Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,3,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (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: | \(9.64580135835\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.2 | ||
Root | \(-4.74052 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.3.d.a.235.12 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −4.74052 | −0.948104 | −0.474052 | − | 0.880497i | \(-0.657209\pi\) | ||||
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 12.4076 | 1.77252 | 0.886259 | − | 0.463191i | \(-0.153296\pi\) | ||||
0.886259 | + | 0.463191i | \(0.153296\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 6.70411i | 0.670411i | ||||||||
\(11\) | − | 1.77650i | − | 0.161500i | −0.996734 | − | 0.0807500i | \(-0.974268\pi\) | ||
0.996734 | − | 0.0807500i | \(-0.0257315\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | − | 3.41653i | − | 0.262810i | −0.991329 | − | 0.131405i | \(-0.958051\pi\) | ||
0.991329 | − | 0.131405i | \(-0.0419488\pi\) | |||||||
\(14\) | − | 17.5470i | − | 1.25336i | ||||||
\(15\) | 8.21082 | 0.547388 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −5.78514 | −0.340302 | −0.170151 | − | 0.985418i | \(-0.554426\pi\) | ||||
−0.170151 | + | 0.985418i | \(0.554426\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 10.5232 | 0.553852 | 0.276926 | − | 0.960891i | \(-0.410684\pi\) | ||||
0.276926 | + | 0.960891i | \(0.410684\pi\) | |||||||
\(20\) | 9.48104 | 0.474052 | ||||||||
\(21\) | −21.4906 | −1.02336 | ||||||||
\(22\) | −2.51235 | −0.114198 | ||||||||
\(23\) | − | 41.0431i | − | 1.78448i | −0.451560 | − | 0.892241i | \(-0.649132\pi\) | ||
0.451560 | − | 0.892241i | \(-0.350868\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | −2.52748 | −0.101099 | ||||||||
\(26\) | −4.83170 | −0.185835 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −24.8152 | −0.886259 | ||||||||
\(29\) | −33.6345 | −1.15981 | −0.579905 | − | 0.814684i | \(-0.696911\pi\) | ||||
−0.579905 | + | 0.814684i | \(0.696911\pi\) | |||||||
\(30\) | − | 11.6119i | − | 0.387062i | ||||||
\(31\) | − | 46.9951i | − | 1.51597i | −0.652272 | − | 0.757985i | \(-0.726184\pi\) | ||
0.652272 | − | 0.757985i | \(-0.273816\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 3.07699i | 0.0932420i | ||||||||
\(34\) | 8.18142i | 0.240630i | ||||||||
\(35\) | −58.8186 | −1.68053 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 41.9921i | − | 1.13492i | −0.823400 | − | 0.567461i | \(-0.807926\pi\) | ||
0.823400 | − | 0.567461i | \(-0.192074\pi\) | |||||||
\(38\) | − | 14.8820i | − | 0.391632i | ||||||
\(39\) | 5.91760i | 0.151733i | ||||||||
\(40\) | − | 13.4082i | − | 0.335205i | ||||||
\(41\) | 23.8134 | 0.580815 | 0.290408 | − | 0.956903i | \(-0.406209\pi\) | ||||
0.290408 | + | 0.956903i | \(0.406209\pi\) | |||||||
\(42\) | 30.3923i | 0.723627i | ||||||||
\(43\) | − | 1.60072i | − | 0.0372260i | −0.999827 | − | 0.0186130i | \(-0.994075\pi\) | ||
0.999827 | − | 0.0186130i | \(-0.00592504\pi\) | |||||||
\(44\) | 3.55300i | 0.0807500i | ||||||||
\(45\) | −14.2216 | −0.316035 | ||||||||
\(46\) | −58.0437 | −1.26182 | ||||||||
\(47\) | − | 6.39642i | − | 0.136094i | −0.997682 | − | 0.0680470i | \(-0.978323\pi\) | ||
0.997682 | − | 0.0680470i | \(-0.0216768\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 104.949 | 2.14182 | ||||||||
\(50\) | 3.57439i | 0.0714879i | ||||||||
\(51\) | 10.0202 | 0.196474 | ||||||||
\(52\) | 6.83305i | 0.131405i | ||||||||
\(53\) | −2.92135 | −0.0551198 | −0.0275599 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275599 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 8.42153i | 0.153119i | ||||||||
\(56\) | 35.0940i | 0.626679i | ||||||||
\(57\) | −18.2267 | −0.319766 | ||||||||
\(58\) | 47.5664i | 0.820110i | ||||||||
\(59\) | 48.0608 | + | 34.2223i | 0.814589 | + | 0.580038i | ||||
\(60\) | −16.4216 | −0.273694 | ||||||||
\(61\) | − | 10.8622i | − | 0.178069i | −0.996029 | − | 0.0890346i | \(-0.971622\pi\) | ||
0.996029 | − | 0.0890346i | \(-0.0283782\pi\) | |||||||
\(62\) | −66.4611 | −1.07195 | ||||||||
\(63\) | 37.2229 | 0.590839 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 16.1961i | 0.249171i | ||||||||
\(66\) | 4.35152 | 0.0659321 | ||||||||
\(67\) | 40.9681i | 0.611464i | 0.952118 | + | 0.305732i | \(0.0989011\pi\) | ||||
−0.952118 | + | 0.305732i | \(0.901099\pi\) | |||||||
\(68\) | 11.5703 | 0.170151 | ||||||||
\(69\) | 71.0887i | 1.03027i | ||||||||
\(70\) | 83.1820i | 1.18831i | ||||||||
\(71\) | −30.6899 | −0.432253 | −0.216126 | − | 0.976365i | \(-0.569342\pi\) | ||||
−0.216126 | + | 0.976365i | \(0.569342\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | − | 118.342i | − | 1.62112i | −0.585655 | − | 0.810561i | \(-0.699162\pi\) | ||
0.585655 | − | 0.810561i | \(-0.300838\pi\) | |||||||
\(74\) | −59.3858 | −0.802511 | ||||||||
\(75\) | 4.37772 | 0.0583696 | ||||||||
\(76\) | −21.0464 | −0.276926 | ||||||||
\(77\) | − | 22.0421i | − | 0.286261i | ||||||
\(78\) | 8.36875 | 0.107292 | ||||||||
\(79\) | 62.0124 | 0.784968 | 0.392484 | − | 0.919759i | \(-0.371616\pi\) | ||||
0.392484 | + | 0.919759i | \(0.371616\pi\) | |||||||
\(80\) | −18.9621 | −0.237026 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 33.6773i | − | 0.410699i | ||||||
\(83\) | − | 57.1672i | − | 0.688762i | −0.938830 | − | 0.344381i | \(-0.888089\pi\) | ||
0.938830 | − | 0.344381i | \(-0.111911\pi\) | |||||||
\(84\) | 42.9813 | 0.511682 | ||||||||
\(85\) | 27.4246 | 0.322642 | ||||||||
\(86\) | −2.26376 | −0.0263227 | ||||||||
\(87\) | 58.2567 | 0.669617 | ||||||||
\(88\) | 5.02470 | 0.0570989 | ||||||||
\(89\) | − | 96.6560i | − | 1.08602i | −0.839725 | − | 0.543011i | \(-0.817284\pi\) | ||
0.839725 | − | 0.543011i | \(-0.182716\pi\) | |||||||
\(90\) | 20.1123i | 0.223470i | ||||||||
\(91\) | − | 42.3910i | − | 0.465835i | ||||||
\(92\) | 82.0862i | 0.892241i | ||||||||
\(93\) | 81.3978i | 0.875246i | ||||||||
\(94\) | −9.04590 | −0.0962330 | ||||||||
\(95\) | −49.8853 | −0.525109 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 73.5083i | 0.757817i | 0.925434 | + | 0.378909i | \(0.123701\pi\) | ||||
−0.925434 | + | 0.378909i | \(0.876299\pi\) | |||||||
\(98\) | − | 148.420i | − | 1.51449i | ||||||
\(99\) | − | 5.32950i | − | 0.0538333i | ||||||
\(100\) | 5.05496 | 0.0505496 | ||||||||
\(101\) | − | 126.711i | − | 1.25456i | −0.778794 | − | 0.627280i | \(-0.784168\pi\) | ||
0.778794 | − | 0.627280i | \(-0.215832\pi\) | |||||||
\(102\) | − | 14.1706i | − | 0.138928i | ||||||
\(103\) | 140.694i | 1.36596i | 0.730438 | + | 0.682979i | \(0.239316\pi\) | ||||
−0.730438 | + | 0.682979i | \(0.760684\pi\) | |||||||
\(104\) | 9.66339 | 0.0929173 | ||||||||
\(105\) | 101.877 | 0.970255 | ||||||||
\(106\) | 4.13141i | 0.0389756i | ||||||||
\(107\) | −76.3548 | −0.713597 | −0.356798 | − | 0.934181i | \(-0.616132\pi\) | ||||
−0.356798 | + | 0.934181i | \(0.616132\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 160.557i | 1.47300i | 0.676439 | + | 0.736499i | \(0.263522\pi\) | ||||
−0.676439 | + | 0.736499i | \(0.736478\pi\) | |||||||
\(110\) | 11.9098 | 0.108271 | ||||||||
\(111\) | 72.7325i | 0.655248i | ||||||||
\(112\) | 49.6305 | 0.443129 | ||||||||
\(113\) | − | 59.5527i | − | 0.527015i | −0.964657 | − | 0.263508i | \(-0.915121\pi\) | ||
0.964657 | − | 0.263508i | \(-0.0848794\pi\) | |||||||
\(114\) | 25.7764i | 0.226109i | ||||||||
\(115\) | 194.565i | 1.69187i | ||||||||
\(116\) | 67.2690 | 0.579905 | ||||||||
\(117\) | − | 10.2496i | − | 0.0876032i | ||||||
\(118\) | 48.3976 | − | 67.9682i | 0.410149 | − | 0.576002i | ||||
\(119\) | −71.7798 | −0.603192 | ||||||||
\(120\) | 23.2237i | 0.193531i | ||||||||
\(121\) | 117.844 | 0.973918 | ||||||||
\(122\) | −15.3615 | −0.125914 | ||||||||
\(123\) | −41.2461 | −0.335334 | ||||||||
\(124\) | 93.9901i | 0.757985i | ||||||||
\(125\) | 130.495 | 1.04396 | ||||||||
\(126\) | − | 52.6411i | − | 0.417786i | ||||||
\(127\) | −19.7373 | −0.155412 | −0.0777058 | − | 0.996976i | \(-0.524759\pi\) | ||||
−0.0777058 | + | 0.996976i | \(0.524759\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 2.77252i | 0.0214924i | ||||||||
\(130\) | 22.9048 | 0.176190 | ||||||||
\(131\) | − | 22.2772i | − | 0.170055i | −0.996379 | − | 0.0850276i | \(-0.972902\pi\) | ||
0.996379 | − | 0.0850276i | \(-0.0270979\pi\) | |||||||
\(132\) | − | 6.15398i | − | 0.0466210i | ||||||
\(133\) | 130.568 | 0.981712 | ||||||||
\(134\) | 57.9376 | 0.432370 | ||||||||
\(135\) | 24.6325 | 0.182463 | ||||||||
\(136\) | − | 16.3628i | − | 0.120315i | ||||||
\(137\) | 103.894 | 0.758353 | 0.379176 | − | 0.925324i | \(-0.376207\pi\) | ||||
0.379176 | + | 0.925324i | \(0.376207\pi\) | |||||||
\(138\) | 100.535 | 0.728512 | ||||||||
\(139\) | −92.2479 | −0.663654 | −0.331827 | − | 0.943340i | \(-0.607665\pi\) | ||||
−0.331827 | + | 0.943340i | \(0.607665\pi\) | |||||||
\(140\) | 117.637 | 0.840265 | ||||||||
\(141\) | 11.0789i | 0.0785739i | ||||||||
\(142\) | 43.4021i | 0.305649i | ||||||||
\(143\) | −6.06946 | −0.0424438 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 159.445 | 1.09962 | ||||||||
\(146\) | −167.361 | −1.14631 | ||||||||
\(147\) | −181.777 | −1.23658 | ||||||||
\(148\) | 83.9843i | 0.567461i | ||||||||
\(149\) | 264.023i | 1.77196i | 0.463719 | + | 0.885982i | \(0.346515\pi\) | ||||
−0.463719 | + | 0.885982i | \(0.653485\pi\) | |||||||
\(150\) | − | 6.19103i | − | 0.0412736i | ||||||
\(151\) | − | 102.361i | − | 0.677886i | −0.940807 | − | 0.338943i | \(-0.889931\pi\) | ||
0.940807 | − | 0.338943i | \(-0.110069\pi\) | |||||||
\(152\) | 29.7641i | 0.195816i | ||||||||
\(153\) | −17.3554 | −0.113434 | ||||||||
\(154\) | −31.1723 | −0.202417 | ||||||||
\(155\) | 222.781i | 1.43730i | ||||||||
\(156\) | − | 11.8352i | − | 0.0758666i | ||||||
\(157\) | − | 198.566i | − | 1.26475i | −0.774662 | − | 0.632375i | \(-0.782080\pi\) | ||
0.774662 | − | 0.632375i | \(-0.217920\pi\) | |||||||
\(158\) | − | 87.6988i | − | 0.555056i | ||||||
\(159\) | 5.05993 | 0.0318234 | ||||||||
\(160\) | 26.8164i | 0.167603i | ||||||||
\(161\) | − | 509.247i | − | 3.16302i | ||||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | −143.430 | −0.879941 | −0.439970 | − | 0.898012i | \(-0.645011\pi\) | ||||
−0.439970 | + | 0.898012i | \(0.645011\pi\) | |||||||
\(164\) | −47.6269 | −0.290408 | ||||||||
\(165\) | − | 14.5865i | − | 0.0884031i | ||||||
\(166\) | −80.8467 | −0.487028 | ||||||||
\(167\) | 9.22359 | 0.0552311 | 0.0276155 | − | 0.999619i | \(-0.491209\pi\) | ||||
0.0276155 | + | 0.999619i | \(0.491209\pi\) | |||||||
\(168\) | − | 60.7847i | − | 0.361814i | ||||||
\(169\) | 157.327 | 0.930931 | ||||||||
\(170\) | − | 38.7842i | − | 0.228142i | ||||||
\(171\) | 31.5695 | 0.184617 | ||||||||
\(172\) | 3.20143i | 0.0186130i | ||||||||
\(173\) | − | 20.9989i | − | 0.121381i | −0.998157 | − | 0.0606903i | \(-0.980670\pi\) | ||
0.998157 | − | 0.0606903i | \(-0.0193302\pi\) | |||||||
\(174\) | − | 82.3874i | − | 0.473491i | ||||||
\(175\) | −31.3600 | −0.179200 | ||||||||
\(176\) | − | 7.10600i | − | 0.0403750i | ||||||
\(177\) | −83.2437 | − | 59.2747i | −0.470303 | − | 0.334885i | ||||
\(178\) | −136.692 | −0.767934 | ||||||||
\(179\) | 226.280i | 1.26413i | 0.774914 | + | 0.632067i | \(0.217793\pi\) | ||||
−0.774914 | + | 0.632067i | \(0.782207\pi\) | |||||||
\(180\) | 28.4431 | 0.158017 | ||||||||
\(181\) | −201.036 | −1.11070 | −0.555349 | − | 0.831618i | \(-0.687415\pi\) | ||||
−0.555349 | + | 0.831618i | \(0.687415\pi\) | |||||||
\(182\) | −59.9499 | −0.329395 | ||||||||
\(183\) | 18.8139i | 0.102808i | ||||||||
\(184\) | 116.087 | 0.630910 | ||||||||
\(185\) | 199.065i | 1.07602i | ||||||||
\(186\) | 115.114 | 0.618892 | ||||||||
\(187\) | 10.2773i | 0.0549588i | ||||||||
\(188\) | 12.7928i | 0.0680470i | ||||||||
\(189\) | −64.4719 | −0.341121 | ||||||||
\(190\) | 70.5485i | 0.371308i | ||||||||
\(191\) | 1.70993i | 0.00895250i | 0.999990 | + | 0.00447625i | \(0.00142484\pi\) | ||||
−0.999990 | + | 0.00447625i | \(0.998575\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 49.8788 | 0.258440 | 0.129220 | − | 0.991616i | \(-0.458753\pi\) | ||||
0.129220 | + | 0.991616i | \(0.458753\pi\) | |||||||
\(194\) | 103.956 | 0.535858 | ||||||||
\(195\) | − | 28.0525i | − | 0.143859i | ||||||
\(196\) | −209.898 | −1.07091 | ||||||||
\(197\) | 146.114 | 0.741694 | 0.370847 | − | 0.928694i | \(-0.379067\pi\) | ||||
0.370847 | + | 0.928694i | \(0.379067\pi\) | |||||||
\(198\) | −7.53705 | −0.0380659 | ||||||||
\(199\) | −372.185 | −1.87027 | −0.935137 | − | 0.354286i | \(-0.884724\pi\) | ||||
−0.935137 | + | 0.354286i | \(0.884724\pi\) | |||||||
\(200\) | − | 7.14879i | − | 0.0357439i | ||||||
\(201\) | − | 70.9588i | − | 0.353029i | ||||||
\(202\) | −179.196 | −0.887108 | ||||||||
\(203\) | −417.324 | −2.05578 | ||||||||
\(204\) | −20.0403 | −0.0982368 | ||||||||
\(205\) | −112.888 | −0.550673 | ||||||||
\(206\) | 198.971 | 0.965878 | ||||||||
\(207\) | − | 123.129i | − | 0.594827i | ||||||
\(208\) | − | 13.6661i | − | 0.0657024i | ||||||
\(209\) | − | 18.6944i | − | 0.0894470i | ||||||
\(210\) | − | 144.075i | − | 0.686074i | ||||||
\(211\) | 155.113i | 0.735131i | 0.929998 | + | 0.367566i | \(0.119809\pi\) | ||||
−0.929998 | + | 0.367566i | \(0.880191\pi\) | |||||||
\(212\) | 5.84270 | 0.0275599 | ||||||||
\(213\) | 53.1565 | 0.249561 | ||||||||
\(214\) | 107.982i | 0.504589i | ||||||||
\(215\) | 7.58823i | 0.0352941i | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | − | 583.097i | − | 2.68708i | ||||||
\(218\) | 227.061 | 1.04157 | ||||||||
\(219\) | 204.974i | 0.935955i | ||||||||
\(220\) | − | 16.8431i | − | 0.0765594i | ||||||
\(221\) | 19.7651i | 0.0894347i | ||||||||
\(222\) | 102.859 | 0.463330 | ||||||||
\(223\) | 425.113 | 1.90634 | 0.953169 | − | 0.302439i | \(-0.0978010\pi\) | ||||
0.953169 | + | 0.302439i | \(0.0978010\pi\) | |||||||
\(224\) | − | 70.1881i | − | 0.313340i | ||||||
\(225\) | −7.58244 | −0.0336997 | ||||||||
\(226\) | −84.2202 | −0.372656 | ||||||||
\(227\) | 140.065i | 0.617028i | 0.951220 | + | 0.308514i | \(0.0998317\pi\) | ||||
−0.951220 | + | 0.308514i | \(0.900168\pi\) | |||||||
\(228\) | 36.4534 | 0.159883 | ||||||||
\(229\) | 433.918i | 1.89484i | 0.319998 | + | 0.947418i | \(0.396318\pi\) | ||||
−0.319998 | + | 0.947418i | \(0.603682\pi\) | |||||||
\(230\) | 275.157 | 1.19634 | ||||||||
\(231\) | 38.1781i | 0.165273i | ||||||||
\(232\) | − | 95.1328i | − | 0.410055i | ||||||
\(233\) | 271.351i | 1.16460i | 0.812975 | + | 0.582298i | \(0.197846\pi\) | ||||
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(234\) | −14.4951 | −0.0619448 | ||||||||
\(235\) | 30.3224i | 0.129031i | ||||||||
\(236\) | −96.1215 | − | 68.4445i | −0.407295 | − | 0.290019i | ||||
\(237\) | −107.409 | −0.453201 | ||||||||
\(238\) | 101.512i | 0.426521i | ||||||||
\(239\) | −213.395 | −0.892866 | −0.446433 | − | 0.894817i | \(-0.647306\pi\) | ||||
−0.446433 | + | 0.894817i | \(0.647306\pi\) | |||||||
\(240\) | 32.8433 | 0.136847 | ||||||||
\(241\) | −53.4060 | −0.221602 | −0.110801 | − | 0.993843i | \(-0.535342\pi\) | ||||
−0.110801 | + | 0.993843i | \(0.535342\pi\) | |||||||
\(242\) | − | 166.657i | − | 0.688664i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 21.7244i | 0.0890346i | ||||||||
\(245\) | −497.513 | −2.03066 | ||||||||
\(246\) | 58.3308i | 0.237117i | ||||||||
\(247\) | − | 35.9527i | − | 0.145558i | ||||||
\(248\) | 132.922 | 0.535976 | ||||||||
\(249\) | 99.0166i | 0.397657i | ||||||||
\(250\) | − | 184.547i | − | 0.738189i | ||||||
\(251\) | −426.149 | −1.69780 | −0.848902 | − | 0.528550i | \(-0.822736\pi\) | ||||
−0.848902 | + | 0.528550i | \(0.822736\pi\) | |||||||
\(252\) | −74.4457 | −0.295420 | ||||||||
\(253\) | −72.9130 | −0.288194 | ||||||||
\(254\) | 27.9127i | 0.109893i | ||||||||
\(255\) | −47.5007 | −0.186277 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 434.787 | 1.69178 | 0.845890 | − | 0.533358i | \(-0.179070\pi\) | ||||
0.845890 | + | 0.533358i | \(0.179070\pi\) | |||||||
\(258\) | 3.92094 | 0.0151974 | ||||||||
\(259\) | − | 521.022i | − | 2.01167i | ||||||
\(260\) | − | 32.3922i | − | 0.124585i | ||||||
\(261\) | −100.904 | −0.386604 | ||||||||
\(262\) | −31.5048 | −0.120247 | ||||||||
\(263\) | 90.5138 | 0.344159 | 0.172080 | − | 0.985083i | \(-0.444951\pi\) | ||||
0.172080 | + | 0.985083i | \(0.444951\pi\) | |||||||
\(264\) | −8.70304 | −0.0329660 | ||||||||
\(265\) | 13.8487 | 0.0522593 | ||||||||
\(266\) | − | 184.651i | − | 0.694175i | ||||||
\(267\) | 167.413i | 0.627015i | ||||||||
\(268\) | − | 81.9361i | − | 0.305732i | ||||||
\(269\) | − | 458.484i | − | 1.70440i | −0.523216 | − | 0.852200i | \(-0.675268\pi\) | ||
0.523216 | − | 0.852200i | \(-0.324732\pi\) | |||||||
\(270\) | − | 34.8356i | − | 0.129021i | ||||||
\(271\) | 76.4145 | 0.281972 | 0.140986 | − | 0.990012i | \(-0.454973\pi\) | ||||
0.140986 | + | 0.990012i | \(0.454973\pi\) | |||||||
\(272\) | −23.1406 | −0.0850756 | ||||||||
\(273\) | 73.4233i | 0.268950i | ||||||||
\(274\) | − | 146.929i | − | 0.536236i | ||||||
\(275\) | 4.49006i | 0.0163275i | ||||||||
\(276\) | − | 142.177i | − | 0.515135i | ||||||
\(277\) | −321.427 | −1.16039 | −0.580193 | − | 0.814479i | \(-0.697023\pi\) | ||||
−0.580193 | + | 0.814479i | \(0.697023\pi\) | |||||||
\(278\) | 130.458i | 0.469274i | ||||||||
\(279\) | − | 140.985i | − | 0.505323i | ||||||
\(280\) | − | 166.364i | − | 0.594157i | ||||||
\(281\) | 30.4551 | 0.108381 | 0.0541906 | − | 0.998531i | \(-0.482742\pi\) | ||||
0.0541906 | + | 0.998531i | \(0.482742\pi\) | |||||||
\(282\) | 15.6680 | 0.0555602 | ||||||||
\(283\) | − | 410.231i | − | 1.44958i | −0.688971 | − | 0.724789i | \(-0.741937\pi\) | ||
0.688971 | − | 0.724789i | \(-0.258063\pi\) | |||||||
\(284\) | 61.3799 | 0.216126 | ||||||||
\(285\) | 86.4040 | 0.303172 | ||||||||
\(286\) | 8.58351i | 0.0300123i | ||||||||
\(287\) | 295.468 | 1.02951 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −255.532 | −0.884194 | ||||||||
\(290\) | − | 225.489i | − | 0.777550i | ||||||
\(291\) | − | 127.320i | − | 0.437526i | ||||||
\(292\) | 236.684i | 0.810561i | ||||||||
\(293\) | −196.579 | −0.670917 | −0.335458 | − | 0.942055i | \(-0.608891\pi\) | ||||
−0.335458 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(294\) | 257.072i | 0.874393i | ||||||||
\(295\) | −227.833 | − | 162.231i | −0.772315 | − | 0.549937i | ||||
\(296\) | 118.772 | 0.401256 | ||||||||
\(297\) | 9.23096i | 0.0310807i | ||||||||
\(298\) | 373.385 | 1.25297 | ||||||||
\(299\) | −140.225 | −0.468979 | ||||||||
\(300\) | −8.75544 | −0.0291848 | ||||||||
\(301\) | − | 19.8611i | − | 0.0659837i | ||||||
\(302\) | −144.760 | −0.479338 | ||||||||
\(303\) | 219.469i | 0.724320i | ||||||||
\(304\) | 42.0927 | 0.138463 | ||||||||
\(305\) | 51.4925i | 0.168828i | ||||||||
\(306\) | 24.5443i | 0.0802100i | ||||||||
\(307\) | 362.671 | 1.18134 | 0.590669 | − | 0.806914i | \(-0.298864\pi\) | ||||
0.590669 | + | 0.806914i | \(0.298864\pi\) | |||||||
\(308\) | 44.0843i | 0.143131i | ||||||||
\(309\) | − | 243.689i | − | 0.788636i | ||||||
\(310\) | 315.060 | 1.01632 | ||||||||
\(311\) | −30.0272 | −0.0965506 | −0.0482753 | − | 0.998834i | \(-0.515372\pi\) | ||||
−0.0482753 | + | 0.998834i | \(0.515372\pi\) | |||||||
\(312\) | −16.7375 | −0.0536458 | ||||||||
\(313\) | 145.855i | 0.465992i | 0.972478 | + | 0.232996i | \(0.0748529\pi\) | ||||
−0.972478 | + | 0.232996i | \(0.925147\pi\) | |||||||
\(314\) | −280.814 | −0.894313 | ||||||||
\(315\) | −176.456 | −0.560177 | ||||||||
\(316\) | −124.025 | −0.392484 | ||||||||
\(317\) | 567.000 | 1.78864 | 0.894322 | − | 0.447424i | \(-0.147659\pi\) | ||||
0.894322 | + | 0.447424i | \(0.147659\pi\) | |||||||
\(318\) | − | 7.15582i | − | 0.0225026i | ||||||
\(319\) | 59.7517i | 0.187309i | ||||||||
\(320\) | 37.9242 | 0.118513 | ||||||||
\(321\) | 132.250 | 0.411995 | ||||||||
\(322\) | −720.184 | −2.23660 | ||||||||
\(323\) | −60.8781 | −0.188477 | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 8.63520i | 0.0265698i | ||||||||
\(326\) | 202.841i | 0.622212i | ||||||||
\(327\) | − | 278.092i | − | 0.850435i | ||||||
\(328\) | 67.3546i | 0.205349i | ||||||||
\(329\) | − | 79.3644i | − | 0.241229i | ||||||
\(330\) | −20.6285 | −0.0625105 | ||||||||
\(331\) | 251.778 | 0.760659 | 0.380329 | − | 0.924851i | \(-0.375811\pi\) | ||||
0.380329 | + | 0.924851i | \(0.375811\pi\) | |||||||
\(332\) | 114.334i | 0.344381i | ||||||||
\(333\) | − | 125.976i | − | 0.378308i | ||||||
\(334\) | − | 13.0441i | − | 0.0390543i | ||||||
\(335\) | − | 194.210i | − | 0.579731i | ||||||
\(336\) | −85.9625 | −0.255841 | ||||||||
\(337\) | 446.903i | 1.32612i | 0.748566 | + | 0.663060i | \(0.230743\pi\) | ||||
−0.748566 | + | 0.663060i | \(0.769257\pi\) | |||||||
\(338\) | − | 222.494i | − | 0.658268i | ||||||
\(339\) | 103.148i | 0.304272i | ||||||||
\(340\) | −54.8491 | −0.161321 | ||||||||
\(341\) | −83.4867 | −0.244829 | ||||||||
\(342\) | − | 44.6461i | − | 0.130544i | ||||||
\(343\) | 694.194 | 2.02389 | ||||||||
\(344\) | 4.52751 | 0.0131614 | ||||||||
\(345\) | − | 336.997i | − | 0.976804i | ||||||
\(346\) | −29.6969 | −0.0858291 | ||||||||
\(347\) | 619.129i | 1.78423i | 0.451804 | + | 0.892117i | \(0.350781\pi\) | ||||
−0.451804 | + | 0.892117i | \(0.649219\pi\) | |||||||
\(348\) | −116.513 | −0.334809 | ||||||||
\(349\) | − | 475.410i | − | 1.36221i | −0.732187 | − | 0.681104i | \(-0.761500\pi\) | ||
0.732187 | − | 0.681104i | \(-0.238500\pi\) | |||||||
\(350\) | 44.3497i | 0.126714i | ||||||||
\(351\) | 17.7528i | 0.0505777i | ||||||||
\(352\) | −10.0494 | −0.0285494 | ||||||||
\(353\) | 584.466i | 1.65571i | 0.560941 | + | 0.827856i | \(0.310439\pi\) | ||||
−0.560941 | + | 0.827856i | \(0.689561\pi\) | |||||||
\(354\) | −83.8271 | + | 117.724i | −0.236800 | + | 0.332555i | ||||
\(355\) | 145.486 | 0.409820 | ||||||||
\(356\) | 193.312i | 0.543011i | ||||||||
\(357\) | 124.326 | 0.348253 | ||||||||
\(358\) | 320.008 | 0.893878 | ||||||||
\(359\) | 458.625 | 1.27751 | 0.638753 | − | 0.769411i | \(-0.279450\pi\) | ||||
0.638753 | + | 0.769411i | \(0.279450\pi\) | |||||||
\(360\) | − | 40.2246i | − | 0.111735i | ||||||
\(361\) | −250.263 | −0.693248 | ||||||||
\(362\) | 284.308i | 0.785381i | ||||||||
\(363\) | −204.112 | −0.562292 | ||||||||
\(364\) | 84.7819i | 0.232917i | ||||||||
\(365\) | 561.002i | 1.53699i | ||||||||
\(366\) | 26.6069 | 0.0726964 | ||||||||
\(367\) | − | 320.755i | − | 0.873991i | −0.899464 | − | 0.436996i | \(-0.856043\pi\) | ||
0.899464 | − | 0.436996i | \(-0.143957\pi\) | |||||||
\(368\) | − | 164.172i | − | 0.446120i | ||||||
\(369\) | 71.4403 | 0.193605 | ||||||||
\(370\) | 281.520 | 0.760864 | ||||||||
\(371\) | −36.2470 | −0.0977008 | ||||||||
\(372\) | − | 162.796i | − | 0.437623i | ||||||
\(373\) | 338.130 | 0.906514 | 0.453257 | − | 0.891380i | \(-0.350262\pi\) | ||||
0.453257 | + | 0.891380i | \(0.350262\pi\) | |||||||
\(374\) | 14.5343 | 0.0388617 | ||||||||
\(375\) | −226.023 | −0.602728 | ||||||||
\(376\) | 18.0918 | 0.0481165 | ||||||||
\(377\) | 114.913i | 0.304810i | ||||||||
\(378\) | 91.1770i | 0.241209i | ||||||||
\(379\) | 174.618 | 0.460735 | 0.230367 | − | 0.973104i | \(-0.426007\pi\) | ||||
0.230367 | + | 0.973104i | \(0.426007\pi\) | |||||||
\(380\) | 99.7707 | 0.262554 | ||||||||
\(381\) | 34.1859 | 0.0897269 | ||||||||
\(382\) | 2.41820 | 0.00633038 | ||||||||
\(383\) | 633.347 | 1.65365 | 0.826824 | − | 0.562461i | \(-0.190145\pi\) | ||||
0.826824 | + | 0.562461i | \(0.190145\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 104.491i | 0.271406i | ||||||||
\(386\) | − | 70.5393i | − | 0.182744i | ||||||
\(387\) | − | 4.80215i | − | 0.0124087i | ||||||
\(388\) | − | 147.017i | − | 0.378909i | ||||||
\(389\) | 4.33499 | 0.0111439 | 0.00557196 | − | 0.999984i | \(-0.498226\pi\) | ||||
0.00557196 | + | 0.999984i | \(0.498226\pi\) | |||||||
\(390\) | −39.6722 | −0.101724 | ||||||||
\(391\) | 237.440i | 0.607263i | ||||||||
\(392\) | 296.841i | 0.757247i | ||||||||
\(393\) | 38.5853i | 0.0981814i | ||||||||
\(394\) | − | 206.636i | − | 0.524457i | ||||||
\(395\) | −293.971 | −0.744231 | ||||||||
\(396\) | 10.6590i | 0.0269167i | ||||||||
\(397\) | − | 52.4426i | − | 0.132097i | −0.997816 | − | 0.0660486i | \(-0.978961\pi\) | ||
0.997816 | − | 0.0660486i | \(-0.0210392\pi\) | |||||||
\(398\) | 526.348i | 1.32248i | ||||||||
\(399\) | −226.150 | −0.566791 | ||||||||
\(400\) | −10.1099 | −0.0252748 | ||||||||
\(401\) | − | 395.028i | − | 0.985108i | −0.870282 | − | 0.492554i | \(-0.836063\pi\) | ||
0.870282 | − | 0.492554i | \(-0.163937\pi\) | |||||||
\(402\) | −100.351 | −0.249629 | ||||||||
\(403\) | −160.560 | −0.398412 | ||||||||
\(404\) | 253.421i | 0.627280i | ||||||||
\(405\) | −42.6647 | −0.105345 | ||||||||
\(406\) | 590.186i | 1.45366i | ||||||||
\(407\) | −74.5990 | −0.183290 | ||||||||
\(408\) | 28.3413i | 0.0694639i | ||||||||
\(409\) | 390.371i | 0.954451i | 0.878781 | + | 0.477226i | \(0.158358\pi\) | ||||
−0.878781 | + | 0.477226i | \(0.841642\pi\) | |||||||
\(410\) | 159.648i | 0.389385i | ||||||||
\(411\) | −179.950 | −0.437835 | ||||||||
\(412\) | − | 281.387i | − | 0.682979i | ||||||
\(413\) | 596.320 | + | 424.617i | 1.44387 | + | 1.02813i | ||||
\(414\) | −174.131 | −0.420606 | ||||||||
\(415\) | 271.002i | 0.653018i | ||||||||
\(416\) | −19.3268 | −0.0464586 | ||||||||
\(417\) | 159.778 | 0.383161 | ||||||||
\(418\) | −26.4379 | −0.0632486 | ||||||||
\(419\) | 11.6755i | 0.0278651i | 0.999903 | + | 0.0139325i | \(0.00443501\pi\) | ||||
−0.999903 | + | 0.0139325i | \(0.995565\pi\) | |||||||
\(420\) | −203.753 | −0.485127 | ||||||||
\(421\) | − | 404.443i | − | 0.960673i | −0.877084 | − | 0.480337i | \(-0.840514\pi\) | ||
0.877084 | − | 0.480337i | \(-0.159486\pi\) | |||||||
\(422\) | 219.362 | 0.519816 | ||||||||
\(423\) | − | 19.1893i | − | 0.0453647i | ||||||
\(424\) | − | 8.26282i | − | 0.0194878i | ||||||
\(425\) | 14.6218 | 0.0344043 | ||||||||
\(426\) | − | 75.1747i | − | 0.176466i | ||||||
\(427\) | − | 134.774i | − | 0.315631i | ||||||
\(428\) | 152.710 | 0.356798 | ||||||||
\(429\) | 10.5126 | 0.0245049 | ||||||||
\(430\) | 10.7314 | 0.0249567 | ||||||||
\(431\) | 195.172i | 0.452835i | 0.974030 | + | 0.226418i | \(0.0727014\pi\) | ||||
−0.974030 | + | 0.226418i | \(0.927299\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | −327.408 | −0.756139 | −0.378070 | − | 0.925777i | \(-0.623412\pi\) | ||||
−0.378070 | + | 0.925777i | \(0.623412\pi\) | |||||||
\(434\) | −824.624 | −1.90005 | ||||||||
\(435\) | −276.167 | −0.634867 | ||||||||
\(436\) | − | 321.113i | − | 0.736499i | ||||||
\(437\) | − | 431.904i | − | 0.988338i | ||||||
\(438\) | 289.877 | 0.661820 | ||||||||
\(439\) | −366.054 | −0.833836 | −0.416918 | − | 0.908944i | \(-0.636890\pi\) | ||||
−0.416918 | + | 0.908944i | \(0.636890\pi\) | |||||||
\(440\) | −23.8197 | −0.0541356 | ||||||||
\(441\) | 314.847 | 0.713939 | ||||||||
\(442\) | 27.9520 | 0.0632399 | ||||||||
\(443\) | 620.656i | 1.40103i | 0.713638 | + | 0.700514i | \(0.247046\pi\) | ||||
−0.713638 | + | 0.700514i | \(0.752954\pi\) | |||||||
\(444\) | − | 145.465i | − | 0.327624i | ||||||
\(445\) | 458.200i | 1.02966i | ||||||||
\(446\) | − | 601.201i | − | 1.34798i | ||||||
\(447\) | − | 457.301i | − | 1.02304i | ||||||
\(448\) | −99.2610 | −0.221565 | ||||||||
\(449\) | −251.128 | −0.559304 | −0.279652 | − | 0.960101i | \(-0.590219\pi\) | ||||
−0.279652 | + | 0.960101i | \(0.590219\pi\) | |||||||
\(450\) | 10.7232i | 0.0238293i | ||||||||
\(451\) | − | 42.3046i | − | 0.0938017i | ||||||
\(452\) | 119.105i | 0.263508i | ||||||||
\(453\) | 177.294i | 0.391378i | ||||||||
\(454\) | 198.082 | 0.436305 | ||||||||
\(455\) | 200.955i | 0.441660i | ||||||||
\(456\) | − | 51.5529i | − | 0.113055i | ||||||
\(457\) | − | 524.698i | − | 1.14814i | −0.818808 | − | 0.574068i | \(-0.805365\pi\) | ||
0.818808 | − | 0.574068i | \(-0.194635\pi\) | |||||||
\(458\) | 613.652 | 1.33985 | ||||||||
\(459\) | 30.0605 | 0.0654912 | ||||||||
\(460\) | − | 389.131i | − | 0.845937i | ||||||
\(461\) | 455.129 | 0.987265 | 0.493632 | − | 0.869671i | \(-0.335669\pi\) | ||||
0.493632 | + | 0.869671i | \(0.335669\pi\) | |||||||
\(462\) | 53.9920 | 0.116866 | ||||||||
\(463\) | 692.510i | 1.49570i | 0.663867 | + | 0.747851i | \(0.268914\pi\) | ||||
−0.663867 | + | 0.747851i | \(0.731086\pi\) | |||||||
\(464\) | −134.538 | −0.289953 | ||||||||
\(465\) | − | 385.868i | − | 0.829824i | ||||||
\(466\) | 383.748 | 0.823494 | ||||||||
\(467\) | 418.310i | 0.895738i | 0.894099 | + | 0.447869i | \(0.147817\pi\) | ||||
−0.894099 | + | 0.447869i | \(0.852183\pi\) | |||||||
\(468\) | 20.4992i | 0.0438016i | ||||||||
\(469\) | 508.316i | 1.08383i | ||||||||
\(470\) | 42.8823 | 0.0912389 | ||||||||
\(471\) | 343.926i | 0.730204i | ||||||||
\(472\) | −96.7952 | + | 135.936i | −0.205075 | + | 0.288001i | ||||
\(473\) | −2.84367 | −0.00601199 | ||||||||
\(474\) | 151.899i | 0.320462i | ||||||||
\(475\) | −26.5971 | −0.0559939 | ||||||||
\(476\) | 143.560 | 0.301596 | ||||||||
\(477\) | −8.76405 | −0.0183733 | ||||||||
\(478\) | 301.786i | 0.631352i | ||||||||
\(479\) | 389.623 | 0.813410 | 0.406705 | − | 0.913560i | \(-0.366678\pi\) | ||||
0.406705 | + | 0.913560i | \(0.366678\pi\) | |||||||
\(480\) | − | 46.4474i | − | 0.0967654i | ||||||
\(481\) | −143.467 | −0.298269 | ||||||||
\(482\) | 75.5275i | 0.156696i | ||||||||
\(483\) | 882.042i | 1.82617i | ||||||||
\(484\) | −235.688 | −0.486959 | ||||||||
\(485\) | − | 348.467i | − | 0.718489i | ||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −667.023 | −1.36966 | −0.684829 | − | 0.728704i | \(-0.740123\pi\) | ||||
−0.684829 | + | 0.728704i | \(0.740123\pi\) | |||||||
\(488\) | 30.7230 | 0.0629569 | ||||||||
\(489\) | 248.429 | 0.508034 | ||||||||
\(490\) | 703.589i | 1.43590i | ||||||||
\(491\) | −276.799 | −0.563746 | −0.281873 | − | 0.959452i | \(-0.590956\pi\) | ||||
−0.281873 | + | 0.959452i | \(0.590956\pi\) | |||||||
\(492\) | 82.4922 | 0.167667 | ||||||||
\(493\) | 194.580 | 0.394686 | ||||||||
\(494\) | −50.8448 | −0.102925 | ||||||||
\(495\) | 25.2646i | 0.0510396i | ||||||||
\(496\) | − | 187.980i | − | 0.378992i | ||||||
\(497\) | −380.789 | −0.766175 | ||||||||
\(498\) | 140.031 | 0.281186 | ||||||||
\(499\) | 573.362 | 1.14902 | 0.574511 | − | 0.818497i | \(-0.305192\pi\) | ||||
0.574511 | + | 0.818497i | \(0.305192\pi\) | |||||||
\(500\) | −260.989 | −0.521978 | ||||||||
\(501\) | −15.9757 | −0.0318877 | ||||||||
\(502\) | 602.666i | 1.20053i | ||||||||
\(503\) | − | 31.1451i | − | 0.0619186i | −0.999521 | − | 0.0309593i | \(-0.990144\pi\) | ||
0.999521 | − | 0.0309593i | \(-0.00985623\pi\) | |||||||
\(504\) | 105.282i | 0.208893i | ||||||||
\(505\) | 600.674i | 1.18945i | ||||||||
\(506\) | 103.115i | 0.203784i | ||||||||
\(507\) | −272.499 | −0.537473 | ||||||||
\(508\) | 39.4745 | 0.0777058 | ||||||||
\(509\) | − | 392.968i | − | 0.772038i | −0.922491 | − | 0.386019i | \(-0.873850\pi\) | ||
0.922491 | − | 0.386019i | \(-0.126150\pi\) | |||||||
\(510\) | 67.1762i | 0.131718i | ||||||||
\(511\) | − | 1468.34i | − | 2.87347i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −54.6801 | −0.106589 | ||||||||
\(514\) | − | 614.882i | − | 1.19627i | ||||||
\(515\) | − | 666.961i | − | 1.29507i | ||||||
\(516\) | − | 5.54504i | − | 0.0107462i | ||||||
\(517\) | −11.3632 | −0.0219792 | ||||||||
\(518\) | −736.837 | −1.42247 | ||||||||
\(519\) | 36.3711i | 0.0700792i | ||||||||
\(520\) | −45.8095 | −0.0880952 | ||||||||
\(521\) | 688.699 | 1.32188 | 0.660939 | − | 0.750439i | \(-0.270158\pi\) | ||||
0.660939 | + | 0.750439i | \(0.270158\pi\) | |||||||
\(522\) | 142.699i | 0.273370i | ||||||||
\(523\) | 511.550 | 0.978106 | 0.489053 | − | 0.872254i | \(-0.337342\pi\) | ||||
0.489053 | + | 0.872254i | \(0.337342\pi\) | |||||||
\(524\) | 44.5545i | 0.0850276i | ||||||||
\(525\) | 54.3171 | 0.103461 | ||||||||
\(526\) | − | 128.006i | − | 0.243357i | ||||||
\(527\) | 271.873i | 0.515888i | ||||||||
\(528\) | 12.3080i | 0.0233105i | ||||||||
\(529\) | −1155.53 | −2.18437 | ||||||||
\(530\) | − | 19.5850i | − | 0.0369529i | ||||||
\(531\) | 144.182 | + | 102.667i | 0.271530 | + | 0.193346i | ||||
\(532\) | −261.135 | −0.490856 | ||||||||
\(533\) | − | 81.3592i | − | 0.152644i | ||||||
\(534\) | 236.758 | 0.443367 | ||||||||
\(535\) | 361.962 | 0.676564 | ||||||||
\(536\) | −115.875 | −0.216185 | ||||||||
\(537\) | − | 391.928i | − | 0.729848i | ||||||
\(538\) | −648.394 | −1.20519 | ||||||||
\(539\) | − | 186.442i | − | 0.345903i | ||||||
\(540\) | −49.2649 | −0.0912313 | ||||||||
\(541\) | − | 17.5878i | − | 0.0325098i | −0.999868 | − | 0.0162549i | \(-0.994826\pi\) | ||
0.999868 | − | 0.0162549i | \(-0.00517432\pi\) | |||||||
\(542\) | − | 108.066i | − | 0.199384i | ||||||
\(543\) | 348.205 | 0.641261 | ||||||||
\(544\) | 32.7257i | 0.0601575i | ||||||||
\(545\) | − | 761.122i | − | 1.39655i | ||||||
\(546\) | 103.836 | 0.190176 | ||||||||
\(547\) | −397.445 | −0.726590 | −0.363295 | − | 0.931674i | \(-0.618348\pi\) | ||||
−0.363295 | + | 0.931674i | \(0.618348\pi\) | |||||||
\(548\) | −207.789 | −0.379176 | ||||||||
\(549\) | − | 32.5866i | − | 0.0593564i | ||||||
\(550\) | 6.34991 | 0.0115453 | ||||||||
\(551\) | −353.942 | −0.642363 | ||||||||
\(552\) | −201.069 | −0.364256 | ||||||||
\(553\) | 769.427 | 1.39137 | ||||||||
\(554\) | 454.567i | 0.820517i | ||||||||
\(555\) | − | 344.790i | − | 0.621243i | ||||||
\(556\) | 184.496 | 0.331827 | ||||||||
\(557\) | 427.468 | 0.767448 | 0.383724 | − | 0.923448i | \(-0.374641\pi\) | ||||
0.383724 | + | 0.923448i | \(0.374641\pi\) | |||||||
\(558\) | −199.383 | −0.357318 | ||||||||
\(559\) | −5.46889 | −0.00978334 | ||||||||
\(560\) | −235.274 | −0.420133 | ||||||||
\(561\) | − | 17.8008i | − | 0.0317305i | ||||||
\(562\) | − | 43.0700i | − | 0.0766370i | ||||||
\(563\) | − | 712.655i | − | 1.26582i | −0.774227 | − | 0.632908i | \(-0.781861\pi\) | ||
0.774227 | − | 0.632908i | \(-0.218139\pi\) | |||||||
\(564\) | − | 22.1578i | − | 0.0392870i | ||||||
\(565\) | 282.311i | 0.499665i | ||||||||
\(566\) | −580.154 | −1.02501 | ||||||||
\(567\) | 111.669 | 0.196946 | ||||||||
\(568\) | − | 86.8043i | − | 0.152824i | ||||||
\(569\) | 104.521i | 0.183693i | 0.995773 | + | 0.0918465i | \(0.0292769\pi\) | ||||
−0.995773 | + | 0.0918465i | \(0.970723\pi\) | |||||||
\(570\) | − | 122.194i | − | 0.214375i | ||||||
\(571\) | − | 691.173i | − | 1.21046i | −0.796050 | − | 0.605231i | \(-0.793081\pi\) | ||
0.796050 | − | 0.605231i | \(-0.206919\pi\) | |||||||
\(572\) | 12.1389 | 0.0212219 | ||||||||
\(573\) | − | 2.96168i | − | 0.00516873i | ||||||
\(574\) | − | 417.855i | − | 0.727970i | ||||||
\(575\) | 103.735i | 0.180410i | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 133.428 | 0.231244 | 0.115622 | − | 0.993293i | \(-0.463114\pi\) | ||||
0.115622 | + | 0.993293i | \(0.463114\pi\) | |||||||
\(578\) | 361.377i | 0.625220i | ||||||||
\(579\) | −86.3927 | −0.149210 | ||||||||
\(580\) | −318.890 | −0.549811 | ||||||||
\(581\) | − | 709.309i | − | 1.22084i | ||||||
\(582\) | −180.058 | −0.309378 | ||||||||
\(583\) | 5.18978i | 0.00890185i | ||||||||
\(584\) | 334.721 | 0.573153 | ||||||||
\(585\) | 48.5883i | 0.0830570i | ||||||||
\(586\) | 278.004i | 0.474410i | ||||||||
\(587\) | − | 244.215i | − | 0.416039i | −0.978125 | − | 0.208020i | \(-0.933298\pi\) | ||
0.978125 | − | 0.208020i | \(-0.0667018\pi\) | |||||||
\(588\) | 363.554 | 0.618289 | ||||||||
\(589\) | − | 494.538i | − | 0.839623i | ||||||
\(590\) | −229.430 | + | 322.204i | −0.388864 | + | 0.546109i | ||||
\(591\) | −253.077 | −0.428217 | ||||||||
\(592\) | − | 167.969i | − | 0.283731i | ||||||
\(593\) | 474.801 | 0.800677 | 0.400338 | − | 0.916367i | \(-0.368893\pi\) | ||||
0.400338 | + | 0.916367i | \(0.368893\pi\) | |||||||
\(594\) | 13.0546 | 0.0219774 | ||||||||
\(595\) | 340.273 | 0.571888 | ||||||||
\(596\) | − | 528.045i | − | 0.885982i | ||||||
\(597\) | 644.643 | 1.07980 | ||||||||
\(598\) | 198.308i | 0.331618i | ||||||||
\(599\) | −314.784 | −0.525515 | −0.262758 | − | 0.964862i | \(-0.584632\pi\) | ||||
−0.262758 | + | 0.964862i | \(0.584632\pi\) | |||||||
\(600\) | 12.3821i | 0.0206368i | ||||||||
\(601\) | − | 353.585i | − | 0.588327i | −0.955755 | − | 0.294164i | \(-0.904959\pi\) | ||
0.955755 | − | 0.294164i | \(-0.0950410\pi\) | |||||||
\(602\) | −28.0878 | −0.0466575 | ||||||||
\(603\) | 122.904i | 0.203821i | ||||||||
\(604\) | 204.722i | 0.338943i | ||||||||
\(605\) | −558.642 | −0.923375 | ||||||||
\(606\) | 310.376 | 0.512172 | ||||||||
\(607\) | 495.558 | 0.816406 | 0.408203 | − | 0.912891i | \(-0.366156\pi\) | ||||
0.408203 | + | 0.912891i | \(0.366156\pi\) | |||||||
\(608\) | − | 59.5281i | − | 0.0979081i | ||||||
\(609\) | 722.827 | 1.18691 | ||||||||
\(610\) | 72.8215 | 0.119379 | ||||||||
\(611\) | −21.8535 | −0.0357668 | ||||||||
\(612\) | 34.7108 | 0.0567170 | ||||||||
\(613\) | 81.5110i | 0.132971i | 0.997787 | + | 0.0664853i | \(0.0211785\pi\) | ||||
−0.997787 | + | 0.0664853i | \(0.978821\pi\) | |||||||
\(614\) | − | 512.894i | − | 0.835332i | ||||||
\(615\) | 195.528 | 0.317931 | ||||||||
\(616\) | 62.3446 | 0.101209 | ||||||||
\(617\) | 972.066 | 1.57547 | 0.787735 | − | 0.616014i | \(-0.211253\pi\) | ||||
0.787735 | + | 0.616014i | \(0.211253\pi\) | |||||||
\(618\) | −344.628 | −0.557650 | ||||||||
\(619\) | −245.762 | −0.397031 | −0.198516 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198516 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(620\) | − | 445.562i | − | 0.718648i | ||||||
\(621\) | 213.266i | 0.343424i | ||||||||
\(622\) | 42.4649i | 0.0682716i | ||||||||
\(623\) | − | 1199.27i | − | 1.92499i | ||||||
\(624\) | 23.6704i | 0.0379333i | ||||||||
\(625\) | −555.425 | −0.888680 | ||||||||
\(626\) | 206.271 | 0.329506 | ||||||||
\(627\) | 32.3797i | 0.0516423i | ||||||||
\(628\) | 397.131i | 0.632375i | ||||||||
\(629\) | 242.930i | 0.386217i | ||||||||
\(630\) | 249.546i | 0.396105i | ||||||||
\(631\) | −502.846 | −0.796904 | −0.398452 | − | 0.917189i | \(-0.630452\pi\) | ||||
−0.398452 | + | 0.917189i | \(0.630452\pi\) | |||||||
\(632\) | 175.398i | 0.277528i | ||||||||
\(633\) | − | 268.663i | − | 0.424428i | ||||||
\(634\) | − | 801.859i | − | 1.26476i | ||||||
\(635\) | 93.5649 | 0.147346 | ||||||||
\(636\) | −10.1199 | −0.0159117 | ||||||||
\(637\) | − | 358.561i | − | 0.562890i | ||||||
\(638\) | 84.5017 | 0.132448 | ||||||||
\(639\) | −92.0698 | −0.144084 | ||||||||
\(640\) | − | 53.6329i | − | 0.0838013i | ||||||
\(641\) | −1162.01 | −1.81281 | −0.906403 | − | 0.422415i | \(-0.861183\pi\) | ||||
−0.906403 | + | 0.422415i | \(0.861183\pi\) | |||||||
\(642\) | − | 187.030i | − | 0.291325i | ||||||
\(643\) | −40.2407 | −0.0625827 | −0.0312913 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312913 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(644\) | 1018.49i | 1.58151i | ||||||||
\(645\) | − | 13.1432i | − | 0.0203770i | ||||||
\(646\) | 86.0946i | 0.133273i | ||||||||
\(647\) | −812.933 | −1.25646 | −0.628232 | − | 0.778026i | \(-0.716221\pi\) | ||||
−0.628232 | + | 0.778026i | \(0.716221\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | 60.7958 | − | 85.3799i | 0.0936762 | − | 0.131556i | ||||
\(650\) | 12.2120 | 0.0187877 | ||||||||
\(651\) | 1009.95i | 1.55139i | ||||||||
\(652\) | 286.861 | 0.439970 | ||||||||
\(653\) | 534.281 | 0.818194 | 0.409097 | − | 0.912491i | \(-0.365844\pi\) | ||||
0.409097 | + | 0.912491i | \(0.365844\pi\) | |||||||
\(654\) | −393.282 | −0.601349 | ||||||||
\(655\) | 105.606i | 0.161230i | ||||||||
\(656\) | 95.2537 | 0.145204 | ||||||||
\(657\) | − | 355.026i | − | 0.540374i | ||||||
\(658\) | −112.238 | −0.170575 | ||||||||
\(659\) | 496.424i | 0.753299i | 0.926356 | + | 0.376650i | \(0.122924\pi\) | ||||
−0.926356 | + | 0.376650i | \(0.877076\pi\) | |||||||
\(660\) | 29.1730i | 0.0442016i | ||||||||
\(661\) | −155.910 | −0.235870 | −0.117935 | − | 0.993021i | \(-0.537627\pi\) | ||||
−0.117935 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(662\) | − | 356.068i | − | 0.537867i | ||||||
\(663\) | − | 34.2341i | − | 0.0516352i | ||||||
\(664\) | 161.693 | 0.243514 | ||||||||
\(665\) | −618.958 | −0.930765 | ||||||||
\(666\) | −178.158 | −0.267504 | ||||||||
\(667\) | 1380.46i | 2.06966i | ||||||||
\(668\) | −18.4472 | −0.0276155 | ||||||||
\(669\) | −736.318 | −1.10062 | ||||||||
\(670\) | −274.654 | −0.409932 | ||||||||
\(671\) | −19.2967 | −0.0287582 | ||||||||
\(672\) | 121.569i | 0.180907i | ||||||||
\(673\) | 566.257i | 0.841393i | 0.907202 | + | 0.420696i | \(0.138214\pi\) | ||||
−0.907202 | + | 0.420696i | \(0.861786\pi\) | |||||||
\(674\) | 632.016 | 0.937709 | ||||||||
\(675\) | 13.1332 | 0.0194565 | ||||||||
\(676\) | −314.655 | −0.465466 | ||||||||
\(677\) | 967.786 | 1.42952 | 0.714761 | − | 0.699369i | \(-0.246536\pi\) | ||||
0.714761 | + | 0.699369i | \(0.246536\pi\) | |||||||
\(678\) | 145.874 | 0.215153 | ||||||||
\(679\) | 912.062i | 1.34324i | ||||||||
\(680\) | 77.5684i | 0.114071i | ||||||||
\(681\) | − | 242.600i | − | 0.356241i | ||||||
\(682\) | 118.068i | 0.173120i | ||||||||
\(683\) | − | 156.240i | − | 0.228755i | −0.993437 | − | 0.114377i | \(-0.963513\pi\) | ||
0.993437 | − | 0.114377i | \(-0.0364873\pi\) | |||||||
\(684\) | −63.1391 | −0.0923086 | ||||||||
\(685\) | −492.513 | −0.718997 | ||||||||
\(686\) | − | 981.739i | − | 1.43111i | ||||||
\(687\) | − | 751.567i | − | 1.09398i | ||||||
\(688\) | − | 6.40287i | − | 0.00930649i | ||||||
\(689\) | 9.98087i | 0.0144860i | ||||||||
\(690\) | −476.586 | −0.690705 | ||||||||
\(691\) | 387.135i | 0.560254i | 0.959963 | + | 0.280127i | \(0.0903766\pi\) | ||||
−0.959963 | + | 0.280127i | \(0.909623\pi\) | |||||||
\(692\) | 41.9977i | 0.0606903i | ||||||||
\(693\) | − | 66.1264i | − | 0.0954205i | ||||||
\(694\) | 875.581 | 1.26164 | ||||||||
\(695\) | 437.303 | 0.629213 | ||||||||
\(696\) | 164.775i | 0.236745i | ||||||||
\(697\) | −137.764 | −0.197653 | ||||||||
\(698\) | −672.332 | −0.963226 | ||||||||
\(699\) | − | 469.994i | − | 0.672380i | ||||||
\(700\) | 62.7200 | 0.0896000 | ||||||||
\(701\) | 376.867i | 0.537613i | 0.963194 | + | 0.268806i | \(0.0866292\pi\) | ||||
−0.963194 | + | 0.268806i | \(0.913371\pi\) | |||||||
\(702\) | 25.1062 | 0.0357639 | ||||||||
\(703\) | − | 441.891i | − | 0.628579i | ||||||
\(704\) | 14.2120i | 0.0201875i | ||||||||
\(705\) | − | 52.5199i | − | 0.0744962i | ||||||
\(706\) | 826.560 | 1.17076 | ||||||||
\(707\) | − | 1572.18i | − | 2.22373i | ||||||
\(708\) | 166.487 | + | 118.549i | 0.235152 | + | 0.167443i | ||||
\(709\) | −728.582 | −1.02762 | −0.513809 | − | 0.857904i | \(-0.671766\pi\) | ||||
−0.513809 | + | 0.857904i | \(0.671766\pi\) | |||||||
\(710\) | − | 205.749i | − | 0.289787i | ||||||
\(711\) | 186.037 | 0.261656 | ||||||||
\(712\) | 273.384 | 0.383967 | ||||||||
\(713\) | −1928.82 | −2.70522 | ||||||||
\(714\) | − | 175.824i | − | 0.246252i | ||||||
\(715\) | 28.7724 | 0.0402411 | ||||||||
\(716\) | − | 452.560i | − | 0.632067i | ||||||
\(717\) | 369.611 | 0.515497 | ||||||||
\(718\) | − | 648.594i | − | 0.903334i | ||||||
\(719\) | − | 456.694i | − | 0.635180i | −0.948228 | − | 0.317590i | \(-0.897126\pi\) | ||
0.948228 | − | 0.317590i | \(-0.102874\pi\) | |||||||
\(720\) | −56.8862 | −0.0790087 | ||||||||
\(721\) | 1745.67i | 2.42118i | ||||||||
\(722\) | 353.925i | 0.490201i | ||||||||
\(723\) | 92.5019 | 0.127942 | ||||||||
\(724\) | 402.072 | 0.555349 | ||||||||
\(725\) | 85.0105 | 0.117256 | ||||||||
\(726\) | 288.658i | 0.397600i | ||||||||
\(727\) | −669.263 | −0.920582 | −0.460291 | − | 0.887768i | \(-0.652255\pi\) | ||||
−0.460291 | + | 0.887768i | \(0.652255\pi\) | |||||||
\(728\) | 119.900 | 0.164697 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 793.376 | 1.08682 | ||||||||
\(731\) | 9.26037i | 0.0126681i | ||||||||
\(732\) | − | 37.6278i | − | 0.0514041i | ||||||
\(733\) | −570.834 | −0.778764 | −0.389382 | − | 0.921076i | \(-0.627311\pi\) | ||||
−0.389382 | + | 0.921076i | \(0.627311\pi\) | |||||||
\(734\) | −453.616 | −0.618005 | ||||||||
\(735\) | 861.718 | 1.17240 | ||||||||
\(736\) | −232.175 | −0.315455 | ||||||||
\(737\) | 72.7798 | 0.0987514 | ||||||||
\(738\) | − | 101.032i | − | 0.136900i | ||||||
\(739\) | − | 1360.08i | − | 1.84043i | −0.391409 | − | 0.920217i | \(-0.628012\pi\) | ||
0.391409 | − | 0.920217i | \(-0.371988\pi\) | |||||||
\(740\) | − | 398.129i | − | 0.538012i | ||||||
\(741\) | 62.2720i | 0.0840377i | ||||||||
\(742\) | 51.2610i | 0.0690849i | ||||||||
\(743\) | 1175.48 | 1.58207 | 0.791035 | − | 0.611771i | \(-0.209542\pi\) | ||||
0.791035 | + | 0.611771i | \(0.209542\pi\) | |||||||
\(744\) | −230.228 | −0.309446 | ||||||||
\(745\) | − | 1251.60i | − | 1.68001i | ||||||
\(746\) | − | 478.187i | − | 0.641002i | ||||||
\(747\) | − | 171.502i | − | 0.229587i | ||||||
\(748\) | − | 20.5546i | − | 0.0274794i | ||||||
\(749\) | −947.382 | −1.26486 | ||||||||
\(750\) | 319.645i | 0.426193i | ||||||||
\(751\) | 734.037i | 0.977413i | 0.872448 | + | 0.488706i | \(0.162531\pi\) | ||||
−0.872448 | + | 0.488706i | \(0.837469\pi\) | |||||||
\(752\) | − | 25.5857i | − | 0.0340235i | ||||||
\(753\) | 738.112 | 0.980228 | ||||||||
\(754\) | 162.512 | 0.215533 | ||||||||
\(755\) | 485.243i | 0.642706i | ||||||||
\(756\) | 128.944 | 0.170561 | ||||||||
\(757\) | −946.059 | −1.24975 | −0.624874 | − | 0.780726i | \(-0.714850\pi\) | ||||
−0.624874 | + | 0.780726i | \(0.714850\pi\) | |||||||
\(758\) | − | 246.948i | − | 0.325789i | ||||||
\(759\) | 126.289 | 0.166389 | ||||||||
\(760\) | − | 141.097i | − | 0.185654i | ||||||
\(761\) | −1135.31 | −1.49187 | −0.745933 | − | 0.666021i | \(-0.767996\pi\) | ||||
−0.745933 | + | 0.666021i | \(0.767996\pi\) | |||||||
\(762\) | − | 48.3462i | − | 0.0634465i | ||||||
\(763\) | 1992.13i | 2.61091i | ||||||||
\(764\) | − | 3.41986i | − | 0.00447625i | ||||||
\(765\) | 82.2737 | 0.107547 | ||||||||
\(766\) | − | 895.688i | − | 1.16931i | ||||||
\(767\) | 116.921 | − | 164.201i | 0.152440 | − | 0.214082i | ||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 764.684i | 0.994387i | 0.867640 | + | 0.497193i | \(0.165636\pi\) | ||||
−0.867640 | + | 0.497193i | \(0.834364\pi\) | |||||||
\(770\) | 147.773 | 0.191913 | ||||||||
\(771\) | −753.074 | −0.976749 | ||||||||
\(772\) | −99.7577 | −0.129220 | ||||||||
\(773\) | − | 685.199i | − | 0.886416i | −0.896419 | − | 0.443208i | \(-0.853840\pi\) | ||
0.896419 | − | 0.443208i | \(-0.146160\pi\) | |||||||
\(774\) | −6.79127 | −0.00877424 | ||||||||
\(775\) | 118.779i | 0.153263i | ||||||||
\(776\) | −207.913 | −0.267929 | ||||||||
\(777\) | 902.437i | 1.16144i | ||||||||
\(778\) | − | 6.13060i | − | 0.00787994i | ||||||
\(779\) | 250.593 | 0.321686 | ||||||||
\(780\) | 56.1050i | 0.0719294i | ||||||||
\(781\) | 54.5207i | 0.0698088i | ||||||||
\(782\) | 335.791 | 0.429400 | ||||||||
\(783\) | 174.770 | 0.223206 | ||||||||
\(784\) | 419.796 | 0.535454 | ||||||||
\(785\) | 941.305i | 1.19911i | ||||||||
\(786\) | 54.5679 | 0.0694248 | ||||||||
\(787\) | −491.981 | −0.625135 | −0.312568 | − | 0.949896i | \(-0.601189\pi\) | ||||
−0.312568 | + | 0.949896i | \(0.601189\pi\) | |||||||
\(788\) | −292.228 | −0.370847 | ||||||||
\(789\) | −156.775 | −0.198700 | ||||||||
\(790\) | 415.738i | 0.526251i | ||||||||
\(791\) | − | 738.907i | − | 0.934143i | ||||||
\(792\) | 15.0741 | 0.0190330 | ||||||||
\(793\) | −37.1110 | −0.0467983 | ||||||||
\(794\) | −74.1650 | −0.0934068 | ||||||||
\(795\) | −23.9867 | −0.0301719 | ||||||||
\(796\) | 744.369 | 0.935137 | ||||||||
\(797\) | − | 1102.47i | − | 1.38328i | −0.722244 | − | 0.691639i | \(-0.756889\pi\) | ||
0.722244 | − | 0.691639i | \(-0.243111\pi\) | |||||||
\(798\) | 319.824i | 0.400782i | ||||||||
\(799\) | 37.0042i | 0.0463131i | ||||||||
\(800\) | 14.2976i | 0.0178720i | ||||||||
\(801\) | − | 289.968i | − | 0.362007i | ||||||
\(802\) | −558.654 | −0.696577 | ||||||||
\(803\) | −210.234 | −0.261811 | ||||||||
\(804\) | 141.918i | 0.176514i | ||||||||
\(805\) | 2414.09i | 2.99888i | ||||||||
\(806\) | 227.066i | 0.281720i | ||||||||
\(807\) | 794.117i | 0.984036i | ||||||||
\(808\) | 358.392 | 0.443554 | ||||||||
\(809\) | 906.426i | 1.12043i | 0.828348 | + | 0.560214i | \(0.189281\pi\) | ||||
−0.828348 | + | 0.560214i | \(0.810719\pi\) | |||||||
\(810\) | 60.3370i | 0.0744901i | ||||||||
\(811\) | − | 1164.85i | − | 1.43631i | −0.695882 | − | 0.718157i | \(-0.744986\pi\) | ||
0.695882 | − | 0.718157i | \(-0.255014\pi\) | |||||||
\(812\) | 834.649 | 1.02789 | ||||||||
\(813\) | −132.354 | −0.162797 | ||||||||
\(814\) | 105.499i | 0.129606i | ||||||||
\(815\) | 679.934 | 0.834275 | ||||||||
\(816\) | 40.0806 | 0.0491184 | ||||||||
\(817\) | − | 16.8446i | − | 0.0206177i | ||||||
\(818\) | 552.067 | 0.674899 | ||||||||
\(819\) | − | 127.173i | − | 0.155278i | ||||||
\(820\) | 225.776 | 0.275337 | ||||||||
\(821\) | 1040.13i | 1.26690i | 0.773783 | + | 0.633451i | \(0.218362\pi\) | ||||
−0.773783 | + | 0.633451i | \(0.781638\pi\) | |||||||
\(822\) | 254.488i | 0.309596i | ||||||||
\(823\) | − | 230.161i | − | 0.279660i | −0.990175 | − | 0.139830i | \(-0.955344\pi\) | ||
0.990175 | − | 0.139830i | \(-0.0446557\pi\) | |||||||
\(824\) | −397.942 | −0.482939 | ||||||||
\(825\) | − | 7.77702i | − | 0.00942669i | ||||||
\(826\) | 600.499 | − | 843.323i | 0.726996 | − | 1.02097i | ||||
\(827\) | −1521.53 | −1.83982 | −0.919908 | − | 0.392134i | \(-0.871737\pi\) | ||||
−0.919908 | + | 0.392134i | \(0.871737\pi\) | |||||||
\(828\) | 246.258i | 0.297414i | ||||||||
\(829\) | −189.919 | −0.229094 | −0.114547 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114547 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(830\) | 383.255 | 0.461753 | ||||||||
\(831\) | 556.728 | 0.669950 | ||||||||
\(832\) | 27.3322i | 0.0328512i | ||||||||
\(833\) | −607.145 | −0.728865 | ||||||||
\(834\) | − | 225.960i | − | 0.270936i | ||||||
\(835\) | −43.7246 | −0.0523648 | ||||||||
\(836\) | 37.3889i | 0.0447235i | ||||||||
\(837\) | 244.194i | 0.291749i | ||||||||
\(838\) | 16.5116 | 0.0197036 | ||||||||
\(839\) | 251.046i | 0.299220i | 0.988745 | + | 0.149610i | \(0.0478018\pi\) | ||||
−0.988745 | + | 0.149610i | \(0.952198\pi\) | |||||||
\(840\) | 288.151i | 0.343037i | ||||||||
\(841\) | 290.281 | 0.345161 | ||||||||
\(842\) | −571.969 | −0.679299 | ||||||||
\(843\) | −52.7498 | −0.0625739 | ||||||||
\(844\) | − | 310.225i | − | 0.367566i | ||||||
\(845\) | −745.813 | −0.882619 | ||||||||
\(846\) | −27.1377 | −0.0320777 | ||||||||
\(847\) | 1462.16 | 1.72629 | ||||||||
\(848\) | −11.6854 | −0.0137799 | ||||||||
\(849\) | 710.540i | 0.836914i | ||||||||
\(850\) | − | 20.6784i | − | 0.0243275i | ||||||
\(851\) | −1723.49 | −2.02525 | ||||||||
\(852\) | −106.313 | −0.124781 | ||||||||
\(853\) | 1323.84 | 1.55198 | 0.775992 | − | 0.630743i | \(-0.217250\pi\) | ||||
0.775992 | + | 0.630743i | \(0.217250\pi\) | |||||||
\(854\) | −190.600 | −0.223185 | ||||||||
\(855\) | −149.656 | −0.175036 | ||||||||
\(856\) | − | 215.964i | − | 0.252295i | ||||||
\(857\) | − | 279.071i | − | 0.325637i | −0.986656 | − | 0.162819i | \(-0.947941\pi\) | ||
0.986656 | − | 0.162819i | \(-0.0520585\pi\) | |||||||
\(858\) | − | 14.8671i | − | 0.0173276i | ||||||
\(859\) | 991.453i | 1.15419i | 0.816676 | + | 0.577097i | \(0.195815\pi\) | ||||
−0.816676 | + | 0.577097i | \(0.804185\pi\) | |||||||
\(860\) | − | 15.1765i | − | 0.0176470i | ||||||
\(861\) | −511.766 | −0.594385 | ||||||||
\(862\) | 276.015 | 0.320203 | ||||||||
\(863\) | − | 1164.79i | − | 1.34970i | −0.737954 | − | 0.674851i | \(-0.764208\pi\) | ||
0.737954 | − | 0.674851i | \(-0.235792\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 99.5455i | 0.115081i | ||||||||
\(866\) | 463.025i | 0.534671i | ||||||||
\(867\) | 442.595 | 0.510490 | ||||||||
\(868\) | 1166.19i | 1.34354i | ||||||||
\(869\) | − | 110.165i | − | 0.126772i | ||||||
\(870\) | 390.559i | 0.448918i | ||||||||
\(871\) | 139.968 | 0.160699 | ||||||||
\(872\) | −454.123 | −0.520783 | ||||||||
\(873\) | 220.525i | 0.252606i | ||||||||
\(874\) | −610.804 | −0.698861 | ||||||||
\(875\) | 1619.13 | 1.85043 | ||||||||
\(876\) | − | 409.948i | − | 0.467977i | ||||||
\(877\) | 1319.14 | 1.50415 | 0.752074 | − | 0.659079i | \(-0.229054\pi\) | ||||
0.752074 | + | 0.659079i | \(0.229054\pi\) | |||||||
\(878\) | 517.679i | 0.589611i | ||||||||
\(879\) | 340.484 | 0.387354 | ||||||||
\(880\) | 33.6861i | 0.0382797i | ||||||||
\(881\) | 349.356i | 0.396544i | 0.980147 | + | 0.198272i | \(0.0635330\pi\) | ||||
−0.980147 | + | 0.198272i | \(0.936467\pi\) | |||||||
\(882\) | − | 445.261i | − | 0.504831i | ||||||
\(883\) | 365.342 | 0.413751 | 0.206875 | − | 0.978367i | \(-0.433671\pi\) | ||||
0.206875 | + | 0.978367i | \(0.433671\pi\) | |||||||
\(884\) | − | 39.5301i | − | 0.0447174i | ||||||
\(885\) | 394.618 | + | 280.993i | 0.445896 | + | 0.317506i | ||||
\(886\) | 877.740 | 0.990677 | ||||||||
\(887\) | 1111.94i | 1.25360i | 0.779181 | + | 0.626799i | \(0.215635\pi\) | ||||
−0.779181 | + | 0.626799i | \(0.784365\pi\) | |||||||
\(888\) | −205.719 | −0.231665 | ||||||||
\(889\) | −244.892 | −0.275470 | ||||||||
\(890\) | 647.992 | 0.728081 | ||||||||
\(891\) | − | 15.9885i | − | 0.0179444i | ||||||
\(892\) | −850.226 | −0.953169 | ||||||||
\(893\) | − | 67.3107i | − | 0.0753759i | ||||||
\(894\) | −646.721 | −0.723402 | ||||||||
\(895\) | − | 1072.68i | − | 1.19853i | ||||||
\(896\) | 140.376i | 0.156670i | ||||||||
\(897\) | 242.876 | 0.270765 | ||||||||
\(898\) | 355.148i | 0.395488i | ||||||||
\(899\) | 1580.66i | 1.75824i | ||||||||
\(900\) | 15.1649 | 0.0168499 | ||||||||
\(901\) | 16.9004 | 0.0187574 | ||||||||
\(902\) | −59.8277 | −0.0663278 | ||||||||
\(903\) | 34.4004i | 0.0380957i | ||||||||
\(904\) | 168.440 | 0.186328 | ||||||||
\(905\) | 953.016 | 1.05306 | ||||||||
\(906\) | 250.732 | 0.276746 | ||||||||
\(907\) | −930.561 | −1.02598 | −0.512988 | − | 0.858396i | \(-0.671462\pi\) | ||||
−0.512988 | + | 0.858396i | \(0.671462\pi\) | |||||||
\(908\) | − | 280.131i | − | 0.308514i | ||||||
\(909\) | − | 380.132i | − | 0.418187i | ||||||
\(910\) | 284.193 | 0.312301 | ||||||||
\(911\) | −144.909 | −0.159066 | −0.0795331 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795331 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(912\) | −72.9067 | −0.0799416 | ||||||||
\(913\) | −101.558 | −0.111235 | ||||||||
\(914\) | −742.035 | −0.811855 | ||||||||
\(915\) | − | 89.1877i | − | 0.0974729i | ||||||
\(916\) | − | 867.835i | − | 0.947418i | ||||||
\(917\) | − | 276.408i | − | 0.301426i | ||||||
\(918\) | − | 42.5119i | − | 0.0463093i | ||||||
\(919\) | − | 1480.93i | − | 1.61146i | −0.592284 | − | 0.805729i | \(-0.701774\pi\) | ||
0.592284 | − | 0.805729i | \(-0.298226\pi\) | |||||||
\(920\) | −550.314 | −0.598168 | ||||||||
\(921\) | −628.164 | −0.682046 | ||||||||
\(922\) | − | 643.650i | − | 0.698102i | ||||||
\(923\) | 104.853i | 0.113600i | ||||||||
\(924\) | − | 76.3562i | − | 0.0826366i | ||||||
\(925\) | 106.134i | 0.114740i | ||||||||
\(926\) | 979.357 | 1.05762 | ||||||||
\(927\) | 422.081i | 0.455319i | ||||||||
\(928\) | 190.266i | 0.205028i | ||||||||
\(929\) | − | 252.022i | − | 0.271283i | −0.990758 | − | 0.135642i | \(-0.956690\pi\) | ||
0.990758 | − | 0.135642i | \(-0.0433096\pi\) | |||||||
\(930\) | −545.700 | −0.586774 | ||||||||
\(931\) | 1104.40 | 1.18625 | ||||||||
\(932\) | − | 542.702i | − | 0.582298i | ||||||
\(933\) | 52.0087 | 0.0557435 | ||||||||
\(934\) | 591.579 | 0.633382 | ||||||||
\(935\) | − | 48.7197i | − | 0.0521066i | ||||||
\(936\) | 28.9902 | 0.0309724 | ||||||||
\(937\) | − | 431.511i | − | 0.460524i | −0.973129 | − | 0.230262i | \(-0.926042\pi\) | ||
0.973129 | − | 0.230262i | \(-0.0739584\pi\) | |||||||
\(938\) | 718.868 | 0.766383 | ||||||||
\(939\) | − | 252.629i | − | 0.269041i | ||||||
\(940\) | − | 60.6447i | − | 0.0645156i | ||||||
\(941\) | 406.044i | 0.431503i | 0.976448 | + | 0.215751i | \(0.0692201\pi\) | ||||
−0.976448 | + | 0.215751i | \(0.930780\pi\) | |||||||
\(942\) | 486.385 | 0.516332 | ||||||||
\(943\) | − | 977.377i | − | 1.03645i | ||||||
\(944\) | 192.243 | + | 136.889i | 0.203647 | + | 0.145010i | ||||
\(945\) | 305.630 | 0.323418 | ||||||||
\(946\) | 4.02156i | 0.00425112i | ||||||||
\(947\) | −340.427 | −0.359480 | −0.179740 | − | 0.983714i | \(-0.557526\pi\) | ||||
−0.179740 | + | 0.983714i | \(0.557526\pi\) | |||||||
\(948\) | 214.817 | 0.226601 | ||||||||
\(949\) | −404.318 | −0.426046 | ||||||||
\(950\) | 37.6140i | 0.0395937i | ||||||||
\(951\) | −982.073 | −1.03267 | ||||||||
\(952\) | − | 203.024i | − | 0.213260i | ||||||
\(953\) | 1104.08 | 1.15853 | 0.579264 | − | 0.815140i | \(-0.303340\pi\) | ||||
0.579264 | + | 0.815140i | \(0.303340\pi\) | |||||||
\(954\) | 12.3942i | 0.0129919i | ||||||||
\(955\) | − | 8.10595i | − | 0.00848790i | ||||||
\(956\) | 426.790 | 0.446433 | ||||||||
\(957\) | − | 103.493i | − | 0.108143i | ||||||
\(958\) | − | 551.011i | − | 0.575168i | ||||||
\(959\) | 1289.08 | 1.34419 | ||||||||
\(960\) | −65.6866 | −0.0684235 | ||||||||
\(961\) | −1247.54 | −1.29816 | ||||||||
\(962\) | 202.893i | 0.210908i | ||||||||
\(963\) | −229.065 | −0.237866 | ||||||||
\(964\) | 106.812 | 0.110801 | ||||||||
\(965\) | −236.452 | −0.245028 | ||||||||
\(966\) | 1247.40 | 1.29130 | ||||||||
\(967\) | 1615.17i | 1.67029i | 0.550033 | + | 0.835143i | \(0.314615\pi\) | ||||
−0.550033 | + | 0.835143i | \(0.685385\pi\) | |||||||
\(968\) | 333.313i | 0.344332i | ||||||||
\(969\) | 105.444 | 0.108817 | ||||||||
\(970\) | −492.807 | −0.508049 | ||||||||
\(971\) | −48.0398 | −0.0494745 | −0.0247373 | − | 0.999694i | \(-0.507875\pi\) | ||||
−0.0247373 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −1144.58 | −1.17634 | ||||||||
\(974\) | 943.314i | 0.968495i | ||||||||
\(975\) | − | 14.9566i | − | 0.0153401i | ||||||
\(976\) | − | 43.4489i | − | 0.0445173i | ||||||
\(977\) | − | 238.680i | − | 0.244299i | −0.992512 | − | 0.122149i | \(-0.961021\pi\) | ||
0.992512 | − | 0.122149i | \(-0.0389787\pi\) | |||||||
\(978\) | − | 351.331i | − | 0.359234i | ||||||
\(979\) | −171.709 | −0.175393 | ||||||||
\(980\) | 995.026 | 1.01533 | ||||||||
\(981\) | 481.670i | 0.490999i | ||||||||
\(982\) | 391.453i | 0.398629i | ||||||||
\(983\) | 1918.33i | 1.95150i | 0.218884 | + | 0.975751i | \(0.429758\pi\) | ||||
−0.218884 | + | 0.975751i | \(0.570242\pi\) | |||||||
\(984\) | − | 116.662i | − | 0.118558i | ||||||
\(985\) | −692.655 | −0.703203 | ||||||||
\(986\) | − | 275.178i | − | 0.279085i | ||||||
\(987\) | 137.463i | 0.139274i | ||||||||
\(988\) | 71.9055i | 0.0727788i | ||||||||
\(989\) | −65.6983 | −0.0664291 | ||||||||
\(990\) | 35.7295 | 0.0360904 | ||||||||
\(991\) | − | 1385.49i | − | 1.39807i | −0.715087 | − | 0.699036i | \(-0.753613\pi\) | ||
0.715087 | − | 0.699036i | \(-0.246387\pi\) | |||||||
\(992\) | −265.844 | −0.267988 | ||||||||
\(993\) | −436.092 | −0.439167 | ||||||||
\(994\) | 538.517i | 0.541768i | ||||||||
\(995\) | 1764.35 | 1.77321 | ||||||||
\(996\) | − | 198.033i | − | 0.198828i | ||||||
\(997\) | 182.890 | 0.183441 | 0.0917203 | − | 0.995785i | \(-0.470763\pi\) | ||||
0.0917203 | + | 0.995785i | \(0.470763\pi\) | |||||||
\(998\) | − | 810.856i | − | 0.812481i | ||||||
\(999\) | 218.198i | 0.218416i |
(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 | 354.3.d.a.235.2 | ✓ | 20 | |
3.2 | odd | 2 | 1062.3.d.f.235.18 | 20 | |||
59.58 | odd | 2 | inner | 354.3.d.a.235.12 | yes | 20 | |
177.176 | even | 2 | 1062.3.d.f.235.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.3.d.a.235.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
354.3.d.a.235.12 | yes | 20 | 59.58 | odd | 2 | inner | |
1062.3.d.f.235.8 | 20 | 177.176 | even | 2 | |||
1062.3.d.f.235.18 | 20 | 3.2 | odd | 2 |