Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,3,Mod(11,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.b (of order \(2\), degree \(1\), 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: | \(0.544960528721\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.11 |
Dual form | 20.3.b.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | + | 1.17557i | −0.809017 | + | 0.587785i | ||||
\(3\) | 3.80423i | 1.26808i | 0.773302 | + | 0.634038i | \(0.218604\pi\) | ||||
−0.773302 | + | 0.634038i | \(0.781396\pi\) | |||||||
\(4\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | −4.47214 | − | 6.15537i | −0.745356 | − | 1.02589i | ||||
\(7\) | − | 8.50651i | − | 1.21522i | −0.794237 | − | 0.607608i | \(-0.792129\pi\) | ||
0.794237 | − | 0.607608i | \(-0.207871\pi\) | |||||||
\(8\) | 2.47214 | + | 7.60845i | 0.309017 | + | 0.951057i | ||||
\(9\) | −5.47214 | −0.608015 | ||||||||
\(10\) | −3.61803 | + | 2.62866i | −0.361803 | + | 0.262866i | ||||
\(11\) | 1.79611i | 0.163283i | 0.996662 | + | 0.0816415i | \(0.0260162\pi\) | ||||
−0.996662 | + | 0.0816415i | \(0.973984\pi\) | |||||||
\(12\) | 14.4721 | + | 4.70228i | 1.20601 | + | 0.391857i | ||||
\(13\) | 0.472136 | 0.0363182 | 0.0181591 | − | 0.999835i | \(-0.494219\pi\) | ||||
0.0181591 | + | 0.999835i | \(0.494219\pi\) | |||||||
\(14\) | 10.0000 | + | 13.7638i | 0.714286 | + | 0.983130i | ||||
\(15\) | 8.50651i | 0.567101i | ||||||||
\(16\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(17\) | −23.8885 | −1.40521 | −0.702604 | − | 0.711581i | \(-0.747980\pi\) | ||||
−0.702604 | + | 0.711581i | \(0.747980\pi\) | |||||||
\(18\) | 8.85410 | − | 6.43288i | 0.491895 | − | 0.357382i | ||||
\(19\) | − | 9.40456i | − | 0.494977i | −0.968891 | − | 0.247489i | \(-0.920395\pi\) | ||
0.968891 | − | 0.247489i | \(-0.0796053\pi\) | |||||||
\(20\) | 2.76393 | − | 8.50651i | 0.138197 | − | 0.425325i | ||||
\(21\) | 32.3607 | 1.54098 | ||||||||
\(22\) | −2.11146 | − | 2.90617i | −0.0959753 | − | 0.132099i | ||||
\(23\) | − | 16.1150i | − | 0.700650i | −0.936628 | − | 0.350325i | \(-0.886071\pi\) | ||
0.936628 | − | 0.350325i | \(-0.113929\pi\) | |||||||
\(24\) | −28.9443 | + | 9.40456i | −1.20601 | + | 0.391857i | ||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | −0.763932 | + | 0.555029i | −0.0293820 | + | 0.0213473i | ||||
\(27\) | 13.4208i | 0.497066i | ||||||||
\(28\) | −32.3607 | − | 10.5146i | −1.15574 | − | 0.375522i | ||||
\(29\) | 6.94427 | 0.239458 | 0.119729 | − | 0.992807i | \(-0.461797\pi\) | ||||
0.119729 | + | 0.992807i | \(0.461797\pi\) | |||||||
\(30\) | −10.0000 | − | 13.7638i | −0.333333 | − | 0.458794i | ||||
\(31\) | 47.4468i | 1.53054i | 0.643708 | + | 0.765271i | \(0.277395\pi\) | ||||
−0.643708 | + | 0.765271i | \(0.722605\pi\) | |||||||
\(32\) | 32.0000 | 1.00000 | ||||||||
\(33\) | −6.83282 | −0.207055 | ||||||||
\(34\) | 38.6525 | − | 28.0827i | 1.13684 | − | 0.825961i | ||||
\(35\) | − | 19.0211i | − | 0.543461i | ||||||
\(36\) | −6.76393 | + | 20.8172i | −0.187887 | + | 0.578257i | ||||
\(37\) | 26.3607 | 0.712451 | 0.356225 | − | 0.934400i | \(-0.384064\pi\) | ||||
0.356225 | + | 0.934400i | \(0.384064\pi\) | |||||||
\(38\) | 11.0557 | + | 15.2169i | 0.290940 | + | 0.400445i | ||||
\(39\) | 1.79611i | 0.0460542i | ||||||||
\(40\) | 5.52786 | + | 17.0130i | 0.138197 | + | 0.425325i | ||||
\(41\) | −41.4164 | −1.01016 | −0.505078 | − | 0.863074i | \(-0.668536\pi\) | ||||
−0.505078 | + | 0.863074i | \(0.668536\pi\) | |||||||
\(42\) | −52.3607 | + | 38.0423i | −1.24668 | + | 0.905768i | ||||
\(43\) | − | 2.00811i | − | 0.0467003i | −0.999727 | − | 0.0233502i | \(-0.992567\pi\) | ||
0.999727 | − | 0.0233502i | \(-0.00743326\pi\) | |||||||
\(44\) | 6.83282 | + | 2.22012i | 0.155291 | + | 0.0504572i | ||||
\(45\) | −12.2361 | −0.271913 | ||||||||
\(46\) | 18.9443 | + | 26.0746i | 0.411832 | + | 0.566838i | ||||
\(47\) | − | 35.3481i | − | 0.752087i | −0.926602 | − | 0.376044i | \(-0.877284\pi\) | ||
0.926602 | − | 0.376044i | \(-0.122716\pi\) | |||||||
\(48\) | 35.7771 | − | 49.2429i | 0.745356 | − | 1.02589i | ||||
\(49\) | −23.3607 | −0.476749 | ||||||||
\(50\) | −8.09017 | + | 5.87785i | −0.161803 | + | 0.117557i | ||||
\(51\) | − | 90.8774i | − | 1.78191i | ||||||
\(52\) | 0.583592 | − | 1.79611i | 0.0112229 | − | 0.0345406i | ||||
\(53\) | −21.6393 | −0.408289 | −0.204145 | − | 0.978941i | \(-0.565441\pi\) | ||||
−0.204145 | + | 0.978941i | \(0.565441\pi\) | |||||||
\(54\) | −15.7771 | − | 21.7153i | −0.292168 | − | 0.402135i | ||||
\(55\) | 4.01623i | 0.0730223i | ||||||||
\(56\) | 64.7214 | − | 21.0292i | 1.15574 | − | 0.375522i | ||||
\(57\) | 35.7771 | 0.627668 | ||||||||
\(58\) | −11.2361 | + | 8.16348i | −0.193725 | + | 0.140750i | ||||
\(59\) | 73.8644i | 1.25194i | 0.779848 | + | 0.625970i | \(0.215297\pi\) | ||||
−0.779848 | + | 0.625970i | \(0.784703\pi\) | |||||||
\(60\) | 32.3607 | + | 10.5146i | 0.539345 | + | 0.175244i | ||||
\(61\) | −26.1378 | −0.428488 | −0.214244 | − | 0.976780i | \(-0.568729\pi\) | ||||
−0.214244 | + | 0.976780i | \(0.568729\pi\) | |||||||
\(62\) | −55.7771 | − | 76.7706i | −0.899630 | − | 1.23824i | ||||
\(63\) | 46.5488i | 0.738869i | ||||||||
\(64\) | −51.7771 | + | 37.6183i | −0.809017 | + | 0.587785i | ||||
\(65\) | 1.05573 | 0.0162420 | ||||||||
\(66\) | 11.0557 | − | 8.03246i | 0.167511 | − | 0.121704i | ||||
\(67\) | 88.8693i | 1.32641i | 0.748439 | + | 0.663204i | \(0.230804\pi\) | ||||
−0.748439 | + | 0.663204i | \(0.769196\pi\) | |||||||
\(68\) | −29.5279 | + | 90.8774i | −0.434233 | + | 1.33643i | ||||
\(69\) | 61.3050 | 0.888478 | ||||||||
\(70\) | 22.3607 | + | 30.7768i | 0.319438 | + | 0.439669i | ||||
\(71\) | − | 39.4144i | − | 0.555132i | −0.960707 | − | 0.277566i | \(-0.910472\pi\) | ||
0.960707 | − | 0.277566i | \(-0.0895277\pi\) | |||||||
\(72\) | −13.5279 | − | 41.6345i | −0.187887 | − | 0.578257i | ||||
\(73\) | 137.554 | 1.88430 | 0.942152 | − | 0.335186i | \(-0.108799\pi\) | ||||
0.942152 | + | 0.335186i | \(0.108799\pi\) | |||||||
\(74\) | −42.6525 | + | 30.9888i | −0.576385 | + | 0.418768i | ||||
\(75\) | 19.0211i | 0.253615i | ||||||||
\(76\) | −35.7771 | − | 11.6247i | −0.470751 | − | 0.152956i | ||||
\(77\) | 15.2786 | 0.198424 | ||||||||
\(78\) | −2.11146 | − | 2.90617i | −0.0270700 | − | 0.0372586i | ||||
\(79\) | − | 113.703i | − | 1.43928i | −0.694350 | − | 0.719638i | \(-0.744308\pi\) | ||
0.694350 | − | 0.719638i | \(-0.255692\pi\) | |||||||
\(80\) | −28.9443 | − | 21.0292i | −0.361803 | − | 0.262866i | ||||
\(81\) | −100.305 | −1.23833 | ||||||||
\(82\) | 67.0132 | − | 48.6879i | 0.817234 | − | 0.593755i | ||||
\(83\) | 21.2412i | 0.255919i | 0.991779 | + | 0.127959i | \(0.0408427\pi\) | ||||
−0.991779 | + | 0.127959i | \(0.959157\pi\) | |||||||
\(84\) | 40.0000 | − | 123.107i | 0.476190 | − | 1.46556i | ||||
\(85\) | −53.4164 | −0.628428 | ||||||||
\(86\) | 2.36068 | + | 3.24920i | 0.0274498 | + | 0.0377814i | ||||
\(87\) | 26.4176i | 0.303650i | ||||||||
\(88\) | −13.6656 | + | 4.44023i | −0.155291 | + | 0.0504572i | ||||
\(89\) | 67.4427 | 0.757783 | 0.378892 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378892 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(90\) | 19.7984 | − | 14.3844i | 0.219982 | − | 0.159826i | ||||
\(91\) | − | 4.01623i | − | 0.0441344i | ||||||
\(92\) | −61.3050 | − | 19.9192i | −0.666358 | − | 0.216513i | ||||
\(93\) | −180.498 | −1.94084 | ||||||||
\(94\) | 41.5542 | + | 57.1944i | 0.442066 | + | 0.608451i | ||||
\(95\) | − | 21.0292i | − | 0.221360i | ||||||
\(96\) | 121.735i | 1.26808i | ||||||||
\(97\) | −39.1672 | −0.403785 | −0.201893 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201893 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(98\) | 37.7984 | − | 27.4621i | 0.385698 | − | 0.280226i | ||||
\(99\) | − | 9.82857i | − | 0.0992785i | ||||||
\(100\) | 6.18034 | − | 19.0211i | 0.0618034 | − | 0.190211i | ||||
\(101\) | 99.8885 | 0.988995 | 0.494498 | − | 0.869179i | \(-0.335352\pi\) | ||||
0.494498 | + | 0.869179i | \(0.335352\pi\) | |||||||
\(102\) | 106.833 | + | 147.043i | 1.04738 | + | 1.44160i | ||||
\(103\) | − | 35.7721i | − | 0.347302i | −0.984807 | − | 0.173651i | \(-0.944444\pi\) | ||
0.984807 | − | 0.173651i | \(-0.0555565\pi\) | |||||||
\(104\) | 1.16718 | + | 3.59222i | 0.0112229 | + | 0.0345406i | ||||
\(105\) | 72.3607 | 0.689149 | ||||||||
\(106\) | 35.0132 | − | 25.4385i | 0.330313 | − | 0.239986i | ||||
\(107\) | − | 121.099i | − | 1.13177i | −0.824485 | − | 0.565884i | \(-0.808535\pi\) | ||
0.824485 | − | 0.565884i | \(-0.191465\pi\) | |||||||
\(108\) | 51.0557 | + | 16.5890i | 0.472738 | + | 0.153602i | ||||
\(109\) | −197.469 | −1.81164 | −0.905821 | − | 0.423660i | \(-0.860745\pi\) | ||||
−0.905821 | + | 0.423660i | \(0.860745\pi\) | |||||||
\(110\) | −4.72136 | − | 6.49839i | −0.0429215 | − | 0.0590763i | ||||
\(111\) | 100.282i | 0.903441i | ||||||||
\(112\) | −80.0000 | + | 110.111i | −0.714286 | + | 0.983130i | ||||
\(113\) | 81.2786 | 0.719280 | 0.359640 | − | 0.933091i | \(-0.382900\pi\) | ||||
0.359640 | + | 0.933091i | \(0.382900\pi\) | |||||||
\(114\) | −57.8885 | + | 42.0585i | −0.507794 | + | 0.368934i | ||||
\(115\) | − | 36.0341i | − | 0.313340i | ||||||
\(116\) | 8.58359 | − | 26.4176i | 0.0739965 | − | 0.227738i | ||||
\(117\) | −2.58359 | −0.0220820 | ||||||||
\(118\) | −86.8328 | − | 119.515i | −0.735871 | − | 1.01284i | ||||
\(119\) | 203.208i | 1.70763i | ||||||||
\(120\) | −64.7214 | + | 21.0292i | −0.539345 | + | 0.175244i | ||||
\(121\) | 117.774 | 0.973339 | ||||||||
\(122\) | 42.2918 | − | 30.7268i | 0.346654 | − | 0.251859i | ||||
\(123\) | − | 157.557i | − | 1.28095i | ||||||
\(124\) | 180.498 | + | 58.6475i | 1.45563 | + | 0.472964i | ||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | −54.7214 | − | 75.3175i | −0.434297 | − | 0.597758i | ||||
\(127\) | − | 1.84616i | − | 0.0145367i | −0.999974 | − | 0.00726834i | \(-0.997686\pi\) | ||
0.999974 | − | 0.00726834i | \(-0.00231361\pi\) | |||||||
\(128\) | 39.5542 | − | 121.735i | 0.309017 | − | 0.951057i | ||||
\(129\) | 7.63932 | 0.0592195 | ||||||||
\(130\) | −1.70820 | + | 1.24108i | −0.0131400 | + | 0.00954679i | ||||
\(131\) | 225.609i | 1.72221i | 0.508428 | + | 0.861105i | \(0.330227\pi\) | ||||
−0.508428 | + | 0.861105i | \(0.669773\pi\) | |||||||
\(132\) | −8.44582 | + | 25.9936i | −0.0639835 | + | 0.196921i | ||||
\(133\) | −80.0000 | −0.601504 | ||||||||
\(134\) | −104.472 | − | 143.794i | −0.779643 | − | 1.07309i | ||||
\(135\) | 30.0098i | 0.222295i | ||||||||
\(136\) | −59.0557 | − | 181.755i | −0.434233 | − | 1.33643i | ||||
\(137\) | −52.8328 | −0.385641 | −0.192820 | − | 0.981234i | \(-0.561764\pi\) | ||||
−0.192820 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(138\) | −99.1935 | + | 72.0683i | −0.718793 | + | 0.522234i | ||||
\(139\) | − | 125.852i | − | 0.905407i | −0.891661 | − | 0.452703i | \(-0.850460\pi\) | ||
0.891661 | − | 0.452703i | \(-0.149540\pi\) | |||||||
\(140\) | −72.3607 | − | 23.5114i | −0.516862 | − | 0.167939i | ||||
\(141\) | 134.472 | 0.953703 | ||||||||
\(142\) | 46.3344 | + | 63.7738i | 0.326298 | + | 0.449111i | ||||
\(143\) | 0.848009i | 0.00593013i | ||||||||
\(144\) | 70.8328 | + | 51.4631i | 0.491895 | + | 0.357382i | ||||
\(145\) | 15.5279 | 0.107089 | ||||||||
\(146\) | −222.567 | + | 161.705i | −1.52443 | + | 1.10757i | ||||
\(147\) | − | 88.8693i | − | 0.604553i | ||||||
\(148\) | 32.5836 | − | 100.282i | 0.220159 | − | 0.677581i | ||||
\(149\) | 132.971 | 0.892420 | 0.446210 | − | 0.894928i | \(-0.352773\pi\) | ||||
0.446210 | + | 0.894928i | \(0.352773\pi\) | |||||||
\(150\) | −22.3607 | − | 30.7768i | −0.149071 | − | 0.205179i | ||||
\(151\) | − | 151.221i | − | 1.00146i | −0.865603 | − | 0.500732i | \(-0.833064\pi\) | ||
0.865603 | − | 0.500732i | \(-0.166936\pi\) | |||||||
\(152\) | 71.5542 | − | 23.2494i | 0.470751 | − | 0.152956i | ||||
\(153\) | 130.721 | 0.854388 | ||||||||
\(154\) | −24.7214 | + | 17.9611i | −0.160528 | + | 0.116631i | ||||
\(155\) | 106.094i | 0.684480i | ||||||||
\(156\) | 6.83282 | + | 2.22012i | 0.0438001 | + | 0.0142315i | ||||
\(157\) | −36.7477 | −0.234062 | −0.117031 | − | 0.993128i | \(-0.537338\pi\) | ||||
−0.117031 | + | 0.993128i | \(0.537338\pi\) | |||||||
\(158\) | 133.666 | + | 183.975i | 0.845985 | + | 1.16440i | ||||
\(159\) | − | 82.3209i | − | 0.517741i | ||||||
\(160\) | 71.5542 | 0.447214 | ||||||||
\(161\) | −137.082 | −0.851441 | ||||||||
\(162\) | 162.297 | − | 117.916i | 1.00183 | − | 0.727874i | ||||
\(163\) | 302.854i | 1.85800i | 0.370079 | + | 0.929000i | \(0.379331\pi\) | ||||
−0.370079 | + | 0.929000i | \(0.620669\pi\) | |||||||
\(164\) | −51.1935 | + | 157.557i | −0.312155 | + | 0.960716i | ||||
\(165\) | −15.2786 | −0.0925978 | ||||||||
\(166\) | −24.9706 | − | 34.3691i | −0.150425 | − | 0.207043i | ||||
\(167\) | 99.3839i | 0.595113i | 0.954704 | + | 0.297557i | \(0.0961717\pi\) | ||||
−0.954704 | + | 0.297557i | \(0.903828\pi\) | |||||||
\(168\) | 80.0000 | + | 246.215i | 0.476190 | + | 1.46556i | ||||
\(169\) | −168.777 | −0.998681 | ||||||||
\(170\) | 86.4296 | − | 62.7948i | 0.508409 | − | 0.369381i | ||||
\(171\) | 51.4631i | 0.300954i | ||||||||
\(172\) | −7.63932 | − | 2.48217i | −0.0444147 | − | 0.0144312i | ||||
\(173\) | −181.639 | −1.04994 | −0.524969 | − | 0.851121i | \(-0.675923\pi\) | ||||
−0.524969 | + | 0.851121i | \(0.675923\pi\) | |||||||
\(174\) | −31.0557 | − | 42.7445i | −0.178481 | − | 0.245658i | ||||
\(175\) | − | 42.5325i | − | 0.243043i | ||||||
\(176\) | 16.8916 | − | 23.2494i | 0.0959753 | − | 0.132099i | ||||
\(177\) | −280.997 | −1.58755 | ||||||||
\(178\) | −109.125 | + | 79.2837i | −0.613060 | + | 0.445414i | ||||
\(179\) | − | 260.907i | − | 1.45758i | −0.684735 | − | 0.728792i | \(-0.740082\pi\) | ||
0.684735 | − | 0.728792i | \(-0.259918\pi\) | |||||||
\(180\) | −15.1246 | + | 46.5488i | −0.0840256 | + | 0.258604i | ||||
\(181\) | 157.777 | 0.871697 | 0.435848 | − | 0.900020i | \(-0.356448\pi\) | ||||
0.435848 | + | 0.900020i | \(0.356448\pi\) | |||||||
\(182\) | 4.72136 | + | 6.49839i | 0.0259415 | + | 0.0357055i | ||||
\(183\) | − | 99.4340i | − | 0.543355i | ||||||
\(184\) | 122.610 | − | 39.8384i | 0.666358 | − | 0.216513i | ||||
\(185\) | 58.9443 | 0.318618 | ||||||||
\(186\) | 292.053 | − | 212.189i | 1.57018 | − | 1.14080i | ||||
\(187\) | − | 42.9065i | − | 0.229447i | ||||||
\(188\) | −134.472 | − | 43.6926i | −0.715277 | − | 0.232408i | ||||
\(189\) | 114.164 | 0.604043 | ||||||||
\(190\) | 24.7214 | + | 34.0260i | 0.130112 | + | 0.179084i | ||||
\(191\) | − | 324.095i | − | 1.69683i | −0.529328 | − | 0.848417i | \(-0.677556\pi\) | ||
0.529328 | − | 0.848417i | \(-0.322444\pi\) | |||||||
\(192\) | −143.108 | − | 196.972i | −0.745356 | − | 1.02589i | ||||
\(193\) | 181.777 | 0.941850 | 0.470925 | − | 0.882173i | \(-0.343920\pi\) | ||||
0.470925 | + | 0.882173i | \(0.343920\pi\) | |||||||
\(194\) | 63.3738 | − | 46.0438i | 0.326669 | − | 0.237339i | ||||
\(195\) | 4.01623i | 0.0205960i | ||||||||
\(196\) | −28.8754 | + | 88.8693i | −0.147323 | + | 0.453415i | ||||
\(197\) | 140.525 | 0.713324 | 0.356662 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356662 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(198\) | 11.5542 | + | 15.9030i | 0.0583544 | + | 0.0803180i | ||||
\(199\) | 168.234i | 0.845397i | 0.906270 | + | 0.422698i | \(0.138917\pi\) | ||||
−0.906270 | + | 0.422698i | \(0.861083\pi\) | |||||||
\(200\) | 12.3607 | + | 38.0423i | 0.0618034 | + | 0.190211i | ||||
\(201\) | −338.079 | −1.68198 | ||||||||
\(202\) | −161.623 | + | 117.426i | −0.800114 | + | 0.581317i | ||||
\(203\) | − | 59.0715i | − | 0.290993i | ||||||
\(204\) | −345.718 | − | 112.331i | −1.69470 | − | 0.550641i | ||||
\(205\) | −92.6099 | −0.451756 | ||||||||
\(206\) | 42.0526 | + | 57.8805i | 0.204139 | + | 0.280973i | ||||
\(207\) | 88.1833i | 0.426006i | ||||||||
\(208\) | −6.11146 | − | 4.44023i | −0.0293820 | − | 0.0213473i | ||||
\(209\) | 16.8916 | 0.0808213 | ||||||||
\(210\) | −117.082 | + | 85.0651i | −0.557534 | + | 0.405072i | ||||
\(211\) | 93.9455i | 0.445240i | 0.974905 | + | 0.222620i | \(0.0714608\pi\) | ||||
−0.974905 | + | 0.222620i | \(0.928539\pi\) | |||||||
\(212\) | −26.7477 | + | 82.3209i | −0.126168 | + | 0.388306i | ||||
\(213\) | 149.941 | 0.703949 | ||||||||
\(214\) | 142.361 | + | 195.943i | 0.665237 | + | 0.915620i | ||||
\(215\) | − | 4.49028i | − | 0.0208850i | ||||||
\(216\) | −102.111 | + | 33.1780i | −0.472738 | + | 0.153602i | ||||
\(217\) | 403.607 | 1.85994 | ||||||||
\(218\) | 319.512 | − | 232.139i | 1.46565 | − | 1.06486i | ||||
\(219\) | 523.287i | 2.38944i | ||||||||
\(220\) | 15.2786 | + | 4.96433i | 0.0694484 | + | 0.0225651i | ||||
\(221\) | −11.2786 | −0.0510346 | ||||||||
\(222\) | −117.889 | − | 162.260i | −0.531029 | − | 0.730899i | ||||
\(223\) | 214.035i | 0.959797i | 0.877324 | + | 0.479899i | \(0.159327\pi\) | ||||
−0.877324 | + | 0.479899i | \(0.840673\pi\) | |||||||
\(224\) | − | 272.208i | − | 1.21522i | ||||||
\(225\) | −27.3607 | −0.121603 | ||||||||
\(226\) | −131.512 | + | 95.5488i | −0.581910 | + | 0.422782i | ||||
\(227\) | − | 41.4225i | − | 0.182478i | −0.995829 | − | 0.0912389i | \(-0.970917\pi\) | ||
0.995829 | − | 0.0912389i | \(-0.0290827\pi\) | |||||||
\(228\) | 44.2229 | − | 136.104i | 0.193960 | − | 0.596948i | ||||
\(229\) | 73.2786 | 0.319994 | 0.159997 | − | 0.987117i | \(-0.448852\pi\) | ||||
0.159997 | + | 0.987117i | \(0.448852\pi\) | |||||||
\(230\) | 42.3607 | + | 58.3045i | 0.184177 | + | 0.253498i | ||||
\(231\) | 58.1234i | 0.251616i | ||||||||
\(232\) | 17.1672 | + | 52.8352i | 0.0739965 | + | 0.227738i | ||||
\(233\) | −307.050 | −1.31781 | −0.658905 | − | 0.752227i | \(-0.728980\pi\) | ||||
−0.658905 | + | 0.752227i | \(0.728980\pi\) | |||||||
\(234\) | 4.18034 | − | 3.03719i | 0.0178647 | − | 0.0129795i | ||||
\(235\) | − | 79.0407i | − | 0.336344i | ||||||
\(236\) | 280.997 | + | 91.3014i | 1.19066 | + | 0.386870i | ||||
\(237\) | 432.551 | 1.82511 | ||||||||
\(238\) | −238.885 | − | 328.798i | −1.00372 | − | 1.38150i | ||||
\(239\) | − | 42.9065i | − | 0.179525i | −0.995963 | − | 0.0897625i | \(-0.971389\pi\) | ||
0.995963 | − | 0.0897625i | \(-0.0286108\pi\) | |||||||
\(240\) | 80.0000 | − | 110.111i | 0.333333 | − | 0.458794i | ||||
\(241\) | −135.082 | −0.560506 | −0.280253 | − | 0.959926i | \(-0.590418\pi\) | ||||
−0.280253 | + | 0.959926i | \(0.590418\pi\) | |||||||
\(242\) | −190.562 | + | 138.452i | −0.787448 | + | 0.572114i | ||||
\(243\) | − | 260.796i | − | 1.07323i | ||||||
\(244\) | −32.3081 | + | 99.4340i | −0.132410 | + | 0.407516i | ||||
\(245\) | −52.2361 | −0.213208 | ||||||||
\(246\) | 185.220 | + | 254.933i | 0.752926 | + | 1.03631i | ||||
\(247\) | − | 4.44023i | − | 0.0179767i | ||||||
\(248\) | −360.997 | + | 117.295i | −1.45563 | + | 0.472964i | ||||
\(249\) | −80.8065 | −0.324524 | ||||||||
\(250\) | −18.0902 | + | 13.1433i | −0.0723607 | + | 0.0525731i | ||||
\(251\) | − | 221.169i | − | 0.881152i | −0.897715 | − | 0.440576i | \(-0.854774\pi\) | ||
0.897715 | − | 0.440576i | \(-0.145226\pi\) | |||||||
\(252\) | 177.082 | + | 57.5374i | 0.702707 | + | 0.228323i | ||||
\(253\) | 28.9443 | 0.114404 | ||||||||
\(254\) | 2.17029 | + | 2.98715i | 0.00854445 | + | 0.0117604i | ||||
\(255\) | − | 203.208i | − | 0.796894i | ||||||
\(256\) | 79.1084 | + | 243.470i | 0.309017 | + | 0.951057i | ||||
\(257\) | −257.056 | −1.00022 | −0.500108 | − | 0.865963i | \(-0.666707\pi\) | ||||
−0.500108 | + | 0.865963i | \(0.666707\pi\) | |||||||
\(258\) | −12.3607 | + | 8.98056i | −0.0479096 | + | 0.0348084i | ||||
\(259\) | − | 224.237i | − | 0.865781i | ||||||
\(260\) | 1.30495 | − | 4.01623i | 0.00501904 | − | 0.0154470i | ||||
\(261\) | −38.0000 | −0.145594 | ||||||||
\(262\) | −265.220 | − | 365.044i | −1.01229 | − | 1.39330i | ||||
\(263\) | − | 164.168i | − | 0.624212i | −0.950047 | − | 0.312106i | \(-0.898966\pi\) | ||
0.950047 | − | 0.312106i | \(-0.101034\pi\) | |||||||
\(264\) | −16.8916 | − | 51.9872i | −0.0639835 | − | 0.196921i | ||||
\(265\) | −48.3870 | −0.182592 | ||||||||
\(266\) | 129.443 | − | 94.0456i | 0.486627 | − | 0.353555i | ||||
\(267\) | 256.567i | 0.960926i | ||||||||
\(268\) | 338.079 | + | 109.849i | 1.26149 | + | 0.409882i | ||||
\(269\) | −35.4752 | −0.131878 | −0.0659391 | − | 0.997824i | \(-0.521004\pi\) | ||||
−0.0659391 | + | 0.997824i | \(0.521004\pi\) | |||||||
\(270\) | −35.2786 | − | 48.5569i | −0.130662 | − | 0.179840i | ||||
\(271\) | 298.950i | 1.10314i | 0.834130 | + | 0.551568i | \(0.185970\pi\) | ||||
−0.834130 | + | 0.551568i | \(0.814030\pi\) | |||||||
\(272\) | 309.220 | + | 224.661i | 1.13684 | + | 0.825961i | ||||
\(273\) | 15.2786 | 0.0559657 | ||||||||
\(274\) | 85.4853 | − | 62.1087i | 0.311990 | − | 0.226674i | ||||
\(275\) | 8.98056i | 0.0326566i | ||||||||
\(276\) | 75.7771 | − | 233.218i | 0.274555 | − | 0.844992i | ||||
\(277\) | −457.246 | −1.65071 | −0.825354 | − | 0.564616i | \(-0.809024\pi\) | ||||
−0.825354 | + | 0.564616i | \(0.809024\pi\) | |||||||
\(278\) | 147.947 | + | 203.632i | 0.532185 | + | 0.732490i | ||||
\(279\) | − | 259.635i | − | 0.930593i | ||||||
\(280\) | 144.721 | − | 47.0228i | 0.516862 | − | 0.167939i | ||||
\(281\) | −5.63932 | −0.0200688 | −0.0100344 | − | 0.999950i | \(-0.503194\pi\) | ||||
−0.0100344 | + | 0.999950i | \(0.503194\pi\) | |||||||
\(282\) | −217.580 | + | 158.081i | −0.771562 | + | 0.560573i | ||||
\(283\) | − | 169.918i | − | 0.600418i | −0.953874 | − | 0.300209i | \(-0.902944\pi\) | ||
0.953874 | − | 0.300209i | \(-0.0970563\pi\) | |||||||
\(284\) | −149.941 | − | 48.7188i | −0.527962 | − | 0.171545i | ||||
\(285\) | 80.0000 | 0.280702 | ||||||||
\(286\) | −0.996894 | − | 1.37211i | −0.00348564 | − | 0.00479758i | ||||
\(287\) | 352.309i | 1.22756i | ||||||||
\(288\) | −175.108 | −0.608015 | ||||||||
\(289\) | 281.663 | 0.974611 | ||||||||
\(290\) | −25.1246 | + | 18.2541i | −0.0866366 | + | 0.0629452i | ||||
\(291\) | − | 149.001i | − | 0.512030i | ||||||
\(292\) | 170.026 | − | 523.287i | 0.582282 | − | 1.79208i | ||||
\(293\) | −26.8591 | −0.0916694 | −0.0458347 | − | 0.998949i | \(-0.514595\pi\) | ||||
−0.0458347 | + | 0.998949i | \(0.514595\pi\) | |||||||
\(294\) | 104.472 | + | 143.794i | 0.355347 | + | 0.489094i | ||||
\(295\) | 165.166i | 0.559884i | ||||||||
\(296\) | 65.1672 | + | 200.564i | 0.220159 | + | 0.677581i | ||||
\(297\) | −24.1052 | −0.0811624 | ||||||||
\(298\) | −215.151 | + | 156.316i | −0.721983 | + | 0.524551i | ||||
\(299\) | − | 7.60845i | − | 0.0254463i | ||||||
\(300\) | 72.3607 | + | 23.5114i | 0.241202 | + | 0.0783714i | ||||
\(301\) | −17.0820 | −0.0567510 | ||||||||
\(302\) | 177.771 | + | 244.681i | 0.588645 | + | 0.810201i | ||||
\(303\) | 379.999i | 1.25412i | ||||||||
\(304\) | −88.4458 | + | 121.735i | −0.290940 | + | 0.400445i | ||||
\(305\) | −58.4458 | −0.191626 | ||||||||
\(306\) | −211.512 | + | 153.672i | −0.691214 | + | 0.502197i | ||||
\(307\) | − | 118.031i | − | 0.384466i | −0.981349 | − | 0.192233i | \(-0.938427\pi\) | ||
0.981349 | − | 0.192233i | \(-0.0615730\pi\) | |||||||
\(308\) | 18.8854 | − | 58.1234i | 0.0613164 | − | 0.188712i | ||||
\(309\) | 136.085 | 0.440405 | ||||||||
\(310\) | −124.721 | − | 171.664i | −0.402327 | − | 0.553756i | ||||
\(311\) | 121.835i | 0.391753i | 0.980629 | + | 0.195877i | \(0.0627552\pi\) | ||||
−0.980629 | + | 0.195877i | \(0.937245\pi\) | |||||||
\(312\) | −13.6656 | + | 4.44023i | −0.0438001 | + | 0.0142315i | ||||
\(313\) | 219.548 | 0.701431 | 0.350716 | − | 0.936482i | \(-0.385938\pi\) | ||||
0.350716 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(314\) | 59.4590 | − | 43.1995i | 0.189360 | − | 0.137578i | ||||
\(315\) | 104.086i | 0.330432i | ||||||||
\(316\) | −432.551 | − | 140.544i | −1.36883 | − | 0.444761i | ||||
\(317\) | 366.859 | 1.15728 | 0.578642 | − | 0.815582i | \(-0.303583\pi\) | ||||
0.578642 | + | 0.815582i | \(0.303583\pi\) | |||||||
\(318\) | 96.7740 | + | 133.198i | 0.304321 | + | 0.418862i | ||||
\(319\) | 12.4727i | 0.0390993i | ||||||||
\(320\) | −115.777 | + | 84.1170i | −0.361803 | + | 0.262866i | ||||
\(321\) | 460.689 | 1.43517 | ||||||||
\(322\) | 221.803 | − | 161.150i | 0.688830 | − | 0.500465i | ||||
\(323\) | 224.661i | 0.695546i | ||||||||
\(324\) | −123.984 | + | 381.583i | −0.382666 | + | 1.17772i | ||||
\(325\) | 2.36068 | 0.00726363 | ||||||||
\(326\) | −356.026 | − | 490.028i | −1.09211 | − | 1.50315i | ||||
\(327\) | − | 751.217i | − | 2.29730i | ||||||
\(328\) | −102.387 | − | 315.115i | −0.312155 | − | 0.960716i | ||||
\(329\) | −300.689 | −0.913948 | ||||||||
\(330\) | 24.7214 | − | 17.9611i | 0.0749132 | − | 0.0544276i | ||||
\(331\) | − | 162.846i | − | 0.491981i | −0.969272 | − | 0.245990i | \(-0.920887\pi\) | ||
0.969272 | − | 0.245990i | \(-0.0791132\pi\) | |||||||
\(332\) | 80.8065 | + | 26.2556i | 0.243393 | + | 0.0790832i | ||||
\(333\) | −144.249 | −0.433181 | ||||||||
\(334\) | −116.833 | − | 160.807i | −0.349799 | − | 0.481457i | ||||
\(335\) | 198.718i | 0.593187i | ||||||||
\(336\) | −418.885 | − | 304.338i | −1.24668 | − | 0.905768i | ||||
\(337\) | 17.1084 | 0.0507666 | 0.0253833 | − | 0.999678i | \(-0.491919\pi\) | ||||
0.0253833 | + | 0.999678i | \(0.491919\pi\) | |||||||
\(338\) | 273.087 | − | 198.409i | 0.807950 | − | 0.587010i | ||||
\(339\) | 309.202i | 0.912101i | ||||||||
\(340\) | −66.0263 | + | 203.208i | −0.194195 | + | 0.597671i | ||||
\(341\) | −85.2198 | −0.249911 | ||||||||
\(342\) | −60.4984 | − | 83.2690i | −0.176896 | − | 0.243477i | ||||
\(343\) | − | 218.101i | − | 0.635863i | ||||||
\(344\) | 15.2786 | − | 4.96433i | 0.0444147 | − | 0.0144312i | ||||
\(345\) | 137.082 | 0.397339 | ||||||||
\(346\) | 293.899 | − | 213.530i | 0.849418 | − | 0.617138i | ||||
\(347\) | 167.498i | 0.482703i | 0.970438 | + | 0.241351i | \(0.0775906\pi\) | ||||
−0.970438 | + | 0.241351i | \(0.922409\pi\) | |||||||
\(348\) | 100.498 | + | 32.6539i | 0.288789 | + | 0.0938331i | ||||
\(349\) | −483.495 | −1.38537 | −0.692687 | − | 0.721239i | \(-0.743573\pi\) | ||||
−0.692687 | + | 0.721239i | \(0.743573\pi\) | |||||||
\(350\) | 50.0000 | + | 68.8191i | 0.142857 | + | 0.196626i | ||||
\(351\) | 6.33644i | 0.0180525i | ||||||||
\(352\) | 57.4756i | 0.163283i | ||||||||
\(353\) | 307.994 | 0.872504 | 0.436252 | − | 0.899825i | \(-0.356306\pi\) | ||||
0.436252 | + | 0.899825i | \(0.356306\pi\) | |||||||
\(354\) | 454.663 | − | 330.332i | 1.28436 | − | 0.933140i | ||||
\(355\) | − | 88.1332i | − | 0.248263i | ||||||
\(356\) | 83.3638 | − | 256.567i | 0.234168 | − | 0.720695i | ||||
\(357\) | −773.050 | −2.16540 | ||||||||
\(358\) | 306.715 | + | 422.157i | 0.856746 | + | 1.17921i | ||||
\(359\) | − | 23.2494i | − | 0.0647615i | −0.999476 | − | 0.0323807i | \(-0.989691\pi\) | ||
0.999476 | − | 0.0323807i | \(-0.0103089\pi\) | |||||||
\(360\) | −30.2492 | − | 93.0975i | −0.0840256 | − | 0.258604i | ||||
\(361\) | 272.554 | 0.754998 | ||||||||
\(362\) | −255.289 | + | 185.478i | −0.705217 | + | 0.512370i | ||||
\(363\) | 448.039i | 1.23427i | ||||||||
\(364\) | −15.2786 | − | 4.96433i | −0.0419743 | − | 0.0136383i | ||||
\(365\) | 307.580 | 0.842686 | ||||||||
\(366\) | 116.892 | + | 160.888i | 0.319376 | + | 0.439583i | ||||
\(367\) | − | 517.325i | − | 1.40960i | −0.709404 | − | 0.704802i | \(-0.751036\pi\) | ||
0.709404 | − | 0.704802i | \(-0.248964\pi\) | |||||||
\(368\) | −151.554 | + | 208.596i | −0.411832 | + | 0.566838i | ||||
\(369\) | 226.636 | 0.614190 | ||||||||
\(370\) | −95.3738 | + | 69.2931i | −0.257767 | + | 0.187279i | ||||
\(371\) | 184.075i | 0.496159i | ||||||||
\(372\) | −223.108 | + | 686.657i | −0.599754 | + | 1.84585i | ||||
\(373\) | −88.3545 | −0.236875 | −0.118438 | − | 0.992961i | \(-0.537789\pi\) | ||||
−0.118438 | + | 0.992961i | \(0.537789\pi\) | |||||||
\(374\) | 50.4396 | + | 69.4242i | 0.134865 | + | 0.185626i | ||||
\(375\) | 42.5325i | 0.113420i | ||||||||
\(376\) | 268.944 | − | 87.3853i | 0.715277 | − | 0.232408i | ||||
\(377\) | 3.27864 | 0.00869666 | ||||||||
\(378\) | −184.721 | + | 134.208i | −0.488681 | + | 0.355047i | ||||
\(379\) | 19.3332i | 0.0510112i | 0.999675 | + | 0.0255056i | \(0.00811956\pi\) | ||||
−0.999675 | + | 0.0255056i | \(0.991880\pi\) | |||||||
\(380\) | −80.0000 | − | 25.9936i | −0.210526 | − | 0.0684041i | ||||
\(381\) | 7.02321 | 0.0184336 | ||||||||
\(382\) | 380.997 | + | 524.397i | 0.997374 | + | 1.37277i | ||||
\(383\) | − | 431.612i | − | 1.12692i | −0.826142 | − | 0.563462i | \(-0.809469\pi\) | ||
0.826142 | − | 0.563462i | \(-0.190531\pi\) | |||||||
\(384\) | 463.108 | + | 150.473i | 1.20601 | + | 0.391857i | ||||
\(385\) | 34.1641 | 0.0887379 | ||||||||
\(386\) | −294.122 | + | 213.692i | −0.761973 | + | 0.553606i | ||||
\(387\) | 10.9887i | 0.0283945i | ||||||||
\(388\) | −48.4133 | + | 149.001i | −0.124777 | + | 0.384023i | ||||
\(389\) | −296.354 | −0.761837 | −0.380918 | − | 0.924609i | \(-0.624392\pi\) | ||||
−0.380918 | + | 0.924609i | \(0.624392\pi\) | |||||||
\(390\) | −4.72136 | − | 6.49839i | −0.0121061 | − | 0.0166625i | ||||
\(391\) | 384.963i | 0.984560i | ||||||||
\(392\) | −57.7508 | − | 177.739i | −0.147323 | − | 0.453415i | ||||
\(393\) | −858.269 | −2.18389 | ||||||||
\(394\) | −227.374 | + | 165.197i | −0.577091 | + | 0.419281i | ||||
\(395\) | − | 254.247i | − | 0.643664i | ||||||
\(396\) | −37.3901 | − | 12.1488i | −0.0944194 | − | 0.0306787i | ||||
\(397\) | −86.1904 | −0.217104 | −0.108552 | − | 0.994091i | \(-0.534621\pi\) | ||||
−0.108552 | + | 0.994091i | \(0.534621\pi\) | |||||||
\(398\) | −197.771 | − | 272.208i | −0.496912 | − | 0.683940i | ||||
\(399\) | − | 304.338i | − | 0.762752i | ||||||
\(400\) | −64.7214 | − | 47.0228i | −0.161803 | − | 0.117557i | ||||
\(401\) | 442.997 | 1.10473 | 0.552365 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552365 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(402\) | 547.023 | − | 397.436i | 1.36075 | − | 0.988646i | ||||
\(403\) | 22.4014i | 0.0555865i | ||||||||
\(404\) | 123.469 | − | 379.999i | 0.305616 | − | 0.940591i | ||||
\(405\) | −224.289 | −0.553799 | ||||||||
\(406\) | 69.4427 | + | 95.5797i | 0.171041 | + | 0.235418i | ||||
\(407\) | 47.3467i | 0.116331i | ||||||||
\(408\) | 691.437 | − | 224.661i | 1.69470 | − | 0.550641i | ||||
\(409\) | 63.4102 | 0.155037 | 0.0775186 | − | 0.996991i | \(-0.475300\pi\) | ||||
0.0775186 | + | 0.996991i | \(0.475300\pi\) | |||||||
\(410\) | 149.846 | − | 108.869i | 0.365478 | − | 0.265535i | ||||
\(411\) | − | 200.988i | − | 0.489022i | ||||||
\(412\) | −136.085 | − | 44.2167i | −0.330304 | − | 0.107322i | ||||
\(413\) | 628.328 | 1.52138 | ||||||||
\(414\) | −103.666 | − | 142.684i | −0.250400 | − | 0.344646i | ||||
\(415\) | 47.4969i | 0.114450i | ||||||||
\(416\) | 15.1084 | 0.0363182 | ||||||||
\(417\) | 478.768 | 1.14812 | ||||||||
\(418\) | −27.3313 | + | 19.8573i | −0.0653858 | + | 0.0475056i | ||||
\(419\) | − | 435.678i | − | 1.03980i | −0.854226 | − | 0.519902i | \(-0.825968\pi\) | ||
0.854226 | − | 0.519902i | \(-0.174032\pi\) | |||||||
\(420\) | 89.4427 | − | 275.276i | 0.212959 | − | 0.655420i | ||||
\(421\) | −582.912 | −1.38459 | −0.692294 | − | 0.721615i | \(-0.743400\pi\) | ||||
−0.692294 | + | 0.721615i | \(0.743400\pi\) | |||||||
\(422\) | −110.440 | − | 152.007i | −0.261705 | − | 0.360206i | ||||
\(423\) | 193.430i | 0.457280i | ||||||||
\(424\) | −53.4953 | − | 164.642i | −0.126168 | − | 0.388306i | ||||
\(425\) | −119.443 | −0.281042 | ||||||||
\(426\) | −242.610 | + | 176.266i | −0.569507 | + | 0.413771i | ||||
\(427\) | 222.341i | 0.520705i | ||||||||
\(428\) | −460.689 | − | 149.687i | −1.07638 | − | 0.349736i | ||||
\(429\) | −3.22602 | −0.00751986 | ||||||||
\(430\) | 5.27864 | + | 7.26543i | 0.0122759 | + | 0.0168963i | ||||
\(431\) | 375.882i | 0.872117i | 0.899918 | + | 0.436058i | \(0.143626\pi\) | ||||
−0.899918 | + | 0.436058i | \(0.856374\pi\) | |||||||
\(432\) | 126.217 | − | 173.722i | 0.292168 | − | 0.402135i | ||||
\(433\) | −368.164 | −0.850263 | −0.425132 | − | 0.905131i | \(-0.639772\pi\) | ||||
−0.425132 | + | 0.905131i | \(0.639772\pi\) | |||||||
\(434\) | −653.050 | + | 474.468i | −1.50472 | + | 1.09324i | ||||
\(435\) | 59.0715i | 0.135797i | ||||||||
\(436\) | −244.085 | + | 751.217i | −0.559828 | + | 1.72297i | ||||
\(437\) | −151.554 | −0.346806 | ||||||||
\(438\) | −615.161 | − | 846.696i | −1.40448 | − | 1.93310i | ||||
\(439\) | 483.549i | 1.10148i | 0.834677 | + | 0.550739i | \(0.185654\pi\) | ||||
−0.834677 | + | 0.550739i | \(0.814346\pi\) | |||||||
\(440\) | −30.5573 | + | 9.92866i | −0.0694484 | + | 0.0225651i | ||||
\(441\) | 127.833 | 0.289870 | ||||||||
\(442\) | 18.2492 | − | 13.2588i | 0.0412878 | − | 0.0299974i | ||||
\(443\) | − | 279.181i | − | 0.630205i | −0.949058 | − | 0.315102i | \(-0.897961\pi\) | ||
0.949058 | − | 0.315102i | \(-0.102039\pi\) | |||||||
\(444\) | 381.495 | + | 123.955i | 0.859224 | + | 0.279179i | ||||
\(445\) | 150.807 | 0.338891 | ||||||||
\(446\) | −251.613 | − | 346.316i | −0.564155 | − | 0.776492i | ||||
\(447\) | 505.850i | 1.13166i | ||||||||
\(448\) | 320.000 | + | 440.442i | 0.714286 | + | 0.983130i | ||||
\(449\) | 756.079 | 1.68392 | 0.841959 | − | 0.539542i | \(-0.181403\pi\) | ||||
0.841959 | + | 0.539542i | \(0.181403\pi\) | |||||||
\(450\) | 44.2705 | − | 32.1644i | 0.0983789 | − | 0.0714765i | ||||
\(451\) | − | 74.3885i | − | 0.164941i | ||||||
\(452\) | 100.466 | − | 309.202i | 0.222270 | − | 0.684076i | ||||
\(453\) | 575.279 | 1.26993 | ||||||||
\(454\) | 48.6950 | + | 67.0230i | 0.107258 | + | 0.147628i | ||||
\(455\) | − | 8.98056i | − | 0.0197375i | ||||||
\(456\) | 88.4458 | + | 272.208i | 0.193960 | + | 0.596948i | ||||
\(457\) | 285.672 | 0.625103 | 0.312551 | − | 0.949901i | \(-0.398816\pi\) | ||||
0.312551 | + | 0.949901i | \(0.398816\pi\) | |||||||
\(458\) | −118.567 | + | 86.1442i | −0.258881 | + | 0.188088i | ||||
\(459\) | − | 320.603i | − | 0.698482i | ||||||
\(460\) | −137.082 | − | 44.5407i | −0.298004 | − | 0.0968275i | ||||
\(461\) | −99.1146 | −0.214999 | −0.107500 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107500 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(462\) | −68.3282 | − | 94.0456i | −0.147896 | − | 0.203562i | ||||
\(463\) | − | 630.603i | − | 1.36199i | −0.732286 | − | 0.680997i | \(-0.761547\pi\) | ||
0.732286 | − | 0.680997i | \(-0.238453\pi\) | |||||||
\(464\) | −89.8885 | − | 65.3078i | −0.193725 | − | 0.140750i | ||||
\(465\) | −403.607 | −0.867972 | ||||||||
\(466\) | 496.817 | − | 360.958i | 1.06613 | − | 0.774589i | ||||
\(467\) | 496.010i | 1.06212i | 0.847334 | + | 0.531060i | \(0.178206\pi\) | ||||
−0.847334 | + | 0.531060i | \(0.821794\pi\) | |||||||
\(468\) | −3.19350 | + | 9.82857i | −0.00682371 | + | 0.0210012i | ||||
\(469\) | 755.967 | 1.61187 | ||||||||
\(470\) | 92.9180 | + | 127.891i | 0.197698 | + | 0.272108i | ||||
\(471\) | − | 139.796i | − | 0.296808i | ||||||
\(472\) | −561.994 | + | 182.603i | −1.19066 | + | 0.386870i | ||||
\(473\) | 3.60680 | 0.00762537 | ||||||||
\(474\) | −699.882 | + | 508.494i | −1.47655 | + | 1.07277i | ||||
\(475\) | − | 47.0228i | − | 0.0989954i | ||||||
\(476\) | 773.050 | + | 251.179i | 1.62405 | + | 0.527687i | ||||
\(477\) | 118.413 | 0.248246 | ||||||||
\(478\) | 50.4396 | + | 69.4242i | 0.105522 | + | 0.145239i | ||||
\(479\) | 579.090i | 1.20896i | 0.796621 | + | 0.604478i | \(0.206618\pi\) | ||||
−0.796621 | + | 0.604478i | \(0.793382\pi\) | |||||||
\(480\) | 272.208i | 0.567101i | ||||||||
\(481\) | 12.4458 | 0.0258749 | ||||||||
\(482\) | 218.567 | − | 158.798i | 0.453459 | − | 0.329457i | ||||
\(483\) | − | 521.491i | − | 1.07969i | ||||||
\(484\) | 145.577 | − | 448.039i | 0.300778 | − | 0.925700i | ||||
\(485\) | −87.5805 | −0.180578 | ||||||||
\(486\) | 306.584 | + | 421.976i | 0.630830 | + | 0.868264i | ||||
\(487\) | 626.363i | 1.28617i | 0.765796 | + | 0.643084i | \(0.222345\pi\) | ||||
−0.765796 | + | 0.643084i | \(0.777655\pi\) | |||||||
\(488\) | −64.6161 | − | 198.868i | −0.132410 | − | 0.407516i | ||||
\(489\) | −1152.13 | −2.35608 | ||||||||
\(490\) | 84.5197 | − | 61.4072i | 0.172489 | − | 0.125321i | ||||
\(491\) | 22.3013i | 0.0454201i | 0.999742 | + | 0.0227100i | \(0.00722945\pi\) | ||||
−0.999742 | + | 0.0227100i | \(0.992771\pi\) | |||||||
\(492\) | −599.384 | − | 194.752i | −1.21826 | − | 0.395837i | ||||
\(493\) | −165.889 | −0.336488 | ||||||||
\(494\) | 5.21981 | + | 7.18445i | 0.0105664 | + | 0.0145434i | ||||
\(495\) | − | 21.9773i | − | 0.0443987i | ||||||
\(496\) | 446.217 | − | 614.165i | 0.899630 | − | 1.23824i | ||||
\(497\) | −335.279 | −0.674605 | ||||||||
\(498\) | 130.748 | − | 94.9937i | 0.262546 | − | 0.190750i | ||||
\(499\) | 627.362i | 1.25724i | 0.777714 | + | 0.628619i | \(0.216379\pi\) | ||||
−0.777714 | + | 0.628619i | \(0.783621\pi\) | |||||||
\(500\) | 13.8197 | − | 42.5325i | 0.0276393 | − | 0.0850651i | ||||
\(501\) | −378.079 | −0.754649 | ||||||||
\(502\) | 260.000 | + | 357.859i | 0.517928 | + | 0.712867i | ||||
\(503\) | 780.853i | 1.55239i | 0.630492 | + | 0.776196i | \(0.282853\pi\) | ||||
−0.630492 | + | 0.776196i | \(0.717147\pi\) | |||||||
\(504\) | −354.164 | + | 115.075i | −0.702707 | + | 0.228323i | ||||
\(505\) | 223.358 | 0.442292 | ||||||||
\(506\) | −46.8328 | + | 34.0260i | −0.0925550 | + | 0.0672451i | ||||
\(507\) | − | 642.066i | − | 1.26640i | ||||||
\(508\) | −7.02321 | − | 2.28198i | −0.0138252 | − | 0.00449208i | ||||
\(509\) | −288.950 | −0.567683 | −0.283841 | − | 0.958871i | \(-0.591609\pi\) | ||||
−0.283841 | + | 0.958871i | \(0.591609\pi\) | |||||||
\(510\) | 238.885 | + | 328.798i | 0.468403 | + | 0.644701i | ||||
\(511\) | − | 1170.11i | − | 2.28984i | ||||||
\(512\) | −414.217 | − | 300.946i | −0.809017 | − | 0.587785i | ||||
\(513\) | 126.217 | 0.246036 | ||||||||
\(514\) | 415.925 | − | 302.187i | 0.809192 | − | 0.587913i | ||||
\(515\) | − | 79.9888i | − | 0.155318i | ||||||
\(516\) | 9.44272 | − | 29.0617i | 0.0182998 | − | 0.0563211i | ||||
\(517\) | 63.4891 | 0.122803 | ||||||||
\(518\) | 263.607 | + | 362.824i | 0.508893 | + | 0.700432i | ||||
\(519\) | − | 690.997i | − | 1.33140i | ||||||
\(520\) | 2.60990 | + | 8.03246i | 0.00501904 | + | 0.0154470i | ||||
\(521\) | −602.984 | −1.15736 | −0.578680 | − | 0.815555i | \(-0.696432\pi\) | ||||
−0.578680 | + | 0.815555i | \(0.696432\pi\) | |||||||
\(522\) | 61.4853 | − | 44.6717i | 0.117788 | − | 0.0855779i | ||||
\(523\) | 367.962i | 0.703560i | 0.936083 | + | 0.351780i | \(0.114423\pi\) | ||||
−0.936083 | + | 0.351780i | \(0.885577\pi\) | |||||||
\(524\) | 858.269 | + | 278.869i | 1.63792 | + | 0.532192i | ||||
\(525\) | 161.803 | 0.308197 | ||||||||
\(526\) | 192.991 | + | 265.629i | 0.366902 | + | 0.504998i | ||||
\(527\) | − | 1133.44i | − | 2.15073i | ||||||
\(528\) | 88.4458 | + | 64.2597i | 0.167511 | + | 0.121704i | ||||
\(529\) | 269.308 | 0.509089 | ||||||||
\(530\) | 78.2918 | − | 56.8823i | 0.147720 | − | 0.107325i | ||||
\(531\) | − | 404.196i | − | 0.761198i | ||||||
\(532\) | −98.8854 | + | 304.338i | −0.185875 | + | 0.572064i | ||||
\(533\) | −19.5542 | −0.0366870 | ||||||||
\(534\) | −301.613 | − | 415.135i | −0.564818 | − | 0.777406i | ||||
\(535\) | − | 270.786i | − | 0.506142i | ||||||
\(536\) | −676.158 | + | 219.697i | −1.26149 | + | 0.409882i | ||||
\(537\) | 992.551 | 1.84833 | ||||||||
\(538\) | 57.4001 | − | 41.7036i | 0.106692 | − | 0.0775161i | ||||
\(539\) | − | 41.9584i | − | 0.0778449i | ||||||
\(540\) | 114.164 | + | 37.0942i | 0.211415 | + | 0.0686929i | ||||
\(541\) | −616.885 | −1.14027 | −0.570134 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570134 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(542\) | −351.437 | − | 483.711i | −0.648407 | − | 0.892455i | ||||
\(543\) | 600.220i | 1.10538i | ||||||||
\(544\) | −764.433 | −1.40521 | ||||||||
\(545\) | −441.554 | −0.810191 | ||||||||
\(546\) | −24.7214 | + | 17.9611i | −0.0452772 | + | 0.0328958i | ||||
\(547\) | − | 97.8499i | − | 0.178885i | −0.995992 | − | 0.0894423i | \(-0.971492\pi\) | ||
0.995992 | − | 0.0894423i | \(-0.0285085\pi\) | |||||||
\(548\) | −65.3050 | + | 200.988i | −0.119170 | + | 0.366766i | ||||
\(549\) | 143.029 | 0.260527 | ||||||||
\(550\) | −10.5573 | − | 14.5309i | −0.0191951 | − | 0.0264197i | ||||
\(551\) | − | 65.3078i | − | 0.118526i | ||||||
\(552\) | 151.554 | + | 466.436i | 0.274555 | + | 0.844992i | ||||
\(553\) | −967.214 | −1.74903 | ||||||||
\(554\) | 739.840 | − | 537.525i | 1.33545 | − | 0.970262i | ||||
\(555\) | 224.237i | 0.404031i | ||||||||
\(556\) | −478.768 | − | 155.561i | −0.861093 | − | 0.279786i | ||||
\(557\) | 896.302 | 1.60916 | 0.804580 | − | 0.593845i | \(-0.202391\pi\) | ||||
0.804580 | + | 0.593845i | \(0.202391\pi\) | |||||||
\(558\) | 305.220 | + | 420.099i | 0.546989 | + | 0.752866i | ||||
\(559\) | − | 0.948103i | − | 0.00169607i | ||||||
\(560\) | −178.885 | + | 246.215i | −0.319438 | + | 0.439669i | ||||
\(561\) | 163.226 | 0.290955 | ||||||||
\(562\) | 9.12461 | − | 6.62942i | 0.0162360 | − | 0.0117961i | ||||
\(563\) | 771.186i | 1.36978i | 0.728647 | + | 0.684890i | \(0.240150\pi\) | ||||
−0.728647 | + | 0.684890i | \(0.759850\pi\) | |||||||
\(564\) | 166.217 | − | 511.562i | 0.294710 | − | 0.907026i | ||||
\(565\) | 181.745 | 0.321672 | ||||||||
\(566\) | 199.751 | + | 274.933i | 0.352917 | + | 0.485748i | ||||
\(567\) | 853.245i | 1.50484i | ||||||||
\(568\) | 299.882 | − | 97.4377i | 0.527962 | − | 0.171545i | ||||
\(569\) | 8.74767 | 0.0153738 | 0.00768688 | − | 0.999970i | \(-0.497553\pi\) | ||||
0.00768688 | + | 0.999970i | \(0.497553\pi\) | |||||||
\(570\) | −129.443 | + | 94.0456i | −0.227092 | + | 0.164992i | ||||
\(571\) | 511.138i | 0.895164i | 0.894243 | + | 0.447582i | \(0.147715\pi\) | ||||
−0.894243 | + | 0.447582i | \(0.852285\pi\) | |||||||
\(572\) | 3.22602 | + | 1.04820i | 0.00563989 | + | 0.00183251i | ||||
\(573\) | 1232.93 | 2.15171 | ||||||||
\(574\) | −414.164 | − | 570.048i | −0.721540 | − | 0.993115i | ||||
\(575\) | − | 80.5748i | − | 0.140130i | ||||||
\(576\) | 283.331 | − | 205.852i | 0.491895 | − | 0.357382i | ||||
\(577\) | −713.712 | −1.23694 | −0.618468 | − | 0.785810i | \(-0.712246\pi\) | ||||
−0.618468 | + | 0.785810i | \(0.712246\pi\) | |||||||
\(578\) | −455.740 | + | 331.114i | −0.788477 | + | 0.572862i | ||||
\(579\) | 691.521i | 1.19434i | ||||||||
\(580\) | 19.1935 | − | 59.0715i | 0.0330922 | − | 0.101847i | ||||
\(581\) | 180.689 | 0.310996 | ||||||||
\(582\) | 175.161 | + | 241.088i | 0.300964 | + | 0.414241i | ||||
\(583\) | − | 38.8666i | − | 0.0666666i | ||||||
\(584\) | 340.053 | + | 1046.57i | 0.582282 | + | 1.79208i | ||||
\(585\) | −5.77709 | −0.00987536 | ||||||||
\(586\) | 43.4590 | − | 31.5748i | 0.0741621 | − | 0.0538819i | ||||
\(587\) | − | 422.169i | − | 0.719198i | −0.933107 | − | 0.359599i | \(-0.882914\pi\) | ||
0.933107 | − | 0.359599i | \(-0.117086\pi\) | |||||||
\(588\) | −338.079 | − | 109.849i | −0.574964 | − | 0.186817i | ||||
\(589\) | 446.217 | 0.757584 | ||||||||
\(590\) | −194.164 | − | 267.244i | −0.329092 | − | 0.452956i | ||||
\(591\) | 534.588i | 0.904548i | ||||||||
\(592\) | −341.220 | − | 247.911i | −0.576385 | − | 0.418768i | ||||
\(593\) | −308.663 | −0.520510 | −0.260255 | − | 0.965540i | \(-0.583807\pi\) | ||||
−0.260255 | + | 0.965540i | \(0.583807\pi\) | |||||||
\(594\) | 39.0031 | − | 28.3374i | 0.0656618 | − | 0.0477061i | ||||
\(595\) | 454.387i | 0.763676i | ||||||||
\(596\) | 164.361 | − | 505.850i | 0.275773 | − | 0.848742i | ||||
\(597\) | −640.000 | −1.07203 | ||||||||
\(598\) | 8.94427 | + | 12.3107i | 0.0149570 | + | 0.0205865i | ||||
\(599\) | − | 462.196i | − | 0.771612i | −0.922580 | − | 0.385806i | \(-0.873923\pi\) | ||
0.922580 | − | 0.385806i | \(-0.126077\pi\) | |||||||
\(600\) | −144.721 | + | 47.0228i | −0.241202 | + | 0.0783714i | ||||
\(601\) | 355.358 | 0.591277 | 0.295639 | − | 0.955300i | \(-0.404468\pi\) | ||||
0.295639 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(602\) | 27.6393 | − | 20.0811i | 0.0459125 | − | 0.0333574i | ||||
\(603\) | − | 486.305i | − | 0.806476i | ||||||
\(604\) | −575.279 | − | 186.919i | −0.952448 | − | 0.309469i | ||||
\(605\) | 263.351 | 0.435290 | ||||||||
\(606\) | −446.715 | − | 614.851i | −0.737154 | − | 1.01461i | ||||
\(607\) | 630.403i | 1.03856i | 0.854605 | + | 0.519278i | \(0.173799\pi\) | ||||
−0.854605 | + | 0.519278i | \(0.826201\pi\) | |||||||
\(608\) | − | 300.946i | − | 0.494977i | ||||||
\(609\) | 224.721 | 0.369001 | ||||||||
\(610\) | 94.5673 | − | 68.7072i | 0.155028 | − | 0.112635i | ||||
\(611\) | − | 16.6891i | − | 0.0273144i | ||||||
\(612\) | 161.580 | − | 497.294i | 0.264020 | − | 0.812571i | ||||
\(613\) | 812.525 | 1.32549 | 0.662745 | − | 0.748846i | \(-0.269392\pi\) | ||||
0.662745 | + | 0.748846i | \(0.269392\pi\) | |||||||
\(614\) | 138.754 | + | 190.978i | 0.225984 | + | 0.311040i | ||||
\(615\) | − | 352.309i | − | 0.572860i | ||||||
\(616\) | 37.7709 | + | 116.247i | 0.0613164 | + | 0.188712i | ||||
\(617\) | −437.935 | −0.709781 | −0.354891 | − | 0.934908i | \(-0.615482\pi\) | ||||
−0.354891 | + | 0.934908i | \(0.615482\pi\) | |||||||
\(618\) | −220.190 | + | 159.978i | −0.356295 | + | 0.258864i | ||||
\(619\) | − | 770.250i | − | 1.24435i | −0.782880 | − | 0.622173i | \(-0.786250\pi\) | ||
0.782880 | − | 0.622173i | \(-0.213750\pi\) | |||||||
\(620\) | 403.607 | + | 131.140i | 0.650979 | + | 0.211516i | ||||
\(621\) | 216.276 | 0.348270 | ||||||||
\(622\) | −143.226 | − | 197.134i | −0.230267 | − | 0.316935i | ||||
\(623\) | − | 573.702i | − | 0.920870i | ||||||
\(624\) | 16.8916 | − | 23.2494i | 0.0270700 | − | 0.0372586i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | −355.236 | + | 258.094i | −0.567470 | + | 0.412291i | ||||
\(627\) | 64.2597i | 0.102487i | ||||||||
\(628\) | −45.4226 | + | 139.796i | −0.0723290 | + | 0.222606i | ||||
\(629\) | −629.718 | −1.00114 | ||||||||
\(630\) | −122.361 | − | 168.415i | −0.194223 | − | 0.267325i | ||||
\(631\) | − | 875.496i | − | 1.38747i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) | ||
0.720228 | − | 0.693737i | \(-0.244037\pi\) | |||||||
\(632\) | 865.102 | − | 281.089i | 1.36883 | − | 0.444761i | ||||
\(633\) | −357.390 | −0.564597 | ||||||||
\(634\) | −593.591 | + | 431.269i | −0.936263 | + | 0.680235i | ||||
\(635\) | − | 4.12814i | − | 0.00650100i | ||||||
\(636\) | −313.167 | − | 101.754i | −0.492401 | − | 0.159991i | ||||
\(637\) | −11.0294 | −0.0173146 | ||||||||
\(638\) | −14.6625 | − | 20.1812i | −0.0229820 | − | 0.0316320i | ||||
\(639\) | 215.681i | 0.337529i | ||||||||
\(640\) | 88.4458 | − | 272.208i | 0.138197 | − | 0.425325i | ||||
\(641\) | 842.571 | 1.31446 | 0.657232 | − | 0.753689i | \(-0.271727\pi\) | ||||
0.657232 | + | 0.753689i | \(0.271727\pi\) | |||||||
\(642\) | −745.410 | + | 541.572i | −1.16108 | + | 0.843570i | ||||
\(643\) | − | 1153.20i | − | 1.79348i | −0.442563 | − | 0.896738i | \(-0.645931\pi\) | ||
0.442563 | − | 0.896738i | \(-0.354069\pi\) | |||||||
\(644\) | −169.443 | + | 521.491i | −0.263110 | + | 0.809769i | ||||
\(645\) | 17.0820 | 0.0264838 | ||||||||
\(646\) | −264.105 | − | 363.510i | −0.408832 | − | 0.562708i | ||||
\(647\) | − | 355.751i | − | 0.549847i | −0.961466 | − | 0.274924i | \(-0.911347\pi\) | ||
0.961466 | − | 0.274924i | \(-0.0886526\pi\) | |||||||
\(648\) | −247.967 | − | 763.165i | −0.382666 | − | 1.17772i | ||||
\(649\) | −132.669 | −0.204420 | ||||||||
\(650\) | −3.81966 | + | 2.77515i | −0.00587640 | + | 0.00426945i | ||||
\(651\) | 1535.41i | 2.35854i | ||||||||
\(652\) | 1152.13 | + | 374.348i | 1.76706 | + | 0.574154i | ||||
\(653\) | −557.915 | −0.854387 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(654\) | 883.108 | + | 1215.49i | 1.35032 | + | 1.85855i | ||||
\(655\) | 504.478i | 0.770195i | ||||||||
\(656\) | 536.105 | + | 389.503i | 0.817234 | + | 0.593755i | ||||
\(657\) | −752.715 | −1.14569 | ||||||||
\(658\) | 486.525 | − | 353.481i | 0.739399 | − | 0.537205i | ||||
\(659\) | 284.157i | 0.431194i | 0.976482 | + | 0.215597i | \(0.0691697\pi\) | ||||
−0.976482 | + | 0.215597i | \(0.930830\pi\) | |||||||
\(660\) | −18.8854 | + | 58.1234i | −0.0286143 | + | 0.0880658i | ||||
\(661\) | 716.735 | 1.08432 | 0.542160 | − | 0.840275i | \(-0.317607\pi\) | ||||
0.542160 | + | 0.840275i | \(0.317607\pi\) | |||||||
\(662\) | 191.437 | + | 263.490i | 0.289179 | + | 0.398021i | ||||
\(663\) | − | 42.9065i | − | 0.0647157i | ||||||
\(664\) | −161.613 | + | 52.5112i | −0.243393 | + | 0.0790832i | ||||
\(665\) | −178.885 | −0.269001 | ||||||||
\(666\) | 233.400 | − | 169.575i | 0.350451 | − | 0.254617i | ||||
\(667\) | − | 111.907i | − | 0.167776i | ||||||
\(668\) | 378.079 | + | 122.845i | 0.565986 | + | 0.183900i | ||||
\(669\) | −814.237 | −1.21710 | ||||||||
\(670\) | −233.607 | − | 321.532i | −0.348667 | − | 0.479899i | ||||
\(671\) | − | 46.9464i | − | 0.0699648i | ||||||
\(672\) | 1035.54 | 1.54098 | ||||||||
\(673\) | −695.378 | −1.03325 | −0.516625 | − | 0.856212i | \(-0.672812\pi\) | ||||
−0.516625 | + | 0.856212i | \(0.672812\pi\) | |||||||
\(674\) | −27.6819 | + | 20.1121i | −0.0410711 | + | 0.0298399i | ||||
\(675\) | 67.1040i | 0.0994133i | ||||||||
\(676\) | −208.620 | + | 642.066i | −0.308609 | + | 0.949802i | ||||
\(677\) | −820.237 | −1.21158 | −0.605788 | − | 0.795626i | \(-0.707142\pi\) | ||||
−0.605788 | + | 0.795626i | \(0.707142\pi\) | |||||||
\(678\) | −363.489 | − | 500.300i | −0.536120 | − | 0.737905i | ||||
\(679\) | 333.176i | 0.490686i | ||||||||
\(680\) | −132.053 | − | 406.416i | −0.194195 | − | 0.597671i | ||||
\(681\) | 157.580 | 0.231396 | ||||||||
\(682\) | 137.889 | − | 100.182i | 0.202183 | − | 0.146894i | ||||
\(683\) | 335.508i | 0.491227i | 0.969368 | + | 0.245613i | \(0.0789894\pi\) | ||||
−0.969368 | + | 0.245613i | \(0.921011\pi\) | |||||||
\(684\) | 195.777 | + | 63.6118i | 0.286224 | + | 0.0929998i | ||||
\(685\) | −118.138 | −0.172464 | ||||||||
\(686\) | 256.393 | + | 352.895i | 0.373751 | + | 0.514424i | ||||
\(687\) | 278.769i | 0.405777i | ||||||||
\(688\) | −18.8854 | + | 25.9936i | −0.0274498 | + | 0.0377814i | ||||
\(689\) | −10.2167 | −0.0148283 | ||||||||
\(690\) | −221.803 | + | 161.150i | −0.321454 | + | 0.233550i | ||||
\(691\) | 336.568i | 0.487074i | 0.969892 | + | 0.243537i | \(0.0783077\pi\) | ||||
−0.969892 | + | 0.243537i | \(0.921692\pi\) | |||||||
\(692\) | −224.519 | + | 690.997i | −0.324449 | + | 0.998551i | ||||
\(693\) | −83.6068 | −0.120645 | ||||||||
\(694\) | −196.906 | − | 271.017i | −0.283726 | − | 0.390515i | ||||
\(695\) | − | 281.413i | − | 0.404910i | ||||||
\(696\) | −200.997 | + | 65.3078i | −0.288789 | + | 0.0938331i | ||||
\(697\) | 989.378 | 1.41948 | ||||||||
\(698\) | 782.312 | − | 568.383i | 1.12079 | − | 0.814302i | ||||
\(699\) | − | 1168.09i | − | 1.67108i | ||||||
\(700\) | −161.803 | − | 52.5731i | −0.231148 | − | 0.0751044i | ||||
\(701\) | −429.364 | −0.612502 | −0.306251 | − | 0.951951i | \(-0.599075\pi\) | ||||
−0.306251 | + | 0.951951i | \(0.599075\pi\) | |||||||
\(702\) | −7.44893 | − | 10.2526i | −0.0106110 | − | 0.0146048i | ||||
\(703\) | − | 247.911i | − | 0.352647i | ||||||
\(704\) | −67.5666 | − | 92.9974i | −0.0959753 | − | 0.132099i | ||||
\(705\) | 300.689 | 0.426509 | ||||||||
\(706\) | −498.344 | + | 362.068i | −0.705870 | + | 0.512845i | ||||
\(707\) | − | 849.703i | − | 1.20184i | ||||||
\(708\) | −347.331 | + | 1068.98i | −0.490581 | + | 1.50985i | ||||
\(709\) | 1224.60 | 1.72722 | 0.863609 | − | 0.504162i | \(-0.168199\pi\) | ||||
0.863609 | + | 0.504162i | \(0.168199\pi\) | |||||||
\(710\) | 103.607 | + | 142.603i | 0.145925 | + | 0.200849i | ||||
\(711\) | 622.197i | 0.875101i | ||||||||
\(712\) | 166.728 | + | 513.135i | 0.234168 | + | 0.720695i | ||||
\(713\) | 764.604 | 1.07238 | ||||||||
\(714\) | 1250.82 | − | 908.774i | 1.75185 | − | 1.27279i | ||||
\(715\) | 1.89621i | 0.00265204i | ||||||||
\(716\) | −992.551 | − | 322.499i | −1.38624 | − | 0.450418i | ||||
\(717\) | 163.226 | 0.227651 | ||||||||
\(718\) | 27.3313 | + | 37.6183i | 0.0380658 | + | 0.0523931i | ||||
\(719\) | 496.022i | 0.689877i | 0.938625 | + | 0.344939i | \(0.112100\pi\) | ||||
−0.938625 | + | 0.344939i | \(0.887900\pi\) | |||||||
\(720\) | 158.387 | + | 115.075i | 0.219982 | + | 0.159826i | ||||
\(721\) | −304.296 | −0.422047 | ||||||||
\(722\) | −441.002 | + | 320.407i | −0.610806 | + | 0.443777i | ||||
\(723\) | − | 513.883i | − | 0.710764i | ||||||
\(724\) | 195.023 | − | 600.220i | 0.269369 | − | 0.829033i | ||||
\(725\) | 34.7214 | 0.0478915 | ||||||||
\(726\) | −526.701 | − | 724.942i | −0.725484 | − | 0.998543i | ||||
\(727\) | − | 152.843i | − | 0.210238i | −0.994460 | − | 0.105119i | \(-0.966478\pi\) | ||
0.994460 | − | 0.105119i | \(-0.0335224\pi\) | |||||||
\(728\) | 30.5573 | − | 9.92866i | 0.0419743 | − | 0.0136383i | ||||
\(729\) | 89.3808 | 0.122607 | ||||||||
\(730\) | −497.676 | + | 361.583i | −0.681748 | + | 0.495319i | ||||
\(731\) | 47.9709i | 0.0656237i | ||||||||
\(732\) | −378.269 | − | 122.907i | −0.516761 | − | 0.167906i | ||||
\(733\) | −761.286 | −1.03859 | −0.519295 | − | 0.854595i | \(-0.673805\pi\) | ||||
−0.519295 | + | 0.854595i | \(0.673805\pi\) | |||||||
\(734\) | 608.152 | + | 837.049i | 0.828544 | + | 1.14039i | ||||
\(735\) | − | 198.718i | − | 0.270364i | ||||||
\(736\) | − | 515.679i | − | 0.700650i | ||||||
\(737\) | −159.619 | −0.216580 | ||||||||
\(738\) | −366.705 | + | 266.427i | −0.496890 | + | 0.361012i | ||||
\(739\) | − | 183.975i | − | 0.248951i | −0.992223 | − | 0.124476i | \(-0.960275\pi\) | ||
0.992223 | − | 0.124476i | \(-0.0397249\pi\) | |||||||
\(740\) | 72.8591 | − | 224.237i | 0.0984583 | − | 0.303023i | ||||
\(741\) | 16.8916 | 0.0227957 | ||||||||
\(742\) | −216.393 | − | 297.840i | −0.291635 | − | 0.401401i | ||||
\(743\) | 495.247i | 0.666551i | 0.942830 | + | 0.333275i | \(0.108154\pi\) | ||||
−0.942830 | + | 0.333275i | \(0.891846\pi\) | |||||||
\(744\) | −446.217 | − | 1373.31i | −0.599754 | − | 1.84585i | ||||
\(745\) | 297.331 | 0.399102 | ||||||||
\(746\) | 142.961 | − | 103.867i | 0.191636 | − | 0.139232i | ||||
\(747\) | − | 116.235i | − | 0.155602i | ||||||
\(748\) | −163.226 | − | 53.0353i | −0.218217 | − | 0.0709029i | ||||
\(749\) | −1030.13 | −1.37534 | ||||||||
\(750\) | −50.0000 | − | 68.8191i | −0.0666667 | − | 0.0917588i | ||||
\(751\) | 800.059i | 1.06533i | 0.846328 | + | 0.532663i | \(0.178809\pi\) | ||||
−0.846328 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(752\) | −332.433 | + | 457.555i | −0.442066 | + | 0.608451i | ||||
\(753\) | 841.378 | 1.11737 | ||||||||
\(754\) | −5.30495 | + | 3.85427i | −0.00703574 | + | 0.00511177i | ||||
\(755\) | − | 338.140i | − | 0.447868i | ||||||
\(756\) | 141.115 | − | 434.306i | 0.186659 | − | 0.574479i | ||||
\(757\) | −276.367 | −0.365082 | −0.182541 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182541 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(758\) | −22.7276 | − | 31.2818i | −0.0299836 | − | 0.0412689i | ||||
\(759\) | 110.111i | 0.145073i | ||||||||
\(760\) | 160.000 | − | 51.9872i | 0.210526 | − | 0.0684041i | ||||
\(761\) | 891.207 | 1.17110 | 0.585550 | − | 0.810636i | \(-0.300879\pi\) | ||||
0.585550 | + | 0.810636i | \(0.300879\pi\) | |||||||
\(762\) | −11.3638 | + | 8.25627i | −0.0149131 | + | 0.0108350i | ||||
\(763\) | 1679.77i | 2.20154i | ||||||||
\(764\) | −1232.93 | − | 400.604i | −1.61379 | − | 0.524351i | ||||
\(765\) | 292.302 | 0.382094 | ||||||||
\(766\) | 507.390 | + | 698.363i | 0.662389 | + | 0.911700i | ||||
\(767\) | 34.8740i | 0.0454681i | ||||||||
\(768\) | −926.217 | + | 300.946i | −1.20601 | + | 0.391857i | ||||
\(769\) | −835.430 | −1.08639 | −0.543193 | − | 0.839608i | \(-0.682785\pi\) | ||||
−0.543193 | + | 0.839608i | \(0.682785\pi\) | |||||||
\(770\) | −55.2786 | + | 40.1623i | −0.0717904 | + | 0.0521588i | ||||
\(771\) | − | 977.898i | − | 1.26835i | ||||||
\(772\) | 224.689 | − | 691.521i | 0.291048 | − | 0.895753i | ||||
\(773\) | 213.522 | 0.276225 | 0.138112 | − | 0.990417i | \(-0.455897\pi\) | ||||
0.138112 | + | 0.990417i | \(0.455897\pi\) | |||||||
\(774\) | −12.9180 | − | 17.7800i | −0.0166899 | − | 0.0229716i | ||||
\(775\) | 237.234i | 0.306109i | ||||||||
\(776\) | −96.8266 | − | 298.002i | −0.124777 | − | 0.384023i | ||||
\(777\) | 853.050 | 1.09788 | ||||||||
\(778\) | 479.512 | − | 348.386i | 0.616339 | − | 0.447796i | ||||
\(779\) | 389.503i | 0.500004i | ||||||||
\(780\) | 15.2786 | + | 4.96433i | 0.0195880 | + | 0.00636453i | ||||
\(781\) | 70.7926 | 0.0906436 | ||||||||
\(782\) | −452.551 | − | 622.883i | −0.578710 | − | 0.796526i | ||||
\(783\) | 93.1976i | 0.119026i | ||||||||
\(784\) | 302.387 | + | 219.697i | 0.385698 | + | 0.280226i | ||||
\(785\) | −82.1703 | −0.104676 | ||||||||
\(786\) | 1388.71 | − | 1008.96i | 1.76681 | − | 1.28366i | ||||
\(787\) | − | 370.182i | − | 0.470371i | −0.971951 | − | 0.235185i | \(-0.924430\pi\) | ||
0.971951 | − | 0.235185i | \(-0.0755697\pi\) | |||||||
\(788\) | 173.698 | − | 534.588i | 0.220429 | − | 0.678411i | ||||
\(789\) | 624.531 | 0.791547 | ||||||||
\(790\) | 298.885 | + | 411.381i | 0.378336 | + | 0.520735i | ||||
\(791\) | − | 691.397i | − | 0.874080i | ||||||
\(792\) | 74.7802 | − | 24.2976i | 0.0944194 | − | 0.0306787i | ||||
\(793\) | −12.3406 | −0.0155619 | ||||||||
\(794\) | 139.459 | − | 101.323i | 0.175641 | − | 0.127611i | ||||
\(795\) | − | 184.075i | − | 0.231541i | ||||||
\(796\) | 640.000 | + | 207.949i | 0.804020 | + | 0.261242i | ||||
\(797\) | 274.426 | 0.344323 | 0.172162 | − | 0.985069i | \(-0.444925\pi\) | ||||
0.172162 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(798\) | 357.771 | + | 492.429i | 0.448334 | + | 0.617079i | ||||
\(799\) | 844.414i | 1.05684i | ||||||||
\(800\) | 160.000 | 0.200000 | ||||||||
\(801\) | −369.056 | −0.460744 | ||||||||
\(802\) | −716.784 | + | 520.774i | −0.893746 | + | 0.649344i | ||||
\(803\) | 247.063i | 0.307675i | ||||||||
\(804\) | −417.889 | + | 1286.13i | −0.519762 | + | 1.59966i | ||||
\(805\) | −306.525 | −0.380776 | ||||||||
\(806\) | −26.3344 | − | 36.2461i | −0.0326729 | − | 0.0449704i | ||||
\(807\) | − | 134.956i | − | 0.167232i | ||||||
\(808\) | 246.938 | + | 759.997i | 0.305616 | + | 0.940591i | ||||
\(809\) | 665.214 | 0.822266 | 0.411133 | − | 0.911575i | \(-0.365133\pi\) | ||||
0.411133 | + | 0.911575i | \(0.365133\pi\) | |||||||
\(810\) | 362.907 | − | 263.667i | 0.448033 | − | 0.325515i | ||||
\(811\) | − | 360.665i | − | 0.444717i | −0.974965 | − | 0.222358i | \(-0.928624\pi\) | ||
0.974965 | − | 0.222358i | \(-0.0713755\pi\) | |||||||
\(812\) | −224.721 | − | 73.0164i | −0.276750 | − | 0.0899217i | ||||
\(813\) | −1137.27 | −1.39886 | ||||||||
\(814\) | −55.6594 | − | 76.6086i | −0.0683777 | − | 0.0941138i | ||||
\(815\) | 677.202i | 0.830923i | ||||||||
\(816\) | −854.663 | + | 1176.34i | −1.04738 | + | 1.44160i | ||||
\(817\) | −18.8854 | −0.0231156 | ||||||||
\(818\) | −102.600 | + | 74.5432i | −0.125428 | + | 0.0911286i | ||||
\(819\) | 21.9773i | 0.0268344i | ||||||||
\(820\) | −114.472 | + | 352.309i | −0.139600 | + | 0.429645i | ||||
\(821\) | −666.899 | −0.812301 | −0.406151 | − | 0.913806i | \(-0.633129\pi\) | ||||
−0.406151 | + | 0.913806i | \(0.633129\pi\) | |||||||
\(822\) | 236.276 | + | 325.205i | 0.287440 | + | 0.395627i | ||||
\(823\) | − | 122.433i | − | 0.148764i | −0.997230 | − | 0.0743822i | \(-0.976302\pi\) | ||
0.997230 | − | 0.0743822i | \(-0.0236985\pi\) | |||||||
\(824\) | 272.170 | − | 88.4335i | 0.330304 | − | 0.107322i | ||||
\(825\) | −34.1641 | −0.0414110 | ||||||||
\(826\) | −1016.66 | + | 738.644i | −1.23082 | + | 0.894242i | ||||
\(827\) | 1532.98i | 1.85366i | 0.375477 | + | 0.926832i | \(0.377479\pi\) | ||||
−0.375477 | + | 0.926832i | \(0.622521\pi\) | |||||||
\(828\) | 335.469 | + | 109.000i | 0.405156 | + | 0.131643i | ||||
\(829\) | −195.475 | −0.235796 | −0.117898 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117898 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(830\) | −55.8359 | − | 76.8516i | −0.0672722 | − | 0.0925922i | ||||
\(831\) | − | 1739.47i | − | 2.09322i | ||||||
\(832\) | −24.4458 | + | 17.7609i | −0.0293820 | + | 0.0213473i | ||||
\(833\) | 558.053 | 0.669931 | ||||||||
\(834\) | −774.663 | + | 562.825i | −0.928852 | + | 0.674850i | ||||
\(835\) | 222.229i | 0.266143i | ||||||||
\(836\) | 20.8792 | − | 64.2597i | 0.0249752 | − | 0.0768656i | ||||
\(837\) | −636.774 | −0.760781 | ||||||||
\(838\) | 512.170 | + | 704.942i | 0.611182 | + | 0.841219i | ||||
\(839\) | − | 1325.97i | − | 1.58041i | −0.612840 | − | 0.790207i | \(-0.709973\pi\) | ||
0.612840 | − | 0.790207i | \(-0.290027\pi\) | |||||||
\(840\) | 178.885 | + | 550.553i | 0.212959 | + | 0.655420i | ||||
\(841\) | −792.777 | −0.942660 | ||||||||
\(842\) | 943.171 | − | 685.254i | 1.12016 | − | 0.813841i | ||||
\(843\) | − | 21.4532i | − | 0.0254487i | ||||||
\(844\) | 357.390 | + | 116.123i | 0.423448 | + | 0.137587i | ||||
\(845\) | −377.397 | −0.446624 | ||||||||
\(846\) | −227.390 | − | 312.976i | −0.268783 | − | 0.369948i | ||||
\(847\) | − | 1001.85i | − | 1.18282i | ||||||
\(848\) | 280.105 | + | 203.508i | 0.330313 | + | 0.239986i | ||||
\(849\) | 646.407 | 0.761375 | ||||||||
\(850\) | 193.262 | − | 140.413i | 0.227368 | − | 0.165192i | ||||
\(851\) | − | 424.801i | − | 0.499179i | ||||||
\(852\) | 185.337 | − | 570.410i | 0.217532 | − | 0.669495i | ||||
\(853\) | 1055.28 | 1.23714 | 0.618570 | − | 0.785730i | \(-0.287712\pi\) | ||||
0.618570 | + | 0.785730i | \(0.287712\pi\) | |||||||
\(854\) | −261.378 | − | 359.756i | −0.306063 | − | 0.421259i | ||||
\(855\) | 115.075i | 0.134591i | ||||||||
\(856\) | 921.378 | − | 299.374i | 1.07638 | − | 0.349736i | ||||
\(857\) | 155.378 | 0.181304 | 0.0906521 | − | 0.995883i | \(-0.471105\pi\) | ||||
0.0906521 | + | 0.995883i | \(0.471105\pi\) | |||||||
\(858\) | 5.21981 | − | 3.79241i | 0.00608369 | − | 0.00442006i | ||||
\(859\) | 226.033i | 0.263136i | 0.991307 | + | 0.131568i | \(0.0420011\pi\) | ||||
−0.991307 | + | 0.131568i | \(0.957999\pi\) | |||||||
\(860\) | −17.0820 | − | 5.55029i | −0.0198628 | − | 0.00645383i | ||||
\(861\) | −1340.26 | −1.55664 | ||||||||
\(862\) | −441.876 | − | 608.190i | −0.512617 | − | 0.705557i | ||||
\(863\) | − | 930.702i | − | 1.07845i | −0.842162 | − | 0.539225i | \(-0.818717\pi\) | ||
0.842162 | − | 0.539225i | \(-0.181283\pi\) | |||||||
\(864\) | 429.465i | 0.497066i | ||||||||
\(865\) | −406.158 | −0.469547 | ||||||||
\(866\) | 595.702 | − | 432.803i | 0.687878 | − | 0.499772i | ||||
\(867\) | 1071.51i | 1.23588i | ||||||||
\(868\) | 498.885 | − | 1535.41i | 0.574753 | − | 1.76891i | ||||
\(869\) | 204.223 | 0.235009 | ||||||||
\(870\) | −69.4427 | − | 95.5797i | −0.0798192 | − | 0.109862i | ||||
\(871\) | 41.9584i | 0.0481727i | ||||||||
\(872\) | −488.170 | − | 1502.43i | −0.559828 | − | 1.72297i | ||||
\(873\) | 214.328 | 0.245508 | ||||||||
\(874\) | 245.220 | − | 178.163i | 0.280572 | − | 0.203847i | ||||
\(875\) | − | 95.1057i | − | 0.108692i | ||||||
\(876\) | 1990.70 | + | 646.819i | 2.27249 | + | 0.738377i | ||||
\(877\) | −33.5217 | −0.0382231 | −0.0191115 | − | 0.999817i | \(-0.506084\pi\) | ||||
−0.0191115 | + | 0.999817i | \(0.506084\pi\) | |||||||
\(878\) | −568.446 | − | 782.399i | −0.647433 | − | 0.891115i | ||||
\(879\) | − | 102.178i | − | 0.116244i | ||||||
\(880\) | 37.7709 | − | 51.9872i | 0.0429215 | − | 0.0590763i | ||||
\(881\) | −933.850 | −1.05999 | −0.529994 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(882\) | −206.838 | + | 150.276i | −0.234510 | + | 0.170382i | ||||
\(883\) | − | 542.308i | − | 0.614166i | −0.951683 | − | 0.307083i | \(-0.900647\pi\) | ||
0.951683 | − | 0.307083i | \(-0.0993529\pi\) | |||||||
\(884\) | −13.9412 | + | 42.9065i | −0.0157706 | + | 0.0485368i | ||||
\(885\) | −628.328 | −0.709975 | ||||||||
\(886\) | 328.197 | + | 451.724i | 0.370425 | + | 0.509846i | ||||
\(887\) | 714.720i | 0.805773i | 0.915250 | + | 0.402886i | \(0.131993\pi\) | ||||
−0.915250 | + | 0.402886i | \(0.868007\pi\) | |||||||
\(888\) | −762.991 | + | 247.911i | −0.859224 | + | 0.279179i | ||||
\(889\) | −15.7044 | −0.0176652 | ||||||||
\(890\) | −244.010 | + | 177.284i | −0.274169 | + | 0.199195i | ||||
\(891\) | − | 180.159i | − | 0.202199i | ||||||
\(892\) | 814.237 | + | 264.562i | 0.912822 | + | 0.296594i | ||||
\(893\) | −332.433 | −0.372266 | ||||||||
\(894\) | −594.663 | − | 818.483i | −0.665171 | − | 0.915529i | ||||
\(895\) | − | 583.407i | − | 0.651851i | ||||||
\(896\) | −1035.54 | − | 336.468i | −1.15574 | − | 0.375522i | ||||
\(897\) | 28.9443 | 0.0322679 | ||||||||
\(898\) | −1223.36 | + | 888.824i | −1.36232 | + | 0.989782i | ||||
\(899\) | 329.484i | 0.366500i | ||||||||
\(900\) | −33.8197 | + | 104.086i | −0.0375774 | + | 0.115651i | ||||
\(901\) | 516.932 | 0.573731 | ||||||||
\(902\) | 87.4489 | + | 120.363i | 0.0969500 | + | 0.133440i | ||||
\(903\) | − | 64.9839i | − | 0.0719645i | ||||||
\(904\) | 200.932 | + | 618.405i | 0.222270 | + | 0.684076i | ||||
\(905\) | 352.800 | 0.389835 | ||||||||
\(906\) | −930.820 | + | 676.281i | −1.02740 | + | 0.746447i | ||||
\(907\) | 347.233i | 0.382837i | 0.981509 | + | 0.191418i | \(0.0613087\pi\) | ||||
−0.981509 | + | 0.191418i | \(0.938691\pi\) | |||||||
\(908\) | −157.580 | − | 51.2010i | −0.173547 | − | 0.0563888i | ||||
\(909\) | −546.604 | −0.601324 | ||||||||
\(910\) | 10.5573 | + | 14.5309i | 0.0116014 | + | 0.0159680i | ||||
\(911\) | 1427.54i | 1.56701i | 0.621386 | + | 0.783504i | \(0.286570\pi\) | ||||
−0.621386 | + | 0.783504i | \(0.713430\pi\) | |||||||
\(912\) | −463.108 | − | 336.468i | −0.507794 | − | 0.368934i | ||||
\(913\) | −38.1517 | −0.0417871 | ||||||||
\(914\) | −462.227 | + | 335.827i | −0.505719 | + | 0.367426i | ||||
\(915\) | − | 222.341i | − | 0.242996i | ||||||
\(916\) | 90.5774 | − | 278.769i | 0.0988836 | − | 0.304332i | ||||
\(917\) | 1919.15 | 2.09286 | ||||||||
\(918\) | 376.892 | + | 518.747i | 0.410557 | + | 0.565084i | ||||
\(919\) | − | 569.162i | − | 0.619327i | −0.950846 | − | 0.309664i | \(-0.899784\pi\) | ||
0.950846 | − | 0.309664i | \(-0.100216\pi\) | |||||||
\(920\) | 274.164 | − | 89.0813i | 0.298004 | − | 0.0968275i | ||||
\(921\) | 449.017 | 0.487532 | ||||||||
\(922\) | 160.371 | − | 116.516i | 0.173938 | − | 0.126373i | ||||
\(923\) | − | 18.6089i | − | 0.0201614i | ||||||
\(924\) | 221.115 | + | 71.8445i | 0.239301 | + | 0.0777538i | ||||
\(925\) | 131.803 | 0.142490 | ||||||||
\(926\) | 741.319 | + | 1020.34i | 0.800560 | + | 1.10188i | ||||
\(927\) | 195.750i | 0.211165i | ||||||||
\(928\) | 222.217 | 0.239458 | ||||||||
\(929\) | 1535.96 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(930\) | 653.050 | − | 474.468i | 0.702204 | − | 0.510181i | ||||
\(931\) | 219.697i | 0.235980i | ||||||||
\(932\) | −379.534 | + | 1168.09i | −0.407225 | + | 1.25331i | ||||
\(933\) | −463.489 | −0.496773 | ||||||||
\(934\) | −583.094 | − | 802.561i | −0.624298 | − | 0.859273i | ||||
\(935\) | − | 95.9418i | − | 0.102612i | ||||||
\(936\) | −6.38699 | − | 19.6571i | −0.00682371 | − | 0.0210012i | ||||
\(937\) | 338.721 | 0.361496 | 0.180748 | − | 0.983529i | \(-0.442148\pi\) | ||||
0.180748 | + | 0.983529i | \(0.442148\pi\) | |||||||
\(938\) | −1223.18 | + | 888.693i | −1.30403 | + | 0.947434i | ||||
\(939\) | 835.210i | 0.889468i | ||||||||
\(940\) | −300.689 | − | 97.6997i | −0.319882 | − | 0.103936i | ||||
\(941\) | 1439.77 | 1.53004 | 0.765022 | − | 0.644004i | \(-0.222728\pi\) | ||||
0.765022 | + | 0.644004i | \(0.222728\pi\) | |||||||
\(942\) | 164.341 | + | 226.195i | 0.174459 | + | 0.240123i | ||||
\(943\) | 667.424i | 0.707766i | ||||||||
\(944\) | 694.663 | − | 956.121i | 0.735871 | − | 1.01284i | ||||
\(945\) | 255.279 | 0.270136 | ||||||||
\(946\) | −5.83592 | + | 4.24005i | −0.00616905 | + | 0.00448208i | ||||
\(947\) | 656.135i | 0.692856i | 0.938077 | + | 0.346428i | \(0.112606\pi\) | ||||
−0.938077 | + | 0.346428i | \(0.887394\pi\) | |||||||
\(948\) | 534.663 | − | 1645.52i | 0.563990 | − | 1.73578i | ||||
\(949\) | 64.9443 | 0.0684344 | ||||||||
\(950\) | 55.2786 | + | 76.0845i | 0.0581880 | + | 0.0800890i | ||||
\(951\) | 1395.62i | 1.46752i | ||||||||
\(952\) | −1546.10 | + | 502.358i | −1.62405 | + | 0.527687i | ||||
\(953\) | 436.675 | 0.458211 | 0.229105 | − | 0.973402i | \(-0.426420\pi\) | ||||
0.229105 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(954\) | −191.597 | + | 139.203i | −0.200835 | + | 0.145915i | ||||
\(955\) | − | 724.699i | − | 0.758847i | ||||||
\(956\) | −163.226 | − | 53.0353i | −0.170739 | − | 0.0554763i | ||||
\(957\) | −47.4489 | −0.0495809 | ||||||||
\(958\) | −680.762 | − | 936.988i | −0.710607 | − | 0.978067i | ||||
\(959\) | 449.423i | 0.468637i | ||||||||
\(960\) | −320.000 | − | 440.442i | −0.333333 | − | 0.458794i | ||||
\(961\) | −1290.20 | −1.34256 | ||||||||
\(962\) | −20.1378 | + | 14.6309i | −0.0209332 | + | 0.0152089i | ||||
\(963\) | 662.671i | 0.688132i | ||||||||
\(964\) | −166.971 | + | 513.883i | −0.173206 | + | 0.533073i | ||||
\(965\) | 406.466 | 0.421208 | ||||||||
\(966\) | 613.050 | + | 843.790i | 0.634627 | + | 0.873489i | ||||
\(967\) | − | 903.436i | − | 0.934267i | −0.884187 | − | 0.467133i | \(-0.845287\pi\) | ||
0.884187 | − | 0.467133i | \(-0.154713\pi\) | |||||||
\(968\) | 291.153 | + | 896.078i | 0.300778 | + | 0.925700i | ||||
\(969\) | −854.663 | −0.882005 | ||||||||
\(970\) | 141.708 | − | 102.957i | 0.146091 | − | 0.106141i | ||||
\(971\) | − | 1866.89i | − | 1.92265i | −0.275420 | − | 0.961324i | \(-0.588817\pi\) | ||
0.275420 | − | 0.961324i | \(-0.411183\pi\) | |||||||
\(972\) | −992.125 | − | 322.361i | −1.02071 | − | 0.331647i | ||||
\(973\) | −1070.56 | −1.10026 | ||||||||
\(974\) | −736.334 | − | 1013.48i | −0.755990 | − | 1.04053i | ||||
\(975\) | 8.98056i | 0.00921083i | ||||||||
\(976\) | 338.334 | + | 245.814i | 0.346654 | + | 0.251859i | ||||
\(977\) | −1073.95 | −1.09923 | −0.549615 | − | 0.835418i | \(-0.685226\pi\) | ||||
−0.549615 | + | 0.835418i | \(0.685226\pi\) | |||||||
\(978\) | 1864.18 | − | 1354.40i | 1.90611 | − | 1.38487i | ||||
\(979\) | 121.135i | 0.123733i | ||||||||
\(980\) | −64.5673 | + | 198.718i | −0.0658850 | + | 0.202773i | ||||
\(981\) | 1080.58 | 1.10151 | ||||||||
\(982\) | −26.2167 | − | 36.0842i | −0.0266973 | − | 0.0367456i | ||||
\(983\) | 534.114i | 0.543351i | 0.962389 | + | 0.271675i | \(0.0875777\pi\) | ||||
−0.962389 | + | 0.271675i | \(0.912422\pi\) | |||||||
\(984\) | 1198.77 | − | 389.503i | 1.21826 | − | 0.395837i | ||||
\(985\) | 314.223 | 0.319008 | ||||||||
\(986\) | 268.413 | − | 195.014i | 0.272224 | − | 0.197783i | ||||
\(987\) | − | 1143.89i | − | 1.15895i | ||||||
\(988\) | −16.8916 | − | 5.48843i | −0.0170968 | − | 0.00555509i | ||||
\(989\) | −32.3607 | −0.0327206 | ||||||||
\(990\) | 25.8359 | + | 35.5601i | 0.0260969 | + | 0.0359193i | ||||
\(991\) | 520.419i | 0.525146i | 0.964912 | + | 0.262573i | \(0.0845710\pi\) | ||||
−0.964912 | + | 0.262573i | \(0.915429\pi\) | |||||||
\(992\) | 1518.30i | 1.53054i | ||||||||
\(993\) | 619.502 | 0.623869 | ||||||||
\(994\) | 542.492 | − | 394.144i | 0.545767 | − | 0.396523i | ||||
\(995\) | 376.183i | 0.378073i | ||||||||
\(996\) | −99.8823 | + | 307.406i | −0.100283 | + | 0.308641i | ||||
\(997\) | 457.680 | 0.459057 | 0.229528 | − | 0.973302i | \(-0.426282\pi\) | ||||
0.229528 | + | 0.973302i | \(0.426282\pi\) | |||||||
\(998\) | −737.508 | − | 1015.09i | −0.738986 | − | 1.01713i | ||||
\(999\) | 353.781i | 0.354135i |
(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 | 20.3.b.a.11.2 | yes | 4 | |
3.2 | odd | 2 | 180.3.c.a.91.3 | 4 | |||
4.3 | odd | 2 | inner | 20.3.b.a.11.1 | ✓ | 4 | |
5.2 | odd | 4 | 100.3.d.b.99.3 | 8 | |||
5.3 | odd | 4 | 100.3.d.b.99.6 | 8 | |||
5.4 | even | 2 | 100.3.b.f.51.3 | 4 | |||
8.3 | odd | 2 | 320.3.b.c.191.4 | 4 | |||
8.5 | even | 2 | 320.3.b.c.191.1 | 4 | |||
12.11 | even | 2 | 180.3.c.a.91.4 | 4 | |||
15.2 | even | 4 | 900.3.f.e.199.6 | 8 | |||
15.8 | even | 4 | 900.3.f.e.199.3 | 8 | |||
15.14 | odd | 2 | 900.3.c.k.451.2 | 4 | |||
16.3 | odd | 4 | 1280.3.g.e.1151.7 | 8 | |||
16.5 | even | 4 | 1280.3.g.e.1151.8 | 8 | |||
16.11 | odd | 4 | 1280.3.g.e.1151.2 | 8 | |||
16.13 | even | 4 | 1280.3.g.e.1151.1 | 8 | |||
20.3 | even | 4 | 100.3.d.b.99.4 | 8 | |||
20.7 | even | 4 | 100.3.d.b.99.5 | 8 | |||
20.19 | odd | 2 | 100.3.b.f.51.4 | 4 | |||
24.5 | odd | 2 | 2880.3.e.e.2431.3 | 4 | |||
24.11 | even | 2 | 2880.3.e.e.2431.4 | 4 | |||
40.3 | even | 4 | 1600.3.h.n.1599.2 | 8 | |||
40.13 | odd | 4 | 1600.3.h.n.1599.7 | 8 | |||
40.19 | odd | 2 | 1600.3.b.s.1151.1 | 4 | |||
40.27 | even | 4 | 1600.3.h.n.1599.8 | 8 | |||
40.29 | even | 2 | 1600.3.b.s.1151.4 | 4 | |||
40.37 | odd | 4 | 1600.3.h.n.1599.1 | 8 | |||
60.23 | odd | 4 | 900.3.f.e.199.5 | 8 | |||
60.47 | odd | 4 | 900.3.f.e.199.4 | 8 | |||
60.59 | even | 2 | 900.3.c.k.451.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.b.a.11.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
20.3.b.a.11.2 | yes | 4 | 1.1 | even | 1 | trivial | |
100.3.b.f.51.3 | 4 | 5.4 | even | 2 | |||
100.3.b.f.51.4 | 4 | 20.19 | odd | 2 | |||
100.3.d.b.99.3 | 8 | 5.2 | odd | 4 | |||
100.3.d.b.99.4 | 8 | 20.3 | even | 4 | |||
100.3.d.b.99.5 | 8 | 20.7 | even | 4 | |||
100.3.d.b.99.6 | 8 | 5.3 | odd | 4 | |||
180.3.c.a.91.3 | 4 | 3.2 | odd | 2 | |||
180.3.c.a.91.4 | 4 | 12.11 | even | 2 | |||
320.3.b.c.191.1 | 4 | 8.5 | even | 2 | |||
320.3.b.c.191.4 | 4 | 8.3 | odd | 2 | |||
900.3.c.k.451.1 | 4 | 60.59 | even | 2 | |||
900.3.c.k.451.2 | 4 | 15.14 | odd | 2 | |||
900.3.f.e.199.3 | 8 | 15.8 | even | 4 | |||
900.3.f.e.199.4 | 8 | 60.47 | odd | 4 | |||
900.3.f.e.199.5 | 8 | 60.23 | odd | 4 | |||
900.3.f.e.199.6 | 8 | 15.2 | even | 4 | |||
1280.3.g.e.1151.1 | 8 | 16.13 | even | 4 | |||
1280.3.g.e.1151.2 | 8 | 16.11 | odd | 4 | |||
1280.3.g.e.1151.7 | 8 | 16.3 | odd | 4 | |||
1280.3.g.e.1151.8 | 8 | 16.5 | even | 4 | |||
1600.3.b.s.1151.1 | 4 | 40.19 | odd | 2 | |||
1600.3.b.s.1151.4 | 4 | 40.29 | even | 2 | |||
1600.3.h.n.1599.1 | 8 | 40.37 | odd | 4 | |||
1600.3.h.n.1599.2 | 8 | 40.3 | even | 4 | |||
1600.3.h.n.1599.7 | 8 | 40.13 | odd | 4 | |||
1600.3.h.n.1599.8 | 8 | 40.27 | even | 4 | |||
2880.3.e.e.2431.3 | 4 | 24.5 | odd | 2 | |||
2880.3.e.e.2431.4 | 4 | 24.11 | even | 2 |