Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,2,Mod(17,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 0, 38]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.bg (of order \(21\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.49370765906\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{21})\) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{21}]$ |
Embedding invariants
Embedding label | 369.2 | ||
Character | \(\chi\) | \(=\) | 688.369 |
Dual form | 688.2.bg.c.289.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.90223 | + | 1.29692i | 1.09825 | + | 0.748775i | 0.970034 | − | 0.242970i | \(-0.0781218\pi\) |
0.128218 | + | 0.991746i | \(0.459074\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.37710 | − | 2.20563i | 1.06307 | − | 0.986388i | 0.0631405 | − | 0.998005i | \(-0.479888\pi\) |
0.999933 | + | 0.0116171i | \(0.00369791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.38418 | − | 2.39748i | 0.523173 | − | 0.906162i | −0.476464 | − | 0.879194i | \(-0.658082\pi\) |
0.999636 | − | 0.0269675i | \(-0.00858507\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.840455 | + | 2.14144i | 0.280152 | + | 0.713814i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.47915 | + | 4.36271i | −1.04900 | + | 1.31541i | −0.101787 | + | 0.994806i | \(0.532456\pi\) |
−0.947215 | + | 0.320600i | \(0.896115\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57105 | + | 0.484606i | 0.435732 | + | 0.134406i | 0.504858 | − | 0.863202i | \(-0.331545\pi\) |
−0.0691260 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.38231 | − | 1.11270i | 1.90610 | − | 0.287299i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.555777 | + | 0.515686i | 0.134796 | + | 0.125072i | 0.744690 | − | 0.667411i | \(-0.232597\pi\) |
−0.609894 | + | 0.792483i | \(0.708788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.795961 | − | 2.02807i | 0.182606 | − | 0.465272i | −0.810033 | − | 0.586384i | \(-0.800551\pi\) |
0.992639 | + | 0.121112i | \(0.0386461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.74237 | − | 2.76538i | 1.25309 | − | 0.603455i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.00139480 | 0.000210232i | −0.000290836 | 4.38364e-5i | 0.148897 | − | 0.988853i | \(-0.452428\pi\) | ||
−0.149188 | + | 0.988809i | \(0.547666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.412168 | − | 5.50000i | 0.0824336 | − | 1.10000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.358374 | − | 1.57014i | 0.0689691 | − | 0.302174i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.87133 | + | 2.63943i | −0.718888 | + | 0.490129i | −0.866665 | − | 0.498891i | \(-0.833741\pi\) |
0.147777 | + | 0.989021i | \(0.452788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.301429 | − | 4.02229i | −0.0541382 | − | 0.722424i | −0.956553 | − | 0.291557i | \(-0.905827\pi\) |
0.902415 | − | 0.430867i | \(-0.141792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.2762 | + | 3.78671i | −2.13701 | + | 0.659181i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.99760 | − | 8.75205i | −0.337656 | − | 1.47937i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.999506 | − | 1.73120i | −0.164318 | − | 0.284607i | 0.772095 | − | 0.635507i | \(-0.219209\pi\) |
−0.936413 | + | 0.350900i | \(0.885876\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.36001 | + | 2.95936i | 0.377904 | + | 0.473877i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.30781 | + | 3.03768i | 0.985115 | + | 0.474406i | 0.855861 | − | 0.517205i | \(-0.173028\pi\) |
0.129253 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.54912 | − | 0.330261i | −0.998731 | − | 0.0503643i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.72108 | + | 3.23670i | 1.00192 | + | 0.482499i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.90255 | + | 6.14760i | 0.715110 | + | 0.896720i | 0.998050 | − | 0.0624180i | \(-0.0198812\pi\) |
−0.282940 | + | 0.959138i | \(0.591310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.331936 | − | 0.574929i | −0.0474194 | − | 0.0821328i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.388413 | + | 1.70175i | 0.0543887 | + | 0.238293i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.76860 | + | 1.16246i | −0.517657 | + | 0.159676i | −0.542565 | − | 0.840014i | \(-0.682547\pi\) |
0.0249081 | + | 0.999690i | \(0.492071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35223 | + | 18.0443i | 0.182335 | + | 2.43310i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.14434 | − | 2.82557i | 0.548932 | − | 0.374255i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.811036 | − | 3.55338i | 0.105588 | − | 0.462611i | −0.894297 | − | 0.447473i | \(-0.852324\pi\) |
0.999885 | − | 0.0151380i | \(-0.00481876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.639001 | + | 8.52687i | −0.0818157 | + | 1.09175i | 0.793618 | + | 0.608416i | \(0.208195\pi\) |
−0.875434 | + | 0.483338i | \(0.839424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.29741 | + | 0.949182i | 0.793399 | + | 0.119586i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.80342 | − | 2.31320i | 0.595791 | − | 0.286918i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.43004 | + | 8.73959i | −0.419046 | + | 1.06771i | 0.553054 | + | 0.833145i | \(0.313462\pi\) |
−0.972100 | + | 0.234566i | \(0.924633\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.00238057 | − | 0.00220885i | −0.000286587 | − | 0.000265914i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.83052 | + | 1.02953i | −0.810633 | + | 0.122183i | −0.541263 | − | 0.840853i | \(-0.682054\pi\) |
−0.269370 | + | 0.963037i | \(0.586816\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.6150 | − | 3.27429i | −1.24239 | − | 0.383226i | −0.397220 | − | 0.917724i | \(-0.630025\pi\) |
−0.845170 | + | 0.534497i | \(0.820501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.91708 | − | 9.92771i | 0.914186 | − | 1.14635i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.64372 | + | 14.3800i | 0.643162 | + | 1.63875i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26980 | − | 5.66346i | 0.367882 | − | 0.637190i | −0.621353 | − | 0.783531i | \(-0.713417\pi\) |
0.989234 | + | 0.146342i | \(0.0467498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.77713 | − | 7.21613i | 0.864126 | − | 0.801792i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.71578 | + | 3.21516i | 0.517624 | + | 0.352910i | 0.793782 | − | 0.608202i | \(-0.208109\pi\) |
−0.276158 | + | 0.961112i | \(0.589061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.45855 | 0.266667 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.7873 | −1.15652 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.13427 | − | 4.86406i | −0.756231 | − | 0.515590i | 0.122755 | − | 0.992437i | \(-0.460827\pi\) |
−0.878986 | + | 0.476847i | \(0.841779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.33646 | − | 3.09578i | 0.349756 | − | 0.324526i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.64319 | − | 8.04224i | 0.481476 | − | 0.833941i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.58110 | − | 6.57654i | −0.264815 | − | 0.674739i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0143 | + | 13.8115i | −1.11833 | + | 1.40234i | −0.213306 | + | 0.976986i | \(0.568423\pi\) |
−0.905026 | + | 0.425357i | \(0.860148\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.2666 | − | 3.78373i | −1.23284 | − | 0.380279i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.98838 | + | 1.50551i | −0.993881 | + | 0.149803i | −0.625794 | − | 0.779988i | \(-0.715225\pi\) |
−0.368086 | + | 0.929792i | \(0.619987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2237 | − | 9.48624i | −1.00737 | − | 0.934707i | −0.00950588 | − | 0.999955i | \(-0.503026\pi\) |
−0.997869 | + | 0.0652474i | \(0.979216\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.55080 | − | 19.2391i | 0.736883 | − | 1.87755i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.73185 | + | 3.24189i | −0.650793 | + | 0.313405i | −0.729994 | − | 0.683453i | \(-0.760477\pi\) |
0.0792013 | + | 0.996859i | \(0.474763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.53258 | + | 1.13535i | 0.721490 | + | 0.108747i | 0.499515 | − | 0.866305i | \(-0.333512\pi\) |
0.221975 | + | 0.975052i | \(0.428750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.343928 | − | 4.58941i | 0.0326442 | − | 0.435607i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.43538 | − | 6.28879i | 0.135029 | − | 0.591600i | −0.861456 | − | 0.507831i | \(-0.830447\pi\) |
0.996485 | − | 0.0837684i | \(-0.0266956\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.00377927 | + | 0.00257667i | −0.000352419 | + | 0.000240275i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.282643 | + | 3.77161i | 0.0261304 | + | 0.348686i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00564 | − | 0.618659i | 0.183857 | − | 0.0567124i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.48106 | − | 19.6328i | −0.407369 | − | 1.78480i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.05927 | + | 13.9591i | 0.726680 | + | 1.25865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.04209 | − | 1.30674i | −0.0932077 | − | 0.116879i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.89399 | + | 3.31997i | 0.611743 | + | 0.294600i | 0.713986 | − | 0.700159i | \(-0.246888\pi\) |
−0.102243 | + | 0.994759i | \(0.532602\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0296 | − | 9.12189i | −1.05915 | − | 0.803138i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7172 | + | 7.56902i | 1.37322 | + | 0.661308i | 0.967543 | − | 0.252708i | \(-0.0813211\pi\) |
0.405678 | + | 0.914016i | \(0.367035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.76051 | − | 4.71553i | −0.326077 | − | 0.408888i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.61125 | − | 4.52283i | −0.224741 | − | 0.389263i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.579094 | − | 2.53718i | −0.0494753 | − | 0.216766i | 0.944147 | − | 0.329524i | \(-0.106888\pi\) |
−0.993622 | + | 0.112759i | \(0.964031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.59006 | + | 2.34122i | −0.643780 | + | 0.198580i | −0.599419 | − | 0.800436i | \(-0.704602\pi\) |
−0.0443616 | + | 0.999016i | \(0.514125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.35284 | + | 18.0523i | 0.113929 | + | 1.52028i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.58012 | + | 5.16804i | −0.633881 | + | 0.432173i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38095 | + | 14.8129i | −0.280773 | + | 1.23015i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.114219 | − | 1.52414i | 0.00942058 | − | 0.125709i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.4553 | + | 2.78168i | 1.51191 | + | 0.227884i | 0.852034 | − | 0.523487i | \(-0.175369\pi\) |
0.659880 | + | 0.751371i | \(0.270607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.42384 | − | 4.05671i | 0.685522 | − | 0.330130i | −0.0584978 | − | 0.998288i | \(-0.518631\pi\) |
0.744020 | + | 0.668158i | \(0.232917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.637207 | + | 1.62358i | −0.0515151 | + | 0.131258i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.58821 | − | 8.89656i | −0.770143 | − | 0.714589i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.46599 | + | 0.220962i | −0.116999 | + | 0.0176347i | −0.207280 | − | 0.978282i | \(-0.566461\pi\) |
0.0902820 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.67635 | − | 2.67630i | −0.688080 | − | 0.212244i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.00243469 | + | 0.00305300i | −0.000191880 | + | 0.000240610i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.31184 | − | 13.5344i | −0.416056 | − | 1.06009i | −0.973258 | − | 0.229715i | \(-0.926220\pi\) |
0.557202 | − | 0.830377i | \(-0.311875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.8297 | + | 36.0781i | −1.62159 | + | 2.80868i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.81721 | − | 5.39758i | 0.450149 | − | 0.417677i | −0.422244 | − | 0.906482i | \(-0.638757\pi\) |
0.872393 | + | 0.488805i | \(0.162567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.50774 | − | 5.80048i | −0.654441 | − | 0.446191i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.01198 | 0.383275 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.73137 | −0.131634 | −0.0658169 | − | 0.997832i | \(-0.520965\pi\) | ||||
−0.0658169 | + | 0.997832i | \(0.520965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.6156 | − | 8.60118i | −0.953651 | − | 0.650188i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.15122 | − | 5.70750i | 0.462354 | − | 0.429002i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.07203 | + | 7.05296i | −0.304358 | + | 0.527163i | −0.977118 | − | 0.212698i | \(-0.931775\pi\) |
0.672761 | + | 0.739860i | \(0.265108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.70194 | − | 11.9804i | −0.349493 | − | 0.890493i | −0.992231 | − | 0.124407i | \(-0.960297\pi\) |
0.642739 | − | 0.766086i | \(-0.277798\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2742 | + | 15.3913i | −0.907333 | + | 1.13776i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.19431 | − | 1.91069i | −0.455414 | − | 0.140477i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.18342 | + | 0.630549i | −0.305922 | + | 0.0461103i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.26832 | − | 3.03256i | −0.237735 | − | 0.220586i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.39153 | − | 13.7374i | 0.390118 | − | 0.994003i | −0.592034 | − | 0.805913i | \(-0.701675\pi\) |
0.982152 | − | 0.188090i | \(-0.0602298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7520 | + | 7.58576i | −1.13385 | + | 0.546035i | −0.904145 | − | 0.427225i | \(-0.859491\pi\) |
−0.229708 | + | 0.973260i | \(0.573777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.1372 | + | 1.82939i | 0.869165 | + | 0.131006i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.204205 | + | 2.72492i | −0.0145490 | + | 0.194143i | 0.985193 | + | 0.171447i | \(0.0548441\pi\) |
−0.999742 | + | 0.0226962i | \(0.992775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.867208 | + | 3.79949i | −0.0614747 | + | 0.269338i | −0.996319 | − | 0.0857186i | \(-0.972681\pi\) |
0.934845 | + | 0.355057i | \(0.115539\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.8592 | + | 12.1762i | −1.25969 | + | 0.858845i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.969336 | + | 12.9349i | 0.0680340 | + | 0.907851i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.6943 | − | 6.69181i | 1.51520 | − | 0.467376i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.000722065 | − | 0.00316357i | −5.01870e−5 | − | 0.000219883i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.07864 | + | 10.5285i | 0.420468 | + | 0.728272i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.26808 | + | 7.85992i | 0.431512 | + | 0.541099i | 0.949284 | − | 0.314419i | \(-0.101810\pi\) |
−0.517772 | + | 0.855519i | \(0.673238\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.3284 | − | 6.90020i | −0.981767 | − | 0.472794i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2964 | + | 13.6599i | −1.11140 | + | 0.931595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0606 | − | 4.84492i | −0.682957 | − | 0.328895i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.9456 | − | 19.9952i | −1.07751 | − | 1.35115i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.623252 | + | 1.07950i | 0.0419244 | + | 0.0726152i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.33401 | − | 14.6072i | −0.223262 | − | 0.978173i | −0.955004 | − | 0.296592i | \(-0.904150\pi\) |
0.731743 | − | 0.681581i | \(-0.238707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.1244 | − | 3.73987i | 0.808290 | − | 0.249324i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.663861 | + | 8.85861i | 0.0440620 | + | 0.587966i | 0.974916 | + | 0.222574i | \(0.0714460\pi\) |
−0.930854 | + | 0.365392i | \(0.880935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7625 | − | 11.4285i | 1.10770 | − | 0.755217i | 0.135829 | − | 0.990732i | \(-0.456630\pi\) |
0.971871 | + | 0.235515i | \(0.0756778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.91398 | + | 34.6734i | −0.520702 | + | 2.28134i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.762419 | − | 10.1738i | 0.0499477 | − | 0.666506i | −0.914897 | − | 0.403687i | \(-0.867729\pi\) |
0.964845 | − | 0.262819i | \(-0.0846524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.2132 | + | 3.80028i | 1.64473 | + | 0.247903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5650 | − | 6.53254i | 0.881139 | − | 0.424334i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.91886 | − | 7.43713i | 0.188805 | − | 0.481068i | −0.804858 | − | 0.593468i | \(-0.797759\pi\) |
0.993663 | + | 0.112400i | \(0.0358538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.16388 | + | 5.71925i | 0.397051 | + | 0.368409i | 0.853280 | − | 0.521453i | \(-0.174610\pi\) |
−0.456229 | + | 0.889862i | \(0.650800\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.3750 | − | 2.92031i | 1.24291 | − | 0.187338i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.05713 | − | 0.634540i | −0.131425 | − | 0.0405392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23331 | − | 2.80049i | 0.142102 | − | 0.178191i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.80069 | + | 12.2320i | 0.304231 | + | 0.775168i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.14704 | + | 15.8431i | −0.577356 | + | 1.00001i | 0.418425 | + | 0.908251i | \(0.362582\pi\) |
−0.995781 | + | 0.0917585i | \(0.970751\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.00576989 | − | 0.00535367i | 0.000362750 | − | 0.000336583i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.67673 | + | 3.18854i | 0.292868 | + | 0.199674i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1765 | 1.19620 | 0.598098 | − | 0.801423i | \(-0.295923\pi\) | ||||
0.598098 | + | 0.801423i | \(0.295923\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.53401 | −0.343866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.90586 | − | 6.07191i | −0.551259 | − | 0.375842i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.1950 | + | 9.45955i | −0.628649 | + | 0.583301i | −0.928796 | − | 0.370592i | \(-0.879155\pi\) |
0.300147 | + | 0.953893i | \(0.402964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.39440 | + | 11.0754i | −0.392805 | + | 0.680358i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.26272 | − | 18.5051i | −0.444471 | − | 1.13249i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.8908 | + | 21.1804i | −1.02985 | + | 1.29139i | −0.0740861 | + | 0.997252i | \(0.523604\pi\) |
−0.955763 | + | 0.294138i | \(0.904967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3810 | − | 5.97823i | −1.17731 | − | 0.363152i | −0.356467 | − | 0.934308i | \(-0.616019\pi\) |
−0.820842 | + | 0.571156i | \(0.806495\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3617 | − | 1.56177i | 0.627118 | − | 0.0945228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.5609 | + | 20.9335i | 1.36047 | + | 1.26234i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.37801 | − | 16.2509i | 0.383218 | − | 0.976423i | −0.600966 | − | 0.799274i | \(-0.705217\pi\) |
0.984184 | − | 0.177149i | \(-0.0566873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.36017 | − | 4.02604i | 0.500510 | − | 0.241033i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.2324 | − | 2.29591i | −0.908688 | − | 0.136963i | −0.321966 | − | 0.946751i | \(-0.604344\pi\) |
−0.586722 | + | 0.809789i | \(0.699582\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21194 | − | 16.1722i | 0.0720423 | − | 0.961338i | −0.837691 | − | 0.546144i | \(-0.816095\pi\) |
0.909733 | − | 0.415193i | \(-0.136286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.61938 | − | 15.8575i | 0.214394 | − | 0.939320i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0140 | − | 10.9181i | 0.945274 | − | 0.644477i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.22746 | − | 16.3793i | −0.0722032 | − | 0.963485i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −38.8640 | + | 11.9880i | −2.27825 | + | 0.702747i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.51144 | + | 19.7659i | 0.263561 | + | 1.15474i | 0.917357 | + | 0.398066i | \(0.130318\pi\) |
−0.653796 | + | 0.756671i | \(0.726824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.90953 | − | 10.2356i | −0.344066 | − | 0.595940i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.60323 | + | 7.02623i | 0.325132 | + | 0.407703i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.00208942 | − | 0.00100621i | −0.000120835 | − | 5.81908e-5i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.85698 | + | 15.2442i | −0.568147 | + | 0.878663i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.9527 | − | 10.0903i | −1.20370 | − | 0.579672i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2882 | + | 21.6787i | 0.989917 | + | 1.24132i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.14771 | + | 7.18404i | 0.236722 | + | 0.410015i | 0.959772 | − | 0.280781i | \(-0.0905936\pi\) |
−0.723050 | + | 0.690796i | \(0.757260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.14501 | − | 31.3043i | −0.406466 | − | 1.78084i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.6492 | − | 8.83711i | 1.62455 | − | 0.501107i | 0.657021 | − | 0.753872i | \(-0.271816\pi\) |
0.967528 | + | 0.252766i | \(0.0813402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.488509 | − | 6.51870i | −0.0276122 | − | 0.368459i | −0.993844 | − | 0.110786i | \(-0.964663\pi\) |
0.966232 | − | 0.257673i | \(-0.0829558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.0631 | − | 11.6334i | 0.961399 | − | 0.655471i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.74389 | − | 7.64049i | 0.0979468 | − | 0.429133i | −0.902050 | − | 0.431631i | \(-0.857938\pi\) |
0.999997 | + | 0.00249843i | \(0.000795277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.95386 | − | 26.0724i | 0.109395 | − | 1.45978i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.0100 | − | 2.56384i | −0.949405 | − | 0.143100i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.48823 | − | 0.716692i | 0.0828071 | − | 0.0398778i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.31287 | − | 8.44106i | 0.183765 | − | 0.468226i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8562 | + | 11.9288i | 0.710951 | + | 0.659666i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.5248 | − | 3.24434i | 1.18670 | − | 0.178866i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.1834 | + | 7.15112i | 1.27427 | + | 0.393061i | 0.856810 | − | 0.515633i | \(-0.172443\pi\) |
0.417463 | + | 0.908694i | \(0.362919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.86722 | − | 3.59538i | 0.157123 | − | 0.197025i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1228 | + | 28.3403i | 0.607701 | + | 1.54840i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5673 | − | 28.6953i | 0.902476 | − | 1.56313i | 0.0782058 | − | 0.996937i | \(-0.475081\pi\) |
0.824270 | − | 0.566197i | \(-0.191586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.8865 | − | 10.1012i | 0.591271 | − | 0.548619i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.5968 | + | 12.6791i | 1.00707 | + | 0.686611i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5407 | 0.947111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0105308 | −0.000566957 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.01977 | + | 2.05885i | 0.162110 | + | 0.110525i | 0.641658 | − | 0.766991i | \(-0.278247\pi\) |
−0.479548 | + | 0.877516i | \(0.659199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.09206 | − | 3.79688i | 0.219043 | − | 0.203242i | −0.563017 | − | 0.826445i | \(-0.690359\pi\) |
0.782060 | + | 0.623203i | \(0.214169\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32392 | − | 2.29310i | 0.0706659 | − | 0.122397i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | − | 3.82194i | −0.0798369 | − | 0.203421i | 0.885382 | − | 0.464864i | \(-0.153897\pi\) |
−0.965219 | + | 0.261443i | \(0.915802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9661 | + | 17.5129i | −0.741242 | + | 0.929488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.61754 | + | 1.42432i | 0.244386 | + | 0.0753832i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.63409 | − | 0.397026i | 0.139022 | − | 0.0209542i | −0.0791625 | − | 0.996862i | \(-0.525225\pi\) |
0.218185 | + | 0.975908i | \(0.429986\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.4485 | + | 9.69475i | 0.549919 | + | 0.510250i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.9381 | − | 43.1576i | 0.889021 | − | 2.26519i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.4548 | + | 15.6294i | −1.69876 | + | 0.818080i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.72302 | − | 0.410430i | −0.142141 | − | 0.0214243i | 0.0775865 | − | 0.996986i | \(-0.475279\pi\) |
−0.219727 | + | 0.975561i | \(0.570517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.20359 | + | 16.0609i | −0.0626566 | + | 0.836095i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.42947 | + | 10.6442i | −0.126132 | + | 0.552619i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.6542 | − | 18.8543i | 1.43188 | − | 0.976241i | 0.434751 | − | 0.900551i | \(-0.356836\pi\) |
0.997131 | − | 0.0756903i | \(-0.0241160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.287561 | − | 3.83724i | −0.0148496 | − | 0.198154i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.36115 | + | 2.27061i | −0.379118 | + | 0.116943i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.61567 | − | 15.8413i | −0.185725 | − | 0.813713i | −0.978838 | − | 0.204638i | \(-0.934398\pi\) |
0.793113 | − | 0.609074i | \(-0.208459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.80822 | + | 15.2563i | 0.451259 | + | 0.781603i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5546 | + | 27.0287i | 1.10139 | + | 1.38110i | 0.917303 | + | 0.398191i | \(0.130362\pi\) |
0.184088 | + | 0.982910i | \(0.441067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.1326 | + | 21.7347i | 2.30017 | + | 1.10770i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.79700 | − | 14.3021i | −0.243845 | − | 0.727018i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.7611 | − | 8.07174i | −0.849823 | − | 0.409253i | −0.0423114 | − | 0.999104i | \(-0.513472\pi\) |
−0.807512 | + | 0.589851i | \(0.799186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.000666784 | 0 | 0.000836120i | −3.37207e−5 | 0 | 4.22844e-5i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0814 | + | 34.7819i | 1.01297 | + | 1.75452i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.71885 | − | 20.6746i | −0.237431 | − | 1.04025i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.0394 | − | 8.95748i | 1.45745 | − | 0.449563i | 0.538057 | − | 0.842909i | \(-0.319159\pi\) |
0.919391 | + | 0.393346i | \(0.128682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.03770 | − | 13.8471i | −0.0519497 | − | 0.693221i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.2339 | + | 21.2949i | −1.55975 | + | 1.06342i | −0.593820 | + | 0.804598i | \(0.702381\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.47566 | − | 6.46531i | 0.0735081 | − | 0.322060i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57095 | − | 34.3070i | 0.127752 | − | 1.70473i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0301 | + | 1.66252i | 0.546743 | + | 0.0824083i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.84798 | + | 1.85309i | −0.190271 | + | 0.0916294i | −0.526593 | − | 0.850117i | \(-0.676531\pi\) |
0.336323 | + | 0.941747i | \(0.390817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.18894 | − | 5.57733i | 0.107972 | − | 0.275109i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.39653 | − | 6.86298i | −0.363960 | − | 0.337705i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3014 | − | 2.75849i | 0.898378 | − | 0.135409i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4744 | − | 5.39014i | −0.855725 | − | 0.263956i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.59816 | + | 9.52780i | −0.371195 | + | 0.465463i | −0.931986 | − | 0.362494i | \(-0.881925\pi\) |
0.560792 | + | 0.827957i | \(0.310497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.62044 | − | 9.22474i | −0.176450 | − | 0.449586i | 0.815099 | − | 0.579322i | \(-0.196682\pi\) |
−0.991549 | + | 0.129735i | \(0.958587\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.04437 | + | 15.6653i | −0.439752 | + | 0.761673i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.06535 | − | 2.84423i | 0.148691 | − | 0.137965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.5585 | + | 13.3348i | 0.946502 | + | 0.645314i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.1216 | −1.01976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.4652 | 0.985772 | 0.492886 | − | 0.870094i | \(-0.335942\pi\) | ||||
0.492886 | + | 0.870094i | \(0.335942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.14039 | − | 0.777507i | −0.0548038 | − | 0.0373646i | 0.535608 | − | 0.844467i | \(-0.320082\pi\) |
−0.590412 | + | 0.807102i | \(0.701035\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.6425 | + | 23.7927i | −1.22946 | + | 1.14077i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.00153657 | + | 0.00266142i | −7.35042e−5 | + | 0.000127313i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.75806 | + | 9.57538i | 0.179362 | + | 0.457008i | 0.992074 | − | 0.125659i | \(-0.0401045\pi\) |
−0.812711 | + | 0.582667i | \(0.802009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.952202 | − | 1.19402i | 0.0453430 | − | 0.0568583i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.22921 | − | 1.61300i | −0.248447 | − | 0.0766358i | 0.168030 | − | 0.985782i | \(-0.446259\pi\) |
−0.416477 | + | 0.909146i | \(0.636736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.6872 | + | 4.17318i | −1.31250 | + | 0.197828i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.4985 | + | 29.2263i | 1.48983 | + | 1.38236i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2240 | − | 26.0503i | 0.482499 | − | 1.22939i | −0.457805 | − | 0.889053i | \(-0.651364\pi\) |
0.940304 | − | 0.340335i | \(-0.110541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.1983 | + | 16.9506i | −1.65742 | + | 0.798173i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.2853 | + | 3.20824i | 1.00007 | + | 0.150736i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10296 | − | 14.7180i | 0.0517076 | − | 0.689990i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.19722 | + | 35.9144i | −0.383450 | + | 1.68000i | 0.303131 | + | 0.952949i | \(0.401968\pi\) |
−0.686581 | + | 0.727054i | \(0.740889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.00888 | − | 0.687840i | 0.0470903 | − | 0.0321056i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.984869 | + | 13.1422i | 0.0458699 | + | 0.612092i | 0.972014 | + | 0.234922i | \(0.0754836\pi\) |
−0.926144 | + | 0.377170i | \(0.876897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.5468 | + | 8.49706i | −1.28021 | + | 0.394892i | −0.858955 | − | 0.512052i | \(-0.828886\pi\) |
−0.421253 | + | 0.906943i | \(0.638409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.70086 | − | 29.3584i | −0.310745 | − | 1.36146i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.62410 | − | 2.81302i | −0.0751544 | − | 0.130171i | 0.825999 | − | 0.563672i | \(-0.190612\pi\) |
−0.901153 | + | 0.433500i | \(0.857278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2052 | + | 20.3207i | 0.748286 | + | 0.938321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.07521 | − | 1.48094i | −0.141698 | − | 0.0682383i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.2262 | − | 27.4229i | 1.11392 | − | 1.26090i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8263 | − | 5.21369i | −0.496747 | − | 0.239221i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.65668 | − | 7.09325i | −0.259002 | − | 0.324778i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1630 | − | 19.3348i | −0.510049 | − | 0.883431i | −0.999932 | − | 0.0116426i | \(-0.996294\pi\) |
0.489883 | − | 0.871788i | \(-0.337039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.731330 | − | 3.20417i | −0.0333458 | − | 0.146097i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.00859082 | + | 0.00264992i | −0.000390896 | + | 0.000120575i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.28091 | + | 57.1247i | 0.194386 | + | 2.59390i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1751 | − | 7.61906i | 0.506393 | − | 0.345253i | −0.283022 | − | 0.959114i | \(-0.591337\pi\) |
0.789414 | + | 0.613861i | \(0.210384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.44860 | − | 32.6344i | 0.336837 | − | 1.47578i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.751481 | + | 10.0278i | −0.0339139 | + | 0.452549i | 0.954236 | + | 0.299055i | \(0.0966715\pi\) |
−0.988150 | + | 0.153494i | \(0.950948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.51271 | − | 0.529456i | −0.158205 | − | 0.0238455i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −37.5044 | + | 18.0612i | −1.68570 | + | 0.811789i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.98641 | + | 17.8011i | −0.313383 | + | 0.798488i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.9853 | + | 16.6880i | 0.805135 | + | 0.747056i | 0.970997 | − | 0.239093i | \(-0.0768502\pi\) |
−0.165862 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0659 | − | 2.72299i | 0.807124 | − | 0.121654i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7167 | + | 5.77333i | 0.834535 | + | 0.257420i | 0.682436 | − | 0.730945i | \(-0.260921\pi\) |
0.152099 | + | 0.988365i | \(0.451397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.4228 | + | 25.6094i | −0.908803 | + | 1.13960i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.66092 | − | 22.0677i | −0.384645 | − | 0.980059i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.13596 | − | 3.69959i | 0.0946747 | − | 0.163981i | −0.814798 | − | 0.579745i | \(-0.803152\pi\) |
0.909473 | + | 0.415763i | \(0.136486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.5431 | + | 20.9170i | −0.997250 | + | 0.925312i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.89911 | − | 1.97658i | −0.127999 | − | 0.0872681i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.2260 | −1.99290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.8769 | −1.92970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.29347 | − | 2.24545i | −0.144567 | − | 0.0985642i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.62150 | − | 2.43239i | 0.114850 | − | 0.106565i | −0.620658 | − | 0.784082i | \(-0.713134\pi\) |
0.735507 | + | 0.677517i | \(0.236944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.344694 | − | 0.597027i | 0.0150724 | − | 0.0261062i | −0.858391 | − | 0.512996i | \(-0.828535\pi\) |
0.873463 | + | 0.486890i | \(0.161869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.8428 | − | 32.7228i | −0.560504 | − | 1.42814i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.90671 | − | 2.39094i | 0.0830576 | − | 0.104151i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9782 | − | 6.77937i | −0.955573 | − | 0.294755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.29100 | − | 1.24967i | 0.359799 | − | 0.0542310i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.43783 | + | 7.82916i | 0.365483 | + | 0.339119i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.85191 | + | 22.5543i | −0.382701 | + | 0.975107i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.8930 | + | 8.13525i | −0.728988 | + | 0.351062i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.66310 | + | 0.552124i | 0.157781 | + | 0.0237817i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.98772 | + | 39.8684i | −0.128452 | + | 1.71408i | 0.445579 | + | 0.895243i | \(0.352998\pi\) |
−0.574031 | + | 0.818834i | \(0.694621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.59336 | − | 28.8874i | 0.282948 | − | 1.23968i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.4099 | − | 13.9152i | 0.874263 | − | 0.596063i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.84068 | − | 37.9062i | −0.121459 | − | 1.62075i | −0.641853 | − | 0.766828i | \(-0.721834\pi\) |
0.520394 | − | 0.853926i | \(-0.325785\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.7969 | + | 5.79806i | −0.802231 | + | 0.247455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.27153 | + | 9.95222i | 0.0967704 | + | 0.423979i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.05202 | − | 15.6786i | −0.384931 | − | 0.666720i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.30498 | − | 11.6681i | −0.394974 | − | 0.495282i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9643 | − | 16.3563i | −1.43911 | − | 0.693040i | −0.458445 | − | 0.888723i | \(-0.651593\pi\) |
−0.980667 | + | 0.195683i | \(0.937308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1290 | − | 3.69260i | −0.428410 | − | 0.156180i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.77558 | − | 4.22610i | −0.370505 | − | 0.178426i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6446 | + | 28.3955i | 0.954357 | + | 1.19673i | 0.980391 | + | 0.197065i | \(0.0631409\pi\) |
−0.0260336 | + | 0.999661i | \(0.508288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4587 | − | 18.1150i | −0.440001 | − | 0.762105i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.53552 | − | 28.6340i | −0.274466 | − | 1.20251i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5039 | − | 8.48383i | 1.15302 | − | 0.355661i | 0.341444 | − | 0.939902i | \(-0.389084\pi\) |
0.811580 | + | 0.584241i | \(0.198608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.35501 | + | 18.0813i | 0.0567052 | + | 0.756679i | 0.950998 | + | 0.309197i | \(0.100060\pi\) |
−0.894293 | + | 0.447482i | \(0.852321\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.0722 | − | 19.1393i | 1.17273 | − | 0.799556i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.00173117 | + | 0.00758474i | −7.21947e−5 | + | 0.000316306i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.994996 | + | 13.2773i | −0.0414222 | + | 0.552741i | 0.937430 | + | 0.348173i | \(0.113198\pi\) |
−0.978852 | + | 0.204568i | \(0.934421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.8020 | − | 5.99918i | −1.65411 | − | 0.249318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.2358 | − | 6.85560i | 0.590600 | − | 0.284418i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.04004 | − | 20.4857i | 0.332984 | − | 0.848430i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.99065 | + | 8.34211i | 0.371718 | + | 0.344904i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.55180 | + | 0.987525i | −0.270422 | + | 0.0407595i | −0.282853 | − | 0.959163i | \(-0.591281\pi\) |
0.0124315 | + | 0.999923i | \(0.496043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.39743 | − | 2.59026i | −0.346010 | − | 0.106730i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.92244 | + | 4.91859i | −0.161348 | + | 0.202324i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.57645 | + | 4.01673i | 0.0647371 | + | 0.164947i | 0.959582 | − | 0.281431i | \(-0.0908089\pi\) |
−0.894844 | + | 0.446378i | \(0.852714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.40309 | − | 5.89433i | 0.139513 | − | 0.241644i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.57725 | + | 6.10279i | −0.269189 | + | 0.249771i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.5509 | − | 12.6478i | −0.757968 | − | 0.516774i | 0.121581 | − | 0.992581i | \(-0.461203\pi\) |
−0.879549 | + | 0.475808i | \(0.842156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.82446 | 0.156003 | 0.0780015 | − | 0.996953i | \(-0.475146\pi\) | ||||
0.0780015 | + | 0.996953i | \(0.475146\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.5981 | −0.879544 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −53.9546 | − | 36.7856i | −2.19357 | − | 1.49555i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.0366 | − | 15.8077i | 0.691495 | − | 0.641613i | −0.254018 | − | 0.967200i | \(-0.581752\pi\) |
0.945512 | + | 0.325586i | \(0.105562\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.9316 | + | 25.8622i | −0.605058 | + | 1.04799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.72300 | + | 12.0340i | 0.191072 | + | 0.486844i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.06228 | − | 2.58602i | 0.0832947 | − | 0.104448i | −0.738438 | − | 0.674321i | \(-0.764436\pi\) |
0.821733 | + | 0.569873i | \(0.193008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 49.9463 | + | 15.4064i | 2.01403 | + | 0.621245i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.6142 | − | 5.21724i | 1.39351 | − | 0.210038i | 0.591000 | − | 0.806672i | \(-0.298733\pi\) |
0.802514 | + | 0.596633i | \(0.203495\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1838 | + | 12.2328i | 0.529903 | + | 0.491678i | 0.899142 | − | 0.437656i | \(-0.144191\pi\) |
−0.369239 | + | 0.929334i | \(0.620382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.000829954 | 0.00211469i | −3.33049e−5 | 8.48595e-5i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.5366 | + | 10.3715i | −0.862847 | + | 0.415525i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9097 | + | 3.30236i | 0.876390 | + | 0.132094i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.09165 | + | 27.9111i | −0.0835324 | + | 1.11466i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.337250 | − | 1.47759i | 0.0134471 | − | 0.0589154i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8020 | + | 14.1826i | −0.828114 | + | 0.564599i | −0.901537 | − | 0.432702i | \(-0.857560\pi\) |
0.0734225 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.72965 | + | 23.0805i | 0.0687473 | + | 0.917369i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.7104 | − | 7.31368i | 0.940917 | − | 0.290235i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.242875 | − | 1.06410i | −0.00962304 | − | 0.0421613i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.94543 | − | 13.7619i | −0.314316 | − | 0.544412i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.6472 | + | 28.3987i | 0.894511 | + | 1.12168i | 0.991974 | + | 0.126442i | \(0.0403557\pi\) |
−0.0974634 | + | 0.995239i | \(0.531073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.99826 | + | 1.44389i | 0.118240 | + | 0.0569413i | 0.492069 | − | 0.870556i | \(-0.336241\pi\) |
−0.373829 | + | 0.927498i | \(0.621955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.7151 | + | 4.84914i | −1.91816 | + | 0.190935i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.9436 | − | 18.2727i | −1.49172 | − | 0.718372i | −0.502464 | − | 0.864598i | \(-0.667573\pi\) |
−0.989251 | + | 0.146226i | \(0.953287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6807 | + | 15.9010i | 0.497759 | + | 0.624171i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8541 | − | 22.2639i | −0.503791 | − | 0.872591i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.31138 | − | 23.2707i | −0.207850 | − | 0.910652i | −0.965994 | − | 0.258564i | \(-0.916751\pi\) |
0.758144 | − | 0.652088i | \(-0.226107\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.0559 | − | 16.6740i | 2.11214 | − | 0.651509i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.90971 | − | 25.4833i | −0.0745048 | − | 0.994197i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.95025 | − | 2.69323i | 0.153880 | − | 0.104913i | −0.483932 | − | 0.875105i | \(-0.660792\pi\) |
0.637812 | + | 0.770192i | \(0.279840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.18440 | − | 13.9518i | 0.123859 | − | 0.542662i | −0.874481 | − | 0.485060i | \(-0.838798\pi\) |
0.998340 | − | 0.0576012i | \(-0.0183452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.214460 | + | 2.86177i | −0.00832893 | + | 0.111142i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.3398 | − | 2.91501i | −0.749966 | − | 0.113039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.00595462 | − | 0.00286759i | 0.000230564 | − | 0.000111034i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.6023 | − | 32.1102i | 0.487234 | − | 1.24145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.9771 | − | 32.4540i | −1.35028 | − | 1.25287i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.9150 | + | 3.45387i | −0.883307 | + | 0.133137i | −0.575003 | − | 0.818151i | \(-0.694999\pi\) |
−0.308303 | + | 0.951288i | \(0.599761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.48806 | − | 2.61822i | −0.326706 | − | 0.100775i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.82015 | − | 11.0601i | 0.338986 | − | 0.425075i | −0.582895 | − | 0.812547i | \(-0.698080\pi\) |
0.921881 | + | 0.387472i | \(0.126652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.8669 | + | 45.5241i | 0.685669 | + | 1.74706i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2261 | + | 17.7121i | −0.391864 | + | 0.678728i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9013 | − | 32.3837i | 1.33546 | − | 1.23913i | 0.387060 | − | 0.922054i | \(-0.373491\pi\) |
0.948401 | − | 0.317073i | \(-0.102700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.97264 | − | 4.75386i | −0.266411 | − | 0.181636i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.7080 | 1.78202 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.48401 | −0.247021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1689 | − | 23.2959i | −1.29985 | − | 0.886220i | −0.302096 | − | 0.953277i | \(-0.597686\pi\) |
−0.997749 | + | 0.0670578i | \(0.978639\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.0506 | + | 24.1714i | −0.989581 | + | 0.918197i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8785 | + | 22.3062i | −0.488509 | + | 0.846122i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.93925 | + | 4.94112i | 0.0734543 | + | 0.187158i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.6448 | − | 18.3640i | 0.553919 | − | 0.694592i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.7066 | + | 14.0986i | 1.72632 | + | 0.532498i | 0.989618 | − | 0.143725i | \(-0.0459079\pi\) |
0.736698 | + | 0.676222i | \(0.236384\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.30656 | + | 0.649110i | −0.162425 | + | 0.0244816i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.0326 | + | 39.9284i | 1.62070 | + | 1.50379i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.2163 | + | 26.0308i | −0.384225 | + | 0.978990i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.2688 | + | 12.6504i | −0.986547 | + | 0.475096i | −0.856352 | − | 0.516392i | \(-0.827275\pi\) |
−0.130195 | + | 0.991488i | \(0.541560\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.8761 | + | 2.24221i | 0.557898 | + | 0.0840896i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.000425181 | 0.00567365i | −1.59232e−5 | 0.000212480i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.61995 | + | 29.0039i | −0.247572 | + | 1.08468i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.1977 | − | 10.3616i | 0.567567 | − | 0.386961i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.145367 | − | 1.93979i | −0.00542127 | − | 0.0723418i | 0.993837 | − | 0.110852i | \(-0.0353579\pi\) |
−0.999258 | + | 0.0385100i | \(0.987739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.8946 | + | 11.3805i | −1.37403 | + | 0.423831i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.30772 | + | 18.8734i | 0.160206 | + | 0.701908i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.9212 | + | 22.3802i | 0.479882 | + | 0.831180i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.86302 | − | 7.35200i | −0.217447 | − | 0.272670i | 0.661129 | − | 0.750272i | \(-0.270078\pi\) |
−0.878576 | + | 0.477602i | \(0.841506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9673 | + | 5.76313i | 0.443232 | + | 0.213449i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.46954 | − | 3.56084i | −0.128326 | − | 0.131702i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3172 | + | 5.45007i | 0.418010 | + | 0.201303i | 0.631053 | − | 0.775740i | \(-0.282623\pi\) |
−0.213043 | + | 0.977043i | \(0.568337\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.09018 | − | 3.87496i | −0.113983 | − | 0.142930i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.1947 | − | 45.3706i | −0.964895 | − | 1.67125i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.29738 | + | 40.7345i | 0.342010 | + | 1.49844i | 0.794825 | + | 0.606838i | \(0.207563\pi\) |
−0.452815 | + | 0.891604i | \(0.649580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.88027 | − | 2.43074i | 0.289489 | − | 0.0892955i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.118093 | − | 1.57585i | −0.00433243 | − | 0.0578122i | 0.994619 | − | 0.103605i | \(-0.0330377\pi\) |
−0.998951 | + | 0.0457926i | \(0.985419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.0054 | − | 34.0931i | 1.83206 | − | 1.24908i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.92169 | + | 12.8008i | −0.106899 | + | 0.468356i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.54577 | + | 20.6269i | −0.0564812 | + | 0.753689i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.12248 | + | 0.922815i | 0.223412 | + | 0.0336740i | 0.259794 | − | 0.965664i | \(-0.416345\pi\) |
−0.0363820 | + | 0.999338i | \(0.511583\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.9470 | + | 18.2743i | −1.38286 | + | 0.665953i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.0767 | − | 28.2231i | 0.403124 | − | 1.02714i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.19269 | + | 3.89025i | 0.152386 | + | 0.141394i | 0.752682 | − | 0.658385i | \(-0.228760\pi\) |
−0.600296 | + | 0.799778i | \(0.704950\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0179189 | − | 0.00270084i | 0.000650415 | − | 9.80343e-5i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3236 | + | 5.03516i | 0.591729 | + | 0.182524i | 0.576136 | − | 0.817354i | \(-0.304560\pi\) |
0.0155937 | + | 0.999878i | \(0.495036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1485 | − | 16.4877i | 0.476006 | − | 0.596893i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.06630 | + | 5.26485i | 0.0747073 | + | 0.190351i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.99617 | − | 5.18952i | 0.108185 | − | 0.187383i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.75024 | − | 1.62399i | 0.0631153 | − | 0.0585624i | −0.647985 | − | 0.761653i | \(-0.724388\pi\) |
0.711100 | + | 0.703091i | \(0.248197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.4780 | + | 24.8703i | 1.31372 | + | 0.895682i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.76858 | 0.0636114 | 0.0318057 | − | 0.999494i | \(-0.489874\pi\) | ||||
0.0318057 | + | 0.999494i | \(0.489874\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.2468 | −0.799130 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.5269 | − | 7.17715i | −0.377652 | − | 0.257479i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.1814 | − | 10.3748i | 0.400616 | − | 0.371717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2728 | − | 33.3815i | 0.689635 | − | 1.19448i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.75689 | + | 7.02443i | 0.0985231 | + | 0.251033i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.99744 | + | 3.75867i | −0.106983 | + | 0.134153i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5189 | − | 9.72230i | −1.12353 | − | 0.346563i | −0.323323 | − | 0.946289i | \(-0.604800\pi\) |
−0.800205 | + | 0.599726i | \(0.795276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.6614 | + | 4.77219i | −1.12718 | + | 0.169894i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.0904 | − | 12.1461i | −0.465442 | − | 0.431867i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.13608 | + | 13.0865i | −0.182387 | + | 0.464716i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.5275 | + | 12.7750i | −0.940834 | + | 0.453082i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3286 | + | 3.36550i | 0.790921 | + | 0.119212i | 0.532065 | − | 0.846704i | \(-0.321416\pi\) |
0.258856 | + | 0.965916i | \(0.416654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.445506 | + | 5.94487i | −0.0157609 | + | 0.210314i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.42008 | − | 19.3657i | 0.156176 | − | 0.684252i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.2158 | − | 34.9184i | 1.80737 | − | 1.23224i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.000946286 | 0.0126273i | 3.33522e−5 | 0.000445054i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −59.5993 | + | 18.3839i | −2.09799 | + | 0.647146i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.39510 | + | 10.4936i | 0.0842072 | + | 0.368936i | 0.999421 | − | 0.0340335i | \(-0.0108353\pi\) |
−0.915213 | + | 0.402969i | \(0.867978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.44394 | + | 16.3574i | 0.331621 | + | 0.574385i | 0.982830 | − | 0.184514i | \(-0.0590710\pi\) |
−0.651208 | + | 0.758899i | \(0.725738\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.1137 | − | 36.5074i | −1.02106 | − | 1.28037i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.4786 | − | 20.4566i | −1.48796 | − | 0.716563i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.88263 | + | 13.0192i | −0.205807 | + | 0.455485i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.43359 | + | 4.54298i | 0.329636 | + | 0.158744i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5066 | − | 37.0001i | −1.02979 | − | 1.29131i | −0.955789 | − | 0.294053i | \(-0.904996\pi\) |
−0.0739969 | − | 0.997258i | \(-0.523576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.551677 | + | 0.955532i | 0.0192302 | + | 0.0333078i | 0.875480 | − | 0.483254i | \(-0.160545\pi\) |
−0.856250 | + | 0.516561i | \(0.827212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.7670 | + | 69.0799i | 0.548938 | + | 2.40505i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0646 | + | 6.49756i | −0.732487 | + | 0.225942i | −0.638490 | − | 0.769630i | \(-0.720441\pi\) |
−0.0939973 | + | 0.995572i | \(0.529965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.82921 | − | 51.0972i | −0.132994 | − | 1.77468i | −0.521518 | − | 0.853241i | \(-0.674634\pi\) |
0.388524 | − | 0.921439i | \(-0.372985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.2085 | − | 22.6412i | 1.15199 | − | 0.785414i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.112001 | − | 0.490707i | 0.00388060 | − | 0.0170020i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.92304 | − | 25.6612i | 0.0665496 | − | 0.888043i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.42358 | − | 0.968199i | −0.222031 | − | 0.0334659i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0756 | + | 4.85214i | −0.347847 | + | 0.167514i | −0.599646 | − | 0.800265i | \(-0.704692\pi\) |
0.251799 | + | 0.967780i | \(0.418978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.57428 | + | 6.55915i | −0.0887682 | + | 0.226178i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9979 | − | 24.1225i | −0.895414 | − | 0.830823i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.0175 | + | 4.97658i | −1.13584 | + | 0.171200i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.2718 | − | 16.4322i | −1.83044 | − | 0.564616i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.2794 | − | 29.1914i | 0.798947 | − | 1.00185i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.00103016 | + | 0.00262480i | 3.53133e−5 | + | 8.99769e-5i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.4719 | + | 18.1379i | −0.358553 | + | 0.621031i | −0.987719 | − | 0.156239i | \(-0.950063\pi\) |
0.629167 | + | 0.777270i | \(0.283396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.9140 | − | 11.0546i | 0.407450 | − | 0.378058i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.50785 | + | 4.43698i | 0.222304 | + | 0.151564i | 0.669351 | − | 0.742946i | \(-0.266572\pi\) |
−0.447047 | + | 0.894510i | \(0.647524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.8104 | 1.46067 | 0.730337 | − | 0.683087i | \(-0.239363\pi\) | ||||
0.730337 | + | 0.683087i | \(0.239363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.6221 | 1.52072 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.563855 | − | 0.384430i | −0.0191939 | − | 0.0130861i | 0.553685 | − | 0.832726i | \(-0.313221\pi\) |
−0.572879 | + | 0.819640i | \(0.694174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.11565 | + | 3.81877i | −0.139936 | + | 0.129842i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.9076 | − | 32.7490i | 0.642137 | − | 1.11221i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3319 | + | 33.9692i | 0.452255 | + | 1.15233i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.62403 | + | 12.0682i | −0.326098 | + | 0.408914i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.8335 | − | 11.9785i | −1.31431 | − | 0.405412i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.57534 | + | 0.689622i | −0.154675 | + | 0.0233135i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.4736 | − | 23.6361i | −0.860183 | − | 0.798133i | 0.120709 | − | 0.992688i | \(-0.461483\pi\) |
−0.980892 | + | 0.194555i | \(0.937674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.0530 | + | 43.4502i | −0.575182 | + | 1.46554i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.50466 | − | 1.68776i | 0.118075 | − | 0.0568620i | −0.373914 | − | 0.927463i | \(-0.621984\pi\) |
0.491989 | + | 0.870602i | \(0.336270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.9489 | − | 5.56915i | −1.24343 | − | 0.187417i | −0.505817 | − | 0.862641i | \(-0.668809\pi\) |
−0.737613 | + | 0.675224i | \(0.764047\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.03346 | − | 27.1346i | 0.0683540 | − | 0.912120i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0666391 | + | 0.291965i | −0.00223752 | + | 0.00980322i | −0.976034 | − | 0.217617i | \(-0.930172\pi\) |
0.973797 | + | 0.227420i | \(0.0730289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.5021 | − | 11.9327i | 0.587002 | − | 0.400211i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.42409 | + | 59.0353i | 0.148212 | + | 1.97776i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.3700 | − | 5.04948i | 0.547802 | − | 0.168975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.87658 | + | 25.7470i | 0.196432 | + | 0.860627i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.00266959 | − | 0.00462386i | −8.91349e−5 | − | 0.000154386i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7835 | + | 14.7760i | 0.393001 | + | 0.492807i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.69397 | − | 1.29735i | −0.0897490 | − | 0.0432209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.5207 | + | 16.2143i | −1.28189 | + | 0.539578i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.6012 | − | 18.1078i | −1.24991 | − | 0.601924i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.3860 | + | 24.3092i | 0.643700 | + | 0.807175i | 0.991460 | − | 0.130409i | \(-0.0416290\pi\) |
−0.347760 | + | 0.937584i | \(0.613058\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.6187 | − | 20.1242i | −0.385369 | − | 0.667479i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.55930 | − | 28.7382i | −0.217319 | − | 0.952139i | −0.959449 | − | 0.281882i | \(-0.909041\pi\) |
0.742130 | − | 0.670256i | \(-0.233816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.4337 | + | 9.38756i | −1.00721 | + | 0.310683i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.77059 | + | 63.6590i | 0.157711 | + | 2.10450i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.9021 | − | 27.2048i | 1.31768 | − | 0.898382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.58384 | − | 15.7018i | 0.118220 | − | 0.517956i | −0.880792 | − | 0.473504i | \(-0.842989\pi\) |
0.999012 | − | 0.0444515i | \(-0.0141540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.42722 | + | 19.0449i | −0.0470285 | + | 0.627551i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.2300 | − | 1.69265i | −0.369641 | − | 0.0557144i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.93354 | + | 4.78374i | −0.326613 | + | 0.157288i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.7217 | − | 29.8663i | 0.384990 | − | 0.980939i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.5691 | − | 15.3739i | −0.543616 | − | 0.504402i | 0.359880 | − | 0.932999i | \(-0.382818\pi\) |
−0.903496 | + | 0.428597i | \(0.859008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.43021 | + | 0.215569i | −0.0468732 | + | 0.00706499i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.9584 | + | 20.3455i | 2.15938 | + | 0.666080i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.55366 | + | 10.7260i | −0.279735 | + | 0.350776i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9474 | + | 30.4414i | 0.390304 | + | 0.994478i | 0.982095 | + | 0.188387i | \(0.0603258\pi\) |
−0.591791 | + | 0.806091i | \(0.701579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.52496 | − | 13.0336i | 0.245568 | − | 0.425336i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.214487 | + | 0.199015i | −0.00699209 | + | 0.00648771i | −0.683661 | − | 0.729800i | \(-0.739613\pi\) |
0.676669 | + | 0.736287i | \(0.263423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.00815951 | − | 0.00556306i | −0.000265710 | − | 0.000181158i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.4578 | −0.470313 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5390 | −0.439959 | −0.219979 | − | 0.975504i | \(-0.570599\pi\) | ||||
−0.219979 | + | 0.975504i | \(0.570599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0900 | − | 10.2882i | −0.489841 | − | 0.333968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.2264 | − | 12.2723i | 0.428894 | − | 0.397956i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.90661 | + | 11.9626i | −0.223727 | + | 0.387507i | −0.955937 | − | 0.293573i | \(-0.905156\pi\) |
0.732210 | + | 0.681079i | \(0.238489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.4834 | − | 44.5469i | −0.565749 | − | 1.44151i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.5305 | − | 47.0617i | 1.21319 | − | 1.52129i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.88440 | − | 2.12356i | −0.222309 | − | 0.0685732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5658 | − | 2.19544i | 0.469865 | − | 0.0708207i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6001 | − | 11.6912i | −0.406034 | − | 0.376744i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.7127 | + | 52.7752i | −0.666767 | + | 1.69889i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3525 | + | 4.98550i | −0.332914 | + | 0.160323i | −0.592871 | − | 0.805297i | \(-0.702006\pi\) |
0.259958 | + | 0.965620i | \(0.416291\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.76044 | + | 0.566795i | 0.120803 | + | 0.0182081i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.68142 | + | 49.1251i | −0.118142 | + | 1.57650i | 0.551729 | + | 0.834023i | \(0.313968\pi\) |
−0.669872 | + | 0.742477i | \(0.733651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.89301 | + | 21.4377i | −0.156863 | + | 0.687261i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.2492 | − | 11.7603i | 0.552416 | − | 0.376631i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.57239 | − | 34.3262i | −0.0822982 | − | 1.09819i | −0.873560 | − | 0.486716i | \(-0.838195\pi\) |
0.791262 | − | 0.611477i | \(-0.209424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.0416 | − | 14.2020i | 1.47150 | − | 0.453897i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.89949 | + | 17.0848i | 0.124501 | + | 0.545476i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.3956 | + | 40.5224i | 0.746205 | + | 1.29247i | 0.949630 | + | 0.313375i | \(0.101460\pi\) |
−0.203424 | + | 0.979091i | \(0.565207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.52476 | + | 6.92783i | 0.176033 | + | 0.220739i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45.1527 | + | 21.7444i | 1.43723 | + | 0.692131i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.00906527 | + | 0.00183748i | 0.000288259 | + | 5.84285e-5i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.0704 | + | 10.1470i | 0.669325 | + | 0.322330i | 0.737503 | − | 0.675343i | \(-0.236005\pi\) |
−0.0681788 | + | 0.997673i | \(0.521719\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.8256 | + | 43.6700i | 1.10516 | + | 1.38582i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.31882 | + | 10.9445i | 0.200320 | + | 0.346964i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0399 | + | 48.3689i | 0.349637 | + | 1.53186i | 0.778007 | + | 0.628255i | \(0.216231\pi\) |
−0.428370 | + | 0.903603i | \(0.640912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.07642 | + | 0.948949i | −0.0973335 | + | 0.0300234i |
(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 | 688.2.bg.c.369.2 | 36 | ||
4.3 | odd | 2 | 43.2.g.a.25.1 | ✓ | 36 | ||
12.11 | even | 2 | 387.2.y.c.154.3 | 36 | |||
43.31 | even | 21 | inner | 688.2.bg.c.289.2 | 36 | ||
172.31 | odd | 42 | 43.2.g.a.31.1 | yes | 36 | ||
172.103 | odd | 42 | 1849.2.a.n.1.14 | 18 | |||
172.155 | even | 42 | 1849.2.a.o.1.5 | 18 | |||
516.203 | even | 42 | 387.2.y.c.289.3 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.25.1 | ✓ | 36 | 4.3 | odd | 2 | ||
43.2.g.a.31.1 | yes | 36 | 172.31 | odd | 42 | ||
387.2.y.c.154.3 | 36 | 12.11 | even | 2 | |||
387.2.y.c.289.3 | 36 | 516.203 | even | 42 | |||
688.2.bg.c.289.2 | 36 | 43.31 | even | 21 | inner | ||
688.2.bg.c.369.2 | 36 | 1.1 | even | 1 | trivial | ||
1849.2.a.n.1.14 | 18 | 172.103 | odd | 42 | |||
1849.2.a.o.1.5 | 18 | 172.155 | even | 42 |