Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.3 | ||
Root | \(0.277956 - 0.213283i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.h.493.3 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 1.86367 | + | 1.87796i | 0.704402 | + | 0.709801i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.74315 | − | 4.75127i | −0.827091 | − | 1.43256i | −0.900311 | − | 0.435247i | \(-0.856661\pi\) |
0.0732202 | − | 0.997316i | \(-0.476672\pi\) | |||||||
\(12\) | −0.258819 | − | 0.965926i | −0.0747146 | − | 0.278839i | ||||
\(13\) | −2.41668 | − | 2.41668i | −0.670266 | − | 0.670266i | 0.287511 | − | 0.957777i | \(-0.407172\pi\) |
−0.957777 | + | 0.287511i | \(0.907172\pi\) | |||||||
\(14\) | 2.28622 | + | 1.33161i | 0.611018 | + | 0.355889i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 2.04607 | + | 0.548242i | 0.496244 | + | 0.132968i | 0.498256 | − | 0.867030i | \(-0.333974\pi\) |
−0.00201209 | + | 0.999998i | \(0.500640\pi\) | |||||||
\(18\) | −0.965926 | − | 0.258819i | −0.227671 | − | 0.0610042i | ||||
\(19\) | 3.49797 | − | 6.05866i | 0.802489 | − | 1.38995i | −0.115485 | − | 0.993309i | \(-0.536842\pi\) |
0.917974 | − | 0.396642i | \(-0.129824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.29632 | − | 1.31412i | 0.501098 | − | 0.286764i | ||||
\(22\) | −3.87940 | − | 3.87940i | −0.827091 | − | 0.827091i | ||||
\(23\) | 0.454069 | + | 1.69461i | 0.0946800 | + | 0.353350i | 0.996971 | − | 0.0777776i | \(-0.0247824\pi\) |
−0.902291 | + | 0.431128i | \(0.858116\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.95981 | − | 1.70885i | −0.580467 | − | 0.335133i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.55297 | + | 0.694523i | 0.482465 | + | 0.131252i | ||||
\(29\) | 0.684610i | 0.127129i | 0.997978 | + | 0.0635644i | \(0.0202468\pi\) | ||||
−0.997978 | + | 0.0635644i | \(0.979753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82932 | − | 2.78821i | 0.867371 | − | 0.500777i | 0.000897301 | − | 1.00000i | \(-0.499714\pi\) |
0.866474 | + | 0.499223i | \(0.166381\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | −5.29936 | + | 1.41996i | −0.922500 | + | 0.247183i | ||||
\(34\) | 2.11825 | 0.363276 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 9.46620 | − | 2.53646i | 1.55623 | − | 0.416992i | 0.624765 | − | 0.780813i | \(-0.285195\pi\) |
0.931469 | + | 0.363821i | \(0.118528\pi\) | |||||||
\(38\) | 1.81068 | − | 6.75755i | 0.293731 | − | 1.09622i | ||||
\(39\) | −2.95981 | + | 1.70885i | −0.473950 | + | 0.273635i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50597i | 0.391366i | 0.980667 | + | 0.195683i | \(0.0626924\pi\) | ||||
−0.980667 | + | 0.195683i | \(0.937308\pi\) | |||||||
\(42\) | 1.87796 | − | 1.86367i | 0.289775 | − | 0.287571i | ||||
\(43\) | 1.95305 | − | 1.95305i | 0.297837 | − | 0.297837i | −0.542329 | − | 0.840166i | \(-0.682457\pi\) |
0.840166 | + | 0.542329i | \(0.182457\pi\) | |||||||
\(44\) | −4.75127 | − | 2.74315i | −0.716282 | − | 0.413545i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.877194 | + | 1.51935i | 0.129335 | + | 0.224015i | ||||
\(47\) | 0.912383 | + | 3.40506i | 0.133085 | + | 0.496679i | 0.999998 | − | 0.00177938i | \(-0.000566396\pi\) |
−0.866914 | + | 0.498458i | \(0.833900\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −0.0534500 | + | 6.99980i | −0.00763571 | + | 0.999971i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05912 | − | 1.83445i | 0.148307 | − | 0.256875i | ||||
\(52\) | −3.30124 | − | 0.884566i | −0.457800 | − | 0.122667i | ||||
\(53\) | −9.08204 | − | 2.43353i | −1.24751 | − | 0.334270i | −0.426138 | − | 0.904658i | \(-0.640126\pi\) |
−0.821376 | + | 0.570388i | \(0.806793\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.64573 | + | 0.0101012i | 0.353551 | + | 0.00134983i | ||||
\(57\) | −4.94687 | − | 4.94687i | −0.655229 | − | 0.655229i | ||||
\(58\) | 0.177190 | + | 0.661282i | 0.0232662 | + | 0.0868306i | ||||
\(59\) | 5.08015 | + | 8.79907i | 0.661379 | + | 1.14554i | 0.980253 | + | 0.197745i | \(0.0633618\pi\) |
−0.318875 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01469 | + | 0.585830i | 0.129917 | + | 0.0750079i | 0.563550 | − | 0.826082i | \(-0.309435\pi\) |
−0.433633 | + | 0.901090i | \(0.642768\pi\) | |||||||
\(62\) | 3.94312 | − | 3.94312i | 0.500777 | − | 0.500777i | ||||
\(63\) | −0.675009 | − | 2.55820i | −0.0850431 | − | 0.322302i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.75127 | + | 2.74315i | −0.584841 | + | 0.337658i | ||||
\(67\) | −2.57606 | + | 9.61398i | −0.314716 | + | 1.17454i | 0.609538 | + | 0.792757i | \(0.291355\pi\) |
−0.924254 | + | 0.381778i | \(0.875312\pi\) | |||||||
\(68\) | 2.04607 | − | 0.548242i | 0.248122 | − | 0.0664841i | ||||
\(69\) | 1.75439 | 0.211204 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9716 | −1.42077 | −0.710383 | − | 0.703816i | \(-0.751478\pi\) | ||||
−0.710383 | + | 0.703816i | \(0.751478\pi\) | |||||||
\(72\) | −0.965926 | + | 0.258819i | −0.113835 | + | 0.0305021i | ||||
\(73\) | −1.26065 | + | 4.70482i | −0.147548 | + | 0.550657i | 0.852081 | + | 0.523411i | \(0.175341\pi\) |
−0.999629 | + | 0.0272467i | \(0.991326\pi\) | |||||||
\(74\) | 8.48716 | − | 4.90007i | 0.986613 | − | 0.569621i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.99593i | − | 0.802489i | ||||||
\(77\) | 3.81036 | − | 14.0063i | 0.434231 | − | 1.59617i | ||||
\(78\) | −2.41668 | + | 2.41668i | −0.273635 | + | 0.273635i | ||||
\(79\) | −7.21474 | − | 4.16543i | −0.811722 | − | 0.468648i | 0.0358316 | − | 0.999358i | \(-0.488592\pi\) |
−0.847553 | + | 0.530710i | \(0.821925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.648592 | + | 2.42058i | 0.0716250 | + | 0.267308i | ||||
\(83\) | −4.05281 | − | 4.05281i | −0.444854 | − | 0.444854i | 0.448786 | − | 0.893639i | \(-0.351857\pi\) |
−0.893639 | + | 0.448786i | \(0.851857\pi\) | |||||||
\(84\) | 1.33161 | − | 2.28622i | 0.145291 | − | 0.249447i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.38101 | − | 2.39198i | 0.148918 | − | 0.257934i | ||||
\(87\) | 0.661282 | + | 0.177190i | 0.0708969 | + | 0.0189968i | ||||
\(88\) | −5.29936 | − | 1.41996i | −0.564913 | − | 0.151368i | ||||
\(89\) | 3.59178 | − | 6.22115i | 0.380728 | − | 0.659440i | −0.610439 | − | 0.792064i | \(-0.709007\pi\) |
0.991166 | + | 0.132623i | \(0.0423401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0345228 | − | 9.04232i | 0.00361897 | − | 0.947892i | ||||
\(92\) | 1.24054 | + | 1.24054i | 0.129335 | + | 0.129335i | ||||
\(93\) | −1.44328 | − | 5.38640i | −0.149661 | − | 0.558544i | ||||
\(94\) | 1.76259 | + | 3.05289i | 0.181797 | + | 0.314882i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −13.1212 | + | 13.1212i | −1.33226 | + | 1.33226i | −0.428909 | + | 0.903348i | \(0.641102\pi\) |
−0.903348 | + | 0.428909i | \(0.858898\pi\) | |||||||
\(98\) | 1.76005 | + | 6.77512i | 0.177792 | + | 0.684390i | ||||
\(99\) | 5.48630i | 0.551394i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.16001 | − | 4.13383i | 0.712447 | − | 0.411332i | −0.0995192 | − | 0.995036i | \(-0.531730\pi\) |
0.811967 | + | 0.583704i | \(0.198397\pi\) | |||||||
\(102\) | 0.548242 | − | 2.04607i | 0.0542841 | − | 0.202591i | ||||
\(103\) | 8.98910 | − | 2.40862i | 0.885722 | − | 0.237329i | 0.212848 | − | 0.977085i | \(-0.431726\pi\) |
0.672874 | + | 0.739757i | \(0.265059\pi\) | |||||||
\(104\) | −3.41770 | −0.335133 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.40242 | −0.913244 | ||||||||
\(107\) | −11.8496 | + | 3.17510i | −1.14555 | + | 0.306949i | −0.781180 | − | 0.624306i | \(-0.785382\pi\) |
−0.364369 | + | 0.931255i | \(0.618715\pi\) | |||||||
\(108\) | −0.258819 | + | 0.965926i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | 0.291523 | − | 0.168311i | 0.0279228 | − | 0.0161213i | −0.485974 | − | 0.873973i | \(-0.661535\pi\) |
0.513896 | + | 0.857852i | \(0.328202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.80013i | − | 0.930188i | ||||||
\(112\) | 2.55820 | − | 0.675009i | 0.241727 | − | 0.0637823i | ||||
\(113\) | −10.1896 | + | 10.1896i | −0.958555 | + | 0.958555i | −0.999175 | − | 0.0406198i | \(-0.987067\pi\) |
0.0406198 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(114\) | −6.05866 | − | 3.49797i | −0.567445 | − | 0.327615i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.342305 | + | 0.592889i | 0.0317822 | + | 0.0550484i | ||||
\(117\) | 0.884566 | + | 3.30124i | 0.0817781 | + | 0.305200i | ||||
\(118\) | 7.18441 | + | 7.18441i | 0.661379 | + | 0.661379i | ||||
\(119\) | 2.78362 | + | 4.86417i | 0.255174 | + | 0.445898i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54974 | + | 16.5406i | −0.868158 | + | 1.50369i | ||||
\(122\) | 1.13174 | + | 0.303248i | 0.102463 | + | 0.0274548i | ||||
\(123\) | 2.42058 | + | 0.648592i | 0.218256 | + | 0.0584816i | ||||
\(124\) | 2.78821 | − | 4.82932i | 0.250388 | − | 0.433686i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.31412 | − | 2.29632i | −0.117071 | − | 0.204573i | ||||
\(127\) | 4.77054 | + | 4.77054i | 0.423317 | + | 0.423317i | 0.886344 | − | 0.463027i | \(-0.153237\pi\) |
−0.463027 | + | 0.886344i | \(0.653237\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | −1.38101 | − | 2.39198i | −0.121591 | − | 0.210602i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7695 | + | 9.10455i | 1.37779 | + | 0.795468i | 0.991893 | − | 0.127074i | \(-0.0405585\pi\) |
0.385898 | + | 0.922542i | \(0.373892\pi\) | |||||||
\(132\) | −3.87940 | + | 3.87940i | −0.337658 | + | 0.337658i | ||||
\(133\) | 17.8970 | − | 4.72232i | 1.55186 | − | 0.409477i | ||||
\(134\) | 9.95313i | 0.859819i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.83445 | − | 1.05912i | 0.157303 | − | 0.0908190i | ||||
\(137\) | −0.565438 | + | 2.11024i | −0.0483086 | + | 0.180290i | −0.985865 | − | 0.167544i | \(-0.946416\pi\) |
0.937556 | + | 0.347835i | \(0.113083\pi\) | |||||||
\(138\) | 1.69461 | − | 0.454069i | 0.144255 | − | 0.0386529i | ||||
\(139\) | 18.1446 | 1.53900 | 0.769501 | − | 0.638645i | \(-0.220505\pi\) | ||||
0.769501 | + | 0.638645i | \(0.220505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.52518 | 0.296873 | ||||||||
\(142\) | −11.5637 | + | 3.09847i | −0.970401 | + | 0.260018i | ||||
\(143\) | −4.85299 | + | 18.1116i | −0.405828 | + | 1.51457i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.87079i | 0.403109i | ||||||||
\(147\) | 6.74745 | + | 1.86331i | 0.556520 | + | 0.153683i | ||||
\(148\) | 6.92974 | − | 6.92974i | 0.569621 | − | 0.569621i | ||||
\(149\) | 0.167711 | + | 0.0968279i | 0.0137394 | + | 0.00793245i | 0.506854 | − | 0.862032i | \(-0.330808\pi\) |
−0.493115 | + | 0.869964i | \(0.664142\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6614 | + | 18.4660i | 0.867610 | + | 1.50274i | 0.864432 | + | 0.502750i | \(0.167678\pi\) |
0.00317777 | + | 0.999995i | \(0.498988\pi\) | |||||||
\(152\) | −1.81068 | − | 6.75755i | −0.146866 | − | 0.548110i | ||||
\(153\) | −1.49783 | − | 1.49783i | −0.121092 | − | 0.121092i | ||||
\(154\) | 0.0554181 | − | 14.5153i | 0.00446571 | − | 1.16967i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.70885 | + | 2.95981i | −0.136817 | + | 0.236975i | ||||
\(157\) | 3.55464 | + | 0.952462i | 0.283691 | + | 0.0760147i | 0.397859 | − | 0.917447i | \(-0.369753\pi\) |
−0.114168 | + | 0.993461i | \(0.536420\pi\) | |||||||
\(158\) | −8.04700 | − | 2.15619i | −0.640185 | − | 0.171537i | ||||
\(159\) | −4.70121 | + | 8.14273i | −0.372830 | + | 0.645761i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.33617 | + | 4.01092i | −0.184116 | + | 0.316105i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 3.64443 | + | 13.6012i | 0.285454 | + | 1.06533i | 0.948507 | + | 0.316756i | \(0.102594\pi\) |
−0.663054 | + | 0.748572i | \(0.730740\pi\) | |||||||
\(164\) | 1.25298 | + | 2.17023i | 0.0978416 | + | 0.169467i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.96366 | − | 2.86577i | −0.385255 | − | 0.222427i | ||||
\(167\) | 6.07259 | − | 6.07259i | 0.469911 | − | 0.469911i | −0.431974 | − | 0.901886i | \(-0.642183\pi\) |
0.901886 | + | 0.431974i | \(0.142183\pi\) | |||||||
\(168\) | 0.694523 | − | 2.55297i | 0.0535836 | − | 0.196966i | ||||
\(169\) | − | 1.31933i | − | 0.101487i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.05866 | + | 3.49797i | −0.463317 | + | 0.267496i | ||||
\(172\) | 0.714864 | − | 2.66791i | 0.0545079 | − | 0.203426i | ||||
\(173\) | 3.91108 | − | 1.04797i | 0.297354 | − | 0.0796757i | −0.107058 | − | 0.994253i | \(-0.534143\pi\) |
0.404412 | + | 0.914577i | \(0.367476\pi\) | |||||||
\(174\) | 0.684610 | 0.0519001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.48630 | −0.413545 | ||||||||
\(177\) | 9.81409 | − | 2.62968i | 0.737672 | − | 0.197659i | ||||
\(178\) | 1.85924 | − | 6.93879i | 0.139356 | − | 0.520084i | ||||
\(179\) | −3.17428 | + | 1.83267i | −0.237256 | + | 0.136980i | −0.613915 | − | 0.789372i | \(-0.710406\pi\) |
0.376659 | + | 0.926352i | \(0.377073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.39985i | − | 0.178379i | −0.996015 | − | 0.0891896i | \(-0.971572\pi\) | ||
0.996015 | − | 0.0891896i | \(-0.0284277\pi\) | |||||||
\(182\) | −2.30698 | − | 8.74314i | −0.171005 | − | 0.648085i | ||||
\(183\) | 0.828489 | − | 0.828489i | 0.0612437 | − | 0.0612437i | ||||
\(184\) | 1.51935 | + | 0.877194i | 0.112008 | + | 0.0646676i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.78821 | − | 4.82932i | −0.204441 | − | 0.354103i | ||||
\(187\) | −3.00782 | − | 11.2253i | −0.219954 | − | 0.820878i | ||||
\(188\) | 2.49268 | + | 2.49268i | 0.181797 | + | 0.181797i | ||||
\(189\) | −2.64573 | − | 0.0101012i | −0.192449 | − | 0.000734752i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.03766 | + | 6.99344i | −0.292155 | + | 0.506027i | −0.974319 | − | 0.225172i | \(-0.927706\pi\) |
0.682164 | + | 0.731199i | \(0.261039\pi\) | |||||||
\(192\) | −0.965926 | − | 0.258819i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | −1.66383 | − | 0.445821i | −0.119765 | − | 0.0320909i | 0.198439 | − | 0.980113i | \(-0.436413\pi\) |
−0.318204 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(194\) | −9.27809 | + | 16.0701i | −0.666128 | + | 1.15377i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.45361 | + | 6.08873i | 0.246686 | + | 0.434909i | ||||
\(197\) | −6.01174 | − | 6.01174i | −0.428319 | − | 0.428319i | 0.459737 | − | 0.888055i | \(-0.347944\pi\) |
−0.888055 | + | 0.459737i | \(0.847944\pi\) | |||||||
\(198\) | 1.41996 | + | 5.29936i | 0.100912 | + | 0.376609i | ||||
\(199\) | −5.50897 | − | 9.54181i | −0.390520 | − | 0.676401i | 0.601998 | − | 0.798498i | \(-0.294372\pi\) |
−0.992518 | + | 0.122097i | \(0.961038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.61966 | + | 4.97656i | 0.607984 | + | 0.351020i | ||||
\(202\) | 5.84612 | − | 5.84612i | 0.411332 | − | 0.411332i | ||||
\(203\) | −1.28567 | + | 1.27589i | −0.0902362 | + | 0.0895498i | ||||
\(204\) | − | 2.11825i | − | 0.148307i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.05941 | − | 4.65310i | 0.561526 | − | 0.324197i | ||||
\(207\) | 0.454069 | − | 1.69461i | 0.0315600 | − | 0.117783i | ||||
\(208\) | −3.30124 | + | 0.884566i | −0.228900 | + | 0.0613336i | ||||
\(209\) | −38.3818 | −2.65492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3323 | 0.711302 | 0.355651 | − | 0.934619i | \(-0.384259\pi\) | ||||
0.355651 | + | 0.934619i | \(0.384259\pi\) | |||||||
\(212\) | −9.08204 | + | 2.43353i | −0.623757 | + | 0.167135i | ||||
\(213\) | −3.09847 | + | 11.5637i | −0.212304 | + | 0.792329i | ||||
\(214\) | −10.6241 | + | 6.13383i | −0.726249 | + | 0.419300i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 14.2364 | + | 3.87295i | 0.966430 | + | 0.262913i | ||||
\(218\) | 0.238027 | − | 0.238027i | 0.0161213 | − | 0.0161213i | ||||
\(219\) | 4.21822 | + | 2.43539i | 0.285041 | + | 0.164569i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.61976 | − | 6.26961i | −0.243492 | − | 0.421740i | ||||
\(222\) | −2.53646 | − | 9.46620i | −0.170236 | − | 0.635330i | ||||
\(223\) | 3.41183 | + | 3.41183i | 0.228473 | + | 0.228473i | 0.812054 | − | 0.583582i | \(-0.198349\pi\) |
−0.583582 | + | 0.812054i | \(0.698349\pi\) | |||||||
\(224\) | 2.29632 | − | 1.31412i | 0.153429 | − | 0.0878032i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.20512 | + | 12.4796i | −0.479277 | + | 0.830133i | ||||
\(227\) | 17.4772 | + | 4.68301i | 1.16000 | + | 0.310822i | 0.786968 | − | 0.616994i | \(-0.211650\pi\) |
0.373037 | + | 0.927816i | \(0.378316\pi\) | |||||||
\(228\) | −6.75755 | − | 1.81068i | −0.447530 | − | 0.119915i | ||||
\(229\) | −4.82375 | + | 8.35497i | −0.318762 | + | 0.552112i | −0.980230 | − | 0.197861i | \(-0.936600\pi\) |
0.661468 | + | 0.749973i | \(0.269934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5429 | − | 7.30563i | −0.825262 | − | 0.480675i | ||||
\(232\) | 0.484092 | + | 0.484092i | 0.0317822 | + | 0.0317822i | ||||
\(233\) | −3.74597 | − | 13.9801i | −0.245407 | − | 0.915870i | −0.973179 | − | 0.230051i | \(-0.926111\pi\) |
0.727772 | − | 0.685819i | \(-0.240556\pi\) | |||||||
\(234\) | 1.70885 | + | 2.95981i | 0.111711 | + | 0.193489i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.79907 | + | 5.08015i | 0.572771 | + | 0.330689i | ||||
\(237\) | −5.89081 | + | 5.89081i | −0.382649 | + | 0.382649i | ||||
\(238\) | 3.94772 | + | 3.97798i | 0.255892 | + | 0.257854i | ||||
\(239\) | − | 29.9736i | − | 1.93883i | −0.245427 | − | 0.969415i | \(-0.578928\pi\) | ||
0.245427 | − | 0.969415i | \(-0.421072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3934 | − | 8.31003i | 0.927161 | − | 0.535296i | 0.0412481 | − | 0.999149i | \(-0.486867\pi\) |
0.885912 | + | 0.463853i | \(0.153533\pi\) | |||||||
\(242\) | −4.94331 | + | 18.4487i | −0.317768 | + | 1.18593i | ||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 1.17166 | 0.0750079 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.50597 | 0.159775 | ||||||||
\(247\) | −23.0953 | + | 6.18836i | −1.46952 | + | 0.393756i | ||||
\(248\) | 1.44328 | − | 5.38640i | 0.0916485 | − | 0.342037i | ||||
\(249\) | −4.96366 | + | 2.86577i | −0.314559 | + | 0.181611i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7660i | 0.679546i | 0.940508 | + | 0.339773i | \(0.110350\pi\) | ||||
−0.940508 | + | 0.339773i | \(0.889650\pi\) | |||||||
\(252\) | −1.86367 | − | 1.87796i | −0.117400 | − | 0.118300i | ||||
\(253\) | 6.80597 | − | 6.80597i | 0.427888 | − | 0.427888i | ||||
\(254\) | 5.84270 | + | 3.37328i | 0.366604 | + | 0.211659i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.89328 | + | 14.5299i | 0.242856 | + | 0.906352i | 0.974449 | + | 0.224610i | \(0.0721107\pi\) |
−0.731593 | + | 0.681742i | \(0.761223\pi\) | |||||||
\(258\) | −1.95305 | − | 1.95305i | −0.121591 | − | 0.121591i | ||||
\(259\) | 22.4053 | + | 13.0500i | 1.39220 | + | 0.810887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.342305 | − | 0.592889i | 0.0211881 | − | 0.0366989i | ||||
\(262\) | 17.5886 | + | 4.71286i | 1.08663 | + | 0.291161i | ||||
\(263\) | 21.7637 | + | 5.83157i | 1.34201 | + | 0.359590i | 0.857179 | − | 0.515019i | \(-0.172215\pi\) |
0.484829 | + | 0.874609i | \(0.338882\pi\) | |||||||
\(264\) | −2.74315 | + | 4.75127i | −0.168829 | + | 0.292421i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.0649 | − | 9.19348i | 0.985003 | − | 0.563689i | ||||
\(267\) | −5.07954 | − | 5.07954i | −0.310863 | − | 0.310863i | ||||
\(268\) | 2.57606 | + | 9.61398i | 0.157358 | + | 0.587268i | ||||
\(269\) | −5.52122 | − | 9.56304i | −0.336635 | − | 0.583069i | 0.647163 | − | 0.762352i | \(-0.275955\pi\) |
−0.983797 | + | 0.179283i | \(0.942622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.34433 | + | 2.50820i | 0.263899 | + | 0.152362i | 0.626112 | − | 0.779733i | \(-0.284645\pi\) |
−0.362213 | + | 0.932095i | \(0.617979\pi\) | |||||||
\(272\) | 1.49783 | − | 1.49783i | 0.0908190 | − | 0.0908190i | ||||
\(273\) | −8.72527 | − | 2.37367i | −0.528077 | − | 0.143661i | ||||
\(274\) | 2.18468i | 0.131982i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.51935 | − | 0.877194i | 0.0914538 | − | 0.0528009i | ||||
\(277\) | −1.63963 | + | 6.11920i | −0.0985161 | + | 0.367667i | −0.997529 | − | 0.0702549i | \(-0.977619\pi\) |
0.899013 | + | 0.437922i | \(0.144285\pi\) | |||||||
\(278\) | 17.5263 | − | 4.69616i | 1.05116 | − | 0.281657i | ||||
\(279\) | −5.57642 | −0.333851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4723 | −1.75817 | −0.879085 | − | 0.476665i | \(-0.841846\pi\) | ||||
−0.879085 | + | 0.476665i | \(0.841846\pi\) | |||||||
\(282\) | 3.40506 | − | 0.912383i | 0.202768 | − | 0.0543316i | ||||
\(283\) | 0.0253192 | − | 0.0944925i | 0.00150507 | − | 0.00561700i | −0.965169 | − | 0.261626i | \(-0.915741\pi\) |
0.966674 | + | 0.256009i | \(0.0824078\pi\) | |||||||
\(284\) | −10.3677 | + | 5.98579i | −0.615210 | + | 0.355191i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.7505i | 1.10874i | ||||||||
\(287\) | −4.70610 | + | 4.67030i | −0.277792 | + | 0.275679i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | −10.8366 | − | 6.25652i | −0.637447 | − | 0.368030i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.27809 | + | 16.0701i | 0.543891 | + | 0.942048i | ||||
\(292\) | 1.26065 | + | 4.70482i | 0.0737741 | + | 0.275329i | ||||
\(293\) | −14.0076 | − | 14.0076i | −0.818330 | − | 0.818330i | 0.167536 | − | 0.985866i | \(-0.446419\pi\) |
−0.985866 | + | 0.167536i | \(0.946419\pi\) | |||||||
\(294\) | 6.99980 | + | 0.0534500i | 0.408236 | + | 0.00311727i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.90007 | − | 8.48716i | 0.284811 | − | 0.493306i | ||||
\(297\) | 5.29936 | + | 1.41996i | 0.307500 | + | 0.0823944i | ||||
\(298\) | 0.187057 | + | 0.0501218i | 0.0108359 | + | 0.00290348i | ||||
\(299\) | 2.99799 | − | 5.19266i | 0.173378 | − | 0.300300i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.30758 | + | 0.0278997i | 0.421202 | + | 0.00160811i | ||||
\(302\) | 15.0775 | + | 15.0775i | 0.867610 | + | 0.867610i | ||||
\(303\) | −2.13983 | − | 7.98595i | −0.122930 | − | 0.458781i | ||||
\(304\) | −3.49797 | − | 6.05866i | −0.200622 | − | 0.347488i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.83445 | − | 1.05912i | −0.104869 | − | 0.0605460i | ||||
\(307\) | −3.05320 | + | 3.05320i | −0.174255 | + | 0.174255i | −0.788846 | − | 0.614591i | \(-0.789321\pi\) |
0.614591 | + | 0.788846i | \(0.289321\pi\) | |||||||
\(308\) | −3.70330 | − | 14.0350i | −0.211015 | − | 0.799720i | ||||
\(309\) | − | 9.30620i | − | 0.529411i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.31386 | + | 4.22266i | −0.414731 | + | 0.239445i | −0.692820 | − | 0.721110i | \(-0.743632\pi\) |
0.278089 | + | 0.960555i | \(0.410299\pi\) | |||||||
\(312\) | −0.884566 | + | 3.30124i | −0.0500787 | + | 0.186896i | ||||
\(313\) | 18.7482 | − | 5.02358i | 1.05971 | − | 0.283949i | 0.313453 | − | 0.949604i | \(-0.398514\pi\) |
0.746260 | + | 0.665654i | \(0.231847\pi\) | |||||||
\(314\) | 3.68003 | 0.207676 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.33087 | −0.468648 | ||||||||
\(317\) | −15.0204 | + | 4.02471i | −0.843632 | + | 0.226050i | −0.654652 | − | 0.755931i | \(-0.727185\pi\) |
−0.188980 | + | 0.981981i | \(0.560518\pi\) | |||||||
\(318\) | −2.43353 | + | 9.08204i | −0.136465 | + | 0.509296i | ||||
\(319\) | 3.25277 | − | 1.87799i | 0.182120 | − | 0.105147i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2677i | 0.684714i | ||||||||
\(322\) | −1.21846 | + | 4.47890i | −0.0679023 | + | 0.249599i | ||||
\(323\) | 10.4787 | − | 10.4787i | 0.583050 | − | 0.583050i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.04050 | + | 12.1945i | 0.389937 | + | 0.675391i | ||||
\(327\) | −0.0871241 | − | 0.325151i | −0.00481797 | − | 0.0179809i | ||||
\(328\) | 1.77199 | + | 1.77199i | 0.0978416 | + | 0.0978416i | ||||
\(329\) | −4.69417 | + | 8.05933i | −0.258798 | + | 0.444325i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.09296 | + | 14.0174i | −0.444830 | + | 0.770467i | −0.998040 | − | 0.0625739i | \(-0.980069\pi\) |
0.553211 | + | 0.833041i | \(0.313402\pi\) | |||||||
\(332\) | −5.53624 | − | 1.48343i | −0.303841 | − | 0.0814139i | ||||
\(333\) | −9.46620 | − | 2.53646i | −0.518745 | − | 0.138997i | ||||
\(334\) | 4.29397 | − | 7.43738i | 0.234956 | − | 0.406955i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0101012 | − | 2.64573i | 0.000551064 | − | 0.144337i | ||||
\(337\) | −19.2055 | − | 19.2055i | −1.04619 | − | 1.04619i | −0.998880 | − | 0.0473073i | \(-0.984936\pi\) |
−0.0473073 | − | 0.998880i | \(-0.515064\pi\) | |||||||
\(338\) | −0.341468 | − | 1.27438i | −0.0185734 | − | 0.0693169i | ||||
\(339\) | 7.20512 | + | 12.4796i | 0.391328 | + | 0.677801i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.4951 | − | 15.2969i | −1.43479 | − | 0.828376i | ||||
\(342\) | −4.94687 | + | 4.94687i | −0.267496 | + | 0.267496i | ||||
\(343\) | −13.2449 | + | 12.9450i | −0.715159 | + | 0.698962i | ||||
\(344\) | − | 2.76202i | − | 0.148918i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.50658 | − | 2.02452i | 0.188515 | − | 0.108839i | ||||
\(347\) | −2.65696 | + | 9.91592i | −0.142633 | + | 0.532315i | 0.857216 | + | 0.514957i | \(0.172192\pi\) |
−0.999849 | + | 0.0173577i | \(0.994475\pi\) | |||||||
\(348\) | 0.661282 | − | 0.177190i | 0.0354484 | − | 0.00949838i | ||||
\(349\) | −6.61441 | −0.354061 | −0.177031 | − | 0.984205i | \(-0.556649\pi\) | ||||
−0.177031 | + | 0.984205i | \(0.556649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.41770 | 0.182423 | ||||||||
\(352\) | −5.29936 | + | 1.41996i | −0.282457 | + | 0.0756841i | ||||
\(353\) | −3.52633 | + | 13.1604i | −0.187688 | + | 0.700460i | 0.806352 | + | 0.591436i | \(0.201439\pi\) |
−0.994039 | + | 0.109023i | \(0.965228\pi\) | |||||||
\(354\) | 8.79907 | − | 5.08015i | 0.467666 | − | 0.270007i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7.18356i | − | 0.380728i | ||||||
\(357\) | 5.41889 | − | 1.42983i | 0.286798 | − | 0.0756749i | ||||
\(358\) | −2.59178 | + | 2.59178i | −0.136980 | + | 0.136980i | ||||
\(359\) | 14.9791 | + | 8.64822i | 0.790569 | + | 0.456435i | 0.840163 | − | 0.542334i | \(-0.182459\pi\) |
−0.0495937 | + | 0.998769i | \(0.515793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9715 | − | 25.9315i | −0.787976 | − | 1.36481i | ||||
\(362\) | −0.621126 | − | 2.31807i | −0.0326457 | − | 0.121835i | ||||
\(363\) | 13.5054 | + | 13.5054i | 0.708848 | + | 0.708848i | ||||
\(364\) | −4.49126 | − | 7.84814i | −0.235406 | − | 0.411354i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.585830 | − | 1.01469i | 0.0306218 | − | 0.0530386i | ||||
\(367\) | 24.9992 | + | 6.69852i | 1.30495 | + | 0.349660i | 0.843319 | − | 0.537413i | \(-0.180598\pi\) |
0.461629 | + | 0.887073i | \(0.347265\pi\) | |||||||
\(368\) | 1.69461 | + | 0.454069i | 0.0883376 | + | 0.0236700i | ||||
\(369\) | 1.25298 | − | 2.17023i | 0.0652277 | − | 0.112978i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.3559 | − | 21.5910i | −0.641486 | − | 1.12095i | ||||
\(372\) | −3.94312 | − | 3.94312i | −0.204441 | − | 0.204441i | ||||
\(373\) | −2.37243 | − | 8.85404i | −0.122840 | − | 0.458445i | 0.876914 | − | 0.480648i | \(-0.159599\pi\) |
−0.999753 | + | 0.0222033i | \(0.992932\pi\) | |||||||
\(374\) | −5.81066 | − | 10.0644i | −0.300462 | − | 0.520416i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.05289 | + | 1.76259i | 0.157441 | + | 0.0908985i | ||||
\(377\) | 1.65448 | − | 1.65448i | 0.0852101 | − | 0.0852101i | ||||
\(378\) | −2.55820 | + | 0.675009i | −0.131579 | + | 0.0347187i | ||||
\(379\) | − | 18.6871i | − | 0.959891i | −0.877298 | − | 0.479946i | \(-0.840656\pi\) | ||
0.877298 | − | 0.479946i | \(-0.159344\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.84270 | − | 3.37328i | 0.299331 | − | 0.172819i | ||||
\(382\) | −2.09005 | + | 7.80016i | −0.106936 | + | 0.399091i | ||||
\(383\) | 19.1654 | − | 5.13534i | 0.979304 | − | 0.262404i | 0.266553 | − | 0.963820i | \(-0.414115\pi\) |
0.712752 | + | 0.701417i | \(0.247449\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.72252 | −0.0876740 | ||||||||
\(387\) | −2.66791 | + | 0.714864i | −0.135618 | + | 0.0363386i | ||||
\(388\) | −4.80269 | + | 17.9239i | −0.243820 | + | 0.909948i | ||||
\(389\) | 4.44026 | − | 2.56359i | 0.225130 | − | 0.129979i | −0.383193 | − | 0.923668i | \(-0.625176\pi\) |
0.608323 | + | 0.793689i | \(0.291842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.71623i | 0.187938i | ||||||||
\(392\) | 4.91181 | + | 4.98740i | 0.248084 | + | 0.251902i | ||||
\(393\) | 12.8758 | − | 12.8758i | 0.649497 | − | 0.649497i | ||||
\(394\) | −7.36285 | − | 4.25094i | −0.370935 | − | 0.214159i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.74315 | + | 4.75127i | 0.137848 | + | 0.238761i | ||||
\(397\) | −6.83113 | − | 25.4941i | −0.342844 | − | 1.27951i | −0.895110 | − | 0.445845i | \(-0.852903\pi\) |
0.552266 | − | 0.833668i | \(-0.313763\pi\) | |||||||
\(398\) | −7.79086 | − | 7.79086i | −0.390520 | − | 0.390520i | ||||
\(399\) | 0.0706671 | − | 18.5094i | 0.00353778 | − | 0.926627i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.61471 | − | 14.9211i | 0.430198 | − | 0.745125i | −0.566692 | − | 0.823930i | \(-0.691777\pi\) |
0.996890 | + | 0.0788050i | \(0.0251104\pi\) | |||||||
\(402\) | 9.61398 | + | 2.57606i | 0.479502 | + | 0.128482i | ||||
\(403\) | −18.4091 | − | 4.93271i | −0.917023 | − | 0.245716i | ||||
\(404\) | 4.13383 | − | 7.16001i | 0.205666 | − | 0.356224i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.911636 | + | 1.56517i | −0.0452437 | + | 0.0776780i | ||||
\(407\) | −38.0186 | − | 38.0186i | −1.88451 | − | 1.88451i | ||||
\(408\) | −0.548242 | − | 2.04607i | −0.0271420 | − | 0.101295i | ||||
\(409\) | 17.8569 | + | 30.9290i | 0.882967 | + | 1.52934i | 0.848027 | + | 0.529954i | \(0.177791\pi\) |
0.0349400 | + | 0.999389i | \(0.488876\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.89199 | + | 1.09234i | 0.0933251 | + | 0.0538813i | ||||
\(412\) | 6.58048 | − | 6.58048i | 0.324197 | − | 0.324197i | ||||
\(413\) | −7.05656 | + | 25.9389i | −0.347230 | + | 1.27637i | ||||
\(414\) | − | 1.75439i | − | 0.0862235i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.95981 | + | 1.70885i | −0.145117 | + | 0.0837832i | ||||
\(417\) | 4.69616 | − | 17.5263i | 0.229972 | − | 0.858267i | ||||
\(418\) | −37.0740 | + | 9.93394i | −1.81335 | + | 0.485885i | ||||
\(419\) | −14.0414 | −0.685966 | −0.342983 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342983 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4332 | 1.19080 | 0.595401 | − | 0.803429i | \(-0.296993\pi\) | ||||
0.595401 | + | 0.803429i | \(0.296993\pi\) | |||||||
\(422\) | 9.98020 | − | 2.67419i | 0.485829 | − | 0.130177i | ||||
\(423\) | 0.912383 | − | 3.40506i | 0.0443616 | − | 0.165560i | ||||
\(424\) | −8.14273 | + | 4.70121i | −0.395446 | + | 0.228311i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.9716i | 0.580025i | ||||||||
\(427\) | 0.790881 | + | 2.99734i | 0.0382734 | + | 0.145051i | ||||
\(428\) | −8.67454 | + | 8.67454i | −0.419300 | + | 0.419300i | ||||
\(429\) | 16.2384 | + | 9.37526i | 0.783999 | + | 0.452642i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3886 | + | 33.5820i | 0.933914 | + | 1.61759i | 0.776559 | + | 0.630044i | \(0.216963\pi\) |
0.157354 | + | 0.987542i | \(0.449704\pi\) | |||||||
\(432\) | 0.258819 | + | 0.965926i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | −7.85700 | − | 7.85700i | −0.377583 | − | 0.377583i | 0.492646 | − | 0.870230i | \(-0.336030\pi\) |
−0.870230 | + | 0.492646i | \(0.836030\pi\) | |||||||
\(434\) | 14.7537 | + | 0.0563283i | 0.708200 | + | 0.00270385i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.168311 | − | 0.291523i | 0.00806063 | − | 0.0139614i | ||||
\(437\) | 11.8554 | + | 3.17664i | 0.567119 | + | 0.151959i | ||||
\(438\) | 4.70482 | + | 1.26065i | 0.224805 | + | 0.0602363i | ||||
\(439\) | −10.5640 | + | 18.2973i | −0.504190 | + | 0.873283i | 0.495798 | + | 0.868438i | \(0.334876\pi\) |
−0.999988 | + | 0.00484487i | \(0.998458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.54619 | − | 6.03528i | 0.168866 | − | 0.287394i | ||||
\(442\) | −5.11912 | − | 5.11912i | −0.243492 | − | 0.243492i | ||||
\(443\) | −1.73709 | − | 6.48289i | −0.0825314 | − | 0.308011i | 0.912304 | − | 0.409514i | \(-0.134302\pi\) |
−0.994835 | + | 0.101503i | \(0.967635\pi\) | |||||||
\(444\) | −4.90007 | − | 8.48716i | −0.232547 | − | 0.402783i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.17862 | + | 2.41253i | 0.197863 | + | 0.114236i | ||||
\(447\) | 0.136935 | − | 0.136935i | 0.00647682 | − | 0.00647682i | ||||
\(448\) | 1.87796 | − | 1.86367i | 0.0887252 | − | 0.0880502i | ||||
\(449\) | 8.28979i | 0.391219i | 0.980682 | + | 0.195610i | \(0.0626685\pi\) | ||||
−0.980682 | + | 0.195610i | \(0.937331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9065 | − | 6.87424i | 0.560657 | − | 0.323695i | ||||
\(452\) | −3.72964 | + | 13.9192i | −0.175428 | + | 0.654705i | ||||
\(453\) | 20.5962 | − | 5.51873i | 0.967693 | − | 0.259293i | ||||
\(454\) | 18.0938 | 0.849182 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.99593 | −0.327615 | ||||||||
\(457\) | 21.3296 | − | 5.71524i | 0.997755 | − | 0.267348i | 0.277250 | − | 0.960798i | \(-0.410577\pi\) |
0.720505 | + | 0.693450i | \(0.243910\pi\) | |||||||
\(458\) | −2.49695 | + | 9.31876i | −0.116675 | + | 0.435437i | ||||
\(459\) | −1.83445 | + | 1.05912i | −0.0856250 | + | 0.0494356i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.0130i | − | 0.885524i | −0.896639 | − | 0.442762i | \(-0.853999\pi\) | ||
0.896639 | − | 0.442762i | \(-0.146001\pi\) | |||||||
\(462\) | −14.0063 | − | 3.81036i | −0.651634 | − | 0.177274i | ||||
\(463\) | 16.6091 | − | 16.6091i | 0.771891 | − | 0.771891i | −0.206546 | − | 0.978437i | \(-0.566222\pi\) |
0.978437 | + | 0.206546i | \(0.0662222\pi\) | |||||||
\(464\) | 0.592889 | + | 0.342305i | 0.0275242 | + | 0.0158911i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.23665 | − | 12.5343i | −0.335232 | − | 0.580638i | ||||
\(467\) | −4.13837 | − | 15.4446i | −0.191501 | − | 0.714691i | −0.993145 | − | 0.116889i | \(-0.962708\pi\) |
0.801644 | − | 0.597802i | \(-0.203959\pi\) | |||||||
\(468\) | 2.41668 | + | 2.41668i | 0.111711 | + | 0.111711i | ||||
\(469\) | −22.8556 | + | 13.0796i | −1.05537 | + | 0.603959i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.84001 | − | 3.18700i | 0.0847834 | − | 0.146849i | ||||
\(472\) | 9.81409 | + | 2.62968i | 0.451730 | + | 0.121041i | ||||
\(473\) | −14.6370 | − | 3.92196i | −0.673008 | − | 0.180332i | ||||
\(474\) | −4.16543 | + | 7.21474i | −0.191325 | + | 0.331384i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.84278 | + | 2.82069i | 0.221968 | + | 0.129286i | ||||
\(477\) | 6.64852 | + | 6.64852i | 0.304415 | + | 0.304415i | ||||
\(478\) | −7.75773 | − | 28.9523i | −0.354831 | − | 1.32425i | ||||
\(479\) | −4.50526 | − | 7.80333i | −0.205850 | − | 0.356543i | 0.744553 | − | 0.667563i | \(-0.232663\pi\) |
−0.950403 | + | 0.311020i | \(0.899329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.0066 | − | 16.7470i | −1.32259 | − | 0.763595i | ||||
\(482\) | 11.7522 | − | 11.7522i | 0.535296 | − | 0.535296i | ||||
\(483\) | 3.26961 | + | 3.29467i | 0.148772 | + | 0.149913i | ||||
\(484\) | 19.0995i | 0.868158i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −2.41740 | + | 9.02186i | −0.109543 | + | 0.408820i | −0.998821 | − | 0.0485475i | \(-0.984541\pi\) |
0.889278 | + | 0.457367i | \(0.151207\pi\) | |||||||
\(488\) | 1.13174 | − | 0.303248i | 0.0512313 | − | 0.0137274i | ||||
\(489\) | 14.0810 | 0.636764 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.08535 | 0.0941107 | 0.0470554 | − | 0.998892i | \(-0.485016\pi\) | ||||
0.0470554 | + | 0.998892i | \(0.485016\pi\) | |||||||
\(492\) | 2.42058 | − | 0.648592i | 0.109128 | − | 0.0292408i | ||||
\(493\) | −0.375332 | + | 1.40076i | −0.0169041 | + | 0.0630870i | ||||
\(494\) | −20.7067 | + | 11.9550i | −0.931637 | + | 0.537881i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.57642i | − | 0.250388i | ||||||
\(497\) | −22.3111 | − | 22.4821i | −1.00079 | − | 1.00846i | ||||
\(498\) | −4.05281 | + | 4.05281i | −0.181611 | + | 0.181611i | ||||
\(499\) | 11.6260 | + | 6.71229i | 0.520452 | + | 0.300483i | 0.737120 | − | 0.675762i | \(-0.236185\pi\) |
−0.216668 | + | 0.976245i | \(0.569519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.29397 | − | 7.43738i | −0.191841 | − | 0.332278i | ||||
\(502\) | 2.78645 | + | 10.3992i | 0.124366 | + | 0.464138i | ||||
\(503\) | −7.19669 | − | 7.19669i | −0.320885 | − | 0.320885i | 0.528222 | − | 0.849106i | \(-0.322859\pi\) |
−0.849106 | + | 0.528222i | \(0.822859\pi\) | |||||||
\(504\) | −2.28622 | − | 1.33161i | −0.101836 | − | 0.0593148i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.81255 | − | 8.33558i | 0.213944 | − | 0.370562i | ||||
\(507\) | −1.27438 | − | 0.341468i | −0.0565970 | − | 0.0151651i | ||||
\(508\) | 6.51668 | + | 1.74614i | 0.289131 | + | 0.0774724i | ||||
\(509\) | −2.14078 | + | 3.70794i | −0.0948884 | + | 0.164352i | −0.909562 | − | 0.415568i | \(-0.863583\pi\) |
0.814674 | + | 0.579920i | \(0.196916\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1849 | + | 6.40079i | −0.494791 | + | 0.283154i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 1.81068 | + | 6.75755i | 0.0799435 | + | 0.298353i | ||||
\(514\) | 7.52124 | + | 13.0272i | 0.331748 | + | 0.574604i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.39198 | − | 1.38101i | −0.105301 | − | 0.0607957i | ||||
\(517\) | 13.6756 | − | 13.6756i | 0.601451 | − | 0.601451i | ||||
\(518\) | 25.0194 | + | 6.80642i | 1.09929 | + | 0.299057i | ||||
\(519\) | − | 4.04905i | − | 0.177733i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.6226 | + | 7.28768i | −0.553007 | + | 0.319279i | −0.750334 | − | 0.661059i | \(-0.770107\pi\) |
0.197327 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(522\) | 0.177190 | − | 0.661282i | 0.00775540 | − | 0.0289435i | ||||
\(523\) | −36.7904 | + | 9.85794i | −1.60873 | + | 0.431058i | −0.947664 | − | 0.319270i | \(-0.896562\pi\) |
−0.661066 | + | 0.750328i | \(0.729896\pi\) | |||||||
\(524\) | 18.2091 | 0.795468 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.5315 | 0.982418 | ||||||||
\(527\) | 11.4097 | − | 3.05723i | 0.497015 | − | 0.133175i | ||||
\(528\) | −1.41996 | + | 5.29936i | −0.0617958 | + | 0.230625i | ||||
\(529\) | 17.2531 | − | 9.96106i | 0.750133 | − | 0.433090i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 10.1603i | − | 0.440919i | ||||||
\(532\) | 13.1381 | − | 13.0381i | 0.569607 | − | 0.565275i | ||||
\(533\) | 6.05612 | − | 6.05612i | 0.262319 | − | 0.262319i | ||||
\(534\) | −6.22115 | − | 3.59178i | −0.269215 | − | 0.155432i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.97656 | + | 8.61966i | 0.214955 | + | 0.372313i | ||||
\(537\) | 0.948659 | + | 3.54044i | 0.0409377 | + | 0.152781i | ||||
\(538\) | −7.80819 | − | 7.80819i | −0.336635 | − | 0.336635i | ||||
\(539\) | 33.4046 | − | 18.9475i | 1.43884 | − | 0.816128i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.43016 | + | 14.6015i | −0.362441 | + | 0.627766i | −0.988362 | − | 0.152121i | \(-0.951390\pi\) |
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(542\) | 4.84547 | + | 1.29834i | 0.208131 | + | 0.0557684i | ||||
\(543\) | −2.31807 | − | 0.621126i | −0.0994781 | − | 0.0266551i | ||||
\(544\) | 1.05912 | − | 1.83445i | 0.0454095 | − | 0.0786516i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.04232 | − | 0.0345228i | −0.386975 | − | 0.00147744i | ||||
\(547\) | 2.04444 | + | 2.04444i | 0.0874141 | + | 0.0874141i | 0.749462 | − | 0.662048i | \(-0.230312\pi\) |
−0.662048 | + | 0.749462i | \(0.730312\pi\) | |||||||
\(548\) | 0.565438 | + | 2.11024i | 0.0241543 | + | 0.0901451i | ||||
\(549\) | −0.585830 | − | 1.01469i | −0.0250026 | − | 0.0433058i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.14781 | + | 2.39474i | 0.176703 | + | 0.102019i | ||||
\(552\) | 1.24054 | − | 1.24054i | 0.0528009 | − | 0.0528009i | ||||
\(553\) | −5.62341 | − | 21.3120i | −0.239132 | − | 0.906278i | ||||
\(554\) | 6.33506i | 0.269151i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.7137 | − | 9.07229i | 0.666408 | − | 0.384751i | ||||
\(557\) | −1.08302 | + | 4.04187i | −0.0458889 | + | 0.171260i | −0.985067 | − | 0.172170i | \(-0.944922\pi\) |
0.939178 | + | 0.343430i | \(0.111589\pi\) | |||||||
\(558\) | −5.38640 | + | 1.44328i | −0.228025 | + | 0.0610990i | ||||
\(559\) | −9.43977 | −0.399260 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.6213 | −0.490653 | ||||||||
\(562\) | −28.4681 | + | 7.62799i | −1.20085 | + | 0.321767i | ||||
\(563\) | −6.48217 | + | 24.1918i | −0.273191 | + | 1.01956i | 0.683853 | + | 0.729620i | \(0.260303\pi\) |
−0.957044 | + | 0.289943i | \(0.906364\pi\) | |||||||
\(564\) | 3.05289 | − | 1.76259i | 0.128550 | − | 0.0742183i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 0.0978259i | − | 0.00411193i | ||||||
\(567\) | −0.694523 | + | 2.55297i | −0.0291672 | + | 0.107215i | ||||
\(568\) | −8.46519 | + | 8.46519i | −0.355191 | + | 0.355191i | ||||
\(569\) | 1.99827 | + | 1.15370i | 0.0837720 | + | 0.0483658i | 0.541301 | − | 0.840829i | \(-0.317932\pi\) |
−0.457529 | + | 0.889195i | \(0.651265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.94325 | − | 13.7581i | −0.332415 | − | 0.575759i | 0.650570 | − | 0.759446i | \(-0.274530\pi\) |
−0.982985 | + | 0.183687i | \(0.941197\pi\) | |||||||
\(572\) | 4.85299 | + | 18.1116i | 0.202914 | + | 0.757285i | ||||
\(573\) | 5.71012 | + | 5.71012i | 0.238544 | + | 0.238544i | ||||
\(574\) | −3.33698 | + | 5.72919i | −0.139283 | + | 0.239132i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −3.86453 | − | 1.03550i | −0.160883 | − | 0.0431084i | 0.177479 | − | 0.984125i | \(-0.443206\pi\) |
−0.338361 | + | 0.941016i | \(0.609873\pi\) | |||||||
\(578\) | −12.0867 | − | 3.23861i | −0.502739 | − | 0.134709i | ||||
\(579\) | −0.861260 | + | 1.49175i | −0.0357928 | + | 0.0619949i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0578953 | − | 15.1641i | 0.00240190 | − | 0.629114i | ||||
\(582\) | 13.1212 | + | 13.1212i | 0.543891 | + | 0.543891i | ||||
\(583\) | 13.3510 | + | 49.8268i | 0.552944 | + | 2.06361i | ||||
\(584\) | 2.43539 | + | 4.21822i | 0.100777 | + | 0.174551i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.1557 | − | 9.90484i | −0.708695 | − | 0.409165i | ||||
\(587\) | −5.31785 | + | 5.31785i | −0.219491 | + | 0.219491i | −0.808284 | − | 0.588793i | \(-0.799603\pi\) |
0.588793 | + | 0.808284i | \(0.299603\pi\) | |||||||
\(588\) | 6.77512 | − | 1.76005i | 0.279401 | − | 0.0725833i | ||||
\(589\) | − | 39.0122i | − | 1.60747i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.36285 | + | 4.25094i | −0.302867 | + | 0.174860i | ||||
\(592\) | 2.53646 | − | 9.46620i | 0.104248 | − | 0.389059i | ||||
\(593\) | −17.0986 | + | 4.58156i | −0.702156 | + | 0.188142i | −0.592196 | − | 0.805794i | \(-0.701739\pi\) |
−0.109960 | + | 0.993936i | \(0.535072\pi\) | |||||||
\(594\) | 5.48630 | 0.225106 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.193656 | 0.00793245 | ||||||||
\(597\) | −10.6425 | + | 2.85165i | −0.435569 | + | 0.116710i | ||||
\(598\) | 1.55187 | − | 5.79167i | 0.0634608 | − | 0.236839i | ||||
\(599\) | 27.0972 | − | 15.6446i | 1.10716 | − | 0.639220i | 0.169069 | − | 0.985604i | \(-0.445924\pi\) |
0.938093 | + | 0.346384i | \(0.112591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 47.5637i | − | 1.94016i | −0.242776 | − | 0.970082i | \(-0.578058\pi\) | ||
0.242776 | − | 0.970082i | \(-0.421942\pi\) | |||||||
\(602\) | 7.06580 | − | 1.86439i | 0.287980 | − | 0.0759869i | ||||
\(603\) | 7.03792 | − | 7.03792i | 0.286606 | − | 0.286606i | ||||
\(604\) | 18.4660 | + | 10.6614i | 0.751372 | + | 0.433805i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.13383 | − | 7.16001i | −0.167925 | − | 0.290855i | ||||
\(607\) | −6.35260 | − | 23.7082i | −0.257844 | − | 0.962287i | −0.966486 | − | 0.256719i | \(-0.917359\pi\) |
0.708642 | − | 0.705568i | \(-0.249308\pi\) | |||||||
\(608\) | −4.94687 | − | 4.94687i | −0.200622 | − | 0.200622i | ||||
\(609\) | 0.899658 | + | 1.57208i | 0.0364560 | + | 0.0637041i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.02400 | − | 10.4339i | 0.243705 | − | 0.422109i | ||||
\(612\) | −2.04607 | − | 0.548242i | −0.0827074 | − | 0.0221614i | ||||
\(613\) | −26.8884 | − | 7.20472i | −1.08601 | − | 0.290996i | −0.328955 | − | 0.944345i | \(-0.606697\pi\) |
−0.757056 | + | 0.653349i | \(0.773363\pi\) | |||||||
\(614\) | −2.15894 | + | 3.73939i | −0.0871277 | + | 0.150910i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.20965 | − | 12.5983i | −0.290485 | − | 0.507600i | ||||
\(617\) | 24.4884 | + | 24.4884i | 0.985865 | + | 0.985865i | 0.999901 | − | 0.0140365i | \(-0.00446811\pi\) |
−0.0140365 | + | 0.999901i | \(0.504468\pi\) | |||||||
\(618\) | −2.40862 | − | 8.98910i | −0.0968890 | − | 0.361595i | ||||
\(619\) | 15.9137 | + | 27.5634i | 0.639627 | + | 1.10787i | 0.985515 | + | 0.169590i | \(0.0542445\pi\) |
−0.345888 | + | 0.938276i | \(0.612422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51935 | − | 0.877194i | −0.0609692 | − | 0.0352006i | ||||
\(622\) | −5.97174 | + | 5.97174i | −0.239445 | + | 0.239445i | ||||
\(623\) | 18.3770 | − | 4.84897i | 0.736257 | − | 0.194270i | ||||
\(624\) | 3.41770i | 0.136817i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.8092 | − | 9.70480i | 0.671831 | − | 0.387882i | ||||
\(627\) | −9.93394 | + | 37.0740i | −0.396723 | + | 1.48059i | ||||
\(628\) | 3.55464 | − | 0.952462i | 0.141845 | − | 0.0380074i | ||||
\(629\) | 20.7591 | 0.827719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9471 | −1.39122 | −0.695610 | − | 0.718419i | \(-0.744866\pi\) | ||||
−0.695610 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(632\) | −8.04700 | + | 2.15619i | −0.320092 | + | 0.0857685i | ||||
\(633\) | 2.67419 | − | 9.98020i | 0.106289 | − | 0.396677i | ||||
\(634\) | −13.4670 | + | 7.77515i | −0.534841 | + | 0.308791i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.40242i | 0.372830i | ||||||||
\(637\) | 17.0454 | − | 16.7871i | 0.675364 | − | 0.665128i | ||||
\(638\) | 2.65587 | − | 2.65587i | 0.105147 | − | 0.105147i | ||||
\(639\) | 10.3677 | + | 5.98579i | 0.410140 | + | 0.236794i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.61488 | + | 9.72526i | 0.221774 | + | 0.384125i | 0.955347 | − | 0.295487i | \(-0.0954818\pi\) |
−0.733572 | + | 0.679611i | \(0.762148\pi\) | |||||||
\(642\) | 3.17510 | + | 11.8496i | 0.125311 | + | 0.467668i | ||||
\(643\) | 9.89036 | + | 9.89036i | 0.390038 | + | 0.390038i | 0.874701 | − | 0.484663i | \(-0.161058\pi\) |
−0.484663 | + | 0.874701i | \(0.661058\pi\) | |||||||
\(644\) | −0.0177214 | + | 4.64164i | −0.000698320 | + | 0.182906i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.40955 | − | 12.8337i | 0.291525 | − | 0.504936i | ||||
\(647\) | −15.1576 | − | 4.06147i | −0.595908 | − | 0.159673i | −0.0517559 | − | 0.998660i | \(-0.516482\pi\) |
−0.544152 | + | 0.838987i | \(0.683148\pi\) | |||||||
\(648\) | 0.965926 | + | 0.258819i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | 27.8712 | − | 48.2744i | 1.09404 | − | 1.89493i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.42563 | − | 12.7489i | 0.291033 | − | 0.499669i | ||||
\(652\) | 9.95676 | + | 9.95676i | 0.389937 | + | 0.389937i | ||||
\(653\) | −4.12761 | − | 15.4045i | −0.161526 | − | 0.602823i | −0.998458 | − | 0.0555160i | \(-0.982320\pi\) |
0.836932 | − | 0.547307i | \(-0.184347\pi\) | |||||||
\(654\) | −0.168311 | − | 0.291523i | −0.00658147 | − | 0.0113994i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.17023 | + | 1.25298i | 0.0847333 | + | 0.0489208i | ||||
\(657\) | 3.44417 | − | 3.44417i | 0.134370 | − | 0.134370i | ||||
\(658\) | −2.44832 | + | 8.99966i | −0.0954453 | + | 0.350843i | ||||
\(659\) | − | 10.4778i | − | 0.408157i | −0.978955 | − | 0.204078i | \(-0.934580\pi\) | ||
0.978955 | − | 0.204078i | \(-0.0654198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9764 | + | 12.1107i | −0.815888 | + | 0.471053i | −0.848996 | − | 0.528399i | \(-0.822793\pi\) |
0.0331084 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(662\) | −4.18923 | + | 15.6344i | −0.162819 | + | 0.607648i | ||||
\(663\) | −6.99285 | + | 1.87373i | −0.271580 | + | 0.0727695i | ||||
\(664\) | −5.73154 | −0.222427 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.80013 | −0.379747 | ||||||||
\(667\) | −1.16015 | + | 0.310860i | −0.0449210 | + | 0.0120366i | ||||
\(668\) | 2.22272 | − | 8.29532i | 0.0859998 | − | 0.320955i | ||||
\(669\) | 4.17862 | − | 2.41253i | 0.161555 | − | 0.0932736i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.42808i | − | 0.248153i | ||||||
\(672\) | −0.675009 | − | 2.55820i | −0.0260390 | − | 0.0986845i | ||||
\(673\) | 1.16725 | − | 1.16725i | 0.0449943 | − | 0.0449943i | −0.684252 | − | 0.729246i | \(-0.739871\pi\) |
0.729246 | + | 0.684252i | \(0.239871\pi\) | |||||||
\(674\) | −23.5218 | − | 13.5803i | −0.906025 | − | 0.523094i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.659666 | − | 1.14257i | −0.0253718 | − | 0.0439452i | ||||
\(677\) | 3.32260 | + | 12.4001i | 0.127698 | + | 0.476575i | 0.999921 | − | 0.0125322i | \(-0.00398922\pi\) |
−0.872223 | + | 0.489108i | \(0.837323\pi\) | |||||||
\(678\) | 10.1896 | + | 10.1896i | 0.391328 | + | 0.391328i | ||||
\(679\) | −49.0947 | − | 0.187439i | −1.88408 | − | 0.00719326i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.04688 | − | 15.6697i | 0.346677 | − | 0.600463i | ||||
\(682\) | −29.5514 | − | 7.91828i | −1.13158 | − | 0.303207i | ||||
\(683\) | 20.6373 | + | 5.52974i | 0.789663 | + | 0.211589i | 0.631040 | − | 0.775750i | \(-0.282628\pi\) |
0.158622 | + | 0.987339i | \(0.449295\pi\) | |||||||
\(684\) | −3.49797 | + | 6.05866i | −0.133748 | + | 0.231658i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.44322 | + | 15.9319i | −0.360544 | + | 0.608283i | ||||
\(687\) | 6.82181 | + | 6.82181i | 0.260268 | + | 0.260268i | ||||
\(688\) | −0.714864 | − | 2.66791i | −0.0272540 | − | 0.101713i | ||||
\(689\) | 16.0673 | + | 27.8294i | 0.612116 | + | 1.06022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0127 | − | 21.3693i | −1.40803 | − | 0.812927i | −0.412833 | − | 0.910807i | \(-0.635461\pi\) |
−0.995198 | + | 0.0978797i | \(0.968794\pi\) | |||||||
\(692\) | 2.86311 | − | 2.86311i | 0.108839 | − | 0.108839i | ||||
\(693\) | −10.3030 | + | 10.2247i | −0.391380 | + | 0.388403i | ||||
\(694\) | 10.2657i | 0.389681i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.592889 | − | 0.342305i | 0.0224734 | − | 0.0129750i | ||||
\(697\) | −1.37388 | + | 5.12738i | −0.0520393 | + | 0.194213i | ||||
\(698\) | −6.38903 | + | 1.71194i | −0.241828 | + | 0.0647977i | ||||
\(699\) | −14.4733 | −0.547431 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.5959 | 1.68436 | 0.842182 | − | 0.539194i | \(-0.181271\pi\) | ||||
0.842182 | + | 0.539194i | \(0.181271\pi\) | |||||||
\(702\) | 3.30124 | − | 0.884566i | 0.124597 | − | 0.0333858i | ||||
\(703\) | 17.7449 | − | 66.2249i | 0.669262 | − | 2.49772i | ||||
\(704\) | −4.75127 | + | 2.74315i | −0.179070 | + | 0.103386i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.6247i | 0.512772i | ||||||||
\(707\) | 21.1071 | + | 5.74208i | 0.793813 | + | 0.215953i | ||||
\(708\) | 7.18441 | − | 7.18441i | 0.270007 | − | 0.270007i | ||||
\(709\) | −35.8750 | − | 20.7125i | −1.34732 | − | 0.777873i | −0.359447 | − | 0.933166i | \(-0.617035\pi\) |
−0.987869 | + | 0.155293i | \(0.950368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.16543 | + | 7.21474i | 0.156216 | + | 0.270574i | ||||
\(712\) | −1.85924 | − | 6.93879i | −0.0696781 | − | 0.260042i | ||||
\(713\) | 6.91777 | + | 6.91777i | 0.259072 | + | 0.259072i | ||||
\(714\) | 4.86417 | − | 2.78362i | 0.182037 | − | 0.104175i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.83267 | + | 3.17428i | −0.0684900 | + | 0.118628i | ||||
\(717\) | −28.9523 | − | 7.75773i | −1.08124 | − | 0.289718i | ||||
\(718\) | 16.7071 | + | 4.47665i | 0.623502 | + | 0.167067i | ||||
\(719\) | 11.7839 | − | 20.4103i | 0.439464 | − | 0.761174i | −0.558184 | − | 0.829717i | \(-0.688502\pi\) |
0.997648 | + | 0.0685431i | \(0.0218351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.2760 | + | 12.3923i | 0.792361 | + | 0.461512i | ||||
\(722\) | −21.1730 | − | 21.1730i | −0.787976 | − | 0.787976i | ||||
\(723\) | −4.30159 | − | 16.0538i | −0.159978 | − | 0.597046i | ||||
\(724\) | −1.19992 | − | 2.07833i | −0.0445948 | − | 0.0772405i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.5406 | + | 9.54974i | 0.613881 | + | 0.354424i | ||||
\(727\) | 3.38556 | − | 3.38556i | 0.125563 | − | 0.125563i | −0.641532 | − | 0.767096i | \(-0.721701\pi\) |
0.767096 | + | 0.641532i | \(0.221701\pi\) | |||||||
\(728\) | −6.36947 | − | 6.41829i | −0.236068 | − | 0.237878i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.06681 | − | 2.92532i | 0.187403 | − | 0.108197i | ||||
\(732\) | 0.303248 | − | 1.13174i | 0.0112084 | − | 0.0418302i | ||||
\(733\) | −37.9373 | + | 10.1653i | −1.40125 | + | 0.375463i | −0.878792 | − | 0.477204i | \(-0.841650\pi\) |
−0.522454 | + | 0.852667i | \(0.674983\pi\) | |||||||
\(734\) | 25.8811 | 0.955288 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75439 | 0.0646676 | ||||||||
\(737\) | 52.7452 | − | 14.1330i | 1.94289 | − | 0.520597i | ||||
\(738\) | 0.648592 | − | 2.42058i | 0.0238750 | − | 0.0891027i | ||||
\(739\) | −38.6211 | + | 22.2979i | −1.42070 | + | 0.820242i | −0.996359 | − | 0.0852593i | \(-0.972828\pi\) |
−0.424343 | + | 0.905502i | \(0.639495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.9100i | 0.878356i | ||||||||
\(742\) | −17.5230 | − | 17.6573i | −0.643291 | − | 0.648222i | ||||
\(743\) | −24.7787 | + | 24.7787i | −0.909041 | + | 0.909041i | −0.996195 | − | 0.0871537i | \(-0.972223\pi\) |
0.0871537 | + | 0.996195i | \(0.472223\pi\) | |||||||
\(744\) | −4.82932 | − | 2.78821i | −0.177051 | − | 0.102221i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.58319 | − | 7.93832i | −0.167802 | − | 0.290642i | ||||
\(747\) | 1.48343 | + | 5.53624i | 0.0542759 | + | 0.202561i | ||||
\(748\) | −8.21752 | − | 8.21752i | −0.300462 | − | 0.300462i | ||||
\(749\) | −28.0466 | − | 16.3358i | −1.02480 | − | 0.596897i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.54731 | + | 4.41207i | −0.0929526 | + | 0.160999i | −0.908752 | − | 0.417336i | \(-0.862964\pi\) |
0.815800 | + | 0.578335i | \(0.196297\pi\) | |||||||
\(752\) | 3.40506 | + | 0.912383i | 0.124170 | + | 0.0332712i | ||||
\(753\) | 10.3992 | + | 2.78645i | 0.378967 | + | 0.101544i | ||||
\(754\) | 1.16989 | − | 2.02632i | 0.0426051 | − | 0.0737941i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.29632 | + | 1.31412i | −0.0835164 | + | 0.0477940i | ||||
\(757\) | −18.2623 | − | 18.2623i | −0.663754 | − | 0.663754i | 0.292509 | − | 0.956263i | \(-0.405510\pi\) |
−0.956263 | + | 0.292509i | \(0.905510\pi\) | |||||||
\(758\) | −4.83657 | − | 18.0503i | −0.175672 | − | 0.655618i | ||||
\(759\) | −4.81255 | − | 8.33558i | −0.174685 | − | 0.302562i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3626 | + | 14.0657i | 0.883142 | + | 0.509882i | 0.871693 | − | 0.490052i | \(-0.163022\pi\) |
0.0114488 | + | 0.999934i | \(0.496356\pi\) | |||||||
\(762\) | 4.77054 | − | 4.77054i | 0.172819 | − | 0.172819i | ||||
\(763\) | 0.859384 | + | 0.233791i | 0.0311118 | + | 0.00846382i | ||||
\(764\) | 8.07532i | 0.292155i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.1832 | − | 9.92072i | 0.620854 | − | 0.358450i | ||||
\(767\) | 8.98745 | − | 33.5416i | 0.324518 | − | 1.21112i | ||||
\(768\) | −0.965926 | + | 0.258819i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | 3.03517 | 0.109451 | 0.0547256 | − | 0.998501i | \(-0.482572\pi\) | ||||
0.0547256 | + | 0.998501i | \(0.482572\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0425 | 0.541742 | ||||||||
\(772\) | −1.66383 | + | 0.445821i | −0.0598825 | + | 0.0160455i | ||||
\(773\) | 12.5554 | − | 46.8575i | 0.451588 | − | 1.68535i | −0.246342 | − | 0.969183i | \(-0.579229\pi\) |
0.697930 | − | 0.716166i | \(-0.254105\pi\) | |||||||
\(774\) | −2.39198 | + | 1.38101i | −0.0859781 | + | 0.0496395i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.5562i | 0.666128i | ||||||||
\(777\) | 18.4042 | − | 18.2642i | 0.660248 | − | 0.655226i | ||||
\(778\) | 3.62546 | − | 3.62546i | 0.129979 | − | 0.129979i | ||||
\(779\) | 15.1828 | + | 8.76579i | 0.543980 | + | 0.314067i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.8398 | + | 56.8803i | 1.17510 | + | 2.03534i | ||||
\(782\) | 0.961830 | + | 3.58960i | 0.0343950 | + | 0.128364i | ||||
\(783\) | −0.484092 | − | 0.484092i | −0.0173000 | − | 0.0173000i | ||||
\(784\) | 6.03528 | + | 3.54619i | 0.215546 | + | 0.126650i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.10455 | − | 15.7695i | 0.324748 | − | 0.562481i | ||||
\(787\) | 36.6884 | + | 9.83063i | 1.30780 | + | 0.350424i | 0.844394 | − | 0.535722i | \(-0.179961\pi\) |
0.463406 | + | 0.886146i | \(0.346627\pi\) | |||||||
\(788\) | −8.21219 | − | 2.20045i | −0.292547 | − | 0.0783878i | ||||
\(789\) | 11.2657 | − | 19.5128i | 0.401070 | − | 0.694674i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.1256 | − | 0.145560i | −1.35559 | − | 0.00517553i | ||||
\(792\) | 3.87940 | + | 3.87940i | 0.137848 | + | 0.137848i | ||||
\(793\) | −1.03641 | − | 3.86794i | −0.0368040 | − | 0.137354i | ||||
\(794\) | −13.1967 | − | 22.8574i | −0.468334 | − | 0.811179i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.54181 | − | 5.50897i | −0.338200 | − | 0.195260i | ||||
\(797\) | −34.4058 | + | 34.4058i | −1.21871 | + | 1.21871i | −0.250632 | + | 0.968082i | \(0.580638\pi\) |
−0.968082 | + | 0.250632i | \(0.919362\pi\) | |||||||
\(798\) | −4.72232 | − | 17.8970i | −0.167168 | − | 0.633546i | ||||
\(799\) | 7.46719i | 0.264170i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.22115 | + | 3.59178i | −0.219813 | + | 0.126909i | ||||
\(802\) | 4.45930 | − | 16.6423i | 0.157463 | − | 0.587661i | ||||
\(803\) | 25.8120 | − | 6.91632i | 0.910887 | − | 0.244071i | ||||
\(804\) | 9.95313 | 0.351020 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.0585 | −0.671307 | ||||||||
\(807\) | −10.6662 | + | 2.85799i | −0.375467 | + | 0.100606i | ||||
\(808\) | 2.13983 | − | 7.98595i | 0.0752789 | − | 0.280945i | ||||
\(809\) | −33.6569 | + | 19.4318i | −1.18331 | + | 0.683186i | −0.956779 | − | 0.290817i | \(-0.906073\pi\) |
−0.226534 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.3545i | − | 0.539168i | −0.962977 | − | 0.269584i | \(-0.913114\pi\) | ||
0.962977 | − | 0.269584i | \(-0.0868862\pi\) | |||||||
\(812\) | −0.475477 | + | 1.74779i | −0.0166860 | + | 0.0613352i | ||||
\(813\) | 3.54713 | − | 3.54713i | 0.124403 | − | 0.124403i | ||||
\(814\) | −46.5631 | − | 26.8832i | −1.63204 | − | 0.942257i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.05912 | − | 1.83445i | −0.0370767 | − | 0.0642187i | ||||
\(817\) | −5.00114 | − | 18.6645i | −0.174968 | − | 0.652989i | ||||
\(818\) | 25.2535 | + | 25.2535i | 0.882967 | + | 0.882967i | ||||
\(819\) | −4.55106 | + | 7.81361i | −0.159027 | + | 0.273030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.9561 | + | 20.7086i | −0.417271 | + | 0.722735i | −0.995664 | − | 0.0930235i | \(-0.970347\pi\) |
0.578393 | + | 0.815758i | \(0.303680\pi\) | |||||||
\(822\) | 2.11024 | + | 0.565438i | 0.0736032 | + | 0.0197219i | ||||
\(823\) | −27.3473 | − | 7.32768i | −0.953267 | − | 0.255427i | −0.251519 | − | 0.967852i | \(-0.580930\pi\) |
−0.701748 | + | 0.712425i | \(0.747597\pi\) | |||||||
\(824\) | 4.65310 | − | 8.05941i | 0.162098 | − | 0.280763i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.102631 | + | 26.8814i | −0.00357099 | + | 0.935324i | ||||
\(827\) | −20.7600 | − | 20.7600i | −0.721898 | − | 0.721898i | 0.247094 | − | 0.968992i | \(-0.420524\pi\) |
−0.968992 | + | 0.247094i | \(0.920524\pi\) | |||||||
\(828\) | −0.454069 | − | 1.69461i | −0.0157800 | − | 0.0588917i | ||||
\(829\) | 4.14106 | + | 7.17253i | 0.143825 | + | 0.249112i | 0.928934 | − | 0.370246i | \(-0.120726\pi\) |
−0.785109 | + | 0.619358i | \(0.787393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.48632 | + | 3.16753i | 0.190318 | + | 0.109880i | ||||
\(832\) | −2.41668 | + | 2.41668i | −0.0837832 | + | 0.0837832i | ||||
\(833\) | −3.94695 | + | 14.2928i | −0.136754 | + | 0.495215i | ||||
\(834\) | − | 18.1446i | − | 0.628295i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −33.2396 | + | 19.1909i | −1.14962 | + | 0.663731i | ||||
\(837\) | −1.44328 | + | 5.38640i | −0.0498871 | + | 0.186181i | ||||
\(838\) | −13.5629 | + | 3.63417i | −0.468523 | + | 0.125540i | ||||
\(839\) | 8.03334 | 0.277342 | 0.138671 | − | 0.990339i | \(-0.455717\pi\) | ||||
0.138671 | + | 0.990339i | \(0.455717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5313 | 0.983838 | ||||||||
\(842\) | 23.6007 | − | 6.32378i | 0.813333 | − | 0.217932i | ||||
\(843\) | −7.62799 | + | 28.4681i | −0.262722 | + | 0.980492i | ||||
\(844\) | 8.94800 | − | 5.16613i | 0.308003 | − | 0.177826i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 3.52518i | − | 0.121198i | ||||||
\(847\) | −48.8602 | + | 12.8923i | −1.67886 | + | 0.442985i | ||||
\(848\) | −6.64852 | + | 6.64852i | −0.228311 | + | 0.228311i | ||||
\(849\) | −0.0847197 | − | 0.0489129i | −0.00290757 | − | 0.00167869i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.59662 | + | 14.8898i | 0.294688 | + | 0.510415i | ||||
\(852\) | 3.09847 | + | 11.5637i | 0.106152 | + | 0.396165i | ||||
\(853\) | −23.8654 | − | 23.8654i | −0.817136 | − | 0.817136i | 0.168556 | − | 0.985692i | \(-0.446089\pi\) |
−0.985692 | + | 0.168556i | \(0.946089\pi\) | |||||||
\(854\) | 1.53970 | + | 2.69051i | 0.0526875 | + | 0.0920673i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.13383 | + | 10.6241i | −0.209650 | + | 0.363124i | ||||
\(857\) | −23.1984 | − | 6.21598i | −0.792441 | − | 0.212334i | −0.160178 | − | 0.987088i | \(-0.551207\pi\) |
−0.632263 | + | 0.774754i | \(0.717874\pi\) | |||||||
\(858\) | 18.1116 | + | 4.85299i | 0.618320 | + | 0.165678i | ||||
\(859\) | −3.26421 | + | 5.65377i | −0.111373 | + | 0.192904i | −0.916324 | − | 0.400437i | \(-0.868858\pi\) |
0.804951 | + | 0.593341i | \(0.202192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.29314 | + | 5.75451i | 0.112230 | + | 0.196113i | ||||
\(862\) | 27.4196 | + | 27.4196i | 0.933914 | + | 0.933914i | ||||
\(863\) | 4.28582 | + | 15.9949i | 0.145891 | + | 0.544473i | 0.999714 | + | 0.0239095i | \(0.00761137\pi\) |
−0.853823 | + | 0.520563i | \(0.825722\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.62282 | − | 5.55574i | −0.326997 | − | 0.188792i | ||||
\(867\) | −8.84805 | + | 8.84805i | −0.300496 | + | 0.300496i | ||||
\(868\) | 14.2656 | − | 3.76413i | 0.484205 | − | 0.127763i | ||||
\(869\) | 45.7056i | 1.55046i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.4594 | − | 17.0084i | 0.998194 | − | 0.576308i | ||||
\(872\) | 0.0871241 | − | 0.325151i | 0.00295039 | − | 0.0110110i | ||||
\(873\) | 17.9239 | − | 4.80269i | 0.606632 | − | 0.162547i | ||||
\(874\) | 12.2736 | 0.415160 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.87079 | 0.164569 | ||||||||
\(877\) | 35.7050 | − | 9.56712i | 1.20567 | − | 0.323059i | 0.400609 | − | 0.916249i | \(-0.368798\pi\) |
0.805062 | + | 0.593190i | \(0.202132\pi\) | |||||||
\(878\) | −5.46830 | + | 20.4080i | −0.184546 | + | 0.688736i | ||||
\(879\) | −17.1557 | + | 9.90484i | −0.578647 | + | 0.334082i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4940i | 0.589386i | 0.955592 | + | 0.294693i | \(0.0952174\pi\) | ||||
−0.955592 | + | 0.294693i | \(0.904783\pi\) | |||||||
\(882\) | 1.86331 | − | 6.74745i | 0.0627409 | − | 0.227198i | ||||
\(883\) | 14.0857 | − | 14.0857i | 0.474022 | − | 0.474022i | −0.429191 | − | 0.903214i | \(-0.641201\pi\) |
0.903214 | + | 0.429191i | \(0.141201\pi\) | |||||||
\(884\) | −6.26961 | − | 3.61976i | −0.210870 | − | 0.121746i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.35579 | − | 5.81240i | −0.112740 | − | 0.195271i | ||||
\(887\) | 10.6152 | + | 39.6163i | 0.356422 | + | 1.33018i | 0.878686 | + | 0.477401i | \(0.158421\pi\) |
−0.522264 | + | 0.852784i | \(0.674912\pi\) | |||||||
\(888\) | −6.92974 | − | 6.92974i | −0.232547 | − | 0.232547i | ||||
\(889\) | −0.0681482 | + | 17.8496i | −0.00228562 | + | 0.598657i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.74315 | − | 4.75127i | 0.0918990 | − | 0.159174i | ||||
\(892\) | 4.66064 | + | 1.24882i | 0.156050 | + | 0.0418134i | ||||
\(893\) | 23.8216 | + | 6.38297i | 0.797158 | + | 0.213598i | ||||
\(894\) | 0.0968279 | − | 0.167711i | 0.00323841 | − | 0.00560909i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.33161 | − | 2.28622i | 0.0444861 | − | 0.0763773i | ||||
\(897\) | −4.23979 | − | 4.23979i | −0.141563 | − | 0.141563i | ||||
\(898\) | 2.14555 | + | 8.00732i | 0.0715981 | + | 0.267208i | ||||
\(899\) | 1.90883 | + | 3.30620i | 0.0636632 | + | 0.110268i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.2483 | − | 9.95832i | −0.574625 | − | 0.331760i | ||||
\(902\) | 9.72165 | − | 9.72165i | 0.323695 | − | 0.323695i | ||||
\(903\) | 1.91829 | − | 7.05136i | 0.0638367 | − | 0.234654i | ||||
\(904\) | 14.4102i | 0.479277i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.4660 | − | 10.6614i | 0.613493 | − | 0.354200i | ||||
\(907\) | −5.17169 | + | 19.3010i | −0.171723 | + | 0.640879i | 0.825364 | + | 0.564602i | \(0.190970\pi\) |
−0.997087 | + | 0.0762776i | \(0.975696\pi\) | |||||||
\(908\) | 17.4772 | − | 4.68301i | 0.580002 | − | 0.155411i | ||||
\(909\) | −8.26766 | −0.274221 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.3131 | −0.706136 | −0.353068 | − | 0.935598i | \(-0.614862\pi\) | ||||
−0.353068 | + | 0.935598i | \(0.614862\pi\) | |||||||
\(912\) | −6.75755 | + | 1.81068i | −0.223765 | + | 0.0599576i | ||||
\(913\) | −8.13855 | + | 30.3735i | −0.269347 | + | 1.00522i | ||||
\(914\) | 19.1236 | − | 11.0410i | 0.632551 | − | 0.365204i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.64749i | 0.318762i | ||||||||
\(917\) | 12.2913 | + | 46.5824i | 0.405894 | + | 1.53829i | ||||
\(918\) | −1.49783 | + | 1.49783i | −0.0494356 | + | 0.0494356i | ||||
\(919\) | 11.4010 | + | 6.58238i | 0.376085 | + | 0.217133i | 0.676114 | − | 0.736797i | \(-0.263663\pi\) |
−0.300029 | + | 0.953930i | \(0.596996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.15894 | + | 3.73939i | 0.0711394 | + | 0.123217i | ||||
\(922\) | −4.92093 | − | 18.3652i | −0.162062 | − | 0.604824i | ||||
\(923\) | 28.9315 | + | 28.9315i | 0.952291 | + | 0.952291i | ||||
\(924\) | −14.5153 | − | 0.0554181i | −0.477518 | − | 0.00182312i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.7444 | − | 20.3419i | 0.385946 | − | 0.668478i | ||||
\(927\) | −8.98910 | − | 2.40862i | −0.295241 | − | 0.0791095i | ||||
\(928\) | 0.661282 | + | 0.177190i | 0.0217076 | + | 0.00581655i | ||||
\(929\) | −2.59922 | + | 4.50199i | −0.0852777 | + | 0.147705i | −0.905510 | − | 0.424326i | \(-0.860511\pi\) |
0.820232 | + | 0.572031i | \(0.193844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.2224 | + | 24.8089i | 1.38378 | + | 0.813078i | ||||
\(932\) | −10.2342 | − | 10.2342i | −0.335232 | − | 0.335232i | ||||
\(933\) | 2.18581 | + | 8.15755i | 0.0715602 | + | 0.267066i | ||||
\(934\) | −7.99472 | − | 13.8473i | −0.261595 | − | 0.453096i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.95981 | + | 1.70885i | 0.0967446 | + | 0.0558555i | ||||
\(937\) | −3.54515 | + | 3.54515i | −0.115815 | + | 0.115815i | −0.762639 | − | 0.646824i | \(-0.776097\pi\) |
0.646824 | + | 0.762639i | \(0.276097\pi\) | |||||||
\(938\) | −18.6916 | + | 18.5494i | −0.610301 | + | 0.605658i | ||||
\(939\) | − | 19.4096i | − | 0.633409i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.88464 | − | 5.12955i | 0.289631 | − | 0.167219i | −0.348144 | − | 0.937441i | \(-0.613188\pi\) |
0.637775 | + | 0.770222i | \(0.279855\pi\) | |||||||
\(942\) | 0.952462 | − | 3.55464i | 0.0310329 | − | 0.115816i | ||||
\(943\) | −4.24663 | + | 1.13788i | −0.138289 | + | 0.0370545i | ||||
\(944\) | 10.1603 | 0.330689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.1533 | −0.492676 | ||||||||
\(947\) | 27.1150 | − | 7.26545i | 0.881120 | − | 0.236096i | 0.210230 | − | 0.977652i | \(-0.432579\pi\) |
0.670890 | + | 0.741556i | \(0.265912\pi\) | |||||||
\(948\) | −2.15619 | + | 8.04700i | −0.0700297 | + | 0.261354i | ||||
\(949\) | 14.4166 | − | 8.32344i | 0.467983 | − | 0.270190i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.5503i | 0.504253i | ||||||||
\(952\) | 5.40781 | + | 1.47117i | 0.175268 | + | 0.0476809i | ||||
\(953\) | 29.6648 | − | 29.6648i | 0.960937 | − | 0.960937i | −0.0383279 | − | 0.999265i | \(-0.512203\pi\) |
0.999265 | + | 0.0383279i | \(0.0122031\pi\) | |||||||
\(954\) | 8.14273 | + | 4.70121i | 0.263631 | + | 0.152207i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.9868 | − | 25.9579i | −0.484708 | − | 0.839538i | ||||
\(957\) | −0.972117 | − | 3.62799i | −0.0314241 | − | 0.117276i | ||||
\(958\) | −6.37140 | − | 6.37140i | −0.205850 | − | 0.205850i | ||||
\(959\) | −5.01674 | + | 2.87093i | −0.161999 | + | 0.0927073i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0482042 | − | 0.0834922i | 0.00155498 | − | 0.00269330i | ||||
\(962\) | −32.3526 | − | 8.66886i | −1.04309 | − | 0.279495i | ||||
\(963\) | 11.8496 | + | 3.17510i | 0.381850 | + | 0.102316i | ||||
\(964\) | 8.31003 | − | 14.3934i | 0.267648 | − | 0.463580i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.01092 | + | 2.33617i | 0.129049 | + | 0.0751650i | ||||
\(967\) | 3.20889 | + | 3.20889i | 0.103191 | + | 0.103191i | 0.756817 | − | 0.653626i | \(-0.226753\pi\) |
−0.653626 | + | 0.756817i | \(0.726753\pi\) | |||||||
\(968\) | 4.94331 | + | 18.4487i | 0.158884 | + | 0.592963i | ||||
\(969\) | −7.40955 | − | 12.8337i | −0.238029 | − | 0.412278i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.1699 | + | 29.5430i | 1.64212 | + | 0.948079i | 0.980078 | + | 0.198612i | \(0.0636433\pi\) |
0.662042 | + | 0.749467i | \(0.269690\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 33.8155 | + | 34.0747i | 1.08408 | + | 1.09239i | ||||
\(974\) | 9.34012i | 0.299277i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.01469 | − | 0.585830i | 0.0324794 | − | 0.0187520i | ||||
\(977\) | 3.06089 | − | 11.4234i | 0.0979266 | − | 0.365467i | −0.899520 | − | 0.436879i | \(-0.856084\pi\) |
0.997447 | + | 0.0714120i | \(0.0227505\pi\) | |||||||
\(978\) | 13.6012 | − | 3.64443i | 0.434918 | − | 0.116536i | ||||
\(979\) | −39.4112 | −1.25959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.336622 | −0.0107475 | ||||||||
\(982\) | 2.01430 | − | 0.539730i | 0.0642788 | − | 0.0172235i | ||||
\(983\) | 9.83561 | − | 36.7070i | 0.313707 | − | 1.17077i | −0.611480 | − | 0.791260i | \(-0.709425\pi\) |
0.925187 | − | 0.379511i | \(-0.123908\pi\) | |||||||
\(984\) | 2.17023 | − | 1.25298i | 0.0691844 | − | 0.0399437i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.45017i | 0.0461829i | ||||||||
\(987\) | 6.56977 | + | 6.62013i | 0.209118 | + | 0.210721i | ||||
\(988\) | −16.9069 | + | 16.9069i | −0.537881 | + | 0.537881i | ||||
\(989\) | 4.19647 | + | 2.42283i | 0.133440 | + | 0.0770416i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00630 | − | 6.93911i | −0.127264 | − | 0.220428i | 0.795352 | − | 0.606148i | \(-0.207286\pi\) |
−0.922616 | + | 0.385720i | \(0.873953\pi\) | |||||||
\(992\) | −1.44328 | − | 5.38640i | −0.0458243 | − | 0.171018i | ||||
\(993\) | 11.4452 | + | 11.4452i | 0.363202 | + | 0.363202i | ||||
\(994\) | −27.3697 | − | 15.9415i | −0.868114 | − | 0.505635i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.86577 | + | 4.96366i | −0.0908054 | + | 0.157280i | ||||
\(997\) | −41.1086 | − | 11.0150i | −1.30192 | − | 0.348849i | −0.459745 | − | 0.888051i | \(-0.652059\pi\) |
−0.842176 | + | 0.539202i | \(0.818726\pi\) | |||||||
\(998\) | 12.9671 | + | 3.47453i | 0.410468 | + | 0.109984i | ||||
\(999\) | −4.90007 | + | 8.48716i | −0.155031 | + | 0.268522i |
(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 | 1050.2.bc.h.607.3 | 16 | ||
5.2 | odd | 4 | 210.2.u.b.103.3 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.g.943.2 | 16 | |||
5.4 | even | 2 | 210.2.u.a.187.1 | yes | 16 | ||
7.3 | odd | 6 | 1050.2.bc.g.157.2 | 16 | |||
15.2 | even | 4 | 630.2.bv.b.523.2 | 16 | |||
15.14 | odd | 2 | 630.2.bv.a.397.4 | 16 | |||
35.2 | odd | 12 | 1470.2.m.e.1273.7 | 16 | |||
35.3 | even | 12 | inner | 1050.2.bc.h.493.3 | 16 | ||
35.9 | even | 6 | 1470.2.m.d.97.6 | 16 | |||
35.12 | even | 12 | 1470.2.m.d.1273.6 | 16 | |||
35.17 | even | 12 | 210.2.u.a.73.1 | ✓ | 16 | ||
35.19 | odd | 6 | 1470.2.m.e.97.7 | 16 | |||
35.24 | odd | 6 | 210.2.u.b.157.3 | yes | 16 | ||
105.17 | odd | 12 | 630.2.bv.a.73.4 | 16 | |||
105.59 | even | 6 | 630.2.bv.b.577.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.73.1 | ✓ | 16 | 35.17 | even | 12 | ||
210.2.u.a.187.1 | yes | 16 | 5.4 | even | 2 | ||
210.2.u.b.103.3 | yes | 16 | 5.2 | odd | 4 | ||
210.2.u.b.157.3 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bv.a.73.4 | 16 | 105.17 | odd | 12 | |||
630.2.bv.a.397.4 | 16 | 15.14 | odd | 2 | |||
630.2.bv.b.523.2 | 16 | 15.2 | even | 4 | |||
630.2.bv.b.577.2 | 16 | 105.59 | even | 6 | |||
1050.2.bc.g.157.2 | 16 | 7.3 | odd | 6 | |||
1050.2.bc.g.943.2 | 16 | 5.3 | odd | 4 | |||
1050.2.bc.h.493.3 | 16 | 35.3 | even | 12 | inner | ||
1050.2.bc.h.607.3 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.d.97.6 | 16 | 35.9 | even | 6 | |||
1470.2.m.d.1273.6 | 16 | 35.12 | even | 12 | |||
1470.2.m.e.97.7 | 16 | 35.19 | odd | 6 | |||
1470.2.m.e.1273.7 | 16 | 35.2 | odd | 12 |