Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(1\) |
Dimension: | \(217\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74777 | −1.94296 | −0.971482 | − | 0.237112i | \(-0.923799\pi\) | ||||
−0.971482 | + | 0.237112i | \(0.923799\pi\) | |||||||
\(3\) | 2.83106 | 1.63452 | 0.817258 | − | 0.576272i | \(-0.195493\pi\) | ||||
0.817258 | + | 0.576272i | \(0.195493\pi\) | |||||||
\(4\) | 5.55022 | 2.77511 | ||||||||
\(5\) | −0.268060 | −0.119880 | −0.0599400 | − | 0.998202i | \(-0.519091\pi\) | ||||
−0.0599400 | + | 0.998202i | \(0.519091\pi\) | |||||||
\(6\) | −7.77911 | −3.17581 | ||||||||
\(7\) | 0.663291 | 0.250700 | 0.125350 | − | 0.992113i | \(-0.459995\pi\) | ||||
0.125350 | + | 0.992113i | \(0.459995\pi\) | |||||||
\(8\) | −9.75518 | −3.44898 | ||||||||
\(9\) | 5.01493 | 1.67164 | ||||||||
\(10\) | 0.736566 | 0.232923 | ||||||||
\(11\) | −0.384723 | −0.115998 | −0.0579992 | − | 0.998317i | \(-0.518472\pi\) | ||||
−0.0579992 | + | 0.998317i | \(0.518472\pi\) | |||||||
\(12\) | 15.7130 | 4.53596 | ||||||||
\(13\) | −5.76370 | −1.59856 | −0.799281 | − | 0.600957i | \(-0.794786\pi\) | ||||
−0.799281 | + | 0.600957i | \(0.794786\pi\) | |||||||
\(14\) | −1.82257 | −0.487102 | ||||||||
\(15\) | −0.758895 | −0.195946 | ||||||||
\(16\) | 15.7045 | 3.92613 | ||||||||
\(17\) | 4.35813 | 1.05700 | 0.528501 | − | 0.848933i | \(-0.322754\pi\) | ||||
0.528501 | + | 0.848933i | \(0.322754\pi\) | |||||||
\(18\) | −13.7799 | −3.24794 | ||||||||
\(19\) | −0.449082 | −0.103026 | −0.0515132 | − | 0.998672i | \(-0.516404\pi\) | ||||
−0.0515132 | + | 0.998672i | \(0.516404\pi\) | |||||||
\(20\) | −1.48779 | −0.332680 | ||||||||
\(21\) | 1.87782 | 0.409774 | ||||||||
\(22\) | 1.05713 | 0.225381 | ||||||||
\(23\) | −6.98624 | −1.45673 | −0.728366 | − | 0.685188i | \(-0.759720\pi\) | ||||
−0.728366 | + | 0.685188i | \(0.759720\pi\) | |||||||
\(24\) | −27.6175 | −5.63741 | ||||||||
\(25\) | −4.92814 | −0.985629 | ||||||||
\(26\) | 15.8373 | 3.10595 | ||||||||
\(27\) | 5.70439 | 1.09781 | ||||||||
\(28\) | 3.68141 | 0.695721 | ||||||||
\(29\) | 8.69575 | 1.61476 | 0.807380 | − | 0.590032i | \(-0.200885\pi\) | ||||
0.807380 | + | 0.590032i | \(0.200885\pi\) | |||||||
\(30\) | 2.08527 | 0.380716 | ||||||||
\(31\) | 3.46104 | 0.621622 | 0.310811 | − | 0.950472i | \(-0.399399\pi\) | ||||
0.310811 | + | 0.950472i | \(0.399399\pi\) | |||||||
\(32\) | −23.6420 | −4.17935 | ||||||||
\(33\) | −1.08918 | −0.189601 | ||||||||
\(34\) | −11.9751 | −2.05372 | ||||||||
\(35\) | −0.177802 | −0.0300540 | ||||||||
\(36\) | 27.8340 | 4.63899 | ||||||||
\(37\) | −7.57075 | −1.24462 | −0.622312 | − | 0.782769i | \(-0.713806\pi\) | ||||
−0.622312 | + | 0.782769i | \(0.713806\pi\) | |||||||
\(38\) | 1.23397 | 0.200177 | ||||||||
\(39\) | −16.3174 | −2.61288 | ||||||||
\(40\) | 2.61497 | 0.413463 | ||||||||
\(41\) | −2.18675 | −0.341514 | −0.170757 | − | 0.985313i | \(-0.554621\pi\) | ||||
−0.170757 | + | 0.985313i | \(0.554621\pi\) | |||||||
\(42\) | −5.15981 | −0.796176 | ||||||||
\(43\) | 2.89706 | 0.441798 | 0.220899 | − | 0.975297i | \(-0.429101\pi\) | ||||
0.220899 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(44\) | −2.13530 | −0.321909 | ||||||||
\(45\) | −1.34430 | −0.200397 | ||||||||
\(46\) | 19.1966 | 2.83038 | ||||||||
\(47\) | −11.2441 | −1.64012 | −0.820061 | − | 0.572276i | \(-0.806061\pi\) | ||||
−0.820061 | + | 0.572276i | \(0.806061\pi\) | |||||||
\(48\) | 44.4605 | 6.41732 | ||||||||
\(49\) | −6.56005 | −0.937149 | ||||||||
\(50\) | 13.5414 | 1.91504 | ||||||||
\(51\) | 12.3382 | 1.72769 | ||||||||
\(52\) | −31.9898 | −4.43619 | ||||||||
\(53\) | 8.78614 | 1.20687 | 0.603435 | − | 0.797412i | \(-0.293798\pi\) | ||||
0.603435 | + | 0.797412i | \(0.293798\pi\) | |||||||
\(54\) | −15.6743 | −2.13301 | ||||||||
\(55\) | 0.103129 | 0.0139059 | ||||||||
\(56\) | −6.47052 | −0.864660 | ||||||||
\(57\) | −1.27138 | −0.168398 | ||||||||
\(58\) | −23.8939 | −3.13742 | ||||||||
\(59\) | −2.66440 | −0.346875 | −0.173437 | − | 0.984845i | \(-0.555487\pi\) | ||||
−0.173437 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(60\) | −4.21203 | −0.543771 | ||||||||
\(61\) | −7.78497 | −0.996764 | −0.498382 | − | 0.866958i | \(-0.666072\pi\) | ||||
−0.498382 | + | 0.866958i | \(0.666072\pi\) | |||||||
\(62\) | −9.51014 | −1.20779 | ||||||||
\(63\) | 3.32636 | 0.419082 | ||||||||
\(64\) | 33.5536 | 4.19420 | ||||||||
\(65\) | 1.54502 | 0.191636 | ||||||||
\(66\) | 2.99280 | 0.368389 | ||||||||
\(67\) | −14.3711 | −1.75571 | −0.877855 | − | 0.478927i | \(-0.841026\pi\) | ||||
−0.877855 | + | 0.478927i | \(0.841026\pi\) | |||||||
\(68\) | 24.1886 | 2.93330 | ||||||||
\(69\) | −19.7785 | −2.38105 | ||||||||
\(70\) | 0.488558 | 0.0583938 | ||||||||
\(71\) | 10.8117 | 1.28312 | 0.641558 | − | 0.767074i | \(-0.278288\pi\) | ||||
0.641558 | + | 0.767074i | \(0.278288\pi\) | |||||||
\(72\) | −48.9215 | −5.76546 | ||||||||
\(73\) | −9.56377 | −1.11935 | −0.559677 | − | 0.828711i | \(-0.689075\pi\) | ||||
−0.559677 | + | 0.828711i | \(0.689075\pi\) | |||||||
\(74\) | 20.8027 | 2.41826 | ||||||||
\(75\) | −13.9519 | −1.61103 | ||||||||
\(76\) | −2.49250 | −0.285910 | ||||||||
\(77\) | −0.255184 | −0.0290809 | ||||||||
\(78\) | 44.8364 | 5.07673 | ||||||||
\(79\) | 2.68890 | 0.302525 | 0.151263 | − | 0.988494i | \(-0.451666\pi\) | ||||
0.151263 | + | 0.988494i | \(0.451666\pi\) | |||||||
\(80\) | −4.20975 | −0.470664 | ||||||||
\(81\) | 1.10472 | 0.122747 | ||||||||
\(82\) | 6.00869 | 0.663549 | ||||||||
\(83\) | −10.9813 | −1.20536 | −0.602680 | − | 0.797983i | \(-0.705900\pi\) | ||||
−0.602680 | + | 0.797983i | \(0.705900\pi\) | |||||||
\(84\) | 10.4223 | 1.13717 | ||||||||
\(85\) | −1.16824 | −0.126713 | ||||||||
\(86\) | −7.96046 | −0.858398 | ||||||||
\(87\) | 24.6182 | 2.63935 | ||||||||
\(88\) | 3.75305 | 0.400076 | ||||||||
\(89\) | 12.7262 | 1.34897 | 0.674486 | − | 0.738288i | \(-0.264365\pi\) | ||||
0.674486 | + | 0.738288i | \(0.264365\pi\) | |||||||
\(90\) | 3.69383 | 0.389363 | ||||||||
\(91\) | −3.82301 | −0.400760 | ||||||||
\(92\) | −38.7752 | −4.04259 | ||||||||
\(93\) | 9.79844 | 1.01605 | ||||||||
\(94\) | 30.8962 | 3.18670 | ||||||||
\(95\) | 0.120381 | 0.0123508 | ||||||||
\(96\) | −66.9320 | −6.83122 | ||||||||
\(97\) | −11.9138 | −1.20966 | −0.604831 | − | 0.796354i | \(-0.706759\pi\) | ||||
−0.604831 | + | 0.796354i | \(0.706759\pi\) | |||||||
\(98\) | 18.0255 | 1.82085 | ||||||||
\(99\) | −1.92936 | −0.193908 | ||||||||
\(100\) | −27.3523 | −2.73523 | ||||||||
\(101\) | 10.3128 | 1.02616 | 0.513081 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513081 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(102\) | −33.9024 | −3.35683 | ||||||||
\(103\) | −4.82667 | −0.475586 | −0.237793 | − | 0.971316i | \(-0.576424\pi\) | ||||
−0.237793 | + | 0.971316i | \(0.576424\pi\) | |||||||
\(104\) | 56.2259 | 5.51341 | ||||||||
\(105\) | −0.503368 | −0.0491237 | ||||||||
\(106\) | −24.1423 | −2.34491 | ||||||||
\(107\) | 17.4002 | 1.68214 | 0.841070 | − | 0.540927i | \(-0.181926\pi\) | ||||
0.841070 | + | 0.540927i | \(0.181926\pi\) | |||||||
\(108\) | 31.6606 | 3.04655 | ||||||||
\(109\) | 13.1502 | 1.25956 | 0.629781 | − | 0.776773i | \(-0.283145\pi\) | ||||
0.629781 | + | 0.776773i | \(0.283145\pi\) | |||||||
\(110\) | −0.283374 | −0.0270187 | ||||||||
\(111\) | −21.4333 | −2.03436 | ||||||||
\(112\) | 10.4167 | 0.984282 | ||||||||
\(113\) | 1.50871 | 0.141928 | 0.0709639 | − | 0.997479i | \(-0.477392\pi\) | ||||
0.0709639 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(114\) | 3.49345 | 0.327192 | ||||||||
\(115\) | 1.87273 | 0.174633 | ||||||||
\(116\) | 48.2633 | 4.48114 | ||||||||
\(117\) | −28.9045 | −2.67223 | ||||||||
\(118\) | 7.32114 | 0.673965 | ||||||||
\(119\) | 2.89071 | 0.264991 | ||||||||
\(120\) | 7.40316 | 0.675813 | ||||||||
\(121\) | −10.8520 | −0.986544 | ||||||||
\(122\) | 21.3913 | 1.93668 | ||||||||
\(123\) | −6.19084 | −0.558210 | ||||||||
\(124\) | 19.2096 | 1.72507 | ||||||||
\(125\) | 2.66134 | 0.238037 | ||||||||
\(126\) | −9.14005 | −0.814261 | ||||||||
\(127\) | −3.14345 | −0.278936 | −0.139468 | − | 0.990227i | \(-0.544539\pi\) | ||||
−0.139468 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(128\) | −44.9136 | −3.96984 | ||||||||
\(129\) | 8.20178 | 0.722126 | ||||||||
\(130\) | −4.24534 | −0.372341 | ||||||||
\(131\) | −6.34072 | −0.553991 | −0.276996 | − | 0.960871i | \(-0.589339\pi\) | ||||
−0.276996 | + | 0.960871i | \(0.589339\pi\) | |||||||
\(132\) | −6.04517 | −0.526165 | ||||||||
\(133\) | −0.297872 | −0.0258288 | ||||||||
\(134\) | 39.4884 | 3.41128 | ||||||||
\(135\) | −1.52912 | −0.131606 | ||||||||
\(136\) | −42.5144 | −3.64558 | ||||||||
\(137\) | −13.1477 | −1.12328 | −0.561641 | − | 0.827381i | \(-0.689830\pi\) | ||||
−0.561641 | + | 0.827381i | \(0.689830\pi\) | |||||||
\(138\) | 54.3467 | 4.62630 | ||||||||
\(139\) | −9.10485 | −0.772263 | −0.386132 | − | 0.922444i | \(-0.626189\pi\) | ||||
−0.386132 | + | 0.922444i | \(0.626189\pi\) | |||||||
\(140\) | −0.986839 | −0.0834031 | ||||||||
\(141\) | −31.8328 | −2.68081 | ||||||||
\(142\) | −29.7081 | −2.49305 | ||||||||
\(143\) | 2.21743 | 0.185431 | ||||||||
\(144\) | 78.7570 | 6.56309 | ||||||||
\(145\) | −2.33098 | −0.193577 | ||||||||
\(146\) | 26.2790 | 2.17487 | ||||||||
\(147\) | −18.5719 | −1.53179 | ||||||||
\(148\) | −42.0193 | −3.45397 | ||||||||
\(149\) | −18.3745 | −1.50530 | −0.752648 | − | 0.658423i | \(-0.771224\pi\) | ||||
−0.752648 | + | 0.658423i | \(0.771224\pi\) | |||||||
\(150\) | 38.3366 | 3.13017 | ||||||||
\(151\) | 14.5444 | 1.18361 | 0.591803 | − | 0.806082i | \(-0.298416\pi\) | ||||
0.591803 | + | 0.806082i | \(0.298416\pi\) | |||||||
\(152\) | 4.38087 | 0.355336 | ||||||||
\(153\) | 21.8557 | 1.76693 | ||||||||
\(154\) | 0.701185 | 0.0565031 | ||||||||
\(155\) | −0.927767 | −0.0745200 | ||||||||
\(156\) | −90.5652 | −7.25102 | ||||||||
\(157\) | 22.9546 | 1.83198 | 0.915990 | − | 0.401201i | \(-0.131407\pi\) | ||||
0.915990 | + | 0.401201i | \(0.131407\pi\) | |||||||
\(158\) | −7.38848 | −0.587796 | ||||||||
\(159\) | 24.8741 | 1.97265 | ||||||||
\(160\) | 6.33747 | 0.501021 | ||||||||
\(161\) | −4.63391 | −0.365203 | ||||||||
\(162\) | −3.03551 | −0.238493 | ||||||||
\(163\) | 0.356555 | 0.0279275 | 0.0139638 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139638 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(164\) | −12.1370 | −0.947738 | ||||||||
\(165\) | 0.291965 | 0.0227294 | ||||||||
\(166\) | 30.1742 | 2.34197 | ||||||||
\(167\) | −6.51146 | −0.503872 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(168\) | −18.3185 | −1.41330 | ||||||||
\(169\) | 20.2202 | 1.55540 | ||||||||
\(170\) | 3.21005 | 0.246200 | ||||||||
\(171\) | −2.25211 | −0.172223 | ||||||||
\(172\) | 16.0794 | 1.22604 | ||||||||
\(173\) | −22.2534 | −1.69190 | −0.845948 | − | 0.533266i | \(-0.820964\pi\) | ||||
−0.845948 | + | 0.533266i | \(0.820964\pi\) | |||||||
\(174\) | −67.6452 | −5.12817 | ||||||||
\(175\) | −3.26879 | −0.247098 | ||||||||
\(176\) | −6.04190 | −0.455425 | ||||||||
\(177\) | −7.54308 | −0.566972 | ||||||||
\(178\) | −34.9686 | −2.62100 | ||||||||
\(179\) | 9.48252 | 0.708757 | 0.354379 | − | 0.935102i | \(-0.384692\pi\) | ||||
0.354379 | + | 0.935102i | \(0.384692\pi\) | |||||||
\(180\) | −7.46117 | −0.556123 | ||||||||
\(181\) | −12.1978 | −0.906658 | −0.453329 | − | 0.891343i | \(-0.649764\pi\) | ||||
−0.453329 | + | 0.891343i | \(0.649764\pi\) | |||||||
\(182\) | 10.5047 | 0.778663 | ||||||||
\(183\) | −22.0398 | −1.62923 | ||||||||
\(184\) | 68.1521 | 5.02424 | ||||||||
\(185\) | 2.02941 | 0.149206 | ||||||||
\(186\) | −26.9238 | −1.97415 | ||||||||
\(187\) | −1.67668 | −0.122611 | ||||||||
\(188\) | −62.4073 | −4.55152 | ||||||||
\(189\) | 3.78367 | 0.275222 | ||||||||
\(190\) | −0.330778 | −0.0239972 | ||||||||
\(191\) | −16.5971 | −1.20093 | −0.600463 | − | 0.799653i | \(-0.705017\pi\) | ||||
−0.600463 | + | 0.799653i | \(0.705017\pi\) | |||||||
\(192\) | 94.9925 | 6.85549 | ||||||||
\(193\) | 0.940517 | 0.0676999 | 0.0338499 | − | 0.999427i | \(-0.489223\pi\) | ||||
0.0338499 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(194\) | 32.7363 | 2.35033 | ||||||||
\(195\) | 4.37404 | 0.313232 | ||||||||
\(196\) | −36.4097 | −2.60069 | ||||||||
\(197\) | 18.2047 | 1.29703 | 0.648515 | − | 0.761202i | \(-0.275390\pi\) | ||||
0.648515 | + | 0.761202i | \(0.275390\pi\) | |||||||
\(198\) | 5.30143 | 0.376756 | ||||||||
\(199\) | −26.0927 | −1.84966 | −0.924830 | − | 0.380382i | \(-0.875793\pi\) | ||||
−0.924830 | + | 0.380382i | \(0.875793\pi\) | |||||||
\(200\) | 48.0749 | 3.39941 | ||||||||
\(201\) | −40.6855 | −2.86973 | ||||||||
\(202\) | −28.3372 | −1.99380 | ||||||||
\(203\) | 5.76781 | 0.404821 | ||||||||
\(204\) | 68.4795 | 4.79452 | ||||||||
\(205\) | 0.586181 | 0.0409407 | ||||||||
\(206\) | 13.2626 | 0.924046 | ||||||||
\(207\) | −35.0355 | −2.43514 | ||||||||
\(208\) | −90.5161 | −6.27616 | ||||||||
\(209\) | 0.172772 | 0.0119509 | ||||||||
\(210\) | 1.38314 | 0.0954456 | ||||||||
\(211\) | 7.01319 | 0.482808 | 0.241404 | − | 0.970425i | \(-0.422392\pi\) | ||||
0.241404 | + | 0.970425i | \(0.422392\pi\) | |||||||
\(212\) | 48.7650 | 3.34920 | ||||||||
\(213\) | 30.6087 | 2.09727 | ||||||||
\(214\) | −47.8116 | −3.26834 | ||||||||
\(215\) | −0.776587 | −0.0529628 | ||||||||
\(216\) | −55.6474 | −3.78632 | ||||||||
\(217\) | 2.29568 | 0.155841 | ||||||||
\(218\) | −36.1337 | −2.44728 | ||||||||
\(219\) | −27.0756 | −1.82960 | ||||||||
\(220\) | 0.572388 | 0.0385904 | ||||||||
\(221\) | −25.1190 | −1.68968 | ||||||||
\(222\) | 58.8937 | 3.95268 | ||||||||
\(223\) | −7.35233 | −0.492349 | −0.246174 | − | 0.969226i | \(-0.579174\pi\) | ||||
−0.246174 | + | 0.969226i | \(0.579174\pi\) | |||||||
\(224\) | −15.6815 | −1.04777 | ||||||||
\(225\) | −24.7143 | −1.64762 | ||||||||
\(226\) | −4.14559 | −0.275761 | ||||||||
\(227\) | −6.32180 | −0.419592 | −0.209796 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209796 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(228\) | −7.05644 | −0.467324 | ||||||||
\(229\) | −8.49816 | −0.561574 | −0.280787 | − | 0.959770i | \(-0.590596\pi\) | ||||
−0.280787 | + | 0.959770i | \(0.590596\pi\) | |||||||
\(230\) | −5.14583 | −0.339306 | ||||||||
\(231\) | −0.722441 | −0.0475332 | ||||||||
\(232\) | −84.8286 | −5.56927 | ||||||||
\(233\) | 4.34378 | 0.284570 | 0.142285 | − | 0.989826i | \(-0.454555\pi\) | ||||
0.142285 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(234\) | 79.4229 | 5.19204 | ||||||||
\(235\) | 3.01409 | 0.196618 | ||||||||
\(236\) | −14.7880 | −0.962616 | ||||||||
\(237\) | 7.61246 | 0.494482 | ||||||||
\(238\) | −7.94299 | −0.514868 | ||||||||
\(239\) | 11.0112 | 0.712253 | 0.356127 | − | 0.934438i | \(-0.384097\pi\) | ||||
0.356127 | + | 0.934438i | \(0.384097\pi\) | |||||||
\(240\) | −11.9181 | −0.769309 | ||||||||
\(241\) | −28.1245 | −1.81166 | −0.905830 | − | 0.423642i | \(-0.860751\pi\) | ||||
−0.905830 | + | 0.423642i | \(0.860751\pi\) | |||||||
\(242\) | 29.8187 | 1.91682 | ||||||||
\(243\) | −13.9856 | −0.897179 | ||||||||
\(244\) | −43.2083 | −2.76613 | ||||||||
\(245\) | 1.75848 | 0.112345 | ||||||||
\(246\) | 17.0110 | 1.08458 | ||||||||
\(247\) | 2.58837 | 0.164694 | ||||||||
\(248\) | −33.7631 | −2.14396 | ||||||||
\(249\) | −31.0889 | −1.97018 | ||||||||
\(250\) | −7.31273 | −0.462498 | ||||||||
\(251\) | −19.8691 | −1.25413 | −0.627063 | − | 0.778969i | \(-0.715743\pi\) | ||||
−0.627063 | + | 0.778969i | \(0.715743\pi\) | |||||||
\(252\) | 18.4620 | 1.16300 | ||||||||
\(253\) | 2.68777 | 0.168979 | ||||||||
\(254\) | 8.63748 | 0.541964 | ||||||||
\(255\) | −3.30736 | −0.207115 | ||||||||
\(256\) | 56.3048 | 3.51905 | ||||||||
\(257\) | −23.1575 | −1.44453 | −0.722263 | − | 0.691619i | \(-0.756898\pi\) | ||||
−0.722263 | + | 0.691619i | \(0.756898\pi\) | |||||||
\(258\) | −22.5366 | −1.40307 | ||||||||
\(259\) | −5.02161 | −0.312028 | ||||||||
\(260\) | 8.57518 | 0.531810 | ||||||||
\(261\) | 43.6086 | 2.69930 | ||||||||
\(262\) | 17.4228 | 1.07639 | ||||||||
\(263\) | 8.06607 | 0.497375 | 0.248687 | − | 0.968584i | \(-0.420001\pi\) | ||||
0.248687 | + | 0.968584i | \(0.420001\pi\) | |||||||
\(264\) | 10.6251 | 0.653931 | ||||||||
\(265\) | −2.35521 | −0.144680 | ||||||||
\(266\) | 0.818483 | 0.0501844 | ||||||||
\(267\) | 36.0286 | 2.20492 | ||||||||
\(268\) | −79.7628 | −4.87229 | ||||||||
\(269\) | 5.08067 | 0.309774 | 0.154887 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154887 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(270\) | 4.20166 | 0.255705 | ||||||||
\(271\) | 23.0088 | 1.39769 | 0.698843 | − | 0.715275i | \(-0.253699\pi\) | ||||
0.698843 | + | 0.715275i | \(0.253699\pi\) | |||||||
\(272\) | 68.4423 | 4.14993 | ||||||||
\(273\) | −10.8232 | −0.655049 | ||||||||
\(274\) | 36.1267 | 2.18250 | ||||||||
\(275\) | 1.89597 | 0.114331 | ||||||||
\(276\) | −109.775 | −6.60769 | ||||||||
\(277\) | −4.15471 | −0.249632 | −0.124816 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124816 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(278\) | 25.0180 | 1.50048 | ||||||||
\(279\) | 17.3569 | 1.03913 | ||||||||
\(280\) | 1.73449 | 0.103655 | ||||||||
\(281\) | −1.15765 | −0.0690598 | −0.0345299 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345299 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(282\) | 87.4691 | 5.20871 | ||||||||
\(283\) | 6.61994 | 0.393515 | 0.196757 | − | 0.980452i | \(-0.436959\pi\) | ||||
0.196757 | + | 0.980452i | \(0.436959\pi\) | |||||||
\(284\) | 60.0075 | 3.56079 | ||||||||
\(285\) | 0.340806 | 0.0201876 | ||||||||
\(286\) | −6.09298 | −0.360286 | ||||||||
\(287\) | −1.45045 | −0.0856176 | ||||||||
\(288\) | −118.563 | −6.98638 | ||||||||
\(289\) | 1.99331 | 0.117253 | ||||||||
\(290\) | 6.40499 | 0.376114 | ||||||||
\(291\) | −33.7287 | −1.97721 | ||||||||
\(292\) | −53.0810 | −3.10633 | ||||||||
\(293\) | −21.8019 | −1.27368 | −0.636839 | − | 0.770997i | \(-0.719758\pi\) | ||||
−0.636839 | + | 0.770997i | \(0.719758\pi\) | |||||||
\(294\) | 51.0313 | 2.97620 | ||||||||
\(295\) | 0.714218 | 0.0415834 | ||||||||
\(296\) | 73.8540 | 4.29268 | ||||||||
\(297\) | −2.19461 | −0.127344 | ||||||||
\(298\) | 50.4888 | 2.92474 | ||||||||
\(299\) | 40.2666 | 2.32868 | ||||||||
\(300\) | −77.4361 | −4.47078 | ||||||||
\(301\) | 1.92160 | 0.110759 | ||||||||
\(302\) | −39.9646 | −2.29971 | ||||||||
\(303\) | 29.1962 | 1.67728 | ||||||||
\(304\) | −7.05261 | −0.404495 | ||||||||
\(305\) | 2.08684 | 0.119492 | ||||||||
\(306\) | −60.0544 | −3.43308 | ||||||||
\(307\) | 8.58297 | 0.489856 | 0.244928 | − | 0.969541i | \(-0.421236\pi\) | ||||
0.244928 | + | 0.969541i | \(0.421236\pi\) | |||||||
\(308\) | −1.41633 | −0.0807026 | ||||||||
\(309\) | −13.6646 | −0.777352 | ||||||||
\(310\) | 2.54929 | 0.144790 | ||||||||
\(311\) | 19.9813 | 1.13304 | 0.566518 | − | 0.824049i | \(-0.308290\pi\) | ||||
0.566518 | + | 0.824049i | \(0.308290\pi\) | |||||||
\(312\) | 159.179 | 9.01175 | ||||||||
\(313\) | 31.5208 | 1.78166 | 0.890831 | − | 0.454335i | \(-0.150123\pi\) | ||||
0.890831 | + | 0.454335i | \(0.150123\pi\) | |||||||
\(314\) | −63.0740 | −3.55947 | ||||||||
\(315\) | −0.891663 | −0.0502395 | ||||||||
\(316\) | 14.9240 | 0.839541 | ||||||||
\(317\) | −19.4533 | −1.09260 | −0.546302 | − | 0.837588i | \(-0.683965\pi\) | ||||
−0.546302 | + | 0.837588i | \(0.683965\pi\) | |||||||
\(318\) | −68.3483 | −3.83278 | ||||||||
\(319\) | −3.34546 | −0.187310 | ||||||||
\(320\) | −8.99438 | −0.502801 | ||||||||
\(321\) | 49.2610 | 2.74948 | ||||||||
\(322\) | 12.7329 | 0.709577 | ||||||||
\(323\) | −1.95716 | −0.108899 | ||||||||
\(324\) | 6.13144 | 0.340636 | ||||||||
\(325\) | 28.4043 | 1.57559 | ||||||||
\(326\) | −0.979730 | −0.0542622 | ||||||||
\(327\) | 37.2291 | 2.05877 | ||||||||
\(328\) | 21.3322 | 1.17787 | ||||||||
\(329\) | −7.45812 | −0.411179 | ||||||||
\(330\) | −0.802251 | −0.0441625 | ||||||||
\(331\) | −19.6916 | −1.08235 | −0.541174 | − | 0.840911i | \(-0.682020\pi\) | ||||
−0.541174 | + | 0.840911i | \(0.682020\pi\) | |||||||
\(332\) | −60.9489 | −3.34501 | ||||||||
\(333\) | −37.9668 | −2.08057 | ||||||||
\(334\) | 17.8920 | 0.979005 | ||||||||
\(335\) | 3.85232 | 0.210474 | ||||||||
\(336\) | 29.4903 | 1.60883 | ||||||||
\(337\) | −22.2381 | −1.21139 | −0.605694 | − | 0.795697i | \(-0.707105\pi\) | ||||
−0.605694 | + | 0.795697i | \(0.707105\pi\) | |||||||
\(338\) | −55.5605 | −3.02209 | ||||||||
\(339\) | 4.27127 | 0.231983 | ||||||||
\(340\) | −6.48399 | −0.351644 | ||||||||
\(341\) | −1.33155 | −0.0721072 | ||||||||
\(342\) | 6.18828 | 0.334624 | ||||||||
\(343\) | −8.99426 | −0.485644 | ||||||||
\(344\) | −28.2614 | −1.52375 | ||||||||
\(345\) | 5.30182 | 0.285441 | ||||||||
\(346\) | 61.1472 | 3.28729 | ||||||||
\(347\) | 6.06202 | 0.325426 | 0.162713 | − | 0.986673i | \(-0.447976\pi\) | ||||
0.162713 | + | 0.986673i | \(0.447976\pi\) | |||||||
\(348\) | 136.637 | 7.32449 | ||||||||
\(349\) | −3.33798 | −0.178678 | −0.0893391 | − | 0.996001i | \(-0.528475\pi\) | ||||
−0.0893391 | + | 0.996001i | \(0.528475\pi\) | |||||||
\(350\) | 8.98188 | 0.480102 | ||||||||
\(351\) | −32.8784 | −1.75492 | ||||||||
\(352\) | 9.09563 | 0.484799 | ||||||||
\(353\) | −14.4259 | −0.767814 | −0.383907 | − | 0.923372i | \(-0.625422\pi\) | ||||
−0.383907 | + | 0.923372i | \(0.625422\pi\) | |||||||
\(354\) | 20.7266 | 1.10161 | ||||||||
\(355\) | −2.89819 | −0.153820 | ||||||||
\(356\) | 70.6331 | 3.74355 | ||||||||
\(357\) | 8.18378 | 0.433132 | ||||||||
\(358\) | −26.0558 | −1.37709 | ||||||||
\(359\) | −0.923414 | −0.0487359 | −0.0243680 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243680 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(360\) | 13.1139 | 0.691163 | ||||||||
\(361\) | −18.7983 | −0.989386 | ||||||||
\(362\) | 33.5168 | 1.76160 | ||||||||
\(363\) | −30.7227 | −1.61252 | ||||||||
\(364\) | −21.2186 | −1.11215 | ||||||||
\(365\) | 2.56366 | 0.134188 | ||||||||
\(366\) | 60.5601 | 3.16553 | ||||||||
\(367\) | 23.1871 | 1.21036 | 0.605178 | − | 0.796090i | \(-0.293102\pi\) | ||||
0.605178 | + | 0.796090i | \(0.293102\pi\) | |||||||
\(368\) | −109.716 | −5.71932 | ||||||||
\(369\) | −10.9664 | −0.570889 | ||||||||
\(370\) | −5.57636 | −0.289901 | ||||||||
\(371\) | 5.82777 | 0.302563 | ||||||||
\(372\) | 54.3835 | 2.81965 | ||||||||
\(373\) | 8.19879 | 0.424517 | 0.212259 | − | 0.977214i | \(-0.431918\pi\) | ||||
0.212259 | + | 0.977214i | \(0.431918\pi\) | |||||||
\(374\) | 4.60711 | 0.238228 | ||||||||
\(375\) | 7.53442 | 0.389076 | ||||||||
\(376\) | 109.688 | 5.65674 | ||||||||
\(377\) | −50.1197 | −2.58130 | ||||||||
\(378\) | −10.3966 | −0.534746 | ||||||||
\(379\) | −7.74294 | −0.397728 | −0.198864 | − | 0.980027i | \(-0.563725\pi\) | ||||
−0.198864 | + | 0.980027i | \(0.563725\pi\) | |||||||
\(380\) | 0.668140 | 0.0342749 | ||||||||
\(381\) | −8.89932 | −0.455926 | ||||||||
\(382\) | 45.6050 | 2.33336 | ||||||||
\(383\) | 13.0305 | 0.665825 | 0.332913 | − | 0.942958i | \(-0.391969\pi\) | ||||
0.332913 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(384\) | −127.153 | −6.48876 | ||||||||
\(385\) | 0.0684045 | 0.00348622 | ||||||||
\(386\) | −2.58432 | −0.131538 | ||||||||
\(387\) | 14.5286 | 0.738529 | ||||||||
\(388\) | −66.1242 | −3.35695 | ||||||||
\(389\) | −1.85451 | −0.0940274 | −0.0470137 | − | 0.998894i | \(-0.514970\pi\) | ||||
−0.0470137 | + | 0.998894i | \(0.514970\pi\) | |||||||
\(390\) | −12.0188 | −0.608598 | ||||||||
\(391\) | −30.4470 | −1.53977 | ||||||||
\(392\) | 63.9944 | 3.23221 | ||||||||
\(393\) | −17.9510 | −0.905508 | ||||||||
\(394\) | −50.0222 | −2.52008 | ||||||||
\(395\) | −0.720787 | −0.0362667 | ||||||||
\(396\) | −10.7084 | −0.538116 | ||||||||
\(397\) | 34.9991 | 1.75655 | 0.878276 | − | 0.478154i | \(-0.158694\pi\) | ||||
0.878276 | + | 0.478154i | \(0.158694\pi\) | |||||||
\(398\) | 71.6965 | 3.59382 | ||||||||
\(399\) | −0.843295 | −0.0422175 | ||||||||
\(400\) | −77.3941 | −3.86971 | ||||||||
\(401\) | 22.6706 | 1.13212 | 0.566059 | − | 0.824365i | \(-0.308467\pi\) | ||||
0.566059 | + | 0.824365i | \(0.308467\pi\) | |||||||
\(402\) | 111.794 | 5.57579 | ||||||||
\(403\) | −19.9484 | −0.993702 | ||||||||
\(404\) | 57.2384 | 2.84772 | ||||||||
\(405\) | −0.296131 | −0.0147149 | ||||||||
\(406\) | −15.8486 | −0.786553 | ||||||||
\(407\) | 2.91265 | 0.144374 | ||||||||
\(408\) | −120.361 | −5.95875 | ||||||||
\(409\) | 8.79769 | 0.435018 | 0.217509 | − | 0.976058i | \(-0.430207\pi\) | ||||
0.217509 | + | 0.976058i | \(0.430207\pi\) | |||||||
\(410\) | −1.61069 | −0.0795463 | ||||||||
\(411\) | −37.2219 | −1.83602 | ||||||||
\(412\) | −26.7891 | −1.31980 | ||||||||
\(413\) | −1.76727 | −0.0869617 | ||||||||
\(414\) | 96.2694 | 4.73138 | ||||||||
\(415\) | 2.94366 | 0.144499 | ||||||||
\(416\) | 136.265 | 6.68096 | ||||||||
\(417\) | −25.7764 | −1.26228 | ||||||||
\(418\) | −0.474738 | −0.0232202 | ||||||||
\(419\) | −1.83358 | −0.0895762 | −0.0447881 | − | 0.998997i | \(-0.514261\pi\) | ||||
−0.0447881 | + | 0.998997i | \(0.514261\pi\) | |||||||
\(420\) | −2.79380 | −0.136324 | ||||||||
\(421\) | −11.2603 | −0.548796 | −0.274398 | − | 0.961616i | \(-0.588479\pi\) | ||||
−0.274398 | + | 0.961616i | \(0.588479\pi\) | |||||||
\(422\) | −19.2706 | −0.938078 | ||||||||
\(423\) | −56.3884 | −2.74170 | ||||||||
\(424\) | −85.7104 | −4.16247 | ||||||||
\(425\) | −21.4775 | −1.04181 | ||||||||
\(426\) | −84.1056 | −4.07493 | ||||||||
\(427\) | −5.16370 | −0.249889 | ||||||||
\(428\) | 96.5749 | 4.66812 | ||||||||
\(429\) | 6.27769 | 0.303090 | ||||||||
\(430\) | 2.13388 | 0.102905 | ||||||||
\(431\) | 29.3399 | 1.41326 | 0.706628 | − | 0.707586i | \(-0.250216\pi\) | ||||
0.706628 | + | 0.707586i | \(0.250216\pi\) | |||||||
\(432\) | 89.5847 | 4.31015 | ||||||||
\(433\) | 35.6164 | 1.71161 | 0.855807 | − | 0.517295i | \(-0.173061\pi\) | ||||
0.855807 | + | 0.517295i | \(0.173061\pi\) | |||||||
\(434\) | −6.30799 | −0.302793 | ||||||||
\(435\) | −6.59916 | −0.316406 | ||||||||
\(436\) | 72.9866 | 3.49543 | ||||||||
\(437\) | 3.13740 | 0.150082 | ||||||||
\(438\) | 74.3975 | 3.55485 | ||||||||
\(439\) | 27.6024 | 1.31739 | 0.658695 | − | 0.752410i | \(-0.271109\pi\) | ||||
0.658695 | + | 0.752410i | \(0.271109\pi\) | |||||||
\(440\) | −1.00604 | −0.0479611 | ||||||||
\(441\) | −32.8982 | −1.56658 | ||||||||
\(442\) | 69.0210 | 3.28300 | ||||||||
\(443\) | −28.2081 | −1.34021 | −0.670104 | − | 0.742267i | \(-0.733751\pi\) | ||||
−0.670104 | + | 0.742267i | \(0.733751\pi\) | |||||||
\(444\) | −118.959 | −5.64557 | ||||||||
\(445\) | −3.41138 | −0.161715 | ||||||||
\(446\) | 20.2025 | 0.956616 | ||||||||
\(447\) | −52.0193 | −2.46043 | ||||||||
\(448\) | 22.2558 | 1.05149 | ||||||||
\(449\) | 19.7510 | 0.932109 | 0.466054 | − | 0.884756i | \(-0.345675\pi\) | ||||
0.466054 | + | 0.884756i | \(0.345675\pi\) | |||||||
\(450\) | 67.9091 | 3.20127 | ||||||||
\(451\) | 0.841296 | 0.0396151 | ||||||||
\(452\) | 8.37370 | 0.393866 | ||||||||
\(453\) | 41.1761 | 1.93462 | ||||||||
\(454\) | 17.3708 | 0.815253 | ||||||||
\(455\) | 1.02480 | 0.0480432 | ||||||||
\(456\) | 12.4025 | 0.580802 | ||||||||
\(457\) | 22.4530 | 1.05031 | 0.525155 | − | 0.851007i | \(-0.324007\pi\) | ||||
0.525155 | + | 0.851007i | \(0.324007\pi\) | |||||||
\(458\) | 23.3510 | 1.09112 | ||||||||
\(459\) | 24.8605 | 1.16039 | ||||||||
\(460\) | 10.3941 | 0.484626 | ||||||||
\(461\) | 31.8776 | 1.48469 | 0.742345 | − | 0.670018i | \(-0.233714\pi\) | ||||
0.742345 | + | 0.670018i | \(0.233714\pi\) | |||||||
\(462\) | 1.98510 | 0.0923552 | ||||||||
\(463\) | −28.7756 | −1.33731 | −0.668657 | − | 0.743571i | \(-0.733130\pi\) | ||||
−0.668657 | + | 0.743571i | \(0.733130\pi\) | |||||||
\(464\) | 136.563 | 6.33976 | ||||||||
\(465\) | −2.62657 | −0.121804 | ||||||||
\(466\) | −11.9357 | −0.552910 | ||||||||
\(467\) | 10.8971 | 0.504257 | 0.252128 | − | 0.967694i | \(-0.418869\pi\) | ||||
0.252128 | + | 0.967694i | \(0.418869\pi\) | |||||||
\(468\) | −160.427 | −7.41572 | ||||||||
\(469\) | −9.53222 | −0.440157 | ||||||||
\(470\) | −8.28203 | −0.382022 | ||||||||
\(471\) | 64.9861 | 2.99440 | ||||||||
\(472\) | 25.9917 | 1.19636 | ||||||||
\(473\) | −1.11457 | −0.0512479 | ||||||||
\(474\) | −20.9173 | −0.960762 | ||||||||
\(475\) | 2.21314 | 0.101546 | ||||||||
\(476\) | 16.0441 | 0.735379 | ||||||||
\(477\) | 44.0619 | 2.01746 | ||||||||
\(478\) | −30.2561 | −1.38388 | ||||||||
\(479\) | 20.8436 | 0.952369 | 0.476185 | − | 0.879345i | \(-0.342019\pi\) | ||||
0.476185 | + | 0.879345i | \(0.342019\pi\) | |||||||
\(480\) | 17.9418 | 0.818927 | ||||||||
\(481\) | 43.6355 | 1.98961 | ||||||||
\(482\) | 77.2796 | 3.51999 | ||||||||
\(483\) | −13.1189 | −0.596931 | ||||||||
\(484\) | −60.2309 | −2.73777 | ||||||||
\(485\) | 3.19361 | 0.145014 | ||||||||
\(486\) | 38.4293 | 1.74319 | ||||||||
\(487\) | −16.1589 | −0.732229 | −0.366115 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366115 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(488\) | 75.9438 | 3.43782 | ||||||||
\(489\) | 1.00943 | 0.0456480 | ||||||||
\(490\) | −4.83191 | −0.218283 | ||||||||
\(491\) | −36.7588 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(492\) | −34.3606 | −1.54909 | ||||||||
\(493\) | 37.8972 | 1.70680 | ||||||||
\(494\) | −7.11224 | −0.319995 | ||||||||
\(495\) | 0.517184 | 0.0232457 | ||||||||
\(496\) | 54.3540 | 2.44057 | ||||||||
\(497\) | 7.17132 | 0.321678 | ||||||||
\(498\) | 85.4251 | 3.82799 | ||||||||
\(499\) | 19.7333 | 0.883384 | 0.441692 | − | 0.897167i | \(-0.354378\pi\) | ||||
0.441692 | + | 0.897167i | \(0.354378\pi\) | |||||||
\(500\) | 14.7710 | 0.660580 | ||||||||
\(501\) | −18.4344 | −0.823587 | ||||||||
\(502\) | 54.5956 | 2.43672 | ||||||||
\(503\) | 35.2246 | 1.57059 | 0.785294 | − | 0.619123i | \(-0.212512\pi\) | ||||
0.785294 | + | 0.619123i | \(0.212512\pi\) | |||||||
\(504\) | −32.4492 | −1.44540 | ||||||||
\(505\) | −2.76445 | −0.123016 | ||||||||
\(506\) | −7.38537 | −0.328320 | ||||||||
\(507\) | 57.2448 | 2.54233 | ||||||||
\(508\) | −17.4469 | −0.774080 | ||||||||
\(509\) | −0.00929338 | −0.000411922 0 | −0.000205961 | − | 1.00000i | \(-0.500066\pi\) | ||||
−0.000205961 | 1.00000i | \(0.500066\pi\) | ||||||||
\(510\) | 9.08786 | 0.402417 | ||||||||
\(511\) | −6.34356 | −0.280623 | ||||||||
\(512\) | −64.8852 | −2.86755 | ||||||||
\(513\) | −2.56174 | −0.113104 | ||||||||
\(514\) | 63.6314 | 2.80666 | ||||||||
\(515\) | 1.29384 | 0.0570132 | ||||||||
\(516\) | 45.5217 | 2.00398 | ||||||||
\(517\) | 4.32587 | 0.190252 | ||||||||
\(518\) | 13.7982 | 0.606259 | ||||||||
\(519\) | −63.0008 | −2.76543 | ||||||||
\(520\) | −15.0719 | −0.660947 | ||||||||
\(521\) | 2.27695 | 0.0997549 | 0.0498774 | − | 0.998755i | \(-0.484117\pi\) | ||||
0.0498774 | + | 0.998755i | \(0.484117\pi\) | |||||||
\(522\) | −119.826 | −5.24465 | ||||||||
\(523\) | −5.79464 | −0.253382 | −0.126691 | − | 0.991942i | \(-0.540436\pi\) | ||||
−0.126691 | + | 0.991942i | \(0.540436\pi\) | |||||||
\(524\) | −35.1924 | −1.53739 | ||||||||
\(525\) | −9.25417 | −0.403885 | ||||||||
\(526\) | −22.1637 | −0.966382 | ||||||||
\(527\) | 15.0837 | 0.657056 | ||||||||
\(528\) | −17.1050 | −0.744400 | ||||||||
\(529\) | 25.8076 | 1.12207 | ||||||||
\(530\) | 6.47157 | 0.281107 | ||||||||
\(531\) | −13.3618 | −0.579851 | ||||||||
\(532\) | −1.65326 | −0.0716777 | ||||||||
\(533\) | 12.6038 | 0.545931 | ||||||||
\(534\) | −98.9982 | −4.28407 | ||||||||
\(535\) | −4.66429 | −0.201655 | ||||||||
\(536\) | 140.193 | 6.05540 | ||||||||
\(537\) | 26.8456 | 1.15847 | ||||||||
\(538\) | −13.9605 | −0.601879 | ||||||||
\(539\) | 2.52380 | 0.108708 | ||||||||
\(540\) | −8.48695 | −0.365220 | ||||||||
\(541\) | −29.4409 | −1.26576 | −0.632881 | − | 0.774249i | \(-0.718128\pi\) | ||||
−0.632881 | + | 0.774249i | \(0.718128\pi\) | |||||||
\(542\) | −63.2229 | −2.71565 | ||||||||
\(543\) | −34.5329 | −1.48195 | ||||||||
\(544\) | −103.035 | −4.41758 | ||||||||
\(545\) | −3.52505 | −0.150996 | ||||||||
\(546\) | 29.7396 | 1.27274 | ||||||||
\(547\) | −22.4891 | −0.961563 | −0.480781 | − | 0.876840i | \(-0.659647\pi\) | ||||
−0.480781 | + | 0.876840i | \(0.659647\pi\) | |||||||
\(548\) | −72.9725 | −3.11723 | ||||||||
\(549\) | −39.0411 | −1.66623 | ||||||||
\(550\) | −5.20969 | −0.222142 | ||||||||
\(551\) | −3.90510 | −0.166363 | ||||||||
\(552\) | 192.943 | 8.21220 | ||||||||
\(553\) | 1.78353 | 0.0758432 | ||||||||
\(554\) | 11.4162 | 0.485026 | ||||||||
\(555\) | 5.74540 | 0.243879 | ||||||||
\(556\) | −50.5339 | −2.14312 | ||||||||
\(557\) | −17.9008 | −0.758480 | −0.379240 | − | 0.925298i | \(-0.623815\pi\) | ||||
−0.379240 | + | 0.925298i | \(0.623815\pi\) | |||||||
\(558\) | −47.6927 | −2.01899 | ||||||||
\(559\) | −16.6978 | −0.706242 | ||||||||
\(560\) | −2.79229 | −0.117996 | ||||||||
\(561\) | −4.74678 | −0.200409 | ||||||||
\(562\) | 3.18096 | 0.134181 | ||||||||
\(563\) | 22.5847 | 0.951833 | 0.475917 | − | 0.879490i | \(-0.342116\pi\) | ||||
0.475917 | + | 0.879490i | \(0.342116\pi\) | |||||||
\(564\) | −176.679 | −7.43953 | ||||||||
\(565\) | −0.404426 | −0.0170143 | ||||||||
\(566\) | −18.1901 | −0.764585 | ||||||||
\(567\) | 0.732751 | 0.0307727 | ||||||||
\(568\) | −105.470 | −4.42544 | ||||||||
\(569\) | −5.26548 | −0.220740 | −0.110370 | − | 0.993891i | \(-0.535204\pi\) | ||||
−0.110370 | + | 0.993891i | \(0.535204\pi\) | |||||||
\(570\) | −0.936455 | −0.0392238 | ||||||||
\(571\) | −39.5292 | −1.65424 | −0.827122 | − | 0.562023i | \(-0.810023\pi\) | ||||
−0.827122 | + | 0.562023i | \(0.810023\pi\) | |||||||
\(572\) | 12.3072 | 0.514591 | ||||||||
\(573\) | −46.9875 | −1.96293 | ||||||||
\(574\) | 3.98551 | 0.166352 | ||||||||
\(575\) | 34.4292 | 1.43580 | ||||||||
\(576\) | 168.269 | 7.01121 | ||||||||
\(577\) | −9.67339 | −0.402709 | −0.201354 | − | 0.979518i | \(-0.564534\pi\) | ||||
−0.201354 | + | 0.979518i | \(0.564534\pi\) | |||||||
\(578\) | −5.47714 | −0.227819 | ||||||||
\(579\) | 2.66266 | 0.110657 | ||||||||
\(580\) | −12.9375 | −0.537199 | ||||||||
\(581\) | −7.28383 | −0.302184 | ||||||||
\(582\) | 92.6787 | 3.84165 | ||||||||
\(583\) | −3.38024 | −0.139995 | ||||||||
\(584\) | 93.2963 | 3.86063 | ||||||||
\(585\) | 7.74815 | 0.320346 | ||||||||
\(586\) | 59.9064 | 2.47471 | ||||||||
\(587\) | −23.0707 | −0.952231 | −0.476115 | − | 0.879383i | \(-0.657956\pi\) | ||||
−0.476115 | + | 0.879383i | \(0.657956\pi\) | |||||||
\(588\) | −103.078 | −4.25087 | ||||||||
\(589\) | −1.55429 | −0.0640435 | ||||||||
\(590\) | −1.96250 | −0.0807950 | ||||||||
\(591\) | 51.5386 | 2.12002 | ||||||||
\(592\) | −118.895 | −4.88655 | ||||||||
\(593\) | 36.1559 | 1.48475 | 0.742373 | − | 0.669987i | \(-0.233700\pi\) | ||||
0.742373 | + | 0.669987i | \(0.233700\pi\) | |||||||
\(594\) | 6.03029 | 0.247426 | ||||||||
\(595\) | −0.774883 | −0.0317671 | ||||||||
\(596\) | −101.982 | −4.17736 | ||||||||
\(597\) | −73.8700 | −3.02330 | ||||||||
\(598\) | −110.643 | −4.52454 | ||||||||
\(599\) | −19.1886 | −0.784025 | −0.392013 | − | 0.919960i | \(-0.628221\pi\) | ||||
−0.392013 | + | 0.919960i | \(0.628221\pi\) | |||||||
\(600\) | 136.103 | 5.55639 | ||||||||
\(601\) | −26.2190 | −1.06950 | −0.534748 | − | 0.845012i | \(-0.679594\pi\) | ||||
−0.534748 | + | 0.845012i | \(0.679594\pi\) | |||||||
\(602\) | −5.28010 | −0.215201 | ||||||||
\(603\) | −72.0700 | −2.93492 | ||||||||
\(604\) | 80.7246 | 3.28464 | ||||||||
\(605\) | 2.90898 | 0.118267 | ||||||||
\(606\) | −80.2244 | −3.25889 | ||||||||
\(607\) | 18.2805 | 0.741983 | 0.370992 | − | 0.928636i | \(-0.379018\pi\) | ||||
0.370992 | + | 0.928636i | \(0.379018\pi\) | |||||||
\(608\) | 10.6172 | 0.430584 | ||||||||
\(609\) | 16.3291 | 0.661687 | ||||||||
\(610\) | −5.73415 | −0.232169 | ||||||||
\(611\) | 64.8077 | 2.62184 | ||||||||
\(612\) | 121.304 | 4.90343 | ||||||||
\(613\) | 23.8259 | 0.962319 | 0.481160 | − | 0.876633i | \(-0.340216\pi\) | ||||
0.481160 | + | 0.876633i | \(0.340216\pi\) | |||||||
\(614\) | −23.5840 | −0.951773 | ||||||||
\(615\) | 1.65952 | 0.0669182 | ||||||||
\(616\) | 2.48936 | 0.100299 | ||||||||
\(617\) | −36.0198 | −1.45010 | −0.725052 | − | 0.688694i | \(-0.758184\pi\) | ||||
−0.725052 | + | 0.688694i | \(0.758184\pi\) | |||||||
\(618\) | 37.5472 | 1.51037 | ||||||||
\(619\) | −24.3879 | −0.980232 | −0.490116 | − | 0.871657i | \(-0.663046\pi\) | ||||
−0.490116 | + | 0.871657i | \(0.663046\pi\) | |||||||
\(620\) | −5.14931 | −0.206801 | ||||||||
\(621\) | −39.8523 | −1.59922 | ||||||||
\(622\) | −54.9040 | −2.20145 | ||||||||
\(623\) | 8.44116 | 0.338188 | ||||||||
\(624\) | −256.257 | −10.2585 | ||||||||
\(625\) | 23.9273 | 0.957093 | ||||||||
\(626\) | −86.6118 | −3.46170 | ||||||||
\(627\) | 0.489130 | 0.0195340 | ||||||||
\(628\) | 127.403 | 5.08395 | ||||||||
\(629\) | −32.9943 | −1.31557 | ||||||||
\(630\) | 2.45008 | 0.0976136 | ||||||||
\(631\) | −28.1607 | −1.12106 | −0.560530 | − | 0.828134i | \(-0.689403\pi\) | ||||
−0.560530 | + | 0.828134i | \(0.689403\pi\) | |||||||
\(632\) | −26.2307 | −1.04340 | ||||||||
\(633\) | 19.8548 | 0.789157 | ||||||||
\(634\) | 53.4530 | 2.12289 | ||||||||
\(635\) | 0.842634 | 0.0334389 | ||||||||
\(636\) | 138.057 | 5.47432 | ||||||||
\(637\) | 37.8101 | 1.49809 | ||||||||
\(638\) | 9.19254 | 0.363936 | ||||||||
\(639\) | 54.2201 | 2.14491 | ||||||||
\(640\) | 12.0395 | 0.475904 | ||||||||
\(641\) | −13.7269 | −0.542182 | −0.271091 | − | 0.962554i | \(-0.587384\pi\) | ||||
−0.271091 | + | 0.962554i | \(0.587384\pi\) | |||||||
\(642\) | −135.358 | −5.34215 | ||||||||
\(643\) | 24.3853 | 0.961661 | 0.480830 | − | 0.876814i | \(-0.340335\pi\) | ||||
0.480830 | + | 0.876814i | \(0.340335\pi\) | |||||||
\(644\) | −25.7192 | −1.01348 | ||||||||
\(645\) | −2.19857 | −0.0865685 | ||||||||
\(646\) | 5.37781 | 0.211587 | ||||||||
\(647\) | −2.39454 | −0.0941390 | −0.0470695 | − | 0.998892i | \(-0.514988\pi\) | ||||
−0.0470695 | + | 0.998892i | \(0.514988\pi\) | |||||||
\(648\) | −10.7768 | −0.423351 | ||||||||
\(649\) | 1.02506 | 0.0402370 | ||||||||
\(650\) | −78.0485 | −3.06131 | ||||||||
\(651\) | 6.49922 | 0.254724 | ||||||||
\(652\) | 1.97896 | 0.0775020 | ||||||||
\(653\) | 2.52179 | 0.0986853 | 0.0493427 | − | 0.998782i | \(-0.484287\pi\) | ||||
0.0493427 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(654\) | −102.297 | −4.00013 | ||||||||
\(655\) | 1.69969 | 0.0664125 | ||||||||
\(656\) | −34.3419 | −1.34083 | ||||||||
\(657\) | −47.9616 | −1.87116 | ||||||||
\(658\) | 20.4932 | 0.798907 | ||||||||
\(659\) | −13.4172 | −0.522660 | −0.261330 | − | 0.965249i | \(-0.584161\pi\) | ||||
−0.261330 | + | 0.965249i | \(0.584161\pi\) | |||||||
\(660\) | 1.62047 | 0.0630767 | ||||||||
\(661\) | −32.0390 | −1.24617 | −0.623086 | − | 0.782153i | \(-0.714122\pi\) | ||||
−0.623086 | + | 0.782153i | \(0.714122\pi\) | |||||||
\(662\) | 54.1079 | 2.10296 | ||||||||
\(663\) | −71.1134 | −2.76182 | ||||||||
\(664\) | 107.125 | 4.15726 | ||||||||
\(665\) | 0.0798475 | 0.00309635 | ||||||||
\(666\) | 104.324 | 4.04247 | ||||||||
\(667\) | −60.7506 | −2.35227 | ||||||||
\(668\) | −36.1400 | −1.39830 | ||||||||
\(669\) | −20.8149 | −0.804752 | ||||||||
\(670\) | −10.5853 | −0.408944 | ||||||||
\(671\) | 2.99506 | 0.115623 | ||||||||
\(672\) | −44.3954 | −1.71259 | ||||||||
\(673\) | −22.0019 | −0.848112 | −0.424056 | − | 0.905636i | \(-0.639394\pi\) | ||||
−0.424056 | + | 0.905636i | \(0.639394\pi\) | |||||||
\(674\) | 61.1052 | 2.35369 | ||||||||
\(675\) | −28.1121 | −1.08203 | ||||||||
\(676\) | 112.227 | 4.31641 | ||||||||
\(677\) | −2.82608 | −0.108615 | −0.0543075 | − | 0.998524i | \(-0.517295\pi\) | ||||
−0.0543075 | + | 0.998524i | \(0.517295\pi\) | |||||||
\(678\) | −11.7364 | −0.450736 | ||||||||
\(679\) | −7.90231 | −0.303263 | ||||||||
\(680\) | 11.3964 | 0.437032 | ||||||||
\(681\) | −17.8974 | −0.685830 | ||||||||
\(682\) | 3.65878 | 0.140102 | ||||||||
\(683\) | −0.781159 | −0.0298902 | −0.0149451 | − | 0.999888i | \(-0.504757\pi\) | ||||
−0.0149451 | + | 0.999888i | \(0.504757\pi\) | |||||||
\(684\) | −12.4997 | −0.477939 | ||||||||
\(685\) | 3.52436 | 0.134659 | ||||||||
\(686\) | 24.7141 | 0.943589 | ||||||||
\(687\) | −24.0589 | −0.917902 | ||||||||
\(688\) | 45.4970 | 1.73456 | ||||||||
\(689\) | −50.6407 | −1.92926 | ||||||||
\(690\) | −14.5682 | −0.554601 | ||||||||
\(691\) | −21.9947 | −0.836716 | −0.418358 | − | 0.908282i | \(-0.637394\pi\) | ||||
−0.418358 | + | 0.908282i | \(0.637394\pi\) | |||||||
\(692\) | −123.511 | −4.69520 | ||||||||
\(693\) | −1.27973 | −0.0486128 | ||||||||
\(694\) | −16.6570 | −0.632292 | ||||||||
\(695\) | 2.44065 | 0.0925790 | ||||||||
\(696\) | −240.155 | −9.10306 | ||||||||
\(697\) | −9.53016 | −0.360981 | ||||||||
\(698\) | 9.17200 | 0.347165 | ||||||||
\(699\) | 12.2975 | 0.465135 | ||||||||
\(700\) | −18.1425 | −0.685723 | ||||||||
\(701\) | −14.7395 | −0.556703 | −0.278351 | − | 0.960479i | \(-0.589788\pi\) | ||||
−0.278351 | + | 0.960479i | \(0.589788\pi\) | |||||||
\(702\) | 90.3422 | 3.40975 | ||||||||
\(703\) | 3.39989 | 0.128229 | ||||||||
\(704\) | −12.9089 | −0.486521 | ||||||||
\(705\) | 8.53310 | 0.321375 | ||||||||
\(706\) | 39.6391 | 1.49184 | ||||||||
\(707\) | 6.84039 | 0.257259 | ||||||||
\(708\) | −41.8658 | −1.57341 | ||||||||
\(709\) | 35.1932 | 1.32171 | 0.660854 | − | 0.750515i | \(-0.270194\pi\) | ||||
0.660854 | + | 0.750515i | \(0.270194\pi\) | |||||||
\(710\) | 7.96355 | 0.298867 | ||||||||
\(711\) | 13.4847 | 0.505714 | ||||||||
\(712\) | −124.146 | −4.65257 | ||||||||
\(713\) | −24.1797 | −0.905537 | ||||||||
\(714\) | −22.4871 | −0.841560 | ||||||||
\(715\) | −0.594404 | −0.0222295 | ||||||||
\(716\) | 52.6301 | 1.96688 | ||||||||
\(717\) | 31.1733 | 1.16419 | ||||||||
\(718\) | 2.53733 | 0.0946922 | ||||||||
\(719\) | 1.76054 | 0.0656570 | 0.0328285 | − | 0.999461i | \(-0.489548\pi\) | ||||
0.0328285 | + | 0.999461i | \(0.489548\pi\) | |||||||
\(720\) | −21.1116 | −0.786783 | ||||||||
\(721\) | −3.20148 | −0.119230 | ||||||||
\(722\) | 51.6534 | 1.92234 | ||||||||
\(723\) | −79.6223 | −2.96119 | ||||||||
\(724\) | −67.7007 | −2.51608 | ||||||||
\(725\) | −42.8539 | −1.59155 | ||||||||
\(726\) | 84.4188 | 3.13307 | ||||||||
\(727\) | 34.4891 | 1.27913 | 0.639565 | − | 0.768737i | \(-0.279115\pi\) | ||||
0.639565 | + | 0.768737i | \(0.279115\pi\) | |||||||
\(728\) | 37.2942 | 1.38221 | ||||||||
\(729\) | −42.9084 | −1.58920 | ||||||||
\(730\) | −7.04434 | −0.260723 | ||||||||
\(731\) | 12.6258 | 0.466982 | ||||||||
\(732\) | −122.326 | −4.52128 | ||||||||
\(733\) | −17.9628 | −0.663473 | −0.331736 | − | 0.943372i | \(-0.607634\pi\) | ||||
−0.331736 | + | 0.943372i | \(0.607634\pi\) | |||||||
\(734\) | −63.7127 | −2.35168 | ||||||||
\(735\) | 4.97838 | 0.183630 | ||||||||
\(736\) | 165.169 | 6.08820 | ||||||||
\(737\) | 5.52890 | 0.203660 | ||||||||
\(738\) | 30.1332 | 1.10922 | ||||||||
\(739\) | −41.6129 | −1.53075 | −0.765377 | − | 0.643582i | \(-0.777448\pi\) | ||||
−0.765377 | + | 0.643582i | \(0.777448\pi\) | |||||||
\(740\) | 11.2637 | 0.414062 | ||||||||
\(741\) | 7.32785 | 0.269195 | ||||||||
\(742\) | −16.0134 | −0.587869 | ||||||||
\(743\) | 4.82500 | 0.177012 | 0.0885061 | − | 0.996076i | \(-0.471791\pi\) | ||||
0.0885061 | + | 0.996076i | \(0.471791\pi\) | |||||||
\(744\) | −95.5856 | −3.50434 | ||||||||
\(745\) | 4.92546 | 0.180455 | ||||||||
\(746\) | −22.5283 | −0.824821 | ||||||||
\(747\) | −55.0707 | −2.01493 | ||||||||
\(748\) | −9.30592 | −0.340258 | ||||||||
\(749\) | 11.5414 | 0.421713 | ||||||||
\(750\) | −20.7028 | −0.755960 | ||||||||
\(751\) | 21.5459 | 0.786221 | 0.393110 | − | 0.919491i | \(-0.371399\pi\) | ||||
0.393110 | + | 0.919491i | \(0.371399\pi\) | |||||||
\(752\) | −176.583 | −6.43933 | ||||||||
\(753\) | −56.2507 | −2.04989 | ||||||||
\(754\) | 137.717 | 5.01537 | ||||||||
\(755\) | −3.89877 | −0.141891 | ||||||||
\(756\) | 21.0002 | 0.763771 | ||||||||
\(757\) | −53.9524 | −1.96093 | −0.980467 | − | 0.196683i | \(-0.936983\pi\) | ||||
−0.980467 | + | 0.196683i | \(0.936983\pi\) | |||||||
\(758\) | 21.2758 | 0.772772 | ||||||||
\(759\) | 7.60926 | 0.276199 | ||||||||
\(760\) | −1.17434 | −0.0425977 | ||||||||
\(761\) | 20.5337 | 0.744347 | 0.372174 | − | 0.928163i | \(-0.378613\pi\) | ||||
0.372174 | + | 0.928163i | \(0.378613\pi\) | |||||||
\(762\) | 24.4533 | 0.885848 | ||||||||
\(763\) | 8.72242 | 0.315773 | ||||||||
\(764\) | −92.1177 | −3.33270 | ||||||||
\(765\) | −5.85864 | −0.211820 | ||||||||
\(766\) | −35.8047 | −1.29367 | ||||||||
\(767\) | 15.3568 | 0.554501 | ||||||||
\(768\) | 159.402 | 5.75194 | ||||||||
\(769\) | 47.4625 | 1.71154 | 0.855770 | − | 0.517357i | \(-0.173084\pi\) | ||||
0.855770 | + | 0.517357i | \(0.173084\pi\) | |||||||
\(770\) | −0.187960 | −0.00677359 | ||||||||
\(771\) | −65.5604 | −2.36110 | ||||||||
\(772\) | 5.22008 | 0.187875 | ||||||||
\(773\) | 5.37205 | 0.193219 | 0.0966096 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966096 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(774\) | −39.9211 | −1.43494 | ||||||||
\(775\) | −17.0565 | −0.612688 | ||||||||
\(776\) | 116.221 | 4.17210 | ||||||||
\(777\) | −14.2165 | −0.510014 | ||||||||
\(778\) | 5.09576 | 0.182692 | ||||||||
\(779\) | 0.982032 | 0.0351849 | ||||||||
\(780\) | 24.2769 | 0.869253 | ||||||||
\(781\) | −4.15953 | −0.148840 | ||||||||
\(782\) | 83.6612 | 2.99172 | ||||||||
\(783\) | 49.6040 | 1.77270 | ||||||||
\(784\) | −103.022 | −3.67937 | ||||||||
\(785\) | −6.15322 | −0.219618 | ||||||||
\(786\) | 49.3251 | 1.75937 | ||||||||
\(787\) | 2.09839 | 0.0747997 | 0.0373998 | − | 0.999300i | \(-0.488092\pi\) | ||||
0.0373998 | + | 0.999300i | \(0.488092\pi\) | |||||||
\(788\) | 101.040 | 3.59940 | ||||||||
\(789\) | 22.8356 | 0.812967 | ||||||||
\(790\) | 1.98055 | 0.0704650 | ||||||||
\(791\) | 1.00072 | 0.0355814 | ||||||||
\(792\) | 18.8213 | 0.668784 | ||||||||
\(793\) | 44.8702 | 1.59339 | ||||||||
\(794\) | −96.1692 | −3.41292 | ||||||||
\(795\) | −6.66776 | −0.236481 | ||||||||
\(796\) | −144.820 | −5.13301 | ||||||||
\(797\) | 45.8513 | 1.62414 | 0.812069 | − | 0.583562i | \(-0.198341\pi\) | ||||
0.812069 | + | 0.583562i | \(0.198341\pi\) | |||||||
\(798\) | 2.31718 | 0.0820272 | ||||||||
\(799\) | −49.0033 | −1.73361 | ||||||||
\(800\) | 116.511 | 4.11929 | ||||||||
\(801\) | 63.8208 | 2.25500 | ||||||||
\(802\) | −62.2936 | −2.19966 | ||||||||
\(803\) | 3.67941 | 0.129843 | ||||||||
\(804\) | −225.814 | −7.96383 | ||||||||
\(805\) | 1.24217 | 0.0437806 | ||||||||
\(806\) | 54.8136 | 1.93073 | ||||||||
\(807\) | 14.3837 | 0.506330 | ||||||||
\(808\) | −100.603 | −3.53921 | ||||||||
\(809\) | −9.69767 | −0.340952 | −0.170476 | − | 0.985362i | \(-0.554531\pi\) | ||||
−0.170476 | + | 0.985362i | \(0.554531\pi\) | |||||||
\(810\) | 0.813700 | 0.0285905 | ||||||||
\(811\) | 18.7242 | 0.657497 | 0.328748 | − | 0.944418i | \(-0.393373\pi\) | ||||
0.328748 | + | 0.944418i | \(0.393373\pi\) | |||||||
\(812\) | 32.0126 | 1.12342 | ||||||||
\(813\) | 65.1395 | 2.28454 | ||||||||
\(814\) | −8.00327 | −0.280514 | ||||||||
\(815\) | −0.0955781 | −0.00334795 | ||||||||
\(816\) | 193.765 | 6.78312 | ||||||||
\(817\) | −1.30102 | −0.0455169 | ||||||||
\(818\) | −24.1740 | −0.845225 | ||||||||
\(819\) | −19.1721 | −0.669928 | ||||||||
\(820\) | 3.25344 | 0.113615 | ||||||||
\(821\) | 36.3840 | 1.26981 | 0.634906 | − | 0.772589i | \(-0.281039\pi\) | ||||
0.634906 | + | 0.772589i | \(0.281039\pi\) | |||||||
\(822\) | 102.277 | 3.56732 | ||||||||
\(823\) | 12.4426 | 0.433723 | 0.216861 | − | 0.976202i | \(-0.430418\pi\) | ||||
0.216861 | + | 0.976202i | \(0.430418\pi\) | |||||||
\(824\) | 47.0850 | 1.64028 | ||||||||
\(825\) | 5.36762 | 0.186877 | ||||||||
\(826\) | 4.85605 | 0.168963 | ||||||||
\(827\) | −11.4381 | −0.397741 | −0.198871 | − | 0.980026i | \(-0.563727\pi\) | ||||
−0.198871 | + | 0.980026i | \(0.563727\pi\) | |||||||
\(828\) | −194.455 | −6.75777 | ||||||||
\(829\) | −43.7258 | −1.51866 | −0.759330 | − | 0.650705i | \(-0.774473\pi\) | ||||
−0.759330 | + | 0.650705i | \(0.774473\pi\) | |||||||
\(830\) | −8.08849 | −0.280755 | ||||||||
\(831\) | −11.7622 | −0.408028 | ||||||||
\(832\) | −193.393 | −6.70470 | ||||||||
\(833\) | −28.5895 | −0.990569 | ||||||||
\(834\) | 70.8276 | 2.45256 | ||||||||
\(835\) | 1.74546 | 0.0604042 | ||||||||
\(836\) | 0.958925 | 0.0331651 | ||||||||
\(837\) | 19.7432 | 0.682423 | ||||||||
\(838\) | 5.03825 | 0.174043 | ||||||||
\(839\) | 25.5731 | 0.882883 | 0.441441 | − | 0.897290i | \(-0.354467\pi\) | ||||
0.441441 | + | 0.897290i | \(0.354467\pi\) | |||||||
\(840\) | 4.91045 | 0.169427 | ||||||||
\(841\) | 46.6161 | 1.60745 | ||||||||
\(842\) | 30.9408 | 1.06629 | ||||||||
\(843\) | −3.27739 | −0.112879 | ||||||||
\(844\) | 38.9248 | 1.33985 | ||||||||
\(845\) | −5.42023 | −0.186462 | ||||||||
\(846\) | 154.942 | 5.32702 | ||||||||
\(847\) | −7.19803 | −0.247327 | ||||||||
\(848\) | 137.982 | 4.73833 | ||||||||
\(849\) | 18.7415 | 0.643206 | ||||||||
\(850\) | 59.0151 | 2.02420 | ||||||||
\(851\) | 52.8911 | 1.81308 | ||||||||
\(852\) | 169.885 | 5.82017 | ||||||||
\(853\) | −25.0225 | −0.856755 | −0.428378 | − | 0.903600i | \(-0.640915\pi\) | ||||
−0.428378 | + | 0.903600i | \(0.640915\pi\) | |||||||
\(854\) | 14.1887 | 0.485526 | ||||||||
\(855\) | 0.603701 | 0.0206461 | ||||||||
\(856\) | −169.742 | −5.80166 | ||||||||
\(857\) | 15.2920 | 0.522365 | 0.261182 | − | 0.965289i | \(-0.415888\pi\) | ||||
0.261182 | + | 0.965289i | \(0.415888\pi\) | |||||||
\(858\) | −17.2496 | −0.588893 | ||||||||
\(859\) | −17.8572 | −0.609279 | −0.304639 | − | 0.952468i | \(-0.598536\pi\) | ||||
−0.304639 | + | 0.952468i | \(0.598536\pi\) | |||||||
\(860\) | −4.31023 | −0.146978 | ||||||||
\(861\) | −4.10633 | −0.139943 | ||||||||
\(862\) | −80.6193 | −2.74591 | ||||||||
\(863\) | −34.1387 | −1.16210 | −0.581048 | − | 0.813870i | \(-0.697357\pi\) | ||||
−0.581048 | + | 0.813870i | \(0.697357\pi\) | |||||||
\(864\) | −134.863 | −4.58814 | ||||||||
\(865\) | 5.96524 | 0.202824 | ||||||||
\(866\) | −97.8655 | −3.32561 | ||||||||
\(867\) | 5.64318 | 0.191652 | ||||||||
\(868\) | 12.7415 | 0.432476 | ||||||||
\(869\) | −1.03448 | −0.0350925 | ||||||||
\(870\) | 18.1330 | 0.614765 | ||||||||
\(871\) | 82.8307 | 2.80661 | ||||||||
\(872\) | −128.283 | −4.34420 | ||||||||
\(873\) | −59.7468 | −2.02212 | ||||||||
\(874\) | −8.62083 | −0.291604 | ||||||||
\(875\) | 1.76524 | 0.0596760 | ||||||||
\(876\) | −150.276 | −5.07735 | ||||||||
\(877\) | −40.8185 | −1.37834 | −0.689171 | − | 0.724599i | \(-0.742025\pi\) | ||||
−0.689171 | + | 0.724599i | \(0.742025\pi\) | |||||||
\(878\) | −75.8449 | −2.55964 | ||||||||
\(879\) | −61.7225 | −2.08185 | ||||||||
\(880\) | 1.61959 | 0.0545964 | ||||||||
\(881\) | 30.3932 | 1.02397 | 0.511986 | − | 0.858994i | \(-0.328910\pi\) | ||||
0.511986 | + | 0.858994i | \(0.328910\pi\) | |||||||
\(882\) | 90.3965 | 3.04381 | ||||||||
\(883\) | 41.1549 | 1.38497 | 0.692486 | − | 0.721431i | \(-0.256515\pi\) | ||||
0.692486 | + | 0.721431i | \(0.256515\pi\) | |||||||
\(884\) | −139.416 | −4.68906 | ||||||||
\(885\) | 2.02200 | 0.0679687 | ||||||||
\(886\) | 77.5093 | 2.60398 | ||||||||
\(887\) | 51.8259 | 1.74014 | 0.870072 | − | 0.492925i | \(-0.164072\pi\) | ||||
0.870072 | + | 0.492925i | \(0.164072\pi\) | |||||||
\(888\) | 209.086 | 7.01645 | ||||||||
\(889\) | −2.08503 | −0.0699295 | ||||||||
\(890\) | 9.37367 | 0.314206 | ||||||||
\(891\) | −0.425012 | −0.0142384 | ||||||||
\(892\) | −40.8071 | −1.36632 | ||||||||
\(893\) | 5.04953 | 0.168976 | ||||||||
\(894\) | 142.937 | 4.78053 | ||||||||
\(895\) | −2.54188 | −0.0849658 | ||||||||
\(896\) | −29.7908 | −0.995240 | ||||||||
\(897\) | 113.997 | 3.80626 | ||||||||
\(898\) | −54.2712 | −1.81105 | ||||||||
\(899\) | 30.0964 | 1.00377 | ||||||||
\(900\) | −137.170 | −4.57233 | ||||||||
\(901\) | 38.2912 | 1.27566 | ||||||||
\(902\) | −2.31168 | −0.0769707 | ||||||||
\(903\) | 5.44017 | 0.181037 | ||||||||
\(904\) | −14.7178 | −0.489506 | ||||||||
\(905\) | 3.26975 | 0.108690 | ||||||||
\(906\) | −113.142 | −3.75890 | ||||||||
\(907\) | 18.2405 | 0.605665 | 0.302833 | − | 0.953044i | \(-0.402068\pi\) | ||||
0.302833 | + | 0.953044i | \(0.402068\pi\) | |||||||
\(908\) | −35.0874 | −1.16442 | ||||||||
\(909\) | 51.7180 | 1.71538 | ||||||||
\(910\) | −2.81590 | −0.0933461 | ||||||||
\(911\) | 32.3369 | 1.07137 | 0.535685 | − | 0.844418i | \(-0.320054\pi\) | ||||
0.535685 | + | 0.844418i | \(0.320054\pi\) | |||||||
\(912\) | −19.9664 | −0.661154 | ||||||||
\(913\) | 4.22478 | 0.139820 | ||||||||
\(914\) | −61.6957 | −2.04071 | ||||||||
\(915\) | 5.90798 | 0.195312 | ||||||||
\(916\) | −47.1667 | −1.55843 | ||||||||
\(917\) | −4.20574 | −0.138886 | ||||||||
\(918\) | −68.3108 | −2.25459 | ||||||||
\(919\) | −10.0951 | −0.333006 | −0.166503 | − | 0.986041i | \(-0.553248\pi\) | ||||
−0.166503 | + | 0.986041i | \(0.553248\pi\) | |||||||
\(920\) | −18.2688 | −0.602306 | ||||||||
\(921\) | 24.2989 | 0.800677 | ||||||||
\(922\) | −87.5923 | −2.88470 | ||||||||
\(923\) | −62.3156 | −2.05114 | ||||||||
\(924\) | −4.00971 | −0.131910 | ||||||||
\(925\) | 37.3097 | 1.22674 | ||||||||
\(926\) | 79.0685 | 2.59835 | ||||||||
\(927\) | −24.2054 | −0.795009 | ||||||||
\(928\) | −205.585 | −6.74865 | ||||||||
\(929\) | −24.2582 | −0.795887 | −0.397943 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(930\) | 7.21720 | 0.236661 | ||||||||
\(931\) | 2.94600 | 0.0965511 | ||||||||
\(932\) | 24.1089 | 0.789714 | ||||||||
\(933\) | 56.5684 | 1.85197 | ||||||||
\(934\) | −29.9426 | −0.979753 | ||||||||
\(935\) | 0.449449 | 0.0146986 | ||||||||
\(936\) | 281.969 | 9.21645 | ||||||||
\(937\) | −11.4323 | −0.373477 | −0.186738 | − | 0.982410i | \(-0.559792\pi\) | ||||
−0.186738 | + | 0.982410i | \(0.559792\pi\) | |||||||
\(938\) | 26.1923 | 0.855210 | ||||||||
\(939\) | 89.2375 | 2.91215 | ||||||||
\(940\) | 16.7289 | 0.545636 | ||||||||
\(941\) | −46.2305 | −1.50707 | −0.753536 | − | 0.657407i | \(-0.771653\pi\) | ||||
−0.753536 | + | 0.657407i | \(0.771653\pi\) | |||||||
\(942\) | −178.567 | −5.81801 | ||||||||
\(943\) | 15.2772 | 0.497494 | ||||||||
\(944\) | −41.8431 | −1.36188 | ||||||||
\(945\) | −1.01425 | −0.0329936 | ||||||||
\(946\) | 3.06258 | 0.0995729 | ||||||||
\(947\) | −29.9459 | −0.973110 | −0.486555 | − | 0.873650i | \(-0.661747\pi\) | ||||
−0.486555 | + | 0.873650i | \(0.661747\pi\) | |||||||
\(948\) | 42.2508 | 1.37224 | ||||||||
\(949\) | 55.1227 | 1.78936 | ||||||||
\(950\) | −6.08119 | −0.197300 | ||||||||
\(951\) | −55.0734 | −1.78588 | ||||||||
\(952\) | −28.1994 | −0.913947 | ||||||||
\(953\) | 31.5644 | 1.02247 | 0.511235 | − | 0.859441i | \(-0.329188\pi\) | ||||
0.511235 | + | 0.859441i | \(0.329188\pi\) | |||||||
\(954\) | −121.072 | −3.91984 | ||||||||
\(955\) | 4.44902 | 0.143967 | ||||||||
\(956\) | 61.1144 | 1.97658 | ||||||||
\(957\) | −9.47121 | −0.306161 | ||||||||
\(958\) | −57.2734 | −1.85042 | ||||||||
\(959\) | −8.72073 | −0.281607 | ||||||||
\(960\) | −25.4637 | −0.821837 | ||||||||
\(961\) | −19.0212 | −0.613586 | ||||||||
\(962\) | −119.900 | −3.86574 | ||||||||
\(963\) | 87.2607 | 2.81194 | ||||||||
\(964\) | −156.097 | −5.02756 | ||||||||
\(965\) | −0.252115 | −0.00811586 | ||||||||
\(966\) | 36.0477 | 1.15982 | ||||||||
\(967\) | 16.6516 | 0.535478 | 0.267739 | − | 0.963491i | \(-0.413723\pi\) | ||||
0.267739 | + | 0.963491i | \(0.413723\pi\) | |||||||
\(968\) | 105.863 | 3.40257 | ||||||||
\(969\) | −5.54084 | −0.177997 | ||||||||
\(970\) | −8.77530 | −0.281758 | ||||||||
\(971\) | −40.4620 | −1.29849 | −0.649244 | − | 0.760580i | \(-0.724915\pi\) | ||||
−0.649244 | + | 0.760580i | \(0.724915\pi\) | |||||||
\(972\) | −77.6234 | −2.48977 | ||||||||
\(973\) | −6.03917 | −0.193607 | ||||||||
\(974\) | 44.4009 | 1.42270 | ||||||||
\(975\) | 80.4145 | 2.57533 | ||||||||
\(976\) | −122.259 | −3.91342 | ||||||||
\(977\) | −31.3387 | −1.00262 | −0.501308 | − | 0.865269i | \(-0.667148\pi\) | ||||
−0.501308 | + | 0.865269i | \(0.667148\pi\) | |||||||
\(978\) | −2.77368 | −0.0886925 | ||||||||
\(979\) | −4.89606 | −0.156479 | ||||||||
\(980\) | 9.75998 | 0.311771 | ||||||||
\(981\) | 65.9474 | 2.10554 | ||||||||
\(982\) | 101.005 | 3.22318 | ||||||||
\(983\) | 15.9832 | 0.509784 | 0.254892 | − | 0.966970i | \(-0.417960\pi\) | ||||
0.254892 | + | 0.966970i | \(0.417960\pi\) | |||||||
\(984\) | 60.3928 | 1.92525 | ||||||||
\(985\) | −4.87994 | −0.155488 | ||||||||
\(986\) | −104.133 | −3.31626 | ||||||||
\(987\) | −21.1144 | −0.672079 | ||||||||
\(988\) | 14.3660 | 0.457045 | ||||||||
\(989\) | −20.2396 | −0.643582 | ||||||||
\(990\) | −1.42110 | −0.0451656 | ||||||||
\(991\) | −47.9200 | −1.52223 | −0.761114 | − | 0.648618i | \(-0.775347\pi\) | ||||
−0.761114 | + | 0.648618i | \(0.775347\pi\) | |||||||
\(992\) | −81.8260 | −2.59798 | ||||||||
\(993\) | −55.7482 | −1.76911 | ||||||||
\(994\) | −19.7051 | −0.625009 | ||||||||
\(995\) | 6.99439 | 0.221737 | ||||||||
\(996\) | −172.550 | −5.46747 | ||||||||
\(997\) | 53.1162 | 1.68221 | 0.841103 | − | 0.540875i | \(-0.181907\pi\) | ||||
0.841103 | + | 0.540875i | \(0.181907\pi\) | |||||||
\(998\) | −54.2225 | −1.71638 | ||||||||
\(999\) | −43.1865 | −1.36636 |
(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 | 6047.2.a.a.1.4 | ✓ | 217 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.a.1.4 | ✓ | 217 | 1.1 | even | 1 | trivial |