Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32654 | −1.64511 | −0.822555 | − | 0.568685i | \(-0.807452\pi\) | ||||
−0.822555 | + | 0.568685i | \(0.807452\pi\) | |||||||
\(3\) | −0.105675 | −0.0610113 | −0.0305056 | − | 0.999535i | \(-0.509712\pi\) | ||||
−0.0305056 | + | 0.999535i | \(0.509712\pi\) | |||||||
\(4\) | 3.41278 | 1.70639 | ||||||||
\(5\) | −1.05522 | −0.471911 | −0.235955 | − | 0.971764i | \(-0.575822\pi\) | ||||
−0.235955 | + | 0.971764i | \(0.575822\pi\) | |||||||
\(6\) | 0.245856 | 0.100370 | ||||||||
\(7\) | 0.945293 | 0.357287 | 0.178644 | − | 0.983914i | \(-0.442829\pi\) | ||||
0.178644 | + | 0.983914i | \(0.442829\pi\) | |||||||
\(8\) | −3.28688 | −1.16209 | ||||||||
\(9\) | −2.98883 | −0.996278 | ||||||||
\(10\) | 2.45502 | 0.776346 | ||||||||
\(11\) | 2.00424 | 0.604300 | 0.302150 | − | 0.953260i | \(-0.402296\pi\) | ||||
0.302150 | + | 0.953260i | \(0.402296\pi\) | |||||||
\(12\) | −0.360644 | −0.104109 | ||||||||
\(13\) | 4.81051 | 1.33420 | 0.667098 | − | 0.744970i | \(-0.267536\pi\) | ||||
0.667098 | + | 0.744970i | \(0.267536\pi\) | |||||||
\(14\) | −2.19926 | −0.587777 | ||||||||
\(15\) | 0.111511 | 0.0287919 | ||||||||
\(16\) | 0.821491 | 0.205373 | ||||||||
\(17\) | 5.66382 | 1.37368 | 0.686839 | − | 0.726810i | \(-0.258998\pi\) | ||||
0.686839 | + | 0.726810i | \(0.258998\pi\) | |||||||
\(18\) | 6.95363 | 1.63899 | ||||||||
\(19\) | 0.270587 | 0.0620770 | 0.0310385 | − | 0.999518i | \(-0.490119\pi\) | ||||
0.0310385 | + | 0.999518i | \(0.490119\pi\) | |||||||
\(20\) | −3.60125 | −0.805263 | ||||||||
\(21\) | −0.0998935 | −0.0217986 | ||||||||
\(22\) | −4.66293 | −0.994140 | ||||||||
\(23\) | 2.04703 | 0.426835 | 0.213418 | − | 0.976961i | \(-0.431540\pi\) | ||||
0.213418 | + | 0.976961i | \(0.431540\pi\) | |||||||
\(24\) | 0.347340 | 0.0709004 | ||||||||
\(25\) | −3.88650 | −0.777300 | ||||||||
\(26\) | −11.1918 | −2.19490 | ||||||||
\(27\) | 0.632868 | 0.121795 | ||||||||
\(28\) | 3.22608 | 0.609671 | ||||||||
\(29\) | −5.94578 | −1.10410 | −0.552052 | − | 0.833810i | \(-0.686155\pi\) | ||||
−0.552052 | + | 0.833810i | \(0.686155\pi\) | |||||||
\(30\) | −0.259433 | −0.0473658 | ||||||||
\(31\) | 3.29742 | 0.592234 | 0.296117 | − | 0.955152i | \(-0.404308\pi\) | ||||
0.296117 | + | 0.955152i | \(0.404308\pi\) | |||||||
\(32\) | 4.66253 | 0.824226 | ||||||||
\(33\) | −0.211797 | −0.0368691 | ||||||||
\(34\) | −13.1771 | −2.25985 | ||||||||
\(35\) | −0.997497 | −0.168608 | ||||||||
\(36\) | −10.2002 | −1.70004 | ||||||||
\(37\) | −5.04927 | −0.830095 | −0.415047 | − | 0.909800i | \(-0.636235\pi\) | ||||
−0.415047 | + | 0.909800i | \(0.636235\pi\) | |||||||
\(38\) | −0.629531 | −0.102123 | ||||||||
\(39\) | −0.508349 | −0.0814010 | ||||||||
\(40\) | 3.46840 | 0.548401 | ||||||||
\(41\) | −5.06296 | −0.790701 | −0.395350 | − | 0.918530i | \(-0.629377\pi\) | ||||
−0.395350 | + | 0.918530i | \(0.629377\pi\) | |||||||
\(42\) | 0.232406 | 0.0358610 | ||||||||
\(43\) | 1.81524 | 0.276822 | 0.138411 | − | 0.990375i | \(-0.455801\pi\) | ||||
0.138411 | + | 0.990375i | \(0.455801\pi\) | |||||||
\(44\) | 6.84001 | 1.03117 | ||||||||
\(45\) | 3.15389 | 0.470154 | ||||||||
\(46\) | −4.76249 | −0.702191 | ||||||||
\(47\) | 12.2205 | 1.78254 | 0.891269 | − | 0.453474i | \(-0.149816\pi\) | ||||
0.891269 | + | 0.453474i | \(0.149816\pi\) | |||||||
\(48\) | −0.0868108 | −0.0125301 | ||||||||
\(49\) | −6.10642 | −0.872346 | ||||||||
\(50\) | 9.04209 | 1.27874 | ||||||||
\(51\) | −0.598522 | −0.0838098 | ||||||||
\(52\) | 16.4172 | 2.27666 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −1.47239 | −0.200367 | ||||||||
\(55\) | −2.11492 | −0.285176 | ||||||||
\(56\) | −3.10706 | −0.415199 | ||||||||
\(57\) | −0.0285942 | −0.00378739 | ||||||||
\(58\) | 13.8331 | 1.81637 | ||||||||
\(59\) | −11.0180 | −1.43442 | −0.717211 | − | 0.696856i | \(-0.754581\pi\) | ||||
−0.717211 | + | 0.696856i | \(0.754581\pi\) | |||||||
\(60\) | 0.380560 | 0.0491301 | ||||||||
\(61\) | −7.84960 | −1.00504 | −0.502519 | − | 0.864566i | \(-0.667593\pi\) | ||||
−0.502519 | + | 0.864566i | \(0.667593\pi\) | |||||||
\(62\) | −7.67157 | −0.974290 | ||||||||
\(63\) | −2.82532 | −0.355957 | ||||||||
\(64\) | −12.4905 | −1.56132 | ||||||||
\(65\) | −5.07617 | −0.629622 | ||||||||
\(66\) | 0.492754 | 0.0606538 | ||||||||
\(67\) | −11.3588 | −1.38769 | −0.693847 | − | 0.720122i | \(-0.744086\pi\) | ||||
−0.693847 | + | 0.720122i | \(0.744086\pi\) | |||||||
\(68\) | 19.3293 | 2.34403 | ||||||||
\(69\) | −0.216319 | −0.0260418 | ||||||||
\(70\) | 2.32071 | 0.277378 | ||||||||
\(71\) | −6.29987 | −0.747657 | −0.373829 | − | 0.927498i | \(-0.621955\pi\) | ||||
−0.373829 | + | 0.927498i | \(0.621955\pi\) | |||||||
\(72\) | 9.82393 | 1.15776 | ||||||||
\(73\) | −1.26449 | −0.147997 | −0.0739985 | − | 0.997258i | \(-0.523576\pi\) | ||||
−0.0739985 | + | 0.997258i | \(0.523576\pi\) | |||||||
\(74\) | 11.7473 | 1.36560 | ||||||||
\(75\) | 0.410705 | 0.0474241 | ||||||||
\(76\) | 0.923454 | 0.105927 | ||||||||
\(77\) | 1.89459 | 0.215909 | ||||||||
\(78\) | 1.18269 | 0.133914 | ||||||||
\(79\) | −9.25154 | −1.04088 | −0.520440 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520440 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(80\) | −0.866858 | −0.0969177 | ||||||||
\(81\) | 8.89962 | 0.988847 | ||||||||
\(82\) | 11.7792 | 1.30079 | ||||||||
\(83\) | −15.9049 | −1.74579 | −0.872893 | − | 0.487912i | \(-0.837759\pi\) | ||||
−0.872893 | + | 0.487912i | \(0.837759\pi\) | |||||||
\(84\) | −0.340914 | −0.0371968 | ||||||||
\(85\) | −5.97660 | −0.648253 | ||||||||
\(86\) | −4.22323 | −0.455402 | ||||||||
\(87\) | 0.628318 | 0.0673628 | ||||||||
\(88\) | −6.58768 | −0.702249 | ||||||||
\(89\) | −9.97305 | −1.05714 | −0.528570 | − | 0.848889i | \(-0.677272\pi\) | ||||
−0.528570 | + | 0.848889i | \(0.677272\pi\) | |||||||
\(90\) | −7.33765 | −0.773456 | ||||||||
\(91\) | 4.54735 | 0.476691 | ||||||||
\(92\) | 6.98606 | 0.728347 | ||||||||
\(93\) | −0.348453 | −0.0361329 | ||||||||
\(94\) | −28.4314 | −2.93247 | ||||||||
\(95\) | −0.285530 | −0.0292948 | ||||||||
\(96\) | −0.492711 | −0.0502871 | ||||||||
\(97\) | 13.8158 | 1.40278 | 0.701389 | − | 0.712779i | \(-0.252564\pi\) | ||||
0.701389 | + | 0.712779i | \(0.252564\pi\) | |||||||
\(98\) | 14.2068 | 1.43511 | ||||||||
\(99\) | −5.99033 | −0.602051 | ||||||||
\(100\) | −13.2638 | −1.32638 | ||||||||
\(101\) | 11.6367 | 1.15790 | 0.578949 | − | 0.815364i | \(-0.303463\pi\) | ||||
0.578949 | + | 0.815364i | \(0.303463\pi\) | |||||||
\(102\) | 1.39248 | 0.137876 | ||||||||
\(103\) | −1.85596 | −0.182873 | −0.0914365 | − | 0.995811i | \(-0.529146\pi\) | ||||
−0.0914365 | + | 0.995811i | \(0.529146\pi\) | |||||||
\(104\) | −15.8116 | −1.55045 | ||||||||
\(105\) | 0.105410 | 0.0102870 | ||||||||
\(106\) | 2.32654 | 0.225973 | ||||||||
\(107\) | 14.4919 | 1.40099 | 0.700493 | − | 0.713660i | \(-0.252964\pi\) | ||||
0.700493 | + | 0.713660i | \(0.252964\pi\) | |||||||
\(108\) | 2.15984 | 0.207830 | ||||||||
\(109\) | 11.5306 | 1.10443 | 0.552215 | − | 0.833702i | \(-0.313783\pi\) | ||||
0.552215 | + | 0.833702i | \(0.313783\pi\) | |||||||
\(110\) | 4.92044 | 0.469146 | ||||||||
\(111\) | 0.533580 | 0.0506451 | ||||||||
\(112\) | 0.776550 | 0.0733771 | ||||||||
\(113\) | 10.6900 | 1.00563 | 0.502814 | − | 0.864395i | \(-0.332298\pi\) | ||||
0.502814 | + | 0.864395i | \(0.332298\pi\) | |||||||
\(114\) | 0.0665255 | 0.00623068 | ||||||||
\(115\) | −2.16008 | −0.201428 | ||||||||
\(116\) | −20.2916 | −1.88403 | ||||||||
\(117\) | −14.3778 | −1.32923 | ||||||||
\(118\) | 25.6338 | 2.35978 | ||||||||
\(119\) | 5.35397 | 0.490798 | ||||||||
\(120\) | −0.366521 | −0.0334587 | ||||||||
\(121\) | −6.98304 | −0.634821 | ||||||||
\(122\) | 18.2624 | 1.65340 | ||||||||
\(123\) | 0.535026 | 0.0482417 | ||||||||
\(124\) | 11.2534 | 1.01058 | ||||||||
\(125\) | 9.37726 | 0.838727 | ||||||||
\(126\) | 6.57322 | 0.585589 | ||||||||
\(127\) | 8.78273 | 0.779341 | 0.389671 | − | 0.920954i | \(-0.372589\pi\) | ||||
0.389671 | + | 0.920954i | \(0.372589\pi\) | |||||||
\(128\) | 19.7346 | 1.74431 | ||||||||
\(129\) | −0.191825 | −0.0168892 | ||||||||
\(130\) | 11.8099 | 1.03580 | ||||||||
\(131\) | −0.515780 | −0.0450639 | −0.0225320 | − | 0.999746i | \(-0.507173\pi\) | ||||
−0.0225320 | + | 0.999746i | \(0.507173\pi\) | |||||||
\(132\) | −0.722816 | −0.0629130 | ||||||||
\(133\) | 0.255784 | 0.0221793 | ||||||||
\(134\) | 26.4266 | 2.28291 | ||||||||
\(135\) | −0.667818 | −0.0574766 | ||||||||
\(136\) | −18.6163 | −1.59633 | ||||||||
\(137\) | 6.81055 | 0.581865 | 0.290932 | − | 0.956744i | \(-0.406035\pi\) | ||||
0.290932 | + | 0.956744i | \(0.406035\pi\) | |||||||
\(138\) | 0.503275 | 0.0428416 | ||||||||
\(139\) | −17.8245 | −1.51186 | −0.755928 | − | 0.654655i | \(-0.772814\pi\) | ||||
−0.755928 | + | 0.654655i | \(0.772814\pi\) | |||||||
\(140\) | −3.40424 | −0.287710 | ||||||||
\(141\) | −1.29139 | −0.108755 | ||||||||
\(142\) | 14.6569 | 1.22998 | ||||||||
\(143\) | 9.64140 | 0.806255 | ||||||||
\(144\) | −2.45530 | −0.204608 | ||||||||
\(145\) | 6.27413 | 0.521039 | ||||||||
\(146\) | 2.94188 | 0.243471 | ||||||||
\(147\) | 0.645294 | 0.0532229 | ||||||||
\(148\) | −17.2320 | −1.41646 | ||||||||
\(149\) | 24.2110 | 1.98345 | 0.991723 | − | 0.128394i | \(-0.0409823\pi\) | ||||
0.991723 | + | 0.128394i | \(0.0409823\pi\) | |||||||
\(150\) | −0.955520 | −0.0780178 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | −0.889387 | −0.0721388 | ||||||||
\(153\) | −16.9282 | −1.36856 | ||||||||
\(154\) | −4.40784 | −0.355194 | ||||||||
\(155\) | −3.47952 | −0.279482 | ||||||||
\(156\) | −1.73488 | −0.138902 | ||||||||
\(157\) | −13.5873 | −1.08439 | −0.542194 | − | 0.840254i | \(-0.682406\pi\) | ||||
−0.542194 | + | 0.840254i | \(0.682406\pi\) | |||||||
\(158\) | 21.5240 | 1.71236 | ||||||||
\(159\) | 0.105675 | 0.00838054 | ||||||||
\(160\) | −4.92001 | −0.388961 | ||||||||
\(161\) | 1.93504 | 0.152503 | ||||||||
\(162\) | −20.7053 | −1.62676 | ||||||||
\(163\) | −11.0521 | −0.865671 | −0.432835 | − | 0.901473i | \(-0.642487\pi\) | ||||
−0.432835 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(164\) | −17.2787 | −1.34924 | ||||||||
\(165\) | 0.223493 | 0.0173989 | ||||||||
\(166\) | 37.0033 | 2.87201 | ||||||||
\(167\) | 13.3755 | 1.03503 | 0.517515 | − | 0.855674i | \(-0.326857\pi\) | ||||
0.517515 | + | 0.855674i | \(0.326857\pi\) | |||||||
\(168\) | 0.328338 | 0.0253318 | ||||||||
\(169\) | 10.1410 | 0.780079 | ||||||||
\(170\) | 13.9048 | 1.06645 | ||||||||
\(171\) | −0.808740 | −0.0618459 | ||||||||
\(172\) | 6.19501 | 0.472365 | ||||||||
\(173\) | −11.2195 | −0.853004 | −0.426502 | − | 0.904487i | \(-0.640254\pi\) | ||||
−0.426502 | + | 0.904487i | \(0.640254\pi\) | |||||||
\(174\) | −1.46181 | −0.110819 | ||||||||
\(175\) | −3.67388 | −0.277719 | ||||||||
\(176\) | 1.64646 | 0.124107 | ||||||||
\(177\) | 1.16432 | 0.0875159 | ||||||||
\(178\) | 23.2027 | 1.73911 | ||||||||
\(179\) | −18.7923 | −1.40460 | −0.702302 | − | 0.711879i | \(-0.747844\pi\) | ||||
−0.702302 | + | 0.711879i | \(0.747844\pi\) | |||||||
\(180\) | 10.7635 | 0.802266 | ||||||||
\(181\) | 9.04545 | 0.672343 | 0.336172 | − | 0.941801i | \(-0.390868\pi\) | ||||
0.336172 | + | 0.941801i | \(0.390868\pi\) | |||||||
\(182\) | −10.5796 | −0.784210 | ||||||||
\(183\) | 0.829503 | 0.0613187 | ||||||||
\(184\) | −6.72834 | −0.496020 | ||||||||
\(185\) | 5.32811 | 0.391731 | ||||||||
\(186\) | 0.810690 | 0.0594427 | ||||||||
\(187\) | 11.3516 | 0.830113 | ||||||||
\(188\) | 41.7057 | 3.04170 | ||||||||
\(189\) | 0.598246 | 0.0435160 | ||||||||
\(190\) | 0.664297 | 0.0481932 | ||||||||
\(191\) | −27.2592 | −1.97240 | −0.986202 | − | 0.165547i | \(-0.947061\pi\) | ||||
−0.986202 | + | 0.165547i | \(0.947061\pi\) | |||||||
\(192\) | 1.31993 | 0.0952579 | ||||||||
\(193\) | −25.5753 | −1.84095 | −0.920476 | − | 0.390798i | \(-0.872199\pi\) | ||||
−0.920476 | + | 0.390798i | \(0.872199\pi\) | |||||||
\(194\) | −32.1429 | −2.30772 | ||||||||
\(195\) | 0.536423 | 0.0384140 | ||||||||
\(196\) | −20.8398 | −1.48856 | ||||||||
\(197\) | −25.1873 | −1.79452 | −0.897259 | − | 0.441504i | \(-0.854445\pi\) | ||||
−0.897259 | + | 0.441504i | \(0.854445\pi\) | |||||||
\(198\) | 13.9367 | 0.990440 | ||||||||
\(199\) | −12.9728 | −0.919620 | −0.459810 | − | 0.888017i | \(-0.652082\pi\) | ||||
−0.459810 | + | 0.888017i | \(0.652082\pi\) | |||||||
\(200\) | 12.7745 | 0.903290 | ||||||||
\(201\) | 1.20033 | 0.0846650 | ||||||||
\(202\) | −27.0733 | −1.90487 | ||||||||
\(203\) | −5.62051 | −0.394482 | ||||||||
\(204\) | −2.04262 | −0.143012 | ||||||||
\(205\) | 5.34256 | 0.373140 | ||||||||
\(206\) | 4.31795 | 0.300846 | ||||||||
\(207\) | −6.11823 | −0.425246 | ||||||||
\(208\) | 3.95179 | 0.274008 | ||||||||
\(209\) | 0.542321 | 0.0375131 | ||||||||
\(210\) | −0.245241 | −0.0169232 | ||||||||
\(211\) | −19.2950 | −1.32832 | −0.664161 | − | 0.747589i | \(-0.731211\pi\) | ||||
−0.664161 | + | 0.747589i | \(0.731211\pi\) | |||||||
\(212\) | −3.41278 | −0.234390 | ||||||||
\(213\) | 0.665737 | 0.0456155 | ||||||||
\(214\) | −33.7160 | −2.30478 | ||||||||
\(215\) | −1.91549 | −0.130635 | ||||||||
\(216\) | −2.08016 | −0.141537 | ||||||||
\(217\) | 3.11703 | 0.211598 | ||||||||
\(218\) | −26.8264 | −1.81691 | ||||||||
\(219\) | 0.133624 | 0.00902949 | ||||||||
\(220\) | −7.21775 | −0.486621 | ||||||||
\(221\) | 27.2459 | 1.83275 | ||||||||
\(222\) | −1.24139 | −0.0833168 | ||||||||
\(223\) | 4.64432 | 0.311007 | 0.155503 | − | 0.987835i | \(-0.450300\pi\) | ||||
0.155503 | + | 0.987835i | \(0.450300\pi\) | |||||||
\(224\) | 4.40745 | 0.294485 | ||||||||
\(225\) | 11.6161 | 0.774407 | ||||||||
\(226\) | −24.8706 | −1.65437 | ||||||||
\(227\) | 18.5004 | 1.22791 | 0.613957 | − | 0.789340i | \(-0.289577\pi\) | ||||
0.613957 | + | 0.789340i | \(0.289577\pi\) | |||||||
\(228\) | −0.0975856 | −0.00646277 | ||||||||
\(229\) | 12.9241 | 0.854047 | 0.427023 | − | 0.904241i | \(-0.359562\pi\) | ||||
0.427023 | + | 0.904241i | \(0.359562\pi\) | |||||||
\(230\) | 5.02550 | 0.331372 | ||||||||
\(231\) | −0.200210 | −0.0131729 | ||||||||
\(232\) | 19.5431 | 1.28306 | ||||||||
\(233\) | 4.88210 | 0.319837 | 0.159919 | − | 0.987130i | \(-0.448877\pi\) | ||||
0.159919 | + | 0.987130i | \(0.448877\pi\) | |||||||
\(234\) | 33.4505 | 2.18673 | ||||||||
\(235\) | −12.8953 | −0.841199 | ||||||||
\(236\) | −37.6020 | −2.44768 | ||||||||
\(237\) | 0.977653 | 0.0635054 | ||||||||
\(238\) | −12.4562 | −0.807416 | ||||||||
\(239\) | 13.1707 | 0.851943 | 0.425971 | − | 0.904737i | \(-0.359932\pi\) | ||||
0.425971 | + | 0.904737i | \(0.359932\pi\) | |||||||
\(240\) | 0.0916049 | 0.00591307 | ||||||||
\(241\) | 2.09034 | 0.134651 | 0.0673253 | − | 0.997731i | \(-0.478553\pi\) | ||||
0.0673253 | + | 0.997731i | \(0.478553\pi\) | |||||||
\(242\) | 16.2463 | 1.04435 | ||||||||
\(243\) | −2.83907 | −0.182126 | ||||||||
\(244\) | −26.7889 | −1.71499 | ||||||||
\(245\) | 6.44365 | 0.411669 | ||||||||
\(246\) | −1.24476 | −0.0793629 | ||||||||
\(247\) | 1.30166 | 0.0828228 | ||||||||
\(248\) | −10.8382 | −0.688227 | ||||||||
\(249\) | 1.68074 | 0.106513 | ||||||||
\(250\) | −21.8165 | −1.37980 | ||||||||
\(251\) | −6.82059 | −0.430512 | −0.215256 | − | 0.976558i | \(-0.569059\pi\) | ||||
−0.215256 | + | 0.976558i | \(0.569059\pi\) | |||||||
\(252\) | −9.64220 | −0.607402 | ||||||||
\(253\) | 4.10273 | 0.257937 | ||||||||
\(254\) | −20.4333 | −1.28210 | ||||||||
\(255\) | 0.631575 | 0.0395508 | ||||||||
\(256\) | −20.9323 | −1.30827 | ||||||||
\(257\) | 9.96701 | 0.621725 | 0.310862 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310862 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(258\) | 0.446288 | 0.0277847 | ||||||||
\(259\) | −4.77304 | −0.296582 | ||||||||
\(260\) | −17.3238 | −1.07438 | ||||||||
\(261\) | 17.7709 | 1.09999 | ||||||||
\(262\) | 1.19998 | 0.0741351 | ||||||||
\(263\) | 17.4636 | 1.07685 | 0.538426 | − | 0.842673i | \(-0.319019\pi\) | ||||
0.538426 | + | 0.842673i | \(0.319019\pi\) | |||||||
\(264\) | 0.696151 | 0.0428451 | ||||||||
\(265\) | 1.05522 | 0.0648219 | ||||||||
\(266\) | −0.595092 | −0.0364874 | ||||||||
\(267\) | 1.05390 | 0.0644975 | ||||||||
\(268\) | −38.7649 | −2.36794 | ||||||||
\(269\) | −3.40003 | −0.207303 | −0.103652 | − | 0.994614i | \(-0.533053\pi\) | ||||
−0.103652 | + | 0.994614i | \(0.533053\pi\) | |||||||
\(270\) | 1.55370 | 0.0945554 | ||||||||
\(271\) | 9.85897 | 0.598890 | 0.299445 | − | 0.954114i | \(-0.403199\pi\) | ||||
0.299445 | + | 0.954114i | \(0.403199\pi\) | |||||||
\(272\) | 4.65278 | 0.282116 | ||||||||
\(273\) | −0.480539 | −0.0290835 | ||||||||
\(274\) | −15.8450 | −0.957232 | ||||||||
\(275\) | −7.78947 | −0.469723 | ||||||||
\(276\) | −0.738249 | −0.0444374 | ||||||||
\(277\) | 27.4781 | 1.65100 | 0.825500 | − | 0.564401i | \(-0.190893\pi\) | ||||
0.825500 | + | 0.564401i | \(0.190893\pi\) | |||||||
\(278\) | 41.4694 | 2.48717 | ||||||||
\(279\) | −9.85543 | −0.590029 | ||||||||
\(280\) | 3.27865 | 0.195937 | ||||||||
\(281\) | −22.4075 | −1.33672 | −0.668360 | − | 0.743838i | \(-0.733004\pi\) | ||||
−0.668360 | + | 0.743838i | \(0.733004\pi\) | |||||||
\(282\) | 3.00448 | 0.178914 | ||||||||
\(283\) | 4.32478 | 0.257081 | 0.128541 | − | 0.991704i | \(-0.458971\pi\) | ||||
0.128541 | + | 0.991704i | \(0.458971\pi\) | |||||||
\(284\) | −21.5001 | −1.27579 | ||||||||
\(285\) | 0.0301733 | 0.00178731 | ||||||||
\(286\) | −22.4311 | −1.32638 | ||||||||
\(287\) | −4.78598 | −0.282507 | ||||||||
\(288\) | −13.9355 | −0.821158 | ||||||||
\(289\) | 15.0788 | 0.886990 | ||||||||
\(290\) | −14.5970 | −0.857166 | ||||||||
\(291\) | −1.45998 | −0.0855853 | ||||||||
\(292\) | −4.31541 | −0.252540 | ||||||||
\(293\) | −10.7815 | −0.629862 | −0.314931 | − | 0.949115i | \(-0.601981\pi\) | ||||
−0.314931 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(294\) | −1.50130 | −0.0875576 | ||||||||
\(295\) | 11.6265 | 0.676919 | ||||||||
\(296\) | 16.5963 | 0.964642 | ||||||||
\(297\) | 1.26842 | 0.0736010 | ||||||||
\(298\) | −56.3279 | −3.26299 | ||||||||
\(299\) | 9.84726 | 0.569482 | ||||||||
\(300\) | 1.40164 | 0.0809239 | ||||||||
\(301\) | 1.71594 | 0.0989049 | ||||||||
\(302\) | 2.32654 | 0.133877 | ||||||||
\(303\) | −1.22971 | −0.0706448 | ||||||||
\(304\) | 0.222285 | 0.0127489 | ||||||||
\(305\) | 8.28309 | 0.474288 | ||||||||
\(306\) | 39.3841 | 2.25144 | ||||||||
\(307\) | −16.9354 | −0.966556 | −0.483278 | − | 0.875467i | \(-0.660554\pi\) | ||||
−0.483278 | + | 0.875467i | \(0.660554\pi\) | |||||||
\(308\) | 6.46582 | 0.368424 | ||||||||
\(309\) | 0.196128 | 0.0111573 | ||||||||
\(310\) | 8.09523 | 0.459778 | ||||||||
\(311\) | 17.4501 | 0.989505 | 0.494753 | − | 0.869034i | \(-0.335259\pi\) | ||||
0.494753 | + | 0.869034i | \(0.335259\pi\) | |||||||
\(312\) | 1.67088 | 0.0945950 | ||||||||
\(313\) | 4.11461 | 0.232571 | 0.116286 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116286 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(314\) | 31.6114 | 1.78394 | ||||||||
\(315\) | 2.98135 | 0.167980 | ||||||||
\(316\) | −31.5734 | −1.77614 | ||||||||
\(317\) | −6.94553 | −0.390100 | −0.195050 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195050 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(318\) | −0.245856 | −0.0137869 | ||||||||
\(319\) | −11.9168 | −0.667210 | ||||||||
\(320\) | 13.1803 | 0.736802 | ||||||||
\(321\) | −1.53143 | −0.0854759 | ||||||||
\(322\) | −4.50195 | −0.250884 | ||||||||
\(323\) | 1.53256 | 0.0852737 | ||||||||
\(324\) | 30.3724 | 1.68736 | ||||||||
\(325\) | −18.6961 | −1.03707 | ||||||||
\(326\) | 25.7132 | 1.42412 | ||||||||
\(327\) | −1.21849 | −0.0673827 | ||||||||
\(328\) | 16.6413 | 0.918863 | ||||||||
\(329\) | 11.5519 | 0.636878 | ||||||||
\(330\) | −0.519966 | −0.0286232 | ||||||||
\(331\) | −2.27204 | −0.124883 | −0.0624414 | − | 0.998049i | \(-0.519889\pi\) | ||||
−0.0624414 | + | 0.998049i | \(0.519889\pi\) | |||||||
\(332\) | −54.2798 | −2.97899 | ||||||||
\(333\) | 15.0914 | 0.827005 | ||||||||
\(334\) | −31.1187 | −1.70274 | ||||||||
\(335\) | 11.9861 | 0.654868 | ||||||||
\(336\) | −0.0820617 | −0.00447683 | ||||||||
\(337\) | −8.13127 | −0.442939 | −0.221469 | − | 0.975167i | \(-0.571085\pi\) | ||||
−0.221469 | + | 0.975167i | \(0.571085\pi\) | |||||||
\(338\) | −23.5935 | −1.28332 | ||||||||
\(339\) | −1.12966 | −0.0613547 | ||||||||
\(340\) | −20.3968 | −1.10617 | ||||||||
\(341\) | 6.60881 | 0.357887 | ||||||||
\(342\) | 1.88156 | 0.101743 | ||||||||
\(343\) | −12.3894 | −0.668965 | ||||||||
\(344\) | −5.96648 | −0.321691 | ||||||||
\(345\) | 0.228265 | 0.0122894 | ||||||||
\(346\) | 26.1026 | 1.40329 | ||||||||
\(347\) | 1.24494 | 0.0668321 | 0.0334161 | − | 0.999442i | \(-0.489361\pi\) | ||||
0.0334161 | + | 0.999442i | \(0.489361\pi\) | |||||||
\(348\) | 2.14431 | 0.114947 | ||||||||
\(349\) | −31.3306 | −1.67709 | −0.838544 | − | 0.544833i | \(-0.816593\pi\) | ||||
−0.838544 | + | 0.544833i | \(0.816593\pi\) | |||||||
\(350\) | 8.54743 | 0.456879 | ||||||||
\(351\) | 3.04442 | 0.162499 | ||||||||
\(352\) | 9.34480 | 0.498080 | ||||||||
\(353\) | −7.46509 | −0.397327 | −0.198663 | − | 0.980068i | \(-0.563660\pi\) | ||||
−0.198663 | + | 0.980068i | \(0.563660\pi\) | |||||||
\(354\) | −2.70884 | −0.143973 | ||||||||
\(355\) | 6.64778 | 0.352828 | ||||||||
\(356\) | −34.0358 | −1.80389 | ||||||||
\(357\) | −0.565779 | −0.0299442 | ||||||||
\(358\) | 43.7210 | 2.31073 | ||||||||
\(359\) | 18.2435 | 0.962854 | 0.481427 | − | 0.876486i | \(-0.340119\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340119\pi\) | |||||||
\(360\) | −10.3665 | −0.546360 | ||||||||
\(361\) | −18.9268 | −0.996146 | ||||||||
\(362\) | −21.0446 | −1.10608 | ||||||||
\(363\) | 0.737930 | 0.0387313 | ||||||||
\(364\) | 15.5191 | 0.813421 | ||||||||
\(365\) | 1.33432 | 0.0698414 | ||||||||
\(366\) | −1.92987 | −0.100876 | ||||||||
\(367\) | 33.6861 | 1.75840 | 0.879199 | − | 0.476455i | \(-0.158078\pi\) | ||||
0.879199 | + | 0.476455i | \(0.158078\pi\) | |||||||
\(368\) | 1.68162 | 0.0876604 | ||||||||
\(369\) | 15.1323 | 0.787758 | ||||||||
\(370\) | −12.3961 | −0.644440 | ||||||||
\(371\) | −0.945293 | −0.0490772 | ||||||||
\(372\) | −1.18919 | −0.0616568 | ||||||||
\(373\) | −31.5618 | −1.63421 | −0.817104 | − | 0.576490i | \(-0.804422\pi\) | ||||
−0.817104 | + | 0.576490i | \(0.804422\pi\) | |||||||
\(374\) | −26.4100 | −1.36563 | ||||||||
\(375\) | −0.990938 | −0.0511718 | ||||||||
\(376\) | −40.1672 | −2.07146 | ||||||||
\(377\) | −28.6022 | −1.47309 | ||||||||
\(378\) | −1.39184 | −0.0715886 | ||||||||
\(379\) | 10.3087 | 0.529523 | 0.264761 | − | 0.964314i | \(-0.414707\pi\) | ||||
0.264761 | + | 0.964314i | \(0.414707\pi\) | |||||||
\(380\) | −0.974451 | −0.0499883 | ||||||||
\(381\) | −0.928112 | −0.0475486 | ||||||||
\(382\) | 63.4195 | 3.24482 | ||||||||
\(383\) | 1.01110 | 0.0516647 | 0.0258323 | − | 0.999666i | \(-0.491776\pi\) | ||||
0.0258323 | + | 0.999666i | \(0.491776\pi\) | |||||||
\(384\) | −2.08545 | −0.106423 | ||||||||
\(385\) | −1.99922 | −0.101890 | ||||||||
\(386\) | 59.5020 | 3.02857 | ||||||||
\(387\) | −5.42545 | −0.275791 | ||||||||
\(388\) | 47.1501 | 2.39368 | ||||||||
\(389\) | 22.5036 | 1.14098 | 0.570488 | − | 0.821306i | \(-0.306754\pi\) | ||||
0.570488 | + | 0.821306i | \(0.306754\pi\) | |||||||
\(390\) | −1.24801 | −0.0631953 | ||||||||
\(391\) | 11.5940 | 0.586334 | ||||||||
\(392\) | 20.0711 | 1.01374 | ||||||||
\(393\) | 0.0545049 | 0.00274941 | ||||||||
\(394\) | 58.5991 | 2.95218 | ||||||||
\(395\) | 9.76245 | 0.491202 | ||||||||
\(396\) | −20.4437 | −1.02733 | ||||||||
\(397\) | 23.3877 | 1.17379 | 0.586896 | − | 0.809662i | \(-0.300350\pi\) | ||||
0.586896 | + | 0.809662i | \(0.300350\pi\) | |||||||
\(398\) | 30.1818 | 1.51288 | ||||||||
\(399\) | −0.0270299 | −0.00135319 | ||||||||
\(400\) | −3.19273 | −0.159636 | ||||||||
\(401\) | 36.5891 | 1.82717 | 0.913587 | − | 0.406644i | \(-0.133301\pi\) | ||||
0.913587 | + | 0.406644i | \(0.133301\pi\) | |||||||
\(402\) | −2.79262 | −0.139283 | ||||||||
\(403\) | 15.8623 | 0.790156 | ||||||||
\(404\) | 39.7135 | 1.97582 | ||||||||
\(405\) | −9.39110 | −0.466648 | ||||||||
\(406\) | 13.0763 | 0.648967 | ||||||||
\(407\) | −10.1199 | −0.501626 | ||||||||
\(408\) | 1.96727 | 0.0973943 | ||||||||
\(409\) | 18.8697 | 0.933047 | 0.466524 | − | 0.884509i | \(-0.345506\pi\) | ||||
0.466524 | + | 0.884509i | \(0.345506\pi\) | |||||||
\(410\) | −12.4297 | −0.613857 | ||||||||
\(411\) | −0.719703 | −0.0355003 | ||||||||
\(412\) | −6.33397 | −0.312052 | ||||||||
\(413\) | −10.4152 | −0.512501 | ||||||||
\(414\) | 14.2343 | 0.699577 | ||||||||
\(415\) | 16.7832 | 0.823855 | ||||||||
\(416\) | 22.4291 | 1.09968 | ||||||||
\(417\) | 1.88360 | 0.0922403 | ||||||||
\(418\) | −1.26173 | −0.0617132 | ||||||||
\(419\) | 13.1710 | 0.643447 | 0.321724 | − | 0.946834i | \(-0.395738\pi\) | ||||
0.321724 | + | 0.946834i | \(0.395738\pi\) | |||||||
\(420\) | 0.359741 | 0.0175536 | ||||||||
\(421\) | −33.5068 | −1.63302 | −0.816510 | − | 0.577331i | \(-0.804094\pi\) | ||||
−0.816510 | + | 0.577331i | \(0.804094\pi\) | |||||||
\(422\) | 44.8905 | 2.18524 | ||||||||
\(423\) | −36.5249 | −1.77590 | ||||||||
\(424\) | 3.28688 | 0.159625 | ||||||||
\(425\) | −22.0124 | −1.06776 | ||||||||
\(426\) | −1.54886 | −0.0750426 | ||||||||
\(427\) | −7.42017 | −0.359087 | ||||||||
\(428\) | 49.4576 | 2.39063 | ||||||||
\(429\) | −1.01885 | −0.0491906 | ||||||||
\(430\) | 4.45645 | 0.214909 | ||||||||
\(431\) | −12.4916 | −0.601700 | −0.300850 | − | 0.953671i | \(-0.597270\pi\) | ||||
−0.300850 | + | 0.953671i | \(0.597270\pi\) | |||||||
\(432\) | 0.519895 | 0.0250135 | ||||||||
\(433\) | −29.8047 | −1.43232 | −0.716162 | − | 0.697935i | \(-0.754103\pi\) | ||||
−0.716162 | + | 0.697935i | \(0.754103\pi\) | |||||||
\(434\) | −7.25188 | −0.348101 | ||||||||
\(435\) | −0.663017 | −0.0317892 | ||||||||
\(436\) | 39.3513 | 1.88459 | ||||||||
\(437\) | 0.553900 | 0.0264966 | ||||||||
\(438\) | −0.310882 | −0.0148545 | ||||||||
\(439\) | −25.7071 | −1.22693 | −0.613467 | − | 0.789721i | \(-0.710225\pi\) | ||||
−0.613467 | + | 0.789721i | \(0.710225\pi\) | |||||||
\(440\) | 6.95149 | 0.331399 | ||||||||
\(441\) | 18.2511 | 0.869099 | ||||||||
\(442\) | −63.3885 | −3.01508 | ||||||||
\(443\) | −1.37364 | −0.0652636 | −0.0326318 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326318 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(444\) | 1.82099 | 0.0864203 | ||||||||
\(445\) | 10.5238 | 0.498876 | ||||||||
\(446\) | −10.8052 | −0.511641 | ||||||||
\(447\) | −2.55849 | −0.121013 | ||||||||
\(448\) | −11.8072 | −0.557838 | ||||||||
\(449\) | −3.08402 | −0.145544 | −0.0727719 | − | 0.997349i | \(-0.523185\pi\) | ||||
−0.0727719 | + | 0.997349i | \(0.523185\pi\) | |||||||
\(450\) | −27.0253 | −1.27398 | ||||||||
\(451\) | −10.1474 | −0.477821 | ||||||||
\(452\) | 36.4825 | 1.71599 | ||||||||
\(453\) | 0.105675 | 0.00496503 | ||||||||
\(454\) | −43.0418 | −2.02005 | ||||||||
\(455\) | −4.79847 | −0.224956 | ||||||||
\(456\) | 0.0939857 | 0.00440128 | ||||||||
\(457\) | 27.5201 | 1.28734 | 0.643669 | − | 0.765304i | \(-0.277411\pi\) | ||||
0.643669 | + | 0.765304i | \(0.277411\pi\) | |||||||
\(458\) | −30.0683 | −1.40500 | ||||||||
\(459\) | 3.58445 | 0.167308 | ||||||||
\(460\) | −7.37186 | −0.343715 | ||||||||
\(461\) | 21.4450 | 0.998792 | 0.499396 | − | 0.866374i | \(-0.333555\pi\) | ||||
0.499396 | + | 0.866374i | \(0.333555\pi\) | |||||||
\(462\) | 0.465797 | 0.0216708 | ||||||||
\(463\) | 5.50370 | 0.255779 | 0.127889 | − | 0.991788i | \(-0.459180\pi\) | ||||
0.127889 | + | 0.991788i | \(0.459180\pi\) | |||||||
\(464\) | −4.88441 | −0.226753 | ||||||||
\(465\) | 0.367697 | 0.0170515 | ||||||||
\(466\) | −11.3584 | −0.526168 | ||||||||
\(467\) | −13.3843 | −0.619351 | −0.309676 | − | 0.950842i | \(-0.600220\pi\) | ||||
−0.309676 | + | 0.950842i | \(0.600220\pi\) | |||||||
\(468\) | −49.0683 | −2.26818 | ||||||||
\(469\) | −10.7374 | −0.495806 | ||||||||
\(470\) | 30.0015 | 1.38387 | ||||||||
\(471\) | 1.43584 | 0.0661598 | ||||||||
\(472\) | 36.2148 | 1.66692 | ||||||||
\(473\) | 3.63817 | 0.167283 | ||||||||
\(474\) | −2.27455 | −0.104473 | ||||||||
\(475\) | −1.05164 | −0.0482524 | ||||||||
\(476\) | 18.2719 | 0.837491 | ||||||||
\(477\) | 2.98883 | 0.136849 | ||||||||
\(478\) | −30.6422 | −1.40154 | ||||||||
\(479\) | −25.0429 | −1.14424 | −0.572119 | − | 0.820171i | \(-0.693878\pi\) | ||||
−0.572119 | + | 0.820171i | \(0.693878\pi\) | |||||||
\(480\) | 0.519921 | 0.0237310 | ||||||||
\(481\) | −24.2896 | −1.10751 | ||||||||
\(482\) | −4.86326 | −0.221515 | ||||||||
\(483\) | −0.204485 | −0.00930439 | ||||||||
\(484\) | −23.8315 | −1.08325 | ||||||||
\(485\) | −14.5787 | −0.661986 | ||||||||
\(486\) | 6.60520 | 0.299618 | ||||||||
\(487\) | −14.1657 | −0.641911 | −0.320956 | − | 0.947094i | \(-0.604004\pi\) | ||||
−0.320956 | + | 0.947094i | \(0.604004\pi\) | |||||||
\(488\) | 25.8007 | 1.16794 | ||||||||
\(489\) | 1.16793 | 0.0528157 | ||||||||
\(490\) | −14.9914 | −0.677242 | ||||||||
\(491\) | −20.4328 | −0.922121 | −0.461061 | − | 0.887369i | \(-0.652531\pi\) | ||||
−0.461061 | + | 0.887369i | \(0.652531\pi\) | |||||||
\(492\) | 1.82592 | 0.0823190 | ||||||||
\(493\) | −33.6758 | −1.51668 | ||||||||
\(494\) | −3.02837 | −0.136253 | ||||||||
\(495\) | 6.32114 | 0.284114 | ||||||||
\(496\) | 2.70880 | 0.121629 | ||||||||
\(497\) | −5.95523 | −0.267129 | ||||||||
\(498\) | −3.91031 | −0.175225 | ||||||||
\(499\) | −24.5326 | −1.09823 | −0.549114 | − | 0.835747i | \(-0.685035\pi\) | ||||
−0.549114 | + | 0.835747i | \(0.685035\pi\) | |||||||
\(500\) | 32.0025 | 1.43119 | ||||||||
\(501\) | −1.41346 | −0.0631485 | ||||||||
\(502\) | 15.8684 | 0.708239 | ||||||||
\(503\) | −27.2903 | −1.21681 | −0.608406 | − | 0.793626i | \(-0.708191\pi\) | ||||
−0.608406 | + | 0.793626i | \(0.708191\pi\) | |||||||
\(504\) | 9.28650 | 0.413653 | ||||||||
\(505\) | −12.2794 | −0.546424 | ||||||||
\(506\) | −9.54516 | −0.424334 | ||||||||
\(507\) | −1.07165 | −0.0475936 | ||||||||
\(508\) | 29.9735 | 1.32986 | ||||||||
\(509\) | 37.3185 | 1.65411 | 0.827057 | − | 0.562117i | \(-0.190013\pi\) | ||||
0.827057 | + | 0.562117i | \(0.190013\pi\) | |||||||
\(510\) | −1.46938 | −0.0650654 | ||||||||
\(511\) | −1.19531 | −0.0528775 | ||||||||
\(512\) | 9.23051 | 0.407935 | ||||||||
\(513\) | 0.171246 | 0.00756069 | ||||||||
\(514\) | −23.1886 | −1.02281 | ||||||||
\(515\) | 1.95845 | 0.0862997 | ||||||||
\(516\) | −0.654656 | −0.0288196 | ||||||||
\(517\) | 24.4927 | 1.07719 | ||||||||
\(518\) | 11.1047 | 0.487911 | ||||||||
\(519\) | 1.18562 | 0.0520429 | ||||||||
\(520\) | 16.6848 | 0.731675 | ||||||||
\(521\) | 29.2842 | 1.28296 | 0.641482 | − | 0.767138i | \(-0.278320\pi\) | ||||
0.641482 | + | 0.767138i | \(0.278320\pi\) | |||||||
\(522\) | −41.3448 | −1.80961 | ||||||||
\(523\) | 31.4200 | 1.37390 | 0.686950 | − | 0.726705i | \(-0.258949\pi\) | ||||
0.686950 | + | 0.726705i | \(0.258949\pi\) | |||||||
\(524\) | −1.76024 | −0.0768965 | ||||||||
\(525\) | 0.388236 | 0.0169440 | ||||||||
\(526\) | −40.6297 | −1.77154 | ||||||||
\(527\) | 18.6760 | 0.813538 | ||||||||
\(528\) | −0.173989 | −0.00757192 | ||||||||
\(529\) | −18.8097 | −0.817812 | ||||||||
\(530\) | −2.45502 | −0.106639 | ||||||||
\(531\) | 32.9310 | 1.42908 | ||||||||
\(532\) | 0.872935 | 0.0378465 | ||||||||
\(533\) | −24.3554 | −1.05495 | ||||||||
\(534\) | −2.45193 | −0.106106 | ||||||||
\(535\) | −15.2922 | −0.661140 | ||||||||
\(536\) | 37.3349 | 1.61262 | ||||||||
\(537\) | 1.98587 | 0.0856966 | ||||||||
\(538\) | 7.91029 | 0.341037 | ||||||||
\(539\) | −12.2387 | −0.527159 | ||||||||
\(540\) | −2.27911 | −0.0980774 | ||||||||
\(541\) | −18.8032 | −0.808415 | −0.404207 | − | 0.914667i | \(-0.632453\pi\) | ||||
−0.404207 | + | 0.914667i | \(0.632453\pi\) | |||||||
\(542\) | −22.9373 | −0.985240 | ||||||||
\(543\) | −0.955875 | −0.0410205 | ||||||||
\(544\) | 26.4077 | 1.13222 | ||||||||
\(545\) | −12.1674 | −0.521193 | ||||||||
\(546\) | 1.11799 | 0.0478456 | ||||||||
\(547\) | −44.2854 | −1.89351 | −0.946754 | − | 0.321958i | \(-0.895659\pi\) | ||||
−0.946754 | + | 0.321958i | \(0.895659\pi\) | |||||||
\(548\) | 23.2429 | 0.992887 | ||||||||
\(549\) | 23.4611 | 1.00130 | ||||||||
\(550\) | 18.1225 | 0.772745 | ||||||||
\(551\) | −1.60885 | −0.0685394 | ||||||||
\(552\) | 0.711015 | 0.0302628 | ||||||||
\(553\) | −8.74542 | −0.371893 | ||||||||
\(554\) | −63.9289 | −2.71608 | ||||||||
\(555\) | −0.563046 | −0.0239000 | ||||||||
\(556\) | −60.8311 | −2.57981 | ||||||||
\(557\) | 24.4583 | 1.03633 | 0.518166 | − | 0.855280i | \(-0.326615\pi\) | ||||
0.518166 | + | 0.855280i | \(0.326615\pi\) | |||||||
\(558\) | 22.9290 | 0.970663 | ||||||||
\(559\) | 8.73224 | 0.369334 | ||||||||
\(560\) | −0.819435 | −0.0346275 | ||||||||
\(561\) | −1.19958 | −0.0506463 | ||||||||
\(562\) | 52.1319 | 2.19905 | ||||||||
\(563\) | −23.3970 | −0.986067 | −0.493033 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493033 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(564\) | −4.40724 | −0.185578 | ||||||||
\(565\) | −11.2803 | −0.474567 | ||||||||
\(566\) | −10.0618 | −0.422927 | ||||||||
\(567\) | 8.41275 | 0.353302 | ||||||||
\(568\) | 20.7069 | 0.868843 | ||||||||
\(569\) | 32.9512 | 1.38138 | 0.690692 | − | 0.723149i | \(-0.257306\pi\) | ||||
0.690692 | + | 0.723149i | \(0.257306\pi\) | |||||||
\(570\) | −0.0701993 | −0.00294033 | ||||||||
\(571\) | −35.6656 | −1.49256 | −0.746280 | − | 0.665632i | \(-0.768162\pi\) | ||||
−0.746280 | + | 0.665632i | \(0.768162\pi\) | |||||||
\(572\) | 32.9040 | 1.37578 | ||||||||
\(573\) | 2.88060 | 0.120339 | ||||||||
\(574\) | 11.1348 | 0.464756 | ||||||||
\(575\) | −7.95578 | −0.331779 | ||||||||
\(576\) | 37.3321 | 1.55550 | ||||||||
\(577\) | 12.4895 | 0.519944 | 0.259972 | − | 0.965616i | \(-0.416287\pi\) | ||||
0.259972 | + | 0.965616i | \(0.416287\pi\) | |||||||
\(578\) | −35.0814 | −1.45920 | ||||||||
\(579\) | 2.70266 | 0.112319 | ||||||||
\(580\) | 21.4122 | 0.889094 | ||||||||
\(581\) | −15.0348 | −0.623747 | ||||||||
\(582\) | 3.39669 | 0.140797 | ||||||||
\(583\) | −2.00424 | −0.0830070 | ||||||||
\(584\) | 4.15621 | 0.171985 | ||||||||
\(585\) | 15.1718 | 0.627278 | ||||||||
\(586\) | 25.0835 | 1.03619 | ||||||||
\(587\) | 11.3770 | 0.469581 | 0.234790 | − | 0.972046i | \(-0.424560\pi\) | ||||
0.234790 | + | 0.972046i | \(0.424560\pi\) | |||||||
\(588\) | 2.20224 | 0.0908190 | ||||||||
\(589\) | 0.892239 | 0.0367641 | ||||||||
\(590\) | −27.0494 | −1.11361 | ||||||||
\(591\) | 2.66166 | 0.109486 | ||||||||
\(592\) | −4.14793 | −0.170479 | ||||||||
\(593\) | −5.62730 | −0.231086 | −0.115543 | − | 0.993302i | \(-0.536861\pi\) | ||||
−0.115543 | + | 0.993302i | \(0.536861\pi\) | |||||||
\(594\) | −2.95102 | −0.121082 | ||||||||
\(595\) | −5.64964 | −0.231613 | ||||||||
\(596\) | 82.6269 | 3.38453 | ||||||||
\(597\) | 1.37090 | 0.0561072 | ||||||||
\(598\) | −22.9100 | −0.936861 | ||||||||
\(599\) | −22.0472 | −0.900823 | −0.450412 | − | 0.892821i | \(-0.648723\pi\) | ||||
−0.450412 | + | 0.892821i | \(0.648723\pi\) | |||||||
\(600\) | −1.34994 | −0.0551109 | ||||||||
\(601\) | 5.80486 | 0.236785 | 0.118393 | − | 0.992967i | \(-0.462226\pi\) | ||||
0.118393 | + | 0.992967i | \(0.462226\pi\) | |||||||
\(602\) | −3.99219 | −0.162709 | ||||||||
\(603\) | 33.9495 | 1.38253 | ||||||||
\(604\) | −3.41278 | −0.138864 | ||||||||
\(605\) | 7.36867 | 0.299579 | ||||||||
\(606\) | 2.86096 | 0.116219 | ||||||||
\(607\) | 17.0397 | 0.691621 | 0.345810 | − | 0.938304i | \(-0.387604\pi\) | ||||
0.345810 | + | 0.938304i | \(0.387604\pi\) | |||||||
\(608\) | 1.26162 | 0.0511654 | ||||||||
\(609\) | 0.593945 | 0.0240679 | ||||||||
\(610\) | −19.2709 | −0.780257 | ||||||||
\(611\) | 58.7867 | 2.37826 | ||||||||
\(612\) | −57.7722 | −2.33530 | ||||||||
\(613\) | −25.1182 | −1.01451 | −0.507256 | − | 0.861795i | \(-0.669340\pi\) | ||||
−0.507256 | + | 0.861795i | \(0.669340\pi\) | |||||||
\(614\) | 39.4009 | 1.59009 | ||||||||
\(615\) | −0.564573 | −0.0227658 | ||||||||
\(616\) | −6.22729 | −0.250905 | ||||||||
\(617\) | −35.5411 | −1.43083 | −0.715414 | − | 0.698700i | \(-0.753762\pi\) | ||||
−0.715414 | + | 0.698700i | \(0.753762\pi\) | |||||||
\(618\) | −0.456298 | −0.0183550 | ||||||||
\(619\) | 9.59120 | 0.385503 | 0.192751 | − | 0.981248i | \(-0.438259\pi\) | ||||
0.192751 | + | 0.981248i | \(0.438259\pi\) | |||||||
\(620\) | −11.8748 | −0.476904 | ||||||||
\(621\) | 1.29550 | 0.0519866 | ||||||||
\(622\) | −40.5983 | −1.62785 | ||||||||
\(623\) | −9.42746 | −0.377703 | ||||||||
\(624\) | −0.417604 | −0.0167176 | ||||||||
\(625\) | 9.53739 | 0.381496 | ||||||||
\(626\) | −9.57279 | −0.382606 | ||||||||
\(627\) | −0.0573096 | −0.00228872 | ||||||||
\(628\) | −46.3705 | −1.85039 | ||||||||
\(629\) | −28.5981 | −1.14028 | ||||||||
\(630\) | −6.93623 | −0.276346 | ||||||||
\(631\) | −17.1033 | −0.680871 | −0.340436 | − | 0.940268i | \(-0.610575\pi\) | ||||
−0.340436 | + | 0.940268i | \(0.610575\pi\) | |||||||
\(632\) | 30.4087 | 1.20959 | ||||||||
\(633\) | 2.03899 | 0.0810426 | ||||||||
\(634\) | 16.1590 | 0.641757 | ||||||||
\(635\) | −9.26775 | −0.367780 | ||||||||
\(636\) | 0.360644 | 0.0143005 | ||||||||
\(637\) | −29.3750 | −1.16388 | ||||||||
\(638\) | 27.7248 | 1.09763 | ||||||||
\(639\) | 18.8293 | 0.744874 | ||||||||
\(640\) | −20.8245 | −0.823159 | ||||||||
\(641\) | 8.39218 | 0.331471 | 0.165736 | − | 0.986170i | \(-0.447000\pi\) | ||||
0.165736 | + | 0.986170i | \(0.447000\pi\) | |||||||
\(642\) | 3.56292 | 0.140617 | ||||||||
\(643\) | 4.57793 | 0.180536 | 0.0902680 | − | 0.995918i | \(-0.471228\pi\) | ||||
0.0902680 | + | 0.995918i | \(0.471228\pi\) | |||||||
\(644\) | 6.60387 | 0.260229 | ||||||||
\(645\) | 0.202418 | 0.00797022 | ||||||||
\(646\) | −3.56555 | −0.140285 | ||||||||
\(647\) | 37.0464 | 1.45644 | 0.728221 | − | 0.685342i | \(-0.240347\pi\) | ||||
0.728221 | + | 0.685342i | \(0.240347\pi\) | |||||||
\(648\) | −29.2520 | −1.14913 | ||||||||
\(649\) | −22.0827 | −0.866821 | ||||||||
\(650\) | 43.4971 | 1.70610 | ||||||||
\(651\) | −0.329391 | −0.0129098 | ||||||||
\(652\) | −37.7185 | −1.47717 | ||||||||
\(653\) | 11.6546 | 0.456079 | 0.228039 | − | 0.973652i | \(-0.426768\pi\) | ||||
0.228039 | + | 0.973652i | \(0.426768\pi\) | |||||||
\(654\) | 2.83487 | 0.110852 | ||||||||
\(655\) | 0.544264 | 0.0212661 | ||||||||
\(656\) | −4.15917 | −0.162388 | ||||||||
\(657\) | 3.77934 | 0.147446 | ||||||||
\(658\) | −26.8760 | −1.04774 | ||||||||
\(659\) | 0.398028 | 0.0155050 | 0.00775248 | − | 0.999970i | \(-0.497532\pi\) | ||||
0.00775248 | + | 0.999970i | \(0.497532\pi\) | |||||||
\(660\) | 0.762733 | 0.0296894 | ||||||||
\(661\) | 1.51832 | 0.0590559 | 0.0295279 | − | 0.999564i | \(-0.490600\pi\) | ||||
0.0295279 | + | 0.999564i | \(0.490600\pi\) | |||||||
\(662\) | 5.28600 | 0.205446 | ||||||||
\(663\) | −2.87920 | −0.111819 | ||||||||
\(664\) | 52.2774 | 2.02875 | ||||||||
\(665\) | −0.269910 | −0.0104667 | ||||||||
\(666\) | −35.1107 | −1.36051 | ||||||||
\(667\) | −12.1712 | −0.471270 | ||||||||
\(668\) | 45.6477 | 1.76616 | ||||||||
\(669\) | −0.490787 | −0.0189749 | ||||||||
\(670\) | −27.8860 | −1.07733 | ||||||||
\(671\) | −15.7325 | −0.607345 | ||||||||
\(672\) | −0.465756 | −0.0179669 | ||||||||
\(673\) | 24.7578 | 0.954343 | 0.477171 | − | 0.878810i | \(-0.341662\pi\) | ||||
0.477171 | + | 0.878810i | \(0.341662\pi\) | |||||||
\(674\) | 18.9177 | 0.728683 | ||||||||
\(675\) | −2.45964 | −0.0946716 | ||||||||
\(676\) | 34.6091 | 1.33112 | ||||||||
\(677\) | −9.46609 | −0.363812 | −0.181906 | − | 0.983316i | \(-0.558227\pi\) | ||||
−0.181906 | + | 0.983316i | \(0.558227\pi\) | |||||||
\(678\) | 2.62819 | 0.100935 | ||||||||
\(679\) | 13.0599 | 0.501195 | ||||||||
\(680\) | 19.6444 | 0.753327 | ||||||||
\(681\) | −1.95502 | −0.0749166 | ||||||||
\(682\) | −15.3756 | −0.588764 | ||||||||
\(683\) | −29.9564 | −1.14625 | −0.573124 | − | 0.819469i | \(-0.694269\pi\) | ||||
−0.573124 | + | 0.819469i | \(0.694269\pi\) | |||||||
\(684\) | −2.76005 | −0.105533 | ||||||||
\(685\) | −7.18666 | −0.274588 | ||||||||
\(686\) | 28.8244 | 1.10052 | ||||||||
\(687\) | −1.36575 | −0.0521065 | ||||||||
\(688\) | 1.49121 | 0.0568517 | ||||||||
\(689\) | −4.81051 | −0.183266 | ||||||||
\(690\) | −0.531068 | −0.0202174 | ||||||||
\(691\) | 13.8166 | 0.525609 | 0.262804 | − | 0.964849i | \(-0.415353\pi\) | ||||
0.262804 | + | 0.964849i | \(0.415353\pi\) | |||||||
\(692\) | −38.2897 | −1.45556 | ||||||||
\(693\) | −5.66262 | −0.215105 | ||||||||
\(694\) | −2.89641 | −0.109946 | ||||||||
\(695\) | 18.8089 | 0.713461 | ||||||||
\(696\) | −2.06521 | −0.0782814 | ||||||||
\(697\) | −28.6757 | −1.08617 | ||||||||
\(698\) | 72.8918 | 2.75900 | ||||||||
\(699\) | −0.515915 | −0.0195137 | ||||||||
\(700\) | −12.5381 | −0.473897 | ||||||||
\(701\) | −25.0831 | −0.947377 | −0.473688 | − | 0.880692i | \(-0.657078\pi\) | ||||
−0.473688 | + | 0.880692i | \(0.657078\pi\) | |||||||
\(702\) | −7.08295 | −0.267329 | ||||||||
\(703\) | −1.36627 | −0.0515297 | ||||||||
\(704\) | −25.0340 | −0.943503 | ||||||||
\(705\) | 1.36271 | 0.0513227 | ||||||||
\(706\) | 17.3678 | 0.653646 | ||||||||
\(707\) | 11.0001 | 0.413702 | ||||||||
\(708\) | 3.97357 | 0.149336 | ||||||||
\(709\) | −39.9093 | −1.49882 | −0.749412 | − | 0.662104i | \(-0.769664\pi\) | ||||
−0.749412 | + | 0.662104i | \(0.769664\pi\) | |||||||
\(710\) | −15.4663 | −0.580441 | ||||||||
\(711\) | 27.6513 | 1.03700 | ||||||||
\(712\) | 32.7802 | 1.22849 | ||||||||
\(713\) | 6.74992 | 0.252786 | ||||||||
\(714\) | 1.31631 | 0.0492615 | ||||||||
\(715\) | −10.1739 | −0.380480 | ||||||||
\(716\) | −64.1340 | −2.39680 | ||||||||
\(717\) | −1.39181 | −0.0519781 | ||||||||
\(718\) | −42.4441 | −1.58400 | ||||||||
\(719\) | 11.7807 | 0.439348 | 0.219674 | − | 0.975573i | \(-0.429501\pi\) | ||||
0.219674 | + | 0.975573i | \(0.429501\pi\) | |||||||
\(720\) | 2.59089 | 0.0965569 | ||||||||
\(721\) | −1.75442 | −0.0653382 | ||||||||
\(722\) | 44.0339 | 1.63877 | ||||||||
\(723\) | −0.220896 | −0.00821521 | ||||||||
\(724\) | 30.8701 | 1.14728 | ||||||||
\(725\) | 23.1083 | 0.858220 | ||||||||
\(726\) | −1.71682 | −0.0637172 | ||||||||
\(727\) | 48.5814 | 1.80178 | 0.900892 | − | 0.434043i | \(-0.142914\pi\) | ||||
0.900892 | + | 0.434043i | \(0.142914\pi\) | |||||||
\(728\) | −14.9466 | −0.553957 | ||||||||
\(729\) | −26.3988 | −0.977735 | ||||||||
\(730\) | −3.10434 | −0.114897 | ||||||||
\(731\) | 10.2812 | 0.380264 | ||||||||
\(732\) | 2.83091 | 0.104633 | ||||||||
\(733\) | −45.4763 | −1.67970 | −0.839852 | − | 0.542815i | \(-0.817358\pi\) | ||||
−0.839852 | + | 0.542815i | \(0.817358\pi\) | |||||||
\(734\) | −78.3719 | −2.89276 | ||||||||
\(735\) | −0.680930 | −0.0251165 | ||||||||
\(736\) | 9.54433 | 0.351809 | ||||||||
\(737\) | −22.7657 | −0.838584 | ||||||||
\(738\) | −35.2059 | −1.29595 | ||||||||
\(739\) | 0.141290 | 0.00519742 | 0.00259871 | − | 0.999997i | \(-0.499173\pi\) | ||||
0.00259871 | + | 0.999997i | \(0.499173\pi\) | |||||||
\(740\) | 18.1837 | 0.668445 | ||||||||
\(741\) | −0.137553 | −0.00505313 | ||||||||
\(742\) | 2.19926 | 0.0807374 | ||||||||
\(743\) | −18.1142 | −0.664545 | −0.332272 | − | 0.943183i | \(-0.607815\pi\) | ||||
−0.332272 | + | 0.943183i | \(0.607815\pi\) | |||||||
\(744\) | 1.14532 | 0.0419896 | ||||||||
\(745\) | −25.5481 | −0.936010 | ||||||||
\(746\) | 73.4297 | 2.68845 | ||||||||
\(747\) | 47.5370 | 1.73929 | ||||||||
\(748\) | 38.7406 | 1.41650 | ||||||||
\(749\) | 13.6991 | 0.500554 | ||||||||
\(750\) | 2.30545 | 0.0841833 | ||||||||
\(751\) | −44.4699 | −1.62273 | −0.811364 | − | 0.584541i | \(-0.801275\pi\) | ||||
−0.811364 | + | 0.584541i | \(0.801275\pi\) | |||||||
\(752\) | 10.0390 | 0.366085 | ||||||||
\(753\) | 0.720763 | 0.0262661 | ||||||||
\(754\) | 66.5442 | 2.42340 | ||||||||
\(755\) | 1.05522 | 0.0384036 | ||||||||
\(756\) | 2.04168 | 0.0742552 | ||||||||
\(757\) | 16.5346 | 0.600959 | 0.300480 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300480 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(758\) | −23.9836 | −0.871123 | ||||||||
\(759\) | −0.433555 | −0.0157370 | ||||||||
\(760\) | 0.938503 | 0.0340431 | ||||||||
\(761\) | −47.3243 | −1.71551 | −0.857753 | − | 0.514063i | \(-0.828140\pi\) | ||||
−0.857753 | + | 0.514063i | \(0.828140\pi\) | |||||||
\(762\) | 2.15929 | 0.0782227 | ||||||||
\(763\) | 10.8998 | 0.394599 | ||||||||
\(764\) | −93.0294 | −3.36569 | ||||||||
\(765\) | 17.8631 | 0.645840 | ||||||||
\(766\) | −2.35236 | −0.0849941 | ||||||||
\(767\) | −53.0022 | −1.91380 | ||||||||
\(768\) | 2.21201 | 0.0798191 | ||||||||
\(769\) | 19.6585 | 0.708903 | 0.354452 | − | 0.935074i | \(-0.384668\pi\) | ||||
0.354452 | + | 0.935074i | \(0.384668\pi\) | |||||||
\(770\) | 4.65126 | 0.167620 | ||||||||
\(771\) | −1.05326 | −0.0379322 | ||||||||
\(772\) | −87.2829 | −3.14138 | ||||||||
\(773\) | −41.1572 | −1.48032 | −0.740160 | − | 0.672431i | \(-0.765250\pi\) | ||||
−0.740160 | + | 0.672431i | \(0.765250\pi\) | |||||||
\(774\) | 12.6225 | 0.453707 | ||||||||
\(775\) | −12.8154 | −0.460343 | ||||||||
\(776\) | −45.4107 | −1.63015 | ||||||||
\(777\) | 0.504389 | 0.0180949 | ||||||||
\(778\) | −52.3554 | −1.87703 | ||||||||
\(779\) | −1.36997 | −0.0490843 | ||||||||
\(780\) | 1.83069 | 0.0655492 | ||||||||
\(781\) | −12.6264 | −0.451809 | ||||||||
\(782\) | −26.9739 | −0.964584 | ||||||||
\(783\) | −3.76289 | −0.134475 | ||||||||
\(784\) | −5.01637 | −0.179156 | ||||||||
\(785\) | 14.3377 | 0.511734 | ||||||||
\(786\) | −0.126808 | −0.00452308 | ||||||||
\(787\) | −9.52652 | −0.339584 | −0.169792 | − | 0.985480i | \(-0.554310\pi\) | ||||
−0.169792 | + | 0.985480i | \(0.554310\pi\) | |||||||
\(788\) | −85.9585 | −3.06215 | ||||||||
\(789\) | −1.84546 | −0.0657001 | ||||||||
\(790\) | −22.7127 | −0.808082 | ||||||||
\(791\) | 10.1052 | 0.359298 | ||||||||
\(792\) | 19.6895 | 0.699635 | ||||||||
\(793\) | −37.7606 | −1.34092 | ||||||||
\(794\) | −54.4123 | −1.93102 | ||||||||
\(795\) | −0.111511 | −0.00395487 | ||||||||
\(796\) | −44.2734 | −1.56923 | ||||||||
\(797\) | 6.28050 | 0.222467 | 0.111233 | − | 0.993794i | \(-0.464520\pi\) | ||||
0.111233 | + | 0.993794i | \(0.464520\pi\) | |||||||
\(798\) | 0.0628861 | 0.00222614 | ||||||||
\(799\) | 69.2145 | 2.44863 | ||||||||
\(800\) | −18.1209 | −0.640671 | ||||||||
\(801\) | 29.8078 | 1.05321 | ||||||||
\(802\) | −85.1260 | −3.00590 | ||||||||
\(803\) | −2.53433 | −0.0894346 | ||||||||
\(804\) | 4.09647 | 0.144471 | ||||||||
\(805\) | −2.04191 | −0.0719678 | ||||||||
\(806\) | −36.9042 | −1.29989 | ||||||||
\(807\) | 0.359297 | 0.0126478 | ||||||||
\(808\) | −38.2485 | −1.34558 | ||||||||
\(809\) | −40.6225 | −1.42821 | −0.714105 | − | 0.700038i | \(-0.753166\pi\) | ||||
−0.714105 | + | 0.700038i | \(0.753166\pi\) | |||||||
\(810\) | 21.8487 | 0.767687 | ||||||||
\(811\) | 3.23697 | 0.113665 | 0.0568327 | − | 0.998384i | \(-0.481900\pi\) | ||||
0.0568327 | + | 0.998384i | \(0.481900\pi\) | |||||||
\(812\) | −19.1815 | −0.673140 | ||||||||
\(813\) | −1.04184 | −0.0365390 | ||||||||
\(814\) | 23.5444 | 0.825231 | ||||||||
\(815\) | 11.6625 | 0.408520 | ||||||||
\(816\) | −0.491680 | −0.0172123 | ||||||||
\(817\) | 0.491181 | 0.0171843 | ||||||||
\(818\) | −43.9011 | −1.53497 | ||||||||
\(819\) | −13.5913 | −0.474917 | ||||||||
\(820\) | 18.2330 | 0.636722 | ||||||||
\(821\) | −4.72802 | −0.165009 | −0.0825046 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825046 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(822\) | 1.67442 | 0.0584019 | ||||||||
\(823\) | −33.8363 | −1.17946 | −0.589729 | − | 0.807601i | \(-0.700765\pi\) | ||||
−0.589729 | + | 0.807601i | \(0.700765\pi\) | |||||||
\(824\) | 6.10031 | 0.212514 | ||||||||
\(825\) | 0.823149 | 0.0286584 | ||||||||
\(826\) | 24.2315 | 0.843120 | ||||||||
\(827\) | −51.8419 | −1.80272 | −0.901360 | − | 0.433070i | \(-0.857430\pi\) | ||||
−0.901360 | + | 0.433070i | \(0.857430\pi\) | |||||||
\(828\) | −20.8802 | −0.725636 | ||||||||
\(829\) | 6.74425 | 0.234238 | 0.117119 | − | 0.993118i | \(-0.462634\pi\) | ||||
0.117119 | + | 0.993118i | \(0.462634\pi\) | |||||||
\(830\) | −39.0468 | −1.35533 | ||||||||
\(831\) | −2.90374 | −0.100730 | ||||||||
\(832\) | −60.0858 | −2.08310 | ||||||||
\(833\) | −34.5856 | −1.19832 | ||||||||
\(834\) | −4.38226 | −0.151745 | ||||||||
\(835\) | −14.1142 | −0.488442 | ||||||||
\(836\) | 1.85082 | 0.0640119 | ||||||||
\(837\) | 2.08683 | 0.0721314 | ||||||||
\(838\) | −30.6429 | −1.05854 | ||||||||
\(839\) | 6.13693 | 0.211870 | 0.105935 | − | 0.994373i | \(-0.466216\pi\) | ||||
0.105935 | + | 0.994373i | \(0.466216\pi\) | |||||||
\(840\) | −0.346470 | −0.0119544 | ||||||||
\(841\) | 6.35230 | 0.219045 | ||||||||
\(842\) | 77.9548 | 2.68650 | ||||||||
\(843\) | 2.36791 | 0.0815551 | ||||||||
\(844\) | −65.8495 | −2.26663 | ||||||||
\(845\) | −10.7011 | −0.368128 | ||||||||
\(846\) | 84.9766 | 2.92156 | ||||||||
\(847\) | −6.60102 | −0.226814 | ||||||||
\(848\) | −0.821491 | −0.0282101 | ||||||||
\(849\) | −0.457019 | −0.0156849 | ||||||||
\(850\) | 51.2127 | 1.75658 | ||||||||
\(851\) | −10.3360 | −0.354314 | ||||||||
\(852\) | 2.27201 | 0.0778378 | ||||||||
\(853\) | −30.3243 | −1.03828 | −0.519142 | − | 0.854688i | \(-0.673748\pi\) | ||||
−0.519142 | + | 0.854688i | \(0.673748\pi\) | |||||||
\(854\) | 17.2633 | 0.590738 | ||||||||
\(855\) | 0.853402 | 0.0291857 | ||||||||
\(856\) | −47.6331 | −1.62807 | ||||||||
\(857\) | −49.2665 | −1.68291 | −0.841456 | − | 0.540325i | \(-0.818301\pi\) | ||||
−0.841456 | + | 0.540325i | \(0.818301\pi\) | |||||||
\(858\) | 2.37040 | 0.0809240 | ||||||||
\(859\) | 52.8682 | 1.80384 | 0.901920 | − | 0.431904i | \(-0.142158\pi\) | ||||
0.901920 | + | 0.431904i | \(0.142158\pi\) | |||||||
\(860\) | −6.53713 | −0.222914 | ||||||||
\(861\) | 0.505757 | 0.0172361 | ||||||||
\(862\) | 29.0622 | 0.989863 | ||||||||
\(863\) | 52.0226 | 1.77087 | 0.885434 | − | 0.464765i | \(-0.153861\pi\) | ||||
0.885434 | + | 0.464765i | \(0.153861\pi\) | |||||||
\(864\) | 2.95076 | 0.100387 | ||||||||
\(865\) | 11.8391 | 0.402542 | ||||||||
\(866\) | 69.3418 | 2.35633 | ||||||||
\(867\) | −1.59345 | −0.0541164 | ||||||||
\(868\) | 10.6377 | 0.361068 | ||||||||
\(869\) | −18.5423 | −0.629003 | ||||||||
\(870\) | 1.54253 | 0.0522968 | ||||||||
\(871\) | −54.6415 | −1.85146 | ||||||||
\(872\) | −37.8997 | −1.28344 | ||||||||
\(873\) | −41.2930 | −1.39756 | ||||||||
\(874\) | −1.28867 | −0.0435899 | ||||||||
\(875\) | 8.86426 | 0.299667 | ||||||||
\(876\) | 0.456030 | 0.0154078 | ||||||||
\(877\) | 9.80581 | 0.331119 | 0.165559 | − | 0.986200i | \(-0.447057\pi\) | ||||
0.165559 | + | 0.986200i | \(0.447057\pi\) | |||||||
\(878\) | 59.8085 | 2.01844 | ||||||||
\(879\) | 1.13933 | 0.0384287 | ||||||||
\(880\) | −1.73739 | −0.0585674 | ||||||||
\(881\) | −43.3366 | −1.46005 | −0.730024 | − | 0.683421i | \(-0.760491\pi\) | ||||
−0.730024 | + | 0.683421i | \(0.760491\pi\) | |||||||
\(882\) | −42.4618 | −1.42976 | ||||||||
\(883\) | 2.69451 | 0.0906774 | 0.0453387 | − | 0.998972i | \(-0.485563\pi\) | ||||
0.0453387 | + | 0.998972i | \(0.485563\pi\) | |||||||
\(884\) | 92.9840 | 3.12739 | ||||||||
\(885\) | −1.22862 | −0.0412997 | ||||||||
\(886\) | 3.19582 | 0.107366 | ||||||||
\(887\) | 12.1789 | 0.408927 | 0.204463 | − | 0.978874i | \(-0.434455\pi\) | ||||
0.204463 | + | 0.978874i | \(0.434455\pi\) | |||||||
\(888\) | −1.75381 | −0.0588540 | ||||||||
\(889\) | 8.30226 | 0.278449 | ||||||||
\(890\) | −24.4840 | −0.820707 | ||||||||
\(891\) | 17.8369 | 0.597560 | ||||||||
\(892\) | 15.8500 | 0.530699 | ||||||||
\(893\) | 3.30670 | 0.110655 | ||||||||
\(894\) | 5.95243 | 0.199079 | ||||||||
\(895\) | 19.8301 | 0.662848 | ||||||||
\(896\) | 18.6550 | 0.623220 | ||||||||
\(897\) | −1.04061 | −0.0347448 | ||||||||
\(898\) | 7.17508 | 0.239436 | ||||||||
\(899\) | −19.6057 | −0.653887 | ||||||||
\(900\) | 39.6432 | 1.32144 | ||||||||
\(901\) | −5.66382 | −0.188689 | ||||||||
\(902\) | 23.6082 | 0.786068 | ||||||||
\(903\) | −0.181331 | −0.00603431 | ||||||||
\(904\) | −35.1366 | −1.16863 | ||||||||
\(905\) | −9.54499 | −0.317286 | ||||||||
\(906\) | −0.245856 | −0.00816802 | ||||||||
\(907\) | −21.4756 | −0.713084 | −0.356542 | − | 0.934279i | \(-0.616044\pi\) | ||||
−0.356542 | + | 0.934279i | \(0.616044\pi\) | |||||||
\(908\) | 63.1377 | 2.09530 | ||||||||
\(909\) | −34.7802 | −1.15359 | ||||||||
\(910\) | 11.1638 | 0.370077 | ||||||||
\(911\) | −3.06655 | −0.101599 | −0.0507997 | − | 0.998709i | \(-0.516177\pi\) | ||||
−0.0507997 | + | 0.998709i | \(0.516177\pi\) | |||||||
\(912\) | −0.0234899 | −0.000777828 0 | ||||||||
\(913\) | −31.8771 | −1.05498 | ||||||||
\(914\) | −64.0266 | −2.11781 | ||||||||
\(915\) | −0.875313 | −0.0289369 | ||||||||
\(916\) | 44.1070 | 1.45734 | ||||||||
\(917\) | −0.487563 | −0.0161008 | ||||||||
\(918\) | −8.33935 | −0.275240 | ||||||||
\(919\) | −31.8045 | −1.04913 | −0.524567 | − | 0.851369i | \(-0.675773\pi\) | ||||
−0.524567 | + | 0.851369i | \(0.675773\pi\) | |||||||
\(920\) | 7.09991 | 0.234077 | ||||||||
\(921\) | 1.78965 | 0.0589708 | ||||||||
\(922\) | −49.8926 | −1.64312 | ||||||||
\(923\) | −30.3056 | −0.997522 | ||||||||
\(924\) | −0.683273 | −0.0224780 | ||||||||
\(925\) | 19.6240 | 0.645233 | ||||||||
\(926\) | −12.8046 | −0.420784 | ||||||||
\(927\) | 5.54715 | 0.182192 | ||||||||
\(928\) | −27.7224 | −0.910031 | ||||||||
\(929\) | 35.0498 | 1.14995 | 0.574973 | − | 0.818172i | \(-0.305012\pi\) | ||||
0.574973 | + | 0.818172i | \(0.305012\pi\) | |||||||
\(930\) | −0.855460 | −0.0280517 | ||||||||
\(931\) | −1.65232 | −0.0541526 | ||||||||
\(932\) | 16.6615 | 0.545767 | ||||||||
\(933\) | −1.84403 | −0.0603710 | ||||||||
\(934\) | 31.1391 | 1.01890 | ||||||||
\(935\) | −11.9785 | −0.391740 | ||||||||
\(936\) | 47.2581 | 1.54468 | ||||||||
\(937\) | 16.7390 | 0.546839 | 0.273419 | − | 0.961895i | \(-0.411845\pi\) | ||||
0.273419 | + | 0.961895i | \(0.411845\pi\) | |||||||
\(938\) | 24.9809 | 0.815655 | ||||||||
\(939\) | −0.434810 | −0.0141895 | ||||||||
\(940\) | −44.0089 | −1.43541 | ||||||||
\(941\) | 21.0001 | 0.684583 | 0.342291 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342291 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(942\) | −3.34053 | −0.108840 | ||||||||
\(943\) | −10.3640 | −0.337499 | ||||||||
\(944\) | −9.05119 | −0.294591 | ||||||||
\(945\) | −0.631284 | −0.0205357 | ||||||||
\(946\) | −8.46435 | −0.275200 | ||||||||
\(947\) | 27.2102 | 0.884214 | 0.442107 | − | 0.896962i | \(-0.354231\pi\) | ||||
0.442107 | + | 0.896962i | \(0.354231\pi\) | |||||||
\(948\) | 3.33651 | 0.108365 | ||||||||
\(949\) | −6.08283 | −0.197457 | ||||||||
\(950\) | 2.44667 | 0.0793806 | ||||||||
\(951\) | 0.733966 | 0.0238005 | ||||||||
\(952\) | −17.5978 | −0.570349 | ||||||||
\(953\) | −58.4981 | −1.89494 | −0.947470 | − | 0.319846i | \(-0.896369\pi\) | ||||
−0.947470 | + | 0.319846i | \(0.896369\pi\) | |||||||
\(954\) | −6.95363 | −0.225132 | ||||||||
\(955\) | 28.7645 | 0.930799 | ||||||||
\(956\) | 44.9487 | 1.45375 | ||||||||
\(957\) | 1.25930 | 0.0407073 | ||||||||
\(958\) | 58.2632 | 1.88240 | ||||||||
\(959\) | 6.43797 | 0.207893 | ||||||||
\(960\) | −1.39282 | −0.0449532 | ||||||||
\(961\) | −20.1270 | −0.649259 | ||||||||
\(962\) | 56.5106 | 1.82197 | ||||||||
\(963\) | −43.3139 | −1.39577 | ||||||||
\(964\) | 7.13387 | 0.229766 | ||||||||
\(965\) | 26.9877 | 0.868766 | ||||||||
\(966\) | 0.475742 | 0.0153068 | ||||||||
\(967\) | −24.8688 | −0.799726 | −0.399863 | − | 0.916575i | \(-0.630942\pi\) | ||||
−0.399863 | + | 0.916575i | \(0.630942\pi\) | |||||||
\(968\) | 22.9524 | 0.737718 | ||||||||
\(969\) | −0.161952 | −0.00520266 | ||||||||
\(970\) | 33.9180 | 1.08904 | ||||||||
\(971\) | −42.4789 | −1.36321 | −0.681606 | − | 0.731719i | \(-0.738718\pi\) | ||||
−0.681606 | + | 0.731719i | \(0.738718\pi\) | |||||||
\(972\) | −9.68910 | −0.310778 | ||||||||
\(973\) | −16.8494 | −0.540167 | ||||||||
\(974\) | 32.9571 | 1.05601 | ||||||||
\(975\) | 1.97570 | 0.0632730 | ||||||||
\(976\) | −6.44838 | −0.206407 | ||||||||
\(977\) | −26.2243 | −0.838990 | −0.419495 | − | 0.907758i | \(-0.637793\pi\) | ||||
−0.419495 | + | 0.907758i | \(0.637793\pi\) | |||||||
\(978\) | −2.71724 | −0.0868876 | ||||||||
\(979\) | −19.9883 | −0.638830 | ||||||||
\(980\) | 21.9907 | 0.702468 | ||||||||
\(981\) | −34.4630 | −1.10032 | ||||||||
\(982\) | 47.5378 | 1.51699 | ||||||||
\(983\) | 52.1294 | 1.66267 | 0.831335 | − | 0.555772i | \(-0.187577\pi\) | ||||
0.831335 | + | 0.555772i | \(0.187577\pi\) | |||||||
\(984\) | −1.75857 | −0.0560610 | ||||||||
\(985\) | 26.5782 | 0.846853 | ||||||||
\(986\) | 78.3480 | 2.49511 | ||||||||
\(987\) | −1.22075 | −0.0388568 | ||||||||
\(988\) | 4.44228 | 0.141328 | ||||||||
\(989\) | 3.71585 | 0.118157 | ||||||||
\(990\) | −14.7064 | −0.467399 | ||||||||
\(991\) | −21.5566 | −0.684768 | −0.342384 | − | 0.939560i | \(-0.611234\pi\) | ||||
−0.342384 | + | 0.939560i | \(0.611234\pi\) | |||||||
\(992\) | 15.3743 | 0.488134 | ||||||||
\(993\) | 0.240097 | 0.00761926 | ||||||||
\(994\) | 13.8551 | 0.439456 | ||||||||
\(995\) | 13.6893 | 0.433978 | ||||||||
\(996\) | 5.73599 | 0.181752 | ||||||||
\(997\) | −9.97917 | −0.316043 | −0.158022 | − | 0.987436i | \(-0.550512\pi\) | ||||
−0.158022 | + | 0.987436i | \(0.550512\pi\) | |||||||
\(998\) | 57.0759 | 1.80671 | ||||||||
\(999\) | −3.19552 | −0.101102 |
(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 | 8003.2.a.b.1.20 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.20 | ✓ | 153 | 1.1 | even | 1 | trivial |