Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.97522\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.97522 | −1.71774 | −0.858872 | − | 0.512191i | \(-0.828834\pi\) | ||||
−0.858872 | + | 0.512191i | \(0.828834\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.840694 | 0.375970 | 0.187985 | − | 0.982172i | \(-0.439804\pi\) | ||||
0.187985 | + | 0.982172i | \(0.439804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.22061 | −1.59524 | −0.797621 | − | 0.603159i | \(-0.793908\pi\) | ||||
−0.797621 | + | 0.603159i | \(0.793908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.85193 | 1.95064 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.71552 | 1.12027 | 0.560135 | − | 0.828401i | \(-0.310749\pi\) | ||||
0.560135 | + | 0.828401i | \(0.310749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07012 | −0.296799 | −0.148400 | − | 0.988927i | \(-0.547412\pi\) | ||||
−0.148400 | + | 0.988927i | \(0.547412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.50125 | −0.645820 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.37513 | 0.333519 | 0.166760 | − | 0.985998i | \(-0.446670\pi\) | ||||
0.166760 | + | 0.985998i | \(0.446670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.5573 | 2.74022 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.51456 | −0.941351 | −0.470676 | − | 0.882306i | \(-0.655990\pi\) | ||||
−0.470676 | + | 0.882306i | \(0.655990\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29323 | −0.858647 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.48511 | −1.63296 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.356792 | 0.0662546 | 0.0331273 | − | 0.999451i | \(-0.489453\pi\) | ||||
0.0331273 | + | 0.999451i | \(0.489453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24901 | −0.763144 | −0.381572 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381572 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.0545 | −1.92434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.54825 | −0.599763 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.55793 | 0.749319 | 0.374659 | − | 0.927163i | \(-0.377760\pi\) | ||||
0.374659 | + | 0.927163i | \(0.377760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.18386 | 0.509825 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9742 | 1.71388 | 0.856942 | − | 0.515412i | \(-0.172361\pi\) | ||||
0.856942 | + | 0.515412i | \(0.172361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.17832 | 0.789686 | 0.394843 | − | 0.918749i | \(-0.370799\pi\) | ||||
0.394843 | + | 0.918749i | \(0.370799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.91968 | 0.733383 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.68548 | −0.683448 | −0.341724 | − | 0.939800i | \(-0.611011\pi\) | ||||
−0.341724 | + | 0.939800i | \(0.611011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.8136 | 1.54480 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09133 | −0.572900 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.12361 | 0.421188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.97522 | 0.394077 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.35327 | 0.957315 | 0.478657 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478657 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.24655 | 0.799789 | 0.399895 | − | 0.916561i | \(-0.369047\pi\) | ||||
0.399895 | + | 0.916561i | \(0.369047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24.6987 | −3.11175 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.899648 | −0.111588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.54664 | 0.433291 | 0.216646 | − | 0.976250i | \(-0.430488\pi\) | ||||
0.216646 | + | 0.976250i | \(0.430488\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.4318 | 1.61700 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.04982 | −0.599303 | −0.299652 | − | 0.954049i | \(-0.596870\pi\) | ||||
−0.299652 | + | 0.954049i | \(0.596870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.95668 | 0.697177 | 0.348589 | − | 0.937276i | \(-0.386661\pi\) | ||||
0.348589 | + | 0.937276i | \(0.386661\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.7733 | 1.47493 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.6818 | −1.78710 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2077 | 1.26096 | 0.630482 | − | 0.776204i | \(-0.282857\pi\) | ||||
0.630482 | + | 0.776204i | \(0.282857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.68928 | 0.854364 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.23503 | −0.355091 | −0.177545 | − | 0.984113i | \(-0.556816\pi\) | ||||
−0.177545 | + | 0.984113i | \(0.556816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15607 | 0.125393 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.06153 | −0.113808 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.365040 | −0.0386942 | −0.0193471 | − | 0.999813i | \(-0.506159\pi\) | ||||
−0.0193471 | + | 0.999813i | \(0.506159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.51658 | 0.473467 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.6417 | 1.31089 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.840694 | −0.0862534 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.23679 | −0.430181 | −0.215090 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215090 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.7429 | 2.18525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.24757 | −0.522153 | −0.261076 | − | 0.965318i | \(-0.584077\pi\) | ||||
−0.261076 | + | 0.965318i | \(0.584077\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5467 | 1.13773 | 0.568867 | − | 0.822429i | \(-0.307382\pi\) | ||||
0.568867 | + | 0.822429i | \(0.307382\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.5568 | 1.03024 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9642 | −1.15662 | −0.578310 | − | 0.815817i | \(-0.696288\pi\) | ||||
−0.578310 | + | 0.815817i | \(0.696288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.53419 | −0.913209 | −0.456605 | − | 0.889670i | \(-0.650935\pi\) | ||||
−0.456605 | + | 0.889670i | \(0.650935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.5608 | −1.28714 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.29833 | −0.686569 | −0.343285 | − | 0.939231i | \(-0.611540\pi\) | ||||
−0.343285 | + | 0.939231i | \(0.611540\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.79537 | −0.353920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.26229 | −0.578949 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.80391 | −0.532044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.80506 | 0.255006 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32.6507 | −2.94401 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.81277 | −0.698795 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5407 | −1.55649 | −0.778245 | − | 0.627961i | \(-0.783890\pi\) | ||||
−0.778245 | + | 0.627961i | \(0.783890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.4066 | −1.35648 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.77183 | −0.154806 | −0.0774028 | − | 0.997000i | \(-0.524663\pi\) | ||||
−0.0774028 | + | 0.997000i | \(0.524663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.22061 | 0.365974 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.13338 | −0.613944 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.58520 | −0.733483 | −0.366741 | − | 0.930323i | \(-0.619527\pi\) | ||||
−0.366741 | + | 0.930323i | \(0.619527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.52199 | −0.298731 | −0.149366 | − | 0.988782i | \(-0.547723\pi\) | ||||
−0.149366 | + | 0.988782i | \(0.547723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.9403 | 1.17399 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.97607 | −0.332495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.299953 | 0.0249097 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.1728 | −2.65357 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.33047 | 0.436689 | 0.218345 | − | 0.975872i | \(-0.429934\pi\) | ||||
0.218345 | + | 0.975872i | \(0.429934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0625813 | −0.00509280 | −0.00254640 | − | 0.999997i | \(-0.500811\pi\) | ||||
−0.00254640 | + | 0.999997i | \(0.500811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.04719 | 0.650577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.57211 | −0.286919 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1905 | 1.13253 | 0.566263 | − | 0.824225i | \(-0.308389\pi\) | ||||
0.566263 | + | 0.824225i | \(0.308389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.97522 | −0.235950 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.0542 | 1.50168 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0663669 | 0.00519825 | 0.00259913 | − | 0.999997i | \(-0.499173\pi\) | ||||
0.00259913 | + | 0.999997i | \(0.499173\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.29343 | −0.723493 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.05248 | 0.390973 | 0.195486 | − | 0.980706i | \(-0.437371\pi\) | ||||
0.195486 | + | 0.980706i | \(0.437371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8548 | −0.911910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.85193 | −0.447508 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.7174 | −1.04292 | −0.521458 | − | 0.853277i | \(-0.674611\pi\) | ||||
−0.521458 | + | 0.853277i | \(0.674611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.1201 | 1.36975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.8776 | −1.64442 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.86867 | 0.139671 | 0.0698355 | − | 0.997559i | \(-0.477753\pi\) | ||||
0.0698355 | + | 0.997559i | \(0.477753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3639 | 0.919001 | 0.459500 | − | 0.888178i | \(-0.348028\pi\) | ||||
0.459500 | + | 0.888178i | \(0.348028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.5849 | −1.37383 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.83182 | 0.281721 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.10934 | 0.373632 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35.8124 | 2.60497 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8145 | −1.07194 | −0.535971 | − | 0.844236i | \(-0.680054\pi\) | ||||
−0.535971 | + | 0.844236i | \(0.680054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.96136 | 0.573071 | 0.286536 | − | 0.958070i | \(-0.407496\pi\) | ||||
0.286536 | + | 0.958070i | \(0.407496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.67665 | 0.191679 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.57542 | −0.682220 | −0.341110 | − | 0.940023i | \(-0.610803\pi\) | ||||
−0.341110 | + | 0.940023i | \(0.610803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.699774 | −0.0496056 | −0.0248028 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248028 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5520 | −0.744284 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.50588 | −0.105692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.22596 | 0.644369 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.4189 | −1.83624 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.71552 | −0.257008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8027 | −1.08790 | −0.543950 | − | 0.839118i | \(-0.683072\pi\) | ||||
−0.543950 | + | 0.839118i | \(0.683072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.0243 | 1.02945 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.35338 | 0.296898 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.9334 | 1.21740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.7224 | −1.19757 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.47157 | −0.0989882 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.10067 | −0.140671 | −0.0703356 | − | 0.997523i | \(-0.522407\pi\) | ||||
−0.0703356 | + | 0.997523i | \(0.522407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.1237 | −1.67491 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.78860 | −0.185086 | −0.0925431 | − | 0.995709i | \(-0.529500\pi\) | ||||
−0.0925431 | + | 0.995709i | \(0.529500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3824 | −1.41299 | −0.706495 | − | 0.707718i | \(-0.749725\pi\) | ||||
−0.706495 | + | 0.707718i | \(0.749725\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 46.6567 | 3.06978 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8652 | −1.03936 | −0.519681 | − | 0.854361i | \(-0.673949\pi\) | ||||
−0.519681 | + | 0.854361i | \(0.673949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.93906 | −0.256956 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.3453 | −2.16601 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.04028 | 0.196659 | 0.0983295 | − | 0.995154i | \(-0.468650\pi\) | ||||
0.0983295 | + | 0.995154i | \(0.468650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.15242 | 0.0742338 | 0.0371169 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371169 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.57804 | 0.165382 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.09092 | 0.580797 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.07012 | 0.0680904 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.62493 | 0.609955 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.88283 | 0.560679 | 0.280340 | − | 0.959901i | \(-0.409553\pi\) | ||||
0.280340 | + | 0.959901i | \(0.409553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.7739 | −1.05457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.43955 | −0.215393 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.86797 | 0.178899 | 0.0894496 | − | 0.995991i | \(-0.471489\pi\) | ||||
0.0894496 | + | 0.995991i | \(0.471489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.2373 | −1.19535 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.08792 | 0.129239 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0299 | −0.680131 | −0.340065 | − | 0.940402i | \(-0.610449\pi\) | ||||
−0.340065 | + | 0.940402i | \(0.610449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.840694 | 0.0516434 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08607 | 0.0664666 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3740 | 0.693488 | 0.346744 | − | 0.937960i | \(-0.387287\pi\) | ||||
0.346744 | + | 0.937960i | \(0.387287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.6727 | −1.80249 | −0.901244 | − | 0.433311i | \(-0.857345\pi\) | ||||
−0.901244 | + | 0.433311i | \(0.857345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.4378 | −0.813294 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.9516 | −0.961916 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.2485 | −1.81745 | −0.908727 | − | 0.417390i | \(-0.862945\pi\) | ||||
−0.908727 | + | 0.417390i | \(0.862945\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.8649 | −1.48862 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.5911 | 1.70560 | 0.852802 | − | 0.522234i | \(-0.174901\pi\) | ||||
0.852802 | + | 0.522234i | \(0.174901\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2731 | −0.907894 | −0.453947 | − | 0.891029i | \(-0.649984\pi\) | ||||
−0.453947 | + | 0.891029i | \(0.649984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.50125 | 0.148161 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −46.3179 | −2.73406 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1090 | −0.888765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.6054 | 0.738940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.0308 | −1.46232 | −0.731158 | − | 0.682208i | \(-0.761020\pi\) | ||||
−0.731158 | + | 0.682208i | \(0.761020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.18185 | 0.359921 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.5266 | −1.82936 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.83114 | 0.279392 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.8557 | −1.25974 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6127 | 0.896925 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.25144 | 0.300697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0251 | 1.25704 | 0.628521 | − | 0.777793i | \(-0.283661\pi\) | ||||
0.628521 | + | 0.777793i | \(0.283661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.3541 | −1.95434 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.76915 | 0.270434 | 0.135217 | − | 0.990816i | \(-0.456827\pi\) | ||||
0.135217 | + | 0.990816i | \(0.456827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7241 | 1.39749 | 0.698745 | − | 0.715371i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715371i | \(0.253742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.7641 | −1.16992 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.67668 | −0.431165 | −0.215583 | − | 0.976486i | \(-0.569165\pi\) | ||||
−0.215583 | + | 0.976486i | \(0.569165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.32567 | 0.0742230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.5960 | 1.98678 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.37513 | −0.0765145 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.59429 | 0.254846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.3663 | 1.56866 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.7756 | 1.09027 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0635 | −1.65244 | −0.826219 | − | 0.563349i | \(-0.809513\pi\) | ||||
−0.826219 | + | 0.563349i | \(0.809513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.6727 | 1.46165 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.98164 | 0.162905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64397 | 0.144026 | 0.0720130 | − | 0.997404i | \(-0.477058\pi\) | ||||
0.0720130 | + | 0.997404i | \(0.477058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.7141 | 1.17935 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7872 | −0.854928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0957 | −0.869084 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.2920 | 0.607943 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.9516 | −1.28579 | −0.642896 | − | 0.765954i | \(-0.722267\pi\) | ||||
−0.642896 | + | 0.765954i | \(0.722267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.59212 | −0.192282 | −0.0961409 | − | 0.995368i | \(-0.530650\pi\) | ||||
−0.0961409 | + | 0.995368i | \(0.530650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.08013 | 0.484661 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.7761 | 0.573554 | 0.286777 | − | 0.957997i | \(-0.407416\pi\) | ||||
0.286777 | + | 0.957997i | \(0.407416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.24535 | −0.225320 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.2679 | 0.913915 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.7132 | −1.25153 | −0.625767 | − | 0.780010i | \(-0.715214\pi\) | ||||
−0.625767 | + | 0.780010i | \(0.715214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.34567 | −0.438034 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.00775 | 0.262118 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.5017 | −1.27898 | −0.639489 | − | 0.768800i | \(-0.720854\pi\) | ||||
−0.639489 | + | 0.768800i | \(0.720854\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 64.2203 | 3.34318 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.22061 | −0.219123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0247 | 0.881505 | 0.440752 | − | 0.897629i | \(-0.354712\pi\) | ||||
0.440752 | + | 0.897629i | \(0.354712\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.2447 | 1.20035 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.381812 | −0.0196643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2487 | 1.14284 | 0.571418 | − | 0.820659i | \(-0.306393\pi\) | ||||
0.571418 | + | 0.820659i | \(0.306393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.1876 | 2.67365 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2777 | −0.780654 | −0.390327 | − | 0.920676i | \(-0.627638\pi\) | ||||
−0.390327 | + | 0.920676i | \(0.627638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1836 | −0.671897 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.3032 | 1.54040 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.2173 | −1.37997 | −0.689987 | − | 0.723822i | \(-0.742384\pi\) | ||||
−0.689987 | + | 0.723822i | \(0.742384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.20813 | −0.313959 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.27159 | 0.265916 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.42224 | 0.474084 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1764 | −0.711492 | −0.355746 | − | 0.934583i | \(-0.615773\pi\) | ||||
−0.355746 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.5573 | −0.628649 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.72260 | −0.235835 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.54697 | 0.226500 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.46433 | 0.321215 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9351 | 0.839440 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3145 | 0.559465 | 0.279733 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279733 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.5428 | 1.25994 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.0353 | −1.52715 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.71967 | −0.133503 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.4787 | 0.513144 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.08754 | −0.248543 | −0.124271 | − | 0.992248i | \(-0.539659\pi\) | ||||
−0.124271 | + | 0.992248i | \(0.539659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1078 | 0.785048 | 0.392524 | − | 0.919742i | \(-0.371602\pi\) | ||||
0.392524 | + | 0.919742i | \(0.371602\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.4191 | −1.33316 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.90377 | −0.286375 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.3643 | −1.27586 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.8297 | 0.571142 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.87058 | 0.379113 | 0.189556 | − | 0.981870i | \(-0.439295\pi\) | ||||
0.189556 | + | 0.981870i | \(0.439295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.98769 | 0.383864 | 0.191932 | − | 0.981408i | \(-0.438525\pi\) | ||||
0.191932 | + | 0.981408i | \(0.438525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.892425 | −0.0427885 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.51456 | 0.215961 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.796487 | −0.0380143 | −0.0190071 | − | 0.999819i | \(-0.506051\pi\) | ||||
−0.0190071 | + | 0.999819i | \(0.506051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63.2803 | 3.01335 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.3640 | 1.30010 | 0.650050 | − | 0.759891i | \(-0.274748\pi\) | ||||
0.650050 | + | 0.759891i | \(0.274748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.306887 | −0.0145478 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.8593 | −0.750120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.3688 | −1.43319 | −0.716597 | − | 0.697488i | \(-0.754301\pi\) | ||||
−0.716597 | + | 0.697488i | \(0.754301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.7749 | 1.92001 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.186193 | 0.00874812 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.79706 | 0.178009 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1263 | 0.801137 | 0.400568 | − | 0.916267i | \(-0.368813\pi\) | ||||
0.400568 | + | 0.916267i | \(0.368813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.6682 | −0.544624 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1700 | −0.846260 | −0.423130 | − | 0.906069i | \(-0.639069\pi\) | ||||
−0.423130 | + | 0.906069i | \(0.639069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8465 | −1.15471 | −0.577357 | − | 0.816492i | \(-0.695916\pi\) | ||||
−0.577357 | + | 0.816492i | \(0.695916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.6278 | 0.492853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0875 | 0.790714 | 0.395357 | − | 0.918528i | \(-0.370621\pi\) | ||||
0.395357 | + | 0.918528i | \(0.370621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9690 | −0.691205 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.2199 | −1.94539 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.2401 | 0.884662 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.29323 | 0.196987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.85193 | 0.267941 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.4945 | 1.62179 | 0.810893 | − | 0.585194i | \(-0.198982\pi\) | ||||
0.810893 | + | 0.585194i | \(0.198982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.87755 | −0.222397 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −56.6905 | −2.57951 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.56184 | −0.161735 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5860 | 0.706269 | 0.353134 | − | 0.935573i | \(-0.385116\pi\) | ||||
0.353134 | + | 0.935573i | \(0.385116\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.197456 | −0.00892927 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.33672 | −0.195713 | −0.0978567 | − | 0.995201i | \(-0.531199\pi\) | ||||
−0.0978567 | + | 0.995201i | \(0.531199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.490637 | 0.0220972 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.2792 | 0.821587 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.3133 | 0.956034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.6908 | −1.15008 | −0.575038 | − | 0.818127i | \(-0.695013\pi\) | ||||
−0.575038 | + | 0.818127i | \(0.695013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.0322 | −0.671591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0218 | 0.536024 | 0.268012 | − | 0.963416i | \(-0.413633\pi\) | ||||
0.268012 | + | 0.963416i | \(0.413633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.41160 | −0.196314 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.2707 | 1.56643 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.8346 | −1.36672 | −0.683361 | − | 0.730081i | \(-0.739482\pi\) | ||||
−0.683361 | + | 0.730081i | \(0.739482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.1409 | −1.11217 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.48511 | 0.374627 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.70728 | 0.427754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4090 | −0.765647 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 40.8123 | 1.79146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.0129 | −1.40251 | −0.701255 | − | 0.712910i | \(-0.747377\pi\) | ||||
−0.701255 | + | 0.712910i | \(0.747377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8228 | 0.604431 | 0.302215 | − | 0.953240i | \(-0.402274\pi\) | ||||
0.302215 | + | 0.953240i | \(0.402274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −53.9112 | −2.35288 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.84296 | −0.254523 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.61874 | −0.113858 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43.0308 | 1.86738 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.7438 | −0.508680 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0582 | −0.434854 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.55971 | −0.239919 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.1780 | 1.73059 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.13116 | 0.349586 | 0.174793 | − | 0.984605i | \(-0.444074\pi\) | ||||
0.174793 | + | 0.984605i | \(0.444074\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.7853 | −1.57861 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.01534 | −0.343339 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.8326 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.5544 | 1.56010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.356792 | −0.0151998 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −47.3033 | −2.01154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.4005 | −0.483925 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.1896 | −0.855461 | −0.427730 | − | 0.903906i | \(-0.640687\pi\) | ||||
−0.427730 | + | 0.903906i | \(0.640687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.54145 | −0.234378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2014 | −0.641803 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.0089 | −1.47545 | −0.737725 | − | 0.675102i | \(-0.764100\pi\) | ||||
−0.737725 | + | 0.675102i | \(0.764100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.13566 | −0.258129 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −32.4535 | −1.36292 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.6655 | 0.824422 | 0.412211 | − | 0.911088i | \(-0.364757\pi\) | ||||
0.412211 | + | 0.911088i | \(0.364757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.832125 | 0.0348234 | 0.0174117 | − | 0.999848i | \(-0.494457\pi\) | ||||
0.0174117 | + | 0.999848i | \(0.494457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.0765 | 1.84132 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.3821 | 0.808288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0792 | −0.586127 | −0.293063 | − | 0.956093i | \(-0.594675\pi\) | ||||
−0.293063 | + | 0.956093i | \(0.594675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.6868 | −0.984389 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6538 | 0.566456 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.71552 | 0.153881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.26467 | −0.217667 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5544 | −0.559451 | −0.279725 | − | 0.960080i | \(-0.590243\pi\) | ||||
−0.279725 | + | 0.960080i | \(0.590243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.24901 | 0.175077 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.4890 | 1.17188 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.31694 | −0.382601 | −0.191301 | − | 0.981532i | \(-0.561271\pi\) | ||||
−0.191301 | + | 0.981532i | \(0.561271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.87932 | −0.200032 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.08198 | 0.0852098 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.2330 | 1.07185 | 0.535926 | − | 0.844265i | \(-0.319963\pi\) | ||||
0.535926 | + | 0.844265i | \(0.319963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0201 | −0.857427 | −0.428713 | − | 0.903441i | \(-0.641033\pi\) | ||||
−0.428713 | + | 0.903441i | \(0.641033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.7547 | 0.845197 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.35820 | 0.0958744 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.61623 | 0.227956 | 0.113978 | − | 0.993483i | \(-0.463641\pi\) | ||||
0.113978 | + | 0.993483i | \(0.463641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.48032 | 0.181552 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.01405 | 0.202847 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −48.9131 | −1.97558 | −0.987790 | − | 0.155790i | \(-0.950208\pi\) | ||||
−0.987790 | + | 0.155790i | \(0.950208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.4493 | −1.10686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.2094 | 1.21618 | 0.608092 | − | 0.793867i | \(-0.291935\pi\) | ||||
0.608092 | + | 0.793867i | \(0.291935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.72482 | −0.390874 | −0.195437 | − | 0.980716i | \(-0.562612\pi\) | ||||
−0.195437 | + | 0.980716i | \(0.562612\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.3066 | 1.53719 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.54069 | 0.0617266 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8980 | 0.595921 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0545 | 0.441473 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.26777 | 0.249912 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.1987 | 1.64009 | 0.820047 | − | 0.572296i | \(-0.193947\pi\) | ||||
0.820047 | + | 0.572296i | \(0.193947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 47.0164 | 1.86873 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.7464 | −0.585193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.5719 | −0.458495 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.5512 | −1.16903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0491 | 0.594403 | 0.297201 | − | 0.954815i | \(-0.403947\pi\) | ||||
0.297201 | + | 0.954815i | \(0.403947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.7314 | 0.817567 | 0.408783 | − | 0.912631i | \(-0.365953\pi\) | ||||
0.408783 | + | 0.912631i | \(0.365953\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.9523 | −0.509995 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.60478 | −0.181033 | −0.0905163 | − | 0.995895i | \(-0.528852\pi\) | ||||
−0.0905163 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3212 | 1.07245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.3558 | −2.09118 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4907 | 0.840994 | 0.420497 | − | 0.907294i | \(-0.361856\pi\) | ||||
0.420497 | + | 0.907294i | \(0.361856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.48957 | −0.0582023 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.8581 | 1.35994 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.4486 | 1.65356 | 0.826782 | − | 0.562523i | \(-0.190169\pi\) | ||||
0.826782 | + | 0.562523i | \(0.190169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.9112 | −0.930039 | −0.465020 | − | 0.885300i | \(-0.653953\pi\) | ||||
−0.465020 | + | 0.885300i | \(0.653953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.37823 | 0.170036 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.54825 | 0.137595 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.61076 | −0.0623688 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.24995 | 0.241637 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.2092 | 0.895980 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.60761 | 0.254705 | 0.127352 | − | 0.991858i | \(-0.459352\pi\) | ||||
0.127352 | + | 0.991858i | \(0.459352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.4286 | 1.40214 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.8559 | −1.83925 | −0.919626 | − | 0.392796i | \(-0.871508\pi\) | ||||
−0.919626 | + | 0.392796i | \(0.871508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.8818 | 0.686242 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.29671 | 0.317930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.39775 | −0.0534835 | −0.0267418 | − | 0.999642i | \(-0.508513\pi\) | ||||
−0.0267418 | + | 0.999642i | \(0.508513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.21752 | −0.275767 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 63.6174 | 2.42716 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.07012 | −0.0407685 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.22951 | 0.198940 | 0.0994699 | − | 0.995041i | \(-0.468285\pi\) | ||||
0.0994699 | + | 0.995041i | \(0.468285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −91.7685 | −3.48600 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.96092 | −0.112314 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0910 | 0.571613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 47.2023 | 1.78536 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.4662 | −1.94385 | −0.971925 | − | 0.235291i | \(-0.924396\pi\) | ||||
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.55793 | −0.171906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.7196 | 0.441384 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.1480 | 0.832960 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.9661 | −0.674732 | −0.337366 | − | 0.941374i | \(-0.609536\pi\) | ||||
−0.337366 | + | 0.941374i | \(0.609536\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 65.5866 | 2.45969 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.1824 | 0.718386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.34265 | −0.125008 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.04548 | −0.337810 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.13026 | −0.116739 | −0.0583695 | − | 0.998295i | \(-0.518590\pi\) | ||||
−0.0583695 | + | 0.998295i | \(0.518590\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.7343 | −1.81496 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.42870 | −0.127515 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.53179 | −0.0568893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.94895 | 0.257722 | 0.128861 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128861 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.7381 | −1.13845 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.12089 | 0.263375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.2491 | 1.33889 | 0.669446 | − | 0.742861i | \(-0.266532\pi\) | ||||
0.669446 | + | 0.742861i | \(0.266532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.0475 | −0.997661 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.1776 | 0.485404 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.968430 | 0.0356243 | 0.0178121 | − | 0.999841i | \(-0.494330\pi\) | ||||
0.0178121 | + | 0.999841i | \(0.494330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.18386 | −0.116962 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.6326 | 1.52735 | 0.763677 | − | 0.645599i | \(-0.223392\pi\) | ||||
0.763677 | + | 0.645599i | \(0.223392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.48129 | 0.164182 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.9312 | −0.692655 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.4962 | 1.84509 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9606 | 1.02030 | 0.510149 | − | 0.860086i | \(-0.329590\pi\) | ||||
0.510149 | + | 0.860086i | \(0.329590\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.4284 | −0.963103 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0526118 | −0.00191474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.32862 | −0.302709 | −0.151354 | − | 0.988480i | \(-0.548363\pi\) | ||||
−0.151354 | + | 0.988480i | \(0.548363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 49.9061 | 1.81148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.42069 | 0.0514998 | 0.0257499 | − | 0.999668i | \(-0.491803\pi\) | ||||
0.0257499 | + | 0.999668i | \(0.491803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.2401 | 1.45679 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.76523 | 0.244597 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.86892 | −0.284130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.3760 | 1.92479 | 0.962394 | − | 0.271657i | \(-0.0875715\pi\) | ||||
0.962394 | + | 0.271657i | \(0.0875715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.53285 | −0.307303 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.5422 | 0.882722 | 0.441361 | − | 0.897330i | \(-0.354496\pi\) | ||||
0.441361 | + | 0.897330i | \(0.354496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.2420 | 0.655271 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 57.2351 | 2.05330 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.9742 | −0.393192 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.7627 | −0.671381 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.02742 | −0.108191 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.9299 | 0.425795 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.6965 | −1.91407 | −0.957036 | − | 0.289969i | \(-0.906355\pi\) | ||||
−0.957036 | + | 0.289969i | \(0.906355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.8163 | 1.16829 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.8034 | 1.09524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.68459 | −0.237377 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.50125 | −0.0887102 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.3147 | 1.42802 | 0.714010 | − | 0.700135i | \(-0.246877\pi\) | ||||
0.714010 | + | 0.700135i | \(0.246877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.44317 | −0.227943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.13619 | −0.0754785 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.1322 | 0.781027 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0188 | 0.564588 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.8403 | −1.19123 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.8672 | −0.417227 | −0.208614 | − | 0.977998i | \(-0.566895\pi\) | ||||
−0.208614 | + | 0.977998i | \(0.566895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.8087 | −0.906266 | −0.453133 | − | 0.891443i | \(-0.649694\pi\) | ||||
−0.453133 | + | 0.891443i | \(0.649694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 88.2828 | 3.09621 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0557942 | 0.00195439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.17832 | −0.181166 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.4307 | 0.923564 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8624 | −1.28651 | −0.643253 | − | 0.765654i | \(-0.722416\pi\) | ||||
−0.643253 | + | 0.765654i | \(0.722416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7764 | −0.898509 | −0.449255 | − | 0.893404i | \(-0.648310\pi\) | ||||
−0.449255 | + | 0.893404i | \(0.648310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 47.4594 | 1.65233 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9229 | 0.588466 | 0.294233 | − | 0.955734i | \(-0.404936\pi\) | ||||
0.294233 | + | 0.955734i | \(0.404936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5392 | 0.956475 | 0.478237 | − | 0.878231i | \(-0.341276\pi\) | ||||
0.478237 | + | 0.878231i | \(0.341276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 89.9958 | 3.12192 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8701 | 0.515220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.24759 | 0.146994 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.0533 | 1.24618 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.5599 | 1.19314 | 0.596570 | − | 0.802561i | \(-0.296530\pi\) | ||||
0.596570 | + | 0.802561i | \(0.296530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8727 | −0.995610 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −85.0649 | −2.92979 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.96629 | −0.342851 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.8391 | −0.406796 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 45.4409 | 1.55953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.5770 | −0.705372 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.3711 | 1.00565 | 0.502824 | − | 0.864389i | \(-0.332294\pi\) | ||||
0.502824 | + | 0.864389i | \(0.332294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.91968 | −0.168250 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.4480 | −1.27920 | −0.639600 | − | 0.768708i | \(-0.720900\pi\) | ||||
−0.639600 | + | 0.768708i | \(0.720900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4648 | 0.357054 | 0.178527 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178527 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 137.806 | 4.69642 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.7941 | −1.79713 | −0.898567 | − | 0.438837i | \(-0.855391\pi\) | ||||
−0.898567 | + | 0.438837i | \(0.855391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5321 | −0.392105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.9526 | 1.52667 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.6424 | 1.41262 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.79535 | −0.128601 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.7934 | −0.839129 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.9747 | 1.11475 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.6830 | −1.71144 | −0.855722 | − | 0.517437i | \(-0.826886\pi\) | ||||
−0.855722 | + | 0.517437i | \(0.826886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 74.4722 | 2.51189 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.8273 | 1.17336 | 0.586681 | − | 0.809818i | \(-0.300434\pi\) | ||||
0.586681 | + | 0.809818i | \(0.300434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.49713 | −0.218646 | −0.109323 | − | 0.994006i | \(-0.534868\pi\) | ||||
−0.109323 | + | 0.994006i | \(0.534868\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.3924 | −0.618253 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 59.3534 | 1.99289 | 0.996447 | − | 0.0842241i | \(-0.0268412\pi\) | ||||
0.996447 | + | 0.0842241i | \(0.0268412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 74.0327 | 2.48298 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.5696 | 0.957119 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.68548 | 0.156794 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.57098 | 0.0525121 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.3737 | −0.479924 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.51601 | −0.0505618 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.37513 | 0.0458124 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.0254 | 2.16391 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.3943 | 0.345517 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.55945 | 0.251007 | 0.125504 | − | 0.992093i | \(-0.459945\pi\) | ||||
0.125504 | + | 0.992093i | \(0.459945\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.7084 | −1.01853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.4756 | 0.910308 | 0.455154 | − | 0.890413i | \(-0.349584\pi\) | ||||
0.455154 | + | 0.890413i | \(0.349584\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0198 | −0.397798 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.6242 | −0.516520 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.47822 | 0.246952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.51453 | −0.247882 | −0.123941 | − | 0.992290i | \(-0.539553\pi\) | ||||
−0.123941 | + | 0.992290i | \(0.539553\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −65.5296 | −2.15927 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.40393 | 0.177873 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.5683 | −0.643400 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 67.5707 | 2.21931 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.0716 | 0.625718 | 0.312859 | − | 0.949800i | \(-0.398713\pi\) | ||||
0.312859 | + | 0.949800i | \(0.398713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.8136 | −0.354401 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.1893 | −0.464536 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.29539 | 0.140474 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.0609918 | −0.00199252 | −0.000996258 | − | 1.00000i | \(-0.500317\pi\) | ||||
−0.000996258 | 1.00000i | \(0.500317\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −73.5597 | −2.40053 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.9013 | −1.75713 | −0.878566 | − | 0.477621i | \(-0.841499\pi\) | ||||
−0.878566 | + | 0.477621i | \(0.841499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.5438 | −1.61337 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.1073 | 0.979389 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.1185 | 1.14120 | 0.570600 | − | 0.821228i | \(-0.306711\pi\) | ||||
0.570600 | + | 0.821228i | \(0.306711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.37439 | −0.206922 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.8398 | 0.740631 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.25933 | 0.202760 | 0.101380 | − | 0.994848i | \(-0.467674\pi\) | ||||
0.101380 | + | 0.994848i | \(0.467674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.4545 | −0.403018 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.94415 | −0.127496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.2348 | 1.17008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9460 | −0.417611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −70.0135 | −2.25615 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.69307 | 0.215457 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.1928 | −0.810147 | −0.405073 | − | 0.914284i | \(-0.632754\pi\) | ||||
−0.405073 | + | 0.914284i | \(0.632754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.09133 | 0.131432 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4247 | −0.398728 | −0.199364 | − | 0.979926i | \(-0.563888\pi\) | ||||
−0.199364 | + | 0.979926i | \(0.563888\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8650 | 0.476549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.6690 | −0.437759 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.2577 | −0.744079 | −0.372040 | − | 0.928217i | \(-0.621341\pi\) | ||||
−0.372040 | + | 0.928217i | \(0.621341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.35631 | −0.0433479 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55.7934 | −1.78135 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.5385 | 1.29298 | 0.646489 | − | 0.762923i | \(-0.276236\pi\) | ||||
0.646489 | + | 0.762923i | \(0.276236\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.05000 | −0.256494 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −58.8368 | −1.87280 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.3778 | −0.743372 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8507 | −1.01177 | −0.505886 | − | 0.862600i | \(-0.668834\pi\) | ||||
−0.505886 | + | 0.862600i | \(0.668834\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 89.4454 | 2.83846 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.588296 | −0.0186502 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.18740 | 0.259297 | 0.129649 | − | 0.991560i | \(-0.458615\pi\) | ||||
0.129649 | + | 0.991560i | \(0.458615\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.6745 | −1.22361 |
(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 | 4028.2.a.d.1.2 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.2 | ✓ | 19 | 1.1 | even | 1 | trivial |