Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(119\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40399 | −1.69988 | −0.849940 | − | 0.526880i | \(-0.823362\pi\) | ||||
−0.849940 | + | 0.526880i | \(0.823362\pi\) | |||||||
\(3\) | −2.26995 | −1.31056 | −0.655279 | − | 0.755387i | \(-0.727449\pi\) | ||||
−0.655279 | + | 0.755387i | \(0.727449\pi\) | |||||||
\(4\) | 3.77918 | 1.88959 | ||||||||
\(5\) | −1.51011 | −0.675340 | −0.337670 | − | 0.941265i | \(-0.609639\pi\) | ||||
−0.337670 | + | 0.941265i | \(0.609639\pi\) | |||||||
\(6\) | 5.45695 | 2.22779 | ||||||||
\(7\) | −2.08665 | −0.788679 | −0.394340 | − | 0.918965i | \(-0.629027\pi\) | ||||
−0.394340 | + | 0.918965i | \(0.629027\pi\) | |||||||
\(8\) | −4.27714 | −1.51220 | ||||||||
\(9\) | 2.15269 | 0.717565 | ||||||||
\(10\) | 3.63028 | 1.14800 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −8.57857 | −2.47642 | ||||||||
\(13\) | 2.52148 | 0.699332 | 0.349666 | − | 0.936874i | \(-0.386295\pi\) | ||||
0.349666 | + | 0.936874i | \(0.386295\pi\) | |||||||
\(14\) | 5.01629 | 1.34066 | ||||||||
\(15\) | 3.42787 | 0.885073 | ||||||||
\(16\) | 2.72384 | 0.680960 | ||||||||
\(17\) | −3.45087 | −0.836959 | −0.418480 | − | 0.908226i | \(-0.637437\pi\) | ||||
−0.418480 | + | 0.908226i | \(0.637437\pi\) | |||||||
\(18\) | −5.17506 | −1.21977 | ||||||||
\(19\) | −2.66540 | −0.611485 | −0.305742 | − | 0.952114i | \(-0.598905\pi\) | ||||
−0.305742 | + | 0.952114i | \(0.598905\pi\) | |||||||
\(20\) | −5.70696 | −1.27612 | ||||||||
\(21\) | 4.73660 | 1.03361 | ||||||||
\(22\) | −2.40399 | −0.512533 | ||||||||
\(23\) | −7.64641 | −1.59439 | −0.797193 | − | 0.603724i | \(-0.793683\pi\) | ||||
−0.797193 | + | 0.603724i | \(0.793683\pi\) | |||||||
\(24\) | 9.70890 | 1.98182 | ||||||||
\(25\) | −2.71958 | −0.543916 | ||||||||
\(26\) | −6.06161 | −1.18878 | ||||||||
\(27\) | 1.92335 | 0.370148 | ||||||||
\(28\) | −7.88582 | −1.49028 | ||||||||
\(29\) | −6.54517 | −1.21541 | −0.607704 | − | 0.794164i | \(-0.707909\pi\) | ||||
−0.607704 | + | 0.794164i | \(0.707909\pi\) | |||||||
\(30\) | −8.24058 | −1.50452 | ||||||||
\(31\) | −4.30054 | −0.772399 | −0.386200 | − | 0.922415i | \(-0.626212\pi\) | ||||
−0.386200 | + | 0.922415i | \(0.626212\pi\) | |||||||
\(32\) | 2.00618 | 0.354645 | ||||||||
\(33\) | −2.26995 | −0.395148 | ||||||||
\(34\) | 8.29587 | 1.42273 | ||||||||
\(35\) | 3.15106 | 0.532627 | ||||||||
\(36\) | 8.13542 | 1.35590 | ||||||||
\(37\) | 9.17839 | 1.50892 | 0.754459 | − | 0.656347i | \(-0.227899\pi\) | ||||
0.754459 | + | 0.656347i | \(0.227899\pi\) | |||||||
\(38\) | 6.40760 | 1.03945 | ||||||||
\(39\) | −5.72364 | −0.916515 | ||||||||
\(40\) | 6.45893 | 1.02125 | ||||||||
\(41\) | −4.82899 | −0.754161 | −0.377080 | − | 0.926181i | \(-0.623072\pi\) | ||||
−0.377080 | + | 0.926181i | \(0.623072\pi\) | |||||||
\(42\) | −11.3868 | −1.75701 | ||||||||
\(43\) | 0.829704 | 0.126529 | 0.0632643 | − | 0.997997i | \(-0.479849\pi\) | ||||
0.0632643 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(44\) | 3.77918 | 0.569733 | ||||||||
\(45\) | −3.25080 | −0.484600 | ||||||||
\(46\) | 18.3819 | 2.71027 | ||||||||
\(47\) | −0.606466 | −0.0884622 | −0.0442311 | − | 0.999021i | \(-0.514084\pi\) | ||||
−0.0442311 | + | 0.999021i | \(0.514084\pi\) | |||||||
\(48\) | −6.18300 | −0.892439 | ||||||||
\(49\) | −2.64589 | −0.377985 | ||||||||
\(50\) | 6.53785 | 0.924592 | ||||||||
\(51\) | 7.83332 | 1.09688 | ||||||||
\(52\) | 9.52911 | 1.32145 | ||||||||
\(53\) | 5.23353 | 0.718881 | 0.359440 | − | 0.933168i | \(-0.382968\pi\) | ||||
0.359440 | + | 0.933168i | \(0.382968\pi\) | |||||||
\(54\) | −4.62371 | −0.629207 | ||||||||
\(55\) | −1.51011 | −0.203623 | ||||||||
\(56\) | 8.92488 | 1.19264 | ||||||||
\(57\) | 6.05034 | 0.801387 | ||||||||
\(58\) | 15.7345 | 2.06605 | ||||||||
\(59\) | −4.33952 | −0.564958 | −0.282479 | − | 0.959274i | \(-0.591157\pi\) | ||||
−0.282479 | + | 0.959274i | \(0.591157\pi\) | |||||||
\(60\) | 12.9545 | 1.67242 | ||||||||
\(61\) | −4.40105 | −0.563497 | −0.281748 | − | 0.959488i | \(-0.590914\pi\) | ||||
−0.281748 | + | 0.959488i | \(0.590914\pi\) | |||||||
\(62\) | 10.3385 | 1.31299 | ||||||||
\(63\) | −4.49192 | −0.565928 | ||||||||
\(64\) | −10.2705 | −1.28381 | ||||||||
\(65\) | −3.80770 | −0.472287 | ||||||||
\(66\) | 5.45695 | 0.671705 | ||||||||
\(67\) | 1.85979 | 0.227210 | 0.113605 | − | 0.993526i | \(-0.463760\pi\) | ||||
0.113605 | + | 0.993526i | \(0.463760\pi\) | |||||||
\(68\) | −13.0415 | −1.58151 | ||||||||
\(69\) | 17.3570 | 2.08954 | ||||||||
\(70\) | −7.57513 | −0.905401 | ||||||||
\(71\) | −8.95640 | −1.06293 | −0.531464 | − | 0.847081i | \(-0.678358\pi\) | ||||
−0.531464 | + | 0.847081i | \(0.678358\pi\) | |||||||
\(72\) | −9.20736 | −1.08510 | ||||||||
\(73\) | −2.96845 | −0.347431 | −0.173715 | − | 0.984796i | \(-0.555577\pi\) | ||||
−0.173715 | + | 0.984796i | \(0.555577\pi\) | |||||||
\(74\) | −22.0648 | −2.56498 | ||||||||
\(75\) | 6.17332 | 0.712834 | ||||||||
\(76\) | −10.0730 | −1.15546 | ||||||||
\(77\) | −2.08665 | −0.237796 | ||||||||
\(78\) | 13.7596 | 1.55797 | ||||||||
\(79\) | 13.1655 | 1.48124 | 0.740618 | − | 0.671926i | \(-0.234533\pi\) | ||||
0.740618 | + | 0.671926i | \(0.234533\pi\) | |||||||
\(80\) | −4.11329 | −0.459880 | ||||||||
\(81\) | −10.8240 | −1.20267 | ||||||||
\(82\) | 11.6088 | 1.28198 | ||||||||
\(83\) | 3.49794 | 0.383949 | 0.191974 | − | 0.981400i | \(-0.438511\pi\) | ||||
0.191974 | + | 0.981400i | \(0.438511\pi\) | |||||||
\(84\) | 17.9005 | 1.95310 | ||||||||
\(85\) | 5.21118 | 0.565232 | ||||||||
\(86\) | −1.99460 | −0.215084 | ||||||||
\(87\) | 14.8572 | 1.59286 | ||||||||
\(88\) | −4.27714 | −0.455944 | ||||||||
\(89\) | −6.65752 | −0.705696 | −0.352848 | − | 0.935681i | \(-0.614787\pi\) | ||||
−0.352848 | + | 0.935681i | \(0.614787\pi\) | |||||||
\(90\) | 7.81489 | 0.823761 | ||||||||
\(91\) | −5.26144 | −0.551548 | ||||||||
\(92\) | −28.8972 | −3.01274 | ||||||||
\(93\) | 9.76203 | 1.01227 | ||||||||
\(94\) | 1.45794 | 0.150375 | ||||||||
\(95\) | 4.02504 | 0.412960 | ||||||||
\(96\) | −4.55393 | −0.464783 | ||||||||
\(97\) | −5.12048 | −0.519906 | −0.259953 | − | 0.965621i | \(-0.583707\pi\) | ||||
−0.259953 | + | 0.965621i | \(0.583707\pi\) | |||||||
\(98\) | 6.36071 | 0.642528 | ||||||||
\(99\) | 2.15269 | 0.216354 | ||||||||
\(100\) | −10.2778 | −1.02778 | ||||||||
\(101\) | −9.99545 | −0.994585 | −0.497292 | − | 0.867583i | \(-0.665672\pi\) | ||||
−0.497292 | + | 0.867583i | \(0.665672\pi\) | |||||||
\(102\) | −18.8312 | −1.86457 | ||||||||
\(103\) | 10.8870 | 1.07273 | 0.536366 | − | 0.843986i | \(-0.319797\pi\) | ||||
0.536366 | + | 0.843986i | \(0.319797\pi\) | |||||||
\(104\) | −10.7847 | −1.05753 | ||||||||
\(105\) | −7.15277 | −0.698039 | ||||||||
\(106\) | −12.5814 | −1.22201 | ||||||||
\(107\) | 10.3963 | 1.00505 | 0.502526 | − | 0.864562i | \(-0.332404\pi\) | ||||
0.502526 | + | 0.864562i | \(0.332404\pi\) | |||||||
\(108\) | 7.26867 | 0.699429 | ||||||||
\(109\) | −18.4807 | −1.77013 | −0.885065 | − | 0.465468i | \(-0.845886\pi\) | ||||
−0.885065 | + | 0.465468i | \(0.845886\pi\) | |||||||
\(110\) | 3.63028 | 0.346134 | ||||||||
\(111\) | −20.8345 | −1.97753 | ||||||||
\(112\) | −5.68370 | −0.537059 | ||||||||
\(113\) | −18.0313 | −1.69624 | −0.848119 | − | 0.529805i | \(-0.822265\pi\) | ||||
−0.848119 | + | 0.529805i | \(0.822265\pi\) | |||||||
\(114\) | −14.5450 | −1.36226 | ||||||||
\(115\) | 11.5469 | 1.07675 | ||||||||
\(116\) | −24.7354 | −2.29662 | ||||||||
\(117\) | 5.42797 | 0.501816 | ||||||||
\(118\) | 10.4322 | 0.960360 | ||||||||
\(119\) | 7.20076 | 0.660093 | ||||||||
\(120\) | −14.6615 | −1.33840 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.5801 | 0.957876 | ||||||||
\(123\) | 10.9616 | 0.988372 | ||||||||
\(124\) | −16.2525 | −1.45952 | ||||||||
\(125\) | 11.6574 | 1.04267 | ||||||||
\(126\) | 10.7985 | 0.962010 | ||||||||
\(127\) | −17.9343 | −1.59141 | −0.795706 | − | 0.605683i | \(-0.792900\pi\) | ||||
−0.795706 | + | 0.605683i | \(0.792900\pi\) | |||||||
\(128\) | 20.6779 | 1.82768 | ||||||||
\(129\) | −1.88339 | −0.165823 | ||||||||
\(130\) | 9.15367 | 0.802830 | ||||||||
\(131\) | −12.7359 | −1.11274 | −0.556370 | − | 0.830935i | \(-0.687806\pi\) | ||||
−0.556370 | + | 0.830935i | \(0.687806\pi\) | |||||||
\(132\) | −8.57857 | −0.746668 | ||||||||
\(133\) | 5.56176 | 0.482266 | ||||||||
\(134\) | −4.47093 | −0.386229 | ||||||||
\(135\) | −2.90446 | −0.249976 | ||||||||
\(136\) | 14.7598 | 1.26565 | ||||||||
\(137\) | −8.49771 | −0.726008 | −0.363004 | − | 0.931788i | \(-0.618249\pi\) | ||||
−0.363004 | + | 0.931788i | \(0.618249\pi\) | |||||||
\(138\) | −41.7261 | −3.55196 | ||||||||
\(139\) | −8.78959 | −0.745523 | −0.372762 | − | 0.927927i | \(-0.621589\pi\) | ||||
−0.372762 | + | 0.927927i | \(0.621589\pi\) | |||||||
\(140\) | 11.9084 | 1.00645 | ||||||||
\(141\) | 1.37665 | 0.115935 | ||||||||
\(142\) | 21.5311 | 1.80685 | ||||||||
\(143\) | 2.52148 | 0.210856 | ||||||||
\(144\) | 5.86360 | 0.488633 | ||||||||
\(145\) | 9.88390 | 0.820813 | ||||||||
\(146\) | 7.13613 | 0.590590 | ||||||||
\(147\) | 6.00606 | 0.495371 | ||||||||
\(148\) | 34.6868 | 2.85124 | ||||||||
\(149\) | −11.3902 | −0.933121 | −0.466560 | − | 0.884489i | \(-0.654507\pi\) | ||||
−0.466560 | + | 0.884489i | \(0.654507\pi\) | |||||||
\(150\) | −14.8406 | −1.21173 | ||||||||
\(151\) | −11.5394 | −0.939065 | −0.469533 | − | 0.882915i | \(-0.655578\pi\) | ||||
−0.469533 | + | 0.882915i | \(0.655578\pi\) | |||||||
\(152\) | 11.4003 | 0.924685 | ||||||||
\(153\) | −7.42867 | −0.600572 | ||||||||
\(154\) | 5.01629 | 0.404224 | ||||||||
\(155\) | 6.49427 | 0.521632 | ||||||||
\(156\) | −21.6307 | −1.73184 | ||||||||
\(157\) | −0.372088 | −0.0296959 | −0.0148479 | − | 0.999890i | \(-0.504726\pi\) | ||||
−0.0148479 | + | 0.999890i | \(0.504726\pi\) | |||||||
\(158\) | −31.6498 | −2.51792 | ||||||||
\(159\) | −11.8799 | −0.942135 | ||||||||
\(160\) | −3.02954 | −0.239506 | ||||||||
\(161\) | 15.9554 | 1.25746 | ||||||||
\(162\) | 26.0208 | 2.04439 | ||||||||
\(163\) | −22.4248 | −1.75645 | −0.878224 | − | 0.478249i | \(-0.841272\pi\) | ||||
−0.878224 | + | 0.478249i | \(0.841272\pi\) | |||||||
\(164\) | −18.2496 | −1.42505 | ||||||||
\(165\) | 3.42787 | 0.266859 | ||||||||
\(166\) | −8.40902 | −0.652666 | ||||||||
\(167\) | 7.77964 | 0.602006 | 0.301003 | − | 0.953623i | \(-0.402679\pi\) | ||||
0.301003 | + | 0.953623i | \(0.402679\pi\) | |||||||
\(168\) | −20.2591 | −1.56302 | ||||||||
\(169\) | −6.64216 | −0.510935 | ||||||||
\(170\) | −12.5276 | −0.960826 | ||||||||
\(171\) | −5.73779 | −0.438780 | ||||||||
\(172\) | 3.13560 | 0.239087 | ||||||||
\(173\) | 20.9192 | 1.59045 | 0.795227 | − | 0.606312i | \(-0.207352\pi\) | ||||
0.795227 | + | 0.606312i | \(0.207352\pi\) | |||||||
\(174\) | −35.7167 | −2.70768 | ||||||||
\(175\) | 5.67481 | 0.428975 | ||||||||
\(176\) | 2.72384 | 0.205317 | ||||||||
\(177\) | 9.85052 | 0.740410 | ||||||||
\(178\) | 16.0046 | 1.19960 | ||||||||
\(179\) | 7.64198 | 0.571188 | 0.285594 | − | 0.958351i | \(-0.407809\pi\) | ||||
0.285594 | + | 0.958351i | \(0.407809\pi\) | |||||||
\(180\) | −12.2853 | −0.915695 | ||||||||
\(181\) | 9.54483 | 0.709461 | 0.354731 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354731 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(182\) | 12.6485 | 0.937566 | ||||||||
\(183\) | 9.99018 | 0.738496 | ||||||||
\(184\) | 32.7047 | 2.41102 | ||||||||
\(185\) | −13.8603 | −1.01903 | ||||||||
\(186\) | −23.4678 | −1.72075 | ||||||||
\(187\) | −3.45087 | −0.252353 | ||||||||
\(188\) | −2.29195 | −0.167157 | ||||||||
\(189\) | −4.01335 | −0.291928 | ||||||||
\(190\) | −9.67616 | −0.701983 | ||||||||
\(191\) | −15.1850 | −1.09875 | −0.549373 | − | 0.835577i | \(-0.685133\pi\) | ||||
−0.549373 | + | 0.835577i | \(0.685133\pi\) | |||||||
\(192\) | 23.3136 | 1.68251 | ||||||||
\(193\) | 9.37732 | 0.674994 | 0.337497 | − | 0.941327i | \(-0.390420\pi\) | ||||
0.337497 | + | 0.941327i | \(0.390420\pi\) | |||||||
\(194\) | 12.3096 | 0.883778 | ||||||||
\(195\) | 8.64330 | 0.618959 | ||||||||
\(196\) | −9.99931 | −0.714236 | ||||||||
\(197\) | −24.6276 | −1.75464 | −0.877322 | − | 0.479902i | \(-0.840672\pi\) | ||||
−0.877322 | + | 0.479902i | \(0.840672\pi\) | |||||||
\(198\) | −5.17506 | −0.367775 | ||||||||
\(199\) | −4.21845 | −0.299038 | −0.149519 | − | 0.988759i | \(-0.547772\pi\) | ||||
−0.149519 | + | 0.988759i | \(0.547772\pi\) | |||||||
\(200\) | 11.6320 | 0.822508 | ||||||||
\(201\) | −4.22164 | −0.297772 | ||||||||
\(202\) | 24.0290 | 1.69067 | ||||||||
\(203\) | 13.6575 | 0.958567 | ||||||||
\(204\) | 29.6035 | 2.07266 | ||||||||
\(205\) | 7.29228 | 0.509315 | ||||||||
\(206\) | −26.1723 | −1.82351 | ||||||||
\(207\) | −16.4604 | −1.14408 | ||||||||
\(208\) | 6.86810 | 0.476217 | ||||||||
\(209\) | −2.66540 | −0.184370 | ||||||||
\(210\) | 17.1952 | 1.18658 | ||||||||
\(211\) | 23.3921 | 1.61038 | 0.805189 | − | 0.593019i | \(-0.202064\pi\) | ||||
0.805189 | + | 0.593019i | \(0.202064\pi\) | |||||||
\(212\) | 19.7785 | 1.35839 | ||||||||
\(213\) | 20.3306 | 1.39303 | ||||||||
\(214\) | −24.9927 | −1.70847 | ||||||||
\(215\) | −1.25294 | −0.0854499 | ||||||||
\(216\) | −8.22642 | −0.559737 | ||||||||
\(217\) | 8.97372 | 0.609176 | ||||||||
\(218\) | 44.4275 | 3.00901 | ||||||||
\(219\) | 6.73824 | 0.455328 | ||||||||
\(220\) | −5.70696 | −0.384763 | ||||||||
\(221\) | −8.70129 | −0.585312 | ||||||||
\(222\) | 50.0861 | 3.36156 | ||||||||
\(223\) | 20.2933 | 1.35894 | 0.679471 | − | 0.733702i | \(-0.262209\pi\) | ||||
0.679471 | + | 0.733702i | \(0.262209\pi\) | |||||||
\(224\) | −4.18619 | −0.279701 | ||||||||
\(225\) | −5.85442 | −0.390295 | ||||||||
\(226\) | 43.3470 | 2.88340 | ||||||||
\(227\) | −22.0826 | −1.46568 | −0.732838 | − | 0.680403i | \(-0.761805\pi\) | ||||
−0.732838 | + | 0.680403i | \(0.761805\pi\) | |||||||
\(228\) | 22.8653 | 1.51429 | ||||||||
\(229\) | −16.7997 | −1.11016 | −0.555078 | − | 0.831798i | \(-0.687312\pi\) | ||||
−0.555078 | + | 0.831798i | \(0.687312\pi\) | |||||||
\(230\) | −27.7586 | −1.83035 | ||||||||
\(231\) | 4.73660 | 0.311645 | ||||||||
\(232\) | 27.9946 | 1.83793 | ||||||||
\(233\) | 9.29069 | 0.608653 | 0.304327 | − | 0.952568i | \(-0.401569\pi\) | ||||
0.304327 | + | 0.952568i | \(0.401569\pi\) | |||||||
\(234\) | −13.0488 | −0.853026 | ||||||||
\(235\) | 0.915828 | 0.0597421 | ||||||||
\(236\) | −16.3998 | −1.06754 | ||||||||
\(237\) | −29.8851 | −1.94125 | ||||||||
\(238\) | −17.3106 | −1.12208 | ||||||||
\(239\) | −25.8064 | −1.66928 | −0.834638 | − | 0.550799i | \(-0.814323\pi\) | ||||
−0.834638 | + | 0.550799i | \(0.814323\pi\) | |||||||
\(240\) | 9.33698 | 0.602699 | ||||||||
\(241\) | −23.9305 | −1.54150 | −0.770750 | − | 0.637138i | \(-0.780118\pi\) | ||||
−0.770750 | + | 0.637138i | \(0.780118\pi\) | |||||||
\(242\) | −2.40399 | −0.154534 | ||||||||
\(243\) | 18.7999 | 1.20602 | ||||||||
\(244\) | −16.6324 | −1.06478 | ||||||||
\(245\) | 3.99558 | 0.255268 | ||||||||
\(246\) | −26.3516 | −1.68011 | ||||||||
\(247\) | −6.72074 | −0.427631 | ||||||||
\(248\) | 18.3940 | 1.16802 | ||||||||
\(249\) | −7.94016 | −0.503187 | ||||||||
\(250\) | −28.0243 | −1.77241 | ||||||||
\(251\) | 17.0822 | 1.07822 | 0.539110 | − | 0.842235i | \(-0.318761\pi\) | ||||
0.539110 | + | 0.842235i | \(0.318761\pi\) | |||||||
\(252\) | −16.9758 | −1.06937 | ||||||||
\(253\) | −7.64641 | −0.480726 | ||||||||
\(254\) | 43.1139 | 2.70521 | ||||||||
\(255\) | −11.8291 | −0.740770 | ||||||||
\(256\) | −29.1685 | −1.82303 | ||||||||
\(257\) | −30.5627 | −1.90645 | −0.953223 | − | 0.302268i | \(-0.902256\pi\) | ||||
−0.953223 | + | 0.302268i | \(0.902256\pi\) | |||||||
\(258\) | 4.52766 | 0.281880 | ||||||||
\(259\) | −19.1521 | −1.19005 | ||||||||
\(260\) | −14.3900 | −0.892428 | ||||||||
\(261\) | −14.0897 | −0.872133 | ||||||||
\(262\) | 30.6170 | 1.89152 | ||||||||
\(263\) | −20.5830 | −1.26920 | −0.634600 | − | 0.772841i | \(-0.718835\pi\) | ||||
−0.634600 | + | 0.772841i | \(0.718835\pi\) | |||||||
\(264\) | 9.70890 | 0.597542 | ||||||||
\(265\) | −7.90319 | −0.485489 | ||||||||
\(266\) | −13.3704 | −0.819793 | ||||||||
\(267\) | 15.1123 | 0.924856 | ||||||||
\(268\) | 7.02849 | 0.429333 | ||||||||
\(269\) | −18.2785 | −1.11446 | −0.557230 | − | 0.830358i | \(-0.688136\pi\) | ||||
−0.557230 | + | 0.830358i | \(0.688136\pi\) | |||||||
\(270\) | 6.98229 | 0.424929 | ||||||||
\(271\) | −5.31546 | −0.322891 | −0.161446 | − | 0.986882i | \(-0.551616\pi\) | ||||
−0.161446 | + | 0.986882i | \(0.551616\pi\) | |||||||
\(272\) | −9.39963 | −0.569936 | ||||||||
\(273\) | 11.9432 | 0.722837 | ||||||||
\(274\) | 20.4284 | 1.23413 | ||||||||
\(275\) | −2.71958 | −0.163997 | ||||||||
\(276\) | 65.5952 | 3.94837 | ||||||||
\(277\) | 1.32154 | 0.0794034 | 0.0397017 | − | 0.999212i | \(-0.487359\pi\) | ||||
0.0397017 | + | 0.999212i | \(0.487359\pi\) | |||||||
\(278\) | 21.1301 | 1.26730 | ||||||||
\(279\) | −9.25774 | −0.554246 | ||||||||
\(280\) | −13.4775 | −0.805436 | ||||||||
\(281\) | 28.2381 | 1.68454 | 0.842271 | − | 0.539055i | \(-0.181218\pi\) | ||||
0.842271 | + | 0.539055i | \(0.181218\pi\) | |||||||
\(282\) | −3.30946 | −0.197075 | ||||||||
\(283\) | 8.30176 | 0.493488 | 0.246744 | − | 0.969081i | \(-0.420639\pi\) | ||||
0.246744 | + | 0.969081i | \(0.420639\pi\) | |||||||
\(284\) | −33.8478 | −2.00850 | ||||||||
\(285\) | −9.13665 | −0.541209 | ||||||||
\(286\) | −6.06161 | −0.358430 | ||||||||
\(287\) | 10.0764 | 0.594791 | ||||||||
\(288\) | 4.31868 | 0.254481 | ||||||||
\(289\) | −5.09149 | −0.299499 | ||||||||
\(290\) | −23.7608 | −1.39528 | ||||||||
\(291\) | 11.6233 | 0.681368 | ||||||||
\(292\) | −11.2183 | −0.656501 | ||||||||
\(293\) | −30.3495 | −1.77304 | −0.886518 | − | 0.462693i | \(-0.846883\pi\) | ||||
−0.886518 | + | 0.462693i | \(0.846883\pi\) | |||||||
\(294\) | −14.4385 | −0.842071 | ||||||||
\(295\) | 6.55314 | 0.381539 | ||||||||
\(296\) | −39.2572 | −2.28178 | ||||||||
\(297\) | 1.92335 | 0.111604 | ||||||||
\(298\) | 27.3819 | 1.58619 | ||||||||
\(299\) | −19.2802 | −1.11501 | ||||||||
\(300\) | 23.3301 | 1.34696 | ||||||||
\(301\) | −1.73130 | −0.0997906 | ||||||||
\(302\) | 27.7407 | 1.59630 | ||||||||
\(303\) | 22.6892 | 1.30346 | ||||||||
\(304\) | −7.26013 | −0.416397 | ||||||||
\(305\) | 6.64605 | 0.380552 | ||||||||
\(306\) | 17.8585 | 1.02090 | ||||||||
\(307\) | 20.6568 | 1.17895 | 0.589473 | − | 0.807788i | \(-0.299335\pi\) | ||||
0.589473 | + | 0.807788i | \(0.299335\pi\) | |||||||
\(308\) | −7.88582 | −0.449337 | ||||||||
\(309\) | −24.7131 | −1.40588 | ||||||||
\(310\) | −15.6122 | −0.886712 | ||||||||
\(311\) | −30.1829 | −1.71151 | −0.855757 | − | 0.517379i | \(-0.826908\pi\) | ||||
−0.855757 | + | 0.517379i | \(0.826908\pi\) | |||||||
\(312\) | 24.4808 | 1.38595 | ||||||||
\(313\) | −30.0485 | −1.69844 | −0.849221 | − | 0.528037i | \(-0.822928\pi\) | ||||
−0.849221 | + | 0.528037i | \(0.822928\pi\) | |||||||
\(314\) | 0.894497 | 0.0504794 | ||||||||
\(315\) | 6.78327 | 0.382194 | ||||||||
\(316\) | 49.7548 | 2.79893 | ||||||||
\(317\) | −8.02485 | −0.450721 | −0.225360 | − | 0.974275i | \(-0.572356\pi\) | ||||
−0.225360 | + | 0.974275i | \(0.572356\pi\) | |||||||
\(318\) | 28.5591 | 1.60152 | ||||||||
\(319\) | −6.54517 | −0.366459 | ||||||||
\(320\) | 15.5096 | 0.867011 | ||||||||
\(321\) | −23.5992 | −1.31718 | ||||||||
\(322\) | −38.3566 | −2.13753 | ||||||||
\(323\) | 9.19796 | 0.511788 | ||||||||
\(324\) | −40.9058 | −2.27255 | ||||||||
\(325\) | −6.85736 | −0.380378 | ||||||||
\(326\) | 53.9091 | 2.98575 | ||||||||
\(327\) | 41.9503 | 2.31986 | ||||||||
\(328\) | 20.6542 | 1.14044 | ||||||||
\(329\) | 1.26548 | 0.0697683 | ||||||||
\(330\) | −8.24058 | −0.453629 | ||||||||
\(331\) | 18.3426 | 1.00820 | 0.504099 | − | 0.863646i | \(-0.331825\pi\) | ||||
0.504099 | + | 0.863646i | \(0.331825\pi\) | |||||||
\(332\) | 13.2193 | 0.725506 | ||||||||
\(333\) | 19.7583 | 1.08275 | ||||||||
\(334\) | −18.7022 | −1.02334 | ||||||||
\(335\) | −2.80848 | −0.153444 | ||||||||
\(336\) | 12.9017 | 0.703848 | ||||||||
\(337\) | −9.26795 | −0.504857 | −0.252429 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252429 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(338\) | 15.9677 | 0.868528 | ||||||||
\(339\) | 40.9302 | 2.22302 | ||||||||
\(340\) | 19.6940 | 1.06806 | ||||||||
\(341\) | −4.30054 | −0.232887 | ||||||||
\(342\) | 13.7936 | 0.745873 | ||||||||
\(343\) | 20.1276 | 1.08679 | ||||||||
\(344\) | −3.54876 | −0.191336 | ||||||||
\(345\) | −26.2109 | −1.41115 | ||||||||
\(346\) | −50.2895 | −2.70358 | ||||||||
\(347\) | −19.1148 | −1.02614 | −0.513068 | − | 0.858348i | \(-0.671491\pi\) | ||||
−0.513068 | + | 0.858348i | \(0.671491\pi\) | |||||||
\(348\) | 56.1482 | 3.00986 | ||||||||
\(349\) | 31.9173 | 1.70849 | 0.854246 | − | 0.519869i | \(-0.174019\pi\) | ||||
0.854246 | + | 0.519869i | \(0.174019\pi\) | |||||||
\(350\) | −13.6422 | −0.729206 | ||||||||
\(351\) | 4.84967 | 0.258856 | ||||||||
\(352\) | 2.00618 | 0.106930 | ||||||||
\(353\) | −15.1290 | −0.805234 | −0.402617 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402617 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(354\) | −23.6806 | −1.25861 | ||||||||
\(355\) | 13.5251 | 0.717838 | ||||||||
\(356\) | −25.1600 | −1.33348 | ||||||||
\(357\) | −16.3454 | −0.865090 | ||||||||
\(358\) | −18.3713 | −0.970951 | ||||||||
\(359\) | −18.0070 | −0.950372 | −0.475186 | − | 0.879885i | \(-0.657619\pi\) | ||||
−0.475186 | + | 0.879885i | \(0.657619\pi\) | |||||||
\(360\) | 13.9041 | 0.732810 | ||||||||
\(361\) | −11.8956 | −0.626086 | ||||||||
\(362\) | −22.9457 | −1.20600 | ||||||||
\(363\) | −2.26995 | −0.119142 | ||||||||
\(364\) | −19.8839 | −1.04220 | ||||||||
\(365\) | 4.48267 | 0.234634 | ||||||||
\(366\) | −24.0163 | −1.25535 | ||||||||
\(367\) | 17.0362 | 0.889283 | 0.444641 | − | 0.895709i | \(-0.353331\pi\) | ||||
0.444641 | + | 0.895709i | \(0.353331\pi\) | |||||||
\(368\) | −20.8276 | −1.08571 | ||||||||
\(369\) | −10.3953 | −0.541159 | ||||||||
\(370\) | 33.3202 | 1.73223 | ||||||||
\(371\) | −10.9205 | −0.566966 | ||||||||
\(372\) | 36.8925 | 1.91278 | ||||||||
\(373\) | −28.6584 | −1.48388 | −0.741938 | − | 0.670469i | \(-0.766093\pi\) | ||||
−0.741938 | + | 0.670469i | \(0.766093\pi\) | |||||||
\(374\) | 8.29587 | 0.428969 | ||||||||
\(375\) | −26.4617 | −1.36648 | ||||||||
\(376\) | 2.59394 | 0.133772 | ||||||||
\(377\) | −16.5035 | −0.849973 | ||||||||
\(378\) | 9.64807 | 0.496243 | ||||||||
\(379\) | 23.3996 | 1.20196 | 0.600978 | − | 0.799265i | \(-0.294778\pi\) | ||||
0.600978 | + | 0.799265i | \(0.294778\pi\) | |||||||
\(380\) | 15.2113 | 0.780325 | ||||||||
\(381\) | 40.7101 | 2.08564 | ||||||||
\(382\) | 36.5045 | 1.86773 | ||||||||
\(383\) | −30.3914 | −1.55293 | −0.776464 | − | 0.630161i | \(-0.782989\pi\) | ||||
−0.776464 | + | 0.630161i | \(0.782989\pi\) | |||||||
\(384\) | −46.9379 | −2.39529 | ||||||||
\(385\) | 3.15106 | 0.160593 | ||||||||
\(386\) | −22.5430 | −1.14741 | ||||||||
\(387\) | 1.78610 | 0.0907925 | ||||||||
\(388\) | −19.3512 | −0.982410 | ||||||||
\(389\) | 25.0239 | 1.26876 | 0.634381 | − | 0.773020i | \(-0.281255\pi\) | ||||
0.634381 | + | 0.773020i | \(0.281255\pi\) | |||||||
\(390\) | −20.7784 | −1.05216 | ||||||||
\(391\) | 26.3868 | 1.33444 | ||||||||
\(392\) | 11.3168 | 0.571587 | ||||||||
\(393\) | 28.9099 | 1.45831 | ||||||||
\(394\) | 59.2046 | 2.98268 | ||||||||
\(395\) | −19.8813 | −1.00034 | ||||||||
\(396\) | 8.13542 | 0.408820 | ||||||||
\(397\) | −28.9668 | −1.45380 | −0.726902 | − | 0.686741i | \(-0.759041\pi\) | ||||
−0.726902 | + | 0.686741i | \(0.759041\pi\) | |||||||
\(398\) | 10.1411 | 0.508328 | ||||||||
\(399\) | −12.6249 | −0.632037 | ||||||||
\(400\) | −7.40771 | −0.370385 | ||||||||
\(401\) | −7.85044 | −0.392032 | −0.196016 | − | 0.980601i | \(-0.562801\pi\) | ||||
−0.196016 | + | 0.980601i | \(0.562801\pi\) | |||||||
\(402\) | 10.1488 | 0.506176 | ||||||||
\(403\) | −10.8437 | −0.540163 | ||||||||
\(404\) | −37.7746 | −1.87936 | ||||||||
\(405\) | 16.3454 | 0.812208 | ||||||||
\(406\) | −32.8325 | −1.62945 | ||||||||
\(407\) | 9.17839 | 0.454956 | ||||||||
\(408\) | −33.5042 | −1.65870 | ||||||||
\(409\) | 7.27346 | 0.359650 | 0.179825 | − | 0.983699i | \(-0.442447\pi\) | ||||
0.179825 | + | 0.983699i | \(0.442447\pi\) | |||||||
\(410\) | −17.5306 | −0.865774 | ||||||||
\(411\) | 19.2894 | 0.951476 | ||||||||
\(412\) | 41.1441 | 2.02702 | ||||||||
\(413\) | 9.05506 | 0.445571 | ||||||||
\(414\) | 39.5706 | 1.94479 | ||||||||
\(415\) | −5.28226 | −0.259296 | ||||||||
\(416\) | 5.05852 | 0.248015 | ||||||||
\(417\) | 19.9520 | 0.977052 | ||||||||
\(418\) | 6.40760 | 0.313406 | ||||||||
\(419\) | 13.7486 | 0.671661 | 0.335831 | − | 0.941922i | \(-0.390983\pi\) | ||||
0.335831 | + | 0.941922i | \(0.390983\pi\) | |||||||
\(420\) | −27.0316 | −1.31901 | ||||||||
\(421\) | 10.2897 | 0.501487 | 0.250744 | − | 0.968053i | \(-0.419325\pi\) | ||||
0.250744 | + | 0.968053i | \(0.419325\pi\) | |||||||
\(422\) | −56.2344 | −2.73745 | ||||||||
\(423\) | −1.30554 | −0.0634773 | ||||||||
\(424\) | −22.3845 | −1.08709 | ||||||||
\(425\) | 9.38492 | 0.455236 | ||||||||
\(426\) | −48.8746 | −2.36798 | ||||||||
\(427\) | 9.18345 | 0.444418 | ||||||||
\(428\) | 39.2896 | 1.89914 | ||||||||
\(429\) | −5.72364 | −0.276340 | ||||||||
\(430\) | 3.01206 | 0.145254 | ||||||||
\(431\) | 9.22181 | 0.444199 | 0.222099 | − | 0.975024i | \(-0.428709\pi\) | ||||
0.222099 | + | 0.975024i | \(0.428709\pi\) | |||||||
\(432\) | 5.23889 | 0.252056 | ||||||||
\(433\) | −12.1809 | −0.585375 | −0.292688 | − | 0.956208i | \(-0.594550\pi\) | ||||
−0.292688 | + | 0.956208i | \(0.594550\pi\) | |||||||
\(434\) | −21.5727 | −1.03553 | ||||||||
\(435\) | −22.4360 | −1.07572 | ||||||||
\(436\) | −69.8419 | −3.34482 | ||||||||
\(437\) | 20.3808 | 0.974943 | ||||||||
\(438\) | −16.1987 | −0.774003 | ||||||||
\(439\) | −14.9755 | −0.714741 | −0.357370 | − | 0.933963i | \(-0.616327\pi\) | ||||
−0.357370 | + | 0.933963i | \(0.616327\pi\) | |||||||
\(440\) | 6.45893 | 0.307917 | ||||||||
\(441\) | −5.69580 | −0.271228 | ||||||||
\(442\) | 20.9178 | 0.994960 | ||||||||
\(443\) | −29.7636 | −1.41411 | −0.707055 | − | 0.707158i | \(-0.749977\pi\) | ||||
−0.707055 | + | 0.707158i | \(0.749977\pi\) | |||||||
\(444\) | −78.7375 | −3.73671 | ||||||||
\(445\) | 10.0536 | 0.476585 | ||||||||
\(446\) | −48.7850 | −2.31004 | ||||||||
\(447\) | 25.8552 | 1.22291 | ||||||||
\(448\) | 21.4310 | 1.01252 | ||||||||
\(449\) | 40.6067 | 1.91635 | 0.958175 | − | 0.286182i | \(-0.0923863\pi\) | ||||
0.958175 | + | 0.286182i | \(0.0923863\pi\) | |||||||
\(450\) | 14.0740 | 0.663454 | ||||||||
\(451\) | −4.82899 | −0.227388 | ||||||||
\(452\) | −68.1434 | −3.20520 | ||||||||
\(453\) | 26.1940 | 1.23070 | ||||||||
\(454\) | 53.0865 | 2.49147 | ||||||||
\(455\) | 7.94533 | 0.372483 | ||||||||
\(456\) | −25.8781 | −1.21185 | ||||||||
\(457\) | 25.2577 | 1.18150 | 0.590752 | − | 0.806853i | \(-0.298831\pi\) | ||||
0.590752 | + | 0.806853i | \(0.298831\pi\) | |||||||
\(458\) | 40.3864 | 1.88713 | ||||||||
\(459\) | −6.63722 | −0.309799 | ||||||||
\(460\) | 43.6378 | 2.03462 | ||||||||
\(461\) | 33.0679 | 1.54013 | 0.770064 | − | 0.637967i | \(-0.220224\pi\) | ||||
0.770064 | + | 0.637967i | \(0.220224\pi\) | |||||||
\(462\) | −11.3868 | −0.529760 | ||||||||
\(463\) | −10.5726 | −0.491350 | −0.245675 | − | 0.969352i | \(-0.579010\pi\) | ||||
−0.245675 | + | 0.969352i | \(0.579010\pi\) | |||||||
\(464\) | −17.8280 | −0.827644 | ||||||||
\(465\) | −14.7417 | −0.683630 | ||||||||
\(466\) | −22.3347 | −1.03464 | ||||||||
\(467\) | −13.2070 | −0.611146 | −0.305573 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305573 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(468\) | 20.5133 | 0.948226 | ||||||||
\(469\) | −3.88073 | −0.179196 | ||||||||
\(470\) | −2.20164 | −0.101554 | ||||||||
\(471\) | 0.844623 | 0.0389182 | ||||||||
\(472\) | 18.5607 | 0.854327 | ||||||||
\(473\) | 0.829704 | 0.0381498 | ||||||||
\(474\) | 71.8436 | 3.29989 | ||||||||
\(475\) | 7.24877 | 0.332596 | ||||||||
\(476\) | 27.2130 | 1.24730 | ||||||||
\(477\) | 11.2662 | 0.515843 | ||||||||
\(478\) | 62.0383 | 2.83757 | ||||||||
\(479\) | −35.2765 | −1.61183 | −0.805913 | − | 0.592034i | \(-0.798325\pi\) | ||||
−0.805913 | + | 0.592034i | \(0.798325\pi\) | |||||||
\(480\) | 6.87691 | 0.313887 | ||||||||
\(481\) | 23.1431 | 1.05523 | ||||||||
\(482\) | 57.5288 | 2.62036 | ||||||||
\(483\) | −36.2180 | −1.64798 | ||||||||
\(484\) | 3.77918 | 0.171781 | ||||||||
\(485\) | 7.73247 | 0.351114 | ||||||||
\(486\) | −45.1949 | −2.05008 | ||||||||
\(487\) | 29.2891 | 1.32721 | 0.663607 | − | 0.748081i | \(-0.269025\pi\) | ||||
0.663607 | + | 0.748081i | \(0.269025\pi\) | |||||||
\(488\) | 18.8239 | 0.852117 | ||||||||
\(489\) | 50.9033 | 2.30193 | ||||||||
\(490\) | −9.60534 | −0.433925 | ||||||||
\(491\) | −8.88302 | −0.400885 | −0.200443 | − | 0.979705i | \(-0.564238\pi\) | ||||
−0.200443 | + | 0.979705i | \(0.564238\pi\) | |||||||
\(492\) | 41.4258 | 1.86762 | ||||||||
\(493\) | 22.5865 | 1.01725 | ||||||||
\(494\) | 16.1566 | 0.726921 | ||||||||
\(495\) | −3.25080 | −0.146112 | ||||||||
\(496\) | −11.7140 | −0.525973 | ||||||||
\(497\) | 18.6889 | 0.838310 | ||||||||
\(498\) | 19.0881 | 0.855358 | ||||||||
\(499\) | 26.4315 | 1.18324 | 0.591618 | − | 0.806218i | \(-0.298489\pi\) | ||||
0.591618 | + | 0.806218i | \(0.298489\pi\) | |||||||
\(500\) | 44.0554 | 1.97022 | ||||||||
\(501\) | −17.6594 | −0.788965 | ||||||||
\(502\) | −41.0655 | −1.83284 | ||||||||
\(503\) | 15.3632 | 0.685013 | 0.342507 | − | 0.939515i | \(-0.388724\pi\) | ||||
0.342507 | + | 0.939515i | \(0.388724\pi\) | |||||||
\(504\) | 19.2125 | 0.855795 | ||||||||
\(505\) | 15.0942 | 0.671683 | ||||||||
\(506\) | 18.3819 | 0.817176 | ||||||||
\(507\) | 15.0774 | 0.669611 | ||||||||
\(508\) | −67.7770 | −3.00712 | ||||||||
\(509\) | 15.2410 | 0.675547 | 0.337774 | − | 0.941227i | \(-0.390326\pi\) | ||||
0.337774 | + | 0.941227i | \(0.390326\pi\) | |||||||
\(510\) | 28.4372 | 1.25922 | ||||||||
\(511\) | 6.19411 | 0.274011 | ||||||||
\(512\) | 28.7650 | 1.27124 | ||||||||
\(513\) | −5.12649 | −0.226340 | ||||||||
\(514\) | 73.4724 | 3.24073 | ||||||||
\(515\) | −16.4406 | −0.724458 | ||||||||
\(516\) | −7.11767 | −0.313338 | ||||||||
\(517\) | −0.606466 | −0.0266724 | ||||||||
\(518\) | 46.0415 | 2.02295 | ||||||||
\(519\) | −47.4855 | −2.08438 | ||||||||
\(520\) | 16.2860 | 0.714190 | ||||||||
\(521\) | −37.5200 | −1.64378 | −0.821890 | − | 0.569646i | \(-0.807080\pi\) | ||||
−0.821890 | + | 0.569646i | \(0.807080\pi\) | |||||||
\(522\) | 33.8716 | 1.48252 | ||||||||
\(523\) | 36.1966 | 1.58277 | 0.791384 | − | 0.611319i | \(-0.209361\pi\) | ||||
0.791384 | + | 0.611319i | \(0.209361\pi\) | |||||||
\(524\) | −48.1312 | −2.10262 | ||||||||
\(525\) | −12.8816 | −0.562198 | ||||||||
\(526\) | 49.4813 | 2.15749 | ||||||||
\(527\) | 14.8406 | 0.646467 | ||||||||
\(528\) | −6.18300 | −0.269080 | ||||||||
\(529\) | 35.4676 | 1.54207 | ||||||||
\(530\) | 18.9992 | 0.825272 | ||||||||
\(531\) | −9.34166 | −0.405394 | ||||||||
\(532\) | 21.0189 | 0.911284 | ||||||||
\(533\) | −12.1762 | −0.527408 | ||||||||
\(534\) | −36.3298 | −1.57214 | ||||||||
\(535\) | −15.6996 | −0.678751 | ||||||||
\(536\) | −7.95458 | −0.343586 | ||||||||
\(537\) | −17.3469 | −0.748576 | ||||||||
\(538\) | 43.9414 | 1.89445 | ||||||||
\(539\) | −2.64589 | −0.113967 | ||||||||
\(540\) | −10.9765 | −0.472352 | ||||||||
\(541\) | −13.5138 | −0.581003 | −0.290501 | − | 0.956875i | \(-0.593822\pi\) | ||||
−0.290501 | + | 0.956875i | \(0.593822\pi\) | |||||||
\(542\) | 12.7783 | 0.548876 | ||||||||
\(543\) | −21.6663 | −0.929791 | ||||||||
\(544\) | −6.92306 | −0.296824 | ||||||||
\(545\) | 27.9078 | 1.19544 | ||||||||
\(546\) | −28.7114 | −1.22874 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −32.1144 | −1.37186 | ||||||||
\(549\) | −9.47411 | −0.404345 | ||||||||
\(550\) | 6.53785 | 0.278775 | ||||||||
\(551\) | 17.4455 | 0.743203 | ||||||||
\(552\) | −74.2383 | −3.15979 | ||||||||
\(553\) | −27.4718 | −1.16822 | ||||||||
\(554\) | −3.17696 | −0.134976 | ||||||||
\(555\) | 31.4624 | 1.33550 | ||||||||
\(556\) | −33.2174 | −1.40873 | ||||||||
\(557\) | 19.9686 | 0.846096 | 0.423048 | − | 0.906107i | \(-0.360960\pi\) | ||||
0.423048 | + | 0.906107i | \(0.360960\pi\) | |||||||
\(558\) | 22.2555 | 0.942152 | ||||||||
\(559\) | 2.09208 | 0.0884855 | ||||||||
\(560\) | 8.58299 | 0.362698 | ||||||||
\(561\) | 7.83332 | 0.330723 | ||||||||
\(562\) | −67.8841 | −2.86352 | ||||||||
\(563\) | 33.3850 | 1.40701 | 0.703506 | − | 0.710690i | \(-0.251617\pi\) | ||||
0.703506 | + | 0.710690i | \(0.251617\pi\) | |||||||
\(564\) | 5.20261 | 0.219070 | ||||||||
\(565\) | 27.2291 | 1.14554 | ||||||||
\(566\) | −19.9574 | −0.838871 | ||||||||
\(567\) | 22.5859 | 0.948518 | ||||||||
\(568\) | 38.3077 | 1.60736 | ||||||||
\(569\) | 38.8166 | 1.62728 | 0.813638 | − | 0.581371i | \(-0.197484\pi\) | ||||
0.813638 | + | 0.581371i | \(0.197484\pi\) | |||||||
\(570\) | 21.9644 | 0.919989 | ||||||||
\(571\) | 13.4426 | 0.562557 | 0.281279 | − | 0.959626i | \(-0.409242\pi\) | ||||
0.281279 | + | 0.959626i | \(0.409242\pi\) | |||||||
\(572\) | 9.52911 | 0.398432 | ||||||||
\(573\) | 34.4692 | 1.43997 | ||||||||
\(574\) | −24.2236 | −1.01107 | ||||||||
\(575\) | 20.7950 | 0.867213 | ||||||||
\(576\) | −22.1093 | −0.921220 | ||||||||
\(577\) | −12.4689 | −0.519087 | −0.259544 | − | 0.965731i | \(-0.583572\pi\) | ||||
−0.259544 | + | 0.965731i | \(0.583572\pi\) | |||||||
\(578\) | 12.2399 | 0.509113 | ||||||||
\(579\) | −21.2861 | −0.884620 | ||||||||
\(580\) | 37.3530 | 1.55100 | ||||||||
\(581\) | −7.29897 | −0.302812 | ||||||||
\(582\) | −27.9422 | −1.15824 | ||||||||
\(583\) | 5.23353 | 0.216751 | ||||||||
\(584\) | 12.6965 | 0.525383 | ||||||||
\(585\) | −8.19680 | −0.338896 | ||||||||
\(586\) | 72.9600 | 3.01395 | ||||||||
\(587\) | 29.6787 | 1.22497 | 0.612485 | − | 0.790482i | \(-0.290170\pi\) | ||||
0.612485 | + | 0.790482i | \(0.290170\pi\) | |||||||
\(588\) | 22.6980 | 0.936049 | ||||||||
\(589\) | 11.4627 | 0.472311 | ||||||||
\(590\) | −15.7537 | −0.648570 | ||||||||
\(591\) | 55.9035 | 2.29956 | ||||||||
\(592\) | 25.0005 | 1.02751 | ||||||||
\(593\) | −28.0727 | −1.15281 | −0.576405 | − | 0.817165i | \(-0.695545\pi\) | ||||
−0.576405 | + | 0.817165i | \(0.695545\pi\) | |||||||
\(594\) | −4.62371 | −0.189713 | ||||||||
\(595\) | −10.8739 | −0.445787 | ||||||||
\(596\) | −43.0456 | −1.76322 | ||||||||
\(597\) | 9.57568 | 0.391906 | ||||||||
\(598\) | 46.3496 | 1.89537 | ||||||||
\(599\) | −22.1345 | −0.904392 | −0.452196 | − | 0.891919i | \(-0.649359\pi\) | ||||
−0.452196 | + | 0.891919i | \(0.649359\pi\) | |||||||
\(600\) | −26.4041 | −1.07794 | ||||||||
\(601\) | 37.8548 | 1.54413 | 0.772064 | − | 0.635544i | \(-0.219224\pi\) | ||||
0.772064 | + | 0.635544i | \(0.219224\pi\) | |||||||
\(602\) | 4.16204 | 0.169632 | ||||||||
\(603\) | 4.00356 | 0.163038 | ||||||||
\(604\) | −43.6096 | −1.77445 | ||||||||
\(605\) | −1.51011 | −0.0613945 | ||||||||
\(606\) | −54.5447 | −2.21573 | ||||||||
\(607\) | 23.2774 | 0.944802 | 0.472401 | − | 0.881384i | \(-0.343387\pi\) | ||||
0.472401 | + | 0.881384i | \(0.343387\pi\) | |||||||
\(608\) | −5.34726 | −0.216860 | ||||||||
\(609\) | −31.0018 | −1.25626 | ||||||||
\(610\) | −15.9771 | −0.646892 | ||||||||
\(611\) | −1.52919 | −0.0618644 | ||||||||
\(612\) | −28.0743 | −1.13484 | ||||||||
\(613\) | −22.6455 | −0.914644 | −0.457322 | − | 0.889301i | \(-0.651191\pi\) | ||||
−0.457322 | + | 0.889301i | \(0.651191\pi\) | |||||||
\(614\) | −49.6588 | −2.00407 | ||||||||
\(615\) | −16.5531 | −0.667487 | ||||||||
\(616\) | 8.92488 | 0.359594 | ||||||||
\(617\) | 30.0028 | 1.20787 | 0.603934 | − | 0.797034i | \(-0.293599\pi\) | ||||
0.603934 | + | 0.797034i | \(0.293599\pi\) | |||||||
\(618\) | 59.4100 | 2.38982 | ||||||||
\(619\) | 4.04243 | 0.162479 | 0.0812395 | − | 0.996695i | \(-0.474112\pi\) | ||||
0.0812395 | + | 0.996695i | \(0.474112\pi\) | |||||||
\(620\) | 24.5430 | 0.985671 | ||||||||
\(621\) | −14.7067 | −0.590160 | ||||||||
\(622\) | 72.5594 | 2.90937 | ||||||||
\(623\) | 13.8919 | 0.556568 | ||||||||
\(624\) | −15.5903 | −0.624111 | ||||||||
\(625\) | −4.00598 | −0.160239 | ||||||||
\(626\) | 72.2364 | 2.88715 | ||||||||
\(627\) | 6.05034 | 0.241627 | ||||||||
\(628\) | −1.40619 | −0.0561130 | ||||||||
\(629\) | −31.6735 | −1.26290 | ||||||||
\(630\) | −16.3069 | −0.649684 | ||||||||
\(631\) | −32.5121 | −1.29429 | −0.647144 | − | 0.762368i | \(-0.724037\pi\) | ||||
−0.647144 | + | 0.762368i | \(0.724037\pi\) | |||||||
\(632\) | −56.3107 | −2.23992 | ||||||||
\(633\) | −53.0990 | −2.11049 | ||||||||
\(634\) | 19.2917 | 0.766171 | ||||||||
\(635\) | 27.0827 | 1.07474 | ||||||||
\(636\) | −44.8962 | −1.78025 | ||||||||
\(637\) | −6.67156 | −0.264337 | ||||||||
\(638\) | 15.7345 | 0.622936 | ||||||||
\(639\) | −19.2804 | −0.762720 | ||||||||
\(640\) | −31.2258 | −1.23431 | ||||||||
\(641\) | −19.5444 | −0.771959 | −0.385979 | − | 0.922507i | \(-0.626136\pi\) | ||||
−0.385979 | + | 0.922507i | \(0.626136\pi\) | |||||||
\(642\) | 56.7323 | 2.23905 | ||||||||
\(643\) | 1.14866 | 0.0452988 | 0.0226494 | − | 0.999743i | \(-0.492790\pi\) | ||||
0.0226494 | + | 0.999743i | \(0.492790\pi\) | |||||||
\(644\) | 60.2982 | 2.37608 | ||||||||
\(645\) | 2.84412 | 0.111987 | ||||||||
\(646\) | −22.1118 | −0.869978 | ||||||||
\(647\) | 23.4719 | 0.922775 | 0.461387 | − | 0.887199i | \(-0.347352\pi\) | ||||
0.461387 | + | 0.887199i | \(0.347352\pi\) | |||||||
\(648\) | 46.2957 | 1.81867 | ||||||||
\(649\) | −4.33952 | −0.170341 | ||||||||
\(650\) | 16.4850 | 0.646596 | ||||||||
\(651\) | −20.3699 | −0.798360 | ||||||||
\(652\) | −84.7475 | −3.31897 | ||||||||
\(653\) | −15.9812 | −0.625393 | −0.312696 | − | 0.949853i | \(-0.601232\pi\) | ||||
−0.312696 | + | 0.949853i | \(0.601232\pi\) | |||||||
\(654\) | −100.848 | −3.94348 | ||||||||
\(655\) | 19.2325 | 0.751477 | ||||||||
\(656\) | −13.1534 | −0.513554 | ||||||||
\(657\) | −6.39016 | −0.249304 | ||||||||
\(658\) | −3.04221 | −0.118598 | ||||||||
\(659\) | 26.4394 | 1.02993 | 0.514966 | − | 0.857210i | \(-0.327804\pi\) | ||||
0.514966 | + | 0.857210i | \(0.327804\pi\) | |||||||
\(660\) | 12.9545 | 0.504255 | ||||||||
\(661\) | 9.92932 | 0.386206 | 0.193103 | − | 0.981179i | \(-0.438145\pi\) | ||||
0.193103 | + | 0.981179i | \(0.438145\pi\) | |||||||
\(662\) | −44.0954 | −1.71382 | ||||||||
\(663\) | 19.7515 | 0.767086 | ||||||||
\(664\) | −14.9612 | −0.580606 | ||||||||
\(665\) | −8.39884 | −0.325693 | ||||||||
\(666\) | −47.4987 | −1.84054 | ||||||||
\(667\) | 50.0470 | 1.93783 | ||||||||
\(668\) | 29.4006 | 1.13755 | ||||||||
\(669\) | −46.0649 | −1.78097 | ||||||||
\(670\) | 6.75157 | 0.260836 | ||||||||
\(671\) | −4.40105 | −0.169901 | ||||||||
\(672\) | 9.50245 | 0.366565 | ||||||||
\(673\) | −20.0206 | −0.771736 | −0.385868 | − | 0.922554i | \(-0.626098\pi\) | ||||
−0.385868 | + | 0.922554i | \(0.626098\pi\) | |||||||
\(674\) | 22.2801 | 0.858196 | ||||||||
\(675\) | −5.23070 | −0.201330 | ||||||||
\(676\) | −25.1019 | −0.965458 | ||||||||
\(677\) | 15.4201 | 0.592641 | 0.296321 | − | 0.955089i | \(-0.404240\pi\) | ||||
0.296321 | + | 0.955089i | \(0.404240\pi\) | |||||||
\(678\) | −98.3958 | −3.77887 | ||||||||
\(679\) | 10.6847 | 0.410039 | ||||||||
\(680\) | −22.2889 | −0.854741 | ||||||||
\(681\) | 50.1266 | 1.92085 | ||||||||
\(682\) | 10.3385 | 0.395880 | ||||||||
\(683\) | −42.0334 | −1.60836 | −0.804182 | − | 0.594384i | \(-0.797396\pi\) | ||||
−0.804182 | + | 0.594384i | \(0.797396\pi\) | |||||||
\(684\) | −21.6841 | −0.829114 | ||||||||
\(685\) | 12.8324 | 0.490302 | ||||||||
\(686\) | −48.3866 | −1.84741 | ||||||||
\(687\) | 38.1346 | 1.45493 | ||||||||
\(688\) | 2.25998 | 0.0861610 | ||||||||
\(689\) | 13.1962 | 0.502736 | ||||||||
\(690\) | 63.0108 | 2.39878 | ||||||||
\(691\) | 9.24275 | 0.351611 | 0.175805 | − | 0.984425i | \(-0.443747\pi\) | ||||
0.175805 | + | 0.984425i | \(0.443747\pi\) | |||||||
\(692\) | 79.0573 | 3.00531 | ||||||||
\(693\) | −4.49192 | −0.170634 | ||||||||
\(694\) | 45.9518 | 1.74431 | ||||||||
\(695\) | 13.2732 | 0.503482 | ||||||||
\(696\) | −63.5464 | −2.40872 | ||||||||
\(697\) | 16.6642 | 0.631202 | ||||||||
\(698\) | −76.7288 | −2.90423 | ||||||||
\(699\) | −21.0894 | −0.797676 | ||||||||
\(700\) | 21.4461 | 0.810588 | ||||||||
\(701\) | 45.6241 | 1.72320 | 0.861599 | − | 0.507589i | \(-0.169463\pi\) | ||||
0.861599 | + | 0.507589i | \(0.169463\pi\) | |||||||
\(702\) | −11.6586 | −0.440025 | ||||||||
\(703\) | −24.4641 | −0.922681 | ||||||||
\(704\) | −10.2705 | −0.387085 | ||||||||
\(705\) | −2.07889 | −0.0782955 | ||||||||
\(706\) | 36.3699 | 1.36880 | ||||||||
\(707\) | 20.8570 | 0.784409 | ||||||||
\(708\) | 37.2269 | 1.39907 | ||||||||
\(709\) | 6.06822 | 0.227897 | 0.113948 | − | 0.993487i | \(-0.463650\pi\) | ||||
0.113948 | + | 0.993487i | \(0.463650\pi\) | |||||||
\(710\) | −32.5143 | −1.22024 | ||||||||
\(711\) | 28.3413 | 1.06288 | ||||||||
\(712\) | 28.4751 | 1.06715 | ||||||||
\(713\) | 32.8837 | 1.23150 | ||||||||
\(714\) | 39.2942 | 1.47055 | ||||||||
\(715\) | −3.80770 | −0.142400 | ||||||||
\(716\) | 28.8804 | 1.07931 | ||||||||
\(717\) | 58.5793 | 2.18768 | ||||||||
\(718\) | 43.2886 | 1.61552 | ||||||||
\(719\) | −6.19591 | −0.231069 | −0.115534 | − | 0.993303i | \(-0.536858\pi\) | ||||
−0.115534 | + | 0.993303i | \(0.536858\pi\) | |||||||
\(720\) | −8.85465 | −0.329993 | ||||||||
\(721\) | −22.7174 | −0.846041 | ||||||||
\(722\) | 28.5970 | 1.06427 | ||||||||
\(723\) | 54.3212 | 2.02023 | ||||||||
\(724\) | 36.0716 | 1.34059 | ||||||||
\(725\) | 17.8001 | 0.661080 | ||||||||
\(726\) | 5.45695 | 0.202527 | ||||||||
\(727\) | 10.8056 | 0.400759 | 0.200380 | − | 0.979718i | \(-0.435782\pi\) | ||||
0.200380 | + | 0.979718i | \(0.435782\pi\) | |||||||
\(728\) | 22.5039 | 0.834049 | ||||||||
\(729\) | −10.2030 | −0.377889 | ||||||||
\(730\) | −10.7763 | −0.398849 | ||||||||
\(731\) | −2.86320 | −0.105899 | ||||||||
\(732\) | 37.7547 | 1.39545 | ||||||||
\(733\) | 39.5114 | 1.45939 | 0.729693 | − | 0.683775i | \(-0.239663\pi\) | ||||
0.729693 | + | 0.683775i | \(0.239663\pi\) | |||||||
\(734\) | −40.9549 | −1.51167 | ||||||||
\(735\) | −9.06978 | −0.334544 | ||||||||
\(736\) | −15.3400 | −0.565441 | ||||||||
\(737\) | 1.85979 | 0.0685063 | ||||||||
\(738\) | 24.9903 | 0.919905 | ||||||||
\(739\) | −40.8264 | −1.50182 | −0.750912 | − | 0.660403i | \(-0.770386\pi\) | ||||
−0.750912 | + | 0.660403i | \(0.770386\pi\) | |||||||
\(740\) | −52.3807 | −1.92555 | ||||||||
\(741\) | 15.2558 | 0.560435 | ||||||||
\(742\) | 26.2529 | 0.963775 | ||||||||
\(743\) | −22.9122 | −0.840568 | −0.420284 | − | 0.907393i | \(-0.638070\pi\) | ||||
−0.420284 | + | 0.907393i | \(0.638070\pi\) | |||||||
\(744\) | −41.7535 | −1.53076 | ||||||||
\(745\) | 17.2004 | 0.630174 | ||||||||
\(746\) | 68.8946 | 2.52241 | ||||||||
\(747\) | 7.52999 | 0.275508 | ||||||||
\(748\) | −13.0415 | −0.476843 | ||||||||
\(749\) | −21.6935 | −0.792663 | ||||||||
\(750\) | 63.6138 | 2.32285 | ||||||||
\(751\) | 18.3110 | 0.668179 | 0.334090 | − | 0.942541i | \(-0.391571\pi\) | ||||
0.334090 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(752\) | −1.65192 | −0.0602393 | ||||||||
\(753\) | −38.7758 | −1.41307 | ||||||||
\(754\) | 39.6743 | 1.44485 | ||||||||
\(755\) | 17.4258 | 0.634188 | ||||||||
\(756\) | −15.1672 | −0.551625 | ||||||||
\(757\) | −22.2201 | −0.807603 | −0.403801 | − | 0.914847i | \(-0.632311\pi\) | ||||
−0.403801 | + | 0.914847i | \(0.632311\pi\) | |||||||
\(758\) | −56.2524 | −2.04318 | ||||||||
\(759\) | 17.3570 | 0.630019 | ||||||||
\(760\) | −17.2156 | −0.624477 | ||||||||
\(761\) | 20.1613 | 0.730848 | 0.365424 | − | 0.930841i | \(-0.380924\pi\) | ||||
0.365424 | + | 0.930841i | \(0.380924\pi\) | |||||||
\(762\) | −97.8667 | −3.54534 | ||||||||
\(763\) | 38.5627 | 1.39606 | ||||||||
\(764\) | −57.3867 | −2.07618 | ||||||||
\(765\) | 11.2181 | 0.405590 | ||||||||
\(766\) | 73.0607 | 2.63979 | ||||||||
\(767\) | −10.9420 | −0.395093 | ||||||||
\(768\) | 66.2111 | 2.38919 | ||||||||
\(769\) | −9.99809 | −0.360540 | −0.180270 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180270 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(770\) | −7.57513 | −0.272989 | ||||||||
\(771\) | 69.3758 | 2.49851 | ||||||||
\(772\) | 35.4386 | 1.27546 | ||||||||
\(773\) | 3.28603 | 0.118190 | 0.0590951 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590951 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(774\) | −4.29377 | −0.154336 | ||||||||
\(775\) | 11.6957 | 0.420120 | ||||||||
\(776\) | 21.9010 | 0.786200 | ||||||||
\(777\) | 43.4744 | 1.55963 | ||||||||
\(778\) | −60.1573 | −2.15674 | ||||||||
\(779\) | 12.8712 | 0.461158 | ||||||||
\(780\) | 32.6646 | 1.16958 | ||||||||
\(781\) | −8.95640 | −0.320485 | ||||||||
\(782\) | −63.4336 | −2.26838 | ||||||||
\(783\) | −12.5886 | −0.449881 | ||||||||
\(784\) | −7.20699 | −0.257393 | ||||||||
\(785\) | 0.561892 | 0.0200548 | ||||||||
\(786\) | −69.4991 | −2.47895 | ||||||||
\(787\) | −1.96656 | −0.0701004 | −0.0350502 | − | 0.999386i | \(-0.511159\pi\) | ||||
−0.0350502 | + | 0.999386i | \(0.511159\pi\) | |||||||
\(788\) | −93.0722 | −3.31556 | ||||||||
\(789\) | 46.7224 | 1.66336 | ||||||||
\(790\) | 47.7945 | 1.70045 | ||||||||
\(791\) | 37.6249 | 1.33779 | ||||||||
\(792\) | −9.20736 | −0.327169 | ||||||||
\(793\) | −11.0971 | −0.394071 | ||||||||
\(794\) | 69.6361 | 2.47129 | ||||||||
\(795\) | 17.9399 | 0.636262 | ||||||||
\(796\) | −15.9423 | −0.565059 | ||||||||
\(797\) | 52.4229 | 1.85691 | 0.928457 | − | 0.371440i | \(-0.121136\pi\) | ||||
0.928457 | + | 0.371440i | \(0.121136\pi\) | |||||||
\(798\) | 30.3503 | 1.07439 | ||||||||
\(799\) | 2.09284 | 0.0740393 | ||||||||
\(800\) | −5.45596 | −0.192897 | ||||||||
\(801\) | −14.3316 | −0.506382 | ||||||||
\(802\) | 18.8724 | 0.666408 | ||||||||
\(803\) | −2.96845 | −0.104754 | ||||||||
\(804\) | −15.9544 | −0.562667 | ||||||||
\(805\) | −24.0943 | −0.849213 | ||||||||
\(806\) | 26.0682 | 0.918213 | ||||||||
\(807\) | 41.4913 | 1.46056 | ||||||||
\(808\) | 42.7519 | 1.50401 | ||||||||
\(809\) | −24.2234 | −0.851650 | −0.425825 | − | 0.904806i | \(-0.640016\pi\) | ||||
−0.425825 | + | 0.904806i | \(0.640016\pi\) | |||||||
\(810\) | −39.2942 | −1.38066 | ||||||||
\(811\) | 29.6743 | 1.04201 | 0.521003 | − | 0.853555i | \(-0.325558\pi\) | ||||
0.521003 | + | 0.853555i | \(0.325558\pi\) | |||||||
\(812\) | 51.6141 | 1.81130 | ||||||||
\(813\) | 12.0658 | 0.423168 | ||||||||
\(814\) | −22.0648 | −0.773370 | ||||||||
\(815\) | 33.8639 | 1.18620 | ||||||||
\(816\) | 21.3367 | 0.746935 | ||||||||
\(817\) | −2.21149 | −0.0773704 | ||||||||
\(818\) | −17.4853 | −0.611361 | ||||||||
\(819\) | −11.3263 | −0.395772 | ||||||||
\(820\) | 27.5588 | 0.962396 | ||||||||
\(821\) | −26.5478 | −0.926524 | −0.463262 | − | 0.886221i | \(-0.653321\pi\) | ||||
−0.463262 | + | 0.886221i | \(0.653321\pi\) | |||||||
\(822\) | −46.3716 | −1.61740 | ||||||||
\(823\) | −11.5568 | −0.402843 | −0.201422 | − | 0.979505i | \(-0.564556\pi\) | ||||
−0.201422 | + | 0.979505i | \(0.564556\pi\) | |||||||
\(824\) | −46.5653 | −1.62218 | ||||||||
\(825\) | 6.17332 | 0.214928 | ||||||||
\(826\) | −21.7683 | −0.757416 | ||||||||
\(827\) | −51.2010 | −1.78043 | −0.890217 | − | 0.455537i | \(-0.849447\pi\) | ||||
−0.890217 | + | 0.455537i | \(0.849447\pi\) | |||||||
\(828\) | −62.2067 | −2.16183 | ||||||||
\(829\) | −20.4453 | −0.710094 | −0.355047 | − | 0.934848i | \(-0.615535\pi\) | ||||
−0.355047 | + | 0.934848i | \(0.615535\pi\) | |||||||
\(830\) | 12.6985 | 0.440772 | ||||||||
\(831\) | −2.99983 | −0.104063 | ||||||||
\(832\) | −25.8969 | −0.897812 | ||||||||
\(833\) | 9.13064 | 0.316358 | ||||||||
\(834\) | −47.9644 | −1.66087 | ||||||||
\(835\) | −11.7481 | −0.406559 | ||||||||
\(836\) | −10.0730 | −0.348383 | ||||||||
\(837\) | −8.27143 | −0.285902 | ||||||||
\(838\) | −33.0514 | −1.14174 | ||||||||
\(839\) | 21.5997 | 0.745705 | 0.372853 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372853 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(840\) | 30.5934 | 1.05557 | ||||||||
\(841\) | 13.8392 | 0.477215 | ||||||||
\(842\) | −24.7363 | −0.852468 | ||||||||
\(843\) | −64.0991 | −2.20769 | ||||||||
\(844\) | 88.4029 | 3.04295 | ||||||||
\(845\) | 10.0304 | 0.345055 | ||||||||
\(846\) | 3.13850 | 0.107904 | ||||||||
\(847\) | −2.08665 | −0.0716981 | ||||||||
\(848\) | 14.2553 | 0.489529 | ||||||||
\(849\) | −18.8446 | −0.646746 | ||||||||
\(850\) | −22.5613 | −0.773846 | ||||||||
\(851\) | −70.1818 | −2.40580 | ||||||||
\(852\) | 76.8330 | 2.63226 | ||||||||
\(853\) | −14.3233 | −0.490422 | −0.245211 | − | 0.969470i | \(-0.578857\pi\) | ||||
−0.245211 | + | 0.969470i | \(0.578857\pi\) | |||||||
\(854\) | −22.0769 | −0.755457 | ||||||||
\(855\) | 8.66467 | 0.296326 | ||||||||
\(856\) | −44.4665 | −1.51983 | ||||||||
\(857\) | −3.80935 | −0.130125 | −0.0650625 | − | 0.997881i | \(-0.520725\pi\) | ||||
−0.0650625 | + | 0.997881i | \(0.520725\pi\) | |||||||
\(858\) | 13.7596 | 0.469744 | ||||||||
\(859\) | 27.9709 | 0.954355 | 0.477178 | − | 0.878807i | \(-0.341660\pi\) | ||||
0.477178 | + | 0.878807i | \(0.341660\pi\) | |||||||
\(860\) | −4.73509 | −0.161465 | ||||||||
\(861\) | −22.8730 | −0.779509 | ||||||||
\(862\) | −22.1692 | −0.755084 | ||||||||
\(863\) | −1.53959 | −0.0524081 | −0.0262041 | − | 0.999657i | \(-0.508342\pi\) | ||||
−0.0262041 | + | 0.999657i | \(0.508342\pi\) | |||||||
\(864\) | 3.85857 | 0.131271 | ||||||||
\(865\) | −31.5901 | −1.07410 | ||||||||
\(866\) | 29.2827 | 0.995067 | ||||||||
\(867\) | 11.5574 | 0.392511 | ||||||||
\(868\) | 33.9133 | 1.15109 | ||||||||
\(869\) | 13.1655 | 0.446609 | ||||||||
\(870\) | 53.9360 | 1.82860 | ||||||||
\(871\) | 4.68942 | 0.158895 | ||||||||
\(872\) | 79.0444 | 2.67678 | ||||||||
\(873\) | −11.0228 | −0.373066 | ||||||||
\(874\) | −48.9952 | −1.65729 | ||||||||
\(875\) | −24.3249 | −0.822331 | ||||||||
\(876\) | 25.4650 | 0.860384 | ||||||||
\(877\) | 23.8958 | 0.806903 | 0.403452 | − | 0.915001i | \(-0.367810\pi\) | ||||
0.403452 | + | 0.915001i | \(0.367810\pi\) | |||||||
\(878\) | 36.0009 | 1.21497 | ||||||||
\(879\) | 68.8920 | 2.32367 | ||||||||
\(880\) | −4.11329 | −0.138659 | ||||||||
\(881\) | −46.0867 | −1.55270 | −0.776351 | − | 0.630301i | \(-0.782931\pi\) | ||||
−0.776351 | + | 0.630301i | \(0.782931\pi\) | |||||||
\(882\) | 13.6927 | 0.461056 | ||||||||
\(883\) | −18.1485 | −0.610745 | −0.305372 | − | 0.952233i | \(-0.598781\pi\) | ||||
−0.305372 | + | 0.952233i | \(0.598781\pi\) | |||||||
\(884\) | −32.8837 | −1.10600 | ||||||||
\(885\) | −14.8753 | −0.500029 | ||||||||
\(886\) | 71.5515 | 2.40382 | ||||||||
\(887\) | 22.6102 | 0.759177 | 0.379588 | − | 0.925155i | \(-0.376066\pi\) | ||||
0.379588 | + | 0.925155i | \(0.376066\pi\) | |||||||
\(888\) | 89.1121 | 2.99041 | ||||||||
\(889\) | 37.4226 | 1.25511 | ||||||||
\(890\) | −24.1687 | −0.810136 | ||||||||
\(891\) | −10.8240 | −0.362617 | ||||||||
\(892\) | 76.6921 | 2.56784 | ||||||||
\(893\) | 1.61648 | 0.0540933 | ||||||||
\(894\) | −62.1557 | −2.07880 | ||||||||
\(895\) | −11.5402 | −0.385746 | ||||||||
\(896\) | −43.1475 | −1.44146 | ||||||||
\(897\) | 43.7653 | 1.46128 | ||||||||
\(898\) | −97.6183 | −3.25756 | ||||||||
\(899\) | 28.1478 | 0.938780 | ||||||||
\(900\) | −22.1249 | −0.737497 | ||||||||
\(901\) | −18.0602 | −0.601674 | ||||||||
\(902\) | 11.6088 | 0.386532 | ||||||||
\(903\) | 3.92998 | 0.130781 | ||||||||
\(904\) | 77.1222 | 2.56504 | ||||||||
\(905\) | −14.4137 | −0.479128 | ||||||||
\(906\) | −62.9701 | −2.09204 | ||||||||
\(907\) | −25.5160 | −0.847246 | −0.423623 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(908\) | −83.4542 | −2.76953 | ||||||||
\(909\) | −21.5172 | −0.713679 | ||||||||
\(910\) | −19.1005 | −0.633176 | ||||||||
\(911\) | 8.30911 | 0.275293 | 0.137647 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137647 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(912\) | 16.4802 | 0.545713 | ||||||||
\(913\) | 3.49794 | 0.115765 | ||||||||
\(914\) | −60.7192 | −2.00841 | ||||||||
\(915\) | −15.0862 | −0.498736 | ||||||||
\(916\) | −63.4892 | −2.09774 | ||||||||
\(917\) | 26.5753 | 0.877595 | ||||||||
\(918\) | 15.9558 | 0.526621 | ||||||||
\(919\) | −40.6810 | −1.34194 | −0.670972 | − | 0.741483i | \(-0.734123\pi\) | ||||
−0.670972 | + | 0.741483i | \(0.734123\pi\) | |||||||
\(920\) | −49.3876 | −1.62826 | ||||||||
\(921\) | −46.8900 | −1.54508 | ||||||||
\(922\) | −79.4951 | −2.61803 | ||||||||
\(923\) | −22.5833 | −0.743340 | ||||||||
\(924\) | 17.9005 | 0.588882 | ||||||||
\(925\) | −24.9614 | −0.820725 | ||||||||
\(926\) | 25.4165 | 0.835237 | ||||||||
\(927\) | 23.4364 | 0.769754 | ||||||||
\(928\) | −13.1308 | −0.431038 | ||||||||
\(929\) | −53.8706 | −1.76744 | −0.883718 | − | 0.468019i | \(-0.844968\pi\) | ||||
−0.883718 | + | 0.468019i | \(0.844968\pi\) | |||||||
\(930\) | 35.4389 | 1.16209 | ||||||||
\(931\) | 7.05237 | 0.231132 | ||||||||
\(932\) | 35.1112 | 1.15010 | ||||||||
\(933\) | 68.5137 | 2.24304 | ||||||||
\(934\) | 31.7495 | 1.03888 | ||||||||
\(935\) | 5.21118 | 0.170424 | ||||||||
\(936\) | −23.2161 | −0.758843 | ||||||||
\(937\) | 20.2956 | 0.663029 | 0.331514 | − | 0.943450i | \(-0.392440\pi\) | ||||
0.331514 | + | 0.943450i | \(0.392440\pi\) | |||||||
\(938\) | 9.32926 | 0.304611 | ||||||||
\(939\) | 68.2088 | 2.22591 | ||||||||
\(940\) | 3.46108 | 0.112888 | ||||||||
\(941\) | 19.0799 | 0.621987 | 0.310994 | − | 0.950412i | \(-0.399338\pi\) | ||||
0.310994 | + | 0.950412i | \(0.399338\pi\) | |||||||
\(942\) | −2.03047 | −0.0661562 | ||||||||
\(943\) | 36.9244 | 1.20242 | ||||||||
\(944\) | −11.8202 | −0.384714 | ||||||||
\(945\) | 6.06059 | 0.197151 | ||||||||
\(946\) | −1.99460 | −0.0648501 | ||||||||
\(947\) | −6.78891 | −0.220610 | −0.110305 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110305 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(948\) | −112.941 | −3.66816 | ||||||||
\(949\) | −7.48487 | −0.242969 | ||||||||
\(950\) | −17.4260 | −0.565374 | ||||||||
\(951\) | 18.2161 | 0.590696 | ||||||||
\(952\) | −30.7986 | −0.998189 | ||||||||
\(953\) | −14.6571 | −0.474790 | −0.237395 | − | 0.971413i | \(-0.576294\pi\) | ||||
−0.237395 | + | 0.971413i | \(0.576294\pi\) | |||||||
\(954\) | −27.0838 | −0.876871 | ||||||||
\(955\) | 22.9309 | 0.742027 | ||||||||
\(956\) | −97.5269 | −3.15425 | ||||||||
\(957\) | 14.8572 | 0.480266 | ||||||||
\(958\) | 84.8045 | 2.73991 | ||||||||
\(959\) | 17.7317 | 0.572588 | ||||||||
\(960\) | −35.2060 | −1.13627 | ||||||||
\(961\) | −12.5054 | −0.403399 | ||||||||
\(962\) | −55.6358 | −1.79377 | ||||||||
\(963\) | 22.3801 | 0.721189 | ||||||||
\(964\) | −90.4377 | −2.91280 | ||||||||
\(965\) | −14.1607 | −0.455851 | ||||||||
\(966\) | 87.0678 | 2.80136 | ||||||||
\(967\) | 32.5328 | 1.04618 | 0.523091 | − | 0.852277i | \(-0.324779\pi\) | ||||
0.523091 | + | 0.852277i | \(0.324779\pi\) | |||||||
\(968\) | −4.27714 | −0.137472 | ||||||||
\(969\) | −20.8789 | −0.670728 | ||||||||
\(970\) | −18.5888 | −0.596851 | ||||||||
\(971\) | −39.3080 | −1.26146 | −0.630728 | − | 0.776004i | \(-0.717243\pi\) | ||||
−0.630728 | + | 0.776004i | \(0.717243\pi\) | |||||||
\(972\) | 71.0483 | 2.27888 | ||||||||
\(973\) | 18.3408 | 0.587979 | ||||||||
\(974\) | −70.4107 | −2.25610 | ||||||||
\(975\) | 15.5659 | 0.498507 | ||||||||
\(976\) | −11.9878 | −0.383719 | ||||||||
\(977\) | 0.321298 | 0.0102792 | 0.00513962 | − | 0.999987i | \(-0.498364\pi\) | ||||
0.00513962 | + | 0.999987i | \(0.498364\pi\) | |||||||
\(978\) | −122.371 | −3.91300 | ||||||||
\(979\) | −6.65752 | −0.212775 | ||||||||
\(980\) | 15.1000 | 0.482352 | ||||||||
\(981\) | −39.7833 | −1.27018 | ||||||||
\(982\) | 21.3547 | 0.681457 | ||||||||
\(983\) | 28.6296 | 0.913143 | 0.456572 | − | 0.889687i | \(-0.349077\pi\) | ||||
0.456572 | + | 0.889687i | \(0.349077\pi\) | |||||||
\(984\) | −46.8842 | −1.49461 | ||||||||
\(985\) | 37.1903 | 1.18498 | ||||||||
\(986\) | −54.2979 | −1.72920 | ||||||||
\(987\) | −2.87259 | −0.0914355 | ||||||||
\(988\) | −25.3989 | −0.808047 | ||||||||
\(989\) | −6.34426 | −0.201736 | ||||||||
\(990\) | 7.81489 | 0.248373 | ||||||||
\(991\) | 50.7278 | 1.61142 | 0.805711 | − | 0.592309i | \(-0.201784\pi\) | ||||
0.805711 | + | 0.592309i | \(0.201784\pi\) | |||||||
\(992\) | −8.62764 | −0.273928 | ||||||||
\(993\) | −41.6368 | −1.32130 | ||||||||
\(994\) | −44.9279 | −1.42503 | ||||||||
\(995\) | 6.37030 | 0.201952 | ||||||||
\(996\) | −30.0073 | −0.950818 | ||||||||
\(997\) | −14.1408 | −0.447844 | −0.223922 | − | 0.974607i | \(-0.571886\pi\) | ||||
−0.223922 | + | 0.974607i | \(0.571886\pi\) | |||||||
\(998\) | −63.5412 | −2.01136 | ||||||||
\(999\) | 17.6532 | 0.558524 |
(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 | 6017.2.a.e.1.9 | ✓ | 119 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.e.1.9 | ✓ | 119 | 1.1 | even | 1 | trivial |