Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Character | \(\chi\) | \(=\) | 63.47 |
Dual form | 63.4.s.a.59.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.33849 | + | 2.50483i | −1.53389 | + | 0.885590i | −0.534709 | + | 0.845036i | \(0.679579\pi\) |
−0.999177 | + | 0.0405535i | \(0.987088\pi\) | |||||||
\(3\) | −5.18070 | + | 0.400483i | −0.997025 | + | 0.0770730i | ||||
\(4\) | 8.54831 | − | 14.8061i | 1.06854 | − | 1.85076i | ||||
\(5\) | 18.5684 | 1.66080 | 0.830402 | − | 0.557164i | \(-0.188111\pi\) | ||||
0.830402 | + | 0.557164i | \(0.188111\pi\) | |||||||
\(6\) | 21.4732 | − | 14.7142i | 1.46107 | − | 1.00118i | ||||
\(7\) | −17.9322 | − | 4.62983i | −0.968249 | − | 0.249987i | ||||
\(8\) | 45.5709i | 2.01397i | ||||||||
\(9\) | 26.6792 | − | 4.14956i | 0.988120 | − | 0.153687i | ||||
\(10\) | −80.5586 | + | 46.5105i | −2.54749 | + | 1.47079i | ||||
\(11\) | 35.1341i | 0.963029i | 0.876438 | + | 0.481515i | \(0.159913\pi\) | ||||
−0.876438 | + | 0.481515i | \(0.840087\pi\) | |||||||
\(12\) | −38.3566 | + | 80.1294i | −0.922716 | + | 1.92761i | ||||
\(13\) | 3.94292 | − | 2.27645i | 0.0841207 | − | 0.0485671i | −0.457350 | − | 0.889287i | \(-0.651201\pi\) |
0.541470 | + | 0.840720i | \(0.317868\pi\) | |||||||
\(14\) | 89.3956 | − | 24.8307i | 1.70657 | − | 0.474019i | ||||
\(15\) | −96.1970 | + | 7.43631i | −1.65586 | + | 0.128003i | ||||
\(16\) | −45.7606 | − | 79.2597i | −0.715010 | − | 1.23843i | ||||
\(17\) | 20.7867 | + | 36.0037i | 0.296560 | + | 0.513658i | 0.975347 | − | 0.220678i | \(-0.0708271\pi\) |
−0.678786 | + | 0.734336i | \(0.737494\pi\) | |||||||
\(18\) | −105.354 | + | 84.8296i | −1.37956 | + | 1.11081i | ||||
\(19\) | 64.8837 | + | 37.4606i | 0.783439 | + | 0.452319i | 0.837648 | − | 0.546211i | \(-0.183930\pi\) |
−0.0542084 | + | 0.998530i | \(0.517264\pi\) | |||||||
\(20\) | 158.728 | − | 274.925i | 1.77463 | − | 3.07376i | ||||
\(21\) | 94.7556 | + | 16.8042i | 0.984636 | + | 0.174618i | ||||
\(22\) | −88.0048 | − | 152.429i | −0.852849 | − | 1.47718i | ||||
\(23\) | 152.700i | 1.38435i | 0.721728 | + | 0.692176i | \(0.243348\pi\) | ||||
−0.721728 | + | 0.692176i | \(0.756652\pi\) | |||||||
\(24\) | −18.2504 | − | 236.089i | −0.155222 | − | 2.00798i | ||||
\(25\) | 219.784 | 1.75827 | ||||||||
\(26\) | −11.4042 | + | 19.7527i | −0.0860211 | + | 0.148993i | ||||
\(27\) | −136.555 | + | 32.1822i | −0.973335 | + | 0.229388i | ||||
\(28\) | −221.840 | + | 225.929i | −1.49728 | + | 1.52488i | ||||
\(29\) | 42.5645 | + | 24.5746i | 0.272552 | + | 0.157358i | 0.630047 | − | 0.776557i | \(-0.283036\pi\) |
−0.357495 | + | 0.933915i | \(0.616369\pi\) | |||||||
\(30\) | 398.723 | − | 273.219i | 2.42655 | − | 1.66276i | ||||
\(31\) | 87.6525 | + | 50.6062i | 0.507834 | + | 0.293198i | 0.731943 | − | 0.681366i | \(-0.238614\pi\) |
−0.224109 | + | 0.974564i | \(0.571947\pi\) | |||||||
\(32\) | 81.3395 | + | 46.9614i | 0.449342 | + | 0.259428i | ||||
\(33\) | −14.0706 | − | 182.019i | −0.0742236 | − | 0.960165i | ||||
\(34\) | −180.366 | − | 104.134i | −0.909780 | − | 0.525262i | ||||
\(35\) | −332.972 | − | 85.9684i | −1.60807 | − | 0.415180i | ||||
\(36\) | 166.623 | − | 430.487i | 0.771404 | − | 1.99300i | ||||
\(37\) | 2.86552 | − | 4.96323i | 0.0127321 | − | 0.0220527i | −0.859589 | − | 0.510986i | \(-0.829280\pi\) |
0.872321 | + | 0.488933i | \(0.162614\pi\) | |||||||
\(38\) | −375.330 | −1.60228 | ||||||||
\(39\) | −19.5154 | + | 13.3727i | −0.0801273 | + | 0.0549061i | ||||
\(40\) | 846.176i | 3.34481i | ||||||||
\(41\) | −6.35071 | − | 10.9998i | −0.0241906 | − | 0.0418993i | 0.853677 | − | 0.520803i | \(-0.174368\pi\) |
−0.877867 | + | 0.478904i | \(0.841034\pi\) | |||||||
\(42\) | −453.187 | + | 164.442i | −1.66496 | + | 0.604140i | ||||
\(43\) | 69.1907 | − | 119.842i | 0.245383 | − | 0.425016i | −0.716856 | − | 0.697221i | \(-0.754420\pi\) |
0.962239 | + | 0.272205i | \(0.0877528\pi\) | |||||||
\(44\) | 520.199 | + | 300.337i | 1.78234 | + | 1.02903i | ||||
\(45\) | 495.390 | − | 77.0506i | 1.64107 | − | 0.255245i | ||||
\(46\) | −382.486 | − | 662.486i | −1.22597 | − | 2.12344i | ||||
\(47\) | 269.089 | + | 466.076i | 0.835121 | + | 1.44647i | 0.893932 | + | 0.448203i | \(0.147936\pi\) |
−0.0588112 | + | 0.998269i | \(0.518731\pi\) | |||||||
\(48\) | 268.814 | + | 392.294i | 0.808333 | + | 1.17964i | ||||
\(49\) | 300.129 | + | 166.046i | 0.875013 | + | 0.484100i | ||||
\(50\) | −953.530 | + | 550.521i | −2.69699 | + | 1.55711i | ||||
\(51\) | −122.109 | − | 178.199i | −0.335267 | − | 0.489273i | ||||
\(52\) | − | 77.8390i | − | 0.207583i | ||||||
\(53\) | 105.466 | − | 60.8907i | 0.273337 | − | 0.157811i | −0.357066 | − | 0.934079i | \(-0.616223\pi\) |
0.630403 | + | 0.776268i | \(0.282890\pi\) | |||||||
\(54\) | 511.832 | − | 481.669i | 1.28984 | − | 1.21383i | ||||
\(55\) | 652.382i | 1.59940i | ||||||||
\(56\) | 210.985 | − | 817.187i | 0.503466 | − | 1.95002i | ||||
\(57\) | −351.145 | − | 168.087i | −0.815971 | − | 0.390591i | ||||
\(58\) | −246.220 | −0.557419 | ||||||||
\(59\) | 156.280 | − | 270.684i | 0.344845 | − | 0.597290i | −0.640480 | − | 0.767975i | \(-0.721265\pi\) |
0.985326 | + | 0.170685i | \(0.0545980\pi\) | |||||||
\(60\) | −712.219 | + | 1487.87i | −1.53245 | + | 3.20139i | ||||
\(61\) | −436.557 | + | 252.047i | −0.916319 | + | 0.529037i | −0.882459 | − | 0.470390i | \(-0.844113\pi\) |
−0.0338600 | + | 0.999427i | \(0.510780\pi\) | |||||||
\(62\) | −507.039 | −1.03861 | ||||||||
\(63\) | −497.630 | − | 49.1094i | −0.995166 | − | 0.0982095i | ||||
\(64\) | 261.650 | 0.511034 | ||||||||
\(65\) | 73.2136 | − | 42.2699i | 0.139708 | − | 0.0806605i | ||||
\(66\) | 516.971 | + | 754.442i | 0.964163 | + | 1.40705i | ||||
\(67\) | 327.373 | − | 567.026i | 0.596939 | − | 1.03393i | −0.396331 | − | 0.918108i | \(-0.629717\pi\) |
0.993270 | − | 0.115821i | \(-0.0369500\pi\) | |||||||
\(68\) | 710.766 | 1.26754 | ||||||||
\(69\) | −61.1537 | − | 791.091i | −0.106696 | − | 1.38023i | ||||
\(70\) | 1659.93 | − | 461.065i | 2.83428 | − | 0.787254i | ||||
\(71\) | − | 891.951i | − | 1.49092i | −0.666552 | − | 0.745459i | \(-0.732230\pi\) | ||
0.666552 | − | 0.745459i | \(-0.267770\pi\) | |||||||
\(72\) | 189.099 | + | 1215.80i | 0.309521 | + | 1.99004i | ||||
\(73\) | −315.436 | + | 182.117i | −0.505740 | + | 0.291989i | −0.731081 | − | 0.682291i | \(-0.760984\pi\) |
0.225341 | + | 0.974280i | \(0.427650\pi\) | |||||||
\(74\) | 28.7105i | 0.0451018i | ||||||||
\(75\) | −1138.63 | + | 88.0198i | −1.75304 | + | 0.135515i | ||||
\(76\) | 1109.29 | − | 640.450i | 1.67427 | − | 0.966640i | ||||
\(77\) | 162.665 | − | 630.032i | 0.240745 | − | 0.932452i | ||||
\(78\) | 51.1711 | − | 106.900i | 0.0742819 | − | 0.155180i | ||||
\(79\) | −242.587 | − | 420.173i | −0.345483 | − | 0.598394i | 0.639958 | − | 0.768410i | \(-0.278952\pi\) |
−0.985441 | + | 0.170016i | \(0.945618\pi\) | |||||||
\(80\) | −849.700 | − | 1471.72i | −1.18749 | − | 2.05680i | ||||
\(81\) | 694.562 | − | 221.414i | 0.952760 | − | 0.303723i | ||||
\(82\) | 55.1049 | + | 31.8149i | 0.0742113 | + | 0.0428459i | ||||
\(83\) | −248.712 | + | 430.783i | −0.328912 | + | 0.569693i | −0.982296 | − | 0.187334i | \(-0.940015\pi\) |
0.653384 | + | 0.757027i | \(0.273349\pi\) | |||||||
\(84\) | 1058.80 | − | 1259.31i | 1.37530 | − | 1.63574i | ||||
\(85\) | 385.976 | + | 668.530i | 0.492529 | + | 0.853085i | ||||
\(86\) | 693.243i | 0.869236i | ||||||||
\(87\) | −230.355 | − | 110.267i | −0.283870 | − | 0.135884i | ||||
\(88\) | −1601.09 | −1.93951 | ||||||||
\(89\) | −685.285 | + | 1186.95i | −0.816181 | + | 1.41367i | 0.0922965 | + | 0.995732i | \(0.470579\pi\) |
−0.908477 | + | 0.417935i | \(0.862754\pi\) | |||||||
\(90\) | −1956.24 | + | 1575.15i | −2.29118 | + | 1.84483i | ||||
\(91\) | −81.2449 | + | 22.5667i | −0.0935910 | + | 0.0259960i | ||||
\(92\) | 2260.89 | + | 1305.32i | 2.56211 | + | 1.47923i | ||||
\(93\) | −474.368 | − | 227.072i | −0.528921 | − | 0.253186i | ||||
\(94\) | −2334.88 | − | 1348.04i | −2.56196 | − | 1.47915i | ||||
\(95\) | 1204.78 | + | 695.583i | 1.30114 | + | 0.751213i | ||||
\(96\) | −440.203 | − | 210.718i | −0.468000 | − | 0.224024i | ||||
\(97\) | −205.065 | − | 118.394i | −0.214652 | − | 0.123929i | 0.388820 | − | 0.921314i | \(-0.372883\pi\) |
−0.603471 | + | 0.797385i | \(0.706216\pi\) | |||||||
\(98\) | −1718.02 | + | 31.3824i | −1.77088 | + | 0.0323480i | ||||
\(99\) | 145.791 | + | 937.350i | 0.148006 | + | 0.951588i | ||||
\(100\) | 1878.78 | − | 3254.15i | 1.87878 | − | 3.25415i | ||||
\(101\) | −354.109 | −0.348863 | −0.174431 | − | 0.984669i | \(-0.555809\pi\) | ||||
−0.174431 | + | 0.984669i | \(0.555809\pi\) | |||||||
\(102\) | 976.125 | + | 467.255i | 0.947557 | + | 0.453580i | ||||
\(103\) | − | 1257.38i | − | 1.20285i | −0.798929 | − | 0.601426i | \(-0.794600\pi\) | ||
0.798929 | − | 0.601426i | \(-0.205400\pi\) | |||||||
\(104\) | 103.740 | + | 179.682i | 0.0978126 | + | 0.169416i | ||||
\(105\) | 1759.46 | + | 312.026i | 1.63529 | + | 0.290006i | ||||
\(106\) | −305.041 | + | 528.347i | −0.279512 | + | 0.484128i | ||||
\(107\) | −182.056 | − | 105.110i | −0.164487 | − | 0.0949663i | 0.415497 | − | 0.909595i | \(-0.363608\pi\) |
−0.579984 | + | 0.814628i | \(0.696941\pi\) | |||||||
\(108\) | −690.822 | + | 2296.95i | −0.615504 | + | 2.04652i | ||||
\(109\) | 78.9687 | + | 136.778i | 0.0693929 | + | 0.120192i | 0.898634 | − | 0.438699i | \(-0.144560\pi\) |
−0.829241 | + | 0.558891i | \(0.811227\pi\) | |||||||
\(110\) | −1634.10 | − | 2830.35i | −1.41642 | − | 2.45330i | ||||
\(111\) | −12.8577 | + | 26.8606i | −0.0109946 | + | 0.0229684i | ||||
\(112\) | 453.631 | + | 1633.17i | 0.382715 | + | 1.37786i | ||||
\(113\) | −385.384 | + | 222.502i | −0.320831 | + | 0.185232i | −0.651763 | − | 0.758423i | \(-0.725970\pi\) |
0.330932 | + | 0.943655i | \(0.392637\pi\) | |||||||
\(114\) | 1944.47 | − | 150.313i | 1.59751 | − | 0.123492i | ||||
\(115\) | 2835.39i | 2.29914i | ||||||||
\(116\) | 727.708 | − | 420.142i | 0.582465 | − | 0.336287i | ||||
\(117\) | 95.7478 | − | 77.0952i | 0.0756572 | − | 0.0609184i | ||||
\(118\) | 1565.81i | 1.22157i | ||||||||
\(119\) | −206.062 | − | 741.865i | −0.158736 | − | 0.571485i | ||||
\(120\) | −338.879 | − | 4383.78i | −0.257794 | − | 3.33486i | ||||
\(121\) | 96.5964 | 0.0725743 | ||||||||
\(122\) | 1262.67 | − | 2187.00i | 0.937019 | − | 1.62296i | ||||
\(123\) | 37.3063 | + | 54.4430i | 0.0273479 | + | 0.0399103i | ||||
\(124\) | 1498.56 | − | 865.194i | 1.08528 | − | 0.626587i | ||||
\(125\) | 1759.99 | 1.25934 | ||||||||
\(126\) | 2281.97 | − | 1033.42i | 1.61344 | − | 0.730666i | ||||
\(127\) | 2066.68 | 1.44400 | 0.722002 | − | 0.691891i | \(-0.243222\pi\) | ||||
0.722002 | + | 0.691891i | \(0.243222\pi\) | |||||||
\(128\) | −1785.88 | + | 1031.08i | −1.23321 | + | 0.711994i | ||||
\(129\) | −310.461 | + | 648.574i | −0.211896 | + | 0.442665i | ||||
\(130\) | −211.757 | + | 366.775i | −0.142864 | + | 0.247448i | ||||
\(131\) | −163.509 | −0.109052 | −0.0545260 | − | 0.998512i | \(-0.517365\pi\) | ||||
−0.0545260 | + | 0.998512i | \(0.517365\pi\) | |||||||
\(132\) | −2815.27 | − | 1347.62i | −1.85635 | − | 0.888603i | ||||
\(133\) | −990.073 | − | 972.153i | −0.645491 | − | 0.633807i | ||||
\(134\) | 3280.05i | 2.11457i | ||||||||
\(135\) | −2535.61 | + | 597.571i | −1.61652 | + | 0.380968i | ||||
\(136\) | −1640.72 | + | 947.270i | −1.03449 | + | 0.597263i | ||||
\(137\) | − | 2624.69i | − | 1.63680i | −0.574646 | − | 0.818402i | \(-0.694860\pi\) | ||
0.574646 | − | 0.818402i | \(-0.305140\pi\) | |||||||
\(138\) | 2246.86 | + | 3278.96i | 1.38598 | + | 2.02263i | ||||
\(139\) | −1161.11 | + | 670.366i | −0.708518 | + | 0.409063i | −0.810512 | − | 0.585722i | \(-0.800811\pi\) |
0.101994 | + | 0.994785i | \(0.467478\pi\) | |||||||
\(140\) | −4119.20 | + | 4195.13i | −2.48669 | + | 2.53253i | ||||
\(141\) | −1580.72 | − | 2306.83i | −0.944121 | − | 1.37780i | ||||
\(142\) | 2234.18 | + | 3869.72i | 1.32034 | + | 2.28690i | ||||
\(143\) | 79.9809 | + | 138.531i | 0.0467716 | + | 0.0810107i | ||||
\(144\) | −1549.75 | − | 1924.70i | −0.896847 | − | 1.11383i | ||||
\(145\) | 790.352 | + | 456.310i | 0.452656 | + | 0.261341i | ||||
\(146\) | 912.343 | − | 1580.22i | 0.517165 | − | 0.895756i | ||||
\(147\) | −1621.38 | − | 740.039i | −0.909721 | − | 0.415220i | ||||
\(148\) | −48.9907 | − | 84.8544i | −0.0272095 | − | 0.0471283i | ||||
\(149\) | 745.154i | 0.409701i | 0.978793 | + | 0.204850i | \(0.0656708\pi\) | ||||
−0.978793 | + | 0.204850i | \(0.934329\pi\) | |||||||
\(150\) | 4719.48 | − | 3233.95i | 2.56896 | − | 1.76034i | ||||
\(151\) | −3412.14 | −1.83891 | −0.919457 | − | 0.393190i | \(-0.871371\pi\) | ||||
−0.919457 | + | 0.393190i | \(0.871371\pi\) | |||||||
\(152\) | −1707.11 | + | 2956.81i | −0.910955 | + | 1.57782i | ||||
\(153\) | 703.974 | + | 874.295i | 0.371980 | + | 0.461977i | ||||
\(154\) | 872.402 | + | 3140.83i | 0.456495 | + | 1.64348i | ||||
\(155\) | 1627.56 | + | 939.674i | 0.843413 | + | 0.486945i | ||||
\(156\) | 31.1732 | + | 403.260i | 0.0159991 | + | 0.206966i | ||||
\(157\) | 2006.44 | + | 1158.42i | 1.01994 | + | 0.588865i | 0.914088 | − | 0.405516i | \(-0.132908\pi\) |
0.105857 | + | 0.994381i | \(0.466242\pi\) | |||||||
\(158\) | 2104.92 | + | 1215.28i | 1.05986 | + | 0.611912i | ||||
\(159\) | −522.001 | + | 357.694i | −0.260361 | + | 0.178408i | ||||
\(160\) | 1510.34 | + | 871.996i | 0.746269 | + | 0.430858i | ||||
\(161\) | 706.974 | − | 2738.25i | 0.346071 | − | 1.34040i | ||||
\(162\) | −2458.74 | + | 2700.36i | −1.19245 | + | 1.30963i | ||||
\(163\) | 730.165 | − | 1264.68i | 0.350865 | − | 0.607716i | −0.635536 | − | 0.772071i | \(-0.719221\pi\) |
0.986401 | + | 0.164355i | \(0.0525544\pi\) | |||||||
\(164\) | −217.151 | −0.103394 | ||||||||
\(165\) | −261.268 | − | 3379.79i | −0.123271 | − | 1.59465i | ||||
\(166\) | − | 2491.93i | − | 1.16513i | ||||||
\(167\) | −1047.84 | − | 1814.91i | −0.485534 | − | 0.840969i | 0.514328 | − | 0.857594i | \(-0.328041\pi\) |
−0.999862 | + | 0.0166244i | \(0.994708\pi\) | |||||||
\(168\) | −765.781 | + | 4318.09i | −0.351674 | + | 1.98302i | ||||
\(169\) | −1088.14 | + | 1884.71i | −0.495282 | + | 0.857854i | ||||
\(170\) | −3349.10 | − | 1933.60i | −1.51097 | − | 0.872357i | ||||
\(171\) | 1886.49 | + | 730.182i | 0.843647 | + | 0.326540i | ||||
\(172\) | −1182.93 | − | 2048.89i | −0.524403 | − | 0.908293i | ||||
\(173\) | 1387.37 | + | 2402.99i | 0.609708 | + | 1.05604i | 0.991288 | + | 0.131709i | \(0.0420465\pi\) |
−0.381581 | + | 0.924336i | \(0.624620\pi\) | |||||||
\(174\) | 1275.59 | − | 98.6071i | 0.555761 | − | 0.0429620i | ||||
\(175\) | −3941.22 | − | 1017.56i | −1.70245 | − | 0.439546i | ||||
\(176\) | 2784.72 | − | 1607.76i | 1.19265 | − | 0.688576i | ||||
\(177\) | −701.233 | + | 1464.92i | −0.297785 | + | 0.622091i | ||||
\(178\) | − | 6866.08i | − | 2.89120i | ||||||
\(179\) | 63.6106 | − | 36.7256i | 0.0265614 | − | 0.0153352i | −0.486661 | − | 0.873591i | \(-0.661785\pi\) |
0.513222 | + | 0.858256i | \(0.328452\pi\) | |||||||
\(180\) | 3093.92 | − | 7993.44i | 1.28115 | − | 3.30998i | ||||
\(181\) | − | 2260.38i | − | 0.928247i | −0.885771 | − | 0.464123i | \(-0.846369\pi\) | ||
0.885771 | − | 0.464123i | \(-0.153631\pi\) | |||||||
\(182\) | 295.954 | − | 301.410i | 0.120536 | − | 0.122758i | ||||
\(183\) | 2160.73 | − | 1480.61i | 0.872819 | − | 0.598087i | ||||
\(184\) | −6958.66 | −2.78804 | ||||||||
\(185\) | 53.2080 | − | 92.1590i | 0.0211456 | − | 0.0366252i | ||||
\(186\) | 2626.81 | − | 203.060i | 1.03552 | − | 0.0800490i | ||||
\(187\) | −1264.96 | + | 730.323i | −0.494667 | + | 0.285596i | ||||
\(188\) | 9201.02 | 3.56943 | ||||||||
\(189\) | 2597.74 | + | 55.1286i | 0.999775 | + | 0.0212170i | ||||
\(190\) | −6969.25 | −2.66107 | ||||||||
\(191\) | 3258.23 | − | 1881.14i | 1.23433 | − | 0.712641i | 0.266401 | − | 0.963862i | \(-0.414165\pi\) |
0.967930 | + | 0.251221i | \(0.0808321\pi\) | |||||||
\(192\) | −1355.53 | + | 104.786i | −0.509514 | + | 0.0393870i | ||||
\(193\) | 70.9018 | − | 122.805i | 0.0264436 | − | 0.0458017i | −0.852501 | − | 0.522726i | \(-0.824915\pi\) |
0.878944 | + | 0.476924i | \(0.158248\pi\) | |||||||
\(194\) | 1186.23 | 0.439002 | ||||||||
\(195\) | −362.369 | + | 248.308i | −0.133076 | + | 0.0911883i | ||||
\(196\) | 5024.10 | − | 3024.33i | 1.83094 | − | 1.10216i | ||||
\(197\) | − | 3470.68i | − | 1.25521i | −0.778533 | − | 0.627603i | \(-0.784036\pi\) | ||
0.778533 | − | 0.627603i | \(-0.215964\pi\) | |||||||
\(198\) | −2980.41 | − | 3701.50i | −1.06974 | − | 1.32856i | ||||
\(199\) | −58.1115 | + | 33.5507i | −0.0207006 | + | 0.0119515i | −0.510315 | − | 0.859988i | \(-0.670471\pi\) |
0.489614 | + | 0.871939i | \(0.337138\pi\) | |||||||
\(200\) | 10015.8i | 3.54110i | ||||||||
\(201\) | −1468.93 | + | 3068.70i | −0.515476 | + | 1.07686i | ||||
\(202\) | 1536.30 | − | 886.980i | 0.535116 | − | 0.308949i | ||||
\(203\) | −649.499 | − | 637.743i | −0.224561 | − | 0.220497i | ||||
\(204\) | −3682.26 | + | 284.650i | −1.26377 | + | 0.0976934i | ||||
\(205\) | −117.922 | − | 204.247i | −0.0401759 | − | 0.0695866i | ||||
\(206\) | 3149.53 | + | 5455.14i | 1.06523 | + | 1.84504i | ||||
\(207\) | 633.637 | + | 4073.91i | 0.212758 | + | 1.36791i | ||||
\(208\) | −360.861 | − | 208.343i | −0.120294 | − | 0.0694520i | ||||
\(209\) | −1316.15 | + | 2279.63i | −0.435596 | + | 0.754475i | ||||
\(210\) | −8414.95 | + | 3053.41i | −2.76517 | + | 1.00336i | ||||
\(211\) | −820.718 | − | 1421.53i | −0.267775 | − | 0.463800i | 0.700512 | − | 0.713641i | \(-0.252955\pi\) |
−0.968287 | + | 0.249841i | \(0.919622\pi\) | |||||||
\(212\) | − | 2082.05i | − | 0.674508i | ||||||
\(213\) | 357.211 | + | 4620.93i | 0.114909 | + | 1.48648i | ||||
\(214\) | 1053.13 | 0.336405 | ||||||||
\(215\) | 1284.76 | − | 2225.27i | 0.407534 | − | 0.705869i | ||||
\(216\) | −1466.57 | − | 6222.94i | −0.461979 | − | 1.96026i | ||||
\(217\) | −1337.51 | − | 1313.30i | −0.418414 | − | 0.410841i | ||||
\(218\) | −685.209 | − | 395.606i | −0.212882 | − | 0.122907i | ||||
\(219\) | 1561.24 | − | 1069.82i | 0.481731 | − | 0.330099i | ||||
\(220\) | 9659.24 | + | 5576.76i | 2.96012 | + | 1.70902i | ||||
\(221\) | 163.921 | + | 94.6398i | 0.0498937 | + | 0.0288062i | ||||
\(222\) | −11.4981 | − | 148.741i | −0.00347613 | − | 0.0449676i | ||||
\(223\) | 2975.62 | + | 1717.98i | 0.893554 | + | 0.515894i | 0.875103 | − | 0.483936i | \(-0.160793\pi\) |
0.0184507 | + | 0.999830i | \(0.494127\pi\) | |||||||
\(224\) | −1241.18 | − | 1218.71i | −0.370221 | − | 0.363520i | ||||
\(225\) | 5863.67 | − | 912.008i | 1.73738 | − | 0.270225i | ||||
\(226\) | 1114.66 | − | 1930.64i | 0.328079 | − | 0.568249i | ||||
\(227\) | −3886.11 | −1.13626 | −0.568129 | − | 0.822940i | \(-0.692332\pi\) | ||||
−0.568129 | + | 0.822940i | \(0.692332\pi\) | |||||||
\(228\) | −5490.42 | + | 3762.23i | −1.59479 | + | 1.09281i | ||||
\(229\) | − | 2280.90i | − | 0.658193i | −0.944296 | − | 0.329097i | \(-0.893256\pi\) | ||
0.944296 | − | 0.329097i | \(-0.106744\pi\) | |||||||
\(230\) | −7102.15 | − | 12301.3i | −2.03609 | − | 3.52662i | ||||
\(231\) | −590.400 | + | 3329.15i | −0.168162 | + | 0.948234i | ||||
\(232\) | −1119.89 | + | 1939.70i | −0.316914 | + | 0.548912i | ||||
\(233\) | 691.417 | + | 399.190i | 0.194404 | + | 0.112239i | 0.594043 | − | 0.804433i | \(-0.297531\pi\) |
−0.399638 | + | 0.916673i | \(0.630864\pi\) | |||||||
\(234\) | −222.290 | + | 574.308i | −0.0621008 | + | 0.160443i | ||||
\(235\) | 4996.54 | + | 8654.27i | 1.38697 | + | 2.40231i | ||||
\(236\) | −2671.85 | − | 4627.79i | −0.736961 | − | 1.27645i | ||||
\(237\) | 1425.04 | + | 2079.64i | 0.390575 | + | 0.569987i | ||||
\(238\) | 2752.24 | + | 2702.42i | 0.749585 | + | 0.736017i | ||||
\(239\) | −4557.37 | + | 2631.20i | −1.23344 | + | 0.712127i | −0.967745 | − | 0.251931i | \(-0.918934\pi\) |
−0.265694 | + | 0.964057i | \(0.585601\pi\) | |||||||
\(240\) | 4991.44 | + | 7284.26i | 1.34248 | + | 1.95915i | ||||
\(241\) | − | 3951.47i | − | 1.05617i | −0.849192 | − | 0.528084i | \(-0.822910\pi\) | ||
0.849192 | − | 0.528084i | \(-0.177090\pi\) | |||||||
\(242\) | −419.082 | + | 241.957i | −0.111321 | + | 0.0642710i | ||||
\(243\) | −3509.64 | + | 1425.24i | −0.926517 | + | 0.376252i | ||||
\(244\) | 8618.28i | 2.26118i | ||||||||
\(245\) | 5572.91 | + | 3083.21i | 1.45323 | + | 0.803996i | ||||
\(246\) | −298.223 | − | 142.754i | −0.0772928 | − | 0.0369988i | ||||
\(247\) | 341.109 | 0.0878713 | ||||||||
\(248\) | −2306.17 | + | 3994.40i | −0.590491 | + | 1.02276i | ||||
\(249\) | 1115.98 | − | 2331.36i | 0.284026 | − | 0.593349i | ||||
\(250\) | −7635.67 | + | 4408.46i | −1.93169 | + | 1.11526i | ||||
\(251\) | −5548.60 | −1.39532 | −0.697658 | − | 0.716431i | \(-0.745775\pi\) | ||||
−0.697658 | + | 0.716431i | \(0.745775\pi\) | |||||||
\(252\) | −4981.01 | + | 6948.15i | −1.24514 | + | 1.73687i | ||||
\(253\) | −5364.97 | −1.33317 | ||||||||
\(254\) | −8966.27 | + | 5176.68i | −2.21494 | + | 1.27879i | ||||
\(255\) | −2267.36 | − | 3308.87i | −0.556814 | − | 0.812587i | ||||
\(256\) | 4118.74 | − | 7133.87i | 1.00555 | − | 1.74167i | ||||
\(257\) | 2783.15 | 0.675518 | 0.337759 | − | 0.941233i | \(-0.390331\pi\) | ||||
0.337759 | + | 0.941233i | \(0.390331\pi\) | |||||||
\(258\) | −277.632 | − | 3591.48i | −0.0669946 | − | 0.866650i | ||||
\(259\) | −74.3641 | + | 75.7348i | −0.0178408 | + | 0.0181696i | ||||
\(260\) | − | 1445.34i | − | 0.344755i | ||||||
\(261\) | 1237.56 | + | 479.007i | 0.293498 | + | 0.113601i | ||||
\(262\) | 709.379 | − | 409.560i | 0.167273 | − | 0.0965753i | ||||
\(263\) | − | 5999.20i | − | 1.40657i | −0.710910 | − | 0.703283i | \(-0.751717\pi\) | ||
0.710910 | − | 0.703283i | \(-0.248283\pi\) | |||||||
\(264\) | 8294.76 | − | 641.210i | 1.93374 | − | 0.149484i | ||||
\(265\) | 1958.33 | − | 1130.64i | 0.453959 | − | 0.262093i | ||||
\(266\) | 6730.49 | + | 1737.71i | 1.55140 | + | 0.400549i | ||||
\(267\) | 3074.90 | − | 6423.66i | 0.704797 | − | 1.47237i | ||||
\(268\) | −5596.96 | − | 9694.23i | −1.27571 | − | 2.20959i | ||||
\(269\) | 1352.02 | + | 2341.76i | 0.306445 | + | 0.530779i | 0.977582 | − | 0.210555i | \(-0.0675269\pi\) |
−0.671137 | + | 0.741334i | \(0.734194\pi\) | |||||||
\(270\) | 9503.88 | − | 8943.80i | 2.14218 | − | 2.01594i | ||||
\(271\) | 1538.06 | + | 887.999i | 0.344762 | + | 0.199048i | 0.662376 | − | 0.749172i | \(-0.269548\pi\) |
−0.317614 | + | 0.948220i | \(0.602882\pi\) | |||||||
\(272\) | 1902.43 | − | 3295.10i | 0.424087 | − | 0.734541i | ||||
\(273\) | 411.868 | − | 149.448i | 0.0913090 | − | 0.0331320i | ||||
\(274\) | 6574.38 | + | 11387.2i | 1.44954 | + | 2.51067i | ||||
\(275\) | 7721.91i | 1.69327i | ||||||||
\(276\) | −12235.7 | − | 5857.04i | −2.66850 | − | 1.27736i | ||||
\(277\) | −873.158 | −0.189397 | −0.0946985 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0946985 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(278\) | 3358.30 | − | 5816.75i | 0.724524 | − | 1.25491i | ||||
\(279\) | 2548.49 | + | 986.415i | 0.546862 | + | 0.211667i | ||||
\(280\) | 3917.65 | − | 15173.8i | 0.836159 | − | 3.23861i | ||||
\(281\) | 1562.82 | + | 902.296i | 0.331780 | + | 0.191553i | 0.656631 | − | 0.754212i | \(-0.271981\pi\) |
−0.324851 | + | 0.945765i | \(0.605314\pi\) | |||||||
\(282\) | 12636.2 | + | 6048.72i | 2.66834 | + | 1.27729i | ||||
\(283\) | 5223.93 | + | 3016.04i | 1.09728 | + | 0.633515i | 0.935505 | − | 0.353313i | \(-0.114945\pi\) |
0.161775 | + | 0.986828i | \(0.448278\pi\) | |||||||
\(284\) | −13206.3 | − | 7624.67i | −2.75933 | − | 1.59310i | ||||
\(285\) | −6520.19 | − | 3121.11i | −1.35517 | − | 0.648696i | ||||
\(286\) | −693.992 | − | 400.676i | −0.143485 | − | 0.0828409i | ||||
\(287\) | 62.9554 | + | 226.653i | 0.0129482 | + | 0.0466163i | ||||
\(288\) | 2364.94 | + | 915.370i | 0.483874 | + | 0.187287i | ||||
\(289\) | 1592.32 | − | 2757.98i | 0.324104 | − | 0.561364i | ||||
\(290\) | −4571.91 | −0.925765 | ||||||||
\(291\) | 1109.80 | + | 531.241i | 0.223565 | + | 0.107017i | ||||
\(292\) | 6227.17i | 1.24801i | ||||||||
\(293\) | 4576.92 | + | 7927.46i | 0.912583 | + | 1.58064i | 0.810402 | + | 0.585874i | \(0.199249\pi\) |
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(294\) | 8887.99 | − | 850.622i | 1.76312 | − | 0.168739i | ||||
\(295\) | 2901.86 | − | 5026.17i | 0.572721 | − | 0.991982i | ||||
\(296\) | 226.179 | + | 130.584i | 0.0444134 | + | 0.0256421i | ||||
\(297\) | −1130.69 | − | 4797.74i | −0.220907 | − | 0.937350i | ||||
\(298\) | −1866.48 | − | 3232.84i | −0.362827 | − | 0.628434i | ||||
\(299\) | 347.613 | + | 602.083i | 0.0672340 | + | 0.116453i | ||||
\(300\) | −8430.17 | + | 17611.2i | −1.62239 | + | 3.38927i | ||||
\(301\) | −1795.59 | + | 1828.69i | −0.343841 | + | 0.350179i | ||||
\(302\) | 14803.5 | − | 8546.82i | 2.82069 | − | 1.62852i | ||||
\(303\) | 1834.53 | − | 141.814i | 0.347825 | − | 0.0268879i | ||||
\(304\) | − | 6856.89i | − | 1.29365i | ||||||
\(305\) | −8106.16 | + | 4680.09i | −1.52183 | + | 0.878627i | ||||
\(306\) | −5244.14 | − | 2029.78i | −0.979697 | − | 0.379199i | ||||
\(307\) | 3205.89i | 0.595993i | 0.954567 | + | 0.297997i | \(0.0963184\pi\) | ||||
−0.954567 | + | 0.297997i | \(0.903682\pi\) | |||||||
\(308\) | −7937.81 | − | 7794.14i | −1.46850 | − | 1.44192i | ||||
\(309\) | 503.561 | + | 6514.12i | 0.0927073 | + | 1.19927i | ||||
\(310\) | −9414.88 | −1.72493 | ||||||||
\(311\) | −2.43583 | + | 4.21898i | −0.000444126 | + | 0.000769249i | −0.866247 | − | 0.499615i | \(-0.833475\pi\) |
0.865803 | + | 0.500385i | \(0.166808\pi\) | |||||||
\(312\) | −609.403 | − | 889.334i | −0.110579 | − | 0.161374i | ||||
\(313\) | 1663.20 | − | 960.246i | 0.300349 | − | 0.173407i | −0.342250 | − | 0.939609i | \(-0.611189\pi\) |
0.642600 | + | 0.766202i | \(0.277856\pi\) | |||||||
\(314\) | −11606.5 | −2.08597 | ||||||||
\(315\) | −9240.17 | − | 911.881i | −1.65278 | − | 0.163107i | ||||
\(316\) | −8294.83 | −1.47665 | ||||||||
\(317\) | −8798.23 | + | 5079.66i | −1.55886 | + | 0.900007i | −0.561491 | + | 0.827483i | \(0.689772\pi\) |
−0.997367 | + | 0.0725240i | \(0.976895\pi\) | |||||||
\(318\) | 1368.73 | − | 2859.37i | 0.241367 | − | 0.504231i | ||||
\(319\) | −863.406 | + | 1495.46i | −0.151541 | + | 0.262476i | ||||
\(320\) | 4858.41 | 0.848729 | ||||||||
\(321\) | 985.274 | + | 471.634i | 0.171317 | + | 0.0820064i | ||||
\(322\) | 3791.64 | + | 13650.7i | 0.656210 | + | 2.36250i | ||||
\(323\) | 3114.74i | 0.536559i | ||||||||
\(324\) | 2659.05 | − | 12176.5i | 0.455941 | − | 2.08787i | ||||
\(325\) | 866.591 | − | 500.327i | 0.147907 | − | 0.0853943i | ||||
\(326\) | 7315.75i | 1.24289i | ||||||||
\(327\) | −463.890 | − | 676.978i | −0.0784501 | − | 0.114486i | ||||
\(328\) | 501.268 | − | 289.407i | 0.0843839 | − | 0.0487191i | ||||
\(329\) | −2667.51 | − | 9603.62i | −0.447005 | − | 1.60931i | ||||
\(330\) | 9599.31 | + | 14008.8i | 1.60129 | + | 2.33684i | ||||
\(331\) | 5754.15 | + | 9966.49i | 0.955519 | + | 1.65501i | 0.733175 | + | 0.680040i | \(0.238038\pi\) |
0.222344 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(332\) | 4252.14 | + | 7364.92i | 0.702911 | + | 1.21748i | ||||
\(333\) | 55.8547 | − | 144.306i | 0.00919164 | − | 0.0237475i | ||||
\(334\) | 9092.06 | + | 5249.30i | 1.48951 | + | 0.859967i | ||||
\(335\) | 6078.77 | − | 10528.7i | 0.991400 | − | 1.71715i | ||||
\(336\) | −3004.18 | − | 8279.27i | −0.487772 | − | 1.34426i | ||||
\(337\) | −4193.55 | − | 7263.44i | −0.677855 | − | 1.17408i | −0.975625 | − | 0.219442i | \(-0.929576\pi\) |
0.297770 | − | 0.954638i | \(-0.403757\pi\) | |||||||
\(338\) | − | 10902.4i | − | 1.75447i | ||||||
\(339\) | 1907.45 | − | 1307.05i | 0.305600 | − | 0.209408i | ||||
\(340\) | 13197.8 | 2.10514 | ||||||||
\(341\) | −1778.00 | + | 3079.59i | −0.282358 | + | 0.489059i | ||||
\(342\) | −10013.5 | + | 1557.45i | −1.58324 | + | 0.246250i | ||||
\(343\) | −4613.22 | − | 4367.13i | −0.726211 | − | 0.687471i | ||||
\(344\) | 5461.30 | + | 3153.08i | 0.855969 | + | 0.494194i | ||||
\(345\) | −1135.52 | − | 14689.3i | −0.177202 | − | 2.29230i | ||||
\(346\) | −12038.1 | − | 6950.22i | −1.87044 | − | 1.07990i | ||||
\(347\) | −10783.9 | − | 6226.07i | −1.66832 | − | 0.963207i | −0.968542 | − | 0.248849i | \(-0.919948\pi\) |
−0.699781 | − | 0.714358i | \(-0.746719\pi\) | |||||||
\(348\) | −3601.77 | + | 2468.06i | −0.554814 | + | 0.380179i | ||||
\(349\) | 1881.46 | + | 1086.26i | 0.288574 | + | 0.166608i | 0.637298 | − | 0.770617i | \(-0.280052\pi\) |
−0.348725 | + | 0.937225i | \(0.613385\pi\) | |||||||
\(350\) | 19647.7 | − | 5457.38i | 3.00062 | − | 0.833455i | ||||
\(351\) | −465.165 | + | 437.752i | −0.0707370 | + | 0.0665684i | ||||
\(352\) | −1649.95 | + | 2857.79i | −0.249836 | + | 0.432729i | ||||
\(353\) | −966.144 | −0.145673 | −0.0728366 | − | 0.997344i | \(-0.523205\pi\) | ||||
−0.0728366 | + | 0.997344i | \(0.523205\pi\) | |||||||
\(354\) | −627.082 | − | 8112.00i | −0.0941498 | − | 1.21793i | ||||
\(355\) | − | 16562.1i | − | 2.47612i | ||||||
\(356\) | 11716.1 | + | 20292.8i | 1.74424 | + | 3.02111i | ||||
\(357\) | 1364.65 | + | 3760.86i | 0.202310 | + | 0.557551i | ||||
\(358\) | −183.983 | + | 318.667i | −0.0271614 | + | 0.0470449i | ||||
\(359\) | 1011.40 | + | 583.931i | 0.148689 | + | 0.0858459i | 0.572499 | − | 0.819905i | \(-0.305974\pi\) |
−0.423809 | + | 0.905751i | \(0.639307\pi\) | |||||||
\(360\) | 3511.26 | + | 22575.3i | 0.514055 | + | 3.30507i | ||||
\(361\) | −622.901 | − | 1078.90i | −0.0908152 | − | 0.157296i | ||||
\(362\) | 5661.86 | + | 9806.63i | 0.822046 | + | 1.42383i | ||||
\(363\) | −500.436 | + | 38.6852i | −0.0723584 | + | 0.00559352i | ||||
\(364\) | −360.382 | + | 1395.83i | −0.0518932 | + | 0.200992i | ||||
\(365\) | −5857.13 | + | 3381.62i | −0.839935 | + | 0.484937i | ||||
\(366\) | −5665.63 | + | 11835.9i | −0.809145 | + | 1.69036i | ||||
\(367\) | − | 8702.02i | − | 1.23772i | −0.785503 | − | 0.618858i | \(-0.787596\pi\) | ||
0.785503 | − | 0.618858i | \(-0.212404\pi\) | |||||||
\(368\) | 12102.9 | − | 6987.64i | 1.71443 | − | 0.989826i | ||||
\(369\) | −215.076 | − | 267.112i | −0.0303426 | − | 0.0376838i | ||||
\(370\) | 533.107i | 0.0749052i | ||||||||
\(371\) | −2173.15 | + | 603.617i | −0.304109 | + | 0.0844697i | ||||
\(372\) | −7417.09 | + | 5082.46i | −1.03376 | + | 0.708369i | ||||
\(373\) | 8449.87 | 1.17297 | 0.586485 | − | 0.809960i | \(-0.300511\pi\) | ||||
0.586485 | + | 0.809960i | \(0.300511\pi\) | |||||||
\(374\) | 3658.66 | − | 6336.99i | 0.505842 | − | 0.876145i | ||||
\(375\) | −9117.95 | + | 704.844i | −1.25560 | + | 0.0970614i | ||||
\(376\) | −21239.5 | + | 12262.6i | −2.91315 | + | 1.68191i | ||||
\(377\) | 223.771 | 0.0305697 | ||||||||
\(378\) | −11408.3 | + | 6267.70i | −1.55233 | + | 0.852846i | ||||
\(379\) | 10435.1 | 1.41428 | 0.707142 | − | 0.707072i | \(-0.249984\pi\) | ||||
0.707142 | + | 0.707072i | \(0.249984\pi\) | |||||||
\(380\) | 20597.7 | − | 11892.1i | 2.78064 | − | 1.60540i | ||||
\(381\) | −10706.9 | + | 827.671i | −1.43971 | + | 0.111294i | ||||
\(382\) | −9423.85 | + | 16322.6i | −1.26222 | + | 2.18622i | ||||
\(383\) | 1729.70 | 0.230767 | 0.115383 | − | 0.993321i | \(-0.463190\pi\) | ||||
0.115383 | + | 0.993321i | \(0.463190\pi\) | |||||||
\(384\) | 8839.17 | − | 6056.92i | 1.17467 | − | 0.804924i | ||||
\(385\) | 3020.42 | − | 11698.7i | 0.399831 | − | 1.54862i | ||||
\(386\) | 710.386i | 0.0936728i | ||||||||
\(387\) | 1348.66 | − | 3484.40i | 0.177148 | − | 0.457679i | ||||
\(388\) | −3505.92 | + | 2024.14i | −0.458727 | + | 0.264846i | ||||
\(389\) | 8787.45i | 1.14535i | 0.819782 | + | 0.572675i | \(0.194094\pi\) | ||||
−0.819782 | + | 0.572675i | \(0.805906\pi\) | |||||||
\(390\) | 950.164 | − | 1984.95i | 0.123368 | − | 0.257723i | ||||
\(391\) | −5497.76 | + | 3174.13i | −0.711083 | + | 0.410544i | ||||
\(392\) | −7566.87 | + | 13677.2i | −0.974961 | + | 1.76225i | ||||
\(393\) | 847.088 | − | 65.4824i | 0.108728 | − | 0.00840496i | ||||
\(394\) | 8693.45 | + | 15057.5i | 1.11160 | + | 1.92534i | ||||
\(395\) | −4504.44 | − | 7801.92i | −0.573780 | − | 0.993816i | ||||
\(396\) | 15124.8 | + | 5854.16i | 1.91931 | + | 0.742885i | ||||
\(397\) | −10427.7 | − | 6020.42i | −1.31826 | − | 0.761099i | −0.334814 | − | 0.942284i | \(-0.608673\pi\) |
−0.983449 | + | 0.181185i | \(0.942007\pi\) | |||||||
\(398\) | 168.077 | − | 291.118i | 0.0211682 | − | 0.0366644i | ||||
\(399\) | 5518.60 | + | 4639.92i | 0.692420 | + | 0.582172i | ||||
\(400\) | −10057.5 | − | 17420.0i | −1.25718 | − | 2.17750i | ||||
\(401\) | 5182.09i | 0.645339i | 0.946512 | + | 0.322670i | \(0.104580\pi\) | ||||
−0.946512 | + | 0.322670i | \(0.895420\pi\) | |||||||
\(402\) | −1313.60 | − | 16992.9i | −0.162977 | − | 2.10828i | ||||
\(403\) | 460.809 | 0.0569592 | ||||||||
\(404\) | −3027.03 | + | 5242.97i | −0.372773 | + | 0.645662i | ||||
\(405\) | 12896.9 | − | 4111.30i | 1.58235 | − | 0.504425i | ||||
\(406\) | 4415.28 | + | 1139.96i | 0.539721 | + | 0.139348i | ||||
\(407\) | 174.378 | + | 100.677i | 0.0212374 | + | 0.0122614i | ||||
\(408\) | 8120.70 | − | 5564.60i | 0.985379 | − | 0.675217i | ||||
\(409\) | −3497.73 | − | 2019.41i | −0.422864 | − | 0.244141i | 0.273438 | − | 0.961890i | \(-0.411839\pi\) |
−0.696302 | + | 0.717749i | \(0.745173\pi\) | |||||||
\(410\) | 1023.21 | + | 590.750i | 0.123250 | + | 0.0711587i | ||||
\(411\) | 1051.14 | + | 13597.7i | 0.126153 | + | 1.63194i | ||||
\(412\) | −18616.9 | − | 10748.5i | −2.22619 | − | 1.28529i | ||||
\(413\) | −4055.66 | + | 4130.42i | −0.483211 | + | 0.492118i | ||||
\(414\) | −12953.5 | − | 16087.5i | −1.53775 | − | 1.90980i | ||||
\(415\) | −4618.18 | + | 7998.93i | −0.546259 | + | 0.946149i | ||||
\(416\) | 427.620 | 0.0503986 | ||||||||
\(417\) | 5746.88 | − | 3937.97i | 0.674882 | − | 0.462454i | ||||
\(418\) | − | 13186.9i | − | 1.54304i | ||||||
\(419\) | −1365.90 | − | 2365.81i | −0.159257 | − | 0.275841i | 0.775344 | − | 0.631539i | \(-0.217577\pi\) |
−0.934601 | + | 0.355698i | \(0.884243\pi\) | |||||||
\(420\) | 19660.3 | − | 23383.4i | 2.28410 | − | 2.71665i | ||||
\(421\) | −4199.36 | + | 7273.51i | −0.486139 | + | 0.842017i | −0.999873 | − | 0.0159323i | \(-0.994928\pi\) |
0.513734 | + | 0.857949i | \(0.328262\pi\) | |||||||
\(422\) | 7121.35 | + | 4111.51i | 0.821473 | + | 0.474278i | ||||
\(423\) | 9113.10 | + | 11317.9i | 1.04750 | + | 1.30094i | ||||
\(424\) | 2774.84 | + | 4806.17i | 0.317826 | + | 0.550491i | ||||
\(425\) | 4568.60 | + | 7913.04i | 0.521434 | + | 0.903150i | ||||
\(426\) | −13124.4 | − | 19153.1i | −1.49267 | − | 2.17833i | ||||
\(427\) | 8995.38 | − | 2498.57i | 1.01948 | − | 0.283171i | ||||
\(428\) | −3112.55 | + | 1797.03i | −0.351520 | + | 0.202950i | ||||
\(429\) | −469.836 | − | 685.656i | −0.0528762 | − | 0.0771649i | ||||
\(430\) | 12872.4i | 1.44363i | ||||||||
\(431\) | 9243.99 | − | 5337.02i | 1.03310 | − | 0.596463i | 0.115231 | − | 0.993339i | \(-0.463239\pi\) |
0.917872 | + | 0.396876i | \(0.129906\pi\) | |||||||
\(432\) | 8799.60 | + | 9350.65i | 0.980026 | + | 1.04140i | ||||
\(433\) | − | 4332.16i | − | 0.480809i | −0.970673 | − | 0.240404i | \(-0.922720\pi\) | ||
0.970673 | − | 0.240404i | \(-0.0772801\pi\) | |||||||
\(434\) | 9092.33 | + | 2347.50i | 1.00564 | + | 0.259640i | ||||
\(435\) | −4277.32 | − | 2047.48i | −0.471452 | − | 0.225676i | ||||
\(436\) | 2700.19 | 0.296596 | ||||||||
\(437\) | −5720.23 | + | 9907.73i | −0.626169 | + | 1.08456i | ||||
\(438\) | −4093.72 | + | 8552.04i | −0.446588 | + | 0.932951i | ||||
\(439\) | −2459.01 | + | 1419.71i | −0.267339 | + | 0.154348i | −0.627678 | − | 0.778473i | \(-0.715995\pi\) |
0.360339 | + | 0.932822i | \(0.382661\pi\) | |||||||
\(440\) | −29729.6 | −3.22115 | ||||||||
\(441\) | 8696.24 | + | 3184.58i | 0.939017 | + | 0.343870i | ||||
\(442\) | −948.225 | −0.102042 | ||||||||
\(443\) | −1669.39 | + | 963.823i | −0.179041 | + | 0.103369i | −0.586842 | − | 0.809701i | \(-0.699629\pi\) |
0.407801 | + | 0.913071i | \(0.366296\pi\) | |||||||
\(444\) | 287.789 | + | 419.985i | 0.0307609 | + | 0.0448910i | ||||
\(445\) | −12724.6 | + | 22039.7i | −1.35552 | + | 2.34782i | ||||
\(446\) | −17212.9 | −1.82748 | ||||||||
\(447\) | −298.422 | − | 3860.42i | −0.0315769 | − | 0.408482i | ||||
\(448\) | −4691.96 | − | 1211.39i | −0.494809 | − | 0.127752i | ||||
\(449\) | − | 13226.6i | − | 1.39020i | −0.718913 | − | 0.695100i | \(-0.755360\pi\) | ||
0.718913 | − | 0.695100i | \(-0.244640\pi\) | |||||||
\(450\) | −23155.0 | + | 18644.2i | −2.42564 | + | 1.95310i | ||||
\(451\) | 386.466 | − | 223.126i | 0.0403503 | − | 0.0232963i | ||||
\(452\) | 7608.05i | 0.791709i | ||||||||
\(453\) | 17677.3 | − | 1366.50i | 1.83344 | − | 0.141731i | ||||
\(454\) | 16859.8 | − | 9734.04i | 1.74289 | − | 1.00626i | ||||
\(455\) | −1508.58 | + | 419.027i | −0.155436 | + | 0.0431742i | ||||
\(456\) | 7659.89 | − | 16002.0i | 0.786638 | − | 1.64334i | ||||
\(457\) | −4106.85 | − | 7113.26i | −0.420372 | − | 0.728106i | 0.575604 | − | 0.817729i | \(-0.304767\pi\) |
−0.995976 | + | 0.0896228i | \(0.971434\pi\) | |||||||
\(458\) | 5713.26 | + | 9895.66i | 0.582889 | + | 1.00959i | ||||
\(459\) | −3997.21 | − | 4247.53i | −0.406479 | − | 0.431934i | ||||
\(460\) | 41981.0 | + | 24237.7i | 4.25516 | + | 2.45672i | ||||
\(461\) | 5491.41 | − | 9511.40i | 0.554795 | − | 0.960933i | −0.443125 | − | 0.896460i | \(-0.646130\pi\) |
0.997919 | − | 0.0644727i | \(-0.0205365\pi\) | |||||||
\(462\) | −5777.50 | − | 15922.3i | −0.581804 | − | 1.60341i | ||||
\(463\) | 6093.85 | + | 10554.9i | 0.611675 | + | 1.05945i | 0.990958 | + | 0.134171i | \(0.0428371\pi\) |
−0.379284 | + | 0.925280i | \(0.623830\pi\) | |||||||
\(464\) | − | 4498.20i | − | 0.450051i | ||||||
\(465\) | −8808.23 | − | 4216.35i | −0.878435 | − | 0.420492i | ||||
\(466\) | −3999.60 | −0.397593 | ||||||||
\(467\) | 3008.23 | − | 5210.40i | 0.298082 | − | 0.516292i | −0.677615 | − | 0.735416i | \(-0.736987\pi\) |
0.975697 | + | 0.219124i | \(0.0703199\pi\) | |||||||
\(468\) | −322.998 | − | 2076.69i | −0.0319030 | − | 0.205117i | ||||
\(469\) | −8495.75 | + | 8652.36i | −0.836455 | + | 0.851874i | ||||
\(470\) | −43354.9 | − | 25030.9i | −4.25492 | − | 2.45658i | ||||
\(471\) | −10858.7 | − | 5197.87i | −1.06230 | − | 0.508504i | ||||
\(472\) | 12335.3 | + | 7121.80i | 1.20292 | + | 0.694507i | ||||
\(473\) | 4210.53 | + | 2430.95i | 0.409303 | + | 0.236311i | ||||
\(474\) | −11391.6 | − | 5452.99i | −1.10387 | − | 0.528405i | ||||
\(475\) | 14260.4 | + | 8233.25i | 1.37750 | + | 0.795300i | ||||
\(476\) | −12745.6 | − | 3290.72i | −1.22730 | − | 0.316870i | ||||
\(477\) | 2561.08 | − | 2062.15i | 0.245836 | − | 0.197945i | ||||
\(478\) | 13181.4 | − | 22830.9i | 1.26130 | − | 2.18464i | ||||
\(479\) | 10557.6 | 1.00708 | 0.503539 | − | 0.863972i | \(-0.332031\pi\) | ||||
0.503539 | + | 0.863972i | \(0.332031\pi\) | |||||||
\(480\) | −8173.84 | − | 3912.68i | −0.777257 | − | 0.372060i | ||||
\(481\) | − | 26.0928i | − | 0.00247345i | ||||||
\(482\) | 9897.75 | + | 17143.4i | 0.935332 | + | 1.62004i | ||||
\(483\) | −2566.00 | + | 14469.2i | −0.241733 | + | 1.36308i | ||||
\(484\) | 825.735 | − | 1430.22i | 0.0775484 | − | 0.134318i | ||||
\(485\) | −3807.73 | − | 2198.39i | −0.356495 | − | 0.205822i | ||||
\(486\) | 11656.6 | − | 14974.4i | 1.08797 | − | 1.39764i | ||||
\(487\) | −1762.23 | − | 3052.27i | −0.163972 | − | 0.284008i | 0.772318 | − | 0.635236i | \(-0.219097\pi\) |
−0.936290 | + | 0.351229i | \(0.885764\pi\) | |||||||
\(488\) | −11486.0 | − | 19894.3i | −1.06546 | − | 1.84544i | ||||
\(489\) | −3276.28 | + | 6844.36i | −0.302983 | + | 0.632950i | ||||
\(490\) | −31900.9 | + | 582.720i | −2.94109 | + | 0.0537237i | ||||
\(491\) | 10853.9 | − | 6266.52i | 0.997619 | − | 0.575976i | 0.0900762 | − | 0.995935i | \(-0.471289\pi\) |
0.907543 | + | 0.419959i | \(0.137956\pi\) | |||||||
\(492\) | 1124.99 | − | 86.9654i | 0.103087 | − | 0.00796891i | ||||
\(493\) | 2043.30i | 0.186665i | ||||||||
\(494\) | −1479.89 | + | 854.418i | −0.134785 | + | 0.0778179i | ||||
\(495\) | 2707.10 | + | 17405.1i | 0.245808 | + | 1.58040i | ||||
\(496\) | − | 9263.09i | − | 0.838558i | ||||||
\(497\) | −4129.58 | + | 15994.7i | −0.372710 | + | 1.44358i | ||||
\(498\) | 997.974 | + | 12909.9i | 0.0897998 | + | 1.16166i | ||||
\(499\) | 9548.65 | 0.856626 | 0.428313 | − | 0.903630i | \(-0.359108\pi\) | ||||
0.428313 | + | 0.903630i | \(0.359108\pi\) | |||||||
\(500\) | 15044.9 | − | 26058.5i | 1.34566 | − | 2.33075i | ||||
\(501\) | 6155.37 | + | 8982.85i | 0.548905 | + | 0.801046i | ||||
\(502\) | 24072.5 | − | 13898.3i | 2.14026 | − | 1.23568i | ||||
\(503\) | 21478.4 | 1.90393 | 0.951963 | − | 0.306214i | \(-0.0990624\pi\) | ||||
0.951963 | + | 0.306214i | \(0.0990624\pi\) | |||||||
\(504\) | 2237.96 | − | 22677.4i | 0.197791 | − | 2.00423i | ||||
\(505\) | −6575.22 | −0.579393 | ||||||||
\(506\) | 23275.8 | − | 13438.3i | 2.04493 | − | 1.18064i | ||||
\(507\) | 4882.51 | − | 10199.9i | 0.427692 | − | 0.893476i | ||||
\(508\) | 17666.6 | − | 30599.5i | 1.54297 | − | 2.67251i | ||||
\(509\) | −16323.8 | −1.42149 | −0.710745 | − | 0.703450i | \(-0.751642\pi\) | ||||
−0.710745 | + | 0.703450i | \(0.751642\pi\) | |||||||
\(510\) | 18125.1 | + | 8676.16i | 1.57371 | + | 0.753307i | ||||
\(511\) | 6499.64 | − | 1805.35i | 0.562675 | − | 0.156290i | ||||
\(512\) | 24769.7i | 2.13804i | ||||||||
\(513\) | −10065.8 | − | 3027.34i | −0.866305 | − | 0.260547i | ||||
\(514\) | −12074.7 | + | 6971.31i | −1.03617 | + | 0.598232i | ||||
\(515\) | − | 23347.5i | − | 1.99770i | ||||||
\(516\) | 6948.93 | + | 10140.9i | 0.592848 | + | 0.865174i | ||||
\(517\) | −16375.2 | + | 9454.20i | −1.39299 | + | 0.804246i | ||||
\(518\) | 132.925 | − | 514.844i | 0.0112749 | − | 0.0436697i | ||||
\(519\) | −8149.87 | − | 11893.5i | −0.689287 | − | 1.00591i | ||||
\(520\) | 1926.28 | + | 3336.41i | 0.162448 | + | 0.281368i | ||||
\(521\) | −7116.33 | − | 12325.8i | −0.598411 | − | 1.03648i | −0.993056 | − | 0.117644i | \(-0.962466\pi\) |
0.394645 | − | 0.918834i | \(-0.370868\pi\) | |||||||
\(522\) | −6568.97 | + | 1021.71i | −0.550797 | + | 0.0856684i | ||||
\(523\) | −4121.11 | − | 2379.33i | −0.344558 | − | 0.198931i | 0.317728 | − | 0.948182i | \(-0.397080\pi\) |
−0.662286 | + | 0.749251i | \(0.730413\pi\) | |||||||
\(524\) | −1397.72 | + | 2420.92i | −0.116526 | + | 0.201829i | ||||
\(525\) | 20825.8 | + | 3693.29i | 1.73126 | + | 0.307026i | ||||
\(526\) | 15027.0 | + | 26027.5i | 1.24564 | + | 2.15751i | ||||
\(527\) | 4207.75i | 0.347804i | ||||||||
\(528\) | −13782.9 | + | 9444.54i | −1.13603 | + | 0.778448i | ||||
\(529\) | −11150.2 | −0.916432 | ||||||||
\(530\) | −5664.12 | + | 9810.54i | −0.464214 | + | 0.804043i | ||||
\(531\) | 3046.20 | − | 7870.14i | 0.248953 | − | 0.643192i | ||||
\(532\) | −22857.2 | + | 6348.86i | −1.86276 | + | 0.517402i | ||||
\(533\) | −50.0807 | − | 28.9141i | −0.00406986 | − | 0.00234974i | ||||
\(534\) | 2749.75 | + | 35571.1i | 0.222834 | + | 2.88260i | ||||
\(535\) | −3380.49 | − | 1951.73i | −0.273180 | − | 0.157721i | ||||
\(536\) | 25839.9 | + | 14918.7i | 2.08230 | + | 1.20222i | ||||
\(537\) | −314.839 | + | 215.739i | −0.0253004 | + | 0.0173368i | ||||
\(538\) | −11731.4 | − | 6773.13i | −0.940105 | − | 0.542770i | ||||
\(539\) | −5833.88 | + | 10544.8i | −0.466202 | + | 0.842663i | ||||
\(540\) | −12827.4 | + | 42650.6i | −1.02223 | + | 3.39887i | ||||
\(541\) | 5255.73 | − | 9103.19i | 0.417674 | − | 0.723432i | −0.578031 | − | 0.816014i | \(-0.696179\pi\) |
0.995705 | + | 0.0925827i | \(0.0295122\pi\) | |||||||
\(542\) | −8897.13 | −0.705101 | ||||||||
\(543\) | 905.244 | + | 11710.3i | 0.0715428 | + | 0.925486i | ||||
\(544\) | 3904.70i | 0.307744i | ||||||||
\(545\) | 1466.32 | + | 2539.74i | 0.115248 | + | 0.199616i | ||||
\(546\) | −1412.54 | + | 1680.04i | −0.110716 | + | 0.131683i | ||||
\(547\) | 11334.1 | − | 19631.2i | 0.885943 | − | 1.53450i | 0.0413133 | − | 0.999146i | \(-0.486846\pi\) |
0.844629 | − | 0.535351i | \(-0.179821\pi\) | |||||||
\(548\) | −38861.4 | − | 22436.6i | −3.02934 | − | 1.74899i | ||||
\(549\) | −10601.1 | + | 8535.93i | −0.824126 | + | 0.663578i | ||||
\(550\) | −19342.0 | − | 33501.4i | −1.49954 | − | 2.59728i | ||||
\(551\) | 1841.16 | + | 3188.98i | 0.142352 | + | 0.246561i | ||||
\(552\) | 36050.7 | − | 2786.83i | 2.77975 | − | 0.214883i | ||||
\(553\) | 2404.79 | + | 8657.77i | 0.184923 | + | 0.665761i | ||||
\(554\) | 3788.18 | − | 2187.11i | 0.290513 | − | 0.167728i | ||||
\(555\) | −238.747 | + | 498.757i | −0.0182599 | + | 0.0381460i | ||||
\(556\) | 22922.0i | 1.74840i | ||||||||
\(557\) | 10244.9 | − | 5914.91i | 0.779338 | − | 0.449951i | −0.0568577 | − | 0.998382i | \(-0.518108\pi\) |
0.836196 | + | 0.548431i | \(0.184775\pi\) | |||||||
\(558\) | −13527.4 | + | 2103.99i | −1.02627 | + | 0.159622i | ||||
\(559\) | − | 630.036i | − | 0.0476703i | ||||||
\(560\) | 8423.18 | + | 30325.2i | 0.635615 | + | 2.28835i | ||||
\(561\) | 6260.87 | − | 4290.18i | 0.471184 | − | 0.322872i | ||||
\(562\) | −9040.38 | −0.678551 | ||||||||
\(563\) | 2833.63 | − | 4907.99i | 0.212119 | − | 0.367401i | −0.740258 | − | 0.672323i | \(-0.765297\pi\) |
0.952378 | + | 0.304921i | \(0.0986302\pi\) | |||||||
\(564\) | −47667.7 | + | 3684.85i | −3.55882 | + | 0.275107i | ||||
\(565\) | −7155.95 | + | 4131.49i | −0.532838 | + | 0.307634i | ||||
\(566\) | −30218.6 | −2.24414 | ||||||||
\(567\) | −13480.2 | + | 754.745i | −0.998436 | + | 0.0559018i | ||||
\(568\) | 40647.0 | 3.00266 | ||||||||
\(569\) | 3471.92 | − | 2004.52i | 0.255801 | − | 0.147687i | −0.366617 | − | 0.930372i | \(-0.619484\pi\) |
0.622417 | + | 0.782685i | \(0.286151\pi\) | |||||||
\(570\) | 36105.6 | − | 2791.07i | 2.65315 | − | 0.205096i | ||||
\(571\) | 3248.70 | − | 5626.91i | 0.238097 | − | 0.412397i | −0.722071 | − | 0.691819i | \(-0.756810\pi\) |
0.960168 | + | 0.279422i | \(0.0901429\pi\) | |||||||
\(572\) | 2734.80 | 0.199909 | ||||||||
\(573\) | −16126.5 | + | 11050.5i | −1.17573 | + | 0.805655i | ||||
\(574\) | −840.857 | − | 825.638i | −0.0611441 | − | 0.0600374i | ||||
\(575\) | 33561.0i | 2.43407i | ||||||||
\(576\) | 6980.61 | − | 1085.73i | 0.504963 | − | 0.0785396i | ||||
\(577\) | 13721.3 | − | 7922.02i | 0.989995 | − | 0.571574i | 0.0847219 | − | 0.996405i | \(-0.473000\pi\) |
0.905273 | + | 0.424831i | \(0.139666\pi\) | |||||||
\(578\) | 15954.0i | 1.14809i | ||||||||
\(579\) | −318.139 | + | 664.613i | −0.0228349 | + | 0.0477036i | ||||
\(580\) | 13512.3 | − | 7801.36i | 0.967361 | − | 0.558506i | ||||
\(581\) | 6454.42 | − | 6573.39i | 0.460885 | − | 0.469381i | ||||
\(582\) | −6145.50 | + | 475.065i | −0.437696 | + | 0.0338352i | ||||
\(583\) | 2139.34 | + | 3705.44i | 0.151977 | + | 0.263231i | ||||
\(584\) | −8299.23 | − | 14374.7i | −0.588056 | − | 1.01854i | ||||
\(585\) | 1777.88 | − | 1431.53i | 0.125652 | − | 0.101174i | ||||
\(586\) | −39713.8 | − | 22928.8i | −2.79960 | − | 1.61635i | ||||
\(587\) | −3651.54 | + | 6324.65i | −0.256755 | + | 0.444713i | −0.965371 | − | 0.260882i | \(-0.915987\pi\) |
0.708616 | + | 0.705595i | \(0.249320\pi\) | |||||||
\(588\) | −24817.1 | + | 17680.2i | −1.74055 | + | 1.24000i | ||||
\(589\) | 3791.48 | + | 6567.04i | 0.265238 | + | 0.459406i | ||||
\(590\) | 29074.6i | 2.02878i | ||||||||
\(591\) | 1389.95 | + | 17980.5i | 0.0967425 | + | 1.25147i | ||||
\(592\) | −524.512 | −0.0364144 | ||||||||
\(593\) | 2546.38 | − | 4410.47i | 0.176336 | − | 0.305424i | −0.764287 | − | 0.644877i | \(-0.776909\pi\) |
0.940623 | + | 0.339453i | \(0.110242\pi\) | |||||||
\(594\) | 16923.0 | + | 17982.7i | 1.16895 | + | 1.24216i | ||||
\(595\) | −3826.23 | − | 13775.2i | −0.263630 | − | 0.949125i | ||||
\(596\) | 11032.8 | + | 6369.81i | 0.758259 | + | 0.437781i | ||||
\(597\) | 287.621 | − | 197.089i | 0.0197179 | − | 0.0135114i | ||||
\(598\) | −3016.23 | − | 1741.42i | −0.206259 | − | 0.119084i | ||||
\(599\) | 1617.80 | + | 934.036i | 0.110353 | + | 0.0637123i | 0.554161 | − | 0.832410i | \(-0.313039\pi\) |
−0.443808 | + | 0.896122i | \(0.646373\pi\) | |||||||
\(600\) | −4011.14 | − | 51888.6i | −0.272923 | − | 3.53057i | ||||
\(601\) | −17969.3 | − | 10374.6i | −1.21960 | − | 0.704139i | −0.254771 | − | 0.967001i | \(-0.582000\pi\) |
−0.964833 | + | 0.262863i | \(0.915333\pi\) | |||||||
\(602\) | 3209.60 | − | 12431.4i | 0.217298 | − | 0.841637i | ||||
\(603\) | 6381.14 | − | 16486.3i | 0.430945 | − | 1.11339i | ||||
\(604\) | −29168.0 | + | 50520.5i | −1.96495 | + | 3.40339i | ||||
\(605\) | 1793.64 | 0.120532 | ||||||||
\(606\) | −7603.86 | + | 5210.44i | −0.509712 | + | 0.349273i | ||||
\(607\) | 3452.62i | 0.230869i | 0.993315 | + | 0.115434i | \(0.0368260\pi\) | ||||
−0.993315 | + | 0.115434i | \(0.963174\pi\) | |||||||
\(608\) | 3518.41 | + | 6094.06i | 0.234688 | + | 0.406491i | ||||
\(609\) | 3620.26 | + | 3043.84i | 0.240887 | + | 0.202533i | ||||
\(610\) | 23445.6 | − | 40609.0i | 1.55621 | − | 2.69543i | ||||
\(611\) | 2121.99 | + | 1225.13i | 0.140502 | + | 0.0811188i | ||||
\(612\) | 18962.7 | − | 2949.37i | 1.25249 | − | 0.194806i | ||||
\(613\) | 8024.21 | + | 13898.3i | 0.528703 | + | 0.915740i | 0.999440 | + | 0.0334664i | \(0.0106547\pi\) |
−0.470737 | + | 0.882273i | \(0.656012\pi\) | |||||||
\(614\) | −8030.20 | − | 13908.7i | −0.527806 | − | 0.914186i | ||||
\(615\) | 692.717 | + | 1010.92i | 0.0454196 | + | 0.0662832i | ||||
\(616\) | 28711.1 | + | 7412.78i | 1.87793 | + | 0.484853i | ||||
\(617\) | 640.877 | − | 370.011i | 0.0418164 | − | 0.0241427i | −0.478946 | − | 0.877844i | \(-0.658981\pi\) |
0.520762 | + | 0.853702i | \(0.325648\pi\) | |||||||
\(618\) | −18501.4 | − | 27000.1i | −1.20427 | − | 1.75745i | ||||
\(619\) | 9135.21i | 0.593174i | 0.955006 | + | 0.296587i | \(0.0958485\pi\) | ||||
−0.955006 | + | 0.296587i | \(0.904151\pi\) | |||||||
\(620\) | 27825.8 | − | 16065.2i | 1.80244 | − | 1.04064i | ||||
\(621\) | −4914.22 | − | 20851.9i | −0.317553 | − | 1.34744i | ||||
\(622\) | − | 24.4053i | − | 0.00157325i | ||||||
\(623\) | 17784.1 | − | 18111.9i | 1.14366 | − | 1.16475i | ||||
\(624\) | 1952.95 | + | 934.844i | 0.125289 | + | 0.0599739i | ||||
\(625\) | 5207.04 | 0.333250 | ||||||||
\(626\) | −4810.50 | + | 8332.03i | −0.307135 | + | 0.531973i | ||||
\(627\) | 5905.59 | − | 12337.2i | 0.376151 | − | 0.785804i | ||||
\(628\) | 34303.3 | − | 19805.0i | 2.17970 | − | 1.25845i | ||||
\(629\) | 238.259 | 0.0151034 | ||||||||
\(630\) | 42372.4 | − | 19188.8i | 2.67962 | − | 1.21349i | ||||
\(631\) | −11586.8 | −0.731004 | −0.365502 | − | 0.930811i | \(-0.619103\pi\) | ||||
−0.365502 | + | 0.930811i | \(0.619103\pi\) | |||||||
\(632\) | 19147.6 | − | 11054.9i | 1.20515 | − | 0.695791i | ||||
\(633\) | 4821.19 | + | 7035.81i | 0.302725 | + | 0.441782i | ||||
\(634\) | 25447.3 | − | 44076.1i | 1.59407 | − | 2.76102i | ||||
\(635\) | 38374.9 | 2.39821 | ||||||||
\(636\) | 833.826 | + | 10786.5i | 0.0519864 | + | 0.672502i | ||||
\(637\) | 1561.38 | − | 28.5211i | 0.0971181 | − | 0.00177401i | ||||
\(638\) | − | 8650.73i | − | 0.536811i | ||||||
\(639\) | −3701.21 | − | 23796.6i | −0.229135 | − | 1.47320i | ||||
\(640\) | −33160.9 | + | 19145.4i | −2.04812 | + | 1.18248i | ||||
\(641\) | 2669.76i | 0.164507i | 0.996611 | + | 0.0822536i | \(0.0262118\pi\) | ||||
−0.996611 | + | 0.0822536i | \(0.973788\pi\) | |||||||
\(642\) | −5455.96 | + | 421.762i | −0.335404 | + | 0.0259277i | ||||
\(643\) | −23669.3 | + | 13665.5i | −1.45167 | + | 0.838124i | −0.998577 | − | 0.0533376i | \(-0.983014\pi\) |
−0.453097 | + | 0.891461i | \(0.649681\pi\) | |||||||
\(644\) | −34499.3 | − | 33874.9i | −2.11097 | − | 2.07276i | ||||
\(645\) | −5764.76 | + | 12043.0i | −0.351918 | + | 0.735180i | ||||
\(646\) | −7801.88 | − | 13513.2i | −0.475171 | − | 0.823021i | ||||
\(647\) | −7270.33 | − | 12592.6i | −0.441771 | − | 0.765170i | 0.556050 | − | 0.831149i | \(-0.312316\pi\) |
−0.997821 | + | 0.0659787i | \(0.978983\pi\) | |||||||
\(648\) | 10090.0 | + | 31651.8i | 0.611688 | + | 1.91883i | ||||
\(649\) | 9510.25 | + | 5490.74i | 0.575208 | + | 0.332096i | ||||
\(650\) | −2506.46 | + | 4341.32i | −0.151249 | + | 0.261970i | ||||
\(651\) | 7455.17 | + | 6268.15i | 0.448834 | + | 0.377370i | ||||
\(652\) | −12483.4 | − | 21621.8i | −0.749825 | − | 1.29873i | ||||
\(653\) | − | 3829.95i | − | 0.229521i | −0.993393 | − | 0.114761i | \(-0.963390\pi\) | ||
0.993393 | − | 0.114761i | \(-0.0366101\pi\) | |||||||
\(654\) | 3708.29 | + | 1775.10i | 0.221721 | + | 0.106134i | ||||
\(655\) | −3036.09 | −0.181114 | ||||||||
\(656\) | −581.225 | + | 1006.71i | −0.0345930 | + | 0.0599169i | ||||
\(657\) | −7659.88 | + | 6167.66i | −0.454856 | + | 0.366246i | ||||
\(658\) | 35628.4 | + | 34983.5i | 2.11085 | + | 2.07264i | ||||
\(659\) | −21012.5 | − | 12131.6i | −1.24208 | − | 0.717116i | −0.272564 | − | 0.962138i | \(-0.587872\pi\) |
−0.969518 | + | 0.245021i | \(0.921205\pi\) | |||||||
\(660\) | −52275.0 | − | 25023.2i | −3.08303 | − | 1.47580i | ||||
\(661\) | 11858.1 | + | 6846.29i | 0.697772 | + | 0.402859i | 0.806517 | − | 0.591211i | \(-0.201350\pi\) |
−0.108745 | + | 0.994070i | \(0.534683\pi\) | |||||||
\(662\) | −49928.6 | − | 28826.3i | −2.93132 | − | 1.69240i | ||||
\(663\) | −887.126 | − | 424.653i | −0.0519655 | − | 0.0248750i | ||||
\(664\) | −19631.1 | − | 11334.0i | −1.14734 | − | 0.662419i | ||||
\(665\) | −18384.0 | − | 18051.3i | −1.07203 | − | 1.05263i | ||||
\(666\) | 119.136 | + | 765.975i | 0.00693158 | + | 0.0445659i | ||||
\(667\) | −3752.54 | + | 6499.58i | −0.217839 | + | 0.377309i | ||||
\(668\) | −35829.0 | −2.07525 | ||||||||
\(669\) | −16103.8 | − | 7708.63i | −0.930658 | − | 0.445490i | ||||
\(670\) | 60905.1i | 3.51189i | ||||||||
\(671\) | −8855.42 | − | 15338.0i | −0.509478 | − | 0.882442i | ||||
\(672\) | 6918.23 | + | 5816.70i | 0.397137 | + | 0.333905i | ||||
\(673\) | −9187.98 | + | 15914.0i | −0.526256 | + | 0.911503i | 0.473276 | + | 0.880914i | \(0.343071\pi\) |
−0.999532 | + | 0.0305886i | \(0.990262\pi\) | |||||||
\(674\) | 36387.3 | + | 21008.2i | 2.07951 | + | 1.20060i | ||||
\(675\) | −30012.6 | + | 7073.14i | −1.71139 | + | 0.403326i | ||||
\(676\) | 18603.4 | + | 32222.1i | 1.05846 | + | 1.83330i | ||||
\(677\) | −1417.84 | − | 2455.77i | −0.0804904 | − | 0.139413i | 0.822970 | − | 0.568084i | \(-0.192315\pi\) |
−0.903461 | + | 0.428671i | \(0.858982\pi\) | |||||||
\(678\) | −5001.50 | + | 10448.5i | −0.283306 | + | 0.591845i | ||||
\(679\) | 3129.13 | + | 3072.49i | 0.176856 | + | 0.173655i | ||||
\(680\) | −30465.5 | + | 17589.3i | −1.71808 | + | 0.991937i | ||||
\(681\) | 20132.8 | − | 1556.32i | 1.13288 | − | 0.0875747i | ||||
\(682\) | − | 17814.3i | − | 1.00021i | ||||||
\(683\) | 14759.6 | − | 8521.44i | 0.826880 | − | 0.477399i | −0.0259033 | − | 0.999664i | \(-0.508246\pi\) |
0.852783 | + | 0.522265i | \(0.174913\pi\) | |||||||
\(684\) | 26937.5 | − | 21689.8i | 1.50582 | − | 1.21247i | ||||
\(685\) | − | 48736.1i | − | 2.71841i | ||||||
\(686\) | 30953.3 | + | 7391.40i | 1.72274 | + | 0.411378i | ||||
\(687\) | 913.463 | + | 11816.7i | 0.0507289 | + | 0.656236i | ||||
\(688\) | −12664.8 | −0.701806 | ||||||||
\(689\) | 277.229 | − | 480.175i | 0.0153289 | − | 0.0265504i | ||||
\(690\) | 41720.5 | + | 60884.9i | 2.30185 | + | 3.35920i | ||||
\(691\) | −4224.31 | + | 2438.91i | −0.232562 | + | 0.134270i | −0.611753 | − | 0.791048i | \(-0.709536\pi\) |
0.379191 | + | 0.925318i | \(0.376202\pi\) | |||||||
\(692\) | 47438.5 | 2.60598 | ||||||||
\(693\) | 1725.41 | − | 17483.8i | 0.0945787 | − | 0.958374i | ||||
\(694\) | 62380.8 | 3.41202 | ||||||||
\(695\) | −21559.9 | + | 12447.6i | −1.17671 | + | 0.679374i | ||||
\(696\) | 5024.97 | − | 10497.5i | 0.273665 | − | 0.571704i | ||||
\(697\) | 264.021 | − | 457.298i | 0.0143479 | − | 0.0248514i | ||||
\(698\) | −10883.6 | −0.590186 | ||||||||
\(699\) | −3741.89 | − | 1791.18i | −0.202477 | − | 0.0969223i | ||||
\(700\) | −48756.9 | + | 49655.6i | −2.63262 | + | 2.68115i | ||||
\(701\) | 18496.2i | 0.996564i | 0.867015 | + | 0.498282i | \(0.166036\pi\) | ||||
−0.867015 | + | 0.498282i | \(0.833964\pi\) | |||||||
\(702\) | 921.619 | − | 3064.34i | 0.0495502 | − | 0.164752i | ||||
\(703\) | 371.851 | − | 214.688i | 0.0199497 | − | 0.0115180i | ||||
\(704\) | 9192.82i | 0.492141i | ||||||||
\(705\) | −29351.5 | − | 42834.1i | −1.56800 | − | 2.28826i | ||||
\(706\) | 4191.60 | − | 2420.02i | 0.223446 | − | 0.129007i | ||||
\(707\) | 6349.96 | + | 1639.46i | 0.337786 | + | 0.0872112i | ||||
\(708\) | 15695.4 | + | 22905.1i | 0.833149 | + | 1.21586i | ||||
\(709\) | 5252.92 | + | 9098.33i | 0.278248 | + | 0.481939i | 0.970949 | − | 0.239285i | \(-0.0769130\pi\) |
−0.692702 | + | 0.721224i | \(0.743580\pi\) | |||||||
\(710\) | 41485.1 | + | 71854.3i | 2.19283 | + | 3.79809i | ||||
\(711\) | −8215.56 | − | 10203.3i | −0.433344 | − | 0.538188i | ||||
\(712\) | −54090.3 | − | 31229.0i | −2.84708 | − | 1.64376i | ||||
\(713\) | −7727.56 | + | 13384.5i | −0.405890 | + | 0.703021i | ||||
\(714\) | −15340.8 | − | 12898.2i | −0.804082 | − | 0.676055i | ||||
\(715\) | 1485.11 | + | 2572.29i | 0.0776785 | + | 0.134543i | ||||
\(716\) | − | 1255.77i | − | 0.0655450i | ||||||
\(717\) | 22556.6 | − | 15456.6i | 1.17488 | − | 0.805073i | ||||
\(718\) | −5850.58 | −0.304097 | ||||||||
\(719\) | −519.987 | + | 900.644i | −0.0269711 | + | 0.0467154i | −0.879196 | − | 0.476460i | \(-0.841920\pi\) |
0.852225 | + | 0.523176i | \(0.175253\pi\) | |||||||
\(720\) | −28776.3 | − | 35738.6i | −1.48949 | − | 1.84986i | ||||
\(721\) | −5821.47 | + | 22547.7i | −0.300697 | + | 1.16466i | ||||
\(722\) | 5404.90 | + | 3120.52i | 0.278600 | + | 0.160850i | ||||
\(723\) | 1582.50 | + | 20471.4i | 0.0814021 | + | 1.05303i | ||||
\(724\) | −33467.4 | − | 19322.4i | −1.71796 | − | 0.991867i | ||||
\(725\) | 9354.99 | + | 5401.11i | 0.479221 | + | 0.276679i | ||||
\(726\) | 2074.24 | − | 1421.34i | 0.106036 | − | 0.0726597i | ||||
\(727\) | 28717.4 | + | 16580.0i | 1.46502 | + | 0.845829i | 0.999236 | − | 0.0390696i | \(-0.0124394\pi\) |
0.465783 | + | 0.884899i | \(0.345773\pi\) | |||||||
\(728\) | −1028.38 | − | 3702.40i | −0.0523550 | − | 0.188489i | ||||
\(729\) | 17611.6 | − | 8789.29i | 0.894763 | − | 0.446542i | ||||
\(730\) | 16940.7 | − | 29342.2i | 0.858910 | − | 1.48768i | ||||
\(731\) | 5753.00 | 0.291084 | ||||||||
\(732\) | −3451.48 | − | 44648.7i | −0.174276 | − | 2.25446i | ||||
\(733\) | − | 10650.5i | − | 0.536677i | −0.963325 | − | 0.268339i | \(-0.913525\pi\) | ||
0.963325 | − | 0.268339i | \(-0.0864746\pi\) | |||||||
\(734\) | 21797.0 | + | 37753.6i | 1.09611 | + | 1.89851i | ||||
\(735\) | −30106.3 | − | 13741.3i | −1.51087 | − | 0.689600i | ||||
\(736\) | −7171.00 | + | 12420.5i | −0.359139 | + | 0.622047i | ||||
\(737\) | 19921.9 | + | 11501.9i | 0.995704 | + | 0.574870i | ||||
\(738\) | 1602.17 | + | 620.134i | 0.0799145 | + | 0.0309315i | ||||
\(739\) | 701.510 | + | 1215.05i | 0.0349194 | + | 0.0604822i | 0.882957 | − | 0.469454i | \(-0.155549\pi\) |
−0.848038 | + | 0.529936i | \(0.822216\pi\) | |||||||
\(740\) | −909.677 | − | 1575.61i | −0.0451897 | − | 0.0782709i | ||||
\(741\) | −1767.18 | + | 136.608i | −0.0876099 | + | 0.00677251i | ||||
\(742\) | 7916.22 | − | 8062.15i | 0.391663 | − | 0.398882i | ||||
\(743\) | −27959.9 | + | 16142.6i | −1.38055 | + | 0.797060i | −0.992224 | − | 0.124463i | \(-0.960279\pi\) |
−0.388324 | + | 0.921523i | \(0.626946\pi\) | |||||||
\(744\) | 10347.9 | − | 21617.4i | 0.509907 | − | 1.06523i | ||||
\(745\) | 13836.3i | 0.680433i | ||||||||
\(746\) | −36659.6 | + | 21165.5i | −1.79920 | + | 1.03877i | ||||
\(747\) | −4847.90 | + | 12525.0i | −0.237450 | + | 0.613475i | ||||
\(748\) | 24972.1i | 1.22068i | ||||||||
\(749\) | 2778.03 | + | 2727.75i | 0.135524 | + | 0.133071i | ||||
\(750\) | 37792.6 | − | 25896.8i | 1.83999 | − | 1.26083i | ||||
\(751\) | −33807.6 | −1.64269 | −0.821344 | − | 0.570433i | \(-0.806775\pi\) | ||||
−0.821344 | + | 0.570433i | \(0.806775\pi\) | |||||||
\(752\) | 24627.4 | − | 42655.9i | 1.19424 | − | 2.06848i | ||||
\(753\) | 28745.6 | − | 2222.12i | 1.39117 | − | 0.107541i | ||||
\(754\) | −970.827 | + | 560.507i | −0.0468905 | + | 0.0270723i | ||||
\(755\) | −63357.9 | −3.05408 | ||||||||
\(756\) | 23022.5 | − | 37991.1i | 1.10757 | − | 1.82767i | ||||
\(757\) | −32096.2 | −1.54102 | −0.770512 | − | 0.637426i | \(-0.779999\pi\) | ||||
−0.770512 | + | 0.637426i | \(0.779999\pi\) | |||||||
\(758\) | −45272.4 | + | 26138.0i | −2.16935 | + | 1.25247i | ||||
\(759\) | 27794.3 | − | 2148.58i | 1.32921 | − | 0.102752i | ||||
\(760\) | −31698.3 | + | 54903.1i | −1.51292 | + | 2.62045i | ||||
\(761\) | 2884.25 | 0.137390 | 0.0686951 | − | 0.997638i | \(-0.478116\pi\) | ||||
0.0686951 | + | 0.997638i | \(0.478116\pi\) | |||||||
\(762\) | 44378.4 | − | 30409.7i | 2.10979 | − | 1.44570i | ||||
\(763\) | −782.826 | − | 2818.34i | −0.0371431 | − | 0.133723i | ||||
\(764\) | − | 64322.2i | − | 3.04594i | ||||||
\(765\) | 13071.6 | + | 16234.2i | 0.617786 | + | 0.767254i | ||||
\(766\) | −7504.29 | + | 4332.60i | −0.353970 | + | 0.204365i | ||||
\(767\) | − | 1423.05i | − | 0.0669926i | ||||||
\(768\) | −18481.0 | + | 38607.9i | −0.868326 | + | 1.81399i | ||||
\(769\) | 15050.9 | − | 8689.61i | 0.705784 | − | 0.407484i | −0.103714 | − | 0.994607i | \(-0.533073\pi\) |
0.809498 | + | 0.587123i | \(0.199739\pi\) | |||||||
\(770\) | 16199.1 | + | 58320.1i | 0.758148 | + | 2.72950i | ||||
\(771\) | −14418.7 | + | 1114.60i | −0.673509 | + | 0.0520642i | ||||
\(772\) | −1212.18 | − | 2099.56i | −0.0565121 | − | 0.0978818i | ||||
\(773\) | −7817.05 | − | 13539.5i | −0.363726 | − | 0.629991i | 0.624845 | − | 0.780749i | \(-0.285162\pi\) |
−0.988571 | + | 0.150758i | \(0.951829\pi\) | |||||||
\(774\) | 2876.65 | + | 18495.2i | 0.133591 | + | 0.858909i | ||||
\(775\) | 19264.6 | + | 11122.4i | 0.892911 | + | 0.515522i | ||||
\(776\) | 5395.34 | − | 9345.00i | 0.249589 | − | 0.432301i | ||||
\(777\) | 354.927 | − | 422.141i | 0.0163873 | − | 0.0194906i | ||||
\(778\) | −22011.0 | − | 38124.2i | −1.01431 | − | 1.75684i | ||||
\(779\) | − | 951.607i | − | 0.0437675i | ||||||
\(780\) | 578.836 | + | 7487.89i | 0.0265713 | + | 0.343730i | ||||
\(781\) | 31337.9 | 1.43580 | ||||||||
\(782\) | 15901.3 | − | 27541.9i | 0.727147 | − | 1.25946i | ||||
\(783\) | −6603.26 | − | 1985.97i | −0.301381 | − | 0.0906421i | ||||
\(784\) | −573.325 | − | 31386.6i | −0.0261172 | − | 1.42978i | ||||
\(785\) | 37256.3 | + | 21509.9i | 1.69393 | + | 0.977990i | ||||
\(786\) | −3511.06 | + | 2405.90i | −0.159332 | + | 0.109180i | ||||
\(787\) | 22839.4 | + | 13186.3i | 1.03448 | + | 0.597258i | 0.918265 | − | 0.395966i | \(-0.129590\pi\) |
0.116216 | + | 0.993224i | \(0.462924\pi\) | |||||||
\(788\) | −51387.2 | − | 29668.4i | −2.32309 | − | 1.34124i | ||||
\(789\) | 2402.58 | + | 31080.1i | 0.108408 | + | 1.40238i | ||||
\(790\) | 39084.9 | + | 22565.7i | 1.76023 | + | 1.01627i | ||||
\(791\) | 7940.94 | − | 2205.69i | 0.356950 | − | 0.0991469i | ||||
\(792\) | −42715.9 | + | 6643.82i | −1.91647 | + | 0.298078i | ||||
\(793\) | −1147.54 | + | 1987.60i | −0.0513876 | + | 0.0890059i | ||||
\(794\) | 60320.5 | 2.69609 | ||||||||
\(795\) | −9692.70 | + | 6641.78i | −0.432408 | + | 0.296302i | ||||
\(796\) | 1147.21i | 0.0510825i | ||||||||
\(797\) | −4401.10 | − | 7622.92i | −0.195602 | − | 0.338793i | 0.751496 | − | 0.659738i | \(-0.229333\pi\) |
−0.947098 | + | 0.320945i | \(0.895999\pi\) | |||||||
\(798\) | −35564.6 | − | 6307.11i | −1.57766 | − | 0.279786i | ||||
\(799\) | −11187.0 | + | 19376.4i | −0.495327 | + | 0.857932i | ||||
\(800\) | 17877.1 | + | 10321.4i | 0.790065 | + | 0.456144i | ||||
\(801\) | −13357.6 | + | 34510.5i | −0.589221 | + | 1.52231i | ||||
\(802\) | −12980.2 | − | 22482.4i | −0.571506 | − | 0.989877i | ||||
\(803\) | −6398.52 | − | 11082.6i | −0.281194 | − | 0.487042i | ||||
\(804\) | 32878.5 | + | 47981.3i | 1.44221 | + | 2.10469i | ||||
\(805\) | 13127.4 | − | 50844.8i | 0.574756 | − | 2.22614i | ||||
\(806\) | −1999.21 | + | 1154.25i | −0.0873689 | + | 0.0504424i | ||||
\(807\) | −7942.22 | − | 11590.5i | −0.346443 | − | 0.505582i | ||||
\(808\) | − | 16137.0i | − | 0.702598i | ||||||
\(809\) | 29529.8 | − | 17049.0i | 1.28333 | − | 0.740930i | 0.305873 | − | 0.952072i | \(-0.401052\pi\) |
0.977455 | + | 0.211142i | \(0.0677183\pi\) | |||||||
\(810\) | −45654.9 | + | 50141.3i | −1.98043 | + | 2.17504i | ||||
\(811\) | 22436.9i | 0.971475i | 0.874105 | + | 0.485737i | \(0.161449\pi\) | ||||
−0.874105 | + | 0.485737i | \(0.838551\pi\) | |||||||
\(812\) | −14994.6 | + | 4164.92i | −0.648039 | + | 0.180000i | ||||
\(813\) | −8323.85 | − | 3984.49i | −0.359078 | − | 0.171884i | ||||
\(814\) | −1008.72 | −0.0434343 | ||||||||
\(815\) | 13558.0 | − | 23483.1i | 0.582718 | − | 1.00930i | ||||
\(816\) | −8536.27 | + | 17832.8i | −0.366212 | + | 0.765041i | ||||
\(817\) | 8978.70 | − | 5183.86i | 0.384486 | − | 0.221983i | ||||
\(818\) | 20233.1 | 0.864835 | ||||||||
\(819\) | −2073.91 | + | 939.193i | −0.0884838 | + | 0.0400709i | ||||
\(820\) | −4032.14 | −0.171718 | ||||||||
\(821\) | 17597.0 | − | 10159.6i | 0.748038 | − | 0.431880i | −0.0769464 | − | 0.997035i | \(-0.524517\pi\) |
0.824985 | + | 0.565155i | \(0.191184\pi\) | |||||||
\(822\) | −38620.3 | − | 56360.5i | −1.63873 | − | 2.39148i | ||||
\(823\) | 5250.28 | − | 9093.75i | 0.222373 | − | 0.385162i | −0.733155 | − | 0.680062i | \(-0.761953\pi\) |
0.955528 | + | 0.294900i | \(0.0952863\pi\) | |||||||
\(824\) | 57300.0 | 2.42250 | ||||||||
\(825\) | −3092.49 | − | 40004.9i | −0.130505 | − | 1.68823i | ||||
\(826\) | 7249.45 | − | 28078.5i | 0.305376 | − | 1.18278i | ||||
\(827\) | 12440.4i | 0.523089i | 0.965191 | + | 0.261545i | \(0.0842319\pi\) | ||||
−0.965191 | + | 0.261545i | \(0.915768\pi\) | |||||||
\(828\) | 65735.3 | + | 25443.4i | 2.75901 | + | 1.06790i | ||||
\(829\) | 25751.9 | − | 14867.9i | 1.07889 | − | 0.622899i | 0.148295 | − | 0.988943i | \(-0.452622\pi\) |
0.930597 | + | 0.366045i | \(0.119288\pi\) | |||||||
\(830\) | − | 46271.0i | − | 1.93505i | ||||||
\(831\) | 4523.57 | − | 349.685i | 0.188834 | − | 0.0145974i | ||||
\(832\) | 1031.66 | − | 595.631i | 0.0429886 | − | 0.0248195i | ||||
\(833\) | 260.432 | + | 14257.3i | 0.0108325 | + | 0.593022i | ||||
\(834\) | −15068.8 | + | 31479.8i | −0.625649 | + | 1.30702i | ||||
\(835\) | −19456.6 | − | 33699.9i | −0.806377 | − | 1.39669i | ||||
\(836\) | 22501.6 | + | 38974.0i | 0.930903 | + | 1.61237i | ||||
\(837\) | −13598.0 | − | 4089.69i | −0.561549 | − | 0.168889i | ||||
\(838\) | 11851.9 | + | 6842.70i | 0.488565 | + | 0.282073i | ||||
\(839\) | −10779.3 | + | 18670.3i | −0.443556 | + | 0.768261i | −0.997950 | − | 0.0639928i | \(-0.979617\pi\) |
0.554395 | + | 0.832254i | \(0.312950\pi\) | |||||||
\(840\) | −14219.3 | + | 80179.9i | −0.584063 | + | 3.29342i | ||||
\(841\) | −10986.7 | − | 19029.5i | −0.450477 | − | 0.780249i | ||||
\(842\) | − | 42074.7i | − | 1.72208i | ||||||
\(843\) | −8457.87 | − | 4048.64i | −0.345557 | − | 0.165412i | ||||
\(844\) | −28063.0 | −1.14451 | ||||||||
\(845\) | −20204.9 | + | 34995.9i | −0.822568 | + | 1.42473i | ||||
\(846\) | −67886.5 | − | 26276.0i | −2.75885 | − | 1.06783i | ||||
\(847\) | −1732.19 | − | 447.225i | −0.0702700 | − | 0.0181426i | ||||
\(848\) | −9652.36 | − | 5572.80i | −0.390877 | − | 0.225673i | ||||
\(849\) | −28271.5 | − | 13533.1i | −1.14284 | − | 0.547060i | ||||
\(850\) | −39641.6 | − | 22887.1i | −1.59964 | − | 0.923553i | ||||
\(851\) | 757.884 | + | 437.565i | 0.0305287 | + | 0.0176258i | ||||
\(852\) | 71471.5 | + | 34212.2i | 2.87391 | + | 1.37569i | ||||
\(853\) | 12410.8 | + | 7165.35i | 0.498167 | + | 0.287617i | 0.727956 | − | 0.685624i | \(-0.240470\pi\) |
−0.229789 | + | 0.973240i | \(0.573804\pi\) | |||||||
\(854\) | −32767.8 | + | 33371.9i | −1.31299 | + | 1.33719i | ||||
\(855\) | 35029.1 | + | 13558.3i | 1.40113 | + | 0.542320i | ||||
\(856\) | 4789.97 | − | 8296.47i | 0.191259 | − | 0.331270i | ||||
\(857\) | −28895.0 | −1.15173 | −0.575866 | − | 0.817544i | \(-0.695335\pi\) | ||||
−0.575866 | + | 0.817544i | \(0.695335\pi\) | |||||||
\(858\) | 3755.82 | + | 1797.85i | 0.149443 | + | 0.0715357i | ||||
\(859\) | 16933.5i | 0.672600i | 0.941755 | + | 0.336300i | \(0.109176\pi\) | ||||
−0.941755 | + | 0.336300i | \(0.890824\pi\) | |||||||
\(860\) | −21965.0 | − | 38044.5i | −0.870931 | − | 1.50850i | ||||
\(861\) | −416.923 | − | 1149.01i | −0.0165026 | − | 0.0454797i | ||||
\(862\) | −26736.6 | + | 46309.2i | −1.05644 | + | 1.82981i | ||||
\(863\) | 659.862 | + | 380.971i | 0.0260278 | + | 0.0150271i | 0.512957 | − | 0.858414i | \(-0.328550\pi\) |
−0.486930 | + | 0.873441i | \(0.661883\pi\) | |||||||
\(864\) | −12618.7 | − | 3795.14i | −0.496869 | − | 0.149436i | ||||
\(865\) | 25761.1 | + | 44619.5i | 1.01261 | + | 1.75388i | ||||
\(866\) | 10851.3 | + | 18795.0i | 0.425799 | + | 0.737506i | ||||
\(867\) | −7144.81 | + | 14926.0i | −0.279874 | + | 0.584674i | ||||
\(868\) | −30878.2 | + | 8576.78i | −1.20746 | + | 0.335386i | ||||
\(869\) | 14762.4 | − | 8523.07i | 0.576271 | − | 0.332710i | ||||
\(870\) | 23685.7 | − | 1830.97i | 0.923011 | − | 0.0713515i | ||||
\(871\) | − | 2980.99i | − | 0.115967i | ||||||
\(872\) | −6233.08 | + | 3598.67i | −0.242063 | + | 0.139755i | ||||
\(873\) | −5962.27 | − | 2307.74i | −0.231148 | − | 0.0894676i | ||||
\(874\) | − | 57312.7i | − | 2.21812i | ||||||
\(875\) | −31560.5 | − | 8148.43i | −1.21936 | − | 0.314820i | ||||
\(876\) | −2493.88 | − | 32261.1i | −0.0961875 | − | 1.24429i | ||||
\(877\) | 9506.85 | 0.366047 | 0.183024 | − | 0.983109i | \(-0.441412\pi\) | ||||
0.183024 | + | 0.983109i | \(0.441412\pi\) | |||||||
\(878\) | 7112.24 | − | 12318.8i | 0.273379 | − | 0.473506i | ||||
\(879\) | −26886.5 | − | 39236.8i | −1.03169 | − | 1.50560i | ||||
\(880\) | 51707.7 | − | 29853.4i | 1.98076 | − | 1.14359i | ||||
\(881\) | 35524.5 | 1.35851 | 0.679257 | − | 0.733901i | \(-0.262302\pi\) | ||||
0.679257 | + | 0.733901i | \(0.262302\pi\) | |||||||
\(882\) | −45705.3 | + | 7966.31i | −1.74487 | + | 0.304126i | ||||
\(883\) | −20779.3 | −0.791934 | −0.395967 | − | 0.918265i | \(-0.629591\pi\) | ||||
−0.395967 | + | 0.918265i | \(0.629591\pi\) | |||||||
\(884\) | 2802.49 | − | 1618.02i | 0.106627 | − | 0.0615610i | ||||
\(885\) | −13020.8 | + | 27201.2i | −0.494562 | + | 1.03317i | ||||
\(886\) | 4828.42 | − | 8363.07i | 0.183086 | − | 0.317114i | ||||
\(887\) | 15097.7 | 0.571512 | 0.285756 | − | 0.958302i | \(-0.407755\pi\) | ||||
0.285756 | + | 0.958302i | \(0.407755\pi\) | |||||||
\(888\) | −1224.06 | − | 585.937i | −0.0462576 | − | 0.0221427i | ||||
\(889\) | −37060.2 | − | 9568.39i | −1.39816 | − | 0.360983i | ||||
\(890\) | − | 127492.i | − | 4.80173i | ||||||
\(891\) | 7779.18 | + | 24402.8i | 0.292494 | + | 0.917536i | ||||
\(892\) | 50873.1 | − | 29371.6i | 1.90959 | − | 1.10250i | ||||
\(893\) | 40321.0i | 1.51096i | ||||||||
\(894\) | 10964.4 | + | 16000.9i | 0.410183 | + | 0.598601i | ||||
\(895\) | 1181.15 | − | 681.935i | 0.0441132 | − | 0.0254688i | ||||
\(896\) | 36798.5 | − | 10221.2i | 1.37204 | − | 0.381101i | ||||
\(897\) | −2042.00 | − | 2980.00i | −0.0760094 | − | 0.110924i | ||||
\(898\) | 33130.2 | + | 57383.2i | 1.23115 | + | 2.13241i | ||||
\(899\) | 2487.25 | + | 4308.05i | 0.0922743 | + | 0.159824i | ||||
\(900\) | 36621.2 | − | 94614.2i | 1.35634 | − | 3.50423i | ||||
\(901\) | 4384.58 | + | 2531.44i | 0.162122 | + | 0.0936010i | ||||
\(902\) | −1117.79 | + | 1936.06i | −0.0412619 | + | 0.0714676i | ||||
\(903\) | 8570.05 | − | 10193.0i | 0.315829 | − | 0.375638i | ||||
\(904\) | −10139.6 | − | 17562.3i | −0.373051 | − | 0.646143i | ||||
\(905\) | − | 41971.6i | − | 1.54164i | ||||||
\(906\) | −73269.7 | + | 50207.0i | −2.68678 | + | 1.84108i | ||||
\(907\) | 668.119 | 0.0244592 | 0.0122296 | − | 0.999925i | \(-0.496107\pi\) | ||||
0.0122296 | + | 0.999925i | \(0.496107\pi\) | |||||||
\(908\) | −33219.7 | + | 57538.2i | −1.21413 | + | 2.10294i | ||||
\(909\) | −9447.34 | + | 1469.40i | −0.344718 | + | 0.0536158i | ||||
\(910\) | 5495.39 | − | 5596.68i | 0.200187 | − | 0.203877i | ||||
\(911\) | 11058.3 | + | 6384.54i | 0.402173 | + | 0.232195i | 0.687421 | − | 0.726259i | \(-0.258743\pi\) |
−0.285248 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(912\) | 2746.07 | + | 35523.5i | 0.0997055 | + | 1.28980i | ||||
\(913\) | −15135.1 | − | 8738.28i | −0.548631 | − | 0.316752i | ||||
\(914\) | 35635.0 | + | 20573.9i | 1.28961 | + | 0.744555i | ||||
\(915\) | 40121.2 | − | 27492.5i | 1.44958 | − | 0.993305i | ||||
\(916\) | −33771.3 | − | 19497.9i | −1.21816 | − | 0.703305i | ||||
\(917\) | 2932.07 | + | 757.017i | 0.105589 | + | 0.0272616i | ||||
\(918\) | 27981.2 | + | 8415.51i | 1.00601 | + | 0.302563i | ||||
\(919\) | −12511.9 | + | 21671.3i | −0.449108 | + | 0.777878i | −0.998328 | − | 0.0577998i | \(-0.981591\pi\) |
0.549220 | + | 0.835678i | \(0.314925\pi\) | |||||||
\(920\) | −129211. | −4.63039 | ||||||||
\(921\) | −1283.91 | − | 16608.8i | −0.0459350 | − | 0.594221i | ||||
\(922\) | 55020.1i | 1.96528i | ||||||||
\(923\) | −2030.48 | − | 3516.89i | −0.0724096 | − | 0.125417i | ||||
\(924\) | 44244.8 | + | 37200.1i | 1.57527 | + | 1.32445i | ||||
\(925\) | 629.796 | − | 1090.84i | 0.0223866 | − | 0.0387747i | ||||
\(926\) | −52876.2 | − | 30528.1i | −1.87648 | − | 1.08339i | ||||
\(927\) | −5217.59 | − | 33546.0i | −0.184863 | − | 1.18856i | ||||
\(928\) | 2308.11 | + | 3997.77i | 0.0816461 | + | 0.141415i | ||||
\(929\) | −6089.03 | − | 10546.5i | −0.215042 | − | 0.372464i | 0.738243 | − | 0.674535i | \(-0.235656\pi\) |
−0.953286 | + | 0.302070i | \(0.902322\pi\) | |||||||
\(930\) | 48775.6 | − | 3770.50i | 1.71980 | − | 0.132946i | ||||
\(931\) | 13253.3 | + | 22016.7i | 0.466552 | + | 0.775048i | ||||
\(932\) | 11820.9 | − | 6824.79i | 0.415457 | − | 0.239864i | ||||
\(933\) | 10.9297 | − | 22.8328i | 0.000383517 | − | 0.000801191i | ||||
\(934\) | 30140.3i | 1.05591i | ||||||||
\(935\) | −23488.2 | + | 13560.9i | −0.821546 | + | 0.474320i | ||||
\(936\) | 3513.30 | + | 4363.31i | 0.122688 | + | 0.152371i | ||||
\(937\) | − | 31836.0i | − | 1.10996i | −0.831863 | − | 0.554982i | \(-0.812725\pi\) | ||
0.831863 | − | 0.554982i | \(-0.187275\pi\) | |||||||
\(938\) | 15186.1 | − | 58818.5i | 0.528616 | − | 2.04743i | ||||
\(939\) | −8231.95 | + | 5640.83i | −0.286091 | + | 0.196040i | ||||
\(940\) | 170848. | 5.92813 | ||||||||
\(941\) | −22435.3 | + | 38859.0i | −0.777226 | + | 1.34619i | 0.156310 | + | 0.987708i | \(0.450040\pi\) |
−0.933535 | + | 0.358486i | \(0.883293\pi\) | |||||||
\(942\) | 60130.0 | − | 4648.23i | 2.07977 | − | 0.160772i | ||||
\(943\) | 1679.66 | − | 969.752i | 0.0580035 | − | 0.0334883i | ||||
\(944\) | −28605.8 | −0.986272 | ||||||||
\(945\) | 48235.7 | + | 1023.65i | 1.66043 | + | 0.0352373i | ||||
\(946\) | −24356.4 | −0.837100 | ||||||||
\(947\) | 10108.1 | − | 5835.91i | 0.346852 | − | 0.200255i | −0.316446 | − | 0.948611i | \(-0.602490\pi\) |
0.663298 | + | 0.748355i | \(0.269156\pi\) | |||||||
\(948\) | 42973.0 | − | 3321.94i | 1.47225 | − | 0.113810i | ||||
\(949\) | −829.160 | + | 1436.15i | −0.0283621 | + | 0.0491246i | ||||
\(950\) | −82491.5 | −2.81724 | ||||||||
\(951\) | 43546.6 | − | 29839.7i | 1.48485 | − | 1.01748i | ||||
\(952\) | 33807.4 | − | 9390.40i | 1.15095 | − | 0.319690i | ||||
\(953\) | − | 4481.70i | − | 0.152336i | −0.997095 | − | 0.0761682i | \(-0.975731\pi\) | ||
0.997095 | − | 0.0761682i | \(-0.0242686\pi\) | |||||||
\(954\) | −5945.86 | + | 15361.7i | −0.201786 | + | 0.521334i | ||||
\(955\) | 60500.0 | − | 34929.7i | 2.04998 | − | 1.18356i | ||||
\(956\) | 89969.2i | 3.04374i | ||||||||
\(957\) | 3874.14 | − | 8093.32i | 0.130860 | − | 0.273375i | ||||
\(958\) | −45804.2 | + | 26445.0i | −1.54474 | + | 0.891859i | ||||
\(959\) | −12151.9 | + | 47066.5i | −0.409180 | + | 1.58483i | ||||
\(960\) | −25169.9 | + | 1945.71i | −0.846204 | + | 0.0654141i | ||||
\(961\) | −9773.53 | − | 16928.2i | −0.328070 | − | 0.568234i | ||||
\(962\) | 65.3580 | + | 113.203i | 0.00219046 | + | 0.00379399i | ||||
\(963\) | −5293.29 | − | 2048.81i | −0.177127 | − | 0.0685586i | ||||
\(964\) | −58505.9 | − | 33778.4i | −1.95472 | − | 1.12856i | ||||
\(965\) | 1316.53 | − | 2280.30i | 0.0439177 | − | 0.0760677i | ||||
\(966\) | −25110.2 | − | 69201.6i | −0.836343 | − | 2.30489i | ||||
\(967\) | 10438.9 | + | 18080.8i | 0.347149 | + | 0.601280i | 0.985742 | − | 0.168265i | \(-0.0538164\pi\) |
−0.638593 | + | 0.769545i | \(0.720483\pi\) | |||||||
\(968\) | 4401.98i | 0.146162i | ||||||||
\(969\) | −1247.40 | − | 16136.5i | −0.0413542 | − | 0.534963i | ||||
\(970\) | 22026.3 | 0.729096 | ||||||||
\(971\) | −9951.75 | + | 17236.9i | −0.328905 | + | 0.569680i | −0.982295 | − | 0.187341i | \(-0.940013\pi\) |
0.653390 | + | 0.757022i | \(0.273346\pi\) | |||||||
\(972\) | −8899.26 | + | 64147.5i | −0.293666 | + | 2.11680i | ||||
\(973\) | 23924.9 | − | 6645.43i | 0.788282 | − | 0.218954i | ||||
\(974\) | 15290.8 | + | 8828.17i | 0.503029 | + | 0.290424i | ||||
\(975\) | −4289.17 | + | 2939.10i | −0.140886 | + | 0.0965399i | ||||
\(976\) | 39954.3 | + | 23067.6i | 1.31035 | + | 0.756533i | ||||
\(977\) | −2735.30 | − | 1579.22i | −0.0895700 | − | 0.0517133i | 0.454546 | − | 0.890723i | \(-0.349802\pi\) |
−0.544116 | + | 0.839010i | \(0.683135\pi\) | |||||||
\(978\) | −2929.83 | − | 37900.7i | −0.0957932 | − | 1.23919i | ||||
\(979\) | −41702.3 | − | 24076.9i | −1.36140 | − | 0.786006i | ||||
\(980\) | 93289.2 | − | 56156.9i | 3.04083 | − | 1.83048i | ||||
\(981\) | 2674.39 | + | 3321.44i | 0.0870405 | + | 0.108099i | ||||
\(982\) | −31393.1 | + | 54374.4i | −1.02016 | + | 1.76696i | ||||
\(983\) | −2682.61 | −0.0870417 | −0.0435208 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435208 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(984\) | −2481.02 | + | 1700.08i | −0.0803780 | + | 0.0550779i | ||||
\(985\) | − | 64444.8i | − | 2.08465i | ||||||
\(986\) | −5118.12 | − | 8864.84i | −0.165308 | − | 0.286323i | ||||
\(987\) | 17665.7 | + | 48685.1i | 0.569711 | + | 1.57008i | ||||
\(988\) | 2915.90 | − | 5050.49i | 0.0938939 | − | 0.162629i | ||||
\(989\) | 18299.8 | + | 10565.4i | 0.588373 | + | 0.339697i | ||||
\(990\) | −55341.4 | − | 68730.8i | −1.77663 | − | 2.20647i | ||||
\(991\) | −186.928 | − | 323.769i | −0.00599189 | − | 0.0103783i | 0.863014 | − | 0.505180i | \(-0.168574\pi\) |
−0.869006 | + | 0.494802i | \(0.835241\pi\) | |||||||
\(992\) | 4753.08 | + | 8232.57i | 0.152127 | + | 0.263492i | ||||
\(993\) | −33801.9 | − | 49328.9i | −1.08023 | − | 1.57644i | ||||
\(994\) | −22147.7 | − | 79736.5i | −0.706724 | − | 2.54436i | ||||
\(995\) | −1079.04 | + | 622.981i | −0.0343796 | + | 0.0198491i | ||||
\(996\) | −24978.6 | − | 36452.5i | −0.794655 | − | 1.15968i | ||||
\(997\) | 48421.0i | 1.53812i | 0.639176 | + | 0.769061i | \(0.279276\pi\) | ||||
−0.639176 | + | 0.769061i | \(0.720724\pi\) | |||||||
\(998\) | −41426.7 | + | 23917.7i | −1.31397 | + | 0.758619i | ||||
\(999\) | −231.574 | + | 769.973i | −0.00733401 | + | 0.0243853i |
(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 | 63.4.s.a.47.2 | yes | 44 | |
3.2 | odd | 2 | 189.4.s.a.89.21 | 44 | |||
7.3 | odd | 6 | 63.4.i.a.38.2 | yes | 44 | ||
9.4 | even | 3 | 189.4.i.a.152.2 | 44 | |||
9.5 | odd | 6 | 63.4.i.a.5.21 | ✓ | 44 | ||
21.17 | even | 6 | 189.4.i.a.143.21 | 44 | |||
63.31 | odd | 6 | 189.4.s.a.17.21 | 44 | |||
63.59 | even | 6 | inner | 63.4.s.a.59.2 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.21 | ✓ | 44 | 9.5 | odd | 6 | ||
63.4.i.a.38.2 | yes | 44 | 7.3 | odd | 6 | ||
63.4.s.a.47.2 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.s.a.59.2 | yes | 44 | 63.59 | even | 6 | inner | |
189.4.i.a.143.21 | 44 | 21.17 | even | 6 | |||
189.4.i.a.152.2 | 44 | 9.4 | even | 3 | |||
189.4.s.a.17.21 | 44 | 63.31 | odd | 6 | |||
189.4.s.a.89.21 | 44 | 3.2 | odd | 2 |