Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(286,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.286");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 120x^{6} + 2874x^{4} + 16920x^{2} + 19881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 286.7 | ||
Root | \(-2.54461i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.286 |
Dual form | 287.3.d.c.286.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | −0.500000 | −0.250000 | − | 0.968246i | \(-0.580431\pi\) | ||||
−0.250000 | + | 0.968246i | \(0.580431\pi\) | |||||||
\(3\) | 4.37780 | 1.45927 | 0.729634 | − | 0.683838i | \(-0.239691\pi\) | ||||
0.729634 | + | 0.683838i | \(0.239691\pi\) | |||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | − | 3.17602i | − | 0.635205i | −0.948224 | − | 0.317602i | \(-0.897122\pi\) | ||
0.948224 | − | 0.317602i | \(-0.102878\pi\) | |||||||
\(6\) | −4.37780 | −0.729634 | ||||||||
\(7\) | −0.818350 | + | 6.95200i | −0.116907 | + | 0.993143i | ||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 10.1652 | 1.12946 | ||||||||
\(10\) | 3.17602i | 0.317602i | ||||||||
\(11\) | 19.4050i | 1.76409i | 0.471162 | + | 0.882047i | \(0.343835\pi\) | ||||
−0.471162 | + | 0.882047i | \(0.656165\pi\) | |||||||
\(12\) | −13.1334 | −1.09445 | ||||||||
\(13\) | −4.37780 | −0.336754 | −0.168377 | − | 0.985723i | \(-0.553853\pi\) | ||||
−0.168377 | + | 0.985723i | \(0.553853\pi\) | |||||||
\(14\) | 0.818350 | − | 6.95200i | 0.0584536 | − | 0.496571i | ||||
\(15\) | − | 13.9040i | − | 0.926933i | ||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 25.3531 | 1.49136 | 0.745680 | − | 0.666304i | \(-0.232125\pi\) | ||||
0.745680 | + | 0.666304i | \(0.232125\pi\) | |||||||
\(18\) | −10.1652 | −0.564731 | ||||||||
\(19\) | 23.3350 | 1.22816 | 0.614079 | − | 0.789244i | \(-0.289528\pi\) | ||||
0.614079 | + | 0.789244i | \(0.289528\pi\) | |||||||
\(20\) | 9.52807i | 0.476403i | ||||||||
\(21\) | −3.58258 | + | 30.4345i | −0.170599 | + | 1.44926i | ||||
\(22\) | − | 19.4050i | − | 0.882047i | ||||||
\(23\) | 0.747727 | 0.0325099 | 0.0162549 | − | 0.999868i | \(-0.494826\pi\) | ||||
0.0162549 | + | 0.999868i | \(0.494826\pi\) | |||||||
\(24\) | 30.6446 | 1.27686 | ||||||||
\(25\) | 14.9129 | 0.596515 | ||||||||
\(26\) | 4.37780 | 0.168377 | ||||||||
\(27\) | 5.10080 | 0.188919 | ||||||||
\(28\) | 2.45505 | − | 20.8560i | 0.0876804 | − | 0.744857i | ||||
\(29\) | − | 11.3049i | − | 0.389824i | −0.980821 | − | 0.194912i | \(-0.937558\pi\) | ||
0.980821 | − | 0.194912i | \(-0.0624422\pi\) | |||||||
\(30\) | 13.9040i | 0.463467i | ||||||||
\(31\) | − | 17.7304i | − | 0.571948i | −0.958237 | − | 0.285974i | \(-0.907683\pi\) | ||
0.958237 | − | 0.285974i | \(-0.0923171\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | 84.9514i | 2.57428i | ||||||||
\(34\) | −25.3531 | −0.745680 | ||||||||
\(35\) | 22.0797 | + | 2.59910i | 0.630849 | + | 0.0742600i | ||||
\(36\) | −30.4955 | −0.847096 | ||||||||
\(37\) | −37.1652 | −1.00446 | −0.502232 | − | 0.864733i | \(-0.667488\pi\) | ||||
−0.502232 | + | 0.864733i | \(0.667488\pi\) | |||||||
\(38\) | −23.3350 | −0.614079 | ||||||||
\(39\) | −19.1652 | −0.491414 | ||||||||
\(40\) | − | 22.2322i | − | 0.555804i | ||||||
\(41\) | 28.1896 | + | 29.7716i | 0.687550 | + | 0.726137i | ||||
\(42\) | 3.58258 | − | 30.4345i | 0.0852994 | − | 0.724630i | ||||
\(43\) | 35.4955 | 0.825476 | 0.412738 | − | 0.910850i | \(-0.364573\pi\) | ||||
0.412738 | + | 0.910850i | \(0.364573\pi\) | |||||||
\(44\) | − | 58.2151i | − | 1.32307i | ||||||
\(45\) | − | 32.2848i | − | 0.717439i | ||||||
\(46\) | −0.747727 | −0.0162549 | ||||||||
\(47\) | −52.0013 | −1.10641 | −0.553206 | − | 0.833045i | \(-0.686596\pi\) | ||||
−0.553206 | + | 0.833045i | \(0.686596\pi\) | |||||||
\(48\) | 21.8890 | 0.456021 | ||||||||
\(49\) | −47.6606 | − | 11.3783i | −0.972665 | − | 0.232211i | ||||
\(50\) | −14.9129 | −0.298258 | ||||||||
\(51\) | 110.991 | 2.17629 | ||||||||
\(52\) | 13.1334 | 0.252566 | ||||||||
\(53\) | 69.2172i | 1.30598i | 0.757365 | + | 0.652992i | \(0.226487\pi\) | ||||
−0.757365 | + | 0.652992i | \(0.773513\pi\) | |||||||
\(54\) | −5.10080 | −0.0944593 | ||||||||
\(55\) | 61.6308 | 1.12056 | ||||||||
\(56\) | −5.72845 | + | 48.6640i | −0.102294 | + | 0.869000i | ||||
\(57\) | 102.156 | 1.79221 | ||||||||
\(58\) | 11.3049i | 0.194912i | ||||||||
\(59\) | 20.9064i | 0.354346i | 0.984180 | + | 0.177173i | \(0.0566952\pi\) | ||||
−0.984180 | + | 0.177173i | \(0.943305\pi\) | |||||||
\(60\) | 41.7120i | 0.695200i | ||||||||
\(61\) | 75.4233i | 1.23645i | 0.786002 | + | 0.618224i | \(0.212148\pi\) | ||||
−0.786002 | + | 0.618224i | \(0.787852\pi\) | |||||||
\(62\) | 17.7304i | 0.285974i | ||||||||
\(63\) | −8.31865 | + | 70.6681i | −0.132042 | + | 1.12172i | ||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | 13.9040i | 0.213908i | ||||||||
\(66\) | − | 84.9514i | − | 1.28714i | ||||||
\(67\) | − | 61.1170i | − | 0.912195i | −0.889930 | − | 0.456097i | \(-0.849247\pi\) | ||
0.889930 | − | 0.456097i | \(-0.150753\pi\) | |||||||
\(68\) | −76.0593 | −1.11852 | ||||||||
\(69\) | 3.27340 | 0.0474406 | ||||||||
\(70\) | −22.0797 | − | 2.59910i | −0.315424 | − | 0.0371300i | ||||
\(71\) | − | 107.724i | − | 1.51725i | −0.651530 | − | 0.758623i | \(-0.725873\pi\) | ||
0.651530 | − | 0.758623i | \(-0.274127\pi\) | |||||||
\(72\) | 71.1561 | 0.988279 | ||||||||
\(73\) | 19.0561i | 0.261043i | 0.991445 | + | 0.130521i | \(0.0416652\pi\) | ||||
−0.991445 | + | 0.130521i | \(0.958335\pi\) | |||||||
\(74\) | 37.1652 | 0.502232 | ||||||||
\(75\) | 65.2856 | 0.870475 | ||||||||
\(76\) | −70.0050 | −0.921119 | ||||||||
\(77\) | −134.904 | − | 15.8801i | −1.75200 | − | 0.206235i | ||||
\(78\) | 19.1652 | 0.245707 | ||||||||
\(79\) | 46.9102i | 0.593800i | 0.954909 | + | 0.296900i | \(0.0959528\pi\) | ||||
−0.954909 | + | 0.296900i | \(0.904047\pi\) | |||||||
\(80\) | − | 15.8801i | − | 0.198501i | ||||||
\(81\) | −69.1561 | −0.853779 | ||||||||
\(82\) | −28.1896 | − | 29.7716i | −0.343775 | − | 0.363068i | ||||
\(83\) | − | 165.401i | − | 1.99278i | −0.0848743 | − | 0.996392i | \(-0.527049\pi\) | ||
0.0848743 | − | 0.996392i | \(-0.472951\pi\) | |||||||
\(84\) | 10.7477 | − | 91.3034i | 0.127949 | − | 1.08695i | ||||
\(85\) | − | 80.5221i | − | 0.947318i | ||||||
\(86\) | −35.4955 | −0.412738 | ||||||||
\(87\) | − | 49.4906i | − | 0.568858i | ||||||
\(88\) | 135.835i | 1.54358i | ||||||||
\(89\) | −70.9187 | −0.796840 | −0.398420 | − | 0.917203i | \(-0.630441\pi\) | ||||
−0.398420 | + | 0.917203i | \(0.630441\pi\) | |||||||
\(90\) | 32.2848i | 0.358719i | ||||||||
\(91\) | 3.58258 | − | 30.4345i | 0.0393690 | − | 0.334445i | ||||
\(92\) | −2.24318 | −0.0243824 | ||||||||
\(93\) | − | 77.6201i | − | 0.834625i | ||||||
\(94\) | 52.0013 | 0.553206 | ||||||||
\(95\) | − | 74.1125i | − | 0.780132i | ||||||
\(96\) | −144.467 | −1.50487 | ||||||||
\(97\) | 100.539 | 1.03648 | 0.518240 | − | 0.855235i | \(-0.326587\pi\) | ||||
0.518240 | + | 0.855235i | \(0.326587\pi\) | |||||||
\(98\) | 47.6606 | + | 11.3783i | 0.486333 | + | 0.116106i | ||||
\(99\) | 197.255i | 1.99248i | ||||||||
\(100\) | −44.7386 | −0.447386 | ||||||||
\(101\) | −87.5162 | −0.866497 | −0.433249 | − | 0.901274i | \(-0.642633\pi\) | ||||
−0.433249 | + | 0.901274i | \(0.642633\pi\) | |||||||
\(102\) | −110.991 | −1.08815 | ||||||||
\(103\) | 112.734i | 1.09451i | 0.836966 | + | 0.547254i | \(0.184327\pi\) | ||||
−0.836966 | + | 0.547254i | \(0.815673\pi\) | |||||||
\(104\) | −30.6446 | −0.294660 | ||||||||
\(105\) | 96.6606 | + | 11.3783i | 0.920577 | + | 0.108365i | ||||
\(106\) | − | 69.2172i | − | 0.652992i | ||||||
\(107\) | −89.6515 | −0.837865 | −0.418932 | − | 0.908017i | \(-0.637596\pi\) | ||||
−0.418932 | + | 0.908017i | \(0.637596\pi\) | |||||||
\(108\) | −15.3024 | −0.141689 | ||||||||
\(109\) | − | 170.053i | − | 1.56012i | −0.625707 | − | 0.780059i | \(-0.715189\pi\) | ||
0.625707 | − | 0.780059i | \(-0.284811\pi\) | |||||||
\(110\) | −61.6308 | −0.560280 | ||||||||
\(111\) | −162.702 | −1.46578 | ||||||||
\(112\) | −4.09175 | + | 34.7600i | −0.0365335 | + | 0.310357i | ||||
\(113\) | 61.4083 | 0.543437 | 0.271718 | − | 0.962377i | \(-0.412408\pi\) | ||||
0.271718 | + | 0.962377i | \(0.412408\pi\) | |||||||
\(114\) | −102.156 | −0.896106 | ||||||||
\(115\) | − | 2.37480i | − | 0.0206504i | ||||||
\(116\) | 33.9147i | 0.292368i | ||||||||
\(117\) | −44.5010 | −0.380351 | ||||||||
\(118\) | − | 20.9064i | − | 0.177173i | ||||||
\(119\) | −20.7477 | + | 176.255i | −0.174351 | + | 1.48113i | ||||
\(120\) | − | 97.3280i | − | 0.811067i | ||||||
\(121\) | −255.555 | −2.11203 | ||||||||
\(122\) | − | 75.4233i | − | 0.618224i | ||||||
\(123\) | 123.408 | + | 130.334i | 1.00332 | + | 1.05963i | ||||
\(124\) | 53.1912i | 0.428961i | ||||||||
\(125\) | − | 126.764i | − | 1.01411i | ||||||
\(126\) | 8.31865 | − | 70.6681i | 0.0660211 | − | 0.560858i | ||||
\(127\) | 71.5644 | 0.563499 | 0.281750 | − | 0.959488i | \(-0.409085\pi\) | ||||
0.281750 | + | 0.959488i | \(0.409085\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | 155.392 | 1.20459 | ||||||||
\(130\) | − | 13.9040i | − | 0.106954i | ||||||
\(131\) | − | 242.951i | − | 1.85459i | −0.374331 | − | 0.927295i | \(-0.622128\pi\) | ||
0.374331 | − | 0.927295i | \(-0.377872\pi\) | |||||||
\(132\) | − | 254.854i | − | 1.93071i | ||||||
\(133\) | −19.0962 | + | 162.225i | −0.143581 | + | 1.21974i | ||||
\(134\) | 61.1170i | 0.456097i | ||||||||
\(135\) | − | 16.2003i | − | 0.120002i | ||||||
\(136\) | 177.472 | 1.30494 | ||||||||
\(137\) | − | 60.8142i | − | 0.443899i | −0.975058 | − | 0.221950i | \(-0.928758\pi\) | ||
0.975058 | − | 0.221950i | \(-0.0712421\pi\) | |||||||
\(138\) | −3.27340 | −0.0237203 | ||||||||
\(139\) | 24.8837i | 0.179019i | 0.995986 | + | 0.0895096i | \(0.0285300\pi\) | ||||
−0.995986 | + | 0.0895096i | \(0.971470\pi\) | |||||||
\(140\) | −66.2391 | − | 7.79730i | −0.473137 | − | 0.0556950i | ||||
\(141\) | −227.652 | −1.61455 | ||||||||
\(142\) | 107.724i | 0.758623i | ||||||||
\(143\) | − | 84.9514i | − | 0.594066i | ||||||
\(144\) | 50.8258 | 0.352957 | ||||||||
\(145\) | −35.9046 | −0.247618 | ||||||||
\(146\) | − | 19.0561i | − | 0.130521i | ||||||
\(147\) | −208.649 | − | 49.8121i | −1.41938 | − | 0.338858i | ||||
\(148\) | 111.495 | 0.753348 | ||||||||
\(149\) | 15.8974i | 0.106694i | 0.998576 | + | 0.0533471i | \(0.0169890\pi\) | ||||
−0.998576 | + | 0.0533471i | \(0.983011\pi\) | |||||||
\(150\) | −65.2856 | −0.435238 | ||||||||
\(151\) | − | 100.230i | − | 0.663774i | −0.943319 | − | 0.331887i | \(-0.892315\pi\) | ||
0.943319 | − | 0.331887i | \(-0.107685\pi\) | |||||||
\(152\) | 163.345 | 1.07464 | ||||||||
\(153\) | 257.718 | 1.68443 | ||||||||
\(154\) | 134.904 | + | 15.8801i | 0.875999 | + | 0.103118i | ||||
\(155\) | −56.3121 | −0.363304 | ||||||||
\(156\) | 57.4955 | 0.368561 | ||||||||
\(157\) | 24.4792 | 0.155919 | 0.0779593 | − | 0.996957i | \(-0.475160\pi\) | ||||
0.0779593 | + | 0.996957i | \(0.475160\pi\) | |||||||
\(158\) | − | 46.9102i | − | 0.296900i | ||||||
\(159\) | 303.019i | 1.90578i | ||||||||
\(160\) | 104.809i | 0.655055i | ||||||||
\(161\) | −0.611903 | + | 5.19820i | −0.00380064 | + | 0.0322869i | ||||
\(162\) | 69.1561 | 0.426889 | ||||||||
\(163\) | 199.808 | 1.22581 | 0.612907 | − | 0.790155i | \(-0.290000\pi\) | ||||
0.612907 | + | 0.790155i | \(0.290000\pi\) | |||||||
\(164\) | −84.5687 | − | 89.3148i | −0.515663 | − | 0.544603i | ||||
\(165\) | 269.808 | 1.63520 | ||||||||
\(166\) | 165.401i | 0.996392i | ||||||||
\(167\) | 6.13391 | 0.0367300 | 0.0183650 | − | 0.999831i | \(-0.494154\pi\) | ||||
0.0183650 | + | 0.999831i | \(0.494154\pi\) | |||||||
\(168\) | −25.0780 | + | 213.041i | −0.149274 | + | 1.26810i | ||||
\(169\) | −149.835 | −0.886597 | ||||||||
\(170\) | 80.5221i | 0.473659i | ||||||||
\(171\) | 237.204 | 1.38716 | ||||||||
\(172\) | −106.486 | −0.619107 | ||||||||
\(173\) | − | 117.236i | − | 0.677666i | −0.940847 | − | 0.338833i | \(-0.889968\pi\) | ||
0.940847 | − | 0.338833i | \(-0.110032\pi\) | |||||||
\(174\) | 49.4906i | 0.284429i | ||||||||
\(175\) | −12.2040 | + | 103.674i | −0.0697369 | + | 0.592425i | ||||
\(176\) | 97.0252i | 0.551279i | ||||||||
\(177\) | 91.5241i | 0.517085i | ||||||||
\(178\) | 70.9187 | 0.398420 | ||||||||
\(179\) | − | 44.9168i | − | 0.250932i | −0.992098 | − | 0.125466i | \(-0.959957\pi\) | ||
0.992098 | − | 0.125466i | \(-0.0400425\pi\) | |||||||
\(180\) | 96.8543i | 0.538079i | ||||||||
\(181\) | 143.705 | 0.793948 | 0.396974 | − | 0.917830i | \(-0.370060\pi\) | ||||
0.396974 | + | 0.917830i | \(0.370060\pi\) | |||||||
\(182\) | −3.58258 | + | 30.4345i | −0.0196845 | + | 0.167222i | ||||
\(183\) | 330.188i | 1.80431i | ||||||||
\(184\) | 5.23409 | 0.0284461 | ||||||||
\(185\) | 118.037i | 0.638040i | ||||||||
\(186\) | 77.6201i | 0.417313i | ||||||||
\(187\) | 491.978i | 2.63090i | ||||||||
\(188\) | 156.004 | 0.829808 | ||||||||
\(189\) | −4.17424 | + | 35.4608i | −0.0220859 | + | 0.187623i | ||||
\(190\) | 74.1125i | 0.390066i | ||||||||
\(191\) | − | 225.366i | − | 1.17993i | −0.807430 | − | 0.589963i | \(-0.799142\pi\) | ||
0.807430 | − | 0.589963i | \(-0.200858\pi\) | |||||||
\(192\) | 56.9114 | 0.296414 | ||||||||
\(193\) | − | 81.7334i | − | 0.423489i | −0.977325 | − | 0.211745i | \(-0.932086\pi\) | ||
0.977325 | − | 0.211745i | \(-0.0679145\pi\) | |||||||
\(194\) | −100.539 | −0.518240 | ||||||||
\(195\) | 60.8690i | 0.312149i | ||||||||
\(196\) | 142.982 | + | 34.1350i | 0.729499 | + | 0.174158i | ||||
\(197\) | −49.6879 | −0.252223 | −0.126111 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126111 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(198\) | − | 197.255i | − | 0.996238i | ||||||
\(199\) | 361.339 | 1.81578 | 0.907888 | − | 0.419213i | \(-0.137694\pi\) | ||||
0.907888 | + | 0.419213i | \(0.137694\pi\) | |||||||
\(200\) | 104.390 | 0.521951 | ||||||||
\(201\) | − | 267.558i | − | 1.33114i | ||||||
\(202\) | 87.5162 | 0.433249 | ||||||||
\(203\) | 78.5917 | + | 9.25137i | 0.387151 | + | 0.0455732i | ||||
\(204\) | −332.973 | −1.63222 | ||||||||
\(205\) | 94.5553 | − | 89.5307i | 0.461245 | − | 0.436735i | ||||
\(206\) | − | 112.734i | − | 0.547254i | ||||||
\(207\) | 7.60076 | 0.0367186 | ||||||||
\(208\) | −21.8890 | −0.105236 | ||||||||
\(209\) | 452.817i | 2.16659i | ||||||||
\(210\) | −96.6606 | − | 11.3783i | −0.460289 | − | 0.0541826i | ||||
\(211\) | 130.031i | 0.616262i | 0.951344 | + | 0.308131i | \(0.0997036\pi\) | ||||
−0.951344 | + | 0.308131i | \(0.900296\pi\) | |||||||
\(212\) | − | 207.651i | − | 0.979488i | ||||||
\(213\) | − | 471.596i | − | 2.21407i | ||||||
\(214\) | 89.6515 | 0.418932 | ||||||||
\(215\) | − | 112.734i | − | 0.524346i | ||||||
\(216\) | 35.7056 | 0.165304 | ||||||||
\(217\) | 123.262 | + | 14.5097i | 0.568026 | + | 0.0668648i | ||||
\(218\) | 170.053i | 0.780059i | ||||||||
\(219\) | 83.4240i | 0.380932i | ||||||||
\(220\) | −184.892 | −0.840420 | ||||||||
\(221\) | −110.991 | −0.502221 | ||||||||
\(222\) | 162.702 | 0.732890 | ||||||||
\(223\) | − | 159.850i | − | 0.716817i | −0.933565 | − | 0.358409i | \(-0.883320\pi\) | ||
0.933565 | − | 0.358409i | \(-0.116680\pi\) | |||||||
\(224\) | 27.0056 | − | 229.416i | 0.120561 | − | 1.02418i | ||||
\(225\) | 151.592 | 0.673741 | ||||||||
\(226\) | −61.4083 | −0.271718 | ||||||||
\(227\) | −41.3072 | −0.181970 | −0.0909851 | − | 0.995852i | \(-0.529002\pi\) | ||||
−0.0909851 | + | 0.995852i | \(0.529002\pi\) | |||||||
\(228\) | −306.468 | −1.34416 | ||||||||
\(229\) | 240.096 | 1.04845 | 0.524227 | − | 0.851579i | \(-0.324354\pi\) | ||||
0.524227 | + | 0.851579i | \(0.324354\pi\) | |||||||
\(230\) | 2.37480i | 0.0103252i | ||||||||
\(231\) | −590.582 | − | 69.5200i | −2.55663 | − | 0.300952i | ||||
\(232\) | − | 79.1343i | − | 0.341096i | ||||||
\(233\) | 406.118i | 1.74300i | 0.490400 | + | 0.871498i | \(0.336851\pi\) | ||||
−0.490400 | + | 0.871498i | \(0.663149\pi\) | |||||||
\(234\) | 44.5010 | 0.190175 | ||||||||
\(235\) | 165.157i | 0.702797i | ||||||||
\(236\) | − | 62.7192i | − | 0.265759i | ||||||
\(237\) | 205.364i | 0.866513i | ||||||||
\(238\) | 20.7477 | − | 176.255i | 0.0871753 | − | 0.740567i | ||||
\(239\) | − | 121.628i | − | 0.508905i | −0.967085 | − | 0.254453i | \(-0.918105\pi\) | ||
0.967085 | − | 0.254453i | \(-0.0818953\pi\) | |||||||
\(240\) | − | 69.5200i | − | 0.289667i | ||||||
\(241\) | 266.509i | 1.10585i | 0.833232 | + | 0.552924i | \(0.186488\pi\) | ||||
−0.833232 | + | 0.552924i | \(0.813512\pi\) | |||||||
\(242\) | 255.555 | 1.05601 | ||||||||
\(243\) | −348.659 | −1.43481 | ||||||||
\(244\) | − | 226.270i | − | 0.927336i | ||||||
\(245\) | −36.1379 | + | 151.371i | −0.147502 | + | 0.617842i | ||||
\(246\) | −123.408 | − | 130.334i | −0.501660 | − | 0.529814i | ||||
\(247\) | −102.156 | −0.413587 | ||||||||
\(248\) | − | 124.113i | − | 0.500455i | ||||||
\(249\) | − | 724.093i | − | 2.90800i | ||||||
\(250\) | 126.764i | 0.507057i | ||||||||
\(251\) | − | 187.109i | − | 0.745453i | −0.927941 | − | 0.372726i | \(-0.878423\pi\) | ||
0.927941 | − | 0.372726i | \(-0.121577\pi\) | |||||||
\(252\) | 24.9560 | − | 212.004i | 0.0990316 | − | 0.841287i | ||||
\(253\) | 14.5097i | 0.0573505i | ||||||||
\(254\) | −71.5644 | −0.281750 | ||||||||
\(255\) | − | 352.510i | − | 1.38239i | ||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | −397.387 | −1.54625 | −0.773126 | − | 0.634253i | \(-0.781308\pi\) | ||||
−0.773126 | + | 0.634253i | \(0.781308\pi\) | |||||||
\(258\) | −155.392 | −0.602295 | ||||||||
\(259\) | 30.4141 | − | 258.372i | 0.117429 | − | 0.997576i | ||||
\(260\) | − | 41.7120i | − | 0.160431i | ||||||
\(261\) | − | 114.916i | − | 0.440291i | ||||||
\(262\) | 242.951i | 0.927295i | ||||||||
\(263\) | 281.588i | 1.07068i | 0.844638 | + | 0.535338i | \(0.179816\pi\) | ||||
−0.844638 | + | 0.535338i | \(0.820184\pi\) | |||||||
\(264\) | 594.660i | 2.25250i | ||||||||
\(265\) | 219.835 | 0.829567 | ||||||||
\(266\) | 19.0962 | − | 162.225i | 0.0717903 | − | 0.609868i | ||||
\(267\) | −310.468 | −1.16280 | ||||||||
\(268\) | 183.351i | 0.684146i | ||||||||
\(269\) | 207.214i | 0.770312i | 0.922852 | + | 0.385156i | \(0.125852\pi\) | ||||
−0.922852 | + | 0.385156i | \(0.874148\pi\) | |||||||
\(270\) | 16.2003i | 0.0600010i | ||||||||
\(271\) | − | 169.626i | − | 0.625927i | −0.949765 | − | 0.312963i | \(-0.898678\pi\) | ||
0.949765 | − | 0.312963i | \(-0.101322\pi\) | |||||||
\(272\) | 126.766 | 0.466050 | ||||||||
\(273\) | 15.6838 | − | 133.236i | 0.0574498 | − | 0.488044i | ||||
\(274\) | 60.8142i | 0.221950i | ||||||||
\(275\) | 289.385i | 1.05231i | ||||||||
\(276\) | −9.82020 | −0.0355804 | ||||||||
\(277\) | −85.9636 | −0.310338 | −0.155169 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155169 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(278\) | − | 24.8837i | − | 0.0895096i | ||||||
\(279\) | − | 180.232i | − | 0.645993i | ||||||
\(280\) | 154.558 | + | 18.1937i | 0.551993 | + | 0.0649775i | ||||
\(281\) | − | 245.074i | − | 0.872149i | −0.899911 | − | 0.436074i | \(-0.856368\pi\) | ||
0.899911 | − | 0.436074i | \(-0.143632\pi\) | |||||||
\(282\) | 227.652 | 0.807275 | ||||||||
\(283\) | − | 203.790i | − | 0.720106i | −0.932932 | − | 0.360053i | \(-0.882759\pi\) | ||
0.932932 | − | 0.360053i | \(-0.117241\pi\) | |||||||
\(284\) | 323.173i | 1.13793i | ||||||||
\(285\) | − | 324.450i | − | 1.13842i | ||||||
\(286\) | 84.9514i | 0.297033i | ||||||||
\(287\) | −230.041 | + | 171.610i | −0.801537 | + | 0.597945i | ||||
\(288\) | −335.450 | −1.16476 | ||||||||
\(289\) | 353.780 | 1.22415 | ||||||||
\(290\) | 35.9046 | 0.123809 | ||||||||
\(291\) | 440.138 | 1.51250 | ||||||||
\(292\) | − | 57.1684i | − | 0.195782i | ||||||
\(293\) | −422.057 | −1.44047 | −0.720233 | − | 0.693732i | \(-0.755965\pi\) | ||||
−0.720233 | + | 0.693732i | \(0.755965\pi\) | |||||||
\(294\) | 208.649 | + | 49.8121i | 0.709689 | + | 0.169429i | ||||
\(295\) | 66.3992 | 0.225082 | ||||||||
\(296\) | −260.156 | −0.878906 | ||||||||
\(297\) | 98.9812i | 0.333270i | ||||||||
\(298\) | − | 15.8974i | − | 0.0533471i | ||||||
\(299\) | −3.27340 | −0.0109478 | ||||||||
\(300\) | −195.857 | −0.652856 | ||||||||
\(301\) | −29.0477 | + | 246.764i | −0.0965040 | + | 0.819815i | ||||
\(302\) | 100.230i | 0.331887i | ||||||||
\(303\) | −383.129 | −1.26445 | ||||||||
\(304\) | 116.675 | 0.383800 | ||||||||
\(305\) | 239.546 | 0.785397 | ||||||||
\(306\) | −257.718 | −0.842216 | ||||||||
\(307\) | − | 402.802i | − | 1.31206i | −0.754736 | − | 0.656029i | \(-0.772235\pi\) | ||
0.754736 | − | 0.656029i | \(-0.227765\pi\) | |||||||
\(308\) | 404.711 | + | 47.6403i | 1.31400 | + | 0.154676i | ||||
\(309\) | 493.529i | 1.59718i | ||||||||
\(310\) | 56.3121 | 0.181652 | ||||||||
\(311\) | −112.670 | −0.362284 | −0.181142 | − | 0.983457i | \(-0.557979\pi\) | ||||
−0.181142 | + | 0.983457i | \(0.557979\pi\) | |||||||
\(312\) | −134.156 | −0.429987 | ||||||||
\(313\) | 412.188 | 1.31690 | 0.658448 | − | 0.752626i | \(-0.271213\pi\) | ||||
0.658448 | + | 0.752626i | \(0.271213\pi\) | |||||||
\(314\) | −24.4792 | −0.0779593 | ||||||||
\(315\) | 224.444 | + | 26.4202i | 0.712519 | + | 0.0838738i | ||||
\(316\) | − | 140.731i | − | 0.445350i | ||||||
\(317\) | 322.391i | 1.01701i | 0.861060 | + | 0.508503i | \(0.169801\pi\) | ||||
−0.861060 | + | 0.508503i | \(0.830199\pi\) | |||||||
\(318\) | − | 303.019i | − | 0.952890i | ||||||
\(319\) | 219.372 | 0.687686 | ||||||||
\(320\) | − | 41.2883i | − | 0.129026i | ||||||
\(321\) | −392.477 | −1.22267 | ||||||||
\(322\) | 0.611903 | − | 5.19820i | 0.00190032 | − | 0.0161435i | ||||
\(323\) | 591.615 | 1.83163 | ||||||||
\(324\) | 207.468 | 0.640334 | ||||||||
\(325\) | −65.2856 | −0.200879 | ||||||||
\(326\) | −199.808 | −0.612907 | ||||||||
\(327\) | − | 744.457i | − | 2.27663i | ||||||
\(328\) | 197.327 | + | 208.401i | 0.601607 | + | 0.635370i | ||||
\(329\) | 42.5553 | − | 361.513i | 0.129347 | − | 1.09882i | ||||
\(330\) | −269.808 | −0.817599 | ||||||||
\(331\) | 320.574i | 0.968502i | 0.874929 | + | 0.484251i | \(0.160908\pi\) | ||||
−0.874929 | + | 0.484251i | \(0.839092\pi\) | |||||||
\(332\) | 496.203i | 1.49459i | ||||||||
\(333\) | −377.789 | −1.13450 | ||||||||
\(334\) | −6.13391 | −0.0183650 | ||||||||
\(335\) | −194.109 | −0.579430 | ||||||||
\(336\) | −17.9129 | + | 152.172i | −0.0533121 | + | 0.452894i | ||||
\(337\) | 264.018 | 0.783437 | 0.391718 | − | 0.920085i | \(-0.371881\pi\) | ||||
0.391718 | + | 0.920085i | \(0.371881\pi\) | |||||||
\(338\) | 149.835 | 0.443298 | ||||||||
\(339\) | 268.834 | 0.793019 | ||||||||
\(340\) | 241.566i | 0.710489i | ||||||||
\(341\) | 344.059 | 1.00897 | ||||||||
\(342\) | −237.204 | −0.693579 | ||||||||
\(343\) | 118.105 | − | 322.025i | 0.344330 | − | 0.938849i | ||||
\(344\) | 248.468 | 0.722291 | ||||||||
\(345\) | − | 10.3964i | − | 0.0301345i | ||||||
\(346\) | 117.236i | 0.338833i | ||||||||
\(347\) | 70.4285i | 0.202964i | 0.994837 | + | 0.101482i | \(0.0323584\pi\) | ||||
−0.994837 | + | 0.101482i | \(0.967642\pi\) | |||||||
\(348\) | 148.472i | 0.426643i | ||||||||
\(349\) | 516.862i | 1.48098i | 0.672068 | + | 0.740489i | \(0.265406\pi\) | ||||
−0.672068 | + | 0.740489i | \(0.734594\pi\) | |||||||
\(350\) | 12.2040 | − | 103.674i | 0.0348685 | − | 0.296212i | ||||
\(351\) | −22.3303 | −0.0636191 | ||||||||
\(352\) | − | 640.366i | − | 1.81922i | ||||||
\(353\) | − | 289.266i | − | 0.819450i | −0.912209 | − | 0.409725i | \(-0.865625\pi\) | ||
0.912209 | − | 0.409725i | \(-0.134375\pi\) | |||||||
\(354\) | − | 91.5241i | − | 0.258543i | ||||||
\(355\) | −342.135 | −0.963761 | ||||||||
\(356\) | 212.756 | 0.597630 | ||||||||
\(357\) | −90.8294 | + | 771.609i | −0.254424 | + | 2.16137i | ||||
\(358\) | 44.9168i | 0.125466i | ||||||||
\(359\) | −606.450 | −1.68928 | −0.844638 | − | 0.535338i | \(-0.820184\pi\) | ||||
−0.844638 | + | 0.535338i | \(0.820184\pi\) | |||||||
\(360\) | − | 225.993i | − | 0.627759i | ||||||
\(361\) | 183.523 | 0.508373 | ||||||||
\(362\) | −143.705 | −0.396974 | ||||||||
\(363\) | −1118.77 | −3.08201 | ||||||||
\(364\) | −10.7477 | + | 91.3034i | −0.0295267 | + | 0.250834i | ||||
\(365\) | 60.5227 | 0.165816 | ||||||||
\(366\) | − | 330.188i | − | 0.902154i | ||||||
\(367\) | − | 443.813i | − | 1.20930i | −0.796491 | − | 0.604650i | \(-0.793313\pi\) | ||
0.796491 | − | 0.604650i | \(-0.206687\pi\) | |||||||
\(368\) | 3.73864 | 0.0101593 | ||||||||
\(369\) | 286.551 | + | 302.633i | 0.776561 | + | 0.820143i | ||||
\(370\) | − | 118.037i | − | 0.319020i | ||||||
\(371\) | −481.198 | − | 56.6439i | −1.29703 | − | 0.152679i | ||||
\(372\) | 232.860i | 0.625969i | ||||||||
\(373\) | 92.4682 | 0.247904 | 0.123952 | − | 0.992288i | \(-0.460443\pi\) | ||||
0.123952 | + | 0.992288i | \(0.460443\pi\) | |||||||
\(374\) | − | 491.978i | − | 1.31545i | ||||||
\(375\) | − | 554.949i | − | 1.47986i | ||||||
\(376\) | −364.009 | −0.968110 | ||||||||
\(377\) | 49.4906i | 0.131275i | ||||||||
\(378\) | 4.17424 | − | 35.4608i | 0.0110430 | − | 0.0938116i | ||||
\(379\) | −325.441 | −0.858683 | −0.429342 | − | 0.903142i | \(-0.641254\pi\) | ||||
−0.429342 | + | 0.903142i | \(0.641254\pi\) | |||||||
\(380\) | 222.338i | 0.585099i | ||||||||
\(381\) | 313.295 | 0.822296 | ||||||||
\(382\) | 225.366i | 0.589963i | ||||||||
\(383\) | 545.025 | 1.42304 | 0.711521 | − | 0.702665i | \(-0.248007\pi\) | ||||
0.711521 | + | 0.702665i | \(0.248007\pi\) | |||||||
\(384\) | 520.958 | 1.35666 | ||||||||
\(385\) | −50.4356 | + | 428.458i | −0.131002 | + | 1.11288i | ||||
\(386\) | 81.7334i | 0.211745i | ||||||||
\(387\) | 360.817 | 0.932343 | ||||||||
\(388\) | −301.616 | −0.777360 | ||||||||
\(389\) | 137.964 | 0.354662 | 0.177331 | − | 0.984151i | \(-0.443254\pi\) | ||||
0.177331 | + | 0.984151i | \(0.443254\pi\) | |||||||
\(390\) | − | 60.8690i | − | 0.156074i | ||||||
\(391\) | 18.9572 | 0.0484839 | ||||||||
\(392\) | −333.624 | − | 79.6484i | −0.851082 | − | 0.203185i | ||||
\(393\) | − | 1063.59i | − | 2.70634i | ||||||
\(394\) | 49.6879 | 0.126111 | ||||||||
\(395\) | 148.988 | 0.377184 | ||||||||
\(396\) | − | 591.765i | − | 1.49436i | ||||||
\(397\) | −509.231 | −1.28270 | −0.641349 | − | 0.767249i | \(-0.721625\pi\) | ||||
−0.641349 | + | 0.767249i | \(0.721625\pi\) | |||||||
\(398\) | −361.339 | −0.907888 | ||||||||
\(399\) | −83.5994 | + | 710.189i | −0.209522 | + | 1.77992i | ||||
\(400\) | 74.5644 | 0.186411 | ||||||||
\(401\) | 29.7568 | 0.0742065 | 0.0371033 | − | 0.999311i | \(-0.488187\pi\) | ||||
0.0371033 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(402\) | 267.558i | 0.665568i | ||||||||
\(403\) | 77.6201i | 0.192606i | ||||||||
\(404\) | 262.549 | 0.649873 | ||||||||
\(405\) | 219.641i | 0.542324i | ||||||||
\(406\) | −78.5917 | − | 9.25137i | −0.193576 | − | 0.0227866i | ||||
\(407\) | − | 721.191i | − | 1.77197i | ||||||
\(408\) | 776.936 | 1.90426 | ||||||||
\(409\) | 9.28024i | 0.0226901i | 0.999936 | + | 0.0113450i | \(0.00361132\pi\) | ||||
−0.999936 | + | 0.0113450i | \(0.996389\pi\) | |||||||
\(410\) | −94.5553 | + | 89.5307i | −0.230623 | + | 0.218368i | ||||
\(411\) | − | 266.233i | − | 0.647768i | ||||||
\(412\) | − | 338.203i | − | 0.820881i | ||||||
\(413\) | −145.341 | − | 17.1088i | −0.351916 | − | 0.0414256i | ||||
\(414\) | −7.60076 | −0.0183593 | ||||||||
\(415\) | −525.317 | −1.26583 | ||||||||
\(416\) | 144.467 | 0.347278 | ||||||||
\(417\) | 108.936i | 0.261237i | ||||||||
\(418\) | − | 452.817i | − | 1.08329i | ||||||
\(419\) | − | 156.674i | − | 0.373924i | −0.982367 | − | 0.186962i | \(-0.940136\pi\) | ||
0.982367 | − | 0.186962i | \(-0.0598641\pi\) | |||||||
\(420\) | −289.982 | − | 34.1350i | −0.690433 | − | 0.0812739i | ||||
\(421\) | − | 149.739i | − | 0.355675i | −0.984060 | − | 0.177838i | \(-0.943090\pi\) | ||
0.984060 | − | 0.177838i | \(-0.0569102\pi\) | |||||||
\(422\) | − | 130.031i | − | 0.308131i | ||||||
\(423\) | −528.601 | −1.24965 | ||||||||
\(424\) | 484.520i | 1.14274i | ||||||||
\(425\) | 378.088 | 0.889619 | ||||||||
\(426\) | 471.596i | 1.10703i | ||||||||
\(427\) | −524.343 | − | 61.7227i | −1.22797 | − | 0.144550i | ||||
\(428\) | 268.955 | 0.628398 | ||||||||
\(429\) | − | 371.900i | − | 0.866901i | ||||||
\(430\) | 112.734i | 0.262173i | ||||||||
\(431\) | −489.408 | −1.13552 | −0.567759 | − | 0.823195i | \(-0.692189\pi\) | ||||
−0.567759 | + | 0.823195i | \(0.692189\pi\) | |||||||
\(432\) | 25.5040 | 0.0590371 | ||||||||
\(433\) | 626.973i | 1.44798i | 0.689813 | + | 0.723988i | \(0.257693\pi\) | ||||
−0.689813 | + | 0.723988i | \(0.742307\pi\) | |||||||
\(434\) | −123.262 | − | 14.5097i | −0.284013 | − | 0.0334324i | ||||
\(435\) | −157.183 | −0.361341 | ||||||||
\(436\) | 510.158i | 1.17009i | ||||||||
\(437\) | 17.4482 | 0.0399273 | ||||||||
\(438\) | − | 83.4240i | − | 0.190466i | ||||||
\(439\) | 245.911 | 0.560163 | 0.280081 | − | 0.959976i | \(-0.409639\pi\) | ||||
0.280081 | + | 0.959976i | \(0.409639\pi\) | |||||||
\(440\) | 431.416 | 0.980490 | ||||||||
\(441\) | −484.477 | − | 115.663i | −1.09859 | − | 0.262273i | ||||
\(442\) | 110.991 | 0.251111 | ||||||||
\(443\) | −664.744 | −1.50055 | −0.750275 | − | 0.661126i | \(-0.770079\pi\) | ||||
−0.750275 | + | 0.661126i | \(0.770079\pi\) | |||||||
\(444\) | 488.105 | 1.09934 | ||||||||
\(445\) | 225.240i | 0.506156i | ||||||||
\(446\) | 159.850i | 0.358409i | ||||||||
\(447\) | 69.5958i | 0.155695i | ||||||||
\(448\) | −10.6386 | + | 90.3760i | −0.0237468 | + | 0.201732i | ||||
\(449\) | 2.79848 | 0.00623270 | 0.00311635 | − | 0.999995i | \(-0.499008\pi\) | ||||
0.00311635 | + | 0.999995i | \(0.499008\pi\) | |||||||
\(450\) | −151.592 | −0.336870 | ||||||||
\(451\) | −577.719 | + | 547.019i | −1.28097 | + | 1.21290i | ||||
\(452\) | −184.225 | −0.407577 | ||||||||
\(453\) | − | 438.787i | − | 0.968624i | ||||||
\(454\) | 41.3072 | 0.0909851 | ||||||||
\(455\) | −96.6606 | − | 11.3783i | −0.212441 | − | 0.0250073i | ||||
\(456\) | 715.092 | 1.56819 | ||||||||
\(457\) | − | 736.912i | − | 1.61250i | −0.591576 | − | 0.806249i | \(-0.701494\pi\) | ||
0.591576 | − | 0.806249i | \(-0.298506\pi\) | |||||||
\(458\) | −240.096 | −0.524227 | ||||||||
\(459\) | 129.321 | 0.281746 | ||||||||
\(460\) | 7.12440i | 0.0154878i | ||||||||
\(461\) | 304.316i | 0.660121i | 0.943960 | + | 0.330061i | \(0.107069\pi\) | ||||
−0.943960 | + | 0.330061i | \(0.892931\pi\) | |||||||
\(462\) | 590.582 | + | 69.5200i | 1.27832 | + | 0.150476i | ||||
\(463\) | − | 438.392i | − | 0.946851i | −0.880834 | − | 0.473426i | \(-0.843017\pi\) | ||
0.880834 | − | 0.473426i | \(-0.156983\pi\) | |||||||
\(464\) | − | 56.5245i | − | 0.121820i | ||||||
\(465\) | −246.523 | −0.530158 | ||||||||
\(466\) | − | 406.118i | − | 0.871498i | ||||||
\(467\) | 205.116i | 0.439220i | 0.975588 | + | 0.219610i | \(0.0704785\pi\) | ||||
−0.975588 | + | 0.219610i | \(0.929522\pi\) | |||||||
\(468\) | 133.503 | 0.285263 | ||||||||
\(469\) | 424.886 | + | 50.0151i | 0.905939 | + | 0.106642i | ||||
\(470\) | − | 165.157i | − | 0.351399i | ||||||
\(471\) | 107.165 | 0.227527 | ||||||||
\(472\) | 146.345i | 0.310053i | ||||||||
\(473\) | 688.790i | 1.45622i | ||||||||
\(474\) | − | 205.364i | − | 0.433256i | ||||||
\(475\) | 347.992 | 0.732615 | ||||||||
\(476\) | 62.2432 | − | 528.765i | 0.130763 | − | 1.11085i | ||||
\(477\) | 703.603i | 1.47506i | ||||||||
\(478\) | 121.628i | 0.254453i | ||||||||
\(479\) | 181.269 | 0.378433 | 0.189216 | − | 0.981935i | \(-0.439405\pi\) | ||||
0.189216 | + | 0.981935i | \(0.439405\pi\) | |||||||
\(480\) | 458.832i | 0.955900i | ||||||||
\(481\) | 162.702 | 0.338257 | ||||||||
\(482\) | − | 266.509i | − | 0.552924i | ||||||
\(483\) | −2.67879 | + | 22.7567i | −0.00554615 | + | 0.0471153i | ||||
\(484\) | 766.666 | 1.58402 | ||||||||
\(485\) | − | 319.313i | − | 0.658377i | ||||||
\(486\) | 348.659 | 0.717405 | ||||||||
\(487\) | −844.083 | −1.73323 | −0.866615 | − | 0.498977i | \(-0.833709\pi\) | ||||
−0.866615 | + | 0.498977i | \(0.833709\pi\) | |||||||
\(488\) | 527.963i | 1.08189i | ||||||||
\(489\) | 874.718 | 1.78879 | ||||||||
\(490\) | 36.1379 | − | 151.371i | 0.0737508 | − | 0.308921i | ||||
\(491\) | 675.459 | 1.37568 | 0.687840 | − | 0.725862i | \(-0.258559\pi\) | ||||
0.687840 | + | 0.725862i | \(0.258559\pi\) | |||||||
\(492\) | −370.225 | − | 391.003i | −0.752490 | − | 0.794721i | ||||
\(493\) | − | 286.614i | − | 0.581368i | ||||||
\(494\) | 102.156 | 0.206794 | ||||||||
\(495\) | 626.487 | 1.26563 | ||||||||
\(496\) | − | 88.6519i | − | 0.178734i | ||||||
\(497\) | 748.900 | + | 88.1563i | 1.50684 | + | 0.177377i | ||||
\(498\) | 724.093i | 1.45400i | ||||||||
\(499\) | 676.880i | 1.35647i | 0.734844 | + | 0.678236i | \(0.237255\pi\) | ||||
−0.734844 | + | 0.678236i | \(0.762745\pi\) | |||||||
\(500\) | 380.293i | 0.760585i | ||||||||
\(501\) | 26.8530 | 0.0535989 | ||||||||
\(502\) | 187.109i | 0.372726i | ||||||||
\(503\) | 286.456 | 0.569495 | 0.284747 | − | 0.958603i | \(-0.408090\pi\) | ||||
0.284747 | + | 0.958603i | \(0.408090\pi\) | |||||||
\(504\) | −58.2306 | + | 494.677i | −0.115537 | + | 0.981502i | ||||
\(505\) | 277.954i | 0.550403i | ||||||||
\(506\) | − | 14.5097i | − | 0.0286752i | ||||||
\(507\) | −655.947 | −1.29378 | ||||||||
\(508\) | −214.693 | −0.422624 | ||||||||
\(509\) | 381.854 | 0.750204 | 0.375102 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375102 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(510\) | 352.510i | 0.691195i | ||||||||
\(511\) | −132.478 | − | 15.5946i | −0.259253 | − | 0.0305178i | ||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 119.027 | 0.232022 | ||||||||
\(514\) | 397.387 | 0.773126 | ||||||||
\(515\) | 358.047 | 0.695237 | ||||||||
\(516\) | −466.176 | −0.903442 | ||||||||
\(517\) | − | 1009.09i | − | 1.95181i | ||||||
\(518\) | −30.4141 | + | 258.372i | −0.0587145 | + | 0.498788i | ||||
\(519\) | − | 513.237i | − | 0.988895i | ||||||
\(520\) | 97.3280i | 0.187169i | ||||||||
\(521\) | 439.901 | 0.844340 | 0.422170 | − | 0.906517i | \(-0.361269\pi\) | ||||
0.422170 | + | 0.906517i | \(0.361269\pi\) | |||||||
\(522\) | 114.916i | 0.220146i | ||||||||
\(523\) | 627.498i | 1.19980i | 0.800073 | + | 0.599902i | \(0.204794\pi\) | ||||
−0.800073 | + | 0.599902i | \(0.795206\pi\) | |||||||
\(524\) | 728.854i | 1.39094i | ||||||||
\(525\) | −53.4265 | + | 453.866i | −0.101765 | + | 0.864506i | ||||
\(526\) | − | 281.588i | − | 0.535338i | ||||||
\(527\) | − | 449.521i | − | 0.852980i | ||||||
\(528\) | 424.757i | 0.804464i | ||||||||
\(529\) | −528.441 | −0.998943 | ||||||||
\(530\) | −219.835 | −0.414784 | ||||||||
\(531\) | 212.517i | 0.400220i | ||||||||
\(532\) | 57.2886 | − | 486.675i | 0.107685 | − | 0.914803i | ||||
\(533\) | −123.408 | − | 130.334i | −0.231535 | − | 0.244529i | ||||
\(534\) | 310.468 | 0.581401 | ||||||||
\(535\) | 284.735i | 0.532215i | ||||||||
\(536\) | − | 427.819i | − | 0.798170i | ||||||
\(537\) | − | 196.637i | − | 0.366176i | ||||||
\(538\) | − | 207.214i | − | 0.385156i | ||||||
\(539\) | 220.797 | − | 924.856i | 0.409642 | − | 1.71587i | ||||
\(540\) | 48.6008i | 0.0900015i | ||||||||
\(541\) | 791.248 | 1.46257 | 0.731283 | − | 0.682074i | \(-0.238922\pi\) | ||||
0.731283 | + | 0.682074i | \(0.238922\pi\) | |||||||
\(542\) | 169.626i | 0.312963i | ||||||||
\(543\) | 629.111 | 1.15858 | ||||||||
\(544\) | −836.653 | −1.53796 | ||||||||
\(545\) | −540.091 | −0.990994 | ||||||||
\(546\) | −15.6838 | + | 133.236i | −0.0287249 | + | 0.244022i | ||||
\(547\) | − | 694.771i | − | 1.27015i | −0.772451 | − | 0.635074i | \(-0.780970\pi\) | ||
0.772451 | − | 0.635074i | \(-0.219030\pi\) | |||||||
\(548\) | 182.443i | 0.332924i | ||||||||
\(549\) | 766.690i | 1.39652i | ||||||||
\(550\) | − | 289.385i | − | 0.526154i | ||||||
\(551\) | − | 263.800i | − | 0.478766i | ||||||
\(552\) | 22.9138 | 0.0415105 | ||||||||
\(553\) | −326.120 | − | 38.3890i | −0.589728 | − | 0.0694195i | ||||
\(554\) | 85.9636 | 0.155169 | ||||||||
\(555\) | 516.744i | 0.931071i | ||||||||
\(556\) | − | 74.6510i | − | 0.134264i | ||||||
\(557\) | 216.837i | 0.389294i | 0.980873 | + | 0.194647i | \(0.0623561\pi\) | ||||
−0.980873 | + | 0.194647i | \(0.937644\pi\) | |||||||
\(558\) | 180.232i | 0.322997i | ||||||||
\(559\) | −155.392 | −0.277982 | ||||||||
\(560\) | 110.399 | + | 12.9955i | 0.197140 | + | 0.0232062i | ||||
\(561\) | 2153.78i | 3.83918i | ||||||||
\(562\) | 245.074i | 0.436074i | ||||||||
\(563\) | −850.335 | −1.51036 | −0.755182 | − | 0.655515i | \(-0.772452\pi\) | ||||
−0.755182 | + | 0.655515i | \(0.772452\pi\) | |||||||
\(564\) | 682.955 | 1.21091 | ||||||||
\(565\) | − | 195.034i | − | 0.345193i | ||||||
\(566\) | 203.790i | 0.360053i | ||||||||
\(567\) | 56.5939 | − | 480.773i | 0.0998128 | − | 0.847924i | ||||
\(568\) | − | 754.071i | − | 1.32759i | ||||||
\(569\) | −21.7932 | −0.0383009 | −0.0191504 | − | 0.999817i | \(-0.506096\pi\) | ||||
−0.0191504 | + | 0.999817i | \(0.506096\pi\) | |||||||
\(570\) | 324.450i | 0.569211i | ||||||||
\(571\) | − | 248.152i | − | 0.434592i | −0.976106 | − | 0.217296i | \(-0.930276\pi\) | ||
0.976106 | − | 0.217296i | \(-0.0697237\pi\) | |||||||
\(572\) | 254.854i | 0.445549i | ||||||||
\(573\) | − | 986.607i | − | 1.72183i | ||||||
\(574\) | 230.041 | − | 171.610i | 0.400769 | − | 0.298973i | ||||
\(575\) | 11.1508 | 0.0193926 | ||||||||
\(576\) | 132.147 | 0.229422 | ||||||||
\(577\) | −919.649 | −1.59384 | −0.796922 | − | 0.604082i | \(-0.793540\pi\) | ||||
−0.796922 | + | 0.604082i | \(0.793540\pi\) | |||||||
\(578\) | −353.780 | −0.612077 | ||||||||
\(579\) | − | 357.813i | − | 0.617984i | ||||||
\(580\) | 107.714 | 0.185714 | ||||||||
\(581\) | 1149.87 | + | 135.356i | 1.97912 | + | 0.232971i | ||||
\(582\) | −440.138 | −0.756251 | ||||||||
\(583\) | −1343.16 | −2.30388 | ||||||||
\(584\) | 133.393i | 0.228413i | ||||||||
\(585\) | 141.336i | 0.241600i | ||||||||
\(586\) | 422.057 | 0.720233 | ||||||||
\(587\) | 284.318 | 0.484358 | 0.242179 | − | 0.970232i | \(-0.422138\pi\) | ||||
0.242179 | + | 0.970232i | \(0.422138\pi\) | |||||||
\(588\) | 625.946 | + | 149.436i | 1.06453 | + | 0.254144i | ||||
\(589\) | − | 413.739i | − | 0.702443i | ||||||
\(590\) | −66.3992 | −0.112541 | ||||||||
\(591\) | −217.524 | −0.368060 | ||||||||
\(592\) | −185.826 | −0.313895 | ||||||||
\(593\) | 875.768 | 1.47684 | 0.738421 | − | 0.674340i | \(-0.235572\pi\) | ||||
0.738421 | + | 0.674340i | \(0.235572\pi\) | |||||||
\(594\) | − | 98.9812i | − | 0.166635i | ||||||
\(595\) | 559.789 | + | 65.8953i | 0.940823 | + | 0.110748i | ||||
\(596\) | − | 47.6923i | − | 0.0800206i | ||||||
\(597\) | 1581.87 | 2.64970 | ||||||||
\(598\) | 3.27340 | 0.00547392 | ||||||||
\(599\) | −353.405 | −0.589991 | −0.294995 | − | 0.955499i | \(-0.595318\pi\) | ||||
−0.294995 | + | 0.955499i | \(0.595318\pi\) | |||||||
\(600\) | 456.999 | 0.761666 | ||||||||
\(601\) | 581.231 | 0.967107 | 0.483553 | − | 0.875315i | \(-0.339346\pi\) | ||||
0.483553 | + | 0.875315i | \(0.339346\pi\) | |||||||
\(602\) | 29.0477 | − | 246.764i | 0.0482520 | − | 0.409908i | ||||
\(603\) | − | 621.264i | − | 1.03029i | ||||||
\(604\) | 300.690i | 0.497831i | ||||||||
\(605\) | 811.649i | 1.34157i | ||||||||
\(606\) | 383.129 | 0.632226 | ||||||||
\(607\) | − | 774.119i | − | 1.27532i | −0.770318 | − | 0.637660i | \(-0.779902\pi\) | ||
0.770318 | − | 0.637660i | \(-0.220098\pi\) | |||||||
\(608\) | −770.055 | −1.26654 | ||||||||
\(609\) | 344.059 | + | 40.5007i | 0.564957 | + | 0.0665035i | ||||
\(610\) | −239.546 | −0.392699 | ||||||||
\(611\) | 227.652 | 0.372588 | ||||||||
\(612\) | −773.155 | −1.26332 | ||||||||
\(613\) | −524.018 | −0.854842 | −0.427421 | − | 0.904053i | \(-0.640578\pi\) | ||||
−0.427421 | + | 0.904053i | \(0.640578\pi\) | |||||||
\(614\) | 402.802i | 0.656029i | ||||||||
\(615\) | 413.944 | − | 391.948i | 0.673080 | − | 0.637313i | ||||
\(616\) | −944.327 | − | 111.161i | −1.53300 | − | 0.180456i | ||||
\(617\) | −897.684 | −1.45492 | −0.727459 | − | 0.686151i | \(-0.759299\pi\) | ||||
−0.727459 | + | 0.686151i | \(0.759299\pi\) | |||||||
\(618\) | − | 493.529i | − | 0.798590i | ||||||
\(619\) | − | 605.790i | − | 0.978660i | −0.872099 | − | 0.489330i | \(-0.837241\pi\) | ||
0.872099 | − | 0.489330i | \(-0.162759\pi\) | |||||||
\(620\) | 168.936 | 0.272478 | ||||||||
\(621\) | 3.81401 | 0.00614172 | ||||||||
\(622\) | 112.670 | 0.181142 | ||||||||
\(623\) | 58.0364 | − | 493.027i | 0.0931563 | − | 0.791376i | ||||
\(624\) | −95.8258 | −0.153567 | ||||||||
\(625\) | −29.7841 | −0.0476545 | ||||||||
\(626\) | −412.188 | −0.658448 | ||||||||
\(627\) | 1982.34i | 3.16163i | ||||||||
\(628\) | −73.4376 | −0.116939 | ||||||||
\(629\) | −942.252 | −1.49802 | ||||||||
\(630\) | −224.444 | − | 26.4202i | −0.356260 | − | 0.0419369i | ||||
\(631\) | 823.492 | 1.30506 | 0.652529 | − | 0.757764i | \(-0.273708\pi\) | ||||
0.652529 | + | 0.757764i | \(0.273708\pi\) | |||||||
\(632\) | 328.371i | 0.519575i | ||||||||
\(633\) | 569.252i | 0.899292i | ||||||||
\(634\) | − | 322.391i | − | 0.508503i | ||||||
\(635\) | − | 227.290i | − | 0.357937i | ||||||
\(636\) | − | 909.057i | − | 1.42934i | ||||||
\(637\) | 208.649 | + | 49.8121i | 0.327549 | + | 0.0781980i | ||||
\(638\) | −219.372 | −0.343843 | ||||||||
\(639\) | − | 1095.03i | − | 1.71367i | ||||||
\(640\) | − | 377.947i | − | 0.590542i | ||||||
\(641\) | − | 207.954i | − | 0.324422i | −0.986756 | − | 0.162211i | \(-0.948138\pi\) | ||
0.986756 | − | 0.162211i | \(-0.0518625\pi\) | |||||||
\(642\) | 392.477 | 0.611334 | ||||||||
\(643\) | 1005.93 | 1.56444 | 0.782218 | − | 0.623004i | \(-0.214088\pi\) | ||||
0.782218 | + | 0.623004i | \(0.214088\pi\) | |||||||
\(644\) | 1.83571 | − | 15.5946i | 0.00285048 | − | 0.0242152i | ||||
\(645\) | − | 493.529i | − | 0.765161i | ||||||
\(646\) | −591.615 | −0.915813 | ||||||||
\(647\) | 1177.11i | 1.81934i | 0.415335 | + | 0.909669i | \(0.363664\pi\) | ||||
−0.415335 | + | 0.909669i | \(0.636336\pi\) | |||||||
\(648\) | −484.092 | −0.747056 | ||||||||
\(649\) | −405.690 | −0.625100 | ||||||||
\(650\) | 65.2856 | 0.100439 | ||||||||
\(651\) | 539.615 | + | 63.5205i | 0.828902 | + | 0.0975737i | ||||
\(652\) | −599.423 | −0.919360 | ||||||||
\(653\) | − | 492.015i | − | 0.753468i | −0.926321 | − | 0.376734i | \(-0.877047\pi\) | ||
0.926321 | − | 0.376734i | \(-0.122953\pi\) | |||||||
\(654\) | 744.457i | 1.13831i | ||||||||
\(655\) | −771.619 | −1.17804 | ||||||||
\(656\) | 140.948 | + | 148.858i | 0.214859 | + | 0.226918i | ||||
\(657\) | 193.709i | 0.294838i | ||||||||
\(658\) | −42.5553 | + | 361.513i | −0.0646737 | + | 0.549412i | ||||
\(659\) | 490.198i | 0.743851i | 0.928263 | + | 0.371925i | \(0.121302\pi\) | ||||
−0.928263 | + | 0.371925i | \(0.878698\pi\) | |||||||
\(660\) | −809.423 | −1.22640 | ||||||||
\(661\) | 925.986i | 1.40089i | 0.713708 | + | 0.700444i | \(0.247014\pi\) | ||||
−0.713708 | + | 0.700444i | \(0.752986\pi\) | |||||||
\(662\) | − | 320.574i | − | 0.484251i | ||||||
\(663\) | −485.896 | −0.732875 | ||||||||
\(664\) | − | 1157.81i | − | 1.74369i | ||||||
\(665\) | 515.230 | + | 60.6500i | 0.774782 | + | 0.0912030i | ||||
\(666\) | 377.789 | 0.567251 | ||||||||
\(667\) | − | 8.45298i | − | 0.0126731i | ||||||
\(668\) | −18.4017 | −0.0275475 | ||||||||
\(669\) | − | 699.793i | − | 1.04603i | ||||||
\(670\) | 194.109 | 0.289715 | ||||||||
\(671\) | −1463.59 | −2.18121 | ||||||||
\(672\) | 118.225 | − | 1004.34i | 0.175930 | − | 1.49455i | ||||
\(673\) | 750.563i | 1.11525i | 0.830093 | + | 0.557625i | \(0.188287\pi\) | ||||
−0.830093 | + | 0.557625i | \(0.811713\pi\) | |||||||
\(674\) | −264.018 | −0.391718 | ||||||||
\(675\) | 76.0676 | 0.112693 | ||||||||
\(676\) | 449.505 | 0.664948 | ||||||||
\(677\) | − | 208.540i | − | 0.308035i | −0.988068 | − | 0.154017i | \(-0.950779\pi\) | ||
0.988068 | − | 0.154017i | \(-0.0492212\pi\) | |||||||
\(678\) | −268.834 | −0.396510 | ||||||||
\(679\) | −82.2758 | + | 698.944i | −0.121172 | + | 1.02937i | ||||
\(680\) | − | 563.654i | − | 0.828904i | ||||||
\(681\) | −180.835 | −0.265543 | ||||||||
\(682\) | −344.059 | −0.504485 | ||||||||
\(683\) | − | 693.080i | − | 1.01476i | −0.861723 | − | 0.507379i | \(-0.830614\pi\) | ||
0.861723 | − | 0.507379i | \(-0.169386\pi\) | |||||||
\(684\) | −711.612 | −1.04037 | ||||||||
\(685\) | −193.147 | −0.281967 | ||||||||
\(686\) | −118.105 | + | 322.025i | −0.172165 | + | 0.469424i | ||||
\(687\) | 1051.09 | 1.52997 | ||||||||
\(688\) | 177.477 | 0.257961 | ||||||||
\(689\) | − | 303.019i | − | 0.439795i | ||||||
\(690\) | 10.3964i | 0.0150672i | ||||||||
\(691\) | 345.402 | 0.499858 | 0.249929 | − | 0.968264i | \(-0.419593\pi\) | ||||
0.249929 | + | 0.968264i | \(0.419593\pi\) | |||||||
\(692\) | 351.708i | 0.508249i | ||||||||
\(693\) | −1371.32 | − | 161.424i | −1.97881 | − | 0.232935i | ||||
\(694\) | − | 70.4285i | − | 0.101482i | ||||||
\(695\) | 79.0311 | 0.113714 | ||||||||
\(696\) | − | 346.434i | − | 0.497750i | ||||||
\(697\) | 714.693 | + | 754.803i | 1.02538 | + | 1.08293i | ||||
\(698\) | − | 516.862i | − | 0.740489i | ||||||
\(699\) | 1777.90i | 2.54350i | ||||||||
\(700\) | 36.6119 | − | 311.023i | 0.0523027 | − | 0.444319i | ||||
\(701\) | −604.359 | −0.862138 | −0.431069 | − | 0.902319i | \(-0.641864\pi\) | ||||
−0.431069 | + | 0.902319i | \(0.641864\pi\) | |||||||
\(702\) | 22.3303 | 0.0318095 | ||||||||
\(703\) | −867.249 | −1.23364 | ||||||||
\(704\) | 252.265i | 0.358332i | ||||||||
\(705\) | 723.026i | 1.02557i | ||||||||
\(706\) | 289.266i | 0.409725i | ||||||||
\(707\) | 71.6189 | − | 608.413i | 0.101300 | − | 0.860556i | ||||
\(708\) | − | 274.572i | − | 0.387814i | ||||||
\(709\) | 581.369i | 0.819984i | 0.912089 | + | 0.409992i | \(0.134469\pi\) | ||||
−0.912089 | + | 0.409992i | \(0.865531\pi\) | |||||||
\(710\) | 342.135 | 0.481880 | ||||||||
\(711\) | 476.849i | 0.670674i | ||||||||
\(712\) | −496.431 | −0.697235 | ||||||||
\(713\) | − | 13.2575i | − | 0.0185940i | ||||||
\(714\) | 90.8294 | − | 771.609i | 0.127212 | − | 1.08068i | ||||
\(715\) | −269.808 | −0.377353 | ||||||||
\(716\) | 134.750i | 0.188199i | ||||||||
\(717\) | − | 532.465i | − | 0.742629i | ||||||
\(718\) | 606.450 | 0.844638 | ||||||||
\(719\) | 320.556 | 0.445836 | 0.222918 | − | 0.974837i | \(-0.428442\pi\) | ||||
0.222918 | + | 0.974837i | \(0.428442\pi\) | |||||||
\(720\) | − | 161.424i | − | 0.224200i | ||||||
\(721\) | −783.729 | − | 92.2562i | −1.08700 | − | 0.127956i | ||||
\(722\) | −183.523 | −0.254187 | ||||||||
\(723\) | 1166.72i | 1.61373i | ||||||||
\(724\) | −431.114 | −0.595461 | ||||||||
\(725\) | − | 168.589i | − | 0.232536i | ||||||
\(726\) | 1118.77 | 1.54101 | ||||||||
\(727\) | 830.527 | 1.14240 | 0.571202 | − | 0.820810i | \(-0.306477\pi\) | ||||
0.571202 | + | 0.820810i | \(0.306477\pi\) | |||||||
\(728\) | 25.0780 | − | 213.041i | 0.0344478 | − | 0.292639i | ||||
\(729\) | −903.955 | −1.23999 | ||||||||
\(730\) | −60.5227 | −0.0829078 | ||||||||
\(731\) | 899.920 | 1.23108 | ||||||||
\(732\) | − | 990.565i | − | 1.35323i | ||||||
\(733\) | − | 1033.69i | − | 1.41022i | −0.709096 | − | 0.705112i | \(-0.750897\pi\) | ||
0.709096 | − | 0.705112i | \(-0.249103\pi\) | |||||||
\(734\) | 443.813i | 0.604650i | ||||||||
\(735\) | −158.204 | + | 662.673i | −0.215244 | + | 0.901596i | ||||
\(736\) | −24.6750 | −0.0335258 | ||||||||
\(737\) | 1185.98 | 1.60920 | ||||||||
\(738\) | −286.551 | − | 302.633i | −0.388281 | − | 0.410072i | ||||
\(739\) | 224.330 | 0.303559 | 0.151780 | − | 0.988414i | \(-0.451500\pi\) | ||||
0.151780 | + | 0.988414i | \(0.451500\pi\) | |||||||
\(740\) | − | 354.112i | − | 0.478530i | ||||||
\(741\) | −447.219 | −0.603534 | ||||||||
\(742\) | 481.198 | + | 56.6439i | 0.648514 | + | 0.0763395i | ||||
\(743\) | 350.661 | 0.471952 | 0.235976 | − | 0.971759i | \(-0.424171\pi\) | ||||
0.235976 | + | 0.971759i | \(0.424171\pi\) | |||||||
\(744\) | − | 543.341i | − | 0.730297i | ||||||
\(745\) | 50.4906 | 0.0677726 | ||||||||
\(746\) | −92.4682 | −0.123952 | ||||||||
\(747\) | − | 1681.33i | − | 2.25077i | ||||||
\(748\) | − | 1475.93i | − | 1.97317i | ||||||
\(749\) | 73.3663 | − | 623.257i | 0.0979524 | − | 0.832119i | ||||
\(750\) | 554.949i | 0.739932i | ||||||||
\(751\) | 378.916i | 0.504548i | 0.967656 | + | 0.252274i | \(0.0811784\pi\) | ||||
−0.967656 | + | 0.252274i | \(0.918822\pi\) | |||||||
\(752\) | −260.007 | −0.345753 | ||||||||
\(753\) | − | 819.125i | − | 1.08781i | ||||||
\(754\) | − | 49.4906i | − | 0.0656374i | ||||||
\(755\) | −318.333 | −0.421633 | ||||||||
\(756\) | 12.5227 | − | 106.382i | 0.0165645 | − | 0.140717i | ||||
\(757\) | 1274.27i | 1.68332i | 0.540008 | + | 0.841660i | \(0.318421\pi\) | ||||
−0.540008 | + | 0.841660i | \(0.681579\pi\) | |||||||
\(758\) | 325.441 | 0.429342 | ||||||||
\(759\) | 63.5205i | 0.0836897i | ||||||||
\(760\) | − | 518.788i | − | 0.682615i | ||||||
\(761\) | − | 1364.03i | − | 1.79242i | −0.443633 | − | 0.896209i | \(-0.646311\pi\) | ||
0.443633 | − | 0.896209i | \(-0.353689\pi\) | |||||||
\(762\) | −313.295 | −0.411148 | ||||||||
\(763\) | 1182.21 | + | 139.163i | 1.54942 | + | 0.182389i | ||||
\(764\) | 676.098i | 0.884945i | ||||||||
\(765\) | − | 818.519i | − | 1.06996i | ||||||
\(766\) | −545.025 | −0.711521 | ||||||||
\(767\) | − | 91.5241i | − | 0.119327i | ||||||
\(768\) | −748.604 | −0.974745 | ||||||||
\(769\) | 978.653i | 1.27263i | 0.771429 | + | 0.636315i | \(0.219542\pi\) | ||||
−0.771429 | + | 0.636315i | \(0.780458\pi\) | |||||||
\(770\) | 50.4356 | − | 428.458i | 0.0655008 | − | 0.556438i | ||||
\(771\) | −1739.68 | −2.25639 | ||||||||
\(772\) | 245.200i | 0.317617i | ||||||||
\(773\) | −226.445 | −0.292943 | −0.146472 | − | 0.989215i | \(-0.546792\pi\) | ||||
−0.146472 | + | 0.989215i | \(0.546792\pi\) | |||||||
\(774\) | −360.817 | −0.466171 | ||||||||
\(775\) | − | 264.411i | − | 0.341176i | ||||||
\(776\) | 703.770 | 0.906920 | ||||||||
\(777\) | 133.147 | − | 1131.10i | 0.171360 | − | 1.45573i | ||||
\(778\) | −137.964 | −0.177331 | ||||||||
\(779\) | 657.804 | + | 694.721i | 0.844421 | + | 0.891811i | ||||
\(780\) | − | 182.607i | − | 0.234111i | ||||||
\(781\) | 2090.40 | 2.67656 | ||||||||
\(782\) | −18.9572 | −0.0242420 | ||||||||
\(783\) | − | 57.6641i | − | 0.0736450i | ||||||
\(784\) | −238.303 | − | 56.8917i | −0.303958 | − | 0.0725660i | ||||
\(785\) | − | 77.7465i | − | 0.0990402i | ||||||
\(786\) | 1063.59i | 1.35317i | ||||||||
\(787\) | 609.986i | 0.775078i | 0.921853 | + | 0.387539i | \(0.126675\pi\) | ||||
−0.921853 | + | 0.387539i | \(0.873325\pi\) | |||||||
\(788\) | 149.064 | 0.189167 | ||||||||
\(789\) | 1232.73i | 1.56240i | ||||||||
\(790\) | −148.988 | −0.188592 | ||||||||
\(791\) | −50.2535 | + | 426.911i | −0.0635316 | + | 0.539710i | ||||
\(792\) | 1380.79i | 1.74342i | ||||||||
\(793\) | − | 330.188i | − | 0.416379i | ||||||
\(794\) | 509.231 | 0.641349 | ||||||||
\(795\) | 962.395 | 1.21056 | ||||||||
\(796\) | −1084.02 | −1.36183 | ||||||||
\(797\) | − | 329.010i | − | 0.412810i | −0.978467 | − | 0.206405i | \(-0.933824\pi\) | ||
0.978467 | − | 0.206405i | \(-0.0661764\pi\) | |||||||
\(798\) | 83.5994 | − | 710.189i | 0.104761 | − | 0.889961i | ||||
\(799\) | −1318.40 | −1.65006 | ||||||||
\(800\) | −492.125 | −0.615156 | ||||||||
\(801\) | −720.900 | −0.900000 | ||||||||
\(802\) | −29.7568 | −0.0371033 | ||||||||
\(803\) | −369.785 | −0.460504 | ||||||||
\(804\) | 802.675i | 0.998352i | ||||||||
\(805\) | 16.5096 | + | 1.94342i | 0.0205088 | + | 0.00241418i | ||||
\(806\) | − | 77.6201i | − | 0.0963029i | ||||||
\(807\) | 907.141i | 1.12409i | ||||||||
\(808\) | −612.614 | −0.758185 | ||||||||
\(809\) | 1030.94i | 1.27434i | 0.770724 | + | 0.637169i | \(0.219895\pi\) | ||||
−0.770724 | + | 0.637169i | \(0.780105\pi\) | |||||||
\(810\) | − | 219.641i | − | 0.271162i | ||||||
\(811\) | − | 1254.91i | − | 1.54736i | −0.633576 | − | 0.773680i | \(-0.718414\pi\) | ||
0.633576 | − | 0.773680i | \(-0.281586\pi\) | |||||||
\(812\) | −235.775 | − | 27.7541i | −0.290363 | − | 0.0341799i | ||||
\(813\) | − | 742.589i | − | 0.913394i | ||||||
\(814\) | 721.191i | 0.885984i | ||||||||
\(815\) | − | 634.593i | − | 0.778642i | ||||||
\(816\) | 554.955 | 0.680091 | ||||||||
\(817\) | 828.287 | 1.01381 | ||||||||
\(818\) | − | 9.28024i | − | 0.0113450i | ||||||
\(819\) | 36.4174 | − | 309.371i | 0.0444657 | − | 0.377742i | ||||
\(820\) | −283.666 | + | 268.592i | −0.345934 | + | 0.327551i | ||||
\(821\) | −83.4303 | −0.101620 | −0.0508102 | − | 0.998708i | \(-0.516180\pi\) | ||||
−0.0508102 | + | 0.998708i | \(0.516180\pi\) | |||||||
\(822\) | 266.233i | 0.323884i | ||||||||
\(823\) | − | 1216.66i | − | 1.47833i | −0.673526 | − | 0.739164i | \(-0.735221\pi\) | ||
0.673526 | − | 0.739164i | \(-0.264779\pi\) | |||||||
\(824\) | 789.141i | 0.957695i | ||||||||
\(825\) | 1266.87i | 1.53560i | ||||||||
\(826\) | 145.341 | + | 17.1088i | 0.175958 | + | 0.0207128i | ||||
\(827\) | 1278.87i | 1.54639i | 0.634168 | + | 0.773195i | \(0.281343\pi\) | ||||
−0.634168 | + | 0.773195i | \(0.718657\pi\) | |||||||
\(828\) | −22.8023 | −0.0275390 | ||||||||
\(829\) | 191.086i | 0.230502i | 0.993336 | + | 0.115251i | \(0.0367672\pi\) | ||||
−0.993336 | + | 0.115251i | \(0.963233\pi\) | |||||||
\(830\) | 525.317 | 0.632913 | ||||||||
\(831\) | −376.332 | −0.452866 | ||||||||
\(832\) | −56.9114 | −0.0684032 | ||||||||
\(833\) | −1208.34 | − | 288.476i | −1.45059 | − | 0.346310i | ||||
\(834\) | − | 108.936i | − | 0.130618i | ||||||
\(835\) | − | 19.4814i | − | 0.0233311i | ||||||
\(836\) | − | 1358.45i | − | 1.62494i | ||||||
\(837\) | − | 90.4392i | − | 0.108052i | ||||||
\(838\) | 156.674i | 0.186962i | ||||||||
\(839\) | −526.074 | −0.627025 | −0.313513 | − | 0.949584i | \(-0.601506\pi\) | ||||
−0.313513 | + | 0.949584i | \(0.601506\pi\) | |||||||
\(840\) | 676.624 | + | 79.6484i | 0.805505 | + | 0.0948195i | ||||
\(841\) | 713.199 | 0.848037 | ||||||||
\(842\) | 149.739i | 0.177838i | ||||||||
\(843\) | − | 1072.88i | − | 1.27270i | ||||||
\(844\) | − | 390.094i | − | 0.462197i | ||||||
\(845\) | 475.879i | 0.563170i | ||||||||
\(846\) | 528.601 | 0.624824 | ||||||||
\(847\) | 209.134 | − | 1776.62i | 0.246911 | − | 2.09754i | ||||
\(848\) | 346.086i | 0.408120i | ||||||||
\(849\) | − | 892.152i | − | 1.05083i | ||||||
\(850\) | −378.088 | −0.444809 | ||||||||
\(851\) | −27.7894 | −0.0326550 | ||||||||
\(852\) | 1414.79i | 1.66055i | ||||||||
\(853\) | − | 336.906i | − | 0.394966i | −0.980306 | − | 0.197483i | \(-0.936723\pi\) | ||
0.980306 | − | 0.197483i | \(-0.0632768\pi\) | |||||||
\(854\) | 524.343 | + | 61.7227i | 0.613985 | + | 0.0722748i | ||||
\(855\) | − | 753.365i | − | 0.881129i | ||||||
\(856\) | −627.561 | −0.733132 | ||||||||
\(857\) | − | 155.873i | − | 0.181882i | −0.995856 | − | 0.0909410i | \(-0.971013\pi\) | ||
0.995856 | − | 0.0909410i | \(-0.0289875\pi\) | |||||||
\(858\) | 371.900i | 0.433450i | ||||||||
\(859\) | 694.996i | 0.809075i | 0.914521 | + | 0.404538i | \(0.132568\pi\) | ||||
−0.914521 | + | 0.404538i | \(0.867432\pi\) | |||||||
\(860\) | 338.203i | 0.393259i | ||||||||
\(861\) | −1007.07 | + | 751.276i | −1.16966 | + | 0.872562i | ||||
\(862\) | 489.408 | 0.567759 | ||||||||
\(863\) | −570.174 | −0.660689 | −0.330344 | − | 0.943861i | \(-0.607165\pi\) | ||||
−0.330344 | + | 0.943861i | \(0.607165\pi\) | |||||||
\(864\) | −168.326 | −0.194822 | ||||||||
\(865\) | −372.345 | −0.430456 | ||||||||
\(866\) | − | 626.973i | − | 0.723988i | ||||||
\(867\) | 1548.78 | 1.78637 | ||||||||
\(868\) | −369.785 | − | 43.5290i | −0.426020 | − | 0.0501486i | ||||
\(869\) | −910.294 | −1.04752 | ||||||||
\(870\) | 157.183 | 0.180670 | ||||||||
\(871\) | 267.558i | 0.307185i | ||||||||
\(872\) | − | 1190.37i | − | 1.36510i | ||||||
\(873\) | 1021.99 | 1.17066 | ||||||||
\(874\) | −17.4482 | −0.0199636 | ||||||||
\(875\) | 881.265 | + | 103.738i | 1.00716 | + | 0.118557i | ||||
\(876\) | − | 250.272i | − | 0.285699i | ||||||
\(877\) | −1146.20 | −1.30696 | −0.653479 | − | 0.756944i | \(-0.726691\pi\) | ||||
−0.653479 | + | 0.756944i | \(0.726691\pi\) | |||||||
\(878\) | −245.911 | −0.280081 | ||||||||
\(879\) | −1847.68 | −2.10203 | ||||||||
\(880\) | 308.154 | 0.350175 | ||||||||
\(881\) | 749.703i | 0.850968i | 0.904966 | + | 0.425484i | \(0.139896\pi\) | ||||
−0.904966 | + | 0.425484i | \(0.860104\pi\) | |||||||
\(882\) | 484.477 | + | 115.663i | 0.549294 | + | 0.131137i | ||||
\(883\) | 1054.71i | 1.19446i | 0.802069 | + | 0.597231i | \(0.203733\pi\) | ||||
−0.802069 | + | 0.597231i | \(0.796267\pi\) | |||||||
\(884\) | 332.973 | 0.376666 | ||||||||
\(885\) | 290.683 | 0.328455 | ||||||||
\(886\) | 664.744 | 0.750275 | ||||||||
\(887\) | −27.7211 | −0.0312527 | −0.0156263 | − | 0.999878i | \(-0.504974\pi\) | ||||
−0.0156263 | + | 0.999878i | \(0.504974\pi\) | |||||||
\(888\) | −1138.91 | −1.28256 | ||||||||
\(889\) | −58.5647 | + | 497.516i | −0.0658771 | + | 0.559635i | ||||
\(890\) | − | 225.240i | − | 0.253078i | ||||||
\(891\) | − | 1341.98i | − | 1.50615i | ||||||
\(892\) | 479.551i | 0.537613i | ||||||||
\(893\) | −1213.45 | −1.35885 | ||||||||
\(894\) | − | 69.5958i | − | 0.0778477i | ||||||
\(895\) | −142.657 | −0.159393 | ||||||||
\(896\) | −97.3837 | + | 827.288i | −0.108687 | + | 0.923312i | ||||
\(897\) | −14.3303 | −0.0159758 | ||||||||
\(898\) | −2.79848 | −0.00311635 | ||||||||
\(899\) | −200.440 | −0.222959 | ||||||||
\(900\) | −454.775 | −0.505306 | ||||||||
\(901\) | 1754.87i | 1.94769i | ||||||||
\(902\) | 577.719 | − | 547.019i | 0.640487 | − | 0.606452i | ||||
\(903\) | −127.165 | + | 1080.29i | −0.140825 | + | 1.19633i | ||||
\(904\) | 429.858 | 0.475507 | ||||||||
\(905\) | − | 456.409i | − | 0.504320i | ||||||
\(906\) | 438.787i | 0.484312i | ||||||||
\(907\) | −491.045 | −0.541395 | −0.270698 | − | 0.962664i | \(-0.587254\pi\) | ||||
−0.270698 | + | 0.962664i | \(0.587254\pi\) | |||||||
\(908\) | 123.922 | 0.136478 | ||||||||
\(909\) | −889.616 | −0.978675 | ||||||||
\(910\) | 96.6606 | + | 11.3783i | 0.106220 | + | 0.0125037i | ||||
\(911\) | 983.070 | 1.07911 | 0.539556 | − | 0.841950i | \(-0.318592\pi\) | ||||
0.539556 | + | 0.841950i | \(0.318592\pi\) | |||||||
\(912\) | 510.780 | 0.560066 | ||||||||
\(913\) | 3209.61 | 3.51546 | ||||||||
\(914\) | 736.912i | 0.806249i | ||||||||
\(915\) | 1048.69 | 1.14610 | ||||||||
\(916\) | −720.288 | −0.786340 | ||||||||
\(917\) | 1689.00 | + | 198.819i | 1.84187 | + | 0.216815i | ||||
\(918\) | −129.321 | −0.140873 | ||||||||
\(919\) | − | 643.092i | − | 0.699773i | −0.936792 | − | 0.349887i | \(-0.886220\pi\) | ||
0.936792 | − | 0.349887i | \(-0.113780\pi\) | |||||||
\(920\) | − | 16.6236i | − | 0.0180691i | ||||||
\(921\) | − | 1763.39i | − | 1.91464i | ||||||
\(922\) | − | 304.316i | − | 0.330061i | ||||||
\(923\) | 471.596i | 0.510938i | ||||||||
\(924\) | 1771.75 | + | 208.560i | 1.91747 | + | 0.225714i | ||||
\(925\) | −554.239 | −0.599178 | ||||||||
\(926\) | 438.392i | 0.473426i | ||||||||
\(927\) | 1145.96i | 1.23620i | ||||||||
\(928\) | 373.062i | 0.402006i | ||||||||
\(929\) | −210.388 | −0.226467 | −0.113234 | − | 0.993568i | \(-0.536121\pi\) | ||||
−0.113234 | + | 0.993568i | \(0.536121\pi\) | |||||||
\(930\) | 246.523 | 0.265079 | ||||||||
\(931\) | −1112.16 | − | 265.514i | −1.19459 | − | 0.285192i | ||||
\(932\) | − | 1218.35i | − | 1.30725i | ||||||
\(933\) | −493.248 | −0.528669 | ||||||||
\(934\) | − | 205.116i | − | 0.219610i | ||||||
\(935\) | 1562.53 | 1.67116 | ||||||||
\(936\) | −311.507 | −0.332807 | ||||||||
\(937\) | −329.915 | −0.352098 | −0.176049 | − | 0.984381i | \(-0.556332\pi\) | ||||
−0.176049 | + | 0.984381i | \(0.556332\pi\) | |||||||
\(938\) | −424.886 | − | 50.0151i | −0.452970 | − | 0.0533210i | ||||
\(939\) | 1804.48 | 1.92170 | ||||||||
\(940\) | − | 495.472i | − | 0.527098i | ||||||
\(941\) | − | 947.198i | − | 1.00659i | −0.864116 | − | 0.503293i | \(-0.832121\pi\) | ||
0.864116 | − | 0.503293i | \(-0.167879\pi\) | |||||||
\(942\) | −107.165 | −0.113763 | ||||||||
\(943\) | 21.0781 | + | 22.2610i | 0.0223522 | + | 0.0236066i | ||||
\(944\) | 104.532i | 0.110733i | ||||||||
\(945\) | 112.624 | + | 13.2575i | 0.119179 | + | 0.0140291i | ||||
\(946\) | − | 688.790i | − | 0.728108i | ||||||
\(947\) | −386.595 | −0.408232 | −0.204116 | − | 0.978947i | \(-0.565432\pi\) | ||||
−0.204116 | + | 0.978947i | \(0.565432\pi\) | |||||||
\(948\) | − | 616.091i | − | 0.649885i | ||||||
\(949\) | − | 83.4240i | − | 0.0879073i | ||||||
\(950\) | −347.992 | −0.366308 | ||||||||
\(951\) | 1411.36i | 1.48408i | ||||||||
\(952\) | −145.234 | + | 1233.78i | −0.152557 | + | 1.29599i | ||||
\(953\) | −979.840 | −1.02816 | −0.514082 | − | 0.857741i | \(-0.671867\pi\) | ||||
−0.514082 | + | 0.857741i | \(0.671867\pi\) | |||||||
\(954\) | − | 703.603i | − | 0.737529i | ||||||
\(955\) | −715.767 | −0.749495 | ||||||||
\(956\) | 364.885i | 0.381679i | ||||||||
\(957\) | 960.367 | 1.00352 | ||||||||
\(958\) | −181.269 | −0.189216 | ||||||||
\(959\) | 422.780 | + | 49.7673i | 0.440855 | + | 0.0518950i | ||||
\(960\) | − | 180.752i | − | 0.188283i | ||||||
\(961\) | 646.633 | 0.672875 | ||||||||
\(962\) | −162.702 | −0.169129 | ||||||||
\(963\) | −911.321 | −0.946336 | ||||||||
\(964\) | − | 799.528i | − | 0.829386i | ||||||
\(965\) | −259.587 | −0.269002 | ||||||||
\(966\) | 2.67879 | − | 22.7567i | 0.00277307 | − | 0.0235576i | ||||
\(967\) | − | 84.0297i | − | 0.0868973i | −0.999056 | − | 0.0434486i | \(-0.986166\pi\) | ||
0.999056 | − | 0.0434486i | \(-0.0138345\pi\) | |||||||
\(968\) | −1788.89 | −1.84802 | ||||||||
\(969\) | 2589.97 | 2.67283 | ||||||||
\(970\) | 319.313i | 0.329188i | ||||||||
\(971\) | 147.565 | 0.151972 | 0.0759861 | − | 0.997109i | \(-0.475790\pi\) | ||||
0.0759861 | + | 0.997109i | \(0.475790\pi\) | |||||||
\(972\) | 1045.98 | 1.07611 | ||||||||
\(973\) | −172.991 | − | 20.3635i | −0.177792 | − | 0.0209286i | ||||
\(974\) | 844.083 | 0.866615 | ||||||||
\(975\) | −285.808 | −0.293136 | ||||||||
\(976\) | 377.117i | 0.386390i | ||||||||
\(977\) | − | 116.077i | − | 0.118810i | −0.998234 | − | 0.0594050i | \(-0.981080\pi\) | ||
0.998234 | − | 0.0594050i | \(-0.0189203\pi\) | |||||||
\(978\) | −874.718 | −0.894395 | ||||||||
\(979\) | − | 1376.18i | − | 1.40570i | ||||||
\(980\) | 108.414 | − | 454.114i | 0.110626 | − | 0.463381i | ||||
\(981\) | − | 1728.61i | − | 1.76209i | ||||||
\(982\) | −675.459 | −0.687840 | ||||||||
\(983\) | 1429.37i | 1.45409i | 0.686589 | + | 0.727046i | \(0.259107\pi\) | ||||
−0.686589 | + | 0.727046i | \(0.740893\pi\) | |||||||
\(984\) | 863.858 | + | 912.339i | 0.877905 | + | 0.927174i | ||||
\(985\) | 157.810i | 0.160213i | ||||||||
\(986\) | 286.614i | 0.290684i | ||||||||
\(987\) | 186.299 | − | 1582.63i | 0.188752 | − | 1.60348i | ||||
\(988\) | 306.468 | 0.310190 | ||||||||
\(989\) | 26.5409 | 0.0268361 | ||||||||
\(990\) | −626.487 | −0.632815 | ||||||||
\(991\) | 1138.18i | 1.14852i | 0.818673 | + | 0.574261i | \(0.194710\pi\) | ||||
−0.818673 | + | 0.574261i | \(0.805290\pi\) | |||||||
\(992\) | 585.103i | 0.589821i | ||||||||
\(993\) | 1403.41i | 1.41330i | ||||||||
\(994\) | −748.900 | − | 88.1563i | −0.753421 | − | 0.0886884i | ||||
\(995\) | − | 1147.62i | − | 1.15339i | ||||||
\(996\) | 2172.28i | 2.18100i | ||||||||
\(997\) | −456.333 | −0.457706 | −0.228853 | − | 0.973461i | \(-0.573498\pi\) | ||||
−0.228853 | + | 0.973461i | \(0.573498\pi\) | |||||||
\(998\) | − | 676.880i | − | 0.678236i | ||||||
\(999\) | −189.572 | −0.189762 |
(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 | 287.3.d.c.286.7 | yes | 8 | |
7.6 | odd | 2 | inner | 287.3.d.c.286.2 | yes | 8 | |
41.40 | even | 2 | inner | 287.3.d.c.286.1 | ✓ | 8 | |
287.286 | odd | 2 | inner | 287.3.d.c.286.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.d.c.286.1 | ✓ | 8 | 41.40 | even | 2 | inner | |
287.3.d.c.286.2 | yes | 8 | 7.6 | odd | 2 | inner | |
287.3.d.c.286.7 | yes | 8 | 1.1 | even | 1 | trivial | |
287.3.d.c.286.8 | yes | 8 | 287.286 | odd | 2 | inner |