Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(26,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.h (of order \(5\), degree \(4\), 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: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 201.2 | ||
Root | \(0.977523 + 0.710212i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.201 |
Dual form | 275.2.h.c.26.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.168506 | + | 0.122427i | −0.119152 | + | 0.0865688i | −0.645765 | − | 0.763536i | \(-0.723462\pi\) |
0.526613 | + | 0.850105i | \(0.323462\pi\) | |||||||
\(3\) | −0.585361 | − | 1.80155i | −0.337958 | − | 1.04013i | −0.965247 | − | 0.261341i | \(-0.915835\pi\) |
0.627288 | − | 0.778787i | \(-0.284165\pi\) | |||||||
\(4\) | −0.604628 | + | 1.86085i | −0.302314 | + | 0.930427i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.319195 | + | 0.231909i | 0.130311 | + | 0.0946765i | ||||
\(7\) | 0.398265 | − | 1.22573i | 0.150530 | − | 0.463284i | −0.847150 | − | 0.531353i | \(-0.821684\pi\) |
0.997681 | + | 0.0680689i | \(0.0216838\pi\) | |||||||
\(8\) | −0.254662 | − | 0.783769i | −0.0900367 | − | 0.277104i | ||||
\(9\) | −0.475901 | + | 0.345762i | −0.158634 | + | 0.115254i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.898964 | − | 3.19247i | 0.271048 | − | 0.962566i | ||||
\(12\) | 3.70635 | 1.06993 | ||||||||
\(13\) | 4.40926 | − | 3.20351i | 1.22291 | − | 0.888494i | 0.226569 | − | 0.973995i | \(-0.427249\pi\) |
0.996338 | + | 0.0855007i | \(0.0272490\pi\) | |||||||
\(14\) | 0.0829527 | + | 0.255302i | 0.0221700 | + | 0.0682324i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.02701 | − | 2.19925i | −0.756752 | − | 0.549812i | ||||
\(17\) | −3.18058 | − | 2.31083i | −0.771404 | − | 0.560458i | 0.130983 | − | 0.991385i | \(-0.458187\pi\) |
−0.902387 | + | 0.430927i | \(0.858187\pi\) | |||||||
\(18\) | 0.0378616 | − | 0.116526i | 0.00892407 | − | 0.0274655i | ||||
\(19\) | 0.693894 | + | 2.13559i | 0.159190 | + | 0.489937i | 0.998561 | − | 0.0536215i | \(-0.0170764\pi\) |
−0.839371 | + | 0.543559i | \(0.817076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.44136 | −0.532748 | ||||||||
\(22\) | 0.239363 | + | 0.648008i | 0.0510324 | + | 0.138156i | ||||
\(23\) | 0.711128 | 0.148280 | 0.0741402 | − | 0.997248i | \(-0.476379\pi\) | ||||
0.0741402 | + | 0.997248i | \(0.476379\pi\) | |||||||
\(24\) | −1.26293 | + | 0.917575i | −0.257795 | + | 0.187299i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.350791 | + | 1.07962i | −0.0687957 | + | 0.211731i | ||||
\(27\) | −3.69600 | − | 2.68530i | −0.711295 | − | 0.516786i | ||||
\(28\) | 2.04011 | + | 1.48223i | 0.385545 | + | 0.280115i | ||||
\(29\) | 1.13043 | − | 3.47910i | 0.209915 | − | 0.646052i | −0.789561 | − | 0.613673i | \(-0.789691\pi\) |
0.999476 | − | 0.0323796i | \(-0.0103085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.22959 | − | 3.79952i | 0.939262 | − | 0.682414i | −0.00898085 | − | 0.999960i | \(-0.502859\pi\) |
0.948243 | + | 0.317546i | \(0.102859\pi\) | |||||||
\(32\) | 2.42752 | 0.429130 | ||||||||
\(33\) | −6.27763 | + | 0.249213i | −1.09279 | + | 0.0433824i | ||||
\(34\) | 0.818854 | 0.140432 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.355670 | − | 1.09464i | −0.0592783 | − | 0.182440i | ||||
\(37\) | −2.55355 | + | 7.85902i | −0.419801 | + | 1.29201i | 0.488085 | + | 0.872796i | \(0.337696\pi\) |
−0.907886 | + | 0.419218i | \(0.862304\pi\) | |||||||
\(38\) | −0.378379 | − | 0.274908i | −0.0613811 | − | 0.0445960i | ||||
\(39\) | −8.35231 | − | 6.06831i | −1.33744 | − | 0.971707i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.90378 | + | 12.0146i | 0.609668 | + | 1.87637i | 0.460789 | + | 0.887510i | \(0.347566\pi\) |
0.148879 | + | 0.988855i | \(0.452434\pi\) | |||||||
\(42\) | 0.411383 | − | 0.298888i | 0.0634779 | − | 0.0461194i | ||||
\(43\) | 1.31169 | 0.200031 | 0.100015 | − | 0.994986i | \(-0.468111\pi\) | ||||
0.100015 | + | 0.994986i | \(0.468111\pi\) | |||||||
\(44\) | 5.39718 | + | 3.60310i | 0.813656 | + | 0.543187i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.119829 | + | 0.0870611i | −0.0176679 | + | 0.0128365i | ||||
\(47\) | −1.39523 | − | 4.29408i | −0.203515 | − | 0.626356i | −0.999771 | − | 0.0213959i | \(-0.993189\pi\) |
0.796256 | − | 0.604960i | \(-0.206811\pi\) | |||||||
\(48\) | −2.19018 | + | 6.74067i | −0.316125 | + | 0.972932i | ||||
\(49\) | 4.31931 | + | 3.13816i | 0.617044 | + | 0.448309i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.30129 | + | 7.08265i | −0.322246 | + | 0.991770i | ||||
\(52\) | 3.29531 | + | 10.1419i | 0.456977 | + | 1.40643i | ||||
\(53\) | −7.86297 | + | 5.71278i | −1.08006 | + | 0.784711i | −0.977694 | − | 0.210035i | \(-0.932642\pi\) |
−0.102369 | + | 0.994747i | \(0.532642\pi\) | |||||||
\(54\) | 0.951551 | 0.129490 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.06212 | −0.141931 | ||||||||
\(57\) | 3.44120 | − | 2.50018i | 0.455798 | − | 0.331157i | ||||
\(58\) | 0.235451 | + | 0.724644i | 0.0309162 | + | 0.0951504i | ||||
\(59\) | 2.75455 | − | 8.47763i | 0.358612 | − | 1.10369i | −0.595274 | − | 0.803523i | \(-0.702956\pi\) |
0.953886 | − | 0.300171i | \(-0.0970436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.48965 | + | 1.08229i | 0.190730 | + | 0.138574i | 0.679052 | − | 0.734090i | \(-0.262391\pi\) |
−0.488322 | + | 0.872663i | \(0.662391\pi\) | |||||||
\(62\) | −0.416055 | + | 1.28048i | −0.0528390 | + | 0.162622i | ||||
\(63\) | 0.234278 | + | 0.721033i | 0.0295162 | + | 0.0908417i | ||||
\(64\) | 5.64496 | − | 4.10130i | 0.705620 | − | 0.512663i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.02731 | − | 0.810544i | 0.126453 | − | 0.0997711i | ||||
\(67\) | 4.30232 | 0.525612 | 0.262806 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262806 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(68\) | 6.22318 | − | 4.52140i | 0.754671 | − | 0.548301i | ||||
\(69\) | −0.416266 | − | 1.28114i | −0.0501126 | − | 0.154231i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.21746 | − | 5.97033i | −0.975233 | − | 0.708548i | −0.0185947 | − | 0.999827i | \(-0.505919\pi\) |
−0.956638 | + | 0.291279i | \(0.905919\pi\) | |||||||
\(72\) | 0.392192 | + | 0.284944i | 0.0462202 | + | 0.0335810i | ||||
\(73\) | −3.70969 | + | 11.4173i | −0.434187 | + | 1.33629i | 0.459731 | + | 0.888058i | \(0.347946\pi\) |
−0.893917 | + | 0.448232i | \(0.852054\pi\) | |||||||
\(74\) | −0.531866 | − | 1.63692i | −0.0618282 | − | 0.190288i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.39356 | −0.503976 | ||||||||
\(77\) | −3.55509 | − | 2.37334i | −0.405141 | − | 0.270467i | ||||
\(78\) | 2.15034 | 0.243478 | ||||||||
\(79\) | −10.3649 | + | 7.53052i | −1.16614 | + | 0.847249i | −0.990542 | − | 0.137213i | \(-0.956186\pi\) |
−0.175597 | + | 0.984462i | \(0.556186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.21956 | + | 9.90878i | −0.357729 | + | 1.10098i | ||||
\(82\) | −2.12872 | − | 1.54661i | −0.235078 | − | 0.170794i | ||||
\(83\) | 10.1477 | + | 7.37274i | 1.11386 | + | 0.809263i | 0.983266 | − | 0.182174i | \(-0.0583133\pi\) |
0.130589 | + | 0.991437i | \(0.458313\pi\) | |||||||
\(84\) | 1.47611 | − | 4.54301i | 0.161057 | − | 0.495683i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.221028 | + | 0.160586i | −0.0238340 | + | 0.0173164i | ||||
\(87\) | −6.92949 | −0.742920 | ||||||||
\(88\) | −2.73109 | + | 0.108421i | −0.291135 | + | 0.0115577i | ||||
\(89\) | −6.28392 | −0.666095 | −0.333047 | − | 0.942910i | \(-0.608077\pi\) | ||||
−0.333047 | + | 0.942910i | \(0.608077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.17060 | − | 6.68043i | −0.227541 | − | 0.700299i | ||||
\(92\) | −0.429968 | + | 1.32330i | −0.0448272 | + | 0.137964i | ||||
\(93\) | −9.90624 | − | 7.19730i | −1.02723 | − | 0.746326i | ||||
\(94\) | 0.760816 | + | 0.552765i | 0.0784722 | + | 0.0570134i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.42098 | − | 4.37332i | −0.145028 | − | 0.446350i | ||||
\(97\) | −0.245459 | + | 0.178336i | −0.0249226 | + | 0.0181073i | −0.600177 | − | 0.799867i | \(-0.704903\pi\) |
0.575254 | + | 0.817975i | \(0.304903\pi\) | |||||||
\(98\) | −1.11202 | −0.112331 | ||||||||
\(99\) | 0.676018 | + | 1.83013i | 0.0679423 | + | 0.183935i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.99821 | − | 3.63141i | 0.497340 | − | 0.361339i | −0.310660 | − | 0.950521i | \(-0.600550\pi\) |
0.808000 | + | 0.589182i | \(0.200550\pi\) | |||||||
\(102\) | −0.479325 | − | 1.47521i | −0.0474602 | − | 0.146068i | ||||
\(103\) | −2.46558 | + | 7.58828i | −0.242941 | + | 0.747695i | 0.753027 | + | 0.657989i | \(0.228593\pi\) |
−0.995968 | + | 0.0897061i | \(0.971407\pi\) | |||||||
\(104\) | −3.63369 | − | 2.64003i | −0.356312 | − | 0.258876i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.625561 | − | 1.92528i | 0.0607598 | − | 0.187000i | ||||
\(107\) | −3.10415 | − | 9.55358i | −0.300089 | − | 0.923580i | −0.981464 | − | 0.191645i | \(-0.938618\pi\) |
0.681375 | − | 0.731934i | \(-0.261382\pi\) | |||||||
\(108\) | 7.23165 | − | 5.25410i | 0.695866 | − | 0.505576i | ||||
\(109\) | 7.63832 | 0.731619 | 0.365809 | − | 0.930690i | \(-0.380792\pi\) | ||||
0.365809 | + | 0.930690i | \(0.380792\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.6532 | 1.48574 | ||||||||
\(112\) | −3.90125 | + | 2.83442i | −0.368633 | + | 0.267828i | ||||
\(113\) | −6.05767 | − | 18.6436i | −0.569858 | − | 1.75384i | −0.653057 | − | 0.757309i | \(-0.726514\pi\) |
0.0831991 | − | 0.996533i | \(-0.473486\pi\) | |||||||
\(114\) | −0.273774 | + | 0.842590i | −0.0256413 | + | 0.0789158i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.79060 | + | 4.20712i | 0.537644 | + | 0.390621i | ||||
\(117\) | −0.990715 | + | 3.04911i | −0.0915916 | + | 0.281890i | ||||
\(118\) | 0.573731 | + | 1.76576i | 0.0528162 | + | 0.162552i | ||||
\(119\) | −4.09918 | + | 2.97823i | −0.375771 | + | 0.273013i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.38373 | − | 5.73983i | −0.853066 | − | 0.521803i | ||||
\(122\) | −0.383517 | −0.0347220 | ||||||||
\(123\) | 19.3598 | − | 14.0657i | 1.74562 | − | 1.26827i | ||||
\(124\) | 3.90839 | + | 12.0288i | 0.350984 | + | 1.08022i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.127751 | − | 0.0928166i | −0.0113810 | − | 0.00826876i | ||||
\(127\) | 13.8869 | + | 10.0894i | 1.23226 | + | 0.895293i | 0.997058 | − | 0.0766526i | \(-0.0244232\pi\) |
0.235207 | + | 0.971945i | \(0.424423\pi\) | |||||||
\(128\) | −1.94939 | + | 5.99961i | −0.172304 | + | 0.530296i | ||||
\(129\) | −0.767812 | − | 2.36308i | −0.0676020 | − | 0.208058i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0223 | 0.875655 | 0.437828 | − | 0.899059i | \(-0.355748\pi\) | ||||
0.437828 | + | 0.899059i | \(0.355748\pi\) | |||||||
\(132\) | 3.33188 | − | 11.8324i | 0.290003 | − | 1.02988i | ||||
\(133\) | 2.89402 | 0.250943 | ||||||||
\(134\) | −0.724967 | + | 0.526720i | −0.0626276 | + | 0.0455016i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00118 | + | 3.08132i | −0.0858506 | + | 0.264221i | ||||
\(137\) | 2.85366 | + | 2.07331i | 0.243805 | + | 0.177134i | 0.702977 | − | 0.711213i | \(-0.251854\pi\) |
−0.459172 | + | 0.888347i | \(0.651854\pi\) | |||||||
\(138\) | 0.226989 | + | 0.164917i | 0.0193226 | + | 0.0140387i | ||||
\(139\) | −2.71237 | + | 8.34781i | −0.230060 | + | 0.708052i | 0.767679 | + | 0.640835i | \(0.221412\pi\) |
−0.997738 | + | 0.0672164i | \(0.978588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.91931 | + | 5.02717i | −0.582711 | + | 0.423364i | ||||
\(142\) | 2.11562 | 0.177539 | ||||||||
\(143\) | −6.26335 | − | 16.9563i | −0.523768 | − | 1.41795i | ||||
\(144\) | 2.20097 | 0.183414 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.772674 | − | 2.37805i | −0.0639469 | − | 0.196808i | ||||
\(147\) | 3.12522 | − | 9.61843i | 0.257763 | − | 0.793314i | ||||
\(148\) | −13.0805 | − | 9.50356i | −1.07521 | − | 0.781188i | ||||
\(149\) | 6.79312 | + | 4.93549i | 0.556514 | + | 0.404331i | 0.830181 | − | 0.557493i | \(-0.188237\pi\) |
−0.273667 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.63804 | − | 8.11906i | −0.214681 | − | 0.660720i | −0.999176 | − | 0.0405849i | \(-0.987078\pi\) |
0.784495 | − | 0.620135i | \(-0.212922\pi\) | |||||||
\(152\) | 1.49710 | − | 1.08771i | 0.121431 | − | 0.0882247i | ||||
\(153\) | 2.31264 | 0.186966 | ||||||||
\(154\) | 0.889616 | − | 0.0353165i | 0.0716873 | − | 0.00284588i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.3423 | − | 11.8734i | 1.30843 | − | 0.950629i | ||||
\(157\) | 3.90892 | + | 12.0304i | 0.311966 | + | 0.960131i | 0.976986 | + | 0.213306i | \(0.0684230\pi\) |
−0.665020 | + | 0.746826i | \(0.731577\pi\) | |||||||
\(158\) | 0.824606 | − | 2.53788i | 0.0656021 | − | 0.201903i | ||||
\(159\) | 14.8946 | + | 10.8215i | 1.18122 | + | 0.858204i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.283218 | − | 0.871654i | 0.0223207 | − | 0.0686960i | ||||
\(162\) | −0.670585 | − | 2.06385i | −0.0526862 | − | 0.162151i | ||||
\(163\) | 6.80311 | − | 4.94275i | 0.532860 | − | 0.387146i | −0.288566 | − | 0.957460i | \(-0.593179\pi\) |
0.821427 | + | 0.570314i | \(0.193179\pi\) | |||||||
\(164\) | −24.7177 | −1.93013 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.61257 | −0.202775 | ||||||||
\(167\) | 15.4725 | − | 11.2414i | 1.19730 | − | 0.869888i | 0.203281 | − | 0.979120i | \(-0.434839\pi\) |
0.994016 | + | 0.109233i | \(0.0348394\pi\) | |||||||
\(168\) | 0.621721 | + | 1.91346i | 0.0479668 | + | 0.147627i | ||||
\(169\) | 5.16183 | − | 15.8865i | 0.397064 | − | 1.22204i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.06863 | − | 0.776405i | −0.0817202 | − | 0.0593732i | ||||
\(172\) | −0.793085 | + | 2.44086i | −0.0604721 | + | 0.186114i | ||||
\(173\) | 3.78197 | + | 11.6397i | 0.287538 | + | 0.884950i | 0.985626 | + | 0.168939i | \(0.0540341\pi\) |
−0.698089 | + | 0.716011i | \(0.745966\pi\) | |||||||
\(174\) | 1.16766 | − | 0.848356i | 0.0885202 | − | 0.0643137i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.74221 | + | 7.68658i | −0.734347 | + | 0.579398i | ||||
\(177\) | −16.8853 | −1.26918 | ||||||||
\(178\) | 1.05888 | − | 0.769321i | 0.0793664 | − | 0.0576630i | ||||
\(179\) | 0.988945 | + | 3.04366i | 0.0739172 | + | 0.227494i | 0.981189 | − | 0.193052i | \(-0.0618386\pi\) |
−0.907271 | + | 0.420546i | \(0.861839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75310 | − | 1.27370i | −0.130307 | − | 0.0946734i | 0.520723 | − | 0.853726i | \(-0.325663\pi\) |
−0.651029 | + | 0.759053i | \(0.725663\pi\) | |||||||
\(182\) | 1.18362 | + | 0.859952i | 0.0877360 | + | 0.0637439i | ||||
\(183\) | 1.07783 | − | 3.31722i | 0.0796754 | − | 0.245216i | ||||
\(184\) | −0.181097 | − | 0.557360i | −0.0133507 | − | 0.0410891i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.55040 | 0.187005 | ||||||||
\(187\) | −10.2365 | + | 8.07655i | −0.748565 | + | 0.590616i | ||||
\(188\) | 8.83425 | 0.644304 | ||||||||
\(189\) | −4.76345 | + | 3.46085i | −0.346490 | + | 0.251740i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.544810 | − | 1.67675i | 0.0394211 | − | 0.121326i | −0.929409 | − | 0.369051i | \(-0.879683\pi\) |
0.968830 | + | 0.247725i | \(0.0796829\pi\) | |||||||
\(192\) | −10.6931 | − | 7.76896i | −0.771705 | − | 0.560677i | ||||
\(193\) | 12.4647 | + | 9.05616i | 0.897231 | + | 0.651877i | 0.937753 | − | 0.347302i | \(-0.112902\pi\) |
−0.0405221 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(194\) | 0.0195282 | − | 0.0601015i | 0.00140204 | − | 0.00431503i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.45123 | + | 6.14018i | −0.603660 | + | 0.438584i | ||||
\(197\) | −1.78727 | −0.127338 | −0.0636689 | − | 0.997971i | \(-0.520280\pi\) | ||||
−0.0636689 | + | 0.997971i | \(0.520280\pi\) | |||||||
\(198\) | −0.337970 | − | 0.225625i | −0.0240185 | − | 0.0160345i | ||||
\(199\) | −19.6066 | −1.38988 | −0.694938 | − | 0.719070i | \(-0.744568\pi\) | ||||
−0.694938 | + | 0.719070i | \(0.744568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.51841 | − | 7.75087i | −0.177635 | − | 0.546704i | ||||
\(202\) | −0.397646 | + | 1.22383i | −0.0279783 | + | 0.0861083i | ||||
\(203\) | −3.81424 | − | 2.77121i | −0.267707 | − | 0.194501i | ||||
\(204\) | −11.7884 | − | 8.56474i | −0.825350 | − | 0.599652i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.513544 | − | 1.58052i | −0.0357803 | − | 0.110120i | ||||
\(207\) | −0.338426 | + | 0.245881i | −0.0235223 | + | 0.0170899i | ||||
\(208\) | −20.3922 | −1.41394 | ||||||||
\(209\) | 7.44159 | − | 0.295420i | 0.514745 | − | 0.0204347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5246 | − | 9.82620i | 0.931072 | − | 0.676464i | −0.0151828 | − | 0.999885i | \(-0.504833\pi\) |
0.946255 | + | 0.323421i | \(0.104833\pi\) | |||||||
\(212\) | −5.87648 | − | 18.0860i | −0.403598 | − | 1.24215i | ||||
\(213\) | −5.94570 | + | 18.2990i | −0.407393 | + | 1.25383i | ||||
\(214\) | 1.69268 | + | 1.22981i | 0.115709 | + | 0.0840678i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.16343 | + | 3.58065i | −0.0791611 | + | 0.243633i | ||||
\(217\) | −2.57444 | − | 7.92331i | −0.174764 | − | 0.537869i | ||||
\(218\) | −1.28710 | + | 0.935136i | −0.0871737 | + | 0.0633354i | ||||
\(219\) | 22.7403 | 1.53665 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.4267 | −1.44132 | ||||||||
\(222\) | −2.63766 | + | 1.91637i | −0.177028 | + | 0.128618i | ||||
\(223\) | 1.84839 | + | 5.68876i | 0.123777 | + | 0.380947i | 0.993676 | − | 0.112283i | \(-0.0358162\pi\) |
−0.869899 | + | 0.493230i | \(0.835816\pi\) | |||||||
\(224\) | 0.966799 | − | 2.97550i | 0.0645970 | − | 0.198809i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.30323 | + | 2.39994i | 0.219728 | + | 0.159641i | ||||
\(227\) | −6.87537 | + | 21.1602i | −0.456334 | + | 1.40445i | 0.413227 | + | 0.910628i | \(0.364401\pi\) |
−0.869562 | + | 0.493825i | \(0.835599\pi\) | |||||||
\(228\) | 2.57182 | + | 7.91525i | 0.170323 | + | 0.524200i | ||||
\(229\) | −4.83195 | + | 3.51062i | −0.319305 | + | 0.231988i | −0.735879 | − | 0.677113i | \(-0.763231\pi\) |
0.416574 | + | 0.909102i | \(0.363231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.19469 | + | 7.79396i | −0.144400 | + | 0.512805i | ||||
\(232\) | −3.01469 | −0.197924 | ||||||||
\(233\) | −14.3479 | + | 10.4243i | −0.939960 | + | 0.682921i | −0.948411 | − | 0.317044i | \(-0.897310\pi\) |
0.00845137 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(234\) | −0.206351 | − | 0.635083i | −0.0134896 | − | 0.0415167i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.1102 | + | 10.2516i | 0.918493 | + | 0.667324i | ||||
\(237\) | 19.6338 | + | 14.2648i | 1.27535 | + | 0.926599i | ||||
\(238\) | 0.326121 | − | 1.00370i | 0.0211393 | − | 0.0650601i | ||||
\(239\) | −5.90708 | − | 18.1801i | −0.382097 | − | 1.17597i | −0.938564 | − | 0.345104i | \(-0.887844\pi\) |
0.556467 | − | 0.830870i | \(-0.312156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.79437 | −0.115586 | −0.0577929 | − | 0.998329i | \(-0.518406\pi\) | ||||
−0.0577929 | + | 0.998329i | \(0.518406\pi\) | |||||||
\(242\) | 2.28392 | − | 0.181623i | 0.146816 | − | 0.0116752i | ||||
\(243\) | 6.03029 | 0.386843 | ||||||||
\(244\) | −2.91468 | + | 2.11764i | −0.186593 | + | 0.135568i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.54023 | + | 4.74033i | −0.0982012 | + | 0.302232i | ||||
\(247\) | 9.90094 | + | 7.19345i | 0.629982 | + | 0.457708i | ||||
\(248\) | −4.30973 | − | 3.13120i | −0.273668 | − | 0.198831i | ||||
\(249\) | 7.34232 | − | 22.5973i | 0.465301 | − | 1.43205i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.55143 | + | 6.21298i | −0.539761 | + | 0.392160i | −0.823996 | − | 0.566595i | \(-0.808260\pi\) |
0.284235 | + | 0.958755i | \(0.408260\pi\) | |||||||
\(252\) | −1.48339 | −0.0934447 | ||||||||
\(253\) | 0.639278 | − | 2.27025i | 0.0401911 | − | 0.142730i | ||||
\(254\) | −3.57525 | −0.224331 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.90634 | + | 12.0225i | 0.244146 | + | 0.751404i | ||||
\(257\) | 1.39033 | − | 4.27900i | 0.0867265 | − | 0.266917i | −0.898283 | − | 0.439418i | \(-0.855185\pi\) |
0.985009 | + | 0.172501i | \(0.0551848\pi\) | |||||||
\(258\) | 0.418686 | + | 0.304193i | 0.0260662 | + | 0.0189382i | ||||
\(259\) | 8.61608 | + | 6.25995i | 0.535377 | + | 0.388974i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.664969 | + | 2.04656i | 0.0411606 | + | 0.126679i | ||||
\(262\) | −1.68882 | + | 1.22700i | −0.104336 | + | 0.0758045i | ||||
\(263\) | 8.87966 | 0.547543 | 0.273772 | − | 0.961795i | \(-0.411729\pi\) | ||||
0.273772 | + | 0.961795i | \(0.411729\pi\) | |||||||
\(264\) | 1.79400 | + | 4.85675i | 0.110413 | + | 0.298912i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.487660 | + | 0.354305i | −0.0299003 | + | 0.0217239i | ||||
\(267\) | 3.67836 | + | 11.3208i | 0.225112 | + | 0.692824i | ||||
\(268\) | −2.60130 | + | 8.00599i | −0.158900 | + | 0.489044i | ||||
\(269\) | 13.5968 | + | 9.87862i | 0.829009 | + | 0.602310i | 0.919279 | − | 0.393607i | \(-0.128773\pi\) |
−0.0902701 | + | 0.995917i | \(0.528773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.18182 | + | 12.8703i | −0.254028 | + | 0.781817i | 0.739992 | + | 0.672616i | \(0.234829\pi\) |
−0.994020 | + | 0.109201i | \(0.965171\pi\) | |||||||
\(272\) | 4.54555 | + | 13.9898i | 0.275615 | + | 0.848255i | ||||
\(273\) | −10.7646 | + | 7.82092i | −0.651501 | + | 0.473343i | ||||
\(274\) | −0.734688 | −0.0443841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.63569 | 0.158650 | ||||||||
\(277\) | 16.5592 | − | 12.0310i | 0.994946 | − | 0.722870i | 0.0339471 | − | 0.999424i | \(-0.489192\pi\) |
0.960999 | + | 0.276553i | \(0.0891922\pi\) | |||||||
\(278\) | −0.564945 | − | 1.73872i | −0.0338832 | − | 0.104282i | ||||
\(279\) | −1.17504 | + | 3.61639i | −0.0703476 | + | 0.216508i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.09848 | + | 5.88389i | 0.483115 | + | 0.351004i | 0.802530 | − | 0.596611i | \(-0.203487\pi\) |
−0.319415 | + | 0.947615i | \(0.603487\pi\) | |||||||
\(282\) | 0.550485 | − | 1.69422i | 0.0327809 | − | 0.100889i | ||||
\(283\) | 0.827516 | + | 2.54683i | 0.0491907 | + | 0.151394i | 0.972635 | − | 0.232340i | \(-0.0746382\pi\) |
−0.923444 | + | 0.383733i | \(0.874638\pi\) | |||||||
\(284\) | 16.0784 | − | 11.6817i | 0.954079 | − | 0.693179i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.13131 | + | 2.09043i | 0.185158 | + | 0.123610i | ||||
\(287\) | 16.2815 | 0.961064 | ||||||||
\(288\) | −1.15526 | + | 0.839346i | −0.0680744 | + | 0.0494589i | ||||
\(289\) | −0.477120 | − | 1.46843i | −0.0280659 | − | 0.0863780i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.464964 | + | 0.337816i | 0.0272567 | + | 0.0198031i | ||||
\(292\) | −19.0029 | − | 13.8064i | −1.11206 | − | 0.807958i | ||||
\(293\) | −7.81514 | + | 24.0525i | −0.456565 | + | 1.40516i | 0.412723 | + | 0.910857i | \(0.364578\pi\) |
−0.869288 | + | 0.494306i | \(0.835422\pi\) | |||||||
\(294\) | 0.650936 | + | 2.00337i | 0.0379633 | + | 0.116839i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.80995 | 0.395820 | ||||||||
\(297\) | −11.8953 | + | 9.38538i | −0.690236 | + | 0.544595i | ||||
\(298\) | −1.74892 | −0.101312 | ||||||||
\(299\) | 3.13554 | − | 2.27811i | 0.181333 | − | 0.131746i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.522401 | − | 1.60778i | 0.0301107 | − | 0.0926711i | ||||
\(302\) | 1.43852 | + | 1.04514i | 0.0827774 | + | 0.0601413i | ||||
\(303\) | −9.46794 | − | 6.87886i | −0.543919 | − | 0.395180i | ||||
\(304\) | 2.59627 | − | 7.99049i | 0.148906 | − | 0.458286i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.389693 | + | 0.283129i | −0.0222773 | + | 0.0161854i | ||||
\(307\) | 8.53224 | 0.486960 | 0.243480 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243480 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(308\) | 6.56595 | − | 5.18052i | 0.374130 | − | 0.295188i | ||||
\(309\) | 15.1140 | 0.859803 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.341159 | − | 1.04998i | −0.0193454 | − | 0.0595389i | 0.940918 | − | 0.338635i | \(-0.109965\pi\) |
−0.960263 | + | 0.279096i | \(0.909965\pi\) | |||||||
\(312\) | −2.62914 | + | 8.09165i | −0.148846 | + | 0.458099i | ||||
\(313\) | 4.52358 | + | 3.28657i | 0.255688 | + | 0.185768i | 0.708244 | − | 0.705968i | \(-0.249488\pi\) |
−0.452556 | + | 0.891736i | \(0.649488\pi\) | |||||||
\(314\) | −2.13152 | − | 1.54864i | −0.120289 | − | 0.0873949i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.74630 | − | 23.8407i | −0.435764 | − | 1.34114i | ||||
\(317\) | −22.9349 | + | 16.6632i | −1.28815 | + | 0.935897i | −0.999766 | − | 0.0216175i | \(-0.993118\pi\) |
−0.288385 | + | 0.957514i | \(0.593118\pi\) | |||||||
\(318\) | −3.83467 | −0.215038 | ||||||||
\(319\) | −10.0907 | − | 6.73644i | −0.564971 | − | 0.377168i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.3943 | + | 11.1846i | −0.859223 | + | 0.624262i | ||||
\(322\) | 0.0589900 | + | 0.181552i | 0.00328738 | + | 0.0101175i | ||||
\(323\) | 2.72799 | − | 8.39588i | 0.151789 | − | 0.467159i | ||||
\(324\) | −16.4921 | − | 11.9822i | −0.916231 | − | 0.665680i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.541240 | + | 1.66577i | −0.0299765 | + | 0.0922582i | ||||
\(327\) | −4.47117 | − | 13.7609i | −0.247256 | − | 0.760977i | ||||
\(328\) | 8.42253 | − | 6.11933i | 0.465056 | − | 0.337883i | ||||
\(329\) | −5.81908 | −0.320816 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6052 | 1.02263 | 0.511317 | − | 0.859392i | \(-0.329158\pi\) | ||||
0.511317 | + | 0.859392i | \(0.329158\pi\) | |||||||
\(332\) | −19.8552 | + | 14.4256i | −1.08969 | + | 0.791709i | ||||
\(333\) | −1.50211 | − | 4.62303i | −0.0823154 | − | 0.253341i | ||||
\(334\) | −1.23096 | + | 3.78850i | −0.0673550 | + | 0.207297i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.39000 | + | 5.36915i | 0.403158 | + | 0.292911i | ||||
\(337\) | 9.10777 | − | 28.0308i | 0.496132 | − | 1.52694i | −0.319054 | − | 0.947737i | \(-0.603365\pi\) |
0.815186 | − | 0.579200i | \(-0.196635\pi\) | |||||||
\(338\) | 1.07513 | + | 3.30891i | 0.0584794 | + | 0.179981i | ||||
\(339\) | −30.0415 | + | 21.8264i | −1.63163 | + | 1.18545i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.42864 | − | 20.1109i | −0.402283 | − | 1.08907i | ||||
\(342\) | 0.275124 | 0.0148770 | ||||||||
\(343\) | 12.8655 | − | 9.34733i | 0.694671 | − | 0.504708i | ||||
\(344\) | −0.334038 | − | 1.02806i | −0.0180101 | − | 0.0554294i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.06230 | − | 1.49835i | −0.110870 | − | 0.0805516i | ||||
\(347\) | −14.3171 | − | 10.4020i | −0.768583 | − | 0.558408i | 0.132948 | − | 0.991123i | \(-0.457556\pi\) |
−0.901531 | + | 0.432715i | \(0.857556\pi\) | |||||||
\(348\) | 4.18977 | − | 12.8948i | 0.224595 | − | 0.691232i | ||||
\(349\) | 0.483116 | + | 1.48688i | 0.0258606 | + | 0.0795908i | 0.963154 | − | 0.268951i | \(-0.0866770\pi\) |
−0.937293 | + | 0.348542i | \(0.886677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.8990 | −1.32901 | ||||||||
\(352\) | 2.18226 | − | 7.74980i | 0.116315 | − | 0.413066i | ||||
\(353\) | −1.66213 | −0.0884663 | −0.0442331 | − | 0.999021i | \(-0.514084\pi\) | ||||
−0.0442331 | + | 0.999021i | \(0.514084\pi\) | |||||||
\(354\) | 2.84528 | − | 2.06722i | 0.151225 | − | 0.109871i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.79944 | − | 11.6935i | 0.201370 | − | 0.619752i | ||||
\(357\) | 7.76493 | + | 5.64155i | 0.410964 | + | 0.298583i | ||||
\(358\) | −0.539269 | − | 0.391802i | −0.0285012 | − | 0.0207074i | ||||
\(359\) | −9.64641 | + | 29.6886i | −0.509118 | + | 1.56690i | 0.284617 | + | 0.958641i | \(0.408134\pi\) |
−0.793735 | + | 0.608263i | \(0.791866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2921 | − | 8.20418i | 0.594320 | − | 0.431799i | ||||
\(362\) | 0.451343 | 0.0237220 | ||||||||
\(363\) | −4.84776 | + | 20.2652i | −0.254441 | + | 1.06365i | ||||
\(364\) | 13.7437 | 0.720366 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.224496 | + | 0.690927i | 0.0117346 | + | 0.0361153i | ||||
\(367\) | −2.88261 | + | 8.87177i | −0.150471 | + | 0.463103i | −0.997674 | − | 0.0681670i | \(-0.978285\pi\) |
0.847203 | + | 0.531270i | \(0.178285\pi\) | |||||||
\(368\) | −2.15259 | − | 1.56395i | −0.112211 | − | 0.0815264i | ||||
\(369\) | −6.01201 | − | 4.36798i | −0.312973 | − | 0.227388i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87081 | + | 11.9131i | 0.200962 | + | 0.618499i | ||||
\(372\) | 19.3827 | − | 14.0824i | 1.00495 | − | 0.730137i | ||||
\(373\) | 9.77497 | 0.506129 | 0.253064 | − | 0.967449i | \(-0.418562\pi\) | ||||
0.253064 | + | 0.967449i | \(0.418562\pi\) | |||||||
\(374\) | 0.736121 | − | 2.61417i | 0.0380639 | − | 0.135175i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.01026 | + | 2.18708i | −0.155242 | + | 0.112790i | ||||
\(377\) | −6.16099 | − | 18.9616i | −0.317307 | − | 0.976571i | ||||
\(378\) | 0.378970 | − | 1.16635i | 0.0194921 | − | 0.0599905i | ||||
\(379\) | −10.8852 | − | 7.90855i | −0.559135 | − | 0.406235i | 0.272007 | − | 0.962295i | \(-0.412312\pi\) |
−0.831142 | + | 0.556060i | \(0.812312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0478 | − | 30.9240i | 0.514765 | − | 1.58428i | ||||
\(382\) | 0.113476 | + | 0.349242i | 0.00580592 | + | 0.0178688i | ||||
\(383\) | 3.16673 | − | 2.30076i | 0.161812 | − | 0.117563i | −0.503933 | − | 0.863743i | \(-0.668114\pi\) |
0.665745 | + | 0.746180i | \(0.268114\pi\) | |||||||
\(384\) | 11.9497 | 0.609807 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.20910 | −0.163339 | ||||||||
\(387\) | −0.624234 | + | 0.453533i | −0.0317316 | + | 0.0230544i | ||||
\(388\) | −0.183446 | − | 0.564590i | −0.00931308 | − | 0.0286627i | ||||
\(389\) | −4.11854 | + | 12.6755i | −0.208818 | + | 0.642676i | 0.790717 | + | 0.612182i | \(0.209708\pi\) |
−0.999535 | + | 0.0304938i | \(0.990292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.26180 | − | 1.64329i | −0.114384 | − | 0.0831049i | ||||
\(392\) | 1.35963 | − | 4.18451i | 0.0686717 | − | 0.211350i | ||||
\(393\) | −5.86668 | − | 18.0558i | −0.295935 | − | 0.910794i | ||||
\(394\) | 0.301166 | − | 0.218810i | 0.0151725 | − | 0.0110235i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.81434 | + | 0.151424i | −0.191678 | + | 0.00760933i | ||||
\(397\) | −8.80209 | −0.441764 | −0.220882 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220882 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(398\) | 3.30383 | − | 2.40038i | 0.165606 | − | 0.120320i | ||||
\(399\) | −1.69404 | − | 5.21373i | −0.0848083 | − | 0.261013i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2728 | − | 9.64323i | −0.662810 | − | 0.481560i | 0.204801 | − | 0.978804i | \(-0.434345\pi\) |
−0.867611 | + | 0.497244i | \(0.834345\pi\) | |||||||
\(402\) | 1.37328 | + | 0.997747i | 0.0684931 | + | 0.0497631i | ||||
\(403\) | 10.8868 | − | 33.5061i | 0.542310 | − | 1.66906i | ||||
\(404\) | 3.73547 | + | 11.4966i | 0.185846 | + | 0.571976i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.981993 | 0.0487355 | ||||||||
\(407\) | 22.7941 | + | 15.2171i | 1.12986 | + | 0.754284i | ||||
\(408\) | 6.13722 | 0.303838 | ||||||||
\(409\) | 9.55575 | − | 6.94266i | 0.472501 | − | 0.343292i | −0.325914 | − | 0.945399i | \(-0.605672\pi\) |
0.798415 | + | 0.602107i | \(0.205672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.06475 | − | 6.35466i | 0.101847 | − | 0.313452i | ||||
\(412\) | −12.6299 | − | 9.17617i | −0.622231 | − | 0.452078i | ||||
\(413\) | −9.29429 | − | 6.75269i | −0.457342 | − | 0.332278i | ||||
\(414\) | 0.0269244 | − | 0.0828649i | 0.00132326 | − | 0.00407259i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.7036 | − | 7.77660i | 0.524786 | − | 0.381279i | ||||
\(417\) | 16.6267 | 0.814215 | ||||||||
\(418\) | −1.21778 | + | 0.960830i | −0.0595638 | + | 0.0469957i | ||||
\(419\) | 26.3901 | 1.28924 | 0.644620 | − | 0.764503i | \(-0.277015\pi\) | ||||
0.644620 | + | 0.764503i | \(0.277015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.51334 | + | 10.8130i | 0.171230 | + | 0.526991i | 0.999441 | − | 0.0334246i | \(-0.0106414\pi\) |
−0.828211 | + | 0.560416i | \(0.810641\pi\) | |||||||
\(422\) | −1.07599 | + | 3.31155i | −0.0523783 | + | 0.161204i | ||||
\(423\) | 2.14872 | + | 1.56114i | 0.104474 | + | 0.0759052i | ||||
\(424\) | 6.47991 | + | 4.70793i | 0.314692 | + | 0.228637i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.23840 | − | 3.81141i | −0.0600007 | − | 0.184663i | ||||
\(427\) | 1.91988 | − | 1.39488i | 0.0929096 | − | 0.0675028i | ||||
\(428\) | 19.6547 | 0.950044 | ||||||||
\(429\) | −26.8813 | + | 21.2093i | −1.29784 | + | 1.02399i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5688 | + | 10.5849i | −0.701756 | + | 0.509856i | −0.880504 | − | 0.474039i | \(-0.842795\pi\) |
0.178747 | + | 0.983895i | \(0.442795\pi\) | |||||||
\(432\) | 5.28217 | + | 16.2568i | 0.254138 | + | 0.782158i | ||||
\(433\) | 11.8233 | − | 36.3883i | 0.568191 | − | 1.74871i | −0.0900851 | − | 0.995934i | \(-0.528714\pi\) |
0.658276 | − | 0.752777i | \(-0.271286\pi\) | |||||||
\(434\) | 1.40383 | + | 1.01995i | 0.0673862 | + | 0.0489589i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.61834 | + | 14.2138i | −0.221179 | + | 0.680718i | ||||
\(437\) | 0.493448 | + | 1.51868i | 0.0236048 | + | 0.0726481i | ||||
\(438\) | −3.83189 | + | 2.78403i | −0.183095 | + | 0.133026i | ||||
\(439\) | −8.67958 | −0.414254 | −0.207127 | − | 0.978314i | \(-0.566411\pi\) | ||||
−0.207127 | + | 0.978314i | \(0.566411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.14062 | −0.149553 | ||||||||
\(442\) | 3.61054 | − | 2.62321i | 0.171736 | − | 0.124773i | ||||
\(443\) | 4.13947 | + | 12.7400i | 0.196672 | + | 0.605295i | 0.999953 | + | 0.00969443i | \(0.00308588\pi\) |
−0.803281 | + | 0.595601i | \(0.796914\pi\) | |||||||
\(444\) | −9.46436 | + | 29.1283i | −0.449159 | + | 1.38237i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.00792 | − | 0.732298i | −0.0477264 | − | 0.0346753i | ||||
\(447\) | 4.91513 | − | 15.1272i | 0.232478 | − | 0.715493i | ||||
\(448\) | −2.77892 | − | 8.55263i | −0.131292 | − | 0.404074i | ||||
\(449\) | 15.8011 | − | 11.4802i | 0.745700 | − | 0.541783i | −0.148791 | − | 0.988869i | \(-0.547538\pi\) |
0.894491 | + | 0.447086i | \(0.147538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.8656 | − | 1.66201i | 1.97137 | − | 0.0782608i | ||||
\(452\) | 38.3556 | 1.80410 | ||||||||
\(453\) | −13.0827 | + | 9.50515i | −0.614680 | + | 0.446591i | ||||
\(454\) | −1.43204 | − | 4.40735i | −0.0672088 | − | 0.206847i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.83591 | − | 2.06041i | −0.132803 | − | 0.0964874i | ||||
\(457\) | −20.8569 | − | 15.1535i | −0.975647 | − | 0.708849i | −0.0189151 | − | 0.999821i | \(-0.506021\pi\) |
−0.956731 | + | 0.290972i | \(0.906021\pi\) | |||||||
\(458\) | 0.384420 | − | 1.18312i | 0.0179627 | − | 0.0552836i | ||||
\(459\) | 5.55016 | + | 17.0816i | 0.259059 | + | 0.797302i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0542 | 0.887441 | 0.443720 | − | 0.896165i | \(-0.353658\pi\) | ||||
0.443720 | + | 0.896165i | \(0.353658\pi\) | |||||||
\(462\) | −0.584371 | − | 1.58202i | −0.0271874 | − | 0.0736022i | ||||
\(463\) | −20.0792 | −0.933161 | −0.466580 | − | 0.884479i | \(-0.654514\pi\) | ||||
−0.466580 | + | 0.884479i | \(0.654514\pi\) | |||||||
\(464\) | −11.0732 | + | 8.04516i | −0.514061 | + | 0.373487i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.14148 | − | 3.51313i | 0.0528782 | − | 0.162742i | ||||
\(467\) | 13.3534 | + | 9.70181i | 0.617921 | + | 0.448946i | 0.852195 | − | 0.523225i | \(-0.175271\pi\) |
−0.234273 | + | 0.972171i | \(0.575271\pi\) | |||||||
\(468\) | −5.07493 | − | 3.68715i | −0.234589 | − | 0.170439i | ||||
\(469\) | 1.71347 | − | 5.27350i | 0.0791205 | − | 0.243508i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.3853 | − | 14.0843i | 0.893228 | − | 0.648968i | ||||
\(472\) | −7.34599 | −0.338127 | ||||||||
\(473\) | 1.17916 | − | 4.18753i | 0.0542179 | − | 0.192543i | ||||
\(474\) | −5.05481 | −0.232175 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.06356 | − | 9.42868i | −0.140418 | − | 0.432163i | ||||
\(477\) | 1.76673 | − | 5.43744i | 0.0808930 | − | 0.248963i | ||||
\(478\) | 3.22111 | + | 2.34028i | 0.147330 | + | 0.107042i | ||||
\(479\) | −4.15087 | − | 3.01578i | −0.189658 | − | 0.137795i | 0.488904 | − | 0.872337i | \(-0.337397\pi\) |
−0.678562 | + | 0.734543i | \(0.737397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9172 | + | 42.8327i | 0.634570 | + | 1.95300i | ||||
\(482\) | 0.302363 | − | 0.219680i | 0.0137723 | − | 0.0100061i | ||||
\(483\) | −1.73612 | −0.0789960 | ||||||||
\(484\) | 16.3547 | − | 13.9913i | 0.743393 | − | 0.635967i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.01614 | + | 0.738269i | −0.0460930 | + | 0.0334886i | ||||
\(487\) | −5.17276 | − | 15.9201i | −0.234400 | − | 0.721409i | −0.997200 | − | 0.0747753i | \(-0.976176\pi\) |
0.762800 | − | 0.646634i | \(-0.223824\pi\) | |||||||
\(488\) | 0.468912 | − | 1.44316i | 0.0212266 | − | 0.0653289i | ||||
\(489\) | −12.8869 | − | 9.36288i | −0.582766 | − | 0.423404i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.238396 | + | 0.733708i | −0.0107587 | + | 0.0331118i | −0.956292 | − | 0.292414i | \(-0.905541\pi\) |
0.945533 | + | 0.325526i | \(0.105541\pi\) | |||||||
\(492\) | 14.4688 | + | 44.5304i | 0.652304 | + | 2.00758i | ||||
\(493\) | −11.6350 | + | 8.45333i | −0.524014 | + | 0.380719i | ||||
\(494\) | −2.54904 | −0.114687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.1861 | −1.08599 | ||||||||
\(497\) | −10.5908 | + | 7.69465i | −0.475061 | + | 0.345152i | ||||
\(498\) | 1.52930 | + | 4.70669i | 0.0685294 | + | 0.210912i | ||||
\(499\) | 5.40385 | − | 16.6313i | 0.241909 | − | 0.744521i | −0.754220 | − | 0.656622i | \(-0.771985\pi\) |
0.996129 | − | 0.0878988i | \(-0.0280152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.3090 | − | 21.2943i | −1.30943 | − | 0.951357i | ||||
\(502\) | 0.680333 | − | 2.09385i | 0.0303647 | − | 0.0934530i | ||||
\(503\) | −12.1050 | − | 37.2553i | −0.539734 | − | 1.66113i | −0.733193 | − | 0.680021i | \(-0.761971\pi\) |
0.193459 | − | 0.981108i | \(-0.438029\pi\) | |||||||
\(504\) | 0.505462 | − | 0.367240i | 0.0225151 | − | 0.0163582i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.170218 | + | 0.460816i | 0.00756710 | + | 0.0204858i | ||||
\(507\) | −31.6419 | −1.40526 | ||||||||
\(508\) | −27.1714 | + | 19.7412i | −1.20554 | + | 0.875873i | ||||
\(509\) | 1.00212 | + | 3.08420i | 0.0444181 | + | 0.136705i | 0.970806 | − | 0.239865i | \(-0.0771033\pi\) |
−0.926388 | + | 0.376570i | \(0.877103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5171 | + | 9.09420i | 0.553724 | + | 0.402304i | ||||
\(512\) | −12.3373 | − | 8.96355i | −0.545235 | − | 0.396137i | ||||
\(513\) | 3.17006 | − | 9.75644i | 0.139962 | − | 0.430757i | ||||
\(514\) | 0.289585 | + | 0.891252i | 0.0127731 | + | 0.0393114i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.86159 | 0.214020 | ||||||||
\(517\) | −14.9630 | + | 0.594010i | −0.658072 | + | 0.0261245i | ||||
\(518\) | −2.21825 | −0.0974642 | ||||||||
\(519\) | 18.7557 | − | 13.6268i | 0.823286 | − | 0.598152i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.60355 | − | 11.0906i | 0.157874 | − | 0.485887i | −0.840567 | − | 0.541708i | \(-0.817778\pi\) |
0.998441 | + | 0.0558215i | \(0.0177778\pi\) | |||||||
\(522\) | −0.362606 | − | 0.263449i | −0.0158708 | − | 0.0115308i | ||||
\(523\) | 4.13469 | + | 3.00403i | 0.180797 | + | 0.131357i | 0.674503 | − | 0.738272i | \(-0.264358\pi\) |
−0.493706 | + | 0.869629i | \(0.664358\pi\) | |||||||
\(524\) | −6.05978 | + | 18.6501i | −0.264723 | + | 0.814733i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.49628 | + | 1.08711i | −0.0652407 | + | 0.0474002i | ||||
\(527\) | −25.4132 | −1.10701 | ||||||||
\(528\) | 19.5505 | + | 13.0517i | 0.850826 | + | 0.568002i | ||||
\(529\) | −22.4943 | −0.978013 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.62035 | + | 4.98693i | 0.0703173 | + | 0.216414i | ||||
\(532\) | −1.74980 | + | 5.38534i | −0.0758636 | + | 0.233484i | ||||
\(533\) | 55.7017 | + | 40.4696i | 2.41271 | + | 1.75293i | ||||
\(534\) | −2.00580 | − | 1.45730i | −0.0867994 | − | 0.0630635i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.09564 | − | 3.37203i | −0.0473244 | − | 0.145649i | ||||
\(537\) | 4.90443 | − | 3.56328i | 0.211642 | − | 0.153767i | ||||
\(538\) | −3.50054 | −0.150919 | ||||||||
\(539\) | 13.9014 | − | 10.9682i | 0.598775 | − | 0.472432i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.3114 | + | 21.2960i | −1.26019 | + | 0.915585i | −0.998767 | − | 0.0496388i | \(-0.984193\pi\) |
−0.261427 | + | 0.965223i | \(0.584193\pi\) | |||||||
\(542\) | −0.871011 | − | 2.68070i | −0.0374131 | − | 0.115146i | ||||
\(543\) | −1.26845 | + | 3.90388i | −0.0544342 | + | 0.167531i | ||||
\(544\) | −7.72093 | − | 5.60959i | −0.331032 | − | 0.240509i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.856405 | − | 2.63574i | 0.0366508 | − | 0.112799i | ||||
\(547\) | −5.91930 | − | 18.2177i | −0.253091 | − | 0.778934i | −0.994200 | − | 0.107549i | \(-0.965700\pi\) |
0.741109 | − | 0.671385i | \(-0.234300\pi\) | |||||||
\(548\) | −5.58352 | + | 4.05667i | −0.238516 | + | 0.173292i | ||||
\(549\) | −1.08314 | −0.0462274 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.21432 | 0.349942 | ||||||||
\(552\) | −0.898108 | + | 0.652513i | −0.0382260 | + | 0.0277728i | ||||
\(553\) | 5.10245 | + | 15.7037i | 0.216978 | + | 0.667790i | ||||
\(554\) | −1.31741 | + | 4.05458i | −0.0559715 | + | 0.172263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.8941 | − | 10.0946i | −0.589240 | − | 0.428108i | ||||
\(557\) | −8.24779 | + | 25.3841i | −0.349470 | + | 1.07556i | 0.609677 | + | 0.792650i | \(0.291299\pi\) |
−0.959147 | + | 0.282908i | \(0.908701\pi\) | |||||||
\(558\) | −0.244742 | − | 0.753239i | −0.0103608 | − | 0.0318872i | ||||
\(559\) | 5.78358 | − | 4.20201i | 0.244619 | − | 0.177726i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.5424 | + | 13.7139i | 0.867300 | + | 0.579000i | ||||
\(562\) | −2.08499 | −0.0879500 | ||||||||
\(563\) | −27.5770 | + | 20.0359i | −1.16223 | + | 0.844412i | −0.990059 | − | 0.140655i | \(-0.955079\pi\) |
−0.172174 | + | 0.985066i | \(0.555079\pi\) | |||||||
\(564\) | −5.17122 | − | 15.9154i | −0.217748 | − | 0.670159i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.451242 | − | 0.327847i | −0.0189671 | − | 0.0137804i | ||||
\(567\) | 10.8633 | + | 7.89265i | 0.456215 | + | 0.331460i | ||||
\(568\) | −2.58669 | + | 7.96101i | −0.108535 | + | 0.334037i | ||||
\(569\) | −7.05363 | − | 21.7088i | −0.295703 | − | 0.910082i | −0.982984 | − | 0.183690i | \(-0.941196\pi\) |
0.687281 | − | 0.726392i | \(-0.258804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9818 | −1.54764 | −0.773820 | − | 0.633406i | \(-0.781656\pi\) | ||||
−0.773820 | + | 0.633406i | \(0.781656\pi\) | |||||||
\(572\) | 35.3401 | − | 1.40295i | 1.47764 | − | 0.0586604i | ||||
\(573\) | −3.33967 | −0.139517 | ||||||||
\(574\) | −2.74352 | + | 1.99329i | −0.114512 | + | 0.0831982i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.26837 | + | 3.90363i | −0.0528486 | + | 0.162651i | ||||
\(577\) | −23.3962 | − | 16.9984i | −0.973999 | − | 0.707651i | −0.0176392 | − | 0.999844i | \(-0.505615\pi\) |
−0.956359 | + | 0.292193i | \(0.905615\pi\) | |||||||
\(578\) | 0.260172 | + | 0.189026i | 0.0108217 | + | 0.00786246i | ||||
\(579\) | 9.01880 | − | 27.7570i | 0.374809 | − | 1.15354i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0785 | − | 9.50209i | 0.542588 | − | 0.394213i | ||||
\(582\) | −0.119707 | −0.00496202 | ||||||||
\(583\) | 11.1694 | + | 30.2379i | 0.462588 | + | 1.25233i | ||||
\(584\) | 9.89322 | 0.409385 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.62778 | − | 5.00978i | −0.0672428 | − | 0.206952i | ||||
\(587\) | 2.23223 | − | 6.87011i | 0.0921341 | − | 0.283560i | −0.894362 | − | 0.447344i | \(-0.852370\pi\) |
0.986496 | + | 0.163784i | \(0.0523701\pi\) | |||||||
\(588\) | 16.0089 | + | 11.6311i | 0.660195 | + | 0.479660i | ||||
\(589\) | 11.7430 | + | 8.53178i | 0.483861 | + | 0.351546i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.04620 | + | 3.21986i | 0.0430348 | + | 0.132448i | ||||
\(592\) | 25.0135 | − | 18.1734i | 1.02805 | − | 0.746922i | ||||
\(593\) | −10.9657 | −0.450308 | −0.225154 | − | 0.974323i | \(-0.572289\pi\) | ||||
−0.225154 | + | 0.974323i | \(0.572289\pi\) | |||||||
\(594\) | 0.855410 | − | 3.03780i | 0.0350979 | − | 0.124642i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.2915 | + | 9.65687i | −0.544442 | + | 0.395561i | ||||
\(597\) | 11.4769 | + | 35.3224i | 0.469720 | + | 1.44565i | ||||
\(598\) | −0.249457 | + | 0.767749i | −0.0102011 | + | 0.0313956i | ||||
\(599\) | −4.69066 | − | 3.40797i | −0.191655 | − | 0.139246i | 0.487820 | − | 0.872944i | \(-0.337792\pi\) |
−0.679475 | + | 0.733699i | \(0.737792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.51599 | + | 7.74343i | −0.102629 | + | 0.315861i | −0.989167 | − | 0.146796i | \(-0.953104\pi\) |
0.886537 | + | 0.462657i | \(0.153104\pi\) | |||||||
\(602\) | 0.108808 | + | 0.334877i | 0.00443469 | + | 0.0136486i | ||||
\(603\) | −2.04748 | + | 1.48758i | −0.0833798 | + | 0.0605789i | ||||
\(604\) | 16.7034 | 0.679652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.43756 | 0.0990192 | ||||||||
\(607\) | −21.5706 | + | 15.6720i | −0.875525 | + | 0.636106i | −0.932064 | − | 0.362294i | \(-0.881994\pi\) |
0.0565387 | + | 0.998400i | \(0.481994\pi\) | |||||||
\(608\) | 1.68445 | + | 5.18419i | 0.0683133 | + | 0.210247i | ||||
\(609\) | −2.75978 | + | 8.49372i | −0.111832 | + | 0.344183i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.9081 | − | 14.4641i | −0.805395 | − | 0.585153i | ||||
\(612\) | −1.39829 | + | 4.30348i | −0.0565223 | + | 0.173958i | ||||
\(613\) | −3.19030 | − | 9.81873i | −0.128855 | − | 0.396575i | 0.865729 | − | 0.500513i | \(-0.166855\pi\) |
−0.994584 | + | 0.103939i | \(0.966855\pi\) | |||||||
\(614\) | −1.43773 | + | 1.04457i | −0.0580222 | + | 0.0421556i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.954805 | + | 3.39078i | −0.0384702 | + | 0.136618i | ||||
\(617\) | 8.79766 | 0.354180 | 0.177090 | − | 0.984195i | \(-0.443332\pi\) | ||||
0.177090 | + | 0.984195i | \(0.443332\pi\) | |||||||
\(618\) | −2.54679 | + | 1.85035i | −0.102447 | + | 0.0744321i | ||||
\(619\) | −4.20736 | − | 12.9489i | −0.169108 | − | 0.520461i | 0.830208 | − | 0.557454i | \(-0.188222\pi\) |
−0.999315 | + | 0.0369937i | \(0.988222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.62833 | − | 1.90959i | −0.105471 | − | 0.0766293i | ||||
\(622\) | 0.186033 | + | 0.135161i | 0.00745925 | + | 0.00541946i | ||||
\(623\) | −2.50267 | + | 7.70242i | −0.100267 | + | 0.308591i | ||||
\(624\) | 11.9368 | + | 36.7376i | 0.477853 | + | 1.47068i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.16462 | −0.0465474 | ||||||||
\(627\) | −4.88823 | − | 13.2335i | −0.195217 | − | 0.528495i | ||||
\(628\) | −24.7503 | −0.987643 | ||||||||
\(629\) | 26.2826 | − | 19.0954i | 1.04796 | − | 0.761384i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10923 | + | 24.9576i | −0.322823 | + | 0.993548i | 0.649590 | + | 0.760285i | \(0.274941\pi\) |
−0.972414 | + | 0.233264i | \(0.925059\pi\) | |||||||
\(632\) | 8.54173 | + | 6.20593i | 0.339772 | + | 0.246859i | ||||
\(633\) | −25.6192 | − | 18.6134i | −1.01827 | − | 0.739818i | ||||
\(634\) | 1.82465 | − | 5.61569i | 0.0724661 | − | 0.223028i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29.1430 | + | 21.1736i | −1.15559 | + | 0.839588i | ||||
\(637\) | 29.0981 | 1.15291 | ||||||||
\(638\) | 2.52507 | − | 0.100242i | 0.0999683 | − | 0.00396860i | ||||
\(639\) | 5.97501 | 0.236368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3908 | + | 38.1350i | 0.489407 | + | 1.50624i | 0.825495 | + | 0.564410i | \(0.190896\pi\) |
−0.336087 | + | 0.941831i | \(0.609104\pi\) | |||||||
\(642\) | 1.22473 | − | 3.76934i | 0.0483363 | − | 0.148764i | ||||
\(643\) | −2.12044 | − | 1.54059i | −0.0836218 | − | 0.0607548i | 0.545189 | − | 0.838313i | \(-0.316458\pi\) |
−0.628811 | + | 0.777558i | \(0.716458\pi\) | |||||||
\(644\) | 1.45078 | + | 1.05405i | 0.0571687 | + | 0.0415355i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.568198 | + | 1.74873i | 0.0223555 | + | 0.0688031i | ||||
\(647\) | −24.4251 | + | 17.7459i | −0.960250 | + | 0.697662i | −0.953209 | − | 0.302313i | \(-0.902241\pi\) |
−0.00704095 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(648\) | 8.58610 | 0.337294 | ||||||||
\(649\) | −24.5883 | − | 16.4149i | −0.965177 | − | 0.644341i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7673 | + | 9.27598i | −0.500390 | + | 0.363554i | ||||
\(652\) | 5.08438 | + | 15.6481i | 0.199120 | + | 0.612827i | ||||
\(653\) | 11.2515 | − | 34.6286i | 0.440305 | − | 1.35512i | −0.447246 | − | 0.894411i | \(-0.647595\pi\) |
0.887551 | − | 0.460709i | \(-0.152405\pi\) | |||||||
\(654\) | 2.43812 | + | 1.77140i | 0.0953380 | + | 0.0692671i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.6063 | − | 44.9537i | 0.570281 | − | 1.75515i | ||||
\(657\) | −2.18221 | − | 6.71616i | −0.0851362 | − | 0.262022i | ||||
\(658\) | 0.980550 | − | 0.712411i | 0.0382258 | − | 0.0277727i | ||||
\(659\) | −32.9001 | −1.28161 | −0.640803 | − | 0.767706i | \(-0.721398\pi\) | ||||
−0.640803 | + | 0.767706i | \(0.721398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0455 | 1.20753 | 0.603766 | − | 0.797162i | \(-0.293666\pi\) | ||||
0.603766 | + | 0.797162i | \(0.293666\pi\) | |||||||
\(662\) | −3.13509 | + | 2.27778i | −0.121849 | + | 0.0885283i | ||||
\(663\) | 12.5424 | + | 38.6015i | 0.487105 | + | 1.49916i | ||||
\(664\) | 3.19429 | − | 9.83102i | 0.123963 | − | 0.381517i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.819099 | + | 0.595110i | 0.0317394 | + | 0.0230601i | ||||
\(667\) | 0.803878 | − | 2.47408i | 0.0311263 | − | 0.0957969i | ||||
\(668\) | 11.5635 | + | 35.5889i | 0.447407 | + | 1.37698i | ||||
\(669\) | 9.16663 | − | 6.65995i | 0.354402 | − | 0.257488i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.79433 | − | 3.78272i | 0.185083 | − | 0.146030i | ||||
\(672\) | −5.92645 | −0.228618 | ||||||||
\(673\) | −3.74637 | + | 2.72189i | −0.144412 | + | 0.104921i | −0.657645 | − | 0.753328i | \(-0.728447\pi\) |
0.513234 | + | 0.858249i | \(0.328447\pi\) | |||||||
\(674\) | 1.89701 | + | 5.83840i | 0.0730701 | + | 0.224887i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.4414 | + | 19.2108i | 1.01698 | + | 0.738877i | ||||
\(677\) | 17.9475 | + | 13.0396i | 0.689780 | + | 0.501154i | 0.876588 | − | 0.481242i | \(-0.159814\pi\) |
−0.186808 | + | 0.982396i | \(0.559814\pi\) | |||||||
\(678\) | 2.39004 | − | 7.35578i | 0.0917888 | − | 0.282497i | ||||
\(679\) | 0.120835 | + | 0.371892i | 0.00463723 | + | 0.0142719i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.1458 | 1.61503 | ||||||||
\(682\) | 3.71389 | + | 2.47935i | 0.142212 | + | 0.0949393i | ||||
\(683\) | −42.5540 | −1.62828 | −0.814142 | − | 0.580665i | \(-0.802793\pi\) | ||||
−0.814142 | + | 0.580665i | \(0.802793\pi\) | |||||||
\(684\) | 2.09090 | − | 1.51913i | 0.0799476 | − | 0.0580853i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.02355 | + | 3.15016i | −0.0390793 | + | 0.120274i | ||||
\(687\) | 9.15301 | + | 6.65005i | 0.349209 | + | 0.253715i | ||||
\(688\) | −3.97050 | − | 2.88473i | −0.151374 | − | 0.109979i | ||||
\(689\) | −16.3689 | + | 50.3783i | −0.623605 | + | 1.91926i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.05397 | − | 2.21884i | 0.116178 | − | 0.0844086i | −0.528179 | − | 0.849133i | \(-0.677125\pi\) |
0.644357 | + | 0.764725i | \(0.277125\pi\) | |||||||
\(692\) | −23.9465 | −0.910308 | ||||||||
\(693\) | 2.51248 | − | 0.0997421i | 0.0954414 | − | 0.00378889i | ||||
\(694\) | 3.68600 | 0.139919 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.76468 | + | 5.43112i | 0.0668900 | + | 0.205866i | ||||
\(697\) | 15.3474 | − | 47.2343i | 0.581323 | − | 1.78913i | ||||
\(698\) | −0.263442 | − | 0.191402i | −0.00997143 | − | 0.00724466i | ||||
\(699\) | 27.1787 | + | 19.7465i | 1.02799 | + | 0.746880i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.265067 | − | 0.815792i | −0.0100114 | − | 0.0308120i | 0.945926 | − | 0.324382i | \(-0.105156\pi\) |
−0.955937 | + | 0.293570i | \(0.905156\pi\) | |||||||
\(702\) | 4.19563 | − | 3.04830i | 0.158354 | − | 0.115051i | ||||
\(703\) | −18.5555 | −0.699834 | ||||||||
\(704\) | −8.01867 | − | 21.7083i | −0.302215 | − | 0.818162i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.280079 | − | 0.203489i | 0.0105409 | − | 0.00765842i | ||||
\(707\) | −2.46053 | − | 7.57274i | −0.0925378 | − | 0.284802i | ||||
\(708\) | 10.2093 | − | 31.4211i | 0.383690 | − | 1.18088i | ||||
\(709\) | −20.0202 | − | 14.5455i | −0.751874 | − | 0.546269i | 0.144533 | − | 0.989500i | \(-0.453832\pi\) |
−0.896407 | + | 0.443231i | \(0.853832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.32888 | − | 7.16756i | 0.0873399 | − | 0.268804i | ||||
\(712\) | 1.60028 | + | 4.92515i | 0.0599729 | + | 0.184578i | ||||
\(713\) | 3.71891 | − | 2.70194i | 0.139274 | − | 0.101189i | ||||
\(714\) | −1.99912 | −0.0748150 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.26175 | −0.234012 | ||||||||
\(717\) | −29.2947 | + | 21.2838i | −1.09403 | + | 0.794860i | ||||
\(718\) | −2.00920 | − | 6.18369i | −0.0749828 | − | 0.230773i | ||||
\(719\) | −5.40434 | + | 16.6329i | −0.201548 | + | 0.620301i | 0.798289 | + | 0.602274i | \(0.205739\pi\) |
−0.999837 | + | 0.0180271i | \(0.994261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.31926 | + | 6.04430i | 0.309826 | + | 0.225101i | ||||
\(722\) | −0.898373 | + | 2.76491i | −0.0334340 | + | 0.102899i | ||||
\(723\) | 1.05036 | + | 3.23266i | 0.0390632 | + | 0.120224i | ||||
\(724\) | 3.43014 | − | 2.49214i | 0.127480 | − | 0.0926198i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.66412 | − | 4.00830i | −0.0617614 | − | 0.148762i | ||||
\(727\) | −13.8835 | −0.514909 | −0.257455 | − | 0.966290i | \(-0.582884\pi\) | ||||
−0.257455 | + | 0.966290i | \(0.582884\pi\) | |||||||
\(728\) | −4.68314 | + | 3.40250i | −0.173569 | + | 0.126105i | ||||
\(729\) | 6.12878 | + | 18.8624i | 0.226992 | + | 0.698609i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.17194 | − | 3.03109i | −0.154305 | − | 0.112109i | ||||
\(732\) | 5.52117 | + | 4.01137i | 0.204068 | + | 0.148264i | ||||
\(733\) | 9.34742 | − | 28.7684i | 0.345255 | − | 1.06259i | −0.616192 | − | 0.787596i | \(-0.711326\pi\) |
0.961447 | − | 0.274990i | \(-0.0886744\pi\) | |||||||
\(734\) | −0.600405 | − | 1.84786i | −0.0221614 | − | 0.0682056i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.72628 | 0.0636315 | ||||||||
\(737\) | 3.86763 | − | 13.7350i | 0.142466 | − | 0.505936i | ||||
\(738\) | 1.54782 | 0.0569759 | ||||||||
\(739\) | 19.8185 | − | 14.3990i | 0.729037 | − | 0.529676i | −0.160222 | − | 0.987081i | \(-0.551221\pi\) |
0.889259 | + | 0.457405i | \(0.151221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.16378 | − | 22.0478i | 0.263168 | − | 0.809948i | ||||
\(742\) | −2.11074 | − | 1.53354i | −0.0774877 | − | 0.0562981i | ||||
\(743\) | 5.37625 | + | 3.90607i | 0.197235 | + | 0.143300i | 0.682020 | − | 0.731334i | \(-0.261102\pi\) |
−0.484784 | + | 0.874634i | \(0.661102\pi\) | |||||||
\(744\) | −3.11828 | + | 9.59709i | −0.114322 | + | 0.351846i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.64714 | + | 1.19672i | −0.0603061 | + | 0.0438150i | ||||
\(747\) | −7.37851 | −0.269966 | ||||||||
\(748\) | −8.84003 | − | 23.9319i | −0.323223 | − | 0.875036i | ||||
\(749\) | −12.9464 | −0.473052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.58167 | − | 17.1786i | −0.203678 | − | 0.626857i | −0.999765 | − | 0.0216746i | \(-0.993100\pi\) |
0.796087 | − | 0.605182i | \(-0.206900\pi\) | |||||||
\(752\) | −5.22038 | + | 16.0667i | −0.190368 | + | 0.585891i | ||||
\(753\) | 16.1987 | + | 11.7690i | 0.590313 | + | 0.428887i | ||||
\(754\) | 3.35957 | + | 2.44087i | 0.122348 | + | 0.0888912i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.56002 | − | 10.9566i | −0.129477 | − | 0.398488i | ||||
\(757\) | 8.56321 | − | 6.22154i | 0.311235 | − | 0.226126i | −0.421191 | − | 0.906972i | \(-0.638388\pi\) |
0.732426 | + | 0.680846i | \(0.238388\pi\) | |||||||
\(758\) | 2.80244 | 0.101789 | ||||||||
\(759\) | −4.46419 | + | 0.177222i | −0.162040 | + | 0.00643276i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.26922 | + | 4.55485i | −0.227259 | + | 0.165113i | −0.695588 | − | 0.718441i | \(-0.744856\pi\) |
0.468329 | + | 0.883554i | \(0.344856\pi\) | |||||||
\(762\) | 2.09281 | + | 6.44100i | 0.0758145 | + | 0.233333i | ||||
\(763\) | 3.04208 | − | 9.36256i | 0.110131 | − | 0.338947i | ||||
\(764\) | 2.79078 | + | 2.02762i | 0.100967 | + | 0.0733569i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.251938 | + | 0.775384i | −0.00910288 | + | 0.0280158i | ||||
\(767\) | −15.0127 | − | 46.2043i | −0.542076 | − | 1.66834i | ||||
\(768\) | 19.3725 | − | 14.0750i | 0.699046 | − | 0.507886i | ||||
\(769\) | −23.9339 | −0.863078 | −0.431539 | − | 0.902094i | \(-0.642029\pi\) | ||||
−0.431539 | + | 0.902094i | \(0.642029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.52270 | −0.306938 | ||||||||
\(772\) | −24.3887 | + | 17.7194i | −0.877769 | + | 0.637737i | ||||
\(773\) | −10.7378 | − | 33.0476i | −0.386212 | − | 1.18864i | −0.935597 | − | 0.353069i | \(-0.885138\pi\) |
0.549385 | − | 0.835569i | \(-0.314862\pi\) | |||||||
\(774\) | 0.0496627 | − | 0.152846i | 0.00178509 | − | 0.00549394i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.202284 | + | 0.146968i | 0.00726156 | + | 0.00527583i | ||||
\(777\) | 6.23413 | − | 19.1867i | 0.223648 | − | 0.688318i | ||||
\(778\) | −0.857829 | − | 2.64013i | −0.0307547 | − | 0.0946531i | ||||
\(779\) | −22.9494 | + | 16.6737i | −0.822248 | + | 0.597398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.4473 | + | 20.8669i | −0.946359 | + | 0.746675i | ||||
\(782\) | 0.582310 | 0.0208234 | ||||||||
\(783\) | −13.5205 | + | 9.82320i | −0.483183 | + | 0.351053i | ||||
\(784\) | −6.17298 | − | 18.9985i | −0.220463 | − | 0.678517i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.19908 | + | 2.32427i | 0.114108 | + | 0.0829040i | ||||
\(787\) | 7.10333 | + | 5.16087i | 0.253206 | + | 0.183965i | 0.707147 | − | 0.707067i | \(-0.249982\pi\) |
−0.453940 | + | 0.891032i | \(0.649982\pi\) | |||||||
\(788\) | 1.08063 | − | 3.32585i | 0.0384960 | − | 0.118478i | ||||
\(789\) | −5.19780 | − | 15.9972i | −0.185047 | − | 0.569515i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.2647 | −0.898308 | ||||||||
\(792\) | 1.26224 | − | 0.995906i | 0.0448518 | − | 0.0353880i | ||||
\(793\) | 10.0354 | 0.356367 | ||||||||
\(794\) | 1.48321 | − | 1.07761i | 0.0526370 | − | 0.0382430i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8547 | − | 36.4850i | 0.420179 | − | 1.29318i | ||||
\(797\) | 40.0732 | + | 29.1149i | 1.41946 | + | 1.03130i | 0.991860 | + | 0.127336i | \(0.0406426\pi\) |
0.427605 | + | 0.903966i | \(0.359357\pi\) | |||||||
\(798\) | 0.923757 | + | 0.671149i | 0.0327007 | + | 0.0237584i | ||||
\(799\) | −5.48523 | + | 16.8818i | −0.194054 | + | 0.597235i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.99052 | − | 2.17274i | 0.105665 | − | 0.0767701i | ||||
\(802\) | 3.41713 | 0.120663 | ||||||||
\(803\) | 33.1144 | + | 22.1068i | 1.16858 | + | 0.780132i | ||||
\(804\) | 15.9459 | 0.562370 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.26756 | + | 6.97882i | 0.0798712 | + | 0.245818i | ||||
\(807\) | 9.83787 | − | 30.2778i | 0.346309 | − | 1.06583i | ||||
\(808\) | −4.11904 | − | 2.99266i | −0.144907 | − | 0.105281i | ||||
\(809\) | 32.0568 | + | 23.2906i | 1.12706 | + | 0.818854i | 0.985264 | − | 0.171042i | \(-0.0547135\pi\) |
0.141792 | + | 0.989896i | \(0.454714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4557 | − | 47.5676i | −0.542722 | − | 1.67033i | −0.726346 | − | 0.687329i | \(-0.758783\pi\) |
0.183624 | − | 0.982997i | \(-0.441217\pi\) | |||||||
\(812\) | 7.46301 | − | 5.42219i | 0.261900 | − | 0.190282i | ||||
\(813\) | 25.6345 | 0.899040 | ||||||||
\(814\) | −5.70393 | + | 0.226438i | −0.199923 | + | 0.00793665i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.5426 | − | 16.3781i | 0.789147 | − | 0.573349i | ||||
\(817\) | 0.910175 | + | 2.80123i | 0.0318430 | + | 0.0980026i | ||||
\(818\) | −0.760234 | + | 2.33976i | −0.0265810 | + | 0.0818078i | ||||
\(819\) | 3.34283 | + | 2.42871i | 0.116808 | + | 0.0848659i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5676 | − | 38.6792i | 0.438613 | − | 1.34991i | −0.450725 | − | 0.892663i | \(-0.648834\pi\) |
0.889338 | − | 0.457250i | \(-0.151166\pi\) | |||||||
\(822\) | 0.430057 | + | 1.32358i | 0.0150000 | + | 0.0461651i | ||||
\(823\) | 24.0661 | − | 17.4851i | 0.838892 | − | 0.609491i | −0.0831687 | − | 0.996535i | \(-0.526504\pi\) |
0.922061 | + | 0.387045i | \(0.126504\pi\) | |||||||
\(824\) | 6.57535 | 0.229063 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.39285 | 0.0832581 | ||||||||
\(827\) | 37.3653 | − | 27.1475i | 1.29932 | − | 0.944011i | 0.299371 | − | 0.954137i | \(-0.403223\pi\) |
0.999949 | + | 0.0101260i | \(0.00322326\pi\) | |||||||
\(828\) | −0.252927 | − | 0.778428i | −0.00878981 | − | 0.0270523i | ||||
\(829\) | −15.1310 | + | 46.5683i | −0.525520 | + | 1.61738i | 0.237766 | + | 0.971323i | \(0.423585\pi\) |
−0.763285 | + | 0.646061i | \(0.776415\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.3675 | − | 22.7898i | −1.08813 | − | 0.790571i | ||||
\(832\) | 11.7515 | − | 36.1674i | 0.407410 | − | 1.25388i | ||||
\(833\) | −6.48616 | − | 19.9623i | −0.224732 | − | 0.691654i | ||||
\(834\) | −2.80171 | + | 2.03556i | −0.0970152 | + | 0.0704856i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.94966 | + | 14.0263i | −0.136602 | + | 0.485110i | ||||
\(837\) | −29.5314 | −1.02075 | ||||||||
\(838\) | −4.44689 | + | 3.23086i | −0.153615 | + | 0.111608i | ||||
\(839\) | −14.2351 | − | 43.8112i | −0.491451 | − | 1.51253i | −0.822415 | − | 0.568889i | \(-0.807374\pi\) |
0.330963 | − | 0.943644i | \(-0.392626\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6352 | + | 9.18004i | 0.435698 | + | 0.316553i | ||||
\(842\) | −1.91582 | − | 1.39192i | −0.0660233 | − | 0.0479688i | ||||
\(843\) | 5.85962 | − | 18.0341i | 0.201816 | − | 0.621126i | ||||
\(844\) | 10.1078 | + | 31.1085i | 0.347924 | + | 1.07080i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.553198 | −0.0190193 | ||||||||
\(847\) | −10.7727 | + | 9.21598i | −0.370155 | + | 0.316665i | ||||
\(848\) | 36.3651 | 1.24878 | ||||||||
\(849\) | 4.10386 | − | 2.98163i | 0.140844 | − | 0.102329i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.81590 | + | 5.58877i | −0.0622482 | + | 0.191580i | ||||
\(852\) | −30.4568 | − | 22.1282i | −1.04343 | − | 0.758099i | ||||
\(853\) | −17.3122 | − | 12.5780i | −0.592757 | − | 0.430663i | 0.250543 | − | 0.968105i | \(-0.419391\pi\) |
−0.843301 | + | 0.537442i | \(0.819391\pi\) | |||||||
\(854\) | −0.152742 | + | 0.470090i | −0.00522671 | + | 0.0160862i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.69730 | + | 4.86587i | −0.228909 | + | 0.166312i | ||||
\(857\) | 10.0178 | 0.342201 | 0.171100 | − | 0.985254i | \(-0.445268\pi\) | ||||
0.171100 | + | 0.985254i | \(0.445268\pi\) | |||||||
\(858\) | 1.93308 | − | 6.86489i | 0.0659941 | − | 0.234363i | ||||
\(859\) | −31.7860 | −1.08452 | −0.542261 | − | 0.840210i | \(-0.682432\pi\) | ||||
−0.542261 | + | 0.840210i | \(0.682432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.53052 | − | 29.3319i | −0.324799 | − | 0.999629i | ||||
\(862\) | 1.15906 | − | 3.56723i | 0.0394779 | − | 0.121500i | ||||
\(863\) | −22.2577 | − | 16.1711i | −0.757660 | − | 0.550472i | 0.140532 | − | 0.990076i | \(-0.455119\pi\) |
−0.898192 | + | 0.439604i | \(0.855119\pi\) | |||||||
\(864\) | −8.97213 | − | 6.51863i | −0.305238 | − | 0.221768i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.46261 | + | 7.57914i | 0.0836830 | + | 0.257550i | ||||
\(867\) | −2.36616 | + | 1.71912i | −0.0803590 | + | 0.0583843i | ||||
\(868\) | 16.3007 | 0.553282 | ||||||||
\(869\) | 14.7233 | + | 39.8592i | 0.499454 | + | 1.35213i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9700 | − | 13.7825i | 0.642775 | − | 0.467003i | ||||
\(872\) | −1.94519 | − | 5.98668i | −0.0658725 | − | 0.202735i | ||||
\(873\) | 0.0551521 | − | 0.169741i | 0.00186662 | − | 0.00574485i | ||||
\(874\) | −0.269076 | − | 0.195495i | −0.00910162 | − | 0.00661271i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.7494 | + | 42.3164i | −0.464551 | + | 1.42974i | ||||
\(877\) | 8.44797 | + | 26.0002i | 0.285268 | + | 0.877964i | 0.986318 | + | 0.164852i | \(0.0527148\pi\) |
−0.701050 | + | 0.713112i | \(0.747285\pi\) | |||||||
\(878\) | 1.46256 | − | 1.06261i | 0.0493591 | − | 0.0358615i | ||||
\(879\) | 47.9066 | 1.61585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.8428 | −1.64555 | −0.822777 | − | 0.568364i | \(-0.807576\pi\) | ||||
−0.822777 | + | 0.568364i | \(0.807576\pi\) | |||||||
\(882\) | 0.529214 | − | 0.384496i | 0.0178195 | − | 0.0129467i | ||||
\(883\) | 14.8801 | + | 45.7961i | 0.500754 | + | 1.54116i | 0.807793 | + | 0.589466i | \(0.200662\pi\) |
−0.307039 | + | 0.951697i | \(0.599338\pi\) | |||||||
\(884\) | 12.9552 | − | 39.8720i | 0.435731 | − | 1.34104i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.25724 | − | 1.63998i | −0.0758335 | − | 0.0550963i | ||||
\(887\) | −18.0406 | + | 55.5232i | −0.605744 | + | 1.86429i | −0.114148 | + | 0.993464i | \(0.536414\pi\) |
−0.491596 | + | 0.870824i | \(0.663586\pi\) | |||||||
\(888\) | −3.98628 | − | 12.2685i | −0.133771 | − | 0.411704i | ||||
\(889\) | 17.8977 | − | 13.0034i | 0.600268 | − | 0.436120i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.7392 | + | 19.1860i | 0.962800 | + | 0.642754i | ||||
\(892\) | −11.7035 | −0.391863 | ||||||||
\(893\) | 8.20224 | − | 5.95928i | 0.274478 | − | 0.199420i | ||||
\(894\) | 1.02375 | + | 3.15077i | 0.0342392 | + | 0.105378i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.57756 | + | 4.77888i | 0.219741 | + | 0.159651i | ||||
\(897\) | −5.93956 | − | 4.31534i | −0.198316 | − | 0.144085i | ||||
\(898\) | −1.25710 | + | 3.86896i | −0.0419500 | + | 0.129109i | ||||
\(899\) | −7.30723 | − | 22.4893i | −0.243710 | − | 0.750061i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.2101 | 1.27296 | ||||||||
\(902\) | −6.85113 | + | 5.40553i | −0.228118 | + | 0.179985i | ||||
\(903\) | −3.20230 | −0.106566 | ||||||||
\(904\) | −13.0696 | + | 9.49563i | −0.434689 | + | 0.315820i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.04083 | − | 3.20335i | 0.0345793 | − | 0.106424i | ||||
\(907\) | 36.4485 | + | 26.4814i | 1.21025 | + | 0.879299i | 0.995254 | − | 0.0973150i | \(-0.0310254\pi\) |
0.214998 | + | 0.976614i | \(0.431025\pi\) | |||||||
\(908\) | −35.2190 | − | 25.5881i | −1.16878 | − | 0.849171i | ||||
\(909\) | −1.12305 | + | 3.45638i | −0.0372491 | + | 0.114641i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.00639 | + | 3.63735i | −0.165869 | + | 0.120511i | −0.667623 | − | 0.744499i | \(-0.732688\pi\) |
0.501754 | + | 0.865010i | \(0.332688\pi\) | |||||||
\(912\) | −15.9150 | −0.527000 | ||||||||
\(913\) | 32.6597 | − | 25.7684i | 1.08088 | − | 0.852810i | ||||
\(914\) | 5.36971 | 0.177614 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.61122 | − | 11.1142i | −0.119318 | − | 0.367223i | ||||
\(917\) | 3.99155 | − | 12.2847i | 0.131813 | − | 0.405677i | ||||
\(918\) | −3.02648 | − | 2.19887i | −0.0998889 | − | 0.0725735i | ||||
\(919\) | −6.73240 | − | 4.89138i | −0.222081 | − | 0.161352i | 0.471182 | − | 0.882036i | \(-0.343828\pi\) |
−0.693263 | + | 0.720685i | \(0.743828\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.99444 | − | 15.3713i | −0.164572 | − | 0.506501i | ||||
\(922\) | −3.21074 | + | 2.33274i | −0.105740 | + | 0.0768247i | ||||
\(923\) | −55.3589 | −1.82216 | ||||||||
\(924\) | −13.1764 | − | 8.79645i | −0.433473 | − | 0.289382i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.38347 | − | 2.45824i | 0.111188 | − | 0.0807826i | ||||
\(927\) | −1.45037 | − | 4.46377i | −0.0476363 | − | 0.146610i | ||||
\(928\) | 2.74414 | − | 8.44559i | 0.0900808 | − | 0.277240i | ||||
\(929\) | −8.60810 | − | 6.25415i | −0.282423 | − | 0.205192i | 0.437551 | − | 0.899194i | \(-0.355846\pi\) |
−0.719973 | + | 0.694002i | \(0.755846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.70467 | + | 11.4018i | −0.121416 | + | 0.373679i | ||||
\(932\) | −10.7230 | − | 33.0021i | −0.351245 | − | 1.08102i | ||||
\(933\) | −1.69190 | + | 1.22923i | −0.0553902 | + | 0.0402433i | ||||
\(934\) | −3.43789 | −0.112491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.64210 | 0.0863596 | ||||||||
\(937\) | 30.8835 | − | 22.4382i | 1.00892 | − | 0.733023i | 0.0449375 | − | 0.998990i | \(-0.485691\pi\) |
0.963982 | + | 0.265967i | \(0.0856911\pi\) | |||||||
\(938\) | 0.356889 | + | 1.09839i | 0.0116528 | + | 0.0358638i | ||||
\(939\) | 3.27302 | − | 10.0733i | 0.106811 | − | 0.328730i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.7729 | + | 23.8109i | 1.06837 | + | 0.776213i | 0.975618 | − | 0.219476i | \(-0.0704349\pi\) |
0.0927480 | + | 0.995690i | \(0.470435\pi\) | |||||||
\(942\) | −1.54225 | + | 4.74656i | −0.0502493 | + | 0.154651i | ||||
\(943\) | 2.77609 | + | 8.54391i | 0.0904018 | + | 0.278228i | ||||
\(944\) | −26.9825 | + | 19.6039i | −0.878204 | + | 0.638053i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.313970 | + | 0.849986i | 0.0102081 | + | 0.0276354i | ||||
\(947\) | 25.2006 | 0.818909 | 0.409455 | − | 0.912330i | \(-0.365719\pi\) | ||||
0.409455 | + | 0.912330i | \(0.365719\pi\) | |||||||
\(948\) | −38.4159 | + | 27.9108i | −1.24769 | + | 0.906500i | ||||
\(949\) | 20.2184 | + | 62.2257i | 0.656316 | + | 2.01993i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.4448 | + | 31.5645i | 1.40879 | + | 1.02355i | ||||
\(952\) | 3.37815 | + | 2.45437i | 0.109486 | + | 0.0795465i | ||||
\(953\) | −6.29862 | + | 19.3852i | −0.204032 | + | 0.627947i | 0.795720 | + | 0.605665i | \(0.207093\pi\) |
−0.999752 | + | 0.0222813i | \(0.992907\pi\) | |||||||
\(954\) | 0.367983 | + | 1.13254i | 0.0119139 | + | 0.0366672i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 37.4021 | 1.20967 | ||||||||
\(957\) | −6.22937 | + | 22.1222i | −0.201367 | + | 0.715109i | ||||
\(958\) | 1.06866 | 0.0345268 | ||||||||
\(959\) | 3.67784 | − | 2.67211i | 0.118764 | − | 0.0862868i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.33274 | − | 10.2571i | 0.107508 | − | 0.330874i | ||||
\(962\) | −7.58901 | − | 5.51374i | −0.244680 | − | 0.177770i | ||||
\(963\) | 4.78053 | + | 3.47326i | 0.154051 | + | 0.111924i | ||||
\(964\) | 1.08493 | − | 3.33907i | 0.0349432 | − | 0.107544i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.292546 | − | 0.212547i | 0.00941252 | − | 0.00683860i | ||||
\(967\) | 4.49928 | 0.144687 | 0.0723436 | − | 0.997380i | \(-0.476952\pi\) | ||||
0.0723436 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(968\) | −2.10902 | + | 8.81640i | −0.0677866 | + | 0.283370i | ||||
\(969\) | −16.7225 | −0.537204 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.5776 | + | 32.5546i | 0.339452 | + | 1.04473i | 0.964487 | + | 0.264129i | \(0.0850845\pi\) |
−0.625035 | + | 0.780596i | \(0.714915\pi\) | |||||||
\(972\) | −3.64608 | + | 11.2215i | −0.116948 | + | 0.359929i | ||||
\(973\) | 9.15195 | + | 6.64928i | 0.293398 | + | 0.213166i | ||||
\(974\) | 2.82069 | + | 2.04935i | 0.0903808 | + | 0.0656655i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.12895 | − | 6.55222i | −0.0681459 | − | 0.209732i | ||||
\(977\) | −35.4877 | + | 25.7833i | −1.13535 | + | 0.824881i | −0.986465 | − | 0.163973i | \(-0.947569\pi\) |
−0.148887 | + | 0.988854i | \(0.547569\pi\) | |||||||
\(978\) | 3.31779 | 0.106091 | ||||||||
\(979\) | −5.64902 | + | 20.0612i | −0.180544 | + | 0.641160i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.63508 | + | 2.64104i | −0.116059 | + | 0.0843220i | ||||
\(982\) | −0.0496543 | − | 0.152820i | −0.00158453 | − | 0.00487669i | ||||
\(983\) | −5.54416 | + | 17.0632i | −0.176831 | + | 0.544231i | −0.999712 | − | 0.0239829i | \(-0.992365\pi\) |
0.822881 | + | 0.568214i | \(0.192365\pi\) | |||||||
\(984\) | −15.9545 | − | 11.5916i | −0.508611 | − | 0.369528i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.925655 | − | 2.84887i | 0.0294789 | − | 0.0907266i | ||||
\(987\) | 3.40626 | + | 10.4834i | 0.108422 | + | 0.333690i | ||||
\(988\) | −19.3723 | + | 14.0748i | −0.616316 | + | 0.447780i | ||||
\(989\) | 0.932779 | 0.0296607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.5351 | −1.06528 | −0.532638 | − | 0.846343i | \(-0.678799\pi\) | ||||
−0.532638 | + | 0.846343i | \(0.678799\pi\) | |||||||
\(992\) | 12.6950 | − | 9.22343i | 0.403065 | − | 0.292844i | ||||
\(993\) | −10.8908 | − | 33.5183i | −0.345608 | − | 1.06367i | ||||
\(994\) | 0.842578 | − | 2.59319i | 0.0267250 | − | 0.0822510i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 37.6110 | + | 27.3260i | 1.19175 | + | 0.865857i | ||||
\(997\) | 6.85905 | − | 21.1100i | 0.217228 | − | 0.668560i | −0.781759 | − | 0.623580i | \(-0.785678\pi\) |
0.998988 | − | 0.0449802i | \(-0.0143225\pi\) | |||||||
\(998\) | 1.12554 | + | 3.46406i | 0.0356283 | + | 0.109653i | ||||
\(999\) | 30.5417 | − | 22.1899i | 0.966298 | − | 0.702056i |
(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 | 275.2.h.c.201.2 | yes | 16 | |
5.2 | odd | 4 | 275.2.z.c.124.4 | 32 | |||
5.3 | odd | 4 | 275.2.z.c.124.5 | 32 | |||
5.4 | even | 2 | 275.2.h.e.201.3 | yes | 16 | ||
11.2 | odd | 10 | 3025.2.a.bm.1.3 | 8 | |||
11.4 | even | 5 | inner | 275.2.h.c.26.2 | ✓ | 16 | |
11.9 | even | 5 | 3025.2.a.bi.1.6 | 8 | |||
55.4 | even | 10 | 275.2.h.e.26.3 | yes | 16 | ||
55.9 | even | 10 | 3025.2.a.bn.1.3 | 8 | |||
55.24 | odd | 10 | 3025.2.a.bj.1.6 | 8 | |||
55.37 | odd | 20 | 275.2.z.c.224.5 | 32 | |||
55.48 | odd | 20 | 275.2.z.c.224.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.h.c.26.2 | ✓ | 16 | 11.4 | even | 5 | inner | |
275.2.h.c.201.2 | yes | 16 | 1.1 | even | 1 | trivial | |
275.2.h.e.26.3 | yes | 16 | 55.4 | even | 10 | ||
275.2.h.e.201.3 | yes | 16 | 5.4 | even | 2 | ||
275.2.z.c.124.4 | 32 | 5.2 | odd | 4 | |||
275.2.z.c.124.5 | 32 | 5.3 | odd | 4 | |||
275.2.z.c.224.4 | 32 | 55.48 | odd | 20 | |||
275.2.z.c.224.5 | 32 | 55.37 | odd | 20 | |||
3025.2.a.bi.1.6 | 8 | 11.9 | even | 5 | |||
3025.2.a.bj.1.6 | 8 | 55.24 | odd | 10 | |||
3025.2.a.bm.1.3 | 8 | 11.2 | odd | 10 | |||
3025.2.a.bn.1.3 | 8 | 55.9 | even | 10 |