Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not 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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.e.116.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | −0.940775 | − | 0.339032i | \(-0.889900\pi\) |
0.763998 | + | 0.645219i | \(0.223234\pi\) | |||||||
\(3\) | 4.00000 | + | 6.92820i | 0.769800 | + | 1.33333i | 0.937671 | + | 0.347524i | \(0.112978\pi\) |
−0.167871 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(4\) | 3.50000 | + | 6.06218i | 0.437500 | + | 0.757772i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −15.0000 | −0.662913 | ||||||||
\(9\) | −18.5000 | + | 32.0429i | −0.685185 | + | 1.18678i | ||||
\(10\) | 2.50000 | + | 4.33013i | 0.0790569 | + | 0.136931i | ||||
\(11\) | −6.00000 | − | 10.3923i | −0.164461 | − | 0.284854i | 0.772003 | − | 0.635619i | \(-0.219255\pi\) |
−0.936464 | + | 0.350765i | \(0.885922\pi\) | |||||||
\(12\) | −28.0000 | + | 48.4974i | −0.673575 | + | 1.16667i | ||||
\(13\) | −78.0000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.0000 | 0.688530 | ||||||||
\(16\) | −20.5000 | + | 35.5070i | −0.320312 | + | 0.554798i | ||||
\(17\) | 47.0000 | + | 81.4064i | 0.670540 | + | 1.16141i | 0.977751 | + | 0.209768i | \(0.0672707\pi\) |
−0.307212 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(18\) | −18.5000 | − | 32.0429i | −0.242250 | − | 0.419589i | ||||
\(19\) | −20.0000 | + | 34.6410i | −0.241490 | + | 0.418273i | −0.961139 | − | 0.276065i | \(-0.910970\pi\) |
0.719649 | + | 0.694338i | \(0.244303\pi\) | |||||||
\(20\) | 35.0000 | 0.391312 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | 0.116291 | ||||||||
\(23\) | −16.0000 | + | 27.7128i | −0.145054 | + | 0.251240i | −0.929393 | − | 0.369092i | \(-0.879669\pi\) |
0.784339 | + | 0.620332i | \(0.213002\pi\) | |||||||
\(24\) | −60.0000 | − | 103.923i | −0.510310 | − | 0.883883i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 39.0000 | − | 67.5500i | 0.294174 | − | 0.509525i | ||||
\(27\) | −80.0000 | −0.570222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −50.0000 | −0.320164 | −0.160082 | − | 0.987104i | \(-0.551176\pi\) | ||||
−0.160082 | + | 0.987104i | \(0.551176\pi\) | |||||||
\(30\) | −20.0000 | + | 34.6410i | −0.121716 | + | 0.210819i | ||||
\(31\) | 124.000 | + | 214.774i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | −80.5000 | − | 139.430i | −0.444704 | − | 0.770250i | ||||
\(33\) | 48.0000 | − | 83.1384i | 0.253204 | − | 0.438562i | ||||
\(34\) | −94.0000 | −0.474143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −259.000 | −1.19907 | ||||||||
\(37\) | 217.000 | − | 375.855i | 0.964178 | − | 1.67001i | 0.252370 | − | 0.967631i | \(-0.418790\pi\) |
0.711808 | − | 0.702374i | \(-0.247877\pi\) | |||||||
\(38\) | −20.0000 | − | 34.6410i | −0.0853797 | − | 0.147882i | ||||
\(39\) | −312.000 | − | 540.400i | −1.28103 | − | 2.21880i | ||||
\(40\) | −37.5000 | + | 64.9519i | −0.148232 | + | 0.256745i | ||||
\(41\) | 402.000 | 1.53126 | 0.765632 | − | 0.643278i | \(-0.222426\pi\) | ||||
0.765632 | + | 0.643278i | \(0.222426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68.0000 | −0.241161 | −0.120580 | − | 0.992704i | \(-0.538476\pi\) | ||||
−0.120580 | + | 0.992704i | \(0.538476\pi\) | |||||||
\(44\) | 42.0000 | − | 72.7461i | 0.143903 | − | 0.249248i | ||||
\(45\) | 92.5000 | + | 160.215i | 0.306424 | + | 0.530742i | ||||
\(46\) | −16.0000 | − | 27.7128i | −0.0512842 | − | 0.0888268i | ||||
\(47\) | −268.000 | + | 464.190i | −0.831741 | + | 1.44062i | 0.0649159 | + | 0.997891i | \(0.479322\pi\) |
−0.896657 | + | 0.442727i | \(0.854011\pi\) | |||||||
\(48\) | −328.000 | −0.986307 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 25.0000 | 0.0707107 | ||||||||
\(51\) | −376.000 | + | 651.251i | −1.03236 | + | 1.78811i | ||||
\(52\) | −273.000 | − | 472.850i | −0.728044 | − | 1.26101i | ||||
\(53\) | −11.0000 | − | 19.0526i | −0.0285088 | − | 0.0493787i | 0.851419 | − | 0.524486i | \(-0.175743\pi\) |
−0.879928 | + | 0.475107i | \(0.842409\pi\) | |||||||
\(54\) | 40.0000 | − | 69.2820i | 0.100802 | − | 0.174594i | ||||
\(55\) | −60.0000 | −0.147098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −320.000 | −0.743597 | ||||||||
\(58\) | 25.0000 | − | 43.3013i | 0.0565976 | − | 0.0980299i | ||||
\(59\) | 280.000 | + | 484.974i | 0.617846 | + | 1.07014i | 0.989878 | + | 0.141920i | \(0.0453277\pi\) |
−0.372032 | + | 0.928220i | \(0.621339\pi\) | |||||||
\(60\) | 140.000 | + | 242.487i | 0.301232 | + | 0.521749i | ||||
\(61\) | 139.000 | − | 240.755i | 0.291756 | − | 0.505337i | −0.682469 | − | 0.730915i | \(-0.739094\pi\) |
0.974225 | + | 0.225578i | \(0.0724271\pi\) | |||||||
\(62\) | −248.000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | −195.000 | + | 337.750i | −0.372104 | + | 0.644503i | ||||
\(66\) | 48.0000 | + | 83.1384i | 0.0895211 | + | 0.155055i | ||||
\(67\) | 82.0000 | + | 142.028i | 0.149521 | + | 0.258978i | 0.931050 | − | 0.364890i | \(-0.118894\pi\) |
−0.781530 | + | 0.623868i | \(0.785560\pi\) | |||||||
\(68\) | −329.000 | + | 569.845i | −0.586722 | + | 1.01623i | ||||
\(69\) | −256.000 | −0.446649 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 672.000 | 1.12326 | 0.561632 | − | 0.827387i | \(-0.310174\pi\) | ||||
0.561632 | + | 0.827387i | \(0.310174\pi\) | |||||||
\(72\) | 277.500 | − | 480.644i | 0.454218 | − | 0.786728i | ||||
\(73\) | −41.0000 | − | 71.0141i | −0.0657354 | − | 0.113857i | 0.831285 | − | 0.555847i | \(-0.187606\pi\) |
−0.897020 | + | 0.441990i | \(0.854273\pi\) | |||||||
\(74\) | 217.000 | + | 375.855i | 0.340888 | + | 0.590436i | ||||
\(75\) | 100.000 | − | 173.205i | 0.153960 | − | 0.266667i | ||||
\(76\) | −280.000 | −0.422608 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 624.000 | 0.905822 | ||||||||
\(79\) | 500.000 | − | 866.025i | 0.712081 | − | 1.23336i | −0.251994 | − | 0.967729i | \(-0.581086\pi\) |
0.964075 | − | 0.265632i | \(-0.0855804\pi\) | |||||||
\(80\) | 102.500 | + | 177.535i | 0.143248 | + | 0.248113i | ||||
\(81\) | 179.500 | + | 310.903i | 0.246228 | + | 0.426479i | ||||
\(82\) | −201.000 | + | 348.142i | −0.270692 | + | 0.468852i | ||||
\(83\) | −448.000 | −0.592463 | −0.296231 | − | 0.955116i | \(-0.595730\pi\) | ||||
−0.296231 | + | 0.955116i | \(0.595730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 470.000 | 0.599749 | ||||||||
\(86\) | 34.0000 | − | 58.8897i | 0.0426316 | − | 0.0738400i | ||||
\(87\) | −200.000 | − | 346.410i | −0.246463 | − | 0.426886i | ||||
\(88\) | 90.0000 | + | 155.885i | 0.109023 | + | 0.188834i | ||||
\(89\) | 435.000 | − | 753.442i | 0.518089 | − | 0.897356i | −0.481690 | − | 0.876342i | \(-0.659977\pi\) |
0.999779 | − | 0.0210147i | \(-0.00668968\pi\) | |||||||
\(90\) | −185.000 | −0.216675 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −224.000 | −0.253844 | ||||||||
\(93\) | −992.000 | + | 1718.19i | −1.10608 | + | 1.91579i | ||||
\(94\) | −268.000 | − | 464.190i | −0.294065 | − | 0.509335i | ||||
\(95\) | 100.000 | + | 173.205i | 0.107998 | + | 0.187058i | ||||
\(96\) | 644.000 | − | 1115.44i | 0.684666 | − | 1.18588i | ||||
\(97\) | 1026.00 | 1.07396 | 0.536982 | − | 0.843594i | \(-0.319564\pi\) | ||||
0.536982 | + | 0.843594i | \(0.319564\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 444.000 | 0.450744 | ||||||||
\(100\) | 87.5000 | − | 151.554i | 0.0875000 | − | 0.151554i | ||||
\(101\) | −241.000 | − | 417.424i | −0.237430 | − | 0.411240i | 0.722546 | − | 0.691322i | \(-0.242972\pi\) |
−0.959976 | + | 0.280082i | \(0.909638\pi\) | |||||||
\(102\) | −376.000 | − | 651.251i | −0.364996 | − | 0.632191i | ||||
\(103\) | −136.000 | + | 235.559i | −0.130102 | + | 0.225343i | −0.923716 | − | 0.383079i | \(-0.874864\pi\) |
0.793614 | + | 0.608422i | \(0.208197\pi\) | |||||||
\(104\) | 1170.00 | 1.10315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.0000 | 0.0201588 | ||||||||
\(107\) | 222.000 | − | 384.515i | 0.200575 | − | 0.347406i | −0.748139 | − | 0.663542i | \(-0.769052\pi\) |
0.948714 | + | 0.316136i | \(0.102386\pi\) | |||||||
\(108\) | −280.000 | − | 484.974i | −0.249472 | − | 0.432099i | ||||
\(109\) | 585.000 | + | 1013.25i | 0.514063 | + | 0.890383i | 0.999867 | + | 0.0163151i | \(0.00519348\pi\) |
−0.485804 | + | 0.874068i | \(0.661473\pi\) | |||||||
\(110\) | 30.0000 | − | 51.9615i | 0.0260035 | − | 0.0450394i | ||||
\(111\) | 3472.00 | 2.96890 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −798.000 | −0.664332 | −0.332166 | − | 0.943221i | \(-0.607779\pi\) | ||||
−0.332166 | + | 0.943221i | \(0.607779\pi\) | |||||||
\(114\) | 160.000 | − | 277.128i | 0.131451 | − | 0.227679i | ||||
\(115\) | 80.0000 | + | 138.564i | 0.0648699 | + | 0.112358i | ||||
\(116\) | −175.000 | − | 303.109i | −0.140072 | − | 0.242612i | ||||
\(117\) | 1443.00 | − | 2499.35i | 1.14022 | − | 1.97491i | ||||
\(118\) | −560.000 | −0.436883 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −600.000 | −0.456435 | ||||||||
\(121\) | 593.500 | − | 1027.97i | 0.445905 | − | 0.772331i | ||||
\(122\) | 139.000 | + | 240.755i | 0.103151 | + | 0.178663i | ||||
\(123\) | 1608.00 | + | 2785.14i | 1.17877 | + | 2.04169i | ||||
\(124\) | −868.000 | + | 1503.42i | −0.628619 | + | 1.08880i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 776.000 | 0.542196 | 0.271098 | − | 0.962552i | \(-0.412613\pi\) | ||||
0.271098 | + | 0.962552i | \(0.412613\pi\) | |||||||
\(128\) | 727.500 | − | 1260.07i | 0.502363 | − | 0.870119i | ||||
\(129\) | −272.000 | − | 471.118i | −0.185645 | − | 0.321547i | ||||
\(130\) | −195.000 | − | 337.750i | −0.131559 | − | 0.227866i | ||||
\(131\) | −556.000 | + | 963.020i | −0.370824 | + | 0.642286i | −0.989693 | − | 0.143209i | \(-0.954258\pi\) |
0.618869 | + | 0.785495i | \(0.287591\pi\) | |||||||
\(132\) | 672.000 | 0.443107 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −164.000 | −0.105727 | ||||||||
\(135\) | −200.000 | + | 346.410i | −0.127506 | + | 0.220846i | ||||
\(136\) | −705.000 | − | 1221.10i | −0.444509 | − | 0.769913i | ||||
\(137\) | 347.000 | + | 601.022i | 0.216396 | + | 0.374808i | 0.953703 | − | 0.300749i | \(-0.0972365\pi\) |
−0.737308 | + | 0.675557i | \(0.763903\pi\) | |||||||
\(138\) | 128.000 | − | 221.703i | 0.0789571 | − | 0.136758i | ||||
\(139\) | 360.000 | 0.219675 | 0.109837 | − | 0.993950i | \(-0.464967\pi\) | ||||
0.109837 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4288.00 | −2.56110 | ||||||||
\(142\) | −336.000 | + | 581.969i | −0.198567 | + | 0.343928i | ||||
\(143\) | 468.000 | + | 810.600i | 0.273679 | + | 0.474026i | ||||
\(144\) | −758.500 | − | 1313.76i | −0.438947 | − | 0.760278i | ||||
\(145\) | −125.000 | + | 216.506i | −0.0715909 | + | 0.123999i | ||||
\(146\) | 82.0000 | 0.0464820 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3038.00 | 1.68731 | ||||||||
\(149\) | −1135.00 | + | 1965.88i | −0.624046 | + | 1.08088i | 0.364679 | + | 0.931133i | \(0.381179\pi\) |
−0.988725 | + | 0.149746i | \(0.952155\pi\) | |||||||
\(150\) | 100.000 | + | 173.205i | 0.0544331 | + | 0.0942809i | ||||
\(151\) | −316.000 | − | 547.328i | −0.170303 | − | 0.294973i | 0.768223 | − | 0.640182i | \(-0.221141\pi\) |
−0.938526 | + | 0.345209i | \(0.887808\pi\) | |||||||
\(152\) | 300.000 | − | 519.615i | 0.160087 | − | 0.277279i | ||||
\(153\) | −3478.00 | −1.83778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1240.00 | 0.642575 | ||||||||
\(156\) | 2184.00 | − | 3782.80i | 1.12090 | − | 1.94145i | ||||
\(157\) | 367.000 | + | 635.663i | 0.186559 | + | 0.323130i | 0.944101 | − | 0.329657i | \(-0.106933\pi\) |
−0.757542 | + | 0.652787i | \(0.773600\pi\) | |||||||
\(158\) | 500.000 | + | 866.025i | 0.251759 | + | 0.436059i | ||||
\(159\) | 88.0000 | − | 152.420i | 0.0438922 | − | 0.0760235i | ||||
\(160\) | −805.000 | −0.397755 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −359.000 | −0.174109 | ||||||||
\(163\) | −1266.00 | + | 2192.78i | −0.608348 | + | 1.05369i | 0.383164 | + | 0.923680i | \(0.374834\pi\) |
−0.991513 | + | 0.130010i | \(0.958499\pi\) | |||||||
\(164\) | 1407.00 | + | 2437.00i | 0.669928 | + | 1.16035i | ||||
\(165\) | −240.000 | − | 415.692i | −0.113236 | − | 0.196131i | ||||
\(166\) | 224.000 | − | 387.979i | 0.104734 | − | 0.181404i | ||||
\(167\) | 416.000 | 0.192761 | 0.0963804 | − | 0.995345i | \(-0.469273\pi\) | ||||
0.0963804 | + | 0.995345i | \(0.469273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3887.00 | 1.76923 | ||||||||
\(170\) | −235.000 | + | 407.032i | −0.106022 | + | 0.183635i | ||||
\(171\) | −740.000 | − | 1281.72i | −0.330931 | − | 0.573189i | ||||
\(172\) | −238.000 | − | 412.228i | −0.105508 | − | 0.182745i | ||||
\(173\) | −1521.00 | + | 2634.45i | −0.668436 | + | 1.15777i | 0.309905 | + | 0.950768i | \(0.399703\pi\) |
−0.978341 | + | 0.206998i | \(0.933631\pi\) | |||||||
\(174\) | 400.000 | 0.174275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 492.000 | 0.210715 | ||||||||
\(177\) | −2240.00 | + | 3879.79i | −0.951236 | + | 1.64759i | ||||
\(178\) | 435.000 | + | 753.442i | 0.183172 | + | 0.317263i | ||||
\(179\) | 90.0000 | + | 155.885i | 0.0375805 | + | 0.0650914i | 0.884204 | − | 0.467101i | \(-0.154702\pi\) |
−0.846623 | + | 0.532192i | \(0.821368\pi\) | |||||||
\(180\) | −647.500 | + | 1121.50i | −0.268121 | + | 0.464399i | ||||
\(181\) | −1958.00 | −0.804072 | −0.402036 | − | 0.915624i | \(-0.631697\pi\) | ||||
−0.402036 | + | 0.915624i | \(0.631697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2224.00 | 0.898376 | ||||||||
\(184\) | 240.000 | − | 415.692i | 0.0961578 | − | 0.166550i | ||||
\(185\) | −1085.00 | − | 1879.28i | −0.431193 | − | 0.746849i | ||||
\(186\) | −992.000 | − | 1718.19i | −0.391059 | − | 0.677334i | ||||
\(187\) | 564.000 | − | 976.877i | 0.220555 | − | 0.382012i | ||||
\(188\) | −3752.00 | −1.45555 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −200.000 | −0.0763659 | ||||||||
\(191\) | 1444.00 | − | 2501.08i | 0.547038 | − | 0.947497i | −0.451438 | − | 0.892302i | \(-0.649089\pi\) |
0.998476 | − | 0.0551944i | \(-0.0175779\pi\) | |||||||
\(192\) | −668.000 | − | 1157.01i | −0.251087 | − | 0.434896i | ||||
\(193\) | −801.000 | − | 1387.37i | −0.298742 | − | 0.517437i | 0.677106 | − | 0.735885i | \(-0.263234\pi\) |
−0.975848 | + | 0.218449i | \(0.929900\pi\) | |||||||
\(194\) | −513.000 | + | 888.542i | −0.189852 | + | 0.328833i | ||||
\(195\) | −3120.00 | −1.14578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4794.00 | −1.73380 | −0.866899 | − | 0.498483i | \(-0.833891\pi\) | ||||
−0.866899 | + | 0.498483i | \(0.833891\pi\) | |||||||
\(198\) | −222.000 | + | 384.515i | −0.0796811 | + | 0.138012i | ||||
\(199\) | −640.000 | − | 1108.51i | −0.227982 | − | 0.394876i | 0.729228 | − | 0.684271i | \(-0.239879\pi\) |
−0.957210 | + | 0.289395i | \(0.906546\pi\) | |||||||
\(200\) | 187.500 | + | 324.760i | 0.0662913 | + | 0.114820i | ||||
\(201\) | −656.000 | + | 1136.23i | −0.230202 | + | 0.398722i | ||||
\(202\) | 482.000 | 0.167888 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5264.00 | −1.80664 | ||||||||
\(205\) | 1005.00 | − | 1740.71i | 0.342401 | − | 0.593056i | ||||
\(206\) | −136.000 | − | 235.559i | −0.0459979 | − | 0.0796707i | ||||
\(207\) | −592.000 | − | 1025.37i | −0.198777 | − | 0.344292i | ||||
\(208\) | 1599.00 | − | 2769.55i | 0.533032 | − | 0.923239i | ||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −68.0000 | −0.0221863 | −0.0110932 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110932 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(212\) | 77.0000 | − | 133.368i | 0.0249452 | − | 0.0432063i | ||||
\(213\) | 2688.00 | + | 4655.75i | 0.864689 | + | 1.49769i | ||||
\(214\) | 222.000 | + | 384.515i | 0.0709141 | + | 0.122827i | ||||
\(215\) | −170.000 | + | 294.449i | −0.0539251 | + | 0.0934011i | ||||
\(216\) | 1200.00 | 0.378008 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1170.00 | −0.363497 | ||||||||
\(219\) | 328.000 | − | 568.113i | 0.101206 | − | 0.175295i | ||||
\(220\) | −210.000 | − | 363.731i | −0.0643554 | − | 0.111467i | ||||
\(221\) | −3666.00 | − | 6349.70i | −1.11585 | − | 1.93270i | ||||
\(222\) | −1736.00 | + | 3006.84i | −0.524832 | + | 0.909036i | ||||
\(223\) | −1728.00 | −0.518903 | −0.259452 | − | 0.965756i | \(-0.583542\pi\) | ||||
−0.259452 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 925.000 | 0.274074 | ||||||||
\(226\) | 399.000 | − | 691.088i | 0.117438 | − | 0.203409i | ||||
\(227\) | 2432.00 | + | 4212.35i | 0.711090 | + | 1.23164i | 0.964448 | + | 0.264272i | \(0.0851317\pi\) |
−0.253358 | + | 0.967373i | \(0.581535\pi\) | |||||||
\(228\) | −1120.00 | − | 1939.90i | −0.325324 | − | 0.563477i | ||||
\(229\) | 2755.00 | − | 4771.80i | 0.795002 | − | 1.37698i | −0.127835 | − | 0.991795i | \(-0.540803\pi\) |
0.922838 | − | 0.385189i | \(-0.125864\pi\) | |||||||
\(230\) | −160.000 | −0.0458699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 750.000 | 0.212241 | ||||||||
\(233\) | −2661.00 | + | 4608.99i | −0.748188 | + | 1.29590i | 0.200502 | + | 0.979693i | \(0.435743\pi\) |
−0.948690 | + | 0.316207i | \(0.897591\pi\) | |||||||
\(234\) | 1443.00 | + | 2499.35i | 0.403128 | + | 0.698238i | ||||
\(235\) | 1340.00 | + | 2320.95i | 0.371966 | + | 0.644264i | ||||
\(236\) | −1960.00 | + | 3394.82i | −0.540615 | + | 0.936373i | ||||
\(237\) | 8000.00 | 2.19264 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1840.00 | −0.497990 | −0.248995 | − | 0.968505i | \(-0.580100\pi\) | ||||
−0.248995 | + | 0.968505i | \(0.580100\pi\) | |||||||
\(240\) | −820.000 | + | 1420.28i | −0.220545 | + | 0.381995i | ||||
\(241\) | 219.000 | + | 379.319i | 0.0585354 | + | 0.101386i | 0.893808 | − | 0.448450i | \(-0.148024\pi\) |
−0.835273 | + | 0.549836i | \(0.814690\pi\) | |||||||
\(242\) | 593.500 | + | 1027.97i | 0.157651 | + | 0.273060i | ||||
\(243\) | −2516.00 | + | 4357.84i | −0.664204 | + | 1.15043i | ||||
\(244\) | 1946.00 | 0.510573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3216.00 | −0.833515 | ||||||||
\(247\) | 1560.00 | − | 2702.00i | 0.401864 | − | 0.696049i | ||||
\(248\) | −1860.00 | − | 3221.61i | −0.476250 | − | 0.824890i | ||||
\(249\) | −1792.00 | − | 3103.84i | −0.456078 | − | 0.789950i | ||||
\(250\) | 62.5000 | − | 108.253i | 0.0158114 | − | 0.0273861i | ||||
\(251\) | 5592.00 | 1.40623 | 0.703115 | − | 0.711076i | \(-0.251792\pi\) | ||||
0.703115 | + | 0.711076i | \(0.251792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 384.000 | 0.0954224 | ||||||||
\(254\) | −388.000 | + | 672.036i | −0.0958476 | + | 0.166013i | ||||
\(255\) | 1880.00 | + | 3256.26i | 0.461687 | + | 0.799665i | ||||
\(256\) | 59.5000 | + | 103.057i | 0.0145264 | + | 0.0251604i | ||||
\(257\) | 987.000 | − | 1709.53i | 0.239562 | − | 0.414933i | −0.721027 | − | 0.692907i | \(-0.756330\pi\) |
0.960589 | + | 0.277974i | \(0.0896629\pi\) | |||||||
\(258\) | 544.000 | 0.131271 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2730.00 | −0.651182 | ||||||||
\(261\) | 925.000 | − | 1602.15i | 0.219372 | − | 0.379963i | ||||
\(262\) | −556.000 | − | 963.020i | −0.131106 | − | 0.227082i | ||||
\(263\) | 364.000 | + | 630.466i | 0.0853430 | + | 0.147818i | 0.905537 | − | 0.424267i | \(-0.139468\pi\) |
−0.820194 | + | 0.572085i | \(0.806135\pi\) | |||||||
\(264\) | −720.000 | + | 1247.08i | −0.167852 | + | 0.290728i | ||||
\(265\) | −110.000 | −0.0254990 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6960.00 | 1.59530 | ||||||||
\(268\) | −574.000 | + | 994.197i | −0.130831 | + | 0.226605i | ||||
\(269\) | −2905.00 | − | 5031.61i | −0.658442 | − | 1.14046i | −0.981019 | − | 0.193912i | \(-0.937882\pi\) |
0.322577 | − | 0.946543i | \(-0.395451\pi\) | |||||||
\(270\) | −200.000 | − | 346.410i | −0.0450800 | − | 0.0780809i | ||||
\(271\) | 3264.00 | − | 5653.41i | 0.731638 | − | 1.26723i | −0.224545 | − | 0.974464i | \(-0.572090\pi\) |
0.956183 | − | 0.292770i | \(-0.0945771\pi\) | |||||||
\(272\) | −3854.00 | −0.859129 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −694.000 | −0.153015 | ||||||||
\(275\) | −150.000 | + | 259.808i | −0.0328921 | + | 0.0569709i | ||||
\(276\) | −896.000 | − | 1551.92i | −0.195409 | − | 0.338458i | ||||
\(277\) | −2563.00 | − | 4439.25i | −0.555941 | − | 0.962919i | −0.997830 | − | 0.0658485i | \(-0.979025\pi\) |
0.441888 | − | 0.897070i | \(-0.354309\pi\) | |||||||
\(278\) | −180.000 | + | 311.769i | −0.0388334 | + | 0.0672614i | ||||
\(279\) | −9176.00 | −1.96901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2358.00 | −0.500592 | −0.250296 | − | 0.968169i | \(-0.580528\pi\) | ||||
−0.250296 | + | 0.968169i | \(0.580528\pi\) | |||||||
\(282\) | 2144.00 | − | 3713.52i | 0.452742 | − | 0.784173i | ||||
\(283\) | −196.000 | − | 339.482i | −0.0411696 | − | 0.0713078i | 0.844706 | − | 0.535230i | \(-0.179775\pi\) |
−0.885876 | + | 0.463922i | \(0.846442\pi\) | |||||||
\(284\) | 2352.00 | + | 4073.78i | 0.491428 | + | 0.851178i | ||||
\(285\) | −800.000 | + | 1385.64i | −0.166273 | + | 0.287994i | ||||
\(286\) | −936.000 | −0.193520 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5957.00 | 1.21882 | ||||||||
\(289\) | −1961.50 | + | 3397.42i | −0.399247 | + | 0.691516i | ||||
\(290\) | −125.000 | − | 216.506i | −0.0253112 | − | 0.0438403i | ||||
\(291\) | 4104.00 | + | 7108.34i | 0.826738 | + | 1.43195i | ||||
\(292\) | 287.000 | − | 497.099i | 0.0575185 | − | 0.0996250i | ||||
\(293\) | 1202.00 | 0.239664 | 0.119832 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119832 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | −3255.00 | + | 5637.83i | −0.639166 | + | 1.10707i | ||||
\(297\) | 480.000 | + | 831.384i | 0.0937792 | + | 0.162430i | ||||
\(298\) | −1135.00 | − | 1965.88i | −0.220634 | − | 0.382148i | ||||
\(299\) | 1248.00 | − | 2161.60i | 0.241384 | − | 0.418089i | ||||
\(300\) | 1400.00 | 0.269430 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 632.000 | 0.120422 | ||||||||
\(303\) | 1928.00 | − | 3339.39i | 0.365547 | − | 0.633146i | ||||
\(304\) | −820.000 | − | 1420.28i | −0.154705 | − | 0.267956i | ||||
\(305\) | −695.000 | − | 1203.78i | −0.130477 | − | 0.225993i | ||||
\(306\) | 1739.00 | − | 3012.04i | 0.324876 | − | 0.562701i | ||||
\(307\) | −6384.00 | −1.18682 | −0.593411 | − | 0.804900i | \(-0.702219\pi\) | ||||
−0.593411 | + | 0.804900i | \(0.702219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2176.00 | −0.400609 | ||||||||
\(310\) | −620.000 | + | 1073.87i | −0.113592 | + | 0.196748i | ||||
\(311\) | 2484.00 | + | 4302.41i | 0.452909 | + | 0.784462i | 0.998565 | − | 0.0535476i | \(-0.0170529\pi\) |
−0.545656 | + | 0.838009i | \(0.683720\pi\) | |||||||
\(312\) | 4680.00 | + | 8106.00i | 0.849208 | + | 1.47087i | ||||
\(313\) | 1379.00 | − | 2388.50i | 0.249028 | − | 0.431329i | −0.714229 | − | 0.699913i | \(-0.753222\pi\) |
0.963256 | + | 0.268584i | \(0.0865556\pi\) | |||||||
\(314\) | −734.000 | −0.131917 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7000.00 | 1.24614 | ||||||||
\(317\) | 3137.00 | − | 5433.44i | 0.555809 | − | 0.962690i | −0.442031 | − | 0.897000i | \(-0.645742\pi\) |
0.997840 | − | 0.0656898i | \(-0.0209248\pi\) | |||||||
\(318\) | 88.0000 | + | 152.420i | 0.0155182 | + | 0.0268784i | ||||
\(319\) | 300.000 | + | 519.615i | 0.0526545 | + | 0.0912002i | ||||
\(320\) | −417.500 | + | 723.131i | −0.0729342 | + | 0.126326i | ||||
\(321\) | 3552.00 | 0.617612 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3760.00 | −0.647715 | ||||||||
\(324\) | −1256.50 | + | 2176.32i | −0.215449 | + | 0.373169i | ||||
\(325\) | 975.000 | + | 1688.75i | 0.166410 | + | 0.288231i | ||||
\(326\) | −1266.00 | − | 2192.78i | −0.215084 | − | 0.372536i | ||||
\(327\) | −4680.00 | + | 8106.00i | −0.791451 | + | 1.37083i | ||||
\(328\) | −6030.00 | −1.01509 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 480.000 | 0.0800701 | ||||||||
\(331\) | −966.000 | + | 1673.16i | −0.160411 | + | 0.277841i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(332\) | −1568.00 | − | 2715.86i | −0.259202 | − | 0.448952i | ||||
\(333\) | 8029.00 | + | 13906.6i | 1.32128 | + | 2.28853i | ||||
\(334\) | −208.000 | + | 360.267i | −0.0340756 | + | 0.0590207i | ||||
\(335\) | 820.000 | 0.133735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2386.00 | 0.385679 | 0.192839 | − | 0.981230i | \(-0.438230\pi\) | ||||
0.192839 | + | 0.981230i | \(0.438230\pi\) | |||||||
\(338\) | −1943.50 | + | 3366.24i | −0.312759 | + | 0.541714i | ||||
\(339\) | −3192.00 | − | 5528.71i | −0.511403 | − | 0.885776i | ||||
\(340\) | 1645.00 | + | 2849.22i | 0.262390 | + | 0.454473i | ||||
\(341\) | 1488.00 | − | 2577.29i | 0.236304 | − | 0.409291i | ||||
\(342\) | 1480.00 | 0.234004 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1020.00 | 0.159868 | ||||||||
\(345\) | −640.000 | + | 1108.51i | −0.0998737 | + | 0.172986i | ||||
\(346\) | −1521.00 | − | 2634.45i | −0.236328 | − | 0.409332i | ||||
\(347\) | −3038.00 | − | 5261.97i | −0.469995 | − | 0.814056i | 0.529416 | − | 0.848362i | \(-0.322411\pi\) |
−0.999411 | + | 0.0343065i | \(0.989078\pi\) | |||||||
\(348\) | 1400.00 | − | 2424.87i | 0.215655 | − | 0.373525i | ||||
\(349\) | 2210.00 | 0.338964 | 0.169482 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169482 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6240.00 | 0.948908 | ||||||||
\(352\) | −966.000 | + | 1673.16i | −0.146273 | + | 0.253352i | ||||
\(353\) | 1299.00 | + | 2249.93i | 0.195861 | + | 0.339241i | 0.947182 | − | 0.320696i | \(-0.103917\pi\) |
−0.751322 | + | 0.659936i | \(0.770583\pi\) | |||||||
\(354\) | −2240.00 | − | 3879.79i | −0.336313 | − | 0.582510i | ||||
\(355\) | 1680.00 | − | 2909.85i | 0.251169 | − | 0.435038i | ||||
\(356\) | 6090.00 | 0.906655 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −180.000 | −0.0265735 | ||||||||
\(359\) | 6660.00 | − | 11535.5i | 0.979112 | − | 1.69587i | 0.313476 | − | 0.949596i | \(-0.398506\pi\) |
0.665636 | − | 0.746276i | \(-0.268160\pi\) | |||||||
\(360\) | −1387.50 | − | 2403.22i | −0.203132 | − | 0.351836i | ||||
\(361\) | 2629.50 | + | 4554.43i | 0.383365 | + | 0.664008i | ||||
\(362\) | 979.000 | − | 1695.68i | 0.142141 | − | 0.246196i | ||||
\(363\) | 9496.00 | 1.37303 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −410.000 | −0.0587956 | ||||||||
\(366\) | −1112.00 | + | 1926.04i | −0.158812 | + | 0.275070i | ||||
\(367\) | −5408.00 | − | 9366.93i | −0.769197 | − | 1.33229i | −0.937999 | − | 0.346638i | \(-0.887323\pi\) |
0.168802 | − | 0.985650i | \(-0.446010\pi\) | |||||||
\(368\) | −656.000 | − | 1136.23i | −0.0929249 | − | 0.160951i | ||||
\(369\) | −7437.00 | + | 12881.3i | −1.04920 | + | 1.81727i | ||||
\(370\) | 2170.00 | 0.304900 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −13888.0 | −1.93564 | ||||||||
\(373\) | 5549.00 | − | 9611.15i | 0.770285 | − | 1.33417i | −0.167122 | − | 0.985936i | \(-0.553447\pi\) |
0.937407 | − | 0.348237i | \(-0.113219\pi\) | |||||||
\(374\) | 564.000 | + | 976.877i | 0.0779779 | + | 0.135062i | ||||
\(375\) | −500.000 | − | 866.025i | −0.0688530 | − | 0.119257i | ||||
\(376\) | 4020.00 | − | 6962.84i | 0.551371 | − | 0.955003i | ||||
\(377\) | 3900.00 | 0.532786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7100.00 | 0.962276 | 0.481138 | − | 0.876645i | \(-0.340224\pi\) | ||||
0.481138 | + | 0.876645i | \(0.340224\pi\) | |||||||
\(380\) | −700.000 | + | 1212.44i | −0.0944980 | + | 0.163675i | ||||
\(381\) | 3104.00 | + | 5376.29i | 0.417383 | + | 0.722928i | ||||
\(382\) | 1444.00 | + | 2501.08i | 0.193407 | + | 0.334991i | ||||
\(383\) | 364.000 | − | 630.466i | 0.0485627 | − | 0.0841131i | −0.840722 | − | 0.541467i | \(-0.817869\pi\) |
0.889285 | + | 0.457353i | \(0.151203\pi\) | |||||||
\(384\) | 11640.0 | 1.54688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1602.00 | 0.211243 | ||||||||
\(387\) | 1258.00 | − | 2178.92i | 0.165240 | − | 0.286203i | ||||
\(388\) | 3591.00 | + | 6219.79i | 0.469859 | + | 0.813820i | ||||
\(389\) | 3405.00 | + | 5897.63i | 0.443806 | + | 0.768694i | 0.997968 | − | 0.0637147i | \(-0.0202948\pi\) |
−0.554163 | + | 0.832408i | \(0.686961\pi\) | |||||||
\(390\) | 1560.00 | − | 2702.00i | 0.202548 | − | 0.350823i | ||||
\(391\) | −3008.00 | −0.389057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8896.00 | −1.14184 | ||||||||
\(394\) | 2397.00 | − | 4151.73i | 0.306495 | − | 0.530865i | ||||
\(395\) | −2500.00 | − | 4330.13i | −0.318452 | − | 0.551576i | ||||
\(396\) | 1554.00 | + | 2691.61i | 0.197201 | + | 0.341561i | ||||
\(397\) | 287.000 | − | 497.099i | 0.0362824 | − | 0.0628430i | −0.847314 | − | 0.531092i | \(-0.821782\pi\) |
0.883596 | + | 0.468249i | \(0.155115\pi\) | |||||||
\(398\) | 1280.00 | 0.161208 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1025.00 | 0.128125 | ||||||||
\(401\) | −3081.00 | + | 5336.45i | −0.383685 | + | 0.664562i | −0.991586 | − | 0.129451i | \(-0.958679\pi\) |
0.607901 | + | 0.794013i | \(0.292012\pi\) | |||||||
\(402\) | −656.000 | − | 1136.23i | −0.0813888 | − | 0.140970i | ||||
\(403\) | −9672.00 | − | 16752.4i | −1.19553 | − | 2.07071i | ||||
\(404\) | 1687.00 | − | 2921.97i | 0.207751 | − | 0.359835i | ||||
\(405\) | 1795.00 | 0.220233 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5208.00 | −0.634278 | ||||||||
\(408\) | 5640.00 | − | 9768.77i | 0.684367 | − | 1.18536i | ||||
\(409\) | −4105.00 | − | 7110.07i | −0.496282 | − | 0.859585i | 0.503709 | − | 0.863873i | \(-0.331968\pi\) |
−0.999991 | + | 0.00428830i | \(0.998635\pi\) | |||||||
\(410\) | 1005.00 | + | 1740.71i | 0.121057 | + | 0.209677i | ||||
\(411\) | −2776.00 | + | 4808.17i | −0.333163 | + | 0.577055i | ||||
\(412\) | −1904.00 | −0.227678 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1184.00 | 0.140557 | ||||||||
\(415\) | −1120.00 | + | 1939.90i | −0.132479 | + | 0.229460i | ||||
\(416\) | 6279.00 | + | 10875.5i | 0.740032 | + | 1.28177i | ||||
\(417\) | 1440.00 | + | 2494.15i | 0.169106 | + | 0.292900i | ||||
\(418\) | −240.000 | + | 415.692i | −0.0280832 | + | 0.0486416i | ||||
\(419\) | 4800.00 | 0.559655 | 0.279827 | − | 0.960050i | \(-0.409723\pi\) | ||||
0.279827 | + | 0.960050i | \(0.409723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9938.00 | −1.15047 | −0.575236 | − | 0.817988i | \(-0.695090\pi\) | ||||
−0.575236 | + | 0.817988i | \(0.695090\pi\) | |||||||
\(422\) | 34.0000 | − | 58.8897i | 0.00392202 | − | 0.00679314i | ||||
\(423\) | −9916.00 | − | 17175.0i | −1.13979 | − | 1.97418i | ||||
\(424\) | 165.000 | + | 285.788i | 0.0188988 | + | 0.0327338i | ||||
\(425\) | 1175.00 | − | 2035.16i | 0.134108 | − | 0.232282i | ||||
\(426\) | −5376.00 | −0.611427 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3108.00 | 0.351007 | ||||||||
\(429\) | −3744.00 | + | 6484.80i | −0.421357 | + | 0.729811i | ||||
\(430\) | −170.000 | − | 294.449i | −0.0190654 | − | 0.0330223i | ||||
\(431\) | 4624.00 | + | 8009.00i | 0.516776 | + | 0.895081i | 0.999810 | + | 0.0194802i | \(0.00620115\pi\) |
−0.483035 | + | 0.875601i | \(0.660466\pi\) | |||||||
\(432\) | 1640.00 | − | 2840.56i | 0.182649 | − | 0.316358i | ||||
\(433\) | −1118.00 | −0.124082 | −0.0620412 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620412 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2000.00 | −0.220443 | ||||||||
\(436\) | −4095.00 | + | 7092.75i | −0.449805 | + | 0.779085i | ||||
\(437\) | −640.000 | − | 1108.51i | −0.0700580 | − | 0.121344i | ||||
\(438\) | 328.000 | + | 568.113i | 0.0357818 | + | 0.0619760i | ||||
\(439\) | 5980.00 | − | 10357.7i | 0.650136 | − | 1.12607i | −0.332953 | − | 0.942943i | \(-0.608045\pi\) |
0.983090 | − | 0.183126i | \(-0.0586215\pi\) | |||||||
\(440\) | 900.000 | 0.0975132 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7332.00 | 0.789022 | ||||||||
\(443\) | −3666.00 | + | 6349.70i | −0.393176 | + | 0.681001i | −0.992867 | − | 0.119231i | \(-0.961957\pi\) |
0.599691 | + | 0.800232i | \(0.295290\pi\) | |||||||
\(444\) | 12152.0 | + | 21047.9i | 1.29889 | + | 2.24975i | ||||
\(445\) | −2175.00 | − | 3767.21i | −0.231696 | − | 0.401310i | ||||
\(446\) | 864.000 | − | 1496.49i | 0.0917300 | − | 0.158881i | ||||
\(447\) | −18160.0 | −1.92156 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1890.00 | 0.198652 | 0.0993259 | − | 0.995055i | \(-0.468331\pi\) | ||||
0.0993259 | + | 0.995055i | \(0.468331\pi\) | |||||||
\(450\) | −462.500 | + | 801.073i | −0.0484499 | + | 0.0839177i | ||||
\(451\) | −2412.00 | − | 4177.71i | −0.251833 | − | 0.436187i | ||||
\(452\) | −2793.00 | − | 4837.62i | −0.290645 | − | 0.503412i | ||||
\(453\) | 2528.00 | − | 4378.62i | 0.262198 | − | 0.454141i | ||||
\(454\) | −4864.00 | −0.502817 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4800.00 | 0.492940 | ||||||||
\(457\) | 3507.00 | − | 6074.30i | 0.358973 | − | 0.621759i | −0.628817 | − | 0.777554i | \(-0.716460\pi\) |
0.987789 | + | 0.155795i | \(0.0497938\pi\) | |||||||
\(458\) | 2755.00 | + | 4771.80i | 0.281076 | + | 0.486837i | ||||
\(459\) | −3760.00 | − | 6512.51i | −0.382357 | − | 0.662261i | ||||
\(460\) | −560.000 | + | 969.948i | −0.0567612 | + | 0.0983132i | ||||
\(461\) | −8318.00 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6432.00 | 0.645616 | 0.322808 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322808 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(464\) | 1025.00 | − | 1775.35i | 0.102553 | − | 0.177626i | ||||
\(465\) | 4960.00 | + | 8590.97i | 0.494655 | + | 0.856767i | ||||
\(466\) | −2661.00 | − | 4608.99i | −0.264525 | − | 0.458170i | ||||
\(467\) | 5032.00 | − | 8715.68i | 0.498615 | − | 0.863626i | −0.501384 | − | 0.865225i | \(-0.667176\pi\) |
0.999999 | + | 0.00159856i | \(0.000508837\pi\) | |||||||
\(468\) | 20202.0 | 1.99538 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2680.00 | −0.263020 | ||||||||
\(471\) | −2936.00 | + | 5085.30i | −0.287227 | + | 0.497491i | ||||
\(472\) | −4200.00 | − | 7274.61i | −0.409578 | − | 0.709409i | ||||
\(473\) | 408.000 | + | 706.677i | 0.0396614 | + | 0.0686956i | ||||
\(474\) | −4000.00 | + | 6928.20i | −0.387608 | + | 0.671356i | ||||
\(475\) | 1000.00 | 0.0965961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 814.000 | 0.0781352 | ||||||||
\(478\) | 920.000 | − | 1593.49i | 0.0880331 | − | 0.152478i | ||||
\(479\) | −700.000 | − | 1212.44i | −0.0667721 | − | 0.115653i | 0.830707 | − | 0.556710i | \(-0.187937\pi\) |
−0.897479 | + | 0.441058i | \(0.854603\pi\) | |||||||
\(480\) | −3220.00 | − | 5577.20i | −0.306192 | − | 0.530340i | ||||
\(481\) | −16926.0 | + | 29316.7i | −1.60449 | + | 2.77906i | ||||
\(482\) | −438.000 | −0.0413908 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8309.00 | 0.780334 | ||||||||
\(485\) | 2565.00 | − | 4442.71i | 0.240146 | − | 0.415945i | ||||
\(486\) | −2516.00 | − | 4357.84i | −0.234831 | − | 0.406740i | ||||
\(487\) | −6688.00 | − | 11584.0i | −0.622304 | − | 1.07786i | −0.989056 | − | 0.147544i | \(-0.952863\pi\) |
0.366751 | − | 0.930319i | \(-0.380470\pi\) | |||||||
\(488\) | −2085.00 | + | 3611.33i | −0.193409 | + | 0.334994i | ||||
\(489\) | −20256.0 | −1.87323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7092.00 | 0.651848 | 0.325924 | − | 0.945396i | \(-0.394325\pi\) | ||||
0.325924 | + | 0.945396i | \(0.394325\pi\) | |||||||
\(492\) | −11256.0 | + | 19496.0i | −1.03142 | + | 1.78648i | ||||
\(493\) | −2350.00 | − | 4070.32i | −0.214683 | − | 0.371842i | ||||
\(494\) | 1560.00 | + | 2702.00i | 0.142080 | + | 0.246090i | ||||
\(495\) | 1110.00 | − | 1922.58i | 0.100789 | − | 0.174572i | ||||
\(496\) | −10168.0 | −0.920477 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3584.00 | 0.322496 | ||||||||
\(499\) | 410.000 | − | 710.141i | 0.0367818 | − | 0.0637080i | −0.847048 | − | 0.531516i | \(-0.821623\pi\) |
0.883830 | + | 0.467808i | \(0.154956\pi\) | |||||||
\(500\) | −437.500 | − | 757.772i | −0.0391312 | − | 0.0677772i | ||||
\(501\) | 1664.00 | + | 2882.13i | 0.148387 | + | 0.257014i | ||||
\(502\) | −2796.00 | + | 4842.81i | −0.248589 | + | 0.430568i | ||||
\(503\) | −4568.00 | −0.404925 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2410.00 | −0.212364 | ||||||||
\(506\) | −192.000 | + | 332.554i | −0.0168685 | + | 0.0292170i | ||||
\(507\) | 15548.0 | + | 26929.9i | 1.36195 | + | 2.35897i | ||||
\(508\) | 2716.00 | + | 4704.25i | 0.237211 | + | 0.410861i | ||||
\(509\) | −9905.00 | + | 17156.0i | −0.862537 | + | 1.49396i | 0.00693487 | + | 0.999976i | \(0.497793\pi\) |
−0.869472 | + | 0.493982i | \(0.835541\pi\) | |||||||
\(510\) | −3760.00 | −0.326462 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11521.0 | 0.994455 | ||||||||
\(513\) | 1600.00 | − | 2771.28i | 0.137703 | − | 0.238509i | ||||
\(514\) | 987.000 | + | 1709.53i | 0.0846979 | + | 0.146701i | ||||
\(515\) | 680.000 | + | 1177.79i | 0.0581833 | + | 0.100776i | ||||
\(516\) | 1904.00 | − | 3297.82i | 0.162440 | − | 0.281354i | ||||
\(517\) | 6432.00 | 0.547155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24336.0 | −2.05825 | ||||||||
\(520\) | 2925.00 | − | 5066.25i | 0.246673 | − | 0.427249i | ||||
\(521\) | 919.000 | + | 1591.75i | 0.0772785 | + | 0.133850i | 0.902075 | − | 0.431580i | \(-0.142044\pi\) |
−0.824796 | + | 0.565430i | \(0.808710\pi\) | |||||||
\(522\) | 925.000 | + | 1602.15i | 0.0775597 | + | 0.134337i | ||||
\(523\) | −1036.00 | + | 1794.40i | −0.0866178 | + | 0.150026i | −0.906079 | − | 0.423108i | \(-0.860939\pi\) |
0.819462 | + | 0.573134i | \(0.194273\pi\) | |||||||
\(524\) | −7784.00 | −0.648942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −728.000 | −0.0603466 | ||||||||
\(527\) | −11656.0 | + | 20188.8i | −0.963460 | + | 1.66876i | ||||
\(528\) | 1968.00 | + | 3408.68i | 0.162209 | + | 0.280954i | ||||
\(529\) | 5571.50 | + | 9650.12i | 0.457919 | + | 0.793139i | ||||
\(530\) | 55.0000 | − | 95.2628i | 0.00450764 | − | 0.00780746i | ||||
\(531\) | −20720.0 | −1.69335 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31356.0 | −2.54818 | ||||||||
\(534\) | −3480.00 | + | 6027.54i | −0.282012 | + | 0.488459i | ||||
\(535\) | −1110.00 | − | 1922.58i | −0.0897000 | − | 0.155365i | ||||
\(536\) | −1230.00 | − | 2130.42i | −0.0991192 | − | 0.171680i | ||||
\(537\) | −720.000 | + | 1247.08i | −0.0578590 | + | 0.100215i | ||||
\(538\) | 5810.00 | 0.465589 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2800.00 | −0.223135 | ||||||||
\(541\) | 1749.00 | − | 3029.36i | 0.138993 | − | 0.240743i | −0.788123 | − | 0.615518i | \(-0.788947\pi\) |
0.927116 | + | 0.374775i | \(0.122280\pi\) | |||||||
\(542\) | 3264.00 | + | 5653.41i | 0.258673 | + | 0.448035i | ||||
\(543\) | −7832.00 | − | 13565.4i | −0.618975 | − | 1.07210i | ||||
\(544\) | 7567.00 | − | 13106.4i | 0.596383 | − | 1.03297i | ||||
\(545\) | 5850.00 | 0.459792 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5076.00 | 0.396772 | 0.198386 | − | 0.980124i | \(-0.436430\pi\) | ||||
0.198386 | + | 0.980124i | \(0.436430\pi\) | |||||||
\(548\) | −2429.00 | + | 4207.15i | −0.189346 | + | 0.327957i | ||||
\(549\) | 5143.00 | + | 8907.94i | 0.399814 | + | 0.692498i | ||||
\(550\) | −150.000 | − | 259.808i | −0.0116291 | − | 0.0201422i | ||||
\(551\) | 1000.00 | − | 1732.05i | 0.0773166 | − | 0.133916i | ||||
\(552\) | 3840.00 | 0.296089 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5126.00 | 0.393110 | ||||||||
\(555\) | 8680.00 | − | 15034.2i | 0.663866 | − | 1.14985i | ||||
\(556\) | 1260.00 | + | 2182.38i | 0.0961077 | + | 0.166463i | ||||
\(557\) | 4337.00 | + | 7511.90i | 0.329918 | + | 0.571436i | 0.982495 | − | 0.186287i | \(-0.0596454\pi\) |
−0.652577 | + | 0.757722i | \(0.726312\pi\) | |||||||
\(558\) | 4588.00 | − | 7946.65i | 0.348074 | − | 0.602883i | ||||
\(559\) | 5304.00 | 0.401315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9024.00 | 0.679133 | ||||||||
\(562\) | 1179.00 | − | 2042.09i | 0.0884931 | − | 0.153275i | ||||
\(563\) | −8036.00 | − | 13918.8i | −0.601558 | − | 1.04193i | −0.992585 | − | 0.121550i | \(-0.961214\pi\) |
0.391028 | − | 0.920379i | \(-0.372120\pi\) | |||||||
\(564\) | −15008.0 | − | 25994.6i | −1.12048 | − | 1.94073i | ||||
\(565\) | −1995.00 | + | 3455.44i | −0.148549 | + | 0.257295i | ||||
\(566\) | 392.000 | 0.0291113 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10080.0 | −0.744626 | ||||||||
\(569\) | −1365.00 | + | 2364.25i | −0.100569 | + | 0.174191i | −0.911919 | − | 0.410370i | \(-0.865400\pi\) |
0.811350 | + | 0.584560i | \(0.198733\pi\) | |||||||
\(570\) | −800.000 | − | 1385.64i | −0.0587865 | − | 0.101821i | ||||
\(571\) | −9966.00 | − | 17261.6i | −0.730410 | − | 1.26511i | −0.956708 | − | 0.291049i | \(-0.905996\pi\) |
0.226298 | − | 0.974058i | \(-0.427338\pi\) | |||||||
\(572\) | −3276.00 | + | 5674.20i | −0.239469 | + | 0.414773i | ||||
\(573\) | 23104.0 | 1.68444 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 800.000 | 0.0580214 | ||||||||
\(576\) | 3089.50 | − | 5351.17i | 0.223488 | − | 0.387093i | ||||
\(577\) | 10027.0 | + | 17367.3i | 0.723448 | + | 1.25305i | 0.959610 | + | 0.281335i | \(0.0907772\pi\) |
−0.236162 | + | 0.971714i | \(0.575890\pi\) | |||||||
\(578\) | −1961.50 | − | 3397.42i | −0.141155 | − | 0.244488i | ||||
\(579\) | 6408.00 | − | 11099.0i | 0.459944 | − | 0.796646i | ||||
\(580\) | −1750.00 | −0.125284 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8208.00 | −0.584592 | ||||||||
\(583\) | −132.000 | + | 228.631i | −0.00937716 | + | 0.0162417i | ||||
\(584\) | 615.000 | + | 1065.21i | 0.0435769 | + | 0.0754773i | ||||
\(585\) | −7215.00 | − | 12496.7i | −0.509921 | − | 0.883208i | ||||
\(586\) | −601.000 | + | 1040.96i | −0.0423670 | + | 0.0733819i | ||||
\(587\) | −2544.00 | −0.178879 | −0.0894396 | − | 0.995992i | \(-0.528508\pi\) | ||||
−0.0894396 | + | 0.995992i | \(0.528508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9920.00 | −0.693967 | ||||||||
\(590\) | −1400.00 | + | 2424.87i | −0.0976900 | + | 0.169204i | ||||
\(591\) | −19176.0 | − | 33213.8i | −1.33468 | − | 2.31173i | ||||
\(592\) | 8897.00 | + | 15410.1i | 0.617676 | + | 1.06985i | ||||
\(593\) | −7101.00 | + | 12299.3i | −0.491742 | + | 0.851722i | −0.999955 | − | 0.00950919i | \(-0.996973\pi\) |
0.508213 | + | 0.861232i | \(0.330306\pi\) | |||||||
\(594\) | −960.000 | −0.0663119 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15890.0 | −1.09208 | ||||||||
\(597\) | 5120.00 | − | 8868.10i | 0.351001 | − | 0.607952i | ||||
\(598\) | 1248.00 | + | 2161.60i | 0.0853420 | + | 0.147817i | ||||
\(599\) | 9800.00 | + | 16974.1i | 0.668476 | + | 1.15783i | 0.978330 | + | 0.207050i | \(0.0663864\pi\) |
−0.309854 | + | 0.950784i | \(0.600280\pi\) | |||||||
\(600\) | −1500.00 | + | 2598.08i | −0.102062 | + | 0.176777i | ||||
\(601\) | −27078.0 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6068.00 | −0.409798 | ||||||||
\(604\) | 2212.00 | − | 3831.30i | 0.149015 | − | 0.258101i | ||||
\(605\) | −2967.50 | − | 5139.86i | −0.199415 | − | 0.345397i | ||||
\(606\) | 1928.00 | + | 3339.39i | 0.129240 | + | 0.223851i | ||||
\(607\) | 1352.00 | − | 2341.73i | 0.0904053 | − | 0.156586i | −0.817276 | − | 0.576246i | \(-0.804517\pi\) |
0.907682 | + | 0.419659i | \(0.137850\pi\) | |||||||
\(608\) | 6440.00 | 0.429567 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1390.00 | 0.0922614 | ||||||||
\(611\) | 20904.0 | − | 36206.8i | 1.38410 | − | 2.39733i | ||||
\(612\) | −12173.0 | − | 21084.3i | −0.804027 | − | 1.39262i | ||||
\(613\) | −6351.00 | − | 11000.3i | −0.418458 | − | 0.724790i | 0.577327 | − | 0.816513i | \(-0.304096\pi\) |
−0.995785 | + | 0.0917233i | \(0.970762\pi\) | |||||||
\(614\) | 3192.00 | − | 5528.71i | 0.209802 | − | 0.363388i | ||||
\(615\) | 16080.0 | 1.05432 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12666.0 | 0.826441 | 0.413220 | − | 0.910631i | \(-0.364404\pi\) | ||||
0.413220 | + | 0.910631i | \(0.364404\pi\) | |||||||
\(618\) | 1088.00 | − | 1884.47i | 0.0708184 | − | 0.122661i | ||||
\(619\) | −480.000 | − | 831.384i | −0.0311677 | − | 0.0539841i | 0.850021 | − | 0.526749i | \(-0.176589\pi\) |
−0.881189 | + | 0.472765i | \(0.843256\pi\) | |||||||
\(620\) | 4340.00 | + | 7517.10i | 0.281127 | + | 0.486926i | ||||
\(621\) | 1280.00 | − | 2217.03i | 0.0827128 | − | 0.143263i | ||||
\(622\) | −4968.00 | −0.320255 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 25584.0 | 1.64131 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1379.00 | + | 2388.50i | 0.0880446 | + | 0.152498i | ||||
\(627\) | 1920.00 | + | 3325.54i | 0.122293 | + | 0.211817i | ||||
\(628\) | −2569.00 | + | 4449.64i | −0.163239 | + | 0.282739i | ||||
\(629\) | 40796.0 | 2.58608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23232.0 | 1.46569 | 0.732846 | − | 0.680395i | \(-0.238192\pi\) | ||||
0.732846 | + | 0.680395i | \(0.238192\pi\) | |||||||
\(632\) | −7500.00 | + | 12990.4i | −0.472047 | + | 0.817610i | ||||
\(633\) | −272.000 | − | 471.118i | −0.0170790 | − | 0.0295818i | ||||
\(634\) | 3137.00 | + | 5433.44i | 0.196508 | + | 0.340362i | ||||
\(635\) | 1940.00 | − | 3360.18i | 0.121239 | − | 0.209992i | ||||
\(636\) | 1232.00 | 0.0768113 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −600.000 | −0.0372323 | ||||||||
\(639\) | −12432.0 | + | 21532.9i | −0.769644 | + | 1.33306i | ||||
\(640\) | −3637.50 | − | 6300.33i | −0.224664 | − | 0.389129i | ||||
\(641\) | −6081.00 | − | 10532.6i | −0.374704 | − | 0.649006i | 0.615579 | − | 0.788075i | \(-0.288922\pi\) |
−0.990283 | + | 0.139069i | \(0.955589\pi\) | |||||||
\(642\) | −1776.00 | + | 3076.12i | −0.109179 | + | 0.189104i | ||||
\(643\) | −488.000 | −0.0299298 | −0.0149649 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149649 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2720.00 | −0.166046 | ||||||||
\(646\) | 1880.00 | − | 3256.26i | 0.114501 | − | 0.198321i | ||||
\(647\) | 1992.00 | + | 3450.25i | 0.121041 | + | 0.209649i | 0.920179 | − | 0.391499i | \(-0.128043\pi\) |
−0.799137 | + | 0.601148i | \(0.794710\pi\) | |||||||
\(648\) | −2692.50 | − | 4663.55i | −0.163227 | − | 0.282718i | ||||
\(649\) | 3360.00 | − | 5819.69i | 0.203223 | − | 0.351992i | ||||
\(650\) | −1950.00 | −0.117670 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17724.0 | −1.06461 | ||||||||
\(653\) | 15269.0 | − | 26446.7i | 0.915042 | − | 1.58490i | 0.108201 | − | 0.994129i | \(-0.465491\pi\) |
0.806840 | − | 0.590769i | \(-0.201176\pi\) | |||||||
\(654\) | −4680.00 | − | 8106.00i | −0.279820 | − | 0.484663i | ||||
\(655\) | 2780.00 | + | 4815.10i | 0.165838 | + | 0.287239i | ||||
\(656\) | −8241.00 | + | 14273.8i | −0.490483 | + | 0.849542i | ||||
\(657\) | 3034.00 | 0.180164 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22740.0 | 1.34420 | 0.672098 | − | 0.740463i | \(-0.265394\pi\) | ||||
0.672098 | + | 0.740463i | \(0.265394\pi\) | |||||||
\(660\) | 1680.00 | − | 2909.85i | 0.0990817 | − | 0.171615i | ||||
\(661\) | 9359.00 | + | 16210.3i | 0.550715 | + | 0.953867i | 0.998223 | + | 0.0595870i | \(0.0189784\pi\) |
−0.447508 | + | 0.894280i | \(0.647688\pi\) | |||||||
\(662\) | −966.000 | − | 1673.16i | −0.0567140 | − | 0.0982315i | ||||
\(663\) | 29328.0 | − | 50797.6i | 1.71796 | − | 2.97559i | ||||
\(664\) | 6720.00 | 0.392751 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16058.0 | −0.934287 | ||||||||
\(667\) | 800.000 | − | 1385.64i | 0.0464410 | − | 0.0804381i | ||||
\(668\) | 1456.00 | + | 2521.87i | 0.0843328 | + | 0.146069i | ||||
\(669\) | −6912.00 | − | 11971.9i | −0.399452 | − | 0.691871i | ||||
\(670\) | −410.000 | + | 710.141i | −0.0236413 | + | 0.0409480i | ||||
\(671\) | −3336.00 | −0.191930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10802.0 | 0.618702 | 0.309351 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309351 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(674\) | −1193.00 | + | 2066.34i | −0.0681790 | + | 0.118089i | ||||
\(675\) | 1000.00 | + | 1732.05i | 0.0570222 | + | 0.0987654i | ||||
\(676\) | 13604.5 | + | 23563.7i | 0.774038 | + | 1.34067i | ||||
\(677\) | −173.000 | + | 299.645i | −0.00982117 | + | 0.0170108i | −0.870894 | − | 0.491471i | \(-0.836460\pi\) |
0.861073 | + | 0.508481i | \(0.169793\pi\) | |||||||
\(678\) | 6384.00 | 0.361617 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7050.00 | −0.397581 | ||||||||
\(681\) | −19456.0 | + | 33698.8i | −1.09480 | + | 1.89624i | ||||
\(682\) | 1488.00 | + | 2577.29i | 0.0835461 | + | 0.144706i | ||||
\(683\) | 5814.00 | + | 10070.1i | 0.325720 | + | 0.564163i | 0.981658 | − | 0.190652i | \(-0.0610601\pi\) |
−0.655938 | + | 0.754815i | \(0.727727\pi\) | |||||||
\(684\) | 5180.00 | − | 8972.02i | 0.289565 | − | 0.501541i | ||||
\(685\) | 3470.00 | 0.193550 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44080.0 | 2.44797 | ||||||||
\(688\) | 1394.00 | − | 2414.48i | 0.0772467 | − | 0.133795i | ||||
\(689\) | 858.000 | + | 1486.10i | 0.0474415 | + | 0.0821711i | ||||
\(690\) | −640.000 | − | 1108.51i | −0.0353107 | − | 0.0611599i | ||||
\(691\) | −1236.00 | + | 2140.81i | −0.0680458 | + | 0.117859i | −0.898041 | − | 0.439912i | \(-0.855010\pi\) |
0.829995 | + | 0.557771i | \(0.188343\pi\) | |||||||
\(692\) | −21294.0 | −1.16976 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6076.00 | 0.332337 | ||||||||
\(695\) | 900.000 | − | 1558.85i | 0.0491208 | − | 0.0850797i | ||||
\(696\) | 3000.00 | + | 5196.15i | 0.163383 | + | 0.282988i | ||||
\(697\) | 18894.0 | + | 32725.4i | 1.02677 | + | 1.77842i | ||||
\(698\) | −1105.00 | + | 1913.92i | −0.0599210 | + | 0.103786i | ||||
\(699\) | −42576.0 | −2.30382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2018.00 | −0.108729 | −0.0543643 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543643 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(702\) | −3120.00 | + | 5404.00i | −0.167745 | + | 0.290542i | ||||
\(703\) | 8680.00 | + | 15034.2i | 0.465679 | + | 0.806580i | ||||
\(704\) | 1002.00 | + | 1735.51i | 0.0536425 | + | 0.0929115i | ||||
\(705\) | −10720.0 | + | 18567.6i | −0.572679 | + | 0.991909i | ||||
\(706\) | −2598.00 | −0.138494 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31360.0 | −1.66466 | ||||||||
\(709\) | −395.000 | + | 684.160i | −0.0209232 | + | 0.0362400i | −0.876297 | − | 0.481771i | \(-0.839994\pi\) |
0.855374 | + | 0.518011i | \(0.173327\pi\) | |||||||
\(710\) | 1680.00 | + | 2909.85i | 0.0888018 | + | 0.153809i | ||||
\(711\) | 18500.0 | + | 32042.9i | 0.975815 | + | 1.69016i | ||||
\(712\) | −6525.00 | + | 11301.6i | −0.343448 | + | 0.594869i | ||||
\(713\) | −7936.00 | −0.416838 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4680.00 | 0.244786 | ||||||||
\(716\) | −630.000 | + | 1091.19i | −0.0328830 | + | 0.0569550i | ||||
\(717\) | −7360.00 | − | 12747.9i | −0.383353 | − | 0.663987i | ||||
\(718\) | 6660.00 | + | 11535.5i | 0.346169 | + | 0.599581i | ||||
\(719\) | −9100.00 | + | 15761.7i | −0.472007 | + | 0.817539i | −0.999487 | − | 0.0320278i | \(-0.989803\pi\) |
0.527480 | + | 0.849567i | \(0.323137\pi\) | |||||||
\(720\) | −7585.00 | −0.392606 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5259.00 | −0.271080 | ||||||||
\(723\) | −1752.00 | + | 3034.55i | −0.0901211 | + | 0.156094i | ||||
\(724\) | −6853.00 | − | 11869.7i | −0.351781 | − | 0.609303i | ||||
\(725\) | 625.000 | + | 1082.53i | 0.0320164 | + | 0.0554541i | ||||
\(726\) | −4748.00 | + | 8223.78i | −0.242720 | + | 0.420404i | ||||
\(727\) | 29056.0 | 1.48229 | 0.741147 | − | 0.671343i | \(-0.234282\pi\) | ||||
0.741147 | + | 0.671343i | \(0.234282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30563.0 | −1.55276 | ||||||||
\(730\) | 205.000 | − | 355.070i | 0.0103937 | − | 0.0180024i | ||||
\(731\) | −3196.00 | − | 5535.63i | −0.161708 | − | 0.280086i | ||||
\(732\) | 7784.00 | + | 13482.3i | 0.393040 | + | 0.680764i | ||||
\(733\) | −3541.00 | + | 6133.19i | −0.178431 | + | 0.309051i | −0.941343 | − | 0.337451i | \(-0.890435\pi\) |
0.762912 | + | 0.646502i | \(0.223769\pi\) | |||||||
\(734\) | 10816.0 | 0.543904 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5152.00 | 0.258023 | ||||||||
\(737\) | 984.000 | − | 1704.34i | 0.0491806 | − | 0.0851833i | ||||
\(738\) | −7437.00 | − | 12881.3i | −0.370948 | − | 0.642501i | ||||
\(739\) | −5530.00 | − | 9578.24i | −0.275270 | − | 0.476781i | 0.694933 | − | 0.719074i | \(-0.255434\pi\) |
−0.970203 | + | 0.242293i | \(0.922100\pi\) | |||||||
\(740\) | 7595.00 | − | 13154.9i | 0.377294 | − | 0.653493i | ||||
\(741\) | 24960.0 | 1.23742 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33072.0 | 1.63297 | 0.816483 | − | 0.577369i | \(-0.195921\pi\) | ||||
0.816483 | + | 0.577369i | \(0.195921\pi\) | |||||||
\(744\) | 14880.0 | − | 25772.9i | 0.733236 | − | 1.27000i | ||||
\(745\) | 5675.00 | + | 9829.39i | 0.279082 | + | 0.483384i | ||||
\(746\) | 5549.00 | + | 9611.15i | 0.272337 | + | 0.471701i | ||||
\(747\) | 8288.00 | − | 14355.2i | 0.405947 | − | 0.703120i | ||||
\(748\) | 7896.00 | 0.385971 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1000.00 | 0.0486864 | ||||||||
\(751\) | −14536.0 | + | 25177.1i | −0.706293 | + | 1.22334i | 0.259930 | + | 0.965628i | \(0.416301\pi\) |
−0.966223 | + | 0.257708i | \(0.917033\pi\) | |||||||
\(752\) | −10988.0 | − | 19031.8i | −0.532834 | − | 0.922895i | ||||
\(753\) | 22368.0 | + | 38742.5i | 1.08252 | + | 1.87497i | ||||
\(754\) | −1950.00 | + | 3377.50i | −0.0941841 | + | 0.163132i | ||||
\(755\) | −3160.00 | −0.152323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13234.0 | −0.635400 | −0.317700 | − | 0.948191i | \(-0.602911\pi\) | ||||
−0.317700 | + | 0.948191i | \(0.602911\pi\) | |||||||
\(758\) | −3550.00 | + | 6148.78i | −0.170108 | + | 0.294636i | ||||
\(759\) | 1536.00 | + | 2660.43i | 0.0734562 | + | 0.127230i | ||||
\(760\) | −1500.00 | − | 2598.08i | −0.0715931 | − | 0.124003i | ||||
\(761\) | 11199.0 | − | 19397.2i | 0.533460 | − | 0.923981i | −0.465776 | − | 0.884903i | \(-0.654225\pi\) |
0.999236 | − | 0.0390778i | \(-0.0124420\pi\) | |||||||
\(762\) | −6208.00 | −0.295134 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20216.0 | 0.957316 | ||||||||
\(765\) | −8695.00 | + | 15060.2i | −0.410939 | + | 0.711767i | ||||
\(766\) | 364.000 | + | 630.466i | 0.0171695 | + | 0.0297385i | ||||
\(767\) | −21840.0 | − | 37828.0i | −1.02816 | − | 1.78082i | ||||
\(768\) | −476.000 | + | 824.456i | −0.0223648 | + | 0.0387370i | ||||
\(769\) | 6890.00 | 0.323095 | 0.161547 | − | 0.986865i | \(-0.448352\pi\) | ||||
0.161547 | + | 0.986865i | \(0.448352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15792.0 | 0.737659 | ||||||||
\(772\) | 5607.00 | − | 9711.61i | 0.261399 | − | 0.452757i | ||||
\(773\) | −8361.00 | − | 14481.7i | −0.389035 | − | 0.673829i | 0.603285 | − | 0.797526i | \(-0.293858\pi\) |
−0.992320 | + | 0.123697i | \(0.960525\pi\) | |||||||
\(774\) | 1258.00 | + | 2178.92i | 0.0584210 | + | 0.101188i | ||||
\(775\) | 3100.00 | − | 5369.36i | 0.143684 | − | 0.248868i | ||||
\(776\) | −15390.0 | −0.711944 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6810.00 | −0.313818 | ||||||||
\(779\) | −8040.00 | + | 13925.7i | −0.369785 | + | 0.640487i | ||||
\(780\) | −10920.0 | − | 18914.0i | −0.501280 | − | 0.868243i | ||||
\(781\) | −4032.00 | − | 6983.63i | −0.184733 | − | 0.319967i | ||||
\(782\) | 1504.00 | − | 2605.00i | 0.0687761 | − | 0.119124i | ||||
\(783\) | 4000.00 | 0.182565 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3670.00 | 0.166864 | ||||||||
\(786\) | 4448.00 | − | 7704.16i | 0.201851 | − | 0.349616i | ||||
\(787\) | 16312.0 | + | 28253.2i | 0.738831 | + | 1.27969i | 0.953022 | + | 0.302901i | \(0.0979552\pi\) |
−0.214191 | + | 0.976792i | \(0.568711\pi\) | |||||||
\(788\) | −16779.0 | − | 29062.1i | −0.758537 | − | 1.31382i | ||||
\(789\) | −2912.00 | + | 5043.73i | −0.131394 | + | 0.227581i | ||||
\(790\) | 5000.00 | 0.225180 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6660.00 | −0.298804 | ||||||||
\(793\) | −10842.0 | + | 18778.9i | −0.485512 | + | 0.840931i | ||||
\(794\) | 287.000 | + | 497.099i | 0.0128278 | + | 0.0222183i | ||||
\(795\) | −440.000 | − | 762.102i | −0.0196292 | − | 0.0339987i | ||||
\(796\) | 4480.00 | − | 7759.59i | 0.199484 | − | 0.345517i | ||||
\(797\) | 11346.0 | 0.504261 | 0.252130 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252130 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50384.0 | −2.23086 | ||||||||
\(800\) | −2012.50 | + | 3485.75i | −0.0889408 | + | 0.154050i | ||||
\(801\) | 16095.0 | + | 27877.4i | 0.709974 | + | 1.22971i | ||||
\(802\) | −3081.00 | − | 5336.45i | −0.135653 | − | 0.234958i | ||||
\(803\) | −492.000 | + | 852.169i | −0.0216218 | + | 0.0374501i | ||||
\(804\) | −9184.00 | −0.402854 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19344.0 | 0.845364 | ||||||||
\(807\) | 23240.0 | − | 40252.9i | 1.01374 | − | 1.75585i | ||||
\(808\) | 3615.00 | + | 6261.36i | 0.157395 | + | 0.272616i | ||||
\(809\) | 17595.0 | + | 30475.4i | 0.764657 | + | 1.32442i | 0.940428 | + | 0.339993i | \(0.110425\pi\) |
−0.175771 | + | 0.984431i | \(0.556242\pi\) | |||||||
\(810\) | −897.500 | + | 1554.52i | −0.0389320 | + | 0.0674322i | ||||
\(811\) | 30432.0 | 1.31765 | 0.658824 | − | 0.752297i | \(-0.271054\pi\) | ||||
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52224.0 | 2.25286 | ||||||||
\(814\) | 2604.00 | − | 4510.26i | 0.112125 | − | 0.194207i | ||||
\(815\) | 6330.00 | + | 10963.9i | 0.272062 | + | 0.471225i | ||||
\(816\) | −15416.0 | − | 26701.3i | −0.661358 | − | 1.14551i | ||||
\(817\) | 1360.00 | − | 2355.59i | 0.0582379 | − | 0.100871i | ||||
\(818\) | 8210.00 | 0.350924 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14070.0 | 0.599202 | ||||||||
\(821\) | −6351.00 | + | 11000.3i | −0.269977 | + | 0.467615i | −0.968856 | − | 0.247626i | \(-0.920350\pi\) |
0.698878 | + | 0.715241i | \(0.253683\pi\) | |||||||
\(822\) | −2776.00 | − | 4808.17i | −0.117791 | − | 0.204020i | ||||
\(823\) | −8476.00 | − | 14680.9i | −0.358997 | − | 0.621802i | 0.628796 | − | 0.777570i | \(-0.283548\pi\) |
−0.987794 | + | 0.155769i | \(0.950215\pi\) | |||||||
\(824\) | 2040.00 | − | 3533.38i | 0.0862461 | − | 0.149383i | ||||
\(825\) | −2400.00 | −0.101282 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25404.0 | −1.06818 | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||||
−0.534089 | + | 0.845428i | \(0.679345\pi\) | |||||||
\(828\) | 4144.00 | − | 7177.62i | 0.173930 | − | 0.301255i | ||||
\(829\) | −13125.0 | − | 22733.2i | −0.549879 | − | 0.952419i | −0.998282 | − | 0.0585876i | \(-0.981340\pi\) |
0.448403 | − | 0.893832i | \(-0.351993\pi\) | |||||||
\(830\) | −1120.00 | − | 1939.90i | −0.0468383 | − | 0.0811263i | ||||
\(831\) | 20504.0 | − | 35514.0i | 0.855928 | − | 1.48251i | ||||
\(832\) | 13026.0 | 0.542783 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2880.00 | −0.119576 | ||||||||
\(835\) | 1040.00 | − | 1801.33i | 0.0431026 | − | 0.0746559i | ||||
\(836\) | 1680.00 | + | 2909.85i | 0.0695024 | + | 0.120382i | ||||
\(837\) | −9920.00 | − | 17181.9i | −0.409660 | − | 0.709552i | ||||
\(838\) | −2400.00 | + | 4156.92i | −0.0989339 | + | 0.171359i | ||||
\(839\) | −15360.0 | −0.632045 | −0.316023 | − | 0.948752i | \(-0.602348\pi\) | ||||
−0.316023 | + | 0.948752i | \(0.602348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | 4969.00 | − | 8606.56i | 0.203377 | − | 0.352259i | ||||
\(843\) | −9432.00 | − | 16336.7i | −0.385356 | − | 0.667457i | ||||
\(844\) | −238.000 | − | 412.228i | −0.00970651 | − | 0.0168122i | ||||
\(845\) | 9717.50 | − | 16831.2i | 0.395612 | − | 0.685220i | ||||
\(846\) | 19832.0 | 0.805955 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 902.000 | 0.0365269 | ||||||||
\(849\) | 1568.00 | − | 2715.86i | 0.0633847 | − | 0.109786i | ||||
\(850\) | 1175.00 | + | 2035.16i | 0.0474143 | + | 0.0821240i | ||||
\(851\) | 6944.00 | + | 12027.4i | 0.279715 | + | 0.484480i | ||||
\(852\) | −18816.0 | + | 32590.3i | −0.756603 | + | 1.31047i | ||||
\(853\) | 10362.0 | 0.415930 | 0.207965 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207965 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7400.00 | −0.295994 | ||||||||
\(856\) | −3330.00 | + | 5767.73i | −0.132964 | + | 0.230300i | ||||
\(857\) | −2253.00 | − | 3902.31i | −0.0898028 | − | 0.155543i | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(858\) | −3744.00 | − | 6484.80i | −0.148972 | − | 0.258027i | ||||
\(859\) | −12100.0 | + | 20957.8i | −0.480613 | + | 0.832446i | −0.999753 | − | 0.0222432i | \(-0.992919\pi\) |
0.519139 | + | 0.854690i | \(0.326253\pi\) | |||||||
\(860\) | −2380.00 | −0.0943690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9248.00 | −0.365415 | ||||||||
\(863\) | 18504.0 | − | 32049.9i | 0.729877 | − | 1.26418i | −0.227058 | − | 0.973881i | \(-0.572911\pi\) |
0.956935 | − | 0.290302i | \(-0.0937558\pi\) | |||||||
\(864\) | 6440.00 | + | 11154.4i | 0.253580 | + | 0.439214i | ||||
\(865\) | 7605.00 | + | 13172.2i | 0.298934 | + | 0.517769i | ||||
\(866\) | 559.000 | − | 968.216i | 0.0219349 | − | 0.0379923i | ||||
\(867\) | −31384.0 | −1.22936 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12000.0 | −0.468437 | ||||||||
\(870\) | 1000.00 | − | 1732.05i | 0.0389692 | − | 0.0674966i | ||||
\(871\) | −6396.00 | − | 11078.2i | −0.248818 | − | 0.430965i | ||||
\(872\) | −8775.00 | − | 15198.7i | −0.340779 | − | 0.590246i | ||||
\(873\) | −18981.0 | + | 32876.1i | −0.735864 | + | 1.27455i | ||||
\(874\) | 1280.00 | 0.0495385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4592.00 | 0.177111 | ||||||||
\(877\) | −1723.00 | + | 2984.32i | −0.0663416 | + | 0.114907i | −0.897288 | − | 0.441445i | \(-0.854466\pi\) |
0.830947 | + | 0.556352i | \(0.187799\pi\) | |||||||
\(878\) | 5980.00 | + | 10357.7i | 0.229858 | + | 0.398126i | ||||
\(879\) | 4808.00 | + | 8327.70i | 0.184494 | + | 0.319552i | ||||
\(880\) | 1230.00 | − | 2130.42i | 0.0471174 | − | 0.0816097i | ||||
\(881\) | −16158.0 | −0.617908 | −0.308954 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308954 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44708.0 | −1.70390 | −0.851950 | − | 0.523623i | \(-0.824580\pi\) | ||||
−0.851950 | + | 0.523623i | \(0.824580\pi\) | |||||||
\(884\) | 25662.0 | − | 44447.9i | 0.976365 | − | 1.69111i | ||||
\(885\) | 11200.0 | + | 19399.0i | 0.425406 | + | 0.736824i | ||||
\(886\) | −3666.00 | − | 6349.70i | −0.139009 | − | 0.240770i | ||||
\(887\) | 11752.0 | − | 20355.1i | 0.444863 | − | 0.770525i | −0.553180 | − | 0.833062i | \(-0.686586\pi\) |
0.998043 | + | 0.0625366i | \(0.0199190\pi\) | |||||||
\(888\) | −52080.0 | −1.96812 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4350.00 | 0.163834 | ||||||||
\(891\) | 2154.00 | − | 3730.84i | 0.0809896 | − | 0.140278i | ||||
\(892\) | −6048.00 | − | 10475.4i | −0.227020 | − | 0.393211i | ||||
\(893\) | −10720.0 | − | 18567.6i | −0.401715 | − | 0.695790i | ||||
\(894\) | 9080.00 | − | 15727.0i | 0.339688 | − | 0.588356i | ||||
\(895\) | 900.000 | 0.0336131 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19968.0 | 0.743269 | ||||||||
\(898\) | −945.000 | + | 1636.79i | −0.0351170 | + | 0.0608244i | ||||
\(899\) | −6200.00 | − | 10738.7i | −0.230013 | − | 0.398394i | ||||
\(900\) | 3237.50 | + | 5607.51i | 0.119907 | + | 0.207686i | ||||
\(901\) | 1034.00 | − | 1790.94i | 0.0382326 | − | 0.0662207i | ||||
\(902\) | 4824.00 | 0.178073 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11970.0 | 0.440394 | ||||||||
\(905\) | −4895.00 | + | 8478.39i | −0.179796 | + | 0.311416i | ||||
\(906\) | 2528.00 | + | 4378.62i | 0.0927011 | + | 0.160563i | ||||
\(907\) | −21218.0 | − | 36750.7i | −0.776772 | − | 1.34541i | −0.933793 | − | 0.357813i | \(-0.883522\pi\) |
0.157021 | − | 0.987595i | \(-0.449811\pi\) | |||||||
\(908\) | −17024.0 | + | 29486.4i | −0.622204 | + | 1.07769i | ||||
\(909\) | 17834.0 | 0.650733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7968.00 | −0.289782 | −0.144891 | − | 0.989448i | \(-0.546283\pi\) | ||||
−0.144891 | + | 0.989448i | \(0.546283\pi\) | |||||||
\(912\) | 6560.00 | − | 11362.3i | 0.238183 | − | 0.412546i | ||||
\(913\) | 2688.00 | + | 4655.75i | 0.0974368 | + | 0.168766i | ||||
\(914\) | 3507.00 | + | 6074.30i | 0.126916 | + | 0.219825i | ||||
\(915\) | 5560.00 | − | 9630.20i | 0.200883 | − | 0.347940i | ||||
\(916\) | 38570.0 | 1.39125 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7520.00 | 0.270367 | ||||||||
\(919\) | −7440.00 | + | 12886.5i | −0.267054 | + | 0.462552i | −0.968100 | − | 0.250565i | \(-0.919384\pi\) |
0.701045 | + | 0.713117i | \(0.252717\pi\) | |||||||
\(920\) | −1200.00 | − | 2078.46i | −0.0430031 | − | 0.0744835i | ||||
\(921\) | −25536.0 | − | 44229.6i | −0.913615 | − | 1.58243i | ||||
\(922\) | 4159.00 | − | 7203.60i | 0.148557 | − | 0.257308i | ||||
\(923\) | −52416.0 | −1.86922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10850.0 | −0.385671 | ||||||||
\(926\) | −3216.00 | + | 5570.28i | −0.114130 | + | 0.197679i | ||||
\(927\) | −5032.00 | − | 8715.68i | −0.178288 | − | 0.308803i | ||||
\(928\) | 4025.00 | + | 6971.50i | 0.142378 | + | 0.246607i | ||||
\(929\) | −13805.0 | + | 23911.0i | −0.487543 | + | 0.844449i | −0.999897 | − | 0.0143250i | \(-0.995440\pi\) |
0.512354 | + | 0.858774i | \(0.328773\pi\) | |||||||
\(930\) | −9920.00 | −0.349774 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −37254.0 | −1.30933 | ||||||||
\(933\) | −19872.0 | + | 34419.3i | −0.697299 | + | 1.20776i | ||||
\(934\) | 5032.00 | + | 8715.68i | 0.176287 | + | 0.305338i | ||||
\(935\) | −2820.00 | − | 4884.38i | −0.0986351 | − | 0.170841i | ||||
\(936\) | −21645.0 | + | 37490.2i | −0.755864 | + | 1.30920i | ||||
\(937\) | −28094.0 | −0.979499 | −0.489750 | − | 0.871863i | \(-0.662912\pi\) | ||||
−0.489750 | + | 0.871863i | \(0.662912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22064.0 | 0.766807 | ||||||||
\(940\) | −9380.00 | + | 16246.6i | −0.325470 | + | 0.563731i | ||||
\(941\) | 6099.00 | + | 10563.8i | 0.211288 | + | 0.365961i | 0.952118 | − | 0.305731i | \(-0.0989010\pi\) |
−0.740830 | + | 0.671692i | \(0.765568\pi\) | |||||||
\(942\) | −2936.00 | − | 5085.30i | −0.101550 | − | 0.175890i | ||||
\(943\) | −6432.00 | + | 11140.6i | −0.222115 | + | 0.384715i | ||||
\(944\) | −22960.0 | −0.791615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −816.000 | −0.0280449 | ||||||||
\(947\) | −15658.0 | + | 27120.5i | −0.537293 | + | 0.930619i | 0.461755 | + | 0.887007i | \(0.347220\pi\) |
−0.999049 | + | 0.0436118i | \(0.986114\pi\) | |||||||
\(948\) | 28000.0 | + | 48497.4i | 0.959280 | + | 1.66152i | ||||
\(949\) | 3198.00 | + | 5539.10i | 0.109390 | + | 0.189470i | ||||
\(950\) | −500.000 | + | 866.025i | −0.0170759 | + | 0.0295764i | ||||
\(951\) | 50192.0 | 1.71145 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27322.0 | 0.928695 | 0.464348 | − | 0.885653i | \(-0.346289\pi\) | ||||
0.464348 | + | 0.885653i | \(0.346289\pi\) | |||||||
\(954\) | −407.000 | + | 704.945i | −0.0138125 | + | 0.0239239i | ||||
\(955\) | −7220.00 | − | 12505.4i | −0.244643 | − | 0.423733i | ||||
\(956\) | −6440.00 | − | 11154.4i | −0.217871 | − | 0.377363i | ||||
\(957\) | −2400.00 | + | 4156.92i | −0.0810669 | + | 0.140412i | ||||
\(958\) | 1400.00 | 0.0472150 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6680.00 | −0.224579 | ||||||||
\(961\) | −15856.5 | + | 27464.3i | −0.532258 | + | 0.921898i | ||||
\(962\) | −16926.0 | − | 29316.7i | −0.567272 | − | 0.982545i | ||||
\(963\) | 8214.00 | + | 14227.1i | 0.274862 | + | 0.476076i | ||||
\(964\) | −1533.00 | + | 2655.23i | −0.0512185 | + | 0.0887130i | ||||
\(965\) | −8010.00 | −0.267203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5296.00 | 0.176120 | 0.0880599 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880599 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(968\) | −8902.50 | + | 15419.6i | −0.295596 | + | 0.511988i | ||||
\(969\) | −15040.0 | − | 26050.0i | −0.498611 | − | 0.863620i | ||||
\(970\) | 2565.00 | + | 4442.71i | 0.0849043 | + | 0.147059i | ||||
\(971\) | −256.000 | + | 443.405i | −0.00846079 | + | 0.0146545i | −0.870225 | − | 0.492655i | \(-0.836027\pi\) |
0.861764 | + | 0.507309i | \(0.169360\pi\) | |||||||
\(972\) | −35224.0 | −1.16236 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13376.0 | 0.440036 | ||||||||
\(975\) | −7800.00 | + | 13510.0i | −0.256205 | + | 0.443760i | ||||
\(976\) | 5699.00 | + | 9870.96i | 0.186906 | + | 0.323731i | ||||
\(977\) | 10367.0 | + | 17956.2i | 0.339478 | + | 0.587993i | 0.984335 | − | 0.176311i | \(-0.0564164\pi\) |
−0.644857 | + | 0.764303i | \(0.723083\pi\) | |||||||
\(978\) | 10128.0 | − | 17542.2i | 0.331143 | − | 0.573556i | ||||
\(979\) | −10440.0 | −0.340821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43290.0 | −1.40891 | ||||||||
\(982\) | −3546.00 | + | 6141.85i | −0.115232 | + | 0.199587i | ||||
\(983\) | 30584.0 | + | 52973.0i | 0.992348 | + | 1.71880i | 0.603104 | + | 0.797662i | \(0.293930\pi\) |
0.389244 | + | 0.921135i | \(0.372736\pi\) | |||||||
\(984\) | −24120.0 | − | 41777.1i | −0.781420 | − | 1.35346i | ||||
\(985\) | −11985.0 | + | 20758.6i | −0.387689 | + | 0.671497i | ||||
\(986\) | 4700.00 | 0.151804 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21840.0 | 0.703262 | ||||||||
\(989\) | 1088.00 | − | 1884.47i | 0.0349812 | − | 0.0605892i | ||||
\(990\) | 1110.00 | + | 1922.58i | 0.0356345 | + | 0.0617207i | ||||
\(991\) | 23964.0 | + | 41506.9i | 0.768155 | + | 1.33048i | 0.938562 | + | 0.345110i | \(0.112158\pi\) |
−0.170407 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(992\) | 19964.0 | − | 34578.7i | 0.638969 | − | 1.10673i | ||||
\(993\) | −15456.0 | −0.493939 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6400.00 | −0.203913 | ||||||||
\(996\) | 12544.0 | − | 21726.8i | 0.399068 | − | 0.691206i | ||||
\(997\) | 4727.00 | + | 8187.40i | 0.150156 | + | 0.260078i | 0.931285 | − | 0.364292i | \(-0.118689\pi\) |
−0.781129 | + | 0.624370i | \(0.785356\pi\) | |||||||
\(998\) | 410.000 | + | 710.141i | 0.0130043 | + | 0.0225242i | ||||
\(999\) | −17360.0 | + | 30068.4i | −0.549796 | + | 0.952274i |
(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 | 245.4.e.e.226.1 | 2 | ||
7.2 | even | 3 | 35.4.a.a.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 245.4.e.b.116.1 | 2 | |||
7.4 | even | 3 | inner | 245.4.e.e.116.1 | 2 | ||
7.5 | odd | 6 | 245.4.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 245.4.e.b.226.1 | 2 | |||
21.2 | odd | 6 | 315.4.a.c.1.1 | 1 | |||
21.5 | even | 6 | 2205.4.a.i.1.1 | 1 | |||
28.23 | odd | 6 | 560.4.a.p.1.1 | 1 | |||
35.2 | odd | 12 | 175.4.b.a.99.2 | 2 | |||
35.9 | even | 6 | 175.4.a.a.1.1 | 1 | |||
35.19 | odd | 6 | 1225.4.a.e.1.1 | 1 | |||
35.23 | odd | 12 | 175.4.b.a.99.1 | 2 | |||
56.37 | even | 6 | 2240.4.a.bk.1.1 | 1 | |||
56.51 | odd | 6 | 2240.4.a.b.1.1 | 1 | |||
105.44 | odd | 6 | 1575.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.a.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
175.4.a.a.1.1 | 1 | 35.9 | even | 6 | |||
175.4.b.a.99.1 | 2 | 35.23 | odd | 12 | |||
175.4.b.a.99.2 | 2 | 35.2 | odd | 12 | |||
245.4.a.d.1.1 | 1 | 7.5 | odd | 6 | |||
245.4.e.b.116.1 | 2 | 7.3 | odd | 6 | |||
245.4.e.b.226.1 | 2 | 7.6 | odd | 2 | |||
245.4.e.e.116.1 | 2 | 7.4 | even | 3 | inner | ||
245.4.e.e.226.1 | 2 | 1.1 | even | 1 | trivial | ||
315.4.a.c.1.1 | 1 | 21.2 | odd | 6 | |||
560.4.a.p.1.1 | 1 | 28.23 | odd | 6 | |||
1225.4.a.e.1.1 | 1 | 35.19 | odd | 6 | |||
1575.4.a.g.1.1 | 1 | 105.44 | odd | 6 | |||
2205.4.a.i.1.1 | 1 | 21.5 | even | 6 | |||
2240.4.a.b.1.1 | 1 | 56.51 | odd | 6 | |||
2240.4.a.bk.1.1 | 1 | 56.37 | even | 6 |