Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.d.47.3 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.292893 | − | 1.70711i | −0.169102 | − | 0.985599i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.23607i | 1.00000i | ||||||||
\(6\) | 1.00000 | − | 1.41421i | 0.408248 | − | 0.577350i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | −1.58114 | + | 1.58114i | −0.500000 | + | 0.500000i | ||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 1.70711 | − | 0.292893i | 0.492799 | − | 0.0845510i | ||||
\(13\) | 4.16228 | + | 4.16228i | 1.15441 | + | 1.15441i | 0.985659 | + | 0.168749i | \(0.0539728\pi\) |
0.168749 | + | 0.985659i | \(0.446027\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.81721 | − | 0.654929i | 0.985599 | − | 0.169102i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.65028 | + | 3.65028i | 0.885323 | + | 0.885323i | 0.994070 | − | 0.108746i | \(-0.0346836\pi\) |
−0.108746 | + | 0.994070i | \(0.534684\pi\) | |||||||
\(18\) | −2.70711 | − | 1.29289i | −0.638071 | − | 0.304738i | ||||
\(19\) | 5.16228i | 1.18431i | 0.805825 | + | 0.592154i | \(0.201722\pi\) | ||||
−0.805825 | + | 0.592154i | \(0.798278\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | − | 2.00000i | 0.426401 | − | 0.426401i | ||||
\(23\) | −0.707107 | + | 0.707107i | −0.147442 | + | 0.147442i | ||||
\(24\) | 1.41421 | + | 1.00000i | 0.288675 | + | 0.204124i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 5.88635i | 1.15441i | ||||||||
\(27\) | 2.53553 | + | 4.53553i | 0.487964 | + | 0.872864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 3.16228 | + | 2.23607i | 0.577350 | + | 0.408248i | ||||
\(31\) | 10.3246 | 1.85434 | 0.927172 | − | 0.374635i | \(-0.122232\pi\) | ||||
0.927172 | + | 0.374635i | \(0.122232\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −4.82843 | + | 0.828427i | −0.840521 | + | 0.144211i | ||||
\(34\) | 5.16228i | 0.885323i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | 5.16228 | − | 5.16228i | 0.848673 | − | 0.848673i | −0.141294 | − | 0.989968i | \(-0.545126\pi\) |
0.989968 | + | 0.141294i | \(0.0451264\pi\) | |||||||
\(38\) | −3.65028 | + | 3.65028i | −0.592154 | + | 0.592154i | ||||
\(39\) | 5.88635 | − | 8.32456i | 0.942570 | − | 1.33300i | ||||
\(40\) | −1.58114 | − | 1.58114i | −0.250000 | − | 0.250000i | ||||
\(41\) | 6.11584i | 0.955134i | 0.878595 | + | 0.477567i | \(0.158481\pi\) | ||||
−0.878595 | + | 0.477567i | \(0.841519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83772 | − | 2.83772i | −0.432749 | − | 0.432749i | 0.456814 | − | 0.889562i | \(-0.348991\pi\) |
−0.889562 | + | 0.456814i | \(0.848991\pi\) | |||||||
\(44\) | 2.82843 | 0.426401 | ||||||||
\(45\) | −2.23607 | − | 6.32456i | −0.333333 | − | 0.942809i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.71478 | − | 8.71478i | −1.27118 | − | 1.27118i | −0.945469 | − | 0.325712i | \(-0.894396\pi\) |
−0.325712 | − | 0.945469i | \(-0.605604\pi\) | |||||||
\(48\) | 0.292893 | + | 1.70711i | 0.0422755 | + | 0.246400i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | −3.53553 | − | 3.53553i | −0.500000 | − | 0.500000i | ||||
\(51\) | 5.16228 | − | 7.30056i | 0.722863 | − | 1.02228i | ||||
\(52\) | −4.16228 | + | 4.16228i | −0.577204 | + | 0.577204i | ||||
\(53\) | −6.70820 | + | 6.70820i | −0.921443 | + | 0.921443i | −0.997131 | − | 0.0756888i | \(-0.975884\pi\) |
0.0756888 | + | 0.997131i | \(0.475884\pi\) | |||||||
\(54\) | −1.41421 | + | 5.00000i | −0.192450 | + | 0.680414i | ||||
\(55\) | 6.32456 | 0.852803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.81256 | − | 1.51200i | 1.16725 | − | 0.200269i | ||||
\(58\) | −3.16228 | − | 3.16228i | −0.415227 | − | 0.415227i | ||||
\(59\) | 9.89949 | 1.28880 | 0.644402 | − | 0.764687i | \(-0.277106\pi\) | ||||
0.644402 | + | 0.764687i | \(0.277106\pi\) | |||||||
\(60\) | 0.654929 | + | 3.81721i | 0.0845510 | + | 0.492799i | ||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 7.30056 | + | 7.30056i | 0.927172 | + | 0.927172i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −9.30714 | + | 9.30714i | −1.15441 | + | 1.15441i | ||||
\(66\) | −4.00000 | − | 2.82843i | −0.492366 | − | 0.348155i | ||||
\(67\) | 5.16228 | − | 5.16228i | 0.630673 | − | 0.630673i | −0.317564 | − | 0.948237i | \(-0.602865\pi\) |
0.948237 | + | 0.317564i | \(0.102865\pi\) | |||||||
\(68\) | −3.65028 | + | 3.65028i | −0.442662 | + | 0.442662i | ||||
\(69\) | 1.41421 | + | 1.00000i | 0.170251 | + | 0.120386i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.05792i | − | 0.362909i | −0.983399 | − | 0.181454i | \(-0.941920\pi\) | ||
0.983399 | − | 0.181454i | \(-0.0580804\pi\) | |||||||
\(72\) | 1.29289 | − | 2.70711i | 0.152369 | − | 0.319036i | ||||
\(73\) | −7.32456 | − | 7.32456i | −0.857274 | − | 0.857274i | 0.133742 | − | 0.991016i | \(-0.457301\pi\) |
−0.991016 | + | 0.133742i | \(0.957301\pi\) | |||||||
\(74\) | 7.30056 | 0.848673 | ||||||||
\(75\) | 1.46447 | + | 8.53553i | 0.169102 | + | 0.985599i | ||||
\(76\) | −5.16228 | −0.592154 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0486 | − | 1.72407i | 1.13778 | − | 0.195213i | ||||
\(79\) | 3.16228i | 0.355784i | 0.984050 | + | 0.177892i | \(0.0569278\pi\) | ||||
−0.984050 | + | 0.177892i | \(0.943072\pi\) | |||||||
\(80\) | − | 2.23607i | − | 0.250000i | ||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | −4.32456 | + | 4.32456i | −0.477567 | + | 0.477567i | ||||
\(83\) | −5.88635 | + | 5.88635i | −0.646111 | + | 0.646111i | −0.952051 | − | 0.305940i | \(-0.901029\pi\) |
0.305940 | + | 0.952051i | \(0.401029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.16228 | + | 8.16228i | −0.885323 | + | 0.885323i | ||||
\(86\) | − | 4.01315i | − | 0.432749i | ||||||
\(87\) | 1.30986 | + | 7.63441i | 0.140432 | + | 0.818495i | ||||
\(88\) | 2.00000 | + | 2.00000i | 0.213201 | + | 0.213201i | ||||
\(89\) | −0.458991 | −0.0486529 | −0.0243264 | − | 0.999704i | \(-0.507744\pi\) | ||||
−0.0243264 | + | 0.999704i | \(0.507744\pi\) | |||||||
\(90\) | 2.89100 | − | 6.05327i | 0.304738 | − | 0.638071i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.707107 | − | 0.707107i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −3.02399 | − | 17.6251i | −0.313573 | − | 1.82764i | ||||
\(94\) | − | 12.3246i | − | 1.27118i | ||||||
\(95\) | −11.5432 | −1.18431 | ||||||||
\(96\) | −1.00000 | + | 1.41421i | −0.102062 | + | 0.144338i | ||||
\(97\) | 1.16228 | − | 1.16228i | 0.118011 | − | 0.118011i | −0.645635 | − | 0.763646i | \(-0.723407\pi\) |
0.763646 | + | 0.645635i | \(0.223407\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | 2.82843 | + | 8.00000i | 0.284268 | + | 0.804030i | ||||
\(100\) | − | 5.00000i | − | 0.500000i | ||||||
\(101\) | − | 1.64371i | − | 0.163555i | −0.996651 | − | 0.0817776i | \(-0.973940\pi\) | ||
0.996651 | − | 0.0817776i | \(-0.0260597\pi\) | |||||||
\(102\) | 8.81256 | − | 1.51200i | 0.872573 | − | 0.149710i | ||||
\(103\) | −11.1623 | − | 11.1623i | −1.09985 | − | 1.09985i | −0.994427 | − | 0.105425i | \(-0.966380\pi\) |
−0.105425 | − | 0.994427i | \(-0.533620\pi\) | |||||||
\(104\) | −5.88635 | −0.577204 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.48683 | −0.921443 | ||||||||
\(107\) | −10.3585 | − | 10.3585i | −1.00139 | − | 1.00139i | −0.999999 | − | 0.00139356i | \(-0.999556\pi\) |
−0.00139356 | − | 0.999999i | \(-0.500444\pi\) | |||||||
\(108\) | −4.53553 | + | 2.53553i | −0.436432 | + | 0.243982i | ||||
\(109\) | − | 14.3246i | − | 1.37204i | −0.727581 | − | 0.686022i | \(-0.759355\pi\) | ||
0.727581 | − | 0.686022i | \(-0.240645\pi\) | |||||||
\(110\) | 4.47214 | + | 4.47214i | 0.426401 | + | 0.426401i | ||||
\(111\) | −10.3246 | − | 7.30056i | −0.979963 | − | 0.692939i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.7793 | − | 13.7793i | 1.29624 | − | 1.29624i | 0.365391 | − | 0.930854i | \(-0.380935\pi\) |
0.930854 | − | 0.365391i | \(-0.119065\pi\) | |||||||
\(114\) | 7.30056 | + | 5.16228i | 0.683760 | + | 0.483492i | ||||
\(115\) | −1.58114 | − | 1.58114i | −0.147442 | − | 0.147442i | ||||
\(116\) | − | 4.47214i | − | 0.415227i | ||||||
\(117\) | −15.9350 | − | 7.61042i | −1.47319 | − | 0.703584i | ||||
\(118\) | 7.00000 | + | 7.00000i | 0.644402 | + | 0.644402i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.23607 | + | 3.16228i | −0.204124 | + | 0.288675i | ||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 5.65685 | + | 5.65685i | 0.512148 | + | 0.512148i | ||||
\(123\) | 10.4404 | − | 1.79129i | 0.941379 | − | 0.161515i | ||||
\(124\) | 10.3246i | 0.927172i | ||||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.16228 | + | 5.16228i | −0.458078 | + | 0.458078i | −0.898024 | − | 0.439946i | \(-0.854998\pi\) |
0.439946 | + | 0.898024i | \(0.354998\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −4.01315 | + | 5.67544i | −0.353338 | + | 0.499695i | ||||
\(130\) | −13.1623 | −1.15441 | ||||||||
\(131\) | − | 7.53006i | − | 0.657904i | −0.944347 | − | 0.328952i | \(-0.893305\pi\) | ||
0.944347 | − | 0.328952i | \(-0.106695\pi\) | |||||||
\(132\) | −0.828427 | − | 4.82843i | −0.0721053 | − | 0.420261i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.30056 | 0.630673 | ||||||||
\(135\) | −10.1418 | + | 5.66963i | −0.872864 | + | 0.487964i | ||||
\(136\) | −5.16228 | −0.442662 | ||||||||
\(137\) | −3.65028 | − | 3.65028i | −0.311865 | − | 0.311865i | 0.533767 | − | 0.845632i | \(-0.320776\pi\) |
−0.845632 | + | 0.533767i | \(0.820776\pi\) | |||||||
\(138\) | 0.292893 | + | 1.70711i | 0.0249327 | + | 0.145319i | ||||
\(139\) | − | 2.32456i | − | 0.197166i | −0.995129 | − | 0.0985831i | \(-0.968569\pi\) | ||
0.995129 | − | 0.0985831i | \(-0.0314310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.3246 | + | 17.4296i | −1.03791 | + | 1.46783i | ||||
\(142\) | 2.16228 | − | 2.16228i | 0.181454 | − | 0.181454i | ||||
\(143\) | 11.7727 | − | 11.7727i | 0.984483 | − | 0.984483i | ||||
\(144\) | 2.82843 | − | 1.00000i | 0.235702 | − | 0.0833333i | ||||
\(145\) | − | 10.0000i | − | 0.830455i | ||||||
\(146\) | − | 10.3585i | − | 0.857274i | ||||||
\(147\) | 11.9497 | − | 2.05025i | 0.985599 | − | 0.169102i | ||||
\(148\) | 5.16228 | + | 5.16228i | 0.424337 | + | 0.424337i | ||||
\(149\) | −19.0733 | −1.56254 | −0.781271 | − | 0.624192i | \(-0.785428\pi\) | ||||
−0.781271 | + | 0.624192i | \(0.785428\pi\) | |||||||
\(150\) | −5.00000 | + | 7.07107i | −0.408248 | + | 0.577350i | ||||
\(151\) | 2.32456 | 0.189170 | 0.0945848 | − | 0.995517i | \(-0.469848\pi\) | ||||
0.0945848 | + | 0.995517i | \(0.469848\pi\) | |||||||
\(152\) | −3.65028 | − | 3.65028i | −0.296077 | − | 0.296077i | ||||
\(153\) | −13.9748 | − | 6.67427i | −1.12980 | − | 0.539583i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.0864i | 1.85434i | ||||||||
\(156\) | 8.32456 | + | 5.88635i | 0.666498 | + | 0.471285i | ||||
\(157\) | −9.48683 | + | 9.48683i | −0.757132 | + | 0.757132i | −0.975799 | − | 0.218668i | \(-0.929829\pi\) |
0.218668 | + | 0.975799i | \(0.429829\pi\) | |||||||
\(158\) | −2.23607 | + | 2.23607i | −0.177892 | + | 0.177892i | ||||
\(159\) | 13.4164 | + | 9.48683i | 1.06399 | + | 0.752355i | ||||
\(160\) | 1.58114 | − | 1.58114i | 0.125000 | − | 0.125000i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.94975 | + | 0.949747i | 0.703159 | + | 0.0746192i | ||||
\(163\) | 16.6491 | + | 16.6491i | 1.30406 | + | 1.30406i | 0.925631 | + | 0.378428i | \(0.123535\pi\) |
0.378428 | + | 0.925631i | \(0.376465\pi\) | |||||||
\(164\) | −6.11584 | −0.477567 | ||||||||
\(165\) | −1.85242 | − | 10.7967i | −0.144211 | − | 0.840521i | ||||
\(166\) | −8.32456 | −0.646111 | ||||||||
\(167\) | 3.28742 | + | 3.28742i | 0.254388 | + | 0.254388i | 0.822767 | − | 0.568379i | \(-0.192429\pi\) |
−0.568379 | + | 0.822767i | \(0.692429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.6491i | 1.66532i | ||||||||
\(170\) | −11.5432 | −0.885323 | ||||||||
\(171\) | −5.16228 | − | 14.6011i | −0.394769 | − | 1.11658i | ||||
\(172\) | 2.83772 | − | 2.83772i | 0.216374 | − | 0.216374i | ||||
\(173\) | −0.229495 | + | 0.229495i | −0.0174482 | + | 0.0174482i | −0.715777 | − | 0.698329i | \(-0.753927\pi\) |
0.698329 | + | 0.715777i | \(0.253927\pi\) | |||||||
\(174\) | −4.47214 | + | 6.32456i | −0.339032 | + | 0.479463i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | −2.89949 | − | 16.8995i | −0.217939 | − | 1.27024i | ||||
\(178\) | −0.324555 | − | 0.324555i | −0.0243264 | − | 0.0243264i | ||||
\(179\) | 4.70163 | 0.351416 | 0.175708 | − | 0.984442i | \(-0.443778\pi\) | ||||
0.175708 | + | 0.984442i | \(0.443778\pi\) | |||||||
\(180\) | 6.32456 | − | 2.23607i | 0.471405 | − | 0.166667i | ||||
\(181\) | 9.67544 | 0.719170 | 0.359585 | − | 0.933112i | \(-0.382918\pi\) | ||||
0.359585 | + | 0.933112i | \(0.382918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.34315 | − | 13.6569i | −0.173210 | − | 1.00954i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 11.5432 | + | 11.5432i | 0.848673 | + | 0.848673i | ||||
\(186\) | 10.3246 | − | 14.6011i | 0.757033 | − | 1.07061i | ||||
\(187\) | 10.3246 | − | 10.3246i | 0.755006 | − | 0.755006i | ||||
\(188\) | 8.71478 | − | 8.71478i | 0.635590 | − | 0.635590i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.16228 | − | 8.16228i | −0.592154 | − | 0.592154i | ||||
\(191\) | 0.458991i | 0.0332114i | 0.999862 | + | 0.0166057i | \(0.00528600\pi\) | ||||
−0.999862 | + | 0.0166057i | \(0.994714\pi\) | |||||||
\(192\) | −1.70711 | + | 0.292893i | −0.123200 | + | 0.0211377i | ||||
\(193\) | 3.00000 | + | 3.00000i | 0.215945 | + | 0.215945i | 0.806787 | − | 0.590842i | \(-0.201204\pi\) |
−0.590842 | + | 0.806787i | \(0.701204\pi\) | |||||||
\(194\) | 1.64371 | 0.118011 | ||||||||
\(195\) | 18.6143 | + | 13.1623i | 1.33300 | + | 0.942570i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −11.5432 | − | 11.5432i | −0.822419 | − | 0.822419i | 0.164035 | − | 0.986454i | \(-0.447549\pi\) |
−0.986454 | + | 0.164035i | \(0.947549\pi\) | |||||||
\(198\) | −3.65685 | + | 7.65685i | −0.259881 | + | 0.544149i | ||||
\(199\) | 8.83772i | 0.626490i | 0.949672 | + | 0.313245i | \(0.101416\pi\) | ||||
−0.949672 | + | 0.313245i | \(0.898584\pi\) | |||||||
\(200\) | 3.53553 | − | 3.53553i | 0.250000 | − | 0.250000i | ||||
\(201\) | −10.3246 | − | 7.30056i | −0.728238 | − | 0.514942i | ||||
\(202\) | 1.16228 | − | 1.16228i | 0.0817776 | − | 0.0817776i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.30056 | + | 5.16228i | 0.511142 | + | 0.361432i | ||||
\(205\) | −13.6754 | −0.955134 | ||||||||
\(206\) | − | 15.7858i | − | 1.09985i | ||||||
\(207\) | 1.29289 | − | 2.70711i | 0.0898623 | − | 0.188157i | ||||
\(208\) | −4.16228 | − | 4.16228i | −0.288602 | − | 0.288602i | ||||
\(209\) | 14.6011 | 1.00998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3246 | 0.986143 | 0.493072 | − | 0.869989i | \(-0.335874\pi\) | ||||
0.493072 | + | 0.869989i | \(0.335874\pi\) | |||||||
\(212\) | −6.70820 | − | 6.70820i | −0.460721 | − | 0.460721i | ||||
\(213\) | −5.22020 | + | 0.895645i | −0.357682 | + | 0.0613686i | ||||
\(214\) | − | 14.6491i | − | 1.00139i | ||||||
\(215\) | 6.34534 | − | 6.34534i | 0.432749 | − | 0.432749i | ||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.1290 | − | 10.1290i | 0.686022 | − | 0.686022i | ||||
\(219\) | −10.3585 | + | 14.6491i | −0.699962 | + | 0.989895i | ||||
\(220\) | 6.32456i | 0.426401i | ||||||||
\(221\) | 30.3870i | 2.04405i | ||||||||
\(222\) | −2.13829 | − | 12.4628i | −0.143512 | − | 0.836451i | ||||
\(223\) | 13.1623 | + | 13.1623i | 0.881411 | + | 0.881411i | 0.993678 | − | 0.112267i | \(-0.0358111\pi\) |
−0.112267 | + | 0.993678i | \(0.535811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.1421 | − | 5.00000i | 0.942809 | − | 0.333333i | ||||
\(226\) | 19.4868 | 1.29624 | ||||||||
\(227\) | −4.24264 | − | 4.24264i | −0.281594 | − | 0.281594i | 0.552151 | − | 0.833744i | \(-0.313807\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(228\) | 1.51200 | + | 8.81256i | 0.100134 | + | 0.583626i | ||||
\(229\) | − | 25.2982i | − | 1.67175i | −0.548917 | − | 0.835877i | \(-0.684960\pi\) | ||
0.548917 | − | 0.835877i | \(-0.315040\pi\) | |||||||
\(230\) | − | 2.23607i | − | 0.147442i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.16228 | − | 3.16228i | 0.207614 | − | 0.207614i | ||||
\(233\) | −5.88635 | + | 5.88635i | −0.385628 | + | 0.385628i | −0.873125 | − | 0.487497i | \(-0.837910\pi\) |
0.487497 | + | 0.873125i | \(0.337910\pi\) | |||||||
\(234\) | −5.88635 | − | 16.6491i | −0.384803 | − | 1.08839i | ||||
\(235\) | 19.4868 | − | 19.4868i | 1.27118 | − | 1.27118i | ||||
\(236\) | 9.89949i | 0.644402i | ||||||||
\(237\) | 5.39835 | − | 0.926210i | 0.350660 | − | 0.0601638i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.34534 | 0.410446 | 0.205223 | − | 0.978715i | \(-0.434208\pi\) | ||||
0.205223 | + | 0.978715i | \(0.434208\pi\) | |||||||
\(240\) | −3.81721 | + | 0.654929i | −0.246400 | + | 0.0422755i | ||||
\(241\) | 8.32456 | 0.536232 | 0.268116 | − | 0.963387i | \(-0.413599\pi\) | ||||
0.268116 | + | 0.963387i | \(0.413599\pi\) | |||||||
\(242\) | 2.12132 | + | 2.12132i | 0.136364 | + | 0.136364i | ||||
\(243\) | −11.7071 | − | 10.2929i | −0.751011 | − | 0.660289i | ||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | −15.6525 | −1.00000 | ||||||||
\(246\) | 8.64911 | + | 6.11584i | 0.551447 | + | 0.389932i | ||||
\(247\) | −21.4868 | + | 21.4868i | −1.36717 | + | 1.36717i | ||||
\(248\) | −7.30056 | + | 7.30056i | −0.463586 | + | 0.463586i | ||||
\(249\) | 11.7727 | + | 8.32456i | 0.746064 | + | 0.527547i | ||||
\(250\) | 7.90569 | − | 7.90569i | 0.500000 | − | 0.500000i | ||||
\(251\) | 5.65685i | 0.357057i | 0.983935 | + | 0.178529i | \(0.0571337\pi\) | ||||
−0.983935 | + | 0.178529i | \(0.942866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | + | 2.00000i | 0.125739 | + | 0.125739i | ||||
\(254\) | −7.30056 | −0.458078 | ||||||||
\(255\) | 16.3246 | + | 11.5432i | 1.02228 | + | 0.722863i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.4743 | + | 16.4743i | 1.02764 | + | 1.02764i | 0.999607 | + | 0.0280335i | \(0.00892451\pi\) |
0.0280335 | + | 0.999607i | \(0.491075\pi\) | |||||||
\(258\) | −6.85087 | + | 1.17542i | −0.426516 | + | 0.0731786i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.30714 | − | 9.30714i | −0.577204 | − | 0.577204i | ||||
\(261\) | 12.6491 | − | 4.47214i | 0.782960 | − | 0.276818i | ||||
\(262\) | 5.32456 | − | 5.32456i | 0.328952 | − | 0.328952i | ||||
\(263\) | 17.4296 | − | 17.4296i | 1.07475 | − | 1.07475i | 0.0777819 | − | 0.996970i | \(-0.475216\pi\) |
0.996970 | − | 0.0777819i | \(-0.0247838\pi\) | |||||||
\(264\) | 2.82843 | − | 4.00000i | 0.174078 | − | 0.246183i | ||||
\(265\) | −15.0000 | − | 15.0000i | −0.921443 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.134435 | + | 0.783546i | 0.00822730 | + | 0.0479522i | ||||
\(268\) | 5.16228 | + | 5.16228i | 0.315336 | + | 0.315336i | ||||
\(269\) | 18.6143 | 1.13493 | 0.567466 | − | 0.823397i | \(-0.307924\pi\) | ||||
0.567466 | + | 0.823397i | \(0.307924\pi\) | |||||||
\(270\) | −11.1803 | − | 3.16228i | −0.680414 | − | 0.192450i | ||||
\(271\) | −6.97367 | −0.423620 | −0.211810 | − | 0.977311i | \(-0.567936\pi\) | ||||
−0.211810 | + | 0.977311i | \(0.567936\pi\) | |||||||
\(272\) | −3.65028 | − | 3.65028i | −0.221331 | − | 0.221331i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.16228i | − | 0.311865i | ||||||
\(275\) | 14.1421i | 0.852803i | ||||||||
\(276\) | −1.00000 | + | 1.41421i | −0.0601929 | + | 0.0851257i | ||||
\(277\) | 4.16228 | − | 4.16228i | 0.250087 | − | 0.250087i | −0.570919 | − | 0.821006i | \(-0.693413\pi\) |
0.821006 | + | 0.570919i | \(0.193413\pi\) | |||||||
\(278\) | 1.64371 | − | 1.64371i | 0.0985831 | − | 0.0985831i | ||||
\(279\) | −29.2023 | + | 10.3246i | −1.74829 | + | 0.618115i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.10270i | − | 0.125437i | −0.998031 | − | 0.0627183i | \(-0.980023\pi\) | ||
0.998031 | − | 0.0627183i | \(-0.0199770\pi\) | |||||||
\(282\) | −21.0393 | + | 3.60978i | −1.25287 | + | 0.214959i | ||||
\(283\) | −16.6491 | − | 16.6491i | −0.989687 | − | 0.989687i | 0.0102605 | − | 0.999947i | \(-0.496734\pi\) |
−0.999947 | + | 0.0102605i | \(0.996734\pi\) | |||||||
\(284\) | 3.05792 | 0.181454 | ||||||||
\(285\) | 3.38093 | + | 19.7055i | 0.200269 | + | 1.16725i | ||||
\(286\) | 16.6491 | 0.984483 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.70711 | + | 1.29289i | 0.159518 | + | 0.0761845i | ||||
\(289\) | 9.64911i | 0.567595i | ||||||||
\(290\) | 7.07107 | − | 7.07107i | 0.415227 | − | 0.415227i | ||||
\(291\) | −2.32456 | − | 1.64371i | −0.136268 | − | 0.0963559i | ||||
\(292\) | 7.32456 | − | 7.32456i | 0.428637 | − | 0.428637i | ||||
\(293\) | 0.133369 | − | 0.133369i | 0.00779148 | − | 0.00779148i | −0.703200 | − | 0.710992i | \(-0.748246\pi\) |
0.710992 | + | 0.703200i | \(0.248246\pi\) | |||||||
\(294\) | 9.89949 | + | 7.00000i | 0.577350 | + | 0.408248i | ||||
\(295\) | 22.1359i | 1.28880i | ||||||||
\(296\) | 7.30056i | 0.424337i | ||||||||
\(297\) | 12.8284 | − | 7.17157i | 0.744381 | − | 0.416137i | ||||
\(298\) | −13.4868 | − | 13.4868i | −0.781271 | − | 0.781271i | ||||
\(299\) | −5.88635 | −0.340416 | ||||||||
\(300\) | −8.53553 | + | 1.46447i | −0.492799 | + | 0.0845510i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.64371 | + | 1.64371i | 0.0945848 | + | 0.0945848i | ||||
\(303\) | −2.80599 | + | 0.481431i | −0.161200 | + | 0.0276575i | ||||
\(304\) | − | 5.16228i | − | 0.296077i | ||||||
\(305\) | 17.8885i | 1.02430i | ||||||||
\(306\) | −5.16228 | − | 14.6011i | −0.295108 | − | 0.834691i | ||||
\(307\) | 2.32456 | − | 2.32456i | 0.132669 | − | 0.132669i | −0.637654 | − | 0.770323i | \(-0.720095\pi\) |
0.770323 | + | 0.637654i | \(0.220095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.7858 | + | 22.3246i | −0.898025 | + | 1.27000i | ||||
\(310\) | −16.3246 | + | 16.3246i | −0.927172 | + | 0.927172i | ||||
\(311\) | 26.6033i | 1.50854i | 0.656567 | + | 0.754268i | \(0.272008\pi\) | ||||
−0.656567 | + | 0.754268i | \(0.727992\pi\) | |||||||
\(312\) | 1.72407 | + | 10.0486i | 0.0976063 | + | 0.568891i | ||||
\(313\) | −9.16228 | − | 9.16228i | −0.517883 | − | 0.517883i | 0.399048 | − | 0.916930i | \(-0.369341\pi\) |
−0.916930 | + | 0.399048i | \(0.869341\pi\) | |||||||
\(314\) | −13.4164 | −0.757132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.16228 | −0.177892 | ||||||||
\(317\) | −2.59893 | − | 2.59893i | −0.145971 | − | 0.145971i | 0.630345 | − | 0.776315i | \(-0.282914\pi\) |
−0.776315 | + | 0.630345i | \(0.782914\pi\) | |||||||
\(318\) | 2.77863 | + | 16.1950i | 0.155818 | + | 0.908173i | ||||
\(319\) | 12.6491i | 0.708214i | ||||||||
\(320\) | 2.23607 | 0.125000 | ||||||||
\(321\) | −14.6491 | + | 20.7170i | −0.817634 | + | 1.15631i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.8438 | + | 18.8438i | −1.04850 | + | 1.04850i | ||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | −20.8114 | − | 20.8114i | −1.15441 | − | 1.15441i | ||||
\(326\) | 23.5454i | 1.30406i | ||||||||
\(327\) | −24.4535 | + | 4.19557i | −1.35228 | + | 0.232015i | ||||
\(328\) | −4.32456 | − | 4.32456i | −0.238784 | − | 0.238784i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.32456 | − | 8.94427i | 0.348155 | − | 0.492366i | ||||
\(331\) | 2.97367 | 0.163447 | 0.0817237 | − | 0.996655i | \(-0.473957\pi\) | ||||
0.0817237 | + | 0.996655i | \(0.473957\pi\) | |||||||
\(332\) | −5.88635 | − | 5.88635i | −0.323055 | − | 0.323055i | ||||
\(333\) | −9.43885 | + | 19.7634i | −0.517246 | + | 1.08303i | ||||
\(334\) | 4.64911i | 0.254388i | ||||||||
\(335\) | 11.5432 | + | 11.5432i | 0.630673 | + | 0.630673i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.48683 | + | 9.48683i | −0.516781 | + | 0.516781i | −0.916596 | − | 0.399815i | \(-0.869074\pi\) |
0.399815 | + | 0.916596i | \(0.369074\pi\) | |||||||
\(338\) | −15.3082 | + | 15.3082i | −0.832658 | + | 0.832658i | ||||
\(339\) | −27.5585 | − | 19.4868i | −1.49677 | − | 1.05838i | ||||
\(340\) | −8.16228 | − | 8.16228i | −0.442662 | − | 0.442662i | ||||
\(341\) | − | 29.2023i | − | 1.58139i | ||||||
\(342\) | 6.67427 | − | 13.9748i | 0.360903 | − | 0.755673i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.01315 | 0.216374 | ||||||||
\(345\) | −2.23607 | + | 3.16228i | −0.120386 | + | 0.170251i | ||||
\(346\) | −0.324555 | −0.0174482 | ||||||||
\(347\) | −0.955223 | − | 0.955223i | −0.0512791 | − | 0.0512791i | 0.681002 | − | 0.732281i | \(-0.261544\pi\) |
−0.732281 | + | 0.681002i | \(0.761544\pi\) | |||||||
\(348\) | −7.63441 | + | 1.30986i | −0.409248 | + | 0.0702158i | ||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.32456 | + | 29.4317i | −0.444332 | + | 1.57095i | ||||
\(352\) | −2.00000 | + | 2.00000i | −0.106600 | + | 0.106600i | ||||
\(353\) | 17.6590 | − | 17.6590i | 0.939896 | − | 0.939896i | −0.0583971 | − | 0.998293i | \(-0.518599\pi\) |
0.998293 | + | 0.0583971i | \(0.0185990\pi\) | |||||||
\(354\) | 9.89949 | − | 14.0000i | 0.526152 | − | 0.744092i | ||||
\(355\) | 6.83772 | 0.362909 | ||||||||
\(356\) | − | 0.458991i | − | 0.0243264i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.32456 | + | 3.32456i | 0.175708 | + | 0.175708i | ||||
\(359\) | 19.7990 | 1.04495 | 0.522475 | − | 0.852654i | \(-0.325009\pi\) | ||||
0.522475 | + | 0.852654i | \(0.325009\pi\) | |||||||
\(360\) | 6.05327 | + | 2.89100i | 0.319036 | + | 0.152369i | ||||
\(361\) | −7.64911 | −0.402585 | ||||||||
\(362\) | 6.84157 | + | 6.84157i | 0.359585 | + | 0.359585i | ||||
\(363\) | −0.878680 | − | 5.12132i | −0.0461187 | − | 0.268800i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.3782 | − | 16.3782i | 0.857274 | − | 0.857274i | ||||
\(366\) | 8.00000 | − | 11.3137i | 0.418167 | − | 0.591377i | ||||
\(367\) | 1.48683 | − | 1.48683i | 0.0776120 | − | 0.0776120i | −0.667235 | − | 0.744847i | \(-0.732522\pi\) |
0.744847 | + | 0.667235i | \(0.232522\pi\) | |||||||
\(368\) | 0.707107 | − | 0.707107i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | −6.11584 | − | 17.2982i | −0.318378 | − | 0.900509i | ||||
\(370\) | 16.3246i | 0.848673i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 17.6251 | − | 3.02399i | 0.913820 | − | 0.156787i | ||||
\(373\) | 13.4868 | + | 13.4868i | 0.698322 | + | 0.698322i | 0.964048 | − | 0.265727i | \(-0.0856119\pi\) |
−0.265727 | + | 0.964048i | \(0.585612\pi\) | |||||||
\(374\) | 14.6011 | 0.755006 | ||||||||
\(375\) | −19.0860 | + | 3.27465i | −0.985599 | + | 0.169102i | ||||
\(376\) | 12.3246 | 0.635590 | ||||||||
\(377\) | −18.6143 | − | 18.6143i | −0.958684 | − | 0.958684i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.48683i | 0.179107i | 0.995982 | + | 0.0895533i | \(0.0285439\pi\) | ||||
−0.995982 | + | 0.0895533i | \(0.971456\pi\) | |||||||
\(380\) | − | 11.5432i | − | 0.592154i | ||||||
\(381\) | 10.3246 | + | 7.30056i | 0.528943 | + | 0.374019i | ||||
\(382\) | −0.324555 | + | 0.324555i | −0.0166057 | + | 0.0166057i | ||||
\(383\) | 6.84157 | − | 6.84157i | 0.349588 | − | 0.349588i | −0.510368 | − | 0.859956i | \(-0.670491\pi\) |
0.859956 | + | 0.510368i | \(0.170491\pi\) | |||||||
\(384\) | −1.41421 | − | 1.00000i | −0.0721688 | − | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.24264i | 0.215945i | ||||||||
\(387\) | 10.8640 | + | 5.18857i | 0.552249 | + | 0.263750i | ||||
\(388\) | 1.16228 | + | 1.16228i | 0.0590057 | + | 0.0590057i | ||||
\(389\) | −12.4984 | −0.633695 | −0.316848 | − | 0.948476i | \(-0.602624\pi\) | ||||
−0.316848 | + | 0.948476i | \(0.602624\pi\) | |||||||
\(390\) | 3.85514 | + | 22.4694i | 0.195213 | + | 1.13778i | ||||
\(391\) | −5.16228 | −0.261068 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | −12.8546 | + | 2.20550i | −0.648429 | + | 0.111253i | ||||
\(394\) | − | 16.3246i | − | 0.822419i | ||||||
\(395\) | −7.07107 | −0.355784 | ||||||||
\(396\) | −8.00000 | + | 2.82843i | −0.402015 | + | 0.142134i | ||||
\(397\) | 6.81139 | − | 6.81139i | 0.341854 | − | 0.341854i | −0.515210 | − | 0.857064i | \(-0.672286\pi\) |
0.857064 | + | 0.515210i | \(0.172286\pi\) | |||||||
\(398\) | −6.24921 | + | 6.24921i | −0.313245 | + | 0.313245i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 19.7990i | 0.988714i | 0.869259 | + | 0.494357i | \(0.164597\pi\) | ||||
−0.869259 | + | 0.494357i | \(0.835403\pi\) | |||||||
\(402\) | −2.13829 | − | 12.4628i | −0.106648 | − | 0.621590i | ||||
\(403\) | 42.9737 | + | 42.9737i | 2.14067 | + | 2.14067i | ||||
\(404\) | 1.64371 | 0.0817776 | ||||||||
\(405\) | 12.6491 | + | 15.6525i | 0.628539 | + | 0.777778i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6011 | − | 14.6011i | −0.723751 | − | 0.723751i | ||||
\(408\) | 1.51200 | + | 8.81256i | 0.0748550 | + | 0.436287i | ||||
\(409\) | 20.0000i | 0.988936i | 0.869196 | + | 0.494468i | \(0.164637\pi\) | ||||
−0.869196 | + | 0.494468i | \(0.835363\pi\) | |||||||
\(410\) | −9.67000 | − | 9.67000i | −0.477567 | − | 0.477567i | ||||
\(411\) | −5.16228 | + | 7.30056i | −0.254636 | + | 0.360110i | ||||
\(412\) | 11.1623 | − | 11.1623i | 0.549926 | − | 0.549926i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.82843 | − | 1.00000i | 0.139010 | − | 0.0491473i | ||||
\(415\) | −13.1623 | − | 13.1623i | −0.646111 | − | 0.646111i | ||||
\(416\) | − | 5.88635i | − | 0.288602i | ||||||
\(417\) | −3.96826 | + | 0.680846i | −0.194327 | + | 0.0333412i | ||||
\(418\) | 10.3246 | + | 10.3246i | 0.504991 | + | 0.504991i | ||||
\(419\) | 26.3738 | 1.28845 | 0.644223 | − | 0.764838i | \(-0.277181\pi\) | ||||
0.644223 | + | 0.764838i | \(0.277181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3509 | 0.553208 | 0.276604 | − | 0.960984i | \(-0.410791\pi\) | ||||
0.276604 | + | 0.960984i | \(0.410791\pi\) | |||||||
\(422\) | 10.1290 | + | 10.1290i | 0.493072 | + | 0.493072i | ||||
\(423\) | 33.3639 | + | 15.9343i | 1.62221 | + | 0.774754i | ||||
\(424\) | − | 9.48683i | − | 0.460721i | ||||||
\(425\) | −18.2514 | − | 18.2514i | −0.885323 | − | 0.885323i | ||||
\(426\) | −4.32456 | − | 3.05792i | −0.209525 | − | 0.148157i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.3585 | − | 10.3585i | 0.500696 | − | 0.500696i | ||||
\(429\) | −23.5454 | − | 16.6491i | −1.13678 | − | 0.803827i | ||||
\(430\) | 8.97367 | 0.432749 | ||||||||
\(431\) | 6.11584i | 0.294590i | 0.989093 | + | 0.147295i | \(0.0470566\pi\) | ||||
−0.989093 | + | 0.147295i | \(0.952943\pi\) | |||||||
\(432\) | −2.53553 | − | 4.53553i | −0.121991 | − | 0.218216i | ||||
\(433\) | 16.1359 | + | 16.1359i | 0.775444 | + | 0.775444i | 0.979052 | − | 0.203608i | \(-0.0652669\pi\) |
−0.203608 | + | 0.979052i | \(0.565267\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.0711 | + | 2.92893i | −0.818495 | + | 0.140432i | ||||
\(436\) | 14.3246 | 0.686022 | ||||||||
\(437\) | −3.65028 | − | 3.65028i | −0.174617 | − | 0.174617i | ||||
\(438\) | −17.6830 | + | 3.03393i | −0.844928 | + | 0.144967i | ||||
\(439\) | − | 11.3509i | − | 0.541748i | −0.962615 | − | 0.270874i | \(-0.912687\pi\) | ||
0.962615 | − | 0.270874i | \(-0.0873127\pi\) | |||||||
\(440\) | −4.47214 | + | 4.47214i | −0.213201 | + | 0.213201i | ||||
\(441\) | −7.00000 | − | 19.7990i | −0.333333 | − | 0.942809i | ||||
\(442\) | −21.4868 | + | 21.4868i | −1.02202 | + | 1.02202i | ||||
\(443\) | 11.3137 | − | 11.3137i | 0.537531 | − | 0.537531i | −0.385272 | − | 0.922803i | \(-0.625893\pi\) |
0.922803 | + | 0.385272i | \(0.125893\pi\) | |||||||
\(444\) | 7.30056 | − | 10.3246i | 0.346469 | − | 0.489982i | ||||
\(445\) | − | 1.02633i | − | 0.0486529i | ||||||
\(446\) | 18.6143i | 0.881411i | ||||||||
\(447\) | 5.58643 | + | 32.5601i | 0.264229 | + | 1.54004i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.65685 | −0.266963 | −0.133482 | − | 0.991051i | \(-0.542616\pi\) | ||||
−0.133482 | + | 0.991051i | \(0.542616\pi\) | |||||||
\(450\) | 13.5355 | + | 6.46447i | 0.638071 | + | 0.304738i | ||||
\(451\) | 17.2982 | 0.814541 | ||||||||
\(452\) | 13.7793 | + | 13.7793i | 0.648122 | + | 0.648122i | ||||
\(453\) | −0.680846 | − | 3.96826i | −0.0319890 | − | 0.186445i | ||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.16228 | + | 7.30056i | −0.241746 | + | 0.341880i | ||||
\(457\) | −19.1623 | + | 19.1623i | −0.896374 | + | 0.896374i | −0.995113 | − | 0.0987397i | \(-0.968519\pi\) |
0.0987397 | + | 0.995113i | \(0.468519\pi\) | |||||||
\(458\) | 17.8885 | − | 17.8885i | 0.835877 | − | 0.835877i | ||||
\(459\) | −7.30056 | + | 25.8114i | −0.340761 | + | 1.20477i | ||||
\(460\) | 1.58114 | − | 1.58114i | 0.0737210 | − | 0.0737210i | ||||
\(461\) | − | 4.01315i | − | 0.186911i | −0.995623 | − | 0.0934554i | \(-0.970209\pi\) | ||
0.995623 | − | 0.0934554i | \(-0.0297913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.1359 | − | 26.1359i | −1.21464 | − | 1.21464i | −0.969483 | − | 0.245157i | \(-0.921161\pi\) |
−0.245157 | − | 0.969483i | \(-0.578839\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | 39.4110 | − | 6.76185i | 1.82764 | − | 0.313573i | ||||
\(466\) | −8.32456 | −0.385628 | ||||||||
\(467\) | −4.70163 | − | 4.70163i | −0.217566 | − | 0.217566i | 0.589906 | − | 0.807472i | \(-0.299165\pi\) |
−0.807472 | + | 0.589906i | \(0.799165\pi\) | |||||||
\(468\) | 7.61042 | − | 15.9350i | 0.351792 | − | 0.736595i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 27.5585 | 1.27118 | ||||||||
\(471\) | 18.9737 | + | 13.4164i | 0.874260 | + | 0.618195i | ||||
\(472\) | −7.00000 | + | 7.00000i | −0.322201 | + | 0.322201i | ||||
\(473\) | −8.02629 | + | 8.02629i | −0.369049 | + | 0.369049i | ||||
\(474\) | 4.47214 | + | 3.16228i | 0.205412 | + | 0.145248i | ||||
\(475\) | − | 25.8114i | − | 1.18431i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2655 | − | 25.6819i | 0.561597 | − | 1.17589i | ||||
\(478\) | 4.48683 | + | 4.48683i | 0.205223 | + | 0.205223i | ||||
\(479\) | −28.2843 | −1.29234 | −0.646171 | − | 0.763193i | \(-0.723631\pi\) | ||||
−0.646171 | + | 0.763193i | \(0.723631\pi\) | |||||||
\(480\) | −3.16228 | − | 2.23607i | −0.144338 | − | 0.102062i | ||||
\(481\) | 42.9737 | 1.95943 | ||||||||
\(482\) | 5.88635 | + | 5.88635i | 0.268116 | + | 0.268116i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000i | 0.136364i | ||||||||
\(485\) | 2.59893 | + | 2.59893i | 0.118011 | + | 0.118011i | ||||
\(486\) | −1.00000 | − | 15.5563i | −0.0453609 | − | 0.705650i | ||||
\(487\) | −23.1623 | + | 23.1623i | −1.04958 | + | 1.04958i | −0.0508781 | + | 0.998705i | \(0.516202\pi\) |
−0.998705 | + | 0.0508781i | \(0.983798\pi\) | |||||||
\(488\) | −5.65685 | + | 5.65685i | −0.256074 | + | 0.256074i | ||||
\(489\) | 23.5454 | − | 33.2982i | 1.06476 | − | 1.50580i | ||||
\(490\) | −11.0680 | − | 11.0680i | −0.500000 | − | 0.500000i | ||||
\(491\) | − | 9.89949i | − | 0.446758i | −0.974732 | − | 0.223379i | \(-0.928291\pi\) | ||
0.974732 | − | 0.223379i | \(-0.0717087\pi\) | |||||||
\(492\) | 1.79129 | + | 10.4404i | 0.0807576 | + | 0.470690i | ||||
\(493\) | −16.3246 | − | 16.3246i | −0.735221 | − | 0.735221i | ||||
\(494\) | −30.3870 | −1.36717 | ||||||||
\(495\) | −17.8885 | + | 6.32456i | −0.804030 | + | 0.284268i | ||||
\(496\) | −10.3246 | −0.463586 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.43821 | + | 14.2109i | 0.109259 | + | 0.636806i | ||||
\(499\) | − | 15.3509i | − | 0.687200i | −0.939116 | − | 0.343600i | \(-0.888354\pi\) | ||
0.939116 | − | 0.343600i | \(-0.111646\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | 4.64911 | − | 6.57484i | 0.207707 | − | 0.293742i | ||||
\(502\) | −4.00000 | + | 4.00000i | −0.178529 | + | 0.178529i | ||||
\(503\) | −15.7858 | + | 15.7858i | −0.703856 | + | 0.703856i | −0.965236 | − | 0.261380i | \(-0.915822\pi\) |
0.261380 | + | 0.965236i | \(0.415822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.67544 | 0.163555 | ||||||||
\(506\) | 2.82843i | 0.125739i | ||||||||
\(507\) | 36.9573 | − | 6.34088i | 1.64133 | − | 0.281608i | ||||
\(508\) | −5.16228 | − | 5.16228i | −0.229039 | − | 0.229039i | ||||
\(509\) | 27.0996 | 1.20117 | 0.600583 | − | 0.799562i | \(-0.294935\pi\) | ||||
0.600583 | + | 0.799562i | \(0.294935\pi\) | |||||||
\(510\) | 3.38093 | + | 19.7055i | 0.149710 | + | 0.872573i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −23.4137 | + | 13.0891i | −1.03374 | + | 0.577899i | ||||
\(514\) | 23.2982i | 1.02764i | ||||||||
\(515\) | 24.9596 | − | 24.9596i | 1.09985 | − | 1.09985i | ||||
\(516\) | −5.67544 | − | 4.01315i | −0.249848 | − | 0.176669i | ||||
\(517\) | −24.6491 | + | 24.6491i | −1.08407 | + | 1.08407i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.458991 | + | 0.324555i | 0.0201474 | + | 0.0142464i | ||||
\(520\) | − | 13.1623i | − | 0.577204i | ||||||
\(521\) | − | 9.40326i | − | 0.411964i | −0.978556 | − | 0.205982i | \(-0.933961\pi\) | ||
0.978556 | − | 0.205982i | \(-0.0660389\pi\) | |||||||
\(522\) | 12.1065 | + | 5.78199i | 0.529889 | + | 0.253071i | ||||
\(523\) | −21.2982 | − | 21.2982i | −0.931306 | − | 0.931306i | 0.0664815 | − | 0.997788i | \(-0.478823\pi\) |
−0.997788 | + | 0.0664815i | \(0.978823\pi\) | |||||||
\(524\) | 7.53006 | 0.328952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.6491 | 1.07475 | ||||||||
\(527\) | 37.6875 | + | 37.6875i | 1.64169 | + | 1.64169i | ||||
\(528\) | 4.82843 | − | 0.828427i | 0.210130 | − | 0.0360527i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | − | 21.2132i | − | 0.921443i | ||||||
\(531\) | −28.0000 | + | 9.89949i | −1.21510 | + | 0.429601i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.4558 | + | 25.4558i | −1.10262 | + | 1.10262i | ||||
\(534\) | −0.458991 | + | 0.649111i | −0.0198625 | + | 0.0280898i | ||||
\(535\) | 23.1623 | − | 23.1623i | 1.00139 | − | 1.00139i | ||||
\(536\) | 7.30056i | 0.315336i | ||||||||
\(537\) | −1.37708 | − | 8.02619i | −0.0594252 | − | 0.346356i | ||||
\(538\) | 13.1623 | + | 13.1623i | 0.567466 | + | 0.567466i | ||||
\(539\) | 19.7990 | 0.852803 | ||||||||
\(540\) | −5.66963 | − | 10.1418i | −0.243982 | − | 0.436432i | ||||
\(541\) | 26.3246 | 1.13178 | 0.565891 | − | 0.824480i | \(-0.308532\pi\) | ||||
0.565891 | + | 0.824480i | \(0.308532\pi\) | |||||||
\(542\) | −4.93113 | − | 4.93113i | −0.211810 | − | 0.211810i | ||||
\(543\) | −2.83387 | − | 16.5170i | −0.121613 | − | 0.708813i | ||||
\(544\) | − | 5.16228i | − | 0.221331i | ||||||
\(545\) | 32.0307 | 1.37204 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.32456 | − | 6.32456i | 0.270418 | − | 0.270418i | −0.558850 | − | 0.829269i | \(-0.688757\pi\) |
0.829269 | + | 0.558850i | \(0.188757\pi\) | |||||||
\(548\) | 3.65028 | − | 3.65028i | 0.155932 | − | 0.155932i | ||||
\(549\) | −22.6274 | + | 8.00000i | −0.965715 | + | 0.341432i | ||||
\(550\) | −10.0000 | + | 10.0000i | −0.426401 | + | 0.426401i | ||||
\(551\) | − | 23.0864i | − | 0.983514i | ||||||
\(552\) | −1.70711 | + | 0.292893i | −0.0726593 | + | 0.0124664i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.88635 | 0.250087 | ||||||||
\(555\) | 16.3246 | − | 23.0864i | 0.692939 | − | 0.979963i | ||||
\(556\) | 2.32456 | 0.0985831 | ||||||||
\(557\) | −22.0351 | − | 22.0351i | −0.933655 | − | 0.933655i | 0.0642767 | − | 0.997932i | \(-0.479526\pi\) |
−0.997932 | + | 0.0642767i | \(0.979526\pi\) | |||||||
\(558\) | −27.9497 | − | 13.3485i | −1.18320 | − | 0.565089i | ||||
\(559\) | − | 23.6228i | − | 0.999137i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.6491 | − | 14.6011i | −0.871806 | − | 0.616460i | ||||
\(562\) | 1.48683 | − | 1.48683i | 0.0627183 | − | 0.0627183i | ||||
\(563\) | 3.05792 | − | 3.05792i | 0.128876 | − | 0.128876i | −0.639727 | − | 0.768603i | \(-0.720952\pi\) |
0.768603 | + | 0.639727i | \(0.220952\pi\) | |||||||
\(564\) | −17.4296 | − | 12.3246i | −0.733917 | − | 0.518957i | ||||
\(565\) | 30.8114 | + | 30.8114i | 1.29624 | + | 1.29624i | ||||
\(566\) | − | 23.5454i | − | 0.989687i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.16228 | + | 2.16228i | 0.0907272 | + | 0.0907272i | ||||
\(569\) | 1.18472 | 0.0496660 | 0.0248330 | − | 0.999692i | \(-0.492095\pi\) | ||||
0.0248330 | + | 0.999692i | \(0.492095\pi\) | |||||||
\(570\) | −11.5432 | + | 16.3246i | −0.483492 | + | 0.683760i | ||||
\(571\) | −17.1623 | −0.718219 | −0.359109 | − | 0.933295i | \(-0.616920\pi\) | ||||
−0.359109 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(572\) | 11.7727 | + | 11.7727i | 0.492241 | + | 0.492241i | ||||
\(573\) | 0.783546 | − | 0.134435i | 0.0327331 | − | 0.00561611i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.53553 | − | 3.53553i | 0.147442 | − | 0.147442i | ||||
\(576\) | 1.00000 | + | 2.82843i | 0.0416667 | + | 0.117851i | ||||
\(577\) | −19.3246 | + | 19.3246i | −0.804492 | + | 0.804492i | −0.983794 | − | 0.179302i | \(-0.942616\pi\) |
0.179302 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(578\) | −6.82295 | + | 6.82295i | −0.283797 | + | 0.283797i | ||||
\(579\) | 4.24264 | − | 6.00000i | 0.176318 | − | 0.249351i | ||||
\(580\) | 10.0000 | 0.415227 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.481431 | − | 2.80599i | −0.0199560 | − | 0.116312i | ||||
\(583\) | 18.9737 | + | 18.9737i | 0.785809 | + | 0.785809i | ||||
\(584\) | 10.3585 | 0.428637 | ||||||||
\(585\) | 17.0174 | − | 35.6317i | 0.703584 | − | 1.47319i | ||||
\(586\) | 0.188612 | 0.00779148 | ||||||||
\(587\) | 7.07107 | + | 7.07107i | 0.291854 | + | 0.291854i | 0.837812 | − | 0.545958i | \(-0.183834\pi\) |
−0.545958 | + | 0.837812i | \(0.683834\pi\) | |||||||
\(588\) | 2.05025 | + | 11.9497i | 0.0845510 | + | 0.492799i | ||||
\(589\) | 53.2982i | 2.19611i | ||||||||
\(590\) | −15.6525 | + | 15.6525i | −0.644402 | + | 0.644402i | ||||
\(591\) | −16.3246 | + | 23.0864i | −0.671502 | + | 0.949648i | ||||
\(592\) | −5.16228 | + | 5.16228i | −0.212168 | + | 0.212168i | ||||
\(593\) | 7.98905 | − | 7.98905i | 0.328071 | − | 0.328071i | −0.523782 | − | 0.851853i | \(-0.675479\pi\) |
0.851853 | + | 0.523782i | \(0.175479\pi\) | |||||||
\(594\) | 14.1421 | + | 4.00000i | 0.580259 | + | 0.164122i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 19.0733i | − | 0.781271i | ||||||
\(597\) | 15.0869 | − | 2.58851i | 0.617467 | − | 0.105941i | ||||
\(598\) | −4.16228 | − | 4.16228i | −0.170208 | − | 0.170208i | ||||
\(599\) | −8.25579 | −0.337322 | −0.168661 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168661 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(600\) | −7.07107 | − | 5.00000i | −0.288675 | − | 0.204124i | ||||
\(601\) | −34.6491 | −1.41337 | −0.706683 | − | 0.707530i | \(-0.749809\pi\) | ||||
−0.706683 | + | 0.707530i | \(0.749809\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.43885 | + | 19.7634i | −0.384380 | + | 0.804828i | ||||
\(604\) | 2.32456i | 0.0945848i | ||||||||
\(605\) | 6.70820i | 0.272727i | ||||||||
\(606\) | −2.32456 | − | 1.64371i | −0.0944286 | − | 0.0667711i | ||||
\(607\) | 0.837722 | − | 0.837722i | 0.0340021 | − | 0.0340021i | −0.689901 | − | 0.723903i | \(-0.742346\pi\) |
0.723903 | + | 0.689901i | \(0.242346\pi\) | |||||||
\(608\) | 3.65028 | − | 3.65028i | 0.148038 | − | 0.148038i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6491 | + | 12.6491i | −0.512148 | + | 0.512148i | ||||
\(611\) | − | 72.5466i | − | 2.93492i | ||||||
\(612\) | 6.67427 | − | 13.9748i | 0.269792 | − | 0.564899i | ||||
\(613\) | −26.4605 | − | 26.4605i | −1.06873 | − | 1.06873i | −0.997457 | − | 0.0712726i | \(-0.977294\pi\) |
−0.0712726 | − | 0.997457i | \(-0.522706\pi\) | |||||||
\(614\) | 3.28742 | 0.132669 | ||||||||
\(615\) | 4.00545 | + | 23.3454i | 0.161515 | + | 0.941379i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.66343 | + | 7.66343i | 0.308518 | + | 0.308518i | 0.844334 | − | 0.535817i | \(-0.179996\pi\) |
−0.535817 | + | 0.844334i | \(0.679996\pi\) | |||||||
\(618\) | −26.9481 | + | 4.62357i | −1.08401 | + | 0.185987i | ||||
\(619\) | − | 18.4605i | − | 0.741990i | −0.928635 | − | 0.370995i | \(-0.879017\pi\) | ||
0.928635 | − | 0.370995i | \(-0.120983\pi\) | |||||||
\(620\) | −23.0864 | −0.927172 | ||||||||
\(621\) | −5.00000 | − | 1.41421i | −0.200643 | − | 0.0567504i | ||||
\(622\) | −18.8114 | + | 18.8114i | −0.754268 | + | 0.754268i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.88635 | + | 8.32456i | −0.235643 | + | 0.333249i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | − | 12.9574i | − | 0.517883i | ||||||
\(627\) | −4.27657 | − | 24.9257i | −0.170790 | − | 0.995436i | ||||
\(628\) | −9.48683 | − | 9.48683i | −0.378566 | − | 0.378566i | ||||
\(629\) | 37.6875 | 1.50270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8114 | −1.10715 | −0.553577 | − | 0.832798i | \(-0.686738\pi\) | ||||
−0.553577 | + | 0.832798i | \(0.686738\pi\) | |||||||
\(632\) | −2.23607 | − | 2.23607i | −0.0889460 | − | 0.0889460i | ||||
\(633\) | −4.19557 | − | 24.4535i | −0.166759 | − | 0.971941i | ||||
\(634\) | − | 3.67544i | − | 0.145971i | ||||||
\(635\) | −11.5432 | − | 11.5432i | −0.458078 | − | 0.458078i | ||||
\(636\) | −9.48683 | + | 13.4164i | −0.376177 | + | 0.531995i | ||||
\(637\) | −29.1359 | + | 29.1359i | −1.15441 | + | 1.15441i | ||||
\(638\) | −8.94427 | + | 8.94427i | −0.354107 | + | 0.354107i | ||||
\(639\) | 3.05792 | + | 8.64911i | 0.120970 | + | 0.342154i | ||||
\(640\) | 1.58114 | + | 1.58114i | 0.0625000 | + | 0.0625000i | ||||
\(641\) | 10.8547i | 0.428736i | 0.976753 | + | 0.214368i | \(0.0687691\pi\) | ||||
−0.976753 | + | 0.214368i | \(0.931231\pi\) | |||||||
\(642\) | −25.0076 | + | 4.29063i | −0.986971 | + | 0.169337i | ||||
\(643\) | −5.16228 | − | 5.16228i | −0.203580 | − | 0.203580i | 0.597952 | − | 0.801532i | \(-0.295981\pi\) |
−0.801532 | + | 0.597952i | \(0.795981\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.6907 | − | 8.97367i | −0.499695 | − | 0.353338i | ||||
\(646\) | −26.6491 | −1.04850 | ||||||||
\(647\) | 19.5695 | + | 19.5695i | 0.769356 | + | 0.769356i | 0.977993 | − | 0.208637i | \(-0.0669027\pi\) |
−0.208637 | + | 0.977993i | \(0.566903\pi\) | |||||||
\(648\) | −0.949747 | + | 8.94975i | −0.0373096 | + | 0.351579i | ||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | − | 29.4317i | − | 1.15441i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.6491 | + | 16.6491i | −0.652029 | + | 0.652029i | ||||
\(653\) | 17.6590 | − | 17.6590i | 0.691052 | − | 0.691052i | −0.271411 | − | 0.962463i | \(-0.587490\pi\) |
0.962463 | + | 0.271411i | \(0.0874904\pi\) | |||||||
\(654\) | −20.2580 | − | 14.3246i | −0.792150 | − | 0.560134i | ||||
\(655\) | 16.8377 | 0.657904 | ||||||||
\(656\) | − | 6.11584i | − | 0.238784i | ||||||
\(657\) | 28.0415 | + | 13.3924i | 1.09400 | + | 0.522488i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.94427 | −0.348419 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(660\) | 10.7967 | − | 1.85242i | 0.420261 | − | 0.0721053i | ||||
\(661\) | −32.6491 | −1.26990 | −0.634952 | − | 0.772552i | \(-0.718980\pi\) | ||||
−0.634952 | + | 0.772552i | \(0.718980\pi\) | |||||||
\(662\) | 2.10270 | + | 2.10270i | 0.0817237 | + | 0.0817237i | ||||
\(663\) | 51.8738 | − | 8.90014i | 2.01461 | − | 0.345653i | ||||
\(664\) | − | 8.32456i | − | 0.323055i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.6491 | + | 7.30056i | −0.800137 | + | 0.282891i | ||||
\(667\) | 3.16228 | − | 3.16228i | 0.122444 | − | 0.122444i | ||||
\(668\) | −3.28742 | + | 3.28742i | −0.127194 | + | 0.127194i | ||||
\(669\) | 18.6143 | − | 26.3246i | 0.719669 | − | 1.01777i | ||||
\(670\) | 16.3246i | 0.630673i | ||||||||
\(671\) | − | 22.6274i | − | 0.873522i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.3246 | + | 31.3246i | 1.20747 | + | 1.20747i | 0.971843 | + | 0.235630i | \(0.0757154\pi\) |
0.235630 | + | 0.971843i | \(0.424285\pi\) | |||||||
\(674\) | −13.4164 | −0.516781 | ||||||||
\(675\) | −12.6777 | − | 22.6777i | −0.487964 | − | 0.872864i | ||||
\(676\) | −21.6491 | −0.832658 | ||||||||
\(677\) | −25.7815 | − | 25.7815i | −0.990862 | − | 0.990862i | 0.00909639 | − | 0.999959i | \(-0.497104\pi\) |
−0.999959 | + | 0.00909639i | \(0.997104\pi\) | |||||||
\(678\) | −5.70756 | − | 33.2661i | −0.219198 | − | 1.27758i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 11.5432i | − | 0.442662i | ||||||
\(681\) | −6.00000 | + | 8.48528i | −0.229920 | + | 0.325157i | ||||
\(682\) | 20.6491 | − | 20.6491i | 0.790695 | − | 0.790695i | ||||
\(683\) | 31.0755 | − | 31.0755i | 1.18907 | − | 1.18907i | 0.211744 | − | 0.977325i | \(-0.432086\pi\) |
0.977325 | − | 0.211744i | \(-0.0679144\pi\) | |||||||
\(684\) | 14.6011 | − | 5.16228i | 0.558288 | − | 0.197385i | ||||
\(685\) | 8.16228 | − | 8.16228i | 0.311865 | − | 0.311865i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.1868 | + | 7.40968i | −1.64768 | + | 0.282697i | ||||
\(688\) | 2.83772 | + | 2.83772i | 0.108187 | + | 0.108187i | ||||
\(689\) | −55.8428 | −2.12744 | ||||||||
\(690\) | −3.81721 | + | 0.654929i | −0.145319 | + | 0.0249327i | ||||
\(691\) | −12.6491 | −0.481195 | −0.240597 | − | 0.970625i | \(-0.577343\pi\) | ||||
−0.240597 | + | 0.970625i | \(0.577343\pi\) | |||||||
\(692\) | −0.229495 | − | 0.229495i | −0.00872410 | − | 0.00872410i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.35089i | − | 0.0512791i | ||||||
\(695\) | 5.19786 | 0.197166 | ||||||||
\(696\) | −6.32456 | − | 4.47214i | −0.239732 | − | 0.169516i | ||||
\(697\) | −22.3246 | + | 22.3246i | −0.845603 | + | 0.845603i | ||||
\(698\) | 9.89949 | − | 9.89949i | 0.374701 | − | 0.374701i | ||||
\(699\) | 11.7727 | + | 8.32456i | 0.445284 | + | 0.314864i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9148i | 0.978790i | 0.872062 | + | 0.489395i | \(0.162782\pi\) | ||||
−0.872062 | + | 0.489395i | \(0.837218\pi\) | |||||||
\(702\) | −26.6977 | + | 14.9250i | −1.00764 | + | 0.563309i | ||||
\(703\) | 26.6491 | + | 26.6491i | 1.00509 | + | 1.00509i | ||||
\(704\) | −2.82843 | −0.106600 | ||||||||
\(705\) | −38.9737 | − | 27.5585i | −1.46783 | − | 1.03791i | ||||
\(706\) | 24.9737 | 0.939896 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 16.8995 | − | 2.89949i | 0.635122 | − | 0.108970i | ||||
\(709\) | 25.9473i | 0.974473i | 0.873270 | + | 0.487236i | \(0.161995\pi\) | ||||
−0.873270 | + | 0.487236i | \(0.838005\pi\) | |||||||
\(710\) | 4.83500 | + | 4.83500i | 0.181454 | + | 0.181454i | ||||
\(711\) | −3.16228 | − | 8.94427i | −0.118595 | − | 0.335436i | ||||
\(712\) | 0.324555 | − | 0.324555i | 0.0121632 | − | 0.0121632i | ||||
\(713\) | −7.30056 | + | 7.30056i | −0.273408 | + | 0.273408i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.3246 | + | 26.3246i | 0.984483 | + | 0.984483i | ||||
\(716\) | 4.70163i | 0.175708i | ||||||||
\(717\) | −1.85851 | − | 10.8322i | −0.0694072 | − | 0.404535i | ||||
\(718\) | 14.0000 | + | 14.0000i | 0.522475 | + | 0.522475i | ||||
\(719\) | −30.3497 | −1.13185 | −0.565927 | − | 0.824455i | \(-0.691482\pi\) | ||||
−0.565927 | + | 0.824455i | \(0.691482\pi\) | |||||||
\(720\) | 2.23607 | + | 6.32456i | 0.0833333 | + | 0.235702i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.40874 | − | 5.40874i | −0.201292 | − | 0.201292i | ||||
\(723\) | −2.43821 | − | 14.2109i | −0.0906778 | − | 0.528509i | ||||
\(724\) | 9.67544i | 0.359585i | ||||||||
\(725\) | 22.3607 | 0.830455 | ||||||||
\(726\) | 3.00000 | − | 4.24264i | 0.111340 | − | 0.157459i | ||||
\(727\) | 13.6754 | − | 13.6754i | 0.507194 | − | 0.507194i | −0.406470 | − | 0.913664i | \(-0.633240\pi\) |
0.913664 | + | 0.406470i | \(0.133240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 23.1623 | 0.857274 | ||||||||
\(731\) | − | 20.7170i | − | 0.766245i | ||||||
\(732\) | 13.6569 | − | 2.34315i | 0.504772 | − | 0.0866052i | ||||
\(733\) | −33.8114 | − | 33.8114i | −1.24885 | − | 1.24885i | −0.956227 | − | 0.292625i | \(-0.905471\pi\) |
−0.292625 | − | 0.956227i | \(-0.594529\pi\) | |||||||
\(734\) | 2.10270 | 0.0776120 | ||||||||
\(735\) | 4.58450 | + | 26.7204i | 0.169102 | + | 0.985599i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −14.6011 | − | 14.6011i | −0.537839 | − | 0.537839i | ||||
\(738\) | 7.90713 | − | 16.5562i | 0.291066 | − | 0.609444i | ||||
\(739\) | − | 52.2719i | − | 1.92285i | −0.275063 | − | 0.961426i | \(-0.588699\pi\) | ||
0.275063 | − | 0.961426i | \(-0.411301\pi\) | |||||||
\(740\) | −11.5432 | + | 11.5432i | −0.424337 | + | 0.424337i | ||||
\(741\) | 42.9737 | + | 30.3870i | 1.57868 | + | 1.11629i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.2448 | + | 16.2448i | −0.595965 | + | 0.595965i | −0.939236 | − | 0.343271i | \(-0.888465\pi\) |
0.343271 | + | 0.939236i | \(0.388465\pi\) | |||||||
\(744\) | 14.6011 | + | 10.3246i | 0.535303 | + | 0.378517i | ||||
\(745\) | − | 42.6491i | − | 1.56254i | ||||||
\(746\) | 19.0733i | 0.698322i | ||||||||
\(747\) | 10.7628 | − | 22.5355i | 0.393789 | − | 0.824529i | ||||
\(748\) | 10.3246 | + | 10.3246i | 0.377503 | + | 0.377503i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.8114 | − | 11.1803i | −0.577350 | − | 0.408248i | ||||
\(751\) | −28.4605 | −1.03854 | −0.519269 | − | 0.854611i | \(-0.673796\pi\) | ||||
−0.519269 | + | 0.854611i | \(0.673796\pi\) | |||||||
\(752\) | 8.71478 | + | 8.71478i | 0.317795 | + | 0.317795i | ||||
\(753\) | 9.65685 | − | 1.65685i | 0.351915 | − | 0.0603791i | ||||
\(754\) | − | 26.3246i | − | 0.958684i | ||||||
\(755\) | 5.19786i | 0.189170i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.48683 | − | 9.48683i | 0.344805 | − | 0.344805i | −0.513365 | − | 0.858170i | \(-0.671601\pi\) |
0.858170 | + | 0.513365i | \(0.171601\pi\) | |||||||
\(758\) | −2.46556 | + | 2.46556i | −0.0895533 | + | 0.0895533i | ||||
\(759\) | 2.82843 | − | 4.00000i | 0.102665 | − | 0.145191i | ||||
\(760\) | 8.16228 | − | 8.16228i | 0.296077 | − | 0.296077i | ||||
\(761\) | 21.1760i | 0.767628i | 0.923410 | + | 0.383814i | \(0.125390\pi\) | ||||
−0.923410 | + | 0.383814i | \(0.874610\pi\) | |||||||
\(762\) | 2.13829 | + | 12.4628i | 0.0774619 | + | 0.451481i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.458991 | −0.0166057 | ||||||||
\(765\) | 14.9241 | − | 31.2487i | 0.539583 | − | 1.12980i | ||||
\(766\) | 9.67544 | 0.349588 | ||||||||
\(767\) | 41.2044 | + | 41.2044i | 1.48781 | + | 1.48781i | ||||
\(768\) | −0.292893 | − | 1.70711i | −0.0105689 | − | 0.0615999i | ||||
\(769\) | − | 3.67544i | − | 0.132540i | −0.997802 | − | 0.0662700i | \(-0.978890\pi\) | ||
0.997802 | − | 0.0662700i | \(-0.0211099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.2982 | − | 32.9487i | 0.839065 | − | 1.18662i | ||||
\(772\) | −3.00000 | + | 3.00000i | −0.107972 | + | 0.107972i | ||||
\(773\) | 17.5629 | − | 17.5629i | 0.631694 | − | 0.631694i | −0.316798 | − | 0.948493i | \(-0.602608\pi\) |
0.948493 | + | 0.316798i | \(0.102608\pi\) | |||||||
\(774\) | 4.01315 | + | 11.3509i | 0.144250 | + | 0.407999i | ||||
\(775\) | −51.6228 | −1.85434 | ||||||||
\(776\) | 1.64371i | 0.0590057i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.83772 | − | 8.83772i | −0.316848 | − | 0.316848i | ||||
\(779\) | −31.5717 | −1.13117 | ||||||||
\(780\) | −13.1623 | + | 18.6143i | −0.471285 | + | 0.666498i | ||||
\(781\) | −8.64911 | −0.309490 | ||||||||
\(782\) | −3.65028 | − | 3.65028i | −0.130534 | − | 0.130534i | ||||
\(783\) | −11.3393 | − | 20.2835i | −0.405232 | − | 0.724874i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | −21.2132 | − | 21.2132i | −0.757132 | − | 0.757132i | ||||
\(786\) | −10.6491 | − | 7.53006i | −0.379841 | − | 0.268588i | ||||
\(787\) | 8.13594 | − | 8.13594i | 0.290015 | − | 0.290015i | −0.547071 | − | 0.837086i | \(-0.684257\pi\) |
0.837086 | + | 0.547071i | \(0.184257\pi\) | |||||||
\(788\) | 11.5432 | − | 11.5432i | 0.411210 | − | 0.411210i | ||||
\(789\) | −34.8591 | − | 24.6491i | −1.24102 | − | 0.877532i | ||||
\(790\) | −5.00000 | − | 5.00000i | −0.177892 | − | 0.177892i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.65685 | − | 3.65685i | −0.272074 | − | 0.129941i | ||||
\(793\) | 33.2982 | + | 33.2982i | 1.18245 | + | 1.18245i | ||||
\(794\) | 9.63276 | 0.341854 | ||||||||
\(795\) | −21.2132 | + | 30.0000i | −0.752355 | + | 1.06399i | ||||
\(796\) | −8.83772 | −0.313245 | ||||||||
\(797\) | −11.9061 | − | 11.9061i | −0.421735 | − | 0.421735i | 0.464066 | − | 0.885801i | \(-0.346390\pi\) |
−0.885801 | + | 0.464066i | \(0.846390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 63.6228i | − | 2.25081i | ||||||
\(800\) | 3.53553 | + | 3.53553i | 0.125000 | + | 0.125000i | ||||
\(801\) | 1.29822 | − | 0.458991i | 0.0458704 | − | 0.0162176i | ||||
\(802\) | −14.0000 | + | 14.0000i | −0.494357 | + | 0.494357i | ||||
\(803\) | −20.7170 | + | 20.7170i | −0.731086 | + | 0.731086i | ||||
\(804\) | 7.30056 | − | 10.3246i | 0.257471 | − | 0.364119i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60.7739i | 2.14067i | ||||||||
\(807\) | −5.45199 | − | 31.7765i | −0.191919 | − | 1.11859i | ||||
\(808\) | 1.16228 | + | 1.16228i | 0.0408888 | + | 0.0408888i | ||||
\(809\) | 40.0570 | 1.40833 | 0.704164 | − | 0.710037i | \(-0.251322\pi\) | ||||
0.704164 | + | 0.710037i | \(0.251322\pi\) | |||||||
\(810\) | −2.12370 | + | 20.0122i | −0.0746192 | + | 0.703159i | ||||
\(811\) | −27.3509 | −0.960420 | −0.480210 | − | 0.877154i | \(-0.659439\pi\) | ||||
−0.480210 | + | 0.877154i | \(0.659439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.04254 | + | 11.9048i | 0.0716350 | + | 0.417519i | ||||
\(814\) | − | 20.6491i | − | 0.723751i | ||||||
\(815\) | −37.2285 | + | 37.2285i | −1.30406 | + | 1.30406i | ||||
\(816\) | −5.16228 | + | 7.30056i | −0.180716 | + | 0.255571i | ||||
\(817\) | 14.6491 | − | 14.6491i | 0.512508 | − | 0.512508i | ||||
\(818\) | −14.1421 | + | 14.1421i | −0.494468 | + | 0.494468i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 13.6754i | − | 0.477567i | ||||||
\(821\) | 0.266737i | 0.00930919i | 0.999989 | + | 0.00465460i | \(0.00148161\pi\) | ||||
−0.999989 | + | 0.00465460i | \(0.998518\pi\) | |||||||
\(822\) | −8.81256 | + | 1.51200i | −0.307373 | + | 0.0527369i | ||||
\(823\) | −31.8114 | − | 31.8114i | −1.10888 | − | 1.10888i | −0.993299 | − | 0.115577i | \(-0.963128\pi\) |
−0.115577 | − | 0.993299i | \(-0.536872\pi\) | |||||||
\(824\) | 15.7858 | 0.549926 | ||||||||
\(825\) | 24.1421 | − | 4.14214i | 0.840521 | − | 0.144211i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2689 | + | 12.2689i | 0.426633 | + | 0.426633i | 0.887480 | − | 0.460847i | \(-0.152454\pi\) |
−0.460847 | + | 0.887480i | \(0.652454\pi\) | |||||||
\(828\) | 2.70711 | + | 1.29289i | 0.0940785 | + | 0.0449311i | ||||
\(829\) | 29.6754i | 1.03067i | 0.856989 | + | 0.515335i | \(0.172333\pi\) | ||||
−0.856989 | + | 0.515335i | \(0.827667\pi\) | |||||||
\(830\) | − | 18.6143i | − | 0.646111i | ||||||
\(831\) | −8.32456 | − | 5.88635i | −0.288776 | − | 0.204195i | ||||
\(832\) | 4.16228 | − | 4.16228i | 0.144301 | − | 0.144301i | ||||
\(833\) | −25.5520 | + | 25.5520i | −0.885323 | + | 0.885323i | ||||
\(834\) | −3.28742 | − | 2.32456i | −0.113834 | − | 0.0804928i | ||||
\(835\) | −7.35089 | + | 7.35089i | −0.254388 | + | 0.254388i | ||||
\(836\) | 14.6011i | 0.504991i | ||||||||
\(837\) | 26.1783 | + | 46.8274i | 0.904853 | + | 1.61859i | ||||
\(838\) | 18.6491 | + | 18.6491i | 0.644223 | + | 0.644223i | ||||
\(839\) | 15.0601 | 0.519933 | 0.259966 | − | 0.965618i | \(-0.416288\pi\) | ||||
0.259966 | + | 0.965618i | \(0.416288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 8.02629 | + | 8.02629i | 0.276604 | + | 0.276604i | ||||
\(843\) | −3.58953 | + | 0.615866i | −0.123630 | + | 0.0212116i | ||||
\(844\) | 14.3246i | 0.493072i | ||||||||
\(845\) | −48.4089 | −1.66532 | ||||||||
\(846\) | 12.3246 | + | 34.8591i | 0.423727 | + | 1.19848i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.70820 | − | 6.70820i | 0.230361 | − | 0.230361i | ||||
\(849\) | −23.5454 | + | 33.2982i | −0.808076 | + | 1.14279i | ||||
\(850\) | − | 25.8114i | − | 0.885323i | ||||||
\(851\) | 7.30056i | 0.250260i | ||||||||
\(852\) | −0.895645 | − | 5.22020i | −0.0306843 | − | 0.178841i | ||||
\(853\) | 17.8377 | + | 17.8377i | 0.610752 | + | 0.610752i | 0.943142 | − | 0.332390i | \(-0.107855\pi\) |
−0.332390 | + | 0.943142i | \(0.607855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.6491 | − | 11.5432i | 1.11658 | − | 0.394769i | ||||
\(856\) | 14.6491 | 0.500696 | ||||||||
\(857\) | −7.07107 | − | 7.07107i | −0.241543 | − | 0.241543i | 0.575945 | − | 0.817488i | \(-0.304634\pi\) |
−0.817488 | + | 0.575945i | \(0.804634\pi\) | |||||||
\(858\) | −4.87641 | − | 28.4218i | −0.166478 | − | 0.970305i | ||||
\(859\) | 17.6754i | 0.603078i | 0.953454 | + | 0.301539i | \(0.0975004\pi\) | ||||
−0.953454 | + | 0.301539i | \(0.902500\pi\) | |||||||
\(860\) | 6.34534 | + | 6.34534i | 0.216374 | + | 0.216374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.32456 | + | 4.32456i | −0.147295 | + | 0.147295i | ||||
\(863\) | −11.3137 | + | 11.3137i | −0.385123 | + | 0.385123i | −0.872944 | − | 0.487821i | \(-0.837792\pi\) |
0.487821 | + | 0.872944i | \(0.337792\pi\) | |||||||
\(864\) | 1.41421 | − | 5.00000i | 0.0481125 | − | 0.170103i | ||||
\(865\) | −0.513167 | − | 0.513167i | −0.0174482 | − | 0.0174482i | ||||
\(866\) | 22.8197i | 0.775444i | ||||||||
\(867\) | 16.4721 | − | 2.82616i | 0.559421 | − | 0.0959814i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.94427 | 0.303414 | ||||||||
\(870\) | −14.1421 | − | 10.0000i | −0.479463 | − | 0.339032i | ||||
\(871\) | 42.9737 | 1.45611 | ||||||||
\(872\) | 10.1290 | + | 10.1290i | 0.343011 | + | 0.343011i | ||||
\(873\) | −2.12514 | + | 4.44970i | −0.0719251 | + | 0.150599i | ||||
\(874\) | − | 5.16228i | − | 0.174617i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.6491 | − | 10.3585i | −0.494948 | − | 0.349981i | ||||
\(877\) | 30.8114 | − | 30.8114i | 1.04043 | − | 1.04043i | 0.0412790 | − | 0.999148i | \(-0.486857\pi\) |
0.999148 | − | 0.0412790i | \(-0.0131432\pi\) | |||||||
\(878\) | 8.02629 | − | 8.02629i | 0.270874 | − | 0.270874i | ||||
\(879\) | −0.266737 | − | 0.188612i | −0.00899682 | − | 0.00636171i | ||||
\(880\) | −6.32456 | −0.213201 | ||||||||
\(881\) | 34.5924i | 1.16545i | 0.812671 | + | 0.582723i | \(0.198013\pi\) | ||||
−0.812671 | + | 0.582723i | \(0.801987\pi\) | |||||||
\(882\) | 9.05025 | − | 18.9497i | 0.304738 | − | 0.638071i | ||||
\(883\) | −22.3246 | − | 22.3246i | −0.751281 | − | 0.751281i | 0.223437 | − | 0.974718i | \(-0.428272\pi\) |
−0.974718 | + | 0.223437i | \(0.928272\pi\) | |||||||
\(884\) | −30.3870 | −1.02202 | ||||||||
\(885\) | 37.7884 | − | 6.48347i | 1.27024 | − | 0.217939i | ||||
\(886\) | 16.0000 | 0.537531 | ||||||||
\(887\) | 13.6831 | + | 13.6831i | 0.459435 | + | 0.459435i | 0.898470 | − | 0.439035i | \(-0.144680\pi\) |
−0.439035 | + | 0.898470i | \(0.644680\pi\) | |||||||
\(888\) | 12.4628 | − | 2.13829i | 0.418226 | − | 0.0717562i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.725728 | − | 0.725728i | 0.0243264 | − | 0.0243264i | ||||
\(891\) | −16.0000 | − | 19.7990i | −0.536020 | − | 0.663291i | ||||
\(892\) | −13.1623 | + | 13.1623i | −0.440706 | + | 0.440706i | ||||
\(893\) | 44.9881 | − | 44.9881i | 1.50547 | − | 1.50547i | ||||
\(894\) | −19.0733 | + | 26.9737i | −0.637905 | + | 0.902134i | ||||
\(895\) | 10.5132i | 0.351416i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.72407 | + | 10.0486i | 0.0575651 | + | 0.335514i | ||||
\(898\) | −4.00000 | − | 4.00000i | −0.133482 | − | 0.133482i | ||||
\(899\) | −46.1728 | −1.53995 | ||||||||
\(900\) | 5.00000 | + | 14.1421i | 0.166667 | + | 0.471405i | ||||
\(901\) | −48.9737 | −1.63155 | ||||||||
\(902\) | 12.2317 | + | 12.2317i | 0.407271 | + | 0.407271i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4868i | 0.648122i | ||||||||
\(905\) | 21.6350i | 0.719170i | ||||||||
\(906\) | 2.32456 | − | 3.28742i | 0.0772282 | − | 0.109217i | ||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 4.24264 | − | 4.24264i | 0.140797 | − | 0.140797i | ||||
\(909\) | 1.64371 | + | 4.64911i | 0.0545184 | + | 0.154201i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.28742i | − | 0.108917i | −0.998516 | − | 0.0544585i | \(-0.982657\pi\) | ||
0.998516 | − | 0.0544585i | \(-0.0173433\pi\) | |||||||
\(912\) | −8.81256 | + | 1.51200i | −0.291813 | + | 0.0500672i | ||||
\(913\) | 16.6491 | + | 16.6491i | 0.551005 | + | 0.551005i | ||||
\(914\) | −27.0996 | −0.896374 | ||||||||
\(915\) | 30.5377 | − | 5.23943i | 1.00954 | − | 0.173210i | ||||
\(916\) | 25.2982 | 0.835877 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −23.4137 | + | 13.0891i | −0.772767 | + | 0.432006i | ||||
\(919\) | − | 18.1359i | − | 0.598250i | −0.954214 | − | 0.299125i | \(-0.903305\pi\) | ||
0.954214 | − | 0.299125i | \(-0.0966947\pi\) | |||||||
\(920\) | 2.23607 | 0.0737210 | ||||||||
\(921\) | −4.64911 | − | 3.28742i | −0.153193 | − | 0.108324i | ||||
\(922\) | 2.83772 | − | 2.83772i | 0.0934554 | − | 0.0934554i | ||||
\(923\) | 12.7279 | − | 12.7279i | 0.418945 | − | 0.418945i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8114 | + | 25.8114i | −0.848673 | + | 0.848673i | ||||
\(926\) | − | 36.9618i | − | 1.21464i | ||||||
\(927\) | 42.7340 | + | 20.4094i | 1.40357 | + | 0.670333i | ||||
\(928\) | 3.16228 | + | 3.16228i | 0.103807 | + | 0.103807i | ||||
\(929\) | −2.36944 | −0.0777387 | −0.0388693 | − | 0.999244i | \(-0.512376\pi\) | ||||
−0.0388693 | + | 0.999244i | \(0.512376\pi\) | |||||||
\(930\) | 32.6491 | + | 23.0864i | 1.07061 | + | 0.757033i | ||||
\(931\) | −36.1359 | −1.18431 | ||||||||
\(932\) | −5.88635 | − | 5.88635i | −0.192814 | − | 0.192814i | ||||
\(933\) | 45.4147 | − | 7.79193i | 1.48681 | − | 0.255096i | ||||
\(934\) | − | 6.64911i | − | 0.217566i | ||||||
\(935\) | 23.0864 | + | 23.0864i | 0.755006 | + | 0.755006i | ||||
\(936\) | 16.6491 | − | 5.88635i | 0.544193 | − | 0.192401i | ||||
\(937\) | 29.8114 | − | 29.8114i | 0.973896 | − | 0.973896i | −0.0257722 | − | 0.999668i | \(-0.508204\pi\) |
0.999668 | + | 0.0257722i | \(0.00820447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9574 | + | 18.3246i | −0.422849 | + | 0.597999i | ||||
\(940\) | 19.4868 | + | 19.4868i | 0.635590 | + | 0.635590i | ||||
\(941\) | − | 11.5804i | − | 0.377512i | −0.982024 | − | 0.188756i | \(-0.939555\pi\) | ||
0.982024 | − | 0.188756i | \(-0.0604455\pi\) | |||||||
\(942\) | 3.92957 | + | 22.9032i | 0.128032 | + | 0.746228i | ||||
\(943\) | −4.32456 | − | 4.32456i | −0.140827 | − | 0.140827i | ||||
\(944\) | −9.89949 | −0.322201 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.3509 | −0.369049 | ||||||||
\(947\) | −18.3475 | − | 18.3475i | −0.596215 | − | 0.596215i | 0.343088 | − | 0.939303i | \(-0.388527\pi\) |
−0.939303 | + | 0.343088i | \(0.888527\pi\) | |||||||
\(948\) | 0.926210 | + | 5.39835i | 0.0300819 | + | 0.175330i | ||||
\(949\) | − | 60.9737i | − | 1.97929i | ||||||
\(950\) | 18.2514 | − | 18.2514i | 0.592154 | − | 0.592154i | ||||
\(951\) | −3.67544 | + | 5.19786i | −0.119184 | + | 0.168552i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.3410 | + | 16.3410i | −0.529336 | + | 0.529336i | −0.920374 | − | 0.391039i | \(-0.872116\pi\) |
0.391039 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(954\) | 26.8328 | − | 9.48683i | 0.868744 | − | 0.307148i | ||||
\(955\) | −1.02633 | −0.0332114 | ||||||||
\(956\) | 6.34534i | 0.205223i | ||||||||
\(957\) | 21.5934 | − | 3.70484i | 0.698015 | − | 0.119760i | ||||
\(958\) | −20.0000 | − | 20.0000i | −0.646171 | − | 0.646171i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.654929 | − | 3.81721i | −0.0211377 | − | 0.123200i | ||||
\(961\) | 75.5964 | 2.43859 | ||||||||
\(962\) | 30.3870 | + | 30.3870i | 0.979715 | + | 0.979715i | ||||
\(963\) | 39.6567 | + | 18.9397i | 1.27792 | + | 0.610324i | ||||
\(964\) | 8.32456i | 0.268116i | ||||||||
\(965\) | −6.70820 | + | 6.70820i | −0.215945 | + | 0.215945i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1623 | − | 35.1623i | 1.13074 | − | 1.13074i | 0.140689 | − | 0.990054i | \(-0.455068\pi\) |
0.990054 | − | 0.140689i | \(-0.0449317\pi\) | |||||||
\(968\) | −2.12132 | + | 2.12132i | −0.0681818 | + | 0.0681818i | ||||
\(969\) | 37.6875 | + | 26.6491i | 1.21070 | + | 0.856093i | ||||
\(970\) | 3.67544i | 0.118011i | ||||||||
\(971\) | 46.6318i | 1.49649i | 0.663425 | + | 0.748243i | \(0.269102\pi\) | ||||
−0.663425 | + | 0.748243i | \(0.730898\pi\) | |||||||
\(972\) | 10.2929 | − | 11.7071i | 0.330145 | − | 0.375506i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32.7564 | −1.04958 | ||||||||
\(975\) | −29.4317 | + | 41.6228i | −0.942570 | + | 1.33300i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 22.7235 | + | 22.7235i | 0.726991 | + | 0.726991i | 0.970019 | − | 0.243029i | \(-0.0781409\pi\) |
−0.243029 | + | 0.970019i | \(0.578141\pi\) | |||||||
\(978\) | 40.1945 | − | 6.89629i | 1.28528 | − | 0.220519i | ||||
\(979\) | 1.29822i | 0.0414913i | ||||||||
\(980\) | − | 15.6525i | − | 0.500000i | ||||||
\(981\) | 14.3246 | + | 40.5160i | 0.457348 | + | 1.29358i | ||||
\(982\) | 7.00000 | − | 7.00000i | 0.223379 | − | 0.223379i | ||||
\(983\) | 14.1421 | − | 14.1421i | 0.451064 | − | 0.451064i | −0.444644 | − | 0.895708i | \(-0.646670\pi\) |
0.895708 | + | 0.444644i | \(0.146670\pi\) | |||||||
\(984\) | −6.11584 | + | 8.64911i | −0.194966 | + | 0.275724i | ||||
\(985\) | 25.8114 | − | 25.8114i | 0.822419 | − | 0.822419i | ||||
\(986\) | − | 23.0864i | − | 0.735221i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.4868 | − | 21.4868i | −0.683587 | − | 0.683587i | ||||
\(989\) | 4.01315 | 0.127611 | ||||||||
\(990\) | −17.1212 | − | 8.17697i | −0.544149 | − | 0.259881i | ||||
\(991\) | 25.2982 | 0.803624 | 0.401812 | − | 0.915722i | \(-0.368380\pi\) | ||||
0.401812 | + | 0.915722i | \(0.368380\pi\) | |||||||
\(992\) | −7.30056 | − | 7.30056i | −0.231793 | − | 0.231793i | ||||
\(993\) | −0.870967 | − | 5.07637i | −0.0276393 | − | 0.161094i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.7617 | −0.626490 | ||||||||
\(996\) | −8.32456 | + | 11.7727i | −0.263774 | + | 0.373032i | ||||
\(997\) | −19.4605 | + | 19.4605i | −0.616320 | + | 0.616320i | −0.944586 | − | 0.328265i | \(-0.893536\pi\) |
0.328265 | + | 0.944586i | \(0.393536\pi\) | |||||||
\(998\) | 10.8547 | − | 10.8547i | 0.343600 | − | 0.343600i | ||||
\(999\) | 36.5028 | + | 10.3246i | 1.15490 | + | 0.326654i |
(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 | 690.2.i.d.323.4 | yes | 8 | |
3.2 | odd | 2 | inner | 690.2.i.d.323.1 | yes | 8 | |
5.2 | odd | 4 | inner | 690.2.i.d.47.2 | ✓ | 8 | |
15.2 | even | 4 | inner | 690.2.i.d.47.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.d.47.2 | ✓ | 8 | 5.2 | odd | 4 | inner | |
690.2.i.d.47.3 | yes | 8 | 15.2 | even | 4 | inner | |
690.2.i.d.323.1 | yes | 8 | 3.2 | odd | 2 | inner | |
690.2.i.d.323.4 | yes | 8 | 1.1 | even | 1 | trivial |