Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(81\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.44759 | −1.41312 | −0.706559 | − | 0.707654i | \(-0.749754\pi\) | ||||
−0.706559 | + | 0.707654i | \(0.749754\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.910070 | 0.406996 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(6\) | 2.44759 | 0.999226 | ||||||||
\(7\) | −1.13462 | −0.428845 | −0.214422 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214422 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.99071 | 0.996905 | ||||||||
\(10\) | −0.910070 | −0.287789 | ||||||||
\(11\) | 1.08567 | 0.327343 | 0.163672 | − | 0.986515i | \(-0.447666\pi\) | ||||
0.163672 | + | 0.986515i | \(0.447666\pi\) | |||||||
\(12\) | −2.44759 | −0.706559 | ||||||||
\(13\) | 0.0487246 | 0.0135138 | 0.00675688 | − | 0.999977i | \(-0.497849\pi\) | ||||
0.00675688 | + | 0.999977i | \(0.497849\pi\) | |||||||
\(14\) | 1.13462 | 0.303239 | ||||||||
\(15\) | −2.22748 | −0.575133 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.38283 | 1.30553 | 0.652764 | − | 0.757561i | \(-0.273609\pi\) | ||||
0.652764 | + | 0.757561i | \(0.273609\pi\) | |||||||
\(18\) | −2.99071 | −0.704918 | ||||||||
\(19\) | 8.07160 | 1.85175 | 0.925876 | − | 0.377827i | \(-0.123328\pi\) | ||||
0.925876 | + | 0.377827i | \(0.123328\pi\) | |||||||
\(20\) | 0.910070 | 0.203498 | ||||||||
\(21\) | 2.77708 | 0.606008 | ||||||||
\(22\) | −1.08567 | −0.231467 | ||||||||
\(23\) | −3.40168 | −0.709298 | −0.354649 | − | 0.934999i | \(-0.615400\pi\) | ||||
−0.354649 | + | 0.934999i | \(0.615400\pi\) | |||||||
\(24\) | 2.44759 | 0.499613 | ||||||||
\(25\) | −4.17177 | −0.834355 | ||||||||
\(26\) | −0.0487246 | −0.00955567 | ||||||||
\(27\) | 0.0227294 | 0.00437428 | ||||||||
\(28\) | −1.13462 | −0.214422 | ||||||||
\(29\) | 3.07113 | 0.570295 | 0.285148 | − | 0.958484i | \(-0.407957\pi\) | ||||
0.285148 | + | 0.958484i | \(0.407957\pi\) | |||||||
\(30\) | 2.22748 | 0.406681 | ||||||||
\(31\) | −9.22104 | −1.65615 | −0.828073 | − | 0.560620i | \(-0.810563\pi\) | ||||
−0.828073 | + | 0.560620i | \(0.810563\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.65729 | −0.462575 | ||||||||
\(34\) | −5.38283 | −0.923148 | ||||||||
\(35\) | −1.03258 | −0.174538 | ||||||||
\(36\) | 2.99071 | 0.498452 | ||||||||
\(37\) | −1.93027 | −0.317335 | −0.158667 | − | 0.987332i | \(-0.550720\pi\) | ||||
−0.158667 | + | 0.987332i | \(0.550720\pi\) | |||||||
\(38\) | −8.07160 | −1.30939 | ||||||||
\(39\) | −0.119258 | −0.0190966 | ||||||||
\(40\) | −0.910070 | −0.143895 | ||||||||
\(41\) | −9.73126 | −1.51977 | −0.759884 | − | 0.650059i | \(-0.774744\pi\) | ||||
−0.759884 | + | 0.650059i | \(0.774744\pi\) | |||||||
\(42\) | −2.77708 | −0.428513 | ||||||||
\(43\) | −11.9523 | −1.82271 | −0.911353 | − | 0.411627i | \(-0.864961\pi\) | ||||
−0.911353 | + | 0.411627i | \(0.864961\pi\) | |||||||
\(44\) | 1.08567 | 0.163672 | ||||||||
\(45\) | 2.72176 | 0.405736 | ||||||||
\(46\) | 3.40168 | 0.501550 | ||||||||
\(47\) | 10.5796 | 1.54320 | 0.771600 | − | 0.636109i | \(-0.219457\pi\) | ||||
0.771600 | + | 0.636109i | \(0.219457\pi\) | |||||||
\(48\) | −2.44759 | −0.353280 | ||||||||
\(49\) | −5.71265 | −0.816092 | ||||||||
\(50\) | 4.17177 | 0.589978 | ||||||||
\(51\) | −13.1750 | −1.84487 | ||||||||
\(52\) | 0.0487246 | 0.00675688 | ||||||||
\(53\) | 7.11073 | 0.976734 | 0.488367 | − | 0.872638i | \(-0.337593\pi\) | ||||
0.488367 | + | 0.872638i | \(0.337593\pi\) | |||||||
\(54\) | −0.0227294 | −0.00309308 | ||||||||
\(55\) | 0.988040 | 0.133227 | ||||||||
\(56\) | 1.13462 | 0.151619 | ||||||||
\(57\) | −19.7560 | −2.61675 | ||||||||
\(58\) | −3.07113 | −0.403260 | ||||||||
\(59\) | −12.3864 | −1.61257 | −0.806287 | − | 0.591524i | \(-0.798526\pi\) | ||||
−0.806287 | + | 0.591524i | \(0.798526\pi\) | |||||||
\(60\) | −2.22748 | −0.287567 | ||||||||
\(61\) | 7.19444 | 0.921153 | 0.460577 | − | 0.887620i | \(-0.347643\pi\) | ||||
0.460577 | + | 0.887620i | \(0.347643\pi\) | |||||||
\(62\) | 9.22104 | 1.17107 | ||||||||
\(63\) | −3.39331 | −0.427517 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0443428 | 0.00550004 | ||||||||
\(66\) | 2.65729 | 0.327090 | ||||||||
\(67\) | −0.822257 | −0.100455 | −0.0502273 | − | 0.998738i | \(-0.515995\pi\) | ||||
−0.0502273 | + | 0.998738i | \(0.515995\pi\) | |||||||
\(68\) | 5.38283 | 0.652764 | ||||||||
\(69\) | 8.32592 | 1.00232 | ||||||||
\(70\) | 1.03258 | 0.123417 | ||||||||
\(71\) | −2.06749 | −0.245366 | −0.122683 | − | 0.992446i | \(-0.539150\pi\) | ||||
−0.122683 | + | 0.992446i | \(0.539150\pi\) | |||||||
\(72\) | −2.99071 | −0.352459 | ||||||||
\(73\) | 10.5136 | 1.23052 | 0.615259 | − | 0.788325i | \(-0.289051\pi\) | ||||
0.615259 | + | 0.788325i | \(0.289051\pi\) | |||||||
\(74\) | 1.93027 | 0.224390 | ||||||||
\(75\) | 10.2108 | 1.17904 | ||||||||
\(76\) | 8.07160 | 0.925876 | ||||||||
\(77\) | −1.23182 | −0.140379 | ||||||||
\(78\) | 0.119258 | 0.0135033 | ||||||||
\(79\) | −3.84611 | −0.432721 | −0.216361 | − | 0.976314i | \(-0.569419\pi\) | ||||
−0.216361 | + | 0.976314i | \(0.569419\pi\) | |||||||
\(80\) | 0.910070 | 0.101749 | ||||||||
\(81\) | −9.02777 | −1.00309 | ||||||||
\(82\) | 9.73126 | 1.07464 | ||||||||
\(83\) | 15.6774 | 1.72082 | 0.860411 | − | 0.509601i | \(-0.170207\pi\) | ||||
0.860411 | + | 0.509601i | \(0.170207\pi\) | |||||||
\(84\) | 2.77708 | 0.303004 | ||||||||
\(85\) | 4.89875 | 0.531344 | ||||||||
\(86\) | 11.9523 | 1.28885 | ||||||||
\(87\) | −7.51689 | −0.805895 | ||||||||
\(88\) | −1.08567 | −0.115733 | ||||||||
\(89\) | −8.57779 | −0.909244 | −0.454622 | − | 0.890684i | \(-0.650226\pi\) | ||||
−0.454622 | + | 0.890684i | \(0.650226\pi\) | |||||||
\(90\) | −2.72176 | −0.286899 | ||||||||
\(91\) | −0.0552837 | −0.00579530 | ||||||||
\(92\) | −3.40168 | −0.354649 | ||||||||
\(93\) | 22.5693 | 2.34033 | ||||||||
\(94\) | −10.5796 | −1.09121 | ||||||||
\(95\) | 7.34572 | 0.753655 | ||||||||
\(96\) | 2.44759 | 0.249806 | ||||||||
\(97\) | 12.7856 | 1.29818 | 0.649092 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649092 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(98\) | 5.71265 | 0.577064 | ||||||||
\(99\) | 3.24694 | 0.326330 | ||||||||
\(100\) | −4.17177 | −0.417177 | ||||||||
\(101\) | 13.0332 | 1.29686 | 0.648428 | − | 0.761276i | \(-0.275427\pi\) | ||||
0.648428 | + | 0.761276i | \(0.275427\pi\) | |||||||
\(102\) | 13.1750 | 1.30452 | ||||||||
\(103\) | −17.8803 | −1.76180 | −0.880899 | − | 0.473305i | \(-0.843061\pi\) | ||||
−0.880899 | + | 0.473305i | \(0.843061\pi\) | |||||||
\(104\) | −0.0487246 | −0.00477784 | ||||||||
\(105\) | 2.52734 | 0.246643 | ||||||||
\(106\) | −7.11073 | −0.690655 | ||||||||
\(107\) | −7.58835 | −0.733593 | −0.366797 | − | 0.930301i | \(-0.619546\pi\) | ||||
−0.366797 | + | 0.930301i | \(0.619546\pi\) | |||||||
\(108\) | 0.0227294 | 0.00218714 | ||||||||
\(109\) | 2.94013 | 0.281613 | 0.140807 | − | 0.990037i | \(-0.455030\pi\) | ||||
0.140807 | + | 0.990037i | \(0.455030\pi\) | |||||||
\(110\) | −0.988040 | −0.0942059 | ||||||||
\(111\) | 4.72452 | 0.448432 | ||||||||
\(112\) | −1.13462 | −0.107211 | ||||||||
\(113\) | 8.38348 | 0.788652 | 0.394326 | − | 0.918971i | \(-0.370978\pi\) | ||||
0.394326 | + | 0.918971i | \(0.370978\pi\) | |||||||
\(114\) | 19.7560 | 1.85032 | ||||||||
\(115\) | −3.09576 | −0.288681 | ||||||||
\(116\) | 3.07113 | 0.285148 | ||||||||
\(117\) | 0.145721 | 0.0134719 | ||||||||
\(118\) | 12.3864 | 1.14026 | ||||||||
\(119\) | −6.10744 | −0.559869 | ||||||||
\(120\) | 2.22748 | 0.203340 | ||||||||
\(121\) | −9.82131 | −0.892846 | ||||||||
\(122\) | −7.19444 | −0.651354 | ||||||||
\(123\) | 23.8182 | 2.14761 | ||||||||
\(124\) | −9.22104 | −0.828073 | ||||||||
\(125\) | −8.34696 | −0.746574 | ||||||||
\(126\) | 3.39331 | 0.302300 | ||||||||
\(127\) | −10.9488 | −0.971546 | −0.485773 | − | 0.874085i | \(-0.661462\pi\) | ||||
−0.485773 | + | 0.874085i | \(0.661462\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 29.2543 | 2.57570 | ||||||||
\(130\) | −0.0443428 | −0.00388912 | ||||||||
\(131\) | −18.0252 | −1.57487 | −0.787435 | − | 0.616397i | \(-0.788591\pi\) | ||||
−0.787435 | + | 0.616397i | \(0.788591\pi\) | |||||||
\(132\) | −2.65729 | −0.231287 | ||||||||
\(133\) | −9.15817 | −0.794114 | ||||||||
\(134\) | 0.822257 | 0.0710322 | ||||||||
\(135\) | 0.0206854 | 0.00178031 | ||||||||
\(136\) | −5.38283 | −0.461574 | ||||||||
\(137\) | −17.6524 | −1.50814 | −0.754072 | − | 0.656792i | \(-0.771913\pi\) | ||||
−0.754072 | + | 0.656792i | \(0.771913\pi\) | |||||||
\(138\) | −8.32592 | −0.708749 | ||||||||
\(139\) | 5.69278 | 0.482855 | 0.241428 | − | 0.970419i | \(-0.422384\pi\) | ||||
0.241428 | + | 0.970419i | \(0.422384\pi\) | |||||||
\(140\) | −1.03258 | −0.0872689 | ||||||||
\(141\) | −25.8947 | −2.18072 | ||||||||
\(142\) | 2.06749 | 0.173500 | ||||||||
\(143\) | 0.0528990 | 0.00442364 | ||||||||
\(144\) | 2.99071 | 0.249226 | ||||||||
\(145\) | 2.79495 | 0.232108 | ||||||||
\(146\) | −10.5136 | −0.870108 | ||||||||
\(147\) | 13.9822 | 1.15324 | ||||||||
\(148\) | −1.93027 | −0.158667 | ||||||||
\(149\) | 1.06058 | 0.0868861 | 0.0434430 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434430 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(150\) | −10.2108 | −0.833709 | ||||||||
\(151\) | 15.7425 | 1.28110 | 0.640552 | − | 0.767914i | \(-0.278705\pi\) | ||||
0.640552 | + | 0.767914i | \(0.278705\pi\) | |||||||
\(152\) | −8.07160 | −0.654693 | ||||||||
\(153\) | 16.0985 | 1.30149 | ||||||||
\(154\) | 1.23182 | 0.0992632 | ||||||||
\(155\) | −8.39179 | −0.674045 | ||||||||
\(156\) | −0.119258 | −0.00954828 | ||||||||
\(157\) | −10.1560 | −0.810540 | −0.405270 | − | 0.914197i | \(-0.632823\pi\) | ||||
−0.405270 | + | 0.914197i | \(0.632823\pi\) | |||||||
\(158\) | 3.84611 | 0.305980 | ||||||||
\(159\) | −17.4042 | −1.38024 | ||||||||
\(160\) | −0.910070 | −0.0719474 | ||||||||
\(161\) | 3.85960 | 0.304179 | ||||||||
\(162\) | 9.02777 | 0.709289 | ||||||||
\(163\) | 9.10486 | 0.713148 | 0.356574 | − | 0.934267i | \(-0.383945\pi\) | ||||
0.356574 | + | 0.934267i | \(0.383945\pi\) | |||||||
\(164\) | −9.73126 | −0.759884 | ||||||||
\(165\) | −2.41832 | −0.188266 | ||||||||
\(166\) | −15.6774 | −1.21680 | ||||||||
\(167\) | 11.1294 | 0.861222 | 0.430611 | − | 0.902538i | \(-0.358298\pi\) | ||||
0.430611 | + | 0.902538i | \(0.358298\pi\) | |||||||
\(168\) | −2.77708 | −0.214256 | ||||||||
\(169\) | −12.9976 | −0.999817 | ||||||||
\(170\) | −4.89875 | −0.375717 | ||||||||
\(171\) | 24.1399 | 1.84602 | ||||||||
\(172\) | −11.9523 | −0.911353 | ||||||||
\(173\) | 6.71172 | 0.510283 | 0.255141 | − | 0.966904i | \(-0.417878\pi\) | ||||
0.255141 | + | 0.966904i | \(0.417878\pi\) | |||||||
\(174\) | 7.51689 | 0.569854 | ||||||||
\(175\) | 4.73336 | 0.357808 | ||||||||
\(176\) | 1.08567 | 0.0818358 | ||||||||
\(177\) | 30.3169 | 2.27876 | ||||||||
\(178\) | 8.57779 | 0.642933 | ||||||||
\(179\) | 14.4469 | 1.07981 | 0.539904 | − | 0.841726i | \(-0.318460\pi\) | ||||
0.539904 | + | 0.841726i | \(0.318460\pi\) | |||||||
\(180\) | 2.72176 | 0.202868 | ||||||||
\(181\) | 18.7339 | 1.39248 | 0.696238 | − | 0.717811i | \(-0.254856\pi\) | ||||
0.696238 | + | 0.717811i | \(0.254856\pi\) | |||||||
\(182\) | 0.0552837 | 0.00409790 | ||||||||
\(183\) | −17.6091 | −1.30170 | ||||||||
\(184\) | 3.40168 | 0.250775 | ||||||||
\(185\) | −1.75668 | −0.129154 | ||||||||
\(186\) | −22.5693 | −1.65486 | ||||||||
\(187\) | 5.84400 | 0.427356 | ||||||||
\(188\) | 10.5796 | 0.771600 | ||||||||
\(189\) | −0.0257892 | −0.00187589 | ||||||||
\(190\) | −7.34572 | −0.532915 | ||||||||
\(191\) | −15.9025 | −1.15067 | −0.575333 | − | 0.817919i | \(-0.695128\pi\) | ||||
−0.575333 | + | 0.817919i | \(0.695128\pi\) | |||||||
\(192\) | −2.44759 | −0.176640 | ||||||||
\(193\) | 14.7163 | 1.05930 | 0.529651 | − | 0.848216i | \(-0.322323\pi\) | ||||
0.529651 | + | 0.848216i | \(0.322323\pi\) | |||||||
\(194\) | −12.7856 | −0.917954 | ||||||||
\(195\) | −0.108533 | −0.00777221 | ||||||||
\(196\) | −5.71265 | −0.408046 | ||||||||
\(197\) | −7.73695 | −0.551235 | −0.275618 | − | 0.961267i | \(-0.588882\pi\) | ||||
−0.275618 | + | 0.961267i | \(0.588882\pi\) | |||||||
\(198\) | −3.24694 | −0.230750 | ||||||||
\(199\) | −20.2276 | −1.43390 | −0.716948 | − | 0.697127i | \(-0.754461\pi\) | ||||
−0.716948 | + | 0.697127i | \(0.754461\pi\) | |||||||
\(200\) | 4.17177 | 0.294989 | ||||||||
\(201\) | 2.01255 | 0.141954 | ||||||||
\(202\) | −13.0332 | −0.917016 | ||||||||
\(203\) | −3.48456 | −0.244568 | ||||||||
\(204\) | −13.1750 | −0.922433 | ||||||||
\(205\) | −8.85613 | −0.618539 | ||||||||
\(206\) | 17.8803 | 1.24578 | ||||||||
\(207\) | −10.1734 | −0.707103 | ||||||||
\(208\) | 0.0487246 | 0.00337844 | ||||||||
\(209\) | 8.76313 | 0.606159 | ||||||||
\(210\) | −2.52734 | −0.174403 | ||||||||
\(211\) | 4.52661 | 0.311625 | 0.155812 | − | 0.987787i | \(-0.450200\pi\) | ||||
0.155812 | + | 0.987787i | \(0.450200\pi\) | |||||||
\(212\) | 7.11073 | 0.488367 | ||||||||
\(213\) | 5.06037 | 0.346731 | ||||||||
\(214\) | 7.58835 | 0.518729 | ||||||||
\(215\) | −10.8774 | −0.741833 | ||||||||
\(216\) | −0.0227294 | −0.00154654 | ||||||||
\(217\) | 10.4623 | 0.710230 | ||||||||
\(218\) | −2.94013 | −0.199131 | ||||||||
\(219\) | −25.7329 | −1.73887 | ||||||||
\(220\) | 0.988040 | 0.0666136 | ||||||||
\(221\) | 0.262276 | 0.0176426 | ||||||||
\(222\) | −4.72452 | −0.317089 | ||||||||
\(223\) | 28.9180 | 1.93649 | 0.968247 | − | 0.249994i | \(-0.0804286\pi\) | ||||
0.968247 | + | 0.249994i | \(0.0804286\pi\) | |||||||
\(224\) | 1.13462 | 0.0758097 | ||||||||
\(225\) | −12.4766 | −0.831772 | ||||||||
\(226\) | −8.38348 | −0.557661 | ||||||||
\(227\) | 7.58439 | 0.503394 | 0.251697 | − | 0.967806i | \(-0.419011\pi\) | ||||
0.251697 | + | 0.967806i | \(0.419011\pi\) | |||||||
\(228\) | −19.7560 | −1.30837 | ||||||||
\(229\) | 4.73632 | 0.312985 | 0.156492 | − | 0.987679i | \(-0.449981\pi\) | ||||
0.156492 | + | 0.987679i | \(0.449981\pi\) | |||||||
\(230\) | 3.09576 | 0.204129 | ||||||||
\(231\) | 3.01500 | 0.198373 | ||||||||
\(232\) | −3.07113 | −0.201630 | ||||||||
\(233\) | −17.6630 | −1.15714 | −0.578570 | − | 0.815633i | \(-0.696389\pi\) | ||||
−0.578570 | + | 0.815633i | \(0.696389\pi\) | |||||||
\(234\) | −0.145721 | −0.00952609 | ||||||||
\(235\) | 9.62821 | 0.628075 | ||||||||
\(236\) | −12.3864 | −0.806287 | ||||||||
\(237\) | 9.41372 | 0.611487 | ||||||||
\(238\) | 6.10744 | 0.395887 | ||||||||
\(239\) | −18.2862 | −1.18284 | −0.591418 | − | 0.806365i | \(-0.701432\pi\) | ||||
−0.591418 | + | 0.806365i | \(0.701432\pi\) | |||||||
\(240\) | −2.22748 | −0.143783 | ||||||||
\(241\) | −6.16062 | −0.396841 | −0.198420 | − | 0.980117i | \(-0.563581\pi\) | ||||
−0.198420 | + | 0.980117i | \(0.563581\pi\) | |||||||
\(242\) | 9.82131 | 0.631338 | ||||||||
\(243\) | 22.0281 | 1.41311 | ||||||||
\(244\) | 7.19444 | 0.460577 | ||||||||
\(245\) | −5.19891 | −0.332146 | ||||||||
\(246\) | −23.8182 | −1.51859 | ||||||||
\(247\) | 0.393285 | 0.0250241 | ||||||||
\(248\) | 9.22104 | 0.585536 | ||||||||
\(249\) | −38.3720 | −2.43172 | ||||||||
\(250\) | 8.34696 | 0.527908 | ||||||||
\(251\) | 24.8064 | 1.56577 | 0.782884 | − | 0.622167i | \(-0.213748\pi\) | ||||
0.782884 | + | 0.622167i | \(0.213748\pi\) | |||||||
\(252\) | −3.39331 | −0.213759 | ||||||||
\(253\) | −3.69311 | −0.232184 | ||||||||
\(254\) | 10.9488 | 0.686986 | ||||||||
\(255\) | −11.9902 | −0.750852 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.1055 | 1.50366 | 0.751830 | − | 0.659356i | \(-0.229171\pi\) | ||||
0.751830 | + | 0.659356i | \(0.229171\pi\) | |||||||
\(258\) | −29.2543 | −1.82129 | ||||||||
\(259\) | 2.19012 | 0.136087 | ||||||||
\(260\) | 0.0443428 | 0.00275002 | ||||||||
\(261\) | 9.18488 | 0.568530 | ||||||||
\(262\) | 18.0252 | 1.11360 | ||||||||
\(263\) | −13.9249 | −0.858645 | −0.429322 | − | 0.903151i | \(-0.641248\pi\) | ||||
−0.429322 | + | 0.903151i | \(0.641248\pi\) | |||||||
\(264\) | 2.65729 | 0.163545 | ||||||||
\(265\) | 6.47126 | 0.397526 | ||||||||
\(266\) | 9.15817 | 0.561523 | ||||||||
\(267\) | 20.9950 | 1.28487 | ||||||||
\(268\) | −0.822257 | −0.0502273 | ||||||||
\(269\) | −23.8294 | −1.45290 | −0.726451 | − | 0.687218i | \(-0.758832\pi\) | ||||
−0.726451 | + | 0.687218i | \(0.758832\pi\) | |||||||
\(270\) | −0.0206854 | −0.00125887 | ||||||||
\(271\) | 16.6051 | 1.00869 | 0.504344 | − | 0.863503i | \(-0.331734\pi\) | ||||
0.504344 | + | 0.863503i | \(0.331734\pi\) | |||||||
\(272\) | 5.38283 | 0.326382 | ||||||||
\(273\) | 0.135312 | 0.00818945 | ||||||||
\(274\) | 17.6524 | 1.06642 | ||||||||
\(275\) | −4.52919 | −0.273120 | ||||||||
\(276\) | 8.32592 | 0.501161 | ||||||||
\(277\) | −5.96770 | −0.358564 | −0.179282 | − | 0.983798i | \(-0.557378\pi\) | ||||
−0.179282 | + | 0.983798i | \(0.557378\pi\) | |||||||
\(278\) | −5.69278 | −0.341430 | ||||||||
\(279\) | −27.5775 | −1.65102 | ||||||||
\(280\) | 1.03258 | 0.0617085 | ||||||||
\(281\) | 6.94096 | 0.414063 | 0.207031 | − | 0.978334i | \(-0.433620\pi\) | ||||
0.207031 | + | 0.978334i | \(0.433620\pi\) | |||||||
\(282\) | 25.8947 | 1.54200 | ||||||||
\(283\) | −11.8000 | −0.701439 | −0.350719 | − | 0.936481i | \(-0.614063\pi\) | ||||
−0.350719 | + | 0.936481i | \(0.614063\pi\) | |||||||
\(284\) | −2.06749 | −0.122683 | ||||||||
\(285\) | −17.9793 | −1.06500 | ||||||||
\(286\) | −0.0528990 | −0.00312798 | ||||||||
\(287\) | 11.0412 | 0.651744 | ||||||||
\(288\) | −2.99071 | −0.176229 | ||||||||
\(289\) | 11.9748 | 0.704403 | ||||||||
\(290\) | −2.79495 | −0.164125 | ||||||||
\(291\) | −31.2940 | −1.83449 | ||||||||
\(292\) | 10.5136 | 0.615259 | ||||||||
\(293\) | 26.1606 | 1.52832 | 0.764160 | − | 0.645027i | \(-0.223154\pi\) | ||||
0.764160 | + | 0.645027i | \(0.223154\pi\) | |||||||
\(294\) | −13.9822 | −0.815461 | ||||||||
\(295\) | −11.2725 | −0.656311 | ||||||||
\(296\) | 1.93027 | 0.112195 | ||||||||
\(297\) | 0.0246768 | 0.00143189 | ||||||||
\(298\) | −1.06058 | −0.0614377 | ||||||||
\(299\) | −0.165745 | −0.00958529 | ||||||||
\(300\) | 10.2108 | 0.589521 | ||||||||
\(301\) | 13.5612 | 0.781657 | ||||||||
\(302\) | −15.7425 | −0.905878 | ||||||||
\(303\) | −31.9001 | −1.83261 | ||||||||
\(304\) | 8.07160 | 0.462938 | ||||||||
\(305\) | 6.54744 | 0.374905 | ||||||||
\(306\) | −16.0985 | −0.920290 | ||||||||
\(307\) | −22.3696 | −1.27670 | −0.638349 | − | 0.769747i | \(-0.720382\pi\) | ||||
−0.638349 | + | 0.769747i | \(0.720382\pi\) | |||||||
\(308\) | −1.23182 | −0.0701897 | ||||||||
\(309\) | 43.7637 | 2.48963 | ||||||||
\(310\) | 8.39179 | 0.476622 | ||||||||
\(311\) | −20.4126 | −1.15749 | −0.578745 | − | 0.815508i | \(-0.696457\pi\) | ||||
−0.578745 | + | 0.815508i | \(0.696457\pi\) | |||||||
\(312\) | 0.119258 | 0.00675165 | ||||||||
\(313\) | 34.8587 | 1.97033 | 0.985166 | − | 0.171603i | \(-0.0548947\pi\) | ||||
0.985166 | + | 0.171603i | \(0.0548947\pi\) | |||||||
\(314\) | 10.1560 | 0.573139 | ||||||||
\(315\) | −3.08815 | −0.173998 | ||||||||
\(316\) | −3.84611 | −0.216361 | ||||||||
\(317\) | 9.73168 | 0.546585 | 0.273293 | − | 0.961931i | \(-0.411887\pi\) | ||||
0.273293 | + | 0.961931i | \(0.411887\pi\) | |||||||
\(318\) | 17.4042 | 0.975978 | ||||||||
\(319\) | 3.33425 | 0.186682 | ||||||||
\(320\) | 0.910070 | 0.0508745 | ||||||||
\(321\) | 18.5732 | 1.03665 | ||||||||
\(322\) | −3.85960 | −0.215087 | ||||||||
\(323\) | 43.4481 | 2.41751 | ||||||||
\(324\) | −9.02777 | −0.501543 | ||||||||
\(325\) | −0.203268 | −0.0112753 | ||||||||
\(326\) | −9.10486 | −0.504272 | ||||||||
\(327\) | −7.19624 | −0.397953 | ||||||||
\(328\) | 9.73126 | 0.537319 | ||||||||
\(329\) | −12.0038 | −0.661793 | ||||||||
\(330\) | 2.41832 | 0.133124 | ||||||||
\(331\) | −20.8701 | −1.14712 | −0.573562 | − | 0.819162i | \(-0.694439\pi\) | ||||
−0.573562 | + | 0.819162i | \(0.694439\pi\) | |||||||
\(332\) | 15.6774 | 0.860411 | ||||||||
\(333\) | −5.77289 | −0.316352 | ||||||||
\(334\) | −11.1294 | −0.608976 | ||||||||
\(335\) | −0.748311 | −0.0408846 | ||||||||
\(336\) | 2.77708 | 0.151502 | ||||||||
\(337\) | −16.0986 | −0.876946 | −0.438473 | − | 0.898744i | \(-0.644480\pi\) | ||||
−0.438473 | + | 0.898744i | \(0.644480\pi\) | |||||||
\(338\) | 12.9976 | 0.706978 | ||||||||
\(339\) | −20.5194 | −1.11446 | ||||||||
\(340\) | 4.89875 | 0.265672 | ||||||||
\(341\) | −10.0110 | −0.542128 | ||||||||
\(342\) | −24.1399 | −1.30533 | ||||||||
\(343\) | 14.4240 | 0.778821 | ||||||||
\(344\) | 11.9523 | 0.644424 | ||||||||
\(345\) | 7.57717 | 0.407941 | ||||||||
\(346\) | −6.71172 | −0.360824 | ||||||||
\(347\) | −21.3465 | −1.14594 | −0.572970 | − | 0.819576i | \(-0.694209\pi\) | ||||
−0.572970 | + | 0.819576i | \(0.694209\pi\) | |||||||
\(348\) | −7.51689 | −0.402948 | ||||||||
\(349\) | −34.7456 | −1.85989 | −0.929945 | − | 0.367700i | \(-0.880145\pi\) | ||||
−0.929945 | + | 0.367700i | \(0.880145\pi\) | |||||||
\(350\) | −4.73336 | −0.253009 | ||||||||
\(351\) | 0.00110748 | 5.91130e−5 0 | ||||||||
\(352\) | −1.08567 | −0.0578666 | ||||||||
\(353\) | 12.3338 | 0.656462 | 0.328231 | − | 0.944597i | \(-0.393548\pi\) | ||||
0.328231 | + | 0.944597i | \(0.393548\pi\) | |||||||
\(354\) | −30.3169 | −1.61133 | ||||||||
\(355\) | −1.88156 | −0.0998627 | ||||||||
\(356\) | −8.57779 | −0.454622 | ||||||||
\(357\) | 14.9485 | 0.791161 | ||||||||
\(358\) | −14.4469 | −0.763540 | ||||||||
\(359\) | −30.4610 | −1.60767 | −0.803834 | − | 0.594853i | \(-0.797210\pi\) | ||||
−0.803834 | + | 0.594853i | \(0.797210\pi\) | |||||||
\(360\) | −2.72176 | −0.143449 | ||||||||
\(361\) | 46.1508 | 2.42899 | ||||||||
\(362\) | −18.7339 | −0.984630 | ||||||||
\(363\) | 24.0386 | 1.26170 | ||||||||
\(364\) | −0.0552837 | −0.00289765 | ||||||||
\(365\) | 9.56807 | 0.500816 | ||||||||
\(366\) | 17.6091 | 0.920440 | ||||||||
\(367\) | −11.3977 | −0.594956 | −0.297478 | − | 0.954729i | \(-0.596145\pi\) | ||||
−0.297478 | + | 0.954729i | \(0.596145\pi\) | |||||||
\(368\) | −3.40168 | −0.177325 | ||||||||
\(369\) | −29.1034 | −1.51506 | ||||||||
\(370\) | 1.75668 | 0.0913256 | ||||||||
\(371\) | −8.06795 | −0.418867 | ||||||||
\(372\) | 22.5693 | 1.17017 | ||||||||
\(373\) | −19.8719 | −1.02893 | −0.514465 | − | 0.857511i | \(-0.672010\pi\) | ||||
−0.514465 | + | 0.857511i | \(0.672010\pi\) | |||||||
\(374\) | −5.84400 | −0.302186 | ||||||||
\(375\) | 20.4300 | 1.05500 | ||||||||
\(376\) | −10.5796 | −0.545603 | ||||||||
\(377\) | 0.149640 | 0.00770684 | ||||||||
\(378\) | 0.0257892 | 0.00132645 | ||||||||
\(379\) | 20.8158 | 1.06923 | 0.534617 | − | 0.845094i | \(-0.320456\pi\) | ||||
0.534617 | + | 0.845094i | \(0.320456\pi\) | |||||||
\(380\) | 7.34572 | 0.376828 | ||||||||
\(381\) | 26.7981 | 1.37291 | ||||||||
\(382\) | 15.9025 | 0.813644 | ||||||||
\(383\) | 2.99342 | 0.152956 | 0.0764782 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764782 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(384\) | 2.44759 | 0.124903 | ||||||||
\(385\) | −1.12105 | −0.0571338 | ||||||||
\(386\) | −14.7163 | −0.749039 | ||||||||
\(387\) | −35.7458 | −1.81706 | ||||||||
\(388\) | 12.7856 | 0.649092 | ||||||||
\(389\) | −12.3423 | −0.625781 | −0.312890 | − | 0.949789i | \(-0.601297\pi\) | ||||
−0.312890 | + | 0.949789i | \(0.601297\pi\) | |||||||
\(390\) | 0.108533 | 0.00549579 | ||||||||
\(391\) | −18.3106 | −0.926009 | ||||||||
\(392\) | 5.71265 | 0.288532 | ||||||||
\(393\) | 44.1184 | 2.22548 | ||||||||
\(394\) | 7.73695 | 0.389782 | ||||||||
\(395\) | −3.50023 | −0.176116 | ||||||||
\(396\) | 3.24694 | 0.163165 | ||||||||
\(397\) | 0.189131 | 0.00949224 | 0.00474612 | − | 0.999989i | \(-0.498489\pi\) | ||||
0.00474612 | + | 0.999989i | \(0.498489\pi\) | |||||||
\(398\) | 20.2276 | 1.01392 | ||||||||
\(399\) | 22.4155 | 1.12218 | ||||||||
\(400\) | −4.17177 | −0.208589 | ||||||||
\(401\) | 18.3476 | 0.916233 | 0.458117 | − | 0.888892i | \(-0.348524\pi\) | ||||
0.458117 | + | 0.888892i | \(0.348524\pi\) | |||||||
\(402\) | −2.01255 | −0.100377 | ||||||||
\(403\) | −0.449291 | −0.0223808 | ||||||||
\(404\) | 13.0332 | 0.648428 | ||||||||
\(405\) | −8.21591 | −0.408252 | ||||||||
\(406\) | 3.48456 | 0.172936 | ||||||||
\(407\) | −2.09565 | −0.103877 | ||||||||
\(408\) | 13.1750 | 0.652259 | ||||||||
\(409\) | −1.28838 | −0.0637063 | −0.0318531 | − | 0.999493i | \(-0.510141\pi\) | ||||
−0.0318531 | + | 0.999493i | \(0.510141\pi\) | |||||||
\(410\) | 8.85613 | 0.437373 | ||||||||
\(411\) | 43.2058 | 2.13119 | ||||||||
\(412\) | −17.8803 | −0.880899 | ||||||||
\(413\) | 14.0538 | 0.691544 | ||||||||
\(414\) | 10.1734 | 0.499997 | ||||||||
\(415\) | 14.2676 | 0.700367 | ||||||||
\(416\) | −0.0487246 | −0.00238892 | ||||||||
\(417\) | −13.9336 | −0.682331 | ||||||||
\(418\) | −8.76313 | −0.428619 | ||||||||
\(419\) | −7.67913 | −0.375150 | −0.187575 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187575 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(420\) | 2.52734 | 0.123321 | ||||||||
\(421\) | 20.2118 | 0.985061 | 0.492531 | − | 0.870295i | \(-0.336072\pi\) | ||||
0.492531 | + | 0.870295i | \(0.336072\pi\) | |||||||
\(422\) | −4.52661 | −0.220352 | ||||||||
\(423\) | 31.6407 | 1.53842 | ||||||||
\(424\) | −7.11073 | −0.345328 | ||||||||
\(425\) | −22.4559 | −1.08927 | ||||||||
\(426\) | −5.06037 | −0.245176 | ||||||||
\(427\) | −8.16292 | −0.395032 | ||||||||
\(428\) | −7.58835 | −0.366797 | ||||||||
\(429\) | −0.129475 | −0.00625113 | ||||||||
\(430\) | 10.8774 | 0.524555 | ||||||||
\(431\) | −6.92743 | −0.333683 | −0.166841 | − | 0.985984i | \(-0.553357\pi\) | ||||
−0.166841 | + | 0.985984i | \(0.553357\pi\) | |||||||
\(432\) | 0.0227294 | 0.00109357 | ||||||||
\(433\) | 20.2457 | 0.972948 | 0.486474 | − | 0.873695i | \(-0.338283\pi\) | ||||
0.486474 | + | 0.873695i | \(0.338283\pi\) | |||||||
\(434\) | −10.4623 | −0.502208 | ||||||||
\(435\) | −6.84090 | −0.327996 | ||||||||
\(436\) | 2.94013 | 0.140807 | ||||||||
\(437\) | −27.4570 | −1.31345 | ||||||||
\(438\) | 25.7329 | 1.22957 | ||||||||
\(439\) | −9.40249 | −0.448756 | −0.224378 | − | 0.974502i | \(-0.572035\pi\) | ||||
−0.224378 | + | 0.974502i | \(0.572035\pi\) | |||||||
\(440\) | −0.988040 | −0.0471030 | ||||||||
\(441\) | −17.0849 | −0.813566 | ||||||||
\(442\) | −0.262276 | −0.0124752 | ||||||||
\(443\) | 4.45869 | 0.211839 | 0.105919 | − | 0.994375i | \(-0.466221\pi\) | ||||
0.105919 | + | 0.994375i | \(0.466221\pi\) | |||||||
\(444\) | 4.72452 | 0.224216 | ||||||||
\(445\) | −7.80639 | −0.370059 | ||||||||
\(446\) | −28.9180 | −1.36931 | ||||||||
\(447\) | −2.59587 | −0.122780 | ||||||||
\(448\) | −1.13462 | −0.0536056 | ||||||||
\(449\) | −22.6462 | −1.06874 | −0.534370 | − | 0.845251i | \(-0.679451\pi\) | ||||
−0.534370 | + | 0.845251i | \(0.679451\pi\) | |||||||
\(450\) | 12.4766 | 0.588151 | ||||||||
\(451\) | −10.5650 | −0.497486 | ||||||||
\(452\) | 8.38348 | 0.394326 | ||||||||
\(453\) | −38.5312 | −1.81035 | ||||||||
\(454\) | −7.58439 | −0.355953 | ||||||||
\(455\) | −0.0503120 | −0.00235866 | ||||||||
\(456\) | 19.7560 | 0.925160 | ||||||||
\(457\) | −19.7359 | −0.923208 | −0.461604 | − | 0.887086i | \(-0.652726\pi\) | ||||
−0.461604 | + | 0.887086i | \(0.652726\pi\) | |||||||
\(458\) | −4.73632 | −0.221313 | ||||||||
\(459\) | 0.122349 | 0.00571074 | ||||||||
\(460\) | −3.09576 | −0.144341 | ||||||||
\(461\) | −33.0477 | −1.53919 | −0.769593 | − | 0.638534i | \(-0.779541\pi\) | ||||
−0.769593 | + | 0.638534i | \(0.779541\pi\) | |||||||
\(462\) | −3.01500 | −0.140271 | ||||||||
\(463\) | −20.2663 | −0.941854 | −0.470927 | − | 0.882172i | \(-0.656080\pi\) | ||||
−0.470927 | + | 0.882172i | \(0.656080\pi\) | |||||||
\(464\) | 3.07113 | 0.142574 | ||||||||
\(465\) | 20.5397 | 0.952505 | ||||||||
\(466\) | 17.6630 | 0.818221 | ||||||||
\(467\) | −3.50005 | −0.161963 | −0.0809814 | − | 0.996716i | \(-0.525805\pi\) | ||||
−0.0809814 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(468\) | 0.145721 | 0.00673597 | ||||||||
\(469\) | 0.932946 | 0.0430794 | ||||||||
\(470\) | −9.62821 | −0.444116 | ||||||||
\(471\) | 24.8579 | 1.14539 | ||||||||
\(472\) | 12.3864 | 0.570131 | ||||||||
\(473\) | −12.9763 | −0.596650 | ||||||||
\(474\) | −9.41372 | −0.432386 | ||||||||
\(475\) | −33.6729 | −1.54502 | ||||||||
\(476\) | −6.10744 | −0.279934 | ||||||||
\(477\) | 21.2662 | 0.973710 | ||||||||
\(478\) | 18.2862 | 0.836392 | ||||||||
\(479\) | −38.0198 | −1.73717 | −0.868585 | − | 0.495540i | \(-0.834970\pi\) | ||||
−0.868585 | + | 0.495540i | \(0.834970\pi\) | |||||||
\(480\) | 2.22748 | 0.101670 | ||||||||
\(481\) | −0.0940517 | −0.00428839 | ||||||||
\(482\) | 6.16062 | 0.280609 | ||||||||
\(483\) | −9.44672 | −0.429841 | ||||||||
\(484\) | −9.82131 | −0.446423 | ||||||||
\(485\) | 11.6358 | 0.528355 | ||||||||
\(486\) | −22.0281 | −0.999216 | ||||||||
\(487\) | 2.64149 | 0.119697 | 0.0598487 | − | 0.998207i | \(-0.480938\pi\) | ||||
0.0598487 | + | 0.998207i | \(0.480938\pi\) | |||||||
\(488\) | −7.19444 | −0.325677 | ||||||||
\(489\) | −22.2850 | −1.00776 | ||||||||
\(490\) | 5.19891 | 0.234863 | ||||||||
\(491\) | 25.7930 | 1.16402 | 0.582011 | − | 0.813181i | \(-0.302266\pi\) | ||||
0.582011 | + | 0.813181i | \(0.302266\pi\) | |||||||
\(492\) | 23.8182 | 1.07381 | ||||||||
\(493\) | 16.5314 | 0.744537 | ||||||||
\(494\) | −0.393285 | −0.0176947 | ||||||||
\(495\) | 2.95494 | 0.132815 | ||||||||
\(496\) | −9.22104 | −0.414037 | ||||||||
\(497\) | 2.34580 | 0.105224 | ||||||||
\(498\) | 38.3720 | 1.71949 | ||||||||
\(499\) | −17.3024 | −0.774562 | −0.387281 | − | 0.921962i | \(-0.626586\pi\) | ||||
−0.387281 | + | 0.921962i | \(0.626586\pi\) | |||||||
\(500\) | −8.34696 | −0.373287 | ||||||||
\(501\) | −27.2403 | −1.21701 | ||||||||
\(502\) | −24.8064 | −1.10717 | ||||||||
\(503\) | −36.5845 | −1.63122 | −0.815610 | − | 0.578602i | \(-0.803599\pi\) | ||||
−0.815610 | + | 0.578602i | \(0.803599\pi\) | |||||||
\(504\) | 3.39331 | 0.151150 | ||||||||
\(505\) | 11.8612 | 0.527815 | ||||||||
\(506\) | 3.69311 | 0.164179 | ||||||||
\(507\) | 31.8129 | 1.41286 | ||||||||
\(508\) | −10.9488 | −0.485773 | ||||||||
\(509\) | 31.1189 | 1.37932 | 0.689661 | − | 0.724132i | \(-0.257759\pi\) | ||||
0.689661 | + | 0.724132i | \(0.257759\pi\) | |||||||
\(510\) | 11.9902 | 0.530933 | ||||||||
\(511\) | −11.9288 | −0.527701 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.183463 | 0.00810008 | ||||||||
\(514\) | −24.1055 | −1.06325 | ||||||||
\(515\) | −16.2723 | −0.717044 | ||||||||
\(516\) | 29.2543 | 1.28785 | ||||||||
\(517\) | 11.4860 | 0.505156 | ||||||||
\(518\) | −2.19012 | −0.0962283 | ||||||||
\(519\) | −16.4276 | −0.721090 | ||||||||
\(520\) | −0.0443428 | −0.00194456 | ||||||||
\(521\) | −12.6352 | −0.553556 | −0.276778 | − | 0.960934i | \(-0.589267\pi\) | ||||
−0.276778 | + | 0.960934i | \(0.589267\pi\) | |||||||
\(522\) | −9.18488 | −0.402011 | ||||||||
\(523\) | −42.0964 | −1.84075 | −0.920373 | − | 0.391042i | \(-0.872115\pi\) | ||||
−0.920373 | + | 0.391042i | \(0.872115\pi\) | |||||||
\(524\) | −18.0252 | −0.787435 | ||||||||
\(525\) | −11.5853 | −0.505626 | ||||||||
\(526\) | 13.9249 | 0.607153 | ||||||||
\(527\) | −49.6353 | −2.16215 | ||||||||
\(528\) | −2.65729 | −0.115644 | ||||||||
\(529\) | −11.4286 | −0.496896 | ||||||||
\(530\) | −6.47126 | −0.281094 | ||||||||
\(531\) | −37.0442 | −1.60758 | ||||||||
\(532\) | −9.15817 | −0.397057 | ||||||||
\(533\) | −0.474152 | −0.0205378 | ||||||||
\(534\) | −20.9950 | −0.908541 | ||||||||
\(535\) | −6.90593 | −0.298569 | ||||||||
\(536\) | 0.822257 | 0.0355161 | ||||||||
\(537\) | −35.3600 | −1.52590 | ||||||||
\(538\) | 23.8294 | 1.02736 | ||||||||
\(539\) | −6.20207 | −0.267142 | ||||||||
\(540\) | 0.0206854 | 0.000890156 0 | ||||||||
\(541\) | 39.8135 | 1.71172 | 0.855859 | − | 0.517210i | \(-0.173029\pi\) | ||||
0.855859 | + | 0.517210i | \(0.173029\pi\) | |||||||
\(542\) | −16.6051 | −0.713250 | ||||||||
\(543\) | −45.8529 | −1.96773 | ||||||||
\(544\) | −5.38283 | −0.230787 | ||||||||
\(545\) | 2.67572 | 0.114615 | ||||||||
\(546\) | −0.135312 | −0.00579082 | ||||||||
\(547\) | 2.82527 | 0.120800 | 0.0604000 | − | 0.998174i | \(-0.480762\pi\) | ||||
0.0604000 | + | 0.998174i | \(0.480762\pi\) | |||||||
\(548\) | −17.6524 | −0.754072 | ||||||||
\(549\) | 21.5165 | 0.918302 | ||||||||
\(550\) | 4.52919 | 0.193125 | ||||||||
\(551\) | 24.7890 | 1.05605 | ||||||||
\(552\) | −8.32592 | −0.354375 | ||||||||
\(553\) | 4.36386 | 0.185570 | ||||||||
\(554\) | 5.96770 | 0.253543 | ||||||||
\(555\) | 4.29965 | 0.182510 | ||||||||
\(556\) | 5.69278 | 0.241428 | ||||||||
\(557\) | −8.49144 | −0.359794 | −0.179897 | − | 0.983685i | \(-0.557576\pi\) | ||||
−0.179897 | + | 0.983685i | \(0.557576\pi\) | |||||||
\(558\) | 27.5775 | 1.16745 | ||||||||
\(559\) | −0.582369 | −0.0246316 | ||||||||
\(560\) | −1.03258 | −0.0436345 | ||||||||
\(561\) | −14.3037 | −0.603904 | ||||||||
\(562\) | −6.94096 | −0.292787 | ||||||||
\(563\) | −8.19666 | −0.345448 | −0.172724 | − | 0.984970i | \(-0.555257\pi\) | ||||
−0.172724 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(564\) | −25.8947 | −1.09036 | ||||||||
\(565\) | 7.62956 | 0.320978 | ||||||||
\(566\) | 11.8000 | 0.495992 | ||||||||
\(567\) | 10.2431 | 0.430168 | ||||||||
\(568\) | 2.06749 | 0.0867498 | ||||||||
\(569\) | −27.2249 | −1.14133 | −0.570665 | − | 0.821183i | \(-0.693314\pi\) | ||||
−0.570665 | + | 0.821183i | \(0.693314\pi\) | |||||||
\(570\) | 17.9793 | 0.753072 | ||||||||
\(571\) | −36.2921 | −1.51878 | −0.759388 | − | 0.650637i | \(-0.774502\pi\) | ||||
−0.759388 | + | 0.650637i | \(0.774502\pi\) | |||||||
\(572\) | 0.0528990 | 0.00221182 | ||||||||
\(573\) | 38.9229 | 1.62603 | ||||||||
\(574\) | −11.0412 | −0.460853 | ||||||||
\(575\) | 14.1910 | 0.591806 | ||||||||
\(576\) | 2.99071 | 0.124613 | ||||||||
\(577\) | −12.4305 | −0.517487 | −0.258744 | − | 0.965946i | \(-0.583309\pi\) | ||||
−0.258744 | + | 0.965946i | \(0.583309\pi\) | |||||||
\(578\) | −11.9748 | −0.498088 | ||||||||
\(579\) | −36.0195 | −1.49692 | ||||||||
\(580\) | 2.79495 | 0.116054 | ||||||||
\(581\) | −17.7879 | −0.737965 | ||||||||
\(582\) | 31.2940 | 1.29718 | ||||||||
\(583\) | 7.71994 | 0.319727 | ||||||||
\(584\) | −10.5136 | −0.435054 | ||||||||
\(585\) | 0.132617 | 0.00548302 | ||||||||
\(586\) | −26.1606 | −1.08069 | ||||||||
\(587\) | −0.218546 | −0.00902038 | −0.00451019 | − | 0.999990i | \(-0.501436\pi\) | ||||
−0.00451019 | + | 0.999990i | \(0.501436\pi\) | |||||||
\(588\) | 13.9822 | 0.576618 | ||||||||
\(589\) | −74.4285 | −3.06677 | ||||||||
\(590\) | 11.2725 | 0.464082 | ||||||||
\(591\) | 18.9369 | 0.778961 | ||||||||
\(592\) | −1.93027 | −0.0793337 | ||||||||
\(593\) | 25.0044 | 1.02681 | 0.513403 | − | 0.858148i | \(-0.328385\pi\) | ||||
0.513403 | + | 0.858148i | \(0.328385\pi\) | |||||||
\(594\) | −0.0246768 | −0.00101250 | ||||||||
\(595\) | −5.55820 | −0.227864 | ||||||||
\(596\) | 1.06058 | 0.0434430 | ||||||||
\(597\) | 49.5089 | 2.02626 | ||||||||
\(598\) | 0.165745 | 0.00677782 | ||||||||
\(599\) | −15.6866 | −0.640937 | −0.320468 | − | 0.947259i | \(-0.603840\pi\) | ||||
−0.320468 | + | 0.947259i | \(0.603840\pi\) | |||||||
\(600\) | −10.2108 | −0.416854 | ||||||||
\(601\) | −48.9474 | −1.99661 | −0.998304 | − | 0.0582164i | \(-0.981459\pi\) | ||||
−0.998304 | + | 0.0582164i | \(0.981459\pi\) | |||||||
\(602\) | −13.5612 | −0.552715 | ||||||||
\(603\) | −2.45913 | −0.100144 | ||||||||
\(604\) | 15.7425 | 0.640552 | ||||||||
\(605\) | −8.93808 | −0.363385 | ||||||||
\(606\) | 31.9001 | 1.29585 | ||||||||
\(607\) | −2.84906 | −0.115640 | −0.0578200 | − | 0.998327i | \(-0.518415\pi\) | ||||
−0.0578200 | + | 0.998327i | \(0.518415\pi\) | |||||||
\(608\) | −8.07160 | −0.327347 | ||||||||
\(609\) | 8.52878 | 0.345604 | ||||||||
\(610\) | −6.54744 | −0.265098 | ||||||||
\(611\) | 0.515488 | 0.0208544 | ||||||||
\(612\) | 16.0985 | 0.650743 | ||||||||
\(613\) | 32.7383 | 1.32229 | 0.661143 | − | 0.750260i | \(-0.270072\pi\) | ||||
0.661143 | + | 0.750260i | \(0.270072\pi\) | |||||||
\(614\) | 22.3696 | 0.902762 | ||||||||
\(615\) | 21.6762 | 0.874069 | ||||||||
\(616\) | 1.23182 | 0.0496316 | ||||||||
\(617\) | 13.1121 | 0.527872 | 0.263936 | − | 0.964540i | \(-0.414979\pi\) | ||||
0.263936 | + | 0.964540i | \(0.414979\pi\) | |||||||
\(618\) | −43.7637 | −1.76043 | ||||||||
\(619\) | 29.8471 | 1.19966 | 0.599829 | − | 0.800128i | \(-0.295235\pi\) | ||||
0.599829 | + | 0.800128i | \(0.295235\pi\) | |||||||
\(620\) | −8.39179 | −0.337022 | ||||||||
\(621\) | −0.0773181 | −0.00310267 | ||||||||
\(622\) | 20.4126 | 0.818469 | ||||||||
\(623\) | 9.73250 | 0.389925 | ||||||||
\(624\) | −0.119258 | −0.00477414 | ||||||||
\(625\) | 13.2625 | 0.530502 | ||||||||
\(626\) | −34.8587 | −1.39324 | ||||||||
\(627\) | −21.4486 | −0.856574 | ||||||||
\(628\) | −10.1560 | −0.405270 | ||||||||
\(629\) | −10.3903 | −0.414289 | ||||||||
\(630\) | 3.08815 | 0.123035 | ||||||||
\(631\) | 8.66878 | 0.345098 | 0.172549 | − | 0.985001i | \(-0.444800\pi\) | ||||
0.172549 | + | 0.985001i | \(0.444800\pi\) | |||||||
\(632\) | 3.84611 | 0.152990 | ||||||||
\(633\) | −11.0793 | −0.440363 | ||||||||
\(634\) | −9.73168 | −0.386494 | ||||||||
\(635\) | −9.96414 | −0.395415 | ||||||||
\(636\) | −17.4042 | −0.690120 | ||||||||
\(637\) | −0.278346 | −0.0110285 | ||||||||
\(638\) | −3.33425 | −0.132004 | ||||||||
\(639\) | −6.18326 | −0.244606 | ||||||||
\(640\) | −0.910070 | −0.0359737 | ||||||||
\(641\) | −20.6921 | −0.817287 | −0.408644 | − | 0.912694i | \(-0.633998\pi\) | ||||
−0.408644 | + | 0.912694i | \(0.633998\pi\) | |||||||
\(642\) | −18.5732 | −0.733025 | ||||||||
\(643\) | 3.80078 | 0.149888 | 0.0749441 | − | 0.997188i | \(-0.476122\pi\) | ||||
0.0749441 | + | 0.997188i | \(0.476122\pi\) | |||||||
\(644\) | 3.85960 | 0.152089 | ||||||||
\(645\) | 26.6235 | 1.04830 | ||||||||
\(646\) | −43.4481 | −1.70944 | ||||||||
\(647\) | −9.70291 | −0.381461 | −0.190730 | − | 0.981642i | \(-0.561086\pi\) | ||||
−0.190730 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(648\) | 9.02777 | 0.354644 | ||||||||
\(649\) | −13.4476 | −0.527865 | ||||||||
\(650\) | 0.203268 | 0.00797282 | ||||||||
\(651\) | −25.6075 | −1.00364 | ||||||||
\(652\) | 9.10486 | 0.356574 | ||||||||
\(653\) | −17.6370 | −0.690188 | −0.345094 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345094 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(654\) | 7.19624 | 0.281395 | ||||||||
\(655\) | −16.4042 | −0.640965 | ||||||||
\(656\) | −9.73126 | −0.379942 | ||||||||
\(657\) | 31.4430 | 1.22671 | ||||||||
\(658\) | 12.0038 | 0.467958 | ||||||||
\(659\) | −9.43569 | −0.367562 | −0.183781 | − | 0.982967i | \(-0.558834\pi\) | ||||
−0.183781 | + | 0.982967i | \(0.558834\pi\) | |||||||
\(660\) | −2.41832 | −0.0941330 | ||||||||
\(661\) | 23.0595 | 0.896910 | 0.448455 | − | 0.893806i | \(-0.351975\pi\) | ||||
0.448455 | + | 0.893806i | \(0.351975\pi\) | |||||||
\(662\) | 20.8701 | 0.811140 | ||||||||
\(663\) | −0.641945 | −0.0249311 | ||||||||
\(664\) | −15.6774 | −0.608402 | ||||||||
\(665\) | −8.33458 | −0.323201 | ||||||||
\(666\) | 5.77289 | 0.223695 | ||||||||
\(667\) | −10.4470 | −0.404510 | ||||||||
\(668\) | 11.1294 | 0.430611 | ||||||||
\(669\) | −70.7796 | −2.73650 | ||||||||
\(670\) | 0.748311 | 0.0289098 | ||||||||
\(671\) | 7.81082 | 0.301533 | ||||||||
\(672\) | −2.77708 | −0.107128 | ||||||||
\(673\) | 37.4441 | 1.44336 | 0.721682 | − | 0.692225i | \(-0.243370\pi\) | ||||
0.721682 | + | 0.692225i | \(0.243370\pi\) | |||||||
\(674\) | 16.0986 | 0.620094 | ||||||||
\(675\) | −0.0948220 | −0.00364970 | ||||||||
\(676\) | −12.9976 | −0.499909 | ||||||||
\(677\) | −28.9796 | −1.11378 | −0.556889 | − | 0.830587i | \(-0.688005\pi\) | ||||
−0.556889 | + | 0.830587i | \(0.688005\pi\) | |||||||
\(678\) | 20.5194 | 0.788041 | ||||||||
\(679\) | −14.5068 | −0.556719 | ||||||||
\(680\) | −4.89875 | −0.187859 | ||||||||
\(681\) | −18.5635 | −0.711355 | ||||||||
\(682\) | 10.0110 | 0.383343 | ||||||||
\(683\) | −36.4558 | −1.39494 | −0.697471 | − | 0.716613i | \(-0.745691\pi\) | ||||
−0.697471 | + | 0.716613i | \(0.745691\pi\) | |||||||
\(684\) | 24.1399 | 0.923010 | ||||||||
\(685\) | −16.0649 | −0.613808 | ||||||||
\(686\) | −14.4240 | −0.550710 | ||||||||
\(687\) | −11.5926 | −0.442284 | ||||||||
\(688\) | −11.9523 | −0.455676 | ||||||||
\(689\) | 0.346467 | 0.0131993 | ||||||||
\(690\) | −7.57717 | −0.288458 | ||||||||
\(691\) | −5.44076 | −0.206976 | −0.103488 | − | 0.994631i | \(-0.533000\pi\) | ||||
−0.103488 | + | 0.994631i | \(0.533000\pi\) | |||||||
\(692\) | 6.71172 | 0.255141 | ||||||||
\(693\) | −3.68403 | −0.139945 | ||||||||
\(694\) | 21.3465 | 0.810302 | ||||||||
\(695\) | 5.18083 | 0.196520 | ||||||||
\(696\) | 7.51689 | 0.284927 | ||||||||
\(697\) | −52.3817 | −1.98410 | ||||||||
\(698\) | 34.7456 | 1.31514 | ||||||||
\(699\) | 43.2318 | 1.63518 | ||||||||
\(700\) | 4.73336 | 0.178904 | ||||||||
\(701\) | −30.9295 | −1.16819 | −0.584095 | − | 0.811686i | \(-0.698550\pi\) | ||||
−0.584095 | + | 0.811686i | \(0.698550\pi\) | |||||||
\(702\) | −0.00110748 | −4.17992e−5 0 | ||||||||
\(703\) | −15.5804 | −0.587626 | ||||||||
\(704\) | 1.08567 | 0.0409179 | ||||||||
\(705\) | −23.5660 | −0.887545 | ||||||||
\(706\) | −12.3338 | −0.464189 | ||||||||
\(707\) | −14.7877 | −0.556150 | ||||||||
\(708\) | 30.3169 | 1.13938 | ||||||||
\(709\) | 35.2450 | 1.32365 | 0.661826 | − | 0.749657i | \(-0.269782\pi\) | ||||
0.661826 | + | 0.749657i | \(0.269782\pi\) | |||||||
\(710\) | 1.88156 | 0.0706136 | ||||||||
\(711\) | −11.5026 | −0.431382 | ||||||||
\(712\) | 8.57779 | 0.321466 | ||||||||
\(713\) | 31.3670 | 1.17470 | ||||||||
\(714\) | −14.9485 | −0.559435 | ||||||||
\(715\) | 0.0481418 | 0.00180040 | ||||||||
\(716\) | 14.4469 | 0.539904 | ||||||||
\(717\) | 44.7572 | 1.67149 | ||||||||
\(718\) | 30.4610 | 1.13679 | ||||||||
\(719\) | 5.43232 | 0.202591 | 0.101296 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101296 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(720\) | 2.72176 | 0.101434 | ||||||||
\(721\) | 20.2873 | 0.755537 | ||||||||
\(722\) | −46.1508 | −1.71755 | ||||||||
\(723\) | 15.0787 | 0.560783 | ||||||||
\(724\) | 18.7339 | 0.696238 | ||||||||
\(725\) | −12.8121 | −0.475829 | ||||||||
\(726\) | −24.0386 | −0.892155 | ||||||||
\(727\) | 17.8288 | 0.661233 | 0.330617 | − | 0.943765i | \(-0.392743\pi\) | ||||
0.330617 | + | 0.943765i | \(0.392743\pi\) | |||||||
\(728\) | 0.0552837 | 0.00204895 | ||||||||
\(729\) | −26.8326 | −0.993799 | ||||||||
\(730\) | −9.56807 | −0.354130 | ||||||||
\(731\) | −64.3371 | −2.37959 | ||||||||
\(732\) | −17.6091 | −0.650850 | ||||||||
\(733\) | −22.8672 | −0.844620 | −0.422310 | − | 0.906452i | \(-0.638781\pi\) | ||||
−0.422310 | + | 0.906452i | \(0.638781\pi\) | |||||||
\(734\) | 11.3977 | 0.420697 | ||||||||
\(735\) | 12.7248 | 0.469362 | ||||||||
\(736\) | 3.40168 | 0.125387 | ||||||||
\(737\) | −0.892703 | −0.0328831 | ||||||||
\(738\) | 29.1034 | 1.07131 | ||||||||
\(739\) | −21.8228 | −0.802765 | −0.401383 | − | 0.915910i | \(-0.631470\pi\) | ||||
−0.401383 | + | 0.915910i | \(0.631470\pi\) | |||||||
\(740\) | −1.75668 | −0.0645769 | ||||||||
\(741\) | −0.962603 | −0.0353621 | ||||||||
\(742\) | 8.06795 | 0.296184 | ||||||||
\(743\) | 36.5836 | 1.34212 | 0.671062 | − | 0.741402i | \(-0.265839\pi\) | ||||
0.671062 | + | 0.741402i | \(0.265839\pi\) | |||||||
\(744\) | −22.5693 | −0.827432 | ||||||||
\(745\) | 0.965202 | 0.0353623 | ||||||||
\(746\) | 19.8719 | 0.727564 | ||||||||
\(747\) | 46.8867 | 1.71549 | ||||||||
\(748\) | 5.84400 | 0.213678 | ||||||||
\(749\) | 8.60986 | 0.314597 | ||||||||
\(750\) | −20.4300 | −0.745996 | ||||||||
\(751\) | −29.9067 | −1.09131 | −0.545655 | − | 0.838010i | \(-0.683719\pi\) | ||||
−0.545655 | + | 0.838010i | \(0.683719\pi\) | |||||||
\(752\) | 10.5796 | 0.385800 | ||||||||
\(753\) | −60.7161 | −2.21262 | ||||||||
\(754\) | −0.149640 | −0.00544956 | ||||||||
\(755\) | 14.3268 | 0.521404 | ||||||||
\(756\) | −0.0257892 | −0.000937943 0 | ||||||||
\(757\) | 30.1331 | 1.09521 | 0.547604 | − | 0.836738i | \(-0.315540\pi\) | ||||
0.547604 | + | 0.836738i | \(0.315540\pi\) | |||||||
\(758\) | −20.8158 | −0.756063 | ||||||||
\(759\) | 9.03924 | 0.328104 | ||||||||
\(760\) | −7.34572 | −0.266457 | ||||||||
\(761\) | −6.63047 | −0.240354 | −0.120177 | − | 0.992752i | \(-0.538346\pi\) | ||||
−0.120177 | + | 0.992752i | \(0.538346\pi\) | |||||||
\(762\) | −26.7981 | −0.970793 | ||||||||
\(763\) | −3.33592 | −0.120768 | ||||||||
\(764\) | −15.9025 | −0.575333 | ||||||||
\(765\) | 14.6508 | 0.529699 | ||||||||
\(766\) | −2.99342 | −0.108157 | ||||||||
\(767\) | −0.603523 | −0.0217919 | ||||||||
\(768\) | −2.44759 | −0.0883199 | ||||||||
\(769\) | 9.81181 | 0.353823 | 0.176911 | − | 0.984227i | \(-0.443389\pi\) | ||||
0.176911 | + | 0.984227i | \(0.443389\pi\) | |||||||
\(770\) | 1.12105 | 0.0403997 | ||||||||
\(771\) | −59.0005 | −2.12485 | ||||||||
\(772\) | 14.7163 | 0.529651 | ||||||||
\(773\) | 4.42529 | 0.159167 | 0.0795833 | − | 0.996828i | \(-0.474641\pi\) | ||||
0.0795833 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(774\) | 35.7458 | 1.28486 | ||||||||
\(775\) | 38.4681 | 1.38181 | ||||||||
\(776\) | −12.7856 | −0.458977 | ||||||||
\(777\) | −5.36052 | −0.192308 | ||||||||
\(778\) | 12.3423 | 0.442494 | ||||||||
\(779\) | −78.5469 | −2.81423 | ||||||||
\(780\) | −0.108533 | −0.00388611 | ||||||||
\(781\) | −2.24462 | −0.0803188 | ||||||||
\(782\) | 18.3106 | 0.654787 | ||||||||
\(783\) | 0.0698051 | 0.00249463 | ||||||||
\(784\) | −5.71265 | −0.204023 | ||||||||
\(785\) | −9.24271 | −0.329886 | ||||||||
\(786\) | −44.1184 | −1.57365 | ||||||||
\(787\) | 25.2309 | 0.899384 | 0.449692 | − | 0.893184i | \(-0.351534\pi\) | ||||
0.449692 | + | 0.893184i | \(0.351534\pi\) | |||||||
\(788\) | −7.73695 | −0.275618 | ||||||||
\(789\) | 34.0824 | 1.21337 | ||||||||
\(790\) | 3.50023 | 0.124533 | ||||||||
\(791\) | −9.51203 | −0.338209 | ||||||||
\(792\) | −3.24694 | −0.115375 | ||||||||
\(793\) | 0.350546 | 0.0124482 | ||||||||
\(794\) | −0.189131 | −0.00671202 | ||||||||
\(795\) | −15.8390 | −0.561752 | ||||||||
\(796\) | −20.2276 | −0.716948 | ||||||||
\(797\) | 3.29307 | 0.116646 | 0.0583232 | − | 0.998298i | \(-0.481425\pi\) | ||||
0.0583232 | + | 0.998298i | \(0.481425\pi\) | |||||||
\(798\) | −22.4155 | −0.793499 | ||||||||
\(799\) | 56.9484 | 2.01469 | ||||||||
\(800\) | 4.17177 | 0.147494 | ||||||||
\(801\) | −25.6537 | −0.906430 | ||||||||
\(802\) | −18.3476 | −0.647875 | ||||||||
\(803\) | 11.4143 | 0.402802 | ||||||||
\(804\) | 2.01255 | 0.0709772 | ||||||||
\(805\) | 3.51250 | 0.123799 | ||||||||
\(806\) | 0.449291 | 0.0158256 | ||||||||
\(807\) | 58.3246 | 2.05312 | ||||||||
\(808\) | −13.0332 | −0.458508 | ||||||||
\(809\) | 10.7813 | 0.379050 | 0.189525 | − | 0.981876i | \(-0.439305\pi\) | ||||
0.189525 | + | 0.981876i | \(0.439305\pi\) | |||||||
\(810\) | 8.21591 | 0.288678 | ||||||||
\(811\) | −19.5475 | −0.686407 | −0.343203 | − | 0.939261i | \(-0.611512\pi\) | ||||
−0.343203 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(812\) | −3.48456 | −0.122284 | ||||||||
\(813\) | −40.6425 | −1.42540 | ||||||||
\(814\) | 2.09565 | 0.0734524 | ||||||||
\(815\) | 8.28606 | 0.290248 | ||||||||
\(816\) | −13.1750 | −0.461216 | ||||||||
\(817\) | −96.4740 | −3.37520 | ||||||||
\(818\) | 1.28838 | 0.0450471 | ||||||||
\(819\) | −0.165338 | −0.00577736 | ||||||||
\(820\) | −8.85613 | −0.309269 | ||||||||
\(821\) | −33.7853 | −1.17911 | −0.589557 | − | 0.807727i | \(-0.700698\pi\) | ||||
−0.589557 | + | 0.807727i | \(0.700698\pi\) | |||||||
\(822\) | −43.2058 | −1.50698 | ||||||||
\(823\) | −25.0633 | −0.873653 | −0.436827 | − | 0.899546i | \(-0.643898\pi\) | ||||
−0.436827 | + | 0.899546i | \(0.643898\pi\) | |||||||
\(824\) | 17.8803 | 0.622889 | ||||||||
\(825\) | 11.0856 | 0.385951 | ||||||||
\(826\) | −14.0538 | −0.488995 | ||||||||
\(827\) | 39.3982 | 1.37001 | 0.685005 | − | 0.728538i | \(-0.259800\pi\) | ||||
0.685005 | + | 0.728538i | \(0.259800\pi\) | |||||||
\(828\) | −10.1734 | −0.353551 | ||||||||
\(829\) | 50.1596 | 1.74212 | 0.871058 | − | 0.491181i | \(-0.163435\pi\) | ||||
0.871058 | + | 0.491181i | \(0.163435\pi\) | |||||||
\(830\) | −14.2676 | −0.495234 | ||||||||
\(831\) | 14.6065 | 0.506694 | ||||||||
\(832\) | 0.0487246 | 0.00168922 | ||||||||
\(833\) | −30.7502 | −1.06543 | ||||||||
\(834\) | 13.9336 | 0.482481 | ||||||||
\(835\) | 10.1286 | 0.350514 | ||||||||
\(836\) | 8.76313 | 0.303079 | ||||||||
\(837\) | −0.209589 | −0.00724445 | ||||||||
\(838\) | 7.67913 | 0.265271 | ||||||||
\(839\) | −1.39646 | −0.0482112 | −0.0241056 | − | 0.999709i | \(-0.507674\pi\) | ||||
−0.0241056 | + | 0.999709i | \(0.507674\pi\) | |||||||
\(840\) | −2.52734 | −0.0872014 | ||||||||
\(841\) | −19.5681 | −0.674763 | ||||||||
\(842\) | −20.2118 | −0.696543 | ||||||||
\(843\) | −16.9886 | −0.585120 | ||||||||
\(844\) | 4.52661 | 0.155812 | ||||||||
\(845\) | −11.8287 | −0.406921 | ||||||||
\(846\) | −31.6407 | −1.08783 | ||||||||
\(847\) | 11.1434 | 0.382892 | ||||||||
\(848\) | 7.11073 | 0.244183 | ||||||||
\(849\) | 28.8817 | 0.991216 | ||||||||
\(850\) | 22.4559 | 0.770232 | ||||||||
\(851\) | 6.56616 | 0.225085 | ||||||||
\(852\) | 5.06037 | 0.173365 | ||||||||
\(853\) | −27.6999 | −0.948428 | −0.474214 | − | 0.880410i | \(-0.657268\pi\) | ||||
−0.474214 | + | 0.880410i | \(0.657268\pi\) | |||||||
\(854\) | 8.16292 | 0.279330 | ||||||||
\(855\) | 21.9690 | 0.751322 | ||||||||
\(856\) | 7.58835 | 0.259364 | ||||||||
\(857\) | −50.1196 | −1.71205 | −0.856027 | − | 0.516931i | \(-0.827074\pi\) | ||||
−0.856027 | + | 0.516931i | \(0.827074\pi\) | |||||||
\(858\) | 0.129475 | 0.00442021 | ||||||||
\(859\) | −41.9628 | −1.43175 | −0.715876 | − | 0.698227i | \(-0.753972\pi\) | ||||
−0.715876 | + | 0.698227i | \(0.753972\pi\) | |||||||
\(860\) | −10.8774 | −0.370917 | ||||||||
\(861\) | −27.0245 | −0.920992 | ||||||||
\(862\) | 6.92743 | 0.235949 | ||||||||
\(863\) | −24.9557 | −0.849502 | −0.424751 | − | 0.905310i | \(-0.639638\pi\) | ||||
−0.424751 | + | 0.905310i | \(0.639638\pi\) | |||||||
\(864\) | −0.0227294 | −0.000773271 0 | ||||||||
\(865\) | 6.10814 | 0.207683 | ||||||||
\(866\) | −20.2457 | −0.687978 | ||||||||
\(867\) | −29.3096 | −0.995405 | ||||||||
\(868\) | 10.4623 | 0.355115 | ||||||||
\(869\) | −4.17563 | −0.141648 | ||||||||
\(870\) | 6.84090 | 0.231928 | ||||||||
\(871\) | −0.0400641 | −0.00135752 | ||||||||
\(872\) | −2.94013 | −0.0995653 | ||||||||
\(873\) | 38.2381 | 1.29416 | ||||||||
\(874\) | 27.4570 | 0.928746 | ||||||||
\(875\) | 9.47059 | 0.320164 | ||||||||
\(876\) | −25.7329 | −0.869434 | ||||||||
\(877\) | −29.9038 | −1.00978 | −0.504890 | − | 0.863184i | \(-0.668467\pi\) | ||||
−0.504890 | + | 0.863184i | \(0.668467\pi\) | |||||||
\(878\) | 9.40249 | 0.317319 | ||||||||
\(879\) | −64.0306 | −2.15970 | ||||||||
\(880\) | 0.988040 | 0.0333068 | ||||||||
\(881\) | 2.81636 | 0.0948857 | 0.0474428 | − | 0.998874i | \(-0.484893\pi\) | ||||
0.0474428 | + | 0.998874i | \(0.484893\pi\) | |||||||
\(882\) | 17.0849 | 0.575278 | ||||||||
\(883\) | 7.11950 | 0.239590 | 0.119795 | − | 0.992799i | \(-0.461776\pi\) | ||||
0.119795 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(884\) | 0.262276 | 0.00882130 | ||||||||
\(885\) | 27.5905 | 0.927445 | ||||||||
\(886\) | −4.45869 | −0.149793 | ||||||||
\(887\) | 44.3183 | 1.48806 | 0.744031 | − | 0.668146i | \(-0.232912\pi\) | ||||
0.744031 | + | 0.668146i | \(0.232912\pi\) | |||||||
\(888\) | −4.72452 | −0.158545 | ||||||||
\(889\) | 12.4226 | 0.416642 | ||||||||
\(890\) | 7.80639 | 0.261671 | ||||||||
\(891\) | −9.80122 | −0.328353 | ||||||||
\(892\) | 28.9180 | 0.968247 | ||||||||
\(893\) | 85.3947 | 2.85762 | ||||||||
\(894\) | 2.59587 | 0.0868188 | ||||||||
\(895\) | 13.1477 | 0.439478 | ||||||||
\(896\) | 1.13462 | 0.0379049 | ||||||||
\(897\) | 0.405677 | 0.0135452 | ||||||||
\(898\) | 22.6462 | 0.755713 | ||||||||
\(899\) | −28.3190 | −0.944493 | ||||||||
\(900\) | −12.4766 | −0.415886 | ||||||||
\(901\) | 38.2758 | 1.27515 | ||||||||
\(902\) | 10.5650 | 0.351776 | ||||||||
\(903\) | −33.1924 | −1.10457 | ||||||||
\(904\) | −8.38348 | −0.278830 | ||||||||
\(905\) | 17.0491 | 0.566732 | ||||||||
\(906\) | 38.5312 | 1.28011 | ||||||||
\(907\) | −18.9151 | −0.628066 | −0.314033 | − | 0.949412i | \(-0.601680\pi\) | ||||
−0.314033 | + | 0.949412i | \(0.601680\pi\) | |||||||
\(908\) | 7.58439 | 0.251697 | ||||||||
\(909\) | 38.9787 | 1.29284 | ||||||||
\(910\) | 0.0503120 | 0.00166783 | ||||||||
\(911\) | −18.3532 | −0.608069 | −0.304035 | − | 0.952661i | \(-0.598334\pi\) | ||||
−0.304035 | + | 0.952661i | \(0.598334\pi\) | |||||||
\(912\) | −19.7560 | −0.654187 | ||||||||
\(913\) | 17.0206 | 0.563299 | ||||||||
\(914\) | 19.7359 | 0.652806 | ||||||||
\(915\) | −16.0255 | −0.529786 | ||||||||
\(916\) | 4.73632 | 0.156492 | ||||||||
\(917\) | 20.4517 | 0.675375 | ||||||||
\(918\) | −0.122349 | −0.00403810 | ||||||||
\(919\) | −5.61543 | −0.185236 | −0.0926180 | − | 0.995702i | \(-0.529524\pi\) | ||||
−0.0926180 | + | 0.995702i | \(0.529524\pi\) | |||||||
\(920\) | 3.09576 | 0.102064 | ||||||||
\(921\) | 54.7516 | 1.80413 | ||||||||
\(922\) | 33.0477 | 1.08837 | ||||||||
\(923\) | −0.100737 | −0.00331581 | ||||||||
\(924\) | 3.01500 | 0.0991863 | ||||||||
\(925\) | 8.05266 | 0.264770 | ||||||||
\(926\) | 20.2663 | 0.665991 | ||||||||
\(927\) | −53.4748 | −1.75634 | ||||||||
\(928\) | −3.07113 | −0.100815 | ||||||||
\(929\) | 37.1097 | 1.21753 | 0.608765 | − | 0.793351i | \(-0.291665\pi\) | ||||
0.608765 | + | 0.793351i | \(0.291665\pi\) | |||||||
\(930\) | −20.5397 | −0.673523 | ||||||||
\(931\) | −46.1102 | −1.51120 | ||||||||
\(932\) | −17.6630 | −0.578570 | ||||||||
\(933\) | 49.9617 | 1.63567 | ||||||||
\(934\) | 3.50005 | 0.114525 | ||||||||
\(935\) | 5.31845 | 0.173932 | ||||||||
\(936\) | −0.145721 | −0.00476305 | ||||||||
\(937\) | 23.6693 | 0.773242 | 0.386621 | − | 0.922239i | \(-0.373642\pi\) | ||||
0.386621 | + | 0.922239i | \(0.373642\pi\) | |||||||
\(938\) | −0.932946 | −0.0304618 | ||||||||
\(939\) | −85.3200 | −2.78431 | ||||||||
\(940\) | 9.62821 | 0.314038 | ||||||||
\(941\) | 8.74151 | 0.284965 | 0.142483 | − | 0.989797i | \(-0.454492\pi\) | ||||
0.142483 | + | 0.989797i | \(0.454492\pi\) | |||||||
\(942\) | −24.8579 | −0.809913 | ||||||||
\(943\) | 33.1026 | 1.07797 | ||||||||
\(944\) | −12.3864 | −0.403144 | ||||||||
\(945\) | −0.0234699 | −0.000763477 0 | ||||||||
\(946\) | 12.9763 | 0.421895 | ||||||||
\(947\) | −36.2954 | −1.17944 | −0.589721 | − | 0.807607i | \(-0.700762\pi\) | ||||
−0.589721 | + | 0.807607i | \(0.700762\pi\) | |||||||
\(948\) | 9.41372 | 0.305743 | ||||||||
\(949\) | 0.512268 | 0.0166289 | ||||||||
\(950\) | 33.6729 | 1.09249 | ||||||||
\(951\) | −23.8192 | −0.772390 | ||||||||
\(952\) | 6.10744 | 0.197943 | ||||||||
\(953\) | 12.2221 | 0.395913 | 0.197956 | − | 0.980211i | \(-0.436570\pi\) | ||||
0.197956 | + | 0.980211i | \(0.436570\pi\) | |||||||
\(954\) | −21.2662 | −0.688517 | ||||||||
\(955\) | −14.4724 | −0.468316 | ||||||||
\(956\) | −18.2862 | −0.591418 | ||||||||
\(957\) | −8.16090 | −0.263804 | ||||||||
\(958\) | 38.0198 | 1.22836 | ||||||||
\(959\) | 20.0287 | 0.646759 | ||||||||
\(960\) | −2.22748 | −0.0718917 | ||||||||
\(961\) | 54.0275 | 1.74282 | ||||||||
\(962\) | 0.0940517 | 0.00303235 | ||||||||
\(963\) | −22.6946 | −0.731322 | ||||||||
\(964\) | −6.16062 | −0.198420 | ||||||||
\(965\) | 13.3929 | 0.431131 | ||||||||
\(966\) | 9.44672 | 0.303943 | ||||||||
\(967\) | 3.17194 | 0.102003 | 0.0510013 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510013 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(968\) | 9.82131 | 0.315669 | ||||||||
\(969\) | −106.343 | −3.41624 | ||||||||
\(970\) | −11.6358 | −0.373603 | ||||||||
\(971\) | −27.5984 | −0.885675 | −0.442837 | − | 0.896602i | \(-0.646028\pi\) | ||||
−0.442837 | + | 0.896602i | \(0.646028\pi\) | |||||||
\(972\) | 22.0281 | 0.706553 | ||||||||
\(973\) | −6.45912 | −0.207070 | ||||||||
\(974\) | −2.64149 | −0.0846389 | ||||||||
\(975\) | 0.497517 | 0.0159333 | ||||||||
\(976\) | 7.19444 | 0.230288 | ||||||||
\(977\) | 17.7441 | 0.567683 | 0.283842 | − | 0.958871i | \(-0.408391\pi\) | ||||
0.283842 | + | 0.958871i | \(0.408391\pi\) | |||||||
\(978\) | 22.2850 | 0.712596 | ||||||||
\(979\) | −9.31269 | −0.297635 | ||||||||
\(980\) | −5.19891 | −0.166073 | ||||||||
\(981\) | 8.79308 | 0.280742 | ||||||||
\(982\) | −25.7930 | −0.823088 | ||||||||
\(983\) | −39.9670 | −1.27475 | −0.637375 | − | 0.770554i | \(-0.719980\pi\) | ||||
−0.637375 | + | 0.770554i | \(0.719980\pi\) | |||||||
\(984\) | −23.8182 | −0.759296 | ||||||||
\(985\) | −7.04117 | −0.224350 | ||||||||
\(986\) | −16.5314 | −0.526467 | ||||||||
\(987\) | 29.3805 | 0.935191 | ||||||||
\(988\) | 0.393285 | 0.0125121 | ||||||||
\(989\) | 40.6578 | 1.29284 | ||||||||
\(990\) | −2.95494 | −0.0939143 | ||||||||
\(991\) | 33.0696 | 1.05049 | 0.525246 | − | 0.850950i | \(-0.323973\pi\) | ||||
0.525246 | + | 0.850950i | \(0.323973\pi\) | |||||||
\(992\) | 9.22104 | 0.292768 | ||||||||
\(993\) | 51.0815 | 1.62102 | ||||||||
\(994\) | −2.34580 | −0.0744044 | ||||||||
\(995\) | −18.4085 | −0.583589 | ||||||||
\(996\) | −38.3720 | −1.21586 | ||||||||
\(997\) | 9.82751 | 0.311240 | 0.155620 | − | 0.987817i | \(-0.450262\pi\) | ||||
0.155620 | + | 0.987817i | \(0.450262\pi\) | |||||||
\(998\) | 17.3024 | 0.547698 | ||||||||
\(999\) | −0.0438740 | −0.00138811 |
(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 | 8026.2.a.b.1.14 | ✓ | 81 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.b.1.14 | ✓ | 81 | 1.1 | even | 1 | trivial |