Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.85243\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85243 | 1.30986 | 0.654932 | − | 0.755688i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.43149 | 0.715745 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.85243 | −0.756251 | ||||||||
\(7\) | −2.79882 | −1.05785 | −0.528927 | − | 0.848667i | \(-0.677406\pi\) | ||||
−0.528927 | + | 0.848667i | \(0.677406\pi\) | |||||||
\(8\) | −1.05312 | −0.372335 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.110799 | 0.0334071 | 0.0167036 | − | 0.999860i | \(-0.494683\pi\) | ||||
0.0167036 | + | 0.999860i | \(0.494683\pi\) | |||||||
\(12\) | −1.43149 | −0.413236 | ||||||||
\(13\) | 6.18763 | 1.71614 | 0.858070 | − | 0.513533i | \(-0.171663\pi\) | ||||
0.858070 | + | 0.513533i | \(0.171663\pi\) | |||||||
\(14\) | −5.18461 | −1.38565 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.81382 | −1.20345 | ||||||||
\(17\) | 4.27451 | 1.03672 | 0.518361 | − | 0.855162i | \(-0.326543\pi\) | ||||
0.518361 | + | 0.855162i | \(0.326543\pi\) | |||||||
\(18\) | 1.85243 | 0.436622 | ||||||||
\(19\) | −0.326031 | −0.0747965 | −0.0373983 | − | 0.999300i | \(-0.511907\pi\) | ||||
−0.0373983 | + | 0.999300i | \(0.511907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.79882 | 0.610753 | ||||||||
\(22\) | 0.205247 | 0.0437588 | ||||||||
\(23\) | −5.33219 | −1.11184 | −0.555919 | − | 0.831237i | \(-0.687633\pi\) | ||||
−0.555919 | + | 0.831237i | \(0.687633\pi\) | |||||||
\(24\) | 1.05312 | 0.214968 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.4621 | 2.24791 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.00648 | −0.757154 | ||||||||
\(29\) | −8.69258 | −1.61417 | −0.807086 | − | 0.590434i | \(-0.798957\pi\) | ||||
−0.807086 | + | 0.590434i | \(0.798957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.01264 | −0.900297 | −0.450148 | − | 0.892954i | \(-0.648629\pi\) | ||||
−0.450148 | + | 0.892954i | \(0.648629\pi\) | |||||||
\(32\) | −6.81100 | −1.20403 | ||||||||
\(33\) | −0.110799 | −0.0192876 | ||||||||
\(34\) | 7.91822 | 1.35796 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.43149 | 0.238582 | ||||||||
\(37\) | −1.49079 | −0.245085 | −0.122542 | − | 0.992463i | \(-0.539105\pi\) | ||||
−0.122542 | + | 0.992463i | \(0.539105\pi\) | |||||||
\(38\) | −0.603948 | −0.0979733 | ||||||||
\(39\) | −6.18763 | −0.990814 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8442 | 1.69358 | 0.846791 | − | 0.531925i | \(-0.178531\pi\) | ||||
0.846791 | + | 0.531925i | \(0.178531\pi\) | |||||||
\(42\) | 5.18461 | 0.800003 | ||||||||
\(43\) | −8.23207 | −1.25538 | −0.627690 | − | 0.778464i | \(-0.715999\pi\) | ||||
−0.627690 | + | 0.778464i | \(0.715999\pi\) | |||||||
\(44\) | 0.158608 | 0.0239110 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.87749 | −1.45636 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 4.81382 | 0.694815 | ||||||||
\(49\) | 0.833398 | 0.119057 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.27451 | −0.598551 | ||||||||
\(52\) | 8.85753 | 1.22832 | ||||||||
\(53\) | −10.6703 | −1.46568 | −0.732840 | − | 0.680401i | \(-0.761806\pi\) | ||||
−0.732840 | + | 0.680401i | \(0.761806\pi\) | |||||||
\(54\) | −1.85243 | −0.252084 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.94750 | 0.393877 | ||||||||
\(57\) | 0.326031 | 0.0431838 | ||||||||
\(58\) | −16.1024 | −2.11435 | ||||||||
\(59\) | 7.90884 | 1.02964 | 0.514822 | − | 0.857297i | \(-0.327858\pi\) | ||||
0.514822 | + | 0.857297i | \(0.327858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.66552 | 1.23754 | 0.618771 | − | 0.785571i | \(-0.287631\pi\) | ||||
0.618771 | + | 0.785571i | \(0.287631\pi\) | |||||||
\(62\) | −9.28556 | −1.17927 | ||||||||
\(63\) | −2.79882 | −0.352618 | ||||||||
\(64\) | −2.98926 | −0.373657 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.205247 | −0.0252642 | ||||||||
\(67\) | −2.31475 | −0.282792 | −0.141396 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141396 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(68\) | 6.11892 | 0.742028 | ||||||||
\(69\) | 5.33219 | 0.641920 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.49207 | −0.533111 | −0.266556 | − | 0.963820i | \(-0.585886\pi\) | ||||
−0.266556 | + | 0.963820i | \(0.585886\pi\) | |||||||
\(72\) | −1.05312 | −0.124112 | ||||||||
\(73\) | −13.0475 | −1.52709 | −0.763546 | − | 0.645753i | \(-0.776544\pi\) | ||||
−0.763546 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(74\) | −2.76159 | −0.321028 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.466710 | −0.0535353 | ||||||||
\(77\) | −0.310106 | −0.0353399 | ||||||||
\(78\) | −11.4621 | −1.29783 | ||||||||
\(79\) | −11.7702 | −1.32425 | −0.662124 | − | 0.749395i | \(-0.730345\pi\) | ||||
−0.662124 | + | 0.749395i | \(0.730345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.0881 | 2.21836 | ||||||||
\(83\) | −17.2486 | −1.89328 | −0.946642 | − | 0.322286i | \(-0.895549\pi\) | ||||
−0.946642 | + | 0.322286i | \(0.895549\pi\) | |||||||
\(84\) | 4.00648 | 0.437143 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.2493 | −1.64438 | ||||||||
\(87\) | 8.69258 | 0.931942 | ||||||||
\(88\) | −0.116685 | −0.0124387 | ||||||||
\(89\) | 5.04142 | 0.534389 | 0.267195 | − | 0.963643i | \(-0.413903\pi\) | ||||
0.267195 | + | 0.963643i | \(0.413903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3181 | −1.81543 | ||||||||
\(92\) | −7.63297 | −0.795792 | ||||||||
\(93\) | 5.01264 | 0.519787 | ||||||||
\(94\) | −1.85243 | −0.191063 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.81100 | 0.695145 | ||||||||
\(97\) | 7.54883 | 0.766467 | 0.383234 | − | 0.923651i | \(-0.374810\pi\) | ||||
0.383234 | + | 0.923651i | \(0.374810\pi\) | |||||||
\(98\) | 1.54381 | 0.155948 | ||||||||
\(99\) | 0.110799 | 0.0111357 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9362 | 1.38671 | 0.693354 | − | 0.720597i | \(-0.256132\pi\) | ||||
0.693354 | + | 0.720597i | \(0.256132\pi\) | |||||||
\(102\) | −7.91822 | −0.784021 | ||||||||
\(103\) | −9.10706 | −0.897345 | −0.448672 | − | 0.893696i | \(-0.648103\pi\) | ||||
−0.448672 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(104\) | −6.51634 | −0.638980 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.7660 | −1.91984 | ||||||||
\(107\) | −15.3830 | −1.48713 | −0.743563 | − | 0.668666i | \(-0.766866\pi\) | ||||
−0.743563 | + | 0.668666i | \(0.766866\pi\) | |||||||
\(108\) | −1.43149 | −0.137745 | ||||||||
\(109\) | −19.5500 | −1.87255 | −0.936276 | − | 0.351266i | \(-0.885751\pi\) | ||||
−0.936276 | + | 0.351266i | \(0.885751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.49079 | 0.141500 | ||||||||
\(112\) | 13.4730 | 1.27308 | ||||||||
\(113\) | −11.7869 | −1.10882 | −0.554410 | − | 0.832244i | \(-0.687056\pi\) | ||||
−0.554410 | + | 0.832244i | \(0.687056\pi\) | |||||||
\(114\) | 0.603948 | 0.0565649 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.4433 | −1.15534 | ||||||||
\(117\) | 6.18763 | 0.572047 | ||||||||
\(118\) | 14.6506 | 1.34869 | ||||||||
\(119\) | −11.9636 | −1.09670 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9877 | −0.998884 | ||||||||
\(122\) | 17.9047 | 1.62101 | ||||||||
\(123\) | −10.8442 | −0.977790 | ||||||||
\(124\) | −7.17554 | −0.644383 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.18461 | −0.461882 | ||||||||
\(127\) | 6.22679 | 0.552538 | 0.276269 | − | 0.961080i | \(-0.410902\pi\) | ||||
0.276269 | + | 0.961080i | \(0.410902\pi\) | |||||||
\(128\) | 8.08462 | 0.714586 | ||||||||
\(129\) | 8.23207 | 0.724794 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.9362 | −1.04287 | −0.521436 | − | 0.853291i | \(-0.674603\pi\) | ||||
−0.521436 | + | 0.853291i | \(0.674603\pi\) | |||||||
\(132\) | −0.158608 | −0.0138050 | ||||||||
\(133\) | 0.912501 | 0.0791239 | ||||||||
\(134\) | −4.28791 | −0.370419 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50159 | −0.386008 | ||||||||
\(137\) | −5.55617 | −0.474696 | −0.237348 | − | 0.971425i | \(-0.576278\pi\) | ||||
−0.237348 | + | 0.971425i | \(0.576278\pi\) | |||||||
\(138\) | 9.87749 | 0.840828 | ||||||||
\(139\) | 2.86890 | 0.243337 | 0.121668 | − | 0.992571i | \(-0.461176\pi\) | ||||
0.121668 | + | 0.992571i | \(0.461176\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | −8.32124 | −0.698303 | ||||||||
\(143\) | 0.685583 | 0.0573313 | ||||||||
\(144\) | −4.81382 | −0.401151 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −24.1695 | −2.00028 | ||||||||
\(147\) | −0.833398 | −0.0687375 | ||||||||
\(148\) | −2.13406 | −0.175418 | ||||||||
\(149\) | 10.6867 | 0.875493 | 0.437746 | − | 0.899099i | \(-0.355777\pi\) | ||||
0.437746 | + | 0.899099i | \(0.355777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8170 | 1.61268 | 0.806340 | − | 0.591452i | \(-0.201445\pi\) | ||||
0.806340 | + | 0.591452i | \(0.201445\pi\) | |||||||
\(152\) | 0.343351 | 0.0278494 | ||||||||
\(153\) | 4.27451 | 0.345574 | ||||||||
\(154\) | −0.574450 | −0.0462905 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.85753 | −0.709170 | ||||||||
\(157\) | −17.6734 | −1.41049 | −0.705246 | − | 0.708962i | \(-0.749164\pi\) | ||||
−0.705246 | + | 0.708962i | \(0.749164\pi\) | |||||||
\(158\) | −21.8034 | −1.73458 | ||||||||
\(159\) | 10.6703 | 0.846211 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.9238 | 1.17616 | ||||||||
\(162\) | 1.85243 | 0.145541 | ||||||||
\(163\) | 18.5616 | 1.45386 | 0.726928 | − | 0.686714i | \(-0.240947\pi\) | ||||
0.726928 | + | 0.686714i | \(0.240947\pi\) | |||||||
\(164\) | 15.5234 | 1.21217 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.9519 | −2.47995 | ||||||||
\(167\) | 11.3201 | 0.875974 | 0.437987 | − | 0.898981i | \(-0.355692\pi\) | ||||
0.437987 | + | 0.898981i | \(0.355692\pi\) | |||||||
\(168\) | −2.94750 | −0.227405 | ||||||||
\(169\) | 25.2868 | 1.94514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.326031 | −0.0249322 | ||||||||
\(172\) | −11.7841 | −0.898532 | ||||||||
\(173\) | −7.40410 | −0.562923 | −0.281462 | − | 0.959572i | \(-0.590819\pi\) | ||||
−0.281462 | + | 0.959572i | \(0.590819\pi\) | |||||||
\(174\) | 16.1024 | 1.22072 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.533366 | −0.0402039 | ||||||||
\(177\) | −7.90884 | −0.594465 | ||||||||
\(178\) | 9.33887 | 0.699978 | ||||||||
\(179\) | −7.94693 | −0.593981 | −0.296991 | − | 0.954880i | \(-0.595983\pi\) | ||||
−0.296991 | + | 0.954880i | \(0.595983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.73162 | −0.203040 | −0.101520 | − | 0.994834i | \(-0.532371\pi\) | ||||
−0.101520 | + | 0.994834i | \(0.532371\pi\) | |||||||
\(182\) | −32.0805 | −2.37796 | ||||||||
\(183\) | −9.66552 | −0.714496 | ||||||||
\(184\) | 5.61545 | 0.413977 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.28556 | 0.680850 | ||||||||
\(187\) | 0.473611 | 0.0346339 | ||||||||
\(188\) | −1.43149 | −0.104402 | ||||||||
\(189\) | 2.79882 | 0.203584 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3177 | 0.891279 | 0.445639 | − | 0.895213i | \(-0.352976\pi\) | ||||
0.445639 | + | 0.895213i | \(0.352976\pi\) | |||||||
\(192\) | 2.98926 | 0.215731 | ||||||||
\(193\) | −19.8624 | −1.42973 | −0.714864 | − | 0.699263i | \(-0.753511\pi\) | ||||
−0.714864 | + | 0.699263i | \(0.753511\pi\) | |||||||
\(194\) | 13.9837 | 1.00397 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.19300 | 0.0852143 | ||||||||
\(197\) | 8.64339 | 0.615816 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(198\) | 0.205247 | 0.0145863 | ||||||||
\(199\) | −6.75750 | −0.479026 | −0.239513 | − | 0.970893i | \(-0.576988\pi\) | ||||
−0.239513 | + | 0.970893i | \(0.576988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.31475 | 0.163270 | ||||||||
\(202\) | 25.8159 | 1.81640 | ||||||||
\(203\) | 24.3290 | 1.70756 | ||||||||
\(204\) | −6.11892 | −0.428410 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.8702 | −1.17540 | ||||||||
\(207\) | −5.33219 | −0.370613 | ||||||||
\(208\) | −29.7861 | −2.06530 | ||||||||
\(209\) | −0.0361238 | −0.00249874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4191 | 0.717281 | 0.358640 | − | 0.933476i | \(-0.383240\pi\) | ||||
0.358640 | + | 0.933476i | \(0.383240\pi\) | |||||||
\(212\) | −15.2744 | −1.04905 | ||||||||
\(213\) | 4.49207 | 0.307792 | ||||||||
\(214\) | −28.4958 | −1.94793 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.05312 | 0.0716560 | ||||||||
\(217\) | 14.0295 | 0.952383 | ||||||||
\(218\) | −36.2150 | −2.45279 | ||||||||
\(219\) | 13.0475 | 0.881667 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.4491 | 1.77916 | ||||||||
\(222\) | 2.76159 | 0.185346 | ||||||||
\(223\) | 25.4295 | 1.70288 | 0.851441 | − | 0.524450i | \(-0.175729\pi\) | ||||
0.851441 | + | 0.524450i | \(0.175729\pi\) | |||||||
\(224\) | 19.0628 | 1.27369 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.8344 | −1.45240 | ||||||||
\(227\) | 0.237644 | 0.0157730 | 0.00788651 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788651 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(228\) | 0.466710 | 0.0309086 | ||||||||
\(229\) | −1.04194 | −0.0688534 | −0.0344267 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344267 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.310106 | 0.0204035 | ||||||||
\(232\) | 9.15436 | 0.601013 | ||||||||
\(233\) | −2.65399 | −0.173869 | −0.0869343 | − | 0.996214i | \(-0.527707\pi\) | ||||
−0.0869343 | + | 0.996214i | \(0.527707\pi\) | |||||||
\(234\) | 11.4621 | 0.749304 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.3214 | 0.736962 | ||||||||
\(237\) | 11.7702 | 0.764555 | ||||||||
\(238\) | −22.1617 | −1.43653 | ||||||||
\(239\) | −3.52751 | −0.228176 | −0.114088 | − | 0.993471i | \(-0.536395\pi\) | ||||
−0.114088 | + | 0.993471i | \(0.536395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4873 | 0.739963 | 0.369981 | − | 0.929039i | \(-0.379364\pi\) | ||||
0.369981 | + | 0.929039i | \(0.379364\pi\) | |||||||
\(242\) | −20.3540 | −1.30840 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.8361 | 0.885765 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.0881 | −1.28077 | ||||||||
\(247\) | −2.01736 | −0.128361 | ||||||||
\(248\) | 5.27893 | 0.335212 | ||||||||
\(249\) | 17.2486 | 1.09309 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6108 | −0.985344 | −0.492672 | − | 0.870215i | \(-0.663980\pi\) | ||||
−0.492672 | + | 0.870215i | \(0.663980\pi\) | |||||||
\(252\) | −4.00648 | −0.252385 | ||||||||
\(253\) | −0.590800 | −0.0371433 | ||||||||
\(254\) | 11.5347 | 0.723750 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9547 | 1.30967 | ||||||||
\(257\) | −17.1122 | −1.06743 | −0.533715 | − | 0.845665i | \(-0.679204\pi\) | ||||
−0.533715 | + | 0.845665i | \(0.679204\pi\) | |||||||
\(258\) | 15.2493 | 0.949382 | ||||||||
\(259\) | 4.17246 | 0.259264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.69258 | −0.538057 | ||||||||
\(262\) | −22.1110 | −1.36602 | ||||||||
\(263\) | −4.66446 | −0.287623 | −0.143811 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143811 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(264\) | 0.116685 | 0.00718146 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.69034 | 0.103642 | ||||||||
\(267\) | −5.04142 | −0.308530 | ||||||||
\(268\) | −3.31354 | −0.202407 | ||||||||
\(269\) | 20.9745 | 1.27884 | 0.639420 | − | 0.768858i | \(-0.279175\pi\) | ||||
0.639420 | + | 0.768858i | \(0.279175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.73864 | −0.470089 | −0.235045 | − | 0.971985i | \(-0.575524\pi\) | ||||
−0.235045 | + | 0.971985i | \(0.575524\pi\) | |||||||
\(272\) | −20.5767 | −1.24765 | ||||||||
\(273\) | 17.3181 | 1.04814 | ||||||||
\(274\) | −10.2924 | −0.621787 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.63297 | 0.459451 | ||||||||
\(277\) | 9.08992 | 0.546161 | 0.273080 | − | 0.961991i | \(-0.411958\pi\) | ||||
0.273080 | + | 0.961991i | \(0.411958\pi\) | |||||||
\(278\) | 5.31443 | 0.318738 | ||||||||
\(279\) | −5.01264 | −0.300099 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4182 | 1.33736 | 0.668678 | − | 0.743552i | \(-0.266860\pi\) | ||||
0.668678 | + | 0.743552i | \(0.266860\pi\) | |||||||
\(282\) | 1.85243 | 0.110310 | ||||||||
\(283\) | −5.26529 | −0.312989 | −0.156495 | − | 0.987679i | \(-0.550019\pi\) | ||||
−0.156495 | + | 0.987679i | \(0.550019\pi\) | |||||||
\(284\) | −6.43036 | −0.381572 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.26999 | 0.0750962 | ||||||||
\(287\) | −30.3510 | −1.79156 | ||||||||
\(288\) | −6.81100 | −0.401342 | ||||||||
\(289\) | 1.27145 | 0.0747909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.54883 | −0.442520 | ||||||||
\(292\) | −18.6773 | −1.09301 | ||||||||
\(293\) | 21.1732 | 1.23695 | 0.618475 | − | 0.785804i | \(-0.287751\pi\) | ||||
0.618475 | + | 0.785804i | \(0.287751\pi\) | |||||||
\(294\) | −1.54381 | −0.0900368 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.56999 | 0.0912538 | ||||||||
\(297\) | −0.110799 | −0.00642920 | ||||||||
\(298\) | 19.7964 | 1.14678 | ||||||||
\(299\) | −32.9936 | −1.90807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.0401 | 1.32801 | ||||||||
\(302\) | 36.7095 | 2.11239 | ||||||||
\(303\) | −13.9362 | −0.800616 | ||||||||
\(304\) | 1.56945 | 0.0900142 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.91822 | 0.452655 | ||||||||
\(307\) | −3.64891 | −0.208254 | −0.104127 | − | 0.994564i | \(-0.533205\pi\) | ||||
−0.104127 | + | 0.994564i | \(0.533205\pi\) | |||||||
\(308\) | −0.443914 | −0.0252943 | ||||||||
\(309\) | 9.10706 | 0.518082 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.4701 | −1.27416 | −0.637082 | − | 0.770796i | \(-0.719859\pi\) | ||||
−0.637082 | + | 0.770796i | \(0.719859\pi\) | |||||||
\(312\) | 6.51634 | 0.368915 | ||||||||
\(313\) | 15.6741 | 0.885952 | 0.442976 | − | 0.896533i | \(-0.353923\pi\) | ||||
0.442976 | + | 0.896533i | \(0.353923\pi\) | |||||||
\(314\) | −32.7387 | −1.84755 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.8489 | −0.947824 | ||||||||
\(317\) | 28.0756 | 1.57688 | 0.788441 | − | 0.615110i | \(-0.210888\pi\) | ||||
0.788441 | + | 0.615110i | \(0.210888\pi\) | |||||||
\(318\) | 19.7660 | 1.10842 | ||||||||
\(319\) | −0.963128 | −0.0539248 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3830 | 0.858593 | ||||||||
\(322\) | 27.6453 | 1.54061 | ||||||||
\(323\) | −1.39362 | −0.0775432 | ||||||||
\(324\) | 1.43149 | 0.0795272 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.3840 | 1.90435 | ||||||||
\(327\) | 19.5500 | 1.08112 | ||||||||
\(328\) | −11.4203 | −0.630581 | ||||||||
\(329\) | 2.79882 | 0.154304 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2874 | 0.785305 | 0.392653 | − | 0.919687i | \(-0.371557\pi\) | ||||
0.392653 | + | 0.919687i | \(0.371557\pi\) | |||||||
\(332\) | −24.6913 | −1.35511 | ||||||||
\(333\) | −1.49079 | −0.0816950 | ||||||||
\(334\) | 20.9696 | 1.14741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.4730 | −0.735013 | ||||||||
\(337\) | −21.5968 | −1.17645 | −0.588227 | − | 0.808696i | \(-0.700174\pi\) | ||||
−0.588227 | + | 0.808696i | \(0.700174\pi\) | |||||||
\(338\) | 46.8419 | 2.54787 | ||||||||
\(339\) | 11.7869 | 0.640178 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.555395 | −0.0300763 | ||||||||
\(342\) | −0.603948 | −0.0326578 | ||||||||
\(343\) | 17.2592 | 0.931910 | ||||||||
\(344\) | 8.66939 | 0.467422 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.7156 | −0.737353 | ||||||||
\(347\) | −7.13924 | −0.383254 | −0.191627 | − | 0.981468i | \(-0.561376\pi\) | ||||
−0.191627 | + | 0.981468i | \(0.561376\pi\) | |||||||
\(348\) | 12.4433 | 0.667033 | ||||||||
\(349\) | 28.1558 | 1.50715 | 0.753574 | − | 0.657364i | \(-0.228328\pi\) | ||||
0.753574 | + | 0.657364i | \(0.228328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.18763 | −0.330271 | ||||||||
\(352\) | −0.754651 | −0.0402231 | ||||||||
\(353\) | 14.0360 | 0.747061 | 0.373530 | − | 0.927618i | \(-0.378147\pi\) | ||||
0.373530 | + | 0.927618i | \(0.378147\pi\) | |||||||
\(354\) | −14.6506 | −0.778669 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.21674 | 0.382486 | ||||||||
\(357\) | 11.9636 | 0.633180 | ||||||||
\(358\) | −14.7211 | −0.778035 | ||||||||
\(359\) | 17.1517 | 0.905230 | 0.452615 | − | 0.891706i | \(-0.350491\pi\) | ||||
0.452615 | + | 0.891706i | \(0.350491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8937 | −0.994405 | ||||||||
\(362\) | −5.06013 | −0.265955 | ||||||||
\(363\) | 10.9877 | 0.576706 | ||||||||
\(364\) | −24.7906 | −1.29938 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.9047 | −0.935892 | ||||||||
\(367\) | 9.03906 | 0.471835 | 0.235918 | − | 0.971773i | \(-0.424190\pi\) | ||||
0.235918 | + | 0.971773i | \(0.424190\pi\) | |||||||
\(368\) | 25.6682 | 1.33805 | ||||||||
\(369\) | 10.8442 | 0.564528 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.8643 | 1.55048 | ||||||||
\(372\) | 7.17554 | 0.372035 | ||||||||
\(373\) | 16.8787 | 0.873944 | 0.436972 | − | 0.899475i | \(-0.356051\pi\) | ||||
0.436972 | + | 0.899475i | \(0.356051\pi\) | |||||||
\(374\) | 0.877331 | 0.0453657 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.05312 | 0.0543107 | ||||||||
\(377\) | −53.7865 | −2.77014 | ||||||||
\(378\) | 5.18461 | 0.266668 | ||||||||
\(379\) | −20.0643 | −1.03064 | −0.515318 | − | 0.856999i | \(-0.672326\pi\) | ||||
−0.515318 | + | 0.856999i | \(0.672326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.22679 | −0.319008 | ||||||||
\(382\) | 22.8177 | 1.16745 | ||||||||
\(383\) | 5.87439 | 0.300167 | 0.150084 | − | 0.988673i | \(-0.452046\pi\) | ||||
0.150084 | + | 0.988673i | \(0.452046\pi\) | |||||||
\(384\) | −8.08462 | −0.412566 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36.7937 | −1.87275 | ||||||||
\(387\) | −8.23207 | −0.418460 | ||||||||
\(388\) | 10.8061 | 0.548595 | ||||||||
\(389\) | 11.7348 | 0.594976 | 0.297488 | − | 0.954725i | \(-0.403851\pi\) | ||||
0.297488 | + | 0.954725i | \(0.403851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7925 | −1.15267 | ||||||||
\(392\) | −0.877671 | −0.0443291 | ||||||||
\(393\) | 11.9362 | 0.602102 | ||||||||
\(394\) | 16.0113 | 0.806635 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.158608 | 0.00797033 | ||||||||
\(397\) | −21.3662 | −1.07234 | −0.536171 | − | 0.844110i | \(-0.680130\pi\) | ||||
−0.536171 | + | 0.844110i | \(0.680130\pi\) | |||||||
\(398\) | −12.5178 | −0.627460 | ||||||||
\(399\) | −0.912501 | −0.0456822 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.57801 | 0.0788023 | 0.0394011 | − | 0.999223i | \(-0.487455\pi\) | ||||
0.0394011 | + | 0.999223i | \(0.487455\pi\) | |||||||
\(402\) | 4.28791 | 0.213862 | ||||||||
\(403\) | −31.0164 | −1.54504 | ||||||||
\(404\) | 19.9496 | 0.992529 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 45.0677 | 2.23667 | ||||||||
\(407\) | −0.165178 | −0.00818758 | ||||||||
\(408\) | 4.50159 | 0.222862 | ||||||||
\(409\) | −32.6960 | −1.61671 | −0.808357 | − | 0.588693i | \(-0.799643\pi\) | ||||
−0.808357 | + | 0.588693i | \(0.799643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.55617 | 0.274066 | ||||||||
\(412\) | −13.0367 | −0.642270 | ||||||||
\(413\) | −22.1354 | −1.08921 | ||||||||
\(414\) | −9.87749 | −0.485452 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −42.1440 | −2.06628 | ||||||||
\(417\) | −2.86890 | −0.140490 | ||||||||
\(418\) | −0.0669168 | −0.00327301 | ||||||||
\(419\) | 26.7978 | 1.30916 | 0.654579 | − | 0.755993i | \(-0.272846\pi\) | ||||
0.654579 | + | 0.755993i | \(0.272846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3115 | −1.67224 | −0.836121 | − | 0.548546i | \(-0.815182\pi\) | ||||
−0.836121 | + | 0.548546i | \(0.815182\pi\) | |||||||
\(422\) | 19.3006 | 0.939541 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | 11.2372 | 0.545725 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.32124 | 0.403166 | ||||||||
\(427\) | −27.0521 | −1.30914 | ||||||||
\(428\) | −22.0206 | −1.06440 | ||||||||
\(429\) | −0.685583 | −0.0331002 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4472 | 1.46659 | 0.733294 | − | 0.679912i | \(-0.237982\pi\) | ||||
0.733294 | + | 0.679912i | \(0.237982\pi\) | |||||||
\(432\) | 4.81382 | 0.231605 | ||||||||
\(433\) | −23.8613 | −1.14670 | −0.573350 | − | 0.819311i | \(-0.694356\pi\) | ||||
−0.573350 | + | 0.819311i | \(0.694356\pi\) | |||||||
\(434\) | 25.9886 | 1.24749 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.9856 | −1.34027 | ||||||||
\(437\) | 1.73846 | 0.0831616 | ||||||||
\(438\) | 24.1695 | 1.15486 | ||||||||
\(439\) | 32.0758 | 1.53089 | 0.765447 | − | 0.643499i | \(-0.222518\pi\) | ||||
0.765447 | + | 0.643499i | \(0.222518\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.833398 | 0.0396856 | ||||||||
\(442\) | 48.9951 | 2.33046 | ||||||||
\(443\) | −16.5191 | −0.784847 | −0.392424 | − | 0.919785i | \(-0.628363\pi\) | ||||
−0.392424 | + | 0.919785i | \(0.628363\pi\) | |||||||
\(444\) | 2.13406 | 0.101278 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.1062 | 2.23055 | ||||||||
\(447\) | −10.6867 | −0.505466 | ||||||||
\(448\) | 8.36640 | 0.395275 | ||||||||
\(449\) | −28.5393 | −1.34685 | −0.673427 | − | 0.739254i | \(-0.735178\pi\) | ||||
−0.673427 | + | 0.739254i | \(0.735178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20153 | 0.0565777 | ||||||||
\(452\) | −16.8729 | −0.793633 | ||||||||
\(453\) | −19.8170 | −0.931082 | ||||||||
\(454\) | 0.440219 | 0.0206605 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.343351 | −0.0160789 | ||||||||
\(457\) | −11.2676 | −0.527076 | −0.263538 | − | 0.964649i | \(-0.584889\pi\) | ||||
−0.263538 | + | 0.964649i | \(0.584889\pi\) | |||||||
\(458\) | −1.93012 | −0.0901886 | ||||||||
\(459\) | −4.27451 | −0.199517 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.5927 | 1.33170 | 0.665848 | − | 0.746088i | \(-0.268070\pi\) | ||||
0.665848 | + | 0.746088i | \(0.268070\pi\) | |||||||
\(462\) | 0.574450 | 0.0267258 | ||||||||
\(463\) | −22.9538 | −1.06675 | −0.533376 | − | 0.845878i | \(-0.679077\pi\) | ||||
−0.533376 | + | 0.845878i | \(0.679077\pi\) | |||||||
\(464\) | 41.8445 | 1.94258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.91632 | −0.227744 | ||||||||
\(467\) | −31.0778 | −1.43811 | −0.719054 | − | 0.694954i | \(-0.755425\pi\) | ||||
−0.719054 | + | 0.694954i | \(0.755425\pi\) | |||||||
\(468\) | 8.85753 | 0.409440 | ||||||||
\(469\) | 6.47857 | 0.299153 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.6734 | 0.814348 | ||||||||
\(472\) | −8.32899 | −0.383373 | ||||||||
\(473\) | −0.912105 | −0.0419386 | ||||||||
\(474\) | 21.8034 | 1.00146 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −17.1258 | −0.784958 | ||||||||
\(477\) | −10.6703 | −0.488560 | ||||||||
\(478\) | −6.53446 | −0.298879 | ||||||||
\(479\) | −30.2841 | −1.38371 | −0.691857 | − | 0.722034i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722034i | \(0.743207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.22448 | −0.420600 | ||||||||
\(482\) | 21.2794 | 0.969251 | ||||||||
\(483\) | −14.9238 | −0.679058 | ||||||||
\(484\) | −15.7288 | −0.714946 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.85243 | −0.0840278 | ||||||||
\(487\) | 12.6556 | 0.573479 | 0.286740 | − | 0.958009i | \(-0.407429\pi\) | ||||
0.286740 | + | 0.958009i | \(0.407429\pi\) | |||||||
\(488\) | −10.1790 | −0.460781 | ||||||||
\(489\) | −18.5616 | −0.839384 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8056 | 0.758426 | 0.379213 | − | 0.925309i | \(-0.376195\pi\) | ||||
0.379213 | + | 0.925309i | \(0.376195\pi\) | |||||||
\(492\) | −15.5234 | −0.699849 | ||||||||
\(493\) | −37.1565 | −1.67345 | ||||||||
\(494\) | −3.73701 | −0.168136 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.1299 | 1.08347 | ||||||||
\(497\) | 12.5725 | 0.563954 | ||||||||
\(498\) | 31.9519 | 1.43180 | ||||||||
\(499\) | −10.2138 | −0.457233 | −0.228617 | − | 0.973517i | \(-0.573420\pi\) | ||||
−0.228617 | + | 0.973517i | \(0.573420\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.3201 | −0.505744 | ||||||||
\(502\) | −28.9179 | −1.29067 | ||||||||
\(503\) | −8.50743 | −0.379327 | −0.189664 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189664 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(504\) | 2.94750 | 0.131292 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.09442 | −0.0486527 | ||||||||
\(507\) | −25.2868 | −1.12303 | ||||||||
\(508\) | 8.91358 | 0.395476 | ||||||||
\(509\) | −2.86892 | −0.127162 | −0.0635812 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635812 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.5176 | 1.61544 | ||||||||
\(512\) | 22.6478 | 1.00090 | ||||||||
\(513\) | 0.326031 | 0.0143946 | ||||||||
\(514\) | −31.6991 | −1.39819 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.7841 | 0.518768 | ||||||||
\(517\) | −0.110799 | −0.00487293 | ||||||||
\(518\) | 7.72919 | 0.339601 | ||||||||
\(519\) | 7.40410 | 0.325004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3430 | −1.54841 | −0.774203 | − | 0.632937i | \(-0.781849\pi\) | ||||
−0.774203 | + | 0.632937i | \(0.781849\pi\) | |||||||
\(522\) | −16.1024 | −0.704782 | ||||||||
\(523\) | −4.53636 | −0.198361 | −0.0991806 | − | 0.995069i | \(-0.531622\pi\) | ||||
−0.0991806 | + | 0.995069i | \(0.531622\pi\) | |||||||
\(524\) | −17.0866 | −0.746430 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.64058 | −0.376747 | ||||||||
\(527\) | −21.4266 | −0.933357 | ||||||||
\(528\) | 0.533366 | 0.0232118 | ||||||||
\(529\) | 5.43221 | 0.236183 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.90884 | 0.343215 | ||||||||
\(532\) | 1.30624 | 0.0566325 | ||||||||
\(533\) | 67.1000 | 2.90643 | ||||||||
\(534\) | −9.33887 | −0.404132 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.43772 | 0.105293 | ||||||||
\(537\) | 7.94693 | 0.342935 | ||||||||
\(538\) | 38.8538 | 1.67511 | ||||||||
\(539\) | 0.0923396 | 0.00397735 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.0858 | 1.85240 | 0.926201 | − | 0.377031i | \(-0.123055\pi\) | ||||
0.926201 | + | 0.377031i | \(0.123055\pi\) | |||||||
\(542\) | −14.3353 | −0.615753 | ||||||||
\(543\) | 2.73162 | 0.117225 | ||||||||
\(544\) | −29.1137 | −1.24824 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 32.0805 | 1.37292 | ||||||||
\(547\) | −13.2062 | −0.564658 | −0.282329 | − | 0.959318i | \(-0.591107\pi\) | ||||
−0.282329 | + | 0.959318i | \(0.591107\pi\) | |||||||
\(548\) | −7.95360 | −0.339761 | ||||||||
\(549\) | 9.66552 | 0.412514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.83405 | 0.120734 | ||||||||
\(552\) | −5.61545 | −0.239010 | ||||||||
\(553\) | 32.9426 | 1.40086 | ||||||||
\(554\) | 16.8384 | 0.715396 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.10680 | 0.174167 | ||||||||
\(557\) | −0.0705045 | −0.00298737 | −0.00149369 | − | 0.999999i | \(-0.500475\pi\) | ||||
−0.00149369 | + | 0.999999i | \(0.500475\pi\) | |||||||
\(558\) | −9.28556 | −0.393089 | ||||||||
\(559\) | −50.9370 | −2.15441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.473611 | −0.0199959 | ||||||||
\(562\) | 41.5281 | 1.75176 | ||||||||
\(563\) | 32.3255 | 1.36236 | 0.681179 | − | 0.732117i | \(-0.261468\pi\) | ||||
0.681179 | + | 0.732117i | \(0.261468\pi\) | |||||||
\(564\) | 1.43149 | 0.0602766 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.75358 | −0.409973 | ||||||||
\(567\) | −2.79882 | −0.117539 | ||||||||
\(568\) | 4.73071 | 0.198496 | ||||||||
\(569\) | −11.1856 | −0.468924 | −0.234462 | − | 0.972125i | \(-0.575333\pi\) | ||||
−0.234462 | + | 0.972125i | \(0.575333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9528 | −0.751303 | −0.375651 | − | 0.926761i | \(-0.622581\pi\) | ||||
−0.375651 | + | 0.926761i | \(0.622581\pi\) | |||||||
\(572\) | 0.981405 | 0.0410346 | ||||||||
\(573\) | −12.3177 | −0.514580 | ||||||||
\(574\) | −56.2231 | −2.34671 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.98926 | −0.124552 | ||||||||
\(577\) | 28.6521 | 1.19280 | 0.596402 | − | 0.802686i | \(-0.296596\pi\) | ||||
0.596402 | + | 0.802686i | \(0.296596\pi\) | |||||||
\(578\) | 2.35526 | 0.0979660 | ||||||||
\(579\) | 19.8624 | 0.825454 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.2759 | 2.00282 | ||||||||
\(582\) | −13.9837 | −0.579641 | ||||||||
\(583\) | −1.18226 | −0.0489642 | ||||||||
\(584\) | 13.7406 | 0.568591 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.2218 | 1.62024 | ||||||||
\(587\) | 13.9680 | 0.576522 | 0.288261 | − | 0.957552i | \(-0.406923\pi\) | ||||
0.288261 | + | 0.957552i | \(0.406923\pi\) | |||||||
\(588\) | −1.19300 | −0.0491985 | ||||||||
\(589\) | 1.63427 | 0.0673391 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.64339 | −0.355541 | ||||||||
\(592\) | 7.17641 | 0.294949 | ||||||||
\(593\) | −8.88459 | −0.364846 | −0.182423 | − | 0.983220i | \(-0.558394\pi\) | ||||
−0.182423 | + | 0.983220i | \(0.558394\pi\) | |||||||
\(594\) | −0.205247 | −0.00842139 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2980 | 0.626629 | ||||||||
\(597\) | 6.75750 | 0.276566 | ||||||||
\(598\) | −61.1183 | −2.49931 | ||||||||
\(599\) | 8.06800 | 0.329650 | 0.164825 | − | 0.986323i | \(-0.447294\pi\) | ||||
0.164825 | + | 0.986323i | \(0.447294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6363 | −0.556235 | −0.278117 | − | 0.960547i | \(-0.589710\pi\) | ||||
−0.278117 | + | 0.960547i | \(0.589710\pi\) | |||||||
\(602\) | 42.6801 | 1.73951 | ||||||||
\(603\) | −2.31475 | −0.0942640 | ||||||||
\(604\) | 28.3678 | 1.15427 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −25.8159 | −1.04870 | ||||||||
\(607\) | 18.5254 | 0.751922 | 0.375961 | − | 0.926635i | \(-0.377313\pi\) | ||||
0.375961 | + | 0.926635i | \(0.377313\pi\) | |||||||
\(608\) | 2.22059 | 0.0900570 | ||||||||
\(609\) | −24.3290 | −0.985860 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.18763 | −0.250325 | ||||||||
\(612\) | 6.11892 | 0.247343 | ||||||||
\(613\) | −19.4600 | −0.785981 | −0.392991 | − | 0.919542i | \(-0.628560\pi\) | ||||
−0.392991 | + | 0.919542i | \(0.628560\pi\) | |||||||
\(614\) | −6.75935 | −0.272785 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.326580 | 0.0131583 | ||||||||
\(617\) | −0.462654 | −0.0186258 | −0.00931288 | − | 0.999957i | \(-0.502964\pi\) | ||||
−0.00931288 | + | 0.999957i | \(0.502964\pi\) | |||||||
\(618\) | 16.8702 | 0.678618 | ||||||||
\(619\) | 23.6431 | 0.950297 | 0.475149 | − | 0.879906i | \(-0.342394\pi\) | ||||
0.475149 | + | 0.879906i | \(0.342394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.33219 | 0.213973 | ||||||||
\(622\) | −41.6243 | −1.66898 | ||||||||
\(623\) | −14.1100 | −0.565306 | ||||||||
\(624\) | 29.7861 | 1.19240 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29.0351 | 1.16048 | ||||||||
\(627\) | 0.0361238 | 0.00144265 | ||||||||
\(628\) | −25.2993 | −1.00955 | ||||||||
\(629\) | −6.37241 | −0.254085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6511 | 0.463821 | 0.231911 | − | 0.972737i | \(-0.425502\pi\) | ||||
0.231911 | + | 0.972737i | \(0.425502\pi\) | |||||||
\(632\) | 12.3954 | 0.493064 | ||||||||
\(633\) | −10.4191 | −0.414122 | ||||||||
\(634\) | 52.0080 | 2.06550 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.2744 | 0.605671 | ||||||||
\(637\) | 5.15676 | 0.204318 | ||||||||
\(638\) | −1.78413 | −0.0706342 | ||||||||
\(639\) | −4.49207 | −0.177704 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.05056 | 0.317978 | 0.158989 | − | 0.987280i | \(-0.449177\pi\) | ||||
0.158989 | + | 0.987280i | \(0.449177\pi\) | |||||||
\(642\) | 28.4958 | 1.12464 | ||||||||
\(643\) | −24.4378 | −0.963732 | −0.481866 | − | 0.876245i | \(-0.660041\pi\) | ||||
−0.481866 | + | 0.876245i | \(0.660041\pi\) | |||||||
\(644\) | 21.3633 | 0.841833 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.58158 | −0.101571 | ||||||||
\(647\) | 49.9579 | 1.96405 | 0.982023 | − | 0.188759i | \(-0.0604465\pi\) | ||||
0.982023 | + | 0.188759i | \(0.0604465\pi\) | |||||||
\(648\) | −1.05312 | −0.0413706 | ||||||||
\(649\) | 0.876291 | 0.0343974 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.0295 | −0.549859 | ||||||||
\(652\) | 26.5707 | 1.04059 | ||||||||
\(653\) | 0.319214 | 0.0124918 | 0.00624591 | − | 0.999980i | \(-0.498012\pi\) | ||||
0.00624591 | + | 0.999980i | \(0.498012\pi\) | |||||||
\(654\) | 36.2150 | 1.41612 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −52.2021 | −2.03815 | ||||||||
\(657\) | −13.0475 | −0.509031 | ||||||||
\(658\) | 5.18461 | 0.202117 | ||||||||
\(659\) | −34.4879 | −1.34346 | −0.671728 | − | 0.740798i | \(-0.734448\pi\) | ||||
−0.671728 | + | 0.740798i | \(0.734448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.1530 | −0.511593 | −0.255797 | − | 0.966731i | \(-0.582338\pi\) | ||||
−0.255797 | + | 0.966731i | \(0.582338\pi\) | |||||||
\(662\) | 26.4663 | 1.02864 | ||||||||
\(663\) | −26.4491 | −1.02720 | ||||||||
\(664\) | 18.1650 | 0.704937 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.76159 | −0.107009 | ||||||||
\(667\) | 46.3505 | 1.79470 | ||||||||
\(668\) | 16.2046 | 0.626974 | ||||||||
\(669\) | −25.4295 | −0.983160 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.07093 | 0.0413427 | ||||||||
\(672\) | −19.0628 | −0.735362 | ||||||||
\(673\) | −27.9380 | −1.07693 | −0.538466 | − | 0.842647i | \(-0.680996\pi\) | ||||
−0.538466 | + | 0.842647i | \(0.680996\pi\) | |||||||
\(674\) | −40.0066 | −1.54100 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 36.1978 | 1.39222 | ||||||||
\(677\) | −13.9989 | −0.538021 | −0.269010 | − | 0.963137i | \(-0.586697\pi\) | ||||
−0.269010 | + | 0.963137i | \(0.586697\pi\) | |||||||
\(678\) | 21.8344 | 0.838546 | ||||||||
\(679\) | −21.1278 | −0.810811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.237644 | −0.00910656 | ||||||||
\(682\) | −1.02883 | −0.0393959 | ||||||||
\(683\) | −10.4197 | −0.398700 | −0.199350 | − | 0.979928i | \(-0.563883\pi\) | ||||
−0.199350 | + | 0.979928i | \(0.563883\pi\) | |||||||
\(684\) | −0.466710 | −0.0178451 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.9715 | 1.22068 | ||||||||
\(687\) | 1.04194 | 0.0397525 | ||||||||
\(688\) | 39.6277 | 1.51079 | ||||||||
\(689\) | −66.0240 | −2.51531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0218 | −0.647541 | −0.323771 | − | 0.946136i | \(-0.604951\pi\) | ||||
−0.323771 | + | 0.946136i | \(0.604951\pi\) | |||||||
\(692\) | −10.5989 | −0.402910 | ||||||||
\(693\) | −0.310106 | −0.0117800 | ||||||||
\(694\) | −13.2249 | −0.502011 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.15436 | −0.346995 | ||||||||
\(697\) | 46.3537 | 1.75577 | ||||||||
\(698\) | 52.1567 | 1.97416 | ||||||||
\(699\) | 2.65399 | 0.100383 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.7666 | −1.12427 | −0.562135 | − | 0.827045i | \(-0.690020\pi\) | ||||
−0.562135 | + | 0.827045i | \(0.690020\pi\) | |||||||
\(702\) | −11.4621 | −0.432611 | ||||||||
\(703\) | 0.486044 | 0.0183315 | ||||||||
\(704\) | −0.331206 | −0.0124828 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.0007 | 0.978548 | ||||||||
\(707\) | −39.0050 | −1.46694 | ||||||||
\(708\) | −11.3214 | −0.425485 | ||||||||
\(709\) | −32.8707 | −1.23449 | −0.617243 | − | 0.786773i | \(-0.711750\pi\) | ||||
−0.617243 | + | 0.786773i | \(0.711750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.7702 | −0.441416 | ||||||||
\(712\) | −5.30924 | −0.198972 | ||||||||
\(713\) | 26.7283 | 1.00098 | ||||||||
\(714\) | 22.1617 | 0.829380 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.3759 | −0.425139 | ||||||||
\(717\) | 3.52751 | 0.131737 | ||||||||
\(718\) | 31.7722 | 1.18573 | ||||||||
\(719\) | 23.8857 | 0.890786 | 0.445393 | − | 0.895335i | \(-0.353064\pi\) | ||||
0.445393 | + | 0.895335i | \(0.353064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.4890 | 0.949261 | ||||||||
\(722\) | −34.9992 | −1.30254 | ||||||||
\(723\) | −11.4873 | −0.427218 | ||||||||
\(724\) | −3.91029 | −0.145325 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.3540 | 0.755407 | ||||||||
\(727\) | 11.3100 | 0.419465 | 0.209732 | − | 0.977759i | \(-0.432741\pi\) | ||||
0.209732 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(728\) | 18.2381 | 0.675948 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.1881 | −1.30148 | ||||||||
\(732\) | −13.8361 | −0.511397 | ||||||||
\(733\) | −9.60626 | −0.354815 | −0.177408 | − | 0.984137i | \(-0.556771\pi\) | ||||
−0.177408 | + | 0.984137i | \(0.556771\pi\) | |||||||
\(734\) | 16.7442 | 0.618040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.3175 | 1.33868 | ||||||||
\(737\) | −0.256472 | −0.00944726 | ||||||||
\(738\) | 20.0881 | 0.739455 | ||||||||
\(739\) | 25.1094 | 0.923665 | 0.461833 | − | 0.886967i | \(-0.347192\pi\) | ||||
0.461833 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.01736 | 0.0741095 | ||||||||
\(742\) | 55.3215 | 2.03091 | ||||||||
\(743\) | −5.32029 | −0.195183 | −0.0975913 | − | 0.995227i | \(-0.531114\pi\) | ||||
−0.0975913 | + | 0.995227i | \(0.531114\pi\) | |||||||
\(744\) | −5.27893 | −0.193535 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.2665 | 1.14475 | ||||||||
\(747\) | −17.2486 | −0.631095 | ||||||||
\(748\) | 0.677970 | 0.0247890 | ||||||||
\(749\) | 43.0541 | 1.57316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.8005 | −1.19691 | −0.598453 | − | 0.801158i | \(-0.704218\pi\) | ||||
−0.598453 | + | 0.801158i | \(0.704218\pi\) | |||||||
\(752\) | 4.81382 | 0.175542 | ||||||||
\(753\) | 15.6108 | 0.568889 | ||||||||
\(754\) | −99.6356 | −3.62851 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00648 | 0.145714 | ||||||||
\(757\) | 27.8566 | 1.01246 | 0.506232 | − | 0.862397i | \(-0.331038\pi\) | ||||
0.506232 | + | 0.862397i | \(0.331038\pi\) | |||||||
\(758\) | −37.1677 | −1.34999 | ||||||||
\(759\) | 0.590800 | 0.0214447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.6841 | −1.40230 | −0.701150 | − | 0.713014i | \(-0.747329\pi\) | ||||
−0.701150 | + | 0.713014i | \(0.747329\pi\) | |||||||
\(762\) | −11.5347 | −0.417857 | ||||||||
\(763\) | 54.7170 | 1.98089 | ||||||||
\(764\) | 17.6327 | 0.637928 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.8819 | 0.393179 | ||||||||
\(767\) | 48.9370 | 1.76701 | ||||||||
\(768\) | −20.9547 | −0.756137 | ||||||||
\(769\) | 21.3157 | 0.768663 | 0.384331 | − | 0.923195i | \(-0.374432\pi\) | ||||
0.384331 | + | 0.923195i | \(0.374432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1122 | 0.616280 | ||||||||
\(772\) | −28.4329 | −1.02332 | ||||||||
\(773\) | 43.1498 | 1.55199 | 0.775995 | − | 0.630739i | \(-0.217248\pi\) | ||||
0.775995 | + | 0.630739i | \(0.217248\pi\) | |||||||
\(774\) | −15.2493 | −0.548126 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.94985 | −0.285383 | ||||||||
\(777\) | −4.17246 | −0.149686 | ||||||||
\(778\) | 21.7378 | 0.779339 | ||||||||
\(779\) | −3.53555 | −0.126674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.497717 | −0.0178097 | ||||||||
\(782\) | −42.2214 | −1.50984 | ||||||||
\(783\) | 8.69258 | 0.310647 | ||||||||
\(784\) | −4.01182 | −0.143279 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22.1110 | 0.788672 | ||||||||
\(787\) | 24.4813 | 0.872663 | 0.436332 | − | 0.899786i | \(-0.356277\pi\) | ||||
0.436332 | + | 0.899786i | \(0.356277\pi\) | |||||||
\(788\) | 12.3729 | 0.440767 | ||||||||
\(789\) | 4.66446 | 0.166059 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.9895 | 1.17297 | ||||||||
\(792\) | −0.116685 | −0.00414622 | ||||||||
\(793\) | 59.8067 | 2.12380 | ||||||||
\(794\) | −39.5794 | −1.40462 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.67329 | −0.342861 | ||||||||
\(797\) | −20.0382 | −0.709789 | −0.354894 | − | 0.934906i | \(-0.615483\pi\) | ||||
−0.354894 | + | 0.934906i | \(0.615483\pi\) | |||||||
\(798\) | −1.69034 | −0.0598375 | ||||||||
\(799\) | −4.27451 | −0.151221 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.04142 | 0.178130 | ||||||||
\(802\) | 2.92316 | 0.103220 | ||||||||
\(803\) | −1.44565 | −0.0510158 | ||||||||
\(804\) | 3.31354 | 0.116860 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −57.4556 | −2.02379 | ||||||||
\(807\) | −20.9745 | −0.738338 | ||||||||
\(808\) | −14.6766 | −0.516320 | ||||||||
\(809\) | 11.6522 | 0.409670 | 0.204835 | − | 0.978796i | \(-0.434334\pi\) | ||||
0.204835 | + | 0.978796i | \(0.434334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1104 | −0.355024 | −0.177512 | − | 0.984119i | \(-0.556805\pi\) | ||||
−0.177512 | + | 0.984119i | \(0.556805\pi\) | |||||||
\(812\) | 34.8267 | 1.22218 | ||||||||
\(813\) | 7.73864 | 0.271406 | ||||||||
\(814\) | −0.305981 | −0.0107246 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.5767 | 0.720329 | ||||||||
\(817\) | 2.68391 | 0.0938981 | ||||||||
\(818\) | −60.5670 | −2.11768 | ||||||||
\(819\) | −17.3181 | −0.605142 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.48739 | 0.0868104 | 0.0434052 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434052 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(822\) | 10.2924 | 0.358989 | ||||||||
\(823\) | 0.648409 | 0.0226021 | 0.0113011 | − | 0.999936i | \(-0.496403\pi\) | ||||
0.0113011 | + | 0.999936i | \(0.496403\pi\) | |||||||
\(824\) | 9.59086 | 0.334113 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.0043 | −1.42672 | ||||||||
\(827\) | 23.6590 | 0.822705 | 0.411352 | − | 0.911476i | \(-0.365057\pi\) | ||||
0.411352 | + | 0.911476i | \(0.365057\pi\) | |||||||
\(828\) | −7.63297 | −0.265264 | ||||||||
\(829\) | −9.72843 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.08992 | −0.315326 | ||||||||
\(832\) | −18.4964 | −0.641248 | ||||||||
\(833\) | 3.56237 | 0.123429 | ||||||||
\(834\) | −5.31443 | −0.184024 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0517109 | −0.00178846 | ||||||||
\(837\) | 5.01264 | 0.173262 | ||||||||
\(838\) | 49.6410 | 1.71482 | ||||||||
\(839\) | 18.9737 | 0.655045 | 0.327523 | − | 0.944843i | \(-0.393786\pi\) | ||||
0.327523 | + | 0.944843i | \(0.393786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.5609 | 1.60555 | ||||||||
\(842\) | −63.5596 | −2.19041 | ||||||||
\(843\) | −22.4182 | −0.772123 | ||||||||
\(844\) | 14.9148 | 0.513390 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.85243 | −0.0636878 | ||||||||
\(847\) | 30.7527 | 1.05667 | ||||||||
\(848\) | 51.3649 | 1.76388 | ||||||||
\(849\) | 5.26529 | 0.180704 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.94919 | 0.272495 | ||||||||
\(852\) | 6.43036 | 0.220300 | ||||||||
\(853\) | −42.6218 | −1.45934 | −0.729671 | − | 0.683799i | \(-0.760327\pi\) | ||||
−0.729671 | + | 0.683799i | \(0.760327\pi\) | |||||||
\(854\) | −50.1120 | −1.71480 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.2002 | 0.553710 | ||||||||
\(857\) | 34.4154 | 1.17561 | 0.587804 | − | 0.809003i | \(-0.299993\pi\) | ||||
0.587804 | + | 0.809003i | \(0.299993\pi\) | |||||||
\(858\) | −1.26999 | −0.0433568 | ||||||||
\(859\) | 22.0619 | 0.752741 | 0.376370 | − | 0.926469i | \(-0.377172\pi\) | ||||
0.376370 | + | 0.926469i | \(0.377172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.3510 | 1.03436 | ||||||||
\(862\) | 56.4012 | 1.92103 | ||||||||
\(863\) | 41.9460 | 1.42786 | 0.713930 | − | 0.700217i | \(-0.246913\pi\) | ||||
0.713930 | + | 0.700217i | \(0.246913\pi\) | |||||||
\(864\) | 6.81100 | 0.231715 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −44.2013 | −1.50202 | ||||||||
\(867\) | −1.27145 | −0.0431806 | ||||||||
\(868\) | 20.0831 | 0.681664 | ||||||||
\(869\) | −1.30412 | −0.0442393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3228 | −0.485311 | ||||||||
\(872\) | 20.5886 | 0.697217 | ||||||||
\(873\) | 7.54883 | 0.255489 | ||||||||
\(874\) | 3.22036 | 0.108930 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.6773 | 0.631049 | ||||||||
\(877\) | −48.5215 | −1.63845 | −0.819227 | − | 0.573469i | \(-0.805597\pi\) | ||||
−0.819227 | + | 0.573469i | \(0.805597\pi\) | |||||||
\(878\) | 59.4181 | 2.00526 | ||||||||
\(879\) | −21.1732 | −0.714154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.5996 | 1.83951 | 0.919754 | − | 0.392495i | \(-0.128388\pi\) | ||||
0.919754 | + | 0.392495i | \(0.128388\pi\) | |||||||
\(882\) | 1.54381 | 0.0519828 | ||||||||
\(883\) | 4.25858 | 0.143313 | 0.0716563 | − | 0.997429i | \(-0.477172\pi\) | ||||
0.0716563 | + | 0.997429i | \(0.477172\pi\) | |||||||
\(884\) | 37.8616 | 1.27342 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.6005 | −1.02804 | ||||||||
\(887\) | 14.5826 | 0.489637 | 0.244818 | − | 0.969569i | \(-0.421272\pi\) | ||||
0.244818 | + | 0.969569i | \(0.421272\pi\) | |||||||
\(888\) | −1.56999 | −0.0526854 | ||||||||
\(889\) | −17.4277 | −0.584505 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.110799 | 0.00371190 | ||||||||
\(892\) | 36.4020 | 1.21883 | ||||||||
\(893\) | 0.326031 | 0.0109102 | ||||||||
\(894\) | −19.7964 | −0.662092 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.6274 | −0.755928 | ||||||||
\(897\) | 32.9936 | 1.10162 | ||||||||
\(898\) | −52.8670 | −1.76420 | ||||||||
\(899\) | 43.5728 | 1.45323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.6104 | −1.51950 | ||||||||
\(902\) | 2.22574 | 0.0741091 | ||||||||
\(903\) | −23.0401 | −0.766727 | ||||||||
\(904\) | 12.4131 | 0.412853 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −36.7095 | −1.21959 | ||||||||
\(907\) | −55.6136 | −1.84662 | −0.923309 | − | 0.384058i | \(-0.874526\pi\) | ||||
−0.923309 | + | 0.384058i | \(0.874526\pi\) | |||||||
\(908\) | 0.340186 | 0.0112895 | ||||||||
\(909\) | 13.9362 | 0.462236 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0612 | 0.532132 | 0.266066 | − | 0.963955i | \(-0.414276\pi\) | ||||
0.266066 | + | 0.963955i | \(0.414276\pi\) | |||||||
\(912\) | −1.56945 | −0.0519697 | ||||||||
\(913\) | −1.91113 | −0.0632492 | ||||||||
\(914\) | −20.8724 | −0.690398 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.49153 | −0.0492815 | ||||||||
\(917\) | 33.4073 | 1.10321 | ||||||||
\(918\) | −7.91822 | −0.261340 | ||||||||
\(919\) | −38.0066 | −1.25372 | −0.626861 | − | 0.779131i | \(-0.715661\pi\) | ||||
−0.626861 | + | 0.779131i | \(0.715661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.64891 | 0.120236 | ||||||||
\(922\) | 52.9659 | 1.74434 | ||||||||
\(923\) | −27.7953 | −0.914893 | ||||||||
\(924\) | 0.443914 | 0.0146037 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −42.5202 | −1.39730 | ||||||||
\(927\) | −9.10706 | −0.299115 | ||||||||
\(928\) | 59.2052 | 1.94351 | ||||||||
\(929\) | −42.8736 | −1.40664 | −0.703318 | − | 0.710876i | \(-0.748299\pi\) | ||||
−0.703318 | + | 0.710876i | \(0.748299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.271713 | −0.00890504 | ||||||||
\(932\) | −3.79916 | −0.124446 | ||||||||
\(933\) | 22.4701 | 0.735638 | ||||||||
\(934\) | −57.5693 | −1.88373 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.51634 | −0.212993 | ||||||||
\(937\) | 9.10412 | 0.297419 | 0.148709 | − | 0.988881i | \(-0.452488\pi\) | ||||
0.148709 | + | 0.988881i | \(0.452488\pi\) | |||||||
\(938\) | 12.0011 | 0.391850 | ||||||||
\(939\) | −15.6741 | −0.511505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.6419 | 0.966298 | 0.483149 | − | 0.875538i | \(-0.339493\pi\) | ||||
0.483149 | + | 0.875538i | \(0.339493\pi\) | |||||||
\(942\) | 32.7387 | 1.06669 | ||||||||
\(943\) | −57.8234 | −1.88299 | ||||||||
\(944\) | −38.0717 | −1.23913 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.68961 | −0.0549339 | ||||||||
\(947\) | 16.9801 | 0.551779 | 0.275889 | − | 0.961189i | \(-0.411028\pi\) | ||||
0.275889 | + | 0.961189i | \(0.411028\pi\) | |||||||
\(948\) | 16.8489 | 0.547226 | ||||||||
\(949\) | −80.7330 | −2.62071 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.0756 | −0.910414 | ||||||||
\(952\) | 12.5991 | 0.408341 | ||||||||
\(953\) | 8.88843 | 0.287924 | 0.143962 | − | 0.989583i | \(-0.454016\pi\) | ||||
0.143962 | + | 0.989583i | \(0.454016\pi\) | |||||||
\(954\) | −19.7660 | −0.639947 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.04960 | −0.163316 | ||||||||
\(957\) | 0.963128 | 0.0311335 | ||||||||
\(958\) | −56.0991 | −1.81248 | ||||||||
\(959\) | 15.5507 | 0.502159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.87344 | −0.189466 | ||||||||
\(962\) | −17.0877 | −0.550929 | ||||||||
\(963\) | −15.3830 | −0.495709 | ||||||||
\(964\) | 16.4440 | 0.529625 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −27.6453 | −0.889474 | ||||||||
\(967\) | −51.1031 | −1.64336 | −0.821682 | − | 0.569946i | \(-0.806964\pi\) | ||||
−0.821682 | + | 0.569946i | \(0.806964\pi\) | |||||||
\(968\) | 11.5714 | 0.371920 | ||||||||
\(969\) | 1.39362 | 0.0447696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.7735 | 1.21221 | 0.606104 | − | 0.795385i | \(-0.292731\pi\) | ||||
0.606104 | + | 0.795385i | \(0.292731\pi\) | |||||||
\(972\) | −1.43149 | −0.0459151 | ||||||||
\(973\) | −8.02953 | −0.257415 | ||||||||
\(974\) | 23.4436 | 0.751180 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.5280 | −1.48933 | ||||||||
\(977\) | −25.3906 | −0.812316 | −0.406158 | − | 0.913803i | \(-0.633132\pi\) | ||||
−0.406158 | + | 0.913803i | \(0.633132\pi\) | |||||||
\(978\) | −34.3840 | −1.09948 | ||||||||
\(979\) | 0.558584 | 0.0178524 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.5500 | −0.624184 | ||||||||
\(982\) | 31.1312 | 0.993436 | ||||||||
\(983\) | 6.19401 | 0.197558 | 0.0987792 | − | 0.995109i | \(-0.468506\pi\) | ||||
0.0987792 | + | 0.995109i | \(0.468506\pi\) | |||||||
\(984\) | 11.4203 | 0.364066 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −68.8298 | −2.19199 | ||||||||
\(987\) | −2.79882 | −0.0890874 | ||||||||
\(988\) | −2.88783 | −0.0918740 | ||||||||
\(989\) | 43.8950 | 1.39578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.6177 | −0.591409 | −0.295705 | − | 0.955279i | \(-0.595554\pi\) | ||||
−0.295705 | + | 0.955279i | \(0.595554\pi\) | |||||||
\(992\) | 34.1411 | 1.08398 | ||||||||
\(993\) | −14.2874 | −0.453396 | ||||||||
\(994\) | 23.2897 | 0.738704 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 24.6913 | 0.782373 | ||||||||
\(997\) | 4.73093 | 0.149830 | 0.0749150 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749150 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(998\) | −18.9204 | −0.598914 | ||||||||
\(999\) | 1.49079 | 0.0471666 |
(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 | 3525.2.a.ba.1.6 | yes | 7 | |
5.4 | even | 2 | 3525.2.a.z.1.2 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.z.1.2 | ✓ | 7 | 5.4 | even | 2 | ||
3525.2.a.ba.1.6 | yes | 7 | 1.1 | even | 1 | trivial |