Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,5,Mod(2,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.930329667755\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.39400128.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(1.89154 - 3.27625i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.2 |
Dual form | 9.5.d.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.67463 | − | 3.27625i | −1.41866 | − | 0.819063i | −0.422477 | − | 0.906374i | \(-0.638839\pi\) |
−0.996181 | + | 0.0873110i | \(0.972173\pi\) | |||||||
\(3\) | −1.11837 | − | 8.93024i | −0.124263 | − | 0.992249i | ||||
\(4\) | 13.4676 | + | 23.3266i | 0.841727 | + | 1.45791i | ||||
\(5\) | 10.2044 | − | 5.89150i | 0.408175 | − | 0.235660i | −0.281830 | − | 0.959464i | \(-0.590942\pi\) |
0.690005 | + | 0.723804i | \(0.257608\pi\) | |||||||
\(6\) | −22.9114 | + | 54.3399i | −0.636427 | + | 1.50944i | ||||
\(7\) | 26.6364 | − | 46.1356i | 0.543600 | − | 0.941544i | −0.455093 | − | 0.890444i | \(-0.650394\pi\) |
0.998694 | − | 0.0510997i | \(-0.0162726\pi\) | |||||||
\(8\) | − | 71.6534i | − | 1.11958i | ||||||
\(9\) | −78.4985 | + | 19.9746i | −0.969117 | + | 0.246601i | ||||
\(10\) | −77.2081 | −0.772081 | ||||||||
\(11\) | 108.228 | + | 62.4856i | 0.894449 | + | 0.516410i | 0.875395 | − | 0.483408i | \(-0.160601\pi\) |
0.0190536 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(12\) | 193.251 | − | 146.357i | 1.34202 | − | 1.01637i | ||||
\(13\) | 37.3052 | + | 64.6145i | 0.220741 | + | 0.382334i | 0.955033 | − | 0.296499i | \(-0.0958192\pi\) |
−0.734292 | + | 0.678833i | \(0.762486\pi\) | |||||||
\(14\) | −302.304 | + | 174.535i | −1.54237 | + | 0.890486i | ||||
\(15\) | −64.0248 | − | 84.5387i | −0.284555 | − | 0.375727i | ||||
\(16\) | −19.2722 | + | 33.3805i | −0.0752822 | + | 0.130393i | ||||
\(17\) | 7.70989i | 0.0266778i | 0.999911 | + | 0.0133389i | \(0.00424603\pi\) | ||||
−0.999911 | + | 0.0133389i | \(0.995754\pi\) | |||||||
\(18\) | 510.892 | + | 143.832i | 1.57683 | + | 0.443926i | ||||
\(19\) | −54.1307 | −0.149946 | −0.0749732 | − | 0.997186i | \(-0.523887\pi\) | ||||
−0.0749732 | + | 0.997186i | \(0.523887\pi\) | |||||||
\(20\) | 274.858 | + | 158.689i | 0.687144 | + | 0.396723i | ||||
\(21\) | −441.792 | − | 186.273i | −1.00180 | − | 0.422388i | ||||
\(22\) | −409.437 | − | 709.166i | −0.845944 | − | 1.46522i | ||||
\(23\) | 346.370 | − | 199.977i | 0.654765 | − | 0.378029i | −0.135515 | − | 0.990775i | \(-0.543269\pi\) |
0.790279 | + | 0.612747i | \(0.209935\pi\) | |||||||
\(24\) | −639.882 | + | 80.1350i | −1.11091 | + | 0.139123i | ||||
\(25\) | −243.080 | + | 421.028i | −0.388929 | + | 0.673644i | ||||
\(26\) | − | 488.885i | − | 0.723202i | ||||||
\(27\) | 266.169 | + | 678.672i | 0.365115 | + | 0.930962i | ||||
\(28\) | 1434.92 | 1.83025 | ||||||||
\(29\) | −468.219 | − | 270.326i | −0.556741 | − | 0.321435i | 0.195095 | − | 0.980784i | \(-0.437498\pi\) |
−0.751836 | + | 0.659350i | \(0.770832\pi\) | |||||||
\(30\) | 86.3473 | + | 689.487i | 0.0959414 | + | 0.766097i | ||||
\(31\) | 766.083 | + | 1326.89i | 0.797173 | + | 1.38074i | 0.921450 | + | 0.388496i | \(0.127005\pi\) |
−0.124278 | + | 0.992247i | \(0.539661\pi\) | |||||||
\(32\) | −774.133 | + | 446.946i | −0.755989 | + | 0.436470i | ||||
\(33\) | 436.973 | − | 1036.39i | 0.401260 | − | 0.951687i | ||||
\(34\) | 25.2595 | − | 43.7508i | 0.0218508 | − | 0.0378467i | ||||
\(35\) | − | 627.714i | − | 0.512419i | ||||||
\(36\) | −1523.13 | − | 1562.09i | −1.17525 | − | 1.20532i | ||||
\(37\) | −1719.10 | −1.25574 | −0.627868 | − | 0.778320i | \(-0.716072\pi\) | ||||
−0.627868 | + | 0.778320i | \(0.716072\pi\) | |||||||
\(38\) | 307.172 | + | 177.346i | 0.212723 | + | 0.122816i | ||||
\(39\) | 535.302 | − | 405.408i | 0.351941 | − | 0.266540i | ||||
\(40\) | −422.146 | − | 731.178i | −0.263841 | − | 0.456986i | ||||
\(41\) | 1090.87 | − | 629.816i | 0.648944 | − | 0.374668i | −0.139108 | − | 0.990277i | \(-0.544423\pi\) |
0.788051 | + | 0.615610i | \(0.211090\pi\) | |||||||
\(42\) | 1896.73 | + | 2504.45i | 1.07524 | + | 1.41976i | ||||
\(43\) | 1303.89 | − | 2258.41i | 0.705189 | − | 1.22142i | −0.261434 | − | 0.965221i | \(-0.584196\pi\) |
0.966623 | − | 0.256202i | \(-0.0824711\pi\) | |||||||
\(44\) | 3366.13i | 1.73871i | ||||||||
\(45\) | −683.348 | + | 666.303i | −0.337456 | + | 0.329038i | ||||
\(46\) | −2620.70 | −1.23852 | ||||||||
\(47\) | −692.850 | − | 400.017i | −0.313649 | − | 0.181085i | 0.334909 | − | 0.942250i | \(-0.391294\pi\) |
−0.648558 | + | 0.761165i | \(0.724628\pi\) | |||||||
\(48\) | 319.649 | + | 134.774i | 0.138737 | + | 0.0584957i | ||||
\(49\) | −218.498 | − | 378.449i | −0.0910029 | − | 0.157622i | ||||
\(50\) | 2758.78 | − | 1592.79i | 1.10351 | − | 0.637114i | ||||
\(51\) | 68.8512 | − | 8.62251i | 0.0264710 | − | 0.00331508i | ||||
\(52\) | −1004.83 | + | 1740.41i | −0.371607 | + | 0.643643i | ||||
\(53\) | 4229.81i | 1.50581i | 0.658131 | + | 0.752904i | \(0.271347\pi\) | ||||
−0.658131 | + | 0.752904i | \(0.728653\pi\) | |||||||
\(54\) | 713.088 | − | 4723.25i | 0.244543 | − | 1.61977i | ||||
\(55\) | 1472.54 | 0.486789 | ||||||||
\(56\) | −3305.77 | − | 1908.59i | −1.05414 | − | 0.608606i | ||||
\(57\) | 60.5381 | + | 483.400i | 0.0186329 | + | 0.148784i | ||||
\(58\) | 1771.31 | + | 3068.01i | 0.526550 | + | 0.912011i | ||||
\(59\) | −2886.63 | + | 1666.60i | −0.829253 | + | 0.478769i | −0.853597 | − | 0.520934i | \(-0.825584\pi\) |
0.0243441 | + | 0.999704i | \(0.492250\pi\) | |||||||
\(60\) | 1109.74 | − | 2632.02i | 0.308261 | − | 0.731116i | ||||
\(61\) | 7.50843 | − | 13.0050i | 0.00201785 | − | 0.00349502i | −0.865015 | − | 0.501746i | \(-0.832691\pi\) |
0.867033 | + | 0.498251i | \(0.166024\pi\) | |||||||
\(62\) | − | 10039.5i | − | 2.61174i | ||||||
\(63\) | −1169.38 | + | 4153.63i | −0.294627 | + | 1.04652i | ||||
\(64\) | 6473.94 | 1.58055 | ||||||||
\(65\) | 761.353 | + | 439.567i | 0.180202 | + | 0.104040i | ||||
\(66\) | −5875.12 | + | 4449.48i | −1.34874 | + | 1.02146i | ||||
\(67\) | −2591.20 | − | 4488.08i | −0.577233 | − | 0.999796i | −0.995795 | − | 0.0916081i | \(-0.970799\pi\) |
0.418563 | − | 0.908188i | \(-0.362534\pi\) | |||||||
\(68\) | −179.846 | + | 103.834i | −0.0388940 | + | 0.0224554i | ||||
\(69\) | −2173.21 | − | 2869.52i | −0.456462 | − | 0.602715i | ||||
\(70\) | −2056.55 | + | 3562.05i | −0.419704 | + | 0.726948i | ||||
\(71\) | 1924.16i | 0.381701i | 0.981619 | + | 0.190851i | \(0.0611246\pi\) | ||||
−0.981619 | + | 0.190851i | \(0.938875\pi\) | |||||||
\(72\) | 1431.25 | + | 5624.68i | 0.276090 | + | 1.08501i | ||||
\(73\) | 949.554 | 0.178186 | 0.0890931 | − | 0.996023i | \(-0.471603\pi\) | ||||
0.0890931 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(74\) | 9755.28 | + | 5632.21i | 1.78146 | + | 1.02853i | ||||
\(75\) | 4031.73 | + | 1699.90i | 0.716753 | + | 0.302205i | ||||
\(76\) | −729.012 | − | 1262.69i | −0.126214 | − | 0.218609i | ||||
\(77\) | 5765.63 | − | 3328.79i | 0.972445 | − | 0.561442i | ||||
\(78\) | −4365.86 | + | 546.754i | −0.717597 | + | 0.0898676i | ||||
\(79\) | 118.990 | − | 206.097i | 0.0190659 | − | 0.0330231i | −0.856335 | − | 0.516421i | \(-0.827264\pi\) |
0.875401 | + | 0.483398i | \(0.160597\pi\) | |||||||
\(80\) | 454.169i | 0.0709640i | ||||||||
\(81\) | 5763.03 | − | 3135.96i | 0.878376 | − | 0.477970i | ||||
\(82\) | −8253.75 | −1.22751 | ||||||||
\(83\) | −11402.0 | − | 6582.95i | −1.65510 | − | 0.955574i | −0.974927 | − | 0.222526i | \(-0.928570\pi\) |
−0.680177 | − | 0.733048i | \(-0.738097\pi\) | |||||||
\(84\) | −1604.77 | − | 12814.2i | −0.227433 | − | 1.81607i | ||||
\(85\) | 45.4228 | + | 78.6746i | 0.00628689 | + | 0.0108892i | ||||
\(86\) | −14798.2 | + | 8543.77i | −2.00084 | + | 1.15519i | ||||
\(87\) | −1890.44 | + | 4483.64i | −0.249761 | + | 0.592368i | ||||
\(88\) | 4477.31 | − | 7754.92i | 0.578164 | − | 1.00141i | ||||
\(89\) | 575.925i | 0.0727086i | 0.999339 | + | 0.0363543i | \(0.0115745\pi\) | ||||
−0.999339 | + | 0.0363543i | \(0.988426\pi\) | |||||||
\(90\) | 6060.72 | − | 1542.20i | 0.748237 | − | 0.190396i | ||||
\(91\) | 3974.71 | 0.479979 | ||||||||
\(92\) | 9329.58 | + | 5386.44i | 1.10227 | + | 0.636394i | ||||
\(93\) | 10992.7 | − | 8325.27i | 1.27098 | − | 0.962570i | ||||
\(94\) | 2621.11 | + | 4539.90i | 0.296640 | + | 0.513796i | ||||
\(95\) | −552.370 | + | 318.911i | −0.0612044 | + | 0.0353364i | ||||
\(96\) | 4857.10 | + | 6413.34i | 0.527029 | + | 0.695892i | ||||
\(97\) | −7561.70 | + | 13097.3i | −0.803667 | + | 1.39199i | 0.113520 | + | 0.993536i | \(0.463787\pi\) |
−0.917187 | + | 0.398456i | \(0.869546\pi\) | |||||||
\(98\) | 2863.41i | 0.298148i | ||||||||
\(99\) | −9743.88 | − | 2743.21i | −0.994172 | − | 0.279890i | ||||
\(100\) | −13094.9 | −1.30949 | ||||||||
\(101\) | 9578.90 | + | 5530.38i | 0.939016 | + | 0.542141i | 0.889652 | − | 0.456640i | \(-0.150947\pi\) |
0.0493643 | + | 0.998781i | \(0.484280\pi\) | |||||||
\(102\) | −418.955 | − | 176.644i | −0.0402686 | − | 0.0169785i | ||||
\(103\) | 1781.46 | + | 3085.58i | 0.167920 | + | 0.290846i | 0.937688 | − | 0.347478i | \(-0.112962\pi\) |
−0.769769 | + | 0.638323i | \(0.779628\pi\) | |||||||
\(104\) | 4629.85 | − | 2673.04i | 0.428055 | − | 0.247138i | ||||
\(105\) | −5605.64 | + | 702.017i | −0.508448 | + | 0.0636750i | ||||
\(106\) | 13857.9 | − | 24002.6i | 1.23335 | − | 2.13623i | ||||
\(107\) | − | 11432.7i | − | 0.998576i | −0.866436 | − | 0.499288i | \(-0.833595\pi\) | ||
0.866436 | − | 0.499288i | \(-0.166405\pi\) | |||||||
\(108\) | −12246.5 | + | 15348.9i | −1.04994 | + | 1.31592i | ||||
\(109\) | −4780.43 | −0.402359 | −0.201180 | − | 0.979554i | \(-0.564478\pi\) | ||||
−0.201180 | + | 0.979554i | \(0.564478\pi\) | |||||||
\(110\) | −8356.10 | − | 4824.40i | −0.690587 | − | 0.398710i | ||||
\(111\) | 1922.59 | + | 15352.0i | 0.156042 | + | 1.24600i | ||||
\(112\) | 1026.69 | + | 1778.27i | 0.0818468 | + | 0.141763i | ||||
\(113\) | 3889.66 | − | 2245.69i | 0.304617 | − | 0.175871i | −0.339898 | − | 0.940462i | \(-0.610393\pi\) |
0.644515 | + | 0.764592i | \(0.277059\pi\) | |||||||
\(114\) | 1240.21 | − | 2941.46i | 0.0954300 | − | 0.226335i | ||||
\(115\) | 2356.33 | − | 4081.28i | 0.178172 | − | 0.308604i | ||||
\(116\) | − | 14562.6i | − | 1.08224i | ||||||
\(117\) | −4219.05 | − | 4326.98i | −0.308208 | − | 0.316092i | ||||
\(118\) | 21840.7 | 1.56857 | ||||||||
\(119\) | 355.701 | + | 205.364i | 0.0251183 | + | 0.0145021i | ||||
\(120\) | −6057.48 | + | 4587.59i | −0.420658 | + | 0.318583i | ||||
\(121\) | 488.406 | + | 845.944i | 0.0333588 | + | 0.0577791i | ||||
\(122\) | −85.2151 | + | 49.1990i | −0.00572528 | + | 0.00330549i | ||||
\(123\) | −6844.42 | − | 9037.40i | −0.452404 | − | 0.597356i | ||||
\(124\) | −20634.7 | + | 35740.3i | −1.34200 | + | 2.32442i | ||||
\(125\) | 13092.8i | 0.837940i | ||||||||
\(126\) | 20244.1 | − | 19739.2i | 1.27514 | − | 1.24333i | ||||
\(127\) | 13521.3 | 0.838322 | 0.419161 | − | 0.907912i | \(-0.362324\pi\) | ||||
0.419161 | + | 0.907912i | \(0.362324\pi\) | |||||||
\(128\) | −24351.1 | − | 14059.1i | −1.48627 | − | 0.858100i | ||||
\(129\) | −21626.4 | − | 9118.35i | −1.29959 | − | 0.547945i | ||||
\(130\) | −2880.26 | − | 4988.76i | −0.170430 | − | 0.295193i | ||||
\(131\) | 2941.86 | − | 1698.48i | 0.171427 | − | 0.0989735i | −0.411831 | − | 0.911260i | \(-0.635111\pi\) |
0.583259 | + | 0.812287i | \(0.301777\pi\) | |||||||
\(132\) | 30060.4 | − | 3764.59i | 1.72523 | − | 0.216057i | ||||
\(133\) | −1441.85 | + | 2497.35i | −0.0815110 | + | 0.141181i | ||||
\(134\) | 33957.6i | 1.89116i | ||||||||
\(135\) | 6714.48 | + | 5357.29i | 0.368421 | + | 0.293953i | ||||
\(136\) | 552.439 | 0.0298680 | ||||||||
\(137\) | 3310.98 | + | 1911.60i | 0.176407 | + | 0.101849i | 0.585603 | − | 0.810598i | \(-0.300858\pi\) |
−0.409197 | + | 0.912446i | \(0.634191\pi\) | |||||||
\(138\) | 2930.91 | + | 23403.5i | 0.153902 | + | 1.22892i | ||||
\(139\) | −1738.31 | − | 3010.85i | −0.0899702 | − | 0.155833i | 0.817528 | − | 0.575889i | \(-0.195344\pi\) |
−0.907498 | + | 0.420056i | \(0.862010\pi\) | |||||||
\(140\) | 14642.4 | − | 8453.82i | 0.747064 | − | 0.431317i | ||||
\(141\) | −2797.39 | + | 6634.68i | −0.140707 | + | 0.333720i | ||||
\(142\) | 6304.02 | − | 10918.9i | 0.312637 | − | 0.541504i | ||||
\(143\) | 9324.16i | 0.455971i | ||||||||
\(144\) | 846.078 | − | 3005.27i | 0.0408024 | − | 0.144930i | ||||
\(145\) | −6370.51 | −0.302997 | ||||||||
\(146\) | −5388.37 | − | 3110.98i | −0.252785 | − | 0.145946i | ||||
\(147\) | −3135.28 | + | 2374.49i | −0.145092 | + | 0.109884i | ||||
\(148\) | −23152.3 | − | 40100.9i | −1.05699 | − | 1.83076i | ||||
\(149\) | 7717.10 | − | 4455.47i | 0.347602 | − | 0.200688i | −0.316027 | − | 0.948750i | \(-0.602349\pi\) |
0.663628 | + | 0.748062i | \(0.269016\pi\) | |||||||
\(150\) | −17309.3 | − | 22855.3i | −0.769302 | − | 1.01579i | ||||
\(151\) | 4957.66 | − | 8586.92i | 0.217432 | − | 0.376603i | −0.736590 | − | 0.676339i | \(-0.763565\pi\) |
0.954022 | + | 0.299736i | \(0.0968987\pi\) | |||||||
\(152\) | 3878.65i | 0.167878i | ||||||||
\(153\) | −154.002 | − | 605.215i | −0.00657876 | − | 0.0258539i | ||||
\(154\) | −43623.8 | −1.83942 | ||||||||
\(155\) | 15634.8 | + | 9026.75i | 0.650772 | + | 0.375723i | ||||
\(156\) | 16666.0 | + | 7026.92i | 0.684831 | + | 0.288746i | ||||
\(157\) | −2823.47 | − | 4890.39i | −0.114547 | − | 0.198401i | 0.803052 | − | 0.595909i | \(-0.203208\pi\) |
−0.917599 | + | 0.397508i | \(0.869875\pi\) | |||||||
\(158\) | −1350.45 | + | 779.684i | −0.0540960 | + | 0.0312323i | ||||
\(159\) | 37773.3 | − | 4730.50i | 1.49414 | − | 0.187117i | ||||
\(160\) | −5266.36 | + | 9121.60i | −0.205717 | + | 0.356313i | ||||
\(161\) | − | 21306.7i | − | 0.821986i | ||||||
\(162\) | −42977.2 | − | 1085.71i | −1.63760 | − | 0.0413698i | ||||
\(163\) | −2153.55 | −0.0810552 | −0.0405276 | − | 0.999178i | \(-0.512904\pi\) | ||||
−0.0405276 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(164\) | 29383.0 | + | 16964.3i | 1.09247 | + | 0.630736i | ||||
\(165\) | −1646.84 | − | 13150.1i | −0.0604900 | − | 0.483016i | ||||
\(166\) | 43134.8 | + | 74711.7i | 1.56535 | + | 2.71127i | ||||
\(167\) | −32060.4 | + | 18510.1i | −1.14957 | + | 0.663706i | −0.948783 | − | 0.315929i | \(-0.897684\pi\) |
−0.200789 | + | 0.979635i | \(0.564351\pi\) | |||||||
\(168\) | −13347.1 | + | 31655.9i | −0.472899 | + | 1.12159i | ||||
\(169\) | 11497.1 | − | 19913.6i | 0.402547 | − | 0.697232i | ||||
\(170\) | − | 595.266i | − | 0.0205974i | ||||||
\(171\) | 4249.18 | − | 1081.24i | 0.145316 | − | 0.0369769i | ||||
\(172\) | 70241.5 | 2.37431 | ||||||||
\(173\) | −42076.2 | − | 24292.7i | −1.40587 | − | 0.811678i | −0.410882 | − | 0.911689i | \(-0.634779\pi\) |
−0.994986 | + | 0.100010i | \(0.968112\pi\) | |||||||
\(174\) | 25417.1 | − | 19249.4i | 0.839512 | − | 0.635799i | ||||
\(175\) | 12949.6 | + | 22429.3i | 0.422844 | + | 0.732387i | ||||
\(176\) | −4171.60 | + | 2408.48i | −0.134672 | + | 0.0777530i | ||||
\(177\) | 18111.4 | + | 23914.4i | 0.578104 | + | 0.763332i | ||||
\(178\) | 1886.87 | − | 3268.16i | 0.0595529 | − | 0.103149i | ||||
\(179\) | − | 47717.9i | − | 1.48928i | −0.667468 | − | 0.744639i | \(-0.732622\pi\) | ||
0.667468 | − | 0.744639i | \(-0.267378\pi\) | |||||||
\(180\) | −24745.7 | − | 6966.68i | −0.763755 | − | 0.215021i | ||||
\(181\) | −45767.2 | −1.39700 | −0.698502 | − | 0.715608i | \(-0.746150\pi\) | ||||
−0.698502 | + | 0.715608i | \(0.746150\pi\) | |||||||
\(182\) | −22555.0 | − | 13022.1i | −0.680927 | − | 0.393133i | ||||
\(183\) | −124.535 | − | 52.5077i | −0.00371868 | − | 0.00156791i | ||||
\(184\) | −14329.0 | − | 24818.6i | −0.423235 | − | 0.733064i | ||||
\(185\) | −17542.4 | + | 10128.1i | −0.512560 | + | 0.295927i | ||||
\(186\) | −89655.3 | + | 11227.9i | −2.59149 | + | 0.324543i | ||||
\(187\) | −481.757 | + | 834.428i | −0.0137767 | + | 0.0238619i | ||||
\(188\) | − | 21549.1i | − | 0.609697i | ||||||
\(189\) | 38400.7 | + | 5797.52i | 1.07502 | + | 0.162300i | ||||
\(190\) | 4179.33 | 0.115771 | ||||||||
\(191\) | 40460.3 | + | 23359.7i | 1.10908 | + | 0.640326i | 0.938590 | − | 0.345034i | \(-0.112133\pi\) |
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(192\) | −7240.26 | − | 57813.8i | −0.196405 | − | 1.56830i | ||||
\(193\) | 13603.9 | + | 23562.6i | 0.365215 | + | 0.632571i | 0.988811 | − | 0.149176i | \(-0.0476621\pi\) |
−0.623596 | + | 0.781747i | \(0.714329\pi\) | |||||||
\(194\) | 85819.8 | − | 49548.1i | 2.28026 | − | 1.31651i | ||||
\(195\) | 3073.97 | − | 7290.66i | 0.0808407 | − | 0.191733i | ||||
\(196\) | 5885.30 | − | 10193.6i | 0.153199 | − | 0.265349i | ||||
\(197\) | 64665.2i | 1.66624i | 0.553090 | + | 0.833122i | \(0.313449\pi\) | ||||
−0.553090 | + | 0.833122i | \(0.686551\pi\) | |||||||
\(198\) | 46305.5 | + | 47490.1i | 1.18114 | + | 1.21136i | ||||
\(199\) | −25841.3 | −0.652542 | −0.326271 | − | 0.945276i | \(-0.605792\pi\) | ||||
−0.326271 | + | 0.945276i | \(0.605792\pi\) | |||||||
\(200\) | 30168.1 | + | 17417.5i | 0.754201 | + | 0.435438i | ||||
\(201\) | −37181.8 | + | 28159.4i | −0.920318 | + | 0.696997i | ||||
\(202\) | −36237.8 | − | 62765.8i | −0.888095 | − | 1.53823i | ||||
\(203\) | −24943.4 | + | 14401.1i | −0.605289 | + | 0.349464i | ||||
\(204\) | 1128.40 | + | 1489.94i | 0.0271145 | + | 0.0358021i | ||||
\(205\) | 7421.13 | − | 12853.8i | 0.176588 | − | 0.305860i | ||||
\(206\) | − | 23346.0i | − | 0.550147i | ||||||
\(207\) | −23195.1 | + | 22616.5i | −0.541322 | + | 0.527819i | ||||
\(208\) | −2875.82 | −0.0664714 | ||||||||
\(209\) | −5858.47 | − | 3382.39i | −0.134119 | − | 0.0774339i | ||||
\(210\) | 34109.9 | + | 14381.8i | 0.773467 | + | 0.326118i | ||||
\(211\) | −23029.3 | − | 39888.0i | −0.517269 | − | 0.895936i | −0.999799 | − | 0.0200565i | \(-0.993615\pi\) |
0.482530 | − | 0.875879i | \(-0.339718\pi\) | |||||||
\(212\) | −98667.3 | + | 56965.6i | −2.19534 | + | 1.26748i | ||||
\(213\) | 17183.2 | − | 2151.92i | 0.378743 | − | 0.0474315i | ||||
\(214\) | −37456.4 | + | 64876.4i | −0.817896 | + | 1.41664i | ||||
\(215\) | − | 30727.6i | − | 0.664739i | ||||||
\(216\) | 48629.1 | − | 19071.9i | 1.04229 | − | 0.408777i | ||||
\(217\) | 81622.8 | 1.73337 | ||||||||
\(218\) | 27127.2 | + | 15661.9i | 0.570810 | + | 0.329558i | ||||
\(219\) | −1061.95 | − | 8479.75i | −0.0221420 | − | 0.176805i | ||||
\(220\) | 19831.6 | + | 34349.3i | 0.409743 | + | 0.709696i | ||||
\(221\) | −498.171 | + | 287.619i | −0.0101998 | + | 0.00588888i | ||||
\(222\) | 39387.0 | − | 93415.9i | 0.799185 | − | 1.89546i | ||||
\(223\) | −10955.5 | + | 18975.6i | −0.220305 | + | 0.381579i | −0.954901 | − | 0.296926i | \(-0.904039\pi\) |
0.734596 | + | 0.678505i | \(0.237372\pi\) | |||||||
\(224\) | 47620.1i | 0.949062i | ||||||||
\(225\) | 10671.6 | − | 37905.5i | 0.210797 | − | 0.748750i | ||||
\(226\) | −29429.8 | −0.576197 | ||||||||
\(227\) | 43115.6 | + | 24892.8i | 0.836726 | + | 0.483084i | 0.856150 | − | 0.516727i | \(-0.172850\pi\) |
−0.0194241 | + | 0.999811i | \(0.506183\pi\) | |||||||
\(228\) | −10460.8 | + | 7922.41i | −0.201231 | + | 0.152401i | ||||
\(229\) | −14260.5 | − | 24699.9i | −0.271934 | − | 0.471003i | 0.697423 | − | 0.716660i | \(-0.254330\pi\) |
−0.969357 | + | 0.245656i | \(0.920996\pi\) | |||||||
\(230\) | −26742.6 | + | 15439.9i | −0.505531 | + | 0.291869i | ||||
\(231\) | −36175.0 | − | 47765.6i | −0.677929 | − | 0.895141i | ||||
\(232\) | −19369.8 | + | 33549.5i | −0.359873 | + | 0.623318i | ||||
\(233\) | − | 44050.2i | − | 0.811403i | −0.914006 | − | 0.405701i | \(-0.867027\pi\) | ||
0.914006 | − | 0.405701i | \(-0.132973\pi\) | |||||||
\(234\) | 9765.30 | + | 38376.7i | 0.178342 | + | 0.700868i | ||||
\(235\) | −9426.80 | −0.170698 | ||||||||
\(236\) | −77752.1 | − | 44890.2i | −1.39601 | − | 0.805986i | ||||
\(237\) | −1973.57 | − | 832.119i | −0.0351363 | − | 0.0148146i | ||||
\(238\) | −1345.65 | − | 2330.73i | −0.0237562 | − | 0.0411470i | ||||
\(239\) | 17818.6 | − | 10287.6i | 0.311945 | − | 0.180102i | −0.335851 | − | 0.941915i | \(-0.609024\pi\) |
0.647797 | + | 0.761813i | \(0.275691\pi\) | |||||||
\(240\) | 4055.84 | − | 507.930i | 0.0704140 | − | 0.00881823i | ||||
\(241\) | 28958.8 | − | 50158.0i | 0.498593 | − | 0.863588i | −0.501406 | − | 0.865212i | \(-0.667184\pi\) |
0.999999 | + | 0.00162435i | \(0.000517045\pi\) | |||||||
\(242\) | − | 6400.56i | − | 0.109292i | ||||||
\(243\) | −34450.1 | − | 47958.1i | −0.583415 | − | 0.812174i | ||||
\(244\) | 404.483 | 0.00679392 | ||||||||
\(245\) | −4459.27 | − | 2574.56i | −0.0742902 | − | 0.0428915i | ||||
\(246\) | 9230.75 | + | 73708.0i | 0.152534 | + | 1.21799i | ||||
\(247\) | −2019.36 | − | 3497.63i | −0.0330993 | − | 0.0573297i | ||||
\(248\) | 95076.5 | − | 54892.4i | 1.54586 | − | 0.892502i | ||||
\(249\) | −46035.7 | + | 109185.i | −0.742499 | + | 1.76102i | ||||
\(250\) | 42895.3 | − | 74296.9i | 0.686325 | − | 1.18875i | ||||
\(251\) | 54140.4i | 0.859357i | 0.902982 | + | 0.429679i | \(0.141373\pi\) | ||||
−0.902982 | + | 0.429679i | \(0.858627\pi\) | |||||||
\(252\) | −112639. | + | 28662.0i | −1.77373 | + | 0.451341i | ||||
\(253\) | 49982.8 | 0.780871 | ||||||||
\(254\) | −76728.4 | − | 44299.2i | −1.18929 | − | 0.686639i | ||||
\(255\) | 651.784 | − | 493.624i | 0.0100236 | − | 0.00759130i | ||||
\(256\) | 40330.8 | + | 69855.0i | 0.615399 | + | 1.06590i | ||||
\(257\) | 98522.7 | − | 56882.1i | 1.49166 | − | 0.861211i | 0.491706 | − | 0.870761i | \(-0.336373\pi\) |
0.999954 | + | 0.00955057i | \(0.00304009\pi\) | |||||||
\(258\) | 92847.8 | + | 122597.i | 1.39487 | + | 1.84179i | ||||
\(259\) | −45790.8 | + | 79311.9i | −0.682619 | + | 1.18233i | ||||
\(260\) | 23679.7i | 0.350292i | ||||||||
\(261\) | 42154.2 | + | 11867.7i | 0.618813 | + | 0.174215i | ||||
\(262\) | −22258.6 | −0.324262 | ||||||||
\(263\) | 38420.1 | + | 22181.8i | 0.555452 | + | 0.320691i | 0.751318 | − | 0.659940i | \(-0.229418\pi\) |
−0.195866 | + | 0.980631i | \(0.562752\pi\) | |||||||
\(264\) | −74260.6 | − | 31310.6i | −1.06549 | − | 0.449245i | ||||
\(265\) | 24919.9 | + | 43162.6i | 0.354859 | + | 0.614633i | ||||
\(266\) | 16363.9 | − | 9447.71i | 0.231272 | − | 0.133525i | ||||
\(267\) | 5143.15 | − | 644.097i | 0.0721451 | − | 0.00903502i | ||||
\(268\) | 69794.6 | − | 120888.i | 0.971745 | − | 1.68311i | ||||
\(269\) | 4429.77i | 0.0612176i | 0.999531 | + | 0.0306088i | \(0.00974461\pi\) | ||||
−0.999531 | + | 0.0306088i | \(0.990255\pi\) | |||||||
\(270\) | −20550.4 | − | 52399.0i | −0.281898 | − | 0.718779i | ||||
\(271\) | −86111.9 | −1.17253 | −0.586266 | − | 0.810119i | \(-0.699403\pi\) | ||||
−0.586266 | + | 0.810119i | \(0.699403\pi\) | |||||||
\(272\) | −257.360 | − | 148.587i | −0.00347859 | − | 0.00200836i | ||||
\(273\) | −4445.20 | − | 35495.1i | −0.0596439 | − | 0.476259i | ||||
\(274\) | −12525.7 | − | 21695.2i | −0.166841 | − | 0.288977i | ||||
\(275\) | −52616.4 | + | 30378.1i | −0.695754 | + | 0.401693i | ||||
\(276\) | 37668.3 | − | 89339.5i | 0.494490 | − | 1.17280i | ||||
\(277\) | −35306.7 | + | 61153.0i | −0.460148 | + | 0.797000i | −0.998968 | − | 0.0454210i | \(-0.985537\pi\) |
0.538820 | + | 0.842421i | \(0.318870\pi\) | |||||||
\(278\) | 22780.6i | 0.294765i | ||||||||
\(279\) | −86640.6 | − | 88857.0i | −1.11305 | − | 1.14152i | ||||
\(280\) | −44977.8 | −0.573697 | ||||||||
\(281\) | −129258. | − | 74627.2i | −1.63699 | − | 0.945114i | −0.981863 | − | 0.189592i | \(-0.939283\pi\) |
−0.655123 | − | 0.755522i | \(-0.727383\pi\) | |||||||
\(282\) | 37611.0 | − | 28484.5i | 0.472952 | − | 0.358187i | ||||
\(283\) | 41963.4 | + | 72682.7i | 0.523959 | + | 0.907524i | 0.999611 | + | 0.0278902i | \(0.00887887\pi\) |
−0.475652 | + | 0.879634i | \(0.657788\pi\) | |||||||
\(284\) | −44884.1 | + | 25913.8i | −0.556488 | + | 0.321288i | ||||
\(285\) | 3465.71 | + | 4576.14i | 0.0426680 | + | 0.0563390i | ||||
\(286\) | 30548.3 | − | 52911.2i | 0.373469 | − | 0.646867i | ||||
\(287\) | − | 67104.2i | − | 0.814678i | ||||||
\(288\) | 51840.7 | − | 50547.6i | 0.625008 | − | 0.609418i | ||||
\(289\) | 83461.6 | 0.999288 | ||||||||
\(290\) | 36150.3 | + | 20871.4i | 0.429849 | + | 0.248174i | ||||
\(291\) | 125418. | + | 52880.3i | 1.48107 | + | 0.624464i | ||||
\(292\) | 12788.2 | + | 22149.9i | 0.149984 | + | 0.259780i | ||||
\(293\) | −31092.9 | + | 17951.5i | −0.362182 | + | 0.209106i | −0.670037 | − | 0.742327i | \(-0.733722\pi\) |
0.307856 | + | 0.951433i | \(0.400389\pi\) | |||||||
\(294\) | 25571.0 | − | 3202.36i | 0.295837 | − | 0.0370489i | ||||
\(295\) | −19637.5 | + | 34013.1i | −0.225653 | + | 0.390843i | ||||
\(296\) | 123180.i | 1.40590i | ||||||||
\(297\) | −13600.2 | + | 90083.2i | −0.154182 | + | 1.02125i | ||||
\(298\) | −58389.0 | −0.657504 | ||||||||
\(299\) | 25842.8 | + | 14920.4i | 0.289067 | + | 0.166893i | ||||
\(300\) | 14644.9 | + | 116940.i | 0.162721 | + | 1.29934i | ||||
\(301\) | −69462.2 | − | 120312.i | −0.766682 | − | 1.32793i | ||||
\(302\) | −56265.8 | + | 32485.1i | −0.616923 | + | 0.356181i | ||||
\(303\) | 38674.9 | − | 91727.0i | 0.421254 | − | 0.999106i | ||||
\(304\) | 1043.22 | − | 1806.91i | 0.0112883 | − | 0.0195519i | ||||
\(305\) | − | 176.944i | − | 0.00190211i | ||||||
\(306\) | −1108.93 | + | 3938.92i | −0.0118430 | + | 0.0420663i | ||||
\(307\) | 7054.30 | 0.0748475 | 0.0374238 | − | 0.999299i | \(-0.488085\pi\) | ||||
0.0374238 | + | 0.999299i | \(0.488085\pi\) | |||||||
\(308\) | 155299. | + | 89661.8i | 1.63707 | + | 0.945161i | ||||
\(309\) | 25562.6 | − | 19359.7i | 0.267725 | − | 0.202760i | ||||
\(310\) | −59147.8 | − | 102447.i | −0.615482 | − | 1.06605i | ||||
\(311\) | 74184.9 | − | 42830.7i | 0.766999 | − | 0.442827i | −0.0648038 | − | 0.997898i | \(-0.520642\pi\) |
0.831803 | + | 0.555071i | \(0.187309\pi\) | |||||||
\(312\) | −29048.8 | − | 38356.2i | −0.298414 | − | 0.394028i | ||||
\(313\) | −36721.2 | + | 63603.1i | −0.374825 | + | 0.649216i | −0.990301 | − | 0.138940i | \(-0.955631\pi\) |
0.615476 | + | 0.788156i | \(0.288964\pi\) | |||||||
\(314\) | 37001.5i | 0.375284i | ||||||||
\(315\) | 12538.4 | + | 49274.6i | 0.126363 | + | 0.496595i | ||||
\(316\) | 6410.07 | 0.0641931 | ||||||||
\(317\) | 42642.8 | + | 24619.8i | 0.424353 | + | 0.245000i | 0.696938 | − | 0.717132i | \(-0.254545\pi\) |
−0.272585 | + | 0.962132i | \(0.587879\pi\) | |||||||
\(318\) | −229848. | − | 96910.8i | −2.27293 | − | 0.958336i | ||||
\(319\) | −33783.0 | − | 58513.9i | −0.331984 | − | 0.575013i | ||||
\(320\) | 66062.5 | − | 38141.2i | 0.645141 | − | 0.372473i | ||||
\(321\) | −102097. | + | 12786.0i | −0.990836 | + | 0.124086i | ||||
\(322\) | −69806.1 | + | 120908.i | −0.673258 | + | 1.16612i | ||||
\(323\) | − | 417.341i | − | 0.00400024i | ||||||
\(324\) | 150766. | + | 92198.1i | 1.43619 | + | 0.878277i | ||||
\(325\) | −36272.7 | −0.343410 | ||||||||
\(326\) | 12220.6 | + | 7055.58i | 0.114990 | + | 0.0663893i | ||||
\(327\) | 5346.29 | + | 42690.4i | 0.0499985 | + | 0.399241i | ||||
\(328\) | −45128.5 | − | 78164.8i | −0.419472 | − | 0.726547i | ||||
\(329\) | −36910.1 | + | 21310.0i | −0.340999 | + | 0.196876i | ||||
\(330\) | −33737.8 | + | 80017.5i | −0.309806 | + | 0.734779i | ||||
\(331\) | 41005.6 | − | 71023.7i | 0.374271 | − | 0.648257i | −0.615946 | − | 0.787788i | \(-0.711226\pi\) |
0.990218 | + | 0.139531i | \(0.0445595\pi\) | |||||||
\(332\) | − | 354627.i | − | 3.21733i | ||||||
\(333\) | 134947. | − | 34338.5i | 1.21696 | − | 0.309665i | ||||
\(334\) | 242575. | 2.17447 | ||||||||
\(335\) | −52883.1 | − | 30532.1i | −0.471224 | − | 0.272061i | ||||
\(336\) | 14732.2 | − | 11157.3i | 0.130494 | − | 0.0988284i | ||||
\(337\) | 23491.4 | + | 40688.3i | 0.206847 | + | 0.358270i | 0.950720 | − | 0.310052i | \(-0.100346\pi\) |
−0.743873 | + | 0.668322i | \(0.767013\pi\) | |||||||
\(338\) | −130484. | + | 75335.0i | −1.14215 | + | 0.659422i | ||||
\(339\) | −24404.7 | − | 32224.1i | −0.212360 | − | 0.280402i | ||||
\(340\) | −1223.48 | + | 2119.12i | −0.0105837 | + | 0.0183315i | ||||
\(341\) | 191477.i | 1.64667i | ||||||||
\(342\) | −27654.9 | − | 7785.72i | −0.236440 | − | 0.0665651i | ||||
\(343\) | 104628. | 0.889324 | ||||||||
\(344\) | −161823. | − | 93428.4i | −1.36749 | − | 0.789518i | ||||
\(345\) | −39082.1 | − | 16478.2i | −0.328352 | − | 0.138443i | ||||
\(346\) | 159178. | + | 275705.i | 1.32963 | + | 2.30299i | ||||
\(347\) | 38382.0 | − | 22159.8i | 0.318763 | − | 0.184038i | −0.332078 | − | 0.943252i | \(-0.607750\pi\) |
0.650841 | + | 0.759214i | \(0.274416\pi\) | |||||||
\(348\) | −130048. | + | 16286.4i | −1.07385 | + | 0.134483i | ||||
\(349\) | 93231.7 | − | 161482.i | 0.765442 | − | 1.32579i | −0.174570 | − | 0.984645i | \(-0.555853\pi\) |
0.940012 | − | 0.341140i | \(-0.110813\pi\) | |||||||
\(350\) | − | 169704.i | − | 1.38534i | ||||||
\(351\) | −33922.6 | + | 42516.4i | −0.275343 | + | 0.345097i | ||||
\(352\) | −111711. | −0.901591 | ||||||||
\(353\) | −146959. | − | 84847.1i | −1.17936 | − | 0.680907i | −0.223497 | − | 0.974705i | \(-0.571747\pi\) |
−0.955868 | + | 0.293798i | \(0.905081\pi\) | |||||||
\(354\) | −24426.0 | − | 195043.i | −0.194916 | − | 1.55641i | ||||
\(355\) | 11336.2 | + | 19634.8i | 0.0899517 | + | 0.155801i | ||||
\(356\) | −13434.4 | + | 7756.35i | −0.106003 | + | 0.0612008i | ||||
\(357\) | 1436.14 | − | 3406.17i | 0.0112684 | − | 0.0267257i | ||||
\(358\) | −156336. | + | 270782.i | −1.21981 | + | 2.11278i | ||||
\(359\) | 69656.7i | 0.540473i | 0.962794 | + | 0.270236i | \(0.0871019\pi\) | ||||
−0.962794 | + | 0.270236i | \(0.912898\pi\) | |||||||
\(360\) | 47742.8 | + | 48964.2i | 0.368386 | + | 0.377810i | ||||
\(361\) | −127391. | −0.977516 | ||||||||
\(362\) | 259712. | + | 149945.i | 1.98187 | + | 1.14423i | ||||
\(363\) | 7008.27 | − | 5307.66i | 0.0531860 | − | 0.0402801i | ||||
\(364\) | 53529.9 | + | 92716.6i | 0.404012 | + | 0.699769i | ||||
\(365\) | 9689.60 | − | 5594.30i | 0.0727311 | − | 0.0419913i | ||||
\(366\) | 534.661 | + | 705.969i | 0.00399132 | + | 0.00527016i | ||||
\(367\) | 88084.2 | − | 152566.i | 0.653982 | − | 1.13273i | −0.328166 | − | 0.944620i | \(-0.606431\pi\) |
0.982148 | − | 0.188110i | \(-0.0602361\pi\) | |||||||
\(368\) | 15416.0i | 0.113835i | ||||||||
\(369\) | −73051.6 | + | 71229.5i | −0.536509 | + | 0.523127i | ||||
\(370\) | 132729. | 0.969531 | ||||||||
\(371\) | 195145. | + | 112667.i | 1.41778 | + | 0.818558i | ||||
\(372\) | 342246. | + | 144302.i | 2.47316 | + | 1.04276i | ||||
\(373\) | −33593.6 | − | 58185.7i | −0.241456 | − | 0.418214i | 0.719673 | − | 0.694313i | \(-0.244292\pi\) |
−0.961129 | + | 0.276099i | \(0.910958\pi\) | |||||||
\(374\) | 5467.59 | − | 3156.71i | 0.0390888 | − | 0.0225679i | ||||
\(375\) | 116922. | − | 14642.6i | 0.831445 | − | 0.104125i | ||||
\(376\) | −28662.6 | + | 49645.0i | −0.202740 | + | 0.351156i | ||||
\(377\) | − | 40338.3i | − | 0.283815i | ||||||
\(378\) | −198916. | − | 158709.i | −1.39215 | − | 1.11076i | ||||
\(379\) | 43976.9 | 0.306158 | 0.153079 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153079 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(380\) | −14878.2 | − | 8589.95i | −0.103035 | − | 0.0594872i | ||||
\(381\) | −15121.8 | − | 120749.i | −0.104173 | − | 0.831825i | ||||
\(382\) | −153065. | − | 265116.i | −1.04893 | − | 1.81681i | ||||
\(383\) | −160336. | + | 92569.8i | −1.09303 | + | 0.631062i | −0.934382 | − | 0.356273i | \(-0.884047\pi\) |
−0.158649 | + | 0.987335i | \(0.550714\pi\) | |||||||
\(384\) | −98317.7 | + | 233184.i | −0.666759 | + | 1.58138i | ||||
\(385\) | 39223.1 | − | 67936.4i | 0.264619 | − | 0.458333i | ||||
\(386\) | − | 178279.i | − | 1.19654i | ||||||
\(387\) | −57242.8 | + | 203327.i | −0.382207 | + | 1.35760i | ||||
\(388\) | −407353. | −2.70587 | ||||||||
\(389\) | −26364.0 | − | 15221.3i | −0.174226 | − | 0.100589i | 0.410351 | − | 0.911928i | \(-0.365406\pi\) |
−0.584577 | + | 0.811338i | \(0.698740\pi\) | |||||||
\(390\) | −41329.7 | + | 31300.8i | −0.271727 | + | 0.205791i | ||||
\(391\) | 1541.80 | + | 2670.48i | 0.0100850 | + | 0.0174677i | ||||
\(392\) | −27117.2 | + | 15656.1i | −0.176471 | + | 0.101885i | ||||
\(393\) | −18458.0 | − | 24372.0i | −0.119508 | − | 0.157800i | ||||
\(394\) | 211860. | − | 366951.i | 1.36476 | − | 2.36383i | ||||
\(395\) | − | 2804.12i | − | 0.0179723i | ||||||
\(396\) | −67237.3 | − | 264236.i | −0.428766 | − | 1.68501i | ||||
\(397\) | −235724. | −1.49563 | −0.747813 | − | 0.663910i | \(-0.768896\pi\) | ||||
−0.747813 | + | 0.663910i | \(0.768896\pi\) | |||||||
\(398\) | 146640. | + | 84662.7i | 0.925734 | + | 0.534473i | ||||
\(399\) | 23914.5 | + | 10083.1i | 0.150216 | + | 0.0633355i | ||||
\(400\) | −9369.41 | − | 16228.3i | −0.0585588 | − | 0.101427i | ||||
\(401\) | 202830. | − | 117104.i | 1.26137 | − | 0.728254i | 0.288032 | − | 0.957621i | \(-0.406999\pi\) |
0.973340 | + | 0.229367i | \(0.0736656\pi\) | |||||||
\(402\) | 303250. | − | 37977.2i | 1.87650 | − | 0.235002i | ||||
\(403\) | −57157.8 | + | 99000.1i | −0.351937 | + | 0.609573i | ||||
\(404\) | 297925.i | 1.82534i | ||||||||
\(405\) | 40332.6 | − | 65953.4i | 0.245893 | − | 0.402093i | ||||
\(406\) | 188726. | 1.14493 | ||||||||
\(407\) | −186056. | − | 107419.i | −1.12319 | − | 0.648475i | ||||
\(408\) | −617.832 | − | 4933.42i | −0.00371150 | − | 0.0296365i | ||||
\(409\) | 148893. | + | 257890.i | 0.890076 | + | 1.54166i | 0.839783 | + | 0.542922i | \(0.182682\pi\) |
0.0502930 | + | 0.998735i | \(0.483984\pi\) | |||||||
\(410\) | −84224.3 | + | 48626.9i | −0.501037 | + | 0.289274i | ||||
\(411\) | 13368.1 | − | 31705.7i | 0.0791382 | − | 0.187696i | ||||
\(412\) | −47984.1 | + | 83110.9i | −0.282685 | + | 0.489625i | ||||
\(413\) | 177569.i | 1.04104i | ||||||||
\(414\) | 205721. | − | 52347.5i | 1.20027 | − | 0.305419i | ||||
\(415\) | −155134. | −0.900763 | ||||||||
\(416\) | −57758.3 | − | 33346.8i | −0.333755 | − | 0.192694i | ||||
\(417\) | −24943.5 | + | 18890.8i | −0.143445 | + | 0.108637i | ||||
\(418\) | 22163.1 | + | 38387.6i | 0.126846 | + | 0.219704i | ||||
\(419\) | −31934.0 | + | 18437.1i | −0.181897 | + | 0.105018i | −0.588184 | − | 0.808727i | \(-0.700157\pi\) |
0.406287 | + | 0.913746i | \(0.366823\pi\) | |||||||
\(420\) | −91870.4 | − | 121306.i | −0.520807 | − | 0.687676i | ||||
\(421\) | −120305. | + | 208374.i | −0.678764 | + | 1.17565i | 0.296589 | + | 0.955005i | \(0.404151\pi\) |
−0.975353 | + | 0.220649i | \(0.929183\pi\) | |||||||
\(422\) | 301799.i | 1.69470i | ||||||||
\(423\) | 62377.9 | + | 17561.3i | 0.348618 | + | 0.0981468i | ||||
\(424\) | 303080. | 1.68588 | ||||||||
\(425\) | −3246.08 | − | 1874.12i | −0.0179714 | − | 0.0103758i | ||||
\(426\) | −104559. | − | 44085.1i | −0.576156 | − | 0.242925i | ||||
\(427\) | −399.995 | − | 692.812i | −0.00219381 | − | 0.00379979i | ||||
\(428\) | 266686. | − | 153971.i | 1.45584 | − | 0.840529i | ||||
\(429\) | 83267.0 | − | 10427.9i | 0.452437 | − | 0.0566605i | ||||
\(430\) | −100671. | + | 174368.i | −0.544463 | + | 0.943038i | ||||
\(431\) | − | 162758.i | − | 0.876169i | −0.898934 | − | 0.438084i | \(-0.855657\pi\) | ||
0.898934 | − | 0.438084i | \(-0.144343\pi\) | |||||||
\(432\) | −27784.1 | − | 4194.67i | −0.148877 | − | 0.0224766i | ||||
\(433\) | 266637. | 1.42215 | 0.711073 | − | 0.703118i | \(-0.248209\pi\) | ||||
0.711073 | + | 0.703118i | \(0.248209\pi\) | |||||||
\(434\) | −463180. | − | 267417.i | −2.45906 | − | 1.41974i | ||||
\(435\) | 7124.59 | + | 56890.2i | 0.0376514 | + | 0.300649i | ||||
\(436\) | −64381.1 | − | 111511.i | −0.338677 | − | 0.586605i | ||||
\(437\) | −18749.3 | + | 10824.9i | −0.0981796 | + | 0.0566840i | ||||
\(438\) | −21755.6 | + | 51598.7i | −0.113402 | + | 0.268962i | ||||
\(439\) | 18408.7 | − | 31884.8i | 0.0955201 | − | 0.165446i | −0.814305 | − | 0.580437i | \(-0.802882\pi\) |
0.909826 | + | 0.414991i | \(0.136215\pi\) | |||||||
\(440\) | − | 105512.i | − | 0.545001i | ||||||
\(441\) | 24711.1 | + | 25343.3i | 0.127062 | + | 0.130312i | ||||
\(442\) | 3769.25 | 0.0192935 | ||||||||
\(443\) | −119117. | − | 68772.0i | −0.606967 | − | 0.350432i | 0.164811 | − | 0.986325i | \(-0.447299\pi\) |
−0.771777 | + | 0.635893i | \(0.780632\pi\) | |||||||
\(444\) | −332218. | + | 251603.i | −1.68522 | + | 1.27629i | ||||
\(445\) | 3393.06 | + | 5876.95i | 0.0171345 | + | 0.0296778i | ||||
\(446\) | 124337. | − | 71786.2i | 0.625075 | − | 0.360887i | ||||
\(447\) | −48419.0 | − | 63932.7i | −0.242326 | − | 0.319969i | ||||
\(448\) | 172442. | − | 298679.i | 0.859188 | − | 1.48816i | ||||
\(449\) | − | 174405.i | − | 0.865101i | −0.901610 | − | 0.432550i | \(-0.857614\pi\) | ||
0.901610 | − | 0.432550i | \(-0.142386\pi\) | |||||||
\(450\) | −184745. | + | 180137.i | −0.912322 | + | 0.889565i | ||||
\(451\) | 157418. | 0.773929 | ||||||||
\(452\) | 104769. | + | 60488.4i | 0.512809 | + | 0.296070i | ||||
\(453\) | −82227.8 | − | 34669.8i | −0.400703 | − | 0.168949i | ||||
\(454\) | −163110. | − | 282515.i | −0.791352 | − | 1.37066i | ||||
\(455\) | 40559.4 | − | 23417.0i | 0.195916 | − | 0.113112i | ||||
\(456\) | 34637.2 | − | 4337.76i | 0.166576 | − | 0.0208610i | ||||
\(457\) | −57654.7 | + | 99860.9i | −0.276059 | + | 0.478149i | −0.970402 | − | 0.241496i | \(-0.922362\pi\) |
0.694342 | + | 0.719645i | \(0.255695\pi\) | |||||||
\(458\) | 186884.i | 0.890923i | ||||||||
\(459\) | −5232.48 | + | 2052.13i | −0.0248360 | + | 0.00974047i | ||||
\(460\) | 126937. | 0.599890 | ||||||||
\(461\) | 351141. | + | 202731.i | 1.65226 | + | 0.953936i | 0.976138 | + | 0.217150i | \(0.0696762\pi\) |
0.676127 | + | 0.736785i | \(0.263657\pi\) | |||||||
\(462\) | 48787.5 | + | 389571.i | 0.228573 | + | 1.82517i | ||||
\(463\) | −36293.4 | − | 62861.9i | −0.169303 | − | 0.293242i | 0.768872 | − | 0.639403i | \(-0.220818\pi\) |
−0.938175 | + | 0.346161i | \(0.887485\pi\) | |||||||
\(464\) | 18047.3 | − | 10419.6i | 0.0838253 | − | 0.0483966i | ||||
\(465\) | 63125.6 | − | 149718.i | 0.291944 | − | 0.692417i | ||||
\(466\) | −144320. | + | 249969.i | −0.664590 | + | 1.15110i | ||||
\(467\) | − | 358806.i | − | 1.64523i | −0.568602 | − | 0.822613i | \(-0.692515\pi\) | ||
0.568602 | − | 0.822613i | \(-0.307485\pi\) | |||||||
\(468\) | 44113.3 | − | 156691.i | 0.201408 | − | 0.715404i | ||||
\(469\) | −276081. | −1.25514 | ||||||||
\(470\) | 53493.6 | + | 30884.6i | 0.242162 | + | 0.139812i | ||||
\(471\) | −40514.7 | + | 30683.5i | −0.182629 | + | 0.138313i | ||||
\(472\) | 119417. | + | 206837.i | 0.536022 | + | 0.928418i | ||||
\(473\) | 282236. | − | 162949.i | 1.26151 | − | 0.728333i | ||||
\(474\) | 8473.07 | + | 11187.9i | 0.0377124 | + | 0.0497956i | ||||
\(475\) | 13158.1 | − | 22790.5i | 0.0583185 | − | 0.101011i | ||||
\(476\) | 11063.1i | 0.0488271i | ||||||||
\(477\) | −84489.0 | − | 332034.i | −0.371333 | − | 1.45930i | ||||
\(478\) | −134819. | −0.590058 | ||||||||
\(479\) | −22169.8 | − | 12799.8i | −0.0966255 | − | 0.0557867i | 0.450909 | − | 0.892570i | \(-0.351100\pi\) |
−0.547534 | + | 0.836783i | \(0.684433\pi\) | |||||||
\(480\) | 87347.9 | + | 36828.5i | 0.379114 | + | 0.159846i | ||||
\(481\) | −64131.5 | − | 111079.i | −0.277192 | − | 0.480111i | ||||
\(482\) | −328661. | + | 189752.i | −1.41466 | + | 0.816757i | ||||
\(483\) | −190274. | + | 23828.8i | −0.815615 | + | 0.102143i | ||||
\(484\) | −13155.4 | + | 22785.7i | −0.0561580 | + | 0.0972685i | ||||
\(485\) | 178199.i | 0.757569i | ||||||||
\(486\) | 38368.8 | + | 385012.i | 0.162445 | + | 1.63005i | ||||
\(487\) | 247261. | 1.04255 | 0.521277 | − | 0.853388i | \(-0.325456\pi\) | ||||
0.521277 | + | 0.853388i | \(0.325456\pi\) | |||||||
\(488\) | −931.850 | − | 538.004i | −0.00391297 | − | 0.00225915i | ||||
\(489\) | 2408.47 | + | 19231.8i | 0.0100722 | + | 0.0804269i | ||||
\(490\) | 16869.8 | + | 29219.4i | 0.0702616 | + | 0.121697i | ||||
\(491\) | −296403. | + | 171128.i | −1.22947 | + | 0.709837i | −0.966920 | − | 0.255081i | \(-0.917898\pi\) |
−0.262554 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(492\) | 118634. | − | 281370.i | 0.490094 | − | 1.16238i | ||||
\(493\) | 2084.19 | − | 3609.92i | 0.00857517 | − | 0.0148526i | ||||
\(494\) | 26463.7i | 0.108442i | ||||||||
\(495\) | −115592. | + | 29413.4i | −0.471755 | + | 0.120042i | ||||
\(496\) | −59056.5 | −0.240052 | ||||||||
\(497\) | 88772.2 | + | 51252.7i | 0.359389 | + | 0.207493i | ||||
\(498\) | 618953. | − | 468760.i | 2.49574 | − | 1.89013i | ||||
\(499\) | 98919.1 | + | 171333.i | 0.397264 | + | 0.688081i | 0.993387 | − | 0.114812i | \(-0.0366265\pi\) |
−0.596124 | + | 0.802893i | \(0.703293\pi\) | |||||||
\(500\) | −305411. | + | 176329.i | −1.22164 | + | 0.705317i | ||||
\(501\) | 201155. | + | 265606.i | 0.801411 | + | 1.05819i | ||||
\(502\) | 177377. | − | 307227.i | 0.703867 | − | 1.21913i | ||||
\(503\) | 187051.i | 0.739305i | 0.929170 | + | 0.369652i | \(0.120523\pi\) | ||||
−0.929170 | + | 0.369652i | \(0.879477\pi\) | |||||||
\(504\) | 297622. | + | 83789.7i | 1.17167 | + | 0.329860i | ||||
\(505\) | 130329. | 0.511044 | ||||||||
\(506\) | −283634. | − | 163756.i | −1.10779 | − | 0.639582i | ||||
\(507\) | −190692. | − | 80401.5i | −0.741850 | − | 0.312787i | ||||
\(508\) | 182100. | + | 315406.i | 0.705639 | + | 1.22220i | ||||
\(509\) | −25011.5 | + | 14440.4i | −0.0965393 | + | 0.0557370i | −0.547492 | − | 0.836811i | \(-0.684417\pi\) |
0.450953 | + | 0.892548i | \(0.351084\pi\) | |||||||
\(510\) | −5315.87 | + | 665.728i | −0.0204378 | + | 0.00255951i | ||||
\(511\) | 25292.7 | − | 43808.3i | 0.0968620 | − | 0.167770i | ||||
\(512\) | − | 78644.0i | − | 0.300003i | ||||||
\(513\) | −14407.9 | − | 36736.9i | −0.0547477 | − | 0.139595i | ||||
\(514\) | −745440. | −2.82154 | ||||||||
\(515\) | 36357.4 | + | 20990.9i | 0.137081 | + | 0.0791439i | ||||
\(516\) | −78556.0 | − | 627274.i | −0.295039 | − | 2.35590i | ||||
\(517\) | −49990.6 | − | 86586.3i | −0.187028 | − | 0.323943i | ||||
\(518\) | 519692. | − | 300044.i | 1.93681 | − | 1.11822i | ||||
\(519\) | −169883. | + | 402919.i | −0.630689 | + | 1.49583i | ||||
\(520\) | 31496.5 | − | 54553.5i | 0.116481 | − | 0.201751i | ||||
\(521\) | 269661.i | 0.993443i | 0.867910 | + | 0.496721i | \(0.165463\pi\) | ||||
−0.867910 | + | 0.496721i | \(0.834537\pi\) | |||||||
\(522\) | −200328. | − | 205453.i | −0.735191 | − | 0.753998i | ||||
\(523\) | −187282. | −0.684689 | −0.342344 | − | 0.939575i | \(-0.611221\pi\) | ||||
−0.342344 | + | 0.939575i | \(0.611221\pi\) | |||||||
\(524\) | 79239.8 | + | 45749.1i | 0.288590 | + | 0.166617i | ||||
\(525\) | 185817. | − | 140727.i | 0.674166 | − | 0.510575i | ||||
\(526\) | −145347. | − | 251748.i | −0.525331 | − | 0.909901i | ||||
\(527\) | −10230.2 | + | 5906.41i | −0.0368352 | + | 0.0212668i | ||||
\(528\) | 26173.7 | + | 34559.9i | 0.0938851 | + | 0.123966i | ||||
\(529\) | −59938.8 | + | 103817.i | −0.214189 | + | 0.370986i | ||||
\(530\) | − | 326576.i | − | 1.16261i | ||||||
\(531\) | 193306. | − | 188485.i | 0.685578 | − | 0.668478i | ||||
\(532\) | −77673.1 | −0.274440 | ||||||||
\(533\) | 81390.6 | + | 46990.9i | 0.286497 | + | 0.165409i | ||||
\(534\) | −31295.7 | − | 13195.2i | −0.109749 | − | 0.0462737i | ||||
\(535\) | −67355.7 | − | 116664.i | −0.235324 | − | 0.407594i | ||||
\(536\) | −321586. | + | 185668.i | −1.11936 | + | 0.646260i | ||||
\(537\) | −426133. | + | 53366.3i | −1.47773 | + | 0.185063i | ||||
\(538\) | 14513.0 | − | 25137.3i | 0.0501411 | − | 0.0868469i | ||||
\(539\) | − | 54611.9i | − | 0.187979i | ||||||
\(540\) | −34539.3 | + | 228776.i | −0.118447 | + | 0.784555i | ||||
\(541\) | −25587.9 | −0.0874259 | −0.0437129 | − | 0.999044i | \(-0.513919\pi\) | ||||
−0.0437129 | + | 0.999044i | \(0.513919\pi\) | |||||||
\(542\) | 488653. | + | 282124.i | 1.66342 | + | 0.960377i | ||||
\(543\) | 51184.7 | + | 408713.i | 0.173596 | + | 1.38618i | ||||
\(544\) | −3445.90 | − | 5968.47i | −0.0116441 | − | 0.0201681i | ||||
\(545\) | −48781.3 | + | 28163.9i | −0.164233 | + | 0.0948200i | ||||
\(546\) | −91066.0 | + | 215985.i | −0.305472 | + | 0.724501i | ||||
\(547\) | 138424. | − | 239758.i | 0.462634 | − | 0.801306i | −0.536457 | − | 0.843928i | \(-0.680238\pi\) |
0.999091 | + | 0.0426215i | \(0.0135710\pi\) | |||||||
\(548\) | 102979.i | 0.342915i | ||||||||
\(549\) | −329.630 | + | 1170.85i | −0.00109366 | + | 0.00388469i | ||||
\(550\) | 398105. | 1.31605 | ||||||||
\(551\) | 25345.0 | + | 14633.0i | 0.0834813 | + | 0.0481980i | ||||
\(552\) | −205611. | + | 155718.i | −0.674790 | + | 0.511047i | ||||
\(553\) | −6338.95 | − | 10979.4i | −0.0207285 | − | 0.0359027i | ||||
\(554\) | 400705. | − | 231347.i | 1.30559 | − | 0.753780i | ||||
\(555\) | 110065. | + | 145331.i | 0.357326 | + | 0.471815i | ||||
\(556\) | 46821.9 | − | 81098.0i | 0.151461 | − | 0.262338i | ||||
\(557\) | − | 461786.i | − | 1.48844i | −0.667936 | − | 0.744219i | \(-0.732822\pi\) | ||
0.667936 | − | 0.744219i | \(-0.267178\pi\) | |||||||
\(558\) | 200536. | + | 788087.i | 0.644056 | + | 2.53108i | ||||
\(559\) | 194568. | 0.622656 | ||||||||
\(560\) | 20953.4 | + | 12097.4i | 0.0668157 | + | 0.0385761i | ||||
\(561\) | 7990.43 | + | 3369.01i | 0.0253889 | + | 0.0107047i | ||||
\(562\) | 488995. | + | 846964.i | 1.54822 | + | 2.68159i | ||||
\(563\) | −154104. | + | 88972.1i | −0.486181 | + | 0.280697i | −0.722989 | − | 0.690860i | \(-0.757232\pi\) |
0.236808 | + | 0.971556i | \(0.423899\pi\) | |||||||
\(564\) | −192439. | + | 24099.9i | −0.604971 | + | 0.0757630i | ||||
\(565\) | 26461.0 | − | 45831.8i | 0.0828914 | − | 0.143572i | ||||
\(566\) | − | 549930.i | − | 1.71662i | ||||||
\(567\) | 8826.98 | − | 349412.i | 0.0274566 | − | 1.08685i | ||||
\(568\) | 137872. | 0.427347 | ||||||||
\(569\) | −5111.83 | − | 2951.31i | −0.0157889 | − | 0.00911572i | 0.492085 | − | 0.870547i | \(-0.336235\pi\) |
−0.507874 | + | 0.861432i | \(0.669568\pi\) | |||||||
\(570\) | −4674.04 | − | 37322.4i | −0.0143861 | − | 0.114874i | ||||
\(571\) | −238346. | − | 412828.i | −0.731031 | − | 1.26618i | −0.956443 | − | 0.291920i | \(-0.905706\pi\) |
0.225411 | − | 0.974264i | \(-0.427627\pi\) | |||||||
\(572\) | −217501. | + | 125574.i | −0.664767 | + | 0.383803i | ||||
\(573\) | 163359. | − | 387445.i | 0.497545 | − | 1.18005i | ||||
\(574\) | −219850. | + | 380792.i | −0.667272 | + | 1.15575i | ||||
\(575\) | 194442.i | 0.588105i | ||||||||
\(576\) | −508194. | + | 129315.i | −1.53174 | + | 0.389765i | ||||
\(577\) | 209901. | 0.630468 | 0.315234 | − | 0.949014i | \(-0.397917\pi\) | ||||
0.315234 | + | 0.949014i | \(0.397917\pi\) | |||||||
\(578\) | −473614. | − | 273441.i | −1.41765 | − | 0.818480i | ||||
\(579\) | 195206. | − | 147838.i | 0.582285 | − | 0.440990i | ||||
\(580\) | −85795.7 | − | 148603.i | −0.255041 | − | 0.441744i | ||||
\(581\) | −607417. | + | 350693.i | −1.79943 | + | 1.03890i | ||||
\(582\) | −538455. | − | 710978.i | −1.58966 | − | 2.09899i | ||||
\(583\) | −264302. | + | 457785.i | −0.777614 | + | 1.34687i | ||||
\(584\) | − | 68038.7i | − | 0.199494i | ||||||
\(585\) | −68545.2 | − | 19297.6i | −0.200293 | − | 0.0563887i | ||||
\(586\) | 235255. | 0.685083 | ||||||||
\(587\) | −156552. | − | 90385.1i | −0.454340 | − | 0.262313i | 0.255321 | − | 0.966856i | \(-0.417819\pi\) |
−0.709661 | + | 0.704543i | \(0.751152\pi\) | |||||||
\(588\) | −97613.6 | − | 41156.9i | −0.282329 | − | 0.119039i | ||||
\(589\) | −41468.6 | − | 71825.7i | −0.119533 | − | 0.207038i | ||||
\(590\) | 222871. | − | 128675.i | 0.640250 | − | 0.369649i | ||||
\(591\) | 577476. | − | 72319.7i | 1.65333 | − | 0.207053i | ||||
\(592\) | 33131.0 | − | 57384.5i | 0.0945346 | − | 0.163739i | ||||
\(593\) | − | 468097.i | − | 1.33115i | −0.746332 | − | 0.665574i | \(-0.768187\pi\) | ||
0.746332 | − | 0.665574i | \(-0.231813\pi\) | |||||||
\(594\) | 372311. | − | 466631.i | 1.05520 | − | 1.32252i | ||||
\(595\) | 4839.60 | 0.0136702 | ||||||||
\(596\) | 207862. | + | 120009.i | 0.585171 | + | 0.337849i | ||||
\(597\) | 28900.2 | + | 230769.i | 0.0810871 | + | 0.647485i | ||||
\(598\) | −97765.8 | − | 169335.i | −0.273391 | − | 0.473527i | ||||
\(599\) | 558557. | − | 322483.i | 1.55673 | − | 0.898780i | 0.559167 | − | 0.829055i | \(-0.311121\pi\) |
0.997566 | − | 0.0697251i | \(-0.0222122\pi\) | |||||||
\(600\) | 121804. | − | 288887.i | 0.338344 | − | 0.802465i | ||||
\(601\) | −127517. | + | 220865.i | −0.353035 | + | 0.611474i | −0.986780 | − | 0.162068i | \(-0.948184\pi\) |
0.633745 | + | 0.773542i | \(0.281517\pi\) | |||||||
\(602\) | 910302.i | 2.51184i | ||||||||
\(603\) | 293053. | + | 300550.i | 0.805956 | + | 0.826574i | ||||
\(604\) | 267072. | 0.732073 | ||||||||
\(605\) | 9967.76 | + | 5754.89i | 0.0272325 | + | 0.0157227i | ||||
\(606\) | −519986. | + | 393808.i | −1.41595 | + | 1.07236i | ||||
\(607\) | 176351. | + | 305449.i | 0.478631 | + | 0.829013i | 0.999700 | − | 0.0245019i | \(-0.00779999\pi\) |
−0.521069 | + | 0.853514i | \(0.674467\pi\) | |||||||
\(608\) | 41904.3 | − | 24193.5i | 0.113358 | − | 0.0654472i | ||||
\(609\) | 156501. | + | 206645.i | 0.421971 | + | 0.557172i | ||||
\(610\) | −579.711 | + | 1004.09i | −0.00155795 | + | 0.00269844i | ||||
\(611\) | − | 59690.9i | − | 0.159892i | ||||||
\(612\) | 12043.6 | − | 11743.2i | 0.0321553 | − | 0.0313532i | ||||
\(613\) | −37013.8 | −0.0985015 | −0.0492508 | − | 0.998786i | \(-0.515683\pi\) | ||||
−0.0492508 | + | 0.998786i | \(0.515683\pi\) | |||||||
\(614\) | −40030.6 | − | 23111.7i | −0.106183 | − | 0.0613048i | ||||
\(615\) | −123087. | − | 51897.2i | −0.325433 | − | 0.137212i | ||||
\(616\) | −238519. | − | 413127.i | −0.628581 | − | 1.08873i | ||||
\(617\) | −493797. | + | 285094.i | −1.29711 | + | 0.748888i | −0.979904 | − | 0.199467i | \(-0.936079\pi\) |
−0.317208 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(618\) | −208486. | + | 26109.5i | −0.545883 | + | 0.0683631i | ||||
\(619\) | 220407. | − | 381756.i | 0.575233 | − | 0.996333i | −0.420783 | − | 0.907161i | \(-0.638245\pi\) |
0.996016 | − | 0.0891715i | \(-0.0284219\pi\) | |||||||
\(620\) | 486276.i | 1.26503i | ||||||||
\(621\) | 227912. | + | 181844.i | 0.590995 | + | 0.471537i | ||||
\(622\) | −561296. | −1.45081 | ||||||||
\(623\) | 26570.7 | + | 15340.6i | 0.0684583 | + | 0.0395244i | ||||
\(624\) | 3216.23 | + | 25681.8i | 0.00825996 | + | 0.0659562i | ||||
\(625\) | −74789.0 | − | 129538.i | −0.191460 | − | 0.331618i | ||||
\(626\) | 416759. | − | 240616.i | 1.06350 | − | 0.614011i | ||||
\(627\) | −23653.6 | + | 56100.3i | −0.0601676 | + | 0.142702i | ||||
\(628\) | 76050.9 | − | 131724.i | 0.192835 | − | 0.333999i | ||||
\(629\) | − | 13254.1i | − | 0.0335003i | ||||||
\(630\) | 90285.3 | − | 320694.i | 0.227476 | − | 0.807997i | ||||
\(631\) | −80926.3 | −0.203250 | −0.101625 | − | 0.994823i | \(-0.532404\pi\) | ||||
−0.101625 | + | 0.994823i | \(0.532404\pi\) | |||||||
\(632\) | −14767.6 | − | 8526.05i | −0.0369721 | − | 0.0213459i | ||||
\(633\) | −330454. | + | 250267.i | −0.824714 | + | 0.624592i | ||||
\(634\) | −161321. | − | 279417.i | −0.401341 | − | 0.695143i | ||||
\(635\) | 137976. | − | 79660.7i | 0.342182 | − | 0.197559i | ||||
\(636\) | 619063. | + | 817414.i | 1.53046 | + | 2.02082i | ||||
\(637\) | 16302.2 | − | 28236.3i | 0.0401761 | − | 0.0695870i | ||||
\(638\) | 442727.i | 1.08766i | ||||||||
\(639\) | −38434.3 | − | 151043.i | −0.0941278 | − | 0.369913i | ||||
\(640\) | −331317. | −0.808879 | ||||||||
\(641\) | −131917. | − | 76162.1i | −0.321058 | − | 0.185363i | 0.330806 | − | 0.943699i | \(-0.392679\pi\) |
−0.651864 | + | 0.758336i | \(0.726013\pi\) | |||||||
\(642\) | 621252. | + | 261939.i | 1.50729 | + | 0.635521i | ||||
\(643\) | −58437.1 | − | 101216.i | −0.141340 | − | 0.244809i | 0.786661 | − | 0.617385i | \(-0.211808\pi\) |
−0.928002 | + | 0.372576i | \(0.878475\pi\) | |||||||
\(644\) | 497013. | − | 286951.i | 1.19838 | − | 0.691888i | ||||
\(645\) | −274405. | + | 34364.8i | −0.659587 | + | 0.0826027i | ||||
\(646\) | −1367.31 | + | 2368.26i | −0.00327645 | + | 0.00567498i | ||||
\(647\) | 481407.i | 1.15002i | 0.818148 | + | 0.575008i | \(0.195001\pi\) | ||||
−0.818148 | + | 0.575008i | \(0.804999\pi\) | |||||||
\(648\) | −224702. | − | 412940.i | −0.535127 | − | 0.983416i | ||||
\(649\) | −416553. | −0.988965 | ||||||||
\(650\) | 205834. | + | 118838.i | 0.487181 | + | 0.281274i | ||||
\(651\) | −91284.6 | − | 728912.i | −0.215395 | − | 1.71994i | ||||
\(652\) | −29003.3 | − | 50235.2i | −0.0682263 | − | 0.118171i | ||||
\(653\) | 399091. | − | 230415.i | 0.935935 | − | 0.540363i | 0.0472516 | − | 0.998883i | \(-0.484954\pi\) |
0.888684 | + | 0.458520i | \(0.151620\pi\) | |||||||
\(654\) | 109526. | − | 259768.i | 0.256072 | − | 0.607338i | ||||
\(655\) | 20013.2 | − | 34663.9i | 0.0466482 | − | 0.0807970i | ||||
\(656\) | 48551.9i | 0.112823i | ||||||||
\(657\) | −74538.5 | + | 18967.0i | −0.172683 | + | 0.0439408i | ||||
\(658\) | 279268. | 0.645015 | ||||||||
\(659\) | 142960. | + | 82538.2i | 0.329189 | + | 0.190057i | 0.655481 | − | 0.755212i | \(-0.272466\pi\) |
−0.326292 | + | 0.945269i | \(0.605799\pi\) | |||||||
\(660\) | 284569. | − | 215516.i | 0.653280 | − | 0.494757i | ||||
\(661\) | 140878. | + | 244008.i | 0.322434 | + | 0.558472i | 0.980990 | − | 0.194060i | \(-0.0621657\pi\) |
−0.658556 | + | 0.752532i | \(0.728832\pi\) | |||||||
\(662\) | −465383. | + | 268689.i | −1.06193 | + | 0.613104i | ||||
\(663\) | 3125.65 | + | 4127.12i | 0.00711071 | + | 0.00938902i | ||||
\(664\) | −471691. | + | 816992.i | −1.06985 | + | 1.85303i | ||||
\(665\) | 33978.6i | 0.0768355i | ||||||||
\(666\) | −878276. | − | 247262.i | −1.98008 | − | 0.557454i | ||||
\(667\) | −216236. | −0.486046 | ||||||||
\(668\) | −863556. | − | 498574.i | −1.93525 | − | 1.11732i | ||||
\(669\) | 181709. | + | 76614.0i | 0.405998 | + | 0.171181i | ||||
\(670\) | 200061. | + | 346517.i | 0.445670 | + | 0.771924i | ||||
\(671\) | 1625.25 | − | 938.337i | 0.00360973 | − | 0.00208408i | ||||
\(672\) | 425259. | − | 53256.9i | 0.941706 | − | 0.117934i | ||||
\(673\) | 378387. | − | 655386.i | 0.835423 | − | 1.44699i | −0.0582627 | − | 0.998301i | \(-0.518556\pi\) |
0.893686 | − | 0.448694i | \(-0.148111\pi\) | |||||||
\(674\) | − | 307855.i | − | 0.677683i | ||||||
\(675\) | −350440. | − | 52907.4i | −0.769141 | − | 0.116120i | ||||
\(676\) | 619357. | 1.35534 | ||||||||
\(677\) | −59053.2 | − | 34094.4i | −0.128845 | − | 0.0743885i | 0.434192 | − | 0.900820i | \(-0.357034\pi\) |
−0.563037 | + | 0.826432i | \(0.690367\pi\) | |||||||
\(678\) | 32913.4 | + | 262815.i | 0.0716002 | + | 0.571731i | ||||
\(679\) | 402833. | + | 697728.i | 0.873747 | + | 1.51337i | ||||
\(680\) | 5637.30 | − | 3254.70i | 0.0121914 | − | 0.00703870i | ||||
\(681\) | 174080. | − | 412873.i | 0.375365 | − | 0.890270i | ||||
\(682\) | 627326. | − | 1.08656e6i | 1.34873 | − | 2.33606i | ||||
\(683\) | 31351.1i | 0.0672066i | 0.999435 | + | 0.0336033i | \(0.0106983\pi\) | ||||
−0.999435 | + | 0.0336033i | \(0.989302\pi\) | |||||||
\(684\) | 82448.1 | + | 84557.2i | 0.176225 | + | 0.180733i | ||||
\(685\) | 45048.7 | 0.0960065 | ||||||||
\(686\) | −593726. | − | 342788.i | −1.26165 | − | 0.728412i | ||||
\(687\) | −204627. | + | 154973.i | −0.433561 | + | 0.328355i | ||||
\(688\) | 50257.9 | + | 87049.3i | 0.106176 | + | 0.183903i | ||||
\(689\) | −273307. | + | 157794.i | −0.575722 | + | 0.332393i | ||||
\(690\) | 167790. | + | 221551.i | 0.352426 | + | 0.465345i | ||||
\(691\) | −187442. | + | 324659.i | −0.392565 | + | 0.679942i | −0.992787 | − | 0.119891i | \(-0.961745\pi\) |
0.600222 | + | 0.799833i | \(0.295079\pi\) | |||||||
\(692\) | − | 1.30866e6i | − | 2.73285i | ||||||
\(693\) | −386102. | + | 376471.i | −0.803962 | + | 0.783908i | ||||
\(694\) | −290405. | −0.602955 | ||||||||
\(695\) | −35476.8 | − | 20482.5i | −0.0734471 | − | 0.0424047i | ||||
\(696\) | 321268. | + | 135456.i | 0.663206 | + | 0.279628i | ||||
\(697\) | 4855.81 | + | 8410.52i | 0.00999531 | + | 0.0173124i | ||||
\(698\) | −1.05811e6 | + | 610901.i | −2.17180 | + | 1.25389i | ||||
\(699\) | −393379. | + | 49264.5i | −0.805114 | + | 0.100828i | ||||
\(700\) | −348801. | + | 604140.i | −0.711838 | + | 1.23294i | ||||
\(701\) | 97448.5i | 0.198308i | 0.995072 | + | 0.0991538i | \(0.0316136\pi\) | ||||
−0.995072 | + | 0.0991538i | \(0.968386\pi\) | |||||||
\(702\) | 331792. | − | 130126.i | 0.673274 | − | 0.264052i | ||||
\(703\) | 93056.2 | 0.188293 | ||||||||
\(704\) | 700663. | + | 404528.i | 1.41372 | + | 0.816212i | ||||
\(705\) | 10542.7 | + | 84183.6i | 0.0212115 | + | 0.169375i | ||||
\(706\) | 555961. | + | 962952.i | 1.11541 | + | 1.93195i | ||||
\(707\) | 510295. | − | 294619.i | 1.02090 | − | 0.589416i | ||||
\(708\) | −313925. | + | 744549.i | −0.626266 | + | 1.48534i | ||||
\(709\) | 146263. | − | 253334.i | 0.290965 | − | 0.503967i | −0.683073 | − | 0.730350i | \(-0.739357\pi\) |
0.974038 | + | 0.226383i | \(0.0726902\pi\) | |||||||
\(710\) | − | 148561.i | − | 0.294704i | ||||||
\(711\) | −5223.84 | + | 18555.1i | −0.0103336 | + | 0.0367049i | ||||
\(712\) | 41267.0 | 0.0814034 | ||||||||
\(713\) | 530697. | + | 306398.i | 1.04392 | + | 0.602708i | ||||
\(714\) | −19309.0 | + | 14623.6i | −0.0378760 | + | 0.0286851i | ||||
\(715\) | 54933.3 | + | 95147.2i | 0.107454 | + | 0.186116i | ||||
\(716\) | 1.11310e6 | − | 642648.i | 2.17124 | − | 1.25357i | ||||
\(717\) | −111798. | − | 147619.i | −0.217469 | − | 0.287147i | ||||
\(718\) | 228213. | − | 395276.i | 0.442681 | − | 0.766746i | ||||
\(719\) | 655579.i | 1.26814i | 0.773276 | + | 0.634070i | \(0.218617\pi\) | ||||
−0.773276 | + | 0.634070i | \(0.781383\pi\) | |||||||
\(720\) | −9071.87 | − | 35651.6i | −0.0174998 | − | 0.0687724i | ||||
\(721\) | 189807. | 0.365125 | ||||||||
\(722\) | 722896. | + | 417364.i | 1.38676 | + | 0.800647i | ||||
\(723\) | −480310. | − | 202513.i | −0.918851 | − | 0.387416i | ||||
\(724\) | −616376. | − | 1.06760e6i | −1.17590 | − | 2.03671i | ||||
\(725\) | 227630. | − | 131422.i | 0.433065 | − | 0.250030i | ||||
\(726\) | −57158.6 | + | 7158.20i | −0.108445 | + | 0.0135810i | ||||
\(727\) | −129630. | + | 224526.i | −0.245266 | + | 0.424814i | −0.962206 | − | 0.272321i | \(-0.912209\pi\) |
0.716940 | + | 0.697135i | \(0.245542\pi\) | |||||||
\(728\) | − | 284801.i | − | 0.537377i | ||||||
\(729\) | −389749. | + | 361282.i | −0.733382 | + | 0.679817i | ||||
\(730\) | −73313.3 | −0.137574 | ||||||||
\(731\) | 17412.1 | + | 10052.9i | 0.0325849 | + | 0.0188129i | ||||
\(732\) | −452.362 | − | 3612.13i | −0.000844236 | − | 0.00674126i | ||||
\(733\) | −41254.4 | − | 71454.8i | −0.0767826 | − | 0.132991i | 0.825077 | − | 0.565020i | \(-0.191131\pi\) |
−0.901860 | + | 0.432028i | \(0.857798\pi\) | |||||||
\(734\) | −999691. | + | 577172.i | −1.85555 | + | 1.07130i | ||||
\(735\) | −18004.3 | + | 42701.7i | −0.0333275 | + | 0.0790442i | ||||
\(736\) | −178758. | + | 309618.i | −0.329996 | + | 0.571571i | ||||
\(737\) | − | 647650.i | − | 1.19235i | ||||||
\(738\) | 647907. | − | 164866.i | 1.18960 | − | 0.302703i | ||||
\(739\) | −730583. | −1.33777 | −0.668884 | − | 0.743367i | \(-0.733228\pi\) | ||||
−0.668884 | + | 0.743367i | \(0.733228\pi\) | |||||||
\(740\) | −472509. | − | 272803.i | −0.862872 | − | 0.498179i | ||||
\(741\) | −28976.3 | + | 21945.0i | −0.0527723 | + | 0.0399667i | ||||
\(742\) | −738251. | − | 1.27869e6i | −1.34090 | − | 2.32251i | ||||
\(743\) | 391257. | − | 225892.i | 0.708735 | − | 0.409189i | −0.101857 | − | 0.994799i | \(-0.532479\pi\) |
0.810593 | + | 0.585611i | \(0.199145\pi\) | |||||||
\(744\) | −596533. | − | 787666.i | −1.07768 | − | 1.42297i | ||||
\(745\) | 52498.8 | − | 90930.6i | 0.0945882 | − | 0.163832i | ||||
\(746\) | 440244.i | 0.791071i | ||||||||
\(747\) | 1.02653e6 | + | 289001.i | 1.83963 | + | 0.517914i | ||||
\(748\) | −25952.5 | −0.0463849 | ||||||||
\(749\) | −527455. | − | 304526.i | −0.940203 | − | 0.542826i | ||||
\(750\) | −711462. | − | 299974.i | −1.26482 | − | 0.533287i | ||||
\(751\) | −290081. | − | 502435.i | −0.514327 | − | 0.890840i | −0.999862 | − | 0.0166228i | \(-0.994709\pi\) |
0.485535 | − | 0.874217i | \(-0.338625\pi\) | |||||||
\(752\) | 26705.5 | − | 15418.4i | 0.0472243 | − | 0.0272650i | ||||
\(753\) | 483487. | − | 60549.0i | 0.852696 | − | 0.106787i | ||||
\(754\) | −132158. | + | 228905.i | −0.232462 | + | 0.402636i | ||||
\(755\) | − | 116832.i | − | 0.204960i | ||||||
\(756\) | 381931. | + | 973838.i | 0.668253 | + | 1.70390i | ||||
\(757\) | 1.00242e6 | 1.74928 | 0.874641 | − | 0.484771i | \(-0.161097\pi\) | ||||
0.874641 | + | 0.484771i | \(0.161097\pi\) | |||||||
\(758\) | −249553. | − | 144079.i | −0.434334 | − | 0.250763i | ||||
\(759\) | −55899.3 | − | 446358.i | −0.0970337 | − | 0.774819i | ||||
\(760\) | 22851.0 | + | 39579.2i | 0.0395620 | + | 0.0685235i | ||||
\(761\) | −73367.2 | + | 42358.6i | −0.126687 | + | 0.0731429i | −0.562004 | − | 0.827134i | \(-0.689970\pi\) |
0.435317 | + | 0.900277i | \(0.356636\pi\) | |||||||
\(762\) | −309792. | + | 734746.i | −0.533531 | + | 1.26540i | ||||
\(763\) | −127334. | + | 220548.i | −0.218723 | + | 0.378839i | ||||
\(764\) | 1.25840e6i | 2.15592i | ||||||||
\(765\) | −5137.12 | − | 5268.53i | −0.00877802 | − | 0.00900258i | ||||
\(766\) | 1.21313e6 | 2.06752 | ||||||||
\(767\) | −215373. | − | 124345.i | −0.366100 | − | 0.211368i | ||||
\(768\) | 578717. | − | 438288.i | 0.981170 | − | 0.743082i | ||||
\(769\) | 341763. | + | 591950.i | 0.577926 | + | 1.00100i | 0.995717 | + | 0.0924535i | \(0.0294710\pi\) |
−0.417791 | + | 0.908543i | \(0.637196\pi\) | |||||||
\(770\) | −445153. | + | 257009.i | −0.750807 | + | 0.433478i | ||||
\(771\) | −618156. | − | 816216.i | −1.03989 | − | 1.37308i | ||||
\(772\) | −366425. | + | 634666.i | −0.614823 | + | 1.06490i | ||||
\(773\) | − | 235888.i | − | 0.394772i | −0.980326 | − | 0.197386i | \(-0.936755\pi\) | ||
0.980326 | − | 0.197386i | \(-0.0632453\pi\) | |||||||
\(774\) | 990981. | − | 966263.i | 1.65418 | − | 1.61292i | ||||
\(775\) | −744879. | −1.24017 | ||||||||
\(776\) | 938462. | + | 541821.i | 1.55845 | + | 0.899773i | ||||
\(777\) | 759486. | + | 320223.i | 1.25799 | + | 0.530408i | ||||
\(778\) | 99737.5 | + | 172750.i | 0.164778 | + | 0.285404i | ||||
\(779\) | −59049.7 | + | 34092.4i | −0.0973068 | + | 0.0561801i | ||||
\(780\) | 211466. | − | 26482.7i | 0.347577 | − | 0.0435284i | ||||
\(781\) | −120232. | + | 208248.i | −0.197114 | + | 0.341412i | ||||
\(782\) | − | 20205.3i | − | 0.0330409i | ||||||
\(783\) | 58837.6 | − | 389720.i | 0.0959690 | − | 0.635665i | ||||
\(784\) | 16843.8 | 0.0274036 | ||||||||
\(785\) | −57623.5 | − | 33268.9i | −0.0935104 | − | 0.0539883i | ||||
\(786\) | 24893.4 | + | 198775.i | 0.0402939 | + | 0.321749i | ||||
\(787\) | 228728. | + | 396169.i | 0.369292 | + | 0.639633i | 0.989455 | − | 0.144840i | \(-0.0462668\pi\) |
−0.620163 | + | 0.784473i | \(0.712933\pi\) | |||||||
\(788\) | −1.50842e6 | + | 870888.i | −2.42924 | + | 1.40252i | ||||
\(789\) | 155121. | − | 367908.i | 0.249183 | − | 0.590997i | ||||
\(790\) | −9187.01 | + | 15912.4i | −0.0147204 | + | 0.0254965i | ||||
\(791\) | − | 239269.i | − | 0.382414i | ||||||
\(792\) | −196560. | + | 698182.i | −0.313361 | + | 1.11306i | ||||
\(793\) | 1120.41 | 0.00178169 | ||||||||
\(794\) | 1.33765e6 | + | 772291.i | 2.12178 | + | 1.22501i | ||||
\(795\) | 357583. | − | 270813.i | 0.565773 | − | 0.428484i | ||||
\(796\) | −348022. | − | 602791.i | −0.549263 | − | 0.951351i | ||||
\(797\) | −148023. | + | 85461.0i | −0.233030 | + | 0.134540i | −0.611969 | − | 0.790882i | \(-0.709622\pi\) |
0.378939 | + | 0.925422i | \(0.376289\pi\) | |||||||
\(798\) | −102671. | − | 135568.i | −0.161229 | − | 0.212888i | ||||
\(799\) | 3084.09 | − | 5341.79i | 0.00483095 | − | 0.00836746i | ||||
\(800\) | − | 434575.i | − | 0.679023i | ||||||
\(801\) | −11503.9 | − | 45209.2i | −0.0179300 | − | 0.0704632i | ||||
\(802\) | −1.53465e6 | −2.38594 | ||||||||
\(803\) | 102769. | + | 59333.5i | 0.159378 | + | 0.0920171i | ||||
\(804\) | −1.15761e6 | − | 488085.i | −1.79082 | − | 0.755064i | ||||
\(805\) | −125528. | − | 217422.i | −0.193709 | − | 0.335514i | ||||
\(806\) | 648699. | − | 374526.i | 0.998557 | − | 0.576517i | ||||
\(807\) | 39558.9 | − | 4954.12i | 0.0607432 | − | 0.00760711i | ||||
\(808\) | 396271. | − | 686361.i | 0.606973 | − | 1.05131i | ||||
\(809\) | 252280.i | 0.385465i | 0.981251 | + | 0.192733i | \(0.0617350\pi\) | ||||
−0.981251 | + | 0.192733i | \(0.938265\pi\) | |||||||
\(810\) | −444952. | + | 242121.i | −0.678178 | + | 0.369031i | ||||
\(811\) | 166784. | 0.253579 | 0.126789 | − | 0.991930i | \(-0.459533\pi\) | ||||
0.126789 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(812\) | −671856. | − | 387896.i | −1.01898 | − | 0.588307i | ||||
\(813\) | 96305.0 | + | 769000.i | 0.145703 | + | 1.16344i | ||||
\(814\) | 703865. | + | 1.21913e6i | 1.06228 | + | 1.83993i | ||||
\(815\) | −21975.7 | + | 12687.7i | −0.0330847 | + | 0.0191015i | ||||
\(816\) | −1039.09 | + | 2464.46i | −0.00156054 | + | 0.00370119i | ||||
\(817\) | −70580.7 | + | 122249.i | −0.105741 | + | 0.183148i | ||||
\(818\) | − | 1.95124e6i | − | 2.91611i | ||||||
\(819\) | −312009. | + | 79393.4i | −0.465156 | + | 0.118363i | ||||
\(820\) | 399780. | 0.594557 | ||||||||
\(821\) | −235829. | − | 136156.i | −0.349873 | − | 0.201999i | 0.314756 | − | 0.949173i | \(-0.398077\pi\) |
−0.664629 | + | 0.747173i | \(0.731411\pi\) | |||||||
\(822\) | −179735. | + | 136121.i | −0.266005 | + | 0.201457i | ||||
\(823\) | −482314. | − | 835392.i | −0.712082 | − | 1.23336i | −0.964074 | − | 0.265633i | \(-0.914419\pi\) |
0.251992 | − | 0.967729i | \(-0.418914\pi\) | |||||||
\(824\) | 221092. | − | 127648.i | 0.325626 | − | 0.188000i | ||||
\(825\) | 330128. | + | 435903.i | 0.485037 | + | 0.640445i | ||||
\(826\) | 581759. | − | 1.00764e6i | 0.852674 | − | 1.47687i | ||||
\(827\) | 430905.i | 0.630043i | 0.949085 | + | 0.315021i | \(0.102012\pi\) | ||||
−0.949085 | + | 0.315021i | \(0.897988\pi\) | |||||||
\(828\) | −839950. | − | 236472.i | −1.22516 | − | 0.344921i | ||||
\(829\) | 462870. | 0.673520 | 0.336760 | − | 0.941591i | \(-0.390669\pi\) | ||||
0.336760 | + | 0.941591i | \(0.390669\pi\) | |||||||
\(830\) | 880328. | + | 508257.i | 1.27787 | + | 0.737781i | ||||
\(831\) | 585597. | + | 246906.i | 0.848002 | + | 0.357544i | ||||
\(832\) | 241511. | + | 418310.i | 0.348892 | + | 0.604299i | ||||
\(833\) | 2917.80 | − | 1684.59i | 0.00420500 | − | 0.00242776i | ||||
\(834\) | 203436. | − | 25477.2i | 0.292480 | − | 0.0366285i | ||||
\(835\) | −218104. | + | 377768.i | −0.312818 | + | 0.541816i | ||||
\(836\) | − | 182211.i | − | 0.260713i | ||||||
\(837\) | −696618. | + | 873097.i | −0.994361 | + | 1.24627i | ||||
\(838\) | 241618. | 0.344066 | ||||||||
\(839\) | −696889. | − | 402349.i | −0.990010 | − | 0.571583i | −0.0847327 | − | 0.996404i | \(-0.527004\pi\) |
−0.905277 | + | 0.424821i | \(0.860337\pi\) | |||||||
\(840\) | 50301.9 | + | 401663.i | 0.0712895 | + | 0.569250i | ||||
\(841\) | −207488. | − | 359379.i | −0.293360 | − | 0.508114i | ||||
\(842\) | 1.36537e6 | − | 788297.i | 1.92587 | − | 1.11190i | ||||
\(843\) | −521880. | + | 1.23777e6i | −0.734372 | + | 1.74174i | ||||
\(844\) | 620301. | − | 1.07439e6i | 0.870799 | − | 1.50827i | ||||
\(845\) | − | 270942.i | − | 0.379457i | ||||||
\(846\) | −296436. | − | 304019.i | −0.414181 | − | 0.424777i | ||||
\(847\) | 52037.6 | 0.0725354 | ||||||||
\(848\) | −141193. | − | 81518.0i | −0.196346 | − | 0.113360i | ||||
\(849\) | 602143. | − | 456029.i | 0.835381 | − | 0.632670i | ||||
\(850\) | 12280.2 | + | 21269.9i | 0.0169968 | + | 0.0294393i | ||||
\(851\) | −595447. | + | 343781.i | −0.822212 | + | 0.474704i | ||||
\(852\) | 281614. | + | 371845.i | 0.387949 | + | 0.512250i | ||||
\(853\) | −105790. | + | 183234.i | −0.145394 | + | 0.251830i | −0.929520 | − | 0.368772i | \(-0.879778\pi\) |
0.784126 | + | 0.620602i | \(0.213112\pi\) | |||||||
\(854\) | 5241.94i | 0.00718747i | ||||||||
\(855\) | 36990.1 | − | 36067.4i | 0.0506003 | − | 0.0493381i | ||||
\(856\) | −819191. | −1.11799 | ||||||||
\(857\) | −245348. | − | 141652.i | −0.334057 | − | 0.192868i | 0.323584 | − | 0.946199i | \(-0.395112\pi\) |
−0.657641 | + | 0.753332i | \(0.728446\pi\) | |||||||
\(858\) | −506674. | − | 213629.i | −0.688262 | − | 0.290192i | ||||
\(859\) | 15498.6 | + | 26844.3i | 0.0210042 | + | 0.0363803i | 0.876336 | − | 0.481700i | \(-0.159980\pi\) |
−0.855332 | + | 0.518080i | \(0.826647\pi\) | |||||||
\(860\) | 716771. | − | 413828.i | 0.969133 | − | 0.559529i | ||||
\(861\) | −599257. | + | 75047.4i | −0.808364 | + | 0.101235i | ||||
\(862\) | −533236. | + | 923592.i | −0.717637 | + | 1.24298i | ||||
\(863\) | 1.35611e6i | 1.82085i | 0.413677 | + | 0.910424i | \(0.364244\pi\) | ||||
−0.413677 | + | 0.910424i | \(0.635756\pi\) | |||||||
\(864\) | −509379. | − | 406419.i | −0.682360 | − | 0.544435i | ||||
\(865\) | −572482. | −0.765120 | ||||||||
\(866\) | −1.51307e6 | − | 873569.i | −2.01754 | − | 1.16483i | ||||
\(867\) | −93340.9 | − | 745332.i | −0.124175 | − | 0.991543i | ||||
\(868\) | 1.09927e6 | + | 1.90399e6i | 1.45903 | + | 2.52711i | ||||
\(869\) | 25756.2 | − | 14870.4i | 0.0341069 | − | 0.0196916i | ||||
\(870\) | 145957. | − | 346173.i | 0.192835 | − | 0.457356i | ||||
\(871\) | 193330. | − | 334858.i | 0.254838 | − | 0.441392i | ||||
\(872\) | 342534.i | 0.450475i | ||||||||
\(873\) | 331969. | − | 1.17916e6i | 0.435582 | − | 1.54719i | ||||
\(874\) | 141860. | 0.185711 | ||||||||
\(875\) | 604045. | + | 348746.i | 0.788957 | + | 0.455504i | ||||
\(876\) | 183502. | − | 138974.i | 0.239129 | − | 0.181103i | ||||
\(877\) | 226465. | + | 392249.i | 0.294443 | + | 0.509991i | 0.974855 | − | 0.222839i | \(-0.0715324\pi\) |
−0.680412 | + | 0.732830i | \(0.738199\pi\) | |||||||
\(878\) | −208926. | + | 120623.i | −0.271021 | + | 0.156474i | ||||
\(879\) | 195085. | + | 257591.i | 0.252491 | + | 0.333390i | ||||
\(880\) | −28379.1 | + | 49154.0i | −0.0366465 | + | 0.0634736i | ||||
\(881\) | 1.13788e6i | 1.46603i | 0.680211 | + | 0.733016i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733016i | \(0.738112\pi\) | |||||||
\(882\) | −57195.7 | − | 224774.i | −0.0735235 | − | 0.288941i | ||||
\(883\) | 970367. | 1.24456 | 0.622279 | − | 0.782796i | \(-0.286207\pi\) | ||||
0.622279 | + | 0.782796i | \(0.286207\pi\) | |||||||
\(884\) | −13418.4 | − | 7747.09i | −0.0171710 | − | 0.00991367i | ||||
\(885\) | 325708. | + | 137328.i | 0.415854 | + | 0.175337i | ||||
\(886\) | 450629. | + | 780512.i | 0.574052 | + | 0.994287i | ||||
\(887\) | 1.12349e6 | − | 648647.i | 1.42798 | − | 0.824444i | 0.431017 | − | 0.902344i | \(-0.358155\pi\) |
0.996961 | + | 0.0779001i | \(0.0248215\pi\) | |||||||
\(888\) | 1.10002e6 | − | 137760.i | 1.39501 | − | 0.174702i | ||||
\(889\) | 360159. | − | 623814.i | 0.455712 | − | 0.789317i | ||||
\(890\) | − | 44466.1i | − | 0.0561369i | ||||||
\(891\) | 819675. | + | 20707.0i | 1.03249 | + | 0.0260832i | ||||
\(892\) | −590181. | −0.741747 | ||||||||
\(893\) | 37504.4 | + | 21653.2i | 0.0470305 | + | 0.0271531i | ||||
\(894\) | 65300.5 | + | 521428.i | 0.0817036 | + | 0.652407i | ||||
\(895\) | −281130. | − | 486932.i | −0.350963 | − | 0.607886i | ||||
\(896\) | −1.29725e6 | + | 748968.i | −1.61588 | + | 0.932927i | ||||
\(897\) | 104341. | − | 247469.i | 0.129679 | − | 0.307565i | ||||
\(898\) | −571395. | + | 989685.i | −0.708572 | + | 1.22728i | ||||
\(899\) | − | 828370.i | − | 1.02496i | ||||||
\(900\) | 1.02793e6 | − | 261565.i | 1.26905 | − | 0.322920i | ||||
\(901\) | −32611.4 | −0.0401716 | ||||||||
\(902\) | −893289. | − | 515740.i | −1.09794 | − | 0.633896i | ||||
\(903\) | −996731. | + | 754867.i | −1.22237 | + | 0.925753i | ||||
\(904\) | −160912. | − | 278707.i | −0.196902 | − | 0.341044i | ||||
\(905\) | −467026. | + | 269638.i | −0.570222 | + | 0.329218i | ||||
\(906\) | 353026. | + | 466137.i | 0.430081 | + | 0.567881i | ||||
\(907\) | −76984.1 | + | 133340.i | −0.0935807 | + | 0.162087i | −0.909015 | − | 0.416763i | \(-0.863165\pi\) |
0.815435 | + | 0.578849i | \(0.196498\pi\) | |||||||
\(908\) | 1.34099e6i | 1.62650i | ||||||||
\(909\) | −862397. | − | 242792.i | −1.04371 | − | 0.293837i | ||||
\(910\) | −306880. | −0.370583 | ||||||||
\(911\) | −927466. | − | 535473.i | −1.11753 | − | 0.645209i | −0.176764 | − | 0.984253i | \(-0.556563\pi\) |
−0.940770 | + | 0.339044i | \(0.889896\pi\) | |||||||
\(912\) | −17302.8 | − | 7295.41i | −0.0208031 | − | 0.00877122i | ||||
\(913\) | −822680. | − | 1.42492e6i | −0.986937 | − | 1.70942i | ||||
\(914\) | 654339. | − | 377783.i | 0.783268 | − | 0.452220i | ||||
\(915\) | −1580.15 | + | 197.888i | −0.00188736 | + | 0.000236362i | ||||
\(916\) | 384110. | − | 665298.i | 0.457788 | − | 0.792912i | ||||
\(917\) | − | 180966.i | − | 0.215208i | ||||||
\(918\) | 36415.7 | + | 5497.83i | 0.0432119 | + | 0.00652388i | ||||
\(919\) | 747688. | 0.885298 | 0.442649 | − | 0.896695i | \(-0.354039\pi\) | ||||
0.442649 | + | 0.896695i | \(0.354039\pi\) | |||||||
\(920\) | −292438. | − | 168839.i | −0.345508 | − | 0.199479i | ||||
\(921\) | −7889.33 | − | 62996.6i | −0.00930081 | − | 0.0742674i | ||||
\(922\) | −1.32840e6 | − | 2.30085e6i | −1.56267 | − | 2.70662i | ||||
\(923\) | −124328. | + | 71781.1i | −0.145938 | + | 0.0842571i | ||||
\(924\) | 627020. | − | 1.48713e6i | 0.734408 | − | 1.74183i | ||||
\(925\) | 417881. | − | 723790.i | 0.488392 | − | 0.845920i | ||||
\(926\) | 475625.i | 0.554680i | ||||||||
\(927\) | −201475. | − | 206629.i | −0.234457 | − | 0.240454i | ||||
\(928\) | 483285. | 0.561187 | ||||||||
\(929\) | 1.28522e6 | + | 742020.i | 1.48917 | + | 0.859774i | 0.999923 | − | 0.0123702i | \(-0.00393765\pi\) |
0.489249 | + | 0.872144i | \(0.337271\pi\) | |||||||
\(930\) | −848728. | + | 642778.i | −0.981302 | + | 0.743182i | ||||
\(931\) | 11827.4 | + | 20485.7i | 0.0136456 | + | 0.0236348i | ||||
\(932\) | 1.02754e6 | − | 593253.i | 1.18296 | − | 0.682980i | ||||
\(933\) | −465455. | − | 614589.i | −0.534705 | − | 0.706027i | ||||
\(934\) | −1.17554e6 | + | 2.03609e6i | −1.34754 | + | 2.33401i | ||||
\(935\) | 11353.1i | 0.0129865i | ||||||||
\(936\) | −310043. | + | 302309.i | −0.353892 | + | 0.345064i | ||||
\(937\) | −650560. | −0.740983 | −0.370491 | − | 0.928836i | \(-0.620811\pi\) | ||||
−0.370491 | + | 0.928836i | \(0.620811\pi\) | |||||||
\(938\) | 1.56666e6 | + | 904510.i | 1.78061 | + | 1.02803i | ||||
\(939\) | 609059. | + | 256798.i | 0.690761 | + | 0.291246i | ||||
\(940\) | −126957. | − | 219895.i | −0.143681 | − | 0.248863i | ||||
\(941\) | −352436. | + | 203479.i | −0.398017 | + | 0.229795i | −0.685628 | − | 0.727952i | \(-0.740472\pi\) |
0.287611 | + | 0.957747i | \(0.407139\pi\) | |||||||
\(942\) | 330433. | − | 41381.4i | 0.372376 | − | 0.0466341i | ||||
\(943\) | 251898. | − | 436300.i | 0.283270 | − | 0.490638i | ||||
\(944\) | − | 128476.i | − | 0.144171i | ||||||
\(945\) | 426012. | − | 167078.i | 0.477043 | − | 0.187092i | ||||
\(946\) | −2.13545e6 | −2.38620 | ||||||||
\(947\) | 718809. | + | 415005.i | 0.801519 | + | 0.462757i | 0.844002 | − | 0.536340i | \(-0.180194\pi\) |
−0.0424832 | + | 0.999097i | \(0.513527\pi\) | |||||||
\(948\) | −7168.83 | − | 57243.5i | −0.00797685 | − | 0.0636956i | ||||
\(949\) | 35423.3 | + | 61355.0i | 0.0393330 | + | 0.0681267i | ||||
\(950\) | −149335. | + | 86218.5i | −0.165468 | + | 0.0955330i | ||||
\(951\) | 172170. | − | 408344.i | 0.190370 | − | 0.451508i | ||||
\(952\) | 14715.0 | − | 25487.1i | 0.0162363 | − | 0.0281221i | ||||
\(953\) | − | 927863.i | − | 1.02164i | −0.859688 | − | 0.510820i | \(-0.829342\pi\) | ||
0.859688 | − | 0.510820i | \(-0.170658\pi\) | |||||||
\(954\) | −608382. | + | 2.16098e6i | −0.668467 | + | 2.37440i | ||||
\(955\) | 550496. | 0.603597 | ||||||||
\(956\) | 479949. | + | 277099.i | 0.525145 | + | 0.303193i | ||||
\(957\) | −484762. | + | 367131.i | −0.529303 | + | 0.400864i | ||||
\(958\) | 83870.5 | + | 145268.i | 0.0913857 | + | 0.158285i | ||||
\(959\) | 176385. | − | 101836.i | 0.191790 | − | 0.110730i | ||||
\(960\) | −414492. | − | 547298.i | −0.449753 | − | 0.593856i | ||||
\(961\) | −712006. | + | 1.23323e6i | −0.770968 | + | 1.33536i | ||||
\(962\) | 840444.i | 0.908152i | ||||||||
\(963\) | 228364. | + | 897450.i | 0.246249 | + | 0.967737i | ||||
\(964\) | 1.56002e6 | 1.67872 | ||||||||
\(965\) | 277639. | + | 160295.i | 0.298143 | + | 0.172133i | ||||
\(966\) | 1.15780e6 | + | 488166.i | 1.24074 | + | 0.523134i | ||||
\(967\) | 556238. | + | 963433.i | 0.594851 | + | 1.03031i | 0.993568 | + | 0.113238i | \(0.0361222\pi\) |
−0.398717 | + | 0.917074i | \(0.630544\pi\) | |||||||
\(968\) | 60614.8 | − | 34995.9i | 0.0646886 | − | 0.0373480i | ||||
\(969\) | −3726.96 | + | 466.742i | −0.00396924 | + | 0.000497084i | ||||
\(970\) | 583825. | − | 1.01121e6i | 0.620496 | − | 1.07473i | ||||
\(971\) | 68160.6i | 0.0722927i | 0.999347 | + | 0.0361464i | \(0.0115083\pi\) | ||||
−0.999347 | + | 0.0361464i | \(0.988492\pi\) | |||||||
\(972\) | 654739. | − | 1.44949e6i | 0.693004 | − | 1.53420i | ||||
\(973\) | −185210. | −0.195631 | ||||||||
\(974\) | −1.40312e6 | − | 810090.i | −1.47903 | − | 0.853917i | ||||
\(975\) | 40566.3 | + | 323924.i | 0.0426733 | + | 0.340748i | ||||
\(976\) | 289.408 | + | 501.270i | 0.000303817 | + | 0.000526226i | ||||
\(977\) | −685124. | + | 395556.i | −0.717761 | + | 0.414399i | −0.813928 | − | 0.580966i | \(-0.802675\pi\) |
0.0961671 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(978\) | 49340.9 | − | 117024.i | 0.0515857 | − | 0.122348i | ||||
\(979\) | −35987.0 | + | 62331.4i | −0.0375475 | + | 0.0650341i | ||||
\(980\) | − | 138693.i | − | 0.144412i | ||||||
\(981\) | 375257. | − | 95487.4i | 0.389933 | − | 0.0992220i | ||||
\(982\) | 2.24263e6 | 2.32560 | ||||||||
\(983\) | −948495. | − | 547614.i | −0.981585 | − | 0.566718i | −0.0788368 | − | 0.996888i | \(-0.525121\pi\) |
−0.902748 | + | 0.430169i | \(0.858454\pi\) | |||||||
\(984\) | −647560. | + | 490425.i | −0.668790 | + | 0.506504i | ||||
\(985\) | 380975. | + | 659868.i | 0.392667 | + | 0.680119i | ||||
\(986\) | −23654.0 | + | 13656.6i | −0.0243305 | + | 0.0140472i | ||||
\(987\) | 231583. | + | 305783.i | 0.237724 | + | 0.313892i | ||||
\(988\) | 54391.9 | − | 94209.5i | 0.0557212 | − | 0.0965119i | ||||
\(989\) | − | 1.04300e6i | − | 1.06633i | ||||||
\(990\) | 752307. | + | 211798.i | 0.767582 | + | 0.216098i | ||||
\(991\) | 278492. | 0.283573 | 0.141787 | − | 0.989897i | \(-0.454715\pi\) | ||||
0.141787 | + | 0.989897i | \(0.454715\pi\) | |||||||
\(992\) | −1.18610e6 | − | 684795.i | −1.20531 | − | 0.695884i | ||||
\(993\) | −680118. | − | 286759.i | −0.689741 | − | 0.290816i | ||||
\(994\) | −335833. | − | 581680.i | −0.339900 | − | 0.588723i | ||||
\(995\) | −263695. | + | 152244.i | −0.266351 | + | 0.153778i | ||||
\(996\) | −3.16691e6 | + | 396605.i | −3.19240 | + | 0.399797i | ||||
\(997\) | −665723. | + | 1.15307e6i | −0.669736 | + | 1.16002i | 0.308242 | + | 0.951308i | \(0.400259\pi\) |
−0.977978 | + | 0.208708i | \(0.933074\pi\) | |||||||
\(998\) | − | 1.29633e6i | − | 1.30154i | ||||||
\(999\) | −457572. | − | 1.16671e6i | −0.458488 | − | 1.16904i |
(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 | 9.5.d.a.2.1 | ✓ | 6 | |
3.2 | odd | 2 | 27.5.d.a.8.3 | 6 | |||
4.3 | odd | 2 | 144.5.q.a.65.2 | 6 | |||
9.2 | odd | 6 | 81.5.b.a.80.1 | 6 | |||
9.4 | even | 3 | 27.5.d.a.17.3 | 6 | |||
9.5 | odd | 6 | inner | 9.5.d.a.5.1 | yes | 6 | |
9.7 | even | 3 | 81.5.b.a.80.6 | 6 | |||
12.11 | even | 2 | 432.5.q.a.305.2 | 6 | |||
36.7 | odd | 6 | 1296.5.e.c.161.4 | 6 | |||
36.11 | even | 6 | 1296.5.e.c.161.3 | 6 | |||
36.23 | even | 6 | 144.5.q.a.113.2 | 6 | |||
36.31 | odd | 6 | 432.5.q.a.17.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.5.d.a.5.1 | yes | 6 | 9.5 | odd | 6 | inner | |
27.5.d.a.8.3 | 6 | 3.2 | odd | 2 | |||
27.5.d.a.17.3 | 6 | 9.4 | even | 3 | |||
81.5.b.a.80.1 | 6 | 9.2 | odd | 6 | |||
81.5.b.a.80.6 | 6 | 9.7 | even | 3 | |||
144.5.q.a.65.2 | 6 | 4.3 | odd | 2 | |||
144.5.q.a.113.2 | 6 | 36.23 | even | 6 | |||
432.5.q.a.17.2 | 6 | 36.31 | odd | 6 | |||
432.5.q.a.305.2 | 6 | 12.11 | even | 2 | |||
1296.5.e.c.161.3 | 6 | 36.11 | even | 6 | |||
1296.5.e.c.161.4 | 6 | 36.7 | odd | 6 |