Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 22x^{5} + 57x^{4} - 72x^{3} - 96x^{2} + 64x + 61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.72116\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72116 | 1.92415 | 0.962076 | − | 0.272782i | \(-0.0879437\pi\) | ||||
0.962076 | + | 0.272782i | \(0.0879437\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.40472 | 2.70236 | ||||||||
\(5\) | 1.58278 | 0.707839 | 0.353920 | − | 0.935276i | \(-0.384849\pi\) | ||||
0.353920 | + | 0.935276i | \(0.384849\pi\) | |||||||
\(6\) | −2.72116 | −1.11091 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 9.26480 | 3.27560 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.30699 | 1.36199 | ||||||||
\(11\) | 5.54221 | 1.67104 | 0.835519 | − | 0.549461i | \(-0.185167\pi\) | ||||
0.835519 | + | 0.549461i | \(0.185167\pi\) | |||||||
\(12\) | −5.40472 | −1.56021 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.72116 | −0.727261 | ||||||||
\(15\) | −1.58278 | −0.408671 | ||||||||
\(16\) | 14.4016 | 3.60039 | ||||||||
\(17\) | 4.80577 | 1.16557 | 0.582785 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582785 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(18\) | 2.72116 | 0.641384 | ||||||||
\(19\) | −0.892533 | −0.204761 | −0.102381 | − | 0.994745i | \(-0.532646\pi\) | ||||
−0.102381 | + | 0.994745i | \(0.532646\pi\) | |||||||
\(20\) | 8.55447 | 1.91284 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 15.0812 | 3.21533 | ||||||||
\(23\) | −4.63015 | −0.965453 | −0.482726 | − | 0.875771i | \(-0.660353\pi\) | ||||
−0.482726 | + | 0.875771i | \(0.660353\pi\) | |||||||
\(24\) | −9.26480 | −1.89117 | ||||||||
\(25\) | −2.49482 | −0.498963 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.40472 | −1.02140 | ||||||||
\(29\) | −1.88217 | −0.349511 | −0.174755 | − | 0.984612i | \(-0.555913\pi\) | ||||
−0.174755 | + | 0.984612i | \(0.555913\pi\) | |||||||
\(30\) | −4.30699 | −0.786346 | ||||||||
\(31\) | −1.47545 | −0.264998 | −0.132499 | − | 0.991183i | \(-0.542300\pi\) | ||||
−0.132499 | + | 0.991183i | \(0.542300\pi\) | |||||||
\(32\) | 20.6594 | 3.65210 | ||||||||
\(33\) | −5.54221 | −0.964775 | ||||||||
\(34\) | 13.0773 | 2.24273 | ||||||||
\(35\) | −1.58278 | −0.267538 | ||||||||
\(36\) | 5.40472 | 0.900787 | ||||||||
\(37\) | −4.99293 | −0.820832 | −0.410416 | − | 0.911898i | \(-0.634617\pi\) | ||||
−0.410416 | + | 0.911898i | \(0.634617\pi\) | |||||||
\(38\) | −2.42873 | −0.393992 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.6641 | 2.31860 | ||||||||
\(41\) | −9.75924 | −1.52414 | −0.762069 | − | 0.647496i | \(-0.775816\pi\) | ||||
−0.762069 | + | 0.647496i | \(0.775816\pi\) | |||||||
\(42\) | 2.72116 | 0.419884 | ||||||||
\(43\) | 1.01270 | 0.154435 | 0.0772174 | − | 0.997014i | \(-0.475396\pi\) | ||||
0.0772174 | + | 0.997014i | \(0.475396\pi\) | |||||||
\(44\) | 29.9541 | 4.51575 | ||||||||
\(45\) | 1.58278 | 0.235946 | ||||||||
\(46\) | −12.5994 | −1.85768 | ||||||||
\(47\) | −12.5703 | −1.83357 | −0.916783 | − | 0.399385i | \(-0.869224\pi\) | ||||
−0.916783 | + | 0.399385i | \(0.869224\pi\) | |||||||
\(48\) | −14.4016 | −2.07869 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.78880 | −0.960081 | ||||||||
\(51\) | −4.80577 | −0.672942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.25784 | 0.859581 | 0.429790 | − | 0.902929i | \(-0.358587\pi\) | ||||
0.429790 | + | 0.902929i | \(0.358587\pi\) | |||||||
\(54\) | −2.72116 | −0.370303 | ||||||||
\(55\) | 8.77208 | 1.18283 | ||||||||
\(56\) | −9.26480 | −1.23806 | ||||||||
\(57\) | 0.892533 | 0.118219 | ||||||||
\(58\) | −5.12170 | −0.672512 | ||||||||
\(59\) | 3.44690 | 0.448749 | 0.224374 | − | 0.974503i | \(-0.427966\pi\) | ||||
0.224374 | + | 0.974503i | \(0.427966\pi\) | |||||||
\(60\) | −8.55447 | −1.10438 | ||||||||
\(61\) | −3.58549 | −0.459075 | −0.229538 | − | 0.973300i | \(-0.573721\pi\) | ||||
−0.229538 | + | 0.973300i | \(0.573721\pi\) | |||||||
\(62\) | −4.01493 | −0.509896 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 27.4144 | 3.42681 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −15.0812 | −1.85637 | ||||||||
\(67\) | 14.7401 | 1.80078 | 0.900392 | − | 0.435079i | \(-0.143280\pi\) | ||||
0.900392 | + | 0.435079i | \(0.143280\pi\) | |||||||
\(68\) | 25.9738 | 3.14979 | ||||||||
\(69\) | 4.63015 | 0.557404 | ||||||||
\(70\) | −4.30699 | −0.514784 | ||||||||
\(71\) | 13.1398 | 1.55940 | 0.779702 | − | 0.626151i | \(-0.215371\pi\) | ||||
0.779702 | + | 0.626151i | \(0.215371\pi\) | |||||||
\(72\) | 9.26480 | 1.09187 | ||||||||
\(73\) | 5.33654 | 0.624595 | 0.312298 | − | 0.949984i | \(-0.398901\pi\) | ||||
0.312298 | + | 0.949984i | \(0.398901\pi\) | |||||||
\(74\) | −13.5866 | −1.57941 | ||||||||
\(75\) | 2.49482 | 0.288077 | ||||||||
\(76\) | −4.82389 | −0.553339 | ||||||||
\(77\) | −5.54221 | −0.631593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.779028 | 0.0876475 | 0.0438237 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438237 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(80\) | 22.7945 | 2.54850 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −26.5565 | −2.93267 | ||||||||
\(83\) | −1.47136 | −0.161503 | −0.0807513 | − | 0.996734i | \(-0.525732\pi\) | ||||
−0.0807513 | + | 0.996734i | \(0.525732\pi\) | |||||||
\(84\) | 5.40472 | 0.589703 | ||||||||
\(85\) | 7.60646 | 0.825036 | ||||||||
\(86\) | 2.75571 | 0.297156 | ||||||||
\(87\) | 1.88217 | 0.201790 | ||||||||
\(88\) | 51.3474 | 5.47365 | ||||||||
\(89\) | −7.65950 | −0.811905 | −0.405953 | − | 0.913894i | \(-0.633060\pi\) | ||||
−0.405953 | + | 0.913894i | \(0.633060\pi\) | |||||||
\(90\) | 4.30699 | 0.453997 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.0247 | −2.60900 | ||||||||
\(93\) | 1.47545 | 0.152997 | ||||||||
\(94\) | −34.2058 | −3.52806 | ||||||||
\(95\) | −1.41268 | −0.144938 | ||||||||
\(96\) | −20.6594 | −2.10854 | ||||||||
\(97\) | 0.758679 | 0.0770322 | 0.0385161 | − | 0.999258i | \(-0.487737\pi\) | ||||
0.0385161 | + | 0.999258i | \(0.487737\pi\) | |||||||
\(98\) | 2.72116 | 0.274879 | ||||||||
\(99\) | 5.54221 | 0.557013 | ||||||||
\(100\) | −13.4838 | −1.34838 | ||||||||
\(101\) | −11.7740 | −1.17156 | −0.585779 | − | 0.810471i | \(-0.699211\pi\) | ||||
−0.585779 | + | 0.810471i | \(0.699211\pi\) | |||||||
\(102\) | −13.0773 | −1.29484 | ||||||||
\(103\) | 9.61981 | 0.947868 | 0.473934 | − | 0.880560i | \(-0.342833\pi\) | ||||
0.473934 | + | 0.880560i | \(0.342833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.58278 | 0.154463 | ||||||||
\(106\) | 17.0286 | 1.65396 | ||||||||
\(107\) | 3.68918 | 0.356647 | 0.178323 | − | 0.983972i | \(-0.442933\pi\) | ||||
0.178323 | + | 0.983972i | \(0.442933\pi\) | |||||||
\(108\) | −5.40472 | −0.520070 | ||||||||
\(109\) | 8.92215 | 0.854587 | 0.427293 | − | 0.904113i | \(-0.359467\pi\) | ||||
0.427293 | + | 0.904113i | \(0.359467\pi\) | |||||||
\(110\) | 23.8702 | 2.27594 | ||||||||
\(111\) | 4.99293 | 0.473908 | ||||||||
\(112\) | −14.4016 | −1.36082 | ||||||||
\(113\) | 16.1353 | 1.51788 | 0.758941 | − | 0.651159i | \(-0.225717\pi\) | ||||
0.758941 | + | 0.651159i | \(0.225717\pi\) | |||||||
\(114\) | 2.42873 | 0.227471 | ||||||||
\(115\) | −7.32849 | −0.683385 | ||||||||
\(116\) | −10.1726 | −0.944504 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.37958 | 0.863460 | ||||||||
\(119\) | −4.80577 | −0.440544 | ||||||||
\(120\) | −14.6641 | −1.33864 | ||||||||
\(121\) | 19.7161 | 1.79237 | ||||||||
\(122\) | −9.75670 | −0.883330 | ||||||||
\(123\) | 9.75924 | 0.879961 | ||||||||
\(124\) | −7.97437 | −0.716120 | ||||||||
\(125\) | −11.8626 | −1.06103 | ||||||||
\(126\) | −2.72116 | −0.242420 | ||||||||
\(127\) | −4.62457 | −0.410364 | −0.205182 | − | 0.978724i | \(-0.565779\pi\) | ||||
−0.205182 | + | 0.978724i | \(0.565779\pi\) | |||||||
\(128\) | 33.2803 | 2.94159 | ||||||||
\(129\) | −1.01270 | −0.0891630 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.78183 | −0.679902 | −0.339951 | − | 0.940443i | \(-0.610410\pi\) | ||||
−0.339951 | + | 0.940443i | \(0.610410\pi\) | |||||||
\(132\) | −29.9541 | −2.60717 | ||||||||
\(133\) | 0.892533 | 0.0773925 | ||||||||
\(134\) | 40.1101 | 3.46498 | ||||||||
\(135\) | −1.58278 | −0.136224 | ||||||||
\(136\) | 44.5245 | 3.81794 | ||||||||
\(137\) | 0.276352 | 0.0236104 | 0.0118052 | − | 0.999930i | \(-0.496242\pi\) | ||||
0.0118052 | + | 0.999930i | \(0.496242\pi\) | |||||||
\(138\) | 12.5994 | 1.07253 | ||||||||
\(139\) | 3.96065 | 0.335938 | 0.167969 | − | 0.985792i | \(-0.446279\pi\) | ||||
0.167969 | + | 0.985792i | \(0.446279\pi\) | |||||||
\(140\) | −8.55447 | −0.722984 | ||||||||
\(141\) | 12.5703 | 1.05861 | ||||||||
\(142\) | 35.7554 | 3.00053 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 14.4016 | 1.20013 | ||||||||
\(145\) | −2.97906 | −0.247398 | ||||||||
\(146\) | 14.5216 | 1.20182 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −26.9854 | −2.21818 | ||||||||
\(149\) | −21.6897 | −1.77689 | −0.888446 | − | 0.458982i | \(-0.848214\pi\) | ||||
−0.888446 | + | 0.458982i | \(0.848214\pi\) | |||||||
\(150\) | 6.78880 | 0.554303 | ||||||||
\(151\) | −5.66673 | −0.461152 | −0.230576 | − | 0.973054i | \(-0.574061\pi\) | ||||
−0.230576 | + | 0.973054i | \(0.574061\pi\) | |||||||
\(152\) | −8.26914 | −0.670716 | ||||||||
\(153\) | 4.80577 | 0.388523 | ||||||||
\(154\) | −15.0812 | −1.21528 | ||||||||
\(155\) | −2.33530 | −0.187576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.06406 | 0.0849216 | 0.0424608 | − | 0.999098i | \(-0.486480\pi\) | ||||
0.0424608 | + | 0.999098i | \(0.486480\pi\) | |||||||
\(158\) | 2.11986 | 0.168647 | ||||||||
\(159\) | −6.25784 | −0.496279 | ||||||||
\(160\) | 32.6992 | 2.58510 | ||||||||
\(161\) | 4.63015 | 0.364907 | ||||||||
\(162\) | 2.72116 | 0.213795 | ||||||||
\(163\) | −7.20618 | −0.564432 | −0.282216 | − | 0.959351i | \(-0.591069\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591069\pi\) | |||||||
\(164\) | −52.7460 | −4.11877 | ||||||||
\(165\) | −8.77208 | −0.682905 | ||||||||
\(166\) | −4.00380 | −0.310756 | ||||||||
\(167\) | 0.468497 | 0.0362534 | 0.0181267 | − | 0.999836i | \(-0.494230\pi\) | ||||
0.0181267 | + | 0.999836i | \(0.494230\pi\) | |||||||
\(168\) | 9.26480 | 0.714795 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 20.6984 | 1.58749 | ||||||||
\(171\) | −0.892533 | −0.0682537 | ||||||||
\(172\) | 5.47335 | 0.417339 | ||||||||
\(173\) | −10.6101 | −0.806670 | −0.403335 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403335 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(174\) | 5.12170 | 0.388275 | ||||||||
\(175\) | 2.49482 | 0.188590 | ||||||||
\(176\) | 79.8165 | 6.01639 | ||||||||
\(177\) | −3.44690 | −0.259085 | ||||||||
\(178\) | −20.8427 | −1.56223 | ||||||||
\(179\) | −19.3674 | −1.44759 | −0.723793 | − | 0.690017i | \(-0.757603\pi\) | ||||
−0.723793 | + | 0.690017i | \(0.757603\pi\) | |||||||
\(180\) | 8.55447 | 0.637612 | ||||||||
\(181\) | −16.0004 | −1.18930 | −0.594649 | − | 0.803986i | \(-0.702709\pi\) | ||||
−0.594649 | + | 0.803986i | \(0.702709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.58549 | 0.265047 | ||||||||
\(184\) | −42.8974 | −3.16244 | ||||||||
\(185\) | −7.90269 | −0.581017 | ||||||||
\(186\) | 4.01493 | 0.294389 | ||||||||
\(187\) | 26.6346 | 1.94771 | ||||||||
\(188\) | −67.9390 | −4.95496 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −3.84413 | −0.278883 | ||||||||
\(191\) | 3.14831 | 0.227804 | 0.113902 | − | 0.993492i | \(-0.463665\pi\) | ||||
0.113902 | + | 0.993492i | \(0.463665\pi\) | |||||||
\(192\) | −27.4144 | −1.97847 | ||||||||
\(193\) | −23.2821 | −1.67588 | −0.837942 | − | 0.545759i | \(-0.816241\pi\) | ||||
−0.837942 | + | 0.545759i | \(0.816241\pi\) | |||||||
\(194\) | 2.06449 | 0.148222 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.40472 | 0.386052 | ||||||||
\(197\) | −17.6425 | −1.25697 | −0.628487 | − | 0.777820i | \(-0.716325\pi\) | ||||
−0.628487 | + | 0.777820i | \(0.716325\pi\) | |||||||
\(198\) | 15.0812 | 1.07178 | ||||||||
\(199\) | 11.9251 | 0.845348 | 0.422674 | − | 0.906282i | \(-0.361091\pi\) | ||||
0.422674 | + | 0.906282i | \(0.361091\pi\) | |||||||
\(200\) | −23.1140 | −1.63440 | ||||||||
\(201\) | −14.7401 | −1.03968 | ||||||||
\(202\) | −32.0390 | −2.25426 | ||||||||
\(203\) | 1.88217 | 0.132103 | ||||||||
\(204\) | −25.9738 | −1.81853 | ||||||||
\(205\) | −15.4467 | −1.07884 | ||||||||
\(206\) | 26.1771 | 1.82384 | ||||||||
\(207\) | −4.63015 | −0.321818 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.94661 | −0.342164 | ||||||||
\(210\) | 4.30699 | 0.297211 | ||||||||
\(211\) | −15.1302 | −1.04161 | −0.520803 | − | 0.853677i | \(-0.674367\pi\) | ||||
−0.520803 | + | 0.853677i | \(0.674367\pi\) | |||||||
\(212\) | 33.8219 | 2.32290 | ||||||||
\(213\) | −13.1398 | −0.900322 | ||||||||
\(214\) | 10.0389 | 0.686243 | ||||||||
\(215\) | 1.60287 | 0.109315 | ||||||||
\(216\) | −9.26480 | −0.630390 | ||||||||
\(217\) | 1.47545 | 0.100160 | ||||||||
\(218\) | 24.2786 | 1.64435 | ||||||||
\(219\) | −5.33654 | −0.360610 | ||||||||
\(220\) | 47.4106 | 3.19642 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 13.5866 | 0.911870 | ||||||||
\(223\) | −19.1562 | −1.28280 | −0.641398 | − | 0.767208i | \(-0.721645\pi\) | ||||
−0.641398 | + | 0.767208i | \(0.721645\pi\) | |||||||
\(224\) | −20.6594 | −1.38036 | ||||||||
\(225\) | −2.49482 | −0.166321 | ||||||||
\(226\) | 43.9068 | 2.92064 | ||||||||
\(227\) | 17.4419 | 1.15766 | 0.578831 | − | 0.815447i | \(-0.303509\pi\) | ||||
0.578831 | + | 0.815447i | \(0.303509\pi\) | |||||||
\(228\) | 4.82389 | 0.319470 | ||||||||
\(229\) | 10.5075 | 0.694354 | 0.347177 | − | 0.937800i | \(-0.387140\pi\) | ||||
0.347177 | + | 0.937800i | \(0.387140\pi\) | |||||||
\(230\) | −19.9420 | −1.31494 | ||||||||
\(231\) | 5.54221 | 0.364650 | ||||||||
\(232\) | −17.4380 | −1.14486 | ||||||||
\(233\) | −9.69049 | −0.634845 | −0.317422 | − | 0.948284i | \(-0.602817\pi\) | ||||
−0.317422 | + | 0.948284i | \(0.602817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.8960 | −1.29787 | ||||||||
\(236\) | 18.6296 | 1.21268 | ||||||||
\(237\) | −0.779028 | −0.0506033 | ||||||||
\(238\) | −13.0773 | −0.847673 | ||||||||
\(239\) | 18.4302 | 1.19215 | 0.596074 | − | 0.802929i | \(-0.296726\pi\) | ||||
0.596074 | + | 0.802929i | \(0.296726\pi\) | |||||||
\(240\) | −22.7945 | −1.47138 | ||||||||
\(241\) | 15.3530 | 0.988977 | 0.494488 | − | 0.869184i | \(-0.335355\pi\) | ||||
0.494488 | + | 0.869184i | \(0.335355\pi\) | |||||||
\(242\) | 53.6506 | 3.44879 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.3786 | −1.24059 | ||||||||
\(245\) | 1.58278 | 0.101120 | ||||||||
\(246\) | 26.5565 | 1.69318 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −13.6697 | −0.868027 | ||||||||
\(249\) | 1.47136 | 0.0932436 | ||||||||
\(250\) | −32.2801 | −2.04157 | ||||||||
\(251\) | 8.62900 | 0.544658 | 0.272329 | − | 0.962204i | \(-0.412206\pi\) | ||||
0.272329 | + | 0.962204i | \(0.412206\pi\) | |||||||
\(252\) | −5.40472 | −0.340465 | ||||||||
\(253\) | −25.6612 | −1.61331 | ||||||||
\(254\) | −12.5842 | −0.789602 | ||||||||
\(255\) | −7.60646 | −0.476335 | ||||||||
\(256\) | 35.7323 | 2.23327 | ||||||||
\(257\) | 2.72949 | 0.170261 | 0.0851305 | − | 0.996370i | \(-0.472869\pi\) | ||||
0.0851305 | + | 0.996370i | \(0.472869\pi\) | |||||||
\(258\) | −2.75571 | −0.171563 | ||||||||
\(259\) | 4.99293 | 0.310245 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.88217 | −0.116504 | ||||||||
\(262\) | −21.1756 | −1.30823 | ||||||||
\(263\) | −5.61419 | −0.346186 | −0.173093 | − | 0.984906i | \(-0.555376\pi\) | ||||
−0.173093 | + | 0.984906i | \(0.555376\pi\) | |||||||
\(264\) | −51.3474 | −3.16022 | ||||||||
\(265\) | 9.90477 | 0.608445 | ||||||||
\(266\) | 2.42873 | 0.148915 | ||||||||
\(267\) | 7.65950 | 0.468754 | ||||||||
\(268\) | 79.6659 | 4.86637 | ||||||||
\(269\) | −0.182236 | −0.0111111 | −0.00555556 | − | 0.999985i | \(-0.501768\pi\) | ||||
−0.00555556 | + | 0.999985i | \(0.501768\pi\) | |||||||
\(270\) | −4.30699 | −0.262115 | ||||||||
\(271\) | 29.3326 | 1.78183 | 0.890914 | − | 0.454173i | \(-0.150065\pi\) | ||||
0.890914 | + | 0.454173i | \(0.150065\pi\) | |||||||
\(272\) | 69.2106 | 4.19651 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.752000 | 0.0454300 | ||||||||
\(275\) | −13.8268 | −0.833787 | ||||||||
\(276\) | 25.0247 | 1.50631 | ||||||||
\(277\) | −16.1748 | −0.971849 | −0.485924 | − | 0.874001i | \(-0.661517\pi\) | ||||
−0.485924 | + | 0.874001i | \(0.661517\pi\) | |||||||
\(278\) | 10.7776 | 0.646395 | ||||||||
\(279\) | −1.47545 | −0.0883326 | ||||||||
\(280\) | −14.6641 | −0.876348 | ||||||||
\(281\) | −3.71644 | −0.221704 | −0.110852 | − | 0.993837i | \(-0.535358\pi\) | ||||
−0.110852 | + | 0.993837i | \(0.535358\pi\) | |||||||
\(282\) | 34.2058 | 2.03693 | ||||||||
\(283\) | 3.77370 | 0.224323 | 0.112162 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112162 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(284\) | 71.0168 | 4.21407 | ||||||||
\(285\) | 1.41268 | 0.0836800 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.75924 | 0.576070 | ||||||||
\(288\) | 20.6594 | 1.21737 | ||||||||
\(289\) | 6.09539 | 0.358553 | ||||||||
\(290\) | −8.10651 | −0.476030 | ||||||||
\(291\) | −0.758679 | −0.0444746 | ||||||||
\(292\) | 28.8425 | 1.68788 | ||||||||
\(293\) | 15.4163 | 0.900631 | 0.450316 | − | 0.892869i | \(-0.351311\pi\) | ||||
0.450316 | + | 0.892869i | \(0.351311\pi\) | |||||||
\(294\) | −2.72116 | −0.158701 | ||||||||
\(295\) | 5.45568 | 0.317642 | ||||||||
\(296\) | −46.2585 | −2.68872 | ||||||||
\(297\) | −5.54221 | −0.321592 | ||||||||
\(298\) | −59.0212 | −3.41901 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.4838 | 0.778487 | ||||||||
\(301\) | −1.01270 | −0.0583709 | ||||||||
\(302\) | −15.4201 | −0.887326 | ||||||||
\(303\) | 11.7740 | 0.676400 | ||||||||
\(304\) | −12.8539 | −0.737221 | ||||||||
\(305\) | −5.67503 | −0.324952 | ||||||||
\(306\) | 13.0773 | 0.747578 | ||||||||
\(307\) | −33.2617 | −1.89834 | −0.949172 | − | 0.314758i | \(-0.898077\pi\) | ||||
−0.949172 | + | 0.314758i | \(0.898077\pi\) | |||||||
\(308\) | −29.9541 | −1.70679 | ||||||||
\(309\) | −9.61981 | −0.547252 | ||||||||
\(310\) | −6.35473 | −0.360925 | ||||||||
\(311\) | −5.28263 | −0.299551 | −0.149775 | − | 0.988720i | \(-0.547855\pi\) | ||||
−0.149775 | + | 0.988720i | \(0.547855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4853 | −0.988329 | −0.494165 | − | 0.869368i | \(-0.664526\pi\) | ||||
−0.494165 | + | 0.869368i | \(0.664526\pi\) | |||||||
\(314\) | 2.89549 | 0.163402 | ||||||||
\(315\) | −1.58278 | −0.0891794 | ||||||||
\(316\) | 4.21043 | 0.236855 | ||||||||
\(317\) | 6.89451 | 0.387234 | 0.193617 | − | 0.981077i | \(-0.437978\pi\) | ||||
0.193617 | + | 0.981077i | \(0.437978\pi\) | |||||||
\(318\) | −17.0286 | −0.954917 | ||||||||
\(319\) | −10.4314 | −0.584046 | ||||||||
\(320\) | 43.3909 | 2.42563 | ||||||||
\(321\) | −3.68918 | −0.205910 | ||||||||
\(322\) | 12.5994 | 0.702136 | ||||||||
\(323\) | −4.28931 | −0.238663 | ||||||||
\(324\) | 5.40472 | 0.300262 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.6092 | −1.08605 | ||||||||
\(327\) | −8.92215 | −0.493396 | ||||||||
\(328\) | −90.4174 | −4.99247 | ||||||||
\(329\) | 12.5703 | 0.693023 | ||||||||
\(330\) | −23.8702 | −1.31401 | ||||||||
\(331\) | 3.00614 | 0.165233 | 0.0826163 | − | 0.996581i | \(-0.473672\pi\) | ||||
0.0826163 | + | 0.996581i | \(0.473672\pi\) | |||||||
\(332\) | −7.95228 | −0.436438 | ||||||||
\(333\) | −4.99293 | −0.273611 | ||||||||
\(334\) | 1.27486 | 0.0697571 | ||||||||
\(335\) | 23.3302 | 1.27467 | ||||||||
\(336\) | 14.4016 | 0.785670 | ||||||||
\(337\) | −7.21913 | −0.393251 | −0.196626 | − | 0.980479i | \(-0.562998\pi\) | ||||
−0.196626 | + | 0.980479i | \(0.562998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1353 | −0.876350 | ||||||||
\(340\) | 41.1108 | 2.22954 | ||||||||
\(341\) | −8.17723 | −0.442822 | ||||||||
\(342\) | −2.42873 | −0.131331 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.38243 | 0.505867 | ||||||||
\(345\) | 7.32849 | 0.394553 | ||||||||
\(346\) | −28.8718 | −1.55216 | ||||||||
\(347\) | 1.92476 | 0.103327 | 0.0516633 | − | 0.998665i | \(-0.483548\pi\) | ||||
0.0516633 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(348\) | 10.1726 | 0.545310 | ||||||||
\(349\) | −3.25971 | −0.174488 | −0.0872441 | − | 0.996187i | \(-0.527806\pi\) | ||||
−0.0872441 | + | 0.996187i | \(0.527806\pi\) | |||||||
\(350\) | 6.78880 | 0.362877 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 114.499 | 6.10280 | ||||||||
\(353\) | 8.91285 | 0.474383 | 0.237192 | − | 0.971463i | \(-0.423773\pi\) | ||||
0.237192 | + | 0.971463i | \(0.423773\pi\) | |||||||
\(354\) | −9.37958 | −0.498519 | ||||||||
\(355\) | 20.7973 | 1.10381 | ||||||||
\(356\) | −41.3974 | −2.19406 | ||||||||
\(357\) | 4.80577 | 0.254348 | ||||||||
\(358\) | −52.7018 | −2.78537 | ||||||||
\(359\) | 20.1320 | 1.06253 | 0.531263 | − | 0.847207i | \(-0.321718\pi\) | ||||
0.531263 | + | 0.847207i | \(0.321718\pi\) | |||||||
\(360\) | 14.6641 | 0.772866 | ||||||||
\(361\) | −18.2034 | −0.958073 | ||||||||
\(362\) | −43.5396 | −2.28839 | ||||||||
\(363\) | −19.7161 | −1.03483 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.44656 | 0.442113 | ||||||||
\(366\) | 9.75670 | 0.509991 | ||||||||
\(367\) | −31.3418 | −1.63603 | −0.818013 | − | 0.575200i | \(-0.804924\pi\) | ||||
−0.818013 | + | 0.575200i | \(0.804924\pi\) | |||||||
\(368\) | −66.6814 | −3.47601 | ||||||||
\(369\) | −9.75924 | −0.508046 | ||||||||
\(370\) | −21.5045 | −1.11797 | ||||||||
\(371\) | −6.25784 | −0.324891 | ||||||||
\(372\) | 7.97437 | 0.413452 | ||||||||
\(373\) | 17.9434 | 0.929077 | 0.464538 | − | 0.885553i | \(-0.346220\pi\) | ||||
0.464538 | + | 0.885553i | \(0.346220\pi\) | |||||||
\(374\) | 72.4769 | 3.74769 | ||||||||
\(375\) | 11.8626 | 0.612583 | ||||||||
\(376\) | −116.461 | −6.00603 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.72116 | 0.139961 | ||||||||
\(379\) | 20.1477 | 1.03492 | 0.517458 | − | 0.855709i | \(-0.326878\pi\) | ||||
0.517458 | + | 0.855709i | \(0.326878\pi\) | |||||||
\(380\) | −7.63515 | −0.391675 | ||||||||
\(381\) | 4.62457 | 0.236924 | ||||||||
\(382\) | 8.56705 | 0.438329 | ||||||||
\(383\) | 37.5129 | 1.91682 | 0.958410 | − | 0.285393i | \(-0.0921242\pi\) | ||||
0.958410 | + | 0.285393i | \(0.0921242\pi\) | |||||||
\(384\) | −33.2803 | −1.69833 | ||||||||
\(385\) | −8.77208 | −0.447067 | ||||||||
\(386\) | −63.3544 | −3.22466 | ||||||||
\(387\) | 1.01270 | 0.0514783 | ||||||||
\(388\) | 4.10045 | 0.208169 | ||||||||
\(389\) | −23.1946 | −1.17601 | −0.588006 | − | 0.808857i | \(-0.700087\pi\) | ||||
−0.588006 | + | 0.808857i | \(0.700087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.2514 | −1.12530 | ||||||||
\(392\) | 9.26480 | 0.467943 | ||||||||
\(393\) | 7.78183 | 0.392541 | ||||||||
\(394\) | −48.0080 | −2.41861 | ||||||||
\(395\) | 1.23303 | 0.0620403 | ||||||||
\(396\) | 29.9541 | 1.50525 | ||||||||
\(397\) | −38.1606 | −1.91522 | −0.957612 | − | 0.288060i | \(-0.906990\pi\) | ||||
−0.957612 | + | 0.288060i | \(0.906990\pi\) | |||||||
\(398\) | 32.4501 | 1.62658 | ||||||||
\(399\) | −0.892533 | −0.0446826 | ||||||||
\(400\) | −35.9293 | −1.79646 | ||||||||
\(401\) | −8.28812 | −0.413889 | −0.206944 | − | 0.978353i | \(-0.566352\pi\) | ||||
−0.206944 | + | 0.978353i | \(0.566352\pi\) | |||||||
\(402\) | −40.1101 | −2.00051 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −63.6353 | −3.16597 | ||||||||
\(405\) | 1.58278 | 0.0786488 | ||||||||
\(406\) | 5.12170 | 0.254186 | ||||||||
\(407\) | −27.6718 | −1.37164 | ||||||||
\(408\) | −44.5245 | −2.20429 | ||||||||
\(409\) | 39.1125 | 1.93399 | 0.966994 | − | 0.254800i | \(-0.0820095\pi\) | ||||
0.966994 | + | 0.254800i | \(0.0820095\pi\) | |||||||
\(410\) | −42.0330 | −2.07586 | ||||||||
\(411\) | −0.276352 | −0.0136315 | ||||||||
\(412\) | 51.9924 | 2.56148 | ||||||||
\(413\) | −3.44690 | −0.169611 | ||||||||
\(414\) | −12.5994 | −0.619226 | ||||||||
\(415\) | −2.32883 | −0.114318 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.96065 | −0.193954 | ||||||||
\(418\) | −13.4605 | −0.658375 | ||||||||
\(419\) | 27.5466 | 1.34574 | 0.672869 | − | 0.739762i | \(-0.265062\pi\) | ||||
0.672869 | + | 0.739762i | \(0.265062\pi\) | |||||||
\(420\) | 8.55447 | 0.417415 | ||||||||
\(421\) | 34.1236 | 1.66308 | 0.831540 | − | 0.555465i | \(-0.187460\pi\) | ||||
0.831540 | + | 0.555465i | \(0.187460\pi\) | |||||||
\(422\) | −41.1717 | −2.00421 | ||||||||
\(423\) | −12.5703 | −0.611189 | ||||||||
\(424\) | 57.9776 | 2.81564 | ||||||||
\(425\) | −11.9895 | −0.581577 | ||||||||
\(426\) | −35.7554 | −1.73236 | ||||||||
\(427\) | 3.58549 | 0.173514 | ||||||||
\(428\) | 19.9390 | 0.963788 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.36168 | 0.210339 | ||||||||
\(431\) | −5.00089 | −0.240884 | −0.120442 | − | 0.992720i | \(-0.538431\pi\) | ||||
−0.120442 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(432\) | −14.4016 | −0.692896 | ||||||||
\(433\) | 14.9136 | 0.716701 | 0.358351 | − | 0.933587i | \(-0.383339\pi\) | ||||
0.358351 | + | 0.933587i | \(0.383339\pi\) | |||||||
\(434\) | 4.01493 | 0.192723 | ||||||||
\(435\) | 2.97906 | 0.142835 | ||||||||
\(436\) | 48.2217 | 2.30940 | ||||||||
\(437\) | 4.13256 | 0.197687 | ||||||||
\(438\) | −14.5216 | −0.693869 | ||||||||
\(439\) | −7.10276 | −0.338996 | −0.169498 | − | 0.985531i | \(-0.554215\pi\) | ||||
−0.169498 | + | 0.985531i | \(0.554215\pi\) | |||||||
\(440\) | 81.2715 | 3.87447 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.63166 | −0.220057 | −0.110028 | − | 0.993928i | \(-0.535094\pi\) | ||||
−0.110028 | + | 0.993928i | \(0.535094\pi\) | |||||||
\(444\) | 26.9854 | 1.28067 | ||||||||
\(445\) | −12.1233 | −0.574698 | ||||||||
\(446\) | −52.1272 | −2.46830 | ||||||||
\(447\) | 21.6897 | 1.02589 | ||||||||
\(448\) | −27.4144 | −1.29521 | ||||||||
\(449\) | −22.5728 | −1.06528 | −0.532639 | − | 0.846343i | \(-0.678800\pi\) | ||||
−0.532639 | + | 0.846343i | \(0.678800\pi\) | |||||||
\(450\) | −6.78880 | −0.320027 | ||||||||
\(451\) | −54.0878 | −2.54689 | ||||||||
\(452\) | 87.2069 | 4.10187 | ||||||||
\(453\) | 5.66673 | 0.266246 | ||||||||
\(454\) | 47.4624 | 2.22752 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.26914 | 0.387238 | ||||||||
\(457\) | 29.8125 | 1.39457 | 0.697286 | − | 0.716793i | \(-0.254391\pi\) | ||||
0.697286 | + | 0.716793i | \(0.254391\pi\) | |||||||
\(458\) | 28.5926 | 1.33604 | ||||||||
\(459\) | −4.80577 | −0.224314 | ||||||||
\(460\) | −39.6085 | −1.84675 | ||||||||
\(461\) | 15.3366 | 0.714299 | 0.357149 | − | 0.934047i | \(-0.383749\pi\) | ||||
0.357149 | + | 0.934047i | \(0.383749\pi\) | |||||||
\(462\) | 15.0812 | 0.701643 | ||||||||
\(463\) | −13.7066 | −0.636998 | −0.318499 | − | 0.947923i | \(-0.603179\pi\) | ||||
−0.318499 | + | 0.947923i | \(0.603179\pi\) | |||||||
\(464\) | −27.1063 | −1.25838 | ||||||||
\(465\) | 2.33530 | 0.108297 | ||||||||
\(466\) | −26.3694 | −1.22154 | ||||||||
\(467\) | −41.2833 | −1.91036 | −0.955182 | − | 0.296020i | \(-0.904341\pi\) | ||||
−0.955182 | + | 0.296020i | \(0.904341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7401 | −0.680633 | ||||||||
\(470\) | −54.1402 | −2.49730 | ||||||||
\(471\) | −1.06406 | −0.0490295 | ||||||||
\(472\) | 31.9349 | 1.46992 | ||||||||
\(473\) | 5.61258 | 0.258067 | ||||||||
\(474\) | −2.11986 | −0.0973684 | ||||||||
\(475\) | 2.22671 | 0.102168 | ||||||||
\(476\) | −25.9738 | −1.19051 | ||||||||
\(477\) | 6.25784 | 0.286527 | ||||||||
\(478\) | 50.1514 | 2.29387 | ||||||||
\(479\) | 3.06705 | 0.140137 | 0.0700685 | − | 0.997542i | \(-0.477678\pi\) | ||||
0.0700685 | + | 0.997542i | \(0.477678\pi\) | |||||||
\(480\) | −32.6992 | −1.49251 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 41.7781 | 1.90294 | ||||||||
\(483\) | −4.63015 | −0.210679 | ||||||||
\(484\) | 106.560 | 4.84363 | ||||||||
\(485\) | 1.20082 | 0.0545264 | ||||||||
\(486\) | −2.72116 | −0.123434 | ||||||||
\(487\) | −8.27973 | −0.375190 | −0.187595 | − | 0.982246i | \(-0.560069\pi\) | ||||
−0.187595 | + | 0.982246i | \(0.560069\pi\) | |||||||
\(488\) | −33.2189 | −1.50375 | ||||||||
\(489\) | 7.20618 | 0.325875 | ||||||||
\(490\) | 4.30699 | 0.194570 | ||||||||
\(491\) | −4.97954 | −0.224724 | −0.112362 | − | 0.993667i | \(-0.535842\pi\) | ||||
−0.112362 | + | 0.993667i | \(0.535842\pi\) | |||||||
\(492\) | 52.7460 | 2.37797 | ||||||||
\(493\) | −9.04529 | −0.407379 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.77208 | 0.394276 | ||||||||
\(496\) | −21.2487 | −0.954096 | ||||||||
\(497\) | −13.1398 | −0.589399 | ||||||||
\(498\) | 4.00380 | 0.179415 | ||||||||
\(499\) | 0.00121934 | 5.45852e−5 0 | 2.72926e−5 | − | 1.00000i | \(-0.499991\pi\) | ||||
2.72926e−5 | 1.00000i | \(0.499991\pi\) | ||||||||
\(500\) | −64.1142 | −2.86727 | ||||||||
\(501\) | −0.468497 | −0.0209309 | ||||||||
\(502\) | 23.4809 | 1.04800 | ||||||||
\(503\) | −13.3194 | −0.593881 | −0.296941 | − | 0.954896i | \(-0.595966\pi\) | ||||
−0.296941 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(504\) | −9.26480 | −0.412687 | ||||||||
\(505\) | −18.6356 | −0.829275 | ||||||||
\(506\) | −69.8284 | −3.10425 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.9945 | −1.10895 | ||||||||
\(509\) | 24.9832 | 1.10736 | 0.553682 | − | 0.832729i | \(-0.313223\pi\) | ||||
0.553682 | + | 0.832729i | \(0.313223\pi\) | |||||||
\(510\) | −20.6984 | −0.916541 | ||||||||
\(511\) | −5.33654 | −0.236075 | ||||||||
\(512\) | 30.6726 | 1.35555 | ||||||||
\(513\) | 0.892533 | 0.0394063 | ||||||||
\(514\) | 7.42738 | 0.327608 | ||||||||
\(515\) | 15.2260 | 0.670939 | ||||||||
\(516\) | −5.47335 | −0.240951 | ||||||||
\(517\) | −69.6672 | −3.06396 | ||||||||
\(518\) | 13.5866 | 0.596959 | ||||||||
\(519\) | 10.6101 | 0.465731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3265 | 1.28482 | 0.642409 | − | 0.766362i | \(-0.277935\pi\) | ||||
0.642409 | + | 0.766362i | \(0.277935\pi\) | |||||||
\(522\) | −5.12170 | −0.224171 | ||||||||
\(523\) | 11.4512 | 0.500726 | 0.250363 | − | 0.968152i | \(-0.419450\pi\) | ||||
0.250363 | + | 0.968152i | \(0.419450\pi\) | |||||||
\(524\) | −42.0586 | −1.83734 | ||||||||
\(525\) | −2.49482 | −0.108883 | ||||||||
\(526\) | −15.2771 | −0.666114 | ||||||||
\(527\) | −7.09065 | −0.308874 | ||||||||
\(528\) | −79.8165 | −3.47357 | ||||||||
\(529\) | −1.56172 | −0.0679010 | ||||||||
\(530\) | 26.9525 | 1.17074 | ||||||||
\(531\) | 3.44690 | 0.149583 | ||||||||
\(532\) | 4.82389 | 0.209142 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.8427 | 0.901953 | ||||||||
\(535\) | 5.83915 | 0.252449 | ||||||||
\(536\) | 136.564 | 5.89865 | ||||||||
\(537\) | 19.3674 | 0.835764 | ||||||||
\(538\) | −0.495894 | −0.0213795 | ||||||||
\(539\) | 5.54221 | 0.238720 | ||||||||
\(540\) | −8.55447 | −0.368126 | ||||||||
\(541\) | −7.24411 | −0.311449 | −0.155724 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155724 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(542\) | 79.8187 | 3.42851 | ||||||||
\(543\) | 16.0004 | 0.686641 | ||||||||
\(544\) | 99.2843 | 4.25678 | ||||||||
\(545\) | 14.1218 | 0.604910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.3579 | 1.04147 | 0.520735 | − | 0.853718i | \(-0.325658\pi\) | ||||
0.520735 | + | 0.853718i | \(0.325658\pi\) | |||||||
\(548\) | 1.49361 | 0.0638038 | ||||||||
\(549\) | −3.58549 | −0.153025 | ||||||||
\(550\) | −37.6249 | −1.60433 | ||||||||
\(551\) | 1.67990 | 0.0715663 | ||||||||
\(552\) | 42.8974 | 1.82583 | ||||||||
\(553\) | −0.779028 | −0.0331276 | ||||||||
\(554\) | −44.0142 | −1.86998 | ||||||||
\(555\) | 7.90269 | 0.335450 | ||||||||
\(556\) | 21.4062 | 0.907825 | ||||||||
\(557\) | −4.14744 | −0.175733 | −0.0878664 | − | 0.996132i | \(-0.528005\pi\) | ||||
−0.0878664 | + | 0.996132i | \(0.528005\pi\) | |||||||
\(558\) | −4.01493 | −0.169965 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −22.7945 | −0.963242 | ||||||||
\(561\) | −26.6346 | −1.12451 | ||||||||
\(562\) | −10.1130 | −0.426593 | ||||||||
\(563\) | −0.967864 | −0.0407906 | −0.0203953 | − | 0.999792i | \(-0.506492\pi\) | ||||
−0.0203953 | + | 0.999792i | \(0.506492\pi\) | |||||||
\(564\) | 67.9390 | 2.86075 | ||||||||
\(565\) | 25.5386 | 1.07442 | ||||||||
\(566\) | 10.2688 | 0.431632 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 121.737 | 5.10798 | ||||||||
\(569\) | −12.1746 | −0.510386 | −0.255193 | − | 0.966890i | \(-0.582139\pi\) | ||||
−0.255193 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(570\) | 3.84413 | 0.161013 | ||||||||
\(571\) | 28.8995 | 1.20941 | 0.604703 | − | 0.796451i | \(-0.293292\pi\) | ||||
0.604703 | + | 0.796451i | \(0.293292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.14831 | −0.131522 | ||||||||
\(574\) | 26.5565 | 1.10845 | ||||||||
\(575\) | 11.5514 | 0.481726 | ||||||||
\(576\) | 27.4144 | 1.14227 | ||||||||
\(577\) | 14.5003 | 0.603657 | 0.301828 | − | 0.953362i | \(-0.402403\pi\) | ||||
0.301828 | + | 0.953362i | \(0.402403\pi\) | |||||||
\(578\) | 16.5866 | 0.689910 | ||||||||
\(579\) | 23.2821 | 0.967572 | ||||||||
\(580\) | −16.1010 | −0.668557 | ||||||||
\(581\) | 1.47136 | 0.0610422 | ||||||||
\(582\) | −2.06449 | −0.0855758 | ||||||||
\(583\) | 34.6823 | 1.43639 | ||||||||
\(584\) | 49.4420 | 2.04592 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.9503 | 1.73295 | ||||||||
\(587\) | 27.7697 | 1.14618 | 0.573090 | − | 0.819493i | \(-0.305745\pi\) | ||||
0.573090 | + | 0.819493i | \(0.305745\pi\) | |||||||
\(588\) | −5.40472 | −0.222887 | ||||||||
\(589\) | 1.31688 | 0.0542613 | ||||||||
\(590\) | 14.8458 | 0.611191 | ||||||||
\(591\) | 17.6425 | 0.725714 | ||||||||
\(592\) | −71.9060 | −2.95532 | ||||||||
\(593\) | 8.09800 | 0.332545 | 0.166273 | − | 0.986080i | \(-0.446827\pi\) | ||||
0.166273 | + | 0.986080i | \(0.446827\pi\) | |||||||
\(594\) | −15.0812 | −0.618791 | ||||||||
\(595\) | −7.60646 | −0.311834 | ||||||||
\(596\) | −117.227 | −4.80180 | ||||||||
\(597\) | −11.9251 | −0.488062 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.8054 | 0.523216 | 0.261608 | − | 0.965174i | \(-0.415747\pi\) | ||||
0.261608 | + | 0.965174i | \(0.415747\pi\) | |||||||
\(600\) | 23.1140 | 0.943624 | ||||||||
\(601\) | −17.8049 | −0.726277 | −0.363138 | − | 0.931735i | \(-0.618295\pi\) | ||||
−0.363138 | + | 0.931735i | \(0.618295\pi\) | |||||||
\(602\) | −2.75571 | −0.112314 | ||||||||
\(603\) | 14.7401 | 0.600262 | ||||||||
\(604\) | −30.6271 | −1.24620 | ||||||||
\(605\) | 31.2061 | 1.26871 | ||||||||
\(606\) | 32.0390 | 1.30150 | ||||||||
\(607\) | 6.10155 | 0.247654 | 0.123827 | − | 0.992304i | \(-0.460483\pi\) | ||||
0.123827 | + | 0.992304i | \(0.460483\pi\) | |||||||
\(608\) | −18.4392 | −0.747809 | ||||||||
\(609\) | −1.88217 | −0.0762695 | ||||||||
\(610\) | −15.4427 | −0.625256 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 25.9738 | 1.04993 | ||||||||
\(613\) | −17.0386 | −0.688184 | −0.344092 | − | 0.938936i | \(-0.611813\pi\) | ||||
−0.344092 | + | 0.938936i | \(0.611813\pi\) | |||||||
\(614\) | −90.5104 | −3.65270 | ||||||||
\(615\) | 15.4467 | 0.622871 | ||||||||
\(616\) | −51.3474 | −2.06885 | ||||||||
\(617\) | 25.3413 | 1.02020 | 0.510102 | − | 0.860114i | \(-0.329608\pi\) | ||||
0.510102 | + | 0.860114i | \(0.329608\pi\) | |||||||
\(618\) | −26.1771 | −1.05300 | ||||||||
\(619\) | 45.5457 | 1.83064 | 0.915319 | − | 0.402731i | \(-0.131939\pi\) | ||||
0.915319 | + | 0.402731i | \(0.131939\pi\) | |||||||
\(620\) | −12.6217 | −0.506898 | ||||||||
\(621\) | 4.63015 | 0.185801 | ||||||||
\(622\) | −14.3749 | −0.576381 | ||||||||
\(623\) | 7.65950 | 0.306871 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.30180 | −0.252072 | ||||||||
\(626\) | −47.5804 | −1.90170 | ||||||||
\(627\) | 4.94661 | 0.197548 | ||||||||
\(628\) | 5.75097 | 0.229489 | ||||||||
\(629\) | −23.9948 | −0.956737 | ||||||||
\(630\) | −4.30699 | −0.171595 | ||||||||
\(631\) | 1.98817 | 0.0791477 | 0.0395739 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395739 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(632\) | 7.21754 | 0.287098 | ||||||||
\(633\) | 15.1302 | 0.601372 | ||||||||
\(634\) | 18.7611 | 0.745097 | ||||||||
\(635\) | −7.31966 | −0.290472 | ||||||||
\(636\) | −33.8219 | −1.34113 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −28.3855 | −1.12379 | ||||||||
\(639\) | 13.1398 | 0.519801 | ||||||||
\(640\) | 52.6753 | 2.08218 | ||||||||
\(641\) | −13.6949 | −0.540917 | −0.270459 | − | 0.962732i | \(-0.587175\pi\) | ||||
−0.270459 | + | 0.962732i | \(0.587175\pi\) | |||||||
\(642\) | −10.0389 | −0.396202 | ||||||||
\(643\) | −19.3516 | −0.763153 | −0.381576 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381576 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(644\) | 25.0247 | 0.986110 | ||||||||
\(645\) | −1.60287 | −0.0631131 | ||||||||
\(646\) | −11.6719 | −0.459225 | ||||||||
\(647\) | −36.6708 | −1.44168 | −0.720839 | − | 0.693103i | \(-0.756243\pi\) | ||||
−0.720839 | + | 0.693103i | \(0.756243\pi\) | |||||||
\(648\) | 9.26480 | 0.363956 | ||||||||
\(649\) | 19.1035 | 0.749876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.47545 | −0.0578273 | ||||||||
\(652\) | −38.9474 | −1.52530 | ||||||||
\(653\) | −15.5962 | −0.610325 | −0.305163 | − | 0.952300i | \(-0.598711\pi\) | ||||
−0.305163 | + | 0.952300i | \(0.598711\pi\) | |||||||
\(654\) | −24.2786 | −0.949368 | ||||||||
\(655\) | −12.3169 | −0.481261 | ||||||||
\(656\) | −140.548 | −5.48749 | ||||||||
\(657\) | 5.33654 | 0.208198 | ||||||||
\(658\) | 34.2058 | 1.33348 | ||||||||
\(659\) | −27.4628 | −1.06980 | −0.534900 | − | 0.844915i | \(-0.679651\pi\) | ||||
−0.534900 | + | 0.844915i | \(0.679651\pi\) | |||||||
\(660\) | −47.4106 | −1.84546 | ||||||||
\(661\) | 15.2896 | 0.594697 | 0.297348 | − | 0.954769i | \(-0.403898\pi\) | ||||
0.297348 | + | 0.954769i | \(0.403898\pi\) | |||||||
\(662\) | 8.18021 | 0.317933 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.6318 | −0.529018 | ||||||||
\(665\) | 1.41268 | 0.0547814 | ||||||||
\(666\) | −13.5866 | −0.526469 | ||||||||
\(667\) | 8.71474 | 0.337436 | ||||||||
\(668\) | 2.53210 | 0.0979698 | ||||||||
\(669\) | 19.1562 | 0.740623 | ||||||||
\(670\) | 63.4853 | 2.45265 | ||||||||
\(671\) | −19.8715 | −0.767132 | ||||||||
\(672\) | 20.6594 | 0.796954 | ||||||||
\(673\) | −24.8576 | −0.958188 | −0.479094 | − | 0.877764i | \(-0.659035\pi\) | ||||
−0.479094 | + | 0.877764i | \(0.659035\pi\) | |||||||
\(674\) | −19.6444 | −0.756675 | ||||||||
\(675\) | 2.49482 | 0.0960256 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.31671 | −0.165905 | −0.0829523 | − | 0.996554i | \(-0.526435\pi\) | ||||
−0.0829523 | + | 0.996554i | \(0.526435\pi\) | |||||||
\(678\) | −43.9068 | −1.68623 | ||||||||
\(679\) | −0.758679 | −0.0291154 | ||||||||
\(680\) | 70.4723 | 2.70249 | ||||||||
\(681\) | −17.4419 | −0.668377 | ||||||||
\(682\) | −22.2516 | −0.852056 | ||||||||
\(683\) | 37.6467 | 1.44051 | 0.720255 | − | 0.693709i | \(-0.244025\pi\) | ||||
0.720255 | + | 0.693709i | \(0.244025\pi\) | |||||||
\(684\) | −4.82389 | −0.184446 | ||||||||
\(685\) | 0.437404 | 0.0167124 | ||||||||
\(686\) | −2.72116 | −0.103894 | ||||||||
\(687\) | −10.5075 | −0.400886 | ||||||||
\(688\) | 14.5844 | 0.556026 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19.9420 | 0.759179 | ||||||||
\(691\) | 50.2964 | 1.91336 | 0.956682 | − | 0.291135i | \(-0.0940330\pi\) | ||||
0.956682 | + | 0.291135i | \(0.0940330\pi\) | |||||||
\(692\) | −57.3446 | −2.17991 | ||||||||
\(693\) | −5.54221 | −0.210531 | ||||||||
\(694\) | 5.23758 | 0.198816 | ||||||||
\(695\) | 6.26882 | 0.237790 | ||||||||
\(696\) | 17.4380 | 0.660984 | ||||||||
\(697\) | −46.9007 | −1.77649 | ||||||||
\(698\) | −8.87020 | −0.335742 | ||||||||
\(699\) | 9.69049 | 0.366528 | ||||||||
\(700\) | 13.4838 | 0.509639 | ||||||||
\(701\) | −12.0336 | −0.454504 | −0.227252 | − | 0.973836i | \(-0.572974\pi\) | ||||
−0.227252 | + | 0.973836i | \(0.572974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.45635 | 0.168075 | ||||||||
\(704\) | 151.937 | 5.72632 | ||||||||
\(705\) | 19.8960 | 0.749326 | ||||||||
\(706\) | 24.2533 | 0.912786 | ||||||||
\(707\) | 11.7740 | 0.442808 | ||||||||
\(708\) | −18.6296 | −0.700141 | ||||||||
\(709\) | −43.2095 | −1.62277 | −0.811383 | − | 0.584515i | \(-0.801285\pi\) | ||||
−0.811383 | + | 0.584515i | \(0.801285\pi\) | |||||||
\(710\) | 56.5929 | 2.12389 | ||||||||
\(711\) | 0.779028 | 0.0292158 | ||||||||
\(712\) | −70.9637 | −2.65948 | ||||||||
\(713\) | 6.83153 | 0.255843 | ||||||||
\(714\) | 13.0773 | 0.489404 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −104.675 | −3.91190 | ||||||||
\(717\) | −18.4302 | −0.688287 | ||||||||
\(718\) | 54.7824 | 2.04446 | ||||||||
\(719\) | 40.9527 | 1.52728 | 0.763639 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763639 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(720\) | 22.7945 | 0.849500 | ||||||||
\(721\) | −9.61981 | −0.358261 | ||||||||
\(722\) | −49.5344 | −1.84348 | ||||||||
\(723\) | −15.3530 | −0.570986 | ||||||||
\(724\) | −86.4775 | −3.21391 | ||||||||
\(725\) | 4.69568 | 0.174393 | ||||||||
\(726\) | −53.6506 | −1.99116 | ||||||||
\(727\) | −24.7078 | −0.916360 | −0.458180 | − | 0.888859i | \(-0.651499\pi\) | ||||
−0.458180 | + | 0.888859i | \(0.651499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.9845 | 0.850693 | ||||||||
\(731\) | 4.86679 | 0.180005 | ||||||||
\(732\) | 19.3786 | 0.716253 | ||||||||
\(733\) | 8.10694 | 0.299437 | 0.149718 | − | 0.988729i | \(-0.452163\pi\) | ||||
0.149718 | + | 0.988729i | \(0.452163\pi\) | |||||||
\(734\) | −85.2860 | −3.14796 | ||||||||
\(735\) | −1.58278 | −0.0583816 | ||||||||
\(736\) | −95.6561 | −3.52593 | ||||||||
\(737\) | 81.6925 | 3.00918 | ||||||||
\(738\) | −26.5565 | −0.977558 | ||||||||
\(739\) | 36.8696 | 1.35627 | 0.678135 | − | 0.734938i | \(-0.262789\pi\) | ||||
0.678135 | + | 0.734938i | \(0.262789\pi\) | |||||||
\(740\) | −42.7118 | −1.57012 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.0286 | −0.625140 | ||||||||
\(743\) | −7.62191 | −0.279621 | −0.139810 | − | 0.990178i | \(-0.544649\pi\) | ||||
−0.139810 | + | 0.990178i | \(0.544649\pi\) | |||||||
\(744\) | 13.6697 | 0.501156 | ||||||||
\(745\) | −34.3300 | −1.25775 | ||||||||
\(746\) | 48.8270 | 1.78768 | ||||||||
\(747\) | −1.47136 | −0.0538342 | ||||||||
\(748\) | 143.952 | 5.26342 | ||||||||
\(749\) | −3.68918 | −0.134800 | ||||||||
\(750\) | 32.2801 | 1.17870 | ||||||||
\(751\) | 20.6711 | 0.754300 | 0.377150 | − | 0.926152i | \(-0.376904\pi\) | ||||
0.377150 | + | 0.926152i | \(0.376904\pi\) | |||||||
\(752\) | −181.032 | −6.60156 | ||||||||
\(753\) | −8.62900 | −0.314458 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.96916 | −0.326421 | ||||||||
\(756\) | 5.40472 | 0.196568 | ||||||||
\(757\) | −2.18816 | −0.0795299 | −0.0397650 | − | 0.999209i | \(-0.512661\pi\) | ||||
−0.0397650 | + | 0.999209i | \(0.512661\pi\) | |||||||
\(758\) | 54.8250 | 1.99133 | ||||||||
\(759\) | 25.6612 | 0.931444 | ||||||||
\(760\) | −13.0882 | −0.474759 | ||||||||
\(761\) | 31.3762 | 1.13739 | 0.568694 | − | 0.822549i | \(-0.307449\pi\) | ||||
0.568694 | + | 0.822549i | \(0.307449\pi\) | |||||||
\(762\) | 12.5842 | 0.455877 | ||||||||
\(763\) | −8.92215 | −0.323003 | ||||||||
\(764\) | 17.0157 | 0.615607 | ||||||||
\(765\) | 7.60646 | 0.275012 | ||||||||
\(766\) | 102.079 | 3.68825 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −35.7323 | −1.28938 | ||||||||
\(769\) | 8.90840 | 0.321245 | 0.160623 | − | 0.987016i | \(-0.448650\pi\) | ||||
0.160623 | + | 0.987016i | \(0.448650\pi\) | |||||||
\(770\) | −23.8702 | −0.860224 | ||||||||
\(771\) | −2.72949 | −0.0983002 | ||||||||
\(772\) | −125.833 | −4.52884 | ||||||||
\(773\) | −3.53796 | −0.127252 | −0.0636258 | − | 0.997974i | \(-0.520266\pi\) | ||||
−0.0636258 | + | 0.997974i | \(0.520266\pi\) | |||||||
\(774\) | 2.75571 | 0.0990521 | ||||||||
\(775\) | 3.68097 | 0.132224 | ||||||||
\(776\) | 7.02901 | 0.252327 | ||||||||
\(777\) | −4.99293 | −0.179120 | ||||||||
\(778\) | −63.1162 | −2.26282 | ||||||||
\(779\) | 8.71045 | 0.312084 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 72.8233 | 2.60582 | ||||||||
\(782\) | −60.5497 | −2.16525 | ||||||||
\(783\) | 1.88217 | 0.0672634 | ||||||||
\(784\) | 14.4016 | 0.514342 | ||||||||
\(785\) | 1.68418 | 0.0601108 | ||||||||
\(786\) | 21.1756 | 0.755309 | ||||||||
\(787\) | −20.5207 | −0.731485 | −0.365742 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365742 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(788\) | −95.3526 | −3.39680 | ||||||||
\(789\) | 5.61419 | 0.199870 | ||||||||
\(790\) | 3.35527 | 0.119375 | ||||||||
\(791\) | −16.1353 | −0.573706 | ||||||||
\(792\) | 51.3474 | 1.82455 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −103.841 | −3.68518 | ||||||||
\(795\) | −9.90477 | −0.351286 | ||||||||
\(796\) | 64.4519 | 2.28444 | ||||||||
\(797\) | −39.8650 | −1.41209 | −0.706045 | − | 0.708167i | \(-0.749522\pi\) | ||||
−0.706045 | + | 0.708167i | \(0.749522\pi\) | |||||||
\(798\) | −2.42873 | −0.0859760 | ||||||||
\(799\) | −60.4099 | −2.13715 | ||||||||
\(800\) | −51.5414 | −1.82227 | ||||||||
\(801\) | −7.65950 | −0.270635 | ||||||||
\(802\) | −22.5533 | −0.796385 | ||||||||
\(803\) | 29.5762 | 1.04372 | ||||||||
\(804\) | −79.6659 | −2.80960 | ||||||||
\(805\) | 7.32849 | 0.258295 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.182236 | 0.00641501 | ||||||||
\(808\) | −109.084 | −3.83756 | ||||||||
\(809\) | 41.6694 | 1.46502 | 0.732509 | − | 0.680757i | \(-0.238349\pi\) | ||||
0.732509 | + | 0.680757i | \(0.238349\pi\) | |||||||
\(810\) | 4.30699 | 0.151332 | ||||||||
\(811\) | −20.6446 | −0.724931 | −0.362465 | − | 0.931997i | \(-0.618065\pi\) | ||||
−0.362465 | + | 0.931997i | \(0.618065\pi\) | |||||||
\(812\) | 10.1726 | 0.356989 | ||||||||
\(813\) | −29.3326 | −1.02874 | ||||||||
\(814\) | −75.2995 | −2.63925 | ||||||||
\(815\) | −11.4058 | −0.399527 | ||||||||
\(816\) | −69.2106 | −2.42286 | ||||||||
\(817\) | −0.903866 | −0.0316223 | ||||||||
\(818\) | 106.431 | 3.72129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −83.4851 | −2.91543 | ||||||||
\(821\) | −14.1363 | −0.493359 | −0.246679 | − | 0.969097i | \(-0.579339\pi\) | ||||
−0.246679 | + | 0.969097i | \(0.579339\pi\) | |||||||
\(822\) | −0.752000 | −0.0262290 | ||||||||
\(823\) | 1.64597 | 0.0573749 | 0.0286874 | − | 0.999588i | \(-0.490867\pi\) | ||||
0.0286874 | + | 0.999588i | \(0.490867\pi\) | |||||||
\(824\) | 89.1256 | 3.10484 | ||||||||
\(825\) | 13.8268 | 0.481387 | ||||||||
\(826\) | −9.37958 | −0.326357 | ||||||||
\(827\) | −10.1980 | −0.354620 | −0.177310 | − | 0.984155i | \(-0.556740\pi\) | ||||
−0.177310 | + | 0.984155i | \(0.556740\pi\) | |||||||
\(828\) | −25.0247 | −0.869667 | ||||||||
\(829\) | −1.67774 | −0.0582703 | −0.0291351 | − | 0.999575i | \(-0.509275\pi\) | ||||
−0.0291351 | + | 0.999575i | \(0.509275\pi\) | |||||||
\(830\) | −6.33713 | −0.219965 | ||||||||
\(831\) | 16.1748 | 0.561097 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.80577 | 0.166510 | ||||||||
\(834\) | −10.7776 | −0.373197 | ||||||||
\(835\) | 0.741527 | 0.0256616 | ||||||||
\(836\) | −26.7350 | −0.924650 | ||||||||
\(837\) | 1.47545 | 0.0509989 | ||||||||
\(838\) | 74.9587 | 2.58940 | ||||||||
\(839\) | −10.7213 | −0.370140 | −0.185070 | − | 0.982725i | \(-0.559251\pi\) | ||||
−0.185070 | + | 0.982725i | \(0.559251\pi\) | |||||||
\(840\) | 14.6641 | 0.505960 | ||||||||
\(841\) | −25.4574 | −0.877842 | ||||||||
\(842\) | 92.8557 | 3.20002 | ||||||||
\(843\) | 3.71644 | 0.128001 | ||||||||
\(844\) | −81.7745 | −2.81480 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −34.2058 | −1.17602 | ||||||||
\(847\) | −19.7161 | −0.677452 | ||||||||
\(848\) | 90.1228 | 3.09483 | ||||||||
\(849\) | −3.77370 | −0.129513 | ||||||||
\(850\) | −32.6254 | −1.11904 | ||||||||
\(851\) | 23.1180 | 0.792475 | ||||||||
\(852\) | −71.0168 | −2.43299 | ||||||||
\(853\) | −5.01741 | −0.171793 | −0.0858964 | − | 0.996304i | \(-0.527375\pi\) | ||||
−0.0858964 | + | 0.996304i | \(0.527375\pi\) | |||||||
\(854\) | 9.75670 | 0.333868 | ||||||||
\(855\) | −1.41268 | −0.0483127 | ||||||||
\(856\) | 34.1795 | 1.16823 | ||||||||
\(857\) | 25.0009 | 0.854015 | 0.427008 | − | 0.904248i | \(-0.359568\pi\) | ||||
0.427008 | + | 0.904248i | \(0.359568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.9200 | 0.611424 | 0.305712 | − | 0.952124i | \(-0.401106\pi\) | ||||
0.305712 | + | 0.952124i | \(0.401106\pi\) | |||||||
\(860\) | 8.66309 | 0.295409 | ||||||||
\(861\) | −9.75924 | −0.332594 | ||||||||
\(862\) | −13.6082 | −0.463498 | ||||||||
\(863\) | 7.10038 | 0.241700 | 0.120850 | − | 0.992671i | \(-0.461438\pi\) | ||||
0.120850 | + | 0.992671i | \(0.461438\pi\) | |||||||
\(864\) | −20.6594 | −0.702847 | ||||||||
\(865\) | −16.7934 | −0.570993 | ||||||||
\(866\) | 40.5823 | 1.37904 | ||||||||
\(867\) | −6.09539 | −0.207010 | ||||||||
\(868\) | 7.97437 | 0.270668 | ||||||||
\(869\) | 4.31753 | 0.146462 | ||||||||
\(870\) | 8.10651 | 0.274836 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 82.6619 | 2.79928 | ||||||||
\(873\) | 0.758679 | 0.0256774 | ||||||||
\(874\) | 11.2454 | 0.380380 | ||||||||
\(875\) | 11.8626 | 0.401030 | ||||||||
\(876\) | −28.8425 | −0.974499 | ||||||||
\(877\) | −26.7489 | −0.903248 | −0.451624 | − | 0.892208i | \(-0.649155\pi\) | ||||
−0.451624 | + | 0.892208i | \(0.649155\pi\) | |||||||
\(878\) | −19.3278 | −0.652280 | ||||||||
\(879\) | −15.4163 | −0.519980 | ||||||||
\(880\) | 126.332 | 4.25864 | ||||||||
\(881\) | 10.0293 | 0.337897 | 0.168949 | − | 0.985625i | \(-0.445963\pi\) | ||||
0.168949 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(882\) | 2.72116 | 0.0916263 | ||||||||
\(883\) | −1.88319 | −0.0633743 | −0.0316871 | − | 0.999498i | \(-0.510088\pi\) | ||||
−0.0316871 | + | 0.999498i | \(0.510088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.45568 | −0.183391 | ||||||||
\(886\) | −12.6035 | −0.423422 | ||||||||
\(887\) | −38.5774 | −1.29530 | −0.647652 | − | 0.761936i | \(-0.724249\pi\) | ||||
−0.647652 | + | 0.761936i | \(0.724249\pi\) | |||||||
\(888\) | 46.2585 | 1.55233 | ||||||||
\(889\) | 4.62457 | 0.155103 | ||||||||
\(890\) | −32.9894 | −1.10581 | ||||||||
\(891\) | 5.54221 | 0.185671 | ||||||||
\(892\) | −103.534 | −3.46658 | ||||||||
\(893\) | 11.2194 | 0.375443 | ||||||||
\(894\) | 59.0212 | 1.97397 | ||||||||
\(895\) | −30.6542 | −1.02466 | ||||||||
\(896\) | −33.2803 | −1.11182 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −61.4243 | −2.04976 | ||||||||
\(899\) | 2.77705 | 0.0926197 | ||||||||
\(900\) | −13.4838 | −0.449460 | ||||||||
\(901\) | 30.0737 | 1.00190 | ||||||||
\(902\) | −147.182 | −4.90061 | ||||||||
\(903\) | 1.01270 | 0.0337005 | ||||||||
\(904\) | 149.490 | 4.97198 | ||||||||
\(905\) | −25.3250 | −0.841831 | ||||||||
\(906\) | 15.4201 | 0.512298 | ||||||||
\(907\) | 36.3170 | 1.20589 | 0.602944 | − | 0.797784i | \(-0.293994\pi\) | ||||
0.602944 | + | 0.797784i | \(0.293994\pi\) | |||||||
\(908\) | 94.2689 | 3.12842 | ||||||||
\(909\) | −11.7740 | −0.390520 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.42183 | 0.179633 | 0.0898167 | − | 0.995958i | \(-0.471372\pi\) | ||||
0.0898167 | + | 0.995958i | \(0.471372\pi\) | |||||||
\(912\) | 12.8539 | 0.425635 | ||||||||
\(913\) | −8.15458 | −0.269877 | ||||||||
\(914\) | 81.1248 | 2.68337 | ||||||||
\(915\) | 5.67503 | 0.187611 | ||||||||
\(916\) | 56.7900 | 1.87640 | ||||||||
\(917\) | 7.78183 | 0.256979 | ||||||||
\(918\) | −13.0773 | −0.431614 | ||||||||
\(919\) | 15.8355 | 0.522364 | 0.261182 | − | 0.965290i | \(-0.415888\pi\) | ||||
0.261182 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(920\) | −67.8970 | −2.23850 | ||||||||
\(921\) | 33.2617 | 1.09601 | ||||||||
\(922\) | 41.7335 | 1.37442 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 29.9541 | 0.985417 | ||||||||
\(925\) | 12.4564 | 0.409565 | ||||||||
\(926\) | −37.2978 | −1.22568 | ||||||||
\(927\) | 9.61981 | 0.315956 | ||||||||
\(928\) | −38.8846 | −1.27645 | ||||||||
\(929\) | 23.0269 | 0.755488 | 0.377744 | − | 0.925910i | \(-0.376700\pi\) | ||||
0.377744 | + | 0.925910i | \(0.376700\pi\) | |||||||
\(930\) | 6.35473 | 0.208380 | ||||||||
\(931\) | −0.892533 | −0.0292516 | ||||||||
\(932\) | −52.3744 | −1.71558 | ||||||||
\(933\) | 5.28263 | 0.172946 | ||||||||
\(934\) | −112.339 | −3.67583 | ||||||||
\(935\) | 42.1566 | 1.37867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.9751 | −1.59995 | −0.799974 | − | 0.600035i | \(-0.795153\pi\) | ||||
−0.799974 | + | 0.600035i | \(0.795153\pi\) | |||||||
\(938\) | −40.1101 | −1.30964 | ||||||||
\(939\) | 17.4853 | 0.570612 | ||||||||
\(940\) | −107.532 | −3.50731 | ||||||||
\(941\) | −31.1637 | −1.01591 | −0.507954 | − | 0.861384i | \(-0.669598\pi\) | ||||
−0.507954 | + | 0.861384i | \(0.669598\pi\) | |||||||
\(942\) | −2.89549 | −0.0943402 | ||||||||
\(943\) | 45.1868 | 1.47148 | ||||||||
\(944\) | 49.6408 | 1.61567 | ||||||||
\(945\) | 1.58278 | 0.0514877 | ||||||||
\(946\) | 15.2727 | 0.496559 | ||||||||
\(947\) | −45.0524 | −1.46401 | −0.732003 | − | 0.681302i | \(-0.761414\pi\) | ||||
−0.732003 | + | 0.681302i | \(0.761414\pi\) | |||||||
\(948\) | −4.21043 | −0.136748 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.05923 | 0.196587 | ||||||||
\(951\) | −6.89451 | −0.223570 | ||||||||
\(952\) | −44.5245 | −1.44305 | ||||||||
\(953\) | 8.73966 | 0.283105 | 0.141553 | − | 0.989931i | \(-0.454791\pi\) | ||||
0.141553 | + | 0.989931i | \(0.454791\pi\) | |||||||
\(954\) | 17.0286 | 0.551321 | ||||||||
\(955\) | 4.98307 | 0.161248 | ||||||||
\(956\) | 99.6099 | 3.22161 | ||||||||
\(957\) | 10.4314 | 0.337199 | ||||||||
\(958\) | 8.34593 | 0.269645 | ||||||||
\(959\) | −0.276352 | −0.00892389 | ||||||||
\(960\) | −43.3909 | −1.40044 | ||||||||
\(961\) | −28.8231 | −0.929776 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.68918 | 0.118882 | ||||||||
\(964\) | 82.9789 | 2.67257 | ||||||||
\(965\) | −36.8504 | −1.18626 | ||||||||
\(966\) | −12.5994 | −0.405379 | ||||||||
\(967\) | −5.92797 | −0.190631 | −0.0953154 | − | 0.995447i | \(-0.530386\pi\) | ||||
−0.0953154 | + | 0.995447i | \(0.530386\pi\) | |||||||
\(968\) | 182.665 | 5.87109 | ||||||||
\(969\) | 4.28931 | 0.137792 | ||||||||
\(970\) | 3.26762 | 0.104917 | ||||||||
\(971\) | −31.4172 | −1.00823 | −0.504114 | − | 0.863637i | \(-0.668181\pi\) | ||||
−0.504114 | + | 0.863637i | \(0.668181\pi\) | |||||||
\(972\) | −5.40472 | −0.173357 | ||||||||
\(973\) | −3.96065 | −0.126973 | ||||||||
\(974\) | −22.5305 | −0.721923 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −51.6367 | −1.65285 | ||||||||
\(977\) | −38.2801 | −1.22469 | −0.612344 | − | 0.790591i | \(-0.709773\pi\) | ||||
−0.612344 | + | 0.790591i | \(0.709773\pi\) | |||||||
\(978\) | 19.6092 | 0.627032 | ||||||||
\(979\) | −42.4505 | −1.35672 | ||||||||
\(980\) | 8.55447 | 0.273262 | ||||||||
\(981\) | 8.92215 | 0.284862 | ||||||||
\(982\) | −13.5501 | −0.432402 | ||||||||
\(983\) | −30.9632 | −0.987572 | −0.493786 | − | 0.869583i | \(-0.664387\pi\) | ||||
−0.493786 | + | 0.869583i | \(0.664387\pi\) | |||||||
\(984\) | 90.4174 | 2.88240 | ||||||||
\(985\) | −27.9241 | −0.889736 | ||||||||
\(986\) | −24.6137 | −0.783860 | ||||||||
\(987\) | −12.5703 | −0.400117 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.68894 | −0.149100 | ||||||||
\(990\) | 23.8702 | 0.758646 | ||||||||
\(991\) | −11.1295 | −0.353540 | −0.176770 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176770 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(992\) | −30.4818 | −0.967799 | ||||||||
\(993\) | −3.00614 | −0.0953971 | ||||||||
\(994\) | −35.7554 | −1.13409 | ||||||||
\(995\) | 18.8748 | 0.598371 | ||||||||
\(996\) | 7.95228 | 0.251978 | ||||||||
\(997\) | 14.2980 | 0.452823 | 0.226412 | − | 0.974032i | \(-0.427301\pi\) | ||||
0.226412 | + | 0.974032i | \(0.427301\pi\) | |||||||
\(998\) | 0.00331802 | 0.000105030 0 | ||||||||
\(999\) | 4.99293 | 0.157969 |
(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 | 3549.2.a.bc.1.8 | 8 | ||
13.2 | odd | 12 | 273.2.bd.b.43.8 | ✓ | 16 | ||
13.7 | odd | 12 | 273.2.bd.b.127.8 | yes | 16 | ||
13.12 | even | 2 | 3549.2.a.ba.1.1 | 8 | |||
39.2 | even | 12 | 819.2.ct.c.316.1 | 16 | |||
39.20 | even | 12 | 819.2.ct.c.127.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bd.b.43.8 | ✓ | 16 | 13.2 | odd | 12 | ||
273.2.bd.b.127.8 | yes | 16 | 13.7 | odd | 12 | ||
819.2.ct.c.127.1 | 16 | 39.20 | even | 12 | |||
819.2.ct.c.316.1 | 16 | 39.2 | even | 12 | |||
3549.2.a.ba.1.1 | 8 | 13.12 | even | 2 | |||
3549.2.a.bc.1.8 | 8 | 1.1 | even | 1 | trivial |