Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.9 | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.4.d.c.287.10 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.92666 | − | 4.82576i | −0.370786 | − | 0.928718i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.6497i | 1.66808i | 0.551704 | + | 0.834040i | \(0.313978\pi\) | ||||
−0.551704 | + | 0.834040i | \(0.686022\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.79314i | 0.258805i | 0.991592 | + | 0.129403i | \(0.0413059\pi\) | ||||
−0.991592 | + | 0.129403i | \(0.958694\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.5759 | + | 18.5952i | −0.725035 | + | 0.688712i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.4244 | 0.505014 | 0.252507 | − | 0.967595i | \(-0.418745\pi\) | ||||
0.252507 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 89.9990 | − | 35.9317i | 1.54918 | − | 0.618501i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.4664i | 0.605860i | 0.953013 | + | 0.302930i | \(0.0979648\pi\) | ||||
−0.953013 | + | 0.302930i | \(0.902035\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.4499i | 0.705754i | 0.935670 | + | 0.352877i | \(0.114797\pi\) | ||||
−0.935670 | + | 0.352877i | \(0.885203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23.1305 | − | 9.23476i | 0.240357 | − | 0.0959614i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.6202 | 0.186940 | 0.0934698 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934698 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −222.811 | −1.78249 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 127.452 | + | 58.6421i | 0.908452 | + | 0.417988i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 65.8695i | − | 0.421781i | −0.977510 | − | 0.210891i | \(-0.932364\pi\) | ||
0.977510 | − | 0.210891i | \(-0.0676364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 129.239i | − | 0.748773i | −0.927273 | − | 0.374386i | \(-0.877853\pi\) | ||
0.927273 | − | 0.374386i | \(-0.122147\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −35.4975 | − | 88.9116i | −0.187252 | − | 0.469016i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −89.3906 | −0.431708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −280.300 | −1.24543 | −0.622717 | − | 0.782447i | \(-0.713971\pi\) | ||||
−0.622717 | + | 0.782447i | \(0.713971\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.0466 | + | 62.7349i | 0.102838 | + | 0.257580i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 49.8512i | − | 0.189889i | −0.995483 | − | 0.0949446i | \(-0.969733\pi\) | ||
0.995483 | − | 0.0949446i | \(-0.0302674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 336.630i | − | 1.19385i | −0.802297 | − | 0.596925i | \(-0.796389\pi\) | ||
0.802297 | − | 0.596925i | \(-0.203611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −346.795 | − | 365.086i | −1.14883 | − | 1.20942i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −482.061 | −1.49608 | −0.748041 | − | 0.663652i | \(-0.769005\pi\) | ||||
−0.748041 | + | 0.663652i | \(0.769005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 320.026 | 0.933020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 204.933 | − | 81.8184i | 0.562673 | − | 0.224645i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 256.465i | − | 0.664682i | −0.943159 | − | 0.332341i | \(-0.892161\pi\) | ||
0.943159 | − | 0.332341i | \(-0.107839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 343.609i | 0.842404i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 282.065 | − | 112.613i | 0.655447 | − | 0.261684i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 96.1273 | 0.212114 | 0.106057 | − | 0.994360i | \(-0.466177\pi\) | ||||
0.106057 | + | 0.994360i | \(0.466177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −275.399 | −0.578053 | −0.289027 | − | 0.957321i | \(-0.593332\pi\) | ||||
−0.289027 | + | 0.957321i | \(0.593332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −89.1295 | − | 93.8302i | −0.178242 | − | 0.187643i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 242.446i | − | 0.462642i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 912.032i | 1.66302i | 0.555508 | + | 0.831511i | \(0.312524\pi\) | ||||
−0.555508 | + | 0.831511i | \(0.687476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −39.7282 | − | 99.5082i | −0.0693146 | − | 0.173614i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −842.688 | −1.40857 | −0.704286 | − | 0.709916i | \(-0.748733\pi\) | ||||
−0.704286 | + | 0.709916i | \(0.748733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −851.253 | −1.36482 | −0.682408 | − | 0.730971i | \(-0.739067\pi\) | ||||
−0.682408 | + | 0.730971i | \(0.739067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 429.282 | + | 1075.23i | 0.660923 | + | 1.65543i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 88.3105i | 0.130700i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 305.206i | − | 0.434663i | −0.976098 | − | 0.217331i | \(-0.930265\pi\) | ||
0.976098 | − | 0.217331i | \(-0.0697353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37.4352 | − | 728.038i | 0.0513515 | − | 0.998681i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −394.418 | −0.521602 | −0.260801 | − | 0.965393i | \(-0.583987\pi\) | ||||
−0.260801 | + | 0.965393i | \(0.583987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −791.986 | −1.01062 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −317.870 | + | 126.908i | −0.391716 | + | 0.156391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1358.54i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 62.3108i | − | 0.0717796i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −623.675 | + | 248.999i | −0.695399 | + | 0.277635i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1090.07 | −1.17725 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 261.640 | 0.273871 | 0.136936 | − | 0.990580i | \(-0.456275\pi\) | ||||
0.136936 | + | 0.990580i | \(0.456275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −360.675 | + | 342.605i | −0.366153 | + | 0.347809i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 136.738i | − | 0.134712i | −0.997729 | − | 0.0673562i | \(-0.978544\pi\) | ||
0.997729 | − | 0.0673562i | \(-0.0214564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1253.06i | 1.19872i | 0.800481 | + | 0.599359i | \(0.204578\pi\) | ||||
−0.800481 | + | 0.599359i | \(0.795422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 172.225 | + | 431.378i | 0.160071 | + | 0.400935i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1030.95 | 0.931454 | 0.465727 | − | 0.884929i | \(-0.345793\pi\) | ||||
0.465727 | + | 0.884929i | \(0.345793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1915.84 | −1.68353 | −0.841764 | − | 0.539846i | \(-0.818483\pi\) | ||||
−0.841764 | + | 0.539846i | \(0.818483\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 540.044 | + | 1352.66i | 0.461790 | + | 1.15666i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 27.0817i | − | 0.0225454i | −0.999936 | − | 0.0112727i | \(-0.996412\pi\) | ||
0.999936 | − | 0.0112727i | \(-0.00358829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 384.561i | 0.311830i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 254.487 | − | 241.738i | 0.201089 | − | 0.191014i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −203.547 | −0.156800 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −991.542 | −0.744961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −240.570 | + | 96.0465i | −0.176354 | + | 0.0704083i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1824.15i | − | 1.30526i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 307.817i | − | 0.215074i | −0.994201 | − | 0.107537i | \(-0.965704\pi\) | ||
0.994201 | − | 0.107537i | \(-0.0342964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1624.50 | + | 648.572i | −1.10875 | + | 0.442664i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1571.57 | 1.04815 | 0.524077 | − | 0.851671i | \(-0.324410\pi\) | ||||
0.524077 | + | 0.851671i | \(0.324410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −280.158 | −0.182653 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1093.66 | + | 2376.95i | −0.697238 | + | 1.51537i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2565.67i | 1.60000i | 0.600001 | + | 0.799999i | \(0.295167\pi\) | ||||
−0.600001 | + | 0.799999i | \(0.704833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1134.72i | − | 0.692413i | −0.938158 | − | 0.346206i | \(-0.887470\pi\) | ||
0.938158 | − | 0.346206i | \(-0.112530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 928.769 | + | 2326.31i | 0.554727 | + | 1.38944i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −239.517 | −0.140066 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1228.45 | 0.703565 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −616.582 | − | 1544.37i | −0.345951 | − | 0.866513i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2873.59i | − | 1.57996i | −0.613133 | − | 0.789980i | \(-0.710091\pi\) | ||
0.613133 | − | 0.789980i | \(-0.289909\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 898.495i | − | 0.484228i | −0.970248 | − | 0.242114i | \(-0.922159\pi\) | ||
0.970248 | − | 0.242114i | \(-0.0778408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −789.672 | − | 831.320i | −0.417263 | − | 0.439270i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2410.26 | 1.24901 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1045.24 | −0.531333 | −0.265666 | − | 0.964065i | \(-0.585592\pi\) | ||||
−0.265666 | + | 0.964065i | \(0.585592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1237.64 | + | 494.121i | −0.617303 | + | 0.246455i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 98.8355i | 0.0483809i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3632.61i | − | 1.74557i | −0.488105 | − | 0.872785i | \(-0.662312\pi\) | ||
0.488105 | − | 0.872785i | \(-0.337688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1658.18 | − | 662.019i | 0.782356 | − | 0.312352i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2154.53 | 0.998339 | 0.499169 | − | 0.866504i | \(-0.333639\pi\) | ||||
0.499169 | + | 0.866504i | \(0.333639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1086.89 | − | 1144.21i | −0.486061 | − | 0.511697i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4197.69i | − | 1.84477i | −0.386275 | − | 0.922384i | \(-0.626238\pi\) | ||
0.386275 | − | 0.922384i | \(-0.373762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1067.97i | − | 0.461318i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −185.205 | − | 463.887i | −0.0786488 | − | 0.196994i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2570.05 | −1.07316 | −0.536578 | − | 0.843851i | \(-0.680283\pi\) | ||||
−0.536578 | + | 0.843851i | \(0.680283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1887.31 | −0.775043 | −0.387522 | − | 0.921861i | \(-0.626669\pi\) | ||||
−0.387522 | + | 0.921861i | \(0.626669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 530.601 | + | 1329.01i | 0.214334 | + | 0.536849i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5227.52i | − | 2.07748i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 782.417i | 0.305968i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −281.080 | + | 610.897i | −0.108177 | + | 0.235112i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 140.357 | 0.0531722 | 0.0265861 | − | 0.999647i | \(-0.491536\pi\) | ||||
0.0265861 | + | 0.999647i | \(0.491536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 236.686 | 0.0882749 | 0.0441374 | − | 0.999025i | \(-0.485946\pi\) | ||||
0.0441374 | + | 0.999025i | \(0.485946\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1169.99 | + | 467.112i | −0.429664 | + | 0.171541i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1004.89i | 0.363428i | 0.983351 | + | 0.181714i | \(0.0581645\pi\) | ||||
−0.983351 | + | 0.181714i | \(0.941836\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 671.172i | 0.239086i | 0.992829 | + | 0.119543i | \(0.0381430\pi\) | ||||
−0.992829 | + | 0.119543i | \(0.961857\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4401.25 | − | 1757.18i | 1.54448 | − | 0.616626i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 315.721 | 0.109159 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 929.711 | 0.316750 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −403.660 | + | 383.437i | −0.135538 | + | 0.128748i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1076.90i | 0.356416i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4598.85i | − | 1.50046i | −0.661174 | − | 0.750232i | \(-0.729942\pi\) | ||
0.661174 | − | 0.750232i | \(-0.270058\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1623.57 | + | 4066.61i | 0.522279 | + | 1.30817i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6278.05 | 1.99144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 619.459 | 0.193786 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1640.08 | + | 4107.94i | 0.506055 | + | 1.26753i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 552.063i | − | 0.168035i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1793.95i | − | 0.538707i | −0.963041 | − | 0.269354i | \(-0.913190\pi\) | ||
0.963041 | − | 0.269354i | \(-0.0868101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4361.74 | − | 4143.23i | 1.29237 | − | 1.22762i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4388.97 | −1.28329 | −0.641644 | − | 0.767003i | \(-0.721747\pi\) | ||||
−0.641644 | + | 0.767003i | \(0.721747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1744.68 | −0.503456 | −0.251728 | − | 0.967798i | \(-0.580999\pi\) | ||||
−0.251728 | + | 0.967798i | \(0.580999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 426.166 | − | 170.145i | 0.121384 | − | 0.0484619i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6046.30i | 1.70003i | 0.526760 | + | 0.850014i | \(0.323407\pi\) | ||||
−0.526760 | + | 0.850014i | \(0.676593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8990.30i | − | 2.49558i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1472.85 | + | 588.029i | −0.403679 | + | 0.161167i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2382.04 | 0.644692 | 0.322346 | − | 0.946622i | \(-0.395529\pi\) | ||||
0.322346 | + | 0.946622i | \(0.395529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4961.66 | −1.32618 | −0.663089 | − | 0.748540i | \(-0.730755\pi\) | ||||
−0.663089 | + | 0.748540i | \(0.730755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3585.46 | + | 1222.03i | −0.946533 | + | 0.322606i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5968.39i | 1.55635i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 759.849i | − | 0.195741i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 759.910 | + | 1903.37i | 0.193403 | + | 0.484421i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4132.31 | 1.03916 | 0.519579 | − | 0.854422i | \(-0.326089\pi\) | ||||
0.519579 | + | 0.854422i | \(0.326089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 379.914 | 0.0944072 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1525.89 | + | 3821.93i | 0.374725 | + | 0.938584i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7269.38i | 1.76440i | 0.470871 | + | 0.882202i | \(0.343940\pi\) | ||||
−0.470871 | + | 0.882202i | \(0.656060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1343.52i | − | 0.322325i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1224.86 | + | 1289.46i | 0.290486 | + | 0.305806i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4002.71 | −0.938470 | −0.469235 | − | 0.883073i | \(-0.655470\pi\) | ||||
−0.469235 | + | 0.883073i | \(0.655470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4782.99 | 1.10874 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6556.00 | − | 2617.45i | 1.50270 | − | 0.599945i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 4028.73i | − | 0.913145i | −0.889686 | − | 0.456572i | \(-0.849077\pi\) | ||
0.889686 | − | 0.456572i | \(-0.150923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3465.52i | 0.776810i | 0.921489 | + | 0.388405i | \(0.126974\pi\) | ||||
−0.921489 | + | 0.388405i | \(0.873026\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −300.697 | + | 120.052i | −0.0666630 | + | 0.0266149i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4105.16 | −0.900184 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9176.56 | 1.99049 | 0.995245 | − | 0.0974014i | \(-0.0310531\pi\) | ||||
0.995245 | + | 0.0974014i | \(0.0310531\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2403.22 | + | 2529.97i | 0.515689 | + | 0.542886i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4185.54i | 0.888570i | 0.895885 | + | 0.444285i | \(0.146542\pi\) | ||||
−0.895885 | + | 0.444285i | \(0.853458\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1604.62i | − | 0.337049i | −0.985697 | − | 0.168525i | \(-0.946100\pi\) | ||
0.985697 | − | 0.168525i | \(-0.0539003\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2100.20 | + | 5260.44i | 0.436510 | + | 1.09334i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 238.944 | 0.0491443 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3109.60 | 0.632934 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −504.092 | − | 1262.61i | −0.101548 | − | 0.254349i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6509.95i | 1.29800i | 0.760786 | + | 0.649002i | \(0.224814\pi\) | ||||
−0.760786 | + | 0.649002i | \(0.775186\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1792.75i | 0.353823i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2348.23 | + | 1080.44i | 0.458782 | + | 0.211090i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −268.063 | −0.0518477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1613.51 | 0.308975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −659.865 | + | 263.448i | −0.125110 | + | 0.0499495i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5136.11i | − | 0.964239i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1209.53i | 0.224859i | 0.993660 | + | 0.112429i | \(0.0358632\pi\) | ||||
−0.993660 | + | 0.112429i | \(0.964137\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6046.98 | − | 2414.23i | 1.11327 | − | 0.444468i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5302.65 | 0.966835 | 0.483418 | − | 0.875390i | \(-0.339395\pi\) | ||||
0.483418 | + | 0.875390i | \(0.339395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1535.70 | −0.277326 | −0.138663 | − | 0.990340i | \(-0.544281\pi\) | ||||
−0.138663 | + | 0.990340i | \(0.544281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1749.91 | − | 1662.24i | 0.313003 | − | 0.297322i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5733.47i | 1.01585i | 0.861402 | + | 0.507924i | \(0.169587\pi\) | ||||
−0.861402 | + | 0.507924i | \(0.830413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1213.60i | − | 0.213006i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1986.29 | − | 4975.11i | −0.345370 | − | 0.865058i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2482.16 | −0.427588 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2896.55 | 0.494374 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3691.18 | + | 9245.40i | 0.624229 | + | 1.56352i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2310.59i | − | 0.387194i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4619.03i | − | 0.767024i | −0.923536 | − | 0.383512i | \(-0.874714\pi\) | ||
0.923536 | − | 0.383512i | \(-0.125286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5487.14 | − | 5212.25i | 0.902984 | − | 0.857746i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17009.1 | −2.77405 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4891.93 | −0.790743 | −0.395371 | − | 0.918521i | \(-0.629384\pi\) | ||||
−0.395371 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −130.690 | + | 52.1773i | −0.0209383 | + | 0.00835954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2381.14i | − | 0.378141i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3177.97i | 0.500275i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1855.80 | − | 740.919i | 0.289602 | − | 0.115622i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2572.15 | −0.397926 | −0.198963 | − | 0.980007i | \(-0.563757\pi\) | ||||
−0.198963 | + | 0.980007i | \(0.563757\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −345.160 | −0.0529398 | −0.0264699 | − | 0.999650i | \(-0.508427\pi\) | ||||
−0.0264699 | + | 0.999650i | \(0.508427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1656.88 | − | 762.348i | −0.251959 | − | 0.115929i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2193.51i | 0.330733i | 0.986232 | + | 0.165366i | \(0.0528807\pi\) | ||||
−0.986232 | + | 0.165366i | \(0.947119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 15715.9i | − | 2.34961i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 392.167 | + | 982.271i | 0.0581391 | + | 0.145623i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9166.56 | −1.34761 | −0.673805 | − | 0.738909i | \(-0.735341\pi\) | ||||
−0.673805 | + | 0.738909i | \(0.735341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3442.61 | 0.501911 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1910.37 | + | 4784.95i | 0.276221 | + | 0.691858i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15875.6i | − | 2.27662i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9153.52i | − | 1.30193i | −0.759106 | − | 0.650967i | \(-0.774363\pi\) | ||
0.759106 | − | 0.650967i | \(-0.225637\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 926.995 | + | 975.885i | 0.130779 | + | 0.137676i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1229.27 | 0.172023 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7204.23 | −1.00006 | −0.500028 | − | 0.866009i | \(-0.666677\pi\) | ||||
−0.500028 | + | 0.866009i | \(0.666677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8802.93 | + | 3514.53i | −1.21222 | + | 0.483972i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 856.303i | 0.116981i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5029.01i | − | 0.681591i | −0.940137 | − | 0.340795i | \(-0.889304\pi\) | ||
0.940137 | − | 0.340795i | \(-0.110696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1485.45 | + | 593.060i | −0.199743 | + | 0.0797464i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −361.928 | −0.0482864 | −0.0241432 | − | 0.999709i | \(-0.507686\pi\) | ||||
−0.0241432 | + | 0.999709i | \(0.507686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1646.97 | −0.218019 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6259.71 | + | 6589.85i | 0.822220 | + | 0.865584i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6275.67i | 0.817966i | 0.912542 | + | 0.408983i | \(0.134117\pi\) | ||||
−0.912542 | + | 0.408983i | \(0.865883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 875.666i | 0.113259i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3027.88 | − | 7584.00i | −0.388642 | − | 0.973441i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5692.00 | 0.725053 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6850.54 | 0.866042 | 0.433021 | − | 0.901384i | \(-0.357448\pi\) | ||||
0.433021 | + | 0.901384i | \(0.357448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 539.771 | + | 1351.98i | 0.0677252 | + | 0.169633i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 170.197i | 0.0211951i | 0.999944 | + | 0.0105976i | \(0.00337337\pi\) | ||||
−0.999944 | + | 0.0105976i | \(0.996627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1680.10i | 0.207672i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13577.7 | + | 698.156i | 1.66588 | + | 0.0856584i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5164.36 | −0.628962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10435.9 | 1.26167 | 0.630836 | − | 0.775916i | \(-0.282712\pi\) | ||||
0.630836 | + | 0.775916i | \(0.282712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12381.3 | − | 4943.18i | 1.48595 | − | 0.593258i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 460.751i | 0.0548961i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7355.77i | − | 0.870074i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5475.87 | + | 2186.21i | −0.643056 | + | 0.256737i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16146.5 | 1.88260 | 0.941300 | − | 0.337572i | \(-0.109606\pi\) | ||||
0.941300 | + | 0.337572i | \(0.109606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3152.04 | −0.364896 | −0.182448 | − | 0.983216i | \(-0.558402\pi\) | ||||
−0.182448 | + | 0.983216i | \(0.558402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9436.80 | − | 8964.04i | 1.08471 | − | 1.03037i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9462.00i | − | 1.07994i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1320.03i | − | 0.149603i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 461.468 | + | 1155.85i | 0.0519345 | + | 0.130082i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3825.08 | 0.427489 | 0.213744 | − | 0.976890i | \(-0.431434\pi\) | ||||
0.213744 | + | 0.976890i | \(0.431434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12260.9 | −1.36079 | −0.680394 | − | 0.732846i | \(-0.738192\pi\) | ||||
−0.680394 | + | 0.732846i | \(0.738192\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2366.80 | − | 5928.19i | −0.260872 | − | 0.653413i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1205.25i | 0.131933i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17157.7i | 1.86535i | 0.360714 | + | 0.932677i | \(0.382533\pi\) | ||||
−0.360714 | + | 0.932677i | \(0.617467\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6264.81 | + | 5950.95i | −0.676472 | + | 0.642582i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11111.1 | 1.19166 | 0.595831 | − | 0.803110i | \(-0.296823\pi\) | ||||
0.595831 | + | 0.803110i | \(0.296823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25336.4 | −2.69901 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13867.3 | + | 5536.44i | −1.46734 | + | 0.585827i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2795.70i | 0.293847i | 0.989148 | + | 0.146924i | \(0.0469371\pi\) | ||||
−0.989148 | + | 0.146924i | \(0.953063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 918.478i | − | 0.0958968i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4335.92 | + | 1731.10i | −0.449711 | + | 0.179545i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1162.08 | 0.119734 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3631.78 | −0.371745 | −0.185872 | − | 0.982574i | \(-0.559511\pi\) | ||||
−0.185872 | + | 0.982574i | \(0.559511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2490.32 | + | 5412.44i | −0.253242 | + | 0.550395i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12251.8i | 1.23780i | 0.785471 | + | 0.618898i | \(0.212421\pi\) | ||||
−0.785471 | + | 0.618898i | \(0.787579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13122.3i | 1.31716i | 0.752510 | + | 0.658581i | \(0.228843\pi\) | ||||
−0.752510 | + | 0.658581i | \(0.771157\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4643.76 | − | 11631.4i | −0.463117 | − | 1.15998i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14522.9 | 1.43905 | 0.719526 | − | 0.694465i | \(-0.244359\pi\) | ||||
0.719526 | + | 0.694465i | \(0.244359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4371.50 | −0.430398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2013.83 | + | 5044.08i | 0.197011 | + | 0.493459i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6202.20i | − | 0.602912i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 13023.3i | − | 1.25800i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4769.02 | + | 5020.54i | 0.457775 | + | 0.481918i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17609.3 | −1.67973 | −0.839864 | − | 0.542797i | \(-0.817365\pi\) | ||||
−0.839864 | + | 0.542797i | \(0.817365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3643.90 | 0.345421 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 476.956 | − | 190.423i | 0.0449322 | − | 0.0179390i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4879.50i | 0.456839i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7159.66i | − | 0.666191i | −0.942893 | − | 0.333096i | \(-0.891907\pi\) | ||
0.942893 | − | 0.333096i | \(-0.108093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17530.1 | + | 6998.81i | −1.62114 | + | 0.647233i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3170.70 | 0.291429 | 0.145714 | − | 0.989327i | \(-0.453452\pi\) | ||||
0.145714 | + | 0.989327i | \(0.453452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2797.24 | 0.255540 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6389.49 | − | 6726.47i | −0.580174 | − | 0.610773i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4039.12i | − | 0.364546i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 397.678i | − | 0.0356764i | −0.999841 | − | 0.0178382i | \(-0.994322\pi\) | ||
0.999841 | − | 0.0178382i | \(-0.00567838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4151.05 | − | 10397.3i | −0.370170 | − | 0.927175i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18268.3 | 1.61937 | 0.809684 | − | 0.586866i | \(-0.199638\pi\) | ||||
0.809684 | + | 0.586866i | \(0.199638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2550.12 | 0.224711 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −325.606 | − | 815.554i | −0.0285220 | − | 0.0714399i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8371.51i | 0.728999i | 0.931204 | + | 0.364500i | \(0.118760\pi\) | ||||
−0.931204 | + | 0.364500i | \(0.881240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4080.17i | − | 0.353221i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3427.63 | + | 7449.58i | −0.294997 | + | 0.641144i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23369.2 | −1.99956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8881.68 | −0.755543 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20257.1 | + | 8087.54i | −1.71327 | + | 0.684015i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10212.7i | − | 0.858781i | −0.903119 | − | 0.429391i | \(-0.858728\pi\) | ||
0.903119 | − | 0.429391i | \(-0.141272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8118.39i | 0.678761i | 0.940649 | + | 0.339381i | \(0.110217\pi\) | ||||
−0.940649 | + | 0.339381i | \(0.889783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5153.75 | + | 2057.61i | −0.428434 | + | 0.171050i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5488.30 | 0.453651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11741.8 | −0.965054 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1881.78 | + | 1787.51i | −0.153790 | + | 0.146085i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 648.066i | 0.0526658i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19226.9i | 1.55374i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4951.63 | + | 12402.5i | 0.397911 | + | 0.996659i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5896.28 | 0.471188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18079.1 | −1.43675 | −0.718376 | − | 0.695655i | \(-0.755114\pi\) | ||||
−0.718376 | + | 0.695655i | \(0.755114\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3636.21 | + | 9107.72i | 0.287375 | + | 0.719797i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 35729.9i | − | 2.80826i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14018.2i | 1.09575i | 0.836561 | + | 0.547873i | \(0.184562\pi\) | ||||
−0.836561 | + | 0.547873i | \(0.815438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5391.20 | − | 5121.11i | 0.419109 | − | 0.398112i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3850.07 | 0.297674 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1462.89 | 0.112493 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25226.7 | + | 10071.7i | −1.92940 | + | 0.770303i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11757.3i | − | 0.894386i | −0.894437 | − | 0.447193i | \(-0.852424\pi\) | ||
0.894437 | − | 0.447193i | \(-0.147576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4376.19i | 0.331115i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3775.76 | − | 1507.45i | 0.284158 | − | 0.113449i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13391.8 | 1.00248 | 0.501241 | − | 0.865308i | \(-0.332877\pi\) | ||||
0.501241 | + | 0.865308i | \(0.332877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 505.066 | 0.0376076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3489.59 | + | 179.432i | 0.258464 | + | 0.0132900i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11097.2i | 0.817610i | 0.912622 | + | 0.408805i | \(0.134054\pi\) | ||||
−0.912622 | + | 0.408805i | \(0.865946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7889.44i | 0.578218i | 0.957296 | + | 0.289109i | \(0.0933591\pi\) | ||||
−0.957296 | + | 0.289109i | \(0.906641\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −270.421 | − | 677.330i | −0.0197155 | − | 0.0493820i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4594.42 | −0.333218 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4722.33 | 0.340716 | 0.170358 | − | 0.985382i | \(-0.445508\pi\) | ||||
0.170358 | + | 0.985382i | \(0.445508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −456.015 | − | 1142.19i | −0.0327311 | − | 0.0819825i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1890.50i | − | 0.134993i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4725.21i | − | 0.335674i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4508.34 | + | 4746.11i | 0.318627 | + | 0.335432i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22243.9 | −1.56406 | −0.782030 | − | 0.623241i | \(-0.785816\pi\) | ||||
−0.782030 | + | 0.623241i | \(0.785816\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7553.99 | 0.528450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4849.35 | − | 1936.08i | 0.337522 | − | 0.134754i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3564.68i | 0.246853i | 0.992354 | + | 0.123426i | \(0.0393883\pi\) | ||||
−0.992354 | + | 0.123426i | \(0.960612\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3796.10i | − | 0.261554i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3238.92 | − | 1293.12i | 0.222044 | − | 0.0886499i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8614.13 | 0.587586 | 0.293793 | − | 0.955869i | \(-0.405082\pi\) | ||||
0.293793 | + | 0.955869i | \(0.405082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6578.32 | −0.446481 | −0.223241 | − | 0.974763i | \(-0.571664\pi\) | ||||
−0.223241 | + | 0.974763i | \(0.571664\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16959.4 | − | 17853.9i | −1.14534 | − | 1.20575i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 18492.0i | − | 1.24265i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26046.8i | 1.74169i | 0.491556 | + | 0.870846i | \(0.336428\pi\) | ||||
−0.491556 | + | 0.870846i | \(0.663572\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −608.289 | − | 1523.60i | −0.0404747 | − | 0.101378i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6266.80 | 0.414939 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10126.5 | 0.667218 | 0.333609 | − | 0.942712i | \(-0.391734\pi\) | ||||
0.333609 | + | 0.942712i | \(0.391734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1791.24 | − | 4486.56i | −0.117447 | − | 0.294172i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4115.13i | 0.268507i | 0.990947 | + | 0.134253i | \(0.0428636\pi\) | ||||
−0.990947 | + | 0.134253i | \(0.957136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7782.81i | 0.505359i | 0.967550 | + | 0.252680i | \(0.0813119\pi\) | ||||
−0.967550 | + | 0.252680i | \(0.918688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2628.09 | + | 1209.21i | 0.169826 | + | 0.0781385i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6511.67 | −0.418756 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6168.51 | 0.394784 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5196.88 | − | 2074.83i | 0.331010 | − | 0.132154i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 11903.3i | − | 0.754559i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19254.9i | − | 1.21478i | −0.794404 | − | 0.607390i | \(-0.792217\pi\) | ||
0.794404 | − | 0.607390i | \(-0.207783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22193.0 | + | 8860.43i | −1.39351 | + | 0.556352i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5740.70 | 0.358760 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4160.34 | −0.258773 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16496.4 | − | 15670.0i | 1.02126 | − | 0.970101i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16504.5i | 1.01699i | 0.861066 | + | 0.508494i | \(0.169798\pi\) | ||||
−0.861066 | + | 0.508494i | \(0.830202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27292.3i | 1.67388i | 0.547297 | + | 0.836938i | \(0.315657\pi\) | ||||
−0.547297 | + | 0.836938i | \(0.684343\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12095.7 | − | 30296.4i | −0.738398 | − | 1.84949i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30929.0 | −1.87936 | −0.939680 | − | 0.342054i | \(-0.888877\pi\) | ||||
−0.939680 | + | 0.342054i | \(0.888877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1771.08 | 0.107120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1193.49 | − | 2989.36i | −0.0718533 | − | 0.179973i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2637.30i | 0.158048i | 0.996873 | + | 0.0790241i | \(0.0251804\pi\) | ||||
−0.996873 | + | 0.0790241i | \(0.974820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29309.2i | 1.74841i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16664.1 | − | 15829.2i | 0.989540 | − | 0.939966i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23789.8 | −1.40625 | −0.703126 | − | 0.711065i | \(-0.748213\pi\) | ||||
−0.703126 | + | 0.711065i | \(0.748213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19417.3 | 1.14258 | 0.571290 | − | 0.820748i | \(-0.306443\pi\) | ||||
0.571290 | + | 0.820748i | \(0.306443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2664.13 | + | 1063.64i | −0.156057 | + | 0.0623052i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5224.87i | − | 0.304680i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1358.24i | − | 0.0788476i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8657.17 | + | 3456.33i | −0.500307 | + | 0.199745i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5074.06 | −0.291925 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12145.5 | 0.695656 | 0.347828 | − | 0.937558i | \(-0.386919\pi\) | ||||
0.347828 | + | 0.937558i | \(0.386919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28397.8 | − | 13066.1i | −1.61931 | − | 0.745060i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22646.3i | 1.28562i | 0.766024 | + | 0.642812i | \(0.222232\pi\) | ||||
−0.766024 | + | 0.642812i | \(0.777768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1254.08i | 0.0708792i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8456.06 | + | 21180.1i | 0.475825 | + | 1.19181i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33551.7 | −1.87968 | −0.939840 | − | 0.341614i | \(-0.889026\pi\) | ||||
−0.939840 | + | 0.341614i | \(0.889026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47849.0 | −2.66893 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3361.40 | + | 8419.39i | 0.186675 | + | 0.467569i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3334.04i | 0.184350i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 19643.0i | − | 1.08141i | −0.841211 | − | 0.540707i | \(-0.818157\pi\) | ||
0.841211 | − | 0.540707i | \(-0.181843\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1642.15 | − | 1728.76i | −0.0900148 | − | 0.0947623i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21162.1 | 1.15500 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2117.00 | 0.115046 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29178.0 | − | 11649.2i | 1.57885 | − | 0.630347i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33965.0i | − | 1.83002i | −0.403435 | − | 0.915008i | \(-0.632184\pi\) | ||
0.403435 | − | 0.915008i | \(-0.367816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16383.5i | − | 0.878971i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43385.0 | + | 17321.3i | −2.31770 | + | 0.925329i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 655.404 | 0.0348642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12160.9 | 0.644166 | 0.322083 | − | 0.946711i | \(-0.395617\pi\) | ||||
0.322083 | + | 0.946711i | \(0.395617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5675.38 | + | 5974.70i | 0.299358 | + | 0.315146i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2664.93i | − | 0.139975i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4466.92i | − | 0.233641i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4589.39 | − | 11495.2i | −0.239043 | − | 0.598737i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30972.1 | 1.60649 | 0.803243 | − | 0.595652i | \(-0.203106\pi\) | ||||
0.803243 | + | 0.595652i | \(0.203106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6006.10 | −0.310234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9559.45 | + | 23943.8i | 0.491729 | + | 1.23165i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14676.5i | 0.751821i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18943.9i | 0.966425i | 0.875503 | + | 0.483212i | \(0.160530\pi\) | ||||
−0.875503 | + | 0.483212i | \(0.839470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12805.2 | + | 14948.2i | 0.650572 | + | 0.759445i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14295.5 | 0.723306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5511.95 | 0.277747 | 0.138873 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138873 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28802.0 | − | 11499.1i | 1.44541 | − | 0.577074i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16803.6i | 0.839850i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13044.0i | 0.649298i | 0.945835 | + | 0.324649i | \(0.105246\pi\) | ||||
−0.945835 | + | 0.324649i | \(0.894754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3666.85 | + | 1463.97i | −0.181788 | + | 0.0725781i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12314.1 | −0.608021 | −0.304010 | − | 0.952669i | \(-0.598326\pi\) | ||||
−0.304010 | + | 0.952669i | \(0.598326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53591.7 | 2.63550 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7721.10 | − | 7334.29i | 0.378180 | − | 0.359234i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4941.48i | 0.241065i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18037.7i | − | 0.876436i | −0.898869 | − | 0.438218i | \(-0.855610\pi\) | ||
0.898869 | − | 0.438218i | \(-0.144390\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7961.56 | − | 19941.5i | −0.385306 | − | 0.965086i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16756.7 | 0.807731 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8852.23 | −0.425020 | −0.212510 | − | 0.977159i | \(-0.568164\pi\) | ||||
−0.212510 | + | 0.977159i | \(0.568164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −731.967 | − | 1833.38i | −0.0350049 | − | 0.0876776i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15773.5i | 0.751365i | 0.926748 | + | 0.375683i | \(0.122592\pi\) | ||||
−0.926748 | + | 0.375683i | \(0.877408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9182.90i | − | 0.435706i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15503.9 | − | 14727.2i | 0.732737 | − | 0.696028i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1249.65 | −0.0588297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15893.5 | 0.745296 | 0.372648 | − | 0.927973i | \(-0.378450\pi\) | ||||
0.372648 | + | 0.927973i | \(0.378450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35080.3 | − | 14005.6i | 1.63863 | − | 0.654217i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12767.1i | 0.594049i | 0.954870 | + | 0.297025i | \(0.0959943\pi\) | ||||
−0.954870 | + | 0.297025i | \(0.904006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28795.9i | 1.33468i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6483.50 | + | 2588.50i | −0.299349 | + | 0.119514i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2913.80 | 0.134015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15526.0 | −0.711349 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3862.73 | − | 8395.22i | 0.176300 | − | 0.383168i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19493.4i | − | 0.886306i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1198.97i | 0.0543057i | 0.999631 | + | 0.0271529i | \(0.00864408\pi\) | ||||
−0.999631 | + | 0.0271529i | \(0.991356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7711.87 | + | 19316.1i | 0.347972 | + | 0.871574i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 129.806 | 0.00583487 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3580.19 | 0.160323 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9215.22 | − | 23081.6i | −0.411107 | − | 1.02971i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40863.5i | 1.81613i | 0.418825 | + | 0.908067i | \(0.362442\pi\) | ||||
−0.418825 | + | 0.908067i | \(0.637558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20471.4i | − | 0.906416i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25262.4 | − | 26594.7i | −1.11436 | − | 1.17313i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15683.8 | −0.689252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1843.25 | −0.0807032 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19441.7 | + | 7762.00i | −0.848054 | + | 0.338582i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6162.20i | 0.267801i | 0.990995 | + | 0.133901i | \(0.0427503\pi\) | ||||
−0.990995 | + | 0.133901i | \(0.957250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30637.4i | − | 1.32654i | −0.748381 | − | 0.663269i | \(-0.769168\pi\) | ||
0.748381 | − | 0.663269i | \(-0.230832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16723.8 | − | 6676.89i | 0.721437 | − | 0.288030i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 67747.1 | 2.91175 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19676.0 | 0.842565 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1158.68 | + | 1219.79i | 0.0494355 | + | 0.0520427i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41698.5i | 1.77258i | 0.463131 | + | 0.886290i | \(0.346726\pi\) | ||||
−0.463131 | + | 0.886290i | \(0.653274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15087.6i | 0.639029i | 0.947581 | + | 0.319514i | \(0.103520\pi\) | ||||
−0.947581 | + | 0.319514i | \(0.896480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7909.26 | + | 19810.5i | 0.333776 | + | 0.836017i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22253.3 | −0.935701 | −0.467850 | − | 0.883808i | \(-0.654971\pi\) | ||||
−0.467850 | + | 0.883808i | \(0.654971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6763.95 | −0.283380 | −0.141690 | − | 0.989911i | \(-0.545254\pi\) | ||||
−0.141690 | + | 0.989911i | \(0.545254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17680.1 | − | 44283.9i | −0.738047 | − | 1.84860i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13590.3i | 0.565279i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40181.4i | 1.66531i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7578.83 | − | 16471.8i | 0.312978 | − | 0.680224i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35137.5 | −1.44586 | −0.722932 | − | 0.690919i | \(-0.757206\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20050.2 | 0.822101 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20198.4 | − | 8064.12i | 0.825232 | − | 0.329470i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3151.80i | 0.128314i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4752.60i | − | 0.192800i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7743.53 | + | 3091.57i | −0.313024 | + | 0.124973i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5779.85 | −0.232821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46756.8 | −1.87681 | −0.938407 | − | 0.345531i | \(-0.887699\pi\) | ||||
−0.938407 | + | 0.345531i | \(0.887699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21339.2 | − | 20270.2i | 0.853551 | − | 0.810790i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 46686.1i | − | 1.86087i | −0.366454 | − | 0.930436i | \(-0.619428\pi\) | ||
0.366454 | − | 0.930436i | \(-0.380572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32547.1i | − | 1.29278i | −0.763009 | − | 0.646388i | \(-0.776279\pi\) | ||
0.763009 | − | 0.646388i | \(-0.223721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −460.364 | − | 1153.09i | −0.0182220 | − | 0.0456412i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19498.4 | 0.769102 | 0.384551 | − | 0.923104i | \(-0.374356\pi\) | ||||
0.384551 | + | 0.923104i | \(0.374356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 78285.8 | 3.07722 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5991.16 | − | 15006.2i | −0.234683 | − | 0.587817i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5623.23i | − | 0.219511i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11856.4i | − | 0.461239i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5121.85 | + | 4865.25i | −0.198566 | + | 0.188618i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8743.42 | 0.337808 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34603.0 | 1.33234 | 0.666170 | − | 0.745800i | \(-0.267933\pi\) | ||||
0.666170 | + | 0.745800i | \(0.267933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31415.5 | − | 12542.5i | 1.20548 | − | 0.481283i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21333.9i | 0.815843i | 0.913017 | + | 0.407922i | \(0.133746\pi\) | ||||
−0.913017 | + | 0.407922i | \(0.866254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28520.0i | 1.08695i | 0.839426 | + | 0.543474i | \(0.182892\pi\) | ||||
−0.839426 | + | 0.543474i | \(0.817108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8651.36 | − | 3454.01i | 0.328601 | − | 0.131193i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43303.3 | −1.63921 | −0.819606 | − | 0.572928i | \(-0.805808\pi\) | ||||
−0.819606 | + | 0.572928i | \(0.805808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1475.41 | 0.0556622 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 689.720 | − | 13413.6i | 0.0259332 | − | 0.504348i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 28176.4i | − | 1.05587i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 47930.7i | − | 1.79011i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 516.466 | + | 1293.61i | 0.0192244 | + | 0.0481519i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8512.89 | −0.315818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10891.1 | 0.402704 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3108.70 | − | 7786.43i | −0.114564 | − | 0.286950i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 35197.8i | − | 1.29283i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41510.0i | 1.51965i | 0.650130 | + | 0.759823i | \(0.274714\pi\) | ||||
−0.650130 | + | 0.759823i | \(0.725286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2542.68 | + | 2676.78i | 0.0927780 | + | 0.0976712i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7424.35 | 0.270010 | 0.135005 | − | 0.990845i | \(-0.456895\pi\) | ||||
0.135005 | + | 0.990845i | \(0.456895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7266.90 | −0.263417 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24785.7 | + | 9895.56i | −0.895507 | + | 0.357527i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7532.73i | 0.271268i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17469.0i | 0.627039i | 0.949582 | + | 0.313519i | \(0.101508\pi\) | ||||
−0.949582 | + | 0.313519i | \(0.898492\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5836.91 | − | 2330.36i | 0.208830 | − | 0.0833745i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10954.9 | 0.390668 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62454.1 | 2.21998 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23301.0 | − | 24529.9i | −0.825571 | − | 0.869112i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44640.1i | 1.57653i | 0.615336 | + | 0.788265i | \(0.289020\pi\) | ||||
−0.615336 | + | 0.788265i | \(0.710980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18705.5i | 0.658483i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10216.4 | − | 25589.3i | −0.358489 | − | 0.897918i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14591.8 | −0.510379 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24243.0 | 0.845235 | 0.422618 | − | 0.906308i | \(-0.361111\pi\) | ||||
0.422618 | + | 0.906308i | \(0.361111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2958.78 | + | 7410.94i | 0.102829 | + | 0.257558i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 45703.7i | − | 1.58331i | −0.610966 | − | 0.791657i | \(-0.709219\pi\) | ||
0.610966 | − | 0.791657i | \(-0.290781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1027.94i | − | 0.0354978i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11393.0 | − | 5242.05i | −0.392186 | − | 0.180449i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33165.0 | 1.13803 | 0.569017 | − | 0.822326i | \(-0.307324\pi\) | ||||
0.569017 | + | 0.822326i | \(0.307324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11066.3 | 0.378532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27668.3 | − | 11046.5i | 0.943436 | − | 0.376662i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 9676.78i | − | 0.328921i | −0.986384 | − | 0.164460i | \(-0.947412\pi\) | ||
0.986384 | − | 0.164460i | \(-0.0525883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2617.62i | 0.0886954i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5856.56 | + | 2338.20i | −0.197822 | + | 0.0789795i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12297.6 | −0.414088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13088.4 | 0.439339 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20181.8 | + | 19170.7i | −0.675336 | + | 0.641503i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4414.13i | 0.147250i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30085.9i | − | 1.00051i | −0.865877 | − | 0.500257i | \(-0.833239\pi\) | ||
0.865877 | − | 0.500257i | \(-0.166761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4782.28 | + | 11978.3i | 0.158544 | + | 0.397109i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23229.4 | −0.767732 | −0.383866 | − | 0.923389i | \(-0.625408\pi\) | ||||
−0.383866 | + | 0.923389i | \(0.625408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5438.85 | 0.179200 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5580.67 | − | 13978.1i | −0.183307 | − | 0.459134i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 10271.5i | − | 0.336351i | −0.985757 | − | 0.168176i | \(-0.946212\pi\) | ||
0.985757 | − | 0.168176i | \(-0.0537876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25030.3i | 0.817131i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37504.5 | − | 35625.5i | 1.22062 | − | 1.15947i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26200.0 | −0.850103 | −0.425052 | − | 0.905169i | \(-0.639744\pi\) | ||||
−0.425052 | + | 0.905169i | \(0.639744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18740.9 | −0.606227 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11150.3 | + | 4451.72i | −0.359594 | + | 0.143566i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6941.38i | − | 0.223178i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33380.1i | 1.06998i | 0.844858 | + | 0.534991i | \(0.179685\pi\) | ||||
−0.844858 | + | 0.534991i | \(0.820315\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22290.4 | + | 8899.32i | −0.712349 | + | 0.284402i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12517.2 | −0.398815 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39447.8 | −1.25308 | −0.626541 | − | 0.779388i | \(-0.715530\pi\) | ||||
−0.626541 | + | 0.779388i | \(0.715530\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35724.9 | − | 16437.4i | −1.13142 | − | 0.520577i |
(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 | 624.4.d.c.287.9 | ✓ | 24 | |
3.2 | odd | 2 | inner | 624.4.d.c.287.15 | yes | 24 | |
4.3 | odd | 2 | inner | 624.4.d.c.287.16 | yes | 24 | |
12.11 | even | 2 | inner | 624.4.d.c.287.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.4.d.c.287.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
624.4.d.c.287.10 | yes | 24 | 12.11 | even | 2 | inner | |
624.4.d.c.287.15 | yes | 24 | 3.2 | odd | 2 | inner | |
624.4.d.c.287.16 | yes | 24 | 4.3 | odd | 2 | inner |