Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60157 | −1.83959 | −0.919794 | − | 0.392401i | \(-0.871644\pi\) | ||||
−0.919794 | + | 0.392401i | \(0.871644\pi\) | |||||||
\(3\) | 0.915852 | 0.528767 | 0.264384 | − | 0.964418i | \(-0.414832\pi\) | ||||
0.264384 | + | 0.964418i | \(0.414832\pi\) | |||||||
\(4\) | 4.76817 | 2.38408 | ||||||||
\(5\) | −4.25711 | −1.90384 | −0.951919 | − | 0.306349i | \(-0.900892\pi\) | ||||
−0.951919 | + | 0.306349i | \(0.900892\pi\) | |||||||
\(6\) | −2.38265 | −0.972714 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.20159 | −2.54615 | ||||||||
\(9\) | −2.16122 | −0.720405 | ||||||||
\(10\) | 11.0752 | 3.50228 | ||||||||
\(11\) | 0.535628 | 0.161498 | 0.0807489 | − | 0.996734i | \(-0.474269\pi\) | ||||
0.0807489 | + | 0.996734i | \(0.474269\pi\) | |||||||
\(12\) | 4.36694 | 1.26063 | ||||||||
\(13\) | 3.11863 | 0.864951 | 0.432476 | − | 0.901646i | \(-0.357640\pi\) | ||||
0.432476 | + | 0.901646i | \(0.357640\pi\) | |||||||
\(14\) | −2.60157 | −0.695299 | ||||||||
\(15\) | −3.89888 | −1.00669 | ||||||||
\(16\) | 9.19910 | 2.29978 | ||||||||
\(17\) | 2.52035 | 0.611274 | 0.305637 | − | 0.952148i | \(-0.401131\pi\) | ||||
0.305637 | + | 0.952148i | \(0.401131\pi\) | |||||||
\(18\) | 5.62256 | 1.32525 | ||||||||
\(19\) | 1.79226 | 0.411173 | 0.205587 | − | 0.978639i | \(-0.434090\pi\) | ||||
0.205587 | + | 0.978639i | \(0.434090\pi\) | |||||||
\(20\) | −20.2986 | −4.53891 | ||||||||
\(21\) | 0.915852 | 0.199855 | ||||||||
\(22\) | −1.39347 | −0.297090 | ||||||||
\(23\) | 1.05441 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(24\) | −6.59559 | −1.34632 | ||||||||
\(25\) | 13.1230 | 2.62460 | ||||||||
\(26\) | −8.11333 | −1.59115 | ||||||||
\(27\) | −4.72691 | −0.909694 | ||||||||
\(28\) | 4.76817 | 0.901099 | ||||||||
\(29\) | 8.42416 | 1.56433 | 0.782164 | − | 0.623073i | \(-0.214116\pi\) | ||||
0.782164 | + | 0.623073i | \(0.214116\pi\) | |||||||
\(30\) | 10.1432 | 1.85189 | ||||||||
\(31\) | −7.53448 | −1.35323 | −0.676616 | − | 0.736336i | \(-0.736554\pi\) | ||||
−0.676616 | + | 0.736336i | \(0.736554\pi\) | |||||||
\(32\) | −9.52894 | −1.68449 | ||||||||
\(33\) | 0.490556 | 0.0853948 | ||||||||
\(34\) | −6.55686 | −1.12449 | ||||||||
\(35\) | −4.25711 | −0.719583 | ||||||||
\(36\) | −10.3050 | −1.71751 | ||||||||
\(37\) | 7.37919 | 1.21313 | 0.606566 | − | 0.795033i | \(-0.292547\pi\) | ||||
0.606566 | + | 0.795033i | \(0.292547\pi\) | |||||||
\(38\) | −4.66270 | −0.756389 | ||||||||
\(39\) | 2.85620 | 0.457358 | ||||||||
\(40\) | 30.6580 | 4.84745 | ||||||||
\(41\) | −11.4021 | −1.78071 | −0.890355 | − | 0.455266i | \(-0.849544\pi\) | ||||
−0.890355 | + | 0.455266i | \(0.849544\pi\) | |||||||
\(42\) | −2.38265 | −0.367651 | ||||||||
\(43\) | 7.82399 | 1.19315 | 0.596574 | − | 0.802558i | \(-0.296528\pi\) | ||||
0.596574 | + | 0.802558i | \(0.296528\pi\) | |||||||
\(44\) | 2.55396 | 0.385025 | ||||||||
\(45\) | 9.20054 | 1.37154 | ||||||||
\(46\) | −2.74313 | −0.404453 | ||||||||
\(47\) | −9.30525 | −1.35731 | −0.678655 | − | 0.734457i | \(-0.737437\pi\) | ||||
−0.678655 | + | 0.734457i | \(0.737437\pi\) | |||||||
\(48\) | 8.42501 | 1.21605 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −34.1404 | −4.82818 | ||||||||
\(51\) | 2.30826 | 0.323221 | ||||||||
\(52\) | 14.8701 | 2.06212 | ||||||||
\(53\) | 5.88495 | 0.808359 | 0.404180 | − | 0.914680i | \(-0.367557\pi\) | ||||
0.404180 | + | 0.914680i | \(0.367557\pi\) | |||||||
\(54\) | 12.2974 | 1.67346 | ||||||||
\(55\) | −2.28023 | −0.307466 | ||||||||
\(56\) | −7.20159 | −0.962353 | ||||||||
\(57\) | 1.64145 | 0.217415 | ||||||||
\(58\) | −21.9161 | −2.87772 | ||||||||
\(59\) | 9.36524 | 1.21925 | 0.609625 | − | 0.792690i | \(-0.291320\pi\) | ||||
0.609625 | + | 0.792690i | \(0.291320\pi\) | |||||||
\(60\) | −18.5905 | −2.40003 | ||||||||
\(61\) | −4.82680 | −0.618009 | −0.309005 | − | 0.951061i | \(-0.599996\pi\) | ||||
−0.309005 | + | 0.951061i | \(0.599996\pi\) | |||||||
\(62\) | 19.6015 | 2.48939 | ||||||||
\(63\) | −2.16122 | −0.272288 | ||||||||
\(64\) | 6.39200 | 0.799000 | ||||||||
\(65\) | −13.2763 | −1.64673 | ||||||||
\(66\) | −1.27621 | −0.157091 | ||||||||
\(67\) | 5.73380 | 0.700495 | 0.350247 | − | 0.936657i | \(-0.386098\pi\) | ||||
0.350247 | + | 0.936657i | \(0.386098\pi\) | |||||||
\(68\) | 12.0174 | 1.45733 | ||||||||
\(69\) | 0.965687 | 0.116255 | ||||||||
\(70\) | 11.0752 | 1.32374 | ||||||||
\(71\) | −14.7838 | −1.75452 | −0.877258 | − | 0.480020i | \(-0.840630\pi\) | ||||
−0.877258 | + | 0.480020i | \(0.840630\pi\) | |||||||
\(72\) | 15.5642 | 1.83426 | ||||||||
\(73\) | −3.90120 | −0.456601 | −0.228300 | − | 0.973591i | \(-0.573317\pi\) | ||||
−0.228300 | + | 0.973591i | \(0.573317\pi\) | |||||||
\(74\) | −19.1975 | −2.23166 | ||||||||
\(75\) | 12.0187 | 1.38780 | ||||||||
\(76\) | 8.54581 | 0.980272 | ||||||||
\(77\) | 0.535628 | 0.0610404 | ||||||||
\(78\) | −7.43060 | −0.841350 | ||||||||
\(79\) | 8.77085 | 0.986797 | 0.493399 | − | 0.869803i | \(-0.335754\pi\) | ||||
0.493399 | + | 0.869803i | \(0.335754\pi\) | |||||||
\(80\) | −39.1616 | −4.37840 | ||||||||
\(81\) | 2.15450 | 0.239389 | ||||||||
\(82\) | 29.6634 | 3.27577 | ||||||||
\(83\) | −1.52254 | −0.167120 | −0.0835601 | − | 0.996503i | \(-0.526629\pi\) | ||||
−0.0835601 | + | 0.996503i | \(0.526629\pi\) | |||||||
\(84\) | 4.36694 | 0.476472 | ||||||||
\(85\) | −10.7294 | −1.16377 | ||||||||
\(86\) | −20.3547 | −2.19490 | ||||||||
\(87\) | 7.71528 | 0.827165 | ||||||||
\(88\) | −3.85737 | −0.411197 | ||||||||
\(89\) | −2.42793 | −0.257360 | −0.128680 | − | 0.991686i | \(-0.541074\pi\) | ||||
−0.128680 | + | 0.991686i | \(0.541074\pi\) | |||||||
\(90\) | −23.9359 | −2.52306 | ||||||||
\(91\) | 3.11863 | 0.326921 | ||||||||
\(92\) | 5.02762 | 0.524166 | ||||||||
\(93\) | −6.90046 | −0.715544 | ||||||||
\(94\) | 24.2083 | 2.49689 | ||||||||
\(95\) | −7.62986 | −0.782807 | ||||||||
\(96\) | −8.72709 | −0.890705 | ||||||||
\(97\) | −16.3991 | −1.66508 | −0.832538 | − | 0.553967i | \(-0.813113\pi\) | ||||
−0.832538 | + | 0.553967i | \(0.813113\pi\) | |||||||
\(98\) | −2.60157 | −0.262798 | ||||||||
\(99\) | −1.15761 | −0.116344 | ||||||||
\(100\) | 62.5727 | 6.25727 | ||||||||
\(101\) | −9.15391 | −0.910848 | −0.455424 | − | 0.890275i | \(-0.650512\pi\) | ||||
−0.455424 | + | 0.890275i | \(0.650512\pi\) | |||||||
\(102\) | −6.00511 | −0.594594 | ||||||||
\(103\) | −7.63561 | −0.752359 | −0.376180 | − | 0.926547i | \(-0.622762\pi\) | ||||
−0.376180 | + | 0.926547i | \(0.622762\pi\) | |||||||
\(104\) | −22.4591 | −2.20229 | ||||||||
\(105\) | −3.89888 | −0.380492 | ||||||||
\(106\) | −15.3101 | −1.48705 | ||||||||
\(107\) | 5.02839 | 0.486113 | 0.243057 | − | 0.970012i | \(-0.421850\pi\) | ||||
0.243057 | + | 0.970012i | \(0.421850\pi\) | |||||||
\(108\) | −22.5387 | −2.16879 | ||||||||
\(109\) | 12.8559 | 1.23137 | 0.615686 | − | 0.787991i | \(-0.288879\pi\) | ||||
0.615686 | + | 0.787991i | \(0.288879\pi\) | |||||||
\(110\) | 5.93217 | 0.565610 | ||||||||
\(111\) | 6.75824 | 0.641464 | ||||||||
\(112\) | 9.19910 | 0.869234 | ||||||||
\(113\) | −2.04921 | −0.192774 | −0.0963868 | − | 0.995344i | \(-0.530729\pi\) | ||||
−0.0963868 | + | 0.995344i | \(0.530729\pi\) | |||||||
\(114\) | −4.27034 | −0.399954 | ||||||||
\(115\) | −4.48876 | −0.418579 | ||||||||
\(116\) | 40.1678 | 3.72949 | ||||||||
\(117\) | −6.74002 | −0.623115 | ||||||||
\(118\) | −24.3643 | −2.24292 | ||||||||
\(119\) | 2.52035 | 0.231040 | ||||||||
\(120\) | 28.0782 | 2.56317 | ||||||||
\(121\) | −10.7131 | −0.973918 | ||||||||
\(122\) | 12.5573 | 1.13688 | ||||||||
\(123\) | −10.4426 | −0.941581 | ||||||||
\(124\) | −35.9257 | −3.22622 | ||||||||
\(125\) | −34.5805 | −3.09298 | ||||||||
\(126\) | 5.62256 | 0.500897 | ||||||||
\(127\) | −8.55230 | −0.758894 | −0.379447 | − | 0.925213i | \(-0.623886\pi\) | ||||
−0.379447 | + | 0.925213i | \(0.623886\pi\) | |||||||
\(128\) | 2.42863 | 0.214663 | ||||||||
\(129\) | 7.16562 | 0.630897 | ||||||||
\(130\) | 34.5393 | 3.02930 | ||||||||
\(131\) | 9.40716 | 0.821907 | 0.410954 | − | 0.911656i | \(-0.365196\pi\) | ||||
0.410954 | + | 0.911656i | \(0.365196\pi\) | |||||||
\(132\) | 2.33905 | 0.203588 | ||||||||
\(133\) | 1.79226 | 0.155409 | ||||||||
\(134\) | −14.9169 | −1.28862 | ||||||||
\(135\) | 20.1230 | 1.73191 | ||||||||
\(136\) | −18.1505 | −1.55639 | ||||||||
\(137\) | −5.29343 | −0.452249 | −0.226124 | − | 0.974098i | \(-0.572606\pi\) | ||||
−0.226124 | + | 0.974098i | \(0.572606\pi\) | |||||||
\(138\) | −2.51230 | −0.213861 | ||||||||
\(139\) | 1.42688 | 0.121026 | 0.0605130 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605130 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(140\) | −20.2986 | −1.71555 | ||||||||
\(141\) | −8.52223 | −0.717701 | ||||||||
\(142\) | 38.4611 | 3.22759 | ||||||||
\(143\) | 1.67042 | 0.139688 | ||||||||
\(144\) | −19.8813 | −1.65677 | ||||||||
\(145\) | −35.8626 | −2.97823 | ||||||||
\(146\) | 10.1492 | 0.839958 | ||||||||
\(147\) | 0.915852 | 0.0755382 | ||||||||
\(148\) | 35.1852 | 2.89221 | ||||||||
\(149\) | 8.13443 | 0.666398 | 0.333199 | − | 0.942856i | \(-0.391872\pi\) | ||||
0.333199 | + | 0.942856i | \(0.391872\pi\) | |||||||
\(150\) | −31.2676 | −2.55299 | ||||||||
\(151\) | −7.31121 | −0.594978 | −0.297489 | − | 0.954725i | \(-0.596149\pi\) | ||||
−0.297489 | + | 0.954725i | \(0.596149\pi\) | |||||||
\(152\) | −12.9071 | −1.04691 | ||||||||
\(153\) | −5.44701 | −0.440365 | ||||||||
\(154\) | −1.39347 | −0.112289 | ||||||||
\(155\) | 32.0751 | 2.57633 | ||||||||
\(156\) | 13.6188 | 1.09038 | ||||||||
\(157\) | 11.5153 | 0.919024 | 0.459512 | − | 0.888172i | \(-0.348024\pi\) | ||||
0.459512 | + | 0.888172i | \(0.348024\pi\) | |||||||
\(158\) | −22.8180 | −1.81530 | ||||||||
\(159\) | 5.38974 | 0.427434 | ||||||||
\(160\) | 40.5658 | 3.20701 | ||||||||
\(161\) | 1.05441 | 0.0830994 | ||||||||
\(162\) | −5.60509 | −0.440377 | ||||||||
\(163\) | −4.62404 | −0.362183 | −0.181091 | − | 0.983466i | \(-0.557963\pi\) | ||||
−0.181091 | + | 0.983466i | \(0.557963\pi\) | |||||||
\(164\) | −54.3672 | −4.24537 | ||||||||
\(165\) | −2.08835 | −0.162578 | ||||||||
\(166\) | 3.96099 | 0.307432 | ||||||||
\(167\) | 19.1535 | 1.48214 | 0.741071 | − | 0.671427i | \(-0.234318\pi\) | ||||
0.741071 | + | 0.671427i | \(0.234318\pi\) | |||||||
\(168\) | −6.59559 | −0.508861 | ||||||||
\(169\) | −3.27417 | −0.251859 | ||||||||
\(170\) | 27.9133 | 2.14085 | ||||||||
\(171\) | −3.87347 | −0.296211 | ||||||||
\(172\) | 37.3061 | 2.84457 | ||||||||
\(173\) | −0.781574 | −0.0594220 | −0.0297110 | − | 0.999559i | \(-0.509459\pi\) | ||||
−0.0297110 | + | 0.999559i | \(0.509459\pi\) | |||||||
\(174\) | −20.0719 | −1.52164 | ||||||||
\(175\) | 13.1230 | 0.992006 | ||||||||
\(176\) | 4.92730 | 0.371409 | ||||||||
\(177\) | 8.57717 | 0.644700 | ||||||||
\(178\) | 6.31643 | 0.473437 | ||||||||
\(179\) | −6.23843 | −0.466282 | −0.233141 | − | 0.972443i | \(-0.574900\pi\) | ||||
−0.233141 | + | 0.972443i | \(0.574900\pi\) | |||||||
\(180\) | 43.8697 | 3.26986 | ||||||||
\(181\) | −2.92533 | −0.217438 | −0.108719 | − | 0.994073i | \(-0.534675\pi\) | ||||
−0.108719 | + | 0.994073i | \(0.534675\pi\) | |||||||
\(182\) | −8.11333 | −0.601400 | ||||||||
\(183\) | −4.42064 | −0.326783 | ||||||||
\(184\) | −7.59346 | −0.559797 | ||||||||
\(185\) | −31.4140 | −2.30961 | ||||||||
\(186\) | 17.9520 | 1.31631 | ||||||||
\(187\) | 1.34997 | 0.0987194 | ||||||||
\(188\) | −44.3690 | −3.23594 | ||||||||
\(189\) | −4.72691 | −0.343832 | ||||||||
\(190\) | 19.8496 | 1.44004 | ||||||||
\(191\) | 9.41099 | 0.680956 | 0.340478 | − | 0.940253i | \(-0.389411\pi\) | ||||
0.340478 | + | 0.940253i | \(0.389411\pi\) | |||||||
\(192\) | 5.85413 | 0.422485 | ||||||||
\(193\) | 7.46634 | 0.537439 | 0.268719 | − | 0.963219i | \(-0.413400\pi\) | ||||
0.268719 | + | 0.963219i | \(0.413400\pi\) | |||||||
\(194\) | 42.6634 | 3.06306 | ||||||||
\(195\) | −12.1592 | −0.870735 | ||||||||
\(196\) | 4.76817 | 0.340584 | ||||||||
\(197\) | 0.0198307 | 0.00141288 | 0.000706438 | − | 1.00000i | \(-0.499775\pi\) | ||||
0.000706438 | 1.00000i | \(0.499775\pi\) | ||||||||
\(198\) | 3.01160 | 0.214025 | ||||||||
\(199\) | −10.7600 | −0.762756 | −0.381378 | − | 0.924419i | \(-0.624550\pi\) | ||||
−0.381378 | + | 0.924419i | \(0.624550\pi\) | |||||||
\(200\) | −94.5065 | −6.68262 | ||||||||
\(201\) | 5.25131 | 0.370399 | ||||||||
\(202\) | 23.8145 | 1.67558 | ||||||||
\(203\) | 8.42416 | 0.591260 | ||||||||
\(204\) | 11.0062 | 0.770587 | ||||||||
\(205\) | 48.5401 | 3.39019 | ||||||||
\(206\) | 19.8646 | 1.38403 | ||||||||
\(207\) | −2.27882 | −0.158389 | ||||||||
\(208\) | 28.6886 | 1.98919 | ||||||||
\(209\) | 0.959985 | 0.0664036 | ||||||||
\(210\) | 10.1432 | 0.699949 | ||||||||
\(211\) | 20.6271 | 1.42003 | 0.710014 | − | 0.704188i | \(-0.248689\pi\) | ||||
0.710014 | + | 0.704188i | \(0.248689\pi\) | |||||||
\(212\) | 28.0604 | 1.92720 | ||||||||
\(213\) | −13.5398 | −0.927730 | ||||||||
\(214\) | −13.0817 | −0.894248 | ||||||||
\(215\) | −33.3076 | −2.27156 | ||||||||
\(216\) | 34.0412 | 2.31621 | ||||||||
\(217\) | −7.53448 | −0.511474 | ||||||||
\(218\) | −33.4456 | −2.26522 | ||||||||
\(219\) | −3.57292 | −0.241436 | ||||||||
\(220\) | −10.8725 | −0.733025 | ||||||||
\(221\) | 7.86002 | 0.528722 | ||||||||
\(222\) | −17.5820 | −1.18003 | ||||||||
\(223\) | 11.4562 | 0.767162 | 0.383581 | − | 0.923507i | \(-0.374691\pi\) | ||||
0.383581 | + | 0.923507i | \(0.374691\pi\) | |||||||
\(224\) | −9.52894 | −0.636679 | ||||||||
\(225\) | −28.3616 | −1.89078 | ||||||||
\(226\) | 5.33117 | 0.354624 | ||||||||
\(227\) | −27.6085 | −1.83244 | −0.916221 | − | 0.400672i | \(-0.868777\pi\) | ||||
−0.916221 | + | 0.400672i | \(0.868777\pi\) | |||||||
\(228\) | 7.82669 | 0.518336 | ||||||||
\(229\) | 14.0866 | 0.930867 | 0.465434 | − | 0.885083i | \(-0.345898\pi\) | ||||
0.465434 | + | 0.885083i | \(0.345898\pi\) | |||||||
\(230\) | 11.6778 | 0.770013 | ||||||||
\(231\) | 0.490556 | 0.0322762 | ||||||||
\(232\) | −60.6674 | −3.98301 | ||||||||
\(233\) | 16.4597 | 1.07831 | 0.539157 | − | 0.842205i | \(-0.318743\pi\) | ||||
0.539157 | + | 0.842205i | \(0.318743\pi\) | |||||||
\(234\) | 17.5346 | 1.14628 | ||||||||
\(235\) | 39.6135 | 2.58410 | ||||||||
\(236\) | 44.6551 | 2.90680 | ||||||||
\(237\) | 8.03279 | 0.521786 | ||||||||
\(238\) | −6.55686 | −0.425018 | ||||||||
\(239\) | 29.5579 | 1.91194 | 0.955972 | − | 0.293458i | \(-0.0948060\pi\) | ||||
0.955972 | + | 0.293458i | \(0.0948060\pi\) | |||||||
\(240\) | −35.8662 | −2.31515 | ||||||||
\(241\) | 10.1956 | 0.656756 | 0.328378 | − | 0.944546i | \(-0.393498\pi\) | ||||
0.328378 | + | 0.944546i | \(0.393498\pi\) | |||||||
\(242\) | 27.8709 | 1.79161 | ||||||||
\(243\) | 16.1539 | 1.03627 | ||||||||
\(244\) | −23.0150 | −1.47339 | ||||||||
\(245\) | −4.25711 | −0.271977 | ||||||||
\(246\) | 27.1673 | 1.73212 | ||||||||
\(247\) | 5.58940 | 0.355645 | ||||||||
\(248\) | 54.2602 | 3.44553 | ||||||||
\(249\) | −1.39442 | −0.0883677 | ||||||||
\(250\) | 89.9637 | 5.68980 | ||||||||
\(251\) | 1.67840 | 0.105940 | 0.0529700 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529700 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(252\) | −10.3050 | −0.649157 | ||||||||
\(253\) | 0.564773 | 0.0355070 | ||||||||
\(254\) | 22.2494 | 1.39605 | ||||||||
\(255\) | −9.82653 | −0.615361 | ||||||||
\(256\) | −19.1023 | −1.19389 | ||||||||
\(257\) | 14.4746 | 0.902902 | 0.451451 | − | 0.892296i | \(-0.350907\pi\) | ||||
0.451451 | + | 0.892296i | \(0.350907\pi\) | |||||||
\(258\) | −18.6419 | −1.16059 | ||||||||
\(259\) | 7.37919 | 0.458521 | ||||||||
\(260\) | −63.3038 | −3.92594 | ||||||||
\(261\) | −18.2064 | −1.12695 | ||||||||
\(262\) | −24.4734 | −1.51197 | ||||||||
\(263\) | 12.7104 | 0.783754 | 0.391877 | − | 0.920018i | \(-0.371826\pi\) | ||||
0.391877 | + | 0.920018i | \(0.371826\pi\) | |||||||
\(264\) | −3.53278 | −0.217428 | ||||||||
\(265\) | −25.0529 | −1.53899 | ||||||||
\(266\) | −4.66270 | −0.285888 | ||||||||
\(267\) | −2.22362 | −0.136084 | ||||||||
\(268\) | 27.3397 | 1.67004 | ||||||||
\(269\) | 3.12545 | 0.190562 | 0.0952809 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952809 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(270\) | −52.3513 | −3.18600 | ||||||||
\(271\) | 20.0376 | 1.21720 | 0.608599 | − | 0.793478i | \(-0.291732\pi\) | ||||
0.608599 | + | 0.793478i | \(0.291732\pi\) | |||||||
\(272\) | 23.1849 | 1.40579 | ||||||||
\(273\) | 2.85620 | 0.172865 | ||||||||
\(274\) | 13.7712 | 0.831951 | ||||||||
\(275\) | 7.02904 | 0.423867 | ||||||||
\(276\) | 4.60456 | 0.277162 | ||||||||
\(277\) | −5.42397 | −0.325895 | −0.162947 | − | 0.986635i | \(-0.552100\pi\) | ||||
−0.162947 | + | 0.986635i | \(0.552100\pi\) | |||||||
\(278\) | −3.71212 | −0.222638 | ||||||||
\(279\) | 16.2836 | 0.974875 | ||||||||
\(280\) | 30.6580 | 1.83216 | ||||||||
\(281\) | 15.4820 | 0.923578 | 0.461789 | − | 0.886990i | \(-0.347208\pi\) | ||||
0.461789 | + | 0.886990i | \(0.347208\pi\) | |||||||
\(282\) | 22.1712 | 1.32027 | ||||||||
\(283\) | 18.8417 | 1.12003 | 0.560013 | − | 0.828484i | \(-0.310796\pi\) | ||||
0.560013 | + | 0.828484i | \(0.310796\pi\) | |||||||
\(284\) | −70.4917 | −4.18291 | ||||||||
\(285\) | −6.98782 | −0.413923 | ||||||||
\(286\) | −4.34572 | −0.256968 | ||||||||
\(287\) | −11.4021 | −0.673045 | ||||||||
\(288\) | 20.5941 | 1.21352 | ||||||||
\(289\) | −10.6479 | −0.626344 | ||||||||
\(290\) | 93.2991 | 5.47871 | ||||||||
\(291\) | −15.0191 | −0.880438 | ||||||||
\(292\) | −18.6016 | −1.08858 | ||||||||
\(293\) | 12.6956 | 0.741684 | 0.370842 | − | 0.928696i | \(-0.379069\pi\) | ||||
0.370842 | + | 0.928696i | \(0.379069\pi\) | |||||||
\(294\) | −2.38265 | −0.138959 | ||||||||
\(295\) | −39.8689 | −2.32126 | ||||||||
\(296\) | −53.1419 | −3.08881 | ||||||||
\(297\) | −2.53186 | −0.146914 | ||||||||
\(298\) | −21.1623 | −1.22590 | ||||||||
\(299\) | 3.28832 | 0.190169 | ||||||||
\(300\) | 57.3073 | 3.30864 | ||||||||
\(301\) | 7.82399 | 0.450968 | ||||||||
\(302\) | 19.0206 | 1.09451 | ||||||||
\(303\) | −8.38362 | −0.481626 | ||||||||
\(304\) | 16.4872 | 0.945606 | ||||||||
\(305\) | 20.5482 | 1.17659 | ||||||||
\(306\) | 14.1708 | 0.810090 | ||||||||
\(307\) | −8.49388 | −0.484771 | −0.242386 | − | 0.970180i | \(-0.577930\pi\) | ||||
−0.242386 | + | 0.970180i | \(0.577930\pi\) | |||||||
\(308\) | 2.55396 | 0.145526 | ||||||||
\(309\) | −6.99309 | −0.397823 | ||||||||
\(310\) | −83.4457 | −4.73939 | ||||||||
\(311\) | −12.7982 | −0.725718 | −0.362859 | − | 0.931844i | \(-0.618199\pi\) | ||||
−0.362859 | + | 0.931844i | \(0.618199\pi\) | |||||||
\(312\) | −20.5692 | −1.16450 | ||||||||
\(313\) | −17.4383 | −0.985670 | −0.492835 | − | 0.870123i | \(-0.664039\pi\) | ||||
−0.492835 | + | 0.870123i | \(0.664039\pi\) | |||||||
\(314\) | −29.9580 | −1.69063 | ||||||||
\(315\) | 9.20054 | 0.518392 | ||||||||
\(316\) | 41.8209 | 2.35261 | ||||||||
\(317\) | −10.3135 | −0.579262 | −0.289631 | − | 0.957138i | \(-0.593533\pi\) | ||||
−0.289631 | + | 0.957138i | \(0.593533\pi\) | |||||||
\(318\) | −14.0218 | −0.786302 | ||||||||
\(319\) | 4.51222 | 0.252636 | ||||||||
\(320\) | −27.2115 | −1.52117 | ||||||||
\(321\) | 4.60526 | 0.257041 | ||||||||
\(322\) | −2.74313 | −0.152869 | ||||||||
\(323\) | 4.51712 | 0.251339 | ||||||||
\(324\) | 10.2730 | 0.570724 | ||||||||
\(325\) | 40.9257 | 2.27015 | ||||||||
\(326\) | 12.0298 | 0.666267 | ||||||||
\(327\) | 11.7741 | 0.651109 | ||||||||
\(328\) | 82.1133 | 4.53395 | ||||||||
\(329\) | −9.30525 | −0.513015 | ||||||||
\(330\) | 5.43299 | 0.299076 | ||||||||
\(331\) | −34.2160 | −1.88068 | −0.940340 | − | 0.340238i | \(-0.889493\pi\) | ||||
−0.940340 | + | 0.340238i | \(0.889493\pi\) | |||||||
\(332\) | −7.25972 | −0.398429 | ||||||||
\(333\) | −15.9480 | −0.873946 | ||||||||
\(334\) | −49.8291 | −2.72653 | ||||||||
\(335\) | −24.4094 | −1.33363 | ||||||||
\(336\) | 8.42501 | 0.459622 | ||||||||
\(337\) | −12.8029 | −0.697418 | −0.348709 | − | 0.937231i | \(-0.613380\pi\) | ||||
−0.348709 | + | 0.937231i | \(0.613380\pi\) | |||||||
\(338\) | 8.51799 | 0.463318 | ||||||||
\(339\) | −1.87677 | −0.101932 | ||||||||
\(340\) | −51.1596 | −2.77452 | ||||||||
\(341\) | −4.03567 | −0.218544 | ||||||||
\(342\) | 10.0771 | 0.544907 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −56.3452 | −3.03793 | ||||||||
\(345\) | −4.11104 | −0.221331 | ||||||||
\(346\) | 2.03332 | 0.109312 | ||||||||
\(347\) | 15.1292 | 0.812176 | 0.406088 | − | 0.913834i | \(-0.366893\pi\) | ||||
0.406088 | + | 0.913834i | \(0.366893\pi\) | |||||||
\(348\) | 36.7878 | 1.97203 | ||||||||
\(349\) | −10.2788 | −0.550211 | −0.275105 | − | 0.961414i | \(-0.588713\pi\) | ||||
−0.275105 | + | 0.961414i | \(0.588713\pi\) | |||||||
\(350\) | −34.1404 | −1.82488 | ||||||||
\(351\) | −14.7415 | −0.786841 | ||||||||
\(352\) | −5.10396 | −0.272042 | ||||||||
\(353\) | −7.99564 | −0.425565 | −0.212782 | − | 0.977100i | \(-0.568253\pi\) | ||||
−0.212782 | + | 0.977100i | \(0.568253\pi\) | |||||||
\(354\) | −22.3141 | −1.18598 | ||||||||
\(355\) | 62.9363 | 3.34031 | ||||||||
\(356\) | −11.5768 | −0.613568 | ||||||||
\(357\) | 2.30826 | 0.122166 | ||||||||
\(358\) | 16.2297 | 0.857767 | ||||||||
\(359\) | −9.55303 | −0.504190 | −0.252095 | − | 0.967703i | \(-0.581119\pi\) | ||||
−0.252095 | + | 0.967703i | \(0.581119\pi\) | |||||||
\(360\) | −66.2585 | −3.49213 | ||||||||
\(361\) | −15.7878 | −0.830937 | ||||||||
\(362\) | 7.61046 | 0.399997 | ||||||||
\(363\) | −9.81161 | −0.514976 | ||||||||
\(364\) | 14.8701 | 0.779407 | ||||||||
\(365\) | 16.6078 | 0.869294 | ||||||||
\(366\) | 11.5006 | 0.601146 | ||||||||
\(367\) | 30.5161 | 1.59293 | 0.796463 | − | 0.604687i | \(-0.206702\pi\) | ||||
0.796463 | + | 0.604687i | \(0.206702\pi\) | |||||||
\(368\) | 9.69966 | 0.505630 | ||||||||
\(369\) | 24.6424 | 1.28283 | ||||||||
\(370\) | 81.7259 | 4.24872 | ||||||||
\(371\) | 5.88495 | 0.305531 | ||||||||
\(372\) | −32.9026 | −1.70592 | ||||||||
\(373\) | 16.3614 | 0.847162 | 0.423581 | − | 0.905858i | \(-0.360773\pi\) | ||||
0.423581 | + | 0.905858i | \(0.360773\pi\) | |||||||
\(374\) | −3.51204 | −0.181603 | ||||||||
\(375\) | −31.6706 | −1.63546 | ||||||||
\(376\) | 67.0126 | 3.45591 | ||||||||
\(377\) | 26.2718 | 1.35307 | ||||||||
\(378\) | 12.2974 | 0.632509 | ||||||||
\(379\) | 30.9380 | 1.58918 | 0.794588 | − | 0.607149i | \(-0.207687\pi\) | ||||
0.794588 | + | 0.607149i | \(0.207687\pi\) | |||||||
\(380\) | −36.3805 | −1.86628 | ||||||||
\(381\) | −7.83264 | −0.401278 | ||||||||
\(382\) | −24.4834 | −1.25268 | ||||||||
\(383\) | −16.6554 | −0.851054 | −0.425527 | − | 0.904946i | \(-0.639911\pi\) | ||||
−0.425527 | + | 0.904946i | \(0.639911\pi\) | |||||||
\(384\) | 2.22427 | 0.113507 | ||||||||
\(385\) | −2.28023 | −0.116211 | ||||||||
\(386\) | −19.4242 | −0.988666 | ||||||||
\(387\) | −16.9093 | −0.859550 | ||||||||
\(388\) | −78.1937 | −3.96968 | ||||||||
\(389\) | 10.0382 | 0.508954 | 0.254477 | − | 0.967079i | \(-0.418097\pi\) | ||||
0.254477 | + | 0.967079i | \(0.418097\pi\) | |||||||
\(390\) | 31.6329 | 1.60179 | ||||||||
\(391\) | 2.65749 | 0.134395 | ||||||||
\(392\) | −7.20159 | −0.363735 | ||||||||
\(393\) | 8.61556 | 0.434597 | ||||||||
\(394\) | −0.0515909 | −0.00259911 | ||||||||
\(395\) | −37.3385 | −1.87870 | ||||||||
\(396\) | −5.51967 | −0.277374 | ||||||||
\(397\) | −14.7559 | −0.740577 | −0.370288 | − | 0.928917i | \(-0.620741\pi\) | ||||
−0.370288 | + | 0.928917i | \(0.620741\pi\) | |||||||
\(398\) | 27.9929 | 1.40316 | ||||||||
\(399\) | 1.64145 | 0.0821751 | ||||||||
\(400\) | 120.720 | 6.03599 | ||||||||
\(401\) | −26.0936 | −1.30305 | −0.651526 | − | 0.758626i | \(-0.725871\pi\) | ||||
−0.651526 | + | 0.758626i | \(0.725871\pi\) | |||||||
\(402\) | −13.6616 | −0.681381 | ||||||||
\(403\) | −23.4972 | −1.17048 | ||||||||
\(404\) | −43.6474 | −2.17154 | ||||||||
\(405\) | −9.17196 | −0.455758 | ||||||||
\(406\) | −21.9161 | −1.08768 | ||||||||
\(407\) | 3.95250 | 0.195918 | ||||||||
\(408\) | −16.6232 | −0.822969 | ||||||||
\(409\) | 32.2198 | 1.59317 | 0.796584 | − | 0.604528i | \(-0.206638\pi\) | ||||
0.796584 | + | 0.604528i | \(0.206638\pi\) | |||||||
\(410\) | −126.280 | −6.23655 | ||||||||
\(411\) | −4.84800 | −0.239134 | ||||||||
\(412\) | −36.4079 | −1.79369 | ||||||||
\(413\) | 9.36524 | 0.460833 | ||||||||
\(414\) | 5.92850 | 0.291370 | ||||||||
\(415\) | 6.48161 | 0.318170 | ||||||||
\(416\) | −29.7172 | −1.45701 | ||||||||
\(417\) | 1.30681 | 0.0639946 | ||||||||
\(418\) | −2.49747 | −0.122155 | ||||||||
\(419\) | 4.72985 | 0.231068 | 0.115534 | − | 0.993304i | \(-0.463142\pi\) | ||||
0.115534 | + | 0.993304i | \(0.463142\pi\) | |||||||
\(420\) | −18.5905 | −0.907125 | ||||||||
\(421\) | 34.0463 | 1.65931 | 0.829657 | − | 0.558274i | \(-0.188536\pi\) | ||||
0.829657 | + | 0.558274i | \(0.188536\pi\) | |||||||
\(422\) | −53.6628 | −2.61227 | ||||||||
\(423\) | 20.1107 | 0.977814 | ||||||||
\(424\) | −42.3810 | −2.05820 | ||||||||
\(425\) | 33.0745 | 1.60435 | ||||||||
\(426\) | 35.2247 | 1.70664 | ||||||||
\(427\) | −4.82680 | −0.233585 | ||||||||
\(428\) | 23.9762 | 1.15894 | ||||||||
\(429\) | 1.52986 | 0.0738623 | ||||||||
\(430\) | 86.6521 | 4.17874 | ||||||||
\(431\) | 19.6125 | 0.944700 | 0.472350 | − | 0.881411i | \(-0.343406\pi\) | ||||
0.472350 | + | 0.881411i | \(0.343406\pi\) | |||||||
\(432\) | −43.4833 | −2.09209 | ||||||||
\(433\) | −19.9898 | −0.960648 | −0.480324 | − | 0.877091i | \(-0.659481\pi\) | ||||
−0.480324 | + | 0.877091i | \(0.659481\pi\) | |||||||
\(434\) | 19.6015 | 0.940901 | ||||||||
\(435\) | −32.8448 | −1.57479 | ||||||||
\(436\) | 61.2992 | 2.93570 | ||||||||
\(437\) | 1.88979 | 0.0904007 | ||||||||
\(438\) | 9.29521 | 0.444142 | ||||||||
\(439\) | 23.0437 | 1.09982 | 0.549908 | − | 0.835225i | \(-0.314663\pi\) | ||||
0.549908 | + | 0.835225i | \(0.314663\pi\) | |||||||
\(440\) | 16.4213 | 0.782853 | ||||||||
\(441\) | −2.16122 | −0.102915 | ||||||||
\(442\) | −20.4484 | −0.972631 | ||||||||
\(443\) | −17.7733 | −0.844434 | −0.422217 | − | 0.906495i | \(-0.638748\pi\) | ||||
−0.422217 | + | 0.906495i | \(0.638748\pi\) | |||||||
\(444\) | 32.2245 | 1.52930 | ||||||||
\(445\) | 10.3360 | 0.489972 | ||||||||
\(446\) | −29.8040 | −1.41126 | ||||||||
\(447\) | 7.44993 | 0.352370 | ||||||||
\(448\) | 6.39200 | 0.301994 | ||||||||
\(449\) | −9.13707 | −0.431205 | −0.215602 | − | 0.976481i | \(-0.569172\pi\) | ||||
−0.215602 | + | 0.976481i | \(0.569172\pi\) | |||||||
\(450\) | 73.7848 | 3.47825 | ||||||||
\(451\) | −6.10729 | −0.287581 | ||||||||
\(452\) | −9.77099 | −0.459588 | ||||||||
\(453\) | −6.69598 | −0.314605 | ||||||||
\(454\) | 71.8256 | 3.37094 | ||||||||
\(455\) | −13.2763 | −0.622404 | ||||||||
\(456\) | −11.8210 | −0.553570 | ||||||||
\(457\) | 24.2242 | 1.13316 | 0.566580 | − | 0.824007i | \(-0.308266\pi\) | ||||
0.566580 | + | 0.824007i | \(0.308266\pi\) | |||||||
\(458\) | −36.6472 | −1.71241 | ||||||||
\(459\) | −11.9134 | −0.556072 | ||||||||
\(460\) | −21.4032 | −0.997927 | ||||||||
\(461\) | 16.8887 | 0.786587 | 0.393294 | − | 0.919413i | \(-0.371336\pi\) | ||||
0.393294 | + | 0.919413i | \(0.371336\pi\) | |||||||
\(462\) | −1.27621 | −0.0593749 | ||||||||
\(463\) | −9.83912 | −0.457263 | −0.228631 | − | 0.973513i | \(-0.573425\pi\) | ||||
−0.228631 | + | 0.973513i | \(0.573425\pi\) | |||||||
\(464\) | 77.4948 | 3.59760 | ||||||||
\(465\) | 29.3760 | 1.36228 | ||||||||
\(466\) | −42.8212 | −1.98365 | ||||||||
\(467\) | −31.0103 | −1.43498 | −0.717492 | − | 0.696567i | \(-0.754710\pi\) | ||||
−0.717492 | + | 0.696567i | \(0.754710\pi\) | |||||||
\(468\) | −32.1376 | −1.48556 | ||||||||
\(469\) | 5.73380 | 0.264762 | ||||||||
\(470\) | −103.057 | −4.75368 | ||||||||
\(471\) | 10.5463 | 0.485950 | ||||||||
\(472\) | −67.4446 | −3.10439 | ||||||||
\(473\) | 4.19075 | 0.192691 | ||||||||
\(474\) | −20.8979 | −0.959872 | ||||||||
\(475\) | 23.5199 | 1.07917 | ||||||||
\(476\) | 12.0174 | 0.550818 | ||||||||
\(477\) | −12.7186 | −0.582346 | ||||||||
\(478\) | −76.8971 | −3.51719 | ||||||||
\(479\) | 9.36654 | 0.427968 | 0.213984 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213984 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(480\) | 37.1522 | 1.69576 | ||||||||
\(481\) | 23.0129 | 1.04930 | ||||||||
\(482\) | −26.5246 | −1.20816 | ||||||||
\(483\) | 0.965687 | 0.0439403 | ||||||||
\(484\) | −51.0819 | −2.32190 | ||||||||
\(485\) | 69.8128 | 3.17004 | ||||||||
\(486\) | −42.0256 | −1.90632 | ||||||||
\(487\) | −40.0607 | −1.81532 | −0.907661 | − | 0.419703i | \(-0.862134\pi\) | ||||
−0.907661 | + | 0.419703i | \(0.862134\pi\) | |||||||
\(488\) | 34.7607 | 1.57354 | ||||||||
\(489\) | −4.23493 | −0.191510 | ||||||||
\(490\) | 11.0752 | 0.500326 | ||||||||
\(491\) | −37.2770 | −1.68229 | −0.841144 | − | 0.540811i | \(-0.818117\pi\) | ||||
−0.841144 | + | 0.540811i | \(0.818117\pi\) | |||||||
\(492\) | −49.7923 | −2.24481 | ||||||||
\(493\) | 21.2318 | 0.956233 | ||||||||
\(494\) | −14.5412 | −0.654240 | ||||||||
\(495\) | 4.92806 | 0.221500 | ||||||||
\(496\) | −69.3104 | −3.11213 | ||||||||
\(497\) | −14.7838 | −0.663145 | ||||||||
\(498\) | 3.62768 | 0.162560 | ||||||||
\(499\) | −5.57734 | −0.249676 | −0.124838 | − | 0.992177i | \(-0.539841\pi\) | ||||
−0.124838 | + | 0.992177i | \(0.539841\pi\) | |||||||
\(500\) | −164.886 | −7.37392 | ||||||||
\(501\) | 17.5418 | 0.783708 | ||||||||
\(502\) | −4.36649 | −0.194886 | ||||||||
\(503\) | −21.6403 | −0.964892 | −0.482446 | − | 0.875926i | \(-0.660251\pi\) | ||||
−0.482446 | + | 0.875926i | \(0.660251\pi\) | |||||||
\(504\) | 15.5642 | 0.693284 | ||||||||
\(505\) | 38.9692 | 1.73411 | ||||||||
\(506\) | −1.46930 | −0.0653182 | ||||||||
\(507\) | −2.99866 | −0.133175 | ||||||||
\(508\) | −40.7788 | −1.80927 | ||||||||
\(509\) | 38.7004 | 1.71537 | 0.857683 | − | 0.514180i | \(-0.171904\pi\) | ||||
0.857683 | + | 0.514180i | \(0.171904\pi\) | |||||||
\(510\) | 25.5644 | 1.13201 | ||||||||
\(511\) | −3.90120 | −0.172579 | ||||||||
\(512\) | 44.8386 | 1.98161 | ||||||||
\(513\) | −8.47186 | −0.374042 | ||||||||
\(514\) | −37.6568 | −1.66097 | ||||||||
\(515\) | 32.5057 | 1.43237 | ||||||||
\(516\) | 34.1669 | 1.50411 | ||||||||
\(517\) | −4.98415 | −0.219203 | ||||||||
\(518\) | −19.1975 | −0.843489 | ||||||||
\(519\) | −0.715806 | −0.0314204 | ||||||||
\(520\) | 95.6107 | 4.19281 | ||||||||
\(521\) | 42.8103 | 1.87555 | 0.937776 | − | 0.347241i | \(-0.112882\pi\) | ||||
0.937776 | + | 0.347241i | \(0.112882\pi\) | |||||||
\(522\) | 47.3653 | 2.07312 | ||||||||
\(523\) | 26.7535 | 1.16985 | 0.584924 | − | 0.811088i | \(-0.301124\pi\) | ||||
0.584924 | + | 0.811088i | \(0.301124\pi\) | |||||||
\(524\) | 44.8549 | 1.95950 | ||||||||
\(525\) | 12.0187 | 0.524540 | ||||||||
\(526\) | −33.0669 | −1.44178 | ||||||||
\(527\) | −18.9895 | −0.827195 | ||||||||
\(528\) | 4.51267 | 0.196389 | ||||||||
\(529\) | −21.8882 | −0.951661 | ||||||||
\(530\) | 65.1768 | 2.83110 | ||||||||
\(531\) | −20.2403 | −0.878355 | ||||||||
\(532\) | 8.54581 | 0.370508 | ||||||||
\(533\) | −35.5589 | −1.54023 | ||||||||
\(534\) | 5.78492 | 0.250338 | ||||||||
\(535\) | −21.4064 | −0.925481 | ||||||||
\(536\) | −41.2924 | −1.78356 | ||||||||
\(537\) | −5.71348 | −0.246555 | ||||||||
\(538\) | −8.13107 | −0.350555 | ||||||||
\(539\) | 0.535628 | 0.0230711 | ||||||||
\(540\) | 95.9498 | 4.12902 | ||||||||
\(541\) | 3.25954 | 0.140139 | 0.0700694 | − | 0.997542i | \(-0.477678\pi\) | ||||
0.0700694 | + | 0.997542i | \(0.477678\pi\) | |||||||
\(542\) | −52.1292 | −2.23914 | ||||||||
\(543\) | −2.67917 | −0.114974 | ||||||||
\(544\) | −24.0162 | −1.02969 | ||||||||
\(545\) | −54.7290 | −2.34433 | ||||||||
\(546\) | −7.43060 | −0.318000 | ||||||||
\(547\) | 16.8610 | 0.720926 | 0.360463 | − | 0.932774i | \(-0.382619\pi\) | ||||
0.360463 | + | 0.932774i | \(0.382619\pi\) | |||||||
\(548\) | −25.2400 | −1.07820 | ||||||||
\(549\) | 10.4318 | 0.445217 | ||||||||
\(550\) | −18.2866 | −0.779741 | ||||||||
\(551\) | 15.0983 | 0.643210 | ||||||||
\(552\) | −6.95448 | −0.296002 | ||||||||
\(553\) | 8.77085 | 0.372974 | ||||||||
\(554\) | 14.1109 | 0.599513 | ||||||||
\(555\) | −28.7706 | −1.22124 | ||||||||
\(556\) | 6.80359 | 0.288536 | ||||||||
\(557\) | 26.3701 | 1.11734 | 0.558668 | − | 0.829391i | \(-0.311313\pi\) | ||||
0.558668 | + | 0.829391i | \(0.311313\pi\) | |||||||
\(558\) | −42.3630 | −1.79337 | ||||||||
\(559\) | 24.4001 | 1.03201 | ||||||||
\(560\) | −39.1616 | −1.65488 | ||||||||
\(561\) | 1.23637 | 0.0521996 | ||||||||
\(562\) | −40.2775 | −1.69900 | ||||||||
\(563\) | −13.9222 | −0.586752 | −0.293376 | − | 0.955997i | \(-0.594779\pi\) | ||||
−0.293376 | + | 0.955997i | \(0.594779\pi\) | |||||||
\(564\) | −40.6354 | −1.71106 | ||||||||
\(565\) | 8.72372 | 0.367010 | ||||||||
\(566\) | −49.0181 | −2.06039 | ||||||||
\(567\) | 2.15450 | 0.0904806 | ||||||||
\(568\) | 106.467 | 4.46725 | ||||||||
\(569\) | −6.44127 | −0.270032 | −0.135016 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135016 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(570\) | 18.1793 | 0.761447 | ||||||||
\(571\) | 30.4970 | 1.27626 | 0.638130 | − | 0.769929i | \(-0.279708\pi\) | ||||
0.638130 | + | 0.769929i | \(0.279708\pi\) | |||||||
\(572\) | 7.96486 | 0.333027 | ||||||||
\(573\) | 8.61907 | 0.360067 | ||||||||
\(574\) | 29.6634 | 1.23813 | ||||||||
\(575\) | 13.8371 | 0.577046 | ||||||||
\(576\) | −13.8145 | −0.575604 | ||||||||
\(577\) | −47.2121 | −1.96546 | −0.982732 | − | 0.185036i | \(-0.940760\pi\) | ||||
−0.982732 | + | 0.185036i | \(0.940760\pi\) | |||||||
\(578\) | 27.7011 | 1.15222 | ||||||||
\(579\) | 6.83806 | 0.284180 | ||||||||
\(580\) | −170.999 | −7.10035 | ||||||||
\(581\) | −1.52254 | −0.0631655 | ||||||||
\(582\) | 39.0734 | 1.61964 | ||||||||
\(583\) | 3.15214 | 0.130548 | ||||||||
\(584\) | 28.0948 | 1.16257 | ||||||||
\(585\) | 28.6930 | 1.18631 | ||||||||
\(586\) | −33.0285 | −1.36439 | ||||||||
\(587\) | 5.61724 | 0.231848 | 0.115924 | − | 0.993258i | \(-0.463017\pi\) | ||||
0.115924 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(588\) | 4.36694 | 0.180089 | ||||||||
\(589\) | −13.5038 | −0.556413 | ||||||||
\(590\) | 103.722 | 4.27016 | ||||||||
\(591\) | 0.0181620 | 0.000747083 0 | ||||||||
\(592\) | 67.8819 | 2.78993 | ||||||||
\(593\) | 14.4608 | 0.593834 | 0.296917 | − | 0.954903i | \(-0.404042\pi\) | ||||
0.296917 | + | 0.954903i | \(0.404042\pi\) | |||||||
\(594\) | 6.58682 | 0.270261 | ||||||||
\(595\) | −10.7294 | −0.439862 | ||||||||
\(596\) | 38.7863 | 1.58875 | ||||||||
\(597\) | −9.85457 | −0.403321 | ||||||||
\(598\) | −8.55480 | −0.349832 | ||||||||
\(599\) | −8.52795 | −0.348442 | −0.174221 | − | 0.984707i | \(-0.555741\pi\) | ||||
−0.174221 | + | 0.984707i | \(0.555741\pi\) | |||||||
\(600\) | −86.5539 | −3.53355 | ||||||||
\(601\) | −28.1144 | −1.14681 | −0.573405 | − | 0.819272i | \(-0.694378\pi\) | ||||
−0.573405 | + | 0.819272i | \(0.694378\pi\) | |||||||
\(602\) | −20.3547 | −0.829595 | ||||||||
\(603\) | −12.3920 | −0.504640 | ||||||||
\(604\) | −34.8611 | −1.41848 | ||||||||
\(605\) | 45.6069 | 1.85418 | ||||||||
\(606\) | 21.8106 | 0.885994 | ||||||||
\(607\) | −17.8727 | −0.725430 | −0.362715 | − | 0.931900i | \(-0.618150\pi\) | ||||
−0.362715 | + | 0.931900i | \(0.618150\pi\) | |||||||
\(608\) | −17.0784 | −0.692619 | ||||||||
\(609\) | 7.71528 | 0.312639 | ||||||||
\(610\) | −53.4577 | −2.16444 | ||||||||
\(611\) | −29.0196 | −1.17401 | ||||||||
\(612\) | −25.9723 | −1.04987 | ||||||||
\(613\) | −35.8608 | −1.44840 | −0.724201 | − | 0.689589i | \(-0.757791\pi\) | ||||
−0.724201 | + | 0.689589i | \(0.757791\pi\) | |||||||
\(614\) | 22.0974 | 0.891779 | ||||||||
\(615\) | 44.4555 | 1.79262 | ||||||||
\(616\) | −3.85737 | −0.155418 | ||||||||
\(617\) | 15.0620 | 0.606374 | 0.303187 | − | 0.952931i | \(-0.401949\pi\) | ||||
0.303187 | + | 0.952931i | \(0.401949\pi\) | |||||||
\(618\) | 18.1930 | 0.731830 | ||||||||
\(619\) | 11.4661 | 0.460861 | 0.230431 | − | 0.973089i | \(-0.425987\pi\) | ||||
0.230431 | + | 0.973089i | \(0.425987\pi\) | |||||||
\(620\) | 152.940 | 6.14220 | ||||||||
\(621\) | −4.98412 | −0.200006 | ||||||||
\(622\) | 33.2954 | 1.33502 | ||||||||
\(623\) | −2.42793 | −0.0972730 | ||||||||
\(624\) | 26.2745 | 1.05182 | ||||||||
\(625\) | 81.5982 | 3.26393 | ||||||||
\(626\) | 45.3669 | 1.81323 | ||||||||
\(627\) | 0.879204 | 0.0351120 | ||||||||
\(628\) | 54.9071 | 2.19103 | ||||||||
\(629\) | 18.5981 | 0.741555 | ||||||||
\(630\) | −23.9359 | −0.953627 | ||||||||
\(631\) | 20.2172 | 0.804836 | 0.402418 | − | 0.915456i | \(-0.368170\pi\) | ||||
0.402418 | + | 0.915456i | \(0.368170\pi\) | |||||||
\(632\) | −63.1640 | −2.51253 | ||||||||
\(633\) | 18.8914 | 0.750864 | ||||||||
\(634\) | 26.8312 | 1.06560 | ||||||||
\(635\) | 36.4081 | 1.44481 | ||||||||
\(636\) | 25.6992 | 1.01904 | ||||||||
\(637\) | 3.11863 | 0.123564 | ||||||||
\(638\) | −11.7388 | −0.464745 | ||||||||
\(639\) | 31.9510 | 1.26396 | ||||||||
\(640\) | −10.3390 | −0.408683 | ||||||||
\(641\) | 17.8100 | 0.703453 | 0.351727 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351727 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(642\) | −11.9809 | −0.472849 | ||||||||
\(643\) | 43.3475 | 1.70946 | 0.854729 | − | 0.519075i | \(-0.173723\pi\) | ||||
0.854729 | + | 0.519075i | \(0.173723\pi\) | |||||||
\(644\) | 5.02762 | 0.198116 | ||||||||
\(645\) | −30.5048 | −1.20113 | ||||||||
\(646\) | −11.7516 | −0.462361 | ||||||||
\(647\) | 32.7663 | 1.28818 | 0.644088 | − | 0.764951i | \(-0.277237\pi\) | ||||
0.644088 | + | 0.764951i | \(0.277237\pi\) | |||||||
\(648\) | −15.5158 | −0.609520 | ||||||||
\(649\) | 5.01628 | 0.196906 | ||||||||
\(650\) | −106.471 | −4.17614 | ||||||||
\(651\) | −6.90046 | −0.270450 | ||||||||
\(652\) | −22.0482 | −0.863475 | ||||||||
\(653\) | 3.57824 | 0.140027 | 0.0700136 | − | 0.997546i | \(-0.477696\pi\) | ||||
0.0700136 | + | 0.997546i | \(0.477696\pi\) | |||||||
\(654\) | −30.6312 | −1.19777 | ||||||||
\(655\) | −40.0473 | −1.56478 | ||||||||
\(656\) | −104.889 | −4.09524 | ||||||||
\(657\) | 8.43134 | 0.328938 | ||||||||
\(658\) | 24.2083 | 0.943737 | ||||||||
\(659\) | −9.47166 | −0.368963 | −0.184482 | − | 0.982836i | \(-0.559061\pi\) | ||||
−0.184482 | + | 0.982836i | \(0.559061\pi\) | |||||||
\(660\) | −9.95761 | −0.387599 | ||||||||
\(661\) | 42.9108 | 1.66904 | 0.834519 | − | 0.550979i | \(-0.185746\pi\) | ||||
0.834519 | + | 0.550979i | \(0.185746\pi\) | |||||||
\(662\) | 89.0152 | 3.45968 | ||||||||
\(663\) | 7.19861 | 0.279571 | ||||||||
\(664\) | 10.9647 | 0.425512 | ||||||||
\(665\) | −7.62986 | −0.295873 | ||||||||
\(666\) | 41.4899 | 1.60770 | ||||||||
\(667\) | 8.88255 | 0.343934 | ||||||||
\(668\) | 91.3271 | 3.53355 | ||||||||
\(669\) | 10.4921 | 0.405650 | ||||||||
\(670\) | 63.5028 | 2.45333 | ||||||||
\(671\) | −2.58537 | −0.0998071 | ||||||||
\(672\) | −8.72709 | −0.336655 | ||||||||
\(673\) | 44.0276 | 1.69714 | 0.848570 | − | 0.529083i | \(-0.177464\pi\) | ||||
0.848570 | + | 0.529083i | \(0.177464\pi\) | |||||||
\(674\) | 33.3076 | 1.28296 | ||||||||
\(675\) | −62.0312 | −2.38758 | ||||||||
\(676\) | −15.6118 | −0.600454 | ||||||||
\(677\) | 24.2095 | 0.930446 | 0.465223 | − | 0.885194i | \(-0.345974\pi\) | ||||
0.465223 | + | 0.885194i | \(0.345974\pi\) | |||||||
\(678\) | 4.88256 | 0.187513 | ||||||||
\(679\) | −16.3991 | −0.629340 | ||||||||
\(680\) | 77.2687 | 2.96312 | ||||||||
\(681\) | −25.2853 | −0.968935 | ||||||||
\(682\) | 10.4991 | 0.402031 | ||||||||
\(683\) | 4.85029 | 0.185591 | 0.0927957 | − | 0.995685i | \(-0.470420\pi\) | ||||
0.0927957 | + | 0.995685i | \(0.470420\pi\) | |||||||
\(684\) | −18.4693 | −0.706193 | ||||||||
\(685\) | 22.5347 | 0.861008 | ||||||||
\(686\) | −2.60157 | −0.0993284 | ||||||||
\(687\) | 12.9012 | 0.492212 | ||||||||
\(688\) | 71.9737 | 2.74397 | ||||||||
\(689\) | 18.3529 | 0.699191 | ||||||||
\(690\) | 10.6951 | 0.407157 | ||||||||
\(691\) | 20.0829 | 0.763991 | 0.381995 | − | 0.924164i | \(-0.375237\pi\) | ||||
0.381995 | + | 0.924164i | \(0.375237\pi\) | |||||||
\(692\) | −3.72668 | −0.141667 | ||||||||
\(693\) | −1.15761 | −0.0439739 | ||||||||
\(694\) | −39.3596 | −1.49407 | ||||||||
\(695\) | −6.07437 | −0.230414 | ||||||||
\(696\) | −55.5623 | −2.10608 | ||||||||
\(697\) | −28.7373 | −1.08850 | ||||||||
\(698\) | 26.7410 | 1.01216 | ||||||||
\(699\) | 15.0747 | 0.570177 | ||||||||
\(700\) | 62.5727 | 2.36503 | ||||||||
\(701\) | 32.5584 | 1.22971 | 0.614856 | − | 0.788639i | \(-0.289214\pi\) | ||||
0.614856 | + | 0.788639i | \(0.289214\pi\) | |||||||
\(702\) | 38.3509 | 1.44746 | ||||||||
\(703\) | 13.2254 | 0.498807 | ||||||||
\(704\) | 3.42373 | 0.129037 | ||||||||
\(705\) | 36.2801 | 1.36639 | ||||||||
\(706\) | 20.8012 | 0.782864 | ||||||||
\(707\) | −9.15391 | −0.344268 | ||||||||
\(708\) | 40.8974 | 1.53702 | ||||||||
\(709\) | 7.40470 | 0.278089 | 0.139045 | − | 0.990286i | \(-0.455597\pi\) | ||||
0.139045 | + | 0.990286i | \(0.455597\pi\) | |||||||
\(710\) | −163.733 | −6.14480 | ||||||||
\(711\) | −18.9557 | −0.710894 | ||||||||
\(712\) | 17.4850 | 0.655277 | ||||||||
\(713\) | −7.94446 | −0.297522 | ||||||||
\(714\) | −6.00511 | −0.224736 | ||||||||
\(715\) | −7.11118 | −0.265943 | ||||||||
\(716\) | −29.7459 | −1.11166 | ||||||||
\(717\) | 27.0707 | 1.01097 | ||||||||
\(718\) | 24.8529 | 0.927501 | ||||||||
\(719\) | 34.7350 | 1.29540 | 0.647698 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647698 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(720\) | 84.6367 | 3.15422 | ||||||||
\(721\) | −7.63561 | −0.284365 | ||||||||
\(722\) | 41.0731 | 1.52858 | ||||||||
\(723\) | 9.33765 | 0.347271 | ||||||||
\(724\) | −13.9485 | −0.518391 | ||||||||
\(725\) | 110.550 | 4.10574 | ||||||||
\(726\) | 25.5256 | 0.947344 | ||||||||
\(727\) | −13.1261 | −0.486819 | −0.243409 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243409 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(728\) | −22.4591 | −0.832388 | ||||||||
\(729\) | 8.33109 | 0.308559 | ||||||||
\(730\) | −43.2065 | −1.59914 | ||||||||
\(731\) | 19.7192 | 0.729340 | ||||||||
\(732\) | −21.0783 | −0.779078 | ||||||||
\(733\) | 18.4536 | 0.681598 | 0.340799 | − | 0.940136i | \(-0.389302\pi\) | ||||
0.340799 | + | 0.940136i | \(0.389302\pi\) | |||||||
\(734\) | −79.3897 | −2.93033 | ||||||||
\(735\) | −3.89888 | −0.143812 | ||||||||
\(736\) | −10.0474 | −0.370354 | ||||||||
\(737\) | 3.07118 | 0.113128 | ||||||||
\(738\) | −64.1090 | −2.35989 | ||||||||
\(739\) | 39.6017 | 1.45677 | 0.728386 | − | 0.685167i | \(-0.240271\pi\) | ||||
0.728386 | + | 0.685167i | \(0.240271\pi\) | |||||||
\(740\) | −149.787 | −5.50630 | ||||||||
\(741\) | 5.11906 | 0.188053 | ||||||||
\(742\) | −15.3101 | −0.562052 | ||||||||
\(743\) | 43.3290 | 1.58959 | 0.794794 | − | 0.606880i | \(-0.207579\pi\) | ||||
0.794794 | + | 0.606880i | \(0.207579\pi\) | |||||||
\(744\) | 49.6943 | 1.82188 | ||||||||
\(745\) | −34.6292 | −1.26871 | ||||||||
\(746\) | −42.5654 | −1.55843 | ||||||||
\(747\) | 3.29053 | 0.120394 | ||||||||
\(748\) | 6.43687 | 0.235355 | ||||||||
\(749\) | 5.02839 | 0.183734 | ||||||||
\(750\) | 82.3934 | 3.00858 | ||||||||
\(751\) | 4.15232 | 0.151520 | 0.0757601 | − | 0.997126i | \(-0.475862\pi\) | ||||
0.0757601 | + | 0.997126i | \(0.475862\pi\) | |||||||
\(752\) | −85.6000 | −3.12151 | ||||||||
\(753\) | 1.53717 | 0.0560176 | ||||||||
\(754\) | −68.3480 | −2.48909 | ||||||||
\(755\) | 31.1246 | 1.13274 | ||||||||
\(756\) | −22.5387 | −0.819725 | ||||||||
\(757\) | 12.0037 | 0.436281 | 0.218141 | − | 0.975917i | \(-0.430001\pi\) | ||||
0.218141 | + | 0.975917i | \(0.430001\pi\) | |||||||
\(758\) | −80.4873 | −2.92343 | ||||||||
\(759\) | 0.517249 | 0.0187749 | ||||||||
\(760\) | 54.9471 | 1.99314 | ||||||||
\(761\) | 47.9326 | 1.73755 | 0.868777 | − | 0.495204i | \(-0.164907\pi\) | ||||
0.868777 | + | 0.495204i | \(0.164907\pi\) | |||||||
\(762\) | 20.3772 | 0.738187 | ||||||||
\(763\) | 12.8559 | 0.465415 | ||||||||
\(764\) | 44.8732 | 1.62346 | ||||||||
\(765\) | 23.1885 | 0.838383 | ||||||||
\(766\) | 43.3303 | 1.56559 | ||||||||
\(767\) | 29.2067 | 1.05459 | ||||||||
\(768\) | −17.4948 | −0.631291 | ||||||||
\(769\) | −25.2413 | −0.910225 | −0.455113 | − | 0.890434i | \(-0.650401\pi\) | ||||
−0.455113 | + | 0.890434i | \(0.650401\pi\) | |||||||
\(770\) | 5.93217 | 0.213781 | ||||||||
\(771\) | 13.2566 | 0.477425 | ||||||||
\(772\) | 35.6008 | 1.28130 | ||||||||
\(773\) | −8.42881 | −0.303163 | −0.151582 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151582 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(774\) | 43.9908 | 1.58122 | ||||||||
\(775\) | −98.8749 | −3.55169 | ||||||||
\(776\) | 118.100 | 4.23953 | ||||||||
\(777\) | 6.75824 | 0.242451 | ||||||||
\(778\) | −26.1150 | −0.936267 | ||||||||
\(779\) | −20.4356 | −0.732181 | ||||||||
\(780\) | −57.9769 | −2.07591 | ||||||||
\(781\) | −7.91862 | −0.283350 | ||||||||
\(782\) | −6.91364 | −0.247231 | ||||||||
\(783\) | −39.8202 | −1.42306 | ||||||||
\(784\) | 9.19910 | 0.328539 | ||||||||
\(785\) | −49.0221 | −1.74967 | ||||||||
\(786\) | −22.4140 | −0.799480 | ||||||||
\(787\) | 34.3142 | 1.22317 | 0.611585 | − | 0.791179i | \(-0.290532\pi\) | ||||
0.611585 | + | 0.791179i | \(0.290532\pi\) | |||||||
\(788\) | 0.0945560 | 0.00336842 | ||||||||
\(789\) | 11.6408 | 0.414423 | ||||||||
\(790\) | 97.1387 | 3.45604 | ||||||||
\(791\) | −2.04921 | −0.0728615 | ||||||||
\(792\) | 8.33661 | 0.296229 | ||||||||
\(793\) | −15.0530 | −0.534548 | ||||||||
\(794\) | 38.3885 | 1.36236 | ||||||||
\(795\) | −22.9447 | −0.813765 | ||||||||
\(796\) | −51.3055 | −1.81848 | ||||||||
\(797\) | −44.5599 | −1.57839 | −0.789196 | − | 0.614141i | \(-0.789503\pi\) | ||||
−0.789196 | + | 0.614141i | \(0.789503\pi\) | |||||||
\(798\) | −4.27034 | −0.151168 | ||||||||
\(799\) | −23.4525 | −0.829688 | ||||||||
\(800\) | −125.048 | −4.42113 | ||||||||
\(801\) | 5.24728 | 0.185404 | ||||||||
\(802\) | 67.8844 | 2.39708 | ||||||||
\(803\) | −2.08959 | −0.0737401 | ||||||||
\(804\) | 25.0391 | 0.883062 | ||||||||
\(805\) | −4.48876 | −0.158208 | ||||||||
\(806\) | 61.1297 | 2.15320 | ||||||||
\(807\) | 2.86244 | 0.100763 | ||||||||
\(808\) | 65.9227 | 2.31915 | ||||||||
\(809\) | 26.5735 | 0.934276 | 0.467138 | − | 0.884184i | \(-0.345285\pi\) | ||||
0.467138 | + | 0.884184i | \(0.345285\pi\) | |||||||
\(810\) | 23.8615 | 0.838407 | ||||||||
\(811\) | −17.9232 | −0.629367 | −0.314684 | − | 0.949197i | \(-0.601898\pi\) | ||||
−0.314684 | + | 0.949197i | \(0.601898\pi\) | |||||||
\(812\) | 40.1678 | 1.40962 | ||||||||
\(813\) | 18.3515 | 0.643614 | ||||||||
\(814\) | −10.2827 | −0.360409 | ||||||||
\(815\) | 19.6851 | 0.689538 | ||||||||
\(816\) | 21.2339 | 0.743337 | ||||||||
\(817\) | 14.0227 | 0.490590 | ||||||||
\(818\) | −83.8221 | −2.93077 | ||||||||
\(819\) | −6.74002 | −0.235516 | ||||||||
\(820\) | 231.447 | 8.08249 | ||||||||
\(821\) | −26.4949 | −0.924680 | −0.462340 | − | 0.886703i | \(-0.652990\pi\) | ||||
−0.462340 | + | 0.886703i | \(0.652990\pi\) | |||||||
\(822\) | 12.6124 | 0.439908 | ||||||||
\(823\) | −11.9771 | −0.417495 | −0.208747 | − | 0.977970i | \(-0.566939\pi\) | ||||
−0.208747 | + | 0.977970i | \(0.566939\pi\) | |||||||
\(824\) | 54.9885 | 1.91562 | ||||||||
\(825\) | 6.43756 | 0.224127 | ||||||||
\(826\) | −24.3643 | −0.847744 | ||||||||
\(827\) | 44.5208 | 1.54814 | 0.774069 | − | 0.633101i | \(-0.218218\pi\) | ||||
0.774069 | + | 0.633101i | \(0.218218\pi\) | |||||||
\(828\) | −10.8658 | −0.377612 | ||||||||
\(829\) | 37.9894 | 1.31943 | 0.659713 | − | 0.751518i | \(-0.270678\pi\) | ||||
0.659713 | + | 0.751518i | \(0.270678\pi\) | |||||||
\(830\) | −16.8624 | −0.585301 | ||||||||
\(831\) | −4.96755 | −0.172323 | ||||||||
\(832\) | 19.9343 | 0.691096 | ||||||||
\(833\) | 2.52035 | 0.0873248 | ||||||||
\(834\) | −3.39975 | −0.117724 | ||||||||
\(835\) | −81.5385 | −2.82176 | ||||||||
\(836\) | 4.57737 | 0.158312 | ||||||||
\(837\) | 35.6148 | 1.23103 | ||||||||
\(838\) | −12.3050 | −0.425071 | ||||||||
\(839\) | −15.4558 | −0.533594 | −0.266797 | − | 0.963753i | \(-0.585965\pi\) | ||||
−0.266797 | + | 0.963753i | \(0.585965\pi\) | |||||||
\(840\) | 28.0782 | 0.968788 | ||||||||
\(841\) | 41.9665 | 1.44712 | ||||||||
\(842\) | −88.5737 | −3.05245 | ||||||||
\(843\) | 14.1792 | 0.488358 | ||||||||
\(844\) | 98.3535 | 3.38547 | ||||||||
\(845\) | 13.9385 | 0.479500 | ||||||||
\(846\) | −52.3193 | −1.79877 | ||||||||
\(847\) | −10.7131 | −0.368107 | ||||||||
\(848\) | 54.1362 | 1.85905 | ||||||||
\(849\) | 17.2562 | 0.592233 | ||||||||
\(850\) | −86.0457 | −2.95134 | ||||||||
\(851\) | 7.78072 | 0.266720 | ||||||||
\(852\) | −64.5600 | −2.21179 | ||||||||
\(853\) | −10.1258 | −0.346699 | −0.173350 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173350 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(854\) | 12.5573 | 0.429701 | ||||||||
\(855\) | 16.4898 | 0.563939 | ||||||||
\(856\) | −36.2124 | −1.23772 | ||||||||
\(857\) | 5.83237 | 0.199230 | 0.0996149 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996149 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(858\) | −3.98004 | −0.135876 | ||||||||
\(859\) | −39.4030 | −1.34441 | −0.672206 | − | 0.740364i | \(-0.734653\pi\) | ||||
−0.672206 | + | 0.740364i | \(0.734653\pi\) | |||||||
\(860\) | −158.816 | −5.41559 | ||||||||
\(861\) | −10.4426 | −0.355884 | ||||||||
\(862\) | −51.0233 | −1.73786 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | 45.0424 | 1.53237 | ||||||||
\(865\) | 3.32725 | 0.113130 | ||||||||
\(866\) | 52.0048 | 1.76720 | ||||||||
\(867\) | −9.75185 | −0.331190 | ||||||||
\(868\) | −35.9257 | −1.21940 | ||||||||
\(869\) | 4.69791 | 0.159366 | ||||||||
\(870\) | 85.4481 | 2.89696 | ||||||||
\(871\) | 17.8816 | 0.605894 | ||||||||
\(872\) | −92.5830 | −3.13526 | ||||||||
\(873\) | 35.4420 | 1.19953 | ||||||||
\(874\) | −4.91641 | −0.166300 | ||||||||
\(875\) | −34.5805 | −1.16904 | ||||||||
\(876\) | −17.0363 | −0.575603 | ||||||||
\(877\) | −53.8729 | −1.81916 | −0.909579 | − | 0.415530i | \(-0.863596\pi\) | ||||
−0.909579 | + | 0.415530i | \(0.863596\pi\) | |||||||
\(878\) | −59.9499 | −2.02321 | ||||||||
\(879\) | 11.6273 | 0.392178 | ||||||||
\(880\) | −20.9760 | −0.707102 | ||||||||
\(881\) | 47.1895 | 1.58985 | 0.794927 | − | 0.606705i | \(-0.207509\pi\) | ||||
0.794927 | + | 0.606705i | \(0.207509\pi\) | |||||||
\(882\) | 5.62256 | 0.189321 | ||||||||
\(883\) | −2.02456 | −0.0681317 | −0.0340659 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340659 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(884\) | 37.4779 | 1.26052 | ||||||||
\(885\) | −36.5140 | −1.22740 | ||||||||
\(886\) | 46.2384 | 1.55341 | ||||||||
\(887\) | 52.3010 | 1.75610 | 0.878048 | − | 0.478572i | \(-0.158846\pi\) | ||||
0.878048 | + | 0.478572i | \(0.158846\pi\) | |||||||
\(888\) | −48.6701 | −1.63326 | ||||||||
\(889\) | −8.55230 | −0.286835 | ||||||||
\(890\) | −26.8898 | −0.901347 | ||||||||
\(891\) | 1.15401 | 0.0386608 | ||||||||
\(892\) | 54.6249 | 1.82898 | ||||||||
\(893\) | −16.6775 | −0.558090 | ||||||||
\(894\) | −19.3815 | −0.648215 | ||||||||
\(895\) | 26.5577 | 0.887726 | ||||||||
\(896\) | 2.42863 | 0.0811349 | ||||||||
\(897\) | 3.01161 | 0.100555 | ||||||||
\(898\) | 23.7707 | 0.793239 | ||||||||
\(899\) | −63.4717 | −2.11690 | ||||||||
\(900\) | −135.233 | −4.50777 | ||||||||
\(901\) | 14.8321 | 0.494129 | ||||||||
\(902\) | 15.8885 | 0.529031 | ||||||||
\(903\) | 7.16562 | 0.238457 | ||||||||
\(904\) | 14.7576 | 0.490830 | ||||||||
\(905\) | 12.4535 | 0.413967 | ||||||||
\(906\) | 17.4201 | 0.578743 | ||||||||
\(907\) | 8.93423 | 0.296656 | 0.148328 | − | 0.988938i | \(-0.452611\pi\) | ||||
0.148328 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(908\) | −131.642 | −4.36870 | ||||||||
\(909\) | 19.7836 | 0.656180 | ||||||||
\(910\) | 34.5393 | 1.14497 | ||||||||
\(911\) | −30.2835 | −1.00334 | −0.501669 | − | 0.865060i | \(-0.667280\pi\) | ||||
−0.501669 | + | 0.865060i | \(0.667280\pi\) | |||||||
\(912\) | 15.0998 | 0.500005 | ||||||||
\(913\) | −0.815513 | −0.0269895 | ||||||||
\(914\) | −63.0209 | −2.08455 | ||||||||
\(915\) | 18.8191 | 0.622142 | ||||||||
\(916\) | 67.1672 | 2.21927 | ||||||||
\(917\) | 9.40716 | 0.310652 | ||||||||
\(918\) | 30.9937 | 1.02294 | ||||||||
\(919\) | −53.1601 | −1.75359 | −0.876795 | − | 0.480864i | \(-0.840323\pi\) | ||||
−0.876795 | + | 0.480864i | \(0.840323\pi\) | |||||||
\(920\) | 32.3262 | 1.06576 | ||||||||
\(921\) | −7.77913 | −0.256331 | ||||||||
\(922\) | −43.9373 | −1.44700 | ||||||||
\(923\) | −46.1052 | −1.51757 | ||||||||
\(924\) | 2.33905 | 0.0769492 | ||||||||
\(925\) | 96.8371 | 3.18399 | ||||||||
\(926\) | 25.5972 | 0.841175 | ||||||||
\(927\) | 16.5022 | 0.542004 | ||||||||
\(928\) | −80.2734 | −2.63510 | ||||||||
\(929\) | 40.2169 | 1.31947 | 0.659737 | − | 0.751497i | \(-0.270668\pi\) | ||||
0.659737 | + | 0.751497i | \(0.270668\pi\) | |||||||
\(930\) | −76.4238 | −2.50604 | ||||||||
\(931\) | 1.79226 | 0.0587390 | ||||||||
\(932\) | 78.4829 | 2.57079 | ||||||||
\(933\) | −11.7212 | −0.383736 | ||||||||
\(934\) | 80.6754 | 2.63978 | ||||||||
\(935\) | −5.74696 | −0.187946 | ||||||||
\(936\) | 48.5389 | 1.58654 | ||||||||
\(937\) | −25.2472 | −0.824789 | −0.412394 | − | 0.911005i | \(-0.635307\pi\) | ||||
−0.412394 | + | 0.911005i | \(0.635307\pi\) | |||||||
\(938\) | −14.9169 | −0.487053 | ||||||||
\(939\) | −15.9709 | −0.521190 | ||||||||
\(940\) | 188.884 | 6.16071 | ||||||||
\(941\) | −26.2736 | −0.856494 | −0.428247 | − | 0.903662i | \(-0.640869\pi\) | ||||
−0.428247 | + | 0.903662i | \(0.640869\pi\) | |||||||
\(942\) | −27.4371 | −0.893947 | ||||||||
\(943\) | −12.0225 | −0.391508 | ||||||||
\(944\) | 86.1518 | 2.80400 | ||||||||
\(945\) | 20.1230 | 0.654600 | ||||||||
\(946\) | −10.9025 | −0.354472 | ||||||||
\(947\) | −26.0790 | −0.847453 | −0.423726 | − | 0.905790i | \(-0.639278\pi\) | ||||
−0.423726 | + | 0.905790i | \(0.639278\pi\) | |||||||
\(948\) | 38.3017 | 1.24398 | ||||||||
\(949\) | −12.1664 | −0.394938 | ||||||||
\(950\) | −61.1886 | −1.98522 | ||||||||
\(951\) | −9.44560 | −0.306294 | ||||||||
\(952\) | −18.1505 | −0.588261 | ||||||||
\(953\) | −38.4418 | −1.24525 | −0.622626 | − | 0.782520i | \(-0.713934\pi\) | ||||
−0.622626 | + | 0.782520i | \(0.713934\pi\) | |||||||
\(954\) | 33.0884 | 1.07128 | ||||||||
\(955\) | −40.0637 | −1.29643 | ||||||||
\(956\) | 140.937 | 4.55824 | ||||||||
\(957\) | 4.13252 | 0.133585 | ||||||||
\(958\) | −24.3677 | −0.787286 | ||||||||
\(959\) | −5.29343 | −0.170934 | ||||||||
\(960\) | −24.9217 | −0.804343 | ||||||||
\(961\) | 25.7683 | 0.831236 | ||||||||
\(962\) | −59.8698 | −1.93028 | ||||||||
\(963\) | −10.8674 | −0.350199 | ||||||||
\(964\) | 48.6143 | 1.56576 | ||||||||
\(965\) | −31.7850 | −1.02320 | ||||||||
\(966\) | −2.51230 | −0.0808320 | ||||||||
\(967\) | 23.8010 | 0.765389 | 0.382695 | − | 0.923875i | \(-0.374996\pi\) | ||||
0.382695 | + | 0.923875i | \(0.374996\pi\) | |||||||
\(968\) | 77.1514 | 2.47974 | ||||||||
\(969\) | 4.13701 | 0.132900 | ||||||||
\(970\) | −181.623 | −5.83156 | ||||||||
\(971\) | 28.1205 | 0.902430 | 0.451215 | − | 0.892415i | \(-0.350991\pi\) | ||||
0.451215 | + | 0.892415i | \(0.350991\pi\) | |||||||
\(972\) | 77.0247 | 2.47057 | ||||||||
\(973\) | 1.42688 | 0.0457435 | ||||||||
\(974\) | 104.221 | 3.33945 | ||||||||
\(975\) | 37.4819 | 1.20038 | ||||||||
\(976\) | −44.4023 | −1.42128 | ||||||||
\(977\) | −43.9649 | −1.40656 | −0.703281 | − | 0.710912i | \(-0.748282\pi\) | ||||
−0.703281 | + | 0.710912i | \(0.748282\pi\) | |||||||
\(978\) | 11.0175 | 0.352300 | ||||||||
\(979\) | −1.30047 | −0.0415631 | ||||||||
\(980\) | −20.2986 | −0.648416 | ||||||||
\(981\) | −27.7844 | −0.887087 | ||||||||
\(982\) | 96.9788 | 3.09472 | ||||||||
\(983\) | −13.2073 | −0.421249 | −0.210624 | − | 0.977567i | \(-0.567550\pi\) | ||||
−0.210624 | + | 0.977567i | \(0.567550\pi\) | |||||||
\(984\) | 75.2036 | 2.39740 | ||||||||
\(985\) | −0.0844214 | −0.00268989 | ||||||||
\(986\) | −55.2361 | −1.75907 | ||||||||
\(987\) | −8.52223 | −0.271266 | ||||||||
\(988\) | 26.6512 | 0.847887 | ||||||||
\(989\) | 8.24973 | 0.262326 | ||||||||
\(990\) | −12.8207 | −0.407469 | ||||||||
\(991\) | −3.49676 | −0.111078 | −0.0555391 | − | 0.998457i | \(-0.517688\pi\) | ||||
−0.0555391 | + | 0.998457i | \(0.517688\pi\) | |||||||
\(992\) | 71.7956 | 2.27951 | ||||||||
\(993\) | −31.3367 | −0.994441 | ||||||||
\(994\) | 38.4611 | 1.21991 | ||||||||
\(995\) | 45.8065 | 1.45217 | ||||||||
\(996\) | −6.64882 | −0.210676 | ||||||||
\(997\) | −22.3740 | −0.708592 | −0.354296 | − | 0.935133i | \(-0.615279\pi\) | ||||
−0.354296 | + | 0.935133i | \(0.615279\pi\) | |||||||
\(998\) | 14.5099 | 0.459301 | ||||||||
\(999\) | −34.8808 | −1.10358 |
(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 | 6041.2.a.f.1.8 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.8 | ✓ | 132 | 1.1 | even | 1 | trivial |