Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.19 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.2 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | ||||||||
\(3\) | 2.90590i | 1.67772i | 0.544343 | + | 0.838862i | \(0.316779\pi\) | ||||
−0.544343 | + | 0.838862i | \(0.683221\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.726535 | − | 2.23605i | −0.324916 | − | 0.999990i | −0.971478 | − | 0.237129i | \(-0.923794\pi\) |
0.646562 | − | 0.762862i | \(-0.276206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | − | 0.809017i | −0.222162 | − | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.44428 | −1.81476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.77283 | − | 1.55079i | −1.43906 | − | 0.467580i | −0.517458 | − | 0.855708i | \(-0.673122\pi\) |
−0.921605 | + | 0.388128i | \(0.873122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.248079 | − | 0.341451i | 0.0688046 | − | 0.0947014i | −0.773228 | − | 0.634128i | \(-0.781359\pi\) |
0.842032 | + | 0.539427i | \(0.181359\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.49774 | − | 2.11124i | 1.67771 | − | 0.545121i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.89651 | + | 1.91589i | 1.43011 | + | 0.464672i | 0.918801 | − | 0.394722i | \(-0.129159\pi\) |
0.511314 | + | 0.859394i | \(0.329159\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.733357 | + | 1.00938i | 0.168244 | + | 0.231567i | 0.884811 | − | 0.465951i | \(-0.154288\pi\) |
−0.716567 | + | 0.697518i | \(0.754288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.35093 | − | 1.70805i | 0.513014 | − | 0.372727i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51563 | − | 1.82771i | −0.524545 | − | 0.381104i | 0.293768 | − | 0.955877i | \(-0.405091\pi\) |
−0.818313 | + | 0.574772i | \(0.805091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.426963 | + | 0.310207i | −0.0853925 | + | 0.0620413i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 7.10286i | − | 1.36695i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.39618 | − | 2.40316i | 1.37344 | − | 0.446256i | 0.472930 | − | 0.881100i | \(-0.343196\pi\) |
0.900506 | + | 0.434844i | \(0.143196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65461 | − | 5.09237i | 0.297177 | − | 0.914617i | −0.685304 | − | 0.728257i | \(-0.740331\pi\) |
0.982481 | − | 0.186360i | \(-0.0596692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50644 | − | 13.8694i | 0.784471 | − | 2.41435i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.38195 | + | 1.90209i | −0.233593 | + | 0.321513i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.61986 | − | 11.1408i | −0.595102 | − | 1.83154i | −0.554218 | − | 0.832372i | \(-0.686982\pi\) |
−0.0408844 | − | 0.999164i | \(-0.513018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.992224 | + | 0.720893i | 0.158883 | + | 0.115435i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.63509 | − | 5.27126i | 0.567705 | − | 0.823232i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.80506 | + | 2.76454i | 0.580266 | + | 0.421588i | 0.838820 | − | 0.544409i | \(-0.183246\pi\) |
−0.258554 | + | 0.965997i | \(0.583246\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.95546 | + | 12.1737i | 0.589646 | + | 1.81474i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.46898 | − | 6.15102i | 0.651868 | − | 0.897219i | −0.347310 | − | 0.937750i | \(-0.612905\pi\) |
0.999178 | + | 0.0405311i | \(0.0129050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.56740 | + | 17.1347i | −0.779592 | + | 2.39934i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.91995 | − | 2.89827i | 1.22525 | − | 0.398108i | 0.376259 | − | 0.926515i | \(-0.377210\pi\) |
0.848991 | + | 0.528407i | \(0.177210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7990i | 1.59097i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.93316 | + | 2.13107i | −0.388507 | + | 0.282267i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.13002 | − | 6.63335i | −1.18863 | − | 0.863589i | −0.195509 | − | 0.980702i | \(-0.562636\pi\) |
−0.993119 | + | 0.117113i | \(0.962636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00070 | + | 2.90668i | −0.512237 | + | 0.372162i | −0.813672 | − | 0.581325i | \(-0.802535\pi\) |
0.301434 | + | 0.953487i | \(0.402535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.20007 | + | 4.40452i | 0.403171 | + | 0.554917i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.943738 | − | 0.306639i | −0.117056 | − | 0.0380339i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.17082 | + | 2.65486i | −0.998224 | + | 0.324343i | −0.762156 | − | 0.647394i | \(-0.775859\pi\) |
−0.236068 | + | 0.971736i | \(0.575859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.31116 | − | 7.31018i | 0.639388 | − | 0.880043i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.69294 | − | 1.19991i | −0.438271 | − | 0.142403i | 0.0815668 | − | 0.996668i | \(-0.474008\pi\) |
−0.519838 | + | 0.854265i | \(0.674008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.525670 | 0.0615250 | 0.0307625 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307625 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.901431 | − | 1.24071i | −0.104088 | − | 0.143265i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.55079 | + | 4.77283i | 0.176729 | + | 0.543915i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5264i | 1.40933i | 0.709542 | + | 0.704663i | \(0.248902\pi\) | ||||
−0.709542 | + | 0.704663i | \(0.751098\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30737 | 0.478597 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.32207 | 0.145116 | 0.0725579 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725579 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 14.5768i | − | 1.58108i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.98337 | + | 21.4926i | 0.748695 | + | 2.30425i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.80911 | − | 7.99555i | −0.615764 | − | 0.847527i | 0.381272 | − | 0.924463i | \(-0.375486\pi\) |
−0.997036 | + | 0.0769361i | \(0.975486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.422057 | −0.0442435 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.7980 | + | 4.80815i | 1.53448 | + | 0.498582i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.72421 | − | 2.37317i | 0.176900 | − | 0.243482i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.11564 | + | 2.31201i | −0.722484 | + | 0.234749i | −0.647100 | − | 0.762405i | \(-0.724018\pi\) |
−0.0753842 | + | 0.997155i | \(0.524018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25.9847 | + | 8.44293i | 2.61156 | + | 0.848546i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.102287 | + | 0.140786i | 0.0101779 | + | 0.0140087i | 0.814076 | − | 0.580759i | \(-0.197244\pi\) |
−0.803898 | + | 0.594768i | \(0.797244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.73237 | − | 4.89135i | 0.663360 | − | 0.481959i | −0.204436 | − | 0.978880i | \(-0.565536\pi\) |
0.867796 | + | 0.496921i | \(0.165536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.52731 | − | 4.01582i | −0.539410 | − | 0.391904i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.43783 | + | 1.77119i | −0.235674 | + | 0.171227i | −0.699354 | − | 0.714776i | \(-0.746529\pi\) |
0.463680 | + | 0.886003i | \(0.346529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.16999i | 0.590978i | 0.955346 | + | 0.295489i | \(0.0954825\pi\) | ||||
−0.955346 | + | 0.295489i | \(0.904517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.3741 | − | 10.5190i | 3.07281 | − | 0.998418i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.59020 | − | 17.2049i | 0.525881 | − | 1.61850i | −0.236685 | − | 0.971587i | \(-0.576061\pi\) |
0.762566 | − | 0.646910i | \(-0.223939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.25915 | + | 6.95296i | −0.210667 | + | 0.648367i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.35061 | + | 1.85896i | −0.124864 | + | 0.171860i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.91589 | − | 5.89651i | −0.175630 | − | 0.540532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.4758 | + | 8.33767i | 1.04326 | + | 0.757970i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.3178 | + | 10.5632i | 1.38116 | + | 0.952453i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.50663 | − | 6.18043i | −0.760856 | − | 0.552794i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.82882 | − | 17.9393i | −0.517224 | − | 1.59185i | −0.779198 | − | 0.626777i | \(-0.784373\pi\) |
0.261974 | − | 0.965075i | \(-0.415627\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.03348 | + | 11.0571i | −0.707308 | + | 0.973526i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.79703 | − | 5.53070i | 0.157008 | − | 0.483220i | −0.841351 | − | 0.540489i | \(-0.818239\pi\) |
0.998359 | + | 0.0572692i | \(0.0182393\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.385549 | − | 1.18660i | 0.0334313 | − | 0.102891i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.8823 | + | 5.16048i | −1.36693 | + | 0.444143i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8668i | 1.35560i | 0.735248 | + | 0.677798i | \(0.237066\pi\) | ||||
−0.735248 | + | 0.677798i | \(0.762934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3953 | + | 10.4588i | −1.22099 | + | 0.887101i | −0.996182 | − | 0.0873019i | \(-0.972176\pi\) |
−0.224808 | + | 0.974403i | \(0.572176\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.8743 | + | 12.9864i | 1.50529 | + | 1.09365i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.71356 | + | 1.24497i | −0.143295 | + | 0.104110i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7472 | − | 14.7922i | −0.892504 | − | 1.22843i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.76368 | − | 0.897974i | −0.227944 | − | 0.0740636i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.08749 | − | 0.678266i | 0.171014 | − | 0.0555657i | −0.222259 | − | 0.974988i | \(-0.571343\pi\) |
0.393272 | + | 0.919422i | \(0.371343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.56570 | + | 6.28414i | −0.371551 | + | 0.511396i | −0.953322 | − | 0.301957i | \(-0.902360\pi\) |
0.581771 | + | 0.813353i | \(0.302360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32.1023 | − | 10.4307i | −2.59532 | − | 0.843269i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5889 | −1.01117 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.58928 | − | 11.8221i | −0.685499 | − | 0.943509i | 0.314484 | − | 0.949263i | \(-0.398168\pi\) |
−0.999983 | + | 0.00575395i | \(0.998168\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.42209 | + | 25.9205i | 0.667915 | + | 2.05563i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.10949i | 0.245062i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3868 | −0.813556 | −0.406778 | − | 0.913527i | \(-0.633348\pi\) | ||||
−0.406778 | + | 0.913527i | \(0.633348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −34.2867 | −2.66922 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.923298i | − | 0.0714470i | −0.999362 | − | 0.0357235i | \(-0.988626\pi\) | ||
0.999362 | − | 0.0357235i | \(-0.0113736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.96218 | + | 12.1943i | 0.304783 | + | 0.938025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.99260 | − | 5.49535i | −0.305322 | − | 0.420240i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.214787 | −0.0163299 | −0.00816496 | − | 0.999967i | \(-0.502599\pi\) | ||||
−0.00816496 | + | 0.999967i | \(0.502599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.501925 | + | 0.163085i | 0.0379419 | + | 0.0123281i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.2759 | − | 26.5310i | 1.44886 | − | 1.99419i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9289 | − | 7.45005i | 1.71379 | − | 0.556843i | 0.722830 | − | 0.691026i | \(-0.242841\pi\) |
0.990957 | + | 0.134183i | \(0.0428409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.62666 | + | 0.528533i | 0.120908 | + | 0.0392855i | 0.368846 | − | 0.929490i | \(-0.379753\pi\) |
−0.247938 | + | 0.968776i | \(0.579753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.44653 | − | 11.6257i | −0.624385 | − | 0.859393i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.2814 | + | 16.1884i | −1.63816 | + | 1.19019i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.1719 | − | 18.2885i | −1.84075 | − | 1.33739i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.74633 | + | 4.17495i | −0.417984 | + | 0.303683i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.33542i | 0.458415i | 0.973378 | + | 0.229208i | \(0.0736135\pi\) | ||||
−0.973378 | + | 0.229208i | \(0.926387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00704 | − | 0.652128i | 0.144470 | − | 0.0469412i | −0.235889 | − | 0.971780i | \(-0.575800\pi\) |
0.380359 | + | 0.924839i | \(0.375800\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.891064 | − | 2.74241i | 0.0638104 | − | 0.196388i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.43110 | + | 7.48217i | −0.173209 | + | 0.533083i | −0.999547 | − | 0.0300917i | \(-0.990420\pi\) |
0.826338 | + | 0.563174i | \(0.190420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2737 | − | 18.2697i | 0.940947 | − | 1.29510i | −0.0144862 | − | 0.999895i | \(-0.504611\pi\) |
0.955433 | − | 0.295207i | \(-0.0953888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.71477 | − | 23.7436i | −0.544158 | − | 1.67475i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.29156 | − | 4.57109i | −0.441581 | − | 0.320828i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.4278 | − | 4.29846i | −1.00768 | − | 0.300218i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.6958 | + | 9.95058i | 0.951924 | + | 0.691613i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.93486 | − | 5.95488i | −0.133837 | − | 0.411908i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.66055 | + | 6.41469i | −0.320845 | + | 0.441606i | −0.938725 | − | 0.344667i | \(-0.887992\pi\) |
0.617880 | + | 0.786273i | \(0.287992\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.48682 | − | 10.7313i | 0.238913 | − | 0.735298i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.41712 | − | 10.5168i | 0.233046 | − | 0.717241i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.09237 | + | 1.65461i | −0.345693 | + | 0.112322i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.52755i | 0.103222i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.11698 | − | 1.53808i | 0.142404 | − | 0.103462i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.66151 | + | 4.83987i | 0.446088 | + | 0.324102i | 0.788049 | − | 0.615612i | \(-0.211091\pi\) |
−0.341961 | + | 0.939714i | \(0.611091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.32451 | − | 1.68885i | 0.154967 | − | 0.112590i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.2206 | − | 20.9494i | −1.01023 | − | 1.39046i | −0.918834 | − | 0.394643i | \(-0.870868\pi\) |
−0.0913924 | − | 0.995815i | \(-0.529132\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7491 | + | 4.14245i | 0.842487 | + | 0.273741i | 0.698296 | − | 0.715809i | \(-0.253942\pi\) |
0.144191 | + | 0.989550i | \(0.453942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.8694 | + | 4.50644i | −0.912540 | + | 0.296502i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.887101 | + | 1.22099i | −0.0581159 | + | 0.0799897i | −0.837086 | − | 0.547072i | \(-0.815742\pi\) |
0.778970 | + | 0.627061i | \(0.215742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.0008 | − | 5.52391i | −1.10901 | − | 0.360340i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −36.4004 | −2.36446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.7379 | + | 24.4141i | 1.14737 | + | 1.57922i | 0.749825 | + | 0.661637i | \(0.230138\pi\) |
0.397545 | + | 0.917583i | \(0.369862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.87693 | + | 15.0097i | 0.314151 | + | 0.966857i | 0.976103 | + | 0.217311i | \(0.0697284\pi\) |
−0.661952 | + | 0.749547i | \(0.730272\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.79175i | − | 0.563991i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.35112 | 0.150207 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.526584 | 0.0335057 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.84181i | 0.243465i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.17207 | − | 12.8403i | −0.263339 | − | 0.810473i | −0.992072 | − | 0.125675i | \(-0.959890\pi\) |
0.728733 | − | 0.684798i | \(-0.240110\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.17229 | + | 12.6246i | 0.576657 | + | 0.793700i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 42.3589 | 2.65262 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00094 | − | 0.975064i | −0.187193 | − | 0.0608228i | 0.213920 | − | 0.976851i | \(-0.431377\pi\) |
−0.401114 | + | 0.916028i | \(0.631377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.88539 | + | 9.47693i | −0.427837 | + | 0.588868i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.2669 | + | 13.0835i | −2.49246 | + | 0.809849i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.81843 | + | 3.19020i | 0.605430 | + | 0.196716i | 0.595661 | − | 0.803236i | \(-0.296890\pi\) |
0.00976941 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9613 | − | 17.8397i | −0.796208 | − | 1.09589i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.2343 | − | 16.8807i | 1.42192 | − | 1.03308i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1783 | − | 12.4808i | −1.04738 | − | 0.760966i | −0.0756673 | − | 0.997133i | \(-0.524109\pi\) |
−0.971712 | + | 0.236167i | \(0.924109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1341 | − | 9.54251i | 0.797842 | − | 0.579666i | −0.112438 | − | 0.993659i | \(-0.535866\pi\) |
0.910280 | + | 0.413993i | \(0.135866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.22646i | − | 0.0742285i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.51889 | − | 0.818436i | 0.151895 | − | 0.0493535i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.48606 | + | 23.0397i | −0.449794 | + | 1.38432i | 0.427346 | + | 0.904088i | \(0.359449\pi\) |
−0.877140 | + | 0.480235i | \(0.840551\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.00818 | + | 27.7243i | −0.539306 | + | 1.65981i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.39227 | − | 8.79820i | 0.381331 | − | 0.524857i | −0.574606 | − | 0.818430i | \(-0.694845\pi\) |
0.955936 | + | 0.293574i | \(0.0948446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.74286 | + | 11.5193i | 0.222490 | + | 0.684754i | 0.998537 | + | 0.0540784i | \(0.0172221\pi\) |
−0.776047 | + | 0.630676i | \(0.782778\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.89621 | + | 5.01039i | 0.408496 | + | 0.296790i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.40119 | + | 0.157521i | −0.377850 | + | 0.00929815i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.3449 | + | 12.6018i | 1.02029 | + | 0.741284i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.71849 | − | 20.6774i | −0.393845 | − | 1.21213i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.35516 | − | 4.61798i | 0.196010 | − | 0.269785i | −0.699687 | − | 0.714450i | \(-0.746677\pi\) |
0.895697 | + | 0.444665i | \(0.146677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.19919 | + | 25.2345i | −0.477375 | + | 1.46921i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.0150 | + | 33.9008i | −0.639156 | + | 1.96712i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.24815 | + | 0.405548i | −0.0721823 | + | 0.0234534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.70331i | − | 0.271094i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.409110 | + | 0.297236i | −0.0235028 | + | 0.0170757i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.40612 | + | 6.83394i | 0.538593 | + | 0.391310i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5160 | − | 13.4527i | 1.05676 | − | 0.767784i | 0.0832770 | − | 0.996526i | \(-0.473461\pi\) |
0.973487 | + | 0.228742i | \(0.0734614\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2138 | + | 19.5636i | 0.808595 | + | 1.11294i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.82919 | − | 2.86878i | −0.500658 | − | 0.162674i | 0.0477917 | − | 0.998857i | \(-0.484782\pi\) |
−0.548449 | + | 0.836184i | \(0.684782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.217363 | − | 0.0706255i | 0.0122861 | − | 0.00399199i | −0.302868 | − | 0.953033i | \(-0.597944\pi\) |
0.315154 | + | 0.949041i | \(0.397944\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.52374 | − | 10.3555i | 0.423915 | − | 0.583469i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.2440 | − | 9.17702i | −1.58634 | − | 0.515433i | −0.622659 | − | 0.782493i | \(-0.713948\pi\) |
−0.963680 | + | 0.267061i | \(0.913948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.0275 | −2.18512 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.14691 | − | 7.08411i | −0.287272 | − | 0.395397i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.39039 | + | 7.35685i | 0.133005 | + | 0.409346i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.222742i | 0.0123555i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.9294 | −0.991498 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.60308 | −0.419172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.3341i | − | 0.952766i | −0.879238 | − | 0.476383i | \(-0.841948\pi\) | ||
0.879238 | − | 0.476383i | \(-0.158052\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.7076 | + | 60.6537i | 1.07997 | + | 3.32380i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8728 | + | 16.3415i | 0.648679 | + | 0.892830i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4045 | −0.730192 | −0.365096 | − | 0.930970i | \(-0.618964\pi\) | ||||
−0.365096 | + | 0.930970i | \(0.618964\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 49.9957 | + | 16.2446i | 2.71539 | + | 0.882284i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7944 | + | 21.7391i | −0.855314 | + | 1.17724i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | − | 0.309017i | 0.0513522 | − | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.2046 | − | 6.56489i | −1.08778 | − | 0.353442i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4823 | + | 21.3096i | 0.831135 | + | 1.14396i | 0.987711 | + | 0.156293i | \(0.0499543\pi\) |
−0.156576 | + | 0.987666i | \(0.550046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3479 | + | 14.0571i | −1.03567 | + | 0.752458i | −0.969436 | − | 0.245346i | \(-0.921099\pi\) |
−0.0662344 | + | 0.997804i | \(0.521099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.42528 | − | 1.76207i | −0.129452 | − | 0.0940521i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7863 | − | 19.4614i | 1.42569 | − | 1.03583i | 0.434892 | − | 0.900482i | \(-0.356786\pi\) |
0.990799 | − | 0.135343i | \(-0.0432136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.12935i | 0.484536i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.1347 | − | 5.56740i | 0.906865 | − | 0.294658i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.82170 | − | 8.68431i | 0.148924 | − | 0.458340i | −0.848571 | − | 0.529082i | \(-0.822537\pi\) |
0.997495 | + | 0.0707414i | \(0.0225365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.39029 | − | 16.5896i | 0.283699 | − | 0.873137i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.2285 | + | 33.3476i | −1.27167 | + | 1.75030i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.381918 | − | 1.17542i | −0.0199905 | − | 0.0615244i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.83816 | + | 2.06204i | 0.148151 | + | 0.107638i | 0.659392 | − | 0.751800i | \(-0.270814\pi\) |
−0.511241 | + | 0.859437i | \(0.670814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.7904 | + | 28.6982i | −1.03025 | + | 1.49397i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.58777 | − | 5.51283i | −0.393937 | − | 0.286212i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.127453 | − | 0.392260i | −0.00659926 | − | 0.0203104i | 0.947703 | − | 0.319155i | \(-0.103399\pi\) |
−0.954302 | + | 0.298844i | \(0.903399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.9597 | − | 24.7195i | 0.927437 | − | 1.27651i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.01427 | − | 3.12160i | 0.0522376 | − | 0.160771i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.73524 | + | 11.4959i | −0.191866 | + | 0.590504i | 0.808132 | + | 0.589001i | \(0.200479\pi\) |
−0.999999 | + | 0.00150332i | \(0.999521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.1298 | − | 16.9380i | 2.67069 | − | 0.867760i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.3337i | 1.54998i | 0.631973 | + | 0.774990i | \(0.282245\pi\) | ||||
−0.631973 | + | 0.774990i | \(0.717755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.54557 | − | 6.93527i | 0.486488 | − | 0.353454i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.7158 | − | 15.0509i | −1.05304 | − | 0.765081i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3750 | − | 9.71751i | 0.678140 | − | 0.492697i | −0.194600 | − | 0.980883i | \(-0.562341\pi\) |
0.872740 | + | 0.488185i | \(0.162341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3317 | − | 15.5968i | −0.573071 | − | 0.788764i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0717 | + | 5.22201i | 0.810709 | + | 0.263415i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0095 | − | 9.10085i | 1.40931 | − | 0.457913i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.67368 | + | 9.18553i | −0.334942 | + | 0.461008i | −0.942956 | − | 0.332918i | \(-0.891967\pi\) |
0.608013 | + | 0.793927i | \(0.291967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.44814 | + | 1.12037i | 0.172623 | + | 0.0560885i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.6870 | 1.98187 | 0.990937 | − | 0.134331i | \(-0.0428885\pi\) | ||||
0.990937 | + | 0.134331i | \(0.0428885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.32832 | − | 1.82828i | −0.0661684 | − | 0.0910730i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.12946 | − | 9.63148i | −0.155504 | − | 0.478592i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 58.7868i | 2.91395i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.81376 | −0.238025 | −0.119012 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119012 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.1075 | −2.27432 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2853i | 0.555315i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.960529 | − | 2.95621i | −0.0471505 | − | 0.145114i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.3922 | − | 41.8313i | −1.48831 | − | 2.04849i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.06373 | 0.100820 | 0.0504099 | − | 0.998729i | \(-0.483947\pi\) | ||||
0.0504099 | + | 0.998729i | \(0.483947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8001 | + | 5.13376i | 0.770049 | + | 0.250204i | 0.667586 | − | 0.744533i | \(-0.267328\pi\) |
0.102463 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.3304 | + | 33.4879i | −1.18298 | + | 1.62824i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.11191 | + | 1.01112i | −0.150950 | + | 0.0490466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.70310 | + | 1.52813i | 0.227599 | + | 0.0739514i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.61777 | − | 4.97943i | −0.174667 | − | 0.240409i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.3663 | − | 22.0624i | 1.46269 | − | 1.06271i | 0.480042 | − | 0.877245i | \(-0.340621\pi\) |
0.982651 | − | 0.185464i | \(-0.0593787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.70515 | + | 1.23887i | 0.0819444 | + | 0.0595361i | 0.628003 | − | 0.778211i | \(-0.283872\pi\) |
−0.546059 | + | 0.837747i | \(0.683872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42.9848 | − | 31.2302i | 2.06096 | − | 1.49738i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.87959i | − | 0.185586i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.09799 | − | 1.33152i | 0.195587 | − | 0.0635499i | −0.209586 | − | 0.977790i | \(-0.567212\pi\) |
0.405172 | + | 0.914240i | \(0.367212\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68238 | − | 5.17782i | 0.0801131 | − | 0.246563i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.99947 | + | 21.5422i | −0.332555 | + | 1.02350i | 0.635359 | + | 0.772217i | \(0.280852\pi\) |
−0.967914 | + | 0.251282i | \(0.919148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6579 | + | 18.7985i | −0.647447 | + | 0.891134i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.97098 | + | 6.06604i | 0.0932240 | + | 0.286914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.57166 | + | 6.22767i | 0.404521 | + | 0.293902i | 0.771380 | − | 0.636375i | \(-0.219567\pi\) |
−0.366859 | + | 0.930277i | \(0.619567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.5243 | + | 19.5216i | −1.20189 | + | 0.919236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.2611 | − | 13.2675i | −0.857982 | − | 0.623360i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.306639 | + | 0.943738i | 0.0143755 | + | 0.0442431i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.120284 | + | 0.165557i | −0.00562667 | + | 0.00774445i | −0.811821 | − | 0.583906i | \(-0.801524\pi\) |
0.806194 | + | 0.591651i | \(0.201524\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6083 | − | 41.8821i | 0.635182 | − | 1.95489i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.45306 | + | 22.9382i | −0.347124 | + | 1.06834i | 0.613313 | + | 0.789840i | \(0.289836\pi\) |
−0.960437 | + | 0.278497i | \(0.910164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7040 | + | 3.47793i | −0.497455 | + | 0.161633i | −0.546990 | − | 0.837139i | \(-0.684226\pi\) |
0.0495342 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 36.5822i | − | 1.69646i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.9050 | − | 19.5476i | 1.24501 | − | 0.904556i | 0.247093 | − | 0.968992i | \(-0.420525\pi\) |
0.997922 | + | 0.0644357i | \(0.0205247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95051 | + | 5.04984i | 0.320945 | + | 0.233180i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.3540 | − | 24.9596i | 1.58295 | − | 1.15008i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8737 | − | 19.0955i | −0.637913 | − | 0.878012i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.626232 | − | 0.203475i | −0.0287335 | − | 0.00933608i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −48.5628 | + | 15.7790i | −2.22354 | + | 0.722471i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.1855 | − | 34.6649i | 1.15076 | − | 1.58388i | 0.410030 | − | 0.912072i | \(-0.365518\pi\) |
0.740726 | − | 0.671808i | \(-0.234482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.70205 | − | 1.52779i | −0.214395 | − | 0.0696611i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.03588 | −0.411147 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3395 | + | 14.2311i | 0.469494 | + | 0.646203i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.17612 | + | 9.77511i | 0.143924 | + | 0.442952i | 0.996871 | − | 0.0790450i | \(-0.0251871\pi\) |
−0.852947 | + | 0.521997i | \(0.825187\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 30.1830i | − | 1.36492i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.5980 | −0.974703 | −0.487352 | − | 0.873206i | \(-0.662037\pi\) | ||||
−0.487352 | + | 0.873206i | \(0.662037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.2159 | 2.17153 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 64.2370i | − | 2.88724i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.19991 | + | 3.69294i | 0.0538232 | + | 0.165651i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7697 | − | 25.8342i | −0.840246 | − | 1.15650i | −0.985928 | − | 0.167168i | \(-0.946538\pi\) |
0.145682 | − | 0.989331i | \(-0.453462\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.68302 | 0.119868 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.6161 | + | 10.2727i | 1.40969 | + | 0.458036i | 0.912311 | − | 0.409497i | \(-0.134296\pi\) |
0.497379 | + | 0.867533i | \(0.334296\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.240488 | − | 0.331004i | 0.0107016 | − | 0.0147295i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.4355 | + | 11.5137i | −1.57375 | + | 0.511342i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.14726 | − | 2.64721i | −0.361121 | − | 0.117335i | 0.122836 | − | 0.992427i | \(-0.460801\pi\) |
−0.483957 | + | 0.875092i | \(0.660801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.308981 | − | 0.425276i | −0.0136685 | − | 0.0188131i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.16948 | − | 5.20893i | 0.316540 | − | 0.229980i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8286 | − | 11.5001i | −0.697491 | − | 0.506757i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.8686 | + | 22.4274i | −1.35760 | + | 0.986355i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.624150i | − | 0.0273971i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.98370 | − | 2.59406i | 0.349772 | − | 0.113648i | −0.128861 | − | 0.991663i | \(-0.541132\pi\) |
0.478634 | + | 0.878015i | \(0.341132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.969993 | + | 2.98533i | −0.0424149 | + | 0.130539i | −0.970022 | − | 0.243019i | \(-0.921862\pi\) |
0.927607 | + | 0.373558i | \(0.121862\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.473910 | + | 1.45855i | −0.0206831 | + | 0.0636561i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.5129 | − | 26.8572i | 0.849995 | − | 1.16992i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.11953 | − | 12.6786i | −0.179110 | − | 0.551244i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.7064 | + | 36.1138i | 2.15708 | + | 1.56721i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.898088 | − | 2.54889i | −0.0389005 | − | 0.110405i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.73163 | + | 4.16428i | 0.247800 | + | 0.180037i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.6491 | + | 66.6292i | 0.934230 | + | 2.87526i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.94977 | − | 4.06002i | 0.127056 | − | 0.174877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6485 | − | 38.9280i | 0.543800 | − | 1.67364i | −0.180027 | − | 0.983662i | \(-0.557619\pi\) |
0.723827 | − | 0.689982i | \(-0.242381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.53587 | + | 4.72691i | −0.0659103 | + | 0.202851i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.7964 | − | 4.48271i | 0.590972 | − | 0.192018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1156i | 0.518024i | 0.965874 | + | 0.259012i | \(0.0833970\pi\) | ||||
−0.965874 | + | 0.259012i | \(0.916603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.7809 | − | 15.8248i | 0.929588 | − | 0.675385i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.84974 | + | 5.70317i | 0.334410 | + | 0.242963i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1340 | − | 7.36282i | 0.430943 | − | 0.313099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −47.0419 | − | 64.7476i | −1.99682 | − | 2.74838i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.6203 | − | 12.2236i | −1.59402 | − | 0.517930i | −0.628405 | − | 0.777887i | \(-0.716292\pi\) |
−0.965620 | + | 0.259957i | \(0.916292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.88791 | − | 0.613418i | 0.0798499 | − | 0.0259448i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 53.1446 | − | 73.1472i | 2.24377 | − | 3.08828i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0115 | + | 4.55261i | 0.590514 | + | 0.191869i | 0.589005 | − | 0.808129i | \(-0.299520\pi\) |
0.00150854 | + | 0.999999i | \(0.499520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.5323 | −1.78935 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.53181 | − | 3.48474i | −0.106326 | − | 0.146345i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1768 | + | 34.3988i | 0.468557 | + | 1.44207i | 0.854453 | + | 0.519528i | \(0.173892\pi\) |
−0.385896 | + | 0.922542i | \(0.626108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.78334i | 0.242025i | 0.992651 | + | 0.121013i | \(0.0386142\pi\) | ||||
−0.992651 | + | 0.121013i | \(0.961386\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.4101 | −0.769095 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.64105 | 0.0684365 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 46.0210i | − | 1.91588i | −0.286968 | − | 0.957940i | \(-0.592647\pi\) | ||
0.286968 | − | 0.957940i | \(-0.407353\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.89502 | + | 5.83227i | 0.0787544 | + | 0.242381i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.777092 | − | 1.06958i | −0.0322392 | − | 0.0443735i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.0681 | −1.94936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.13798 | + | 1.66943i | 0.212429 | + | 0.0690224i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.85118 | + | 13.5590i | −0.406602 | + | 0.559639i | −0.962386 | − | 0.271687i | \(-0.912418\pi\) |
0.555784 | + | 0.831327i | \(0.312418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.35356 | − | 2.06440i | 0.261794 | − | 0.0850620i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.7425 | − | 7.06456i | −0.894366 | − | 0.290597i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4632 | − | 15.7777i | −0.470737 | − | 0.647914i | 0.505955 | − | 0.862560i | \(-0.331140\pi\) |
−0.976692 | + | 0.214646i | \(0.931140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7929 | + | 8.56805i | −0.483462 | + | 0.351256i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.0899 | + | 38.5721i | 2.17283 | + | 1.57865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.56803 | − | 3.31887i | 0.186645 | − | 0.135605i | −0.490539 | − | 0.871419i | \(-0.663200\pi\) |
0.677184 | + | 0.735814i | \(0.263200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.2231i | − | 0.580172i | −0.957001 | − | 0.290086i | \(-0.906316\pi\) | ||
0.957001 | − | 0.290086i | \(-0.0936839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.4842 | − | 14.4538i | 1.81154 | − | 0.588604i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3058 | − | 31.7181i | 0.418991 | − | 1.28952i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.11043 | + | 9.57292i | −0.126248 | + | 0.388553i | −0.994126 | − | 0.108225i | \(-0.965483\pi\) |
0.867878 | + | 0.496777i | \(0.165483\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.2831 | − | 18.2827i | 0.538260 | − | 0.740852i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.991614 | − | 3.05187i | −0.0401164 | − | 0.123466i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8404 | + | 24.5865i | 1.36680 | + | 0.993038i | 0.997979 | + | 0.0635371i | \(0.0202381\pi\) |
0.368820 | + | 0.929501i | \(0.379762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.4909 | − | 41.9258i | 0.503683 | − | 1.69061i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.3094 | − | 13.3025i | −0.737107 | − | 0.535540i | 0.154697 | − | 0.987962i | \(-0.450560\pi\) |
−0.891804 | + | 0.452422i | \(0.850560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8023 | + | 33.2459i | 0.434180 | + | 1.33627i | 0.893925 | + | 0.448217i | \(0.147941\pi\) |
−0.459745 | + | 0.888051i | \(0.652059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.9820 | + | 17.8682i | −0.520949 | + | 0.717025i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.05403 | + | 9.39934i | −0.122357 | + | 0.376576i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.45478 | + | 26.0211i | −0.338191 | + | 1.04085i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3043 | − | 5.62251i | 0.691068 | − | 0.224542i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 72.6271i | − | 2.89583i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.2156 | + | 29.2183i | −1.60096 | + | 1.16316i | −0.715306 | + | 0.698812i | \(0.753713\pi\) |
−0.885651 | + | 0.464351i | \(0.846287\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.6405 | − | 13.5431i | −0.740893 | − | 0.538290i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.8782 | + | 26.0670i | −1.42378 | + | 1.03444i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.248079 | + | 0.341451i | 0.00982923 | + | 0.0135288i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.1054 | + | 6.53264i | 0.795357 | + | 0.258427i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.2980 | + | 4.64570i | −0.564737 | + | 0.183494i | −0.577451 | − | 0.816425i | \(-0.695953\pi\) |
0.0127146 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4655 | + | 28.1684i | −0.807081 | + | 1.11085i | 0.184686 | + | 0.982798i | \(0.440873\pi\) |
−0.991767 | + | 0.128055i | \(0.959127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.5609 | + | 9.92983i | 1.20333 | + | 0.390987i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3856 | −0.998012 | −0.499006 | − | 0.866599i | \(-0.666301\pi\) | ||||
−0.499006 | + | 0.866599i | \(0.666301\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.2892 | + | 45.8186i | 1.30671 | + | 1.79854i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.80815 | − | 14.7980i | −0.188446 | − | 0.579978i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 12.1027i | − | 0.473615i | −0.971557 | − | 0.236808i | \(-0.923899\pi\) | ||
0.971557 | − | 0.236808i | \(-0.0761011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.6725 | −0.534229 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.86189 | −0.111653 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.99529i | 0.194589i | 0.995256 | + | 0.0972945i | \(0.0310189\pi\) | ||||
−0.995256 | + | 0.0972945i | \(0.968981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.93165 | − | 24.4111i | −0.308505 | − | 0.949482i | −0.978346 | − | 0.206977i | \(-0.933637\pi\) |
0.669840 | − | 0.742505i | \(-0.266363\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.46951 | + | 6.15175i | 0.173581 | + | 0.238914i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.93340 | −0.113752 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.9983 | − | 7.47261i | −0.890499 | − | 0.289341i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0642 | + | 19.3577i | −0.543754 | + | 0.748413i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.6023 | − | 7.66886i | 0.911157 | − | 0.296053i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.8851 | − | 6.46106i | −0.766514 | − | 0.249056i | −0.100442 | − | 0.994943i | \(-0.532026\pi\) |
−0.666072 | + | 0.745887i | \(0.732026\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.20335 | + | 3.03265i | 0.0848071 | + | 0.116727i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.9123 | + | 7.92828i | −0.419395 | + | 0.304708i | −0.777394 | − | 0.629013i | \(-0.783459\pi\) |
0.357999 | + | 0.933722i | \(0.383459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.05293 | + | 4.39771i | 0.232290 | + | 0.168769i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 60.8769 | − | 44.2296i | 2.33281 | − | 1.69488i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.4682i | − | 0.744930i | −0.928046 | − | 0.372465i | \(-0.878513\pi\) | ||
0.928046 | − | 0.372465i | \(-0.121487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.4790 | − | 11.5278i | 1.35558 | − | 0.440455i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.0376 | + | 37.0478i | −0.459261 | + | 1.41346i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.22323 | − | 3.76472i | 0.0466015 | − | 0.143425i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.8862 | + | 20.4891i | −0.566297 | + | 0.779441i | −0.992110 | − | 0.125370i | \(-0.959988\pi\) |
0.425813 | + | 0.904811i | \(0.359988\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.44293 | − | 25.9847i | −0.320720 | − | 0.987076i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.8450 | + | 24.5898i | 1.28381 | + | 0.932744i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5335 | − | 24.1176i | 1.19442 | − | 0.913519i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.54808 | − | 2.57783i | −0.134201 | − | 0.0975025i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.50977 | + | 16.9573i | 0.208101 | + | 0.640469i | 0.999572 | + | 0.0292620i | \(0.00931570\pi\) |
−0.791471 | + | 0.611207i | \(0.790684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.59064 | − | 11.8240i | 0.324002 | − | 0.445951i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0520 | − | 49.4028i | 0.604552 | − | 1.86062i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0537754 | − | 0.165504i | 0.00202243 | − | 0.00622440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5175 | + | 6.34162i | −0.732995 | + | 0.238164i | −0.651648 | − | 0.758521i | \(-0.725922\pi\) |
−0.0813467 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 68.1971i | − | 2.55759i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.4698 | + | 9.78637i | −0.504448 | + | 0.366503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.02877 | + | 2.92707i | 0.150668 | + | 0.109466i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −70.9452 | + | 51.5447i | −2.64950 | + | 1.92497i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.18710 | + | 7.13943i | 0.193446 | + | 0.266256i | 0.894711 | − | 0.446645i | \(-0.147381\pi\) |
−0.701265 | + | 0.712900i | \(0.747381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.91437 | − | 2.57153i | −0.294747 | − | 0.0957690i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.6166 | + | 14.1719i | −1.62212 | + | 0.527059i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.41241 | + | 3.32040i | −0.0895948 | + | 0.123317i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.79091 | + | 2.53142i | 0.288949 | + | 0.0938852i | 0.449905 | − | 0.893076i | \(-0.351458\pi\) |
−0.160956 | + | 0.986962i | \(0.551458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.4701 | 1.42482 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.1400 | + | 23.5912i | 0.633946 | + | 0.872552i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.73236 | + | 17.6424i | 0.211729 | + | 0.651636i | 0.999370 | + | 0.0355008i | \(0.0113026\pi\) |
−0.787640 | + | 0.616135i | \(0.788697\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.83212i | 0.252007i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.1151 | 1.58816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1266 | 1.40251 | 0.701256 | − | 0.712910i | \(-0.252623\pi\) | ||||
0.701256 | + | 0.712910i | \(0.252623\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.53020i | 0.0562134i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.54675 | + | 26.3042i | 0.313550 | + | 0.965007i | 0.976347 | + | 0.216209i | \(0.0693691\pi\) |
−0.662797 | + | 0.748799i | \(0.730631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.03327 | − | 4.17493i | −0.111130 | − | 0.152958i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.19772 | −0.263351 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.86585 | + | 0.931170i | 0.104716 | + | 0.0340242i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6308 | − | 18.7612i | 0.497395 | − | 0.684606i | −0.484335 | − | 0.874883i | \(-0.660938\pi\) |
0.981731 | + | 0.190276i | \(0.0609384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 37.3127 | − | 12.1236i | 1.35975 | − | 0.441810i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.3688 | + | 5.64345i | 0.632114 | + | 0.205386i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00729 | + | 11.0211i | 0.291030 | + | 0.400568i | 0.929348 | − | 0.369204i | \(-0.120370\pi\) |
−0.638318 | + | 0.769772i | \(0.720370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.6858 | + | 26.6538i | −1.33161 | + | 0.967472i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5410 | + | 16.3770i | 0.817111 | + | 0.593666i | 0.915884 | − | 0.401444i | \(-0.131492\pi\) |
−0.0987723 | + | 0.995110i | \(0.531492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.99163 | − | 3.62663i | 0.180709 | − | 0.131293i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 79.3604i | 2.86928i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.52993 | + | 1.47186i | −0.163566 | + | 0.0531459i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.18457 | + | 25.1895i | −0.295143 | + | 0.908357i | 0.688030 | + | 0.725682i | \(0.258476\pi\) |
−0.983173 | + | 0.182675i | \(0.941524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.83344 | − | 8.72044i | 0.102044 | − | 0.314059i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.59401 | − | 7.69950i | 0.201203 | − | 0.276932i | −0.696478 | − | 0.717578i | \(-0.745251\pi\) |
0.897681 | + | 0.440646i | \(0.145251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.873230 | + | 2.68753i | 0.0313673 | + | 0.0965388i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.5391 | − | 20.0083i | −0.987958 | − | 0.717793i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.98651 | − | 0.196532i | 0.286147 | − | 0.00704150i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.7650 | + | 11.4539i | 0.564115 | + | 0.409854i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.0693 | − | 52.5340i | −0.610008 | − | 1.87741i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1944 | + | 27.7952i | −0.720769 | + | 0.992054i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.83279 | + | 27.1845i | −0.314855 | + | 0.969024i | 0.660959 | + | 0.750422i | \(0.270150\pi\) |
−0.975814 | + | 0.218602i | \(0.929850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.27042 | + | 28.5314i | −0.330036 | + | 1.01575i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.2049 | + | 5.59020i | −0.611734 | + | 0.198765i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.08713i | 0.0741161i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 51.8406 | − | 37.6644i | 1.83860 | − | 1.33582i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.7194 | + | 22.3190i | 1.08814 | + | 0.790579i | 0.979084 | − | 0.203457i | \(-0.0652177\pi\) |
0.109054 | + | 0.994036i | \(0.465218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.1361 | − | 27.7075i | 1.34916 | − | 0.980221i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.6264 | + | 43.5301i | 1.11747 | + | 1.53806i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.50893 | − | 0.815202i | −0.0885384 | − | 0.0287679i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.95296 | − | 2.25915i | 0.245060 | − | 0.0796247i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.2679 | − | 49.9185i | 1.27669 | − | 1.75722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3720 | + | 8.24386i | 0.892031 | + | 0.289839i | 0.718944 | − | 0.695068i | \(-0.244626\pi\) |
0.173087 | + | 0.984906i | \(0.444626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.0874 | −1.33743 | −0.668715 | − | 0.743518i | \(-0.733156\pi\) | ||||
−0.668715 | + | 0.743518i | \(0.733156\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7296 | + | 38.1666i | 0.972520 | + | 1.33856i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.54637 | + | 23.2253i | 0.264338 | + | 0.813548i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.86814i | 0.205300i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.29780 | 0.0802915 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.5541 | −1.24085 | −0.620423 | − | 0.784267i | \(-0.713039\pi\) | ||||
−0.620423 | + | 0.784267i | \(0.713039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.9971i | − | 0.557623i | −0.960346 | − | 0.278812i | \(-0.910059\pi\) | ||
0.960346 | − | 0.278812i | \(-0.0899405\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.37830 | + | 7.31965i | 0.0828017 | + | 0.254837i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6402 | + | 17.3978i | 0.439544 | + | 0.604981i | 0.970111 | − | 0.242663i | \(-0.0780208\pi\) |
−0.530567 | + | 0.847643i | \(0.678021\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.11213 | −0.0386258 | −0.0193129 | − | 0.999813i | \(-0.506148\pi\) | ||||
−0.0193129 | + | 0.999813i | \(0.506148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −66.9512 | − | 21.7538i | −2.32251 | − | 0.754630i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.64424 | + | 5.01587i | −0.126266 | + | 0.173790i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.06454 | + | 0.670809i | −0.0714463 | + | 0.0232143i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.1704 | − | 11.7525i | −1.25023 | − | 0.406225i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.2982 | − | 34.8200i | −0.873392 | − | 1.20212i | −0.978208 | − | 0.207629i | \(-0.933425\pi\) |
0.104816 | − | 0.994492i | \(-0.466575\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.4667 | − | 18.5027i | 0.878164 | − | 0.638023i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.5667 | + | 18.5753i | 0.880565 | + | 0.639768i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.3884 | − | 17.7192i | 0.838987 | − | 0.609559i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.1849i | − | 0.487399i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.4741 | + | 10.8764i | −1.14883 | + | 0.373277i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2559 | + | 34.6422i | −0.385848 | + | 1.18752i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0190 | + | 36.9908i | −0.411524 | + | 1.26654i | 0.503800 | + | 0.863820i | \(0.331935\pi\) |
−0.915324 | + | 0.402719i | \(0.868065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.38708 | + | 12.9202i | −0.321031 | + | 0.441862i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.47298 | + | 4.53337i | 0.0503161 | + | 0.154857i | 0.973057 | − | 0.230563i | \(-0.0740567\pi\) |
−0.922741 | + | 0.385420i | \(0.874057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9500 | + | 7.95567i | 0.373610 | + | 0.271444i | 0.758706 | − | 0.651433i | \(-0.225832\pi\) |
−0.385096 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.457740 | − | 18.6012i | −0.0155997 | − | 0.633929i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0360 | − | 11.6508i | −0.545872 | − | 0.396599i | 0.280389 | − | 0.959886i | \(-0.409536\pi\) |
−0.826261 | + | 0.563287i | \(0.809536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.156050 | + | 0.480273i | 0.00530586 | + | 0.0163298i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.6197 | + | 50.4027i | −1.24367 | + | 1.71177i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.4257 | − | 59.7863i | 0.658973 | − | 2.02811i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12050 | + | 3.44855i | −0.0379667 | + | 0.116850i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.7396 | − | 12.5873i | 1.31114 | − | 0.426014i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5148i | 0.355464i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2499 | − | 7.44696i | 0.346113 | − | 0.251466i | −0.401123 | − | 0.916024i | \(-0.631380\pi\) |
0.747237 | + | 0.664558i | \(0.231380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.4194 | + | 9.74976i | 0.452625 | + | 0.328851i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.1736 | + | 27.7348i | −1.28610 | + | 0.934408i | −0.999719 | − | 0.0237066i | \(-0.992453\pi\) |
−0.286384 | + | 0.958115i | \(0.592453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.2691 | − | 32.0272i | −0.783069 | − | 1.07780i | −0.994937 | − | 0.100503i | \(-0.967955\pi\) |
0.211868 | − | 0.977298i | \(-0.432045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −73.3291 | − | 23.8261i | −2.46493 | − | 0.800905i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0475 | − | 7.81351i | 0.807437 | − | 0.262352i | 0.123925 | − | 0.992292i | \(-0.460452\pi\) |
0.683512 | + | 0.729939i | \(0.260452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.0871 | + | 15.2601i | −0.371849 | + | 0.511806i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5584 | − | 6.67982i | −0.688731 | − | 0.223782i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.48607 | 0.317439 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.3173 | − | 45.8574i | −1.11368 | − | 1.53284i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17848 | − | 3.62700i | −0.0393484 | − | 0.121102i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 41.6404i | − | 1.38879i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.1494 | 1.93724 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.6674 | 0.454822 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.02128i | − | 0.133672i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.2576 | + | 34.6473i | 0.373802 | + | 1.15044i | 0.944283 | + | 0.329133i | \(0.106757\pi\) |
−0.570482 | + | 0.821310i | \(0.693243\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.556878 | − | 0.766477i | −0.0184705 | − | 0.0254225i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.5202 | −1.27623 | −0.638116 | − | 0.769940i | \(-0.720286\pi\) | ||||
−0.638116 | + | 0.769940i | \(0.720286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.31001 | − | 2.05025i | −0.208831 | − | 0.0678533i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.8588 | + | 27.3333i | −0.656511 | + | 0.903610i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.53070 | + | 1.79703i | −0.182640 | + | 0.0593433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8337 | − | 3.84500i | −0.390357 | − | 0.126835i | 0.107261 | − | 0.994231i | \(-0.465792\pi\) |
−0.497618 | + | 0.867396i | \(0.665792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0922 | + | 53.8057i | 1.28813 | + | 1.77296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.32585 | + | 0.963285i | −0.0436408 | + | 0.0317069i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00150 | + | 3.63380i | 0.164448 | + | 0.119479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.6529 | + | 26.6299i | −1.20384 | + | 0.874641i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.97735i | − | 0.130493i | −0.997869 | − | 0.0652463i | \(-0.979217\pi\) | ||
0.997869 | − | 0.0652463i | \(-0.0207833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.18660 | + | 0.385549i | −0.0388891 | + | 0.0126358i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.33640 | − | 25.6568i | 0.272921 | − | 0.839966i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.6056 | + | 69.5728i | −0.739282 | + | 2.27527i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.9362 | + | 28.8162i | −0.683956 | + | 0.941385i | −0.999973 | − | 0.00736901i | \(-0.997654\pi\) |
0.316017 | + | 0.948754i | \(0.397654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.205231 | + | 0.631636i | 0.00669746 | + | 0.0206127i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.4388 | + | 16.3027i | 0.731484 | + | 0.531454i | 0.890033 | − | 0.455897i | \(-0.150681\pi\) |
−0.158548 | + | 0.987351i | \(0.550681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.7789 | + | 6.61664i | −0.611524 | + | 0.215468i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5103 | + | 9.81581i | 0.439490 | + | 0.319308i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6811 | + | 39.0285i | 0.412081 | + | 1.26826i | 0.914836 | + | 0.403826i | \(0.132320\pi\) |
−0.502755 | + | 0.864429i | \(0.667680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.130407 | − | 0.179490i | 0.00423320 | − | 0.00582650i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.6675 | − | 82.0742i | 0.864754 | − | 2.66144i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.2387 | + | 34.5891i | −0.364056 | + | 1.12045i | 0.586513 | + | 0.809939i | \(0.300500\pi\) |
−0.950570 | + | 0.310511i | \(0.899500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.1663 | − | 4.60291i | 0.458411 | − | 0.148947i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 113.410i | − | 3.66603i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8365 | − | 9.32630i | 0.414514 | − | 0.301162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.88500 | + | 1.36953i | 0.0608064 | + | 0.0441784i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.2723 | − | 9.64286i | 0.427693 | − | 0.310737i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.91637 | − | 4.01405i | −0.0938814 | − | 0.129217i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3418 | − | 5.63471i | −0.557676 | − | 0.181200i | 0.0165991 | − | 0.999862i | \(-0.494716\pi\) |
−0.574275 | + | 0.818662i | \(0.694716\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.3783 | + | 6.94623i | −0.686770 | + | 0.223145i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.88857 | − | 6.72854i | 0.156882 | − | 0.215929i | −0.723340 | − | 0.690492i | \(-0.757394\pi\) |
0.880222 | + | 0.474563i | \(0.157394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9226 | + | 5.49850i | 0.542515 | + | 0.176274i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.647268 | −0.0207292 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.1268 | + | 22.1966i | 0.515941 | + | 0.710132i | 0.984907 | − | 0.173084i | \(-0.0553733\pi\) |
−0.468966 | + | 0.883216i | \(0.655373\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3265 | + | 47.1701i | 0.489837 | + | 1.50756i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 33.5912i | − | 1.07248i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.3735 | −1.44719 | −0.723594 | − | 0.690226i | \(-0.757511\pi\) | ||||
−0.723594 | + | 0.690226i | \(0.757511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.4968 | 0.589356 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 22.0938i | − | 0.703255i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.51934 | − | 13.9091i | −0.143707 | − | 0.442284i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2903 | + | 29.3036i | 0.676310 | + | 0.930861i | 0.999882 | − | 0.0153429i | \(-0.00488398\pi\) |
−0.323573 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50.3711 | 1.59848 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.4956 | − | 16.4070i | −1.60082 | − | 0.520138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.2454 | − | 37.5001i | 0.862871 | − | 1.18764i | −0.118006 | − | 0.993013i | \(-0.537650\pi\) |
0.980877 | − | 0.194627i | \(-0.0623497\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −79.1315 | + | 25.7114i | −2.50361 | + | 0.813472i |
(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 | 1148.2.ba.a.113.19 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.2 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.19 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.2 | yes | 80 | 41.4 | even | 10 | inner |