Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Relative dimension: | \(38\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.17 | ||
Character | \(\chi\) | \(=\) | 76.7 |
Dual form | 76.5.g.a.11.17 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.485536 | − | 3.97042i | −0.121384 | − | 0.992606i | ||||
\(3\) | 7.19063 | − | 4.15151i | 0.798958 | − | 0.461279i | −0.0441484 | − | 0.999025i | \(-0.514057\pi\) |
0.843107 | + | 0.537746i | \(0.180724\pi\) | |||||||
\(4\) | −15.5285 | + | 3.85556i | −0.970532 | + | 0.240973i | ||||
\(5\) | −24.3962 | − | 42.2554i | −0.975847 | − | 1.69022i | −0.677110 | − | 0.735882i | \(-0.736768\pi\) |
−0.298737 | − | 0.954335i | \(-0.596565\pi\) | |||||||
\(6\) | −19.9746 | − | 26.5341i | −0.554849 | − | 0.737059i | ||||
\(7\) | 41.7489i | 0.852019i | 0.904719 | + | 0.426010i | \(0.140081\pi\) | ||||
−0.904719 | + | 0.426010i | \(0.859919\pi\) | |||||||
\(8\) | 22.8479 | + | 59.7827i | 0.356998 | + | 0.934105i | ||||
\(9\) | −6.02993 | + | 10.4441i | −0.0744436 | + | 0.128940i | ||||
\(10\) | −155.927 | + | 117.380i | −1.55927 | + | 1.17380i | ||||
\(11\) | − | 125.138i | − | 1.03420i | −0.855925 | − | 0.517100i | \(-0.827012\pi\) | ||
0.855925 | − | 0.517100i | \(-0.172988\pi\) | |||||||
\(12\) | −95.6533 | + | 92.1907i | −0.664259 | + | 0.640213i | ||||
\(13\) | −25.2283 | + | 43.6968i | −0.149280 | + | 0.258561i | −0.930962 | − | 0.365117i | \(-0.881029\pi\) |
0.781681 | + | 0.623678i | \(0.214362\pi\) | |||||||
\(14\) | 165.761 | − | 20.2706i | 0.845719 | − | 0.103421i | ||||
\(15\) | −350.848 | − | 202.562i | −1.55932 | − | 0.900276i | ||||
\(16\) | 226.269 | − | 119.742i | 0.883864 | − | 0.467744i | ||||
\(17\) | 6.72503 | + | 11.6481i | 0.0232700 | + | 0.0403048i | 0.877426 | − | 0.479712i | \(-0.159259\pi\) |
−0.854156 | + | 0.520017i | \(0.825926\pi\) | |||||||
\(18\) | 44.3954 | + | 18.8704i | 0.137023 | + | 0.0582418i | ||||
\(19\) | −292.291 | − | 211.865i | −0.809671 | − | 0.586883i | ||||
\(20\) | 541.755 | + | 562.103i | 1.35439 | + | 1.40526i | ||||
\(21\) | 173.321 | + | 300.201i | 0.393019 | + | 0.680728i | ||||
\(22\) | −496.851 | + | 60.7591i | −1.02655 | + | 0.125535i | ||||
\(23\) | −155.132 | − | 89.5655i | −0.293255 | − | 0.169311i | 0.346154 | − | 0.938178i | \(-0.387488\pi\) |
−0.639409 | + | 0.768867i | \(0.720821\pi\) | |||||||
\(24\) | 412.479 | + | 335.022i | 0.716110 | + | 0.581636i | ||||
\(25\) | −877.848 | + | 1520.48i | −1.40456 | + | 2.43276i | ||||
\(26\) | 185.744 | + | 78.9508i | 0.274769 | + | 0.116791i | ||||
\(27\) | 772.678i | 1.05991i | ||||||||
\(28\) | −160.966 | − | 648.299i | −0.205313 | − | 0.826912i | ||||
\(29\) | 578.800 | − | 1002.51i | 0.688229 | − | 1.19205i | −0.284182 | − | 0.958770i | \(-0.591722\pi\) |
0.972410 | − | 0.233277i | \(-0.0749448\pi\) | |||||||
\(30\) | −633.908 | + | 1491.36i | −0.704342 | + | 1.65707i | ||||
\(31\) | − | 1654.61i | − | 1.72176i | −0.508806 | − | 0.860881i | \(-0.669913\pi\) | ||
0.508806 | − | 0.860881i | \(-0.330087\pi\) | |||||||
\(32\) | −585.290 | − | 840.245i | −0.571572 | − | 0.820552i | ||||
\(33\) | −519.512 | − | 899.822i | −0.477054 | − | 0.826282i | ||||
\(34\) | 42.9826 | − | 32.3568i | 0.0371822 | − | 0.0279903i | ||||
\(35\) | 1764.12 | − | 1018.51i | 1.44010 | − | 0.831441i | ||||
\(36\) | 53.3677 | − | 185.431i | 0.0411788 | − | 0.143079i | ||||
\(37\) | −901.700 | −0.658656 | −0.329328 | − | 0.944216i | \(-0.606822\pi\) | ||||
−0.329328 | + | 0.944216i | \(0.606822\pi\) | |||||||
\(38\) | −699.275 | + | 1263.39i | −0.484263 | + | 0.874923i | ||||
\(39\) | 418.943i | 0.275439i | ||||||||
\(40\) | 1968.74 | − | 2423.92i | 1.23047 | − | 1.51495i | ||||
\(41\) | −267.347 | − | 463.058i | −0.159040 | − | 0.275466i | 0.775483 | − | 0.631369i | \(-0.217507\pi\) |
−0.934523 | + | 0.355903i | \(0.884173\pi\) | |||||||
\(42\) | 1107.77 | − | 833.917i | 0.627988 | − | 0.472742i | ||||
\(43\) | 1585.27 | − | 915.257i | 0.857367 | − | 0.495001i | −0.00576278 | − | 0.999983i | \(-0.501834\pi\) |
0.863130 | + | 0.504982i | \(0.168501\pi\) | |||||||
\(44\) | 482.478 | + | 1943.21i | 0.249214 | + | 1.00372i | ||||
\(45\) | 588.429 | 0.290582 | ||||||||
\(46\) | −280.291 | + | 659.427i | −0.132463 | + | 0.311639i | ||||
\(47\) | −2719.96 | − | 1570.37i | −1.23131 | − | 0.710896i | −0.264006 | − | 0.964521i | \(-0.585044\pi\) |
−0.967303 | + | 0.253625i | \(0.918377\pi\) | |||||||
\(48\) | 1129.91 | − | 1800.38i | 0.490411 | − | 0.781416i | ||||
\(49\) | 658.026 | 0.274063 | ||||||||
\(50\) | 6463.16 | + | 2747.18i | 2.58526 | + | 1.09887i | ||||
\(51\) | 96.7144 | + | 55.8381i | 0.0371835 | + | 0.0214679i | ||||
\(52\) | 223.283 | − | 775.815i | 0.0825750 | − | 0.286914i | ||||
\(53\) | 996.465 | − | 1725.93i | 0.354740 | − | 0.614428i | −0.632333 | − | 0.774696i | \(-0.717903\pi\) |
0.987073 | + | 0.160269i | \(0.0512360\pi\) | |||||||
\(54\) | 3067.86 | − | 375.163i | 1.05208 | − | 0.128657i | ||||
\(55\) | −5287.77 | + | 3052.89i | −1.74802 | + | 1.00922i | ||||
\(56\) | −2495.87 | + | 953.874i | −0.795876 | + | 0.304169i | ||||
\(57\) | −2981.32 | − | 309.991i | −0.917611 | − | 0.0954111i | ||||
\(58\) | −4261.42 | − | 1811.33i | −1.26677 | − | 0.538444i | ||||
\(59\) | 2738.87 | − | 1581.28i | 0.786804 | − | 0.454262i | −0.0520320 | − | 0.998645i | \(-0.516570\pi\) |
0.838836 | + | 0.544384i | \(0.183236\pi\) | |||||||
\(60\) | 6229.13 | + | 1792.77i | 1.73031 | + | 0.497992i | ||||
\(61\) | 150.641 | − | 260.918i | 0.0404840 | − | 0.0701203i | −0.845073 | − | 0.534650i | \(-0.820443\pi\) |
0.885557 | + | 0.464530i | \(0.153777\pi\) | |||||||
\(62\) | −6569.52 | + | 803.374i | −1.70903 | + | 0.208994i | ||||
\(63\) | −436.032 | − | 251.743i | −0.109859 | − | 0.0634273i | ||||
\(64\) | −3051.95 | + | 2731.82i | −0.745105 | + | 0.666947i | ||||
\(65\) | 2461.90 | 0.582698 | ||||||||
\(66\) | −3320.43 | + | 2499.58i | −0.762266 | + | 0.573824i | ||||
\(67\) | 1439.68 | + | 831.198i | 0.320712 | + | 0.185163i | 0.651710 | − | 0.758468i | \(-0.274052\pi\) |
−0.330998 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(68\) | −149.340 | − | 154.949i | −0.0322966 | − | 0.0335097i | ||||
\(69\) | −1487.33 | −0.312398 | ||||||||
\(70\) | −4900.48 | − | 6509.77i | −1.00010 | − | 1.32853i | ||||
\(71\) | 4871.88 | − | 2812.78i | 0.966452 | − | 0.557981i | 0.0682992 | − | 0.997665i | \(-0.478243\pi\) |
0.898153 | + | 0.439684i | \(0.144909\pi\) | |||||||
\(72\) | −762.150 | − | 121.859i | −0.147020 | − | 0.0235068i | ||||
\(73\) | 1680.02 | + | 2909.88i | 0.315260 | + | 0.546047i | 0.979493 | − | 0.201479i | \(-0.0645748\pi\) |
−0.664232 | + | 0.747526i | \(0.731241\pi\) | |||||||
\(74\) | 437.808 | + | 3580.13i | 0.0799503 | + | 0.653786i | ||||
\(75\) | 14577.6i | 2.59157i | ||||||||
\(76\) | 5355.71 | + | 2163.00i | 0.927235 | + | 0.374480i | ||||
\(77\) | 5224.39 | 0.881158 | ||||||||
\(78\) | 1663.38 | − | 203.412i | 0.273402 | − | 0.0334339i | ||||
\(79\) | −362.777 | + | 209.450i | −0.0581281 | + | 0.0335603i | −0.528782 | − | 0.848757i | \(-0.677351\pi\) |
0.470654 | + | 0.882318i | \(0.344018\pi\) | |||||||
\(80\) | −10579.9 | − | 6639.85i | −1.65310 | − | 1.03748i | ||||
\(81\) | 2719.36 | + | 4710.06i | 0.414473 | + | 0.717888i | ||||
\(82\) | −1708.73 | + | 1286.31i | −0.254124 | + | 0.191301i | ||||
\(83\) | 92.4292i | 0.0134169i | 0.999977 | + | 0.00670846i | \(0.00213539\pi\) | ||||
−0.999977 | + | 0.00670846i | \(0.997865\pi\) | |||||||
\(84\) | −3848.86 | − | 3993.42i | −0.545474 | − | 0.565961i | ||||
\(85\) | 328.130 | − | 568.338i | 0.0454159 | − | 0.0786627i | ||||
\(86\) | −4403.66 | − | 5849.81i | −0.595411 | − | 0.790942i | ||||
\(87\) | − | 9611.58i | − | 1.26986i | ||||||
\(88\) | 7481.10 | − | 2859.14i | 0.966051 | − | 0.369207i | ||||
\(89\) | −4333.45 | + | 7505.75i | −0.547083 | + | 0.947576i | 0.451389 | + | 0.892327i | \(0.350929\pi\) |
−0.998473 | + | 0.0552491i | \(0.982405\pi\) | |||||||
\(90\) | −285.703 | − | 2336.31i | −0.0352720 | − | 0.288434i | ||||
\(91\) | −1824.29 | − | 1053.26i | −0.220299 | − | 0.127190i | ||||
\(92\) | 2754.30 | + | 792.698i | 0.325413 | + | 0.0936552i | ||||
\(93\) | −6869.15 | − | 11897.7i | −0.794213 | − | 1.37562i | ||||
\(94\) | −4914.39 | + | 11561.9i | −0.556178 | + | 1.30849i | ||||
\(95\) | −1821.65 | + | 17519.6i | −0.201845 | + | 1.94123i | ||||
\(96\) | −7696.89 | − | 3612.05i | −0.835166 | − | 0.391933i | ||||
\(97\) | 5910.96 | + | 10238.1i | 0.628224 | + | 1.08812i | 0.987908 | + | 0.155041i | \(0.0495511\pi\) |
−0.359684 | + | 0.933074i | \(0.617116\pi\) | |||||||
\(98\) | −319.495 | − | 2612.64i | −0.0332669 | − | 0.272037i | ||||
\(99\) | 1306.96 | + | 754.574i | 0.133350 | + | 0.0769895i | ||||
\(100\) | 7769.37 | − | 26995.3i | 0.776937 | − | 2.69953i | ||||
\(101\) | −9364.27 | + | 16219.4i | −0.917976 | + | 1.58998i | −0.115492 | + | 0.993308i | \(0.536844\pi\) |
−0.802485 | + | 0.596673i | \(0.796489\pi\) | |||||||
\(102\) | 174.742 | − | 411.108i | 0.0167957 | − | 0.0395144i | ||||
\(103\) | − | 5543.03i | − | 0.522483i | −0.965273 | − | 0.261242i | \(-0.915868\pi\) | ||
0.965273 | − | 0.261242i | \(-0.0841320\pi\) | |||||||
\(104\) | −3188.73 | − | 509.841i | −0.294816 | − | 0.0471377i | ||||
\(105\) | 8456.75 | − | 14647.5i | 0.767052 | − | 1.32857i | ||||
\(106\) | −7336.48 | − | 3118.39i | −0.652944 | − | 0.277535i | ||||
\(107\) | 1419.11i | 0.123950i | 0.998078 | + | 0.0619751i | \(0.0197400\pi\) | ||||
−0.998078 | + | 0.0619751i | \(0.980260\pi\) | |||||||
\(108\) | −2979.11 | − | 11998.5i | −0.255411 | − | 1.02868i | ||||
\(109\) | −10812.2 | − | 18727.3i | −0.910044 | − | 1.57624i | −0.814000 | − | 0.580865i | \(-0.802714\pi\) |
−0.0960437 | − | 0.995377i | \(-0.530619\pi\) | |||||||
\(110\) | 14688.7 | + | 19512.4i | 1.21394 | + | 1.61259i | ||||
\(111\) | −6483.79 | + | 3743.42i | −0.526239 | + | 0.303824i | ||||
\(112\) | 4999.12 | + | 9446.50i | 0.398527 | + | 0.753069i | ||||
\(113\) | −530.320 | −0.0415318 | −0.0207659 | − | 0.999784i | \(-0.506610\pi\) | ||||
−0.0207659 | + | 0.999784i | \(0.506610\pi\) | |||||||
\(114\) | 216.742 | + | 11987.6i | 0.0166776 | + | 0.922407i | ||||
\(115\) | 8740.23i | 0.660887i | ||||||||
\(116\) | −5122.66 | + | 17799.1i | −0.380697 | + | 1.32276i | ||||
\(117\) | −304.250 | − | 526.977i | −0.0222259 | − | 0.0384964i | ||||
\(118\) | −7608.19 | − | 10106.7i | −0.546408 | − | 0.725846i | ||||
\(119\) | −486.296 | + | 280.763i | −0.0343405 | + | 0.0198265i | ||||
\(120\) | 4093.59 | − | 25602.7i | 0.284277 | − | 1.77797i | ||||
\(121\) | −1018.55 | −0.0695686 | ||||||||
\(122\) | −1109.09 | − | 471.423i | −0.0745159 | − | 0.0316731i | ||||
\(123\) | −3844.78 | − | 2219.79i | −0.254133 | − | 0.146724i | ||||
\(124\) | 6379.47 | + | 25693.7i | 0.414898 | + | 1.67103i | ||||
\(125\) | 55169.3 | 3.53083 | ||||||||
\(126\) | −787.818 | + | 1853.46i | −0.0496232 | + | 0.116746i | ||||
\(127\) | 12314.3 | + | 7109.68i | 0.763490 | + | 0.440801i | 0.830547 | − | 0.556948i | \(-0.188028\pi\) |
−0.0670574 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(128\) | 12328.3 | + | 10791.1i | 0.752459 | + | 0.658639i | ||||
\(129\) | 7599.40 | − | 13162.5i | 0.456667 | − | 0.790970i | ||||
\(130\) | −1195.34 | − | 9774.79i | −0.0707302 | − | 0.578390i | ||||
\(131\) | 9162.58 | − | 5290.02i | 0.533919 | − | 0.308258i | −0.208692 | − | 0.977981i | \(-0.566921\pi\) |
0.742611 | + | 0.669723i | \(0.233587\pi\) | |||||||
\(132\) | 11536.6 | + | 11969.9i | 0.662108 | + | 0.686976i | ||||
\(133\) | 8845.14 | − | 12202.9i | 0.500036 | − | 0.689856i | ||||
\(134\) | 2601.19 | − | 6119.70i | 0.144865 | − | 0.340817i | ||||
\(135\) | 32649.8 | − | 18850.4i | 1.79149 | − | 1.03432i | ||||
\(136\) | −542.702 | + | 668.175i | −0.0293416 | + | 0.0361254i | ||||
\(137\) | −6374.78 | + | 11041.5i | −0.339644 | + | 0.588281i | −0.984366 | − | 0.176136i | \(-0.943640\pi\) |
0.644721 | + | 0.764418i | \(0.276973\pi\) | |||||||
\(138\) | 722.151 | + | 5905.32i | 0.0379202 | + | 0.310088i | ||||
\(139\) | −4743.50 | − | 2738.66i | −0.245510 | − | 0.141745i | 0.372196 | − | 0.928154i | \(-0.378605\pi\) |
−0.617707 | + | 0.786409i | \(0.711938\pi\) | |||||||
\(140\) | −23467.2 | + | 22617.7i | −1.19731 | + | 1.15396i | ||||
\(141\) | −26077.6 | −1.31169 | ||||||||
\(142\) | −13533.4 | − | 17977.7i | −0.671167 | − | 0.891576i | ||||
\(143\) | 5468.13 | + | 3157.03i | 0.267403 | + | 0.154385i | ||||
\(144\) | −113.781 | + | 3085.23i | −0.00548713 | + | 0.148786i | ||||
\(145\) | −56482.1 | −2.68643 | ||||||||
\(146\) | 10737.8 | − | 8083.25i | 0.503742 | − | 0.379211i | ||||
\(147\) | 4731.62 | − | 2731.80i | 0.218965 | − | 0.126420i | ||||
\(148\) | 14002.1 | − | 3476.56i | 0.639247 | − | 0.158718i | ||||
\(149\) | −9375.16 | − | 16238.2i | −0.422285 | − | 0.731420i | 0.573877 | − | 0.818941i | \(-0.305439\pi\) |
−0.996163 | + | 0.0875216i | \(0.972105\pi\) | |||||||
\(150\) | 57879.1 | − | 7077.93i | 2.57241 | − | 0.314575i | ||||
\(151\) | − | 32292.3i | − | 1.41627i | −0.706079 | − | 0.708133i | \(-0.749538\pi\) | ||
0.706079 | − | 0.708133i | \(-0.250462\pi\) | |||||||
\(152\) | 5987.63 | − | 22314.6i | 0.259160 | − | 0.965834i | ||||
\(153\) | −162.206 | −0.00692921 | ||||||||
\(154\) | −2536.63 | − | 20743.0i | −0.106958 | − | 0.874642i | ||||
\(155\) | −69916.4 | + | 40366.3i | −2.91015 | + | 1.68018i | ||||
\(156\) | −1615.26 | − | 6505.56i | −0.0663733 | − | 0.267322i | ||||
\(157\) | 17475.1 | + | 30267.8i | 0.708959 | + | 1.22795i | 0.965244 | + | 0.261351i | \(0.0841681\pi\) |
−0.256285 | + | 0.966601i | \(0.582499\pi\) | |||||||
\(158\) | 1007.74 | + | 1338.68i | 0.0403679 | + | 0.0536246i | ||||
\(159\) | − | 16547.3i | − | 0.654536i | ||||||
\(160\) | −21226.1 | + | 45230.4i | −0.829144 | + | 1.76681i | ||||
\(161\) | 3739.27 | − | 6476.60i | 0.144256 | − | 0.249859i | ||||
\(162\) | 17380.6 | − | 13083.9i | 0.662269 | − | 0.498548i | ||||
\(163\) | − | 45639.8i | − | 1.71779i | −0.512156 | − | 0.858893i | \(-0.671153\pi\) | ||
0.512156 | − | 0.858893i | \(-0.328847\pi\) | |||||||
\(164\) | 5936.85 | + | 6159.83i | 0.220734 | + | 0.229024i | ||||
\(165\) | −25348.2 | + | 43904.4i | −0.931065 | + | 1.61265i | ||||
\(166\) | 366.983 | − | 44.8777i | 0.0133177 | − | 0.00162860i | ||||
\(167\) | 12344.2 | + | 7126.91i | 0.442618 | + | 0.255546i | 0.704707 | − | 0.709498i | \(-0.251078\pi\) |
−0.262090 | + | 0.965044i | \(0.584412\pi\) | |||||||
\(168\) | −13986.8 | + | 17220.6i | −0.495565 | + | 0.610139i | ||||
\(169\) | 13007.6 | + | 22529.8i | 0.455431 | + | 0.788829i | ||||
\(170\) | −2415.86 | − | 1026.87i | −0.0835938 | − | 0.0355317i | ||||
\(171\) | 3975.24 | − | 1775.20i | 0.135948 | − | 0.0607094i | ||||
\(172\) | −21088.1 | + | 20324.7i | −0.712820 | + | 0.687016i | ||||
\(173\) | −7286.53 | − | 12620.6i | −0.243460 | − | 0.421686i | 0.718237 | − | 0.695798i | \(-0.244949\pi\) |
−0.961698 | + | 0.274112i | \(0.911616\pi\) | |||||||
\(174\) | −38162.0 | + | 4666.77i | −1.26047 | + | 0.154141i | ||||
\(175\) | −63478.3 | − | 36649.2i | −2.07276 | − | 1.19671i | ||||
\(176\) | −14984.3 | − | 28314.9i | −0.483740 | − | 0.914092i | ||||
\(177\) | 13129.4 | − | 22740.9i | 0.419083 | − | 0.725872i | ||||
\(178\) | 31905.1 | + | 13561.3i | 1.00698 | + | 0.428018i | ||||
\(179\) | 19239.7i | 0.600471i | 0.953865 | + | 0.300236i | \(0.0970653\pi\) | ||||
−0.953865 | + | 0.300236i | \(0.902935\pi\) | |||||||
\(180\) | −9137.43 | + | 2268.73i | −0.282019 | + | 0.0700224i | ||||
\(181\) | −1593.83 | + | 2760.59i | −0.0486502 | + | 0.0842646i | −0.889325 | − | 0.457276i | \(-0.848825\pi\) |
0.840675 | + | 0.541540i | \(0.182159\pi\) | |||||||
\(182\) | −3296.11 | + | 7754.61i | −0.0995083 | + | 0.234108i | ||||
\(183\) | − | 2501.55i | − | 0.0746976i | ||||||
\(184\) | 1810.04 | − | 11320.6i | 0.0534628 | − | 0.334375i | ||||
\(185\) | 21998.1 | + | 38101.7i | 0.642748 | + | 1.11327i | ||||
\(186\) | −43903.7 | + | 33050.2i | −1.26904 | + | 0.955318i | ||||
\(187\) | 1457.62 | − | 841.558i | 0.0416832 | − | 0.0240658i | ||||
\(188\) | 48291.6 | + | 13898.5i | 1.36633 | + | 0.393236i | ||||
\(189\) | −32258.5 | −0.903068 | ||||||||
\(190\) | 70444.7 | − | 1273.68i | 1.95138 | − | 0.0352819i | ||||
\(191\) | − | 15034.1i | − | 0.412109i | −0.978541 | − | 0.206054i | \(-0.933938\pi\) | ||
0.978541 | − | 0.206054i | \(-0.0660624\pi\) | |||||||
\(192\) | −10604.3 | + | 32313.7i | −0.287659 | + | 0.876564i | ||||
\(193\) | −18523.3 | − | 32083.4i | −0.497284 | − | 0.861321i | 0.502711 | − | 0.864455i | \(-0.332336\pi\) |
−0.999995 | + | 0.00313314i | \(0.999003\pi\) | |||||||
\(194\) | 37779.5 | − | 28440.0i | 1.00381 | − | 0.755658i | ||||
\(195\) | 17702.6 | − | 10220.6i | 0.465552 | − | 0.268786i | ||||
\(196\) | −10218.2 | + | 2537.06i | −0.265987 | + | 0.0660418i | ||||
\(197\) | 7186.57 | 0.185178 | 0.0925890 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925890 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(198\) | 2361.40 | − | 5555.56i | 0.0602337 | − | 0.141709i | ||||
\(199\) | 33711.6 | + | 19463.4i | 0.851283 | + | 0.491488i | 0.861083 | − | 0.508464i | \(-0.169786\pi\) |
−0.00980084 | + | 0.999952i | \(0.503120\pi\) | |||||||
\(200\) | −110955. | − | 17740.5i | −2.77388 | − | 0.443512i | ||||
\(201\) | 13802.9 | 0.341648 | ||||||||
\(202\) | 68944.6 | + | 29305.0i | 1.68965 | + | 0.718190i | ||||
\(203\) | 41853.8 | + | 24164.3i | 1.01565 | + | 0.586384i | ||||
\(204\) | −1717.12 | − | 494.193i | −0.0412610 | − | 0.0118751i | ||||
\(205\) | −13044.5 | + | 22593.7i | −0.310398 | + | 0.537625i | ||||
\(206\) | −22008.2 | + | 2691.34i | −0.518620 | + | 0.0634211i | ||||
\(207\) | 1870.87 | − | 1080.15i | 0.0436619 | − | 0.0252082i | ||||
\(208\) | −476.044 | + | 12908.1i | −0.0110032 | + | 0.298357i | ||||
\(209\) | −26512.4 | + | 36576.8i | −0.606955 | + | 0.837362i | ||||
\(210\) | −62262.9 | − | 26465.0i | −1.41186 | − | 0.600113i | ||||
\(211\) | 15892.0 | − | 9175.27i | 0.356956 | − | 0.206088i | −0.310789 | − | 0.950479i | \(-0.600593\pi\) |
0.667745 | + | 0.744391i | \(0.267260\pi\) | |||||||
\(212\) | −8819.19 | + | 30643.0i | −0.196226 | + | 0.681804i | ||||
\(213\) | 23354.6 | − | 40451.4i | 0.514770 | − | 0.891608i | ||||
\(214\) | 5634.45 | − | 689.027i | 0.123034 | − | 0.0150456i | ||||
\(215\) | −77349.1 | − | 44657.5i | −1.67332 | − | 0.966091i | ||||
\(216\) | −46192.8 | + | 17654.0i | −0.990072 | + | 0.378387i | ||||
\(217\) | 69078.4 | 1.46697 | ||||||||
\(218\) | −69105.7 | + | 52021.9i | −1.45412 | + | 1.09464i | ||||
\(219\) | 24160.8 | + | 13949.3i | 0.503760 | + | 0.290846i | ||||
\(220\) | 70340.5 | − | 67794.2i | 1.45332 | − | 1.40071i | ||||
\(221\) | −678.645 | −0.0138950 | ||||||||
\(222\) | 18011.1 | + | 23925.8i | 0.365455 | + | 0.485468i | ||||
\(223\) | −62678.5 | + | 36187.5i | −1.26040 | + | 0.727693i | −0.973152 | − | 0.230162i | \(-0.926074\pi\) |
−0.287250 | + | 0.957856i | \(0.592741\pi\) | |||||||
\(224\) | 35079.4 | − | 24435.2i | 0.699126 | − | 0.486990i | ||||
\(225\) | −10586.7 | − | 18336.7i | −0.209120 | − | 0.362207i | ||||
\(226\) | 257.489 | + | 2105.59i | 0.00504129 | + | 0.0412247i | ||||
\(227\) | 40616.4i | 0.788225i | 0.919062 | + | 0.394112i | \(0.128948\pi\) | ||||
−0.919062 | + | 0.394112i | \(0.871052\pi\) | |||||||
\(228\) | 47490.6 | − | 6680.97i | 0.913562 | − | 0.128520i | ||||
\(229\) | 48369.8 | 0.922367 | 0.461183 | − | 0.887305i | \(-0.347425\pi\) | ||||
0.461183 | + | 0.887305i | \(0.347425\pi\) | |||||||
\(230\) | 34702.4 | − | 4243.69i | 0.656000 | − | 0.0802211i | ||||
\(231\) | 37566.6 | − | 21689.1i | 0.704009 | − | 0.406460i | ||||
\(232\) | 73157.2 | + | 11697.0i | 1.35919 | + | 0.217320i | ||||
\(233\) | −33382.0 | − | 57819.2i | −0.614894 | − | 1.06503i | −0.990403 | − | 0.138208i | \(-0.955866\pi\) |
0.375510 | − | 0.926818i | \(-0.377468\pi\) | |||||||
\(234\) | −1944.60 | + | 1463.87i | −0.0355138 | + | 0.0267344i | ||||
\(235\) | 153244.i | 2.77490i | ||||||||
\(236\) | −36433.8 | + | 35114.9i | −0.654154 | + | 0.630474i | ||||
\(237\) | −1739.06 | + | 3012.15i | −0.0309613 | + | 0.0536265i | ||||
\(238\) | 1350.86 | + | 1794.48i | 0.0238483 | + | 0.0316799i | ||||
\(239\) | − | 58780.7i | − | 1.02906i | −0.857473 | − | 0.514528i | \(-0.827967\pi\) | ||
0.857473 | − | 0.514528i | \(-0.172033\pi\) | |||||||
\(240\) | −103641. | − | 3822.22i | −1.79933 | − | 0.0663580i | ||||
\(241\) | 23438.7 | − | 40596.9i | 0.403551 | − | 0.698971i | −0.590600 | − | 0.806964i | \(-0.701109\pi\) |
0.994152 | + | 0.107993i | \(0.0344424\pi\) | |||||||
\(242\) | 494.544 | + | 4044.09i | 0.00844451 | + | 0.0690542i | ||||
\(243\) | −15094.1 | − | 8714.59i | −0.255620 | − | 0.147582i | ||||
\(244\) | −1333.24 | + | 4632.47i | −0.0223939 | + | 0.0778095i | ||||
\(245\) | −16053.3 | − | 27805.2i | −0.267444 | − | 0.463226i | ||||
\(246\) | −6946.71 | + | 16343.2i | −0.114791 | + | 0.270064i | ||||
\(247\) | 16631.8 | − | 7427.19i | 0.272613 | − | 0.121739i | ||||
\(248\) | 98917.3 | − | 37804.4i | 1.60831 | − | 0.614666i | ||||
\(249\) | 383.721 | + | 664.624i | 0.00618894 | + | 0.0107196i | ||||
\(250\) | −26786.7 | − | 219045.i | −0.428587 | − | 3.50473i | ||||
\(251\) | 27585.2 | + | 15926.3i | 0.437853 | + | 0.252794i | 0.702686 | − | 0.711500i | \(-0.251984\pi\) |
−0.264834 | + | 0.964294i | \(0.585317\pi\) | |||||||
\(252\) | 7741.54 | + | 2228.05i | 0.121906 | + | 0.0350851i | ||||
\(253\) | −11208.1 | + | 19412.9i | −0.175101 | + | 0.303284i | ||||
\(254\) | 22249.4 | − | 52345.1i | 0.344866 | − | 0.811351i | ||||
\(255\) | − | 5448.94i | − | 0.0837976i | ||||||
\(256\) | 36859.5 | − | 54188.0i | 0.562432 | − | 0.826844i | ||||
\(257\) | 31844.8 | − | 55156.9i | 0.482139 | − | 0.835090i | −0.517650 | − | 0.855592i | \(-0.673193\pi\) |
0.999790 | + | 0.0205022i | \(0.00652651\pi\) | |||||||
\(258\) | −55950.6 | − | 23781.9i | −0.840554 | − | 0.357279i | ||||
\(259\) | − | 37645.0i | − | 0.561188i | ||||||
\(260\) | −38229.6 | + | 9492.02i | −0.565527 | + | 0.140414i | ||||
\(261\) | 6980.25 | + | 12090.1i | 0.102468 | + | 0.177480i | ||||
\(262\) | −25452.4 | − | 33810.8i | −0.370788 | − | 0.492553i | ||||
\(263\) | 79937.2 | − | 46151.7i | 1.15568 | − | 0.667232i | 0.205414 | − | 0.978675i | \(-0.434146\pi\) |
0.950265 | + | 0.311444i | \(0.100812\pi\) | |||||||
\(264\) | 41924.0 | − | 51616.9i | 0.601527 | − | 0.740600i | ||||
\(265\) | −97239.7 | −1.38469 | ||||||||
\(266\) | −52745.1 | − | 29194.0i | −0.745451 | − | 0.412601i | ||||
\(267\) | 71961.4i | 1.00943i | ||||||||
\(268\) | −25560.8 | − | 7356.50i | −0.355881 | − | 0.102424i | ||||
\(269\) | 30684.0 | + | 53146.2i | 0.424040 | + | 0.734459i | 0.996330 | − | 0.0855922i | \(-0.0272782\pi\) |
−0.572290 | + | 0.820051i | \(0.693945\pi\) | |||||||
\(270\) | −90696.7 | − | 120481.i | −1.24412 | − | 1.65269i | ||||
\(271\) | −101084. | + | 58361.1i | −1.37640 | + | 0.794667i | −0.991725 | − | 0.128384i | \(-0.959021\pi\) |
−0.384678 | + | 0.923051i | \(0.625688\pi\) | |||||||
\(272\) | 2916.44 | + | 1830.33i | 0.0394198 | + | 0.0247396i | ||||
\(273\) | −17490.4 | −0.234679 | ||||||||
\(274\) | 46934.4 | + | 19949.6i | 0.625159 | + | 0.265725i | ||||
\(275\) | 190270. | + | 109852.i | 2.51596 | + | 1.45259i | ||||
\(276\) | 23096.0 | − | 5734.49i | 0.303193 | − | 0.0752795i | ||||
\(277\) | 11380.1 | 0.148316 | 0.0741580 | − | 0.997247i | \(-0.476373\pi\) | ||||
0.0741580 | + | 0.997247i | \(0.476373\pi\) | |||||||
\(278\) | −8570.51 | + | 20163.4i | −0.110896 | + | 0.260900i | ||||
\(279\) | 17281.0 | + | 9977.20i | 0.222004 | + | 0.128174i | ||||
\(280\) | 101196. | + | 82193.0i | 1.29077 | + | 1.04838i | ||||
\(281\) | 1830.04 | − | 3169.73i | 0.0231765 | − | 0.0401429i | −0.854205 | − | 0.519937i | \(-0.825955\pi\) |
0.877381 | + | 0.479794i | \(0.159289\pi\) | |||||||
\(282\) | 12661.6 | + | 103539.i | 0.159218 | + | 1.30199i | ||||
\(283\) | 42423.2 | − | 24493.0i | 0.529700 | − | 0.305823i | −0.211194 | − | 0.977444i | \(-0.567735\pi\) |
0.740894 | + | 0.671622i | \(0.234402\pi\) | |||||||
\(284\) | −64808.2 | + | 62462.2i | −0.803514 | + | 0.774427i | ||||
\(285\) | 59634.0 | + | 133539.i | 0.734183 | + | 1.64407i | ||||
\(286\) | 9879.76 | − | 23243.6i | 0.120785 | − | 0.284166i | ||||
\(287\) | 19332.2 | − | 11161.4i | 0.234702 | − | 0.135505i | ||||
\(288\) | 12304.9 | − | 1046.23i | 0.148352 | − | 0.0126137i | ||||
\(289\) | 41670.0 | − | 72174.6i | 0.498917 | − | 0.864150i | ||||
\(290\) | 27424.1 | + | 224258.i | 0.326089 | + | 2.66656i | ||||
\(291\) | 85007.0 | + | 49078.8i | 1.00385 | + | 0.579573i | ||||
\(292\) | −37307.5 | − | 38708.7i | −0.437553 | − | 0.453987i | ||||
\(293\) | −50882.9 | −0.592702 | −0.296351 | − | 0.955079i | \(-0.595770\pi\) | ||||
−0.296351 | + | 0.955079i | \(0.595770\pi\) | |||||||
\(294\) | −13143.8 | − | 17460.1i | −0.152064 | − | 0.202001i | ||||
\(295\) | −133636. | − | 77154.6i | −1.53560 | − | 0.886580i | ||||
\(296\) | −20601.9 | − | 53906.1i | −0.235139 | − | 0.615254i | ||||
\(297\) | 96691.5 | 1.09616 | ||||||||
\(298\) | −59920.7 | + | 45107.6i | −0.674753 | + | 0.507945i | ||||
\(299\) | 7827.45 | − | 4519.18i | 0.0875544 | − | 0.0505495i | ||||
\(300\) | −56204.8 | − | 226368.i | −0.624498 | − | 2.51520i | ||||
\(301\) | 38211.0 | + | 66183.4i | 0.421750 | + | 0.730493i | ||||
\(302\) | −128214. | + | 15679.1i | −1.40579 | + | 0.171912i | ||||
\(303\) | 155504.i | 1.69377i | ||||||||
\(304\) | −91505.8 | − | 12938.9i | −0.990151 | − | 0.140007i | ||||
\(305\) | −14700.2 | −0.158025 | ||||||||
\(306\) | 78.7567 | + | 644.026i | 0.000841094 | + | 0.00687797i | ||||
\(307\) | −62506.5 | + | 36088.2i | −0.663206 | + | 0.382902i | −0.793498 | − | 0.608573i | \(-0.791742\pi\) |
0.130291 | + | 0.991476i | \(0.458409\pi\) | |||||||
\(308\) | −81126.9 | + | 20143.0i | −0.855192 | + | 0.212335i | ||||
\(309\) | −23011.9 | − | 39857.8i | −0.241011 | − | 0.417443i | ||||
\(310\) | 194218. | + | 257998.i | 2.02100 | + | 2.68469i | ||||
\(311\) | − | 143148.i | − | 1.48001i | −0.672601 | − | 0.740005i | \(-0.734823\pi\) | ||
0.672601 | − | 0.740005i | \(-0.265177\pi\) | |||||||
\(312\) | −25045.5 | + | 9571.95i | −0.257289 | + | 0.0983312i | ||||
\(313\) | −68761.2 | + | 119098.i | −0.701867 | + | 1.21567i | 0.265944 | + | 0.963988i | \(0.414316\pi\) |
−0.967811 | + | 0.251680i | \(0.919017\pi\) | |||||||
\(314\) | 111691. | − | 84079.7i | 1.13282 | − | 0.852770i | ||||
\(315\) | 24566.3i | 0.247582i | ||||||||
\(316\) | 4825.84 | − | 4651.15i | 0.0483280 | − | 0.0465786i | ||||
\(317\) | 37746.5 | − | 65378.8i | 0.375628 | − | 0.650607i | −0.614793 | − | 0.788689i | \(-0.710760\pi\) |
0.990421 | + | 0.138082i | \(0.0440937\pi\) | |||||||
\(318\) | −65699.9 | + | 8034.32i | −0.649696 | + | 0.0794502i | ||||
\(319\) | −125452. | − | 72430.0i | −1.23281 | − | 0.711766i | ||||
\(320\) | 189890. | + | 62315.6i | 1.85439 | + | 0.608550i | ||||
\(321\) | 5891.44 | + | 10204.3i | 0.0571757 | + | 0.0990311i | ||||
\(322\) | −27530.4 | − | 11701.8i | −0.265522 | − | 0.112861i | ||||
\(323\) | 502.154 | − | 4829.44i | 0.00481318 | − | 0.0462904i | ||||
\(324\) | −60387.5 | − | 62655.6i | −0.575250 | − | 0.596856i | ||||
\(325\) | −44293.3 | − | 76718.2i | −0.419345 | − | 0.726326i | ||||
\(326\) | −181209. | + | 22159.8i | −1.70508 | + | 0.208512i | ||||
\(327\) | −155493. | − | 89774.2i | −1.45417 | − | 0.839568i | ||||
\(328\) | 21574.6 | − | 26562.6i | 0.200537 | − | 0.246901i | ||||
\(329\) | 65561.3 | − | 113555.i | 0.605697 | − | 1.04910i | ||||
\(330\) | 186627. | + | 79326.0i | 1.71374 | + | 0.728430i | ||||
\(331\) | − | 128182.i | − | 1.16996i | −0.811049 | − | 0.584978i | \(-0.801103\pi\) | ||
0.811049 | − | 0.584978i | \(-0.198897\pi\) | |||||||
\(332\) | −356.367 | − | 1435.29i | −0.00323311 | − | 0.0130216i | ||||
\(333\) | 5437.19 | − | 9417.49i | 0.0490327 | − | 0.0849272i | ||||
\(334\) | 22303.3 | − | 52472.0i | 0.199929 | − | 0.470364i | ||||
\(335\) | − | 81112.2i | − | 0.722764i | ||||||
\(336\) | 75164.0 | + | 47172.4i | 0.665781 | + | 0.417839i | ||||
\(337\) | 82577.5 | + | 143028.i | 0.727113 | + | 1.25940i | 0.958098 | + | 0.286440i | \(0.0924719\pi\) |
−0.230985 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(338\) | 83137.0 | − | 62584.5i | 0.727715 | − | 0.547815i | ||||
\(339\) | −3813.33 | + | 2201.63i | −0.0331822 | + | 0.0191577i | ||||
\(340\) | −2904.11 | + | 10090.6i | −0.0251220 | + | 0.0872887i | ||||
\(341\) | −207055. | −1.78065 | ||||||||
\(342\) | −8978.43 | − | 14921.5i | −0.0767623 | − | 0.127573i | ||||
\(343\) | 127711.i | 1.08553i | ||||||||
\(344\) | 90936.6 | + | 73860.2i | 0.768461 | + | 0.624156i | ||||
\(345\) | 36285.1 | + | 62847.7i | 0.304853 | + | 0.528021i | ||||
\(346\) | −46571.4 | + | 35058.4i | −0.389016 | + | 0.292846i | ||||
\(347\) | −127569. | + | 73652.2i | −1.05947 | + | 0.611683i | −0.925285 | − | 0.379274i | \(-0.876174\pi\) |
−0.134182 | + | 0.990957i | \(0.542841\pi\) | |||||||
\(348\) | 37058.1 | + | 149254.i | 0.306002 | + | 1.23244i | ||||
\(349\) | −178203. | −1.46306 | −0.731532 | − | 0.681808i | \(-0.761194\pi\) | ||||
−0.731532 | + | 0.681808i | \(0.761194\pi\) | |||||||
\(350\) | −114692. | + | 269830.i | −0.936260 | + | 2.20270i | ||||
\(351\) | −33763.5 | − | 19493.4i | −0.274052 | − | 0.158224i | ||||
\(352\) | −105147. | + | 73242.0i | −0.848614 | + | 0.591119i | ||||
\(353\) | −109873. | −0.881744 | −0.440872 | − | 0.897570i | \(-0.645331\pi\) | ||||
−0.440872 | + | 0.897570i | \(0.645331\pi\) | |||||||
\(354\) | −96665.6 | − | 41087.9i | −0.771375 | − | 0.327875i | ||||
\(355\) | −237711. | − | 137242.i | −1.88622 | − | 1.08901i | ||||
\(356\) | 38353.1 | − | 133261.i | 0.302622 | − | 1.05149i | ||||
\(357\) | −2331.18 | + | 4037.72i | −0.0182911 | + | 0.0316811i | ||||
\(358\) | 76389.7 | − | 9341.56i | 0.596031 | − | 0.0728876i | ||||
\(359\) | 53195.8 | − | 30712.6i | 0.412751 | − | 0.238302i | −0.279220 | − | 0.960227i | \(-0.590076\pi\) |
0.691971 | + | 0.721925i | \(0.256743\pi\) | |||||||
\(360\) | 13444.3 | + | 35177.9i | 0.103737 | + | 0.271434i | ||||
\(361\) | 40547.5 | + | 123853.i | 0.311136 | + | 0.950365i | ||||
\(362\) | 11734.6 | + | 4987.81i | 0.0895468 | + | 0.0380621i | ||||
\(363\) | −7324.04 | + | 4228.54i | −0.0555824 | + | 0.0320905i | ||||
\(364\) | 32389.5 | + | 9321.82i | 0.244456 | + | 0.0703555i | ||||
\(365\) | 81972.3 | − | 141980.i | 0.615292 | − | 1.06572i | ||||
\(366\) | −9932.20 | + | 1214.59i | −0.0741453 | + | 0.00906709i | ||||
\(367\) | 18268.6 | + | 10547.4i | 0.135636 | + | 0.0783092i | 0.566282 | − | 0.824211i | \(-0.308381\pi\) |
−0.430647 | + | 0.902521i | \(0.641715\pi\) | |||||||
\(368\) | −45826.4 | − | 1690.05i | −0.338392 | − | 0.0124797i | ||||
\(369\) | 6448.33 | 0.0473581 | ||||||||
\(370\) | 140599. | − | 105841.i | 1.02702 | − | 0.773129i | ||||
\(371\) | 72055.7 | + | 41601.3i | 0.523504 | + | 0.302245i | ||||
\(372\) | 152540. | + | 158269.i | 1.10229 | + | 1.14370i | ||||
\(373\) | −91821.3 | −0.659972 | −0.329986 | − | 0.943986i | \(-0.607044\pi\) | ||||
−0.329986 | + | 0.943986i | \(0.607044\pi\) | |||||||
\(374\) | −4049.07 | − | 5378.76i | −0.0289475 | − | 0.0384538i | ||||
\(375\) | 396702. | − | 229036.i | 2.82099 | − | 1.62870i | ||||
\(376\) | 31735.7 | − | 198486.i | 0.224477 | − | 1.40396i | ||||
\(377\) | 29204.3 | + | 50583.4i | 0.205478 | + | 0.355898i | ||||
\(378\) | 15662.7 | + | 128080.i | 0.109618 | + | 0.896390i | ||||
\(379\) | − | 25481.9i | − | 0.177400i | −0.996058 | − | 0.0887001i | \(-0.971729\pi\) | ||
0.996058 | − | 0.0887001i | \(-0.0282713\pi\) | |||||||
\(380\) | −39260.4 | − | 279077.i | −0.271887 | − | 1.93266i | ||||
\(381\) | 118064. | 0.813329 | ||||||||
\(382\) | −59691.9 | + | 7299.62i | −0.409062 | + | 0.0500234i | ||||
\(383\) | 128962. | − | 74456.3i | 0.879153 | − | 0.507579i | 0.00877385 | − | 0.999962i | \(-0.497207\pi\) |
0.870379 | + | 0.492382i | \(0.163874\pi\) | |||||||
\(384\) | 133448. | + | 26414.0i | 0.905000 | + | 0.179131i | ||||
\(385\) | −127455. | − | 220759.i | −0.859876 | − | 1.48935i | ||||
\(386\) | −118391. | + | 89123.1i | −0.794590 | + | 0.598158i | ||||
\(387\) | 22075.7i | 0.147399i | ||||||||
\(388\) | −131262. | − | 136192.i | −0.871917 | − | 0.904666i | ||||
\(389\) | −49207.3 | + | 85229.5i | −0.325185 | + | 0.563237i | −0.981550 | − | 0.191207i | \(-0.938760\pi\) |
0.656365 | + | 0.754444i | \(0.272093\pi\) | |||||||
\(390\) | −49175.4 | − | 65324.4i | −0.323309 | − | 0.429483i | ||||
\(391\) | − | 2409.32i | − | 0.0157595i | ||||||
\(392\) | 15034.5 | + | 39338.6i | 0.0978400 | + | 0.256004i | ||||
\(393\) | 43923.1 | − | 76077.1i | 0.284386 | − | 0.492571i | ||||
\(394\) | −3489.34 | − | 28533.7i | −0.0224776 | − | 0.183809i | ||||
\(395\) | 17700.8 | + | 10219.5i | 0.113448 | + | 0.0654994i | ||||
\(396\) | −23204.5 | − | 6678.34i | −0.147973 | − | 0.0425871i | ||||
\(397\) | 14682.9 | + | 25431.6i | 0.0931605 | + | 0.161359i | 0.908839 | − | 0.417146i | \(-0.136970\pi\) |
−0.815679 | + | 0.578505i | \(0.803636\pi\) | |||||||
\(398\) | 60909.8 | − | 143300.i | 0.384522 | − | 0.904647i | ||||
\(399\) | 12941.8 | − | 124467.i | 0.0812921 | − | 0.781822i | ||||
\(400\) | −16564.5 | + | 449153.i | −0.103528 | + | 2.80720i | ||||
\(401\) | −19941.1 | − | 34539.0i | −0.124011 | − | 0.214794i | 0.797335 | − | 0.603537i | \(-0.206243\pi\) |
−0.921346 | + | 0.388744i | \(0.872909\pi\) | |||||||
\(402\) | −6701.81 | − | 54803.4i | −0.0414705 | − | 0.339121i | ||||
\(403\) | 72301.3 | + | 41743.2i | 0.445180 | + | 0.257025i | ||||
\(404\) | 82878.3 | − | 287968.i | 0.507783 | − | 1.76433i | ||||
\(405\) | 132684. | − | 229815.i | 0.808924 | − | 1.40110i | ||||
\(406\) | 75621.0 | − | 177910.i | 0.458765 | − | 1.07931i | ||||
\(407\) | 112837.i | 0.681182i | ||||||||
\(408\) | −1128.43 | + | 7057.63i | −0.00677885 | + | 0.0423973i | ||||
\(409\) | −99124.0 | + | 171688.i | −0.592560 | + | 1.02634i | 0.401326 | + | 0.915935i | \(0.368549\pi\) |
−0.993886 | + | 0.110409i | \(0.964784\pi\) | |||||||
\(410\) | 96040.1 | + | 40822.1i | 0.571327 | + | 0.242844i | ||||
\(411\) | 105860.i | 0.626683i | ||||||||
\(412\) | 21371.5 | + | 86074.9i | 0.125904 | + | 0.507087i | ||||
\(413\) | 66017.0 | + | 114345.i | 0.387040 | + | 0.670372i | ||||
\(414\) | −5197.02 | − | 6903.70i | −0.0303217 | − | 0.0402792i | ||||
\(415\) | 3905.63 | − | 2254.92i | 0.0226775 | − | 0.0130929i | ||||
\(416\) | 51481.9 | − | 4377.27i | 0.297487 | − | 0.0252939i | ||||
\(417\) | −45478.3 | −0.261537 | ||||||||
\(418\) | 158098. | + | 87506.0i | 0.904845 | + | 0.500824i | ||||
\(419\) | − | 183253.i | − | 1.04381i | −0.853002 | − | 0.521907i | \(-0.825221\pi\) | ||
0.853002 | − | 0.521907i | \(-0.174779\pi\) | |||||||
\(420\) | −74846.3 | + | 260060.i | −0.424299 | + | 1.47426i | ||||
\(421\) | 56093.6 | + | 97157.0i | 0.316482 | + | 0.548163i | 0.979751 | − | 0.200218i | \(-0.0641649\pi\) |
−0.663269 | + | 0.748381i | \(0.730832\pi\) | |||||||
\(422\) | −44145.8 | − | 58643.1i | −0.247893 | − | 0.329300i | ||||
\(423\) | 32802.3 | − | 18938.4i | 0.183326 | − | 0.105843i | ||||
\(424\) | 125948. | + | 20137.6i | 0.700582 | + | 0.112015i | ||||
\(425\) | −23614.2 | −0.130736 | ||||||||
\(426\) | −171948. | − | 73087.0i | −0.947500 | − | 0.402737i | ||||
\(427\) | 10893.0 | + | 6289.10i | 0.0597438 | + | 0.0344931i | ||||
\(428\) | −5471.46 | − | 22036.6i | −0.0298686 | − | 0.120298i | ||||
\(429\) | 52425.7 | 0.284859 | ||||||||
\(430\) | −139754. | + | 328792.i | −0.755833 | + | 1.77821i | ||||
\(431\) | 259188. | + | 149642.i | 1.39527 | + | 0.805562i | 0.993893 | − | 0.110349i | \(-0.0351968\pi\) |
0.401382 | + | 0.915911i | \(0.368530\pi\) | |||||||
\(432\) | 92522.3 | + | 174833.i | 0.495768 | + | 0.936821i | ||||
\(433\) | −20272.2 | + | 35112.4i | −0.108124 | + | 0.187277i | −0.915010 | − | 0.403430i | \(-0.867818\pi\) |
0.806886 | + | 0.590707i | \(0.201151\pi\) | |||||||
\(434\) | −33540.0 | − | 274270.i | −0.178067 | − | 1.45613i | ||||
\(435\) | −406142. | + | 234486.i | −2.14634 | + | 1.23919i | ||||
\(436\) | 240102. | + | 249120.i | 1.26306 | + | 1.31050i | ||||
\(437\) | 26368.0 | + | 59046.3i | 0.138075 | + | 0.309193i | ||||
\(438\) | 43653.5 | − | 102702.i | 0.227547 | − | 0.535339i | ||||
\(439\) | −251746. | + | 145346.i | −1.30627 | + | 0.754176i | −0.981472 | − | 0.191606i | \(-0.938630\pi\) |
−0.324800 | + | 0.945783i | \(0.605297\pi\) | |||||||
\(440\) | −303324. | − | 246365.i | −1.56676 | − | 1.27255i | ||||
\(441\) | −3967.85 | + | 6872.51i | −0.0204022 | + | 0.0353377i | ||||
\(442\) | 329.507 | + | 2694.51i | 0.00168663 | + | 0.0137922i | ||||
\(443\) | −67175.9 | − | 38784.0i | −0.342300 | − | 0.197627i | 0.318989 | − | 0.947758i | \(-0.396657\pi\) |
−0.661288 | + | 0.750132i | \(0.729990\pi\) | |||||||
\(444\) | 86250.6 | − | 83128.4i | 0.437518 | − | 0.421680i | ||||
\(445\) | 422878. | 2.13548 | ||||||||
\(446\) | 174112. | + | 231290.i | 0.875305 | + | 1.16275i | ||||
\(447\) | −134827. | − | 77842.1i | −0.674777 | − | 0.389583i | ||||
\(448\) | −114050. | − | 127416.i | −0.568252 | − | 0.634844i | ||||
\(449\) | 108138. | 0.536395 | 0.268198 | − | 0.963364i | \(-0.413572\pi\) | ||||
0.268198 | + | 0.963364i | \(0.413572\pi\) | |||||||
\(450\) | −67664.3 | + | 50936.9i | −0.334145 | + | 0.251540i | ||||
\(451\) | −57946.3 | + | 33455.3i | −0.284887 | + | 0.164479i | ||||
\(452\) | 8235.07 | − | 2044.68i | 0.0403079 | − | 0.0100080i | ||||
\(453\) | −134062. | − | 232202.i | −0.653294 | − | 1.13154i | ||||
\(454\) | 161264. | − | 19720.7i | 0.782396 | − | 0.0956779i | ||||
\(455\) | 102782.i | 0.496470i | ||||||||
\(456\) | −49584.7 | − | 185314.i | −0.238461 | − | 0.891207i | ||||
\(457\) | −231408. | −1.10801 | −0.554007 | − | 0.832512i | \(-0.686902\pi\) | ||||
−0.554007 | + | 0.832512i | \(0.686902\pi\) | |||||||
\(458\) | −23485.3 | − | 192049.i | −0.111961 | − | 0.915546i | ||||
\(459\) | −9000.22 | + | 5196.28i | −0.0427197 | + | 0.0246642i | ||||
\(460\) | −33698.5 | − | 135723.i | −0.159256 | − | 0.641412i | ||||
\(461\) | −82425.9 | − | 142766.i | −0.387848 | − | 0.671773i | 0.604312 | − | 0.796748i | \(-0.293448\pi\) |
−0.992160 | + | 0.124975i | \(0.960115\pi\) | |||||||
\(462\) | −104355. | − | 138624.i | −0.488909 | − | 0.649465i | ||||
\(463\) | − | 178426.i | − | 0.832330i | −0.909289 | − | 0.416165i | \(-0.863374\pi\) | ||
0.909289 | − | 0.416165i | \(-0.136626\pi\) | |||||||
\(464\) | 10921.6 | − | 296144.i | 0.0507284 | − | 1.37552i | ||||
\(465\) | −335162. | + | 580517.i | −1.55006 | + | 2.68478i | ||||
\(466\) | −213359. | + | 160614.i | −0.982513 | + | 0.739624i | ||||
\(467\) | − | 104345.i | − | 0.478452i | −0.970964 | − | 0.239226i | \(-0.923106\pi\) | ||
0.970964 | − | 0.239226i | \(-0.0768937\pi\) | |||||||
\(468\) | 6756.34 | + | 7010.11i | 0.0308475 | + | 0.0320061i | ||||
\(469\) | −34701.6 | + | 60105.0i | −0.157763 | + | 0.273253i | ||||
\(470\) | 608444. | − | 74405.5i | 2.75439 | − | 0.336829i | ||||
\(471\) | 251314. | + | 145096.i | 1.13286 | + | 0.654055i | ||||
\(472\) | 157111. | + | 127608.i | 0.705216 | + | 0.572787i | ||||
\(473\) | −114534. | − | 198378.i | −0.511930 | − | 0.886688i | ||||
\(474\) | 12803.9 | + | 5442.31i | 0.0569882 | + | 0.0242229i | ||||
\(475\) | 578723. | − | 258437.i | 2.56498 | − | 1.14543i | ||||
\(476\) | 6468.95 | − | 6234.77i | 0.0285509 | − | 0.0275174i | ||||
\(477\) | 12017.2 | + | 20814.4i | 0.0528162 | + | 0.0914804i | ||||
\(478\) | −233384. | + | 28540.2i | −1.02145 | + | 0.124911i | ||||
\(479\) | −173716. | − | 100295.i | −0.757127 | − | 0.437127i | 0.0711365 | − | 0.997467i | \(-0.477337\pi\) |
−0.828263 | + | 0.560339i | \(0.810671\pi\) | |||||||
\(480\) | 35145.7 | + | 413356.i | 0.152542 | + | 1.79408i | ||||
\(481\) | 22748.4 | − | 39401.4i | 0.0983243 | − | 0.170303i | ||||
\(482\) | −172567. | − | 73350.1i | −0.742787 | − | 0.315723i | ||||
\(483\) | − | 62094.4i | − | 0.266169i | ||||||
\(484\) | 15816.6 | − | 3927.10i | 0.0675185 | − | 0.0167641i | ||||
\(485\) | 288410. | − | 499540.i | 1.22610 | − | 2.12367i | ||||
\(486\) | −27271.9 | + | 64161.2i | −0.115463 | + | 0.271644i | ||||
\(487\) | 408545.i | 1.72259i | 0.508105 | + | 0.861295i | \(0.330346\pi\) | ||||
−0.508105 | + | 0.861295i | \(0.669654\pi\) | |||||||
\(488\) | 19040.2 | + | 3044.31i | 0.0799524 | + | 0.0127835i | ||||
\(489\) | −189474. | − | 328179.i | −0.792378 | − | 1.37244i | ||||
\(490\) | −102604. | + | 77238.8i | −0.427338 | + | 0.321695i | ||||
\(491\) | −284451. | + | 164228.i | −1.17990 | + | 0.681215i | −0.955991 | − | 0.293395i | \(-0.905215\pi\) |
−0.223908 | + | 0.974610i | \(0.571881\pi\) | |||||||
\(492\) | 68262.3 | + | 19646.2i | 0.282001 | + | 0.0811610i | ||||
\(493\) | 15569.8 | 0.0640603 | ||||||||
\(494\) | −37564.4 | − | 62429.2i | −0.153930 | − | 0.255820i | ||||
\(495\) | − | 73634.9i | − | 0.300520i | ||||||
\(496\) | −198127. | − | 374388.i | −0.805343 | − | 1.52180i | ||||
\(497\) | 117431. | + | 203396.i | 0.475411 | + | 0.823436i | ||||
\(498\) | 2452.53 | − | 1846.23i | 0.00988906 | − | 0.00744436i | ||||
\(499\) | −101644. | + | 58684.2i | −0.408207 | + | 0.235678i | −0.690019 | − | 0.723791i | \(-0.742398\pi\) |
0.281812 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(500\) | −856697. | + | 212709.i | −3.42679 | + | 0.850835i | ||||
\(501\) | 118350. | 0.471511 | ||||||||
\(502\) | 49840.6 | − | 117258.i | 0.197777 | − | 0.465300i | ||||
\(503\) | 243658. | + | 140676.i | 0.963042 | + | 0.556013i | 0.897108 | − | 0.441811i | \(-0.145664\pi\) |
0.0659340 | + | 0.997824i | \(0.478997\pi\) | |||||||
\(504\) | 5087.49 | − | 31819.0i | 0.0200282 | − | 0.125264i | ||||
\(505\) | 913810. | 3.58322 | ||||||||
\(506\) | 82519.5 | + | 35075.1i | 0.322296 | + | 0.136993i | ||||
\(507\) | 187065. | + | 108002.i | 0.727741 | + | 0.420161i | ||||
\(508\) | −218635. | − | 62924.1i | −0.847213 | − | 0.243831i | ||||
\(509\) | −96492.0 | + | 167129.i | −0.372440 | + | 0.645084i | −0.989940 | − | 0.141486i | \(-0.954812\pi\) |
0.617501 | + | 0.786570i | \(0.288145\pi\) | |||||||
\(510\) | −21634.6 | + | 2645.66i | −0.0831780 | + | 0.0101717i | ||||
\(511\) | −121485. | + | 70139.2i | −0.465243 | + | 0.268608i | ||||
\(512\) | −233046. | − | 120038.i | −0.889000 | − | 0.457908i | ||||
\(513\) | 163703. | − | 225847.i | 0.622046 | − | 0.858183i | ||||
\(514\) | −234458. | − | 99656.8i | −0.887439 | − | 0.377208i | ||||
\(515\) | −234223. | + | 135229.i | −0.883110 | + | 0.509864i | ||||
\(516\) | −67258.3 | + | 233695.i | −0.252608 | + | 0.877706i | ||||
\(517\) | −196513. | + | 340371.i | −0.735208 | + | 1.27342i | ||||
\(518\) | −149467. | + | 18278.0i | −0.557038 | + | 0.0681192i | ||||
\(519\) | −104789. | − | 60500.2i | −0.389030 | − | 0.224606i | ||||
\(520\) | 56249.2 | + | 147179.i | 0.208022 | + | 0.544302i | ||||
\(521\) | 198823. | 0.732473 | 0.366236 | − | 0.930522i | \(-0.380646\pi\) | ||||
0.366236 | + | 0.930522i | \(0.380646\pi\) | |||||||
\(522\) | 44613.8 | − | 33584.7i | 0.163730 | − | 0.123254i | ||||
\(523\) | 292097. | + | 168642.i | 1.06788 | + | 0.616542i | 0.927602 | − | 0.373570i | \(-0.121866\pi\) |
0.140280 | + | 0.990112i | \(0.455200\pi\) | |||||||
\(524\) | −121885. | + | 117473.i | −0.443903 | + | 0.427834i | ||||
\(525\) | −608598. | −2.20807 | ||||||||
\(526\) | −222054. | − | 294976.i | −0.802579 | − | 1.06614i | ||||
\(527\) | 19273.1 | − | 11127.3i | 0.0693953 | − | 0.0400654i | ||||
\(528\) | −225296. | − | 141394.i | −0.808140 | − | 0.507182i | ||||
\(529\) | −123877. | − | 214560.i | −0.442668 | − | 0.766723i | ||||
\(530\) | 47213.4 | + | 386083.i | 0.168079 | + | 1.37445i | ||||
\(531\) | 38140.1i | 0.135267i | ||||||||
\(532\) | −90302.9 | + | 223595.i | −0.319064 | + | 0.790022i | ||||
\(533\) | 26978.9 | 0.0949662 | ||||||||
\(534\) | 285717. | − | 34939.8i | 1.00197 | − | 0.122529i | ||||
\(535\) | 59965.0 | − | 34620.8i | 0.209503 | − | 0.120957i | ||||
\(536\) | −16797.7 | + | 105059.i | −0.0584684 | + | 0.365682i | ||||
\(537\) | 79873.8 | + | 138345.i | 0.276985 | + | 0.479752i | ||||
\(538\) | 196115. | − | 147633.i | 0.677556 | − | 0.510056i | ||||
\(539\) | − | 82344.1i | − | 0.283436i | ||||||
\(540\) | −434324. | + | 418602.i | −1.48945 | + | 1.43554i | ||||
\(541\) | 111884. | − | 193789.i | 0.382274 | − | 0.662118i | −0.609113 | − | 0.793084i | \(-0.708474\pi\) |
0.991387 | + | 0.130965i | \(0.0418077\pi\) | |||||||
\(542\) | 280798. | + | 373011.i | 0.955864 | + | 1.26977i | ||||
\(543\) | 26467.2i | 0.0897652i | ||||||||
\(544\) | 5851.17 | − | 12468.2i | 0.0197717 | − | 0.0421313i | ||||
\(545\) | −527554. | + | 913751.i | −1.77613 | + | 3.07634i | ||||
\(546\) | 8492.22 | + | 69444.3i | 0.0284863 | + | 0.232944i | ||||
\(547\) | −156042. | − | 90091.0i | −0.521515 | − | 0.301097i | 0.216039 | − | 0.976385i | \(-0.430686\pi\) |
−0.737554 | + | 0.675288i | \(0.764019\pi\) | |||||||
\(548\) | 56419.9 | − | 196036.i | 0.187876 | − | 0.652791i | ||||
\(549\) | 1816.71 | + | 3146.63i | 0.00602754 | + | 0.0104400i | ||||
\(550\) | 343777. | − | 808788.i | 1.13645 | − | 2.67368i | ||||
\(551\) | −381575. | + | 170398.i | −1.25683 | + | 0.561257i | ||||
\(552\) | −33982.3 | − | 88916.6i | −0.111526 | − | 0.291813i | ||||
\(553\) | −8744.30 | − | 15145.6i | −0.0285940 | − | 0.0495262i | ||||
\(554\) | −5525.47 | − | 45184.0i | −0.0180032 | − | 0.147219i | ||||
\(555\) | 316360. | + | 182650.i | 1.02706 | + | 0.592972i | ||||
\(556\) | 84218.6 | + | 24238.5i | 0.272432 | + | 0.0784071i | ||||
\(557\) | −6985.50 | + | 12099.2i | −0.0225158 | + | 0.0389985i | −0.877064 | − | 0.480374i | \(-0.840501\pi\) |
0.854548 | + | 0.519372i | \(0.173834\pi\) | |||||||
\(558\) | 31223.2 | − | 73457.2i | 0.100279 | − | 0.235921i | ||||
\(559\) | 92361.6i | 0.295575i | ||||||||
\(560\) | 277207. | − | 441698.i | 0.883950 | − | 1.40848i | ||||
\(561\) | 6987.47 | − | 12102.7i | 0.0222021 | − | 0.0384552i | ||||
\(562\) | −13473.7 | − | 5727.03i | −0.0426594 | − | 0.0181325i | ||||
\(563\) | 285750.i | 0.901507i | 0.892649 | + | 0.450753i | \(0.148845\pi\) | ||||
−0.892649 | + | 0.450753i | \(0.851155\pi\) | |||||||
\(564\) | 404947. | − | 100544.i | 1.27303 | − | 0.316081i | ||||
\(565\) | 12937.8 | + | 22408.9i | 0.0405287 | + | 0.0701978i | ||||
\(566\) | −117846. | − | 156546.i | −0.367858 | − | 0.488662i | ||||
\(567\) | −196640. | + | 113530.i | −0.611654 | + | 0.353139i | ||||
\(568\) | 279468. | + | 226988.i | 0.866235 | + | 0.703570i | ||||
\(569\) | 166473. | 0.514185 | 0.257093 | − | 0.966387i | \(-0.417235\pi\) | ||||
0.257093 | + | 0.966387i | \(0.417235\pi\) | |||||||
\(570\) | 501254. | − | 301610.i | 1.54279 | − | 0.928317i | ||||
\(571\) | − | 538668.i | − | 1.65215i | −0.563562 | − | 0.826074i | \(-0.690569\pi\) | ||
0.563562 | − | 0.826074i | \(-0.309431\pi\) | |||||||
\(572\) | −97084.1 | − | 27941.2i | −0.296726 | − | 0.0853990i | ||||
\(573\) | −62414.4 | − | 108105.i | −0.190097 | − | 0.329258i | ||||
\(574\) | −53702.1 | − | 71337.7i | −0.162993 | − | 0.216519i | ||||
\(575\) | 272365. | − | 157250.i | 0.823787 | − | 0.475614i | ||||
\(576\) | −10128.4 | − | 48347.7i | −0.0305279 | − | 0.145724i | ||||
\(577\) | 121393. | 0.364621 | 0.182311 | − | 0.983241i | \(-0.441642\pi\) | ||||
0.182311 | + | 0.983241i | \(0.441642\pi\) | |||||||
\(578\) | −306796. | − | 130404.i | −0.918320 | − | 0.390334i | ||||
\(579\) | −266389. | − | 153800.i | −0.794619 | − | 0.458773i | ||||
\(580\) | 877083. | − | 217770.i | 2.60726 | − | 0.647355i | ||||
\(581\) | −3858.82 | −0.0114315 | ||||||||
\(582\) | 153590. | − | 361343.i | 0.453436 | − | 1.06678i | ||||
\(583\) | −215979. | − | 124696.i | −0.635441 | − | 0.366872i | ||||
\(584\) | −135576. | + | 166921.i | −0.397518 | + | 0.489424i | ||||
\(585\) | −14845.1 | + | 25712.4i | −0.0433781 | + | 0.0751331i | ||||
\(586\) | 24705.5 | + | 202027.i | 0.0719445 | + | 0.588319i | ||||
\(587\) | 504606. | − | 291335.i | 1.46446 | − | 0.845504i | 0.465244 | − | 0.885183i | \(-0.345967\pi\) |
0.999213 | + | 0.0396783i | \(0.0126333\pi\) | |||||||
\(588\) | −62942.3 | + | 60663.8i | −0.182049 | + | 0.175459i | ||||
\(589\) | −350555. | + | 483629.i | −1.01047 | + | 1.39406i | ||||
\(590\) | −241452. | + | 568052.i | −0.693627 | + | 1.63186i | ||||
\(591\) | 51676.0 | − | 29835.1i | 0.147950 | − | 0.0854187i | ||||
\(592\) | −204027. | + | 107972.i | −0.582163 | + | 0.308082i | ||||
\(593\) | 294349. | − | 509827.i | 0.837052 | − | 1.44982i | −0.0552967 | − | 0.998470i | \(-0.517610\pi\) |
0.892349 | − | 0.451347i | \(-0.149056\pi\) | |||||||
\(594\) | −46947.2 | − | 383906.i | −0.133057 | − | 1.08806i | ||||
\(595\) | 23727.5 | + | 13699.1i | 0.0670221 | + | 0.0386953i | ||||
\(596\) | 208190. | + | 216009.i | 0.586094 | + | 0.608107i | ||||
\(597\) | 323210. | 0.906853 | ||||||||
\(598\) | −21743.6 | − | 28884.0i | −0.0608034 | − | 0.0807710i | ||||
\(599\) | −90957.4 | − | 52514.3i | −0.253504 | − | 0.146360i | 0.367864 | − | 0.929880i | \(-0.380089\pi\) |
−0.621368 | + | 0.783519i | \(0.713423\pi\) | |||||||
\(600\) | −871487. | + | 333066.i | −2.42080 | + | 0.925185i | ||||
\(601\) | 241571. | 0.668801 | 0.334400 | − | 0.942431i | \(-0.391466\pi\) | ||||
0.334400 | + | 0.942431i | \(0.391466\pi\) | |||||||
\(602\) | 244223. | − | 183848.i | 0.673898 | − | 0.507302i | ||||
\(603\) | −17362.3 | + | 10024.1i | −0.0477499 | + | 0.0275684i | ||||
\(604\) | 124505. | + | 501451.i | 0.341282 | + | 1.37453i | ||||
\(605\) | 24848.8 | + | 43039.4i | 0.0678883 | + | 0.117586i | ||||
\(606\) | 617415. | − | 75502.5i | 1.68125 | − | 0.205597i | ||||
\(607\) | 178255.i | 0.483797i | 0.970302 | + | 0.241899i | \(0.0777701\pi\) | ||||
−0.970302 | + | 0.241899i | \(0.922230\pi\) | |||||||
\(608\) | −6943.39 | + | 369599.i | −0.0187830 | + | 0.999824i | ||||
\(609\) | 401273. | 1.08195 | ||||||||
\(610\) | 7137.50 | + | 58366.2i | 0.0191817 | + | 0.156856i | ||||
\(611\) | 137240. | − | 79235.6i | 0.367620 | − | 0.212245i | ||||
\(612\) | 2518.81 | − | 625.395i | 0.00672502 | − | 0.00166975i | ||||
\(613\) | 70839.7 | + | 122698.i | 0.188519 | + | 0.326525i | 0.944757 | − | 0.327772i | \(-0.106298\pi\) |
−0.756237 | + | 0.654297i | \(0.772965\pi\) | |||||||
\(614\) | 173634. | + | 230655.i | 0.460574 | + | 0.611824i | ||||
\(615\) | 216617.i | 0.572721i | ||||||||
\(616\) | 119366. | + | 312328.i | 0.314572 | + | 0.823094i | ||||
\(617\) | −150873. | + | 261320.i | −0.396316 | + | 0.686440i | −0.993268 | − | 0.115837i | \(-0.963045\pi\) |
0.596952 | + | 0.802277i | \(0.296378\pi\) | |||||||
\(618\) | −147079. | + | 110719.i | −0.385101 | + | 0.289899i | ||||
\(619\) | − | 234852.i | − | 0.612933i | −0.951881 | − | 0.306466i | \(-0.900853\pi\) | ||
0.951881 | − | 0.306466i | \(-0.0991467\pi\) | |||||||
\(620\) | 930063. | − | 896395.i | 2.41952 | − | 2.33193i | ||||
\(621\) | 69205.3 | − | 119867.i | 0.179455 | − | 0.310826i | ||||
\(622\) | −568358. | + | 69503.5i | −1.46907 | + | 0.179650i | ||||
\(623\) | −313357. | − | 180917.i | −0.807353 | − | 0.466126i | ||||
\(624\) | 50165.2 | + | 94793.9i | 0.128835 | + | 0.243451i | ||||
\(625\) | −797266. | − | 1.38090e6i | −2.04100 | − | 3.53512i | ||||
\(626\) | 506255. | + | 215185.i | 1.29187 | + | 0.549114i | ||||
\(627\) | −38791.7 | + | 373077.i | −0.0986742 | + | 0.948993i | ||||
\(628\) | −388062. | − | 402637.i | −0.983970 | − | 1.02093i | ||||
\(629\) | −6063.96 | − | 10503.1i | −0.0153269 | − | 0.0265470i | ||||
\(630\) | 97538.5 | − | 11927.8i | 0.245751 | − | 0.0300524i | ||||
\(631\) | 495965. | + | 286345.i | 1.24564 | + | 0.719170i | 0.970236 | − | 0.242160i | \(-0.0778557\pi\) |
0.275402 | + | 0.961329i | \(0.411189\pi\) | |||||||
\(632\) | −20810.2 | − | 16902.3i | −0.0521004 | − | 0.0423168i | ||||
\(633\) | 76182.4 | − | 131952.i | 0.190129 | − | 0.329312i | ||||
\(634\) | −277909. | − | 118126.i | −0.691391 | − | 0.293877i | ||||
\(635\) | − | 693796.i | − | 1.72062i | ||||||
\(636\) | 63799.3 | + | 256955.i | 0.157725 | + | 0.635248i | ||||
\(637\) | −16600.9 | + | 28753.6i | −0.0409122 | + | 0.0708620i | ||||
\(638\) | −226666. | + | 533267.i | −0.556859 | + | 1.31010i | ||||
\(639\) | 67843.5i | 0.166152i | ||||||||
\(640\) | 155221. | − | 784200.i | 0.378957 | − | 1.91455i | ||||
\(641\) | −155350. | − | 269073.i | −0.378089 | − | 0.654870i | 0.612695 | − | 0.790319i | \(-0.290085\pi\) |
−0.990784 | + | 0.135450i | \(0.956752\pi\) | |||||||
\(642\) | 37654.7 | − | 28346.0i | 0.0913587 | − | 0.0687737i | ||||
\(643\) | 542339. | − | 313120.i | 1.31174 | − | 0.757336i | 0.329359 | − | 0.944205i | \(-0.393167\pi\) |
0.982385 | + | 0.186869i | \(0.0598341\pi\) | |||||||
\(644\) | −33094.3 | + | 114989.i | −0.0797960 | + | 0.277258i | ||||
\(645\) | −741585. | −1.78255 | ||||||||
\(646\) | −19418.7 | + | 351.100i | −0.0465324 | + | 0.000841330i | ||||
\(647\) | − | 208021.i | − | 0.496933i | −0.968640 | − | 0.248467i | \(-0.920073\pi\) | ||
0.968640 | − | 0.248467i | \(-0.0799267\pi\) | |||||||
\(648\) | −219449. | + | 270185.i | −0.522617 | + | 0.643446i | ||||
\(649\) | −197879. | − | 342737.i | −0.469797 | − | 0.813713i | ||||
\(650\) | −283098. | + | 213112.i | −0.670054 | + | 0.504408i | ||||
\(651\) | 496717. | − | 286780.i | 1.17205 | − | 0.676685i | ||||
\(652\) | 175967. | + | 708719.i | 0.413940 | + | 1.66717i | ||||
\(653\) | 294086. | 0.689682 | 0.344841 | − | 0.938661i | \(-0.387933\pi\) | ||||
0.344841 | + | 0.938661i | \(0.387933\pi\) | |||||||
\(654\) | −280944. | + | 660963.i | −0.656846 | + | 1.54533i | ||||
\(655\) | −447064. | − | 258112.i | −1.04205 | − | 0.601626i | ||||
\(656\) | −115940. | − | 72763.1i | −0.269418 | − | 0.169084i | ||||
\(657\) | −40521.7 | −0.0938764 | ||||||||
\(658\) | −482695. | − | 205171.i | −1.11486 | − | 0.473875i | ||||
\(659\) | 285292. | + | 164713.i | 0.656930 | + | 0.379279i | 0.791106 | − | 0.611679i | \(-0.209506\pi\) |
−0.134176 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(660\) | 224344. | − | 779502.i | 0.515023 | − | 1.78949i | ||||
\(661\) | 60352.9 | − | 104534.i | 0.138132 | − | 0.239252i | −0.788657 | − | 0.614833i | \(-0.789223\pi\) |
0.926790 | + | 0.375581i | \(0.122557\pi\) | |||||||
\(662\) | −508935. | + | 62236.8i | −1.16131 | + | 0.142014i | ||||
\(663\) | −4879.88 | + | 2817.40i | −0.0111015 | + | 0.00640947i | ||||
\(664\) | −5525.67 | + | 2111.81i | −0.0125328 | + | 0.00478981i | ||||
\(665\) | −731425. | − | 76051.9i | −1.65396 | − | 0.171976i | ||||
\(666\) | −40031.4 | − | 17015.4i | −0.0902510 | − | 0.0383614i | ||||
\(667\) | −179581. | + | 103681.i | −0.403653 | + | 0.233049i | ||||
\(668\) | −219165. | − | 63076.6i | −0.491154 | − | 0.141356i | ||||
\(669\) | −300465. | + | 520421.i | −0.671339 | + | 1.16279i | ||||
\(670\) | −322050. | + | 39382.9i | −0.717420 | + | 0.0877320i | ||||
\(671\) | −32650.7 | − | 18850.9i | −0.0725184 | − | 0.0418685i | ||||
\(672\) | 150799. | − | 321337.i | 0.333934 | − | 0.711577i | ||||
\(673\) | 356173. | 0.786377 | 0.393188 | − | 0.919458i | \(-0.371372\pi\) | ||||
0.393188 | + | 0.919458i | \(0.371372\pi\) | |||||||
\(674\) | 527789. | − | 397313.i | 1.16182 | − | 0.874607i | ||||
\(675\) | −1.17484e6 | − | 678293.i | −2.57852 | − | 1.48871i | ||||
\(676\) | −288853. | − | 299702.i | −0.632097 | − | 0.655838i | ||||
\(677\) | −171465. | −0.374108 | −0.187054 | − | 0.982350i | \(-0.559894\pi\) | ||||
−0.187054 | + | 0.982350i | \(0.559894\pi\) | |||||||
\(678\) | 10592.9 | + | 14071.6i | 0.0230439 | + | 0.0306114i | ||||
\(679\) | −427429. | + | 246776.i | −0.927095 | + | 0.535259i | ||||
\(680\) | 41473.9 | + | 6631.20i | 0.0896926 | + | 0.0143408i | ||||
\(681\) | 168620. | + | 292058.i | 0.363591 | + | 0.629759i | ||||
\(682\) | 100533. | + | 822097.i | 0.216142 | + | 1.76748i | ||||
\(683\) | 87088.4i | 0.186689i | 0.995634 | + | 0.0933445i | \(0.0297558\pi\) | ||||
−0.995634 | + | 0.0933445i | \(0.970244\pi\) | |||||||
\(684\) | −54885.2 | + | 42893.1i | −0.117312 | + | 0.0916800i | ||||
\(685\) | 622082. | 1.32576 | ||||||||
\(686\) | 507067. | − | 62008.3i | 1.07750 | − | 0.131765i | ||||
\(687\) | 347809. | − | 200808.i | 0.736933 | − | 0.425468i | ||||
\(688\) | 249103. | − | 396919.i | 0.526262 | − | 0.838541i | ||||
\(689\) | 50278.3 | + | 87084.6i | 0.105911 | + | 0.183444i | ||||
\(690\) | 231914. | − | 174582.i | 0.487113 | − | 0.366692i | ||||
\(691\) | 659632.i | 1.38148i | 0.723102 | + | 0.690742i | \(0.242716\pi\) | ||||
−0.723102 | + | 0.690742i | \(0.757284\pi\) | |||||||
\(692\) | 161809. | + | 167886.i | 0.337901 | + | 0.350592i | ||||
\(693\) | −31502.7 | + | 54564.2i | −0.0655965 | + | 0.113617i | ||||
\(694\) | 354370. | + | 470743.i | 0.735762 | + | 0.977384i | ||||
\(695\) | 267252.i | 0.553287i | ||||||||
\(696\) | 574607. | − | 219604.i | 1.18618 | − | 0.453338i | ||||
\(697\) | 3595.83 | − | 6228.16i | 0.00740174 | − | 0.0128202i | ||||
\(698\) | 86523.7 | + | 707539.i | 0.177592 | + | 1.45224i | ||||
\(699\) | −480074. | − | 277171.i | −0.982549 | − | 0.567275i | ||||
\(700\) | 1.12703e6 | + | 324363.i | 2.30005 | + | 0.661965i | ||||
\(701\) | −210193. | − | 364065.i | −0.427742 | − | 0.740871i | 0.568930 | − | 0.822386i | \(-0.307358\pi\) |
−0.996672 | + | 0.0815147i | \(0.974024\pi\) | |||||||
\(702\) | −61003.5 | + | 143520.i | −0.123789 | + | 0.291232i | ||||
\(703\) | 263559. | + | 191039.i | 0.533295 | + | 0.386554i | ||||
\(704\) | 341854. | + | 381915.i | 0.689757 | + | 0.770587i | ||||
\(705\) | 636194. | + | 1.10192e6i | 1.28000 | + | 2.21703i | ||||
\(706\) | 53347.4 | + | 436243.i | 0.107030 | + | 0.875224i | ||||
\(707\) | −677143. | − | 390949.i | −1.35469 | − | 0.782133i | ||||
\(708\) | −116202. | + | 403753.i | −0.231818 | + | 0.805470i | ||||
\(709\) | −169519. | + | 293616.i | −0.337230 | + | 0.584100i | −0.983911 | − | 0.178661i | \(-0.942823\pi\) |
0.646680 | + | 0.762761i | \(0.276157\pi\) | |||||||
\(710\) | −429493. | + | 1.01045e6i | −0.852000 | + | 2.00446i | ||||
\(711\) | − | 5051.86i | − | 0.00999338i | ||||||
\(712\) | −547724. | − | 87574.9i | −1.08044 | − | 0.172751i | ||||
\(713\) | −148196. | + | 256684.i | −0.291513 | + | 0.504916i | ||||
\(714\) | 17163.3 | + | 7295.31i | 0.0336671 | + | 0.0143103i | ||||
\(715\) | − | 308078.i | − | 0.602626i | ||||||
\(716\) | −74179.9 | − | 298764.i | −0.144697 | − | 0.582776i | ||||
\(717\) | −244029. | − | 422670.i | −0.474682 | − | 0.822173i | ||||
\(718\) | −147770. | − | 196298.i | −0.286641 | − | 0.380773i | ||||
\(719\) | −131742. | + | 76061.4i | −0.254840 | + | 0.147132i | −0.621978 | − | 0.783034i | \(-0.713671\pi\) |
0.367139 | + | 0.930166i | \(0.380337\pi\) | |||||||
\(720\) | 133143. | − | 70459.9i | 0.256835 | − | 0.135918i | ||||
\(721\) | 231416. | 0.445166 | ||||||||
\(722\) | 472060. | − | 221126.i | 0.905571 | − | 0.424194i | ||||
\(723\) | − | 389223.i | − | 0.744599i | ||||||
\(724\) | 14106.1 | − | 49013.0i | 0.0269111 | − | 0.0935048i | ||||
\(725\) | 1.01620e6 | + | 1.76011e6i | 1.93331 | + | 3.34859i | ||||
\(726\) | 20345.2 | + | 27026.4i | 0.0386001 | + | 0.0512762i | ||||
\(727\) | −382980. | + | 221114.i | −0.724615 | + | 0.418357i | −0.816449 | − | 0.577418i | \(-0.804060\pi\) |
0.0918341 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(728\) | 21285.3 | − | 133126.i | 0.0401622 | − | 0.251189i | ||||
\(729\) | −585250. | −1.10125 | ||||||||
\(730\) | −603522. | − | 256528.i | −1.13252 | − | 0.481381i | ||||
\(731\) | 21322.0 | + | 12310.3i | 0.0399019 | + | 0.0230373i | ||||
\(732\) | 9644.88 | + | 38845.3i | 0.0180001 | + | 0.0724964i | ||||
\(733\) | 759847. | 1.41422 | 0.707112 | − | 0.707102i | \(-0.249998\pi\) | ||||
0.707112 | + | 0.707102i | \(0.249998\pi\) | |||||||
\(734\) | 33007.5 | − | 77655.3i | 0.0612662 | − | 0.144138i | ||||
\(735\) | −230867. | − | 133291.i | −0.427353 | − | 0.246732i | ||||
\(736\) | 15540.2 | + | 182771.i | 0.0286880 | + | 0.337405i | ||||
\(737\) | 104015. | − | 180159.i | 0.191496 | − | 0.331680i | ||||
\(738\) | −3130.89 | − | 25602.6i | −0.00574852 | − | 0.0470079i | ||||
\(739\) | −113550. | + | 65558.3i | −0.207922 | + | 0.120044i | −0.600345 | − | 0.799741i | \(-0.704970\pi\) |
0.392423 | + | 0.919785i | \(0.371637\pi\) | |||||||
\(740\) | −488501. | − | 506848.i | −0.892076 | − | 0.925581i | ||||
\(741\) | 88759.3 | − | 122453.i | 0.161651 | − | 0.223015i | ||||
\(742\) | 130189. | − | 306290.i | 0.236465 | − | 0.556321i | ||||
\(743\) | 740254. | − | 427386.i | 1.34092 | − | 0.774181i | 0.353978 | − | 0.935254i | \(-0.384829\pi\) |
0.986942 | + | 0.161073i | \(0.0514955\pi\) | |||||||
\(744\) | 554332. | − | 682494.i | 1.00144 | − | 1.23297i | ||||
\(745\) | −457436. | + | 792303.i | −0.824172 | + | 1.42751i | ||||
\(746\) | 44582.5 | + | 364569.i | 0.0801100 | + | 0.655092i | ||||
\(747\) | −965.344 | − | 557.341i | −0.00172998 | − | 0.000998804i | ||||
\(748\) | −19390.0 | + | 18688.1i | −0.0346557 | + | 0.0334012i | ||||
\(749\) | −59246.2 | −0.105608 | ||||||||
\(750\) | −1.10198e6 | − | 1.46387e6i | −1.95908 | − | 2.60243i | ||||
\(751\) | 130920. | + | 75586.7i | 0.232127 | + | 0.134019i | 0.611553 | − | 0.791203i | \(-0.290545\pi\) |
−0.379426 | + | 0.925222i | \(0.623878\pi\) | |||||||
\(752\) | −803483. | − | 29631.9i | −1.42083 | − | 0.0523992i | ||||
\(753\) | 264473. | 0.466435 | ||||||||
\(754\) | 186658. | − | 140514.i | 0.328325 | − | 0.247159i | ||||
\(755\) | −1.36453e6 | + | 787809.i | −2.39380 | + | 1.38206i | ||||
\(756\) | 500926. | − | 124375.i | 0.876456 | − | 0.217615i | ||||
\(757\) | −540486. | − | 936148.i | −0.943175 | − | 1.63363i | −0.759364 | − | 0.650666i | \(-0.774490\pi\) |
−0.183811 | − | 0.982962i | \(-0.558843\pi\) | |||||||
\(758\) | −101174. | + | 12372.4i | −0.176088 | + | 0.0215335i | ||||
\(759\) | 186122.i | 0.323082i | ||||||||
\(760\) | −1.08899e6 | + | 291382.i | −1.88537 | + | 0.504471i | ||||
\(761\) | −705470. | −1.21817 | −0.609086 | − | 0.793104i | \(-0.708464\pi\) | ||||
−0.609086 | + | 0.793104i | \(0.708464\pi\) | |||||||
\(762\) | −57324.1 | − | 468763.i | −0.0987251 | − | 0.807315i | ||||
\(763\) | 781846. | − | 451399.i | 1.34299 | − | 0.775375i | ||||
\(764\) | 57965.1 | + | 233458.i | 0.0993070 | + | 0.399965i | ||||
\(765\) | 3957.20 | + | 6854.08i | 0.00676185 | + | 0.0117119i | ||||
\(766\) | −358239. | − | 475883.i | −0.610541 | − | 0.811040i | ||||
\(767\) | 159573.i | 0.271249i | ||||||||
\(768\) | 40081.0 | − | 542669.i | 0.0679542 | − | 0.920052i | ||||
\(769\) | −162612. | + | 281651.i | −0.274978 | + | 0.476277i | −0.970130 | − | 0.242587i | \(-0.922004\pi\) |
0.695151 | + | 0.718863i | \(0.255337\pi\) | |||||||
\(770\) | −814621. | + | 613237.i | −1.37396 | + | 1.03430i | ||||
\(771\) | − | 528817.i | − | 0.889603i | ||||||
\(772\) | 411339. | + | 426789.i | 0.690185 | + | 0.716108i | ||||
\(773\) | −279762. | + | 484561.i | −0.468197 | + | 0.810942i | −0.999339 | − | 0.0363411i | \(-0.988430\pi\) |
0.531142 | + | 0.847283i | \(0.321763\pi\) | |||||||
\(774\) | 87650.0 | − | 10718.6i | 0.146309 | − | 0.0178918i | ||||
\(775\) | 2.51580e6 | + | 1.45250e6i | 4.18864 | + | 2.41831i | ||||
\(776\) | −477008. | + | 587292.i | −0.792140 | + | 0.975282i | ||||
\(777\) | −156284. | − | 270691.i | −0.258864 | − | 0.448366i | ||||
\(778\) | 362289. | + | 153992.i | 0.598544 | + | 0.254412i | ||||
\(779\) | −19962.6 | + | 191989.i | −0.0328960 | + | 0.316375i | ||||
\(780\) | −235489. | + | 226964.i | −0.387063 | + | 0.373051i | ||||
\(781\) | −351987. | − | 609659.i | −0.577064 | − | 0.999504i | ||||
\(782\) | −9566.03 | + | 1169.81i | −0.0156429 | + | 0.00191295i | ||||
\(783\) | 774619. | + | 447226.i | 1.26347 | + | 0.729464i | ||||
\(784\) | 148891. | − | 78793.5i | 0.242235 | − | 0.128191i | ||||
\(785\) | 852653. | − | 1.47684e6i | 1.38367 | − | 2.39659i | ||||
\(786\) | −323384. | − | 137455.i | −0.523449 | − | 0.222493i | ||||
\(787\) | − | 304244.i | − | 0.491216i | −0.969369 | − | 0.245608i | \(-0.921012\pi\) | ||
0.969369 | − | 0.245608i | \(-0.0789876\pi\) | |||||||
\(788\) | −111597. | + | 27708.3i | −0.179721 | + | 0.0446229i | ||||
\(789\) | 383199. | − | 663720.i | 0.615560 | − | 1.06618i | ||||
\(790\) | 31981.5 | − | 75241.5i | 0.0512443 | − | 0.120560i | ||||
\(791\) | − | 22140.3i | − | 0.0353859i | ||||||
\(792\) | −15249.2 | + | 95374.1i | −0.0243107 | + | 0.152048i | ||||
\(793\) | 7600.84 | + | 13165.0i | 0.0120869 | + | 0.0209351i | ||||
\(794\) | 93845.1 | − | 70645.4i | 0.148857 | − | 0.112058i | ||||
\(795\) | −699215. | + | 403692.i | −1.10631 | + | 0.638728i | ||||
\(796\) | −598534. | − | 172261.i | −0.944632 | − | 0.271869i | ||||
\(797\) | −112818. | −0.177607 | −0.0888036 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888036 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(798\) | −500470. | + | 9048.75i | −0.785909 | + | 0.0142096i | ||||
\(799\) | − | 42243.1i | − | 0.0661702i | ||||||
\(800\) | 1.79137e6 | − | 152312.i | 2.79901 | − | 0.237987i | ||||
\(801\) | −52260.8 | − | 90518.3i | −0.0814537 | − | 0.141082i | ||||
\(802\) | −127452. | + | 95944.6i | −0.198152 | + | 0.149167i | ||||
\(803\) | 364138. | − | 210235.i | 0.564722 | − | 0.326042i | ||||
\(804\) | −214339. | + | 53218.0i | −0.331580 | + | 0.0823278i | ||||
\(805\) | −364895. | −0.563088 | ||||||||
\(806\) | 130633. | − | 307334.i | 0.201087 | − | 0.473087i | ||||
\(807\) | 441274. | + | 254770.i | 0.677581 | + | 0.391201i | ||||
\(808\) | −1.18359e6 | − | 189243.i | −1.81293 | − | 0.289866i | ||||
\(809\) | 269220. | 0.411348 | 0.205674 | − | 0.978621i | \(-0.434061\pi\) | ||||
0.205674 | + | 0.978621i | \(0.434061\pi\) | |||||||
\(810\) | −976886. | − | 415227.i | −1.48893 | − | 0.632872i | ||||
\(811\) | −41674.7 | − | 24060.9i | −0.0633623 | − | 0.0365823i | 0.467984 | − | 0.883737i | \(-0.344980\pi\) |
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(812\) | −743094. | − | 213866.i | −1.12702 | − | 0.324361i | ||||
\(813\) | −484573. | + | 839306.i | −0.733126 | + | 1.26981i | ||||
\(814\) | 448011. | − | 54786.5i | 0.676145 | − | 0.0826846i | ||||
\(815\) | −1.92853e6 | + | 1.11344e6i | −2.90343 | + | 1.67630i | ||||
\(816\) | 28569.7 | + | 1053.63i | 0.0429067 | + | 0.00158237i | ||||
\(817\) | −657272. | − | 68341.7i | −0.984693 | − | 0.102386i | ||||
\(818\) | 729801. | + | 310204.i | 1.09068 | + | 0.463597i | ||||
\(819\) | 22000.7 | − | 12702.1i | 0.0327996 | − | 0.0189369i | ||||
\(820\) | 115450. | − | 401141.i | 0.171698 | − | 0.596580i | ||||
\(821\) | 199651. | − | 345805.i | 0.296200 | − | 0.513033i | −0.679064 | − | 0.734079i | \(-0.737614\pi\) |
0.975263 | + | 0.221047i | \(0.0709473\pi\) | |||||||
\(822\) | 420309. | − | 51398.8i | 0.622049 | − | 0.0760693i | ||||
\(823\) | 559664. | + | 323122.i | 0.826281 | + | 0.477053i | 0.852577 | − | 0.522601i | \(-0.175038\pi\) |
−0.0262968 | + | 0.999654i | \(0.508372\pi\) | |||||||
\(824\) | 331377. | − | 126646.i | 0.488054 | − | 0.186526i | ||||
\(825\) | 1.82421e6 | 2.68020 | ||||||||
\(826\) | 421943. | − | 317634.i | 0.618435 | − | 0.465550i | ||||
\(827\) | 755424. | + | 436144.i | 1.10454 | + | 0.637704i | 0.937409 | − | 0.348231i | \(-0.113218\pi\) |
0.167127 | + | 0.985935i | \(0.446551\pi\) | |||||||
\(828\) | −24887.3 | + | 23986.3i | −0.0363008 | + | 0.0349867i | ||||
\(829\) | −275564. | −0.400972 | −0.200486 | − | 0.979697i | \(-0.564252\pi\) | ||||
−0.200486 | + | 0.979697i | \(0.564252\pi\) | |||||||
\(830\) | −10849.3 | − | 14412.2i | −0.0157487 | − | 0.0209206i | ||||
\(831\) | 81830.3 | − | 47244.8i | 0.118498 | − | 0.0684151i | ||||
\(832\) | −42375.9 | − | 202279.i | −0.0612170 | − | 0.292217i | ||||
\(833\) | 4425.24 | + | 7664.74i | 0.00637745 | + | 0.0110461i | ||||
\(834\) | 22081.4 | + | 180568.i | 0.0317464 | + | 0.259603i | ||||
\(835\) | − | 695478.i | − | 0.997494i | ||||||
\(836\) | 270674. | − | 670203.i | 0.387287 | − | 0.958946i | ||||
\(837\) | 1.27848e6 | 1.82492 | ||||||||
\(838\) | −727592. | + | 88975.9i | −1.03610 | + | 0.126702i | ||||
\(839\) | 206062. | − | 118970.i | 0.292735 | − | 0.169010i | −0.346440 | − | 0.938072i | \(-0.612609\pi\) |
0.639174 | + | 0.769062i | \(0.279276\pi\) | |||||||
\(840\) | 1.06889e6 | + | 170903.i | 1.51486 | + | 0.242209i | ||||
\(841\) | −316379. | − | 547985.i | −0.447318 | − | 0.774777i | ||||
\(842\) | 358519. | − | 269889.i | 0.505694 | − | 0.380680i | ||||
\(843\) | − | 30389.8i | − | 0.0427634i | ||||||
\(844\) | −211404. | + | 203751.i | −0.296775 | + | 0.286032i | ||||
\(845\) | 634670. | − | 1.09928e6i | 0.888862 | − | 1.53955i | ||||
\(846\) | −91120.3 | − | 121044.i | −0.127313 | − | 0.169123i | ||||
\(847\) | − | 42523.6i | − | 0.0592738i | ||||||
\(848\) | 18802.7 | − | 509843.i | 0.0261474 | − | 0.708998i | ||||
\(849\) | 203366. | − | 352240.i | 0.282139 | − | 0.488679i | ||||
\(850\) | 11465.5 | + | 93758.4i | 0.0158693 | + | 0.129769i | ||||
\(851\) | 139883. | + | 80761.3i | 0.193154 | + | 0.111518i | ||||
\(852\) | −206699. | + | 718194.i | −0.284747 | + | 0.989379i | ||||
\(853\) | 161401. | + | 279555.i | 0.221824 | + | 0.384211i | 0.955362 | − | 0.295438i | \(-0.0954656\pi\) |
−0.733538 | + | 0.679649i | \(0.762132\pi\) | |||||||
\(854\) | 19681.4 | − | 46303.5i | 0.0269861 | − | 0.0634890i | ||||
\(855\) | −171993. | − | 124667.i | −0.235276 | − | 0.170538i | ||||
\(856\) | −84838.1 | + | 32423.6i | −0.115783 | + | 0.0442500i | ||||
\(857\) | −276113. | − | 478243.i | −0.375946 | − | 0.651158i | 0.614522 | − | 0.788900i | \(-0.289349\pi\) |
−0.990468 | + | 0.137742i | \(0.956016\pi\) | |||||||
\(858\) | −25454.6 | − | 208152.i | −0.0345773 | − | 0.282753i | ||||
\(859\) | −610607. | − | 352534.i | −0.827514 | − | 0.477766i | 0.0254866 | − | 0.999675i | \(-0.491886\pi\) |
−0.853001 | + | 0.521910i | \(0.825220\pi\) | |||||||
\(860\) | 1.37330e6 | + | 395241.i | 1.85681 | + | 0.534398i | ||||
\(861\) | 92673.7 | − | 160516.i | 0.125012 | − | 0.216526i | ||||
\(862\) | 468297. | − | 1.10174e6i | 0.630242 | − | 1.48274i | ||||
\(863\) | 110750.i | 0.148703i | 0.997232 | + | 0.0743516i | \(0.0236887\pi\) | ||||
−0.997232 | + | 0.0743516i | \(0.976311\pi\) | |||||||
\(864\) | 649239. | − | 452240.i | 0.869715 | − | 0.605817i | ||||
\(865\) | −355527. | + | 615791.i | −0.475161 | + | 0.823002i | ||||
\(866\) | 149254. | + | 63440.7i | 0.199017 | + | 0.0845925i | ||||
\(867\) | − | 691974.i | − | 0.920560i | ||||||
\(868\) | −1.07268e6 | + | 266336.i | −1.42375 | + | 0.353501i | ||||
\(869\) | 26210.1 | + | 45397.3i | 0.0347080 | + | 0.0601160i | ||||
\(870\) | 1.12820e6 | + | 1.49870e6i | 1.49056 | + | 1.98005i | ||||
\(871\) | −72641.3 | + | 41939.5i | −0.0957519 | + | 0.0552824i | ||||
\(872\) | 872535. | − | 1.07426e6i | 1.14749 | − | 1.41279i | ||||
\(873\) | −142571. | −0.187069 | ||||||||
\(874\) | 221636. | − | 133361.i | 0.290147 | − | 0.174585i | ||||
\(875\) | 2.30326e6i | 3.00834i | ||||||||
\(876\) | −428964. | − | 123458.i | −0.559001 | − | 0.160883i | ||||
\(877\) | 159963. | + | 277065.i | 0.207980 | + | 0.360232i | 0.951078 | − | 0.308951i | \(-0.0999778\pi\) |
−0.743098 | + | 0.669182i | \(0.766644\pi\) | |||||||
\(878\) | 699315. | + | 928968.i | 0.907160 | + | 1.20507i | ||||
\(879\) | −365880. | + | 211241.i | −0.473544 | + | 0.273401i | ||||
\(880\) | −830898. | + | 1.32395e6i | −1.07296 | + | 1.70964i | ||||
\(881\) | 320946. | 0.413504 | 0.206752 | − | 0.978393i | \(-0.433711\pi\) | ||||
0.206752 | + | 0.978393i | \(0.433711\pi\) | |||||||
\(882\) | 29213.3 | + | 12417.2i | 0.0375529 | + | 0.0159619i | ||||
\(883\) | −284526. | − | 164271.i | −0.364922 | − | 0.210688i | 0.306316 | − | 0.951930i | \(-0.400904\pi\) |
−0.671238 | + | 0.741242i | \(0.734237\pi\) | |||||||
\(884\) | 10538.3 | − | 2616.56i | 0.0134855 | − | 0.00334831i | ||||
\(885\) | −1.28123e6 | −1.63584 | ||||||||
\(886\) | −121373. | + | 285548.i | −0.154616 | + | 0.363757i | ||||
\(887\) | −194291. | − | 112174.i | −0.246948 | − | 0.142576i | 0.371418 | − | 0.928466i | \(-0.378872\pi\) |
−0.618366 | + | 0.785890i | \(0.712205\pi\) | |||||||
\(888\) | −371933. | − | 302090.i | −0.471670 | − | 0.383098i | ||||
\(889\) | −296822. | + | 514110.i | −0.375571 | + | 0.650508i | ||||
\(890\) | −205323. | − | 1.67901e6i | −0.259213 | − | 2.11969i | ||||
\(891\) | 589408. | − | 340295.i | 0.742439 | − | 0.428648i | ||||
\(892\) | 833781. | − | 803599.i | 1.04791 | − | 1.00997i | ||||
\(893\) | 462315. | + | 1.03527e6i | 0.579742 | + | 1.29823i | ||||
\(894\) | −243603. | + | 573113.i | −0.304795 | + | 0.717077i | ||||
\(895\) | 812982. | − | 469375.i | 1.01493 | − | 0.585968i | ||||
\(896\) | −450518. | + | 514693.i | −0.561173 | + | 0.641110i | ||||
\(897\) | 37522.8 | − | 64991.5i | 0.0466349 | − | 0.0807740i | ||||
\(898\) | −52504.8 | − | 429353.i | −0.0651098 | − | 0.532429i | ||||
\(899\) | −1.65877e6 | − | 957691.i | −2.05242 | − | 1.18497i | ||||
\(900\) | 235094. | + | 243924.i | 0.290240 | + | 0.301141i | ||||
\(901\) | 26805.0 | 0.0330192 | ||||||||
\(902\) | 160967. | + | 213827.i | 0.197844 | + | 0.262815i | ||||
\(903\) | 549522. | + | 317267.i | 0.673922 | + | 0.389089i | ||||
\(904\) | −12116.7 | − | 31704.0i | −0.0148268 | − | 0.0387951i | ||||
\(905\) | 155533. | 0.189901 | ||||||||
\(906\) | −856848. | + | 645024.i | −1.04387 | + | 0.785814i | ||||
\(907\) | 780633. | − | 450699.i | 0.948926 | − | 0.547863i | 0.0561789 | − | 0.998421i | \(-0.482108\pi\) |
0.892747 | + | 0.450558i | \(0.148775\pi\) | |||||||
\(908\) | −156599. | − | 630713.i | −0.189941 | − | 0.764997i | ||||
\(909\) | −112932. | − | 195604.i | −0.136675 | − | 0.236728i | ||||
\(910\) | 408087. | − | 49904.2i | 0.492799 | − | 0.0602635i | ||||
\(911\) | 177558.i | 0.213946i | 0.994262 | + | 0.106973i | \(0.0341158\pi\) | ||||
−0.994262 | + | 0.106973i | \(0.965884\pi\) | |||||||
\(912\) | −711699. | + | 286849.i | −0.855671 | + | 0.344876i | ||||
\(913\) | 11566.4 | 0.0138758 | ||||||||
\(914\) | 112357. | + | 918786.i | 0.134495 | + | 1.09982i | ||||
\(915\) | −105704. | + | 61028.2i | −0.126255 | + | 0.0728935i | ||||
\(916\) | −751111. | + | 186493.i | −0.895186 | + | 0.222265i | ||||
\(917\) | 220853. | + | 382528.i | 0.262642 | + | 0.454909i | ||||
\(918\) | 25001.4 | + | 33211.7i | 0.0296673 | + | 0.0394099i | ||||
\(919\) | − | 93227.2i | − | 0.110385i | −0.998476 | − | 0.0551927i | \(-0.982423\pi\) | ||
0.998476 | − | 0.0551927i | \(-0.0175773\pi\) | |||||||
\(920\) | −522515. | + | 199696.i | −0.617338 | + | 0.235935i | ||||
\(921\) | −299641. | + | 518993.i | −0.353250 | + | 0.611846i | ||||
\(922\) | −526820. | + | 396584.i | −0.619727 | + | 0.466523i | ||||
\(923\) | 283847.i | 0.333182i | ||||||||
\(924\) | −499730. | + | 481640.i | −0.585317 | + | 0.564129i | ||||
\(925\) | 791556. | − | 1.37101e6i | 0.925120 | − | 1.60235i | ||||
\(926\) | −708425. | + | 86632.1i | −0.826175 | + | 0.101031i | ||||
\(927\) | 57892.2 | + | 33424.1i | 0.0673690 | + | 0.0388955i | ||||
\(928\) | −1.18112e6 | + | 100425.i | −1.37151 | + | 0.116613i | ||||
\(929\) | 619863. | + | 1.07363e6i | 0.718232 | + | 1.24401i | 0.961700 | + | 0.274105i | \(0.0883815\pi\) |
−0.243468 | + | 0.969909i | \(0.578285\pi\) | |||||||
\(930\) | 2.46763e6 | + | 1.04887e6i | 2.85308 | + | 1.21271i | ||||
\(931\) | −192335. | − | 139413.i | −0.221901 | − | 0.160843i | ||||
\(932\) | 741298. | + | 769140.i | 0.853416 | + | 0.885470i | ||||
\(933\) | −594281. | − | 1.02932e6i | −0.682698 | − | 1.18247i | ||||
\(934\) | −414294. | + | 50663.3i | −0.474914 | + | 0.0580764i | ||||
\(935\) | −71120.8 | − | 41061.6i | −0.0813529 | − | 0.0469691i | ||||
\(936\) | 24552.6 | − | 30229.2i | 0.0280251 | − | 0.0345044i | ||||
\(937\) | 647852. | − | 1.12211e6i | 0.737899 | − | 1.27808i | −0.215541 | − | 0.976495i | \(-0.569152\pi\) |
0.953440 | − | 0.301583i | \(-0.0975151\pi\) | |||||||
\(938\) | 255491. | + | 108597.i | 0.290382 | + | 0.123428i | ||||
\(939\) | 1.14185e6i | 1.29502i | ||||||||
\(940\) | −590843. | − | 2.37965e6i | −0.668677 | − | 2.69313i | ||||
\(941\) | −410840. | + | 711597.i | −0.463974 | + | 0.803627i | −0.999155 | − | 0.0411108i | \(-0.986910\pi\) |
0.535180 | + | 0.844738i | \(0.320244\pi\) | |||||||
\(942\) | 454072. | − | 1.06827e6i | 0.511708 | − | 1.20387i | ||||
\(943\) | 95780.2i | 0.107709i | ||||||||
\(944\) | 430374. | − | 685754.i | 0.482950 | − | 0.769528i | ||||
\(945\) | 786984. | + | 1.36310e6i | 0.881256 | + | 1.52638i | ||||
\(946\) | −732034. | + | 551066.i | −0.817992 | + | 0.615774i | ||||
\(947\) | 269585. | − | 155645.i | 0.300605 | − | 0.173554i | −0.342110 | − | 0.939660i | \(-0.611142\pi\) |
0.642714 | + | 0.766106i | \(0.277808\pi\) | |||||||
\(948\) | 15391.5 | − | 53479.2i | 0.0171264 | − | 0.0595071i | ||||
\(949\) | −169537. | −0.188248 | ||||||||
\(950\) | −1.30710e6 | − | 2.17229e6i | −1.44831 | − | 2.40697i | ||||
\(951\) | − | 626819.i | − | 0.693077i | ||||||
\(952\) | −27895.6 | − | 22657.2i | −0.0307795 | − | 0.0249996i | ||||
\(953\) | 169941. | + | 294347.i | 0.187117 | + | 0.324096i | 0.944288 | − | 0.329121i | \(-0.106752\pi\) |
−0.757171 | + | 0.653217i | \(0.773419\pi\) | |||||||
\(954\) | 76807.3 | − | 57819.6i | 0.0843929 | − | 0.0635299i | ||||
\(955\) | −635274. | + | 366776.i | −0.696554 | + | 0.402155i | ||||
\(956\) | 226633. | + | 912777.i | 0.247975 | + | 0.998732i | ||||
\(957\) | −1.20278e6 | −1.31329 | ||||||||
\(958\) | −313868. | + | 738422.i | −0.341992 | + | 0.804588i | ||||
\(959\) | −460969. | − | 266141.i | −0.501227 | − | 0.289384i | ||||
\(960\) | 1.62413e6 | − | 340242.i | 1.76230 | − | 0.369187i | ||||
\(961\) | −1.81423e6 | −1.96447 | ||||||||
\(962\) | −167485. | − | 71190.0i | −0.180978 | − | 0.0769252i | ||||
\(963\) | −14821.4 | − | 8557.11i | −0.0159822 | − | 0.00922730i | ||||
\(964\) | −207443. | + | 720779.i | −0.223226 | + | 0.775619i | ||||
\(965\) | −903798. | + | 1.56542e6i | −0.970547 | + | 1.68104i | ||||
\(966\) | −246541. | + | 30149.1i | −0.264201 | + | 0.0323087i | ||||
\(967\) | 1.00903e6 | − | 582563.i | 1.07907 | − | 0.623003i | 0.148426 | − | 0.988923i | \(-0.452579\pi\) |
0.930646 | + | 0.365921i | \(0.119246\pi\) | |||||||
\(968\) | −23271.8 | − | 60891.9i | −0.0248359 | − | 0.0649844i | ||||
\(969\) | −16438.6 | − | 36811.4i | −0.0175073 | − | 0.0392044i | ||||
\(970\) | −2.12342e6 | − | 902563.i | −2.25680 | − | 0.959255i | ||||
\(971\) | 219836. | − | 126922.i | 0.233163 | − | 0.134617i | −0.378867 | − | 0.925451i | \(-0.623686\pi\) |
0.612031 | + | 0.790834i | \(0.290353\pi\) | |||||||
\(972\) | 267989. | + | 77128.3i | 0.283651 | + | 0.0816359i | ||||
\(973\) | 114336. | − | 198036.i | 0.120770 | − | 0.209179i | ||||
\(974\) | 1.62210e6 | − | 198363.i | 1.70985 | − | 0.209095i | ||||
\(975\) | −636993. | − | 367768.i | −0.670078 | − | 0.386870i | ||||
\(976\) | 2842.50 | − | 77075.7i | 0.00298402 | − | 0.0809129i | ||||
\(977\) | −523166. | −0.548089 | −0.274044 | − | 0.961717i | \(-0.588361\pi\) | ||||
−0.274044 | + | 0.961717i | \(0.588361\pi\) | |||||||
\(978\) | −1.21101e6 | + | 911636.i | −1.26611 | + | 0.953111i | ||||
\(979\) | 939256. | + | 542280.i | 0.979983 | + | 0.565793i | ||||
\(980\) | 356489. | + | 369878.i | 0.371188 | + | 0.385129i | ||||
\(981\) | 260788. | 0.270988 | ||||||||
\(982\) | 790166. | + | 1.04965e6i | 0.819399 | + | 1.08849i | ||||
\(983\) | 199300. | − | 115066.i | 0.206253 | − | 0.119080i | −0.393316 | − | 0.919403i | \(-0.628672\pi\) |
0.599569 | + | 0.800323i | \(0.295339\pi\) | |||||||
\(984\) | 44859.8 | − | 280569.i | 0.0463305 | − | 0.289767i | ||||
\(985\) | −175325. | − | 303672.i | −0.180705 | − | 0.312991i | ||||
\(986\) | −7559.70 | − | 61818.7i | −0.00777590 | − | 0.0635866i | ||||
\(987\) | − | 1.08871e6i | − | 1.11758i | ||||||
\(988\) | −229632. | + | 179458.i | −0.235244 | + | 0.183844i | ||||
\(989\) | −327902. | −0.335237 | ||||||||
\(990\) | −292362. | + | 35752.4i | −0.298298 | + | 0.0364783i | ||||
\(991\) | −1.20592e6 | + | 696241.i | −1.22793 | + | 0.708944i | −0.966596 | − | 0.256305i | \(-0.917495\pi\) |
−0.261332 | + | 0.965249i | \(0.584162\pi\) | |||||||
\(992\) | −1.39028e6 | + | 968428.i | −1.41280 | + | 0.984111i | ||||
\(993\) | −532147. | − | 921706.i | −0.539676 | − | 0.934747i | ||||
\(994\) | 750551. | − | 565006.i | 0.759640 | − | 0.571847i | ||||
\(995\) | − | 1.89933e6i | − | 1.91847i | ||||||
\(996\) | −8521.11 | − | 8841.16i | −0.00858969 | − | 0.00891231i | ||||
\(997\) | −140911. | + | 244066.i | −0.141761 | + | 0.245537i | −0.928160 | − | 0.372182i | \(-0.878610\pi\) |
0.786399 | + | 0.617719i | \(0.211943\pi\) | |||||||
\(998\) | 282353. | + | 375076.i | 0.283486 | + | 0.376581i | ||||
\(999\) | − | 696724.i | − | 0.698120i |
(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 | 76.5.g.a.7.17 | yes | 76 | |
4.3 | odd | 2 | inner | 76.5.g.a.7.9 | ✓ | 76 | |
19.11 | even | 3 | inner | 76.5.g.a.11.9 | yes | 76 | |
76.11 | odd | 6 | inner | 76.5.g.a.11.17 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.g.a.7.9 | ✓ | 76 | 4.3 | odd | 2 | inner | |
76.5.g.a.7.17 | yes | 76 | 1.1 | even | 1 | trivial | |
76.5.g.a.11.9 | yes | 76 | 19.11 | even | 3 | inner | |
76.5.g.a.11.17 | yes | 76 | 76.11 | odd | 6 | inner |