685150\pi\) | ||
0.549417 | − | 0.835548i | \(-0.314850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60453.7i | 2.04841i | ||||||||
\(956\) | 4134.65 | − | 2668.76i | 0.139879 | − | 0.0902865i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40544.4 | + | 11948.5i | −1.36736 | + | 0.402963i | ||||
\(959\) | −7203.08 | + | 12476.1i | −0.242544 | + | 0.420098i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5397.50 | − | 9348.74i | −0.181179 | − | 0.313811i | ||||
\(962\) | −10698.9 | − | 10181.2i | −0.358572 | − | 0.341221i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1741.15 | − | 35089.3i | −0.0581728 | − | 1.17235i | ||||
\(965\) | −20259.8 | + | 11697.0i | −0.675842 | + | 0.390197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14625.7 | − | 8444.18i | −0.486383 | − | 0.280813i | 0.236690 | − | 0.971585i | \(-0.423938\pi\) |
−0.723073 | + | 0.690772i | \(0.757271\pi\) | |||||||
\(968\) | −8720.83 | − | 24957.1i | −0.289564 | − | 0.828670i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23995.4 | + | 5796.06i | 0.794273 | + | 0.191856i | ||||
\(971\) | −22501.6 | −0.743677 | −0.371838 | − | 0.928297i | \(-0.621272\pi\) | ||||
−0.371838 | + | 0.928297i | \(0.621272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59396.6 | −1.95701 | ||||||||
\(974\) | −16314.8 | − | 3940.83i | −0.536714 | − | 0.129643i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20141.6 | − | 44570.3i | 0.660572 | − | 1.46174i | ||||
\(977\) | −11920.1 | − | 6882.06i | −0.390335 | − | 0.225360i | 0.291970 | − | 0.956427i | \(-0.405689\pi\) |
−0.682305 | + | 0.731068i | \(0.739022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3070.40 | − | 1772.70i | 0.100235 | − | 0.0578710i | ||||
\(980\) | −20002.1 | + | 992.515i | −0.651983 | + | 0.0323518i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41112.0 | + | 39122.6i | 1.33598 | + | 1.27134i | ||||
\(983\) | 3892.24 | + | 6741.57i | 0.126290 | + | 0.218741i | 0.922237 | − | 0.386626i | \(-0.126360\pi\) |
−0.795946 | + | 0.605367i | \(0.793026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7235.40 | + | 12532.1i | −0.234050 | + | 0.405386i | ||||
\(986\) | 371.831 | − | 109.579i | 0.0120096 | − | 0.00353927i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2689.27 | − | 4166.43i | −0.0865962 | − | 0.134162i | ||||
\(989\) | − | 14678.0i | − | 0.471925i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47880.3i | 1.53478i | 0.641179 | + | 0.767391i | \(0.278445\pi\) | ||||
−0.641179 | + | 0.767391i | \(0.721555\pi\) | |||||||
\(992\) | 24712.5 | + | 3428.35i | 0.790950 | + | 0.109728i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 403.523 | + | 1369.26i | 0.0128762 | + | 0.0436923i | ||||
\(995\) | 12256.4 | − | 21228.7i | 0.390506 | − | 0.676376i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1245.57 | − | 2157.40i | −0.0395664 | − | 0.0685310i | 0.845564 | − | 0.533874i | \(-0.179264\pi\) |
−0.885130 | + | 0.465343i | \(0.845931\pi\) | |||||||
\(998\) | −18345.0 | + | 19277.9i | −0.581864 | + | 0.611453i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.4.h.b.71.6 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.23.7 | yes | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.71.1 | 24 | ||
9.2 | odd | 6 | inner | 108.4.h.b.35.1 | 24 | ||
9.4 | even | 3 | 324.4.b.c.323.7 | 24 | |||
9.5 | odd | 6 | 324.4.b.c.323.18 | 24 | |||
9.7 | even | 3 | 36.4.h.b.11.12 | yes | 24 | ||
12.11 | even | 2 | 36.4.h.b.23.12 | yes | 24 | ||
36.7 | odd | 6 | 36.4.h.b.11.7 | ✓ | 24 | ||
36.11 | even | 6 | inner | 108.4.h.b.35.6 | 24 | ||
36.23 | even | 6 | 324.4.b.c.323.8 | 24 | |||
36.31 | odd | 6 | 324.4.b.c.323.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.7 | ✓ | 24 | 36.7 | odd | 6 | ||
36.4.h.b.11.12 | yes | 24 | 9.7 | even | 3 | ||
36.4.h.b.23.7 | yes | 24 | 3.2 | odd | 2 | ||
36.4.h.b.23.12 | yes | 24 | 12.11 | even | 2 | ||
108.4.h.b.35.1 | 24 | 9.2 | odd | 6 | inner | ||
108.4.h.b.35.6 | 24 | 36.11 | even | 6 | inner | ||
108.4.h.b.71.1 | 24 | 4.3 | odd | 2 | inner | ||
108.4.h.b.71.6 | 24 | 1.1 | even | 1 | trivial | ||
324.4.b.c.323.7 | 24 | 9.4 | even | 3 | |||
324.4.b.c.323.8 | 24 | 36.23 | even | 6 | |||
324.4.b.c.323.17 | 24 | 36.31 | odd | 6 | |||
324.4.b.c.323.18 | 24 | 9.5 | odd | 6 |