Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05386 | −1.45230 | −0.726149 | − | 0.687537i | \(-0.758692\pi\) | ||||
−0.726149 | + | 0.687537i | \(0.758692\pi\) | |||||||
\(3\) | −1.85254 | −1.06957 | −0.534783 | − | 0.844989i | \(-0.679607\pi\) | ||||
−0.534783 | + | 0.844989i | \(0.679607\pi\) | |||||||
\(4\) | 2.21834 | 1.10917 | ||||||||
\(5\) | −0.958510 | −0.428659 | −0.214329 | − | 0.976761i | \(-0.568757\pi\) | ||||
−0.214329 | + | 0.976761i | \(0.568757\pi\) | |||||||
\(6\) | 3.80486 | 1.55333 | ||||||||
\(7\) | 0.0563033 | 0.0212806 | 0.0106403 | − | 0.999943i | \(-0.496613\pi\) | ||||
0.0106403 | + | 0.999943i | \(0.496613\pi\) | |||||||
\(8\) | −0.448438 | −0.158547 | ||||||||
\(9\) | 0.431918 | 0.143973 | ||||||||
\(10\) | 1.96864 | 0.622540 | ||||||||
\(11\) | 3.83257 | 1.15556 | 0.577782 | − | 0.816191i | \(-0.303918\pi\) | ||||
0.577782 | + | 0.816191i | \(0.303918\pi\) | |||||||
\(12\) | −4.10957 | −1.18633 | ||||||||
\(13\) | −2.53430 | −0.702889 | −0.351445 | − | 0.936209i | \(-0.614309\pi\) | ||||
−0.351445 | + | 0.936209i | \(0.614309\pi\) | |||||||
\(14\) | −0.115639 | −0.0309058 | ||||||||
\(15\) | 1.77568 | 0.458479 | ||||||||
\(16\) | −3.51565 | −0.878912 | ||||||||
\(17\) | 3.80932 | 0.923897 | 0.461948 | − | 0.886907i | \(-0.347151\pi\) | ||||
0.461948 | + | 0.886907i | \(0.347151\pi\) | |||||||
\(18\) | −0.887100 | −0.209091 | ||||||||
\(19\) | −6.70558 | −1.53837 | −0.769183 | − | 0.639029i | \(-0.779336\pi\) | ||||
−0.769183 | + | 0.639029i | \(0.779336\pi\) | |||||||
\(20\) | −2.12630 | −0.475455 | ||||||||
\(21\) | −0.104304 | −0.0227611 | ||||||||
\(22\) | −7.87157 | −1.67822 | ||||||||
\(23\) | −0.340043 | −0.0709038 | −0.0354519 | − | 0.999371i | \(-0.511287\pi\) | ||||
−0.0354519 | + | 0.999371i | \(0.511287\pi\) | |||||||
\(24\) | 0.830751 | 0.169576 | ||||||||
\(25\) | −4.08126 | −0.816252 | ||||||||
\(26\) | 5.20510 | 1.02080 | ||||||||
\(27\) | 4.75748 | 0.915578 | ||||||||
\(28\) | 0.124900 | 0.0236038 | ||||||||
\(29\) | 4.99000 | 0.926619 | 0.463310 | − | 0.886196i | \(-0.346662\pi\) | ||||
0.463310 | + | 0.886196i | \(0.346662\pi\) | |||||||
\(30\) | −3.64700 | −0.665848 | ||||||||
\(31\) | 7.03132 | 1.26286 | 0.631431 | − | 0.775432i | \(-0.282468\pi\) | ||||
0.631431 | + | 0.775432i | \(0.282468\pi\) | |||||||
\(32\) | 8.11753 | 1.43499 | ||||||||
\(33\) | −7.10001 | −1.23595 | ||||||||
\(34\) | −7.82382 | −1.34177 | ||||||||
\(35\) | −0.0539672 | −0.00912213 | ||||||||
\(36\) | 0.958141 | 0.159690 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 13.7723 | 2.23417 | ||||||||
\(39\) | 4.69491 | 0.751787 | ||||||||
\(40\) | 0.429832 | 0.0679624 | ||||||||
\(41\) | 2.40185 | 0.375107 | 0.187553 | − | 0.982254i | \(-0.439944\pi\) | ||||
0.187553 | + | 0.982254i | \(0.439944\pi\) | |||||||
\(42\) | 0.214226 | 0.0330559 | ||||||||
\(43\) | −0.985503 | −0.150288 | −0.0751439 | − | 0.997173i | \(-0.523942\pi\) | ||||
−0.0751439 | + | 0.997173i | \(0.523942\pi\) | |||||||
\(44\) | 8.50195 | 1.28172 | ||||||||
\(45\) | −0.413998 | −0.0617152 | ||||||||
\(46\) | 0.698400 | 0.102973 | ||||||||
\(47\) | −0.377730 | −0.0550976 | −0.0275488 | − | 0.999620i | \(-0.508770\pi\) | ||||
−0.0275488 | + | 0.999620i | \(0.508770\pi\) | |||||||
\(48\) | 6.51289 | 0.940055 | ||||||||
\(49\) | −6.99683 | −0.999547 | ||||||||
\(50\) | 8.38233 | 1.18544 | ||||||||
\(51\) | −7.05694 | −0.988169 | ||||||||
\(52\) | −5.62194 | −0.779623 | ||||||||
\(53\) | −5.64693 | −0.775665 | −0.387833 | − | 0.921730i | \(-0.626776\pi\) | ||||
−0.387833 | + | 0.921730i | \(0.626776\pi\) | |||||||
\(54\) | −9.77120 | −1.32969 | ||||||||
\(55\) | −3.67356 | −0.495343 | ||||||||
\(56\) | −0.0252485 | −0.00337398 | ||||||||
\(57\) | 12.4224 | 1.64538 | ||||||||
\(58\) | −10.2488 | −1.34573 | ||||||||
\(59\) | −9.01439 | −1.17357 | −0.586787 | − | 0.809742i | \(-0.699607\pi\) | ||||
−0.586787 | + | 0.809742i | \(0.699607\pi\) | |||||||
\(60\) | 3.93906 | 0.508531 | ||||||||
\(61\) | −3.77455 | −0.483281 | −0.241641 | − | 0.970366i | \(-0.577686\pi\) | ||||
−0.241641 | + | 0.970366i | \(0.577686\pi\) | |||||||
\(62\) | −14.4413 | −1.83405 | ||||||||
\(63\) | 0.0243184 | 0.00306383 | ||||||||
\(64\) | −9.64096 | −1.20512 | ||||||||
\(65\) | 2.42915 | 0.301300 | ||||||||
\(66\) | 14.5824 | 1.79497 | ||||||||
\(67\) | 2.76583 | 0.337900 | 0.168950 | − | 0.985625i | \(-0.445962\pi\) | ||||
0.168950 | + | 0.985625i | \(0.445962\pi\) | |||||||
\(68\) | 8.45037 | 1.02476 | ||||||||
\(69\) | 0.629944 | 0.0758364 | ||||||||
\(70\) | 0.110841 | 0.0132481 | ||||||||
\(71\) | −13.4217 | −1.59286 | −0.796429 | − | 0.604732i | \(-0.793280\pi\) | ||||
−0.796429 | + | 0.604732i | \(0.793280\pi\) | |||||||
\(72\) | −0.193689 | −0.0228264 | ||||||||
\(73\) | 8.50848 | 0.995842 | 0.497921 | − | 0.867222i | \(-0.334097\pi\) | ||||
0.497921 | + | 0.867222i | \(0.334097\pi\) | |||||||
\(74\) | −2.05386 | −0.238756 | ||||||||
\(75\) | 7.56071 | 0.873036 | ||||||||
\(76\) | −14.8753 | −1.70631 | ||||||||
\(77\) | 0.215787 | 0.0245912 | ||||||||
\(78\) | −9.64268 | −1.09182 | ||||||||
\(79\) | 5.69589 | 0.640838 | 0.320419 | − | 0.947276i | \(-0.396176\pi\) | ||||
0.320419 | + | 0.947276i | \(0.396176\pi\) | |||||||
\(80\) | 3.36978 | 0.376753 | ||||||||
\(81\) | −10.1092 | −1.12324 | ||||||||
\(82\) | −4.93307 | −0.544766 | ||||||||
\(83\) | −4.06456 | −0.446143 | −0.223071 | − | 0.974802i | \(-0.571608\pi\) | ||||
−0.223071 | + | 0.974802i | \(0.571608\pi\) | |||||||
\(84\) | −0.231382 | −0.0252459 | ||||||||
\(85\) | −3.65127 | −0.396036 | ||||||||
\(86\) | 2.02409 | 0.218263 | ||||||||
\(87\) | −9.24419 | −0.991081 | ||||||||
\(88\) | −1.71867 | −0.183211 | ||||||||
\(89\) | 7.77938 | 0.824612 | 0.412306 | − | 0.911045i | \(-0.364723\pi\) | ||||
0.412306 | + | 0.911045i | \(0.364723\pi\) | |||||||
\(90\) | 0.850293 | 0.0896288 | ||||||||
\(91\) | −0.142690 | −0.0149579 | ||||||||
\(92\) | −0.754330 | −0.0786444 | ||||||||
\(93\) | −13.0258 | −1.35071 | ||||||||
\(94\) | 0.775805 | 0.0800182 | ||||||||
\(95\) | 6.42736 | 0.659434 | ||||||||
\(96\) | −15.0381 | −1.53482 | ||||||||
\(97\) | −0.109519 | −0.0111200 | −0.00555999 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00555999 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(98\) | 14.3705 | 1.45164 | ||||||||
\(99\) | 1.65536 | 0.166370 | ||||||||
\(100\) | −9.05362 | −0.905362 | ||||||||
\(101\) | 9.30723 | 0.926104 | 0.463052 | − | 0.886331i | \(-0.346754\pi\) | ||||
0.463052 | + | 0.886331i | \(0.346754\pi\) | |||||||
\(102\) | 14.4940 | 1.43512 | ||||||||
\(103\) | −13.5145 | −1.33162 | −0.665812 | − | 0.746120i | \(-0.731915\pi\) | ||||
−0.665812 | + | 0.746120i | \(0.731915\pi\) | |||||||
\(104\) | 1.13648 | 0.111441 | ||||||||
\(105\) | 0.0999767 | 0.00975673 | ||||||||
\(106\) | 11.5980 | 1.12650 | ||||||||
\(107\) | −5.84344 | −0.564907 | −0.282453 | − | 0.959281i | \(-0.591148\pi\) | ||||
−0.282453 | + | 0.959281i | \(0.591148\pi\) | |||||||
\(108\) | 10.5537 | 1.01553 | ||||||||
\(109\) | −4.35881 | −0.417498 | −0.208749 | − | 0.977969i | \(-0.566939\pi\) | ||||
−0.208749 | + | 0.977969i | \(0.566939\pi\) | |||||||
\(110\) | 7.54497 | 0.719385 | ||||||||
\(111\) | −1.85254 | −0.175836 | ||||||||
\(112\) | −0.197943 | −0.0187038 | ||||||||
\(113\) | −7.50002 | −0.705542 | −0.352771 | − | 0.935710i | \(-0.614761\pi\) | ||||
−0.352771 | + | 0.935710i | \(0.614761\pi\) | |||||||
\(114\) | −25.5138 | −2.38959 | ||||||||
\(115\) | 0.325934 | 0.0303935 | ||||||||
\(116\) | 11.0695 | 1.02778 | ||||||||
\(117\) | −1.09461 | −0.101197 | ||||||||
\(118\) | 18.5143 | 1.70438 | ||||||||
\(119\) | 0.214477 | 0.0196611 | ||||||||
\(120\) | −0.796283 | −0.0726904 | ||||||||
\(121\) | 3.68862 | 0.335329 | ||||||||
\(122\) | 7.75239 | 0.701869 | ||||||||
\(123\) | −4.44954 | −0.401201 | ||||||||
\(124\) | 15.5978 | 1.40073 | ||||||||
\(125\) | 8.70447 | 0.778552 | ||||||||
\(126\) | −0.0499466 | −0.00444960 | ||||||||
\(127\) | 8.71271 | 0.773128 | 0.386564 | − | 0.922263i | \(-0.373662\pi\) | ||||
0.386564 | + | 0.922263i | \(0.373662\pi\) | |||||||
\(128\) | 3.56613 | 0.315204 | ||||||||
\(129\) | 1.82569 | 0.160743 | ||||||||
\(130\) | −4.98914 | −0.437577 | ||||||||
\(131\) | 15.2478 | 1.33221 | 0.666103 | − | 0.745860i | \(-0.267961\pi\) | ||||
0.666103 | + | 0.745860i | \(0.267961\pi\) | |||||||
\(132\) | −15.7502 | −1.37088 | ||||||||
\(133\) | −0.377546 | −0.0327374 | ||||||||
\(134\) | −5.68063 | −0.490732 | ||||||||
\(135\) | −4.56009 | −0.392470 | ||||||||
\(136\) | −1.70825 | −0.146481 | ||||||||
\(137\) | 0.852102 | 0.0728000 | 0.0364000 | − | 0.999337i | \(-0.488411\pi\) | ||||
0.0364000 | + | 0.999337i | \(0.488411\pi\) | |||||||
\(138\) | −1.29382 | −0.110137 | ||||||||
\(139\) | 21.4579 | 1.82003 | 0.910016 | − | 0.414573i | \(-0.136069\pi\) | ||||
0.910016 | + | 0.414573i | \(0.136069\pi\) | |||||||
\(140\) | −0.119718 | −0.0101180 | ||||||||
\(141\) | 0.699762 | 0.0589306 | ||||||||
\(142\) | 27.5662 | 2.31331 | ||||||||
\(143\) | −9.71291 | −0.812234 | ||||||||
\(144\) | −1.51847 | −0.126539 | ||||||||
\(145\) | −4.78296 | −0.397203 | ||||||||
\(146\) | −17.4752 | −1.44626 | ||||||||
\(147\) | 12.9619 | 1.06908 | ||||||||
\(148\) | 2.21834 | 0.182346 | ||||||||
\(149\) | 20.9928 | 1.71980 | 0.859898 | − | 0.510465i | \(-0.170527\pi\) | ||||
0.859898 | + | 0.510465i | \(0.170527\pi\) | |||||||
\(150\) | −15.5286 | −1.26791 | ||||||||
\(151\) | 18.7916 | 1.52924 | 0.764619 | − | 0.644482i | \(-0.222927\pi\) | ||||
0.764619 | + | 0.644482i | \(0.222927\pi\) | |||||||
\(152\) | 3.00704 | 0.243903 | ||||||||
\(153\) | 1.64532 | 0.133016 | ||||||||
\(154\) | −0.443195 | −0.0357137 | ||||||||
\(155\) | −6.73959 | −0.541337 | ||||||||
\(156\) | 10.4149 | 0.833859 | ||||||||
\(157\) | 12.2168 | 0.975008 | 0.487504 | − | 0.873121i | \(-0.337907\pi\) | ||||
0.487504 | + | 0.873121i | \(0.337907\pi\) | |||||||
\(158\) | −11.6986 | −0.930687 | ||||||||
\(159\) | 10.4612 | 0.829625 | ||||||||
\(160\) | −7.78073 | −0.615121 | ||||||||
\(161\) | −0.0191455 | −0.00150888 | ||||||||
\(162\) | 20.7629 | 1.63129 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | 5.32813 | 0.416057 | ||||||||
\(165\) | 6.80543 | 0.529802 | ||||||||
\(166\) | 8.34803 | 0.647933 | ||||||||
\(167\) | 0.941954 | 0.0728906 | 0.0364453 | − | 0.999336i | \(-0.488397\pi\) | ||||
0.0364453 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(168\) | 0.0467740 | 0.00360869 | ||||||||
\(169\) | −6.57731 | −0.505947 | ||||||||
\(170\) | 7.49920 | 0.575163 | ||||||||
\(171\) | −2.89626 | −0.221483 | ||||||||
\(172\) | −2.18618 | −0.166695 | ||||||||
\(173\) | 11.4985 | 0.874218 | 0.437109 | − | 0.899409i | \(-0.356002\pi\) | ||||
0.437109 | + | 0.899409i | \(0.356002\pi\) | |||||||
\(174\) | 18.9863 | 1.43935 | ||||||||
\(175\) | −0.229788 | −0.0173704 | ||||||||
\(176\) | −13.4740 | −1.01564 | ||||||||
\(177\) | 16.6995 | 1.25521 | ||||||||
\(178\) | −15.9777 | −1.19758 | ||||||||
\(179\) | 12.1970 | 0.911647 | 0.455823 | − | 0.890070i | \(-0.349345\pi\) | ||||
0.455823 | + | 0.890070i | \(0.349345\pi\) | |||||||
\(180\) | −0.918388 | −0.0684526 | ||||||||
\(181\) | −20.2170 | −1.50272 | −0.751361 | − | 0.659892i | \(-0.770602\pi\) | ||||
−0.751361 | + | 0.659892i | \(0.770602\pi\) | |||||||
\(182\) | 0.293064 | 0.0217234 | ||||||||
\(183\) | 6.99252 | 0.516902 | ||||||||
\(184\) | 0.152488 | 0.0112416 | ||||||||
\(185\) | −0.958510 | −0.0704710 | ||||||||
\(186\) | 26.7532 | 1.96164 | ||||||||
\(187\) | 14.5995 | 1.06762 | ||||||||
\(188\) | −0.837934 | −0.0611126 | ||||||||
\(189\) | 0.267862 | 0.0194841 | ||||||||
\(190\) | −13.2009 | −0.957694 | ||||||||
\(191\) | −9.77549 | −0.707329 | −0.353665 | − | 0.935372i | \(-0.615065\pi\) | ||||
−0.353665 | + | 0.935372i | \(0.615065\pi\) | |||||||
\(192\) | 17.8603 | 1.28896 | ||||||||
\(193\) | −1.00629 | −0.0724342 | −0.0362171 | − | 0.999344i | \(-0.511531\pi\) | ||||
−0.0362171 | + | 0.999344i | \(0.511531\pi\) | |||||||
\(194\) | 0.224937 | 0.0161495 | ||||||||
\(195\) | −4.50011 | −0.322260 | ||||||||
\(196\) | −15.5213 | −1.10867 | ||||||||
\(197\) | 13.9173 | 0.991570 | 0.495785 | − | 0.868445i | \(-0.334880\pi\) | ||||
0.495785 | + | 0.868445i | \(0.334880\pi\) | |||||||
\(198\) | −3.39987 | −0.241619 | ||||||||
\(199\) | −4.69309 | −0.332684 | −0.166342 | − | 0.986068i | \(-0.553196\pi\) | ||||
−0.166342 | + | 0.986068i | \(0.553196\pi\) | |||||||
\(200\) | 1.83019 | 0.129414 | ||||||||
\(201\) | −5.12383 | −0.361407 | ||||||||
\(202\) | −19.1158 | −1.34498 | ||||||||
\(203\) | 0.280953 | 0.0197191 | ||||||||
\(204\) | −15.6547 | −1.09605 | ||||||||
\(205\) | −2.30220 | −0.160793 | ||||||||
\(206\) | 27.7569 | 1.93391 | ||||||||
\(207\) | −0.146871 | −0.0102082 | ||||||||
\(208\) | 8.90972 | 0.617778 | ||||||||
\(209\) | −25.6996 | −1.77768 | ||||||||
\(210\) | −0.205338 | −0.0141697 | ||||||||
\(211\) | −2.03273 | −0.139939 | −0.0699696 | − | 0.997549i | \(-0.522290\pi\) | ||||
−0.0699696 | + | 0.997549i | \(0.522290\pi\) | |||||||
\(212\) | −12.5268 | −0.860344 | ||||||||
\(213\) | 24.8642 | 1.70367 | ||||||||
\(214\) | 12.0016 | 0.820413 | ||||||||
\(215\) | 0.944615 | 0.0644222 | ||||||||
\(216\) | −2.13344 | −0.145162 | ||||||||
\(217\) | 0.395886 | 0.0268745 | ||||||||
\(218\) | 8.95238 | 0.606331 | ||||||||
\(219\) | −15.7623 | −1.06512 | ||||||||
\(220\) | −8.14920 | −0.549419 | ||||||||
\(221\) | −9.65398 | −0.649397 | ||||||||
\(222\) | 3.80486 | 0.255366 | ||||||||
\(223\) | 18.4323 | 1.23432 | 0.617159 | − | 0.786838i | \(-0.288283\pi\) | ||||
0.617159 | + | 0.786838i | \(0.288283\pi\) | |||||||
\(224\) | 0.457043 | 0.0305375 | ||||||||
\(225\) | −1.76277 | −0.117518 | ||||||||
\(226\) | 15.4040 | 1.02466 | ||||||||
\(227\) | −4.13819 | −0.274661 | −0.137331 | − | 0.990525i | \(-0.543852\pi\) | ||||
−0.137331 | + | 0.990525i | \(0.543852\pi\) | |||||||
\(228\) | 27.5571 | 1.82501 | ||||||||
\(229\) | −18.8481 | −1.24552 | −0.622760 | − | 0.782413i | \(-0.713989\pi\) | ||||
−0.622760 | + | 0.782413i | \(0.713989\pi\) | |||||||
\(230\) | −0.669423 | −0.0441405 | ||||||||
\(231\) | −0.399754 | −0.0263019 | ||||||||
\(232\) | −2.23770 | −0.146913 | ||||||||
\(233\) | 5.05162 | 0.330943 | 0.165471 | − | 0.986215i | \(-0.447085\pi\) | ||||
0.165471 | + | 0.986215i | \(0.447085\pi\) | |||||||
\(234\) | 2.24818 | 0.146968 | ||||||||
\(235\) | 0.362058 | 0.0236181 | ||||||||
\(236\) | −19.9970 | −1.30169 | ||||||||
\(237\) | −10.5519 | −0.685419 | ||||||||
\(238\) | −0.440507 | −0.0285538 | ||||||||
\(239\) | −17.3176 | −1.12018 | −0.560090 | − | 0.828432i | \(-0.689233\pi\) | ||||
−0.560090 | + | 0.828432i | \(0.689233\pi\) | |||||||
\(240\) | −6.24267 | −0.402963 | ||||||||
\(241\) | −6.88953 | −0.443794 | −0.221897 | − | 0.975070i | \(-0.571225\pi\) | ||||
−0.221897 | + | 0.975070i | \(0.571225\pi\) | |||||||
\(242\) | −7.57591 | −0.486998 | ||||||||
\(243\) | 4.45529 | 0.285807 | ||||||||
\(244\) | −8.37323 | −0.536041 | ||||||||
\(245\) | 6.70653 | 0.428464 | ||||||||
\(246\) | 9.13873 | 0.582664 | ||||||||
\(247\) | 16.9940 | 1.08130 | ||||||||
\(248\) | −3.15311 | −0.200223 | ||||||||
\(249\) | 7.52977 | 0.477180 | ||||||||
\(250\) | −17.8778 | −1.13069 | ||||||||
\(251\) | −30.4901 | −1.92452 | −0.962260 | − | 0.272133i | \(-0.912271\pi\) | ||||
−0.962260 | + | 0.272133i | \(0.912271\pi\) | |||||||
\(252\) | 0.0539465 | 0.00339831 | ||||||||
\(253\) | −1.30324 | −0.0819339 | ||||||||
\(254\) | −17.8947 | −1.12281 | ||||||||
\(255\) | 6.76414 | 0.423587 | ||||||||
\(256\) | 11.9576 | 0.747350 | ||||||||
\(257\) | 8.16392 | 0.509252 | 0.254626 | − | 0.967040i | \(-0.418048\pi\) | ||||
0.254626 | + | 0.967040i | \(0.418048\pi\) | |||||||
\(258\) | −3.74971 | −0.233447 | ||||||||
\(259\) | 0.0563033 | 0.00349852 | ||||||||
\(260\) | 5.38869 | 0.334192 | ||||||||
\(261\) | 2.15527 | 0.133408 | ||||||||
\(262\) | −31.3168 | −1.93476 | ||||||||
\(263\) | −30.9868 | −1.91073 | −0.955363 | − | 0.295433i | \(-0.904536\pi\) | ||||
−0.955363 | + | 0.295433i | \(0.904536\pi\) | |||||||
\(264\) | 3.18392 | 0.195956 | ||||||||
\(265\) | 5.41263 | 0.332495 | ||||||||
\(266\) | 0.775427 | 0.0475445 | ||||||||
\(267\) | −14.4116 | −0.881978 | ||||||||
\(268\) | 6.13556 | 0.374789 | ||||||||
\(269\) | 0.506775 | 0.0308986 | 0.0154493 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154493 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(270\) | 9.36579 | 0.569984 | ||||||||
\(271\) | −1.54990 | −0.0941500 | −0.0470750 | − | 0.998891i | \(-0.514990\pi\) | ||||
−0.0470750 | + | 0.998891i | \(0.514990\pi\) | |||||||
\(272\) | −13.3922 | −0.812024 | ||||||||
\(273\) | 0.264339 | 0.0159985 | ||||||||
\(274\) | −1.75010 | −0.105727 | ||||||||
\(275\) | −15.6417 | −0.943232 | ||||||||
\(276\) | 1.39743 | 0.0841154 | ||||||||
\(277\) | 26.8991 | 1.61621 | 0.808104 | − | 0.589040i | \(-0.200494\pi\) | ||||
0.808104 | + | 0.589040i | \(0.200494\pi\) | |||||||
\(278\) | −44.0714 | −2.64323 | ||||||||
\(279\) | 3.03695 | 0.181818 | ||||||||
\(280\) | 0.0242010 | 0.00144628 | ||||||||
\(281\) | 3.77180 | 0.225007 | 0.112503 | − | 0.993651i | \(-0.464113\pi\) | ||||
0.112503 | + | 0.993651i | \(0.464113\pi\) | |||||||
\(282\) | −1.43721 | −0.0855848 | ||||||||
\(283\) | 31.1252 | 1.85020 | 0.925101 | − | 0.379720i | \(-0.123980\pi\) | ||||
0.925101 | + | 0.379720i | \(0.123980\pi\) | |||||||
\(284\) | −29.7738 | −1.76675 | ||||||||
\(285\) | −11.9070 | −0.705308 | ||||||||
\(286\) | 19.9489 | 1.17961 | ||||||||
\(287\) | 0.135232 | 0.00798251 | ||||||||
\(288\) | 3.50611 | 0.206599 | ||||||||
\(289\) | −2.48905 | −0.146415 | ||||||||
\(290\) | 9.82353 | 0.576858 | ||||||||
\(291\) | 0.202889 | 0.0118936 | ||||||||
\(292\) | 18.8747 | 1.10456 | ||||||||
\(293\) | −18.0105 | −1.05219 | −0.526093 | − | 0.850427i | \(-0.676344\pi\) | ||||
−0.526093 | + | 0.850427i | \(0.676344\pi\) | |||||||
\(294\) | −26.6220 | −1.55263 | ||||||||
\(295\) | 8.64038 | 0.503062 | ||||||||
\(296\) | −0.448438 | −0.0260649 | ||||||||
\(297\) | 18.2334 | 1.05801 | ||||||||
\(298\) | −43.1163 | −2.49766 | ||||||||
\(299\) | 0.861772 | 0.0498375 | ||||||||
\(300\) | 16.7722 | 0.968345 | ||||||||
\(301\) | −0.0554871 | −0.00319822 | ||||||||
\(302\) | −38.5953 | −2.22091 | ||||||||
\(303\) | −17.2421 | −0.990530 | ||||||||
\(304\) | 23.5745 | 1.35209 | ||||||||
\(305\) | 3.61794 | 0.207163 | ||||||||
\(306\) | −3.37925 | −0.193179 | ||||||||
\(307\) | 14.4907 | 0.827028 | 0.413514 | − | 0.910498i | \(-0.364301\pi\) | ||||
0.413514 | + | 0.910498i | \(0.364301\pi\) | |||||||
\(308\) | 0.478688 | 0.0272758 | ||||||||
\(309\) | 25.0362 | 1.42426 | ||||||||
\(310\) | 13.8422 | 0.786182 | ||||||||
\(311\) | −4.14032 | −0.234776 | −0.117388 | − | 0.993086i | \(-0.537452\pi\) | ||||
−0.117388 | + | 0.993086i | \(0.537452\pi\) | |||||||
\(312\) | −2.10538 | −0.119193 | ||||||||
\(313\) | 24.3406 | 1.37581 | 0.687905 | − | 0.725801i | \(-0.258531\pi\) | ||||
0.687905 | + | 0.725801i | \(0.258531\pi\) | |||||||
\(314\) | −25.0916 | −1.41600 | ||||||||
\(315\) | −0.0233094 | −0.00131334 | ||||||||
\(316\) | 12.6354 | 0.710798 | ||||||||
\(317\) | 16.7292 | 0.939606 | 0.469803 | − | 0.882771i | \(-0.344325\pi\) | ||||
0.469803 | + | 0.882771i | \(0.344325\pi\) | |||||||
\(318\) | −21.4858 | −1.20486 | ||||||||
\(319\) | 19.1245 | 1.07077 | ||||||||
\(320\) | 9.24095 | 0.516585 | ||||||||
\(321\) | 10.8252 | 0.604205 | ||||||||
\(322\) | 0.0393222 | 0.00219134 | ||||||||
\(323\) | −25.5437 | −1.42129 | ||||||||
\(324\) | −22.4256 | −1.24587 | ||||||||
\(325\) | 10.3431 | 0.573735 | ||||||||
\(326\) | −2.05386 | −0.113753 | ||||||||
\(327\) | 8.07488 | 0.446542 | ||||||||
\(328\) | −1.07708 | −0.0594719 | ||||||||
\(329\) | −0.0212675 | −0.00117251 | ||||||||
\(330\) | −13.9774 | −0.769430 | ||||||||
\(331\) | −13.7376 | −0.755084 | −0.377542 | − | 0.925992i | \(-0.623231\pi\) | ||||
−0.377542 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(332\) | −9.01656 | −0.494848 | ||||||||
\(333\) | 0.431918 | 0.0236690 | ||||||||
\(334\) | −1.93464 | −0.105859 | ||||||||
\(335\) | −2.65108 | −0.144844 | ||||||||
\(336\) | 0.366697 | 0.0200050 | ||||||||
\(337\) | 21.2041 | 1.15506 | 0.577529 | − | 0.816370i | \(-0.304017\pi\) | ||||
0.577529 | + | 0.816370i | \(0.304017\pi\) | |||||||
\(338\) | 13.5089 | 0.734785 | ||||||||
\(339\) | 13.8941 | 0.754624 | ||||||||
\(340\) | −8.09976 | −0.439271 | ||||||||
\(341\) | 26.9480 | 1.45932 | ||||||||
\(342\) | 5.94852 | 0.321659 | ||||||||
\(343\) | −0.788068 | −0.0425516 | ||||||||
\(344\) | 0.441937 | 0.0238277 | ||||||||
\(345\) | −0.603807 | −0.0325079 | ||||||||
\(346\) | −23.6164 | −1.26963 | ||||||||
\(347\) | 32.7467 | 1.75793 | 0.878966 | − | 0.476884i | \(-0.158234\pi\) | ||||
0.878966 | + | 0.476884i | \(0.158234\pi\) | |||||||
\(348\) | −20.5067 | −1.09928 | ||||||||
\(349\) | −21.9300 | −1.17389 | −0.586943 | − | 0.809628i | \(-0.699669\pi\) | ||||
−0.586943 | + | 0.809628i | \(0.699669\pi\) | |||||||
\(350\) | 0.471953 | 0.0252269 | ||||||||
\(351\) | −12.0569 | −0.643550 | ||||||||
\(352\) | 31.1110 | 1.65822 | ||||||||
\(353\) | −27.2823 | −1.45209 | −0.726046 | − | 0.687646i | \(-0.758644\pi\) | ||||
−0.726046 | + | 0.687646i | \(0.758644\pi\) | |||||||
\(354\) | −34.2985 | −1.82295 | ||||||||
\(355\) | 12.8648 | 0.682793 | ||||||||
\(356\) | 17.2573 | 0.914635 | ||||||||
\(357\) | −0.397329 | −0.0210289 | ||||||||
\(358\) | −25.0509 | −1.32398 | ||||||||
\(359\) | −14.0569 | −0.741894 | −0.370947 | − | 0.928654i | \(-0.620967\pi\) | ||||
−0.370947 | + | 0.928654i | \(0.620967\pi\) | |||||||
\(360\) | 0.185652 | 0.00978474 | ||||||||
\(361\) | 25.9648 | 1.36657 | ||||||||
\(362\) | 41.5230 | 2.18240 | ||||||||
\(363\) | −6.83334 | −0.358657 | ||||||||
\(364\) | −0.316534 | −0.0165909 | ||||||||
\(365\) | −8.15546 | −0.426876 | ||||||||
\(366\) | −14.3616 | −0.750695 | ||||||||
\(367\) | 18.6970 | 0.975974 | 0.487987 | − | 0.872851i | \(-0.337731\pi\) | ||||
0.487987 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(368\) | 1.19547 | 0.0623182 | ||||||||
\(369\) | 1.03740 | 0.0540051 | ||||||||
\(370\) | 1.96864 | 0.102345 | ||||||||
\(371\) | −0.317941 | −0.0165067 | ||||||||
\(372\) | −28.8957 | −1.49817 | ||||||||
\(373\) | −24.5199 | −1.26959 | −0.634797 | − | 0.772679i | \(-0.718916\pi\) | ||||
−0.634797 | + | 0.772679i | \(0.718916\pi\) | |||||||
\(374\) | −29.9854 | −1.55051 | ||||||||
\(375\) | −16.1254 | −0.832713 | ||||||||
\(376\) | 0.169389 | 0.00873555 | ||||||||
\(377\) | −12.6462 | −0.651311 | ||||||||
\(378\) | −0.550151 | −0.0282967 | ||||||||
\(379\) | −18.6504 | −0.958007 | −0.479003 | − | 0.877813i | \(-0.659002\pi\) | ||||
−0.479003 | + | 0.877813i | \(0.659002\pi\) | |||||||
\(380\) | 14.2581 | 0.731424 | ||||||||
\(381\) | −16.1407 | −0.826912 | ||||||||
\(382\) | 20.0775 | 1.02725 | ||||||||
\(383\) | 11.3134 | 0.578090 | 0.289045 | − | 0.957316i | \(-0.406662\pi\) | ||||
0.289045 | + | 0.957316i | \(0.406662\pi\) | |||||||
\(384\) | −6.60641 | −0.337132 | ||||||||
\(385\) | −0.206833 | −0.0105412 | ||||||||
\(386\) | 2.06677 | 0.105196 | ||||||||
\(387\) | −0.425657 | −0.0216374 | ||||||||
\(388\) | −0.242951 | −0.0123340 | ||||||||
\(389\) | 23.7954 | 1.20647 | 0.603237 | − | 0.797562i | \(-0.293878\pi\) | ||||
0.603237 | + | 0.797562i | \(0.293878\pi\) | |||||||
\(390\) | 9.24260 | 0.468017 | ||||||||
\(391\) | −1.29533 | −0.0655078 | ||||||||
\(392\) | 3.13765 | 0.158475 | ||||||||
\(393\) | −28.2472 | −1.42488 | ||||||||
\(394\) | −28.5843 | −1.44005 | ||||||||
\(395\) | −5.45956 | −0.274701 | ||||||||
\(396\) | 3.67215 | 0.184532 | ||||||||
\(397\) | −14.0753 | −0.706417 | −0.353208 | − | 0.935545i | \(-0.614909\pi\) | ||||
−0.353208 | + | 0.935545i | \(0.614909\pi\) | |||||||
\(398\) | 9.63895 | 0.483157 | ||||||||
\(399\) | 0.699421 | 0.0350148 | ||||||||
\(400\) | 14.3483 | 0.717414 | ||||||||
\(401\) | −30.3567 | −1.51594 | −0.757971 | − | 0.652288i | \(-0.773809\pi\) | ||||
−0.757971 | + | 0.652288i | \(0.773809\pi\) | |||||||
\(402\) | 10.5236 | 0.524871 | ||||||||
\(403\) | −17.8195 | −0.887652 | ||||||||
\(404\) | 20.6466 | 1.02721 | ||||||||
\(405\) | 9.68977 | 0.481488 | ||||||||
\(406\) | −0.577039 | −0.0286379 | ||||||||
\(407\) | 3.83257 | 0.189974 | ||||||||
\(408\) | 3.16460 | 0.156671 | ||||||||
\(409\) | 7.58009 | 0.374811 | 0.187406 | − | 0.982283i | \(-0.439992\pi\) | ||||
0.187406 | + | 0.982283i | \(0.439992\pi\) | |||||||
\(410\) | 4.72840 | 0.233519 | ||||||||
\(411\) | −1.57856 | −0.0778644 | ||||||||
\(412\) | −29.9797 | −1.47700 | ||||||||
\(413\) | −0.507540 | −0.0249744 | ||||||||
\(414\) | 0.301652 | 0.0148254 | ||||||||
\(415\) | 3.89592 | 0.191243 | ||||||||
\(416\) | −20.5723 | −1.00864 | ||||||||
\(417\) | −39.7516 | −1.94665 | ||||||||
\(418\) | 52.7834 | 2.58172 | ||||||||
\(419\) | −19.8612 | −0.970281 | −0.485141 | − | 0.874436i | \(-0.661232\pi\) | ||||
−0.485141 | + | 0.874436i | \(0.661232\pi\) | |||||||
\(420\) | 0.221782 | 0.0108219 | ||||||||
\(421\) | −32.0566 | −1.56234 | −0.781172 | − | 0.624315i | \(-0.785378\pi\) | ||||
−0.781172 | + | 0.624315i | \(0.785378\pi\) | |||||||
\(422\) | 4.17495 | 0.203233 | ||||||||
\(423\) | −0.163149 | −0.00793256 | ||||||||
\(424\) | 2.53230 | 0.122979 | ||||||||
\(425\) | −15.5468 | −0.754132 | ||||||||
\(426\) | −51.0676 | −2.47423 | ||||||||
\(427\) | −0.212519 | −0.0102845 | ||||||||
\(428\) | −12.9627 | −0.626577 | ||||||||
\(429\) | 17.9936 | 0.868738 | ||||||||
\(430\) | −1.94011 | −0.0935602 | ||||||||
\(431\) | 40.3574 | 1.94395 | 0.971973 | − | 0.235092i | \(-0.0755390\pi\) | ||||
0.971973 | + | 0.235092i | \(0.0755390\pi\) | |||||||
\(432\) | −16.7256 | −0.804713 | ||||||||
\(433\) | 35.9150 | 1.72596 | 0.862982 | − | 0.505234i | \(-0.168594\pi\) | ||||
0.862982 | + | 0.505234i | \(0.168594\pi\) | |||||||
\(434\) | −0.813095 | −0.0390298 | ||||||||
\(435\) | 8.86064 | 0.424835 | ||||||||
\(436\) | −9.66931 | −0.463076 | ||||||||
\(437\) | 2.28018 | 0.109076 | ||||||||
\(438\) | 32.3736 | 1.54687 | ||||||||
\(439\) | −30.5617 | −1.45863 | −0.729315 | − | 0.684178i | \(-0.760161\pi\) | ||||
−0.729315 | + | 0.684178i | \(0.760161\pi\) | |||||||
\(440\) | 1.64736 | 0.0785350 | ||||||||
\(441\) | −3.02206 | −0.143908 | ||||||||
\(442\) | 19.8279 | 0.943118 | ||||||||
\(443\) | −2.71698 | −0.129087 | −0.0645437 | − | 0.997915i | \(-0.520559\pi\) | ||||
−0.0645437 | + | 0.997915i | \(0.520559\pi\) | |||||||
\(444\) | −4.10957 | −0.195032 | ||||||||
\(445\) | −7.45661 | −0.353477 | ||||||||
\(446\) | −37.8574 | −1.79260 | ||||||||
\(447\) | −38.8901 | −1.83944 | ||||||||
\(448\) | −0.542818 | −0.0256457 | ||||||||
\(449\) | 13.4967 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(450\) | 3.62048 | 0.170671 | ||||||||
\(451\) | 9.20528 | 0.433460 | ||||||||
\(452\) | −16.6376 | −0.782566 | ||||||||
\(453\) | −34.8123 | −1.63562 | ||||||||
\(454\) | 8.49926 | 0.398890 | ||||||||
\(455\) | 0.136769 | 0.00641185 | ||||||||
\(456\) | −5.57067 | −0.260870 | ||||||||
\(457\) | −21.3425 | −0.998360 | −0.499180 | − | 0.866498i | \(-0.666365\pi\) | ||||
−0.499180 | + | 0.866498i | \(0.666365\pi\) | |||||||
\(458\) | 38.7114 | 1.80887 | ||||||||
\(459\) | 18.1228 | 0.845900 | ||||||||
\(460\) | 0.723033 | 0.0337116 | ||||||||
\(461\) | −21.1165 | −0.983494 | −0.491747 | − | 0.870738i | \(-0.663642\pi\) | ||||
−0.491747 | + | 0.870738i | \(0.663642\pi\) | |||||||
\(462\) | 0.821039 | 0.0381982 | ||||||||
\(463\) | 15.8408 | 0.736183 | 0.368091 | − | 0.929790i | \(-0.380011\pi\) | ||||
0.368091 | + | 0.929790i | \(0.380011\pi\) | |||||||
\(464\) | −17.5431 | −0.814417 | ||||||||
\(465\) | 12.4854 | 0.578995 | ||||||||
\(466\) | −10.3753 | −0.480628 | ||||||||
\(467\) | −33.3353 | −1.54257 | −0.771286 | − | 0.636489i | \(-0.780386\pi\) | ||||
−0.771286 | + | 0.636489i | \(0.780386\pi\) | |||||||
\(468\) | −2.42822 | −0.112245 | ||||||||
\(469\) | 0.155726 | 0.00719074 | ||||||||
\(470\) | −0.743617 | −0.0343005 | ||||||||
\(471\) | −22.6322 | −1.04284 | ||||||||
\(472\) | 4.04240 | 0.186066 | ||||||||
\(473\) | −3.77701 | −0.173667 | ||||||||
\(474\) | 21.6721 | 0.995432 | ||||||||
\(475\) | 27.3672 | 1.25569 | ||||||||
\(476\) | 0.475784 | 0.0218075 | ||||||||
\(477\) | −2.43901 | −0.111675 | ||||||||
\(478\) | 35.5678 | 1.62683 | ||||||||
\(479\) | −21.0463 | −0.961628 | −0.480814 | − | 0.876823i | \(-0.659659\pi\) | ||||
−0.480814 | + | 0.876823i | \(0.659659\pi\) | |||||||
\(480\) | 14.4141 | 0.657912 | ||||||||
\(481\) | −2.53430 | −0.115554 | ||||||||
\(482\) | 14.1501 | 0.644520 | ||||||||
\(483\) | 0.0354679 | 0.00161385 | ||||||||
\(484\) | 8.18262 | 0.371937 | ||||||||
\(485\) | 0.104975 | 0.00476668 | ||||||||
\(486\) | −9.15053 | −0.415077 | ||||||||
\(487\) | −31.8625 | −1.44383 | −0.721914 | − | 0.691983i | \(-0.756737\pi\) | ||||
−0.721914 | + | 0.691983i | \(0.756737\pi\) | |||||||
\(488\) | 1.69265 | 0.0766227 | ||||||||
\(489\) | −1.85254 | −0.0837749 | ||||||||
\(490\) | −13.7743 | −0.622258 | ||||||||
\(491\) | −28.5135 | −1.28680 | −0.643399 | − | 0.765531i | \(-0.722476\pi\) | ||||
−0.643399 | + | 0.765531i | \(0.722476\pi\) | |||||||
\(492\) | −9.87059 | −0.445000 | ||||||||
\(493\) | 19.0085 | 0.856100 | ||||||||
\(494\) | −34.9032 | −1.57037 | ||||||||
\(495\) | −1.58668 | −0.0713158 | ||||||||
\(496\) | −24.7196 | −1.10994 | ||||||||
\(497\) | −0.755684 | −0.0338971 | ||||||||
\(498\) | −15.4651 | −0.693007 | ||||||||
\(499\) | 34.8206 | 1.55878 | 0.779392 | − | 0.626537i | \(-0.215528\pi\) | ||||
0.779392 | + | 0.626537i | \(0.215528\pi\) | |||||||
\(500\) | 19.3095 | 0.863546 | ||||||||
\(501\) | −1.74501 | −0.0779614 | ||||||||
\(502\) | 62.6224 | 2.79498 | ||||||||
\(503\) | −28.6418 | −1.27707 | −0.638536 | − | 0.769592i | \(-0.720460\pi\) | ||||
−0.638536 | + | 0.769592i | \(0.720460\pi\) | |||||||
\(504\) | −0.0109053 | −0.000485761 0 | ||||||||
\(505\) | −8.92107 | −0.396983 | ||||||||
\(506\) | 2.67667 | 0.118992 | ||||||||
\(507\) | 12.1847 | 0.541144 | ||||||||
\(508\) | 19.3277 | 0.857530 | ||||||||
\(509\) | −4.20427 | −0.186351 | −0.0931755 | − | 0.995650i | \(-0.529702\pi\) | ||||
−0.0931755 | + | 0.995650i | \(0.529702\pi\) | |||||||
\(510\) | −13.8926 | −0.615175 | ||||||||
\(511\) | 0.479056 | 0.0211922 | ||||||||
\(512\) | −31.6915 | −1.40058 | ||||||||
\(513\) | −31.9017 | −1.40849 | ||||||||
\(514\) | −16.7676 | −0.739585 | ||||||||
\(515\) | 12.9538 | 0.570812 | ||||||||
\(516\) | 4.05000 | 0.178291 | ||||||||
\(517\) | −1.44768 | −0.0636689 | ||||||||
\(518\) | −0.115639 | −0.00508089 | ||||||||
\(519\) | −21.3016 | −0.935035 | ||||||||
\(520\) | −1.08933 | −0.0477701 | ||||||||
\(521\) | −36.1845 | −1.58527 | −0.792637 | − | 0.609694i | \(-0.791292\pi\) | ||||
−0.792637 | + | 0.609694i | \(0.791292\pi\) | |||||||
\(522\) | −4.42662 | −0.193748 | ||||||||
\(523\) | 11.8257 | 0.517100 | 0.258550 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258550 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(524\) | 33.8248 | 1.47764 | ||||||||
\(525\) | 0.425693 | 0.0185788 | ||||||||
\(526\) | 63.6425 | 2.77494 | ||||||||
\(527\) | 26.7846 | 1.16675 | ||||||||
\(528\) | 24.9611 | 1.08629 | ||||||||
\(529\) | −22.8844 | −0.994973 | ||||||||
\(530\) | −11.1168 | −0.482882 | ||||||||
\(531\) | −3.89348 | −0.168963 | ||||||||
\(532\) | −0.837526 | −0.0363113 | ||||||||
\(533\) | −6.08703 | −0.263658 | ||||||||
\(534\) | 29.5995 | 1.28089 | ||||||||
\(535\) | 5.60099 | 0.242152 | ||||||||
\(536\) | −1.24031 | −0.0535730 | ||||||||
\(537\) | −22.5955 | −0.975067 | ||||||||
\(538\) | −1.04084 | −0.0448740 | ||||||||
\(539\) | −26.8159 | −1.15504 | ||||||||
\(540\) | −10.1158 | −0.435316 | ||||||||
\(541\) | 42.5447 | 1.82914 | 0.914571 | − | 0.404426i | \(-0.132529\pi\) | ||||
0.914571 | + | 0.404426i | \(0.132529\pi\) | |||||||
\(542\) | 3.18329 | 0.136734 | ||||||||
\(543\) | 37.4530 | 1.60726 | ||||||||
\(544\) | 30.9223 | 1.32578 | ||||||||
\(545\) | 4.17796 | 0.178964 | ||||||||
\(546\) | −0.542915 | −0.0232346 | ||||||||
\(547\) | 27.2665 | 1.16583 | 0.582915 | − | 0.812533i | \(-0.301912\pi\) | ||||
0.582915 | + | 0.812533i | \(0.301912\pi\) | |||||||
\(548\) | 1.89025 | 0.0807475 | ||||||||
\(549\) | −1.63030 | −0.0695794 | ||||||||
\(550\) | 32.1259 | 1.36985 | ||||||||
\(551\) | −33.4608 | −1.42548 | ||||||||
\(552\) | −0.282491 | −0.0120236 | ||||||||
\(553\) | 0.320697 | 0.0136374 | ||||||||
\(554\) | −55.2469 | −2.34722 | ||||||||
\(555\) | 1.77568 | 0.0753735 | ||||||||
\(556\) | 47.6008 | 2.01872 | ||||||||
\(557\) | −24.4021 | −1.03395 | −0.516976 | − | 0.856000i | \(-0.672942\pi\) | ||||
−0.516976 | + | 0.856000i | \(0.672942\pi\) | |||||||
\(558\) | −6.23748 | −0.264054 | ||||||||
\(559\) | 2.49756 | 0.105636 | ||||||||
\(560\) | 0.189730 | 0.00801755 | ||||||||
\(561\) | −27.0462 | −1.14189 | ||||||||
\(562\) | −7.74674 | −0.326777 | ||||||||
\(563\) | 9.58770 | 0.404073 | 0.202037 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202037 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(564\) | 1.55231 | 0.0653640 | ||||||||
\(565\) | 7.18884 | 0.302437 | ||||||||
\(566\) | −63.9268 | −2.68705 | ||||||||
\(567\) | −0.569181 | −0.0239034 | ||||||||
\(568\) | 6.01879 | 0.252543 | ||||||||
\(569\) | −23.7459 | −0.995481 | −0.497741 | − | 0.867326i | \(-0.665837\pi\) | ||||
−0.497741 | + | 0.867326i | \(0.665837\pi\) | |||||||
\(570\) | 24.4552 | 1.02432 | ||||||||
\(571\) | −26.8817 | −1.12496 | −0.562482 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562482 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(572\) | −21.5465 | −0.900905 | ||||||||
\(573\) | 18.1095 | 0.756536 | ||||||||
\(574\) | −0.277748 | −0.0115930 | ||||||||
\(575\) | 1.38780 | 0.0578754 | ||||||||
\(576\) | −4.16411 | −0.173504 | ||||||||
\(577\) | 6.86305 | 0.285712 | 0.142856 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142856 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(578\) | 5.11217 | 0.212638 | ||||||||
\(579\) | 1.86419 | 0.0774732 | ||||||||
\(580\) | −10.6102 | −0.440566 | ||||||||
\(581\) | −0.228848 | −0.00949421 | ||||||||
\(582\) | −0.416706 | −0.0172730 | ||||||||
\(583\) | −21.6423 | −0.896331 | ||||||||
\(584\) | −3.81553 | −0.157888 | ||||||||
\(585\) | 1.04920 | 0.0433789 | ||||||||
\(586\) | 36.9911 | 1.52809 | ||||||||
\(587\) | 43.0689 | 1.77764 | 0.888821 | − | 0.458254i | \(-0.151525\pi\) | ||||
0.888821 | + | 0.458254i | \(0.151525\pi\) | |||||||
\(588\) | 28.7540 | 1.18579 | ||||||||
\(589\) | −47.1491 | −1.94274 | ||||||||
\(590\) | −17.7461 | −0.730596 | ||||||||
\(591\) | −25.7825 | −1.06055 | ||||||||
\(592\) | −3.51565 | −0.144492 | ||||||||
\(593\) | −0.585805 | −0.0240561 | −0.0120281 | − | 0.999928i | \(-0.503829\pi\) | ||||
−0.0120281 | + | 0.999928i | \(0.503829\pi\) | |||||||
\(594\) | −37.4489 | −1.53655 | ||||||||
\(595\) | −0.205579 | −0.00842791 | ||||||||
\(596\) | 46.5691 | 1.90755 | ||||||||
\(597\) | 8.69415 | 0.355828 | ||||||||
\(598\) | −1.76996 | −0.0723790 | ||||||||
\(599\) | −11.0842 | −0.452887 | −0.226443 | − | 0.974024i | \(-0.572710\pi\) | ||||
−0.226443 | + | 0.974024i | \(0.572710\pi\) | |||||||
\(600\) | −3.39051 | −0.138417 | ||||||||
\(601\) | −46.7263 | −1.90600 | −0.953002 | − | 0.302965i | \(-0.902024\pi\) | ||||
−0.953002 | + | 0.302965i | \(0.902024\pi\) | |||||||
\(602\) | 0.113963 | 0.00464477 | ||||||||
\(603\) | 1.19461 | 0.0486485 | ||||||||
\(604\) | 41.6861 | 1.69619 | ||||||||
\(605\) | −3.53558 | −0.143742 | ||||||||
\(606\) | 35.4128 | 1.43855 | ||||||||
\(607\) | −0.0151401 | −0.000614518 0 | −0.000307259 | − | 1.00000i | \(-0.500098\pi\) | ||||
−0.000307259 | 1.00000i | \(0.500098\pi\) | ||||||||
\(608\) | −54.4327 | −2.20754 | ||||||||
\(609\) | −0.520478 | −0.0210908 | ||||||||
\(610\) | −7.43074 | −0.300862 | ||||||||
\(611\) | 0.957283 | 0.0387275 | ||||||||
\(612\) | 3.64987 | 0.147537 | ||||||||
\(613\) | 16.2083 | 0.654647 | 0.327323 | − | 0.944912i | \(-0.393853\pi\) | ||||
0.327323 | + | 0.944912i | \(0.393853\pi\) | |||||||
\(614\) | −29.7618 | −1.20109 | ||||||||
\(615\) | 4.26493 | 0.171978 | ||||||||
\(616\) | −0.0967669 | −0.00389885 | ||||||||
\(617\) | −33.3267 | −1.34168 | −0.670841 | − | 0.741601i | \(-0.734067\pi\) | ||||
−0.670841 | + | 0.741601i | \(0.734067\pi\) | |||||||
\(618\) | −51.4208 | −2.06845 | ||||||||
\(619\) | −42.3955 | −1.70402 | −0.852011 | − | 0.523525i | \(-0.824617\pi\) | ||||
−0.852011 | + | 0.523525i | \(0.824617\pi\) | |||||||
\(620\) | −14.9507 | −0.600434 | ||||||||
\(621\) | −1.61775 | −0.0649180 | ||||||||
\(622\) | 8.50364 | 0.340965 | ||||||||
\(623\) | 0.438005 | 0.0175483 | ||||||||
\(624\) | −16.5057 | −0.660755 | ||||||||
\(625\) | 12.0630 | 0.482519 | ||||||||
\(626\) | −49.9921 | −1.99809 | ||||||||
\(627\) | 47.6097 | 1.90135 | ||||||||
\(628\) | 27.1010 | 1.08145 | ||||||||
\(629\) | 3.80932 | 0.151888 | ||||||||
\(630\) | 0.0478743 | 0.00190736 | ||||||||
\(631\) | −2.35799 | −0.0938701 | −0.0469351 | − | 0.998898i | \(-0.514945\pi\) | ||||
−0.0469351 | + | 0.998898i | \(0.514945\pi\) | |||||||
\(632\) | −2.55425 | −0.101603 | ||||||||
\(633\) | 3.76573 | 0.149674 | ||||||||
\(634\) | −34.3594 | −1.36459 | ||||||||
\(635\) | −8.35122 | −0.331408 | ||||||||
\(636\) | 23.2064 | 0.920195 | ||||||||
\(637\) | 17.7321 | 0.702571 | ||||||||
\(638\) | −39.2791 | −1.55507 | ||||||||
\(639\) | −5.79706 | −0.229328 | ||||||||
\(640\) | −3.41817 | −0.135115 | ||||||||
\(641\) | −3.93575 | −0.155453 | −0.0777263 | − | 0.996975i | \(-0.524766\pi\) | ||||
−0.0777263 | + | 0.996975i | \(0.524766\pi\) | |||||||
\(642\) | −22.2335 | −0.877486 | ||||||||
\(643\) | −19.6361 | −0.774371 | −0.387186 | − | 0.922002i | \(-0.626553\pi\) | ||||
−0.387186 | + | 0.922002i | \(0.626553\pi\) | |||||||
\(644\) | −0.0424713 | −0.00167360 | ||||||||
\(645\) | −1.74994 | −0.0689038 | ||||||||
\(646\) | 52.4632 | 2.06414 | ||||||||
\(647\) | 4.54425 | 0.178653 | 0.0893265 | − | 0.996002i | \(-0.471529\pi\) | ||||
0.0893265 | + | 0.996002i | \(0.471529\pi\) | |||||||
\(648\) | 4.53335 | 0.178087 | ||||||||
\(649\) | −34.5483 | −1.35614 | ||||||||
\(650\) | −21.2434 | −0.833234 | ||||||||
\(651\) | −0.733397 | −0.0287441 | ||||||||
\(652\) | 2.21834 | 0.0868769 | ||||||||
\(653\) | −24.5445 | −0.960501 | −0.480250 | − | 0.877131i | \(-0.659454\pi\) | ||||
−0.480250 | + | 0.877131i | \(0.659454\pi\) | |||||||
\(654\) | −16.5847 | −0.648512 | ||||||||
\(655\) | −14.6152 | −0.571062 | ||||||||
\(656\) | −8.44408 | −0.329686 | ||||||||
\(657\) | 3.67497 | 0.143374 | ||||||||
\(658\) | 0.0436804 | 0.00170284 | ||||||||
\(659\) | 42.6076 | 1.65976 | 0.829879 | − | 0.557943i | \(-0.188409\pi\) | ||||
0.829879 | + | 0.557943i | \(0.188409\pi\) | |||||||
\(660\) | 15.0967 | 0.587640 | ||||||||
\(661\) | −16.4090 | −0.638235 | −0.319117 | − | 0.947715i | \(-0.603386\pi\) | ||||
−0.319117 | + | 0.947715i | \(0.603386\pi\) | |||||||
\(662\) | 28.2150 | 1.09661 | ||||||||
\(663\) | 17.8844 | 0.694573 | ||||||||
\(664\) | 1.82270 | 0.0707345 | ||||||||
\(665\) | 0.361882 | 0.0140332 | ||||||||
\(666\) | −0.887100 | −0.0343744 | ||||||||
\(667\) | −1.69681 | −0.0657008 | ||||||||
\(668\) | 2.08957 | 0.0808481 | ||||||||
\(669\) | −34.1467 | −1.32019 | ||||||||
\(670\) | 5.44494 | 0.210356 | ||||||||
\(671\) | −14.4662 | −0.558463 | ||||||||
\(672\) | −0.846693 | −0.0326619 | ||||||||
\(673\) | −14.6717 | −0.565553 | −0.282776 | − | 0.959186i | \(-0.591255\pi\) | ||||
−0.282776 | + | 0.959186i | \(0.591255\pi\) | |||||||
\(674\) | −43.5502 | −1.67749 | ||||||||
\(675\) | −19.4165 | −0.747342 | ||||||||
\(676\) | −14.5907 | −0.561181 | ||||||||
\(677\) | −25.8030 | −0.991690 | −0.495845 | − | 0.868411i | \(-0.665142\pi\) | ||||
−0.495845 | + | 0.868411i | \(0.665142\pi\) | |||||||
\(678\) | −28.5365 | −1.09594 | ||||||||
\(679\) | −0.00616629 | −0.000236640 0 | ||||||||
\(680\) | 1.63737 | 0.0627903 | ||||||||
\(681\) | 7.66617 | 0.293768 | ||||||||
\(682\) | −55.3475 | −2.11937 | ||||||||
\(683\) | 7.03626 | 0.269235 | 0.134618 | − | 0.990898i | \(-0.457019\pi\) | ||||
0.134618 | + | 0.990898i | \(0.457019\pi\) | |||||||
\(684\) | −6.42489 | −0.245662 | ||||||||
\(685\) | −0.816748 | −0.0312063 | ||||||||
\(686\) | 1.61858 | 0.0617977 | ||||||||
\(687\) | 34.9170 | 1.33217 | ||||||||
\(688\) | 3.46468 | 0.132090 | ||||||||
\(689\) | 14.3110 | 0.545207 | ||||||||
\(690\) | 1.24014 | 0.0472112 | ||||||||
\(691\) | −25.7042 | −0.977832 | −0.488916 | − | 0.872331i | \(-0.662608\pi\) | ||||
−0.488916 | + | 0.872331i | \(0.662608\pi\) | |||||||
\(692\) | 25.5077 | 0.969656 | ||||||||
\(693\) | 0.0932021 | 0.00354046 | ||||||||
\(694\) | −67.2570 | −2.55304 | ||||||||
\(695\) | −20.5676 | −0.780172 | ||||||||
\(696\) | 4.14545 | 0.157133 | ||||||||
\(697\) | 9.14944 | 0.346560 | ||||||||
\(698\) | 45.0412 | 1.70483 | ||||||||
\(699\) | −9.35836 | −0.353966 | ||||||||
\(700\) | −0.509748 | −0.0192667 | ||||||||
\(701\) | 26.0313 | 0.983187 | 0.491593 | − | 0.870825i | \(-0.336415\pi\) | ||||
0.491593 | + | 0.870825i | \(0.336415\pi\) | |||||||
\(702\) | 24.7632 | 0.934627 | ||||||||
\(703\) | −6.70558 | −0.252906 | ||||||||
\(704\) | −36.9497 | −1.39259 | ||||||||
\(705\) | −0.670729 | −0.0252611 | ||||||||
\(706\) | 56.0341 | 2.10887 | ||||||||
\(707\) | 0.524028 | 0.0197081 | ||||||||
\(708\) | 37.0453 | 1.39225 | ||||||||
\(709\) | −32.4586 | −1.21901 | −0.609505 | − | 0.792782i | \(-0.708632\pi\) | ||||
−0.609505 | + | 0.792782i | \(0.708632\pi\) | |||||||
\(710\) | −26.4225 | −0.991618 | ||||||||
\(711\) | 2.46016 | 0.0922632 | ||||||||
\(712\) | −3.48857 | −0.130740 | ||||||||
\(713\) | −2.39095 | −0.0895417 | ||||||||
\(714\) | 0.816058 | 0.0305402 | ||||||||
\(715\) | 9.30991 | 0.348171 | ||||||||
\(716\) | 27.0571 | 1.01117 | ||||||||
\(717\) | 32.0815 | 1.19811 | ||||||||
\(718\) | 28.8709 | 1.07745 | ||||||||
\(719\) | −23.0618 | −0.860061 | −0.430030 | − | 0.902814i | \(-0.641497\pi\) | ||||
−0.430030 | + | 0.902814i | \(0.641497\pi\) | |||||||
\(720\) | 1.45547 | 0.0542422 | ||||||||
\(721\) | −0.760911 | −0.0283378 | ||||||||
\(722\) | −53.3281 | −1.98466 | ||||||||
\(723\) | 12.7632 | 0.474667 | ||||||||
\(724\) | −44.8483 | −1.66677 | ||||||||
\(725\) | −20.3655 | −0.756355 | ||||||||
\(726\) | 14.0347 | 0.520877 | ||||||||
\(727\) | −6.73471 | −0.249777 | −0.124888 | − | 0.992171i | \(-0.539857\pi\) | ||||
−0.124888 | + | 0.992171i | \(0.539857\pi\) | |||||||
\(728\) | 0.0639875 | 0.00237153 | ||||||||
\(729\) | 22.0740 | 0.817555 | ||||||||
\(730\) | 16.7502 | 0.619952 | ||||||||
\(731\) | −3.75410 | −0.138850 | ||||||||
\(732\) | 15.5118 | 0.573332 | ||||||||
\(733\) | −16.5693 | −0.612002 | −0.306001 | − | 0.952031i | \(-0.598991\pi\) | ||||
−0.306001 | + | 0.952031i | \(0.598991\pi\) | |||||||
\(734\) | −38.4010 | −1.41741 | ||||||||
\(735\) | −12.4241 | −0.458271 | ||||||||
\(736\) | −2.76031 | −0.101746 | ||||||||
\(737\) | 10.6003 | 0.390466 | ||||||||
\(738\) | −2.13068 | −0.0784315 | ||||||||
\(739\) | 7.36184 | 0.270810 | 0.135405 | − | 0.990790i | \(-0.456766\pi\) | ||||
0.135405 | + | 0.990790i | \(0.456766\pi\) | |||||||
\(740\) | −2.12630 | −0.0781643 | ||||||||
\(741\) | −31.4821 | −1.15652 | ||||||||
\(742\) | 0.653005 | 0.0239726 | ||||||||
\(743\) | −0.397775 | −0.0145930 | −0.00729648 | − | 0.999973i | \(-0.502323\pi\) | ||||
−0.00729648 | + | 0.999973i | \(0.502323\pi\) | |||||||
\(744\) | 5.84128 | 0.214152 | ||||||||
\(745\) | −20.1218 | −0.737206 | ||||||||
\(746\) | 50.3605 | 1.84383 | ||||||||
\(747\) | −1.75556 | −0.0642324 | ||||||||
\(748\) | 32.3867 | 1.18417 | ||||||||
\(749\) | −0.329005 | −0.0120216 | ||||||||
\(750\) | 33.1193 | 1.20935 | ||||||||
\(751\) | −13.9193 | −0.507921 | −0.253961 | − | 0.967215i | \(-0.581733\pi\) | ||||
−0.253961 | + | 0.967215i | \(0.581733\pi\) | |||||||
\(752\) | 1.32797 | 0.0484260 | ||||||||
\(753\) | 56.4843 | 2.05840 | ||||||||
\(754\) | 25.9735 | 0.945897 | ||||||||
\(755\) | −18.0119 | −0.655521 | ||||||||
\(756\) | 0.594209 | 0.0216112 | ||||||||
\(757\) | 31.4329 | 1.14245 | 0.571224 | − | 0.820794i | \(-0.306469\pi\) | ||||
0.571224 | + | 0.820794i | \(0.306469\pi\) | |||||||
\(758\) | 38.3053 | 1.39131 | ||||||||
\(759\) | 2.41431 | 0.0876338 | ||||||||
\(760\) | −2.88227 | −0.104551 | ||||||||
\(761\) | −13.3332 | −0.483327 | −0.241663 | − | 0.970360i | \(-0.577693\pi\) | ||||
−0.241663 | + | 0.970360i | \(0.577693\pi\) | |||||||
\(762\) | 33.1507 | 1.20092 | ||||||||
\(763\) | −0.245415 | −0.00888462 | ||||||||
\(764\) | −21.6853 | −0.784548 | ||||||||
\(765\) | −1.57705 | −0.0570184 | ||||||||
\(766\) | −23.2362 | −0.839559 | ||||||||
\(767\) | 22.8452 | 0.824892 | ||||||||
\(768\) | −22.1520 | −0.799340 | ||||||||
\(769\) | −31.3330 | −1.12990 | −0.564948 | − | 0.825127i | \(-0.691104\pi\) | ||||
−0.564948 | + | 0.825127i | \(0.691104\pi\) | |||||||
\(770\) | 0.424807 | 0.0153090 | ||||||||
\(771\) | −15.1240 | −0.544679 | ||||||||
\(772\) | −2.23229 | −0.0803418 | ||||||||
\(773\) | 12.9743 | 0.466653 | 0.233327 | − | 0.972398i | \(-0.425039\pi\) | ||||
0.233327 | + | 0.972398i | \(0.425039\pi\) | |||||||
\(774\) | 0.874240 | 0.0314239 | ||||||||
\(775\) | −28.6966 | −1.03081 | ||||||||
\(776\) | 0.0491126 | 0.00176304 | ||||||||
\(777\) | −0.104304 | −0.00374190 | ||||||||
\(778\) | −48.8723 | −1.75216 | ||||||||
\(779\) | −16.1058 | −0.577051 | ||||||||
\(780\) | −9.98278 | −0.357441 | ||||||||
\(781\) | −51.4395 | −1.84065 | ||||||||
\(782\) | 2.66043 | 0.0951368 | ||||||||
\(783\) | 23.7398 | 0.848392 | ||||||||
\(784\) | 24.5984 | 0.878514 | ||||||||
\(785\) | −11.7099 | −0.417946 | ||||||||
\(786\) | 58.0158 | 2.06936 | ||||||||
\(787\) | 25.7833 | 0.919075 | 0.459538 | − | 0.888158i | \(-0.348015\pi\) | ||||
0.459538 | + | 0.888158i | \(0.348015\pi\) | |||||||
\(788\) | 30.8734 | 1.09982 | ||||||||
\(789\) | 57.4044 | 2.04365 | ||||||||
\(790\) | 11.2132 | 0.398947 | ||||||||
\(791\) | −0.422276 | −0.0150144 | ||||||||
\(792\) | −0.742326 | −0.0263774 | ||||||||
\(793\) | 9.56585 | 0.339693 | ||||||||
\(794\) | 28.9086 | 1.02593 | ||||||||
\(795\) | −10.0271 | −0.355626 | ||||||||
\(796\) | −10.4109 | −0.369003 | ||||||||
\(797\) | −10.0199 | −0.354924 | −0.177462 | − | 0.984128i | \(-0.556789\pi\) | ||||
−0.177462 | + | 0.984128i | \(0.556789\pi\) | |||||||
\(798\) | −1.43651 | −0.0508520 | ||||||||
\(799\) | −1.43890 | −0.0509045 | ||||||||
\(800\) | −33.1297 | −1.17131 | ||||||||
\(801\) | 3.36006 | 0.118722 | ||||||||
\(802\) | 62.3484 | 2.20160 | ||||||||
\(803\) | 32.6094 | 1.15076 | ||||||||
\(804\) | −11.3664 | −0.400862 | ||||||||
\(805\) | 0.0183512 | 0.000646794 0 | ||||||||
\(806\) | 36.5987 | 1.28914 | ||||||||
\(807\) | −0.938822 | −0.0330481 | ||||||||
\(808\) | −4.17372 | −0.146831 | ||||||||
\(809\) | 46.1402 | 1.62220 | 0.811101 | − | 0.584906i | \(-0.198869\pi\) | ||||
0.811101 | + | 0.584906i | \(0.198869\pi\) | |||||||
\(810\) | −19.9014 | −0.699265 | ||||||||
\(811\) | 9.40500 | 0.330254 | 0.165127 | − | 0.986272i | \(-0.447197\pi\) | ||||
0.165127 | + | 0.986272i | \(0.447197\pi\) | |||||||
\(812\) | 0.623250 | 0.0218718 | ||||||||
\(813\) | 2.87126 | 0.100700 | ||||||||
\(814\) | −7.87157 | −0.275898 | ||||||||
\(815\) | −0.958510 | −0.0335751 | ||||||||
\(816\) | 24.8097 | 0.868514 | ||||||||
\(817\) | 6.60837 | 0.231198 | ||||||||
\(818\) | −15.5684 | −0.544338 | ||||||||
\(819\) | −0.0616303 | −0.00215354 | ||||||||
\(820\) | −5.10706 | −0.178346 | ||||||||
\(821\) | −18.1631 | −0.633898 | −0.316949 | − | 0.948443i | \(-0.602658\pi\) | ||||
−0.316949 | + | 0.948443i | \(0.602658\pi\) | |||||||
\(822\) | 3.24213 | 0.113082 | ||||||||
\(823\) | 4.05041 | 0.141189 | 0.0705943 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705943 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(824\) | 6.06042 | 0.211125 | ||||||||
\(825\) | 28.9770 | 1.00885 | ||||||||
\(826\) | 1.04242 | 0.0362703 | ||||||||
\(827\) | 44.3747 | 1.54306 | 0.771529 | − | 0.636194i | \(-0.219492\pi\) | ||||
0.771529 | + | 0.636194i | \(0.219492\pi\) | |||||||
\(828\) | −0.325809 | −0.0113226 | ||||||||
\(829\) | −28.0699 | −0.974906 | −0.487453 | − | 0.873149i | \(-0.662074\pi\) | ||||
−0.487453 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(830\) | −8.00166 | −0.277742 | ||||||||
\(831\) | −49.8317 | −1.72864 | ||||||||
\(832\) | 24.4331 | 0.847066 | ||||||||
\(833\) | −26.6532 | −0.923478 | ||||||||
\(834\) | 81.6443 | 2.82711 | ||||||||
\(835\) | −0.902872 | −0.0312452 | ||||||||
\(836\) | −57.0105 | −1.97175 | ||||||||
\(837\) | 33.4514 | 1.15625 | ||||||||
\(838\) | 40.7920 | 1.40914 | ||||||||
\(839\) | −23.3457 | −0.805982 | −0.402991 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402991 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(840\) | −0.0448334 | −0.00154690 | ||||||||
\(841\) | −4.09993 | −0.141377 | ||||||||
\(842\) | 65.8398 | 2.26899 | ||||||||
\(843\) | −6.98742 | −0.240660 | ||||||||
\(844\) | −4.50929 | −0.155216 | ||||||||
\(845\) | 6.30441 | 0.216878 | ||||||||
\(846\) | 0.335084 | 0.0115204 | ||||||||
\(847\) | 0.207682 | 0.00713602 | ||||||||
\(848\) | 19.8526 | 0.681742 | ||||||||
\(849\) | −57.6608 | −1.97891 | ||||||||
\(850\) | 31.9310 | 1.09522 | ||||||||
\(851\) | −0.340043 | −0.0116565 | ||||||||
\(852\) | 55.1573 | 1.88966 | ||||||||
\(853\) | −19.1047 | −0.654131 | −0.327066 | − | 0.945002i | \(-0.606060\pi\) | ||||
−0.327066 | + | 0.945002i | \(0.606060\pi\) | |||||||
\(854\) | 0.436485 | 0.0149362 | ||||||||
\(855\) | 2.77610 | 0.0949405 | ||||||||
\(856\) | 2.62042 | 0.0895642 | ||||||||
\(857\) | −47.0141 | −1.60597 | −0.802985 | − | 0.595999i | \(-0.796756\pi\) | ||||
−0.802985 | + | 0.595999i | \(0.796756\pi\) | |||||||
\(858\) | −36.9563 | −1.26167 | ||||||||
\(859\) | 23.6627 | 0.807361 | 0.403681 | − | 0.914900i | \(-0.367731\pi\) | ||||
0.403681 | + | 0.914900i | \(0.367731\pi\) | |||||||
\(860\) | 2.09548 | 0.0714551 | ||||||||
\(861\) | −0.250524 | −0.00853782 | ||||||||
\(862\) | −82.8884 | −2.82319 | ||||||||
\(863\) | 23.9208 | 0.814273 | 0.407136 | − | 0.913367i | \(-0.366527\pi\) | ||||
0.407136 | + | 0.913367i | \(0.366527\pi\) | |||||||
\(864\) | 38.6190 | 1.31385 | ||||||||
\(865\) | −11.0215 | −0.374741 | ||||||||
\(866\) | −73.7644 | −2.50662 | ||||||||
\(867\) | 4.61108 | 0.156601 | ||||||||
\(868\) | 0.878210 | 0.0298084 | ||||||||
\(869\) | 21.8299 | 0.740529 | ||||||||
\(870\) | −18.1985 | −0.616988 | ||||||||
\(871\) | −7.00946 | −0.237507 | ||||||||
\(872\) | 1.95465 | 0.0661930 | ||||||||
\(873\) | −0.0473033 | −0.00160098 | ||||||||
\(874\) | −4.68318 | −0.158411 | ||||||||
\(875\) | 0.490091 | 0.0165681 | ||||||||
\(876\) | −34.9662 | −1.18140 | ||||||||
\(877\) | 1.24176 | 0.0419312 | 0.0209656 | − | 0.999780i | \(-0.493326\pi\) | ||||
0.0209656 | + | 0.999780i | \(0.493326\pi\) | |||||||
\(878\) | 62.7694 | 2.11836 | ||||||||
\(879\) | 33.3653 | 1.12538 | ||||||||
\(880\) | 12.9149 | 0.435363 | ||||||||
\(881\) | −13.2922 | −0.447827 | −0.223913 | − | 0.974609i | \(-0.571883\pi\) | ||||
−0.223913 | + | 0.974609i | \(0.571883\pi\) | |||||||
\(882\) | 6.20688 | 0.208997 | ||||||||
\(883\) | 23.3807 | 0.786823 | 0.393411 | − | 0.919362i | \(-0.371295\pi\) | ||||
0.393411 | + | 0.919362i | \(0.371295\pi\) | |||||||
\(884\) | −21.4158 | −0.720292 | ||||||||
\(885\) | −16.0067 | −0.538059 | ||||||||
\(886\) | 5.58029 | 0.187473 | ||||||||
\(887\) | −23.8031 | −0.799229 | −0.399614 | − | 0.916683i | \(-0.630856\pi\) | ||||
−0.399614 | + | 0.916683i | \(0.630856\pi\) | |||||||
\(888\) | 0.830751 | 0.0278782 | ||||||||
\(889\) | 0.490554 | 0.0164527 | ||||||||
\(890\) | 15.3148 | 0.513354 | ||||||||
\(891\) | −38.7443 | −1.29798 | ||||||||
\(892\) | 40.8891 | 1.36907 | ||||||||
\(893\) | 2.53290 | 0.0847603 | ||||||||
\(894\) | 79.8747 | 2.67141 | ||||||||
\(895\) | −11.6909 | −0.390785 | ||||||||
\(896\) | 0.200785 | 0.00670775 | ||||||||
\(897\) | −1.59647 | −0.0533046 | ||||||||
\(898\) | −27.7204 | −0.925041 | ||||||||
\(899\) | 35.0863 | 1.17019 | ||||||||
\(900\) | −3.91042 | −0.130347 | ||||||||
\(901\) | −21.5110 | −0.716634 | ||||||||
\(902\) | −18.9064 | −0.629513 | ||||||||
\(903\) | 0.102792 | 0.00342071 | ||||||||
\(904\) | 3.36329 | 0.111861 | ||||||||
\(905\) | 19.3782 | 0.644154 | ||||||||
\(906\) | 71.4995 | 2.37541 | ||||||||
\(907\) | −42.2449 | −1.40272 | −0.701359 | − | 0.712809i | \(-0.747423\pi\) | ||||
−0.701359 | + | 0.712809i | \(0.747423\pi\) | |||||||
\(908\) | −9.17990 | −0.304646 | ||||||||
\(909\) | 4.01996 | 0.133334 | ||||||||
\(910\) | −0.280905 | −0.00931191 | ||||||||
\(911\) | −13.9966 | −0.463728 | −0.231864 | − | 0.972748i | \(-0.574483\pi\) | ||||
−0.231864 | + | 0.972748i | \(0.574483\pi\) | |||||||
\(912\) | −43.6727 | −1.44615 | ||||||||
\(913\) | −15.5777 | −0.515547 | ||||||||
\(914\) | 43.8345 | 1.44992 | ||||||||
\(915\) | −6.70239 | −0.221574 | ||||||||
\(916\) | −41.8116 | −1.38149 | ||||||||
\(917\) | 0.858501 | 0.0283502 | ||||||||
\(918\) | −37.2217 | −1.22850 | ||||||||
\(919\) | 47.8002 | 1.57678 | 0.788392 | − | 0.615173i | \(-0.210914\pi\) | ||||
0.788392 | + | 0.615173i | \(0.210914\pi\) | |||||||
\(920\) | −0.146161 | −0.00481880 | ||||||||
\(921\) | −26.8446 | −0.884561 | ||||||||
\(922\) | 43.3703 | 1.42833 | ||||||||
\(923\) | 34.0146 | 1.11960 | ||||||||
\(924\) | −0.886790 | −0.0291732 | ||||||||
\(925\) | −4.08126 | −0.134191 | ||||||||
\(926\) | −32.5347 | −1.06916 | ||||||||
\(927\) | −5.83716 | −0.191717 | ||||||||
\(928\) | 40.5064 | 1.32969 | ||||||||
\(929\) | −4.10494 | −0.134679 | −0.0673394 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673394 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(930\) | −25.6432 | −0.840874 | ||||||||
\(931\) | 46.9178 | 1.53767 | ||||||||
\(932\) | 11.2062 | 0.367072 | ||||||||
\(933\) | 7.67012 | 0.251109 | ||||||||
\(934\) | 68.4659 | 2.24027 | ||||||||
\(935\) | −13.9938 | −0.457645 | ||||||||
\(936\) | 0.490866 | 0.0160444 | ||||||||
\(937\) | 34.4731 | 1.12619 | 0.563094 | − | 0.826393i | \(-0.309611\pi\) | ||||
0.563094 | + | 0.826393i | \(0.309611\pi\) | |||||||
\(938\) | −0.319838 | −0.0104431 | ||||||||
\(939\) | −45.0920 | −1.47152 | ||||||||
\(940\) | 0.803168 | 0.0261964 | ||||||||
\(941\) | 3.84126 | 0.125222 | 0.0626108 | − | 0.998038i | \(-0.480057\pi\) | ||||
0.0626108 | + | 0.998038i | \(0.480057\pi\) | |||||||
\(942\) | 46.4833 | 1.51451 | ||||||||
\(943\) | −0.816733 | −0.0265965 | ||||||||
\(944\) | 31.6914 | 1.03147 | ||||||||
\(945\) | −0.256748 | −0.00835202 | ||||||||
\(946\) | 7.75746 | 0.252217 | ||||||||
\(947\) | 18.5936 | 0.604211 | 0.302106 | − | 0.953274i | \(-0.402310\pi\) | ||||
0.302106 | + | 0.953274i | \(0.402310\pi\) | |||||||
\(948\) | −23.4077 | −0.760245 | ||||||||
\(949\) | −21.5631 | −0.699967 | ||||||||
\(950\) | −56.2084 | −1.82364 | ||||||||
\(951\) | −30.9916 | −1.00497 | ||||||||
\(952\) | −0.0961799 | −0.00311721 | ||||||||
\(953\) | −55.7455 | −1.80577 | −0.902887 | − | 0.429878i | \(-0.858557\pi\) | ||||
−0.902887 | + | 0.429878i | \(0.858557\pi\) | |||||||
\(954\) | 5.00939 | 0.162185 | ||||||||
\(955\) | 9.36990 | 0.303203 | ||||||||
\(956\) | −38.4162 | −1.24247 | ||||||||
\(957\) | −35.4290 | −1.14526 | ||||||||
\(958\) | 43.2261 | 1.39657 | ||||||||
\(959\) | 0.0479762 | 0.00154923 | ||||||||
\(960\) | −17.1193 | −0.552522 | ||||||||
\(961\) | 18.4394 | 0.594820 | ||||||||
\(962\) | 5.20510 | 0.167819 | ||||||||
\(963\) | −2.52389 | −0.0813312 | ||||||||
\(964\) | −15.2833 | −0.492242 | ||||||||
\(965\) | 0.964537 | 0.0310495 | ||||||||
\(966\) | −0.0728461 | −0.00234379 | ||||||||
\(967\) | −21.1291 | −0.679468 | −0.339734 | − | 0.940522i | \(-0.610337\pi\) | ||||
−0.339734 | + | 0.940522i | \(0.610337\pi\) | |||||||
\(968\) | −1.65412 | −0.0531654 | ||||||||
\(969\) | 47.3209 | 1.52017 | ||||||||
\(970\) | −0.215604 | −0.00692264 | ||||||||
\(971\) | 48.9789 | 1.57181 | 0.785903 | − | 0.618349i | \(-0.212198\pi\) | ||||
0.785903 | + | 0.618349i | \(0.212198\pi\) | |||||||
\(972\) | 9.88334 | 0.317008 | ||||||||
\(973\) | 1.20815 | 0.0387315 | ||||||||
\(974\) | 65.4411 | 2.09687 | ||||||||
\(975\) | −19.1611 | −0.613648 | ||||||||
\(976\) | 13.2700 | 0.424762 | ||||||||
\(977\) | −39.0304 | −1.24869 | −0.624346 | − | 0.781148i | \(-0.714634\pi\) | ||||
−0.624346 | + | 0.781148i | \(0.714634\pi\) | |||||||
\(978\) | 3.80486 | 0.121666 | ||||||||
\(979\) | 29.8150 | 0.952893 | ||||||||
\(980\) | 14.8774 | 0.475240 | ||||||||
\(981\) | −1.88265 | −0.0601083 | ||||||||
\(982\) | 58.5628 | 1.86881 | ||||||||
\(983\) | 36.7464 | 1.17203 | 0.586013 | − | 0.810301i | \(-0.300697\pi\) | ||||
0.586013 | + | 0.810301i | \(0.300697\pi\) | |||||||
\(984\) | 1.99534 | 0.0636092 | ||||||||
\(985\) | −13.3399 | −0.425045 | ||||||||
\(986\) | −39.0408 | −1.24331 | ||||||||
\(987\) | 0.0393989 | 0.00125408 | ||||||||
\(988\) | 37.6984 | 1.19935 | ||||||||
\(989\) | 0.335113 | 0.0106560 | ||||||||
\(990\) | 3.25881 | 0.103572 | ||||||||
\(991\) | −18.3602 | −0.583231 | −0.291615 | − | 0.956536i | \(-0.594193\pi\) | ||||
−0.291615 | + | 0.956536i | \(0.594193\pi\) | |||||||
\(992\) | 57.0769 | 1.81219 | ||||||||
\(993\) | 25.4494 | 0.807613 | ||||||||
\(994\) | 1.55207 | 0.0492286 | ||||||||
\(995\) | 4.49837 | 0.142608 | ||||||||
\(996\) | 16.7036 | 0.529273 | ||||||||
\(997\) | −49.9808 | −1.58291 | −0.791455 | − | 0.611228i | \(-0.790676\pi\) | ||||
−0.791455 | + | 0.611228i | \(0.790676\pi\) | |||||||
\(998\) | −71.5166 | −2.26382 | ||||||||
\(999\) | 4.75748 | 0.150520 |
(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 | 6031.2.a.b.1.20 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.b.1.20 | ✓ | 109 | 1.1 | even | 1 | trivial |