Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (of order \(6\), degree \(2\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.1 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.a.1187.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −3.19684 | − | 1.84570i | −1.42967 | − | 0.825421i | −0.432577 | − | 0.901597i | \(-0.642396\pi\) |
−0.997094 | + | 0.0761754i | \(0.975729\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52985 | − | 2.15860i | −0.578228 | − | 0.815875i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.19684 | − | 1.84570i | 1.01093 | − | 0.583661i | ||||
\(11\) | 0.412474 | + | 3.29088i | 0.124365 | + | 0.992236i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.60520i | − | 1.55460i | −0.629129 | − | 0.777301i | \(-0.716588\pi\) | ||
0.629129 | − | 0.777301i | \(-0.283412\pi\) | |||||||
\(14\) | 2.63433 | − | 0.245585i | 0.704054 | − | 0.0656352i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.39461 | − | 2.41554i | −0.338243 | − | 0.585855i | 0.645859 | − | 0.763457i | \(-0.276499\pi\) |
−0.984102 | + | 0.177602i | \(0.943166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.14631 | − | 1.23917i | −0.492398 | − | 0.284286i | 0.233171 | − | 0.972436i | \(-0.425090\pi\) |
−0.725569 | + | 0.688150i | \(0.758423\pi\) | |||||||
\(20\) | 3.69140i | 0.825421i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.05622 | − | 1.28823i | −0.651588 | − | 0.274651i | ||||
\(23\) | 3.26215 | + | 1.88340i | 0.680206 | + | 0.392717i | 0.799933 | − | 0.600090i | \(-0.204869\pi\) |
−0.119727 | + | 0.992807i | \(0.538202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.31321 | + | 7.47069i | 0.862641 | + | 1.49414i | ||||
\(26\) | 4.85424 | + | 2.80260i | 0.951995 | + | 0.549635i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.10448 | + | 2.40419i | −0.208727 | + | 0.454349i | ||||
\(29\) | −1.51011 | −0.280421 | −0.140210 | − | 0.990122i | \(-0.544778\pi\) | ||||
−0.140210 | + | 0.990122i | \(0.544778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.70296 | − | 2.94961i | −0.305860 | − | 0.529766i | 0.671592 | − | 0.740921i | \(-0.265611\pi\) |
−0.977453 | + | 0.211155i | \(0.932277\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.78923 | 0.478348 | ||||||||
\(35\) | 0.906550 | + | 9.72435i | 0.153235 | + | 1.64372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.85865 | − | 4.95132i | 0.469959 | − | 0.813993i | −0.529451 | − | 0.848340i | \(-0.677602\pi\) |
0.999410 | + | 0.0343479i | \(0.0109354\pi\) | |||||||
\(38\) | 2.14631 | − | 1.23917i | 0.348178 | − | 0.201021i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.19684 | − | 1.84570i | −0.505465 | − | 0.291831i | ||||
\(41\) | −6.24731 | −0.975666 | −0.487833 | − | 0.872937i | \(-0.662213\pi\) | ||||
−0.487833 | + | 0.872937i | \(0.662213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.72006i | 1.17730i | 0.808389 | + | 0.588649i | \(0.200340\pi\) | ||||
−0.808389 | + | 0.588649i | \(0.799660\pi\) | |||||||
\(44\) | 2.64375 | − | 2.00265i | 0.398560 | − | 0.301911i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.26215 | + | 1.88340i | −0.480978 | + | 0.277693i | ||||
\(47\) | 8.98162 | + | 5.18554i | 1.31010 | + | 0.756389i | 0.982113 | − | 0.188292i | \(-0.0602953\pi\) |
0.327991 | + | 0.944681i | \(0.393629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.31914 | + | 6.60467i | −0.331305 | + | 0.943524i | ||||
\(50\) | −8.62641 | −1.21996 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.85424 | + | 2.80260i | −0.673162 | + | 0.388650i | ||||
\(53\) | −9.27677 | + | 5.35595i | −1.27426 | + | 0.735696i | −0.975787 | − | 0.218721i | \(-0.929811\pi\) |
−0.298475 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.75535 | − | 11.2817i | 0.641211 | − | 1.52123i | ||||
\(56\) | −1.52985 | − | 2.15860i | −0.204434 | − | 0.288456i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.755057 | − | 1.30780i | 0.0991438 | − | 0.171722i | ||||
\(59\) | −11.6232 | + | 6.71066i | −1.51321 | + | 0.873654i | −0.513333 | + | 0.858190i | \(0.671589\pi\) |
−0.999880 | + | 0.0154644i | \(0.995077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13230 | − | 1.23108i | −0.273013 | − | 0.157624i | 0.357243 | − | 0.934011i | \(-0.383717\pi\) |
−0.630256 | + | 0.776387i | \(0.717050\pi\) | |||||||
\(62\) | 3.40592 | 0.432552 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.3455 | + | 17.9189i | −1.28320 | + | 2.22257i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.66594 | + | 9.81369i | 0.692204 | + | 1.19893i | 0.971114 | + | 0.238616i | \(0.0766936\pi\) |
−0.278910 | + | 0.960317i | \(0.589973\pi\) | |||||||
\(68\) | −1.39461 | + | 2.41554i | −0.169122 | + | 0.292927i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.87481 | − | 4.07708i | −1.06074 | − | 0.487304i | ||||
\(71\) | 5.15087i | 0.611296i | 0.952145 | + | 0.305648i | \(0.0988730\pi\) | ||||
−0.952145 | + | 0.305648i | \(0.901127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.53946 | + | 2.62086i | −0.531303 | + | 0.306748i | −0.741547 | − | 0.670901i | \(-0.765908\pi\) |
0.210244 | + | 0.977649i | \(0.432574\pi\) | |||||||
\(74\) | 2.85865 | + | 4.95132i | 0.332311 | + | 0.575580i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.47835i | 0.284286i | ||||||||
\(77\) | 6.47267 | − | 5.92490i | 0.737630 | − | 0.675205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.250209 | − | 0.144458i | −0.0281507 | − | 0.0162528i | 0.485859 | − | 0.874037i | \(-0.338507\pi\) |
−0.514009 | + | 0.857785i | \(0.671840\pi\) | |||||||
\(80\) | 3.19684 | − | 1.84570i | 0.357418 | − | 0.206355i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.12366 | − | 5.41033i | 0.344950 | − | 0.597471i | ||||
\(83\) | −10.2522 | −1.12533 | −0.562664 | − | 0.826685i | \(-0.690224\pi\) | ||||
−0.562664 | + | 0.826685i | \(0.690224\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2961i | 1.11677i | ||||||||
\(86\) | −6.68577 | − | 3.86003i | −0.720945 | − | 0.416238i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.412474 | + | 3.29088i | 0.0439698 | + | 0.350809i | ||||
\(89\) | 13.7391 | + | 7.93225i | 1.45634 | + | 0.840816i | 0.998829 | − | 0.0483889i | \(-0.0154087\pi\) |
0.457508 | + | 0.889205i | \(0.348742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0994 | + | 8.57509i | −1.26836 | + | 0.898914i | ||||
\(92\) | − | 3.76681i | − | 0.392717i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.98162 | + | 5.18554i | −0.926383 | + | 0.534848i | ||||
\(95\) | 4.57428 | + | 7.92289i | 0.469311 | + | 0.812871i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.58628 | 0.465666 | 0.232833 | − | 0.972517i | \(-0.425200\pi\) | ||||
0.232833 | + | 0.972517i | \(0.425200\pi\) | |||||||
\(98\) | −4.56024 | − | 5.31076i | −0.460654 | − | 0.536468i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.31321 | − | 7.47069i | 0.431321 | − | 0.747069i | ||||
\(101\) | −1.45801 | − | 2.52536i | −0.145078 | − | 0.251282i | 0.784324 | − | 0.620351i | \(-0.213010\pi\) |
−0.929402 | + | 0.369069i | \(0.879677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.61616 | + | 7.99543i | −0.454844 | + | 0.787813i | −0.998679 | − | 0.0513790i | \(-0.983638\pi\) |
0.543835 | + | 0.839192i | \(0.316972\pi\) | |||||||
\(104\) | − | 5.60520i | − | 0.549635i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 10.7119i | − | 1.04043i | ||||||
\(107\) | 1.81237 | − | 3.13911i | 0.175208 | − | 0.303469i | −0.765025 | − | 0.644000i | \(-0.777274\pi\) |
0.940233 | + | 0.340531i | \(0.110607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9355 | − | 8.04565i | 1.33478 | − | 0.770634i | 0.348749 | − | 0.937216i | \(-0.386607\pi\) |
0.986028 | + | 0.166583i | \(0.0532732\pi\) | |||||||
\(110\) | 7.39258 | + | 9.75911i | 0.704855 | + | 0.930495i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.63433 | − | 0.245585i | 0.248921 | − | 0.0232056i | ||||
\(113\) | − | 18.8371i | − | 1.77204i | −0.463643 | − | 0.886022i | \(-0.653458\pi\) | ||
0.463643 | − | 0.886022i | \(-0.346542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.95239 | − | 12.0419i | −0.648314 | − | 1.12291i | ||||
\(116\) | 0.755057 | + | 1.30780i | 0.0701052 | + | 0.121426i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 13.4213i | − | 1.23553i | ||||||
\(119\) | −3.08065 | + | 6.70582i | −0.282403 | + | 0.614722i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6597 | + | 2.71480i | −0.969066 | + | 0.246800i | ||||
\(122\) | 2.13230 | − | 1.23108i | 0.193049 | − | 0.111457i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.70296 | + | 2.94961i | −0.152930 | + | 0.264883i | ||||
\(125\) | − | 13.3865i | − | 1.19733i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.08283i | − | 0.717235i | −0.933485 | − | 0.358618i | \(-0.883248\pi\) | ||
0.933485 | − | 0.358618i | \(-0.116752\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.3455 | − | 17.9189i | −0.907361 | − | 1.57159i | ||||
\(131\) | 7.83557 | − | 13.5716i | 0.684597 | − | 1.18576i | −0.288967 | − | 0.957339i | \(-0.593312\pi\) |
0.973563 | − | 0.228417i | \(-0.0733549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.608644 | + | 6.52878i | 0.0527761 | + | 0.566117i | ||||
\(134\) | −11.3319 | −0.978925 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.39461 | − | 2.41554i | −0.119587 | − | 0.207131i | ||||
\(137\) | −2.55426 | + | 1.47471i | −0.218226 | + | 0.125993i | −0.605128 | − | 0.796128i | \(-0.706878\pi\) |
0.386903 | + | 0.922120i | \(0.373545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00952i | 0.340083i | 0.985437 | + | 0.170042i | \(0.0543902\pi\) | ||||
−0.985437 | + | 0.170042i | \(0.945610\pi\) | |||||||
\(140\) | 7.96826 | − | 5.64727i | 0.673441 | − | 0.477282i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.46078 | − | 2.57543i | −0.374341 | − | 0.216126i | ||||
\(143\) | 18.4460 | − | 2.31200i | 1.54253 | − | 0.193339i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.82759 | + | 2.78721i | 0.400910 | + | 0.231465i | ||||
\(146\) | − | 5.24171i | − | 0.433807i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.71730 | −0.469959 | ||||||||
\(149\) | 3.23457 | − | 5.60244i | 0.264986 | − | 0.458969i | −0.702574 | − | 0.711611i | \(-0.747966\pi\) |
0.967560 | + | 0.252641i | \(0.0812993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3957 | + | 7.73400i | −1.09012 | + | 0.629384i | −0.933610 | − | 0.358292i | \(-0.883359\pi\) |
−0.156515 | + | 0.987676i | \(0.550026\pi\) | |||||||
\(152\) | −2.14631 | − | 1.23917i | −0.174089 | − | 0.100510i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.89478 | + | 8.56795i | 0.152686 | + | 0.690425i | ||||
\(155\) | 12.5726i | 1.00985i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.34257 | + | 16.1818i | 0.745618 | + | 1.29145i | 0.949905 | + | 0.312538i | \(0.101179\pi\) |
−0.204287 | + | 0.978911i | \(0.565488\pi\) | |||||||
\(158\) | 0.250209 | − | 0.144458i | 0.0199056 | − | 0.0114925i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.69140i | 0.291831i | ||||||||
\(161\) | −0.925070 | − | 9.92301i | −0.0729057 | − | 0.782043i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62801 | − | 8.01595i | 0.362494 | − | 0.627858i | −0.625877 | − | 0.779922i | \(-0.715259\pi\) |
0.988371 | + | 0.152064i | \(0.0485920\pi\) | |||||||
\(164\) | 3.12366 | + | 5.41033i | 0.243917 | + | 0.422476i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.12612 | − | 8.87869i | 0.397864 | − | 0.689120i | ||||
\(167\) | 16.3875 | 1.26811 | 0.634053 | − | 0.773289i | \(-0.281390\pi\) | ||||
0.634053 | + | 0.773289i | \(0.281390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.4182 | −1.41679 | ||||||||
\(170\) | −8.91672 | − | 5.14807i | −0.683881 | − | 0.394839i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.68577 | − | 3.86003i | 0.509785 | − | 0.294325i | ||||
\(173\) | −10.4622 | + | 18.1210i | −0.795424 | + | 1.37771i | 0.127146 | + | 0.991884i | \(0.459418\pi\) |
−0.922570 | + | 0.385831i | \(0.873915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.52771 | − | 20.7395i | 0.720228 | − | 1.56776i | ||||
\(176\) | −3.05622 | − | 1.28823i | −0.230371 | − | 0.0971036i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7391 | + | 7.93225i | −1.02979 | + | 0.594547i | ||||
\(179\) | −12.9584 | + | 7.48153i | −0.968555 | + | 0.559196i | −0.898795 | − | 0.438368i | \(-0.855557\pi\) |
−0.0697596 | + | 0.997564i | \(0.522223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1125 | −0.751657 | −0.375828 | − | 0.926689i | \(-0.622642\pi\) | ||||
−0.375828 | + | 0.926689i | \(0.622642\pi\) | |||||||
\(182\) | −1.37655 | − | 14.7659i | −0.102037 | − | 1.09452i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.26215 | + | 1.88340i | 0.240489 | + | 0.138846i | ||||
\(185\) | −18.2773 | + | 10.5524i | −1.34377 | + | 0.775828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.37400 | − | 5.58584i | 0.539240 | − | 0.408477i | ||||
\(188\) | − | 10.3711i | − | 0.756389i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.14856 | −0.663707 | ||||||||
\(191\) | −4.57254 | − | 2.63995i | −0.330857 | − | 0.191020i | 0.325364 | − | 0.945589i | \(-0.394513\pi\) |
−0.656222 | + | 0.754568i | \(0.727846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.8361 | − | 11.4524i | 1.42784 | − | 0.824362i | 0.430886 | − | 0.902406i | \(-0.358201\pi\) |
0.996950 | + | 0.0780447i | \(0.0248677\pi\) | |||||||
\(194\) | −2.29314 | + | 3.97184i | −0.164638 | + | 0.285161i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.87938 | − | 1.29390i | 0.491384 | − | 0.0924215i | ||||
\(197\) | 8.56673 | 0.610354 | 0.305177 | − | 0.952296i | \(-0.401284\pi\) | ||||
0.305177 | + | 0.952296i | \(0.401284\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.28887 | + | 3.96444i | 0.162254 | + | 0.281032i | 0.935677 | − | 0.352859i | \(-0.114790\pi\) |
−0.773423 | + | 0.633890i | \(0.781457\pi\) | |||||||
\(200\) | 4.31321 | + | 7.47069i | 0.304990 | + | 0.528258i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.91603 | 0.205171 | ||||||||
\(203\) | 2.31024 | + | 3.25974i | 0.162147 | + | 0.228789i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.9717 | + | 11.5307i | 1.39488 | + | 0.805336i | ||||
\(206\) | −4.61616 | − | 7.99543i | −0.321623 | − | 0.557068i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.85424 | + | 2.80260i | 0.336581 | + | 0.194325i | ||||
\(209\) | 3.19267 | − | 7.57437i | 0.220842 | − | 0.523930i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0586i | 0.692463i | 0.938149 | + | 0.346231i | \(0.112539\pi\) | ||||
−0.938149 | + | 0.346231i | \(0.887461\pi\) | |||||||
\(212\) | 9.27677 | + | 5.35595i | 0.637131 | + | 0.367848i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.81237 | + | 3.13911i | 0.123891 | + | 0.214585i | ||||
\(215\) | 14.2489 | − | 24.6798i | 0.971767 | − | 1.68315i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.76177 | + | 8.18846i | −0.255366 | + | 0.555869i | ||||
\(218\) | 16.0913i | 1.08984i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.1479 | + | 1.52260i | −0.819013 | + | 0.102654i | ||||
\(221\) | −13.5396 | + | 7.81708i | −0.910770 | + | 0.525834i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7430 | 0.987266 | 0.493633 | − | 0.869670i | \(-0.335669\pi\) | ||||
0.493633 | + | 0.869670i | \(0.335669\pi\) | |||||||
\(224\) | −1.10448 | + | 2.40419i | −0.0737963 | + | 0.160637i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.3134 | + | 9.41854i | 1.08515 | + | 0.626512i | ||||
\(227\) | −9.41469 | − | 16.3067i | −0.624875 | − | 1.08232i | −0.988565 | − | 0.150795i | \(-0.951817\pi\) |
0.363690 | − | 0.931520i | \(-0.381517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.82233 | + | 11.8166i | −0.450832 | + | 0.780865i | −0.998438 | − | 0.0558720i | \(-0.982206\pi\) |
0.547606 | + | 0.836737i | \(0.315539\pi\) | |||||||
\(230\) | 13.9048 | 0.916854 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.51011 | −0.0991438 | ||||||||
\(233\) | −3.51518 | + | 6.08847i | −0.230287 | + | 0.398869i | −0.957893 | − | 0.287127i | \(-0.907300\pi\) |
0.727606 | + | 0.685996i | \(0.240633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.1419 | − | 33.1547i | −1.24868 | − | 2.16278i | ||||
\(236\) | 11.6232 | + | 6.71066i | 0.756607 | + | 0.436827i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.26709 | − | 6.02083i | −0.276594 | − | 0.390273i | ||||
\(239\) | −10.3908 | −0.672126 | −0.336063 | − | 0.941840i | \(-0.609095\pi\) | ||||
−0.336063 | + | 0.941840i | \(0.609095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.24972 | + | 5.34033i | −0.595827 | + | 0.344001i | −0.767398 | − | 0.641171i | \(-0.778449\pi\) |
0.171571 | + | 0.985172i | \(0.445116\pi\) | |||||||
\(242\) | 2.97878 | − | 10.5890i | 0.191483 | − | 0.680687i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.46216i | 0.157624i | ||||||||
\(245\) | 19.6041 | − | 16.8337i | 1.25246 | − | 1.07546i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.94581 | + | 12.0305i | −0.441951 | + | 0.765482i | ||||
\(248\) | −1.70296 | − | 2.94961i | −0.108138 | − | 0.187300i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5931 | + | 6.69326i | 0.733210 | + | 0.423319i | ||||
\(251\) | − | 9.19949i | − | 0.580667i | −0.956926 | − | 0.290333i | \(-0.906234\pi\) | ||
0.956926 | − | 0.290333i | \(-0.0937662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.85250 | + | 11.5122i | −0.305074 | + | 0.723765i | ||||
\(254\) | 6.99993 | + | 4.04141i | 0.439215 | + | 0.253581i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −17.8743 | − | 10.3197i | −1.11497 | − | 0.643728i | −0.174858 | − | 0.984594i | \(-0.555947\pi\) |
−0.940112 | + | 0.340865i | \(0.889280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0612 | + | 1.40408i | −0.935860 | + | 0.0872453i | ||||
\(260\) | 20.6910 | 1.28320 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.83557 | + | 13.5716i | 0.484083 | + | 0.838456i | ||||
\(263\) | −13.1613 | − | 22.7960i | −0.811561 | − | 1.40566i | −0.911771 | − | 0.410698i | \(-0.865285\pi\) |
0.100211 | − | 0.994966i | \(-0.468048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.5419 | 2.42904 | ||||||||
\(266\) | −5.95841 | − | 2.73729i | −0.365334 | − | 0.167834i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.66594 | − | 9.81369i | 0.346102 | − | 0.599467i | ||||
\(269\) | −7.04033 | + | 4.06473i | −0.429256 | + | 0.247831i | −0.699030 | − | 0.715093i | \(-0.746385\pi\) |
0.269773 | + | 0.962924i | \(0.413051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6065 | + | 7.27836i | 0.765790 | + | 0.442129i | 0.831371 | − | 0.555718i | \(-0.187557\pi\) |
−0.0655809 | + | 0.997847i | \(0.520890\pi\) | |||||||
\(272\) | 2.78923 | 0.169122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 2.94941i | − | 0.178180i | ||||||
\(275\) | −22.8060 | + | 17.2757i | −1.37526 | + | 1.04176i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.9763 | + | 14.9974i | −1.56077 | + | 0.901109i | −0.563587 | + | 0.826057i | \(0.690579\pi\) |
−0.997180 | + | 0.0750526i | \(0.976088\pi\) | |||||||
\(278\) | −3.47235 | − | 2.00476i | −0.208258 | − | 0.120238i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.906550 | + | 9.72435i | 0.0541767 | + | 0.581141i | ||||
\(281\) | 12.8423 | 0.766110 | 0.383055 | − | 0.923726i | \(-0.374872\pi\) | ||||
0.383055 | + | 0.923726i | \(0.374872\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.35099 | + | 3.66675i | −0.377527 | + | 0.217965i | −0.676742 | − | 0.736220i | \(-0.736609\pi\) |
0.299215 | + | 0.954186i | \(0.403275\pi\) | |||||||
\(284\) | 4.46078 | − | 2.57543i | 0.264699 | − | 0.152824i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.22076 | + | 17.1307i | −0.426972 | + | 1.01296i | ||||
\(287\) | 9.55743 | + | 13.4855i | 0.564157 | + | 0.796022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.61011 | − | 7.98495i | 0.271183 | − | 0.469703i | ||||
\(290\) | −4.82759 | + | 2.78721i | −0.283486 | + | 0.163671i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.53946 | + | 2.62086i | 0.265652 | + | 0.153374i | ||||
\(293\) | −6.05343 | −0.353645 | −0.176823 | − | 0.984243i | \(-0.556582\pi\) | ||||
−0.176823 | + | 0.984243i | \(0.556582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 49.5434 | 2.88453 | ||||||||
\(296\) | 2.85865 | − | 4.95132i | 0.166156 | − | 0.287790i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.23457 | + | 5.60244i | 0.187373 | + | 0.324540i | ||||
\(299\) | 10.5569 | − | 18.2850i | 0.610518 | − | 1.05745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6646 | − | 11.8105i | 0.960529 | − | 0.680747i | ||||
\(302\) | − | 15.4680i | − | 0.890083i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.14631 | − | 1.23917i | 0.123099 | − | 0.0710715i | ||||
\(305\) | 4.54441 | + | 7.87116i | 0.260212 | + | 0.450701i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.24654i | 0.356509i | 0.983984 | + | 0.178255i | \(0.0570450\pi\) | ||||
−0.983984 | + | 0.178255i | \(0.942955\pi\) | |||||||
\(308\) | −8.36745 | − | 2.64305i | −0.476780 | − | 0.150602i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.8882 | − | 6.28629i | −0.618407 | − | 0.357038i | ||||
\(311\) | −8.45677 | + | 4.88252i | −0.479539 | + | 0.276862i | −0.720225 | − | 0.693741i | \(-0.755961\pi\) |
0.240685 | + | 0.970603i | \(0.422628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0158 | + | 27.7402i | −0.905266 | + | 1.56797i | −0.0847068 | + | 0.996406i | \(0.526995\pi\) |
−0.820559 | + | 0.571561i | \(0.806338\pi\) | |||||||
\(314\) | −18.6851 | −1.05446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.288917i | 0.0162528i | ||||||||
\(317\) | −18.5774 | − | 10.7256i | −1.04341 | − | 0.602412i | −0.122612 | − | 0.992455i | \(-0.539127\pi\) |
−0.920797 | + | 0.390042i | \(0.872460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.622882 | − | 4.96959i | −0.0348747 | − | 0.278244i | ||||
\(320\) | −3.19684 | − | 1.84570i | −0.178709 | − | 0.103178i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.05612 | + | 4.16037i | 0.504678 | + | 0.231848i | ||||
\(323\) | 6.91267i | 0.384631i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.8747 | − | 24.1764i | 2.32279 | − | 1.34106i | ||||
\(326\) | 4.62801 | + | 8.01595i | 0.256322 | + | 0.443963i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.24731 | −0.344950 | ||||||||
\(329\) | −2.54698 | − | 27.3208i | −0.140419 | − | 1.50625i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3327 | − | 26.5569i | 0.842759 | − | 1.45970i | −0.0447947 | − | 0.998996i | \(-0.514263\pi\) |
0.887553 | − | 0.460705i | \(-0.152403\pi\) | |||||||
\(332\) | 5.12612 | + | 8.87869i | 0.281332 | + | 0.487282i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.19377 | + | 14.1920i | −0.448343 | + | 0.776554i | ||||
\(335\) | − | 41.8304i | − | 2.28544i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.3731i | 1.81795i | 0.416853 | + | 0.908974i | \(0.363133\pi\) | ||||
−0.416853 | + | 0.908974i | \(0.636867\pi\) | |||||||
\(338\) | 9.20911 | − | 15.9507i | 0.500910 | − | 0.867601i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.91672 | − | 5.14807i | 0.483577 | − | 0.279193i | ||||
\(341\) | 9.00438 | − | 6.82086i | 0.487614 | − | 0.369370i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8048 | − | 5.09803i | 0.961368 | − | 0.275268i | ||||
\(344\) | 7.72006i | 0.416238i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.4622 | − | 18.1210i | −0.562450 | − | 0.974191i | ||||
\(347\) | 10.0767 | + | 17.4533i | 0.540943 | + | 0.936941i | 0.998850 | + | 0.0479408i | \(0.0152659\pi\) |
−0.457907 | + | 0.889000i | \(0.651401\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.8276i | − | 1.38252i | −0.722607 | − | 0.691259i | \(-0.757056\pi\) | ||
0.722607 | − | 0.691259i | \(-0.242944\pi\) | |||||||
\(350\) | 13.1971 | + | 18.6210i | 0.705414 | + | 0.995334i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.64375 | − | 2.00265i | 0.140912 | − | 0.106742i | ||||
\(353\) | −8.21248 | + | 4.74148i | −0.437106 | + | 0.252363i | −0.702369 | − | 0.711813i | \(-0.747875\pi\) |
0.265263 | + | 0.964176i | \(0.414541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.50695 | − | 16.4665i | 0.504577 | − | 0.873952i | ||||
\(356\) | − | 15.8645i | − | 0.840816i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 14.9631i | − | 0.790822i | ||||||
\(359\) | −5.42112 | + | 9.38966i | −0.286116 | + | 0.495567i | −0.972879 | − | 0.231314i | \(-0.925698\pi\) |
0.686763 | + | 0.726881i | \(0.259031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.42890 | − | 11.1352i | −0.338363 | − | 0.586062i | ||||
\(362\) | 5.05625 | − | 8.75769i | 0.265751 | − | 0.460294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.4759 | + | 6.19084i | 0.706331 | + | 0.324488i | ||||
\(365\) | 19.3492 | 1.01279 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.46446 | + | 7.73268i | 0.233043 | + | 0.403642i | 0.958702 | − | 0.284412i | \(-0.0917983\pi\) |
−0.725659 | + | 0.688054i | \(0.758465\pi\) | |||||||
\(368\) | −3.26215 | + | 1.88340i | −0.170051 | + | 0.0981792i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 21.1048i | − | 1.09719i | ||||||
\(371\) | 25.7534 | + | 11.8311i | 1.33705 | + | 0.614240i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8877 | − | 7.44073i | −0.667301 | − | 0.385266i | 0.127752 | − | 0.991806i | \(-0.459224\pi\) |
−0.795053 | + | 0.606540i | \(0.792557\pi\) | |||||||
\(374\) | 1.15048 | + | 9.17900i | 0.0594900 | + | 0.474635i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.98162 | + | 5.18554i | 0.463192 | + | 0.267424i | ||||
\(377\) | 8.46448i | 0.435943i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2827 | 1.55552 | 0.777759 | − | 0.628563i | \(-0.216356\pi\) | ||||
0.777759 | + | 0.628563i | \(0.216356\pi\) | |||||||
\(380\) | 4.57428 | − | 7.92289i | 0.234656 | − | 0.406436i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.57254 | − | 2.63995i | 0.233951 | − | 0.135072i | ||||
\(383\) | 18.4934 | + | 10.6772i | 0.944969 | + | 0.545578i | 0.891514 | − | 0.452992i | \(-0.149643\pi\) |
0.0534545 | + | 0.998570i | \(0.482977\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.6277 | + | 6.99438i | −1.61190 | + | 0.356467i | ||||
\(386\) | 22.9048i | 1.16582i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.29314 | − | 3.97184i | −0.116417 | − | 0.201639i | ||||
\(389\) | 6.05094 | − | 3.49351i | 0.306795 | − | 0.177128i | −0.338696 | − | 0.940896i | \(-0.609986\pi\) |
0.645491 | + | 0.763768i | \(0.276653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.5065i | − | 0.531335i | ||||||
\(392\) | −2.31914 | + | 6.60467i | −0.117134 | + | 0.333586i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.28337 | + | 7.41901i | −0.215793 | + | 0.373764i | ||||
\(395\) | 0.533253 | + | 0.923622i | 0.0268309 | + | 0.0464725i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.27929 | + | 9.14400i | −0.264960 | + | 0.458924i | −0.967553 | − | 0.252668i | \(-0.918692\pi\) |
0.702593 | + | 0.711592i | \(0.252025\pi\) | |||||||
\(398\) | −4.57774 | −0.229462 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.62641 | −0.431321 | ||||||||
\(401\) | 8.21248 | + | 4.74148i | 0.410112 | + | 0.236778i | 0.690838 | − | 0.723010i | \(-0.257242\pi\) |
−0.280726 | + | 0.959788i | \(0.590575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.5331 | + | 9.54542i | −0.823575 | + | 0.475491i | ||||
\(404\) | −1.45801 | + | 2.52536i | −0.0725389 | + | 0.125641i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.97813 | + | 0.370860i | −0.197431 | + | 0.0184055i | ||||
\(407\) | 17.4733 | + | 7.36517i | 0.866120 | + | 0.365078i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.48918 | + | 0.859778i | −0.0736351 | + | 0.0425133i | −0.536366 | − | 0.843986i | \(-0.680203\pi\) |
0.462730 | + | 0.886499i | \(0.346870\pi\) | |||||||
\(410\) | −19.9717 | + | 11.5307i | −0.986331 | + | 0.569459i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.23233 | 0.454844 | ||||||||
\(413\) | 32.2674 | + | 14.8236i | 1.58777 | + | 0.729422i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.7748 | + | 18.9225i | 1.60885 | + | 0.928870i | ||||
\(416\) | −4.85424 | + | 2.80260i | −0.237999 | + | 0.137409i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.96326 | + | 6.55212i | 0.242761 | + | 0.320475i | ||||
\(419\) | 5.34038i | 0.260895i | 0.991455 | + | 0.130447i | \(0.0416414\pi\) | ||||
−0.991455 | + | 0.130447i | \(0.958359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1036 | −1.32095 | −0.660475 | − | 0.750848i | \(-0.729645\pi\) | ||||
−0.660475 | + | 0.750848i | \(0.729645\pi\) | |||||||
\(422\) | −8.71101 | − | 5.02930i | −0.424045 | − | 0.244823i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.27677 | + | 5.35595i | −0.450520 | + | 0.260108i | ||||
\(425\) | 12.0305 | − | 20.8374i | 0.583565 | − | 1.01076i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.604670 | + | 6.48615i | 0.0292620 | + | 0.313887i | ||||
\(428\) | −3.62473 | −0.175208 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.2489 | + | 24.6798i | 0.687143 | + | 1.19017i | ||||
\(431\) | 3.80062 | + | 6.58286i | 0.183069 | + | 0.317085i | 0.942924 | − | 0.333007i | \(-0.108063\pi\) |
−0.759855 | + | 0.650093i | \(0.774730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.9514 | −1.53549 | −0.767744 | − | 0.640757i | \(-0.778621\pi\) | ||||
−0.767744 | + | 0.640757i | \(0.778621\pi\) | |||||||
\(434\) | −5.21053 | − | 7.35202i | −0.250113 | − | 0.352908i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9355 | − | 8.04565i | −0.667388 | − | 0.385317i | ||||
\(437\) | −4.66773 | − | 8.08475i | −0.223288 | − | 0.386746i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.37246 | − | 1.94709i | −0.160959 | − | 0.0929294i | 0.417357 | − | 0.908743i | \(-0.362956\pi\) |
−0.578316 | + | 0.815813i | \(0.696290\pi\) | |||||||
\(440\) | 4.75535 | − | 11.2817i | 0.226702 | − | 0.537835i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 15.6342i | − | 0.743641i | ||||||
\(443\) | 4.84958 | + | 2.79991i | 0.230410 | + | 0.133028i | 0.610761 | − | 0.791815i | \(-0.290863\pi\) |
−0.380351 | + | 0.924842i | \(0.624197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.2811 | − | 50.7163i | −1.38806 | − | 2.40418i | ||||
\(446\) | −7.37151 | + | 12.7678i | −0.349051 | + | 0.604575i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.52985 | − | 2.15860i | −0.0722785 | − | 0.101984i | ||||
\(449\) | 19.7608i | 0.932570i | 0.884635 | + | 0.466285i | \(0.154408\pi\) | ||||
−0.884635 | + | 0.466285i | \(0.845592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.57685 | − | 20.5591i | −0.121339 | − | 0.968092i | ||||
\(452\) | −16.3134 | + | 9.41854i | −0.767318 | + | 0.443011i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.8294 | 0.883707 | ||||||||
\(455\) | 54.5069 | − | 5.08139i | 2.55532 | − | 0.238219i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7231 | + | 9.65507i | 0.782272 | + | 0.451645i | 0.837235 | − | 0.546843i | \(-0.184171\pi\) |
−0.0549627 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(458\) | −6.82233 | − | 11.8166i | −0.318787 | − | 0.552155i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.95239 | + | 12.0419i | −0.324157 | + | 0.561456i | ||||
\(461\) | 6.95967 | 0.324144 | 0.162072 | − | 0.986779i | \(-0.448182\pi\) | ||||
0.162072 | + | 0.986779i | \(0.448182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2724 | 0.756243 | 0.378121 | − | 0.925756i | \(-0.376570\pi\) | ||||
0.378121 | + | 0.925756i | \(0.376570\pi\) | |||||||
\(464\) | 0.755057 | − | 1.30780i | 0.0350526 | − | 0.0607129i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.51518 | − | 6.08847i | −0.162837 | − | 0.282043i | ||||
\(467\) | −1.39696 | − | 0.806535i | −0.0646436 | − | 0.0373220i | 0.467330 | − | 0.884083i | \(-0.345216\pi\) |
−0.531973 | + | 0.846761i | \(0.678549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5158 | − | 27.2440i | 0.577928 | − | 1.25801i | ||||
\(470\) | 38.2838 | 1.76590 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.6232 | + | 6.71066i | −0.535002 | + | 0.308883i | ||||
\(473\) | −25.4058 | + | 3.18432i | −1.16816 | + | 0.146415i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 21.3792i | − | 0.980947i | ||||||
\(476\) | 7.34774 | − | 0.684991i | 0.336783 | − | 0.0313965i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.19541 | − | 8.99871i | 0.237632 | − | 0.411591i | ||||
\(479\) | −16.9520 | − | 29.3616i | −0.774555 | − | 1.34157i | −0.935045 | − | 0.354530i | \(-0.884641\pi\) |
0.160490 | − | 0.987037i | \(-0.448693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.7531 | − | 16.0233i | −1.26543 | − | 0.730599i | ||||
\(482\) | − | 10.6807i | − | 0.486490i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.68095 | + | 7.87420i | 0.349134 | + | 0.357918i | ||||
\(485\) | −14.6616 | − | 8.46489i | −0.665750 | − | 0.384371i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52594 | − | 2.64300i | −0.0691468 | − | 0.119766i | 0.829379 | − | 0.558686i | \(-0.188694\pi\) |
−0.898526 | + | 0.438920i | \(0.855361\pi\) | |||||||
\(488\) | −2.13230 | − | 1.23108i | −0.0965246 | − | 0.0557285i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.77630 | + | 25.3945i | 0.215771 | + | 1.14721i | ||||
\(491\) | −35.7449 | −1.61315 | −0.806573 | − | 0.591134i | \(-0.798680\pi\) | ||||
−0.806573 | + | 0.591134i | \(0.798680\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.10602 | + | 3.64774i | 0.0948505 | + | 0.164286i | ||||
\(494\) | −6.94581 | − | 12.0305i | −0.312507 | − | 0.541278i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.40592 | 0.152930 | ||||||||
\(497\) | 11.1187 | − | 7.88004i | 0.498741 | − | 0.353468i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75597 | + | 6.50553i | −0.168140 | + | 0.291227i | −0.937766 | − | 0.347268i | \(-0.887109\pi\) |
0.769626 | + | 0.638495i | \(0.220443\pi\) | |||||||
\(500\) | −11.5931 | + | 6.69326i | −0.518458 | + | 0.299332i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.96699 | + | 4.59974i | 0.355584 | + | 0.205297i | ||||
\(503\) | −21.5419 | −0.960507 | −0.480253 | − | 0.877130i | \(-0.659455\pi\) | ||||
−0.480253 | + | 0.877130i | \(0.659455\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7642i | 0.479002i | ||||||||
\(506\) | −7.54360 | − | 9.95848i | −0.335354 | − | 0.442709i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.99993 | + | 4.04141i | −0.310572 | + | 0.179309i | ||||
\(509\) | −26.1028 | − | 15.0705i | −1.15699 | − | 0.667986i | −0.206406 | − | 0.978466i | \(-0.566177\pi\) |
−0.950580 | + | 0.310480i | \(0.899510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6021 | + | 5.78938i | 0.557483 | + | 0.256107i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.8743 | − | 10.3197i | 0.788403 | − | 0.455185i | ||||
\(515\) | 29.5143 | − | 17.0401i | 1.30056 | − | 0.750876i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.3603 | + | 31.6963i | −0.587585 | + | 1.39400i | ||||
\(518\) | 6.31465 | − | 13.7455i | 0.277450 | − | 0.603941i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.3455 | + | 17.9189i | −0.453680 | + | 0.785797i | ||||
\(521\) | 27.8685 | − | 16.0899i | 1.22094 | − | 0.704909i | 0.255821 | − | 0.966724i | \(-0.417654\pi\) |
0.965118 | + | 0.261815i | \(0.0843209\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.03873 | + | 1.75441i | 0.132874 | + | 0.0767149i | 0.564964 | − | 0.825116i | \(-0.308890\pi\) |
−0.432089 | + | 0.901831i | \(0.642224\pi\) | |||||||
\(524\) | −15.6711 | −0.684597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.3226 | 1.14772 | ||||||||
\(527\) | −4.74993 | + | 8.22713i | −0.206910 | + | 0.358379i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.40558 | − | 7.63068i | −0.191547 | − | 0.331769i | ||||
\(530\) | −19.7709 | + | 34.2443i | −0.858794 | + | 1.48748i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.34977 | − | 3.79149i | 0.231942 | − | 0.164382i | ||||
\(533\) | 35.0174i | 1.51677i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5877 | + | 6.69016i | −0.500980 | + | 0.289241i | ||||
\(536\) | 5.66594 | + | 9.81369i | 0.244731 | + | 0.423887i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 8.12947i | − | 0.350486i | ||||||
\(539\) | −22.6917 | − | 4.90774i | −0.977401 | − | 0.211391i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.92948 | − | 2.26869i | −0.168942 | − | 0.0975385i | 0.413145 | − | 0.910665i | \(-0.364430\pi\) |
−0.582087 | + | 0.813127i | \(0.697764\pi\) | |||||||
\(542\) | −12.6065 | + | 7.27836i | −0.541495 | + | 0.312632i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.39461 | + | 2.41554i | −0.0597935 | + | 0.103565i | ||||
\(545\) | −59.3994 | −2.54439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.8271i | − | 0.719477i | −0.933053 | − | 0.359738i | \(-0.882866\pi\) | ||
0.933053 | − | 0.359738i | \(-0.117134\pi\) | |||||||
\(548\) | 2.55426 | + | 1.47471i | 0.109113 | + | 0.0629963i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.55817 | − | 28.3884i | −0.151721 | − | 1.21049i | ||||
\(551\) | 3.24117 | + | 1.87129i | 0.138079 | + | 0.0797197i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0709535 | + | 0.761102i | 0.00301725 | + | 0.0323653i | ||||
\(554\) | − | 29.9949i | − | 1.27436i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.47235 | − | 2.00476i | 0.147260 | − | 0.0850208i | ||||
\(557\) | −6.67157 | − | 11.5555i | −0.282684 | − | 0.489622i | 0.689361 | − | 0.724418i | \(-0.257891\pi\) |
−0.972045 | + | 0.234795i | \(0.924558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.2725 | 1.83023 | ||||||||
\(560\) | −8.87481 | − | 4.07708i | −0.375029 | − | 0.172288i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.42117 | + | 11.1218i | −0.270861 | + | 0.469144i | ||||
\(563\) | 16.4049 | + | 28.4141i | 0.691384 | + | 1.19751i | 0.971385 | + | 0.237512i | \(0.0763318\pi\) |
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.7676 | + | 60.2192i | −1.46268 | + | 2.53344i | ||||
\(566\) | − | 7.33349i | − | 0.308250i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.15087i | 0.216126i | ||||||||
\(569\) | 2.97076 | − | 5.14551i | 0.124541 | − | 0.215711i | −0.797012 | − | 0.603963i | \(-0.793588\pi\) |
0.921553 | + | 0.388252i | \(0.126921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8007 | + | 18.3601i | −1.33082 | + | 0.768348i | −0.985425 | − | 0.170110i | \(-0.945588\pi\) |
−0.345393 | + | 0.938458i | \(0.612254\pi\) | |||||||
\(572\) | −11.2253 | − | 14.8187i | −0.469351 | − | 0.619602i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.4575 | + | 1.53424i | −0.686922 | + | 0.0640381i | ||||
\(575\) | 32.4940i | 1.35510i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.409992 | + | 0.710127i | 0.0170682 | + | 0.0295630i | 0.874433 | − | 0.485146i | \(-0.161233\pi\) |
−0.857365 | + | 0.514709i | \(0.827900\pi\) | |||||||
\(578\) | 4.61011 | + | 7.98495i | 0.191755 | + | 0.332130i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 5.57443i | − | 0.231465i | ||||||
\(581\) | 15.6843 | + | 22.1305i | 0.650696 | + | 0.918128i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.4522 | − | 28.3195i | −0.888459 | − | 1.17287i | ||||
\(584\) | −4.53946 | + | 2.62086i | −0.187844 | + | 0.108452i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.02672 | − | 5.24243i | 0.125032 | − | 0.216563i | ||||
\(587\) | − | 42.0341i | − | 1.73493i | −0.497494 | − | 0.867467i | \(-0.665746\pi\) | ||
0.497494 | − | 0.867467i | \(-0.334254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.44105i | 0.347807i | ||||||||
\(590\) | −24.7717 | + | 42.9059i | −1.01984 | + | 1.76641i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.85865 | + | 4.95132i | 0.117490 | + | 0.203498i | ||||
\(593\) | −13.1169 | + | 22.7191i | −0.538645 | + | 0.932960i | 0.460333 | + | 0.887747i | \(0.347730\pi\) |
−0.998977 | + | 0.0452135i | \(0.985603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.2253 | − | 15.7515i | 0.911148 | − | 0.645749i | ||||
\(596\) | −6.46913 | −0.264986 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.5569 | + | 18.2850i | 0.431702 | + | 0.747729i | ||||
\(599\) | 22.7563 | − | 13.1384i | 0.929798 | − | 0.536819i | 0.0430501 | − | 0.999073i | \(-0.486292\pi\) |
0.886748 | + | 0.462254i | \(0.152959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0989i | 1.51329i | 0.653824 | + | 0.756647i | \(0.273164\pi\) | ||||
−0.653824 | + | 0.756647i | \(0.726836\pi\) | |||||||
\(602\) | 1.89593 | + | 20.3372i | 0.0772722 | + | 0.828882i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.3957 | + | 7.73400i | 0.545062 | + | 0.314692i | ||||
\(605\) | 39.0882 | + | 10.9959i | 1.58916 | + | 0.447045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.72911 | + | 0.998300i | 0.0701822 | + | 0.0405197i | 0.534680 | − | 0.845054i | \(-0.320432\pi\) |
−0.464498 | + | 0.885574i | \(0.653765\pi\) | |||||||
\(608\) | 2.47835i | 0.100510i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.08883 | −0.367996 | ||||||||
\(611\) | 29.0660 | − | 50.3437i | 1.17588 | − | 2.03669i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.55742 | + | 3.78593i | −0.264852 | + | 0.152912i | −0.626546 | − | 0.779385i | \(-0.715532\pi\) |
0.361694 | + | 0.932297i | \(0.382199\pi\) | |||||||
\(614\) | −5.40966 | − | 3.12327i | −0.218316 | − | 0.126045i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.47267 | − | 5.92490i | 0.260792 | − | 0.238721i | ||||
\(617\) | 17.2159i | 0.693084i | 0.938034 | + | 0.346542i | \(0.112644\pi\) | ||||
−0.938034 | + | 0.346542i | \(0.887356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3426 | − | 31.7703i | −0.737250 | − | 1.27695i | −0.953729 | − | 0.300667i | \(-0.902791\pi\) |
0.216479 | − | 0.976287i | \(-0.430543\pi\) | |||||||
\(620\) | 10.8882 | − | 6.28629i | 0.437280 | − | 0.252464i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 9.76504i | − | 0.391542i | ||||||
\(623\) | −3.89607 | − | 41.7923i | −0.156093 | − | 1.67437i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.14145 | + | 5.44116i | −0.125658 | + | 0.217646i | ||||
\(626\) | −16.0158 | − | 27.7402i | −0.640120 | − | 1.10872i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.34257 | − | 16.1818i | 0.372809 | − | 0.645725i | ||||
\(629\) | −15.9468 | −0.635842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −47.4286 | −1.88810 | −0.944051 | − | 0.329801i | \(-0.893019\pi\) | ||||
−0.944051 | + | 0.329801i | \(0.893019\pi\) | |||||||
\(632\) | −0.250209 | − | 0.144458i | −0.00995279 | − | 0.00574625i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.5774 | − | 10.7256i | 0.737802 | − | 0.425970i | ||||
\(635\) | −14.9185 | + | 25.8395i | −0.592021 | + | 1.02541i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.0204 | + | 12.9992i | 1.46680 | + | 0.515048i | ||||
\(638\) | 4.61524 | + | 1.94537i | 0.182719 | + | 0.0770178i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.19684 | − | 1.84570i | 0.126366 | − | 0.0729576i | ||||
\(641\) | −28.5801 | + | 16.5007i | −1.12884 | + | 0.651739i | −0.943644 | − | 0.330962i | \(-0.892627\pi\) |
−0.185200 | + | 0.982701i | \(0.559293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.8847 | −1.65177 | −0.825885 | − | 0.563838i | \(-0.809324\pi\) | ||||
−0.825885 | + | 0.563838i | \(0.809324\pi\) | |||||||
\(644\) | −8.13105 | + | 5.76264i | −0.320408 | + | 0.227080i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.98655 | − | 3.45634i | −0.235538 | − | 0.135988i | ||||
\(647\) | 17.9616 | − | 10.3701i | 0.706142 | − | 0.407691i | −0.103489 | − | 0.994631i | \(-0.533001\pi\) |
0.809631 | + | 0.586939i | \(0.199667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.8782 | − | 35.4826i | −1.05506 | − | 1.39281i | ||||
\(650\) | 48.3527i | 1.89655i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.25602 | −0.362494 | ||||||||
\(653\) | 6.73045 | + | 3.88583i | 0.263383 | + | 0.152064i | 0.625877 | − | 0.779922i | \(-0.284741\pi\) |
−0.362494 | + | 0.931986i | \(0.618075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.0982 | + | 28.9242i | −1.95750 | + | 1.13016i | ||||
\(656\) | 3.12366 | − | 5.41033i | 0.121958 | − | 0.211238i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.9340 | + | 11.4547i | 0.972029 | + | 0.446549i | ||||
\(659\) | −44.6638 | −1.73986 | −0.869928 | − | 0.493180i | \(-0.835835\pi\) | ||||
−0.869928 | + | 0.493180i | \(0.835835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.14521 | + | 5.44767i | 0.122335 | + | 0.211890i | 0.920688 | − | 0.390300i | \(-0.127629\pi\) |
−0.798353 | + | 0.602189i | \(0.794295\pi\) | |||||||
\(662\) | 15.3327 | + | 26.5569i | 0.595920 | + | 1.03216i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.2522 | −0.397864 | ||||||||
\(665\) | 10.1044 | − | 21.9949i | 0.391833 | − | 0.852924i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.92622 | − | 2.84415i | −0.190744 | − | 0.110126i | ||||
\(668\) | −8.19377 | − | 14.1920i | −0.317027 | − | 0.549106i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 36.2262 | + | 20.9152i | 1.39954 | + | 0.808025i | ||||
\(671\) | 3.17182 | − | 7.52491i | 0.122447 | − | 0.290496i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.96695i | 0.191462i | 0.995407 | + | 0.0957309i | \(0.0305188\pi\) | ||||
−0.995407 | + | 0.0957309i | \(0.969481\pi\) | |||||||
\(674\) | −28.9019 | − | 16.6865i | −1.11326 | − | 0.642742i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.20911 | + | 15.9507i | 0.354197 | + | 0.613487i | ||||
\(677\) | −12.5168 | + | 21.6798i | −0.481061 | + | 0.833222i | −0.999764 | − | 0.0217327i | \(-0.993082\pi\) |
0.518703 | + | 0.854955i | \(0.326415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.01631 | − | 9.89996i | −0.269261 | − | 0.379926i | ||||
\(680\) | 10.2961i | 0.394839i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.40485 | + | 11.2084i | 0.0537945 | + | 0.429194i | ||||
\(683\) | −37.1556 | + | 21.4518i | −1.42172 | + | 0.820831i | −0.996446 | − | 0.0842334i | \(-0.973156\pi\) |
−0.425275 | + | 0.905064i | \(0.639823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8874 | 0.415988 | ||||||||
\(686\) | −4.48737 | + | 17.9684i | −0.171328 | + | 0.686037i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.68577 | − | 3.86003i | −0.254893 | − | 0.147162i | ||||
\(689\) | 30.0211 | + | 51.9981i | 1.14371 | + | 1.98097i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.04518 | + | 5.27440i | −0.115844 | + | 0.200648i | −0.918117 | − | 0.396310i | \(-0.870291\pi\) |
0.802273 | + | 0.596958i | \(0.203624\pi\) | |||||||
\(692\) | 20.9243 | 0.795424 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.1533 | −0.765009 | ||||||||
\(695\) | 7.40037 | − | 12.8178i | 0.280712 | − | 0.486207i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.71258 | + | 15.0906i | 0.330013 | + | 0.571599i | ||||
\(698\) | 22.3673 | + | 12.9138i | 0.846616 | + | 0.488794i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.7248 | + | 2.11851i | −0.858917 | + | 0.0800723i | ||||
\(701\) | −49.6670 | −1.87590 | −0.937948 | − | 0.346777i | \(-0.887276\pi\) | ||||
−0.937948 | + | 0.346777i | \(0.887276\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.2711 | + | 7.08472i | −0.462813 | + | 0.267205i | ||||
\(704\) | 0.412474 | + | 3.29088i | 0.0155457 | + | 0.124030i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 9.48296i | − | 0.356896i | ||||||
\(707\) | −3.22070 | + | 7.01068i | −0.121127 | + | 0.263664i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.37833 | + | 2.38734i | −0.0517643 | + | 0.0896584i | −0.890746 | − | 0.454500i | \(-0.849818\pi\) |
0.838982 | + | 0.544159i | \(0.183151\pi\) | |||||||
\(710\) | 9.50695 | + | 16.4665i | 0.356789 | + | 0.617978i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.7391 | + | 7.93225i | 0.514893 | + | 0.297274i | ||||
\(713\) | − | 12.8294i | − | 0.480466i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63.2362 | − | 26.6547i | −2.36490 | − | 0.996828i | ||||
\(716\) | 12.9584 | + | 7.48153i | 0.484278 | + | 0.279598i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.42112 | − | 9.38966i | −0.202314 | − | 0.350419i | ||||
\(719\) | 34.4448 | + | 19.8867i | 1.28457 | + | 0.741650i | 0.977681 | − | 0.210094i | \(-0.0673771\pi\) |
0.306894 | + | 0.951744i | \(0.400710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.3210 | − | 2.26732i | 0.905761 | − | 0.0844393i | ||||
\(722\) | 12.8578 | 0.478518 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.05625 | + | 8.75769i | 0.187914 | + | 0.325477i | ||||
\(725\) | −6.51343 | − | 11.2816i | −0.241903 | − | 0.418988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4901 | 0.945376 | 0.472688 | − | 0.881230i | \(-0.343284\pi\) | ||||
0.472688 | + | 0.881230i | \(0.343284\pi\) | |||||||
\(728\) | −12.0994 | + | 8.57509i | −0.448433 | + | 0.317814i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.67462 | + | 16.7569i | −0.358074 | + | 0.620202i | ||||
\(731\) | 18.6481 | − | 10.7665i | 0.689726 | − | 0.398213i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.1323 | − | 24.3251i | −1.55619 | − | 0.898467i | −0.997616 | − | 0.0690128i | \(-0.978015\pi\) |
−0.558575 | − | 0.829454i | \(-0.688652\pi\) | |||||||
\(734\) | −8.92893 | −0.329573 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.76681i | − | 0.138846i | ||||||
\(737\) | −29.9586 | + | 22.6938i | −1.10354 | + | 0.835936i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9783 | − | 6.33835i | 0.403845 | − | 0.233160i | −0.284297 | − | 0.958736i | \(-0.591760\pi\) |
0.688142 | + | 0.725576i | \(0.258427\pi\) | |||||||
\(740\) | 18.2773 | + | 10.5524i | 0.671887 | + | 0.387914i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.1227 | + | 16.3876i | −0.848862 | + | 0.601606i | ||||
\(743\) | −18.4512 | −0.676910 | −0.338455 | − | 0.940983i | \(-0.609904\pi\) | ||||
−0.338455 | + | 0.940983i | \(0.609904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.6808 | + | 11.9401i | −0.757686 | + | 0.437450i | ||||
\(746\) | 12.8877 | − | 7.44073i | 0.471853 | − | 0.272424i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.52448 | − | 3.59315i | −0.311686 | − | 0.131379i | ||||
\(749\) | −9.54873 | + | 0.890178i | −0.348903 | + | 0.0325264i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5428 | − | 44.2414i | 0.932070 | − | 1.61439i | 0.152293 | − | 0.988335i | \(-0.451334\pi\) |
0.779777 | − | 0.626057i | \(-0.215332\pi\) | |||||||
\(752\) | −8.98162 | + | 5.18554i | −0.327526 | + | 0.189097i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.33046 | − | 4.23224i | −0.266959 | − | 0.154129i | ||||
\(755\) | 57.0985 | 2.07803 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3898 | 0.486659 | 0.243329 | − | 0.969944i | \(-0.421760\pi\) | ||||
0.243329 | + | 0.969944i | \(0.421760\pi\) | |||||||
\(758\) | −15.1414 | + | 26.2256i | −0.549959 | + | 0.952556i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.57428 | + | 7.92289i | 0.165927 | + | 0.287393i | ||||
\(761\) | 3.48214 | − | 6.03125i | 0.126228 | − | 0.218633i | −0.795985 | − | 0.605317i | \(-0.793046\pi\) |
0.922212 | + | 0.386684i | \(0.126380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.6865 | − | 17.7726i | −1.40055 | − | 0.643410i | ||||
\(764\) | 5.27991i | 0.191020i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.4934 | + | 10.6772i | −0.668194 | + | 0.385782i | ||||
\(767\) | 37.6146 | + | 65.1504i | 1.35818 | + | 2.35244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.40816i | − | 0.0868404i | −0.999057 | − | 0.0434202i | \(-0.986175\pi\) | ||
0.999057 | − | 0.0434202i | \(-0.0138254\pi\) | |||||||
\(770\) | 9.75654 | − | 30.8876i | 0.351601 | − | 1.11311i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.8361 | − | 11.4524i | −0.713918 | − | 0.412181i | ||||
\(773\) | 11.9339 | − | 6.89002i | 0.429231 | − | 0.247817i | −0.269788 | − | 0.962920i | \(-0.586954\pi\) |
0.699019 | + | 0.715103i | \(0.253620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6904 | − | 25.4445i | 0.527695 | − | 0.913995i | ||||
\(776\) | 4.58628 | 0.164638 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.98703i | 0.250497i | ||||||||
\(779\) | 13.4087 | + | 7.74151i | 0.480416 | + | 0.277368i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.9509 | + | 2.12460i | −0.606550 | + | 0.0760241i | ||||
\(782\) | 9.09888 | + | 5.25324i | 0.325375 | + | 0.187855i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.56024 | − | 5.31076i | −0.162866 | − | 0.189670i | ||||
\(785\) | − | 68.9743i | − | 2.46180i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.15993 | − | 2.40174i | 0.148285 | − | 0.0856127i | −0.424022 | − | 0.905652i | \(-0.639382\pi\) |
0.572307 | + | 0.820039i | \(0.306049\pi\) | |||||||
\(788\) | −4.28337 | − | 7.41901i | −0.152589 | − | 0.264291i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.06651 | −0.0379446 | ||||||||
\(791\) | −40.6618 | + | 28.8179i | −1.44577 | + | 1.02465i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.90046 | + | 11.9519i | −0.245042 | + | 0.424426i | ||||
\(794\) | −5.27929 | − | 9.14400i | −0.187355 | − | 0.324508i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.28887 | − | 3.96444i | 0.0811269 | − | 0.140516i | ||||
\(797\) | − | 17.4411i | − | 0.617794i | −0.951096 | − | 0.308897i | \(-0.900040\pi\) | ||
0.951096 | − | 0.308897i | \(-0.0999598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 28.9273i | − | 1.02337i | ||||||
\(800\) | 4.31321 | − | 7.47069i | 0.152495 | − | 0.264129i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.21248 | + | 4.74148i | −0.289993 | + | 0.167427i | ||||
\(803\) | −10.4973 | − | 13.8578i | −0.370442 | − | 0.489030i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.3576 | + | 33.4297i | −0.541284 | + | 1.17824i | ||||
\(806\) | − | 19.0908i | − | 0.672446i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.45801 | − | 2.52536i | −0.0512928 | − | 0.0888417i | ||||
\(809\) | −9.83186 | − | 17.0293i | −0.345670 | − | 0.598717i | 0.639806 | − | 0.768537i | \(-0.279015\pi\) |
−0.985475 | + | 0.169819i | \(0.945682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.2535i | − | 1.44861i | −0.689481 | − | 0.724304i | \(-0.742161\pi\) | ||
0.689481 | − | 0.724304i | \(-0.257839\pi\) | |||||||
\(812\) | 1.66789 | − | 3.63060i | 0.0585316 | − | 0.127409i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.1151 | + | 11.4497i | −0.529783 | + | 0.401313i | ||||
\(815\) | −29.5901 | + | 17.0838i | −1.03649 | + | 0.598420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.56650 | − | 16.5697i | 0.334689 | − | 0.579699i | ||||
\(818\) | − | 1.71956i | − | 0.0601228i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 23.0613i | − | 0.805336i | ||||||
\(821\) | −6.89065 | + | 11.9350i | −0.240485 | + | 0.416533i | −0.960853 | − | 0.277060i | \(-0.910640\pi\) |
0.720367 | + | 0.693593i | \(0.243973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.8569 | + | 41.3214i | 0.831600 | + | 1.44037i | 0.896769 | + | 0.442500i | \(0.145908\pi\) |
−0.0651682 | + | 0.997874i | \(0.520758\pi\) | |||||||
\(824\) | −4.61616 | + | 7.99543i | −0.160812 | + | 0.278534i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.9713 | + | 20.5326i | −1.00804 | + | 0.714420i | ||||
\(827\) | 12.5107 | 0.435040 | 0.217520 | − | 0.976056i | \(-0.430203\pi\) | ||||
0.217520 | + | 0.976056i | \(0.430203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.7935 | − | 36.0153i | −0.722187 | − | 1.25086i | −0.960121 | − | 0.279583i | \(-0.909804\pi\) |
0.237935 | − | 0.971281i | \(-0.423530\pi\) | |||||||
\(830\) | −32.7748 | + | 18.9225i | −1.13763 | + | 0.656811i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.60520i | − | 0.194325i | ||||||
\(833\) | 19.1881 | − | 3.60898i | 0.664829 | − | 0.125044i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.3884 | − | 30.2465i | −1.81298 | − | 1.04672i | ||||
\(836\) | −8.15594 | + | 1.02225i | −0.282079 | + | 0.0353554i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.62491 | − | 2.67019i | −0.159765 | − | 0.0922402i | ||||
\(839\) | 20.8388i | 0.719436i | 0.933061 | + | 0.359718i | \(0.117127\pi\) | ||||
−0.933061 | + | 0.359718i | \(0.882873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7196 | −0.921364 | ||||||||
\(842\) | 13.5518 | − | 23.4724i | 0.467026 | − | 0.808914i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.71101 | − | 5.02930i | 0.299845 | − | 0.173116i | ||||
\(845\) | 58.8802 | + | 33.9945i | 2.02554 | + | 1.16945i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.1679 | + | 18.8569i | 0.761699 | + | 0.647931i | ||||
\(848\) | − | 10.7119i | − | 0.367848i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0305 | + | 20.8374i | 0.412643 | + | 0.714718i | ||||
\(851\) | 18.6507 | − | 10.7680i | 0.639337 | − | 0.369122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.8753i | − | 0.748994i | −0.927228 | − | 0.374497i | \(-0.877815\pi\) | ||
0.927228 | − | 0.374497i | \(-0.122185\pi\) | |||||||
\(854\) | −5.91951 | − | 2.71942i | −0.202561 | − | 0.0930565i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.81237 | − | 3.13911i | 0.0619454 | − | 0.107293i | ||||
\(857\) | 25.9670 | + | 44.9762i | 0.887016 | + | 1.53636i | 0.843386 | + | 0.537309i | \(0.180559\pi\) |
0.0436301 | + | 0.999048i | \(0.486108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.70523 | + | 6.41764i | −0.126421 | + | 0.218967i | −0.922287 | − | 0.386505i | \(-0.873682\pi\) |
0.795867 | + | 0.605472i | \(0.207016\pi\) | |||||||
\(860\) | −28.4978 | −0.971767 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.60124 | −0.258899 | ||||||||
\(863\) | −8.57220 | − | 4.94916i | −0.291801 | − | 0.168471i | 0.346953 | − | 0.937883i | \(-0.387216\pi\) |
−0.638754 | + | 0.769411i | \(0.720550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.8918 | − | 38.6200i | 2.27439 | − | 1.31312i | ||||
\(866\) | 15.9757 | − | 27.6707i | 0.542877 | − | 0.940290i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.97230 | − | 0.836440i | 0.304540 | − | 0.0283906i | ||||
\(869\) | 0.372190 | − | 0.882993i | 0.0126257 | − | 0.0299535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.0077 | − | 31.7587i | 1.86386 | − | 1.07610i | ||||
\(872\) | 13.9355 | − | 8.04565i | 0.471915 | − | 0.272460i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.33546 | 0.315777 | ||||||||
\(875\) | −28.8962 | + | 20.4793i | −0.976869 | + | 0.692328i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.3992 | + | 17.5510i | 1.02651 | + | 0.592655i | 0.915983 | − | 0.401218i | \(-0.131413\pi\) |
0.110526 | + | 0.993873i | \(0.464746\pi\) | |||||||
\(878\) | 3.37246 | − | 1.94709i | 0.113815 | − | 0.0657110i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.39258 | + | 9.75911i | 0.249204 | + | 0.328980i | ||||
\(881\) | − | 23.3064i | − | 0.785212i | −0.919707 | − | 0.392606i | \(-0.871574\pi\) | ||
0.919707 | − | 0.392606i | \(-0.128426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2116 | −0.814786 | −0.407393 | − | 0.913253i | \(-0.633562\pi\) | ||||
−0.407393 | + | 0.913253i | \(0.633562\pi\) | |||||||
\(884\) | 13.5396 | + | 7.81708i | 0.455385 | + | 0.262917i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.84958 | + | 2.79991i | −0.162925 | + | 0.0940647i | ||||
\(887\) | 19.5859 | − | 33.9237i | 0.657629 | − | 1.13905i | −0.323599 | − | 0.946194i | \(-0.604893\pi\) |
0.981228 | − | 0.192852i | \(-0.0617737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4476 | + | 12.3655i | −0.585174 | + | 0.414725i | ||||
\(890\) | 58.5621 | 1.96301 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.37151 | − | 12.7678i | −0.246817 | − | 0.427499i | ||||
\(893\) | −12.8516 | − | 22.2596i | −0.430061 | − | 0.744888i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.2346 | 1.84629 | ||||||||
\(896\) | 2.63433 | − | 0.245585i | 0.0880067 | − | 0.00820440i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.1134 | − | 9.88040i | −0.571080 | − | 0.329713i | ||||
\(899\) | 2.57166 | + | 4.45425i | 0.0857696 | + | 0.148557i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.8750 | + | 14.9389i | 0.862022 | + | 0.497688i | ||||
\(902\) | 19.0932 | + | 8.04795i | 0.635733 | + | 0.267967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 18.8371i | − | 0.626512i | ||||||
\(905\) | 32.3281 | + | 18.6646i | 1.07462 | + | 0.620433i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.18723 | + | 7.25250i | 0.139035 | + | 0.240815i | 0.927132 | − | 0.374736i | \(-0.122267\pi\) |
−0.788097 | + | 0.615551i | \(0.788933\pi\) | |||||||
\(908\) | −9.41469 | + | 16.3067i | −0.312437 | + | 0.541158i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.8528 | + | 49.7451i | −0.757564 | + | 1.64903i | ||||
\(911\) | − | 11.1411i | − | 0.369121i | −0.982821 | − | 0.184560i | \(-0.940914\pi\) | ||
0.982821 | − | 0.184560i | \(-0.0590861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.22877 | − | 33.7388i | −0.139952 | − | 1.11659i | ||||
\(914\) | −16.7231 | + | 9.65507i | −0.553150 | + | 0.319361i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.6447 | 0.450832 | ||||||||
\(917\) | −41.2829 | + | 3.84859i | −1.36328 | + | 0.127092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.7054 | − | 22.3466i | −1.27677 | − | 0.737146i | −0.300520 | − | 0.953776i | \(-0.597160\pi\) |
−0.976254 | + | 0.216630i | \(0.930494\pi\) | |||||||
\(920\) | −6.95239 | − | 12.0419i | −0.229214 | − | 0.397010i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.47983 | + | 6.02725i | −0.114602 | + | 0.198497i | ||||
\(923\) | 28.8716 | 0.950321 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.3197 | 1.62162 | ||||||||
\(926\) | −8.13620 | + | 14.0923i | −0.267372 | + | 0.463102i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.755057 | + | 1.30780i | 0.0247859 | + | 0.0429305i | ||||
\(929\) | −5.89281 | − | 3.40222i | −0.193337 | − | 0.111623i | 0.400207 | − | 0.916425i | \(-0.368938\pi\) |
−0.593544 | + | 0.804802i | \(0.702272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1619 | − | 11.3019i | 0.431365 | − | 0.370403i | ||||
\(932\) | 7.03035 | 0.230287 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.39696 | − | 0.806535i | 0.0457099 | − | 0.0263906i | ||||
\(935\) | −33.8833 | + | 4.24689i | −1.10810 | + | 0.138888i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2645i | 1.83808i | 0.394165 | + | 0.919040i | \(0.371034\pi\) | ||||
−0.394165 | + | 0.919040i | \(0.628966\pi\) | |||||||
\(938\) | 17.3360 | + | 24.4610i | 0.566041 | + | 0.798681i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.1419 | + | 33.1547i | −0.624339 | + | 1.08139i | ||||
\(941\) | 20.2704 | + | 35.1093i | 0.660796 | + | 1.14453i | 0.980407 | + | 0.196983i | \(0.0631144\pi\) |
−0.319611 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3797 | − | 11.7662i | −0.663654 | − | 0.383161i | ||||
\(944\) | − | 13.4213i | − | 0.436827i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.94518 | − | 23.5942i | 0.323346 | − | 0.767114i | ||||
\(947\) | 10.9708 | + | 6.33401i | 0.356504 | + | 0.205828i | 0.667546 | − | 0.744568i | \(-0.267345\pi\) |
−0.311042 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6904 | + | 25.4445i | 0.476871 | + | 0.825965i | ||||
\(950\) | 18.5150 | + | 10.6896i | 0.600705 | + | 0.346817i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.08065 | + | 6.70582i | −0.0998444 | + | 0.217337i | ||||
\(953\) | −4.11699 | −0.133362 | −0.0666812 | − | 0.997774i | \(-0.521241\pi\) | ||||
−0.0666812 | + | 0.997774i | \(0.521241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.74512 | + | 16.8790i | 0.315345 | + | 0.546193i | ||||
\(956\) | 5.19541 | + | 8.99871i | 0.168031 | + | 0.291039i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.9039 | 1.09539 | ||||||||
\(959\) | 7.09094 | + | 3.25757i | 0.228978 | + | 0.105192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.69987 | − | 16.8007i | 0.312899 | − | 0.541957i | ||||
\(962\) | 27.7531 | − | 16.0233i | 0.894797 | − | 0.516611i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.24972 | + | 5.34033i | 0.297913 | + | 0.172000i | ||||
\(965\) | −84.5507 | −2.72178 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.53643i | 0.0815661i | 0.999168 | + | 0.0407831i | \(0.0129853\pi\) | ||||
−0.999168 | + | 0.0407831i | \(0.987015\pi\) | |||||||
\(968\) | −10.6597 | + | 2.71480i | −0.342617 | + | 0.0872569i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.6616 | − | 8.46489i | 0.470756 | − | 0.271791i | ||||
\(971\) | 4.36761 | + | 2.52164i | 0.140163 | + | 0.0809234i | 0.568442 | − | 0.822723i | \(-0.307546\pi\) |
−0.428278 | + | 0.903647i | \(0.640880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.65497 | − | 6.13395i | 0.277466 | − | 0.196646i | ||||
\(974\) | 3.05187 | 0.0977883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.13230 | − | 1.23108i | 0.0682532 | − | 0.0394060i | ||||
\(977\) | −51.9446 | + | 29.9902i | −1.66185 | + | 0.959472i | −0.690025 | + | 0.723786i | \(0.742400\pi\) |
−0.971829 | + | 0.235686i | \(0.924266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.4370 | + | 48.4854i | −0.653171 | + | 1.54960i | ||||
\(980\) | −24.3804 | − | 8.56086i | −0.778805 | − | 0.273467i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.8725 | − | 30.9560i | 0.570334 | − | 0.987847i | ||||
\(983\) | −19.0455 | + | 10.9959i | −0.607458 | + | 0.350716i | −0.771970 | − | 0.635659i | \(-0.780728\pi\) |
0.164512 | + | 0.986375i | \(0.447395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.3865 | − | 15.8116i | −0.872607 | − | 0.503800i | ||||
\(986\) | −4.21205 | −0.134139 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.8916 | 0.441951 | ||||||||
\(989\) | −14.5400 | + | 25.1840i | −0.462345 | + | 0.800805i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.59341 | + | 11.4201i | 0.209446 | + | 0.362772i | 0.951540 | − | 0.307524i | \(-0.0995005\pi\) |
−0.742094 | + | 0.670296i | \(0.766167\pi\) | |||||||
\(992\) | −1.70296 | + | 2.94961i | −0.0540690 | + | 0.0936502i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.26497 | + | 13.5691i | 0.0401225 | + | 0.430385i | ||||
\(995\) | − | 16.8983i | − | 0.535711i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.2987 | + | 23.8438i | −1.30794 | + | 0.755141i | −0.981753 | − | 0.190162i | \(-0.939099\pi\) |
−0.326191 | + | 0.945304i | \(0.605765\pi\) | |||||||
\(998\) | −3.75597 | − | 6.50553i | −0.118893 | − | 0.205929i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.ba.a.989.1 | ✓ | 32 | |
3.2 | odd | 2 | 1386.2.ba.b.989.16 | yes | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.a.1187.16 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.b.989.1 | yes | 32 | ||
21.11 | odd | 6 | 1386.2.ba.b.1187.1 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.a.989.16 | yes | 32 | |
77.32 | odd | 6 | 1386.2.ba.b.1187.16 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.a.1187.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.a.989.16 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.a.1187.1 | yes | 32 | 231.32 | even | 6 | inner | |
1386.2.ba.a.1187.16 | yes | 32 | 7.4 | even | 3 | inner | |
1386.2.ba.b.989.1 | yes | 32 | 11.10 | odd | 2 | ||
1386.2.ba.b.989.16 | yes | 32 | 3.2 | odd | 2 | ||
1386.2.ba.b.1187.1 | yes | 32 | 21.11 | odd | 6 | ||
1386.2.ba.b.1187.16 | yes | 32 | 77.32 | odd | 6 |