Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
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([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + 5832 x^{10} - 32373 x^{9} + 52488 x^{8} - 6561 x^{7} - 40824 x^{6} + 1673055 x^{5} + \cdots + 387420489 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Root | \(-1.07135 + 2.80218i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.c.22.8 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.21232 | − | 3.83185i | 0.782173 | − | 1.35476i | −0.148501 | − | 0.988912i | \(-0.547445\pi\) |
0.930674 | − | 0.365851i | \(-0.119222\pi\) | |||||||
\(3\) | −4.03378 | − | 3.27546i | −0.776301 | − | 0.630362i | ||||
\(4\) | −5.78871 | − | 10.0263i | −0.723588 | − | 1.25329i | ||||
\(5\) | −1.92707 | − | 3.33779i | −0.172363 | − | 0.298541i | 0.766883 | − | 0.641787i | \(-0.221807\pi\) |
−0.939245 | + | 0.343246i | \(0.888473\pi\) | |||||||
\(6\) | −21.4751 | + | 8.21047i | −1.46119 | + | 0.558651i | ||||
\(7\) | −3.50000 | + | 6.06218i | −0.188982 | + | 0.327327i | ||||
\(8\) | −15.8288 | −0.699539 | ||||||||
\(9\) | 5.54273 | + | 26.4250i | 0.205286 | + | 0.978702i | ||||
\(10\) | −17.0532 | −0.539270 | ||||||||
\(11\) | 19.8164 | − | 34.3229i | 0.543169 | − | 0.940796i | −0.455551 | − | 0.890210i | \(-0.650558\pi\) |
0.998720 | − | 0.0505861i | \(-0.0161089\pi\) | |||||||
\(12\) | −9.49049 | + | 59.4047i | −0.228306 | + | 1.42905i | ||||
\(13\) | −31.7297 | − | 54.9575i | −0.676941 | − | 1.17250i | −0.975897 | − | 0.218230i | \(-0.929972\pi\) |
0.298956 | − | 0.954267i | \(-0.403362\pi\) | |||||||
\(14\) | 15.4862 | + | 26.8229i | 0.295634 | + | 0.512052i | ||||
\(15\) | −3.15941 | + | 19.7760i | −0.0543837 | + | 0.340409i | ||||
\(16\) | 11.2914 | − | 19.5573i | 0.176428 | − | 0.305582i | ||||
\(17\) | 10.5049 | 0.149872 | 0.0749360 | − | 0.997188i | \(-0.476125\pi\) | ||||
0.0749360 | + | 0.997188i | \(0.476125\pi\) | |||||||
\(18\) | 113.519 | + | 37.2215i | 1.48648 | + | 0.487400i | ||||
\(19\) | −8.40311 | −0.101463 | −0.0507317 | − | 0.998712i | \(-0.516155\pi\) | ||||
−0.0507317 | + | 0.998712i | \(0.516155\pi\) | |||||||
\(20\) | −22.3105 | + | 38.6430i | −0.249439 | + | 0.432042i | ||||
\(21\) | 33.9746 | − | 12.9894i | 0.353042 | − | 0.134977i | ||||
\(22\) | −87.6802 | − | 151.867i | −0.849703 | − | 1.47173i | ||||
\(23\) | 87.2126 | + | 151.057i | 0.790656 | + | 1.36946i | 0.925561 | + | 0.378598i | \(0.123594\pi\) |
−0.134905 | + | 0.990858i | \(0.543073\pi\) | |||||||
\(24\) | 63.8497 | + | 51.8465i | 0.543053 | + | 0.440963i | ||||
\(25\) | 55.0728 | − | 95.3888i | 0.440582 | − | 0.763111i | ||||
\(26\) | −280.785 | −2.11794 | ||||||||
\(27\) | 64.1957 | − | 124.747i | 0.457573 | − | 0.889172i | ||||
\(28\) | 81.0419 | 0.546981 | ||||||||
\(29\) | 42.0688 | − | 72.8654i | 0.269379 | − | 0.466578i | −0.699323 | − | 0.714806i | \(-0.746515\pi\) |
0.968702 | + | 0.248228i | \(0.0798483\pi\) | |||||||
\(30\) | 68.7889 | + | 55.8571i | 0.418636 | + | 0.339935i | ||||
\(31\) | 11.4889 | + | 19.8994i | 0.0665635 | + | 0.115291i | 0.897386 | − | 0.441245i | \(-0.145463\pi\) |
−0.830823 | + | 0.556537i | \(0.812130\pi\) | |||||||
\(32\) | −113.275 | − | 196.199i | −0.625764 | − | 1.08386i | ||||
\(33\) | −192.358 | + | 73.5434i | −1.01470 | + | 0.387948i | ||||
\(34\) | 23.2403 | − | 40.2534i | 0.117226 | − | 0.203041i | ||||
\(35\) | 26.9790 | 0.130294 | ||||||||
\(36\) | 232.860 | − | 208.540i | 1.07806 | − | 0.965461i | ||||
\(37\) | 302.219 | 1.34282 | 0.671412 | − | 0.741084i | \(-0.265688\pi\) | ||||
0.671412 | + | 0.741084i | \(0.265688\pi\) | |||||||
\(38\) | −18.5904 | + | 32.1995i | −0.0793620 | + | 0.137459i | ||||
\(39\) | −52.0203 | + | 325.616i | −0.213588 | + | 1.33693i | ||||
\(40\) | 30.5032 | + | 52.8331i | 0.120574 | + | 0.208841i | ||||
\(41\) | 179.082 | + | 310.180i | 0.682146 | + | 1.18151i | 0.974325 | + | 0.225148i | \(0.0722865\pi\) |
−0.292179 | + | 0.956364i | \(0.594380\pi\) | |||||||
\(42\) | 25.3894 | − | 158.922i | 0.0932779 | − | 0.583863i | ||||
\(43\) | −170.966 | + | 296.121i | −0.606326 | + | 1.05019i | 0.385514 | + | 0.922702i | \(0.374024\pi\) |
−0.991840 | + | 0.127486i | \(0.959309\pi\) | |||||||
\(44\) | −458.844 | −1.57212 | ||||||||
\(45\) | 77.5197 | − | 69.4233i | 0.256799 | − | 0.229978i | ||||
\(46\) | 771.768 | 2.47372 | ||||||||
\(47\) | −153.122 | + | 265.216i | −0.475217 | + | 0.823100i | −0.999597 | − | 0.0283840i | \(-0.990964\pi\) |
0.524380 | + | 0.851484i | \(0.324297\pi\) | |||||||
\(48\) | −109.606 | + | 41.9052i | −0.329589 | + | 0.126010i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −243.677 | − | 422.061i | −0.689223 | − | 1.19377i | ||||
\(51\) | −42.3746 | − | 34.4085i | −0.116346 | − | 0.0944737i | ||||
\(52\) | −367.348 | + | 636.265i | −0.979654 | + | 1.69681i | ||||
\(53\) | −192.951 | −0.500073 | −0.250036 | − | 0.968236i | \(-0.580443\pi\) | ||||
−0.250036 | + | 0.968236i | \(0.580443\pi\) | |||||||
\(54\) | −335.992 | − | 521.969i | −0.846716 | − | 1.31539i | ||||
\(55\) | −152.750 | −0.374488 | ||||||||
\(56\) | 55.4007 | − | 95.9567i | 0.132200 | − | 0.228978i | ||||
\(57\) | 33.8963 | + | 27.5241i | 0.0787662 | + | 0.0639588i | ||||
\(58\) | −186.139 | − | 322.403i | −0.421402 | − | 0.729889i | ||||
\(59\) | 151.531 | + | 262.459i | 0.334366 | + | 0.579140i | 0.983363 | − | 0.181652i | \(-0.0581444\pi\) |
−0.648997 | + | 0.760791i | \(0.724811\pi\) | |||||||
\(60\) | 216.569 | − | 82.8000i | 0.465983 | − | 0.178157i | ||||
\(61\) | 204.728 | − | 354.599i | 0.429716 | − | 0.744290i | −0.567132 | − | 0.823627i | \(-0.691947\pi\) |
0.996848 | + | 0.0793371i | \(0.0252803\pi\) | |||||||
\(62\) | 101.669 | 0.208257 | ||||||||
\(63\) | −179.592 | − | 58.8863i | −0.359151 | − | 0.117762i | ||||
\(64\) | −821.743 | −1.60497 | ||||||||
\(65\) | −122.291 | + | 211.814i | −0.233359 | + | 0.404190i | ||||
\(66\) | −143.750 | + | 899.789i | −0.268097 | + | 1.67813i | ||||
\(67\) | −196.183 | − | 339.799i | −0.357725 | − | 0.619598i | 0.629855 | − | 0.776713i | \(-0.283114\pi\) |
−0.987580 | + | 0.157114i | \(0.949781\pi\) | |||||||
\(68\) | −60.8101 | − | 105.326i | −0.108446 | − | 0.187833i | ||||
\(69\) | 142.984 | − | 894.990i | 0.249467 | − | 1.56151i | ||||
\(70\) | 59.6862 | − | 103.380i | 0.101912 | − | 0.176518i | ||||
\(71\) | 901.317 | 1.50657 | 0.753286 | − | 0.657693i | \(-0.228467\pi\) | ||||
0.753286 | + | 0.657693i | \(0.228467\pi\) | |||||||
\(72\) | −87.7346 | − | 418.274i | −0.143606 | − | 0.684640i | ||||
\(73\) | −1139.05 | −1.82624 | −0.913120 | − | 0.407691i | \(-0.866334\pi\) | ||||
−0.913120 | + | 0.407691i | \(0.866334\pi\) | |||||||
\(74\) | 668.605 | − | 1158.06i | 1.05032 | − | 1.81921i | ||||
\(75\) | −534.594 | + | 204.389i | −0.823061 | + | 0.314677i | ||||
\(76\) | 48.6432 | + | 84.2524i | 0.0734178 | + | 0.127163i | ||||
\(77\) | 138.714 | + | 240.261i | 0.205298 | + | 0.355587i | ||||
\(78\) | 1132.62 | + | 919.700i | 1.64416 | + | 1.33507i | ||||
\(79\) | −242.087 | + | 419.307i | −0.344771 | + | 0.597161i | −0.985312 | − | 0.170763i | \(-0.945377\pi\) |
0.640541 | + | 0.767924i | \(0.278710\pi\) | |||||||
\(80\) | −87.0375 | −0.121639 | ||||||||
\(81\) | −667.556 | + | 292.933i | −0.915715 | + | 0.401828i | ||||
\(82\) | 1584.75 | 2.13422 | ||||||||
\(83\) | −51.9270 | + | 89.9401i | −0.0686714 | + | 0.118942i | −0.898317 | − | 0.439349i | \(-0.855209\pi\) |
0.829645 | + | 0.558291i | \(0.188543\pi\) | |||||||
\(84\) | −326.905 | − | 265.449i | −0.424622 | − | 0.344797i | ||||
\(85\) | −20.2438 | − | 35.0633i | −0.0258324 | − | 0.0447430i | ||||
\(86\) | 756.462 | + | 1310.23i | 0.948504 | + | 1.64286i | ||||
\(87\) | −408.364 | + | 156.128i | −0.503232 | + | 0.192399i | ||||
\(88\) | −313.668 | + | 543.289i | −0.379968 | + | 0.658123i | ||||
\(89\) | 1424.71 | 1.69684 | 0.848422 | − | 0.529321i | \(-0.177553\pi\) | ||||
0.848422 | + | 0.529321i | \(0.177553\pi\) | |||||||
\(90\) | −94.5214 | − | 450.630i | −0.110705 | − | 0.527785i | ||||
\(91\) | 444.216 | 0.511720 | ||||||||
\(92\) | 1009.70 | − | 1748.85i | 1.14422 | − | 1.98185i | ||||
\(93\) | 18.8359 | − | 117.901i | 0.0210020 | − | 0.131460i | ||||
\(94\) | 677.511 | + | 1173.48i | 0.743404 | + | 1.28761i | ||||
\(95\) | 16.1934 | + | 28.0478i | 0.0174885 | + | 0.0302910i | ||||
\(96\) | −185.713 | + | 1162.45i | −0.197440 | + | 1.23586i | ||||
\(97\) | 752.514 | − | 1303.39i | 0.787693 | − | 1.36432i | −0.139684 | − | 0.990196i | \(-0.544609\pi\) |
0.927377 | − | 0.374128i | \(-0.122058\pi\) | |||||||
\(98\) | −216.807 | −0.223478 | ||||||||
\(99\) | 1016.82 | + | 333.403i | 1.03226 | + | 0.338468i | ||||
\(100\) | −1275.20 | −1.27520 | ||||||||
\(101\) | 769.021 | − | 1331.98i | 0.757628 | − | 1.31225i | −0.186429 | − | 0.982468i | \(-0.559691\pi\) |
0.944057 | − | 0.329782i | \(-0.106975\pi\) | |||||||
\(102\) | −225.594 | + | 86.2505i | −0.218992 | + | 0.0837262i | ||||
\(103\) | 710.125 | + | 1229.97i | 0.679327 | + | 1.17663i | 0.975184 | + | 0.221396i | \(0.0710614\pi\) |
−0.295857 | + | 0.955232i | \(0.595605\pi\) | |||||||
\(104\) | 502.242 | + | 869.908i | 0.473547 | + | 0.820207i | ||||
\(105\) | −108.827 | − | 88.3688i | −0.101147 | − | 0.0821325i | ||||
\(106\) | −426.869 | + | 739.359i | −0.391143 | + | 0.677480i | ||||
\(107\) | −1105.83 | −0.999112 | −0.499556 | − | 0.866282i | \(-0.666504\pi\) | ||||
−0.499556 | + | 0.866282i | \(0.666504\pi\) | |||||||
\(108\) | −1622.37 | + | 78.4785i | −1.44549 | + | 0.0699222i | ||||
\(109\) | −2138.26 | −1.87898 | −0.939488 | − | 0.342583i | \(-0.888698\pi\) | ||||
−0.939488 | + | 0.342583i | \(0.888698\pi\) | |||||||
\(110\) | −337.932 | + | 585.316i | −0.292915 | + | 0.507343i | ||||
\(111\) | −1219.08 | − | 989.906i | −1.04244 | − | 0.846466i | ||||
\(112\) | 79.0398 | + | 136.901i | 0.0666836 | + | 0.115499i | ||||
\(113\) | −216.248 | − | 374.553i | −0.180026 | − | 0.311814i | 0.761863 | − | 0.647738i | \(-0.224285\pi\) |
−0.941889 | + | 0.335924i | \(0.890951\pi\) | |||||||
\(114\) | 180.457 | − | 68.9935i | 0.148258 | − | 0.0566827i | ||||
\(115\) | 336.130 | − | 582.195i | 0.272559 | − | 0.472087i | ||||
\(116\) | −974.097 | −0.779678 | ||||||||
\(117\) | 1276.38 | − | 1143.07i | 1.00856 | − | 0.903222i | ||||
\(118\) | 1340.94 | 1.04613 | ||||||||
\(119\) | −36.7673 | + | 63.6829i | −0.0283231 | + | 0.0490571i | ||||
\(120\) | 50.0095 | − | 313.029i | 0.0380435 | − | 0.238129i | ||||
\(121\) | −119.876 | − | 207.631i | −0.0900645 | − | 0.155996i | ||||
\(122\) | −905.845 | − | 1568.97i | −0.672224 | − | 1.16433i | ||||
\(123\) | 293.603 | − | 1837.77i | 0.215230 | − | 1.34721i | ||||
\(124\) | 133.012 | − | 230.383i | 0.0963292 | − | 0.166847i | ||||
\(125\) | −906.286 | −0.648485 | ||||||||
\(126\) | −622.959 | + | 557.895i | −0.440457 | + | 0.394454i | ||||
\(127\) | −489.245 | −0.341839 | −0.170919 | − | 0.985285i | \(-0.554674\pi\) | ||||
−0.170919 | + | 0.985285i | \(0.554674\pi\) | |||||||
\(128\) | −911.753 | + | 1579.20i | −0.629597 | + | 1.09049i | ||||
\(129\) | 1659.57 | − | 634.497i | 1.13269 | − | 0.433057i | ||||
\(130\) | 541.093 | + | 937.201i | 0.365054 | + | 0.632292i | ||||
\(131\) | 339.589 | + | 588.186i | 0.226489 | + | 0.392291i | 0.956765 | − | 0.290862i | \(-0.0939419\pi\) |
−0.730276 | + | 0.683152i | \(0.760609\pi\) | |||||||
\(132\) | 1850.88 | + | 1502.93i | 1.22044 | + | 0.991007i | ||||
\(133\) | 29.4109 | − | 50.9412i | 0.0191748 | − | 0.0332117i | ||||
\(134\) | −1736.08 | −1.11921 | ||||||||
\(135\) | −540.091 | + | 26.1257i | −0.344323 | + | 0.0166559i | ||||
\(136\) | −166.280 | −0.104841 | ||||||||
\(137\) | 405.842 | − | 702.940i | 0.253091 | − | 0.438366i | −0.711284 | − | 0.702904i | \(-0.751886\pi\) |
0.964375 | + | 0.264538i | \(0.0852195\pi\) | |||||||
\(138\) | −3113.14 | − | 2527.90i | −1.92035 | − | 1.55934i | ||||
\(139\) | 88.5339 | + | 153.345i | 0.0540241 | + | 0.0935725i | 0.891773 | − | 0.452484i | \(-0.149462\pi\) |
−0.837749 | + | 0.546056i | \(0.816129\pi\) | |||||||
\(140\) | −156.174 | − | 270.501i | −0.0942792 | − | 0.163296i | ||||
\(141\) | 1486.37 | − | 568.276i | 0.887763 | − | 0.339415i | ||||
\(142\) | 1994.00 | − | 3453.71i | 1.17840 | − | 2.04105i | ||||
\(143\) | −2515.07 | −1.47077 | ||||||||
\(144\) | 579.385 | + | 189.974i | 0.335292 | + | 0.109939i | ||||
\(145\) | −324.279 | −0.185724 | ||||||||
\(146\) | −2519.94 | + | 4364.66i | −1.42844 | + | 2.47412i | ||||
\(147\) | −40.1674 | + | 251.423i | −0.0225371 | + | 0.141068i | ||||
\(148\) | −1749.46 | − | 3030.15i | −0.971652 | − | 1.68295i | ||||
\(149\) | 1493.35 | + | 2586.56i | 0.821075 | + | 1.42214i | 0.904882 | + | 0.425662i | \(0.139959\pi\) |
−0.0838066 | + | 0.996482i | \(0.526708\pi\) | |||||||
\(150\) | −399.504 | + | 2500.65i | −0.217463 | + | 1.36118i | ||||
\(151\) | −698.478 | + | 1209.80i | −0.376432 | + | 0.652000i | −0.990540 | − | 0.137222i | \(-0.956183\pi\) |
0.614108 | + | 0.789222i | \(0.289516\pi\) | |||||||
\(152\) | 133.011 | 0.0709777 | ||||||||
\(153\) | 58.2261 | + | 277.593i | 0.0307667 | + | 0.146680i | ||||
\(154\) | 1227.52 | 0.642315 | ||||||||
\(155\) | 44.2800 | − | 76.6952i | 0.0229462 | − | 0.0397439i | ||||
\(156\) | 3565.86 | − | 1363.32i | 1.83011 | − | 0.699698i | ||||
\(157\) | 1732.01 | + | 2999.93i | 0.880443 | + | 1.52497i | 0.850849 | + | 0.525410i | \(0.176088\pi\) |
0.0295941 | + | 0.999562i | \(0.490579\pi\) | |||||||
\(158\) | 1071.15 | + | 1855.28i | 0.539341 | + | 0.934165i | ||||
\(159\) | 778.322 | + | 632.003i | 0.388207 | + | 0.315227i | ||||
\(160\) | −436.580 | + | 756.179i | −0.215717 | + | 0.373633i | ||||
\(161\) | −1220.98 | −0.597680 | ||||||||
\(162\) | −354.373 | + | 3206.03i | −0.171865 | + | 1.55488i | ||||
\(163\) | −2922.25 | −1.40422 | −0.702111 | − | 0.712067i | \(-0.747759\pi\) | ||||
−0.702111 | + | 0.712067i | \(0.747759\pi\) | |||||||
\(164\) | 2073.31 | − | 3591.08i | 0.987186 | − | 1.70986i | ||||
\(165\) | 616.161 | + | 500.328i | 0.290716 | + | 0.236063i | ||||
\(166\) | 229.758 | + | 397.952i | 0.107426 | + | 0.186067i | ||||
\(167\) | −1315.23 | − | 2278.04i | −0.609433 | − | 1.05557i | −0.991334 | − | 0.131366i | \(-0.958064\pi\) |
0.381901 | − | 0.924203i | \(-0.375270\pi\) | |||||||
\(168\) | −537.776 | + | 205.606i | −0.246966 | + | 0.0944215i | ||||
\(169\) | −915.049 | + | 1584.91i | −0.416499 | + | 0.721398i | ||||
\(170\) | −179.143 | −0.0808215 | ||||||||
\(171\) | −46.5762 | − | 222.052i | −0.0208291 | − | 0.0993025i | ||||
\(172\) | 3958.68 | 1.75492 | ||||||||
\(173\) | −568.028 | + | 983.853i | −0.249632 | + | 0.432376i | −0.963424 | − | 0.267983i | \(-0.913643\pi\) |
0.713792 | + | 0.700358i | \(0.246976\pi\) | |||||||
\(174\) | −305.173 | + | 1910.19i | −0.132960 | + | 0.832250i | ||||
\(175\) | 385.509 | + | 667.722i | 0.166524 | + | 0.288429i | ||||
\(176\) | −447.509 | − | 775.108i | −0.191660 | − | 0.331966i | ||||
\(177\) | 248.432 | − | 1555.03i | 0.105499 | − | 0.660359i | ||||
\(178\) | 3151.91 | − | 5459.28i | 1.32722 | − | 2.29882i | ||||
\(179\) | 2482.26 | 1.03650 | 0.518248 | − | 0.855230i | \(-0.326584\pi\) | ||||
0.518248 | + | 0.855230i | \(0.326584\pi\) | |||||||
\(180\) | −1144.80 | − | 375.367i | −0.474047 | − | 0.155435i | ||||
\(181\) | 147.725 | 0.0606648 | 0.0303324 | − | 0.999540i | \(-0.490343\pi\) | ||||
0.0303324 | + | 0.999540i | \(0.490343\pi\) | |||||||
\(182\) | 982.747 | − | 1702.17i | 0.400253 | − | 0.693259i | ||||
\(183\) | −1987.30 | + | 759.795i | −0.802761 | + | 0.306916i | ||||
\(184\) | −1380.47 | − | 2391.04i | −0.553095 | − | 0.957988i | ||||
\(185\) | −582.399 | − | 1008.74i | −0.231453 | − | 0.400888i | ||||
\(186\) | −410.108 | − | 333.011i | −0.161670 | − | 0.131277i | ||||
\(187\) | 208.170 | − | 360.561i | 0.0814058 | − | 0.140999i | ||||
\(188\) | 3545.52 | 1.37545 | ||||||||
\(189\) | 531.556 | + | 825.782i | 0.204577 | + | 0.317814i | ||||
\(190\) | 143.300 | 0.0547162 | ||||||||
\(191\) | 149.334 | − | 258.654i | 0.0565730 | − | 0.0979873i | −0.836352 | − | 0.548193i | \(-0.815316\pi\) |
0.892925 | + | 0.450206i | \(0.148649\pi\) | |||||||
\(192\) | 3314.73 | + | 2691.58i | 1.24594 | + | 1.01171i | ||||
\(193\) | −1189.32 | − | 2059.97i | −0.443572 | − | 0.768289i | 0.554379 | − | 0.832264i | \(-0.312956\pi\) |
−0.997952 | + | 0.0639746i | \(0.979622\pi\) | |||||||
\(194\) | −3329.60 | − | 5767.04i | −1.23222 | − | 2.13427i | ||||
\(195\) | 1187.08 | − | 453.853i | 0.435943 | − | 0.166672i | ||||
\(196\) | −283.647 | + | 491.290i | −0.103370 | + | 0.179042i | ||||
\(197\) | −281.450 | −0.101789 | −0.0508945 | − | 0.998704i | \(-0.516207\pi\) | ||||
−0.0508945 | + | 0.998704i | \(0.516207\pi\) | |||||||
\(198\) | 3527.08 | − | 3158.70i | 1.26595 | − | 1.13373i | ||||
\(199\) | 77.5836 | 0.0276370 | 0.0138185 | − | 0.999905i | \(-0.495601\pi\) | ||||
0.0138185 | + | 0.999905i | \(0.495601\pi\) | |||||||
\(200\) | −871.733 | + | 1509.89i | −0.308204 | + | 0.533826i | ||||
\(201\) | −321.639 | + | 2013.26i | −0.112869 | + | 0.706491i | ||||
\(202\) | −3402.64 | − | 5893.54i | −1.18519 | − | 2.05281i | ||||
\(203\) | 294.482 | + | 510.058i | 0.101816 | + | 0.176350i | ||||
\(204\) | −99.6971 | + | 624.043i | −0.0342166 | + | 0.214175i | ||||
\(205\) | 690.211 | − | 1195.48i | 0.235153 | − | 0.407297i | ||||
\(206\) | 6284.09 | 2.12540 | ||||||||
\(207\) | −3508.27 | + | 3141.86i | −1.17798 | + | 1.05495i | ||||
\(208\) | −1433.09 | −0.477726 | ||||||||
\(209\) | −166.519 | + | 288.419i | −0.0551118 | + | 0.0954564i | ||||
\(210\) | −579.377 | + | 221.511i | −0.190385 | + | 0.0727889i | ||||
\(211\) | 1168.35 | + | 2023.65i | 0.381198 | + | 0.660253i | 0.991234 | − | 0.132120i | \(-0.0421784\pi\) |
−0.610036 | + | 0.792374i | \(0.708845\pi\) | |||||||
\(212\) | 1116.94 | + | 1934.59i | 0.361847 | + | 0.626737i | ||||
\(213\) | −3635.71 | − | 2952.23i | −1.16955 | − | 0.949687i | ||||
\(214\) | −2446.46 | + | 4237.39i | −0.781478 | + | 1.35356i | ||||
\(215\) | 1317.86 | 0.418033 | ||||||||
\(216\) | −1016.14 | + | 1974.60i | −0.320090 | + | 0.622010i | ||||
\(217\) | −160.845 | −0.0503173 | ||||||||
\(218\) | −4730.52 | + | 8193.49i | −1.46968 | + | 2.54557i | ||||
\(219\) | 4594.67 | + | 3730.91i | 1.41771 | + | 1.15119i | ||||
\(220\) | 884.227 | + | 1531.53i | 0.270975 | + | 0.469343i | ||||
\(221\) | −333.319 | − | 577.325i | −0.101455 | − | 0.175724i | ||||
\(222\) | −6490.17 | + | 2481.36i | −1.96213 | + | 0.750171i | ||||
\(223\) | −1157.33 | + | 2004.55i | −0.347535 | + | 0.601948i | −0.985811 | − | 0.167860i | \(-0.946314\pi\) |
0.638276 | + | 0.769807i | \(0.279648\pi\) | |||||||
\(224\) | 1585.86 | 0.473033 | ||||||||
\(225\) | 2825.90 | + | 926.580i | 0.837303 | + | 0.274542i | ||||
\(226\) | −1913.64 | −0.563245 | ||||||||
\(227\) | −529.952 | + | 917.904i | −0.154952 | + | 0.268385i | −0.933042 | − | 0.359768i | \(-0.882856\pi\) |
0.778089 | + | 0.628154i | \(0.216189\pi\) | |||||||
\(228\) | 79.7497 | − | 499.184i | 0.0231647 | − | 0.144997i | ||||
\(229\) | −1171.23 | − | 2028.63i | −0.337978 | − | 0.585395i | 0.646074 | − | 0.763275i | \(-0.276410\pi\) |
−0.984052 | + | 0.177880i | \(0.943076\pi\) | |||||||
\(230\) | −1487.26 | − | 2576.00i | −0.426377 | − | 0.738506i | ||||
\(231\) | 227.420 | − | 1423.51i | 0.0647755 | − | 0.405455i | ||||
\(232\) | −665.898 | + | 1153.37i | −0.188441 | + | 0.326389i | ||||
\(233\) | 502.705 | 0.141345 | 0.0706723 | − | 0.997500i | \(-0.477486\pi\) | ||||
0.0706723 | + | 0.997500i | \(0.477486\pi\) | |||||||
\(234\) | −1556.32 | − | 7419.73i | −0.434784 | − | 2.07283i | ||||
\(235\) | 1180.31 | 0.327639 | ||||||||
\(236\) | 1754.33 | − | 3038.60i | 0.483887 | − | 0.838117i | ||||
\(237\) | 2349.95 | − | 898.445i | 0.644074 | − | 0.246246i | ||||
\(238\) | 162.682 | + | 281.774i | 0.0443072 | + | 0.0767423i | ||||
\(239\) | 2022.28 | + | 3502.69i | 0.547323 | + | 0.947992i | 0.998457 | + | 0.0555351i | \(0.0176865\pi\) |
−0.451134 | + | 0.892456i | \(0.648980\pi\) | |||||||
\(240\) | 351.090 | + | 285.088i | 0.0944282 | + | 0.0766764i | ||||
\(241\) | 296.441 | − | 513.451i | 0.0792342 | − | 0.137238i | −0.823686 | − | 0.567047i | \(-0.808086\pi\) |
0.902920 | + | 0.429809i | \(0.141419\pi\) | |||||||
\(242\) | −1060.81 | −0.281784 | ||||||||
\(243\) | 3652.26 | + | 1004.93i | 0.964168 | + | 0.265293i | ||||
\(244\) | −4740.43 | −1.24375 | ||||||||
\(245\) | −94.4267 | + | 163.552i | −0.0246233 | + | 0.0426487i | ||||
\(246\) | −6392.53 | − | 5190.78i | −1.65680 | − | 1.34533i | ||||
\(247\) | 266.628 | + | 461.814i | 0.0686848 | + | 0.118966i | ||||
\(248\) | −181.855 | − | 314.982i | −0.0465638 | − | 0.0806508i | ||||
\(249\) | 504.057 | − | 192.714i | 0.128286 | − | 0.0490472i | ||||
\(250\) | −2004.99 | + | 3472.75i | −0.507228 | + | 0.878544i | ||||
\(251\) | −2663.71 | −0.669848 | −0.334924 | − | 0.942245i | \(-0.608711\pi\) | ||||
−0.334924 | + | 0.942245i | \(0.608711\pi\) | |||||||
\(252\) | 449.194 | + | 2141.53i | 0.112288 | + | 0.535332i | ||||
\(253\) | 6912.94 | 1.71784 | ||||||||
\(254\) | −1082.37 | + | 1874.71i | −0.267377 | + | 0.463110i | ||||
\(255\) | −33.1894 | + | 207.745i | −0.00815059 | + | 0.0510178i | ||||
\(256\) | 747.207 | + | 1294.20i | 0.182424 | + | 0.315967i | ||||
\(257\) | −819.857 | − | 1420.03i | −0.198993 | − | 0.344667i | 0.749209 | − | 0.662334i | \(-0.230434\pi\) |
−0.948202 | + | 0.317667i | \(0.897101\pi\) | |||||||
\(258\) | 1240.21 | − | 7762.94i | 0.299271 | − | 1.87325i | ||||
\(259\) | −1057.77 | + | 1832.11i | −0.253770 | + | 0.439543i | ||||
\(260\) | 2831.63 | 0.675424 | ||||||||
\(261\) | 2158.64 | + | 707.794i | 0.511941 | + | 0.167860i | ||||
\(262\) | 3005.12 | 0.708614 | ||||||||
\(263\) | 1966.25 | − | 3405.64i | 0.461004 | − | 0.798482i | −0.538007 | − | 0.842940i | \(-0.680823\pi\) |
0.999011 | + | 0.0444579i | \(0.0141561\pi\) | |||||||
\(264\) | 3044.79 | − | 1164.10i | 0.709825 | − | 0.271384i | ||||
\(265\) | 371.831 | + | 644.030i | 0.0861940 | + | 0.149292i | ||||
\(266\) | −130.133 | − | 225.396i | −0.0299960 | − | 0.0519546i | ||||
\(267\) | −5746.97 | − | 4666.58i | −1.31726 | − | 1.06963i | ||||
\(268\) | −2271.29 | + | 3934.00i | −0.517691 | + | 0.896668i | ||||
\(269\) | −859.514 | −0.194816 | −0.0974080 | − | 0.995245i | \(-0.531055\pi\) | ||||
−0.0974080 | + | 0.995245i | \(0.531055\pi\) | |||||||
\(270\) | −1094.74 | + | 2127.34i | −0.246755 | + | 0.479504i | ||||
\(271\) | 4260.30 | 0.954963 | 0.477482 | − | 0.878642i | \(-0.341550\pi\) | ||||
0.477482 | + | 0.878642i | \(0.341550\pi\) | |||||||
\(272\) | 118.616 | − | 205.448i | 0.0264416 | − | 0.0457983i | ||||
\(273\) | −1791.87 | − | 1455.01i | −0.397248 | − | 0.322569i | ||||
\(274\) | −1795.71 | − | 3110.25i | −0.395922 | − | 0.685756i | ||||
\(275\) | −2182.68 | − | 3780.52i | −0.478621 | − | 0.828996i | ||||
\(276\) | −9801.16 | + | 3747.24i | −2.13754 | + | 0.817236i | ||||
\(277\) | 2031.16 | − | 3518.07i | 0.440579 | − | 0.763106i | −0.557153 | − | 0.830410i | \(-0.688106\pi\) |
0.997733 | + | 0.0673041i | \(0.0214398\pi\) | |||||||
\(278\) | 783.461 | 0.169025 | ||||||||
\(279\) | −462.160 | + | 413.891i | −0.0991714 | + | 0.0888136i | ||||
\(280\) | −427.045 | −0.0911457 | ||||||||
\(281\) | −1535.16 | + | 2658.98i | −0.325908 | + | 0.564490i | −0.981696 | − | 0.190456i | \(-0.939003\pi\) |
0.655787 | + | 0.754946i | \(0.272337\pi\) | |||||||
\(282\) | 1110.77 | − | 6952.74i | 0.234558 | − | 1.46819i | ||||
\(283\) | 2717.14 | + | 4706.23i | 0.570733 | + | 0.988539i | 0.996491 | + | 0.0837015i | \(0.0266742\pi\) |
−0.425758 | + | 0.904837i | \(0.639992\pi\) | |||||||
\(284\) | −5217.46 | − | 9036.91i | −1.09014 | − | 1.88818i | ||||
\(285\) | 26.5489 | − | 166.180i | 0.00551796 | − | 0.0345391i | ||||
\(286\) | −5564.13 | + | 9637.36i | −1.15040 | + | 1.99255i | ||||
\(287\) | −2507.15 | −0.515654 | ||||||||
\(288\) | 4556.69 | − | 4080.77i | 0.932310 | − | 0.834937i | ||||
\(289\) | −4802.65 | −0.977538 | ||||||||
\(290\) | −717.409 | + | 1242.59i | −0.145268 | + | 0.251611i | ||||
\(291\) | −7304.68 | + | 2792.77i | −1.47151 | + | 0.562594i | ||||
\(292\) | 6593.62 | + | 11420.5i | 1.32145 | + | 2.28881i | ||||
\(293\) | 4472.88 | + | 7747.25i | 0.891837 | + | 1.54471i | 0.837670 | + | 0.546176i | \(0.183917\pi\) |
0.0541670 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(294\) | 874.552 | + | 710.143i | 0.173486 | + | 0.140872i | ||||
\(295\) | 584.022 | − | 1011.56i | 0.115265 | − | 0.199644i | ||||
\(296\) | −4783.75 | −0.939358 | ||||||||
\(297\) | −3009.57 | − | 4675.42i | −0.587990 | − | 0.913453i | ||||
\(298\) | 13215.1 | 2.56889 | ||||||||
\(299\) | 5534.46 | − | 9585.97i | 1.07046 | − | 1.85408i | ||||
\(300\) | 5143.88 | + | 4176.87i | 0.989939 | + | 0.803838i | ||||
\(301\) | −1196.76 | − | 2072.85i | −0.229170 | − | 0.396934i | ||||
\(302\) | 3090.51 | + | 5352.92i | 0.588870 | + | 1.01995i | ||||
\(303\) | −7464.92 | + | 2854.03i | −1.41534 | + | 0.541121i | ||||
\(304\) | −94.8829 | + | 164.342i | −0.0179010 | + | 0.0310055i | ||||
\(305\) | −1578.10 | −0.296268 | ||||||||
\(306\) | 1192.51 | + | 391.010i | 0.222782 | + | 0.0730476i | ||||
\(307\) | 3114.75 | 0.579050 | 0.289525 | − | 0.957170i | \(-0.406503\pi\) | ||||
0.289525 | + | 0.957170i | \(0.406503\pi\) | |||||||
\(308\) | 1605.95 | − | 2781.60i | 0.297103 | − | 0.514598i | ||||
\(309\) | 1164.24 | − | 7287.42i | 0.214340 | − | 1.34164i | ||||
\(310\) | −195.923 | − | 339.348i | −0.0358957 | − | 0.0621732i | ||||
\(311\) | 392.347 | + | 679.564i | 0.0715368 | + | 0.123905i | 0.899575 | − | 0.436766i | \(-0.143876\pi\) |
−0.828038 | + | 0.560672i | \(0.810543\pi\) | |||||||
\(312\) | 823.417 | − | 5154.09i | 0.149413 | − | 0.935234i | ||||
\(313\) | 2295.78 | − | 3976.40i | 0.414584 | − | 0.718081i | −0.580800 | − | 0.814046i | \(-0.697260\pi\) |
0.995385 | + | 0.0959649i | \(0.0305936\pi\) | |||||||
\(314\) | 15327.0 | 2.75463 | ||||||||
\(315\) | 149.538 | + | 712.920i | 0.0267476 | + | 0.127519i | ||||
\(316\) | 5605.48 | 0.997889 | ||||||||
\(317\) | 2097.90 | − | 3633.66i | 0.371702 | − | 0.643807i | −0.618125 | − | 0.786080i | \(-0.712108\pi\) |
0.989828 | + | 0.142272i | \(0.0454409\pi\) | |||||||
\(318\) | 4143.64 | − | 1584.22i | 0.730703 | − | 0.279366i | ||||
\(319\) | −1667.30 | − | 2887.85i | −0.292636 | − | 0.506861i | ||||
\(320\) | 1583.56 | + | 2742.80i | 0.276636 | + | 0.479148i | ||||
\(321\) | 4460.69 | + | 3622.11i | 0.775612 | + | 0.629803i | ||||
\(322\) | −2701.19 | + | 4678.60i | −0.467489 | + | 0.809714i | ||||
\(323\) | −88.2743 | −0.0152065 | ||||||||
\(324\) | 6801.33 | + | 4997.44i | 1.16621 | + | 0.856900i | ||||
\(325\) | −6989.77 | −1.19299 | ||||||||
\(326\) | −6464.95 | + | 11197.6i | −1.09834 | + | 1.90239i | ||||
\(327\) | 8625.27 | + | 7003.79i | 1.45865 | + | 1.18444i | ||||
\(328\) | −2834.65 | − | 4909.76i | −0.477188 | − | 0.826513i | ||||
\(329\) | −1071.86 | − | 1856.51i | −0.179615 | − | 0.311103i | ||||
\(330\) | 3280.32 | − | 1254.15i | 0.547200 | − | 0.209208i | ||||
\(331\) | 3416.58 | − | 5917.69i | 0.567348 | − | 0.982676i | −0.429479 | − | 0.903077i | \(-0.641303\pi\) |
0.996827 | − | 0.0795989i | \(-0.0253639\pi\) | |||||||
\(332\) | 1202.36 | 0.198759 | ||||||||
\(333\) | 1675.12 | + | 7986.12i | 0.275664 | + | 1.31422i | ||||
\(334\) | −11638.8 | −1.90673 | ||||||||
\(335\) | −756.119 | + | 1309.64i | −0.123317 | + | 0.213591i | ||||
\(336\) | 129.584 | − | 811.120i | 0.0210399 | − | 0.131697i | ||||
\(337\) | −2594.16 | − | 4493.21i | −0.419325 | − | 0.726293i | 0.576546 | − | 0.817064i | \(-0.304400\pi\) |
−0.995872 | + | 0.0907716i | \(0.971067\pi\) | |||||||
\(338\) | 4048.76 | + | 7012.66i | 0.651549 | + | 1.12852i | ||||
\(339\) | −354.535 | + | 2219.18i | −0.0568015 | + | 0.355543i | ||||
\(340\) | −234.371 | + | 405.943i | −0.0373840 | + | 0.0647510i | ||||
\(341\) | 910.674 | 0.144621 | ||||||||
\(342\) | −953.910 | − | 312.776i | −0.150823 | − | 0.0494533i | ||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 2706.18 | − | 4687.23i | 0.424149 | − | 0.734648i | ||||
\(345\) | −3262.83 | + | 1247.46i | −0.509174 | + | 0.194670i | ||||
\(346\) | 2513.32 | + | 4353.19i | 0.390511 | + | 0.676385i | ||||
\(347\) | 2.25987 | + | 3.91421i | 0.000349614 | + | 0.000605549i | 0.866200 | − | 0.499697i | \(-0.166555\pi\) |
−0.865851 | + | 0.500303i | \(0.833222\pi\) | |||||||
\(348\) | 3929.29 | + | 3190.61i | 0.605265 | + | 0.491480i | ||||
\(349\) | 276.840 | − | 479.501i | 0.0424610 | − | 0.0735447i | −0.844014 | − | 0.536321i | \(-0.819814\pi\) |
0.886475 | + | 0.462777i | \(0.153147\pi\) | |||||||
\(350\) | 3411.48 | 0.521003 | ||||||||
\(351\) | −8892.71 | + | 430.165i | −1.35230 | + | 0.0654146i | ||||
\(352\) | −8978.82 | −1.35958 | ||||||||
\(353\) | −5834.63 | + | 10105.9i | −0.879734 | + | 1.52374i | −0.0281006 | + | 0.999605i | \(0.508946\pi\) |
−0.851633 | + | 0.524138i | \(0.824387\pi\) | |||||||
\(354\) | −5409.04 | − | 4392.18i | −0.812111 | − | 0.659441i | ||||
\(355\) | −1736.91 | − | 3008.41i | −0.259677 | − | 0.449774i | ||||
\(356\) | −8247.23 | − | 14284.6i | −1.22782 | − | 2.12664i | ||||
\(357\) | 356.902 | − | 136.453i | 0.0529111 | − | 0.0202293i | ||||
\(358\) | 5491.55 | − | 9511.64i | 0.810719 | − | 1.40421i | ||||
\(359\) | −4813.47 | −0.707646 | −0.353823 | − | 0.935312i | \(-0.615119\pi\) | ||||
−0.353823 | + | 0.935312i | \(0.615119\pi\) | |||||||
\(360\) | −1227.04 | + | 1098.89i | −0.179641 | + | 0.160879i | ||||
\(361\) | −6788.39 | −0.989705 | ||||||||
\(362\) | 326.815 | − | 566.061i | 0.0474504 | − | 0.0821864i | ||||
\(363\) | −196.534 | + | 1230.19i | −0.0284170 | + | 0.177873i | ||||
\(364\) | −2571.44 | − | 4453.86i | −0.370274 | − | 0.641334i | ||||
\(365\) | 2195.03 | + | 3801.91i | 0.314776 | + | 0.545208i | ||||
\(366\) | −1485.12 | + | 9295.93i | −0.212099 | + | 1.32761i | ||||
\(367\) | 3263.41 | − | 5652.40i | 0.464166 | − | 0.803959i | −0.534998 | − | 0.844854i | \(-0.679688\pi\) |
0.999163 | + | 0.0408948i | \(0.0130208\pi\) | |||||||
\(368\) | 3939.01 | 0.557976 | ||||||||
\(369\) | −7203.88 | + | 6451.49i | −1.01631 | + | 0.910166i | ||||
\(370\) | −5153.81 | −0.724145 | ||||||||
\(371\) | 675.329 | − | 1169.70i | 0.0945049 | − | 0.163687i | ||||
\(372\) | −1291.15 | + | 493.640i | −0.179955 | + | 0.0688012i | ||||
\(373\) | −2602.17 | − | 4507.09i | −0.361221 | − | 0.625652i | 0.626941 | − | 0.779066i | \(-0.284307\pi\) |
−0.988162 | + | 0.153414i | \(0.950973\pi\) | |||||||
\(374\) | −921.076 | − | 1595.35i | −0.127347 | − | 0.220571i | ||||
\(375\) | 3655.76 | + | 2968.50i | 0.503420 | + | 0.408781i | ||||
\(376\) | 2423.74 | − | 4198.04i | 0.332433 | − | 0.575791i | ||||
\(377\) | −5339.33 | −0.729415 | ||||||||
\(378\) | 4340.24 | − | 209.950i | 0.590576 | − | 0.0285678i | ||||
\(379\) | 9918.32 | 1.34425 | 0.672124 | − | 0.740439i | \(-0.265382\pi\) | ||||
0.672124 | + | 0.740439i | \(0.265382\pi\) | |||||||
\(380\) | 187.478 | − | 324.721i | 0.0253090 | − | 0.0438365i | ||||
\(381\) | 1973.51 | + | 1602.50i | 0.265370 | + | 0.215482i | ||||
\(382\) | −660.750 | − | 1144.45i | −0.0884997 | − | 0.153286i | ||||
\(383\) | 964.048 | + | 1669.78i | 0.128618 | + | 0.222772i | 0.923141 | − | 0.384461i | \(-0.125613\pi\) |
−0.794524 | + | 0.607233i | \(0.792279\pi\) | |||||||
\(384\) | 8850.42 | − | 3383.74i | 1.17616 | − | 0.449677i | ||||
\(385\) | 534.626 | − | 926.000i | 0.0707716 | − | 0.122580i | ||||
\(386\) | −10524.7 | −1.38780 | ||||||||
\(387\) | −8772.61 | − | 2876.44i | −1.15229 | − | 0.377824i | ||||
\(388\) | −17424.3 | −2.27986 | ||||||||
\(389\) | 1241.45 | − | 2150.25i | 0.161810 | − | 0.280263i | −0.773708 | − | 0.633542i | \(-0.781600\pi\) |
0.935518 | + | 0.353280i | \(0.114934\pi\) | |||||||
\(390\) | 887.114 | − | 5552.79i | 0.115181 | − | 0.720966i | ||||
\(391\) | 916.164 | + | 1586.84i | 0.118497 | + | 0.205243i | ||||
\(392\) | 387.805 | + | 671.697i | 0.0499671 | + | 0.0865455i | ||||
\(393\) | 556.751 | − | 3484.92i | 0.0714616 | − | 0.447306i | ||||
\(394\) | −622.656 | + | 1078.47i | −0.0796166 | + | 0.137900i | ||||
\(395\) | 1866.08 | 0.237703 | ||||||||
\(396\) | −2543.25 | − | 12124.9i | −0.322735 | − | 1.53864i | ||||
\(397\) | −603.393 | −0.0762806 | −0.0381403 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381403 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(398\) | 171.640 | − | 297.289i | 0.0216169 | − | 0.0374415i | ||||
\(399\) | −285.493 | + | 109.151i | −0.0358208 | + | 0.0136952i | ||||
\(400\) | −1243.70 | − | 2154.15i | −0.155462 | − | 0.269268i | ||||
\(401\) | −1325.70 | − | 2296.18i | −0.165093 | − | 0.285949i | 0.771595 | − | 0.636114i | \(-0.219459\pi\) |
−0.936688 | + | 0.350164i | \(0.886126\pi\) | |||||||
\(402\) | 7002.95 | + | 5686.45i | 0.868845 | + | 0.705509i | ||||
\(403\) | 729.080 | − | 1262.80i | 0.0901192 | − | 0.156091i | ||||
\(404\) | −17806.5 | −2.19284 | ||||||||
\(405\) | 2264.18 | + | 1663.66i | 0.277797 | + | 0.204118i | ||||
\(406\) | 2605.95 | 0.318550 | ||||||||
\(407\) | 5988.88 | − | 10373.0i | 0.729380 | − | 1.26332i | ||||
\(408\) | 670.738 | + | 544.644i | 0.0813884 | + | 0.0660880i | ||||
\(409\) | 4376.21 | + | 7579.82i | 0.529070 | + | 0.916376i | 0.999425 | + | 0.0338991i | \(0.0107925\pi\) |
−0.470355 | + | 0.882477i | \(0.655874\pi\) | |||||||
\(410\) | −3053.93 | − | 5289.56i | −0.367861 | − | 0.637154i | ||||
\(411\) | −3939.53 | + | 1506.18i | −0.472804 | + | 0.180765i | ||||
\(412\) | 8221.41 | − | 14239.9i | 0.983106 | − | 1.70279i | ||||
\(413\) | −2121.43 | −0.252757 | ||||||||
\(414\) | 4277.71 | + | 20393.9i | 0.507821 | + | 2.42103i | ||||
\(415\) | 400.269 | 0.0473456 | ||||||||
\(416\) | −7188.39 | + | 12450.7i | −0.847211 | + | 1.46741i | ||||
\(417\) | 145.150 | − | 908.550i | 0.0170456 | − | 0.106695i | ||||
\(418\) | 736.786 | + | 1276.15i | 0.0862139 | + | 0.149327i | ||||
\(419\) | −5712.54 | − | 9894.41i | −0.666052 | − | 1.15364i | −0.978999 | − | 0.203866i | \(-0.934649\pi\) |
0.312946 | − | 0.949771i | \(-0.398684\pi\) | |||||||
\(420\) | −256.044 | + | 1602.68i | −0.0297469 | + | 0.186197i | ||||
\(421\) | −5436.83 | + | 9416.87i | −0.629394 | + | 1.09014i | 0.358279 | + | 0.933615i | \(0.383364\pi\) |
−0.987673 | + | 0.156528i | \(0.949970\pi\) | |||||||
\(422\) | 10339.1 | 1.19265 | ||||||||
\(423\) | −7857.04 | − | 2576.23i | −0.903126 | − | 0.296125i | ||||
\(424\) | 3054.18 | 0.349820 | ||||||||
\(425\) | 578.537 | − | 1002.05i | 0.0660309 | − | 0.114369i | ||||
\(426\) | −19355.8 | + | 7400.23i | −2.20139 | + | 0.841649i | ||||
\(427\) | 1433.09 | + | 2482.19i | 0.162417 | + | 0.281315i | ||||
\(428\) | 6401.35 | + | 11087.5i | 0.722946 | + | 1.25218i | ||||
\(429\) | 10145.2 | + | 8238.01i | 1.14176 | + | 0.927120i | ||||
\(430\) | 2915.52 | − | 5049.82i | 0.326974 | − | 0.566335i | ||||
\(431\) | 15702.7 | 1.75493 | 0.877465 | − | 0.479641i | \(-0.159233\pi\) | ||||
0.877465 | + | 0.479641i | \(0.159233\pi\) | |||||||
\(432\) | −1714.86 | − | 2664.07i | −0.190987 | − | 0.296701i | ||||
\(433\) | 9870.43 | 1.09548 | 0.547739 | − | 0.836649i | \(-0.315489\pi\) | ||||
0.547739 | + | 0.836649i | \(0.315489\pi\) | |||||||
\(434\) | −355.840 | + | 616.333i | −0.0393568 | + | 0.0681680i | ||||
\(435\) | 1308.07 | + | 1062.16i | 0.144177 | + | 0.117073i | ||||
\(436\) | 12377.8 | + | 21438.9i | 1.35960 | + | 2.35490i | ||||
\(437\) | −732.857 | − | 1269.35i | −0.0802227 | − | 0.138950i | ||||
\(438\) | 24461.1 | − | 9352.12i | 2.66849 | − | 1.02023i | ||||
\(439\) | −1675.28 | + | 2901.67i | −0.182134 | + | 0.315465i | −0.942607 | − | 0.333904i | \(-0.891634\pi\) |
0.760473 | + | 0.649369i | \(0.224967\pi\) | |||||||
\(440\) | 2417.85 | 0.261969 | ||||||||
\(441\) | 985.552 | − | 882.619i | 0.106420 | − | 0.0953049i | ||||
\(442\) | −2949.63 | −0.317420 | ||||||||
\(443\) | −2841.43 | + | 4921.49i | −0.304741 | + | 0.527827i | −0.977204 | − | 0.212304i | \(-0.931903\pi\) |
0.672463 | + | 0.740131i | \(0.265237\pi\) | |||||||
\(444\) | −2868.21 | + | 17953.2i | −0.306575 | + | 1.91897i | ||||
\(445\) | −2745.52 | − | 4755.39i | −0.292473 | − | 0.506577i | ||||
\(446\) | 5120.74 | + | 8869.39i | 0.543664 | + | 0.941654i | ||||
\(447\) | 2448.33 | − | 15325.0i | 0.259065 | − | 1.62159i | ||||
\(448\) | 2876.10 | − | 4981.55i | 0.303310 | − | 0.525348i | ||||
\(449\) | −12959.0 | −1.36208 | −0.681041 | − | 0.732245i | \(-0.738473\pi\) | ||||
−0.681041 | + | 0.732245i | \(0.738473\pi\) | |||||||
\(450\) | 9802.30 | − | 8778.52i | 1.02686 | − | 0.919608i | ||||
\(451\) | 14195.0 | 1.48208 | ||||||||
\(452\) | −2503.60 | + | 4336.35i | −0.260529 | + | 0.451250i | ||||
\(453\) | 6780.15 | − | 2592.22i | 0.703221 | − | 0.268859i | ||||
\(454\) | 2344.85 | + | 4061.39i | 0.242399 | + | 0.419847i | ||||
\(455\) | −856.037 | − | 1482.70i | −0.0882014 | − | 0.152769i | ||||
\(456\) | −536.536 | − | 435.672i | −0.0551000 | − | 0.0447416i | ||||
\(457\) | −1120.67 | + | 1941.07i | −0.114711 | + | 0.198685i | −0.917664 | − | 0.397357i | \(-0.869928\pi\) |
0.802953 | + | 0.596042i | \(0.203261\pi\) | |||||||
\(458\) | −10364.5 | −1.05743 | ||||||||
\(459\) | 674.373 | − | 1310.46i | 0.0685774 | − | 0.133262i | ||||
\(460\) | −7783.04 | −0.788883 | ||||||||
\(461\) | −6238.22 | + | 10804.9i | −0.630244 | + | 1.09162i | 0.357257 | + | 0.934006i | \(0.383712\pi\) |
−0.987502 | + | 0.157609i | \(0.949621\pi\) | |||||||
\(462\) | −4951.55 | − | 4020.70i | −0.498630 | − | 0.404892i | ||||
\(463\) | 4874.71 | + | 8443.24i | 0.489302 | + | 0.847496i | 0.999924 | − | 0.0123094i | \(-0.00391830\pi\) |
−0.510622 | + | 0.859805i | \(0.670585\pi\) | |||||||
\(464\) | −950.032 | − | 1645.50i | −0.0950520 | − | 0.164635i | ||||
\(465\) | −429.828 | + | 164.334i | −0.0428662 | + | 0.0163888i | ||||
\(466\) | 1112.14 | − | 1926.29i | 0.110556 | − | 0.191488i | ||||
\(467\) | −5947.85 | −0.589365 | −0.294683 | − | 0.955595i | \(-0.595214\pi\) | ||||
−0.294683 | + | 0.955595i | \(0.595214\pi\) | |||||||
\(468\) | −18849.4 | − | 6180.50i | −1.86178 | − | 0.610457i | ||||
\(469\) | 2746.56 | 0.270415 | ||||||||
\(470\) | 2611.23 | − | 4522.78i | 0.256270 | − | 0.443873i | ||||
\(471\) | 2839.60 | − | 17774.2i | 0.277796 | − | 1.73884i | ||||
\(472\) | −2398.54 | − | 4154.40i | −0.233902 | − | 0.405131i | ||||
\(473\) | 6775.84 | + | 11736.1i | 0.658675 | + | 1.14086i | ||||
\(474\) | 1756.13 | − | 10992.3i | 0.170172 | − | 1.06517i | ||||
\(475\) | −462.783 | + | 801.563i | −0.0447030 | + | 0.0774279i | ||||
\(476\) | 851.341 | 0.0819772 | ||||||||
\(477\) | −1069.48 | − | 5098.72i | −0.102658 | − | 0.489422i | ||||
\(478\) | 17895.7 | 1.71240 | ||||||||
\(479\) | 5604.82 | − | 9707.83i | 0.534636 | − | 0.926017i | −0.464545 | − | 0.885550i | \(-0.653782\pi\) |
0.999181 | − | 0.0404673i | \(-0.0128846\pi\) | |||||||
\(480\) | 4237.90 | − | 1620.26i | 0.402985 | − | 0.154072i | ||||
\(481\) | −9589.32 | − | 16609.2i | −0.909014 | − | 1.57446i | ||||
\(482\) | −1311.64 | − | 2271.83i | −0.123950 | − | 0.214687i | ||||
\(483\) | 4925.15 | + | 3999.26i | 0.463979 | + | 0.376755i | ||||
\(484\) | −1387.85 | + | 2403.83i | −0.130339 | + | 0.225754i | ||||
\(485\) | −5800.60 | −0.543076 | ||||||||
\(486\) | 11930.7 | − | 11771.7i | 1.11355 | − | 1.09871i | ||||
\(487\) | −11643.7 | −1.08342 | −0.541709 | − | 0.840566i | \(-0.682223\pi\) | ||||
−0.541709 | + | 0.840566i | \(0.682223\pi\) | |||||||
\(488\) | −3240.58 | + | 5612.85i | −0.300603 | + | 0.520660i | ||||
\(489\) | 11787.7 | + | 9571.71i | 1.09010 | + | 0.885169i | ||||
\(490\) | 417.804 | + | 723.657i | 0.0385193 | + | 0.0667173i | ||||
\(491\) | −6256.33 | − | 10836.3i | −0.575039 | − | 0.995997i | −0.996037 | − | 0.0889358i | \(-0.971653\pi\) |
0.420998 | − | 0.907062i | \(-0.361680\pi\) | |||||||
\(492\) | −20125.7 | + | 7694.58i | −1.84418 | + | 0.705078i | ||||
\(493\) | 441.931 | − | 765.447i | 0.0403724 | − | 0.0699270i | ||||
\(494\) | 2359.47 | 0.214894 | ||||||||
\(495\) | −846.655 | − | 4036.42i | −0.0768774 | − | 0.366512i | ||||
\(496\) | 518.904 | 0.0469747 | ||||||||
\(497\) | −3154.61 | + | 5463.94i | −0.284715 | + | 0.493142i | ||||
\(498\) | 376.684 | − | 2357.81i | 0.0338948 | − | 0.212161i | ||||
\(499\) | −334.598 | − | 579.541i | −0.0300174 | − | 0.0519916i | 0.850626 | − | 0.525771i | \(-0.176223\pi\) |
−0.880644 | + | 0.473779i | \(0.842890\pi\) | |||||||
\(500\) | 5246.22 | + | 9086.73i | 0.469237 | + | 0.812742i | ||||
\(501\) | −2156.29 | + | 13497.1i | −0.192288 | + | 1.20360i | ||||
\(502\) | −5892.97 | + | 10206.9i | −0.523937 | + | 0.907485i | ||||
\(503\) | −7651.80 | −0.678284 | −0.339142 | − | 0.940735i | \(-0.610137\pi\) | ||||
−0.339142 | + | 0.940735i | \(0.610137\pi\) | |||||||
\(504\) | 2842.72 | + | 932.097i | 0.251240 | + | 0.0823788i | ||||
\(505\) | −5927.84 | −0.522348 | ||||||||
\(506\) | 15293.6 | − | 26489.4i | 1.34365 | − | 2.32726i | ||||
\(507\) | 8882.42 | − | 3395.98i | 0.778071 | − | 0.297476i | ||||
\(508\) | 2832.10 | + | 4905.34i | 0.247350 | + | 0.428424i | ||||
\(509\) | 9999.11 | + | 17319.0i | 0.870732 | + | 1.50815i | 0.861240 | + | 0.508198i | \(0.169688\pi\) |
0.00949201 | + | 0.999955i | \(0.496979\pi\) | |||||||
\(510\) | 722.624 | + | 586.776i | 0.0627418 | + | 0.0509468i | ||||
\(511\) | 3986.67 | − | 6905.11i | 0.345127 | − | 0.597777i | ||||
\(512\) | −7975.81 | −0.688446 | ||||||||
\(513\) | −539.444 | + | 1048.27i | −0.0464269 | + | 0.0902185i | ||||
\(514\) | −7255.14 | −0.622589 | ||||||||
\(515\) | 2736.93 | − | 4740.49i | 0.234181 | − | 0.405614i | ||||
\(516\) | −15968.5 | − | 12966.5i | −1.36235 | − | 1.10624i | ||||
\(517\) | 6068.66 | + | 10511.2i | 0.516246 | + | 0.894165i | ||||
\(518\) | 4680.23 | + | 8106.40i | 0.396984 | + | 0.687596i | ||||
\(519\) | 5513.87 | − | 2108.09i | 0.466343 | − | 0.178295i | ||||
\(520\) | 1935.72 | − | 3352.76i | 0.163244 | − | 0.282746i | ||||
\(521\) | 826.109 | 0.0694673 | 0.0347337 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347337 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(522\) | 7487.76 | − | 6705.72i | 0.627836 | − | 0.562263i | ||||
\(523\) | −5294.65 | −0.442675 | −0.221338 | − | 0.975197i | \(-0.571042\pi\) | ||||
−0.221338 | + | 0.975197i | \(0.571042\pi\) | |||||||
\(524\) | 3931.57 | − | 6809.68i | 0.327770 | − | 0.567714i | ||||
\(525\) | 632.036 | − | 3956.16i | 0.0525416 | − | 0.328878i | ||||
\(526\) | −8699.93 | − | 15068.7i | −0.721169 | − | 1.24910i | ||||
\(527\) | 120.690 | + | 209.042i | 0.00997601 | + | 0.0172790i | ||||
\(528\) | −733.683 | + | 4592.41i | −0.0604725 | + | 0.378521i | ||||
\(529\) | −9128.58 | + | 15811.2i | −0.750273 | + | 1.29951i | ||||
\(530\) | 3290.44 | 0.269674 | ||||||||
\(531\) | −6095.57 | + | 5458.93i | −0.498164 | + | 0.446135i | ||||
\(532\) | −681.004 | −0.0554986 | ||||||||
\(533\) | 11364.5 | − | 19683.8i | 0.923546 | − | 1.59963i | ||||
\(534\) | −30595.8 | + | 11697.5i | −2.47942 | + | 0.947944i | ||||
\(535\) | 2131.02 | + | 3691.04i | 0.172210 | + | 0.298276i | ||||
\(536\) | 3105.34 | + | 5378.60i | 0.250243 | + | 0.433433i | ||||
\(537\) | −10012.9 | − | 8130.54i | −0.804633 | − | 0.653368i | ||||
\(538\) | −1901.52 | + | 3293.53i | −0.152380 | + | 0.263929i | ||||
\(539\) | −1942.00 | −0.155191 | ||||||||
\(540\) | 3388.37 | + | 5263.90i | 0.270023 | + | 0.419485i | ||||
\(541\) | 5643.29 | 0.448473 | 0.224237 | − | 0.974535i | \(-0.428011\pi\) | ||||
0.224237 | + | 0.974535i | \(0.428011\pi\) | |||||||
\(542\) | 9425.15 | − | 16324.8i | 0.746946 | − | 1.29375i | ||||
\(543\) | −595.891 | − | 483.868i | −0.0470942 | − | 0.0382408i | ||||
\(544\) | −1189.95 | − | 2061.06i | −0.0937845 | − | 0.162440i | ||||
\(545\) | 4120.59 | + | 7137.07i | 0.323865 | + | 0.560951i | ||||
\(546\) | −9539.57 | + | 3647.22i | −0.747721 | + | 0.285873i | ||||
\(547\) | −9850.94 | + | 17062.3i | −0.770010 | + | 1.33370i | 0.167546 | + | 0.985864i | \(0.446416\pi\) |
−0.937557 | + | 0.347833i | \(0.886918\pi\) | |||||||
\(548\) | −9397.21 | −0.732534 | ||||||||
\(549\) | 10505.0 | + | 3444.47i | 0.816653 | + | 0.267771i | ||||
\(550\) | −19315.2 | −1.49746 | ||||||||
\(551\) | −353.509 | + | 612.296i | −0.0273321 | + | 0.0473406i | ||||
\(552\) | −2263.25 | + | 14166.6i | −0.174512 | + | 1.09234i | ||||
\(553\) | −1694.61 | − | 2935.15i | −0.130311 | − | 0.225705i | ||||
\(554\) | −8987.14 | − | 15566.2i | −0.689218 | − | 1.19376i | ||||
\(555\) | −954.833 | + | 5976.67i | −0.0730278 | + | 0.457109i | ||||
\(556\) | 1024.99 | − | 1775.34i | 0.0781824 | − | 0.135416i | ||||
\(557\) | 4658.25 | 0.354356 | 0.177178 | − | 0.984179i | \(-0.443303\pi\) | ||||
0.177178 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(558\) | 563.522 | + | 2686.59i | 0.0427523 | + | 0.203821i | ||||
\(559\) | 21698.8 | 1.64179 | ||||||||
\(560\) | 304.631 | − | 527.637i | 0.0229875 | − | 0.0398156i | ||||
\(561\) | −2020.71 | + | 772.570i | −0.152076 | + | 0.0581425i | ||||
\(562\) | 6792.55 | + | 11765.0i | 0.509833 | + | 0.883057i | ||||
\(563\) | −4467.06 | − | 7737.17i | −0.334394 | − | 0.579188i | 0.648974 | − | 0.760811i | \(-0.275198\pi\) |
−0.983368 | + | 0.181623i | \(0.941865\pi\) | |||||||
\(564\) | −14301.9 | − | 11613.2i | −1.06776 | − | 0.867030i | ||||
\(565\) | −833.453 | + | 1443.58i | −0.0620595 | + | 0.107490i | ||||
\(566\) | 24044.8 | 1.78565 | ||||||||
\(567\) | 560.635 | − | 5072.11i | 0.0415246 | − | 0.375677i | ||||
\(568\) | −14266.7 | −1.05391 | ||||||||
\(569\) | 517.761 | − | 896.788i | 0.0381470 | − | 0.0660726i | −0.846322 | − | 0.532672i | \(-0.821188\pi\) |
0.884469 | + | 0.466600i | \(0.154521\pi\) | |||||||
\(570\) | −578.041 | − | 469.374i | −0.0424762 | − | 0.0344910i | ||||
\(571\) | −213.177 | − | 369.234i | −0.0156238 | − | 0.0270612i | 0.858108 | − | 0.513470i | \(-0.171640\pi\) |
−0.873732 | + | 0.486408i | \(0.838307\pi\) | |||||||
\(572\) | 14559.0 | + | 25216.9i | 1.06423 | + | 1.84331i | ||||
\(573\) | −1449.59 | + | 554.217i | −0.105685 | + | 0.0404062i | ||||
\(574\) | −5546.63 | + | 9607.04i | −0.403330 | + | 0.698589i | ||||
\(575\) | 19212.2 | 1.39340 | ||||||||
\(576\) | −4554.70 | − | 21714.5i | −0.329478 | − | 1.57078i | ||||
\(577\) | −19507.3 | −1.40745 | −0.703726 | − | 0.710471i | \(-0.748482\pi\) | ||||
−0.703726 | + | 0.710471i | \(0.748482\pi\) | |||||||
\(578\) | −10625.0 | + | 18403.0i | −0.764604 | + | 1.32433i | ||||
\(579\) | −1949.88 | + | 12205.0i | −0.139955 | + | 0.876035i | ||||
\(580\) | 1877.16 | + | 3251.33i | 0.134387 | + | 0.232766i | ||||
\(581\) | −363.489 | − | 629.581i | −0.0259553 | − | 0.0449560i | ||||
\(582\) | −5458.83 | + | 34168.9i | −0.388790 | + | 2.43359i | ||||
\(583\) | −3823.59 | + | 6622.65i | −0.271624 | + | 0.470467i | ||||
\(584\) | 18029.7 | 1.27753 | ||||||||
\(585\) | −6275.01 | − | 2057.50i | −0.443487 | − | 0.145414i | ||||
\(586\) | 39581.7 | 2.79028 | ||||||||
\(587\) | −956.651 | + | 1656.97i | −0.0672661 | + | 0.116508i | −0.897697 | − | 0.440613i | \(-0.854761\pi\) |
0.830431 | + | 0.557122i | \(0.188094\pi\) | |||||||
\(588\) | 2753.37 | − | 1052.68i | 0.193107 | − | 0.0738298i | ||||
\(589\) | −96.5426 | − | 167.217i | −0.00675377 | − | 0.0116979i | ||||
\(590\) | −2584.09 | − | 4475.77i | −0.180314 | − | 0.312313i | ||||
\(591\) | 1135.30 | + | 921.876i | 0.0790190 | + | 0.0641640i | ||||
\(592\) | 3412.48 | − | 5910.58i | 0.236912 | − | 0.410344i | ||||
\(593\) | −26311.5 | −1.82206 | −0.911031 | − | 0.412337i | \(-0.864713\pi\) | ||||
−0.911031 | + | 0.412337i | \(0.864713\pi\) | |||||||
\(594\) | −24573.6 | + | 1188.70i | −1.69742 | + | 0.0821090i | ||||
\(595\) | 283.413 | 0.0195274 | ||||||||
\(596\) | 17289.2 | − | 29945.7i | 1.18824 | − | 2.05809i | ||||
\(597\) | −312.955 | − | 254.122i | −0.0214546 | − | 0.0174213i | ||||
\(598\) | −24488.0 | − | 42414.4i | −1.67456 | − | 2.90043i | ||||
\(599\) | −5780.20 | − | 10011.6i | −0.394278 | − | 0.682910i | 0.598730 | − | 0.800951i | \(-0.295672\pi\) |
−0.993009 | + | 0.118040i | \(0.962339\pi\) | |||||||
\(600\) | 8461.95 | − | 3235.22i | 0.575763 | − | 0.220129i | ||||
\(601\) | −5780.33 | + | 10011.8i | −0.392320 | + | 0.679519i | −0.992755 | − | 0.120155i | \(-0.961661\pi\) |
0.600435 | + | 0.799674i | \(0.294994\pi\) | |||||||
\(602\) | −10590.5 | −0.717002 | ||||||||
\(603\) | 7891.79 | − | 7067.55i | 0.532966 | − | 0.477301i | ||||
\(604\) | 16173.1 | 1.08953 | ||||||||
\(605\) | −462.019 | + | 800.241i | −0.0310475 | + | 0.0537759i | ||||
\(606\) | −5578.57 | + | 34918.4i | −0.373950 | + | 2.34070i | ||||
\(607\) | 2416.25 | + | 4185.06i | 0.161569 | + | 0.279846i | 0.935432 | − | 0.353508i | \(-0.115011\pi\) |
−0.773862 | + | 0.633354i | \(0.781678\pi\) | |||||||
\(608\) | 951.866 | + | 1648.68i | 0.0634922 | + | 0.109972i | ||||
\(609\) | 482.798 | − | 3022.02i | 0.0321248 | − | 0.201081i | ||||
\(610\) | −3491.26 | + | 6047.04i | −0.231733 | + | 0.401373i | ||||
\(611\) | 19434.1 | 1.28678 | ||||||||
\(612\) | 2446.18 | − | 2190.70i | 0.161570 | − | 0.144696i | ||||
\(613\) | −1202.99 | −0.0792631 | −0.0396316 | − | 0.999214i | \(-0.512618\pi\) | ||||
−0.0396316 | + | 0.999214i | \(0.512618\pi\) | |||||||
\(614\) | 6890.83 | − | 11935.3i | 0.452917 | − | 0.784475i | ||||
\(615\) | −6699.90 | + | 2561.54i | −0.439295 | + | 0.167954i | ||||
\(616\) | −2195.68 | − | 3803.03i | −0.143614 | − | 0.248747i | ||||
\(617\) | 6269.06 | + | 10858.3i | 0.409049 | + | 0.708493i | 0.994783 | − | 0.102010i | \(-0.0325273\pi\) |
−0.585735 | + | 0.810503i | \(0.699194\pi\) | |||||||
\(618\) | −25348.6 | − | 20583.3i | −1.64995 | − | 1.33977i | ||||
\(619\) | −13211.3 | + | 22882.6i | −0.857847 | + | 1.48583i | 0.0161321 | + | 0.999870i | \(0.494865\pi\) |
−0.873979 | + | 0.485964i | \(0.838469\pi\) | |||||||
\(620\) | −1025.30 | −0.0664143 | ||||||||
\(621\) | 24442.6 | − | 1182.36i | 1.57946 | − | 0.0764031i | ||||
\(622\) | 3471.98 | 0.223817 | ||||||||
\(623\) | −4986.49 | + | 8636.85i | −0.320673 | + | 0.555422i | ||||
\(624\) | 5780.77 | + | 4694.03i | 0.370859 | + | 0.301141i | ||||
\(625\) | −5137.62 | − | 8898.61i | −0.328807 | − | 0.569511i | ||||
\(626\) | −10158.0 | − | 17594.1i | −0.648553 | − | 1.12333i | ||||
\(627\) | 1616.41 | − | 617.994i | 0.102955 | − | 0.0393625i | ||||
\(628\) | 20052.2 | − | 34731.5i | 1.27416 | − | 2.20690i | ||||
\(629\) | 3174.80 | 0.201252 | ||||||||
\(630\) | 3062.63 | + | 1004.20i | 0.193679 | + | 0.0635053i | ||||
\(631\) | −10485.8 | −0.661545 | −0.330773 | − | 0.943711i | \(-0.607309\pi\) | ||||
−0.330773 | + | 0.943711i | \(0.607309\pi\) | |||||||
\(632\) | 3831.93 | − | 6637.10i | 0.241181 | − | 0.417737i | ||||
\(633\) | 1915.49 | − | 11989.8i | 0.120275 | − | 0.752848i | ||||
\(634\) | −9282.43 | − | 16077.6i | −0.581471 | − | 1.00714i | ||||
\(635\) | 942.812 | + | 1633.00i | 0.0589203 | + | 0.102053i | ||||
\(636\) | 1831.20 | − | 11462.2i | 0.114170 | − | 0.714632i | ||||
\(637\) | −1554.76 | + | 2692.92i | −0.0967059 | + | 0.167500i | ||||
\(638\) | −14754.4 | −0.915569 | ||||||||
\(639\) | 4995.76 | + | 23817.3i | 0.309279 | + | 1.47449i | ||||
\(640\) | 7028.07 | 0.434076 | ||||||||
\(641\) | 2172.72 | − | 3763.25i | 0.133880 | − | 0.231887i | −0.791289 | − | 0.611442i | \(-0.790590\pi\) |
0.925169 | + | 0.379555i | \(0.123923\pi\) | |||||||
\(642\) | 23747.9 | − | 9079.41i | 1.45990 | − | 0.558155i | ||||
\(643\) | −14240.9 | − | 24666.0i | −0.873416 | − | 1.51280i | −0.858440 | − | 0.512914i | \(-0.828566\pi\) |
−0.0149760 | − | 0.999888i | \(-0.504767\pi\) | |||||||
\(644\) | 7067.87 | + | 12241.9i | 0.432474 | + | 0.749067i | ||||
\(645\) | −5315.94 | − | 4316.58i | −0.324519 | − | 0.263512i | ||||
\(646\) | −195.291 | + | 338.254i | −0.0118941 | + | 0.0206013i | ||||
\(647\) | 9196.04 | 0.558785 | 0.279392 | − | 0.960177i | \(-0.409867\pi\) | ||||
0.279392 | + | 0.960177i | \(0.409867\pi\) | |||||||
\(648\) | 10566.6 | − | 4636.76i | 0.640578 | − | 0.281095i | ||||
\(649\) | 12011.1 | 0.726470 | ||||||||
\(650\) | −15463.6 | + | 26783.7i | −0.933127 | + | 1.61622i | ||||
\(651\) | 648.812 | + | 526.841i | 0.0390614 | + | 0.0317181i | ||||
\(652\) | 16916.0 | + | 29299.4i | 1.01608 | + | 1.75990i | ||||
\(653\) | 7451.10 | + | 12905.7i | 0.446530 | + | 0.773413i | 0.998157 | − | 0.0606781i | \(-0.0193263\pi\) |
−0.551627 | + | 0.834091i | \(0.685993\pi\) | |||||||
\(654\) | 45919.3 | − | 17556.1i | 2.74555 | − | 1.04969i | ||||
\(655\) | 1308.83 | − | 2266.96i | 0.0780766 | − | 0.135233i | ||||
\(656\) | 8088.37 | 0.481399 | ||||||||
\(657\) | −6313.44 | − | 30099.3i | −0.374902 | − | 1.78734i | ||||
\(658\) | −9485.16 | −0.561961 | ||||||||
\(659\) | −9210.71 | + | 15953.4i | −0.544459 | + | 0.943031i | 0.454182 | + | 0.890909i | \(0.349932\pi\) |
−0.998641 | + | 0.0521216i | \(0.983402\pi\) | |||||||
\(660\) | 1449.68 | − | 9074.09i | 0.0854978 | − | 0.535164i | ||||
\(661\) | −1583.27 | − | 2742.30i | −0.0931649 | − | 0.161366i | 0.815676 | − | 0.578509i | \(-0.196365\pi\) |
−0.908841 | + | 0.417142i | \(0.863032\pi\) | |||||||
\(662\) | −15117.1 | − | 26183.6i | −0.887528 | − | 1.53724i | ||||
\(663\) | −546.471 | + | 3420.58i | −0.0320108 | + | 0.200368i | ||||
\(664\) | 821.939 | − | 1423.64i | 0.0480383 | − | 0.0832048i | ||||
\(665\) | −226.708 | −0.0132201 | ||||||||
\(666\) | 34307.5 | + | 11249.0i | 1.99608 | + | 0.654492i | ||||
\(667\) | 14675.7 | 0.851944 | ||||||||
\(668\) | −15226.9 | + | 26373.8i | −0.881958 | + | 1.52760i | ||||
\(669\) | 11234.2 | − | 4295.12i | 0.649237 | − | 0.248220i | ||||
\(670\) | 3345.55 | + | 5794.67i | 0.192910 | + | 0.334131i | ||||
\(671\) | −8113.91 | − | 14053.7i | −0.466817 | − | 0.808550i | ||||
\(672\) | −6396.99 | − | 5194.40i | −0.367216 | − | 0.298182i | ||||
\(673\) | −7829.88 | + | 13561.7i | −0.448469 | + | 0.776771i | −0.998287 | − | 0.0585137i | \(-0.981364\pi\) |
0.549818 | + | 0.835285i | \(0.314697\pi\) | |||||||
\(674\) | −22956.4 | −1.31194 | ||||||||
\(675\) | −8364.07 | − | 12993.7i | −0.476938 | − | 0.740932i | ||||
\(676\) | 21187.8 | 1.20550 | ||||||||
\(677\) | −6337.73 | + | 10977.3i | −0.359791 | + | 0.623177i | −0.987926 | − | 0.154928i | \(-0.950485\pi\) |
0.628135 | + | 0.778105i | \(0.283819\pi\) | |||||||
\(678\) | 7719.20 | + | 6268.05i | 0.437248 | + | 0.355049i | ||||
\(679\) | 5267.60 | + | 9123.75i | 0.297720 | + | 0.515666i | ||||
\(680\) | 320.435 | + | 555.009i | 0.0180707 | + | 0.0312994i | ||||
\(681\) | 5144.27 | − | 1966.78i | 0.289469 | − | 0.110672i | ||||
\(682\) | 2014.70 | − | 3489.56i | 0.113119 | − | 0.195927i | ||||
\(683\) | −21325.5 | −1.19473 | −0.597363 | − | 0.801971i | \(-0.703785\pi\) | ||||
−0.597363 | + | 0.801971i | \(0.703785\pi\) | |||||||
\(684\) | −1956.75 | + | 1752.38i | −0.109383 | + | 0.0979591i | ||||
\(685\) | −3128.35 | −0.174494 | ||||||||
\(686\) | 758.825 | − | 1314.32i | 0.0422334 | − | 0.0731503i | ||||
\(687\) | −1920.21 | + | 12019.3i | −0.106638 | + | 0.667491i | ||||
\(688\) | 3860.89 | + | 6687.25i | 0.213946 | + | 0.370566i | ||||
\(689\) | 6122.28 | + | 10604.1i | 0.338520 | + | 0.586334i | ||||
\(690\) | −2438.33 | + | 15262.5i | −0.134530 | + | 0.842075i | ||||
\(691\) | 3743.95 | − | 6484.70i | 0.206116 | − | 0.357004i | −0.744372 | − | 0.667766i | \(-0.767251\pi\) |
0.950488 | + | 0.310762i | \(0.100584\pi\) | |||||||
\(692\) | 13152.6 | 0.722524 | ||||||||
\(693\) | −5580.02 | + | 4997.22i | −0.305869 | + | 0.273923i | ||||
\(694\) | 19.9982 | 0.00109383 | ||||||||
\(695\) | 341.223 | − | 591.016i | 0.0186235 | − | 0.0322568i | ||||
\(696\) | 6463.89 | − | 2471.31i | 0.352031 | − | 0.134590i | ||||
\(697\) | 1881.25 | + | 3258.42i | 0.102235 | + | 0.177076i | ||||
\(698\) | −1224.92 | − | 2121.62i | −0.0664237 | − | 0.115049i | ||||
\(699\) | −2027.80 | − | 1646.59i | −0.109726 | − | 0.0890983i | ||||
\(700\) | 4463.20 | − | 7730.49i | 0.240990 | − | 0.417407i | ||||
\(701\) | 17119.4 | 0.922381 | 0.461191 | − | 0.887301i | \(-0.347422\pi\) | ||||
0.461191 | + | 0.887301i | \(0.347422\pi\) | |||||||
\(702\) | −18025.2 | + | 35027.2i | −0.969112 | + | 1.88321i | ||||
\(703\) | −2539.58 | −0.136248 | ||||||||
\(704\) | −16283.9 | + | 28204.6i | −0.871767 | + | 1.50995i | ||||
\(705\) | −4761.12 | − | 3866.07i | −0.254347 | − | 0.206531i | ||||
\(706\) | 25816.1 | + | 44714.8i | 1.37621 | + | 2.38366i | ||||
\(707\) | 5383.15 | + | 9323.88i | 0.286357 | + | 0.495984i | ||||
\(708\) | −17029.4 | + | 6510.77i | −0.903960 | + | 0.345607i | ||||
\(709\) | 14829.8 | − | 25686.0i | 0.785538 | − | 1.36059i | −0.143140 | − | 0.989702i | \(-0.545720\pi\) |
0.928677 | − | 0.370889i | \(-0.120947\pi\) | |||||||
\(710\) | −15370.4 | −0.812449 | ||||||||
\(711\) | −12422.0 | − | 4073.03i | −0.655219 | − | 0.214839i | ||||
\(712\) | −22551.4 | −1.18701 | ||||||||
\(713\) | −2003.96 | + | 3470.95i | −0.105258 | + | 0.182312i | ||||
\(714\) | 266.715 | − | 1669.47i | 0.0139798 | − | 0.0875047i | ||||
\(715\) | 4846.73 | + | 8394.77i | 0.253507 | + | 0.439086i | ||||
\(716\) | −14369.1 | − | 24888.0i | −0.749996 | − | 1.29903i | ||||
\(717\) | 3315.49 | − | 20752.9i | 0.172691 | − | 1.08094i | ||||
\(718\) | −10648.9 | + | 18444.5i | −0.553502 | + | 0.958693i | ||||
\(719\) | 10886.1 | 0.564649 | 0.282325 | − | 0.959319i | \(-0.408895\pi\) | ||||
0.282325 | + | 0.959319i | \(0.408895\pi\) | |||||||
\(720\) | −482.426 | − | 2299.96i | −0.0249707 | − | 0.119048i | ||||
\(721\) | −9941.74 | −0.513523 | ||||||||
\(722\) | −15018.1 | + | 26012.1i | −0.774120 | + | 1.34082i | ||||
\(723\) | −2877.57 | + | 1100.17i | −0.148019 | + | 0.0565915i | ||||
\(724\) | −855.138 | − | 1481.14i | −0.0438964 | − | 0.0760307i | ||||
\(725\) | −4633.70 | − | 8025.80i | −0.237367 | − | 0.411132i | ||||
\(726\) | 4279.09 | + | 3474.65i | 0.218749 | + | 0.177626i | ||||
\(727\) | 9576.19 | − | 16586.4i | 0.488530 | − | 0.846158i | −0.511383 | − | 0.859353i | \(-0.670867\pi\) |
0.999913 | + | 0.0131946i | \(0.00420008\pi\) | |||||||
\(728\) | −7031.39 | −0.357968 | ||||||||
\(729\) | −11440.8 | − | 16016.5i | −0.581254 | − | 0.813722i | ||||
\(730\) | 19424.4 | 0.984836 | ||||||||
\(731\) | −1795.99 | + | 3110.74i | −0.0908714 | + | 0.157394i | ||||
\(732\) | 19121.8 | + | 15527.1i | 0.965524 | + | 0.784013i | ||||
\(733\) | −11109.0 | − | 19241.4i | −0.559783 | − | 0.969572i | −0.997514 | − | 0.0704661i | \(-0.977551\pi\) |
0.437732 | − | 0.899106i | \(-0.355782\pi\) | |||||||
\(734\) | −14439.4 | − | 25009.8i | −0.726116 | − | 1.25767i | ||||
\(735\) | 916.603 | − | 350.441i | 0.0459992 | − | 0.0175867i | ||||
\(736\) | 19758.1 | − | 34222.0i | 0.989528 | − | 1.71391i | ||||
\(737\) | −15550.5 | −0.777220 | ||||||||
\(738\) | 8783.85 | + | 41876.9i | 0.438127 | + | 2.08877i | ||||
\(739\) | 6173.20 | 0.307287 | 0.153643 | − | 0.988126i | \(-0.450899\pi\) | ||||
0.153643 | + | 0.988126i | \(0.450899\pi\) | |||||||
\(740\) | −6742.67 | + | 11678.6i | −0.334953 | + | 0.580156i | ||||
\(741\) | 437.133 | − | 2736.18i | 0.0216714 | − | 0.135649i | ||||
\(742\) | −2988.08 | − | 5175.51i | −0.147838 | − | 0.256063i | ||||
\(743\) | 1591.20 | + | 2756.05i | 0.0785674 | + | 0.136083i | 0.902632 | − | 0.430413i | \(-0.141632\pi\) |
−0.824065 | + | 0.566496i | \(0.808299\pi\) | |||||||
\(744\) | −298.149 | + | 1866.23i | −0.0146917 | + | 0.0919614i | ||||
\(745\) | 5755.61 | − | 9969.00i | 0.283046 | − | 0.490250i | ||||
\(746\) | −23027.3 | −1.13015 | ||||||||
\(747\) | −2664.48 | − | 873.653i | −0.130506 | − | 0.0427916i | ||||
\(748\) | −4820.14 | −0.235617 | ||||||||
\(749\) | 3870.42 | − | 6703.76i | 0.188814 | − | 0.327036i | ||||
\(750\) | 19462.6 | − | 7441.03i | 0.947562 | − | 0.362277i | ||||
\(751\) | 11697.0 | + | 20259.7i | 0.568347 | + | 0.984405i | 0.996730 | + | 0.0808081i | \(0.0257501\pi\) |
−0.428383 | + | 0.903597i | \(0.640917\pi\) | |||||||
\(752\) | 3457.93 | + | 5989.32i | 0.167683 | + | 0.290436i | ||||
\(753\) | 10744.8 | + | 8724.87i | 0.520004 | + | 0.422247i | ||||
\(754\) | −11812.3 | + | 20459.5i | −0.570529 | + | 0.988184i | ||||
\(755\) | 5384.07 | 0.259532 | ||||||||
\(756\) | 5202.54 | − | 10109.8i | 0.250284 | − | 0.486361i | ||||
\(757\) | −21168.6 | −1.01636 | −0.508182 | − | 0.861250i | \(-0.669682\pi\) | ||||
−0.508182 | + | 0.861250i | \(0.669682\pi\) | |||||||
\(758\) | 21942.5 | − | 38005.5i | 1.05143 | − | 1.82114i | ||||
\(759\) | −27885.3 | − | 22643.1i | −1.33356 | − | 1.08286i | ||||
\(760\) | −256.322 | − | 443.962i | −0.0122339 | − | 0.0211897i | ||||
\(761\) | −17753.7 | − | 30750.4i | −0.845694 | − | 1.46478i | −0.885018 | − | 0.465558i | \(-0.845854\pi\) |
0.0393241 | − | 0.999227i | \(-0.487480\pi\) | |||||||
\(762\) | 10506.6 | − | 4016.93i | 0.499492 | − | 0.190969i | ||||
\(763\) | 7483.92 | − | 12962.5i | 0.355093 | − | 0.615039i | ||||
\(764\) | −3457.81 | −0.163742 | ||||||||
\(765\) | 814.341 | − | 729.289i | 0.0384870 | − | 0.0344673i | ||||
\(766\) | 8531.13 | 0.402405 | ||||||||
\(767\) | 9616.05 | − | 16655.5i | 0.452693 | − | 0.784087i | ||||
\(768\) | 1225.03 | − | 7667.96i | 0.0575581 | − | 0.360278i | ||||
\(769\) | −14514.9 | − | 25140.6i | −0.680653 | − | 1.17893i | −0.974782 | − | 0.223160i | \(-0.928363\pi\) |
0.294129 | − | 0.955766i | \(-0.404971\pi\) | |||||||
\(770\) | −2365.53 | − | 4097.21i | −0.110711 | − | 0.191758i | ||||
\(771\) | −1344.14 | + | 8413.51i | −0.0627862 | + | 0.393003i | ||||
\(772\) | −13769.3 | + | 23849.1i | −0.641927 | + | 1.11185i | ||||
\(773\) | 17176.5 | 0.799220 | 0.399610 | − | 0.916685i | \(-0.369146\pi\) | ||||
0.399610 | + | 0.916685i | \(0.369146\pi\) | |||||||
\(774\) | −30429.9 | + | 27251.7i | −1.41315 | + | 1.26556i | ||||
\(775\) | 2530.91 | 0.117307 | ||||||||
\(776\) | −11911.4 | + | 20631.1i | −0.551022 | + | 0.954398i | ||||
\(777\) | 10267.8 | − | 3925.64i | 0.474073 | − | 0.181250i | ||||
\(778\) | −5492.97 | − | 9514.10i | −0.253126 | − | 0.438428i | ||||
\(779\) | −1504.85 | − | 2606.48i | −0.0692129 | − | 0.119880i | ||||
\(780\) | −11422.2 | − | 9274.88i | −0.524332 | − | 0.425762i | ||||
\(781\) | 17860.8 | − | 30935.8i | 0.818323 | − | 1.41738i | ||||
\(782\) | 8107.39 | 0.370741 | ||||||||
\(783\) | −6389.13 | − | 9925.62i | −0.291608 | − | 0.453018i | ||||
\(784\) | −1106.56 | −0.0504080 | ||||||||
\(785\) | 6675.43 | − | 11562.2i | 0.303511 | − | 0.525697i | ||||
\(786\) | −12122.0 | − | 9843.15i | −0.550098 | − | 0.446684i | ||||
\(787\) | −9166.30 | − | 15876.5i | −0.415176 | − | 0.719105i | 0.580271 | − | 0.814423i | \(-0.302947\pi\) |
−0.995447 | + | 0.0953181i | \(0.969613\pi\) | |||||||
\(788\) | 1629.23 | + | 2821.91i | 0.0736534 | + | 0.127571i | ||||
\(789\) | −19086.4 | + | 7297.24i | −0.861211 | + | 0.329263i | ||||
\(790\) | 4128.36 | − | 7150.53i | 0.185925 | − | 0.322031i | ||||
\(791\) | 3027.48 | 0.136087 | ||||||||
\(792\) | −16095.0 | − | 5277.36i | −0.722109 | − | 0.236771i | ||||
\(793\) | −25983.8 | −1.16357 | ||||||||
\(794\) | −1334.90 | + | 2312.11i | −0.0596646 | + | 0.103342i | ||||
\(795\) | 609.611 | − | 3815.79i | 0.0271958 | − | 0.170229i | ||||
\(796\) | −449.109 | − | 777.879i | −0.0199978 | − | 0.0346372i | ||||
\(797\) | 3577.12 | + | 6195.76i | 0.158981 | + | 0.275364i | 0.934502 | − | 0.355959i | \(-0.115846\pi\) |
−0.775520 | + | 0.631323i | \(0.782512\pi\) | |||||||
\(798\) | −213.350 | + | 1335.44i | −0.00946430 | + | 0.0592408i | ||||
\(799\) | −1608.54 | + | 2786.08i | −0.0712218 | + | 0.123360i | ||||
\(800\) | −24953.6 | −1.10280 | ||||||||
\(801\) | 7896.79 | + | 37647.9i | 0.348339 | + | 1.66070i | ||||
\(802\) | −11731.5 | −0.516525 | ||||||||
\(803\) | −22571.8 | + | 39095.5i | −0.991956 | + | 1.71812i | ||||
\(804\) | 22047.5 | − | 8429.34i | 0.967110 | − | 0.369751i | ||||
\(805\) | 2352.91 | + | 4075.36i | 0.103018 | + | 0.178432i | ||||
\(806\) | −3225.91 | − | 5587.45i | −0.140978 | − | 0.244180i | ||||
\(807\) | 3467.09 | + | 2815.30i | 0.151236 | + | 0.122805i | ||||
\(808\) | −12172.6 | + | 21083.6i | −0.529990 | + | 0.917970i | ||||
\(809\) | 33931.9 | 1.47464 | 0.737318 | − | 0.675546i | \(-0.236092\pi\) | ||||
0.737318 | + | 0.675546i | \(0.236092\pi\) | |||||||
\(810\) | 11384.0 | − | 4995.45i | 0.493818 | − | 0.216694i | ||||
\(811\) | −41265.7 | −1.78673 | −0.893363 | − | 0.449336i | \(-0.851660\pi\) | ||||
−0.893363 | + | 0.449336i | \(0.851660\pi\) | |||||||
\(812\) | 3409.34 | − | 5905.15i | 0.147345 | − | 0.255209i | ||||
\(813\) | −17185.1 | − | 13954.5i | −0.741339 | − | 0.601973i | ||||
\(814\) | −26498.6 | − | 45897.0i | −1.14100 | − | 1.97627i | ||||
\(815\) | 5631.39 | + | 9753.86i | 0.242036 | + | 0.419218i | ||||
\(816\) | −1151.41 | + | 440.212i | −0.0493962 | + | 0.0188854i | ||||
\(817\) | 1436.64 | − | 2488.34i | 0.0615200 | − | 0.106556i | ||||
\(818\) | 38726.3 | 1.65530 | ||||||||
\(819\) | 2462.17 | + | 11738.4i | 0.105049 | + | 0.500821i | ||||
\(820\) | −15981.7 | −0.680616 | ||||||||
\(821\) | 8273.49 | − | 14330.1i | 0.351702 | − | 0.609165i | −0.634846 | − | 0.772639i | \(-0.718937\pi\) |
0.986548 | + | 0.163474i | \(0.0522699\pi\) | |||||||
\(822\) | −2944.03 | + | 18427.8i | −0.124921 | + | 0.781927i | ||||
\(823\) | 4178.02 | + | 7236.55i | 0.176958 | + | 0.306501i | 0.940837 | − | 0.338859i | \(-0.110041\pi\) |
−0.763879 | + | 0.645360i | \(0.776708\pi\) | |||||||
\(824\) | −11240.4 | − | 19468.9i | −0.475215 | − | 0.823097i | ||||
\(825\) | −3578.47 | + | 22399.1i | −0.151014 | + | 0.945255i | ||||
\(826\) | −4693.28 | + | 8129.00i | −0.197700 | + | 0.342426i | ||||
\(827\) | −2525.94 | −0.106210 | −0.0531050 | − | 0.998589i | \(-0.516912\pi\) | ||||
−0.0531050 | + | 0.998589i | \(0.516912\pi\) | |||||||
\(828\) | 51809.6 | + | 16987.8i | 2.17453 | + | 0.713003i | ||||
\(829\) | 42284.4 | 1.77153 | 0.885764 | − | 0.464135i | \(-0.153635\pi\) | ||||
0.885764 | + | 0.464135i | \(0.153635\pi\) | |||||||
\(830\) | 885.522 | − | 1533.77i | 0.0370324 | − | 0.0641420i | ||||
\(831\) | −19716.5 | + | 7538.13i | −0.823055 | + | 0.314675i | ||||
\(832\) | 26073.7 | + | 45160.9i | 1.08647 | + | 1.88182i | ||||
\(833\) | −257.371 | − | 445.780i | −0.0107051 | − | 0.0185419i | ||||
\(834\) | −3160.31 | − | 2566.19i | −0.131214 | − | 0.106547i | ||||
\(835\) | −5069.08 | + | 8779.91i | −0.210087 | + | 0.363882i | ||||
\(836\) | 3855.72 | 0.159513 | ||||||||
\(837\) | 3219.93 | − | 155.757i | 0.132972 | − | 0.00643221i | ||||
\(838\) | −50551.9 | −2.08387 | ||||||||
\(839\) | −5120.57 | + | 8869.09i | −0.210705 | + | 0.364952i | −0.951935 | − | 0.306299i | \(-0.900909\pi\) |
0.741230 | + | 0.671251i | \(0.234243\pi\) | |||||||
\(840\) | 1722.60 | + | 1398.77i | 0.0707565 | + | 0.0574548i | ||||
\(841\) | 8654.92 | + | 14990.8i | 0.354870 | + | 0.614653i | ||||
\(842\) | 24056.0 | + | 41666.2i | 0.984590 | + | 1.70536i | ||||
\(843\) | 14901.9 | − | 5697.38i | 0.608836 | − | 0.232774i | ||||
\(844\) | 13526.5 | − | 23428.6i | 0.551660 | − | 0.955503i | ||||
\(845\) | 7053.47 | 0.287156 | ||||||||
\(846\) | −27254.0 | + | 24407.5i | −1.10758 | + | 0.991900i | ||||
\(847\) | 1678.26 | 0.0680823 | ||||||||
\(848\) | −2178.69 | + | 3773.60i | −0.0882269 | + | 0.152814i | ||||
\(849\) | 4454.71 | − | 27883.8i | 0.180077 | − | 1.12717i | ||||
\(850\) | −2559.81 | − | 4433.73i | −0.103295 | − | 0.178913i | ||||
\(851\) | 26357.3 | + | 45652.2i | 1.06171 | + | 1.83894i | ||||
\(852\) | −8553.94 | + | 53542.5i | −0.343959 | + | 2.15297i | ||||
\(853\) | −5091.41 | + | 8818.58i | −0.204369 | + | 0.353977i | −0.949931 | − | 0.312459i | \(-0.898847\pi\) |
0.745563 | + | 0.666435i | \(0.232181\pi\) | |||||||
\(854\) | 12681.8 | 0.508154 | ||||||||
\(855\) | −651.407 | + | 583.372i | −0.0260557 | + | 0.0233344i | ||||
\(856\) | 17504.0 | 0.698918 | ||||||||
\(857\) | 457.041 | − | 791.619i | 0.0182173 | − | 0.0315533i | −0.856773 | − | 0.515694i | \(-0.827534\pi\) |
0.874990 | + | 0.484140i | \(0.160868\pi\) | |||||||
\(858\) | 54011.3 | − | 20649.9i | 2.14908 | − | 0.821650i | ||||
\(859\) | −13430.7 | − | 23262.7i | −0.533470 | − | 0.923997i | −0.999236 | − | 0.0390890i | \(-0.987554\pi\) |
0.465766 | − | 0.884908i | \(-0.345779\pi\) | |||||||
\(860\) | −7628.68 | − | 13213.3i | −0.302483 | − | 0.523917i | ||||
\(861\) | 10113.3 | + | 8212.08i | 0.400303 | + | 0.325049i | ||||
\(862\) | 34739.5 | − | 60170.5i | 1.37266 | − | 2.37751i | ||||
\(863\) | 33250.8 | 1.31155 | 0.655777 | − | 0.754954i | \(-0.272341\pi\) | ||||
0.655777 | + | 0.754954i | \(0.272341\pi\) | |||||||
\(864\) | −31747.1 | + | 1535.69i | −1.25007 | + | 0.0604692i | ||||
\(865\) | 4378.53 | 0.172109 | ||||||||
\(866\) | 21836.5 | − | 37822.0i | 0.856854 | − | 1.48411i | ||||
\(867\) | 19372.8 | + | 15730.9i | 0.758864 | + | 0.616203i | ||||
\(868\) | 931.083 | + | 1612.68i | 0.0364090 | + | 0.0630623i | ||||
\(869\) | 9594.56 | + | 16618.3i | 0.374537 | + | 0.648718i | ||||
\(870\) | 6963.92 | − | 2662.48i | 0.271378 | − | 0.103755i | ||||
\(871\) | −12449.7 | + | 21563.5i | −0.484318 | + | 0.838863i | ||||
\(872\) | 33846.0 | 1.31442 | ||||||||
\(873\) | 38613.1 | + | 12660.8i | 1.49697 | + | 0.490839i | ||||
\(874\) | −6485.26 | −0.250992 | ||||||||
\(875\) | 3172.00 | − | 5494.07i | 0.122552 | − | 0.212267i | ||||
\(876\) | 10810.1 | − | 67664.8i | 0.416941 | − | 2.60980i | ||||
\(877\) | 11576.9 | + | 20051.7i | 0.445750 | + | 0.772061i | 0.998104 | − | 0.0615482i | \(-0.0196038\pi\) |
−0.552354 | + | 0.833609i | \(0.686270\pi\) | |||||||
\(878\) | 7412.50 | + | 12838.8i | 0.284920 | + | 0.493496i | ||||
\(879\) | 7333.21 | − | 45901.4i | 0.281391 | − | 1.76134i | ||||
\(880\) | −1724.77 | + | 2987.38i | −0.0660703 | + | 0.114437i | ||||
\(881\) | −23462.3 | −0.897236 | −0.448618 | − | 0.893724i | \(-0.648084\pi\) | ||||
−0.448618 | + | 0.893724i | \(0.648084\pi\) | |||||||
\(882\) | −1201.70 | − | 5729.12i | −0.0458770 | − | 0.218718i | ||||
\(883\) | 1599.37 | 0.0609549 | 0.0304775 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304775 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(884\) | −3858.97 | + | 6683.93i | −0.146823 | + | 0.254304i | ||||
\(885\) | −5669.12 | + | 2167.45i | −0.215328 | + | 0.0823255i | ||||
\(886\) | 12572.3 | + | 21775.8i | 0.476720 | + | 0.825703i | ||||
\(887\) | −10238.6 | − | 17733.8i | −0.387574 | − | 0.671298i | 0.604549 | − | 0.796568i | \(-0.293354\pi\) |
−0.992123 | + | 0.125270i | \(0.960020\pi\) | |||||||
\(888\) | 19296.6 | + | 15669.0i | 0.729224 | + | 0.592136i | ||||
\(889\) | 1712.36 | − | 2965.89i | 0.0646014 | − | 0.111893i | ||||
\(890\) | −24295.9 | −0.915057 | ||||||||
\(891\) | −3174.21 | + | 28717.3i | −0.119349 | + | 1.07976i | ||||
\(892\) | 26797.7 | 1.00589 | ||||||||
\(893\) | 1286.71 | − | 2228.64i | 0.0482172 | − | 0.0835146i | ||||
\(894\) | −53306.7 | − | 43285.5i | −1.99423 | − | 1.61933i | ||||
\(895\) | −4783.50 | − | 8285.26i | −0.178653 | − | 0.309437i | ||||
\(896\) | −6382.27 | − | 11054.4i | −0.237965 | − | 0.412168i | ||||
\(897\) | −53723.2 | + | 20539.8i | −1.99974 | + | 0.764552i | ||||
\(898\) | −28669.5 | + | 49657.1i | −1.06538 | + | 1.84530i | ||||
\(899\) | 1933.30 | 0.0717233 | ||||||||
\(900\) | −7068.10 | − | 33697.1i | −0.261781 | − | 1.24804i | ||||
\(901\) | −2026.94 | −0.0749469 | ||||||||
\(902\) | 31404.0 | − | 54393.3i | 1.15924 | − | 2.00787i | ||||
\(903\) | −1962.07 | + | 12281.4i | −0.0723074 | + | 0.452600i | ||||
\(904\) | 3422.94 | + | 5928.71i | 0.125935 | + | 0.218126i | ||||
\(905\) | −284.678 | − | 493.076i | −0.0104564 | − | 0.0181109i | ||||
\(906\) | 5066.84 | − | 31715.3i | 0.185800 | − | 1.16299i | ||||
\(907\) | 14862.7 | − | 25742.9i | 0.544109 | − | 0.942424i | −0.454554 | − | 0.890719i | \(-0.650201\pi\) |
0.998662 | − | 0.0517044i | \(-0.0164654\pi\) | |||||||
\(908\) | 12270.9 | 0.448487 | ||||||||
\(909\) | 39460.1 | + | 12938.5i | 1.43983 | + | 0.472105i | ||||
\(910\) | −7575.31 | −0.275955 | ||||||||
\(911\) | 1412.43 | − | 2446.40i | 0.0513676 | − | 0.0889713i | −0.839198 | − | 0.543826i | \(-0.816975\pi\) |
0.890566 | + | 0.454854i | \(0.150309\pi\) | |||||||
\(912\) | 921.032 | − | 352.134i | 0.0334413 | − | 0.0127854i | ||||
\(913\) | 2058.01 | + | 3564.57i | 0.0746003 | + | 0.129211i | ||||
\(914\) | 4958.58 | + | 8588.51i | 0.179448 | + | 0.310813i | ||||
\(915\) | 6365.71 | + | 5169.01i | 0.229993 | + | 0.186756i | ||||
\(916\) | −13559.8 | + | 23486.3i | −0.489114 | + | 0.847170i | ||||
\(917\) | −4754.25 | −0.171210 | ||||||||
\(918\) | −3529.58 | − | 5483.26i | −0.126899 | − | 0.197140i | ||||
\(919\) | 1150.69 | 0.0413034 | 0.0206517 | − | 0.999787i | \(-0.493426\pi\) | ||||
0.0206517 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(920\) | −5320.53 | + | 9215.42i | −0.190666 | + | 0.330243i | ||||
\(921\) | −12564.2 | − | 10202.2i | −0.449517 | − | 0.365011i | ||||
\(922\) | 27601.8 | + | 47807.8i | 0.985920 | + | 1.70766i | ||||
\(923\) | −28598.5 | − | 49534.1i | −1.01986 | − | 1.76645i | ||||
\(924\) | −15589.1 | + | 5960.10i | −0.555025 | + | 0.212200i | ||||
\(925\) | 16644.0 | − | 28828.3i | 0.591624 | − | 1.02472i | ||||
\(926\) | 43137.6 | 1.53087 | ||||||||
\(927\) | −28565.9 | + | 25582.4i | −1.01211 | + | 0.906404i | ||||
\(928\) | −19061.5 | −0.674271 | ||||||||
\(929\) | −8032.09 | + | 13912.0i | −0.283664 | + | 0.491321i | −0.972284 | − | 0.233801i | \(-0.924884\pi\) |
0.688620 | + | 0.725122i | \(0.258217\pi\) | |||||||
\(930\) | −321.212 | + | 2010.59i | −0.0113258 | + | 0.0708924i | ||||
\(931\) | 205.876 | + | 356.588i | 0.00724739 | + | 0.0125529i | ||||
\(932\) | −2910.01 | − | 5040.29i | −0.102275 | − | 0.177146i | ||||
\(933\) | 643.246 | − | 4026.33i | 0.0225712 | − | 0.141282i | ||||
\(934\) | −13158.5 | + | 22791.3i | −0.460985 | + | 0.798450i | ||||
\(935\) | −1604.63 | −0.0561253 | ||||||||
\(936\) | −20203.5 | + | 18093.4i | −0.705526 | + | 0.631839i | ||||
\(937\) | −7995.92 | −0.278778 | −0.139389 | − | 0.990238i | \(-0.544514\pi\) | ||||
−0.139389 | + | 0.990238i | \(0.544514\pi\) | |||||||
\(938\) | 6076.27 | − | 10524.4i | 0.211511 | − | 0.366348i | ||||
\(939\) | −22285.2 | + | 8520.20i | −0.774494 | + | 0.296109i | ||||
\(940\) | −6832.49 | − | 11834.2i | −0.237076 | − | 0.410627i | ||||
\(941\) | −9716.25 | − | 16829.0i | −0.336600 | − | 0.583009i | 0.647191 | − | 0.762328i | \(-0.275944\pi\) |
−0.983791 | + | 0.179320i | \(0.942610\pi\) | |||||||
\(942\) | −61825.9 | − | 50203.1i | −2.13843 | − | 1.73642i | ||||
\(943\) | −31236.5 | + | 54103.2i | −1.07869 | + | 1.86834i | ||||
\(944\) | 6843.98 | 0.235967 | ||||||||
\(945\) | 1731.94 | − | 3365.57i | 0.0596190 | − | 0.115854i | ||||
\(946\) | 59961.2 | 2.06079 | ||||||||
\(947\) | −20478.3 | + | 35469.4i | −0.702697 | + | 1.21711i | 0.264819 | + | 0.964298i | \(0.414688\pi\) |
−0.967516 | + | 0.252809i | \(0.918646\pi\) | |||||||
\(948\) | −22611.3 | − | 18360.5i | −0.774662 | − | 0.629032i | ||||
\(949\) | 36141.7 | + | 62599.2i | 1.23626 | + | 2.14126i | ||||
\(950\) | 2047.65 | + | 3546.63i | 0.0699309 | + | 0.121124i | ||||
\(951\) | −20364.4 | + | 7785.82i | −0.694385 | + | 0.265481i | ||||
\(952\) | 581.981 | − | 1008.02i | 0.0198131 | − | 0.0343174i | ||||
\(953\) | 7968.49 | 0.270855 | 0.135427 | − | 0.990787i | \(-0.456759\pi\) | ||||
0.135427 | + | 0.990787i | \(0.456759\pi\) | |||||||
\(954\) | −21903.6 | − | 7181.93i | −0.743348 | − | 0.243735i | ||||
\(955\) | −1151.11 | −0.0390043 | ||||||||
\(956\) | 23412.7 | − | 40552.1i | 0.792073 | − | 1.37191i | ||||
\(957\) | −2733.52 | + | 17110.1i | −0.0923323 | + | 0.577944i | ||||
\(958\) | −24799.3 | − | 42953.6i | −0.836356 | − | 1.44861i | ||||
\(959\) | 2840.90 | + | 4920.58i | 0.0956594 | + | 0.165687i | ||||
\(960\) | 2596.22 | − | 16250.8i | 0.0872840 | − | 0.546344i | ||||
\(961\) | 14631.5 | − | 25342.5i | 0.491139 | − | 0.850677i | ||||
\(962\) | −84858.6 | −2.84402 | ||||||||
\(963\) | −6129.34 | − | 29221.6i | −0.205104 | − | 0.977833i | ||||
\(964\) | −6864.04 | −0.229332 | ||||||||
\(965\) | −4583.83 | + | 7939.43i | −0.152911 | + | 0.264849i | ||||
\(966\) | 26220.5 | − | 10024.8i | 0.873325 | − | 0.333895i | ||||
\(967\) | 21570.6 | + | 37361.4i | 0.717337 | + | 1.24246i | 0.962051 | + | 0.272869i | \(0.0879725\pi\) |
−0.244714 | + | 0.969595i | \(0.578694\pi\) | |||||||
\(968\) | 1897.49 | + | 3286.54i | 0.0630036 | + | 0.109125i | ||||
\(969\) | 356.079 | + | 289.139i | 0.0118048 | + | 0.00958563i | ||||
\(970\) | −12832.8 | + | 22227.0i | −0.424779 | + | 0.735739i | ||||
\(971\) | 15809.2 | 0.522492 | 0.261246 | − | 0.965272i | \(-0.415867\pi\) | ||||
0.261246 | + | 0.965272i | \(0.415867\pi\) | |||||||
\(972\) | −11066.1 | − | 42436.0i | −0.365172 | − | 1.40035i | ||||
\(973\) | −1239.48 | −0.0408384 | ||||||||
\(974\) | −25759.5 | + | 44616.8i | −0.847420 | + | 1.46778i | ||||
\(975\) | 28195.2 | + | 22894.7i | 0.926122 | + | 0.752018i | ||||
\(976\) | −4623.32 | − | 8007.83i | −0.151628 | − | 0.262627i | ||||
\(977\) | −5380.65 | − | 9319.55i | −0.176195 | − | 0.305178i | 0.764379 | − | 0.644767i | \(-0.223045\pi\) |
−0.940574 | + | 0.339589i | \(0.889712\pi\) | |||||||
\(978\) | 62755.5 | − | 23993.0i | 2.05184 | − | 0.784471i | ||||
\(979\) | 28232.6 | − | 48900.3i | 0.921672 | − | 1.59638i | ||||
\(980\) | 2186.43 | 0.0712684 | ||||||||
\(981\) | −11851.8 | − | 56503.5i | −0.385728 | − | 1.83896i | ||||
\(982\) | −55364.0 | −1.79912 | ||||||||
\(983\) | 88.2920 | − | 152.926i | 0.00286478 | − | 0.00496194i | −0.864589 | − | 0.502479i | \(-0.832421\pi\) |
0.867454 | + | 0.497517i | \(0.165755\pi\) | |||||||
\(984\) | −4647.37 | + | 29089.7i | −0.150562 | + | 0.942424i | ||||
\(985\) | 542.374 | + | 939.420i | 0.0175447 | + | 0.0303882i | ||||
\(986\) | −1955.38 | − | 3386.83i | −0.0631563 | − | 0.109390i | ||||
\(987\) | −1757.29 | + | 10999.6i | −0.0566720 | + | 0.354732i | ||||
\(988\) | 3086.87 | − | 5346.61i | 0.0993991 | − | 0.172164i | ||||
\(989\) | −59641.5 | −1.91758 | ||||||||
\(990\) | −17340.0 | − | 5685.60i | −0.556669 | − | 0.182525i | ||||
\(991\) | −60295.8 | −1.93275 | −0.966377 | − | 0.257129i | \(-0.917224\pi\) | ||||
−0.966377 | + | 0.257129i | \(0.917224\pi\) | |||||||
\(992\) | 2602.82 | − | 4508.22i | 0.0833061 | − | 0.144290i | ||||
\(993\) | −33164.9 | + | 12679.8i | −1.05987 | + | 0.405217i | ||||
\(994\) | 13958.0 | + | 24176.0i | 0.445393 | + | 0.771444i | ||||
\(995\) | −149.509 | − | 258.958i | −0.00476358 | − | 0.00825077i | ||||
\(996\) | −4850.05 | − | 3938.28i | −0.154297 | − | 0.125290i | ||||
\(997\) | −8722.95 | + | 15108.6i | −0.277090 | + | 0.479934i | −0.970660 | − | 0.240455i | \(-0.922703\pi\) |
0.693570 | + | 0.720389i | \(0.256037\pi\) | |||||||
\(998\) | −2960.95 | −0.0939151 | ||||||||
\(999\) | 19401.2 | − | 37701.0i | 0.614440 | − | 1.19400i |
(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.f.c.43.8 | yes | 18 | |
3.2 | odd | 2 | 189.4.f.c.127.2 | 18 | |||
9.2 | odd | 6 | 567.4.a.k.1.8 | 9 | |||
9.4 | even | 3 | inner | 63.4.f.c.22.8 | ✓ | 18 | |
9.5 | odd | 6 | 189.4.f.c.64.2 | 18 | |||
9.7 | even | 3 | 567.4.a.j.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.c.22.8 | ✓ | 18 | 9.4 | even | 3 | inner | |
63.4.f.c.43.8 | yes | 18 | 1.1 | even | 1 | trivial | |
189.4.f.c.64.2 | 18 | 9.5 | odd | 6 | |||
189.4.f.c.127.2 | 18 | 3.2 | odd | 2 | |||
567.4.a.j.1.2 | 9 | 9.7 | even | 3 | |||
567.4.a.k.1.8 | 9 | 9.2 | odd | 6 |