Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(197,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.11 | ||
Character | \(\chi\) | \(=\) | 735.197 |
Dual form | 735.2.j.h.638.11 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.54414 | − | 1.54414i | 1.09187 | − | 1.09187i | 0.0965442 | − | 0.995329i | \(-0.469221\pi\) |
0.995329 | − | 0.0965442i | \(-0.0307789\pi\) | |||||||
\(3\) | 1.73204 | − | 0.00622252i | 0.999994 | − | 0.00359257i | ||||
\(4\) | − | 2.76875i | − | 1.38437i | ||||||
\(5\) | 0.252500 | + | 2.22177i | 0.112921 | + | 0.993604i | ||||
\(6\) | 2.66491 | − | 2.68412i | 1.08794 | − | 1.09579i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.18705 | − | 1.18705i | −0.419686 | − | 0.419686i | ||||
\(9\) | 2.99992 | − | 0.0215553i | 0.999974 | − | 0.00718510i | ||||
\(10\) | 3.82062 | + | 3.04083i | 1.20819 | + | 0.961593i | ||||
\(11\) | 3.38507i | 1.02064i | 0.859986 | + | 0.510318i | \(0.170472\pi\) | ||||
−0.859986 | + | 0.510318i | \(0.829528\pi\) | |||||||
\(12\) | −0.0172286 | − | 4.79558i | −0.00497346 | − | 1.38436i | ||||
\(13\) | 0.206632 | − | 0.206632i | 0.0573094 | − | 0.0573094i | −0.677871 | − | 0.735181i | \(-0.737097\pi\) |
0.735181 | + | 0.677871i | \(0.237097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.451165 | + | 3.84662i | 0.116490 | + | 0.993192i | ||||
\(16\) | 1.87154 | 0.467884 | ||||||||
\(17\) | −0.167409 | + | 0.167409i | −0.0406026 | + | 0.0406026i | −0.727117 | − | 0.686514i | \(-0.759140\pi\) |
0.686514 | + | 0.727117i | \(0.259140\pi\) | |||||||
\(18\) | 4.59902 | − | 4.66559i | 1.08400 | − | 1.09969i | ||||
\(19\) | − | 5.31419i | − | 1.21916i | −0.792725 | − | 0.609579i | \(-0.791338\pi\) | ||
0.792725 | − | 0.609579i | \(-0.208662\pi\) | |||||||
\(20\) | 6.15151 | − | 0.699108i | 1.37552 | − | 0.156325i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.22702 | + | 5.22702i | 1.11440 | + | 1.11440i | ||||
\(23\) | −5.07773 | − | 5.07773i | −1.05878 | − | 1.05878i | −0.998161 | − | 0.0606179i | \(-0.980693\pi\) |
−0.0606179 | − | 0.998161i | \(-0.519307\pi\) | |||||||
\(24\) | −2.06341 | − | 2.04864i | −0.421191 | − | 0.418176i | ||||
\(25\) | −4.87249 | + | 1.12199i | −0.974497 | + | 0.224398i | ||||
\(26\) | − | 0.638138i | − | 0.125149i | ||||||
\(27\) | 5.19585 | − | 0.0560017i | 0.999942 | − | 0.0107775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.84268 | −0.527872 | −0.263936 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263936 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(30\) | 6.63638 | + | 5.24306i | 1.21163 | + | 0.957247i | ||||
\(31\) | −9.11776 | −1.63760 | −0.818799 | − | 0.574081i | \(-0.805360\pi\) | ||||
−0.818799 | + | 0.574081i | \(0.805360\pi\) | |||||||
\(32\) | 5.26402 | − | 5.26402i | 0.930557 | − | 0.930557i | ||||
\(33\) | 0.0210636 | + | 5.86307i | 0.00366671 | + | 1.02063i | ||||
\(34\) | 0.517005i | 0.0886657i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0596812 | − | 8.30602i | −0.00994686 | − | 1.38434i | ||||
\(37\) | −5.27013 | − | 5.27013i | −0.866404 | − | 0.866404i | 0.125668 | − | 0.992072i | \(-0.459893\pi\) |
−0.992072 | + | 0.125668i | \(0.959893\pi\) | |||||||
\(38\) | −8.20586 | − | 8.20586i | −1.33117 | − | 1.33117i | ||||
\(39\) | 0.356609 | − | 0.359180i | 0.0571031 | − | 0.0575149i | ||||
\(40\) | 2.33762 | − | 2.93708i | 0.369611 | − | 0.464394i | ||||
\(41\) | − | 0.0314968i | − | 0.00491898i | −0.999997 | − | 0.00245949i | \(-0.999217\pi\) | ||
0.999997 | − | 0.00245949i | \(-0.000782881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.76875 | + | 3.76875i | −0.574728 | + | 0.574728i | −0.933446 | − | 0.358718i | \(-0.883214\pi\) |
0.358718 | + | 0.933446i | \(0.383214\pi\) | |||||||
\(44\) | 9.37239 | 1.41294 | ||||||||
\(45\) | 0.805371 | + | 6.65968i | 0.120058 | + | 0.992767i | ||||
\(46\) | −15.6815 | −2.31210 | ||||||||
\(47\) | 3.56639 | − | 3.56639i | 0.520211 | − | 0.520211i | −0.397424 | − | 0.917635i | \(-0.630096\pi\) |
0.917635 | + | 0.397424i | \(0.130096\pi\) | |||||||
\(48\) | 3.24158 | − | 0.0116457i | 0.467881 | − | 0.00168091i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.79130 | + | 9.25632i | −0.819013 | + | 1.30904i | ||||
\(51\) | −0.288917 | + | 0.291000i | −0.0404564 | + | 0.0407482i | ||||
\(52\) | −0.572111 | − | 0.572111i | −0.0793376 | − | 0.0793376i | ||||
\(53\) | 3.55291 | + | 3.55291i | 0.488030 | + | 0.488030i | 0.907684 | − | 0.419654i | \(-0.137849\pi\) |
−0.419654 | + | 0.907684i | \(0.637849\pi\) | |||||||
\(54\) | 7.93665 | − | 8.10960i | 1.08004 | − | 1.10358i | ||||
\(55\) | −7.52082 | + | 0.854729i | −1.01411 | + | 0.115252i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0330677 | − | 9.20439i | −0.00437992 | − | 1.21915i | ||||
\(58\) | −4.38949 | + | 4.38949i | −0.576369 | + | 0.576369i | ||||
\(59\) | 10.3168 | 1.34313 | 0.671565 | − | 0.740946i | \(-0.265622\pi\) | ||||
0.671565 | + | 0.740946i | \(0.265622\pi\) | |||||||
\(60\) | 10.6503 | − | 1.24916i | 1.37495 | − | 0.161266i | ||||
\(61\) | 6.80634 | 0.871462 | 0.435731 | − | 0.900077i | \(-0.356490\pi\) | ||||
0.435731 | + | 0.900077i | \(0.356490\pi\) | |||||||
\(62\) | −14.0791 | + | 14.0791i | −1.78805 | + | 1.78805i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 12.5137i | − | 1.56422i | ||||||
\(65\) | 0.511262 | + | 0.406913i | 0.0634143 | + | 0.0504714i | ||||
\(66\) | 9.08593 | + | 9.02088i | 1.11840 | + | 1.11039i | ||||
\(67\) | 6.34806 | + | 6.34806i | 0.775539 | + | 0.775539i | 0.979069 | − | 0.203530i | \(-0.0652413\pi\) |
−0.203530 | + | 0.979069i | \(0.565241\pi\) | |||||||
\(68\) | 0.463512 | + | 0.463512i | 0.0562091 | + | 0.0562091i | ||||
\(69\) | −8.82642 | − | 8.76323i | −1.06258 | − | 1.05497i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.95454i | 0.469318i | 0.972078 | + | 0.234659i | \(0.0753973\pi\) | ||||
−0.972078 | + | 0.234659i | \(0.924603\pi\) | |||||||
\(72\) | −3.58665 | − | 3.53548i | −0.422691 | − | 0.416660i | ||||
\(73\) | −8.61099 | + | 8.61099i | −1.00784 | + | 1.00784i | −0.00787086 | + | 0.999969i | \(0.502505\pi\) |
−0.999969 | + | 0.00787086i | \(0.997495\pi\) | |||||||
\(74\) | −16.2757 | −1.89201 | ||||||||
\(75\) | −8.43236 | + | 1.97365i | −0.973685 | + | 0.227898i | ||||
\(76\) | −14.7136 | −1.68777 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.00397083 | − | 1.10528i | −0.000449608 | − | 0.125148i | ||||
\(79\) | − | 11.4449i | − | 1.28766i | −0.765170 | − | 0.643828i | \(-0.777345\pi\) | ||
0.765170 | − | 0.643828i | \(-0.222655\pi\) | |||||||
\(80\) | 0.472563 | + | 4.15812i | 0.0528342 | + | 0.464892i | ||||
\(81\) | 8.99907 | − | 0.129328i | 0.999897 | − | 0.0143698i | ||||
\(82\) | −0.0486356 | − | 0.0486356i | −0.00537090 | − | 0.00537090i | ||||
\(83\) | −3.88059 | − | 3.88059i | −0.425951 | − | 0.425951i | 0.461296 | − | 0.887246i | \(-0.347385\pi\) |
−0.887246 | + | 0.461296i | \(0.847385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.414214 | − | 0.329672i | −0.0449278 | − | 0.0357580i | ||||
\(86\) | 11.6390i | 1.25506i | ||||||||
\(87\) | −4.92363 | + | 0.0176886i | −0.527868 | + | 0.00189642i | ||||
\(88\) | 4.01825 | − | 4.01825i | 0.428347 | − | 0.428347i | ||||
\(89\) | −2.00190 | −0.212201 | −0.106100 | − | 0.994355i | \(-0.533836\pi\) | ||||
−0.106100 | + | 0.994355i | \(0.533836\pi\) | |||||||
\(90\) | 11.5271 | + | 9.03989i | 1.21506 | + | 0.952888i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.0589 | + | 14.0589i | −1.46574 | + | 1.46574i | ||||
\(93\) | −15.7923 | + | 0.0567354i | −1.63759 | + | 0.00588319i | ||||
\(94\) | − | 11.0140i | − | 1.13601i | ||||||
\(95\) | 11.8069 | − | 1.34183i | 1.21136 | − | 0.137669i | ||||
\(96\) | 9.08474 | − | 9.15025i | 0.927208 | − | 0.933894i | ||||
\(97\) | −2.26760 | − | 2.26760i | −0.230240 | − | 0.230240i | 0.582553 | − | 0.812793i | \(-0.302054\pi\) |
−0.812793 | + | 0.582553i | \(0.802054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0729661 | + | 10.1549i | 0.00733337 | + | 1.02061i | ||||
\(100\) | 3.10651 | + | 13.4907i | 0.310651 | + | 1.34907i | ||||
\(101\) | 8.63630i | 0.859344i | 0.902985 | + | 0.429672i | \(0.141371\pi\) | ||||
−0.902985 | + | 0.429672i | \(0.858629\pi\) | |||||||
\(102\) | 0.00321708 | + | 0.895474i | 0.000318538 | + | 0.0886651i | ||||
\(103\) | −0.964332 | + | 0.964332i | −0.0950185 | + | 0.0950185i | −0.753018 | − | 0.658000i | \(-0.771403\pi\) |
0.658000 | + | 0.753018i | \(0.271403\pi\) | |||||||
\(104\) | −0.490566 | −0.0481039 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9724 | 1.06573 | ||||||||
\(107\) | −2.95847 | + | 2.95847i | −0.286007 | + | 0.286007i | −0.835499 | − | 0.549492i | \(-0.814821\pi\) |
0.549492 | + | 0.835499i | \(0.314821\pi\) | |||||||
\(108\) | −0.155055 | − | 14.3860i | −0.0149201 | − | 1.38429i | ||||
\(109\) | − | 2.82182i | − | 0.270281i | −0.990826 | − | 0.135141i | \(-0.956851\pi\) | ||
0.990826 | − | 0.135141i | \(-0.0431486\pi\) | |||||||
\(110\) | −10.2934 | + | 12.9330i | −0.981436 | + | 1.23312i | ||||
\(111\) | −9.16087 | − | 9.09528i | −0.869511 | − | 0.863286i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.01798 | + | 2.01798i | 0.189835 | + | 0.189835i | 0.795625 | − | 0.605790i | \(-0.207143\pi\) |
−0.605790 | + | 0.795625i | \(0.707143\pi\) | |||||||
\(114\) | −14.2639 | − | 14.1618i | −1.33594 | − | 1.32638i | ||||
\(115\) | 9.99939 | − | 12.5636i | 0.932448 | − | 1.17157i | ||||
\(116\) | 7.87065i | 0.730771i | ||||||||
\(117\) | 0.615426 | − | 0.624334i | 0.0568961 | − | 0.0577197i | ||||
\(118\) | 15.9306 | − | 15.9306i | 1.46653 | − | 1.46653i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.03058 | − | 5.10169i | 0.367940 | − | 0.465719i | ||||
\(121\) | −0.458667 | −0.0416970 | ||||||||
\(122\) | 10.5099 | − | 10.5099i | 0.951526 | − | 0.951526i | ||||
\(123\) | −0.000195990 | − | 0.0545538i | −1.76718e−5 | − | 0.00491895i | ||||
\(124\) | 25.2448i | 2.26705i | ||||||||
\(125\) | −3.72311 | − | 10.5422i | −0.333005 | − | 0.942925i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6271 | − | 11.6271i | −1.03174 | − | 1.03174i | −0.999480 | − | 0.0322583i | \(-0.989730\pi\) |
−0.0322583 | − | 0.999480i | \(-0.510270\pi\) | |||||||
\(128\) | −8.79491 | − | 8.79491i | −0.777367 | − | 0.777367i | ||||
\(129\) | −6.50417 | + | 6.55107i | −0.572660 | + | 0.576789i | ||||
\(130\) | 1.41779 | − | 0.161130i | 0.124349 | − | 0.0141320i | ||||
\(131\) | 12.7013i | 1.10972i | 0.831943 | + | 0.554861i | \(0.187228\pi\) | ||||
−0.831943 | + | 0.554861i | \(0.812772\pi\) | |||||||
\(132\) | 16.2333 | − | 0.0583199i | 1.41293 | − | 0.00507609i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 19.6046 | 1.69358 | ||||||||
\(135\) | 1.43638 | + | 11.5298i | 0.123623 | + | 0.992329i | ||||
\(136\) | 0.397446 | 0.0340807 | ||||||||
\(137\) | −5.19451 | + | 5.19451i | −0.443797 | + | 0.443797i | −0.893286 | − | 0.449489i | \(-0.851606\pi\) |
0.449489 | + | 0.893286i | \(0.351606\pi\) | |||||||
\(138\) | −27.1609 | + | 0.0975782i | −2.31209 | + | 0.00830641i | ||||
\(139\) | 12.3138i | 1.04444i | 0.852810 | + | 0.522221i | \(0.174897\pi\) | ||||
−0.852810 | + | 0.522221i | \(0.825103\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.15493 | − | 6.19932i | 0.518339 | − | 0.522077i | ||||
\(142\) | 6.10637 | + | 6.10637i | 0.512435 | + | 0.512435i | ||||
\(143\) | 0.699463 | + | 0.699463i | 0.0584920 | + | 0.0584920i | ||||
\(144\) | 5.61447 | − | 0.0403416i | 0.467872 | − | 0.00336180i | ||||
\(145\) | −0.717776 | − | 6.31576i | −0.0596080 | − | 0.524495i | ||||
\(146\) | 26.5932i | 2.20087i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.5917 | + | 14.5917i | −1.19943 | + | 1.19943i | ||||
\(149\) | 18.9350 | 1.55121 | 0.775607 | − | 0.631216i | \(-0.217444\pi\) | ||||
0.775607 | + | 0.631216i | \(0.217444\pi\) | |||||||
\(150\) | −9.97316 | + | 16.0684i | −0.814305 | + | 1.31198i | ||||
\(151\) | −1.90527 | −0.155049 | −0.0775243 | − | 0.996990i | \(-0.524702\pi\) | ||||
−0.0775243 | + | 0.996990i | \(0.524702\pi\) | |||||||
\(152\) | −6.30822 | + | 6.30822i | −0.511665 | + | 0.511665i | ||||
\(153\) | −0.498604 | + | 0.505822i | −0.0403098 | + | 0.0408933i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.30223 | − | 20.2575i | −0.184920 | − | 1.62712i | ||||
\(156\) | −0.994479 | − | 0.987359i | −0.0796221 | − | 0.0790520i | ||||
\(157\) | 4.31728 | + | 4.31728i | 0.344557 | + | 0.344557i | 0.858077 | − | 0.513521i | \(-0.171659\pi\) |
−0.513521 | + | 0.858077i | \(0.671659\pi\) | |||||||
\(158\) | −17.6726 | − | 17.6726i | −1.40596 | − | 1.40596i | ||||
\(159\) | 6.17589 | + | 6.13167i | 0.489780 | + | 0.486273i | ||||
\(160\) | 13.0246 | + | 10.3663i | 1.02968 | + | 0.819525i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.6961 | − | 14.0955i | 1.07607 | − | 1.10745i | ||||
\(163\) | 3.57655 | − | 3.57655i | 0.280137 | − | 0.280137i | −0.553027 | − | 0.833164i | \(-0.686527\pi\) |
0.833164 | + | 0.553027i | \(0.186527\pi\) | |||||||
\(164\) | −0.0872068 | −0.00680970 | ||||||||
\(165\) | −13.0210 | + | 1.52722i | −1.01369 | + | 0.118894i | ||||
\(166\) | −11.9844 | −0.930168 | ||||||||
\(167\) | 6.39241 | − | 6.39241i | 0.494659 | − | 0.494659i | −0.415111 | − | 0.909771i | \(-0.636257\pi\) |
0.909771 | + | 0.415111i | \(0.136257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9146i | 0.993431i | ||||||||
\(170\) | −1.14866 | + | 0.130544i | −0.0880986 | + | 0.0100123i | ||||
\(171\) | −0.114549 | − | 15.9422i | −0.00875978 | − | 1.21913i | ||||
\(172\) | 10.4347 | + | 10.4347i | 0.795638 | + | 0.795638i | ||||
\(173\) | −3.88791 | − | 3.88791i | −0.295592 | − | 0.295592i | 0.543692 | − | 0.839285i | \(-0.317026\pi\) |
−0.839285 | + | 0.543692i | \(0.817026\pi\) | |||||||
\(174\) | −7.57546 | + | 7.63009i | −0.574294 | + | 0.578436i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.33528i | 0.477540i | ||||||||
\(177\) | 17.8691 | − | 0.0641964i | 1.34312 | − | 0.00482529i | ||||
\(178\) | −3.09121 | + | 3.09121i | −0.231696 | + | 0.231696i | ||||
\(179\) | −14.6322 | −1.09366 | −0.546832 | − | 0.837242i | \(-0.684166\pi\) | ||||
−0.546832 | + | 0.837242i | \(0.684166\pi\) | |||||||
\(180\) | 18.4390 | − | 2.22987i | 1.37436 | − | 0.166205i | ||||
\(181\) | 9.83718 | 0.731192 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7888 | − | 0.0423526i | 0.871456 | − | 0.00313079i | ||||
\(184\) | 12.0551i | 0.888710i | ||||||||
\(185\) | 10.3783 | − | 13.0397i | 0.763027 | − | 0.958698i | ||||
\(186\) | −24.2980 | + | 24.4732i | −1.78161 | + | 1.79446i | ||||
\(187\) | −0.566689 | − | 0.566689i | −0.0414404 | − | 0.0414404i | ||||
\(188\) | −9.87442 | − | 9.87442i | −0.720166 | − | 0.720166i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.1595 | − | 20.3035i | 1.17234 | − | 1.47297i | ||||
\(191\) | − | 6.37886i | − | 0.461558i | −0.973006 | − | 0.230779i | \(-0.925873\pi\) | ||
0.973006 | − | 0.230779i | \(-0.0741275\pi\) | |||||||
\(192\) | −0.0778669 | − | 21.6743i | −0.00561956 | − | 1.56421i | ||||
\(193\) | 7.56336 | − | 7.56336i | 0.544422 | − | 0.544422i | −0.380400 | − | 0.924822i | \(-0.624214\pi\) |
0.924822 | + | 0.380400i | \(0.124214\pi\) | |||||||
\(194\) | −7.00299 | −0.502785 | ||||||||
\(195\) | 0.888059 | + | 0.701608i | 0.0635952 | + | 0.0502432i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01490 | + | 1.01490i | −0.0723090 | + | 0.0723090i | −0.742336 | − | 0.670027i | \(-0.766282\pi\) |
0.670027 | + | 0.742336i | \(0.266282\pi\) | |||||||
\(198\) | 15.7933 | + | 15.5680i | 1.12238 | + | 1.10637i | ||||
\(199\) | − | 9.40041i | − | 0.666378i | −0.942860 | − | 0.333189i | \(-0.891875\pi\) | ||
0.942860 | − | 0.333189i | \(-0.108125\pi\) | |||||||
\(200\) | 7.11576 | + | 4.45204i | 0.503160 | + | 0.314806i | ||||
\(201\) | 11.0346 | + | 10.9556i | 0.778320 | + | 0.772748i | ||||
\(202\) | 13.3357 | + | 13.3357i | 0.938295 | + | 0.938295i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.805705 | + | 0.799937i | 0.0564107 | + | 0.0560068i | ||||
\(205\) | 0.0699786 | − | 0.00795295i | 0.00488752 | − | 0.000555458i | ||||
\(206\) | 2.97813i | 0.207496i | ||||||||
\(207\) | −15.3422 | − | 15.1233i | −1.06636 | − | 1.05114i | ||||
\(208\) | 0.386719 | − | 0.386719i | 0.0268142 | − | 0.0268142i | ||||
\(209\) | 17.9889 | 1.24432 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.29157 | −0.570815 | −0.285407 | − | 0.958406i | \(-0.592129\pi\) | ||||
−0.285407 | + | 0.958406i | \(0.592129\pi\) | |||||||
\(212\) | 9.83710 | − | 9.83710i | 0.675615 | − | 0.675615i | ||||
\(213\) | 0.0246072 | + | 6.84942i | 0.00168606 | + | 0.469315i | ||||
\(214\) | 9.13661i | 0.624566i | ||||||||
\(215\) | −9.32488 | − | 7.42166i | −0.635952 | − | 0.506153i | ||||
\(216\) | −6.23422 | − | 6.10127i | −0.424185 | − | 0.415139i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.35729 | − | 4.35729i | −0.295113 | − | 0.295113i | ||||
\(219\) | −14.8610 | + | 14.9682i | −1.00421 | + | 1.01145i | ||||
\(220\) | 2.36653 | + | 20.8232i | 0.159551 | + | 1.40390i | ||||
\(221\) | 0.0691839i | 0.00465382i | ||||||||
\(222\) | −28.1901 | + | 0.101276i | −1.89199 | + | 0.00679717i | ||||
\(223\) | −3.86020 | + | 3.86020i | −0.258498 | + | 0.258498i | −0.824443 | − | 0.565945i | \(-0.808511\pi\) |
0.565945 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.5929 | + | 3.47092i | −0.972860 | + | 0.231394i | ||||
\(226\) | 6.23208 | 0.414552 | ||||||||
\(227\) | −1.50739 | + | 1.50739i | −0.100049 | + | 0.100049i | −0.755360 | − | 0.655310i | \(-0.772538\pi\) |
0.655310 | + | 0.755360i | \(0.272538\pi\) | |||||||
\(228\) | −25.4846 | + | 0.0915560i | −1.68776 | + | 0.00606344i | ||||
\(229\) | 6.26009i | 0.413678i | 0.978375 | + | 0.206839i | \(0.0663177\pi\) | ||||
−0.978375 | + | 0.206839i | \(0.933682\pi\) | |||||||
\(230\) | −3.95957 | − | 34.8405i | −0.261086 | − | 2.29732i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.37440 | + | 3.37440i | 0.221541 | + | 0.221541i | ||||
\(233\) | −2.67422 | − | 2.67422i | −0.175194 | − | 0.175194i | 0.614063 | − | 0.789257i | \(-0.289534\pi\) |
−0.789257 | + | 0.614063i | \(0.789534\pi\) | |||||||
\(234\) | −0.0137553 | − | 1.91436i | −0.000899209 | − | 0.125146i | ||||
\(235\) | 8.82419 | + | 7.02317i | 0.575627 | + | 0.458141i | ||||
\(236\) | − | 28.5645i | − | 1.85939i | ||||||
\(237\) | −0.0712164 | − | 19.8231i | −0.00462600 | − | 1.28765i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.08521 | 0.134881 | 0.0674406 | − | 0.997723i | \(-0.478517\pi\) | ||||
0.0674406 | + | 0.997723i | \(0.478517\pi\) | |||||||
\(240\) | 0.844372 | + | 7.19909i | 0.0545040 | + | 0.464699i | ||||
\(241\) | 5.43686 | 0.350219 | 0.175110 | − | 0.984549i | \(-0.443972\pi\) | ||||
0.175110 | + | 0.984549i | \(0.443972\pi\) | |||||||
\(242\) | −0.708247 | + | 0.708247i | −0.0455279 | + | 0.0455279i | ||||
\(243\) | 15.5859 | − | 0.279999i | 0.999839 | − | 0.0179619i | ||||
\(244\) | − | 18.8450i | − | 1.20643i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0845414 | − | 0.0839361i | −0.00539016 | − | 0.00535157i | ||||
\(247\) | −1.09808 | − | 1.09808i | −0.0698692 | − | 0.0698692i | ||||
\(248\) | 10.8233 | + | 10.8233i | 0.687278 | + | 0.687278i | ||||
\(249\) | −6.74549 | − | 6.69720i | −0.427478 | − | 0.424418i | ||||
\(250\) | −22.0277 | − | 10.5297i | −1.39315 | − | 0.665956i | ||||
\(251\) | 23.3428i | 1.47339i | 0.676227 | + | 0.736693i | \(0.263614\pi\) | ||||
−0.676227 | + | 0.736693i | \(0.736386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.1884 | − | 17.1884i | 1.08063 | − | 1.08063i | ||||
\(254\) | −35.9078 | −2.25305 | ||||||||
\(255\) | −0.719486 | − | 0.568428i | −0.0450559 | − | 0.0355963i | ||||
\(256\) | −2.13372 | −0.133358 | ||||||||
\(257\) | −10.9273 | + | 10.9273i | −0.681627 | + | 0.681627i | −0.960367 | − | 0.278740i | \(-0.910083\pi\) |
0.278740 | + | 0.960367i | \(0.410083\pi\) | |||||||
\(258\) | 0.0724236 | + | 20.1591i | 0.00450890 | + | 1.25505i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.12664 | − | 1.41556i | 0.0698712 | − | 0.0877890i | ||||
\(261\) | −8.52781 | + | 0.0612747i | −0.527858 | + | 0.00379281i | ||||
\(262\) | 19.6127 | + | 19.6127i | 1.21167 | + | 1.21167i | ||||
\(263\) | 18.1808 | + | 18.1808i | 1.12108 | + | 1.12108i | 0.991580 | + | 0.129497i | \(0.0413364\pi\) |
0.129497 | + | 0.991580i | \(0.458664\pi\) | |||||||
\(264\) | 6.93477 | − | 6.98477i | 0.426805 | − | 0.429883i | ||||
\(265\) | −6.99662 | + | 8.79084i | −0.429799 | + | 0.540017i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.46737 | + | 0.0124569i | −0.212199 | + | 0.000762347i | ||||
\(268\) | 17.5762 | − | 17.5762i | 1.07364 | − | 1.07364i | ||||
\(269\) | −28.5125 | −1.73844 | −0.869219 | − | 0.494428i | \(-0.835378\pi\) | ||||
−0.869219 | + | 0.494428i | \(0.835378\pi\) | |||||||
\(270\) | 20.0216 | + | 15.5857i | 1.21848 | + | 0.948516i | ||||
\(271\) | −3.12214 | −0.189656 | −0.0948282 | − | 0.995494i | \(-0.530230\pi\) | ||||
−0.0948282 | + | 0.995494i | \(0.530230\pi\) | |||||||
\(272\) | −0.313312 | + | 0.313312i | −0.0189973 | + | 0.0189973i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0421i | 0.969139i | ||||||||
\(275\) | −3.79802 | − | 16.4937i | −0.229029 | − | 0.994607i | ||||
\(276\) | −24.2631 | + | 24.4381i | −1.46047 | + | 1.47100i | ||||
\(277\) | 12.2472 | + | 12.2472i | 0.735861 | + | 0.735861i | 0.971774 | − | 0.235913i | \(-0.0758081\pi\) |
−0.235913 | + | 0.971774i | \(0.575808\pi\) | |||||||
\(278\) | 19.0142 | + | 19.0142i | 1.14040 | + | 1.14040i | ||||
\(279\) | −27.3526 | + | 0.196536i | −1.63756 | + | 0.0117663i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7181i | 0.758698i | 0.925254 | + | 0.379349i | \(0.123852\pi\) | ||||
−0.925254 | + | 0.379349i | \(0.876148\pi\) | |||||||
\(282\) | −0.0685349 | − | 19.0767i | −0.00408120 | − | 1.13600i | ||||
\(283\) | 19.8271 | − | 19.8271i | 1.17860 | − | 1.17860i | 0.198495 | − | 0.980102i | \(-0.436395\pi\) |
0.980102 | − | 0.198495i | \(-0.0636053\pi\) | |||||||
\(284\) | 10.9491 | 0.649711 | ||||||||
\(285\) | 20.4416 | − | 2.39758i | 1.21086 | − | 0.142020i | ||||
\(286\) | 2.16014 | 0.127732 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 15.6782 | − | 15.9051i | 0.923847 | − | 0.937219i | ||||
\(289\) | 16.9439i | 0.996703i | ||||||||
\(290\) | −10.8608 | − | 8.64408i | −0.637767 | − | 0.507598i | ||||
\(291\) | −3.94168 | − | 3.91346i | −0.231066 | − | 0.229411i | ||||
\(292\) | 23.8416 | + | 23.8416i | 1.39523 | + | 1.39523i | ||||
\(293\) | 6.72836 | + | 6.72836i | 0.393075 | + | 0.393075i | 0.875782 | − | 0.482707i | \(-0.160346\pi\) |
−0.482707 | + | 0.875782i | \(0.660346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.60499 | + | 22.9215i | 0.151668 | + | 1.33454i | ||||
\(296\) | 12.5118i | 0.727236i | ||||||||
\(297\) | 0.189570 | + | 17.5883i | 0.0109999 | + | 1.02058i | ||||
\(298\) | 29.2383 | − | 29.2383i | 1.69373 | − | 1.69373i | ||||
\(299\) | −2.09844 | −0.121356 | ||||||||
\(300\) | 5.46455 | + | 23.3471i | 0.315496 | + | 1.34794i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.94201 | + | 2.94201i | −0.169293 | + | 0.169293i | ||||
\(303\) | 0.0537396 | + | 14.9584i | 0.00308726 | + | 0.859339i | ||||
\(304\) | − | 9.94571i | − | 0.570426i | ||||||
\(305\) | 1.71860 | + | 15.1221i | 0.0984068 | + | 0.865888i | ||||
\(306\) | 0.0111442 | + | 1.55098i | 0.000637072 | + | 0.0886634i | ||||
\(307\) | −10.1105 | − | 10.1105i | −0.577034 | − | 0.577034i | 0.357051 | − | 0.934085i | \(-0.383782\pi\) |
−0.934085 | + | 0.357051i | \(0.883782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.66426 | + | 1.67626i | −0.0946765 | + | 0.0953592i | ||||
\(310\) | −34.8355 | − | 27.7255i | −1.97852 | − | 1.57470i | ||||
\(311\) | 0.394155i | 0.0223505i | 0.999938 | + | 0.0111752i | \(0.00355726\pi\) | ||||
−0.999938 | + | 0.0111752i | \(0.996443\pi\) | |||||||
\(312\) | −0.849680 | + | 0.00305256i | −0.0481036 | + | 0.000172817i | ||||
\(313\) | 10.3810 | − | 10.3810i | 0.586767 | − | 0.586767i | −0.349987 | − | 0.936754i | \(-0.613814\pi\) |
0.936754 | + | 0.349987i | \(0.113814\pi\) | |||||||
\(314\) | 13.3330 | 0.752424 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −31.6881 | −1.78260 | ||||||||
\(317\) | −19.8075 | + | 19.8075i | −1.11250 | + | 1.11250i | −0.119688 | + | 0.992812i | \(0.538190\pi\) |
−0.992812 | + | 0.119688i | \(0.961810\pi\) | |||||||
\(318\) | 19.0046 | − | 0.0682759i | 1.06573 | − | 0.00382872i | ||||
\(319\) | − | 9.62264i | − | 0.538764i | ||||||
\(320\) | 27.8026 | − | 3.15971i | 1.55421 | − | 0.176633i | ||||
\(321\) | −5.10579 | + | 5.14260i | −0.284977 | + | 0.287032i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.889642 | + | 0.889642i | 0.0495010 | + | 0.0495010i | ||||
\(324\) | −0.358078 | − | 24.9161i | −0.0198932 | − | 1.38423i | ||||
\(325\) | −0.774972 | + | 1.23865i | −0.0429877 | + | 0.0687080i | ||||
\(326\) | − | 11.0454i | − | 0.611748i | ||||||
\(327\) | −0.0175588 | − | 4.88750i | −0.000971005 | − | 0.270279i | ||||
\(328\) | −0.0373884 | + | 0.0373884i | −0.00206443 | + | 0.00206443i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −17.7481 | + | 22.4646i | −0.977000 | + | 1.23663i | ||||
\(331\) | −24.7348 | −1.35955 | −0.679774 | − | 0.733422i | \(-0.737922\pi\) | ||||
−0.679774 | + | 0.733422i | \(0.737922\pi\) | |||||||
\(332\) | −10.7444 | + | 10.7444i | −0.589674 | + | 0.589674i | ||||
\(333\) | −15.9236 | − | 15.6964i | −0.872607 | − | 0.860157i | ||||
\(334\) | − | 19.7416i | − | 1.08021i | ||||||
\(335\) | −12.5010 | + | 15.7068i | −0.683004 | + | 0.858154i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40139 | − | 3.40139i | −0.185286 | − | 0.185286i | 0.608369 | − | 0.793655i | \(-0.291824\pi\) |
−0.793655 | + | 0.608369i | \(0.791824\pi\) | |||||||
\(338\) | 19.9420 | + | 19.9420i | 1.08470 | + | 1.08470i | ||||
\(339\) | 3.50777 | + | 3.48266i | 0.190516 | + | 0.189152i | ||||
\(340\) | −0.912779 | + | 1.14685i | −0.0495024 | + | 0.0621968i | ||||
\(341\) | − | 30.8642i | − | 1.67139i | ||||||
\(342\) | −24.7938 | − | 24.4401i | −1.34070 | − | 1.32157i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.94740 | 0.482411 | ||||||||
\(345\) | 17.2412 | − | 21.8229i | 0.928233 | − | 1.17491i | ||||
\(346\) | −12.0070 | −0.645498 | ||||||||
\(347\) | 24.0324 | − | 24.0324i | 1.29013 | − | 1.29013i | 0.355421 | − | 0.934706i | \(-0.384337\pi\) |
0.934706 | − | 0.355421i | \(-0.115663\pi\) | |||||||
\(348\) | 0.0489753 | + | 13.6323i | 0.00262535 | + | 0.730766i | ||||
\(349\) | − | 9.37078i | − | 0.501607i | −0.968038 | − | 0.250803i | \(-0.919305\pi\) | ||
0.968038 | − | 0.250803i | \(-0.0806947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06206 | − | 1.08520i | 0.0566884 | − | 0.0579237i | ||||
\(352\) | 17.8191 | + | 17.8191i | 0.949759 | + | 0.949759i | ||||
\(353\) | −14.5888 | − | 14.5888i | −0.776481 | − | 0.776481i | 0.202750 | − | 0.979231i | \(-0.435012\pi\) |
−0.979231 | + | 0.202750i | \(0.935012\pi\) | |||||||
\(354\) | 27.4932 | − | 27.6915i | 1.46125 | − | 1.47179i | ||||
\(355\) | −8.78606 | + | 0.998522i | −0.466316 | + | 0.0529960i | ||||
\(356\) | 5.54275i | 0.293765i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.5942 | + | 22.5942i | −1.19414 | + | 1.19414i | ||||
\(359\) | 27.2654 | 1.43901 | 0.719506 | − | 0.694486i | \(-0.244368\pi\) | ||||
0.719506 | + | 0.694486i | \(0.244368\pi\) | |||||||
\(360\) | 6.94938 | − | 8.86141i | 0.366264 | − | 0.467037i | ||||
\(361\) | −9.24062 | −0.486349 | ||||||||
\(362\) | 15.1900 | − | 15.1900i | 0.798369 | − | 0.798369i | ||||
\(363\) | −0.794430 | + | 0.00285407i | −0.0416968 | + | 0.000149800i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.3059 | − | 16.9573i | −1.11520 | − | 0.887587i | ||||
\(366\) | 18.1382 | − | 18.2690i | 0.948101 | − | 0.954938i | ||||
\(367\) | −15.9239 | − | 15.9239i | −0.831218 | − | 0.831218i | 0.156465 | − | 0.987683i | \(-0.449990\pi\) |
−0.987683 | + | 0.156465i | \(0.949990\pi\) | |||||||
\(368\) | −9.50315 | − | 9.50315i | −0.495386 | − | 0.495386i | ||||
\(369\) | −0.000678924 | − | 0.0944881i | −3.53434e−5 | − | 0.00491885i | ||||
\(370\) | −4.10960 | − | 36.1607i | −0.213648 | − | 1.87990i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.157086 | + | 43.7249i | 0.00814453 | + | 2.26703i | ||||
\(373\) | 23.3283 | − | 23.3283i | 1.20790 | − | 1.20790i | 0.236189 | − | 0.971707i | \(-0.424102\pi\) |
0.971707 | − | 0.236189i | \(-0.0758984\pi\) | |||||||
\(374\) | −1.75010 | −0.0904954 | ||||||||
\(375\) | −6.51417 | − | 18.2364i | −0.336390 | − | 0.941723i | ||||
\(376\) | −8.46698 | −0.436651 | ||||||||
\(377\) | −0.587387 | + | 0.587387i | −0.0302520 | + | 0.0302520i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 37.4477i | − | 1.92356i | −0.273828 | − | 0.961779i | \(-0.588290\pi\) | ||
0.273828 | − | 0.961779i | \(-0.411710\pi\) | |||||||
\(380\) | −3.71520 | − | 32.6903i | −0.190586 | − | 1.67698i | ||||
\(381\) | −20.2109 | − | 20.0662i | −1.03544 | − | 1.02802i | ||||
\(382\) | −9.84986 | − | 9.84986i | −0.503963 | − | 0.503963i | ||||
\(383\) | 4.95443 | + | 4.95443i | 0.253159 | + | 0.253159i | 0.822265 | − | 0.569105i | \(-0.192710\pi\) |
−0.569105 | + | 0.822265i | \(0.692710\pi\) | |||||||
\(384\) | −15.2879 | − | 15.1784i | −0.780155 | − | 0.774570i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 23.3578i | − | 1.18888i | ||||||
\(387\) | −11.2247 | + | 11.3872i | −0.570584 | + | 0.578843i | ||||
\(388\) | −6.27841 | + | 6.27841i | −0.318738 | + | 0.318738i | ||||
\(389\) | 9.20279 | 0.466600 | 0.233300 | − | 0.972405i | \(-0.425048\pi\) | ||||
0.233300 | + | 0.972405i | \(0.425048\pi\) | |||||||
\(390\) | 2.45467 | − | 0.287905i | 0.124297 | − | 0.0145787i | ||||
\(391\) | 1.70011 | 0.0859783 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0790344 | + | 21.9992i | 0.00398676 | + | 1.10971i | ||||
\(394\) | 3.13431i | 0.157904i | ||||||||
\(395\) | 25.4280 | − | 2.88985i | 1.27942 | − | 0.145404i | ||||
\(396\) | 28.1164 | − | 0.202025i | 1.41290 | − | 0.0101521i | ||||
\(397\) | −21.9242 | − | 21.9242i | −1.10034 | − | 1.10034i | −0.994369 | − | 0.105976i | \(-0.966203\pi\) |
−0.105976 | − | 0.994369i | \(-0.533797\pi\) | |||||||
\(398\) | −14.5156 | − | 14.5156i | −0.727600 | − | 0.727600i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.11904 | + | 2.09985i | −0.455952 | + | 0.104993i | ||||
\(401\) | 25.7514i | 1.28596i | 0.765882 | + | 0.642982i | \(0.222303\pi\) | ||||
−0.765882 | + | 0.642982i | \(0.777697\pi\) | |||||||
\(402\) | 33.9560 | − | 0.121990i | 1.69357 | − | 0.00608431i | ||||
\(403\) | −1.88402 | + | 1.88402i | −0.0938497 | + | 0.0938497i | ||||
\(404\) | 23.9117 | 1.18965 | ||||||||
\(405\) | 2.55960 | + | 19.9612i | 0.127188 | + | 0.991879i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.8397 | − | 17.8397i | 0.884283 | − | 0.884283i | ||||
\(408\) | 0.688392 | − | 0.00247311i | 0.0340805 | − | 0.000122437i | ||||
\(409\) | 10.9496i | 0.541425i | 0.962660 | + | 0.270712i | \(0.0872592\pi\) | ||||
−0.962660 | + | 0.270712i | \(0.912741\pi\) | |||||||
\(410\) | 0.0957764 | − | 0.120337i | 0.00473006 | − | 0.00594304i | ||||
\(411\) | −8.96477 | + | 9.02942i | −0.442200 | + | 0.445388i | ||||
\(412\) | 2.66999 | + | 2.66999i | 0.131541 | + | 0.131541i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −47.0431 | + | 0.338019i | −2.31204 | + | 0.0166127i | ||||
\(415\) | 7.64192 | − | 9.60162i | 0.375127 | − | 0.471325i | ||||
\(416\) | − | 2.17543i | − | 0.106659i | ||||||
\(417\) | 0.0766229 | + | 21.3280i | 0.00375224 | + | 1.04444i | ||||
\(418\) | 27.7774 | − | 27.7774i | 1.35864 | − | 1.35864i | ||||
\(419\) | 5.86958 | 0.286748 | 0.143374 | − | 0.989669i | \(-0.454205\pi\) | ||||
0.143374 | + | 0.989669i | \(0.454205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8842 | 1.31026 | 0.655129 | − | 0.755517i | \(-0.272614\pi\) | ||||
0.655129 | + | 0.755517i | \(0.272614\pi\) | |||||||
\(422\) | −12.8034 | + | 12.8034i | −0.623257 | + | 0.623257i | ||||
\(423\) | 10.6220 | − | 10.7758i | 0.516460 | − | 0.523936i | ||||
\(424\) | − | 8.43498i | − | 0.409639i | ||||||
\(425\) | 0.627865 | − | 1.00353i | 0.0304559 | − | 0.0486782i | ||||
\(426\) | 10.6145 | + | 10.5385i | 0.514273 | + | 0.510591i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.19126 | + | 8.19126i | 0.395940 | + | 0.395940i | ||||
\(429\) | 1.21585 | + | 1.20714i | 0.0587018 | + | 0.0582815i | ||||
\(430\) | −25.8590 | + | 2.93884i | −1.24703 | + | 0.141723i | ||||
\(431\) | 4.18118i | 0.201400i | 0.994917 | + | 0.100700i | \(0.0321083\pi\) | ||||
−0.994917 | + | 0.100700i | \(0.967892\pi\) | |||||||
\(432\) | 9.72423 | − | 0.104809i | 0.467857 | − | 0.00504264i | ||||
\(433\) | 2.20877 | − | 2.20877i | 0.106146 | − | 0.106146i | −0.652039 | − | 0.758185i | \(-0.726086\pi\) |
0.758185 | + | 0.652039i | \(0.226086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.28252 | − | 10.9347i | −0.0614919 | − | 0.524278i | ||||
\(436\) | −7.81290 | −0.374170 | ||||||||
\(437\) | −26.9840 | + | 26.9840i | −1.29082 | + | 1.29082i | ||||
\(438\) | 0.165477 | + | 46.0604i | 0.00790678 | + | 2.20085i | ||||
\(439\) | 27.6028i | 1.31741i | 0.752401 | + | 0.658706i | \(0.228896\pi\) | ||||
−0.752401 | + | 0.658706i | \(0.771104\pi\) | |||||||
\(440\) | 9.94222 | + | 7.91300i | 0.473977 | + | 0.377238i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.106830 | + | 0.106830i | 0.00508138 | + | 0.00508138i | ||||
\(443\) | 12.3040 | + | 12.3040i | 0.584582 | + | 0.584582i | 0.936159 | − | 0.351577i | \(-0.114354\pi\) |
−0.351577 | + | 0.936159i | \(0.614354\pi\) | |||||||
\(444\) | −25.1825 | + | 25.3641i | −1.19511 | + | 1.20373i | ||||
\(445\) | −0.505479 | − | 4.44775i | −0.0239620 | − | 0.210843i | ||||
\(446\) | 11.9214i | 0.564494i | ||||||||
\(447\) | 32.7961 | − | 0.117823i | 1.55120 | − | 0.00557285i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.1859 | −1.61333 | −0.806666 | − | 0.591008i | \(-0.798730\pi\) | ||||
−0.806666 | + | 0.591008i | \(0.798730\pi\) | |||||||
\(450\) | −17.1739 | + | 27.8931i | −0.809586 | + | 1.31489i | ||||
\(451\) | 0.106619 | 0.00502049 | ||||||||
\(452\) | 5.58726 | − | 5.58726i | 0.262803 | − | 0.262803i | ||||
\(453\) | −3.30000 | + | 0.0118556i | −0.155048 | + | 0.000557024i | ||||
\(454\) | 4.65526i | 0.218482i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.8868 | + | 10.9653i | −0.509823 | + | 0.513499i | ||||
\(457\) | −9.31021 | − | 9.31021i | −0.435513 | − | 0.435513i | 0.454986 | − | 0.890499i | \(-0.349644\pi\) |
−0.890499 | + | 0.454986i | \(0.849644\pi\) | |||||||
\(458\) | 9.66646 | + | 9.66646i | 0.451684 | + | 0.451684i | ||||
\(459\) | −0.860455 | + | 0.879206i | −0.0401626 | + | 0.0410378i | ||||
\(460\) | −34.7855 | − | 27.6858i | −1.62188 | − | 1.29086i | ||||
\(461\) | − | 25.6579i | − | 1.19501i | −0.801865 | − | 0.597505i | \(-0.796159\pi\) | ||
0.801865 | − | 0.597505i | \(-0.203841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2170 | − | 13.2170i | 0.614248 | − | 0.614248i | −0.329802 | − | 0.944050i | \(-0.606982\pi\) |
0.944050 | + | 0.329802i | \(0.106982\pi\) | |||||||
\(464\) | −5.32017 | −0.246983 | ||||||||
\(465\) | −4.11361 | − | 35.0725i | −0.190764 | − | 1.62645i | ||||
\(466\) | −8.25874 | −0.382579 | ||||||||
\(467\) | 19.6659 | − | 19.6659i | 0.910031 | − | 0.910031i | −0.0862431 | − | 0.996274i | \(-0.527486\pi\) |
0.996274 | + | 0.0862431i | \(0.0274862\pi\) | |||||||
\(468\) | −1.72862 | − | 1.70396i | −0.0799056 | − | 0.0787655i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.4706 | − | 2.78104i | 1.12874 | − | 0.128280i | ||||
\(471\) | 7.50457 | + | 7.45084i | 0.345792 | + | 0.343317i | ||||
\(472\) | −12.2466 | − | 12.2466i | −0.563693 | − | 0.563693i | ||||
\(473\) | −12.7575 | − | 12.7575i | −0.586588 | − | 0.586588i | ||||
\(474\) | −30.7196 | − | 30.4997i | −1.41100 | − | 1.40090i | ||||
\(475\) | 5.96248 | + | 25.8933i | 0.273577 | + | 1.18807i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7350 | + | 10.5819i | 0.491524 | + | 0.484510i | ||||
\(478\) | 3.21986 | − | 3.21986i | 0.147273 | − | 0.147273i | ||||
\(479\) | 26.9725 | 1.23240 | 0.616202 | − | 0.787588i | \(-0.288670\pi\) | ||||
0.616202 | + | 0.787588i | \(0.288670\pi\) | |||||||
\(480\) | 22.6236 | + | 17.8737i | 1.03262 | + | 0.815821i | ||||
\(481\) | −2.17795 | −0.0993062 | ||||||||
\(482\) | 8.39528 | − | 8.39528i | 0.382395 | − | 0.382395i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.26993i | 0.0577242i | ||||||||
\(485\) | 4.46551 | − | 5.61064i | 0.202768 | − | 0.254766i | ||||
\(486\) | 23.6345 | − | 24.4993i | 1.07208 | − | 1.11131i | ||||
\(487\) | −28.6505 | − | 28.6505i | −1.29828 | − | 1.29828i | −0.929529 | − | 0.368749i | \(-0.879786\pi\) |
−0.368749 | − | 0.929529i | \(-0.620214\pi\) | |||||||
\(488\) | −8.07948 | − | 8.07948i | −0.365741 | − | 0.365741i | ||||
\(489\) | 6.17247 | − | 6.21698i | 0.279129 | − | 0.281141i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.74522i | 0.123890i | 0.998080 | + | 0.0619450i | \(0.0197303\pi\) | ||||
−0.998080 | + | 0.0619450i | \(0.980270\pi\) | |||||||
\(492\) | −0.151046 | 0.000542646i | −0.00680966 | 2.44644e-5i | ||||||
\(493\) | 0.475888 | − | 0.475888i | 0.0214329 | − | 0.0214329i | ||||
\(494\) | −3.39119 | −0.152577 | ||||||||
\(495\) | −22.5435 | + | 2.72623i | −1.01325 | + | 0.122535i | ||||
\(496\) | −17.0642 | −0.766206 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −20.7574 | + | 0.0745730i | −0.930162 | + | 0.00334170i | ||||
\(499\) | 30.3151i | 1.35709i | 0.734558 | + | 0.678546i | \(0.237389\pi\) | ||||
−0.734558 | + | 0.678546i | \(0.762611\pi\) | |||||||
\(500\) | −29.1887 | + | 10.3083i | −1.30536 | + | 0.461003i | ||||
\(501\) | 11.0321 | − | 11.1117i | 0.492879 | − | 0.496433i | ||||
\(502\) | 36.0446 | + | 36.0446i | 1.60875 | + | 1.60875i | ||||
\(503\) | 0.331820 | + | 0.331820i | 0.0147951 | + | 0.0147951i | 0.714466 | − | 0.699671i | \(-0.246670\pi\) |
−0.699671 | + | 0.714466i | \(0.746670\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.1878 | + | 2.18067i | −0.853848 | + | 0.0970384i | ||||
\(506\) | − | 53.0827i | − | 2.35982i | ||||||
\(507\) | 0.0803614 | + | 22.3686i | 0.00356898 | + | 0.993425i | ||||
\(508\) | −32.1925 | + | 32.1925i | −1.42831 | + | 1.42831i | ||||
\(509\) | −14.6491 | −0.649311 | −0.324656 | − | 0.945832i | \(-0.605248\pi\) | ||||
−0.324656 | + | 0.945832i | \(0.605248\pi\) | |||||||
\(510\) | −1.98872 | + | 0.233255i | −0.0880620 | + | 0.0103287i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.2950 | − | 14.2950i | 0.631758 | − | 0.631758i | ||||
\(513\) | −0.297604 | − | 27.6117i | −0.0131395 | − | 1.21909i | ||||
\(514\) | 33.7466i | 1.48850i | ||||||||
\(515\) | −2.38601 | − | 1.89903i | −0.105140 | − | 0.0836811i | ||||
\(516\) | 18.1382 | + | 18.0084i | 0.798492 | + | 0.792775i | ||||
\(517\) | 12.0725 | + | 12.0725i | 0.530946 | + | 0.530946i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.75820 | − | 6.70982i | −0.296652 | − | 0.294528i | ||||
\(520\) | −0.123868 | − | 1.08992i | −0.00543197 | − | 0.0477963i | ||||
\(521\) | 24.6501i | 1.07994i | 0.841683 | + | 0.539971i | \(0.181565\pi\) | ||||
−0.841683 | + | 0.539971i | \(0.818435\pi\) | |||||||
\(522\) | −13.0735 | + | 13.2628i | −0.572212 | + | 0.580495i | ||||
\(523\) | 23.4069 | − | 23.4069i | 1.02351 | − | 1.02351i | 0.0237950 | − | 0.999717i | \(-0.492425\pi\) |
0.999717 | − | 0.0237950i | \(-0.00757491\pi\) | |||||||
\(524\) | 35.1668 | 1.53627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 56.1475 | 2.44815 | ||||||||
\(527\) | 1.52639 | − | 1.52639i | 0.0664907 | − | 0.0664907i | ||||
\(528\) | 0.0394214 | + | 10.9730i | 0.00171560 | + | 0.477536i | ||||
\(529\) | 28.5666i | 1.24203i | ||||||||
\(530\) | 2.77053 | + | 24.3781i | 0.120344 | + | 1.05892i | ||||
\(531\) | 30.9495 | − | 0.222381i | 1.34310 | − | 0.00965053i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.00650825 | − | 0.00650825i | −0.000281904 | − | 0.000281904i | ||||
\(534\) | −5.33487 | + | 5.37334i | −0.230862 | + | 0.232527i | ||||
\(535\) | −7.32005 | − | 5.82602i | −0.316473 | − | 0.251881i | ||||
\(536\) | − | 15.0710i | − | 0.650967i | ||||||
\(537\) | −25.3436 | + | 0.0910493i | −1.09366 | + | 0.00392907i | ||||
\(538\) | −44.0273 | + | 44.0273i | −1.89815 | + | 1.89815i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 31.9232 | − | 3.97696i | 1.37375 | − | 0.171141i | ||||
\(541\) | −27.2143 | −1.17003 | −0.585017 | − | 0.811021i | \(-0.698912\pi\) | ||||
−0.585017 | + | 0.811021i | \(0.698912\pi\) | |||||||
\(542\) | −4.82102 | + | 4.82102i | −0.207081 | + | 0.207081i | ||||
\(543\) | 17.0384 | − | 0.0612121i | 0.731187 | − | 0.00262686i | ||||
\(544\) | 1.76249i | 0.0755660i | ||||||||
\(545\) | 6.26942 | − | 0.712509i | 0.268552 | − | 0.0305205i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.63475 | − | 3.63475i | −0.155411 | − | 0.155411i | 0.625119 | − | 0.780530i | \(-0.285051\pi\) |
−0.780530 | + | 0.625119i | \(0.785051\pi\) | |||||||
\(548\) | 14.3823 | + | 14.3823i | 0.614380 | + | 0.614380i | ||||
\(549\) | 20.4185 | − | 0.146713i | 0.871440 | − | 0.00626154i | ||||
\(550\) | −31.3333 | − | 19.6039i | −1.33605 | − | 0.835914i | ||||
\(551\) | 15.1065i | 0.643559i | ||||||||
\(552\) | 0.0750128 | + | 20.8798i | 0.00319276 | + | 0.888705i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 37.8227 | 1.60693 | ||||||||
\(555\) | 17.8945 | − | 22.6499i | 0.759578 | − | 0.961433i | ||||
\(556\) | 34.0938 | 1.44590 | ||||||||
\(557\) | 5.91751 | − | 5.91751i | 0.250733 | − | 0.250733i | −0.570538 | − | 0.821271i | \(-0.693265\pi\) |
0.821271 | + | 0.570538i | \(0.193265\pi\) | |||||||
\(558\) | −41.9328 | + | 42.5397i | −1.77516 | + | 1.80085i | ||||
\(559\) | 1.55749i | 0.0658747i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.985055 | − | 0.978002i | −0.0415890 | − | 0.0412913i | ||||
\(562\) | 19.6385 | + | 19.6385i | 0.828402 | + | 0.828402i | ||||
\(563\) | 13.8267 | + | 13.8267i | 0.582728 | + | 0.582728i | 0.935652 | − | 0.352924i | \(-0.114813\pi\) |
−0.352924 | + | 0.935652i | \(0.614813\pi\) | |||||||
\(564\) | −17.1643 | − | 17.0414i | −0.722749 | − | 0.717574i | ||||
\(565\) | −3.97393 | + | 4.99301i | −0.167185 | + | 0.210058i | ||||
\(566\) | − | 61.2316i | − | 2.57376i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.69425 | − | 4.69425i | 0.196966 | − | 0.196966i | ||||
\(569\) | −6.82232 | −0.286007 | −0.143003 | − | 0.989722i | \(-0.545676\pi\) | ||||
−0.143003 | + | 0.989722i | \(0.545676\pi\) | |||||||
\(570\) | 27.8626 | − | 35.2670i | 1.16704 | − | 1.47717i | ||||
\(571\) | 19.7545 | 0.826701 | 0.413351 | − | 0.910572i | \(-0.364358\pi\) | ||||
0.413351 | + | 0.910572i | \(0.364358\pi\) | |||||||
\(572\) | 1.93663 | − | 1.93663i | 0.0809747 | − | 0.0809747i | ||||
\(573\) | −0.0396926 | − | 11.0484i | −0.00165818 | − | 0.461555i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.4383 | + | 19.0440i | 1.26937 | + | 0.794189i | ||||
\(576\) | −0.269737 | − | 37.5402i | −0.0112390 | − | 1.56417i | ||||
\(577\) | −1.10727 | − | 1.10727i | −0.0460964 | − | 0.0460964i | 0.683683 | − | 0.729779i | \(-0.260377\pi\) |
−0.729779 | + | 0.683683i | \(0.760377\pi\) | |||||||
\(578\) | 26.1639 | + | 26.1639i | 1.08827 | + | 1.08827i | ||||
\(579\) | 13.0530 | − | 13.1471i | 0.542463 | − | 0.546375i | ||||
\(580\) | −17.4867 | + | 1.98734i | −0.726097 | + | 0.0825197i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.1295 | + | 0.0435762i | −0.502782 | + | 0.00180629i | ||||
\(583\) | −12.0268 | + | 12.0268i | −0.498100 | + | 0.498100i | ||||
\(584\) | 20.4434 | 0.845953 | ||||||||
\(585\) | 1.54252 | + | 1.20969i | 0.0637753 | + | 0.0500144i | ||||
\(586\) | 20.7791 | 0.858376 | ||||||||
\(587\) | −7.76708 | + | 7.76708i | −0.320582 | + | 0.320582i | −0.848990 | − | 0.528408i | \(-0.822789\pi\) |
0.528408 | + | 0.848990i | \(0.322789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.4535i | 1.99649i | ||||||||
\(590\) | 39.4165 | + | 31.3715i | 1.62275 | + | 1.29154i | ||||
\(591\) | −1.75154 | + | 1.76417i | −0.0720487 | + | 0.0725683i | ||||
\(592\) | −9.86325 | − | 9.86325i | −0.405377 | − | 0.405377i | ||||
\(593\) | 8.01301 | + | 8.01301i | 0.329055 | + | 0.329055i | 0.852227 | − | 0.523172i | \(-0.175252\pi\) |
−0.523172 | + | 0.852227i | \(0.675252\pi\) | |||||||
\(594\) | 27.4515 | + | 26.8661i | 1.12635 | + | 1.10233i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 52.4261i | − | 2.14746i | ||||||
\(597\) | −0.0584943 | − | 16.2819i | −0.00239401 | − | 0.666373i | ||||
\(598\) | −3.24029 | + | 3.24029i | −0.132505 | + | 0.132505i | ||||
\(599\) | −20.3742 | −0.832467 | −0.416233 | − | 0.909258i | \(-0.636650\pi\) | ||||
−0.416233 | + | 0.909258i | \(0.636650\pi\) | |||||||
\(600\) | 12.3525 | + | 7.66682i | 0.504288 | + | 0.312997i | ||||
\(601\) | 32.4833 | 1.32502 | 0.662511 | − | 0.749052i | \(-0.269491\pi\) | ||||
0.662511 | + | 0.749052i | \(0.269491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.1805 | + | 18.9069i | 0.781092 | + | 0.769947i | ||||
\(604\) | 5.27521i | 0.214645i | ||||||||
\(605\) | −0.115814 | − | 1.01905i | −0.00470849 | − | 0.0414303i | ||||
\(606\) | 23.1809 | + | 23.0149i | 0.941660 | + | 0.934918i | ||||
\(607\) | 0.0701607 | + | 0.0701607i | 0.00284774 | + | 0.00284774i | 0.708529 | − | 0.705681i | \(-0.249359\pi\) |
−0.705681 | + | 0.708529i | \(0.749359\pi\) | |||||||
\(608\) | −27.9740 | − | 27.9740i | −1.13450 | − | 1.13450i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.0044 | + | 20.6969i | 1.05289 | + | 0.837992i | ||||
\(611\) | − | 1.47386i | − | 0.0596260i | ||||||
\(612\) | 1.40049 | + | 1.38051i | 0.0566115 | + | 0.0558038i | ||||
\(613\) | −26.6840 | + | 26.6840i | −1.07776 | + | 1.07776i | −0.0810445 | + | 0.996710i | \(0.525826\pi\) |
−0.996710 | + | 0.0810445i | \(0.974174\pi\) | |||||||
\(614\) | −31.2239 | −1.26010 | ||||||||
\(615\) | 0.121156 | − | 0.0142103i | 0.00488549 | − | 0.000573014i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.37294 | − | 6.37294i | 0.256565 | − | 0.256565i | −0.567090 | − | 0.823656i | \(-0.691931\pi\) |
0.823656 | + | 0.567090i | \(0.191931\pi\) | |||||||
\(618\) | 0.0185315 | + | 5.15824i | 0.000745446 | + | 0.207495i | ||||
\(619\) | 17.7676i | 0.714139i | 0.934078 | + | 0.357070i | \(0.116224\pi\) | ||||
−0.934078 | + | 0.357070i | \(0.883776\pi\) | |||||||
\(620\) | −56.0879 | + | 6.37430i | −2.25255 | + | 0.255998i | ||||
\(621\) | −26.6675 | − | 26.0987i | −1.07013 | − | 1.04731i | ||||
\(622\) | 0.608631 | + | 0.608631i | 0.0244039 | + | 0.0244039i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.667407 | − | 0.672220i | 0.0267177 | − | 0.0269103i | ||||
\(625\) | 22.4823 | − | 10.9338i | 0.899291 | − | 0.437351i | ||||
\(626\) | − | 32.0594i | − | 1.28135i | ||||||
\(627\) | 31.1575 | − | 0.111936i | 1.24431 | − | 0.00447030i | ||||
\(628\) | 11.9535 | − | 11.9535i | 0.476995 | − | 0.476995i | ||||
\(629\) | 1.76453 | 0.0703565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8248 | 0.709592 | 0.354796 | − | 0.934944i | \(-0.384550\pi\) | ||||
0.354796 | + | 0.934944i | \(0.384550\pi\) | |||||||
\(632\) | −13.5857 | + | 13.5857i | −0.540412 | + | 0.540412i | ||||
\(633\) | −14.3613 | + | 0.0515944i | −0.570811 | + | 0.00205070i | ||||
\(634\) | 61.1712i | 2.42942i | ||||||||
\(635\) | 22.8968 | − | 28.7685i | 0.908633 | − | 1.14164i | ||||
\(636\) | 16.9770 | − | 17.0995i | 0.673183 | − | 0.678038i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.8587 | − | 14.8587i | −0.588262 | − | 0.588262i | ||||
\(639\) | 0.0852413 | + | 11.8633i | 0.00337210 | + | 0.469306i | ||||
\(640\) | 17.3195 | − | 21.7609i | 0.684614 | − | 0.860177i | ||||
\(641\) | 14.8270i | 0.585630i | 0.956169 | + | 0.292815i | \(0.0945920\pi\) | ||||
−0.956169 | + | 0.292815i | \(0.905408\pi\) | |||||||
\(642\) | 0.0568527 | + | 15.8250i | 0.00224380 | + | 0.624562i | ||||
\(643\) | 32.7229 | − | 32.7229i | 1.29047 | − | 1.29047i | 0.355968 | − | 0.934498i | \(-0.384151\pi\) |
0.934498 | − | 0.355968i | \(-0.115849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.1972 | − | 12.7966i | −0.637766 | − | 0.503865i | ||||
\(646\) | 2.74747 | 0.108098 | ||||||||
\(647\) | 27.0564 | − | 27.0564i | 1.06370 | − | 1.06370i | 0.0658674 | − | 0.997828i | \(-0.479019\pi\) |
0.997828 | − | 0.0658674i | \(-0.0209814\pi\) | |||||||
\(648\) | −10.8359 | − | 10.5289i | −0.425674 | − | 0.413612i | ||||
\(649\) | 34.9230i | 1.37085i | ||||||||
\(650\) | 0.715985 | + | 3.10932i | 0.0280833 | + | 0.121958i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.90255 | − | 9.90255i | −0.387814 | − | 0.387814i | ||||
\(653\) | −4.04918 | − | 4.04918i | −0.158457 | − | 0.158457i | 0.623426 | − | 0.781883i | \(-0.285740\pi\) |
−0.781883 | + | 0.623426i | \(0.785740\pi\) | |||||||
\(654\) | −7.57410 | − | 7.51988i | −0.296171 | − | 0.294050i | ||||
\(655\) | −28.2194 | + | 3.20709i | −1.10262 | + | 0.125311i | ||||
\(656\) | − | 0.0589475i | − | 0.00230151i | ||||||
\(657\) | −25.6467 | + | 26.0179i | −1.00057 | + | 1.01506i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.5870 | 0.451366 | 0.225683 | − | 0.974201i | \(-0.427539\pi\) | ||||
0.225683 | + | 0.974201i | \(0.427539\pi\) | |||||||
\(660\) | 4.22849 | + | 36.0520i | 0.164594 | + | 1.40332i | ||||
\(661\) | 15.1550 | 0.589462 | 0.294731 | − | 0.955580i | \(-0.404770\pi\) | ||||
0.294731 | + | 0.955580i | \(0.404770\pi\) | |||||||
\(662\) | −38.1940 | + | 38.1940i | −1.48445 | + | 1.48445i | ||||
\(663\) | 0.000430499 | 0.119829i | 1.67192e−5 | 0.00465379i | ||||||
\(664\) | 9.21294i | 0.357531i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −48.8257 | + | 0.350827i | −1.89196 | + | 0.0135943i | ||||
\(667\) | 14.4343 | + | 14.4343i | 0.558899 | + | 0.558899i | ||||
\(668\) | −17.6990 | − | 17.6990i | −0.684793 | − | 0.684793i | ||||
\(669\) | −6.66199 | + | 6.71003i | −0.257568 | + | 0.259425i | ||||
\(670\) | 4.95017 | + | 43.5569i | 0.191242 | + | 1.68275i | ||||
\(671\) | 23.0399i | 0.889445i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7667 | + | 13.7667i | −0.530666 | + | 0.530666i | −0.920770 | − | 0.390105i | \(-0.872439\pi\) |
0.390105 | + | 0.920770i | \(0.372439\pi\) | |||||||
\(674\) | −10.5045 | −0.404617 | ||||||||
\(675\) | −25.2539 | + | 6.10257i | −0.972022 | + | 0.234888i | ||||
\(676\) | 35.7573 | 1.37528 | ||||||||
\(677\) | −16.3594 | + | 16.3594i | −0.628742 | + | 0.628742i | −0.947752 | − | 0.319009i | \(-0.896650\pi\) |
0.319009 | + | 0.947752i | \(0.396650\pi\) | |||||||
\(678\) | 10.7942 | − | 0.0387793i | 0.414549 | − | 0.00148931i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.100355 | + | 0.883031i | 0.00384844 | + | 0.0338627i | ||||
\(681\) | −2.60148 | + | 2.62024i | −0.0996891 | + | 0.100408i | ||||
\(682\) | −47.6587 | − | 47.6587i | −1.82495 | − | 1.82495i | ||||
\(683\) | 5.85622 | + | 5.85622i | 0.224082 | + | 0.224082i | 0.810215 | − | 0.586133i | \(-0.199350\pi\) |
−0.586133 | + | 0.810215i | \(0.699350\pi\) | |||||||
\(684\) | −44.1398 | + | 0.317157i | −1.68773 | + | 0.0121268i | ||||
\(685\) | −12.8526 | − | 10.2294i | −0.491072 | − | 0.390844i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0389535 | + | 10.8427i | 0.00148617 | + | 0.413676i | ||||
\(688\) | −7.05335 | + | 7.05335i | −0.268906 | + | 0.268906i | ||||
\(689\) | 1.46829 | 0.0559373 | ||||||||
\(690\) | −7.07492 | − | 60.3205i | −0.269338 | − | 2.29636i | ||||
\(691\) | −25.9095 | −0.985642 | −0.492821 | − | 0.870131i | \(-0.664034\pi\) | ||||
−0.492821 | + | 0.870131i | \(0.664034\pi\) | |||||||
\(692\) | −10.7646 | + | 10.7646i | −0.409210 | + | 0.409210i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 74.2189i | − | 2.81731i | ||||||
\(695\) | −27.3584 | + | 3.10923i | −1.03776 | + | 0.117940i | ||||
\(696\) | 5.86560 | + | 5.82361i | 0.222335 | + | 0.220743i | ||||
\(697\) | 0.00527284 | + | 0.00527284i | 0.000199723 | + | 0.000199723i | ||||
\(698\) | −14.4698 | − | 14.4698i | −0.547691 | − | 0.547691i | ||||
\(699\) | −4.64849 | − | 4.61521i | −0.175822 | − | 0.174563i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.9089i | 1.43180i | 0.698204 | + | 0.715899i | \(0.253983\pi\) | ||||
−0.698204 | + | 0.715899i | \(0.746017\pi\) | |||||||
\(702\) | −0.0357368 | − | 3.31567i | −0.00134880 | − | 0.125142i | ||||
\(703\) | −28.0065 | + | 28.0065i | −1.05628 | + | 1.05628i | ||||
\(704\) | 42.3598 | 1.59649 | ||||||||
\(705\) | 15.3276 | + | 12.1095i | 0.577269 | + | 0.456070i | ||||
\(706\) | −45.0542 | −1.69564 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.177743 | − | 49.4749i | −0.00668001 | − | 1.85938i | ||||
\(709\) | − | 16.6841i | − | 0.626586i | −0.949656 | − | 0.313293i | \(-0.898568\pi\) | ||
0.949656 | − | 0.313293i | \(-0.101432\pi\) | |||||||
\(710\) | −12.0251 | + | 15.1088i | −0.451293 | + | 0.567023i | ||||
\(711\) | −0.246699 | − | 34.3339i | −0.00925194 | − | 1.28762i | ||||
\(712\) | 2.37636 | + | 2.37636i | 0.0890578 | + | 0.0890578i | ||||
\(713\) | 46.2975 | + | 46.2975i | 1.73385 | + | 1.73385i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.37743 | + | 1.73066i | −0.0515129 | + | 0.0647229i | ||||
\(716\) | 40.5129i | 1.51404i | ||||||||
\(717\) | 3.61167 | − | 0.0129753i | 0.134880 | − | 0.000484570i | ||||
\(718\) | 42.1016 | − | 42.1016i | 1.57122 | − | 1.57122i | ||||
\(719\) | −13.0709 | −0.487464 | −0.243732 | − | 0.969843i | \(-0.578372\pi\) | ||||
−0.243732 | + | 0.969843i | \(0.578372\pi\) | |||||||
\(720\) | 1.50728 | + | 12.4638i | 0.0561731 | + | 0.464500i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.2688 | + | 14.2688i | −0.531031 | + | 0.531031i | ||||
\(723\) | 9.41686 | − | 0.0338310i | 0.350217 | − | 0.00125819i | ||||
\(724\) | − | 27.2367i | − | 1.01224i | ||||||
\(725\) | 13.8509 | − | 3.18946i | 0.514409 | − | 0.118454i | ||||
\(726\) | −1.22231 | + | 1.23112i | −0.0453640 | + | 0.0456911i | ||||
\(727\) | −19.4878 | − | 19.4878i | −0.722761 | − | 0.722761i | 0.246406 | − | 0.969167i | \(-0.420750\pi\) |
−0.969167 | + | 0.246406i | \(0.920750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9937 | − | 0.581953i | 0.999768 | − | 0.0215538i | ||||
\(730\) | −59.0838 | + | 6.71478i | −2.18679 | + | 0.248525i | ||||
\(731\) | − | 1.26184i | − | 0.0466709i | ||||||
\(732\) | −0.117264 | − | 32.6403i | −0.00433418 | − | 1.20642i | ||||
\(733\) | −24.5624 | + | 24.5624i | −0.907232 | + | 0.907232i | −0.996048 | − | 0.0888162i | \(-0.971692\pi\) |
0.0888162 | + | 0.996048i | \(0.471692\pi\) | |||||||
\(734\) | −49.1774 | −1.81517 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.4585 | −1.97051 | ||||||||
\(737\) | −21.4886 | + | 21.4886i | −0.791543 | + | 0.791543i | ||||
\(738\) | −0.146951 | − | 0.144855i | −0.00540935 | − | 0.00533217i | ||||
\(739\) | − | 25.3925i | − | 0.934079i | −0.884236 | − | 0.467040i | \(-0.845321\pi\) | ||
0.884236 | − | 0.467040i | \(-0.154679\pi\) | |||||||
\(740\) | −36.1036 | − | 28.7348i | −1.32720 | − | 1.05631i | ||||
\(741\) | −1.90875 | − | 1.89509i | −0.0701198 | − | 0.0696178i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.4447 | − | 14.4447i | −0.529923 | − | 0.529923i | 0.390626 | − | 0.920549i | \(-0.372258\pi\) |
−0.920549 | + | 0.390626i | \(0.872258\pi\) | |||||||
\(744\) | 18.8137 | + | 18.6790i | 0.689742 | + | 0.684804i | ||||
\(745\) | 4.78108 | + | 42.0691i | 0.175165 | + | 1.54129i | ||||
\(746\) | − | 72.0445i | − | 2.63774i | ||||||
\(747\) | −11.7251 | − | 11.5578i | −0.429000 | − | 0.422879i | ||||
\(748\) | −1.56902 | + | 1.56902i | −0.0573690 | + | 0.0573690i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −38.2184 | − | 18.1008i | −1.39554 | − | 0.660946i | ||||
\(751\) | 27.4358 | 1.00115 | 0.500573 | − | 0.865694i | \(-0.333123\pi\) | ||||
0.500573 | + | 0.865694i | \(0.333123\pi\) | |||||||
\(752\) | 6.67463 | − | 6.67463i | 0.243399 | − | 0.243399i | ||||
\(753\) | 0.145251 | + | 40.4307i | 0.00529325 | + | 1.47338i | ||||
\(754\) | 1.81402i | 0.0660627i | ||||||||
\(755\) | −0.481081 | − | 4.23306i | −0.0175083 | − | 0.154057i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9760 | − | 11.9760i | −0.435274 | − | 0.435274i | 0.455144 | − | 0.890418i | \(-0.349588\pi\) |
−0.890418 | + | 0.455144i | \(0.849588\pi\) | |||||||
\(758\) | −57.8245 | − | 57.8245i | −2.10028 | − | 2.10028i | ||||
\(759\) | 29.6641 | − | 29.8780i | 1.07674 | − | 1.08450i | ||||
\(760\) | −15.6082 | − | 12.4226i | −0.566170 | − | 0.450614i | ||||
\(761\) | 41.1635i | 1.49217i | 0.665848 | + | 0.746087i | \(0.268070\pi\) | ||||
−0.665848 | + | 0.746087i | \(0.731930\pi\) | |||||||
\(762\) | −62.1937 | + | 0.223437i | −2.25304 | + | 0.00809426i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.6614 | −0.638969 | ||||||||
\(765\) | −1.24971 | − | 0.980062i | −0.0451835 | − | 0.0354342i | ||||
\(766\) | 15.3007 | 0.552836 | ||||||||
\(767\) | 2.13178 | − | 2.13178i | 0.0769740 | − | 0.0769740i | ||||
\(768\) | −3.69569 | + | 0.0132771i | −0.133357 | + | 0.000479097i | ||||
\(769\) | − | 3.96520i | − | 0.142989i | −0.997441 | − | 0.0714944i | \(-0.977223\pi\) | ||
0.997441 | − | 0.0714944i | \(-0.0227768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8585 | + | 18.9945i | −0.679174 | + | 0.684071i | ||||
\(772\) | −20.9410 | − | 20.9410i | −0.753684 | − | 0.753684i | ||||
\(773\) | 5.99943 | + | 5.99943i | 0.215785 | + | 0.215785i | 0.806719 | − | 0.590935i | \(-0.201241\pi\) |
−0.590935 | + | 0.806719i | \(0.701241\pi\) | |||||||
\(774\) | 0.250881 | + | 34.9160i | 0.00901774 | + | 1.25503i | ||||
\(775\) | 44.4262 | − | 10.2301i | 1.59583 | − | 0.367474i | ||||
\(776\) | 5.38352i | 0.193257i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.2104 | − | 14.2104i | 0.509468 | − | 0.509468i | ||||
\(779\) | −0.167380 | −0.00599702 | ||||||||
\(780\) | 1.94258 | − | 2.45881i | 0.0695554 | − | 0.0880395i | ||||
\(781\) | −13.3864 | −0.479002 | ||||||||
\(782\) | 2.62521 | − | 2.62521i | 0.0938774 | − | 0.0938774i | ||||
\(783\) | −14.7701 | + | 0.159195i | −0.527841 | + | 0.00568916i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.50188 | + | 10.6821i | −0.303445 | + | 0.381261i | ||||
\(786\) | 34.0920 | + | 33.8479i | 1.21602 | + | 1.20731i | ||||
\(787\) | −15.8108 | − | 15.8108i | −0.563593 | − | 0.563593i | 0.366733 | − | 0.930326i | \(-0.380476\pi\) |
−0.930326 | + | 0.366733i | \(0.880476\pi\) | |||||||
\(788\) | 2.81001 | + | 2.81001i | 0.100103 | + | 0.100103i | ||||
\(789\) | 31.6030 | + | 31.3768i | 1.12510 | + | 1.11704i | ||||
\(790\) | 34.8021 | − | 43.7267i | 1.23820 | − | 1.55573i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.9678 | − | 12.1411i | 0.425258 | − | 0.431414i | ||||
\(793\) | 1.40641 | − | 1.40641i | 0.0499429 | − | 0.0499429i | ||||
\(794\) | −67.7082 | −2.40287 | ||||||||
\(795\) | −12.0637 | + | 15.2696i | −0.427856 | + | 0.541558i | ||||
\(796\) | −26.0274 | −0.922515 | ||||||||
\(797\) | −8.46554 | + | 8.46554i | −0.299865 | + | 0.299865i | −0.840961 | − | 0.541096i | \(-0.818010\pi\) |
0.541096 | + | 0.840961i | \(0.318010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19409i | 0.0422438i | ||||||||
\(800\) | −19.7427 | + | 31.5551i | −0.698010 | + | 1.11564i | ||||
\(801\) | −6.00554 | + | 0.0431515i | −0.212195 | + | 0.00152468i | ||||
\(802\) | 39.7638 | + | 39.7638i | 1.40411 | + | 1.40411i | ||||
\(803\) | −29.1488 | − | 29.1488i | −1.02864 | − | 1.02864i | ||||
\(804\) | 30.3333 | − | 30.5520i | 1.06977 | − | 1.07749i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.81839i | 0.204944i | ||||||||
\(807\) | −49.3848 | + | 0.177420i | −1.73843 | + | 0.00624547i | ||||
\(808\) | 10.2517 | − | 10.2517i | 0.360655 | − | 0.360655i | ||||
\(809\) | 25.5350 | 0.897764 | 0.448882 | − | 0.893591i | \(-0.351822\pi\) | ||||
0.448882 | + | 0.893591i | \(0.351822\pi\) | |||||||
\(810\) | 34.7753 | + | 26.8705i | 1.22188 | + | 0.944133i | ||||
\(811\) | 1.94760 | 0.0683895 | 0.0341947 | − | 0.999415i | \(-0.489113\pi\) | ||||
0.0341947 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.40767 | + | 0.0194276i | −0.189655 | + | 0.000681355i | ||||
\(814\) | − | 55.0942i | − | 1.93105i | ||||||
\(815\) | 8.84933 | + | 7.04317i | 0.309978 | + | 0.246712i | ||||
\(816\) | −0.540719 | + | 0.544618i | −0.0189289 | + | 0.0190654i | ||||
\(817\) | 20.0278 | + | 20.0278i | 0.700685 | + | 0.700685i | ||||
\(818\) | 16.9078 | + | 16.9078i | 0.591167 | + | 0.591167i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0220197 | − | 0.193753i | −0.000768962 | − | 0.00676615i | ||||
\(821\) | − | 21.6742i | − | 0.756434i | −0.925717 | − | 0.378217i | \(-0.876537\pi\) | ||
0.925717 | − | 0.378217i | \(-0.123463\pi\) | |||||||
\(822\) | 0.0998224 | + | 27.7856i | 0.00348171 | + | 0.969133i | ||||
\(823\) | 8.35207 | − | 8.35207i | 0.291135 | − | 0.291135i | −0.546394 | − | 0.837528i | \(-0.684000\pi\) |
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(824\) | 2.28943 | 0.0797559 | ||||||||
\(825\) | −6.68095 | − | 28.5441i | −0.232601 | − | 0.993778i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1747 | + | 14.1747i | −0.492902 | + | 0.492902i | −0.909219 | − | 0.416318i | \(-0.863320\pi\) |
0.416318 | + | 0.909219i | \(0.363320\pi\) | |||||||
\(828\) | −41.8727 | + | 42.4788i | −1.45518 | + | 1.47624i | ||||
\(829\) | 19.3836i | 0.673219i | 0.941644 | + | 0.336610i | \(0.109280\pi\) | ||||
−0.941644 | + | 0.336610i | \(0.890720\pi\) | |||||||
\(830\) | −3.02605 | − | 26.6265i | −0.105036 | − | 0.924218i | ||||
\(831\) | 21.2888 | + | 21.1364i | 0.738500 | + | 0.733213i | ||||
\(832\) | −2.58573 | − | 2.58573i | −0.0896442 | − | 0.0896442i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 33.0517 | + | 32.8151i | 1.14449 | + | 1.13629i | ||||
\(835\) | 15.8165 | + | 12.5884i | 0.547353 | + | 0.435638i | ||||
\(836\) | − | 49.8066i | − | 1.72260i | ||||||
\(837\) | −47.3745 | + | 0.510610i | −1.63750 | + | 0.0176493i | ||||
\(838\) | 9.06346 | − | 9.06346i | 0.313092 | − | 0.313092i | ||||
\(839\) | −26.2528 | −0.906346 | −0.453173 | − | 0.891423i | \(-0.649708\pi\) | ||||
−0.453173 | + | 0.891423i | \(0.649708\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.9192 | −0.721352 | ||||||||
\(842\) | 41.5131 | − | 41.5131i | 1.43063 | − | 1.43063i | ||||
\(843\) | 0.0791386 | + | 22.0282i | 0.00272568 | + | 0.758693i | ||||
\(844\) | 22.9572i | 0.790221i | ||||||||
\(845\) | −28.6932 | + | 3.26094i | −0.987077 | + | 0.112180i | ||||
\(846\) | −0.237410 | − | 33.0412i | −0.00816234 | − | 1.13598i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.64940 | + | 6.64940i | 0.228341 | + | 0.228341i | ||||
\(849\) | 34.2179 | − | 34.4646i | 1.17435 | − | 1.18282i | ||||
\(850\) | −0.580076 | − | 2.51910i | −0.0198964 | − | 0.0864045i | ||||
\(851\) | 53.5206i | 1.83466i | ||||||||
\(852\) | 18.9643 | − | 0.0681311i | 0.649707 | − | 0.00233413i | ||||
\(853\) | −29.8920 | + | 29.8920i | −1.02348 | + | 1.02348i | −0.0237636 | + | 0.999718i | \(0.507565\pi\) |
−0.999718 | + | 0.0237636i | \(0.992435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35.3908 | − | 4.27990i | 1.21034 | − | 0.146369i | ||||
\(856\) | 7.02373 | 0.240066 | ||||||||
\(857\) | −5.92367 | + | 5.92367i | −0.202349 | + | 0.202349i | −0.801006 | − | 0.598657i | \(-0.795701\pi\) |
0.598657 | + | 0.801006i | \(0.295701\pi\) | |||||||
\(858\) | 3.74145 | − | 0.0134415i | 0.127731 | − | 0.000458885i | ||||
\(859\) | − | 10.3620i | − | 0.353548i | −0.984252 | − | 0.176774i | \(-0.943434\pi\) | ||
0.984252 | − | 0.176774i | \(-0.0565661\pi\) | |||||||
\(860\) | −20.5487 | + | 25.8182i | −0.700705 | + | 0.880394i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.45633 | + | 6.45633i | 0.219904 | + | 0.219904i | ||||
\(863\) | −13.2818 | − | 13.2818i | −0.452118 | − | 0.452118i | 0.443939 | − | 0.896057i | \(-0.353581\pi\) |
−0.896057 | + | 0.443939i | \(0.853581\pi\) | |||||||
\(864\) | 27.0563 | − | 27.6459i | 0.920474 | − | 0.940532i | ||||
\(865\) | 7.65632 | − | 9.61971i | 0.260323 | − | 0.327080i | ||||
\(866\) | − | 6.82129i | − | 0.231797i | ||||||
\(867\) | 0.105434 | + | 29.3476i | 0.00358073 | + | 0.996696i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.7419 | 1.31423 | ||||||||
\(870\) | −18.8651 | − | 14.9043i | −0.639586 | − | 0.505303i | ||||
\(871\) | 2.62342 | 0.0888913 | ||||||||
\(872\) | −3.34965 | + | 3.34965i | −0.113433 | + | 0.113433i | ||||
\(873\) | −6.85150 | − | 6.75374i | −0.231888 | − | 0.228580i | ||||
\(874\) | 83.3342i | 2.81882i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.4430 | + | 41.1463i | 1.40023 | + | 1.39020i | ||||
\(877\) | 4.84197 | + | 4.84197i | 0.163502 | + | 0.163502i | 0.784116 | − | 0.620614i | \(-0.213117\pi\) |
−0.620614 | + | 0.784116i | \(0.713117\pi\) | |||||||
\(878\) | 42.6227 | + | 42.6227i | 1.43845 | + | 1.43845i | ||||
\(879\) | 11.6957 | + | 11.6119i | 0.394485 | + | 0.391660i | ||||
\(880\) | −14.0755 | + | 1.59966i | −0.474485 | + | 0.0539245i | ||||
\(881\) | − | 17.0394i | − | 0.574073i | −0.957920 | − | 0.287036i | \(-0.907330\pi\) | ||
0.957920 | − | 0.287036i | \(-0.0926701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2389 | − | 12.2389i | 0.411871 | − | 0.411871i | −0.470519 | − | 0.882390i | \(-0.655933\pi\) |
0.882390 | + | 0.470519i | \(0.155933\pi\) | |||||||
\(884\) | 0.191553 | 0.00644262 | ||||||||
\(885\) | 4.65457 | + | 39.6847i | 0.156462 | + | 1.33399i | ||||
\(886\) | 37.9983 | 1.27658 | ||||||||
\(887\) | 41.0767 | − | 41.0767i | 1.37922 | − | 1.37922i | 0.533287 | − | 0.845934i | \(-0.320957\pi\) |
0.845934 | − | 0.533287i | \(-0.179043\pi\) | |||||||
\(888\) | 0.0778552 | + | 21.6710i | 0.00261265 | + | 0.727231i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.64848 | − | 6.08742i | −0.256378 | − | 0.204051i | ||||
\(891\) | 0.437785 | + | 30.4624i | 0.0146664 | + | 1.02053i | ||||
\(892\) | 10.6879 | + | 10.6879i | 0.357858 | + | 0.357858i | ||||
\(893\) | −18.9525 | − | 18.9525i | −0.634220 | − | 0.634220i | ||||
\(894\) | 50.4599 | − | 50.8238i | 1.68763 | − | 1.69980i | ||||
\(895\) | −3.69464 | − | 32.5094i | −0.123498 | − | 1.08667i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.63458 | + | 0.0130576i | −0.121355 | + | 0.000435980i | ||||
\(898\) | −52.7879 | + | 52.7879i | −1.76155 | + | 1.76155i | ||||
\(899\) | 25.9188 | 0.864441 | ||||||||
\(900\) | 9.61009 | + | 40.4040i | 0.320336 | + | 1.34680i | ||||
\(901\) | −1.18958 | −0.0396305 | ||||||||
\(902\) | 0.164635 | − | 0.164635i | 0.00548173 | − | 0.00548173i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.79089i | − | 0.159343i | ||||||
\(905\) | 2.48389 | + | 21.8559i | 0.0825673 | + | 0.726515i | ||||
\(906\) | −5.07736 | + | 5.11398i | −0.168684 | + | 0.169901i | ||||
\(907\) | 24.8992 | + | 24.8992i | 0.826765 | + | 0.826765i | 0.987068 | − | 0.160303i | \(-0.0512470\pi\) |
−0.160303 | + | 0.987068i | \(0.551247\pi\) | |||||||
\(908\) | 4.17359 | + | 4.17359i | 0.138505 | + | 0.138505i | ||||
\(909\) | 0.186158 | + | 25.9082i | 0.00617448 | + | 0.859322i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.4322i | 0.776342i | 0.921587 | + | 0.388171i | \(0.126893\pi\) | ||||
−0.921587 | + | 0.388171i | \(0.873107\pi\) | |||||||
\(912\) | −0.0618874 | − | 17.2264i | −0.00204930 | − | 0.570422i | ||||
\(913\) | 13.1361 | − | 13.1361i | 0.434740 | − | 0.434740i | ||||
\(914\) | −28.7526 | −0.951050 | ||||||||
\(915\) | 3.07078 | + | 26.1814i | 0.101517 | + | 0.865529i | ||||
\(916\) | 17.3326 | 0.572685 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0289532 | + | 2.68628i | 0.000955598 | + | 0.0886605i | ||||
\(919\) | 31.9950i | 1.05542i | 0.849425 | + | 0.527710i | \(0.176949\pi\) | ||||
−0.849425 | + | 0.527710i | \(0.823051\pi\) | |||||||
\(920\) | −26.7835 | + | 3.04390i | −0.883026 | + | 0.100354i | ||||
\(921\) | −17.5746 | − | 17.4488i | −0.579103 | − | 0.574957i | ||||
\(922\) | −39.6195 | − | 39.6195i | −1.30480 | − | 1.30480i | ||||
\(923\) | 0.817134 | + | 0.817134i | 0.0268963 | + | 0.0268963i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.5917 | + | 19.7656i | 1.03873 | + | 0.649889i | ||||
\(926\) | − | 40.8180i | − | 1.34136i | ||||||
\(927\) | −2.87214 | + | 2.91371i | −0.0943333 | + | 0.0956987i | ||||
\(928\) | −14.9639 | + | 14.9639i | −0.491214 | + | 0.491214i | ||||
\(929\) | 49.7858 | 1.63342 | 0.816709 | − | 0.577050i | \(-0.195796\pi\) | ||||
0.816709 | + | 0.577050i | \(0.195796\pi\) | |||||||
\(930\) | −60.5089 | − | 47.8049i | −1.98417 | − | 1.56758i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.40423 | + | 7.40423i | −0.242534 | + | 0.242534i | ||||
\(933\) | 0.00245264 | + | 0.682692i | 8.02958e−5 | + | 0.0223503i | ||||
\(934\) | − | 60.7340i | − | 1.98728i | ||||||
\(935\) | 1.11596 | − | 1.40214i | 0.0364959 | − | 0.0458549i | ||||
\(936\) | −1.47166 | + | 0.0105743i | −0.0481027 | + | 0.000345632i | ||||
\(937\) | −18.0919 | − | 18.0919i | −0.591035 | − | 0.591035i | 0.346876 | − | 0.937911i | \(-0.387243\pi\) |
−0.937911 | + | 0.346876i | \(0.887243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.9157 | − | 18.0449i | 0.584656 | − | 0.588872i | ||||
\(940\) | 19.4454 | − | 24.4319i | 0.634238 | − | 0.796882i | ||||
\(941\) | 61.0502i | 1.99018i | 0.0989766 | + | 0.995090i | \(0.468443\pi\) | ||||
−0.0989766 | + | 0.995090i | \(0.531557\pi\) | |||||||
\(942\) | 23.0933 | − | 0.0829648i | 0.752419 | − | 0.00270314i | ||||
\(943\) | −0.159932 | + | 0.159932i | −0.00520811 | + | 0.00520811i | ||||
\(944\) | 19.3082 | 0.628430 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.3986 | −1.28096 | ||||||||
\(947\) | 28.1297 | − | 28.1297i | 0.914093 | − | 0.914093i | −0.0824986 | − | 0.996591i | \(-0.526290\pi\) |
0.996591 | + | 0.0824986i | \(0.0262900\pi\) | |||||||
\(948\) | −54.8851 | + | 0.197180i | −1.78259 | + | 0.00640411i | ||||
\(949\) | 3.55861i | 0.115517i | ||||||||
\(950\) | 49.1899 | + | 30.7761i | 1.59593 | + | 0.998507i | ||||
\(951\) | −34.1841 | + | 34.4306i | −1.10850 | + | 1.11649i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.4406 | − | 16.4406i | −0.532564 | − | 0.532564i | 0.388771 | − | 0.921335i | \(-0.372900\pi\) |
−0.921335 | + | 0.388771i | \(0.872900\pi\) | |||||||
\(954\) | 32.9163 | − | 0.236513i | 1.06571 | − | 0.00765740i | ||||
\(955\) | 14.1723 | − | 1.61066i | 0.458606 | − | 0.0521198i | ||||
\(956\) | − | 5.77342i | − | 0.186726i | ||||||
\(957\) | −0.0598771 | − | 16.6668i | −0.00193555 | − | 0.538761i | ||||
\(958\) | 41.6493 | − | 41.6493i | 1.34563 | − | 1.34563i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 48.1355 | − | 5.64575i | 1.55357 | − | 0.182216i | ||||
\(961\) | 52.1335 | 1.68173 | ||||||||
\(962\) | −3.36307 | + | 3.36307i | −0.108430 | + | 0.108430i | ||||
\(963\) | −8.81142 | + | 8.93897i | −0.283944 | + | 0.288054i | ||||
\(964\) | − | 15.0533i | − | 0.484834i | ||||||
\(965\) | 18.7138 | + | 14.8943i | 0.602417 | + | 0.479463i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.29391 | − | 3.29391i | −0.105925 | − | 0.105925i | 0.652158 | − | 0.758083i | \(-0.273864\pi\) |
−0.758083 | + | 0.652158i | \(0.773864\pi\) | |||||||
\(968\) | 0.544462 | + | 0.544462i | 0.0174997 | + | 0.0174997i | ||||
\(969\) | 1.54643 | + | 1.53536i | 0.0496785 | + | 0.0493228i | ||||
\(970\) | −1.76825 | − | 15.5590i | −0.0567752 | − | 0.499569i | ||||
\(971\) | 32.3161i | 1.03707i | 0.855056 | + | 0.518536i | \(0.173523\pi\) | ||||
−0.855056 | + | 0.518536i | \(0.826477\pi\) | |||||||
\(972\) | −0.775246 | − | 43.1535i | −0.0248660 | − | 1.38415i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −88.4809 | −2.83511 | ||||||||
\(975\) | −1.33457 | + | 2.15021i | −0.0427406 | + | 0.0688620i | ||||
\(976\) | 12.7383 | 0.407744 | ||||||||
\(977\) | −8.42742 | + | 8.42742i | −0.269617 | + | 0.269617i | −0.828946 | − | 0.559329i | \(-0.811059\pi\) |
0.559329 | + | 0.828946i | \(0.311059\pi\) | |||||||
\(978\) | −0.0687302 | − | 19.1311i | −0.00219775 | − | 0.611744i | ||||
\(979\) | − | 6.77655i | − | 0.216580i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0608251 | − | 8.46523i | −0.00194200 | − | 0.270274i | ||||
\(982\) | 4.23900 | + | 4.23900i | 0.135272 | + | 0.135272i | ||||
\(983\) | −43.2280 | − | 43.2280i | −1.37876 | − | 1.37876i | −0.846718 | − | 0.532042i | \(-0.821425\pi\) |
−0.532042 | − | 0.846718i | \(-0.678575\pi\) | |||||||
\(984\) | −0.0645255 | + | 0.0649908i | −0.00205700 | + | 0.00207183i | ||||
\(985\) | −2.51114 | − | 1.99862i | −0.0800117 | − | 0.0636812i | ||||
\(986\) | − | 1.46968i | − | 0.0468041i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.04031 | + | 3.04031i | −0.0967251 | + | 0.0967251i | ||||
\(989\) | 38.2733 | 1.21702 | ||||||||
\(990\) | −30.6006 | + | 39.0200i | −0.972551 | + | 1.24014i | ||||
\(991\) | −25.2971 | −0.803590 | −0.401795 | − | 0.915730i | \(-0.631614\pi\) | ||||
−0.401795 | + | 0.915730i | \(0.631614\pi\) | |||||||
\(992\) | −47.9961 | + | 47.9961i | −1.52388 | + | 1.52388i | ||||
\(993\) | −42.8417 | + | 0.153913i | −1.35954 | + | 0.00488428i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.8855 | − | 2.37360i | 0.662115 | − | 0.0752483i | ||||
\(996\) | −18.5428 | + | 18.6765i | −0.587552 | + | 0.591789i | ||||
\(997\) | 23.3279 | + | 23.3279i | 0.738803 | + | 0.738803i | 0.972346 | − | 0.233543i | \(-0.0750321\pi\) |
−0.233543 | + | 0.972346i | \(0.575032\pi\) | |||||||
\(998\) | 46.8108 | + | 46.8108i | 1.48177 | + | 1.48177i | ||||
\(999\) | −27.6779 | − | 27.0877i | −0.875691 | − | 0.857016i |
(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 | 735.2.j.h.197.11 | 24 | ||
3.2 | odd | 2 | inner | 735.2.j.h.197.2 | 24 | ||
5.3 | odd | 4 | inner | 735.2.j.h.638.2 | 24 | ||
7.2 | even | 3 | 735.2.y.g.557.2 | 48 | |||
7.3 | odd | 6 | 735.2.y.j.422.11 | 48 | |||
7.4 | even | 3 | 735.2.y.g.422.11 | 48 | |||
7.5 | odd | 6 | 735.2.y.j.557.2 | 48 | |||
7.6 | odd | 2 | 105.2.j.a.92.11 | yes | 24 | ||
15.8 | even | 4 | inner | 735.2.j.h.638.11 | 24 | ||
21.2 | odd | 6 | 735.2.y.g.557.11 | 48 | |||
21.5 | even | 6 | 735.2.y.j.557.11 | 48 | |||
21.11 | odd | 6 | 735.2.y.g.422.2 | 48 | |||
21.17 | even | 6 | 735.2.y.j.422.2 | 48 | |||
21.20 | even | 2 | 105.2.j.a.92.2 | yes | 24 | ||
35.3 | even | 12 | 735.2.y.j.128.11 | 48 | |||
35.13 | even | 4 | 105.2.j.a.8.2 | ✓ | 24 | ||
35.18 | odd | 12 | 735.2.y.g.128.11 | 48 | |||
35.23 | odd | 12 | 735.2.y.g.263.2 | 48 | |||
35.27 | even | 4 | 525.2.j.b.218.11 | 24 | |||
35.33 | even | 12 | 735.2.y.j.263.2 | 48 | |||
35.34 | odd | 2 | 525.2.j.b.407.2 | 24 | |||
105.23 | even | 12 | 735.2.y.g.263.11 | 48 | |||
105.38 | odd | 12 | 735.2.y.j.128.2 | 48 | |||
105.53 | even | 12 | 735.2.y.g.128.2 | 48 | |||
105.62 | odd | 4 | 525.2.j.b.218.2 | 24 | |||
105.68 | odd | 12 | 735.2.y.j.263.11 | 48 | |||
105.83 | odd | 4 | 105.2.j.a.8.11 | yes | 24 | ||
105.104 | even | 2 | 525.2.j.b.407.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.2 | ✓ | 24 | 35.13 | even | 4 | ||
105.2.j.a.8.11 | yes | 24 | 105.83 | odd | 4 | ||
105.2.j.a.92.2 | yes | 24 | 21.20 | even | 2 | ||
105.2.j.a.92.11 | yes | 24 | 7.6 | odd | 2 | ||
525.2.j.b.218.2 | 24 | 105.62 | odd | 4 | |||
525.2.j.b.218.11 | 24 | 35.27 | even | 4 | |||
525.2.j.b.407.2 | 24 | 35.34 | odd | 2 | |||
525.2.j.b.407.11 | 24 | 105.104 | even | 2 | |||
735.2.j.h.197.2 | 24 | 3.2 | odd | 2 | inner | ||
735.2.j.h.197.11 | 24 | 1.1 | even | 1 | trivial | ||
735.2.j.h.638.2 | 24 | 5.3 | odd | 4 | inner | ||
735.2.j.h.638.11 | 24 | 15.8 | even | 4 | inner | ||
735.2.y.g.128.2 | 48 | 105.53 | even | 12 | |||
735.2.y.g.128.11 | 48 | 35.18 | odd | 12 | |||
735.2.y.g.263.2 | 48 | 35.23 | odd | 12 | |||
735.2.y.g.263.11 | 48 | 105.23 | even | 12 | |||
735.2.y.g.422.2 | 48 | 21.11 | odd | 6 | |||
735.2.y.g.422.11 | 48 | 7.4 | even | 3 | |||
735.2.y.g.557.2 | 48 | 7.2 | even | 3 | |||
735.2.y.g.557.11 | 48 | 21.2 | odd | 6 | |||
735.2.y.j.128.2 | 48 | 105.38 | odd | 12 | |||
735.2.y.j.128.11 | 48 | 35.3 | even | 12 | |||
735.2.y.j.263.2 | 48 | 35.33 | even | 12 | |||
735.2.y.j.263.11 | 48 | 105.68 | odd | 12 | |||
735.2.y.j.422.2 | 48 | 21.17 | even | 6 | |||
735.2.y.j.422.11 | 48 | 7.3 | odd | 6 | |||
735.2.y.j.557.2 | 48 | 7.5 | odd | 6 | |||
735.2.y.j.557.11 | 48 | 21.5 | even | 6 |