Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.10281 | −1.48691 | −0.743457 | − | 0.668784i | \(-0.766815\pi\) | ||||
−0.743457 | + | 0.668784i | \(0.766815\pi\) | |||||||
\(3\) | −1.04272 | −0.602014 | −0.301007 | − | 0.953622i | \(-0.597323\pi\) | ||||
−0.301007 | + | 0.953622i | \(0.597323\pi\) | |||||||
\(4\) | 2.42182 | 1.21091 | ||||||||
\(5\) | 3.50696 | 1.56836 | 0.784180 | − | 0.620534i | \(-0.213084\pi\) | ||||
0.784180 | + | 0.620534i | \(0.213084\pi\) | |||||||
\(6\) | 2.19264 | 0.895143 | ||||||||
\(7\) | −3.91864 | −1.48111 | −0.740554 | − | 0.671997i | \(-0.765437\pi\) | ||||
−0.740554 | + | 0.671997i | \(0.765437\pi\) | |||||||
\(8\) | −0.887016 | −0.313608 | ||||||||
\(9\) | −1.91274 | −0.637579 | ||||||||
\(10\) | −7.37448 | −2.33201 | ||||||||
\(11\) | −0.686935 | −0.207119 | −0.103559 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103559 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(12\) | −2.52528 | −0.728986 | ||||||||
\(13\) | −0.0835199 | −0.0231643 | −0.0115821 | − | 0.999933i | \(-0.503687\pi\) | ||||
−0.0115821 | + | 0.999933i | \(0.503687\pi\) | |||||||
\(14\) | 8.24017 | 2.20228 | ||||||||
\(15\) | −3.65677 | −0.944174 | ||||||||
\(16\) | −2.97842 | −0.744604 | ||||||||
\(17\) | −6.13443 | −1.48782 | −0.743909 | − | 0.668281i | \(-0.767030\pi\) | ||||
−0.743909 | + | 0.668281i | \(0.767030\pi\) | |||||||
\(18\) | 4.02213 | 0.948025 | ||||||||
\(19\) | −2.60752 | −0.598206 | −0.299103 | − | 0.954221i | \(-0.596687\pi\) | ||||
−0.299103 | + | 0.954221i | \(0.596687\pi\) | |||||||
\(20\) | 8.49323 | 1.89914 | ||||||||
\(21\) | 4.08604 | 0.891648 | ||||||||
\(22\) | 1.44450 | 0.307968 | ||||||||
\(23\) | 6.11523 | 1.27511 | 0.637557 | − | 0.770403i | \(-0.279945\pi\) | ||||
0.637557 | + | 0.770403i | \(0.279945\pi\) | |||||||
\(24\) | 0.924909 | 0.188796 | ||||||||
\(25\) | 7.29875 | 1.45975 | ||||||||
\(26\) | 0.175627 | 0.0344433 | ||||||||
\(27\) | 5.12260 | 0.985846 | ||||||||
\(28\) | −9.49026 | −1.79349 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 7.68951 | 1.40391 | ||||||||
\(31\) | 8.22281 | 1.47686 | 0.738430 | − | 0.674330i | \(-0.235567\pi\) | ||||
0.738430 | + | 0.674330i | \(0.235567\pi\) | |||||||
\(32\) | 8.03709 | 1.42077 | ||||||||
\(33\) | 0.716281 | 0.124688 | ||||||||
\(34\) | 12.8996 | 2.21226 | ||||||||
\(35\) | −13.7425 | −2.32291 | ||||||||
\(36\) | −4.63231 | −0.772052 | ||||||||
\(37\) | 3.10413 | 0.510315 | 0.255158 | − | 0.966899i | \(-0.417873\pi\) | ||||
0.255158 | + | 0.966899i | \(0.417873\pi\) | |||||||
\(38\) | 5.48312 | 0.889480 | ||||||||
\(39\) | 0.0870878 | 0.0139452 | ||||||||
\(40\) | −3.11073 | −0.491849 | ||||||||
\(41\) | 2.48308 | 0.387792 | 0.193896 | − | 0.981022i | \(-0.437888\pi\) | ||||
0.193896 | + | 0.981022i | \(0.437888\pi\) | |||||||
\(42\) | −8.59219 | −1.32580 | ||||||||
\(43\) | 3.60914 | 0.550389 | 0.275194 | − | 0.961389i | \(-0.411258\pi\) | ||||
0.275194 | + | 0.961389i | \(0.411258\pi\) | |||||||
\(44\) | −1.66364 | −0.250803 | ||||||||
\(45\) | −6.70789 | −0.999953 | ||||||||
\(46\) | −12.8592 | −1.89598 | ||||||||
\(47\) | 4.95268 | 0.722422 | 0.361211 | − | 0.932484i | \(-0.382363\pi\) | ||||
0.361211 | + | 0.932484i | \(0.382363\pi\) | |||||||
\(48\) | 3.10565 | 0.448262 | ||||||||
\(49\) | 8.35576 | 1.19368 | ||||||||
\(50\) | −15.3479 | −2.17052 | ||||||||
\(51\) | 6.39649 | 0.895688 | ||||||||
\(52\) | −0.202271 | −0.0280499 | ||||||||
\(53\) | 2.09829 | 0.288222 | 0.144111 | − | 0.989562i | \(-0.453968\pi\) | ||||
0.144111 | + | 0.989562i | \(0.453968\pi\) | |||||||
\(54\) | −10.7719 | −1.46587 | ||||||||
\(55\) | −2.40905 | −0.324837 | ||||||||
\(56\) | 3.47590 | 0.464487 | ||||||||
\(57\) | 2.71891 | 0.360128 | ||||||||
\(58\) | 2.10281 | 0.276113 | ||||||||
\(59\) | 0.107135 | 0.0139479 | 0.00697393 | − | 0.999976i | \(-0.497780\pi\) | ||||
0.00697393 | + | 0.999976i | \(0.497780\pi\) | |||||||
\(60\) | −8.85606 | −1.14331 | ||||||||
\(61\) | 5.60696 | 0.717898 | 0.358949 | − | 0.933357i | \(-0.383135\pi\) | ||||
0.358949 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(62\) | −17.2910 | −2.19596 | ||||||||
\(63\) | 7.49533 | 0.944323 | ||||||||
\(64\) | −10.9437 | −1.36796 | ||||||||
\(65\) | −0.292901 | −0.0363299 | ||||||||
\(66\) | −1.50620 | −0.185401 | ||||||||
\(67\) | 4.35469 | 0.532010 | 0.266005 | − | 0.963972i | \(-0.414296\pi\) | ||||
0.266005 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(68\) | −14.8565 | −1.80162 | ||||||||
\(69\) | −6.37647 | −0.767637 | ||||||||
\(70\) | 28.8979 | 3.45396 | ||||||||
\(71\) | −13.1621 | −1.56205 | −0.781027 | − | 0.624497i | \(-0.785304\pi\) | ||||
−0.781027 | + | 0.624497i | \(0.785304\pi\) | |||||||
\(72\) | 1.69663 | 0.199950 | ||||||||
\(73\) | −6.23169 | −0.729364 | −0.364682 | − | 0.931132i | \(-0.618822\pi\) | ||||
−0.364682 | + | 0.931132i | \(0.618822\pi\) | |||||||
\(74\) | −6.52740 | −0.758795 | ||||||||
\(75\) | −7.61055 | −0.878791 | ||||||||
\(76\) | −6.31495 | −0.724374 | ||||||||
\(77\) | 2.69185 | 0.306765 | ||||||||
\(78\) | −0.183129 | −0.0207353 | ||||||||
\(79\) | 7.29203 | 0.820417 | 0.410209 | − | 0.911992i | \(-0.365456\pi\) | ||||
0.410209 | + | 0.911992i | \(0.365456\pi\) | |||||||
\(80\) | −10.4452 | −1.16781 | ||||||||
\(81\) | 0.396773 | 0.0440858 | ||||||||
\(82\) | −5.22146 | −0.576614 | ||||||||
\(83\) | 0.984862 | 0.108103 | 0.0540513 | − | 0.998538i | \(-0.482787\pi\) | ||||
0.0540513 | + | 0.998538i | \(0.482787\pi\) | |||||||
\(84\) | 9.89568 | 1.07971 | ||||||||
\(85\) | −21.5132 | −2.33343 | ||||||||
\(86\) | −7.58935 | −0.818381 | ||||||||
\(87\) | 1.04272 | 0.111791 | ||||||||
\(88\) | 0.609323 | 0.0649541 | ||||||||
\(89\) | −12.9439 | −1.37205 | −0.686026 | − | 0.727577i | \(-0.740646\pi\) | ||||
−0.686026 | + | 0.727577i | \(0.740646\pi\) | |||||||
\(90\) | 14.1054 | 1.48684 | ||||||||
\(91\) | 0.327285 | 0.0343088 | ||||||||
\(92\) | 14.8100 | 1.54405 | ||||||||
\(93\) | −8.57408 | −0.889091 | ||||||||
\(94\) | −10.4146 | −1.07418 | ||||||||
\(95\) | −9.14446 | −0.938202 | ||||||||
\(96\) | −8.38043 | −0.855324 | ||||||||
\(97\) | −10.0691 | −1.02236 | −0.511179 | − | 0.859475i | \(-0.670791\pi\) | ||||
−0.511179 | + | 0.859475i | \(0.670791\pi\) | |||||||
\(98\) | −17.5706 | −1.77490 | ||||||||
\(99\) | 1.31393 | 0.132055 | ||||||||
\(100\) | 17.6763 | 1.76763 | ||||||||
\(101\) | −7.28969 | −0.725351 | −0.362675 | − | 0.931916i | \(-0.618137\pi\) | ||||
−0.362675 | + | 0.931916i | \(0.618137\pi\) | |||||||
\(102\) | −13.4506 | −1.33181 | ||||||||
\(103\) | 0.147878 | 0.0145708 | 0.00728542 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728542 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(104\) | 0.0740836 | 0.00726449 | ||||||||
\(105\) | 14.3296 | 1.39842 | ||||||||
\(106\) | −4.41231 | −0.428562 | ||||||||
\(107\) | −0.866579 | −0.0837754 | −0.0418877 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418877 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(108\) | 12.4060 | 1.19377 | ||||||||
\(109\) | −1.24876 | −0.119610 | −0.0598048 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598048 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(110\) | 5.06579 | 0.483004 | ||||||||
\(111\) | −3.23673 | −0.307217 | ||||||||
\(112\) | 11.6714 | 1.10284 | ||||||||
\(113\) | −8.99068 | −0.845772 | −0.422886 | − | 0.906183i | \(-0.638983\pi\) | ||||
−0.422886 | + | 0.906183i | \(0.638983\pi\) | |||||||
\(114\) | −5.71736 | −0.535480 | ||||||||
\(115\) | 21.4459 | 1.99984 | ||||||||
\(116\) | −2.42182 | −0.224861 | ||||||||
\(117\) | 0.159752 | 0.0147690 | ||||||||
\(118\) | −0.225286 | −0.0207392 | ||||||||
\(119\) | 24.0386 | 2.20362 | ||||||||
\(120\) | 3.24362 | 0.296100 | ||||||||
\(121\) | −10.5281 | −0.957102 | ||||||||
\(122\) | −11.7904 | −1.06745 | ||||||||
\(123\) | −2.58916 | −0.233456 | ||||||||
\(124\) | 19.9142 | 1.78835 | ||||||||
\(125\) | 8.06163 | 0.721054 | ||||||||
\(126\) | −15.7613 | −1.40413 | ||||||||
\(127\) | 3.40450 | 0.302101 | 0.151050 | − | 0.988526i | \(-0.451734\pi\) | ||||
0.151050 | + | 0.988526i | \(0.451734\pi\) | |||||||
\(128\) | 6.93830 | 0.613265 | ||||||||
\(129\) | −3.76332 | −0.331342 | ||||||||
\(130\) | 0.615916 | 0.0540194 | ||||||||
\(131\) | −3.71368 | −0.324465 | −0.162233 | − | 0.986753i | \(-0.551870\pi\) | ||||
−0.162233 | + | 0.986753i | \(0.551870\pi\) | |||||||
\(132\) | 1.73471 | 0.150987 | ||||||||
\(133\) | 10.2179 | 0.886007 | ||||||||
\(134\) | −9.15710 | −0.791053 | ||||||||
\(135\) | 17.9648 | 1.54616 | ||||||||
\(136\) | 5.44134 | 0.466591 | ||||||||
\(137\) | 19.8097 | 1.69245 | 0.846227 | − | 0.532823i | \(-0.178869\pi\) | ||||
0.846227 | + | 0.532823i | \(0.178869\pi\) | |||||||
\(138\) | 13.4085 | 1.14141 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | −33.2819 | −2.81284 | ||||||||
\(141\) | −5.16425 | −0.434908 | ||||||||
\(142\) | 27.6774 | 2.32264 | ||||||||
\(143\) | 0.0573728 | 0.00479776 | ||||||||
\(144\) | 5.69693 | 0.474744 | ||||||||
\(145\) | −3.50696 | −0.291237 | ||||||||
\(146\) | 13.1041 | 1.08450 | ||||||||
\(147\) | −8.71271 | −0.718612 | ||||||||
\(148\) | 7.51765 | 0.617947 | ||||||||
\(149\) | −5.54235 | −0.454047 | −0.227023 | − | 0.973889i | \(-0.572899\pi\) | ||||
−0.227023 | + | 0.973889i | \(0.572899\pi\) | |||||||
\(150\) | 16.0036 | 1.30669 | ||||||||
\(151\) | −9.93145 | −0.808210 | −0.404105 | − | 0.914713i | \(-0.632417\pi\) | ||||
−0.404105 | + | 0.914713i | \(0.632417\pi\) | |||||||
\(152\) | 2.31291 | 0.187602 | ||||||||
\(153\) | 11.7336 | 0.948602 | ||||||||
\(154\) | −5.66047 | −0.456133 | ||||||||
\(155\) | 28.8370 | 2.31625 | ||||||||
\(156\) | 0.210911 | 0.0168864 | ||||||||
\(157\) | −8.23938 | −0.657574 | −0.328787 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328787 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(158\) | −15.3338 | −1.21989 | ||||||||
\(159\) | −2.18793 | −0.173514 | ||||||||
\(160\) | 28.1857 | 2.22828 | ||||||||
\(161\) | −23.9634 | −1.88858 | ||||||||
\(162\) | −0.834339 | −0.0655518 | ||||||||
\(163\) | 5.27298 | 0.413012 | 0.206506 | − | 0.978445i | \(-0.433791\pi\) | ||||
0.206506 | + | 0.978445i | \(0.433791\pi\) | |||||||
\(164\) | 6.01359 | 0.469582 | ||||||||
\(165\) | 2.51197 | 0.195556 | ||||||||
\(166\) | −2.07098 | −0.160739 | ||||||||
\(167\) | −7.03096 | −0.544072 | −0.272036 | − | 0.962287i | \(-0.587697\pi\) | ||||
−0.272036 | + | 0.962287i | \(0.587697\pi\) | |||||||
\(168\) | −3.62439 | −0.279628 | ||||||||
\(169\) | −12.9930 | −0.999463 | ||||||||
\(170\) | 45.2382 | 3.46961 | ||||||||
\(171\) | 4.98750 | 0.381403 | ||||||||
\(172\) | 8.74070 | 0.666472 | ||||||||
\(173\) | −12.9429 | −0.984028 | −0.492014 | − | 0.870587i | \(-0.663739\pi\) | ||||
−0.492014 | + | 0.870587i | \(0.663739\pi\) | |||||||
\(174\) | −2.19264 | −0.166224 | ||||||||
\(175\) | −28.6012 | −2.16205 | ||||||||
\(176\) | 2.04598 | 0.154222 | ||||||||
\(177\) | −0.111712 | −0.00839680 | ||||||||
\(178\) | 27.2186 | 2.04012 | ||||||||
\(179\) | −8.23835 | −0.615763 | −0.307882 | − | 0.951425i | \(-0.599620\pi\) | ||||
−0.307882 | + | 0.951425i | \(0.599620\pi\) | |||||||
\(180\) | −16.2453 | −1.21085 | ||||||||
\(181\) | −2.63754 | −0.196047 | −0.0980234 | − | 0.995184i | \(-0.531252\pi\) | ||||
−0.0980234 | + | 0.995184i | \(0.531252\pi\) | |||||||
\(182\) | −0.688219 | −0.0510142 | ||||||||
\(183\) | −5.84649 | −0.432185 | ||||||||
\(184\) | −5.42431 | −0.399886 | ||||||||
\(185\) | 10.8860 | 0.800358 | ||||||||
\(186\) | 18.0297 | 1.32200 | ||||||||
\(187\) | 4.21396 | 0.308155 | ||||||||
\(188\) | 11.9945 | 0.874790 | ||||||||
\(189\) | −20.0737 | −1.46014 | ||||||||
\(190\) | 19.2291 | 1.39502 | ||||||||
\(191\) | −9.09683 | −0.658223 | −0.329112 | − | 0.944291i | \(-0.606749\pi\) | ||||
−0.329112 | + | 0.944291i | \(0.606749\pi\) | |||||||
\(192\) | 11.4112 | 0.823530 | ||||||||
\(193\) | 4.90942 | 0.353388 | 0.176694 | − | 0.984266i | \(-0.443460\pi\) | ||||
0.176694 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(194\) | 21.1733 | 1.52016 | ||||||||
\(195\) | 0.305413 | 0.0218711 | ||||||||
\(196\) | 20.2362 | 1.44544 | ||||||||
\(197\) | −10.4899 | −0.747376 | −0.373688 | − | 0.927554i | \(-0.621907\pi\) | ||||
−0.373688 | + | 0.927554i | \(0.621907\pi\) | |||||||
\(198\) | −2.76294 | −0.196354 | ||||||||
\(199\) | −6.71681 | −0.476142 | −0.238071 | − | 0.971248i | \(-0.576515\pi\) | ||||
−0.238071 | + | 0.971248i | \(0.576515\pi\) | |||||||
\(200\) | −6.47411 | −0.457789 | ||||||||
\(201\) | −4.54072 | −0.320277 | ||||||||
\(202\) | 15.3288 | 1.07853 | ||||||||
\(203\) | 3.91864 | 0.275035 | ||||||||
\(204\) | 15.4912 | 1.08460 | ||||||||
\(205\) | 8.70806 | 0.608198 | ||||||||
\(206\) | −0.310960 | −0.0216656 | ||||||||
\(207\) | −11.6968 | −0.812986 | ||||||||
\(208\) | 0.248757 | 0.0172482 | ||||||||
\(209\) | 1.79120 | 0.123900 | ||||||||
\(210\) | −30.1324 | −2.07934 | ||||||||
\(211\) | −10.4311 | −0.718108 | −0.359054 | − | 0.933317i | \(-0.616901\pi\) | ||||
−0.359054 | + | 0.933317i | \(0.616901\pi\) | |||||||
\(212\) | 5.08169 | 0.349012 | ||||||||
\(213\) | 13.7244 | 0.940379 | ||||||||
\(214\) | 1.82225 | 0.124567 | ||||||||
\(215\) | 12.6571 | 0.863207 | ||||||||
\(216\) | −4.54383 | −0.309169 | ||||||||
\(217\) | −32.2222 | −2.18739 | ||||||||
\(218\) | 2.62591 | 0.177849 | ||||||||
\(219\) | 6.49790 | 0.439087 | ||||||||
\(220\) | −5.83430 | −0.393349 | ||||||||
\(221\) | 0.512347 | 0.0344642 | ||||||||
\(222\) | 6.80625 | 0.456805 | ||||||||
\(223\) | 18.0043 | 1.20566 | 0.602828 | − | 0.797871i | \(-0.294040\pi\) | ||||
0.602828 | + | 0.797871i | \(0.294040\pi\) | |||||||
\(224\) | −31.4945 | −2.10431 | ||||||||
\(225\) | −13.9606 | −0.930706 | ||||||||
\(226\) | 18.9057 | 1.25759 | ||||||||
\(227\) | 23.4123 | 1.55393 | 0.776963 | − | 0.629546i | \(-0.216759\pi\) | ||||
0.776963 | + | 0.629546i | \(0.216759\pi\) | |||||||
\(228\) | 6.58472 | 0.436084 | ||||||||
\(229\) | 16.6858 | 1.10263 | 0.551314 | − | 0.834298i | \(-0.314127\pi\) | ||||
0.551314 | + | 0.834298i | \(0.314127\pi\) | |||||||
\(230\) | −45.0967 | −2.97359 | ||||||||
\(231\) | −2.80685 | −0.184677 | ||||||||
\(232\) | 0.887016 | 0.0582355 | ||||||||
\(233\) | −3.34132 | −0.218897 | −0.109449 | − | 0.993992i | \(-0.534909\pi\) | ||||
−0.109449 | + | 0.993992i | \(0.534909\pi\) | |||||||
\(234\) | −0.335928 | −0.0219603 | ||||||||
\(235\) | 17.3688 | 1.13302 | ||||||||
\(236\) | 0.259463 | 0.0168896 | ||||||||
\(237\) | −7.60354 | −0.493903 | ||||||||
\(238\) | −50.5488 | −3.27659 | ||||||||
\(239\) | 18.0675 | 1.16869 | 0.584344 | − | 0.811506i | \(-0.301352\pi\) | ||||
0.584344 | + | 0.811506i | \(0.301352\pi\) | |||||||
\(240\) | 10.8914 | 0.703036 | ||||||||
\(241\) | −17.7528 | −1.14356 | −0.571779 | − | 0.820407i | \(-0.693747\pi\) | ||||
−0.571779 | + | 0.820407i | \(0.693747\pi\) | |||||||
\(242\) | 22.1387 | 1.42313 | ||||||||
\(243\) | −15.7815 | −1.01239 | ||||||||
\(244\) | 13.5791 | 0.869311 | ||||||||
\(245\) | 29.3033 | 1.87212 | ||||||||
\(246\) | 5.44451 | 0.347130 | ||||||||
\(247\) | 0.217780 | 0.0138570 | ||||||||
\(248\) | −7.29377 | −0.463155 | ||||||||
\(249\) | −1.02693 | −0.0650793 | ||||||||
\(250\) | −16.9521 | −1.07215 | ||||||||
\(251\) | 9.22426 | 0.582230 | 0.291115 | − | 0.956688i | \(-0.405974\pi\) | ||||
0.291115 | + | 0.956688i | \(0.405974\pi\) | |||||||
\(252\) | 18.1524 | 1.14349 | ||||||||
\(253\) | −4.20077 | −0.264100 | ||||||||
\(254\) | −7.15903 | −0.449198 | ||||||||
\(255\) | 22.4322 | 1.40476 | ||||||||
\(256\) | 7.29737 | 0.456086 | ||||||||
\(257\) | −5.31611 | −0.331610 | −0.165805 | − | 0.986159i | \(-0.553022\pi\) | ||||
−0.165805 | + | 0.986159i | \(0.553022\pi\) | |||||||
\(258\) | 7.91356 | 0.492677 | ||||||||
\(259\) | −12.1640 | −0.755832 | ||||||||
\(260\) | −0.709354 | −0.0439923 | ||||||||
\(261\) | 1.91274 | 0.118395 | ||||||||
\(262\) | 7.80917 | 0.482452 | ||||||||
\(263\) | −0.378874 | −0.0233624 | −0.0116812 | − | 0.999932i | \(-0.503718\pi\) | ||||
−0.0116812 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(264\) | −0.635353 | −0.0391033 | ||||||||
\(265\) | 7.35862 | 0.452036 | ||||||||
\(266\) | −21.4864 | −1.31742 | ||||||||
\(267\) | 13.4969 | 0.825994 | ||||||||
\(268\) | 10.5463 | 0.644217 | ||||||||
\(269\) | 19.8767 | 1.21190 | 0.605952 | − | 0.795501i | \(-0.292792\pi\) | ||||
0.605952 | + | 0.795501i | \(0.292792\pi\) | |||||||
\(270\) | −37.7765 | −2.29901 | ||||||||
\(271\) | −15.6441 | −0.950311 | −0.475155 | − | 0.879902i | \(-0.657608\pi\) | ||||
−0.475155 | + | 0.879902i | \(0.657608\pi\) | |||||||
\(272\) | 18.2709 | 1.10784 | ||||||||
\(273\) | −0.341266 | −0.0206544 | ||||||||
\(274\) | −41.6560 | −2.51653 | ||||||||
\(275\) | −5.01377 | −0.302342 | ||||||||
\(276\) | −15.4427 | −0.929541 | ||||||||
\(277\) | 11.8379 | 0.711271 | 0.355635 | − | 0.934625i | \(-0.384264\pi\) | ||||
0.355635 | + | 0.934625i | \(0.384264\pi\) | |||||||
\(278\) | 2.10281 | 0.126118 | ||||||||
\(279\) | −15.7281 | −0.941615 | ||||||||
\(280\) | 12.1898 | 0.728482 | ||||||||
\(281\) | −25.6727 | −1.53150 | −0.765752 | − | 0.643136i | \(-0.777633\pi\) | ||||
−0.765752 | + | 0.643136i | \(0.777633\pi\) | |||||||
\(282\) | 10.8595 | 0.646671 | ||||||||
\(283\) | −13.2895 | −0.789979 | −0.394989 | − | 0.918686i | \(-0.629252\pi\) | ||||
−0.394989 | + | 0.918686i | \(0.629252\pi\) | |||||||
\(284\) | −31.8763 | −1.89151 | ||||||||
\(285\) | 9.53510 | 0.564811 | ||||||||
\(286\) | −0.120644 | −0.00713385 | ||||||||
\(287\) | −9.73031 | −0.574362 | ||||||||
\(288\) | −15.3728 | −0.905853 | ||||||||
\(289\) | 20.6313 | 1.21360 | ||||||||
\(290\) | 7.37448 | 0.433044 | ||||||||
\(291\) | 10.4992 | 0.615474 | ||||||||
\(292\) | −15.0920 | −0.883195 | ||||||||
\(293\) | 1.18986 | 0.0695124 | 0.0347562 | − | 0.999396i | \(-0.488935\pi\) | ||||
0.0347562 | + | 0.999396i | \(0.488935\pi\) | |||||||
\(294\) | 18.3212 | 1.06851 | ||||||||
\(295\) | 0.375720 | 0.0218752 | ||||||||
\(296\) | −2.75341 | −0.160039 | ||||||||
\(297\) | −3.51890 | −0.204187 | ||||||||
\(298\) | 11.6545 | 0.675128 | ||||||||
\(299\) | −0.510744 | −0.0295371 | ||||||||
\(300\) | −18.4314 | −1.06414 | ||||||||
\(301\) | −14.1429 | −0.815185 | ||||||||
\(302\) | 20.8840 | 1.20174 | ||||||||
\(303\) | 7.60109 | 0.436671 | ||||||||
\(304\) | 7.76628 | 0.445427 | ||||||||
\(305\) | 19.6634 | 1.12592 | ||||||||
\(306\) | −24.6735 | −1.41049 | ||||||||
\(307\) | 7.28607 | 0.415838 | 0.207919 | − | 0.978146i | \(-0.433331\pi\) | ||||
0.207919 | + | 0.978146i | \(0.433331\pi\) | |||||||
\(308\) | 6.51920 | 0.371466 | ||||||||
\(309\) | −0.154195 | −0.00877185 | ||||||||
\(310\) | −60.6389 | −3.44406 | ||||||||
\(311\) | −2.83001 | −0.160475 | −0.0802375 | − | 0.996776i | \(-0.525568\pi\) | ||||
−0.0802375 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(312\) | −0.0772484 | −0.00437333 | ||||||||
\(313\) | −22.1222 | −1.25042 | −0.625211 | − | 0.780456i | \(-0.714987\pi\) | ||||
−0.625211 | + | 0.780456i | \(0.714987\pi\) | |||||||
\(314\) | 17.3259 | 0.977756 | ||||||||
\(315\) | 26.2858 | 1.48104 | ||||||||
\(316\) | 17.6600 | 0.993453 | ||||||||
\(317\) | 3.17373 | 0.178254 | 0.0891272 | − | 0.996020i | \(-0.471592\pi\) | ||||
0.0891272 | + | 0.996020i | \(0.471592\pi\) | |||||||
\(318\) | 4.60080 | 0.258000 | ||||||||
\(319\) | 0.686935 | 0.0384610 | ||||||||
\(320\) | −38.3790 | −2.14545 | ||||||||
\(321\) | 0.903599 | 0.0504340 | ||||||||
\(322\) | 50.3906 | 2.80816 | ||||||||
\(323\) | 15.9956 | 0.890021 | ||||||||
\(324\) | 0.960913 | 0.0533841 | ||||||||
\(325\) | −0.609591 | −0.0338141 | ||||||||
\(326\) | −11.0881 | −0.614113 | ||||||||
\(327\) | 1.30211 | 0.0720067 | ||||||||
\(328\) | −2.20253 | −0.121615 | ||||||||
\(329\) | −19.4078 | −1.06999 | ||||||||
\(330\) | −5.28220 | −0.290775 | ||||||||
\(331\) | −36.1564 | −1.98734 | −0.993668 | − | 0.112358i | \(-0.964160\pi\) | ||||
−0.993668 | + | 0.112358i | \(0.964160\pi\) | |||||||
\(332\) | 2.38516 | 0.130903 | ||||||||
\(333\) | −5.93738 | −0.325366 | ||||||||
\(334\) | 14.7848 | 0.808988 | ||||||||
\(335\) | 15.2717 | 0.834383 | ||||||||
\(336\) | −12.1699 | −0.663925 | ||||||||
\(337\) | −17.4664 | −0.951455 | −0.475728 | − | 0.879593i | \(-0.657815\pi\) | ||||
−0.475728 | + | 0.879593i | \(0.657815\pi\) | |||||||
\(338\) | 27.3219 | 1.48612 | ||||||||
\(339\) | 9.37475 | 0.509167 | ||||||||
\(340\) | −52.1012 | −2.82558 | ||||||||
\(341\) | −5.64854 | −0.305886 | ||||||||
\(342\) | −10.4878 | −0.567114 | ||||||||
\(343\) | −5.31273 | −0.286860 | ||||||||
\(344\) | −3.20137 | −0.172606 | ||||||||
\(345\) | −22.3620 | −1.20393 | ||||||||
\(346\) | 27.2164 | 1.46316 | ||||||||
\(347\) | −19.8394 | −1.06503 | −0.532517 | − | 0.846419i | \(-0.678754\pi\) | ||||
−0.532517 | + | 0.846419i | \(0.678754\pi\) | |||||||
\(348\) | 2.52528 | 0.135369 | ||||||||
\(349\) | −27.3702 | −1.46509 | −0.732547 | − | 0.680717i | \(-0.761668\pi\) | ||||
−0.732547 | + | 0.680717i | \(0.761668\pi\) | |||||||
\(350\) | 60.1430 | 3.21478 | ||||||||
\(351\) | −0.427840 | −0.0228364 | ||||||||
\(352\) | −5.52096 | −0.294268 | ||||||||
\(353\) | 7.01146 | 0.373182 | 0.186591 | − | 0.982438i | \(-0.440256\pi\) | ||||
0.186591 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(354\) | 0.234910 | 0.0124853 | ||||||||
\(355\) | −46.1589 | −2.44986 | ||||||||
\(356\) | −31.3479 | −1.66143 | ||||||||
\(357\) | −25.0656 | −1.32661 | ||||||||
\(358\) | 17.3237 | 0.915587 | ||||||||
\(359\) | −26.2224 | −1.38397 | −0.691983 | − | 0.721913i | \(-0.743263\pi\) | ||||
−0.691983 | + | 0.721913i | \(0.743263\pi\) | |||||||
\(360\) | 5.95001 | 0.313593 | ||||||||
\(361\) | −12.2008 | −0.642150 | ||||||||
\(362\) | 5.54626 | 0.291505 | ||||||||
\(363\) | 10.9779 | 0.576189 | ||||||||
\(364\) | 0.792626 | 0.0415449 | ||||||||
\(365\) | −21.8543 | −1.14390 | ||||||||
\(366\) | 12.2941 | 0.642621 | ||||||||
\(367\) | −8.27547 | −0.431976 | −0.215988 | − | 0.976396i | \(-0.569297\pi\) | ||||
−0.215988 | + | 0.976396i | \(0.569297\pi\) | |||||||
\(368\) | −18.2137 | −0.949456 | ||||||||
\(369\) | −4.74948 | −0.247248 | ||||||||
\(370\) | −22.8913 | −1.19006 | ||||||||
\(371\) | −8.22245 | −0.426888 | ||||||||
\(372\) | −20.7649 | −1.07661 | ||||||||
\(373\) | −23.9075 | −1.23788 | −0.618942 | − | 0.785437i | \(-0.712438\pi\) | ||||
−0.618942 | + | 0.785437i | \(0.712438\pi\) | |||||||
\(374\) | −8.86117 | −0.458200 | ||||||||
\(375\) | −8.40602 | −0.434085 | ||||||||
\(376\) | −4.39311 | −0.226557 | ||||||||
\(377\) | 0.0835199 | 0.00430150 | ||||||||
\(378\) | 42.2111 | 2.17111 | ||||||||
\(379\) | −5.46090 | −0.280508 | −0.140254 | − | 0.990116i | \(-0.544792\pi\) | ||||
−0.140254 | + | 0.990116i | \(0.544792\pi\) | |||||||
\(380\) | −22.1463 | −1.13608 | ||||||||
\(381\) | −3.54994 | −0.181869 | ||||||||
\(382\) | 19.1289 | 0.978721 | ||||||||
\(383\) | −25.3897 | −1.29735 | −0.648677 | − | 0.761064i | \(-0.724677\pi\) | ||||
−0.648677 | + | 0.761064i | \(0.724677\pi\) | |||||||
\(384\) | −7.23470 | −0.369194 | ||||||||
\(385\) | 9.44022 | 0.481118 | ||||||||
\(386\) | −10.3236 | −0.525457 | ||||||||
\(387\) | −6.90334 | −0.350916 | ||||||||
\(388\) | −24.3855 | −1.23798 | ||||||||
\(389\) | 12.6637 | 0.642076 | 0.321038 | − | 0.947066i | \(-0.395968\pi\) | ||||
0.321038 | + | 0.947066i | \(0.395968\pi\) | |||||||
\(390\) | −0.642227 | −0.0325204 | ||||||||
\(391\) | −37.5135 | −1.89714 | ||||||||
\(392\) | −7.41169 | −0.374347 | ||||||||
\(393\) | 3.87232 | 0.195333 | ||||||||
\(394\) | 22.0583 | 1.11128 | ||||||||
\(395\) | 25.5728 | 1.28671 | ||||||||
\(396\) | 3.18210 | 0.159906 | ||||||||
\(397\) | −17.3326 | −0.869900 | −0.434950 | − | 0.900455i | \(-0.643234\pi\) | ||||
−0.434950 | + | 0.900455i | \(0.643234\pi\) | |||||||
\(398\) | 14.1242 | 0.707982 | ||||||||
\(399\) | −10.6544 | −0.533389 | ||||||||
\(400\) | −21.7387 | −1.08694 | ||||||||
\(401\) | 3.45185 | 0.172377 | 0.0861885 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861885 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(402\) | 9.54828 | 0.476225 | ||||||||
\(403\) | −0.686769 | −0.0342104 | ||||||||
\(404\) | −17.6543 | −0.878336 | ||||||||
\(405\) | 1.39146 | 0.0691424 | ||||||||
\(406\) | −8.24017 | −0.408953 | ||||||||
\(407\) | −2.13234 | −0.105696 | ||||||||
\(408\) | −5.67379 | −0.280895 | ||||||||
\(409\) | 27.1946 | 1.34469 | 0.672343 | − | 0.740240i | \(-0.265288\pi\) | ||||
0.672343 | + | 0.740240i | \(0.265288\pi\) | |||||||
\(410\) | −18.3114 | −0.904337 | ||||||||
\(411\) | −20.6559 | −1.01888 | ||||||||
\(412\) | 0.358134 | 0.0176440 | ||||||||
\(413\) | −0.419826 | −0.0206583 | ||||||||
\(414\) | 24.5963 | 1.20884 | ||||||||
\(415\) | 3.45387 | 0.169544 | ||||||||
\(416\) | −0.671257 | −0.0329111 | ||||||||
\(417\) | 1.04272 | 0.0510622 | ||||||||
\(418\) | −3.76655 | −0.184228 | ||||||||
\(419\) | 35.8510 | 1.75143 | 0.875717 | − | 0.482824i | \(-0.160389\pi\) | ||||
0.875717 | + | 0.482824i | \(0.160389\pi\) | |||||||
\(420\) | 34.7037 | 1.69337 | ||||||||
\(421\) | −36.3630 | −1.77222 | −0.886111 | − | 0.463473i | \(-0.846603\pi\) | ||||
−0.886111 | + | 0.463473i | \(0.846603\pi\) | |||||||
\(422\) | 21.9347 | 1.06776 | ||||||||
\(423\) | −9.47317 | −0.460601 | ||||||||
\(424\) | −1.86122 | −0.0903887 | ||||||||
\(425\) | −44.7737 | −2.17184 | ||||||||
\(426\) | −28.8598 | −1.39826 | ||||||||
\(427\) | −21.9717 | −1.06328 | ||||||||
\(428\) | −2.09870 | −0.101445 | ||||||||
\(429\) | −0.0598237 | −0.00288832 | ||||||||
\(430\) | −26.6155 | −1.28351 | ||||||||
\(431\) | 0.321407 | 0.0154816 | 0.00774081 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00774081 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(432\) | −15.2573 | −0.734065 | ||||||||
\(433\) | 29.1376 | 1.40027 | 0.700133 | − | 0.714012i | \(-0.253124\pi\) | ||||
0.700133 | + | 0.714012i | \(0.253124\pi\) | |||||||
\(434\) | 67.7574 | 3.25246 | ||||||||
\(435\) | 3.65677 | 0.175329 | ||||||||
\(436\) | −3.02428 | −0.144837 | ||||||||
\(437\) | −15.9456 | −0.762781 | ||||||||
\(438\) | −13.6639 | −0.652885 | ||||||||
\(439\) | −18.5092 | −0.883395 | −0.441697 | − | 0.897164i | \(-0.645624\pi\) | ||||
−0.441697 | + | 0.897164i | \(0.645624\pi\) | |||||||
\(440\) | 2.13687 | 0.101871 | ||||||||
\(441\) | −15.9824 | −0.761065 | ||||||||
\(442\) | −1.07737 | −0.0512453 | ||||||||
\(443\) | 22.5793 | 1.07277 | 0.536387 | − | 0.843972i | \(-0.319789\pi\) | ||||
0.536387 | + | 0.843972i | \(0.319789\pi\) | |||||||
\(444\) | −7.83880 | −0.372013 | ||||||||
\(445\) | −45.3937 | −2.15187 | ||||||||
\(446\) | −37.8597 | −1.79271 | ||||||||
\(447\) | 5.77911 | 0.273343 | ||||||||
\(448\) | 42.8843 | 2.02609 | ||||||||
\(449\) | 19.2916 | 0.910429 | 0.455215 | − | 0.890382i | \(-0.349563\pi\) | ||||
0.455215 | + | 0.890382i | \(0.349563\pi\) | |||||||
\(450\) | 29.3565 | 1.38388 | ||||||||
\(451\) | −1.70572 | −0.0803191 | ||||||||
\(452\) | −21.7738 | −1.02416 | ||||||||
\(453\) | 10.3557 | 0.486554 | ||||||||
\(454\) | −49.2316 | −2.31055 | ||||||||
\(455\) | 1.14777 | 0.0538085 | ||||||||
\(456\) | −2.41172 | −0.112939 | ||||||||
\(457\) | 10.7219 | 0.501550 | 0.250775 | − | 0.968045i | \(-0.419315\pi\) | ||||
0.250775 | + | 0.968045i | \(0.419315\pi\) | |||||||
\(458\) | −35.0871 | −1.63951 | ||||||||
\(459\) | −31.4243 | −1.46676 | ||||||||
\(460\) | 51.9381 | 2.42163 | ||||||||
\(461\) | −16.9188 | −0.787988 | −0.393994 | − | 0.919113i | \(-0.628907\pi\) | ||||
−0.393994 | + | 0.919113i | \(0.628907\pi\) | |||||||
\(462\) | 5.90228 | 0.274599 | ||||||||
\(463\) | 34.7591 | 1.61539 | 0.807697 | − | 0.589598i | \(-0.200714\pi\) | ||||
0.807697 | + | 0.589598i | \(0.200714\pi\) | |||||||
\(464\) | 2.97842 | 0.138270 | ||||||||
\(465\) | −30.0689 | −1.39441 | ||||||||
\(466\) | 7.02618 | 0.325481 | ||||||||
\(467\) | 6.99023 | 0.323469 | 0.161735 | − | 0.986834i | \(-0.448291\pi\) | ||||
0.161735 | + | 0.986834i | \(0.448291\pi\) | |||||||
\(468\) | 0.386890 | 0.0178840 | ||||||||
\(469\) | −17.0645 | −0.787964 | ||||||||
\(470\) | −36.5234 | −1.68470 | ||||||||
\(471\) | 8.59136 | 0.395869 | ||||||||
\(472\) | −0.0950309 | −0.00437415 | ||||||||
\(473\) | −2.47925 | −0.113996 | ||||||||
\(474\) | 15.9888 | 0.734391 | ||||||||
\(475\) | −19.0316 | −0.873231 | ||||||||
\(476\) | 58.2174 | 2.66839 | ||||||||
\(477\) | −4.01348 | −0.183765 | ||||||||
\(478\) | −37.9925 | −1.73774 | ||||||||
\(479\) | 29.5808 | 1.35158 | 0.675790 | − | 0.737095i | \(-0.263803\pi\) | ||||
0.675790 | + | 0.737095i | \(0.263803\pi\) | |||||||
\(480\) | −29.3898 | −1.34145 | ||||||||
\(481\) | −0.259257 | −0.0118211 | ||||||||
\(482\) | 37.3308 | 1.70037 | ||||||||
\(483\) | 24.9871 | 1.13695 | ||||||||
\(484\) | −25.4972 | −1.15897 | ||||||||
\(485\) | −35.3117 | −1.60342 | ||||||||
\(486\) | 33.1856 | 1.50533 | ||||||||
\(487\) | −35.9514 | −1.62911 | −0.814556 | − | 0.580085i | \(-0.803019\pi\) | ||||
−0.814556 | + | 0.580085i | \(0.803019\pi\) | |||||||
\(488\) | −4.97347 | −0.225138 | ||||||||
\(489\) | −5.49824 | −0.248639 | ||||||||
\(490\) | −61.6193 | −2.78368 | ||||||||
\(491\) | −0.944071 | −0.0426053 | −0.0213027 | − | 0.999773i | \(-0.506781\pi\) | ||||
−0.0213027 | + | 0.999773i | \(0.506781\pi\) | |||||||
\(492\) | −6.27048 | −0.282695 | ||||||||
\(493\) | 6.13443 | 0.276281 | ||||||||
\(494\) | −0.457950 | −0.0206042 | ||||||||
\(495\) | 4.60789 | 0.207109 | ||||||||
\(496\) | −24.4910 | −1.09968 | ||||||||
\(497\) | 51.5776 | 2.31357 | ||||||||
\(498\) | 2.15945 | 0.0967673 | ||||||||
\(499\) | 17.6273 | 0.789107 | 0.394553 | − | 0.918873i | \(-0.370899\pi\) | ||||
0.394553 | + | 0.918873i | \(0.370899\pi\) | |||||||
\(500\) | 19.5238 | 0.873133 | ||||||||
\(501\) | 7.33132 | 0.327539 | ||||||||
\(502\) | −19.3969 | −0.865726 | ||||||||
\(503\) | −9.28633 | −0.414057 | −0.207028 | − | 0.978335i | \(-0.566379\pi\) | ||||
−0.207028 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(504\) | −6.64848 | −0.296147 | ||||||||
\(505\) | −25.5646 | −1.13761 | ||||||||
\(506\) | 8.83344 | 0.392694 | ||||||||
\(507\) | 13.5481 | 0.601691 | ||||||||
\(508\) | 8.24510 | 0.365817 | ||||||||
\(509\) | −32.2608 | −1.42994 | −0.714968 | − | 0.699157i | \(-0.753559\pi\) | ||||
−0.714968 | + | 0.699157i | \(0.753559\pi\) | |||||||
\(510\) | −47.1708 | −2.08876 | ||||||||
\(511\) | 24.4197 | 1.08027 | ||||||||
\(512\) | −29.2216 | −1.29143 | ||||||||
\(513\) | −13.3573 | −0.589739 | ||||||||
\(514\) | 11.1788 | 0.493075 | ||||||||
\(515\) | 0.518602 | 0.0228523 | ||||||||
\(516\) | −9.11410 | −0.401226 | ||||||||
\(517\) | −3.40217 | −0.149627 | ||||||||
\(518\) | 25.5785 | 1.12386 | ||||||||
\(519\) | 13.4958 | 0.592399 | ||||||||
\(520\) | 0.259808 | 0.0113933 | ||||||||
\(521\) | −6.49922 | −0.284736 | −0.142368 | − | 0.989814i | \(-0.545472\pi\) | ||||
−0.142368 | + | 0.989814i | \(0.545472\pi\) | |||||||
\(522\) | −4.02213 | −0.176044 | ||||||||
\(523\) | −2.79653 | −0.122284 | −0.0611419 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611419 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(524\) | −8.99387 | −0.392899 | ||||||||
\(525\) | 29.8230 | 1.30158 | ||||||||
\(526\) | 0.796701 | 0.0347378 | ||||||||
\(527\) | −50.4423 | −2.19730 | ||||||||
\(528\) | −2.13338 | −0.0928436 | ||||||||
\(529\) | 14.3961 | 0.625916 | ||||||||
\(530\) | −15.4738 | −0.672139 | ||||||||
\(531\) | −0.204922 | −0.00889286 | ||||||||
\(532\) | 24.7460 | 1.07288 | ||||||||
\(533\) | −0.207387 | −0.00898292 | ||||||||
\(534\) | −28.3814 | −1.22818 | ||||||||
\(535\) | −3.03906 | −0.131390 | ||||||||
\(536\) | −3.86268 | −0.166842 | ||||||||
\(537\) | 8.59029 | 0.370698 | ||||||||
\(538\) | −41.7970 | −1.80200 | ||||||||
\(539\) | −5.73987 | −0.247234 | ||||||||
\(540\) | 43.5075 | 1.87226 | ||||||||
\(541\) | −13.7229 | −0.589996 | −0.294998 | − | 0.955498i | \(-0.595319\pi\) | ||||
−0.294998 | + | 0.955498i | \(0.595319\pi\) | |||||||
\(542\) | 32.8966 | 1.41303 | ||||||||
\(543\) | 2.75021 | 0.118023 | ||||||||
\(544\) | −49.3030 | −2.11385 | ||||||||
\(545\) | −4.37935 | −0.187591 | ||||||||
\(546\) | 0.717619 | 0.0307113 | ||||||||
\(547\) | 2.06811 | 0.0884258 | 0.0442129 | − | 0.999022i | \(-0.485922\pi\) | ||||
0.0442129 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(548\) | 47.9755 | 2.04941 | ||||||||
\(549\) | −10.7246 | −0.457717 | ||||||||
\(550\) | 10.5430 | 0.449556 | ||||||||
\(551\) | 2.60752 | 0.111084 | ||||||||
\(552\) | 5.65603 | 0.240737 | ||||||||
\(553\) | −28.5749 | −1.21513 | ||||||||
\(554\) | −24.8929 | −1.05760 | ||||||||
\(555\) | −11.3511 | −0.481827 | ||||||||
\(556\) | −2.42182 | −0.102708 | ||||||||
\(557\) | −36.6618 | −1.55341 | −0.776705 | − | 0.629864i | \(-0.783110\pi\) | ||||
−0.776705 | + | 0.629864i | \(0.783110\pi\) | |||||||
\(558\) | 33.0732 | 1.40010 | ||||||||
\(559\) | −0.301435 | −0.0127494 | ||||||||
\(560\) | 40.9309 | 1.72965 | ||||||||
\(561\) | −4.39398 | −0.185514 | ||||||||
\(562\) | 53.9849 | 2.27721 | ||||||||
\(563\) | 0.432140 | 0.0182125 | 0.00910626 | − | 0.999959i | \(-0.497101\pi\) | ||||
0.00910626 | + | 0.999959i | \(0.497101\pi\) | |||||||
\(564\) | −12.5069 | −0.526636 | ||||||||
\(565\) | −31.5299 | −1.32647 | ||||||||
\(566\) | 27.9453 | 1.17463 | ||||||||
\(567\) | −1.55481 | −0.0652959 | ||||||||
\(568\) | 11.6750 | 0.489872 | ||||||||
\(569\) | 8.64233 | 0.362305 | 0.181153 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181153 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(570\) | −20.0505 | −0.839825 | ||||||||
\(571\) | −8.99945 | −0.376615 | −0.188308 | − | 0.982110i | \(-0.560300\pi\) | ||||
−0.188308 | + | 0.982110i | \(0.560300\pi\) | |||||||
\(572\) | 0.138947 | 0.00580966 | ||||||||
\(573\) | 9.48544 | 0.396260 | ||||||||
\(574\) | 20.4610 | 0.854027 | ||||||||
\(575\) | 44.6336 | 1.86135 | ||||||||
\(576\) | 20.9323 | 0.872181 | ||||||||
\(577\) | 22.2843 | 0.927709 | 0.463855 | − | 0.885911i | \(-0.346466\pi\) | ||||
0.463855 | + | 0.885911i | \(0.346466\pi\) | |||||||
\(578\) | −43.3837 | −1.80452 | ||||||||
\(579\) | −5.11914 | −0.212744 | ||||||||
\(580\) | −8.49323 | −0.352662 | ||||||||
\(581\) | −3.85932 | −0.160112 | ||||||||
\(582\) | −22.0778 | −0.915156 | ||||||||
\(583\) | −1.44139 | −0.0596963 | ||||||||
\(584\) | 5.52761 | 0.228734 | ||||||||
\(585\) | 0.560242 | 0.0231632 | ||||||||
\(586\) | −2.50206 | −0.103359 | ||||||||
\(587\) | −29.8291 | −1.23118 | −0.615590 | − | 0.788067i | \(-0.711082\pi\) | ||||
−0.615590 | + | 0.788067i | \(0.711082\pi\) | |||||||
\(588\) | −21.1006 | −0.870176 | ||||||||
\(589\) | −21.4411 | −0.883466 | ||||||||
\(590\) | −0.790068 | −0.0325266 | ||||||||
\(591\) | 10.9380 | 0.449931 | ||||||||
\(592\) | −9.24539 | −0.379983 | ||||||||
\(593\) | 17.0650 | 0.700777 | 0.350388 | − | 0.936604i | \(-0.386050\pi\) | ||||
0.350388 | + | 0.936604i | \(0.386050\pi\) | |||||||
\(594\) | 7.39959 | 0.303609 | ||||||||
\(595\) | 84.3025 | 3.45607 | ||||||||
\(596\) | −13.4226 | −0.549811 | ||||||||
\(597\) | 7.00375 | 0.286644 | ||||||||
\(598\) | 1.07400 | 0.0439191 | ||||||||
\(599\) | −5.31383 | −0.217117 | −0.108559 | − | 0.994090i | \(-0.534624\pi\) | ||||
−0.108559 | + | 0.994090i | \(0.534624\pi\) | |||||||
\(600\) | 6.75068 | 0.275595 | ||||||||
\(601\) | −25.0796 | −1.02302 | −0.511509 | − | 0.859278i | \(-0.670913\pi\) | ||||
−0.511509 | + | 0.859278i | \(0.670913\pi\) | |||||||
\(602\) | 29.7399 | 1.21211 | ||||||||
\(603\) | −8.32937 | −0.339198 | ||||||||
\(604\) | −24.0522 | −0.978671 | ||||||||
\(605\) | −36.9217 | −1.50108 | ||||||||
\(606\) | −15.9837 | −0.649293 | ||||||||
\(607\) | 47.4201 | 1.92472 | 0.962360 | − | 0.271776i | \(-0.0876111\pi\) | ||||
0.962360 | + | 0.271776i | \(0.0876111\pi\) | |||||||
\(608\) | −20.9569 | −0.849913 | ||||||||
\(609\) | −4.08604 | −0.165575 | ||||||||
\(610\) | −41.3484 | −1.67415 | ||||||||
\(611\) | −0.413647 | −0.0167344 | ||||||||
\(612\) | 28.4166 | 1.14867 | ||||||||
\(613\) | 28.8690 | 1.16601 | 0.583004 | − | 0.812470i | \(-0.301877\pi\) | ||||
0.583004 | + | 0.812470i | \(0.301877\pi\) | |||||||
\(614\) | −15.3212 | −0.618315 | ||||||||
\(615\) | −9.08007 | −0.366144 | ||||||||
\(616\) | −2.38772 | −0.0962039 | ||||||||
\(617\) | 39.7252 | 1.59928 | 0.799638 | − | 0.600483i | \(-0.205025\pi\) | ||||
0.799638 | + | 0.600483i | \(0.205025\pi\) | |||||||
\(618\) | 0.324244 | 0.0130430 | ||||||||
\(619\) | −9.67869 | −0.389019 | −0.194510 | − | 0.980901i | \(-0.562312\pi\) | ||||
−0.194510 | + | 0.980901i | \(0.562312\pi\) | |||||||
\(620\) | 69.8382 | 2.80477 | ||||||||
\(621\) | 31.3259 | 1.25707 | ||||||||
\(622\) | 5.95097 | 0.238612 | ||||||||
\(623\) | 50.7225 | 2.03216 | ||||||||
\(624\) | −0.259384 | −0.0103837 | ||||||||
\(625\) | −8.22197 | −0.328879 | ||||||||
\(626\) | 46.5189 | 1.85927 | ||||||||
\(627\) | −1.86772 | −0.0745894 | ||||||||
\(628\) | −19.9543 | −0.796264 | ||||||||
\(629\) | −19.0421 | −0.759257 | ||||||||
\(630\) | −55.2742 | −2.20217 | ||||||||
\(631\) | −14.5200 | −0.578031 | −0.289015 | − | 0.957324i | \(-0.593328\pi\) | ||||
−0.289015 | + | 0.957324i | \(0.593328\pi\) | |||||||
\(632\) | −6.46815 | −0.257289 | ||||||||
\(633\) | 10.8767 | 0.432311 | ||||||||
\(634\) | −6.67376 | −0.265049 | ||||||||
\(635\) | 11.9394 | 0.473802 | ||||||||
\(636\) | −5.29877 | −0.210110 | ||||||||
\(637\) | −0.697872 | −0.0276507 | ||||||||
\(638\) | −1.44450 | −0.0571882 | ||||||||
\(639\) | 25.1756 | 0.995933 | ||||||||
\(640\) | 24.3323 | 0.961820 | ||||||||
\(641\) | 9.89790 | 0.390944 | 0.195472 | − | 0.980709i | \(-0.437376\pi\) | ||||
0.195472 | + | 0.980709i | \(0.437376\pi\) | |||||||
\(642\) | −1.90010 | −0.0749909 | ||||||||
\(643\) | 15.5904 | 0.614826 | 0.307413 | − | 0.951576i | \(-0.400537\pi\) | ||||
0.307413 | + | 0.951576i | \(0.400537\pi\) | |||||||
\(644\) | −58.0352 | −2.28691 | ||||||||
\(645\) | −13.1978 | −0.519663 | ||||||||
\(646\) | −33.6359 | −1.32338 | ||||||||
\(647\) | 42.4093 | 1.66728 | 0.833641 | − | 0.552307i | \(-0.186252\pi\) | ||||
0.833641 | + | 0.552307i | \(0.186252\pi\) | |||||||
\(648\) | −0.351944 | −0.0138257 | ||||||||
\(649\) | −0.0735952 | −0.00288886 | ||||||||
\(650\) | 1.28186 | 0.0502786 | ||||||||
\(651\) | 33.5988 | 1.31684 | ||||||||
\(652\) | 12.7702 | 0.500121 | ||||||||
\(653\) | 27.8273 | 1.08897 | 0.544483 | − | 0.838772i | \(-0.316726\pi\) | ||||
0.544483 | + | 0.838772i | \(0.316726\pi\) | |||||||
\(654\) | −2.73809 | −0.107068 | ||||||||
\(655\) | −13.0237 | −0.508878 | ||||||||
\(656\) | −7.39565 | −0.288752 | ||||||||
\(657\) | 11.9196 | 0.465027 | ||||||||
\(658\) | 40.8109 | 1.59098 | ||||||||
\(659\) | 25.8774 | 1.00804 | 0.504021 | − | 0.863691i | \(-0.331853\pi\) | ||||
0.504021 | + | 0.863691i | \(0.331853\pi\) | |||||||
\(660\) | 6.08354 | 0.236801 | ||||||||
\(661\) | −30.2353 | −1.17602 | −0.588008 | − | 0.808855i | \(-0.700088\pi\) | ||||
−0.588008 | + | 0.808855i | \(0.700088\pi\) | |||||||
\(662\) | 76.0302 | 2.95500 | ||||||||
\(663\) | −0.534234 | −0.0207479 | ||||||||
\(664\) | −0.873589 | −0.0339018 | ||||||||
\(665\) | 35.8339 | 1.38958 | ||||||||
\(666\) | 12.4852 | 0.483792 | ||||||||
\(667\) | −6.11523 | −0.236783 | ||||||||
\(668\) | −17.0277 | −0.658823 | ||||||||
\(669\) | −18.7734 | −0.725822 | ||||||||
\(670\) | −32.1136 | −1.24065 | ||||||||
\(671\) | −3.85162 | −0.148690 | ||||||||
\(672\) | 32.8399 | 1.26683 | ||||||||
\(673\) | −2.51537 | −0.0969604 | −0.0484802 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484802 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(674\) | 36.7286 | 1.41473 | ||||||||
\(675\) | 37.3886 | 1.43909 | ||||||||
\(676\) | −31.4668 | −1.21026 | ||||||||
\(677\) | −2.60433 | −0.100093 | −0.0500463 | − | 0.998747i | \(-0.515937\pi\) | ||||
−0.0500463 | + | 0.998747i | \(0.515937\pi\) | |||||||
\(678\) | −19.7134 | −0.757087 | ||||||||
\(679\) | 39.4570 | 1.51422 | ||||||||
\(680\) | 19.0826 | 0.731783 | ||||||||
\(681\) | −24.4124 | −0.935486 | ||||||||
\(682\) | 11.8778 | 0.454825 | ||||||||
\(683\) | 19.2096 | 0.735035 | 0.367518 | − | 0.930017i | \(-0.380208\pi\) | ||||
0.367518 | + | 0.930017i | \(0.380208\pi\) | |||||||
\(684\) | 12.0788 | 0.461846 | ||||||||
\(685\) | 69.4716 | 2.65437 | ||||||||
\(686\) | 11.1717 | 0.426537 | ||||||||
\(687\) | −17.3986 | −0.663797 | ||||||||
\(688\) | −10.7495 | −0.409822 | ||||||||
\(689\) | −0.175249 | −0.00667646 | ||||||||
\(690\) | 47.0231 | 1.79014 | ||||||||
\(691\) | −38.0600 | −1.44787 | −0.723936 | − | 0.689867i | \(-0.757669\pi\) | ||||
−0.723936 | + | 0.689867i | \(0.757669\pi\) | |||||||
\(692\) | −31.3453 | −1.19157 | ||||||||
\(693\) | −5.14881 | −0.195587 | ||||||||
\(694\) | 41.7185 | 1.58361 | ||||||||
\(695\) | −3.50696 | −0.133026 | ||||||||
\(696\) | −0.924909 | −0.0350586 | ||||||||
\(697\) | −15.2323 | −0.576964 | ||||||||
\(698\) | 57.5544 | 2.17847 | ||||||||
\(699\) | 3.48406 | 0.131779 | ||||||||
\(700\) | −69.2671 | −2.61805 | ||||||||
\(701\) | −39.8972 | −1.50689 | −0.753447 | − | 0.657508i | \(-0.771610\pi\) | ||||
−0.753447 | + | 0.657508i | \(0.771610\pi\) | |||||||
\(702\) | 0.899667 | 0.0339557 | ||||||||
\(703\) | −8.09407 | −0.305274 | ||||||||
\(704\) | 7.51759 | 0.283330 | ||||||||
\(705\) | −18.1108 | −0.682093 | ||||||||
\(706\) | −14.7438 | −0.554890 | ||||||||
\(707\) | 28.5657 | 1.07432 | ||||||||
\(708\) | −0.270547 | −0.0101678 | ||||||||
\(709\) | 39.0083 | 1.46499 | 0.732494 | − | 0.680773i | \(-0.238356\pi\) | ||||
0.732494 | + | 0.680773i | \(0.238356\pi\) | |||||||
\(710\) | 97.0636 | 3.64273 | ||||||||
\(711\) | −13.9477 | −0.523081 | ||||||||
\(712\) | 11.4815 | 0.430286 | ||||||||
\(713\) | 50.2844 | 1.88317 | ||||||||
\(714\) | 52.7082 | 1.97255 | ||||||||
\(715\) | 0.201204 | 0.00752460 | ||||||||
\(716\) | −19.9518 | −0.745635 | ||||||||
\(717\) | −18.8393 | −0.703567 | ||||||||
\(718\) | 55.1409 | 2.05784 | ||||||||
\(719\) | 4.19148 | 0.156316 | 0.0781579 | − | 0.996941i | \(-0.475096\pi\) | ||||
0.0781579 | + | 0.996941i | \(0.475096\pi\) | |||||||
\(720\) | 19.9789 | 0.744569 | ||||||||
\(721\) | −0.579481 | −0.0215810 | ||||||||
\(722\) | 25.6561 | 0.954821 | ||||||||
\(723\) | 18.5112 | 0.688438 | ||||||||
\(724\) | −6.38766 | −0.237395 | ||||||||
\(725\) | −7.29875 | −0.271069 | ||||||||
\(726\) | −23.0844 | −0.856743 | ||||||||
\(727\) | 20.7800 | 0.770689 | 0.385344 | − | 0.922773i | \(-0.374083\pi\) | ||||
0.385344 | + | 0.922773i | \(0.374083\pi\) | |||||||
\(728\) | −0.290307 | −0.0107595 | ||||||||
\(729\) | 15.2654 | 0.565385 | ||||||||
\(730\) | 45.9554 | 1.70089 | ||||||||
\(731\) | −22.1400 | −0.818878 | ||||||||
\(732\) | −14.1592 | −0.523338 | ||||||||
\(733\) | −12.7192 | −0.469794 | −0.234897 | − | 0.972020i | \(-0.575475\pi\) | ||||
−0.234897 | + | 0.972020i | \(0.575475\pi\) | |||||||
\(734\) | 17.4018 | 0.642311 | ||||||||
\(735\) | −30.5551 | −1.12704 | ||||||||
\(736\) | 49.1487 | 1.81164 | ||||||||
\(737\) | −2.99139 | −0.110189 | ||||||||
\(738\) | 9.98727 | 0.367637 | ||||||||
\(739\) | 40.3992 | 1.48611 | 0.743055 | − | 0.669231i | \(-0.233376\pi\) | ||||
0.743055 | + | 0.669231i | \(0.233376\pi\) | |||||||
\(740\) | 26.3641 | 0.969163 | ||||||||
\(741\) | −0.227083 | −0.00834211 | ||||||||
\(742\) | 17.2903 | 0.634746 | ||||||||
\(743\) | 43.4824 | 1.59521 | 0.797607 | − | 0.603178i | \(-0.206099\pi\) | ||||
0.797607 | + | 0.603178i | \(0.206099\pi\) | |||||||
\(744\) | 7.60535 | 0.278826 | ||||||||
\(745\) | −19.4368 | −0.712109 | ||||||||
\(746\) | 50.2730 | 1.84063 | ||||||||
\(747\) | −1.88378 | −0.0689240 | ||||||||
\(748\) | 10.2055 | 0.373149 | ||||||||
\(749\) | 3.39581 | 0.124080 | ||||||||
\(750\) | 17.6763 | 0.645447 | ||||||||
\(751\) | −13.5066 | −0.492864 | −0.246432 | − | 0.969160i | \(-0.579258\pi\) | ||||
−0.246432 | + | 0.969160i | \(0.579258\pi\) | |||||||
\(752\) | −14.7511 | −0.537919 | ||||||||
\(753\) | −9.61831 | −0.350511 | ||||||||
\(754\) | −0.175627 | −0.00639595 | ||||||||
\(755\) | −34.8292 | −1.26756 | ||||||||
\(756\) | −48.6149 | −1.76811 | ||||||||
\(757\) | 1.47513 | 0.0536144 | 0.0268072 | − | 0.999641i | \(-0.491466\pi\) | ||||
0.0268072 | + | 0.999641i | \(0.491466\pi\) | |||||||
\(758\) | 11.4833 | 0.417091 | ||||||||
\(759\) | 4.38022 | 0.158992 | ||||||||
\(760\) | 8.11128 | 0.294227 | ||||||||
\(761\) | 22.4140 | 0.812506 | 0.406253 | − | 0.913761i | \(-0.366835\pi\) | ||||
0.406253 | + | 0.913761i | \(0.366835\pi\) | |||||||
\(762\) | 7.46486 | 0.270423 | ||||||||
\(763\) | 4.89345 | 0.177155 | ||||||||
\(764\) | −22.0309 | −0.797050 | ||||||||
\(765\) | 41.1491 | 1.48775 | ||||||||
\(766\) | 53.3899 | 1.92905 | ||||||||
\(767\) | −0.00894795 | −0.000323092 0 | ||||||||
\(768\) | −7.60911 | −0.274570 | ||||||||
\(769\) | −37.8544 | −1.36506 | −0.682532 | − | 0.730856i | \(-0.739121\pi\) | ||||
−0.682532 | + | 0.730856i | \(0.739121\pi\) | |||||||
\(770\) | −19.8510 | −0.715381 | ||||||||
\(771\) | 5.54321 | 0.199634 | ||||||||
\(772\) | 11.8897 | 0.427921 | ||||||||
\(773\) | 6.70940 | 0.241320 | 0.120660 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120660 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(774\) | 14.5164 | 0.521782 | ||||||||
\(775\) | 60.0163 | 2.15585 | ||||||||
\(776\) | 8.93141 | 0.320619 | ||||||||
\(777\) | 12.6836 | 0.455022 | ||||||||
\(778\) | −26.6294 | −0.954712 | ||||||||
\(779\) | −6.47468 | −0.231980 | ||||||||
\(780\) | 0.739657 | 0.0264840 | ||||||||
\(781\) | 9.04151 | 0.323531 | ||||||||
\(782\) | 78.8838 | 2.82088 | ||||||||
\(783\) | −5.12260 | −0.183067 | ||||||||
\(784\) | −24.8869 | −0.888819 | ||||||||
\(785\) | −28.8952 | −1.03131 | ||||||||
\(786\) | −8.14277 | −0.290443 | ||||||||
\(787\) | 20.7250 | 0.738765 | 0.369382 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369382 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(788\) | −25.4047 | −0.905006 | ||||||||
\(789\) | 0.395059 | 0.0140645 | ||||||||
\(790\) | −53.7749 | −1.91323 | ||||||||
\(791\) | 35.2313 | 1.25268 | ||||||||
\(792\) | −1.16547 | −0.0414133 | ||||||||
\(793\) | −0.468293 | −0.0166296 | ||||||||
\(794\) | 36.4473 | 1.29347 | ||||||||
\(795\) | −7.67297 | −0.272132 | ||||||||
\(796\) | −16.2669 | −0.576566 | ||||||||
\(797\) | −2.54925 | −0.0902991 | −0.0451495 | − | 0.998980i | \(-0.514376\pi\) | ||||
−0.0451495 | + | 0.998980i | \(0.514376\pi\) | |||||||
\(798\) | 22.4043 | 0.793103 | ||||||||
\(799\) | −30.3819 | −1.07483 | ||||||||
\(800\) | 58.6607 | 2.07397 | ||||||||
\(801\) | 24.7583 | 0.874791 | ||||||||
\(802\) | −7.25859 | −0.256310 | ||||||||
\(803\) | 4.28077 | 0.151065 | ||||||||
\(804\) | −10.9968 | −0.387828 | ||||||||
\(805\) | −84.0387 | −2.96197 | ||||||||
\(806\) | 1.44415 | 0.0508679 | ||||||||
\(807\) | −20.7258 | −0.729584 | ||||||||
\(808\) | 6.46607 | 0.227476 | ||||||||
\(809\) | 43.2595 | 1.52092 | 0.760462 | − | 0.649383i | \(-0.224973\pi\) | ||||
0.760462 | + | 0.649383i | \(0.224973\pi\) | |||||||
\(810\) | −2.92599 | −0.102809 | ||||||||
\(811\) | 22.8573 | 0.802630 | 0.401315 | − | 0.915940i | \(-0.368553\pi\) | ||||
0.401315 | + | 0.915940i | \(0.368553\pi\) | |||||||
\(812\) | 9.49026 | 0.333043 | ||||||||
\(813\) | 16.3124 | 0.572101 | ||||||||
\(814\) | 4.48390 | 0.157161 | ||||||||
\(815\) | 18.4921 | 0.647751 | ||||||||
\(816\) | −19.0514 | −0.666933 | ||||||||
\(817\) | −9.41090 | −0.329246 | ||||||||
\(818\) | −57.1852 | −1.99943 | ||||||||
\(819\) | −0.626010 | −0.0218745 | ||||||||
\(820\) | 21.0894 | 0.736474 | ||||||||
\(821\) | −18.6341 | −0.650334 | −0.325167 | − | 0.945657i | \(-0.605421\pi\) | ||||
−0.325167 | + | 0.945657i | \(0.605421\pi\) | |||||||
\(822\) | 43.4355 | 1.51499 | ||||||||
\(823\) | −22.0827 | −0.769754 | −0.384877 | − | 0.922968i | \(-0.625756\pi\) | ||||
−0.384877 | + | 0.922968i | \(0.625756\pi\) | |||||||
\(824\) | −0.131170 | −0.00456953 | ||||||||
\(825\) | 5.22796 | 0.182014 | ||||||||
\(826\) | 0.882815 | 0.0307171 | ||||||||
\(827\) | −35.4039 | −1.23112 | −0.615558 | − | 0.788092i | \(-0.711069\pi\) | ||||
−0.615558 | + | 0.788092i | \(0.711069\pi\) | |||||||
\(828\) | −28.3277 | −0.984454 | ||||||||
\(829\) | −51.9060 | −1.80277 | −0.901385 | − | 0.433018i | \(-0.857449\pi\) | ||||
−0.901385 | + | 0.433018i | \(0.857449\pi\) | |||||||
\(830\) | −7.26284 | −0.252097 | ||||||||
\(831\) | −12.3436 | −0.428195 | ||||||||
\(832\) | 0.914014 | 0.0316877 | ||||||||
\(833\) | −51.2578 | −1.77598 | ||||||||
\(834\) | −2.19264 | −0.0759250 | ||||||||
\(835\) | −24.6573 | −0.853300 | ||||||||
\(836\) | 4.33796 | 0.150032 | ||||||||
\(837\) | 42.1222 | 1.45596 | ||||||||
\(838\) | −75.3879 | −2.60423 | ||||||||
\(839\) | −32.9816 | −1.13865 | −0.569326 | − | 0.822112i | \(-0.692796\pi\) | ||||
−0.569326 | + | 0.822112i | \(0.692796\pi\) | |||||||
\(840\) | −12.7106 | −0.438556 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 76.4645 | 2.63514 | ||||||||
\(843\) | 26.7694 | 0.921987 | ||||||||
\(844\) | −25.2623 | −0.869566 | ||||||||
\(845\) | −45.5660 | −1.56752 | ||||||||
\(846\) | 19.9203 | 0.684874 | ||||||||
\(847\) | 41.2559 | 1.41757 | ||||||||
\(848\) | −6.24958 | −0.214612 | ||||||||
\(849\) | 13.8572 | 0.475578 | ||||||||
\(850\) | 94.1507 | 3.22934 | ||||||||
\(851\) | 18.9825 | 0.650711 | ||||||||
\(852\) | 33.2380 | 1.13872 | ||||||||
\(853\) | −40.7871 | −1.39652 | −0.698261 | − | 0.715843i | \(-0.746043\pi\) | ||||
−0.698261 | + | 0.715843i | \(0.746043\pi\) | |||||||
\(854\) | 46.2023 | 1.58101 | ||||||||
\(855\) | 17.4909 | 0.598178 | ||||||||
\(856\) | 0.768670 | 0.0262726 | ||||||||
\(857\) | 46.5297 | 1.58942 | 0.794711 | − | 0.606987i | \(-0.207622\pi\) | ||||
0.794711 | + | 0.606987i | \(0.207622\pi\) | |||||||
\(858\) | 0.125798 | 0.00429468 | ||||||||
\(859\) | 31.4868 | 1.07432 | 0.537158 | − | 0.843481i | \(-0.319498\pi\) | ||||
0.537158 | + | 0.843481i | \(0.319498\pi\) | |||||||
\(860\) | 30.6533 | 1.04527 | ||||||||
\(861\) | 10.1460 | 0.345774 | ||||||||
\(862\) | −0.675859 | −0.0230198 | ||||||||
\(863\) | 13.7283 | 0.467316 | 0.233658 | − | 0.972319i | \(-0.424930\pi\) | ||||
0.233658 | + | 0.972319i | \(0.424930\pi\) | |||||||
\(864\) | 41.1708 | 1.40066 | ||||||||
\(865\) | −45.3901 | −1.54331 | ||||||||
\(866\) | −61.2710 | −2.08207 | ||||||||
\(867\) | −21.5126 | −0.730606 | ||||||||
\(868\) | −78.0366 | −2.64873 | ||||||||
\(869\) | −5.00915 | −0.169924 | ||||||||
\(870\) | −7.68951 | −0.260699 | ||||||||
\(871\) | −0.363703 | −0.0123236 | ||||||||
\(872\) | 1.10767 | 0.0375105 | ||||||||
\(873\) | 19.2594 | 0.651833 | ||||||||
\(874\) | 33.5306 | 1.13419 | ||||||||
\(875\) | −31.5906 | −1.06796 | ||||||||
\(876\) | 15.7368 | 0.531696 | ||||||||
\(877\) | 8.48767 | 0.286608 | 0.143304 | − | 0.989679i | \(-0.454227\pi\) | ||||
0.143304 | + | 0.989679i | \(0.454227\pi\) | |||||||
\(878\) | 38.9213 | 1.31353 | ||||||||
\(879\) | −1.24069 | −0.0418475 | ||||||||
\(880\) | 7.17517 | 0.241875 | ||||||||
\(881\) | 34.8625 | 1.17455 | 0.587274 | − | 0.809388i | \(-0.300201\pi\) | ||||
0.587274 | + | 0.809388i | \(0.300201\pi\) | |||||||
\(882\) | 33.6079 | 1.13164 | ||||||||
\(883\) | −30.4512 | −1.02476 | −0.512382 | − | 0.858758i | \(-0.671237\pi\) | ||||
−0.512382 | + | 0.858758i | \(0.671237\pi\) | |||||||
\(884\) | 1.24082 | 0.0417331 | ||||||||
\(885\) | −0.391770 | −0.0131692 | ||||||||
\(886\) | −47.4801 | −1.59512 | ||||||||
\(887\) | −22.8188 | −0.766180 | −0.383090 | − | 0.923711i | \(-0.625140\pi\) | ||||
−0.383090 | + | 0.923711i | \(0.625140\pi\) | |||||||
\(888\) | 2.87104 | 0.0963456 | ||||||||
\(889\) | −13.3410 | −0.447444 | ||||||||
\(890\) | 95.4546 | 3.19964 | ||||||||
\(891\) | −0.272557 | −0.00913101 | ||||||||
\(892\) | 43.6032 | 1.45994 | ||||||||
\(893\) | −12.9142 | −0.432157 | ||||||||
\(894\) | −12.1524 | −0.406437 | ||||||||
\(895\) | −28.8916 | −0.965738 | ||||||||
\(896\) | −27.1887 | −0.908311 | ||||||||
\(897\) | 0.532563 | 0.0177817 | ||||||||
\(898\) | −40.5667 | −1.35373 | ||||||||
\(899\) | −8.22281 | −0.274246 | ||||||||
\(900\) | −33.8101 | −1.12700 | ||||||||
\(901\) | −12.8718 | −0.428822 | ||||||||
\(902\) | 3.58680 | 0.119428 | ||||||||
\(903\) | 14.7471 | 0.490753 | ||||||||
\(904\) | 7.97488 | 0.265241 | ||||||||
\(905\) | −9.24974 | −0.307472 | ||||||||
\(906\) | −21.7761 | −0.723463 | ||||||||
\(907\) | −51.2352 | −1.70124 | −0.850619 | − | 0.525783i | \(-0.823772\pi\) | ||||
−0.850619 | + | 0.525783i | \(0.823772\pi\) | |||||||
\(908\) | 56.7004 | 1.88167 | ||||||||
\(909\) | 13.9433 | 0.462468 | ||||||||
\(910\) | −2.41355 | −0.0800086 | ||||||||
\(911\) | 43.8551 | 1.45298 | 0.726492 | − | 0.687175i | \(-0.241149\pi\) | ||||
0.726492 | + | 0.687175i | \(0.241149\pi\) | |||||||
\(912\) | −8.09805 | −0.268153 | ||||||||
\(913\) | −0.676537 | −0.0223901 | ||||||||
\(914\) | −22.5462 | −0.745761 | ||||||||
\(915\) | −20.5034 | −0.677821 | ||||||||
\(916\) | 40.4100 | 1.33518 | ||||||||
\(917\) | 14.5526 | 0.480568 | ||||||||
\(918\) | 66.0794 | 2.18094 | ||||||||
\(919\) | −37.0033 | −1.22063 | −0.610313 | − | 0.792160i | \(-0.708956\pi\) | ||||
−0.610313 | + | 0.792160i | \(0.708956\pi\) | |||||||
\(920\) | −19.0228 | −0.627164 | ||||||||
\(921\) | −7.59732 | −0.250340 | ||||||||
\(922\) | 35.5771 | 1.17167 | ||||||||
\(923\) | 1.09930 | 0.0361838 | ||||||||
\(924\) | −6.79769 | −0.223628 | ||||||||
\(925\) | 22.6563 | 0.744933 | ||||||||
\(926\) | −73.0920 | −2.40195 | ||||||||
\(927\) | −0.282851 | −0.00929006 | ||||||||
\(928\) | −8.03709 | −0.263830 | ||||||||
\(929\) | −47.8652 | −1.57041 | −0.785203 | − | 0.619239i | \(-0.787441\pi\) | ||||
−0.785203 | + | 0.619239i | \(0.787441\pi\) | |||||||
\(930\) | 63.2294 | 2.07337 | ||||||||
\(931\) | −21.7878 | −0.714066 | ||||||||
\(932\) | −8.09209 | −0.265065 | ||||||||
\(933\) | 2.95090 | 0.0966082 | ||||||||
\(934\) | −14.6991 | −0.480971 | ||||||||
\(935\) | 14.7782 | 0.483298 | ||||||||
\(936\) | −0.141702 | −0.00463169 | ||||||||
\(937\) | −10.2772 | −0.335741 | −0.167870 | − | 0.985809i | \(-0.553689\pi\) | ||||
−0.167870 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(938\) | 35.8834 | 1.17163 | ||||||||
\(939\) | 23.0673 | 0.752771 | ||||||||
\(940\) | 42.0642 | 1.37198 | ||||||||
\(941\) | 11.6758 | 0.380619 | 0.190309 | − | 0.981724i | \(-0.439051\pi\) | ||||
0.190309 | + | 0.981724i | \(0.439051\pi\) | |||||||
\(942\) | −18.0660 | −0.588623 | ||||||||
\(943\) | 15.1846 | 0.494479 | ||||||||
\(944\) | −0.319094 | −0.0103856 | ||||||||
\(945\) | −70.3975 | −2.29003 | ||||||||
\(946\) | 5.21339 | 0.169502 | ||||||||
\(947\) | −26.1893 | −0.851037 | −0.425518 | − | 0.904950i | \(-0.639908\pi\) | ||||
−0.425518 | + | 0.904950i | \(0.639908\pi\) | |||||||
\(948\) | −18.4144 | −0.598073 | ||||||||
\(949\) | 0.520470 | 0.0168952 | ||||||||
\(950\) | 40.0200 | 1.29842 | ||||||||
\(951\) | −3.30931 | −0.107312 | ||||||||
\(952\) | −21.3227 | −0.691072 | ||||||||
\(953\) | −54.0727 | −1.75159 | −0.875794 | − | 0.482685i | \(-0.839662\pi\) | ||||
−0.875794 | + | 0.482685i | \(0.839662\pi\) | |||||||
\(954\) | 8.43959 | 0.273242 | ||||||||
\(955\) | −31.9022 | −1.03233 | ||||||||
\(956\) | 43.7563 | 1.41518 | ||||||||
\(957\) | −0.716281 | −0.0231541 | ||||||||
\(958\) | −62.2028 | −2.00968 | ||||||||
\(959\) | −77.6270 | −2.50671 | ||||||||
\(960\) | 40.0185 | 1.29159 | ||||||||
\(961\) | 36.6146 | 1.18112 | ||||||||
\(962\) | 0.545168 | 0.0175769 | ||||||||
\(963\) | 1.65754 | 0.0534134 | ||||||||
\(964\) | −42.9942 | −1.38475 | ||||||||
\(965\) | 17.2171 | 0.554239 | ||||||||
\(966\) | −52.5432 | −1.69055 | ||||||||
\(967\) | 27.0777 | 0.870761 | 0.435381 | − | 0.900247i | \(-0.356614\pi\) | ||||
0.435381 | + | 0.900247i | \(0.356614\pi\) | |||||||
\(968\) | 9.33862 | 0.300154 | ||||||||
\(969\) | −16.6790 | −0.535806 | ||||||||
\(970\) | 74.2540 | 2.38415 | ||||||||
\(971\) | −53.2776 | −1.70976 | −0.854880 | − | 0.518825i | \(-0.826370\pi\) | ||||
−0.854880 | + | 0.518825i | \(0.826370\pi\) | |||||||
\(972\) | −38.2201 | −1.22591 | ||||||||
\(973\) | 3.91864 | 0.125626 | ||||||||
\(974\) | 75.5990 | 2.42235 | ||||||||
\(975\) | 0.635633 | 0.0203565 | ||||||||
\(976\) | −16.6999 | −0.534550 | ||||||||
\(977\) | −55.1915 | −1.76573 | −0.882866 | − | 0.469625i | \(-0.844389\pi\) | ||||
−0.882866 | + | 0.469625i | \(0.844389\pi\) | |||||||
\(978\) | 11.5618 | 0.369705 | ||||||||
\(979\) | 8.89163 | 0.284178 | ||||||||
\(980\) | 70.9674 | 2.26697 | ||||||||
\(981\) | 2.38855 | 0.0762606 | ||||||||
\(982\) | 1.98521 | 0.0633505 | ||||||||
\(983\) | −12.5933 | −0.401664 | −0.200832 | − | 0.979626i | \(-0.564365\pi\) | ||||
−0.200832 | + | 0.979626i | \(0.564365\pi\) | |||||||
\(984\) | 2.29662 | 0.0732137 | ||||||||
\(985\) | −36.7877 | −1.17215 | ||||||||
\(986\) | −12.8996 | −0.410806 | ||||||||
\(987\) | 20.2369 | 0.644146 | ||||||||
\(988\) | 0.527424 | 0.0167796 | ||||||||
\(989\) | 22.0707 | 0.701809 | ||||||||
\(990\) | −9.68952 | −0.307953 | ||||||||
\(991\) | 52.1016 | 1.65506 | 0.827532 | − | 0.561419i | \(-0.189744\pi\) | ||||
0.827532 | + | 0.561419i | \(0.189744\pi\) | |||||||
\(992\) | 66.0874 | 2.09828 | ||||||||
\(993\) | 37.7010 | 1.19640 | ||||||||
\(994\) | −108.458 | −3.44008 | ||||||||
\(995\) | −23.5556 | −0.746762 | ||||||||
\(996\) | −2.48705 | −0.0788053 | ||||||||
\(997\) | 20.6417 | 0.653729 | 0.326864 | − | 0.945071i | \(-0.394008\pi\) | ||||
0.326864 | + | 0.945071i | \(0.394008\pi\) | |||||||
\(998\) | −37.0670 | −1.17333 | ||||||||
\(999\) | 15.9012 | 0.503092 |
(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 | 4031.2.a.c.1.9 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.9 | ✓ | 61 | 1.1 | even | 1 | trivial |