Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.m (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Root | \(1.24483i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.43 |
Dual form | 770.2.m.e.197.4 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 2.22529 | + | 2.22529i | 1.28477 | + | 1.28477i | 0.937918 | + | 0.346856i | \(0.112751\pi\) |
0.346856 | + | 0.937918i | \(0.387249\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.07027 | − | 0.844975i | 0.925853 | − | 0.377884i | ||||
\(6\) | − | 3.14704i | − | 1.28477i | ||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 6.90387i | 2.30129i | ||||||||
\(10\) | −2.06139 | − | 0.866414i | −0.651869 | − | 0.273984i | ||||
\(11\) | −2.91525 | − | 1.58156i | −0.878979 | − | 0.476860i | ||||
\(12\) | −2.22529 | + | 2.22529i | −0.642387 | + | 0.642387i | ||||
\(13\) | −1.58156 | + | 1.58156i | −0.438647 | + | 0.438647i | −0.891557 | − | 0.452909i | \(-0.850386\pi\) |
0.452909 | + | 0.891557i | \(0.350386\pi\) | |||||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 6.48728 | + | 2.72664i | 1.67501 | + | 0.704016i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.76045 | + | 2.76045i | 0.669508 | + | 0.669508i | 0.957602 | − | 0.288094i | \(-0.0930216\pi\) |
−0.288094 | + | 0.957602i | \(0.593022\pi\) | |||||||
\(18\) | 4.88177 | − | 4.88177i | 1.15064 | − | 1.15064i | ||||
\(19\) | 4.12278 | 0.945830 | 0.472915 | − | 0.881108i | \(-0.343202\pi\) | ||||
0.472915 | + | 0.881108i | \(0.343202\pi\) | |||||||
\(20\) | 0.844975 | + | 2.07027i | 0.188942 | + | 0.462926i | ||||
\(21\) | 3.14704i | 0.686741i | ||||||||
\(22\) | 0.943055 | + | 3.17972i | 0.201060 | + | 0.677920i | ||||
\(23\) | 1.38343 | + | 1.38343i | 0.288465 | + | 0.288465i | 0.836473 | − | 0.548008i | \(-0.184614\pi\) |
−0.548008 | + | 0.836473i | \(0.684614\pi\) | |||||||
\(24\) | 3.14704 | 0.642387 | ||||||||
\(25\) | 3.57203 | − | 3.49865i | 0.714407 | − | 0.699731i | ||||
\(26\) | 2.23667 | 0.438647 | ||||||||
\(27\) | −8.68726 | + | 8.68726i | −1.67186 | + | 1.67186i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −9.22628 | −1.71328 | −0.856639 | − | 0.515916i | \(-0.827452\pi\) | ||||
−0.856639 | + | 0.515916i | \(0.827452\pi\) | |||||||
\(30\) | −2.65917 | − | 6.51522i | −0.485496 | − | 1.18951i | ||||
\(31\) | 3.90387 | 0.701156 | 0.350578 | − | 0.936534i | \(-0.385985\pi\) | ||||
0.350578 | + | 0.936534i | \(0.385985\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −2.96783 | − | 10.0067i | −0.516633 | − | 1.74195i | ||||
\(34\) | − | 3.90387i | − | 0.669508i | ||||||
\(35\) | 2.06139 | + | 0.866414i | 0.348438 | + | 0.146451i | ||||
\(36\) | −6.90387 | −1.15064 | ||||||||
\(37\) | 2.14054 | − | 2.14054i | 0.351903 | − | 0.351903i | −0.508915 | − | 0.860817i | \(-0.669953\pi\) |
0.860817 | + | 0.508915i | \(0.169953\pi\) | |||||||
\(38\) | −2.91525 | − | 2.91525i | −0.472915 | − | 0.472915i | ||||
\(39\) | −7.03889 | −1.12712 | ||||||||
\(40\) | 0.866414 | − | 2.06139i | 0.136992 | − | 0.325934i | ||||
\(41\) | − | 6.93512i | − | 1.08308i | −0.840674 | − | 0.541542i | \(-0.817841\pi\) | ||
0.840674 | − | 0.541542i | \(-0.182159\pi\) | |||||||
\(42\) | 2.22529 | − | 2.22529i | 0.343370 | − | 0.343370i | ||||
\(43\) | −3.60160 | + | 3.60160i | −0.549240 | + | 0.549240i | −0.926221 | − | 0.376981i | \(-0.876962\pi\) |
0.376981 | + | 0.926221i | \(0.376962\pi\) | |||||||
\(44\) | 1.58156 | − | 2.91525i | 0.238430 | − | 0.439490i | ||||
\(45\) | 5.83360 | + | 14.2929i | 0.869622 | + | 2.13066i | ||||
\(46\) | − | 1.95646i | − | 0.288465i | ||||||
\(47\) | 5.45059 | − | 5.45059i | 0.795050 | − | 0.795050i | −0.187260 | − | 0.982310i | \(-0.559961\pi\) |
0.982310 | + | 0.187260i | \(0.0599608\pi\) | |||||||
\(48\) | −2.22529 | − | 2.22529i | −0.321194 | − | 0.321194i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −4.99973 | − | 0.0518870i | −0.707069 | − | 0.00733793i | ||||
\(51\) | 12.2856i | 1.72033i | ||||||||
\(52\) | −1.58156 | − | 1.58156i | −0.219324 | − | 0.219324i | ||||
\(53\) | −3.66720 | − | 3.66720i | −0.503729 | − | 0.503729i | 0.408866 | − | 0.912594i | \(-0.365924\pi\) |
−0.912594 | + | 0.408866i | \(0.865924\pi\) | |||||||
\(54\) | 12.2856 | 1.67186 | ||||||||
\(55\) | −7.37173 | − | 0.810955i | −0.994003 | − | 0.109349i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 9.17440 | + | 9.17440i | 1.21518 | + | 1.21518i | ||||
\(58\) | 6.52397 | + | 6.52397i | 0.856639 | + | 0.856639i | ||||
\(59\) | − | 7.92746i | − | 1.03207i | −0.856568 | − | 0.516033i | \(-0.827408\pi\) | ||
0.856568 | − | 0.516033i | \(-0.172592\pi\) | |||||||
\(60\) | −2.72664 | + | 6.48728i | −0.352008 | + | 0.837504i | ||||
\(61\) | 10.7554i | 1.37708i | 0.725196 | + | 0.688542i | \(0.241749\pi\) | ||||
−0.725196 | + | 0.688542i | \(0.758251\pi\) | |||||||
\(62\) | −2.76045 | − | 2.76045i | −0.350578 | − | 0.350578i | ||||
\(63\) | −4.88177 | + | 4.88177i | −0.615046 | + | 0.615046i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −1.93788 | + | 4.61065i | −0.240365 | + | 0.571881i | ||||
\(66\) | −4.97725 | + | 9.17440i | −0.612657 | + | 1.12929i | ||||
\(67\) | −3.07069 | + | 3.07069i | −0.375144 | + | 0.375144i | −0.869347 | − | 0.494203i | \(-0.835460\pi\) |
0.494203 | + | 0.869347i | \(0.335460\pi\) | |||||||
\(68\) | −2.76045 | + | 2.76045i | −0.334754 | + | 0.334754i | ||||
\(69\) | 6.15707i | 0.741224i | ||||||||
\(70\) | −0.844975 | − | 2.07027i | −0.100994 | − | 0.247445i | ||||
\(71\) | −14.2077 | −1.68614 | −0.843072 | − | 0.537801i | \(-0.819255\pi\) | ||||
−0.843072 | + | 0.537801i | \(0.819255\pi\) | |||||||
\(72\) | 4.88177 | + | 4.88177i | 0.575322 | + | 0.575322i | ||||
\(73\) | 6.02736 | − | 6.02736i | 0.705449 | − | 0.705449i | −0.260126 | − | 0.965575i | \(-0.583764\pi\) |
0.965575 | + | 0.260126i | \(0.0837641\pi\) | |||||||
\(74\) | −3.02718 | −0.351903 | ||||||||
\(75\) | 15.7344 | + | 0.163291i | 1.81685 | + | 0.0188552i | ||||
\(76\) | 4.12278i | 0.472915i | ||||||||
\(77\) | −0.943055 | − | 3.17972i | −0.107471 | − | 0.362363i | ||||
\(78\) | 4.97725 | + | 4.97725i | 0.563562 | + | 0.563562i | ||||
\(79\) | 11.7150 | 1.31804 | 0.659021 | − | 0.752124i | \(-0.270971\pi\) | ||||
0.659021 | + | 0.752124i | \(0.270971\pi\) | |||||||
\(80\) | −2.07027 | + | 0.844975i | −0.231463 | + | 0.0944711i | ||||
\(81\) | −17.9518 | −1.99465 | ||||||||
\(82\) | −4.90387 | + | 4.90387i | −0.541542 | + | 0.541542i | ||||
\(83\) | 6.05876 | − | 6.05876i | 0.665035 | − | 0.665035i | −0.291527 | − | 0.956562i | \(-0.594163\pi\) |
0.956562 | + | 0.291527i | \(0.0941635\pi\) | |||||||
\(84\) | −3.14704 | −0.343370 | ||||||||
\(85\) | 8.04740 | + | 3.38237i | 0.872863 | + | 0.366869i | ||||
\(86\) | 5.09344 | 0.549240 | ||||||||
\(87\) | −20.5312 | − | 20.5312i | −2.20118 | − | 2.20118i | ||||
\(88\) | −3.17972 | + | 0.943055i | −0.338960 | + | 0.100530i | ||||
\(89\) | − | 3.23314i | − | 0.342712i | −0.985209 | − | 0.171356i | \(-0.945185\pi\) | ||
0.985209 | − | 0.171356i | \(-0.0548149\pi\) | |||||||
\(90\) | 5.98161 | − | 14.2316i | 0.630517 | − | 1.50014i | ||||
\(91\) | −2.23667 | −0.234467 | ||||||||
\(92\) | −1.38343 | + | 1.38343i | −0.144232 | + | 0.144232i | ||||
\(93\) | 8.68726 | + | 8.68726i | 0.900827 | + | 0.900827i | ||||
\(94\) | −7.70830 | −0.795050 | ||||||||
\(95\) | 8.53526 | − | 3.48365i | 0.875700 | − | 0.357415i | ||||
\(96\) | 3.14704i | 0.321194i | ||||||||
\(97\) | 3.90387 | − | 3.90387i | 0.396378 | − | 0.396378i | −0.480575 | − | 0.876953i | \(-0.659572\pi\) |
0.876953 | + | 0.480575i | \(0.159572\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 10.9189 | − | 20.1265i | 1.09739 | − | 2.02279i | ||||
\(100\) | 3.49865 | + | 3.57203i | 0.349865 | + | 0.357203i | ||||
\(101\) | 12.5093i | 1.24472i | 0.782731 | + | 0.622360i | \(0.213826\pi\) | ||||
−0.782731 | + | 0.622360i | \(0.786174\pi\) | |||||||
\(102\) | 8.68726 | − | 8.68726i | 0.860167 | − | 0.860167i | ||||
\(103\) | −8.83049 | − | 8.83049i | −0.870094 | − | 0.870094i | 0.122388 | − | 0.992482i | \(-0.460945\pi\) |
−0.992482 | + | 0.122388i | \(0.960945\pi\) | |||||||
\(104\) | 2.23667i | 0.219324i | ||||||||
\(105\) | 2.65917 | + | 6.51522i | 0.259509 | + | 0.635821i | ||||
\(106\) | 5.18620i | 0.503729i | ||||||||
\(107\) | 0.422388 | + | 0.422388i | 0.0408338 | + | 0.0408338i | 0.727229 | − | 0.686395i | \(-0.240808\pi\) |
−0.686395 | + | 0.727229i | \(0.740808\pi\) | |||||||
\(108\) | −8.68726 | − | 8.68726i | −0.835932 | − | 0.835932i | ||||
\(109\) | −12.2856 | −1.17675 | −0.588375 | − | 0.808588i | \(-0.700232\pi\) | ||||
−0.588375 | + | 0.808588i | \(0.700232\pi\) | |||||||
\(110\) | 4.63917 | + | 5.78603i | 0.442327 | + | 0.551676i | ||||
\(111\) | 9.52666 | 0.904231 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | 9.73436 | + | 9.73436i | 0.915732 | + | 0.915732i | 0.996715 | − | 0.0809839i | \(-0.0258062\pi\) |
−0.0809839 | + | 0.996715i | \(0.525806\pi\) | |||||||
\(114\) | − | 12.9746i | − | 1.21518i | ||||||
\(115\) | 4.03303 | + | 1.69511i | 0.376082 | + | 0.158070i | ||||
\(116\) | − | 9.22628i | − | 0.856639i | ||||||
\(117\) | −10.9189 | − | 10.9189i | −1.00945 | − | 1.00945i | ||||
\(118\) | −5.60556 | + | 5.60556i | −0.516033 | + | 0.516033i | ||||
\(119\) | 3.90387i | 0.357867i | ||||||||
\(120\) | 6.51522 | − | 2.65917i | 0.594756 | − | 0.242748i | ||||
\(121\) | 5.99731 | + | 9.22130i | 0.545210 | + | 0.838300i | ||||
\(122\) | 7.60520 | − | 7.60520i | 0.688542 | − | 0.688542i | ||||
\(123\) | 15.4327 | − | 15.4327i | 1.39152 | − | 1.39152i | ||||
\(124\) | 3.90387i | 0.350578i | ||||||||
\(125\) | 4.43880 | − | 10.2614i | 0.397018 | − | 0.917811i | ||||
\(126\) | 6.90387 | 0.615046 | ||||||||
\(127\) | −13.4331 | − | 13.4331i | −1.19200 | − | 1.19200i | −0.976506 | − | 0.215491i | \(-0.930865\pi\) |
−0.215491 | − | 0.976506i | \(-0.569135\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −16.0293 | −1.41130 | ||||||||
\(130\) | 4.63051 | − | 1.88993i | 0.406123 | − | 0.165758i | ||||
\(131\) | − | 7.19093i | − | 0.628274i | −0.949378 | − | 0.314137i | \(-0.898285\pi\) | ||
0.949378 | − | 0.314137i | \(-0.101715\pi\) | |||||||
\(132\) | 10.0067 | − | 2.96783i | 0.870974 | − | 0.258317i | ||||
\(133\) | 2.91525 | + | 2.91525i | 0.252784 | + | 0.252784i | ||||
\(134\) | 4.34261 | 0.375144 | ||||||||
\(135\) | −10.6444 | + | 25.3255i | −0.916128 | + | 2.17967i | ||||
\(136\) | 3.90387 | 0.334754 | ||||||||
\(137\) | 5.37721 | − | 5.37721i | 0.459406 | − | 0.459406i | −0.439054 | − | 0.898460i | \(-0.644686\pi\) |
0.898460 | + | 0.439054i | \(0.144686\pi\) | |||||||
\(138\) | 4.35371 | − | 4.35371i | 0.370612 | − | 0.370612i | ||||
\(139\) | 5.64575 | 0.478867 | 0.239433 | − | 0.970913i | \(-0.423038\pi\) | ||||
0.239433 | + | 0.970913i | \(0.423038\pi\) | |||||||
\(140\) | −0.866414 | + | 2.06139i | −0.0732253 | + | 0.174219i | ||||
\(141\) | 24.2583 | 2.04292 | ||||||||
\(142\) | 10.0464 | + | 10.0464i | 0.843072 | + | 0.843072i | ||||
\(143\) | 7.11199 | − | 2.10930i | 0.594735 | − | 0.176389i | ||||
\(144\) | − | 6.90387i | − | 0.575322i | ||||||
\(145\) | −19.1009 | + | 7.79598i | −1.58624 | + | 0.647421i | ||||
\(146\) | −8.52397 | −0.705449 | ||||||||
\(147\) | −2.22529 | + | 2.22529i | −0.183539 | + | 0.183539i | ||||
\(148\) | 2.14054 | + | 2.14054i | 0.175951 | + | 0.175951i | ||||
\(149\) | 20.7387 | 1.69898 | 0.849492 | − | 0.527601i | \(-0.176908\pi\) | ||||
0.849492 | + | 0.527601i | \(0.176908\pi\) | |||||||
\(150\) | −11.0104 | − | 11.2413i | −0.898996 | − | 0.917851i | ||||
\(151\) | − | 14.5718i | − | 1.18584i | −0.805262 | − | 0.592919i | \(-0.797976\pi\) | ||
0.805262 | − | 0.592919i | \(-0.202024\pi\) | |||||||
\(152\) | 2.91525 | − | 2.91525i | 0.236458 | − | 0.236458i | ||||
\(153\) | −19.0578 | + | 19.0578i | −1.54073 | + | 1.54073i | ||||
\(154\) | −1.58156 | + | 2.91525i | −0.127446 | + | 0.234917i | ||||
\(155\) | 8.08206 | − | 3.29867i | 0.649167 | − | 0.264956i | ||||
\(156\) | − | 7.03889i | − | 0.563562i | ||||||
\(157\) | −10.2960 | + | 10.2960i | −0.821709 | + | 0.821709i | −0.986353 | − | 0.164644i | \(-0.947352\pi\) |
0.164644 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(158\) | −8.28377 | − | 8.28377i | −0.659021 | − | 0.659021i | ||||
\(159\) | − | 16.3212i | − | 1.29436i | ||||||
\(160\) | 2.06139 | + | 0.866414i | 0.162967 | + | 0.0684960i | ||||
\(161\) | 1.95646i | 0.154191i | ||||||||
\(162\) | 12.6938 | + | 12.6938i | 0.997323 | + | 0.997323i | ||||
\(163\) | −12.6139 | − | 12.6139i | −0.987995 | − | 0.987995i | 0.0119335 | − | 0.999929i | \(-0.496201\pi\) |
−0.999929 | + | 0.0119335i | \(0.996201\pi\) | |||||||
\(164\) | 6.93512 | 0.541542 | ||||||||
\(165\) | −14.5996 | − | 18.2089i | −1.13658 | − | 1.41756i | ||||
\(166\) | −8.56838 | −0.665035 | ||||||||
\(167\) | −8.58525 | − | 8.58525i | −0.664346 | − | 0.664346i | 0.292055 | − | 0.956402i | \(-0.405661\pi\) |
−0.956402 | + | 0.292055i | \(0.905661\pi\) | |||||||
\(168\) | 2.22529 | + | 2.22529i | 0.171685 | + | 0.171685i | ||||
\(169\) | 7.99731i | 0.615178i | ||||||||
\(170\) | −3.29867 | − | 8.08206i | −0.252997 | − | 0.619866i | ||||
\(171\) | 28.4631i | 2.17663i | ||||||||
\(172\) | −3.60160 | − | 3.60160i | −0.274620 | − | 0.274620i | ||||
\(173\) | 8.20306 | − | 8.20306i | 0.623667 | − | 0.623667i | −0.322800 | − | 0.946467i | \(-0.604624\pi\) |
0.946467 | + | 0.322800i | \(0.104624\pi\) | |||||||
\(174\) | 29.0355i | 2.20118i | ||||||||
\(175\) | 4.99973 | + | 0.0518870i | 0.377944 | + | 0.00392229i | ||||
\(176\) | 2.91525 | + | 1.58156i | 0.219745 | + | 0.119215i | ||||
\(177\) | 17.6409 | − | 17.6409i | 1.32597 | − | 1.32597i | ||||
\(178\) | −2.28618 | + | 2.28618i | −0.171356 | + | 0.171356i | ||||
\(179\) | 12.2356i | 0.914530i | 0.889331 | + | 0.457265i | \(0.151171\pi\) | ||||
−0.889331 | + | 0.457265i | \(0.848829\pi\) | |||||||
\(180\) | −14.2929 | + | 5.83360i | −1.06533 | + | 0.434811i | ||||
\(181\) | −7.66720 | −0.569898 | −0.284949 | − | 0.958543i | \(-0.591977\pi\) | ||||
−0.284949 | + | 0.958543i | \(0.591977\pi\) | |||||||
\(182\) | 1.58156 | + | 1.58156i | 0.117233 | + | 0.117233i | ||||
\(183\) | −23.9339 | + | 23.9339i | −1.76924 | + | 1.76924i | ||||
\(184\) | 1.95646 | 0.144232 | ||||||||
\(185\) | 2.62279 | − | 6.24020i | 0.192831 | − | 0.458788i | ||||
\(186\) | − | 12.2856i | − | 0.900827i | ||||||
\(187\) | −3.68156 | − | 12.4132i | −0.269222 | − | 0.907745i | ||||
\(188\) | 5.45059 | + | 5.45059i | 0.397525 | + | 0.397525i | ||||
\(189\) | −12.2856 | −0.893649 | ||||||||
\(190\) | −8.49865 | − | 3.57203i | −0.616557 | − | 0.259143i | ||||
\(191\) | −22.2077 | −1.60689 | −0.803446 | − | 0.595377i | \(-0.797003\pi\) | ||||
−0.803446 | + | 0.595377i | \(0.797003\pi\) | |||||||
\(192\) | 2.22529 | − | 2.22529i | 0.160597 | − | 0.160597i | ||||
\(193\) | 5.22337 | − | 5.22337i | 0.375986 | − | 0.375986i | −0.493666 | − | 0.869652i | \(-0.664343\pi\) |
0.869652 | + | 0.493666i | \(0.164343\pi\) | |||||||
\(194\) | −5.52091 | −0.396378 | ||||||||
\(195\) | −14.5724 | + | 5.94769i | −1.04355 | + | 0.425923i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −17.6867 | − | 17.6867i | −1.26012 | − | 1.26012i | −0.951032 | − | 0.309092i | \(-0.899975\pi\) |
−0.309092 | − | 0.951032i | \(-0.600025\pi\) | |||||||
\(198\) | −21.9524 | + | 6.51073i | −1.56009 | + | 0.462697i | ||||
\(199\) | − | 3.75711i | − | 0.266335i | −0.991094 | − | 0.133167i | \(-0.957485\pi\) | ||
0.991094 | − | 0.133167i | \(-0.0425147\pi\) | |||||||
\(200\) | 0.0518870 | − | 4.99973i | 0.00366897 | − | 0.353534i | ||||
\(201\) | −13.6664 | −0.963951 | ||||||||
\(202\) | 8.84539 | − | 8.84539i | 0.622360 | − | 0.622360i | ||||
\(203\) | −6.52397 | − | 6.52397i | −0.457893 | − | 0.457893i | ||||
\(204\) | −12.2856 | −0.860167 | ||||||||
\(205\) | −5.86000 | − | 14.3576i | −0.409280 | − | 1.00278i | ||||
\(206\) | 12.4882i | 0.870094i | ||||||||
\(207\) | −9.55101 | + | 9.55101i | −0.663841 | + | 0.663841i | ||||
\(208\) | 1.58156 | − | 1.58156i | 0.109662 | − | 0.109662i | ||||
\(209\) | −12.0189 | − | 6.52044i | −0.831365 | − | 0.451028i | ||||
\(210\) | 2.72664 | − | 6.48728i | 0.188156 | − | 0.447665i | ||||
\(211\) | 14.6844i | 1.01091i | 0.862852 | + | 0.505457i | \(0.168676\pi\) | ||||
−0.862852 | + | 0.505457i | \(0.831324\pi\) | |||||||
\(212\) | 3.66720 | − | 3.66720i | 0.251864 | − | 0.251864i | ||||
\(213\) | −31.6163 | − | 31.6163i | −2.16631 | − | 2.16631i | ||||
\(214\) | − | 0.597347i | − | 0.0408338i | ||||||
\(215\) | −4.41303 | + | 10.4996i | −0.300966 | + | 0.716064i | ||||
\(216\) | 12.2856i | 0.835932i | ||||||||
\(217\) | 2.76045 | + | 2.76045i | 0.187392 | + | 0.187392i | ||||
\(218\) | 8.68726 | + | 8.68726i | 0.588375 | + | 0.588375i | ||||
\(219\) | 26.8253 | 1.81268 | ||||||||
\(220\) | 0.810955 | − | 7.37173i | 0.0546745 | − | 0.497002i | ||||
\(221\) | −8.73167 | −0.587356 | ||||||||
\(222\) | −6.73637 | − | 6.73637i | −0.452115 | − | 0.452115i | ||||
\(223\) | −5.56947 | − | 5.56947i | −0.372959 | − | 0.372959i | 0.495595 | − | 0.868554i | \(-0.334950\pi\) |
−0.868554 | + | 0.495595i | \(0.834950\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | 24.1542 | + | 24.6609i | 1.61028 | + | 1.64406i | ||||
\(226\) | − | 13.7665i | − | 0.915732i | ||||||
\(227\) | −13.9068 | − | 13.9068i | −0.923027 | − | 0.923027i | 0.0742149 | − | 0.997242i | \(-0.476355\pi\) |
−0.997242 | + | 0.0742149i | \(0.976355\pi\) | |||||||
\(228\) | −9.17440 | + | 9.17440i | −0.607589 | + | 0.607589i | ||||
\(229\) | 28.0669i | 1.85471i | 0.374179 | + | 0.927357i | \(0.377925\pi\) | ||||
−0.374179 | + | 0.927357i | \(0.622075\pi\) | |||||||
\(230\) | −1.65316 | − | 4.05041i | −0.109006 | − | 0.267076i | ||||
\(231\) | 4.97725 | − | 9.17440i | 0.327479 | − | 0.603631i | ||||
\(232\) | −6.52397 | + | 6.52397i | −0.428319 | + | 0.428319i | ||||
\(233\) | −7.66140 | + | 7.66140i | −0.501915 | + | 0.501915i | −0.912033 | − | 0.410118i | \(-0.865488\pi\) |
0.410118 | + | 0.912033i | \(0.365488\pi\) | |||||||
\(234\) | 15.4417i | 1.00945i | ||||||||
\(235\) | 6.67858 | − | 15.8898i | 0.435662 | − | 1.03654i | ||||
\(236\) | 7.92746 | 0.516033 | ||||||||
\(237\) | 26.0694 | + | 26.0694i | 1.69339 | + | 1.69339i | ||||
\(238\) | 2.76045 | − | 2.76045i | 0.178934 | − | 0.178934i | ||||
\(239\) | 4.67613 | 0.302474 | 0.151237 | − | 0.988498i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988498i | \(0.451674\pi\) | |||||||
\(240\) | −6.48728 | − | 2.72664i | −0.418752 | − | 0.176004i | ||||
\(241\) | 23.8981i | 1.53941i | 0.638400 | + | 0.769705i | \(0.279597\pi\) | ||||
−0.638400 | + | 0.769705i | \(0.720403\pi\) | |||||||
\(242\) | 2.27970 | − | 10.7612i | 0.146545 | − | 0.691755i | ||||
\(243\) | −13.8863 | − | 13.8863i | −0.890805 | − | 0.890805i | ||||
\(244\) | −10.7554 | −0.688542 | ||||||||
\(245\) | 0.844975 | + | 2.07027i | 0.0539835 | + | 0.132265i | ||||
\(246\) | −21.8251 | −1.39152 | ||||||||
\(247\) | −6.52044 | + | 6.52044i | −0.414886 | + | 0.414886i | ||||
\(248\) | 2.76045 | − | 2.76045i | 0.175289 | − | 0.175289i | ||||
\(249\) | 26.9650 | 1.70884 | ||||||||
\(250\) | −10.3946 | + | 4.11723i | −0.657414 | + | 0.260396i | ||||
\(251\) | 27.5429 | 1.73849 | 0.869247 | − | 0.494378i | \(-0.164604\pi\) | ||||
0.869247 | + | 0.494378i | \(0.164604\pi\) | |||||||
\(252\) | −4.88177 | − | 4.88177i | −0.307523 | − | 0.307523i | ||||
\(253\) | −1.84505 | − | 6.22101i | −0.115997 | − | 0.391112i | ||||
\(254\) | 18.9973i | 1.19200i | ||||||||
\(255\) | 10.3811 | + | 25.4346i | 0.650087 | + | 1.59278i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.92662 | − | 9.92662i | 0.619206 | − | 0.619206i | −0.326122 | − | 0.945328i | \(-0.605742\pi\) |
0.945328 | + | 0.326122i | \(0.105742\pi\) | |||||||
\(258\) | 11.3344 | + | 11.3344i | 0.705649 | + | 0.705649i | ||||
\(259\) | 3.02718 | 0.188100 | ||||||||
\(260\) | −4.61065 | − | 1.93788i | −0.285940 | − | 0.120182i | ||||
\(261\) | − | 63.6971i | − | 3.94275i | ||||||
\(262\) | −5.08475 | + | 5.08475i | −0.314137 | + | 0.314137i | ||||
\(263\) | 15.6563 | − | 15.6563i | 0.965410 | − | 0.965410i | −0.0340116 | − | 0.999421i | \(-0.510828\pi\) |
0.999421 | + | 0.0340116i | \(0.0108283\pi\) | |||||||
\(264\) | −9.17440 | − | 4.97725i | −0.564645 | − | 0.306328i | ||||
\(265\) | −10.6908 | − | 4.49340i | −0.656730 | − | 0.276027i | ||||
\(266\) | − | 4.12278i | − | 0.252784i | ||||||
\(267\) | 7.19469 | − | 7.19469i | 0.440308 | − | 0.440308i | ||||
\(268\) | −3.07069 | − | 3.07069i | −0.187572 | − | 0.187572i | ||||
\(269\) | − | 7.24103i | − | 0.441493i | −0.975331 | − | 0.220747i | \(-0.929151\pi\) | ||
0.975331 | − | 0.220747i | \(-0.0708494\pi\) | |||||||
\(270\) | 25.4346 | − | 10.3811i | 1.54790 | − | 0.631771i | ||||
\(271\) | 1.44258i | 0.0876306i | 0.999040 | + | 0.0438153i | \(0.0139513\pi\) | ||||
−0.999040 | + | 0.0438153i | \(0.986049\pi\) | |||||||
\(272\) | −2.76045 | − | 2.76045i | −0.167377 | − | 0.167377i | ||||
\(273\) | −4.97725 | − | 4.97725i | −0.301237 | − | 0.301237i | ||||
\(274\) | −7.60452 | −0.459406 | ||||||||
\(275\) | −15.9467 | + | 4.55003i | −0.961622 | + | 0.274377i | ||||
\(276\) | −6.15707 | −0.370612 | ||||||||
\(277\) | 16.4245 | + | 16.4245i | 0.986853 | + | 0.986853i | 0.999915 | − | 0.0130618i | \(-0.00415782\pi\) |
−0.0130618 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(278\) | −3.99215 | − | 3.99215i | −0.239433 | − | 0.239433i | ||||
\(279\) | 26.9518i | 1.61356i | ||||||||
\(280\) | 2.07027 | − | 0.844975i | 0.123722 | − | 0.0504969i | ||||
\(281\) | − | 23.1287i | − | 1.37974i | −0.723932 | − | 0.689871i | \(-0.757667\pi\) | ||
0.723932 | − | 0.689871i | \(-0.242333\pi\) | |||||||
\(282\) | −17.1532 | − | 17.1532i | −1.02146 | − | 1.02146i | ||||
\(283\) | 3.86756 | − | 3.86756i | 0.229903 | − | 0.229903i | −0.582749 | − | 0.812652i | \(-0.698023\pi\) |
0.812652 | + | 0.582749i | \(0.198023\pi\) | |||||||
\(284\) | − | 14.2077i | − | 0.843072i | ||||||
\(285\) | 26.7456 | + | 11.2413i | 1.58427 | + | 0.665879i | ||||
\(286\) | −6.52044 | − | 3.53744i | −0.385562 | − | 0.209173i | ||||
\(287\) | 4.90387 | − | 4.90387i | 0.289466 | − | 0.289466i | ||||
\(288\) | −4.88177 | + | 4.88177i | −0.287661 | + | 0.287661i | ||||
\(289\) | − | 1.75980i | − | 0.103518i | ||||||
\(290\) | 19.0190 | + | 7.99378i | 1.11683 | + | 0.469411i | ||||
\(291\) | 17.3745 | 1.01851 | ||||||||
\(292\) | 6.02736 | + | 6.02736i | 0.352724 | + | 0.352724i | ||||
\(293\) | −1.42953 | + | 1.42953i | −0.0835139 | + | 0.0835139i | −0.747630 | − | 0.664116i | \(-0.768808\pi\) |
0.664116 | + | 0.747630i | \(0.268808\pi\) | |||||||
\(294\) | 3.14704 | 0.183539 | ||||||||
\(295\) | −6.69850 | − | 16.4120i | −0.390002 | − | 0.955542i | ||||
\(296\) | − | 3.02718i | − | 0.175951i | ||||||
\(297\) | 39.0649 | − | 11.5860i | 2.26678 | − | 0.672290i | ||||
\(298\) | −14.6645 | − | 14.6645i | −0.849492 | − | 0.849492i | ||||
\(299\) | −4.37596 | −0.253068 | ||||||||
\(300\) | −0.163291 | + | 15.7344i | −0.00942759 | + | 0.908424i | ||||
\(301\) | −5.09344 | −0.293581 | ||||||||
\(302\) | −10.3038 | + | 10.3038i | −0.592919 | + | 0.592919i | ||||
\(303\) | −27.8368 | + | 27.8368i | −1.59918 | + | 1.59918i | ||||
\(304\) | −4.12278 | −0.236458 | ||||||||
\(305\) | 9.08802 | + | 22.2665i | 0.520379 | + | 1.27498i | ||||
\(306\) | 26.9518 | 1.54073 | ||||||||
\(307\) | 4.64835 | + | 4.64835i | 0.265295 | + | 0.265295i | 0.827201 | − | 0.561906i | \(-0.189932\pi\) |
−0.561906 | + | 0.827201i | \(0.689932\pi\) | |||||||
\(308\) | 3.17972 | − | 0.943055i | 0.181182 | − | 0.0537355i | ||||
\(309\) | − | 39.3009i | − | 2.23575i | ||||||
\(310\) | −8.04740 | − | 3.38237i | −0.457061 | − | 0.192106i | ||||
\(311\) | 16.8121 | 0.953327 | 0.476663 | − | 0.879086i | \(-0.341846\pi\) | ||||
0.476663 | + | 0.879086i | \(0.341846\pi\) | |||||||
\(312\) | −4.97725 | + | 4.97725i | −0.281781 | + | 0.281781i | ||||
\(313\) | −3.35715 | − | 3.35715i | −0.189757 | − | 0.189757i | 0.605834 | − | 0.795591i | \(-0.292840\pi\) |
−0.795591 | + | 0.605834i | \(0.792840\pi\) | |||||||
\(314\) | 14.5607 | 0.821709 | ||||||||
\(315\) | −5.98161 | + | 14.2316i | −0.337025 | + | 0.801858i | ||||
\(316\) | 11.7150i | 0.659021i | ||||||||
\(317\) | 6.33171 | − | 6.33171i | 0.355624 | − | 0.355624i | −0.506573 | − | 0.862197i | \(-0.669088\pi\) |
0.862197 | + | 0.506573i | \(0.169088\pi\) | |||||||
\(318\) | −11.5408 | + | 11.5408i | −0.647178 | + | 0.647178i | ||||
\(319\) | 26.8969 | + | 14.5920i | 1.50594 | + | 0.816993i | ||||
\(320\) | −0.844975 | − | 2.07027i | −0.0472356 | − | 0.115732i | ||||
\(321\) | 1.87988i | 0.104924i | ||||||||
\(322\) | 1.38343 | − | 1.38343i | 0.0770955 | − | 0.0770955i | ||||
\(323\) | 11.3807 | + | 11.3807i | 0.633241 | + | 0.633241i | ||||
\(324\) | − | 17.9518i | − | 0.997323i | ||||||
\(325\) | −0.116054 | + | 11.1827i | −0.00643752 | + | 0.620307i | ||||
\(326\) | 17.8387i | 0.987995i | ||||||||
\(327\) | −27.3392 | − | 27.3392i | −1.51186 | − | 1.51186i | ||||
\(328\) | −4.90387 | − | 4.90387i | −0.270771 | − | 0.270771i | ||||
\(329\) | 7.70830 | 0.424972 | ||||||||
\(330\) | −2.55211 | + | 23.1991i | −0.140489 | + | 1.27707i | ||||
\(331\) | −33.9210 | −1.86447 | −0.932233 | − | 0.361859i | \(-0.882142\pi\) | ||||
−0.932233 | + | 0.361859i | \(0.882142\pi\) | |||||||
\(332\) | 6.05876 | + | 6.05876i | 0.332518 | + | 0.332518i | ||||
\(333\) | 14.7780 | + | 14.7780i | 0.809830 | + | 0.809830i | ||||
\(334\) | 12.1414i | 0.664346i | ||||||||
\(335\) | −3.76250 | + | 8.95181i | −0.205567 | + | 0.489089i | ||||
\(336\) | − | 3.14704i | − | 0.171685i | ||||||
\(337\) | 20.0027 | + | 20.0027i | 1.08962 | + | 1.08962i | 0.995567 | + | 0.0940508i | \(0.0299816\pi\) |
0.0940508 | + | 0.995567i | \(0.470018\pi\) | |||||||
\(338\) | 5.65495 | − | 5.65495i | 0.307589 | − | 0.307589i | ||||
\(339\) | 43.3236i | 2.35302i | ||||||||
\(340\) | −3.38237 | + | 8.04740i | −0.183435 | + | 0.436431i | ||||
\(341\) | −11.3807 | − | 6.17422i | −0.616301 | − | 0.334353i | ||||
\(342\) | 20.1265 | − | 20.1265i | 1.08831 | − | 1.08831i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 5.09344i | 0.274620i | ||||||||
\(345\) | 5.20257 | + | 12.7468i | 0.280097 | + | 0.686265i | ||||
\(346\) | −11.6009 | −0.623667 | ||||||||
\(347\) | −18.1500 | − | 18.1500i | −0.974345 | − | 0.974345i | 0.0253338 | − | 0.999679i | \(-0.491935\pi\) |
−0.999679 | + | 0.0253338i | \(0.991935\pi\) | |||||||
\(348\) | 20.5312 | − | 20.5312i | 1.10059 | − | 1.10059i | ||||
\(349\) | −10.6850 | −0.571952 | −0.285976 | − | 0.958237i | \(-0.592318\pi\) | ||||
−0.285976 | + | 0.958237i | \(0.592318\pi\) | |||||||
\(350\) | −3.49865 | − | 3.57203i | −0.187011 | − | 0.190933i | ||||
\(351\) | − | 27.4789i | − | 1.46672i | ||||||
\(352\) | −0.943055 | − | 3.17972i | −0.0502650 | − | 0.169480i | ||||
\(353\) | 9.09344 | + | 9.09344i | 0.483995 | + | 0.483995i | 0.906405 | − | 0.422410i | \(-0.138816\pi\) |
−0.422410 | + | 0.906405i | \(0.638816\pi\) | |||||||
\(354\) | −24.9480 | −1.32597 | ||||||||
\(355\) | −29.4138 | + | 12.0052i | −1.56112 | + | 0.637168i | ||||
\(356\) | 3.23314 | 0.171356 | ||||||||
\(357\) | −8.68726 | + | 8.68726i | −0.459778 | + | 0.459778i | ||||
\(358\) | 8.65186 | − | 8.65186i | 0.457265 | − | 0.457265i | ||||
\(359\) | −7.50456 | −0.396075 | −0.198038 | − | 0.980194i | \(-0.563457\pi\) | ||||
−0.198038 | + | 0.980194i | \(0.563457\pi\) | |||||||
\(360\) | 14.2316 | + | 5.98161i | 0.750069 | + | 0.315258i | ||||
\(361\) | −2.00269 | −0.105405 | ||||||||
\(362\) | 5.42153 | + | 5.42153i | 0.284949 | + | 0.284949i | ||||
\(363\) | −7.17432 | + | 33.8659i | −0.376554 | + | 1.77750i | ||||
\(364\) | − | 2.23667i | − | 0.117233i | ||||||
\(365\) | 7.38528 | − | 17.5712i | 0.386563 | − | 0.919720i | ||||
\(366\) | 33.8476 | 1.76924 | ||||||||
\(367\) | 10.8532 | − | 10.8532i | 0.566535 | − | 0.566535i | −0.364621 | − | 0.931156i | \(-0.618802\pi\) |
0.931156 | + | 0.364621i | \(0.118802\pi\) | |||||||
\(368\) | −1.38343 | − | 1.38343i | −0.0721162 | − | 0.0721162i | ||||
\(369\) | 47.8792 | 2.49249 | ||||||||
\(370\) | −6.26708 | + | 2.55789i | −0.325810 | + | 0.132978i | ||||
\(371\) | − | 5.18620i | − | 0.269254i | ||||||
\(372\) | −8.68726 | + | 8.68726i | −0.450413 | + | 0.450413i | ||||
\(373\) | 9.54490 | − | 9.54490i | 0.494216 | − | 0.494216i | −0.415416 | − | 0.909632i | \(-0.636364\pi\) |
0.909632 | + | 0.415416i | \(0.136364\pi\) | |||||||
\(374\) | −6.17422 | + | 11.3807i | −0.319261 | + | 0.588484i | ||||
\(375\) | 32.7123 | − | 12.9571i | 1.68926 | − | 0.669101i | ||||
\(376\) | − | 7.70830i | − | 0.397525i | ||||||
\(377\) | 14.5920 | − | 14.5920i | 0.751524 | − | 0.751524i | ||||
\(378\) | 8.68726 | + | 8.68726i | 0.446824 | + | 0.446824i | ||||
\(379\) | 9.80068i | 0.503427i | 0.967802 | + | 0.251714i | \(0.0809941\pi\) | ||||
−0.967802 | + | 0.251714i | \(0.919006\pi\) | |||||||
\(380\) | 3.48365 | + | 8.53526i | 0.178707 | + | 0.437850i | ||||
\(381\) | − | 59.7853i | − | 3.06289i | ||||||
\(382\) | 15.7032 | + | 15.7032i | 0.803446 | + | 0.803446i | ||||
\(383\) | 8.54403 | + | 8.54403i | 0.436579 | + | 0.436579i | 0.890859 | − | 0.454280i | \(-0.150103\pi\) |
−0.454280 | + | 0.890859i | \(0.650103\pi\) | |||||||
\(384\) | −3.14704 | −0.160597 | ||||||||
\(385\) | −4.63917 | − | 5.78603i | −0.236434 | − | 0.294883i | ||||
\(386\) | −7.38696 | −0.375986 | ||||||||
\(387\) | −24.8650 | − | 24.8650i | −1.26396 | − | 1.26396i | ||||
\(388\) | 3.90387 | + | 3.90387i | 0.198189 | + | 0.198189i | ||||
\(389\) | 7.53371i | 0.381974i | 0.981593 | + | 0.190987i | \(0.0611689\pi\) | ||||
−0.981593 | + | 0.190987i | \(0.938831\pi\) | |||||||
\(390\) | 14.5099 | + | 6.09859i | 0.734737 | + | 0.308814i | ||||
\(391\) | 7.63778i | 0.386259i | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 16.0019 | − | 16.0019i | 0.807191 | − | 0.807191i | ||||
\(394\) | 25.0127i | 1.26012i | ||||||||
\(395\) | 24.2533 | − | 9.89890i | 1.22031 | − | 0.498068i | ||||
\(396\) | 20.1265 | + | 10.9189i | 1.01139 | + | 0.548696i | ||||
\(397\) | 0.435686 | − | 0.435686i | 0.0218665 | − | 0.0218665i | −0.696089 | − | 0.717955i | \(-0.745078\pi\) |
0.717955 | + | 0.696089i | \(0.245078\pi\) | |||||||
\(398\) | −2.65668 | + | 2.65668i | −0.133167 | + | 0.133167i | ||||
\(399\) | 12.9746i | 0.649540i | ||||||||
\(400\) | −3.57203 | + | 3.49865i | −0.178602 | + | 0.174933i | ||||
\(401\) | −19.7517 | −0.986354 | −0.493177 | − | 0.869929i | \(-0.664165\pi\) | ||||
−0.493177 | + | 0.869929i | \(0.664165\pi\) | |||||||
\(402\) | 9.66358 | + | 9.66358i | 0.481976 | + | 0.481976i | ||||
\(403\) | −6.17422 | + | 6.17422i | −0.307560 | + | 0.307560i | ||||
\(404\) | −12.5093 | −0.622360 | ||||||||
\(405\) | −37.1651 | + | 15.1688i | −1.84675 | + | 0.753745i | ||||
\(406\) | 9.22628i | 0.457893i | ||||||||
\(407\) | −9.62560 | + | 2.85480i | −0.477123 | + | 0.141507i | ||||
\(408\) | 8.68726 | + | 8.68726i | 0.430083 | + | 0.430083i | ||||
\(409\) | 10.9124 | 0.539583 | 0.269792 | − | 0.962919i | \(-0.413045\pi\) | ||||
0.269792 | + | 0.962919i | \(0.413045\pi\) | |||||||
\(410\) | −6.00868 | + | 14.2960i | −0.296748 | + | 0.706028i | ||||
\(411\) | 23.9317 | 1.18047 | ||||||||
\(412\) | 8.83049 | − | 8.83049i | 0.435047 | − | 0.435047i | ||||
\(413\) | 5.60556 | − | 5.60556i | 0.275831 | − | 0.275831i | ||||
\(414\) | 13.5072 | 0.663841 | ||||||||
\(415\) | 7.42376 | − | 17.6628i | 0.364418 | − | 0.867031i | ||||
\(416\) | −2.23667 | −0.109662 | ||||||||
\(417\) | 12.5635 | + | 12.5635i | 0.615236 | + | 0.615236i | ||||
\(418\) | 3.88801 | + | 13.1093i | 0.190169 | + | 0.641197i | ||||
\(419\) | − | 5.85215i | − | 0.285896i | −0.989730 | − | 0.142948i | \(-0.954342\pi\) | ||
0.989730 | − | 0.142948i | \(-0.0456582\pi\) | |||||||
\(420\) | −6.51522 | + | 2.65917i | −0.317910 | + | 0.129754i | ||||
\(421\) | −15.8375 | −0.771875 | −0.385937 | − | 0.922525i | \(-0.626122\pi\) | ||||
−0.385937 | + | 0.922525i | \(0.626122\pi\) | |||||||
\(422\) | 10.3834 | − | 10.3834i | 0.505457 | − | 0.505457i | ||||
\(423\) | 37.6302 | + | 37.6302i | 1.82964 | + | 1.82964i | ||||
\(424\) | −5.18620 | −0.251864 | ||||||||
\(425\) | 19.5183 | + | 0.202560i | 0.946776 | + | 0.00982561i | ||||
\(426\) | 44.7122i | 2.16631i | ||||||||
\(427\) | −7.60520 | + | 7.60520i | −0.368041 | + | 0.368041i | ||||
\(428\) | −0.422388 | + | 0.422388i | −0.0204169 | + | 0.0204169i | ||||
\(429\) | 20.5201 | + | 11.1325i | 0.990720 | + | 0.537480i | ||||
\(430\) | 10.5448 | − | 4.30383i | 0.508515 | − | 0.207549i | ||||
\(431\) | − | 3.19648i | − | 0.153969i | −0.997032 | − | 0.0769846i | \(-0.975471\pi\) | ||
0.997032 | − | 0.0769846i | \(-0.0245292\pi\) | |||||||
\(432\) | 8.68726 | − | 8.68726i | 0.417966 | − | 0.417966i | ||||
\(433\) | 15.5719 | + | 15.5719i | 0.748338 | + | 0.748338i | 0.974167 | − | 0.225829i | \(-0.0725091\pi\) |
−0.225829 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(434\) | − | 3.90387i | − | 0.187392i | ||||||
\(435\) | −59.8535 | − | 25.1568i | −2.86975 | − | 1.20617i | ||||
\(436\) | − | 12.2856i | − | 0.588375i | ||||||
\(437\) | 5.70357 | + | 5.70357i | 0.272839 | + | 0.272839i | ||||
\(438\) | −18.9683 | − | 18.9683i | −0.906342 | − | 0.906342i | ||||
\(439\) | −28.9831 | −1.38329 | −0.691644 | − | 0.722238i | \(-0.743113\pi\) | ||||
−0.691644 | + | 0.722238i | \(0.743113\pi\) | |||||||
\(440\) | −5.78603 | + | 4.63917i | −0.275838 | + | 0.221164i | ||||
\(441\) | −6.90387 | −0.328756 | ||||||||
\(442\) | 6.17422 | + | 6.17422i | 0.293678 | + | 0.293678i | ||||
\(443\) | 14.8548 | + | 14.8548i | 0.705775 | + | 0.705775i | 0.965644 | − | 0.259869i | \(-0.0836794\pi\) |
−0.259869 | + | 0.965644i | \(0.583679\pi\) | |||||||
\(444\) | 9.52666i | 0.452115i | ||||||||
\(445\) | −2.73193 | − | 6.69348i | −0.129506 | − | 0.317301i | ||||
\(446\) | 7.87642i | 0.372959i | ||||||||
\(447\) | 46.1498 | + | 46.1498i | 2.18281 | + | 2.18281i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 10.7089i | 0.505385i | 0.967547 | + | 0.252693i | \(0.0813161\pi\) | ||||
−0.967547 | + | 0.252693i | \(0.918684\pi\) | |||||||
\(450\) | 0.358221 | − | 34.5175i | 0.0168867 | − | 1.62717i | ||||
\(451\) | −10.9683 | + | 20.2176i | −0.516479 | + | 0.952008i | ||||
\(452\) | −9.73436 | + | 9.73436i | −0.457866 | + | 0.457866i | ||||
\(453\) | 32.4266 | − | 32.4266i | 1.52353 | − | 1.52353i | ||||
\(454\) | 19.6672i | 0.923027i | ||||||||
\(455\) | −4.63051 | + | 1.88993i | −0.217082 | + | 0.0886013i | ||||
\(456\) | 12.9746 | 0.607589 | ||||||||
\(457\) | 15.8229 | + | 15.8229i | 0.740164 | + | 0.740164i | 0.972609 | − | 0.232446i | \(-0.0746728\pi\) |
−0.232446 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(458\) | 19.8463 | − | 19.8463i | 0.927357 | − | 0.927357i | ||||
\(459\) | −47.9615 | −2.23865 | ||||||||
\(460\) | −1.69511 | + | 4.03303i | −0.0790348 | + | 0.188041i | ||||
\(461\) | 22.8434i | 1.06392i | 0.846768 | + | 0.531962i | \(0.178545\pi\) | ||||
−0.846768 | + | 0.531962i | \(0.821455\pi\) | |||||||
\(462\) | −10.0067 | + | 2.96783i | −0.465555 | + | 0.138076i | ||||
\(463\) | −0.862988 | − | 0.862988i | −0.0401064 | − | 0.0401064i | 0.686769 | − | 0.726876i | \(-0.259028\pi\) |
−0.726876 | + | 0.686769i | \(0.759028\pi\) | |||||||
\(464\) | 9.22628 | 0.428319 | ||||||||
\(465\) | 25.3255 | + | 10.6444i | 1.17444 | + | 0.493624i | ||||
\(466\) | 10.8349 | 0.501915 | ||||||||
\(467\) | −24.1744 | + | 24.1744i | −1.11866 | + | 1.11866i | −0.126720 | + | 0.991939i | \(0.540445\pi\) |
−0.991939 | + | 0.126720i | \(0.959555\pi\) | |||||||
\(468\) | 10.9189 | − | 10.9189i | 0.504727 | − | 0.504727i | ||||
\(469\) | −4.34261 | −0.200523 | ||||||||
\(470\) | −15.9583 | + | 6.51332i | −0.736099 | + | 0.300437i | ||||
\(471\) | −45.8232 | −2.11142 | ||||||||
\(472\) | −5.60556 | − | 5.60556i | −0.258017 | − | 0.258017i | ||||
\(473\) | 16.1957 | − | 4.80339i | 0.744680 | − | 0.220860i | ||||
\(474\) | − | 36.8677i | − | 1.69339i | ||||||
\(475\) | 14.7267 | − | 14.4242i | 0.675708 | − | 0.661827i | ||||
\(476\) | −3.90387 | −0.178934 | ||||||||
\(477\) | 25.3179 | − | 25.3179i | 1.15923 | − | 1.15923i | ||||
\(478\) | −3.30652 | − | 3.30652i | −0.151237 | − | 0.151237i | ||||
\(479\) | −9.69812 | −0.443118 | −0.221559 | − | 0.975147i | \(-0.571115\pi\) | ||||
−0.221559 | + | 0.975147i | \(0.571115\pi\) | |||||||
\(480\) | 2.65917 | + | 6.51522i | 0.121374 | + | 0.297378i | ||||
\(481\) | 6.77080i | 0.308722i | ||||||||
\(482\) | 16.8985 | − | 16.8985i | 0.769705 | − | 0.769705i | ||||
\(483\) | −4.35371 | + | 4.35371i | −0.198101 | + | 0.198101i | ||||
\(484\) | −9.22130 | + | 5.99731i | −0.419150 | + | 0.272605i | ||||
\(485\) | 4.78339 | − | 11.3807i | 0.217203 | − | 0.516773i | ||||
\(486\) | 19.6382i | 0.890805i | ||||||||
\(487\) | −6.57107 | + | 6.57107i | −0.297764 | + | 0.297764i | −0.840137 | − | 0.542374i | \(-0.817526\pi\) |
0.542374 | + | 0.840137i | \(0.317526\pi\) | |||||||
\(488\) | 7.60520 | + | 7.60520i | 0.344271 | + | 0.344271i | ||||
\(489\) | − | 56.1392i | − | 2.53870i | ||||||
\(490\) | 0.866414 | − | 2.06139i | 0.0391406 | − | 0.0931241i | ||||
\(491\) | − | 6.25193i | − | 0.282146i | −0.989999 | − | 0.141073i | \(-0.954945\pi\) | ||
0.989999 | − | 0.141073i | \(-0.0450552\pi\) | |||||||
\(492\) | 15.4327 | + | 15.4327i | 0.695759 | + | 0.695759i | ||||
\(493\) | −25.4687 | − | 25.4687i | −1.14705 | − | 1.14705i | ||||
\(494\) | 9.22130 | 0.414886 | ||||||||
\(495\) | 5.59872 | − | 50.8934i | 0.251644 | − | 2.28749i | ||||
\(496\) | −3.90387 | −0.175289 | ||||||||
\(497\) | −10.0464 | − | 10.0464i | −0.450641 | − | 0.450641i | ||||
\(498\) | −19.0672 | − | 19.0672i | −0.854420 | − | 0.854420i | ||||
\(499\) | − | 30.8329i | − | 1.38027i | −0.723680 | − | 0.690136i | \(-0.757551\pi\) | ||
0.723680 | − | 0.690136i | \(-0.242449\pi\) | |||||||
\(500\) | 10.2614 | + | 4.43880i | 0.458905 | + | 0.198509i | ||||
\(501\) | − | 38.2094i | − | 1.70707i | ||||||
\(502\) | −19.4758 | − | 19.4758i | −0.869247 | − | 0.869247i | ||||
\(503\) | −19.2257 | + | 19.2257i | −0.857234 | + | 0.857234i | −0.991011 | − | 0.133778i | \(-0.957289\pi\) |
0.133778 | + | 0.991011i | \(0.457289\pi\) | |||||||
\(504\) | 6.90387i | 0.307523i | ||||||||
\(505\) | 10.5700 | + | 25.8976i | 0.470360 | + | 1.15243i | ||||
\(506\) | −3.09427 | + | 5.70357i | −0.137557 | + | 0.253555i | ||||
\(507\) | −17.7964 | + | 17.7964i | −0.790364 | + | 0.790364i | ||||
\(508\) | 13.4331 | − | 13.4331i | 0.595999 | − | 0.595999i | ||||
\(509\) | 40.8197i | 1.80930i | 0.426156 | + | 0.904650i | \(0.359867\pi\) | ||||
−0.426156 | + | 0.904650i | \(0.640133\pi\) | |||||||
\(510\) | 10.6444 | − | 25.3255i | 0.471344 | − | 1.12143i | ||||
\(511\) | 8.52397 | 0.377078 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −35.8156 | + | 35.8156i | −1.58130 | + | 1.58130i | ||||
\(514\) | −14.0384 | −0.619206 | ||||||||
\(515\) | −25.7430 | − | 10.8199i | −1.13437 | − | 0.476784i | ||||
\(516\) | − | 16.0293i | − | 0.705649i | ||||||
\(517\) | −24.5103 | + | 7.26934i | −1.07796 | + | 0.319705i | ||||
\(518\) | −2.14054 | − | 2.14054i | −0.0940499 | − | 0.0940499i | ||||
\(519\) | 36.5084 | 1.60254 | ||||||||
\(520\) | 1.88993 | + | 4.63051i | 0.0828790 | + | 0.203061i | ||||
\(521\) | −0.939626 | −0.0411657 | −0.0205829 | − | 0.999788i | \(-0.506552\pi\) | ||||
−0.0205829 | + | 0.999788i | \(0.506552\pi\) | |||||||
\(522\) | −45.0406 | + | 45.0406i | −1.97137 | + | 1.97137i | ||||
\(523\) | 4.96198 | − | 4.96198i | 0.216972 | − | 0.216972i | −0.590249 | − | 0.807221i | \(-0.700970\pi\) |
0.807221 | + | 0.590249i | \(0.200970\pi\) | |||||||
\(524\) | 7.19093 | 0.314137 | ||||||||
\(525\) | 11.0104 | + | 11.2413i | 0.480534 | + | 0.490612i | ||||
\(526\) | −22.1414 | −0.965410 | ||||||||
\(527\) | 10.7764 | + | 10.7764i | 0.469429 | + | 0.469429i | ||||
\(528\) | 2.96783 | + | 10.0067i | 0.129158 | + | 0.435487i | ||||
\(529\) | − | 19.1723i | − | 0.833576i | ||||||
\(530\) | 4.38221 | + | 10.7368i | 0.190351 | + | 0.466379i | ||||
\(531\) | 54.7301 | 2.37508 | ||||||||
\(532\) | −2.91525 | + | 2.91525i | −0.126392 | + | 0.126392i | ||||
\(533\) | 10.9683 | + | 10.9683i | 0.475091 | + | 0.475091i | ||||
\(534\) | −10.1748 | −0.440308 | ||||||||
\(535\) | 1.23137 | + | 0.517550i | 0.0532366 | + | 0.0223756i | ||||
\(536\) | 4.34261i | 0.187572i | ||||||||
\(537\) | −27.2278 | + | 27.2278i | −1.17496 | + | 1.17496i | ||||
\(538\) | −5.12018 | + | 5.12018i | −0.220747 | + | 0.220747i | ||||
\(539\) | 1.58156 | − | 2.91525i | 0.0681228 | − | 0.125568i | ||||
\(540\) | −25.3255 | − | 10.6444i | −1.08984 | − | 0.458064i | ||||
\(541\) | 10.5183i | 0.452218i | 0.974102 | + | 0.226109i | \(0.0726006\pi\) | ||||
−0.974102 | + | 0.226109i | \(0.927399\pi\) | |||||||
\(542\) | 1.02006 | − | 1.02006i | 0.0438153 | − | 0.0438153i | ||||
\(543\) | −17.0618 | − | 17.0618i | −0.732191 | − | 0.732191i | ||||
\(544\) | 3.90387i | 0.167377i | ||||||||
\(545\) | −25.4346 | + | 10.3811i | −1.08950 | + | 0.444676i | ||||
\(546\) | 7.03889i | 0.301237i | ||||||||
\(547\) | 6.47829 | + | 6.47829i | 0.276992 | + | 0.276992i | 0.831907 | − | 0.554915i | \(-0.187249\pi\) |
−0.554915 | + | 0.831907i | \(0.687249\pi\) | |||||||
\(548\) | 5.37721 | + | 5.37721i | 0.229703 | + | 0.229703i | ||||
\(549\) | −74.2537 | −3.16907 | ||||||||
\(550\) | 14.4934 | + | 8.05866i | 0.618000 | + | 0.343622i | ||||
\(551\) | −38.0379 | −1.62047 | ||||||||
\(552\) | 4.35371 | + | 4.35371i | 0.185306 | + | 0.185306i | ||||
\(553\) | 8.28377 | + | 8.28377i | 0.352262 | + | 0.352262i | ||||
\(554\) | − | 23.2278i | − | 0.986853i | ||||||
\(555\) | 19.7228 | − | 8.04979i | 0.837184 | − | 0.341695i | ||||
\(556\) | 5.64575i | 0.239433i | ||||||||
\(557\) | −13.5850 | − | 13.5850i | −0.575614 | − | 0.575614i | 0.358078 | − | 0.933692i | \(-0.383432\pi\) |
−0.933692 | + | 0.358078i | \(0.883432\pi\) | |||||||
\(558\) | 19.0578 | − | 19.0578i | 0.806781 | − | 0.806781i | ||||
\(559\) | − | 11.3923i | − | 0.481845i | ||||||
\(560\) | −2.06139 | − | 0.866414i | −0.0871096 | − | 0.0366127i | ||||
\(561\) | 19.4305 | − | 35.8156i | 0.820358 | − | 1.51214i | ||||
\(562\) | −16.3545 | + | 16.3545i | −0.689871 | + | 0.689871i | ||||
\(563\) | −14.0945 | + | 14.0945i | −0.594011 | + | 0.594011i | −0.938712 | − | 0.344702i | \(-0.887980\pi\) |
0.344702 | + | 0.938712i | \(0.387980\pi\) | |||||||
\(564\) | 24.2583i | 1.02146i | ||||||||
\(565\) | 28.3780 | + | 11.9275i | 1.19387 | + | 0.501792i | ||||
\(566\) | −5.46955 | −0.229903 | ||||||||
\(567\) | −12.6938 | − | 12.6938i | −0.533091 | − | 0.533091i | ||||
\(568\) | −10.0464 | + | 10.0464i | −0.421536 | + | 0.421536i | ||||
\(569\) | 21.3400 | 0.894619 | 0.447309 | − | 0.894379i | \(-0.352382\pi\) | ||||
0.447309 | + | 0.894379i | \(0.352382\pi\) | |||||||
\(570\) | −10.9632 | − | 26.8608i | −0.459197 | − | 1.12508i | ||||
\(571\) | 37.1655i | 1.55533i | 0.628680 | + | 0.777664i | \(0.283596\pi\) | ||||
−0.628680 | + | 0.777664i | \(0.716404\pi\) | |||||||
\(572\) | 2.10930 | + | 7.11199i | 0.0881943 | + | 0.297367i | ||||
\(573\) | −49.4187 | − | 49.4187i | −2.06449 | − | 2.06449i | ||||
\(574\) | −6.93512 | −0.289466 | ||||||||
\(575\) | 9.78179 | + | 0.101515i | 0.407929 | + | 0.00423347i | ||||
\(576\) | 6.90387 | 0.287661 | ||||||||
\(577\) | −19.7344 | + | 19.7344i | −0.821552 | + | 0.821552i | −0.986331 | − | 0.164778i | \(-0.947309\pi\) |
0.164778 | + | 0.986331i | \(0.447309\pi\) | |||||||
\(578\) | −1.24437 | + | 1.24437i | −0.0517589 | + | 0.0517589i | ||||
\(579\) | 23.2471 | 0.966115 | ||||||||
\(580\) | −7.79598 | − | 19.1009i | −0.323711 | − | 0.793122i | ||||
\(581\) | 8.56838 | 0.355476 | ||||||||
\(582\) | −12.2856 | − | 12.2856i | −0.509256 | − | 0.509256i | ||||
\(583\) | 4.89087 | + | 16.4907i | 0.202559 | + | 0.682975i | ||||
\(584\) | − | 8.52397i | − | 0.352724i | ||||||
\(585\) | −31.8313 | − | 13.3789i | −1.31606 | − | 0.553149i | ||||
\(586\) | 2.02166 | 0.0835139 | ||||||||
\(587\) | −24.4555 | + | 24.4555i | −1.00939 | + | 1.00939i | −0.00943040 | + | 0.999956i | \(0.503002\pi\) |
−0.999956 | + | 0.00943040i | \(0.996998\pi\) | |||||||
\(588\) | −2.22529 | − | 2.22529i | −0.0917696 | − | 0.0917696i | ||||
\(589\) | 16.0948 | 0.663174 | ||||||||
\(590\) | −6.86846 | + | 16.3416i | −0.282770 | + | 0.672772i | ||||
\(591\) | − | 78.7161i | − | 3.23795i | ||||||
\(592\) | −2.14054 | + | 2.14054i | −0.0879756 | + | 0.0879756i | ||||
\(593\) | −30.8716 | + | 30.8716i | −1.26775 | + | 1.26775i | −0.320495 | + | 0.947250i | \(0.603849\pi\) |
−0.947250 | + | 0.320495i | \(0.896151\pi\) | |||||||
\(594\) | −35.8156 | − | 19.4305i | −1.46953 | − | 0.797244i | ||||
\(595\) | 3.29867 | + | 8.08206i | 0.135232 | + | 0.331332i | ||||
\(596\) | 20.7387i | 0.849492i | ||||||||
\(597\) | 8.36068 | − | 8.36068i | 0.342180 | − | 0.342180i | ||||
\(598\) | 3.09427 | + | 3.09427i | 0.126534 | + | 0.126534i | ||||
\(599\) | − | 21.3065i | − | 0.870561i | −0.900295 | − | 0.435280i | \(-0.856649\pi\) | ||
0.900295 | − | 0.435280i | \(-0.143351\pi\) | |||||||
\(600\) | 11.2413 | − | 11.0104i | 0.458926 | − | 0.449498i | ||||
\(601\) | 16.9962i | 0.693290i | 0.937996 | + | 0.346645i | \(0.112679\pi\) | ||||
−0.937996 | + | 0.346645i | \(0.887321\pi\) | |||||||
\(602\) | 3.60160 | + | 3.60160i | 0.146790 | + | 0.146790i | ||||
\(603\) | −21.1996 | − | 21.1996i | −0.863315 | − | 0.863315i | ||||
\(604\) | 14.5718 | 0.592919 | ||||||||
\(605\) | 20.2078 | + | 14.0230i | 0.821564 | + | 0.570116i | ||||
\(606\) | 39.3672 | 1.59918 | ||||||||
\(607\) | −3.70538 | − | 3.70538i | −0.150397 | − | 0.150397i | 0.627899 | − | 0.778295i | \(-0.283915\pi\) |
−0.778295 | + | 0.627899i | \(0.783915\pi\) | |||||||
\(608\) | 2.91525 | + | 2.91525i | 0.118229 | + | 0.118229i | ||||
\(609\) | − | 29.0355i | − | 1.17658i | ||||||
\(610\) | 9.31860 | − | 22.1710i | 0.377299 | − | 0.897678i | ||||
\(611\) | 17.2409i | 0.697493i | ||||||||
\(612\) | −19.0578 | − | 19.0578i | −0.770366 | − | 0.770366i | ||||
\(613\) | 13.2403 | − | 13.2403i | 0.534771 | − | 0.534771i | −0.387218 | − | 0.921988i | \(-0.626564\pi\) |
0.921988 | + | 0.387218i | \(0.126564\pi\) | |||||||
\(614\) | − | 6.57376i | − | 0.265295i | ||||||
\(615\) | 18.9096 | − | 44.9900i | 0.762508 | − | 1.81417i | ||||
\(616\) | −2.91525 | − | 1.58156i | −0.117459 | − | 0.0637230i | ||||
\(617\) | −25.1525 | + | 25.1525i | −1.01260 | + | 1.01260i | −0.0126799 | + | 0.999920i | \(0.504036\pi\) |
−0.999920 | + | 0.0126799i | \(0.995964\pi\) | |||||||
\(618\) | −27.7899 | + | 27.7899i | −1.11787 | + | 1.11787i | ||||
\(619\) | 9.30030i | 0.373811i | 0.982378 | + | 0.186905i | \(0.0598458\pi\) | ||||
−0.982378 | + | 0.186905i | \(0.940154\pi\) | |||||||
\(620\) | 3.29867 | + | 8.08206i | 0.132478 | + | 0.324583i | ||||
\(621\) | −24.0364 | −0.964548 | ||||||||
\(622\) | −11.8880 | − | 11.8880i | −0.476663 | − | 0.476663i | ||||
\(623\) | 2.28618 | − | 2.28618i | 0.0915938 | − | 0.0915938i | ||||
\(624\) | 7.03889 | 0.281781 | ||||||||
\(625\) | 0.518842 | − | 24.9946i | 0.0207537 | − | 0.999785i | ||||
\(626\) | 4.74773i | 0.189757i | ||||||||
\(627\) | −12.2357 | − | 41.2555i | −0.488647 | − | 1.64759i | ||||
\(628\) | −10.2960 | − | 10.2960i | −0.410854 | − | 0.410854i | ||||
\(629\) | 11.8177 | 0.471203 | ||||||||
\(630\) | 14.2929 | − | 5.83360i | 0.569442 | − | 0.232416i | ||||
\(631\) | 16.2478 | 0.646815 | 0.323408 | − | 0.946260i | \(-0.395171\pi\) | ||||
0.323408 | + | 0.946260i | \(0.395171\pi\) | |||||||
\(632\) | 8.28377 | − | 8.28377i | 0.329511 | − | 0.329511i | ||||
\(633\) | −32.6771 | + | 32.6771i | −1.29880 | + | 1.29880i | ||||
\(634\) | −8.95439 | −0.355624 | ||||||||
\(635\) | −39.1609 | − | 16.4595i | −1.55405 | − | 0.653177i | ||||
\(636\) | 16.3212 | 0.647178 | ||||||||
\(637\) | −1.58156 | − | 1.58156i | −0.0626639 | − | 0.0626639i | ||||
\(638\) | −8.70089 | − | 29.3370i | −0.344472 | − | 1.16146i | ||||
\(639\) | − | 98.0881i | − | 3.88031i | ||||||
\(640\) | −0.866414 | + | 2.06139i | −0.0342480 | + | 0.0814836i | ||||
\(641\) | −25.9440 | −1.02473 | −0.512363 | − | 0.858769i | \(-0.671230\pi\) | ||||
−0.512363 | + | 0.858769i | \(0.671230\pi\) | |||||||
\(642\) | 1.32927 | − | 1.32927i | 0.0524622 | − | 0.0524622i | ||||
\(643\) | 28.4381 | + | 28.4381i | 1.12149 | + | 1.12149i | 0.991518 | + | 0.129972i | \(0.0414889\pi\) |
0.129972 | + | 0.991518i | \(0.458511\pi\) | |||||||
\(644\) | −1.95646 | −0.0770955 | ||||||||
\(645\) | −33.1849 | + | 13.5443i | −1.30665 | + | 0.533308i | ||||
\(646\) | − | 16.0948i | − | 0.633241i | ||||||
\(647\) | 29.0101 | − | 29.0101i | 1.14050 | − | 1.14050i | 0.152145 | − | 0.988358i | \(-0.451382\pi\) |
0.988358 | − | 0.152145i | \(-0.0486180\pi\) | |||||||
\(648\) | −12.6938 | + | 12.6938i | −0.498661 | + | 0.498661i | ||||
\(649\) | −12.5378 | + | 23.1105i | −0.492151 | + | 0.907166i | ||||
\(650\) | 7.98946 | − | 7.82533i | 0.313372 | − | 0.306935i | ||||
\(651\) | 12.2856i | 0.481512i | ||||||||
\(652\) | 12.6139 | − | 12.6139i | 0.493998 | − | 0.493998i | ||||
\(653\) | 28.2965 | + | 28.2965i | 1.10733 | + | 1.10733i | 0.993500 | + | 0.113828i | \(0.0363112\pi\) |
0.113828 | + | 0.993500i | \(0.463689\pi\) | |||||||
\(654\) | 38.6634i | 1.51186i | ||||||||
\(655\) | −6.07616 | − | 14.8872i | −0.237415 | − | 0.581690i | ||||
\(656\) | 6.93512i | 0.270771i | ||||||||
\(657\) | 41.6121 | + | 41.6121i | 1.62344 | + | 1.62344i | ||||
\(658\) | −5.45059 | − | 5.45059i | −0.212486 | − | 0.212486i | ||||
\(659\) | −5.21956 | −0.203325 | −0.101663 | − | 0.994819i | \(-0.532416\pi\) | ||||
−0.101663 | + | 0.994819i | \(0.532416\pi\) | |||||||
\(660\) | 18.2089 | − | 14.5996i | 0.708779 | − | 0.568291i | ||||
\(661\) | 6.23474 | 0.242503 | 0.121252 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121252 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(662\) | 23.9858 | + | 23.9858i | 0.932233 | + | 0.932233i | ||||
\(663\) | −19.4305 | − | 19.4305i | −0.754619 | − | 0.754619i | ||||
\(664\) | − | 8.56838i | − | 0.332518i | ||||||
\(665\) | 8.49865 | + | 3.57203i | 0.329564 | + | 0.138518i | ||||
\(666\) | − | 20.8993i | − | 0.809830i | ||||||
\(667\) | −12.7639 | − | 12.7639i | −0.494220 | − | 0.494220i | ||||
\(668\) | 8.58525 | − | 8.58525i | 0.332173 | − | 0.332173i | ||||
\(669\) | − | 24.7874i | − | 0.958337i | ||||||
\(670\) | 8.99037 | − | 3.66940i | 0.347328 | − | 0.141761i | ||||
\(671\) | 17.0103 | − | 31.3545i | 0.656676 | − | 1.21043i | ||||
\(672\) | −2.22529 | + | 2.22529i | −0.0858426 | + | 0.0858426i | ||||
\(673\) | −5.36642 | + | 5.36642i | −0.206860 | + | 0.206860i | −0.802932 | − | 0.596071i | \(-0.796728\pi\) |
0.596071 | + | 0.802932i | \(0.296728\pi\) | |||||||
\(674\) | − | 28.2881i | − | 1.08962i | ||||||
\(675\) | −0.637465 | + | 61.4249i | −0.0245360 | + | 2.36424i | ||||
\(676\) | −7.99731 | −0.307589 | ||||||||
\(677\) | −10.8856 | − | 10.8856i | −0.418366 | − | 0.418366i | 0.466274 | − | 0.884640i | \(-0.345596\pi\) |
−0.884640 | + | 0.466274i | \(0.845596\pi\) | |||||||
\(678\) | 30.6344 | − | 30.6344i | 1.17651 | − | 1.17651i | ||||
\(679\) | 5.52091 | 0.211873 | ||||||||
\(680\) | 8.08206 | − | 3.29867i | 0.309933 | − | 0.126498i | ||||
\(681\) | − | 61.8935i | − | 2.37176i | ||||||
\(682\) | 3.68156 | + | 12.4132i | 0.140974 | + | 0.475327i | ||||
\(683\) | 16.8040 | + | 16.8040i | 0.642985 | + | 0.642985i | 0.951288 | − | 0.308303i | \(-0.0997610\pi\) |
−0.308303 | + | 0.951288i | \(0.599761\pi\) | |||||||
\(684\) | −28.4631 | −1.08831 | ||||||||
\(685\) | 6.58866 | − | 15.6759i | 0.251740 | − | 0.598945i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −62.4571 | + | 62.4571i | −2.38289 | + | 2.38289i | ||||
\(688\) | 3.60160 | − | 3.60160i | 0.137310 | − | 0.137310i | ||||
\(689\) | 11.5998 | 0.441918 | ||||||||
\(690\) | 5.33457 | − | 12.6921i | 0.203084 | − | 0.483181i | ||||
\(691\) | 5.60413 | 0.213191 | 0.106596 | − | 0.994302i | \(-0.466005\pi\) | ||||
0.106596 | + | 0.994302i | \(0.466005\pi\) | |||||||
\(692\) | 8.20306 | + | 8.20306i | 0.311833 | + | 0.311833i | ||||
\(693\) | 21.9524 | − | 6.51073i | 0.833903 | − | 0.247322i | ||||
\(694\) | 25.6680i | 0.974345i | ||||||||
\(695\) | 11.6882 | − | 4.77052i | 0.443360 | − | 0.180956i | ||||
\(696\) | −29.0355 | −1.10059 | ||||||||
\(697\) | 19.1441 | − | 19.1441i | 0.725133 | − | 0.725133i | ||||
\(698\) | 7.55540 | + | 7.55540i | 0.285976 | + | 0.285976i | ||||
\(699\) | −34.0977 | −1.28969 | ||||||||
\(700\) | −0.0518870 | + | 4.99973i | −0.00196114 | + | 0.188972i | ||||
\(701\) | 44.3044i | 1.67335i | 0.547697 | + | 0.836676i | \(0.315505\pi\) | ||||
−0.547697 | + | 0.836676i | \(0.684495\pi\) | |||||||
\(702\) | −19.4305 | + | 19.4305i | −0.733358 | + | 0.733358i | ||||
\(703\) | 8.82497 | − | 8.82497i | 0.332840 | − | 0.332840i | ||||
\(704\) | −1.58156 | + | 2.91525i | −0.0596075 | + | 0.109872i | ||||
\(705\) | 50.2213 | − | 20.4977i | 1.89144 | − | 0.771988i | ||||
\(706\) | − | 12.8601i | − | 0.483995i | ||||||
\(707\) | −8.84539 | + | 8.84539i | −0.332665 | + | 0.332665i | ||||
\(708\) | 17.6409 | + | 17.6409i | 0.662986 | + | 0.662986i | ||||
\(709\) | 13.6279i | 0.511807i | 0.966702 | + | 0.255904i | \(0.0823730\pi\) | ||||
−0.966702 | + | 0.255904i | \(0.917627\pi\) | |||||||
\(710\) | 29.2876 | + | 12.3097i | 1.09914 | + | 0.461977i | ||||
\(711\) | 80.8790i | 3.03320i | ||||||||
\(712\) | −2.28618 | − | 2.28618i | −0.0856781 | − | 0.0856781i | ||||
\(713\) | 5.40072 | + | 5.40072i | 0.202259 | + | 0.202259i | ||||
\(714\) | 12.2856 | 0.459778 | ||||||||
\(715\) | 12.9414 | − | 10.3763i | 0.483982 | − | 0.388051i | ||||
\(716\) | −12.2356 | −0.457265 | ||||||||
\(717\) | 10.4058 | + | 10.4058i | 0.388610 | + | 0.388610i | ||||
\(718\) | 5.30652 | + | 5.30652i | 0.198038 | + | 0.198038i | ||||
\(719\) | − | 14.8104i | − | 0.552336i | −0.961109 | − | 0.276168i | \(-0.910935\pi\) | ||
0.961109 | − | 0.276168i | \(-0.0890646\pi\) | |||||||
\(720\) | −5.83360 | − | 14.2929i | −0.217405 | − | 0.532664i | ||||
\(721\) | − | 12.4882i | − | 0.465085i | ||||||
\(722\) | 1.41612 | + | 1.41612i | 0.0527024 | + | 0.0527024i | ||||
\(723\) | −53.1802 | + | 53.1802i | −1.97779 | + | 1.97779i | ||||
\(724\) | − | 7.66720i | − | 0.284949i | ||||||
\(725\) | −32.9566 | + | 32.2796i | −1.22398 | + | 1.19883i | ||||
\(726\) | 29.0198 | − | 18.8738i | 1.07703 | − | 0.700472i | ||||
\(727\) | −23.2654 | + | 23.2654i | −0.862865 | + | 0.862865i | −0.991670 | − | 0.128805i | \(-0.958886\pi\) |
0.128805 | + | 0.991670i | \(0.458886\pi\) | |||||||
\(728\) | −1.58156 | + | 1.58156i | −0.0586167 | + | 0.0586167i | ||||
\(729\) | − | 7.94668i | − | 0.294321i | ||||||
\(730\) | −17.6469 | + | 7.20254i | −0.653142 | + | 0.266578i | ||||
\(731\) | −19.8841 | −0.735441 | ||||||||
\(732\) | −23.9339 | − | 23.9339i | −0.884621 | − | 0.884621i | ||||
\(733\) | −24.5188 | + | 24.5188i | −0.905623 | + | 0.905623i | −0.995915 | − | 0.0902927i | \(-0.971220\pi\) |
0.0902927 | + | 0.995915i | \(0.471220\pi\) | |||||||
\(734\) | −15.3488 | −0.566535 | ||||||||
\(735\) | −2.72664 | + | 6.48728i | −0.100574 | + | 0.239287i | ||||
\(736\) | 1.95646i | 0.0721162i | ||||||||
\(737\) | 13.8083 | − | 4.09532i | 0.508635 | − | 0.150853i | ||||
\(738\) | −33.8557 | − | 33.8557i | −1.24624 | − | 1.24624i | ||||
\(739\) | 7.21925 | 0.265565 | 0.132782 | − | 0.991145i | \(-0.457609\pi\) | ||||
0.132782 | + | 0.991145i | \(0.457609\pi\) | |||||||
\(740\) | 6.24020 | + | 2.62279i | 0.229394 | + | 0.0964157i | ||||
\(741\) | −29.0198 | −1.06607 | ||||||||
\(742\) | −3.66720 | + | 3.66720i | −0.134627 | + | 0.134627i | ||||
\(743\) | 2.04782 | − | 2.04782i | 0.0751271 | − | 0.0751271i | −0.668545 | − | 0.743672i | \(-0.733082\pi\) |
0.743672 | + | 0.668545i | \(0.233082\pi\) | |||||||
\(744\) | 12.2856 | 0.450413 | ||||||||
\(745\) | 42.9348 | − | 17.5237i | 1.57301 | − | 0.642020i | ||||
\(746\) | −13.4985 | −0.494216 | ||||||||
\(747\) | 41.8289 | + | 41.8289i | 1.53044 | + | 1.53044i | ||||
\(748\) | 12.4132 | − | 3.68156i | 0.453873 | − | 0.134611i | ||||
\(749\) | 0.597347i | 0.0218266i | ||||||||
\(750\) | −32.2932 | − | 13.9691i | −1.17918 | − | 0.510078i | ||||
\(751\) | −25.8549 | −0.943459 | −0.471730 | − | 0.881743i | \(-0.656370\pi\) | ||||
−0.471730 | + | 0.881743i | \(0.656370\pi\) | |||||||
\(752\) | −5.45059 | + | 5.45059i | −0.198763 | + | 0.198763i | ||||
\(753\) | 61.2911 | + | 61.2911i | 2.23357 | + | 2.23357i | ||||
\(754\) | −20.6362 | −0.751524 | ||||||||
\(755\) | −12.3128 | − | 30.1676i | −0.448110 | − | 1.09791i | ||||
\(756\) | − | 12.2856i | − | 0.446824i | ||||||
\(757\) | 28.8452 | − | 28.8452i | 1.04840 | − | 1.04840i | 0.0496275 | − | 0.998768i | \(-0.484197\pi\) |
0.998768 | − | 0.0496275i | \(-0.0158034\pi\) | |||||||
\(758\) | 6.93013 | − | 6.93013i | 0.251714 | − | 0.251714i | ||||
\(759\) | 9.73781 | − | 17.9494i | 0.353460 | − | 0.651521i | ||||
\(760\) | 3.57203 | − | 8.49865i | 0.129571 | − | 0.308279i | ||||
\(761\) | 35.8344i | 1.29900i | 0.760363 | + | 0.649498i | \(0.225021\pi\) | ||||
−0.760363 | + | 0.649498i | \(0.774979\pi\) | |||||||
\(762\) | −42.2746 | + | 42.2746i | −1.53145 | + | 1.53145i | ||||
\(763\) | −8.68726 | − | 8.68726i | −0.314500 | − | 0.314500i | ||||
\(764\) | − | 22.2077i | − | 0.803446i | ||||||
\(765\) | −23.3514 | + | 55.5582i | −0.844272 | + | 2.00871i | ||||
\(766\) | − | 12.0831i | − | 0.436579i | ||||||
\(767\) | 12.5378 | + | 12.5378i | 0.452713 | + | 0.452713i | ||||
\(768\) | 2.22529 | + | 2.22529i | 0.0802984 | + | 0.0802984i | ||||
\(769\) | −11.9050 | −0.429305 | −0.214652 | − | 0.976691i | \(-0.568862\pi\) | ||||
−0.214652 | + | 0.976691i | \(0.568862\pi\) | |||||||
\(770\) | −0.810955 | + | 7.37173i | −0.0292248 | + | 0.265659i | ||||
\(771\) | 44.1793 | 1.59108 | ||||||||
\(772\) | 5.22337 | + | 5.22337i | 0.187993 | + | 0.187993i | ||||
\(773\) | −23.2034 | − | 23.2034i | −0.834567 | − | 0.834567i | 0.153570 | − | 0.988138i | \(-0.450923\pi\) |
−0.988138 | + | 0.153570i | \(0.950923\pi\) | |||||||
\(774\) | 35.1644i | 1.26396i | ||||||||
\(775\) | 13.9448 | − | 13.6583i | 0.500910 | − | 0.490620i | ||||
\(776\) | − | 5.52091i | − | 0.198189i | ||||||
\(777\) | 6.73637 | + | 6.73637i | 0.241666 | + | 0.241666i | ||||
\(778\) | 5.32714 | − | 5.32714i | 0.190987 | − | 0.190987i | ||||
\(779\) | − | 28.5920i | − | 1.02441i | ||||||
\(780\) | −5.94769 | − | 14.5724i | −0.212962 | − | 0.521776i | ||||
\(781\) | 41.4189 | + | 22.4704i | 1.48209 | + | 0.804054i | ||||
\(782\) | 5.40072 | − | 5.40072i | 0.193130 | − | 0.193130i | ||||
\(783\) | 80.1511 | − | 80.1511i | 2.86437 | − | 2.86437i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −12.6156 | + | 30.0153i | −0.450270 | + | 1.07129i | ||||
\(786\) | −22.6302 | −0.807191 | ||||||||
\(787\) | 29.5830 | + | 29.5830i | 1.05452 | + | 1.05452i | 0.998425 | + | 0.0560954i | \(0.0178651\pi\) |
0.0560954 | + | 0.998425i | \(0.482135\pi\) | |||||||
\(788\) | 17.6867 | − | 17.6867i | 0.630062 | − | 0.630062i | ||||
\(789\) | 69.6798 | 2.48067 | ||||||||
\(790\) | −24.1492 | − | 10.1501i | −0.859191 | − | 0.361123i | ||||
\(791\) | 13.7665i | 0.489479i | ||||||||
\(792\) | −6.51073 | − | 21.9524i | −0.231349 | − | 0.780045i | ||||
\(793\) | −17.0103 | − | 17.0103i | −0.604054 | − | 0.604054i | ||||
\(794\) | −0.616153 | −0.0218665 | ||||||||
\(795\) | −13.7910 | − | 33.7893i | −0.489117 | − | 1.19838i | ||||
\(796\) | 3.75711 | 0.133167 | ||||||||
\(797\) | 14.4647 | − | 14.4647i | 0.512364 | − | 0.512364i | −0.402886 | − | 0.915250i | \(-0.631993\pi\) |
0.915250 | + | 0.402886i | \(0.131993\pi\) | |||||||
\(798\) | 9.17440 | − | 9.17440i | 0.324770 | − | 0.324770i | ||||
\(799\) | 30.0922 | 1.06458 | ||||||||
\(800\) | 4.99973 | + | 0.0518870i | 0.176767 | + | 0.00183448i | ||||
\(801\) | 22.3212 | 0.788681 | ||||||||
\(802\) | 13.9666 | + | 13.9666i | 0.493177 | + | 0.493177i | ||||
\(803\) | −27.1039 | + | 8.03857i | −0.956475 | + | 0.283675i | ||||
\(804\) | − | 13.6664i | − | 0.481976i | ||||||
\(805\) | 1.65316 | + | 4.05041i | 0.0582664 | + | 0.142758i | ||||
\(806\) | 8.73167 | 0.307560 | ||||||||
\(807\) | 16.1134 | − | 16.1134i | 0.567219 | − | 0.567219i | ||||
\(808\) | 8.84539 | + | 8.84539i | 0.311180 | + | 0.311180i | ||||
\(809\) | −23.8253 | −0.837652 | −0.418826 | − | 0.908066i | \(-0.637558\pi\) | ||||
−0.418826 | + | 0.908066i | \(0.637558\pi\) | |||||||
\(810\) | 37.0057 | + | 15.5537i | 1.30025 | + | 0.546501i | ||||
\(811\) | 19.5470i | 0.686388i | 0.939265 | + | 0.343194i | \(0.111509\pi\) | ||||
−0.939265 | + | 0.343194i | \(0.888491\pi\) | |||||||
\(812\) | 6.52397 | − | 6.52397i | 0.228946 | − | 0.228946i | ||||
\(813\) | −3.21017 | + | 3.21017i | −0.112585 | + | 0.112585i | ||||
\(814\) | 8.82497 | + | 4.78768i | 0.309315 | + | 0.167808i | ||||
\(815\) | −36.7725 | − | 15.4557i | −1.28809 | − | 0.541390i | ||||
\(816\) | − | 12.2856i | − | 0.430083i | ||||||
\(817\) | −14.8486 | + | 14.8486i | −0.519487 | + | 0.519487i | ||||
\(818\) | −7.71623 | − | 7.71623i | −0.269792 | − | 0.269792i | ||||
\(819\) | − | 15.4417i | − | 0.539576i | ||||||
\(820\) | 14.3576 | − | 5.86000i | 0.501388 | − | 0.204640i | ||||
\(821\) | − | 7.72090i | − | 0.269461i | −0.990882 | − | 0.134731i | \(-0.956983\pi\) | ||
0.990882 | − | 0.134731i | \(-0.0430169\pi\) | |||||||
\(822\) | −16.9223 | − | 16.9223i | −0.590233 | − | 0.590233i | ||||
\(823\) | 30.4590 | + | 30.4590i | 1.06173 | + | 1.06173i | 0.997965 | + | 0.0637683i | \(0.0203119\pi\) |
0.0637683 | + | 0.997965i | \(0.479688\pi\) | |||||||
\(824\) | −12.4882 | −0.435047 | ||||||||
\(825\) | −45.6113 | − | 25.3609i | −1.58798 | − | 0.882954i | ||||
\(826\) | −7.92746 | −0.275831 | ||||||||
\(827\) | −32.3550 | − | 32.3550i | −1.12509 | − | 1.12509i | −0.990964 | − | 0.134129i | \(-0.957176\pi\) |
−0.134129 | − | 0.990964i | \(-0.542824\pi\) | |||||||
\(828\) | −9.55101 | − | 9.55101i | −0.331921 | − | 0.331921i | ||||
\(829\) | − | 26.3534i | − | 0.915290i | −0.889135 | − | 0.457645i | \(-0.848693\pi\) | ||
0.889135 | − | 0.457645i | \(-0.151307\pi\) | |||||||
\(830\) | −17.7389 | + | 7.24007i | −0.615724 | + | 0.251306i | ||||
\(831\) | 73.0987i | 2.53577i | ||||||||
\(832\) | 1.58156 | + | 1.58156i | 0.0548309 | + | 0.0548309i | ||||
\(833\) | −2.76045 | + | 2.76045i | −0.0956440 | + | 0.0956440i | ||||
\(834\) | − | 17.7674i | − | 0.615236i | ||||||
\(835\) | −25.0281 | − | 10.5195i | −0.866133 | − | 0.364041i | ||||
\(836\) | 6.52044 | − | 12.0189i | 0.225514 | − | 0.415683i | ||||
\(837\) | −33.9139 | + | 33.9139i | −1.17224 | + | 1.17224i | ||||
\(838\) | −4.13809 | + | 4.13809i | −0.142948 | + | 0.142948i | ||||
\(839\) | 41.7918i | 1.44281i | 0.692511 | + | 0.721407i | \(0.256504\pi\) | ||||
−0.692511 | + | 0.721407i | \(0.743496\pi\) | |||||||
\(840\) | 6.48728 | + | 2.72664i | 0.223832 | + | 0.0940780i | ||||
\(841\) | 56.1243 | 1.93532 | ||||||||
\(842\) | 11.1988 | + | 11.1988i | 0.385937 | + | 0.385937i | ||||
\(843\) | 51.4682 | − | 51.4682i | 1.77266 | − | 1.77266i | ||||
\(844\) | −14.6844 | −0.505457 | ||||||||
\(845\) | 6.75753 | + | 16.5566i | 0.232466 | + | 0.569564i | ||||
\(846\) | − | 53.2171i | − | 1.82964i | ||||||
\(847\) | −2.27970 | + | 10.7612i | −0.0783316 | + | 0.369758i | ||||
\(848\) | 3.66720 | + | 3.66720i | 0.125932 | + | 0.125932i | ||||
\(849\) | 17.2129 | 0.590746 | ||||||||
\(850\) | −13.6583 | − | 13.9448i | −0.468475 | − | 0.478301i | ||||
\(851\) | 5.92257 | 0.203023 | ||||||||
\(852\) | 31.6163 | − | 31.6163i | 1.08316 | − | 1.08316i | ||||
\(853\) | 3.00806 | − | 3.00806i | 0.102994 | − | 0.102994i | −0.653732 | − | 0.756726i | \(-0.726798\pi\) |
0.756726 | + | 0.653732i | \(0.226798\pi\) | |||||||
\(854\) | 10.7554 | 0.368041 | ||||||||
\(855\) | 24.0506 | + | 58.9264i | 0.822515 | + | 2.01524i | ||||
\(856\) | 0.597347 | 0.0204169 | ||||||||
\(857\) | −17.9833 | − | 17.9833i | −0.614297 | − | 0.614297i | 0.329766 | − | 0.944063i | \(-0.393030\pi\) |
−0.944063 | + | 0.329766i | \(0.893030\pi\) | |||||||
\(858\) | −6.63806 | − | 22.3817i | −0.226620 | − | 0.764100i | ||||
\(859\) | − | 4.95264i | − | 0.168982i | −0.996424 | − | 0.0844909i | \(-0.973074\pi\) | ||
0.996424 | − | 0.0844909i | \(-0.0269264\pi\) | |||||||
\(860\) | −10.4996 | − | 4.41303i | −0.358032 | − | 0.150483i | ||||
\(861\) | 21.8251 | 0.743798 | ||||||||
\(862\) | −2.26026 | + | 2.26026i | −0.0769846 | + | 0.0769846i | ||||
\(863\) | 8.16951 | + | 8.16951i | 0.278093 | + | 0.278093i | 0.832347 | − | 0.554254i | \(-0.186996\pi\) |
−0.554254 | + | 0.832347i | \(0.686996\pi\) | |||||||
\(864\) | −12.2856 | −0.417966 | ||||||||
\(865\) | 10.0512 | − | 23.9139i | 0.341750 | − | 0.813098i | ||||
\(866\) | − | 22.0220i | − | 0.748338i | ||||||
\(867\) | 3.91608 | − | 3.91608i | 0.132997 | − | 0.132997i | ||||
\(868\) | −2.76045 | + | 2.76045i | −0.0936959 | + | 0.0936959i | ||||
\(869\) | −34.1522 | − | 18.5281i | −1.15853 | − | 0.628521i | ||||
\(870\) | 24.5343 | + | 60.1113i | 0.831790 | + | 2.03796i | ||||
\(871\) | − | 9.71298i | − | 0.329112i | ||||||
\(872\) | −8.68726 | + | 8.68726i | −0.294188 | + | 0.294188i | ||||
\(873\) | 26.9518 | + | 26.9518i | 0.912180 | + | 0.912180i | ||||
\(874\) | − | 8.06607i | − | 0.272839i | ||||||
\(875\) | 10.3946 | − | 4.11723i | 0.351403 | − | 0.139188i | ||||
\(876\) | 26.8253i | 0.906342i | ||||||||
\(877\) | 0.936314 | + | 0.936314i | 0.0316171 | + | 0.0316171i | 0.722739 | − | 0.691122i | \(-0.242883\pi\) |
−0.691122 | + | 0.722739i | \(0.742883\pi\) | |||||||
\(878\) | 20.4942 | + | 20.4942i | 0.691644 | + | 0.691644i | ||||
\(879\) | −6.36224 | −0.214593 | ||||||||
\(880\) | 7.37173 | + | 0.810955i | 0.248501 | + | 0.0273373i | ||||
\(881\) | −39.4249 | −1.32826 | −0.664129 | − | 0.747618i | \(-0.731197\pi\) | ||||
−0.664129 | + | 0.747618i | \(0.731197\pi\) | |||||||
\(882\) | 4.88177 | + | 4.88177i | 0.164378 | + | 0.164378i | ||||
\(883\) | 8.47956 | + | 8.47956i | 0.285360 | + | 0.285360i | 0.835242 | − | 0.549882i | \(-0.185327\pi\) |
−0.549882 | + | 0.835242i | \(0.685327\pi\) | |||||||
\(884\) | − | 8.73167i | − | 0.293678i | ||||||
\(885\) | 21.6153 | − | 51.4276i | 0.726591 | − | 1.72872i | ||||
\(886\) | − | 21.0079i | − | 0.705775i | ||||||
\(887\) | 4.44520 | + | 4.44520i | 0.149255 | + | 0.149255i | 0.777785 | − | 0.628530i | \(-0.216343\pi\) |
−0.628530 | + | 0.777785i | \(0.716343\pi\) | |||||||
\(888\) | 6.73637 | − | 6.73637i | 0.226058 | − | 0.226058i | ||||
\(889\) | − | 18.9973i | − | 0.637149i | ||||||
\(890\) | −2.80124 | + | 6.66477i | −0.0938978 | + | 0.223403i | ||||
\(891\) | 52.3339 | + | 28.3919i | 1.75325 | + | 0.951166i | ||||
\(892\) | 5.56947 | − | 5.56947i | 0.186480 | − | 0.186480i | ||||
\(893\) | 22.4716 | − | 22.4716i | 0.751983 | − | 0.751983i | ||||
\(894\) | − | 65.2657i | − | 2.18281i | ||||||
\(895\) | 10.3388 | + | 25.3309i | 0.345587 | + | 0.846720i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −9.73781 | − | 9.73781i | −0.325136 | − | 0.325136i | ||||
\(898\) | 7.57235 | − | 7.57235i | 0.252693 | − | 0.252693i | ||||
\(899\) | −36.0182 | −1.20127 | ||||||||
\(900\) | −24.6609 | + | 24.1542i | −0.822028 | + | 0.805142i | ||||
\(901\) | − | 20.2463i | − | 0.674501i | ||||||
\(902\) | 22.0518 | − | 6.54020i | 0.734244 | − | 0.217765i | ||||
\(903\) | −11.3344 | − | 11.3344i | −0.377185 | − | 0.377185i | ||||
\(904\) | 13.7665 | 0.457866 | ||||||||
\(905\) | −15.8732 | + | 6.47859i | −0.527642 | + | 0.215356i | ||||
\(906\) | −45.8581 | −1.52353 | ||||||||
\(907\) | 30.0504 | − | 30.0504i | 0.997806 | − | 0.997806i | −0.00219146 | − | 0.999998i | \(-0.500698\pi\) |
0.999998 | + | 0.00219146i | \(0.000697565\pi\) | |||||||
\(908\) | 13.9068 | − | 13.9068i | 0.461514 | − | 0.461514i | ||||
\(909\) | −86.3624 | −2.86446 | ||||||||
\(910\) | 4.61065 | + | 1.93788i | 0.152841 | + | 0.0642402i | ||||
\(911\) | 35.6225 | 1.18023 | 0.590114 | − | 0.807320i | \(-0.299083\pi\) | ||||
0.590114 | + | 0.807320i | \(0.299083\pi\) | |||||||
\(912\) | −9.17440 | − | 9.17440i | −0.303795 | − | 0.303795i | ||||
\(913\) | −27.2451 | + | 8.08045i | −0.901680 | + | 0.267424i | ||||
\(914\) | − | 22.3770i | − | 0.740164i | ||||||
\(915\) | −29.3260 | + | 69.7731i | −0.969489 | + | 2.30663i | ||||
\(916\) | −28.0669 | −0.927357 | ||||||||
\(917\) | 5.08475 | − | 5.08475i | 0.167913 | − | 0.167913i | ||||
\(918\) | 33.9139 | + | 33.9139i | 1.11933 | + | 1.11933i | ||||
\(919\) | −39.9989 | −1.31944 | −0.659721 | − | 0.751510i | \(-0.729326\pi\) | ||||
−0.659721 | + | 0.751510i | \(0.729326\pi\) | |||||||
\(920\) | 4.05041 | − | 1.65316i | 0.133538 | − | 0.0545032i | ||||
\(921\) | 20.6879i | 0.681689i | ||||||||
\(922\) | 16.1527 | − | 16.1527i | 0.531962 | − | 0.531962i | ||||
\(923\) | 22.4704 | − | 22.4704i | 0.739622 | − | 0.739622i | ||||
\(924\) | 9.17440 | + | 4.97725i | 0.301815 | + | 0.163739i | ||||
\(925\) | 0.157071 | − | 15.1351i | 0.00516447 | − | 0.497639i | ||||
\(926\) | 1.22045i | 0.0401064i | ||||||||
\(927\) | 60.9646 | − | 60.9646i | 2.00234 | − | 2.00234i | ||||
\(928\) | −6.52397 | − | 6.52397i | −0.214160 | − | 0.214160i | ||||
\(929\) | − | 6.66174i | − | 0.218565i | −0.994011 | − | 0.109282i | \(-0.965145\pi\) | ||
0.994011 | − | 0.109282i | \(-0.0348553\pi\) | |||||||
\(930\) | −10.3811 | − | 25.4346i | −0.340408 | − | 0.834033i | ||||
\(931\) | 4.12278i | 0.135119i | ||||||||
\(932\) | −7.66140 | − | 7.66140i | −0.250957 | − | 0.250957i | ||||
\(933\) | 37.4119 | + | 37.4119i | 1.22481 | + | 1.22481i | ||||
\(934\) | 34.1878 | 1.11866 | ||||||||
\(935\) | −18.1107 | − | 22.5879i | −0.592283 | − | 0.738703i | ||||
\(936\) | −15.4417 | −0.504727 | ||||||||
\(937\) | −22.2171 | − | 22.2171i | −0.725802 | − | 0.725802i | 0.243979 | − | 0.969781i | \(-0.421547\pi\) |
−0.969781 | + | 0.243979i | \(0.921547\pi\) | |||||||
\(938\) | 3.07069 | + | 3.07069i | 0.100261 | + | 0.100261i | ||||
\(939\) | − | 14.9413i | − | 0.487591i | ||||||
\(940\) | 15.8898 | + | 6.67858i | 0.518268 | + | 0.217831i | ||||
\(941\) | 15.6402i | 0.509857i | 0.966960 | + | 0.254928i | \(0.0820519\pi\) | ||||
−0.966960 | + | 0.254928i | \(0.917948\pi\) | |||||||
\(942\) | 32.4019 | + | 32.4019i | 1.05571 | + | 1.05571i | ||||
\(943\) | 9.59424 | − | 9.59424i | 0.312431 | − | 0.312431i | ||||
\(944\) | 7.92746i | 0.258017i | ||||||||
\(945\) | −25.4346 | + | 10.3811i | −0.827387 | + | 0.337696i | ||||
\(946\) | −14.8486 | − | 8.05560i | −0.482770 | − | 0.261910i | ||||
\(947\) | 4.12401 | − | 4.12401i | 0.134012 | − | 0.134012i | −0.636919 | − | 0.770931i | \(-0.719791\pi\) |
0.770931 | + | 0.636919i | \(0.219791\pi\) | |||||||
\(948\) | −26.0694 | + | 26.0694i | −0.846694 | + | 0.846694i | ||||
\(949\) | 19.0653i | 0.618886i | ||||||||
\(950\) | −20.6128 | − | 0.213919i | −0.668767 | − | 0.00694044i | ||||
\(951\) | 28.1798 | 0.913793 | ||||||||
\(952\) | 2.76045 | + | 2.76045i | 0.0894668 | + | 0.0894668i | ||||
\(953\) | −27.5538 | + | 27.5538i | −0.892556 | + | 0.892556i | −0.994763 | − | 0.102207i | \(-0.967409\pi\) |
0.102207 | + | 0.994763i | \(0.467409\pi\) | |||||||
\(954\) | −35.8049 | −1.15923 | ||||||||
\(955\) | −45.9759 | + | 18.7650i | −1.48775 | + | 0.607220i | ||||
\(956\) | 4.67613i | 0.151237i | ||||||||
\(957\) | 27.3821 | + | 92.3249i | 0.885136 | + | 2.98444i | ||||
\(958\) | 6.85760 | + | 6.85760i | 0.221559 | + | 0.221559i | ||||
\(959\) | 7.60452 | 0.245563 | ||||||||
\(960\) | 2.72664 | − | 6.48728i | 0.0880019 | − | 0.209376i | ||||
\(961\) | −15.7598 | −0.508381 | ||||||||
\(962\) | 4.78768 | − | 4.78768i | 0.154361 | − | 0.154361i | ||||
\(963\) | −2.91611 | + | 2.91611i | −0.0939704 | + | 0.0939704i | ||||
\(964\) | −23.8981 | −0.769705 | ||||||||
\(965\) | 6.40016 | − | 15.2274i | 0.206028 | − | 0.490187i | ||||
\(966\) | 6.15707 | 0.198101 | ||||||||
\(967\) | 15.7565 | + | 15.7565i | 0.506694 | + | 0.506694i | 0.913510 | − | 0.406816i | \(-0.133361\pi\) |
−0.406816 | + | 0.913510i | \(0.633361\pi\) | |||||||
\(968\) | 10.7612 | + | 2.27970i | 0.345877 | + | 0.0732725i | ||||
\(969\) | 50.6510i | 1.62714i | ||||||||
\(970\) | −11.4298 | + | 4.66503i | −0.366988 | + | 0.149785i | ||||
\(971\) | −30.5405 | −0.980091 | −0.490046 | − | 0.871697i | \(-0.663020\pi\) | ||||
−0.490046 | + | 0.871697i | \(0.663020\pi\) | |||||||
\(972\) | 13.8863 | − | 13.8863i | 0.445402 | − | 0.445402i | ||||
\(973\) | 3.99215 | + | 3.99215i | 0.127982 | + | 0.127982i | ||||
\(974\) | 9.29289 | 0.297764 | ||||||||
\(975\) | −25.1432 | + | 24.6266i | −0.805226 | + | 0.788684i | ||||
\(976\) | − | 10.7554i | − | 0.344271i | ||||||
\(977\) | 25.4712 | − | 25.4712i | 0.814894 | − | 0.814894i | −0.170469 | − | 0.985363i | \(-0.554528\pi\) |
0.985363 | + | 0.170469i | \(0.0545282\pi\) | |||||||
\(978\) | −39.6964 | + | 39.6964i | −1.26935 | + | 1.26935i | ||||
\(979\) | −5.11342 | + | 9.42540i | −0.163426 | + | 0.301237i | ||||
\(980\) | −2.07027 | + | 0.844975i | −0.0661323 | + | 0.0269917i | ||||
\(981\) | − | 84.8184i | − | 2.70804i | ||||||
\(982\) | −4.42078 | + | 4.42078i | −0.141073 | + | 0.141073i | ||||
\(983\) | −1.64285 | − | 1.64285i | −0.0523988 | − | 0.0523988i | 0.680422 | − | 0.732821i | \(-0.261797\pi\) |
−0.732821 | + | 0.680422i | \(0.761797\pi\) | |||||||
\(984\) | − | 21.8251i | − | 0.695759i | ||||||
\(985\) | −51.5610 | − | 21.6714i | −1.64287 | − | 0.690508i | ||||
\(986\) | 36.0182i | 1.14705i | ||||||||
\(987\) | 17.1532 | + | 17.1532i | 0.545993 | + | 0.545993i | ||||
\(988\) | −6.52044 | − | 6.52044i | −0.207443 | − | 0.207443i | ||||
\(989\) | −9.96513 | −0.316873 | ||||||||
\(990\) | −39.9460 | + | 32.0282i | −1.26957 | + | 1.01792i | ||||
\(991\) | −43.1539 | −1.37083 | −0.685414 | − | 0.728154i | \(-0.740379\pi\) | ||||
−0.685414 | + | 0.728154i | \(0.740379\pi\) | |||||||
\(992\) | 2.76045 | + | 2.76045i | 0.0876445 | + | 0.0876445i | ||||
\(993\) | −75.4842 | − | 75.4842i | −2.39542 | − | 2.39542i | ||||
\(994\) | 14.2077i | 0.450641i | ||||||||
\(995\) | −3.17467 | − | 7.77823i | −0.100644 | − | 0.246587i | ||||
\(996\) | 26.9650i | 0.854420i | ||||||||
\(997\) | −40.5419 | − | 40.5419i | −1.28398 | − | 1.28398i | −0.938385 | − | 0.345591i | \(-0.887678\pi\) |
−0.345591 | − | 0.938385i | \(-0.612322\pi\) | |||||||
\(998\) | −21.8022 | + | 21.8022i | −0.690136 | + | 0.690136i | ||||
\(999\) | 37.1908i | 1.17667i |
(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 | 770.2.m.e.43.4 | ✓ | 16 | |
5.2 | odd | 4 | inner | 770.2.m.e.197.8 | yes | 16 | |
11.10 | odd | 2 | inner | 770.2.m.e.43.8 | yes | 16 | |
55.32 | even | 4 | inner | 770.2.m.e.197.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.e.43.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
770.2.m.e.43.8 | yes | 16 | 11.10 | odd | 2 | inner | |
770.2.m.e.197.4 | yes | 16 | 55.32 | even | 4 | inner | |
770.2.m.e.197.8 | yes | 16 | 5.2 | odd | 4 | inner |