Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(97,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.g (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: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.7 | ||
Root | \(1.01089 + 0.750919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.293 |
Dual form | 490.2.g.c.97.7 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.204875 | − | 0.204875i | 0.118285 | − | 0.118285i | −0.645487 | − | 0.763771i | \(-0.723345\pi\) |
0.763771 | + | 0.645487i | \(0.223345\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.42962 | − | 1.71936i | 0.639345 | − | 0.768920i | ||||
\(6\) | − | 0.289737i | − | 0.118285i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.91605i | 0.972018i | ||||||||
\(10\) | −0.204875 | − | 2.22666i | −0.0647871 | − | 0.704133i | ||||
\(11\) | 5.62576 | 1.69623 | 0.848115 | − | 0.529812i | \(-0.177737\pi\) | ||||
0.848115 | + | 0.529812i | \(0.177737\pi\) | |||||||
\(12\) | −0.204875 | − | 0.204875i | −0.0591423 | − | 0.0591423i | ||||
\(13\) | 1.42962 | − | 1.42962i | 0.396505 | − | 0.396505i | −0.480493 | − | 0.876998i | \(-0.659542\pi\) |
0.876998 | + | 0.480493i | \(0.159542\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0593598 | − | 0.645146i | −0.0153266 | − | 0.166576i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.75384 | − | 3.75384i | −0.910440 | − | 0.910440i | 0.0858670 | − | 0.996307i | \(-0.472634\pi\) |
−0.996307 | + | 0.0858670i | \(0.972634\pi\) | |||||||
\(18\) | 2.06196 | + | 2.06196i | 0.486009 | + | 0.486009i | ||||
\(19\) | −3.89180 | −0.892841 | −0.446420 | − | 0.894823i | \(-0.647301\pi\) | ||||
−0.446420 | + | 0.894823i | \(0.647301\pi\) | |||||||
\(20\) | −1.71936 | − | 1.42962i | −0.384460 | − | 0.319673i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.97801 | − | 3.97801i | 0.848115 | − | 0.848115i | ||||
\(23\) | −0.794732 | − | 0.794732i | −0.165713 | − | 0.165713i | 0.619379 | − | 0.785092i | \(-0.287384\pi\) |
−0.785092 | + | 0.619379i | \(0.787384\pi\) | |||||||
\(24\) | −0.289737 | −0.0591423 | ||||||||
\(25\) | −0.912375 | − | 4.91605i | −0.182475 | − | 0.983211i | ||||
\(26\) | − | 2.02179i | − | 0.396505i | ||||||
\(27\) | 1.21205 | + | 1.21205i | 0.233259 | + | 0.233259i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.15502i | 0.585872i | 0.956132 | + | 0.292936i | \(0.0946322\pi\) | ||||
−0.956132 | + | 0.292936i | \(0.905368\pi\) | |||||||
\(30\) | −0.498161 | − | 0.414214i | −0.0909513 | − | 0.0756247i | ||||
\(31\) | − | 3.84846i | − | 0.691204i | −0.938381 | − | 0.345602i | \(-0.887675\pi\) | ||
0.938381 | − | 0.345602i | \(-0.112325\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.15258 | − | 1.15258i | 0.200638 | − | 0.200638i | ||||
\(34\) | −5.30873 | −0.910440 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.91605 | 0.486009 | ||||||||
\(37\) | −3.56380 | + | 3.56380i | −0.585885 | + | 0.585885i | −0.936514 | − | 0.350629i | \(-0.885968\pi\) |
0.350629 | + | 0.936514i | \(0.385968\pi\) | |||||||
\(38\) | −2.75192 | + | 2.75192i | −0.446420 | + | 0.446420i | ||||
\(39\) | − | 0.585786i | − | 0.0938009i | ||||||
\(40\) | −2.22666 | + | 0.204875i | −0.352066 | + | 0.0323936i | ||||
\(41\) | 7.21050i | 1.12609i | 0.826426 | + | 0.563046i | \(0.190371\pi\) | ||||
−0.826426 | + | 0.563046i | \(0.809629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85669 | + | 1.85669i | 0.283143 | + | 0.283143i | 0.834361 | − | 0.551218i | \(-0.185837\pi\) |
−0.551218 | + | 0.834361i | \(0.685837\pi\) | |||||||
\(44\) | − | 5.62576i | − | 0.848115i | ||||||
\(45\) | 5.01373 | + | 4.16885i | 0.747403 | + | 0.621455i | ||||
\(46\) | −1.12392 | −0.165713 | ||||||||
\(47\) | 4.16885 | + | 4.16885i | 0.608089 | + | 0.608089i | 0.942446 | − | 0.334358i | \(-0.108519\pi\) |
−0.334358 | + | 0.942446i | \(0.608519\pi\) | |||||||
\(48\) | −0.204875 | + | 0.204875i | −0.0295711 | + | 0.0295711i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.12132 | − | 2.83103i | −0.582843 | − | 0.400368i | ||||
\(51\) | −1.53813 | −0.215382 | ||||||||
\(52\) | −1.42962 | − | 1.42962i | −0.198253 | − | 0.198253i | ||||
\(53\) | −0.978013 | − | 0.978013i | −0.134340 | − | 0.134340i | 0.636739 | − | 0.771079i | \(-0.280283\pi\) |
−0.771079 | + | 0.636739i | \(0.780283\pi\) | |||||||
\(54\) | 1.71410 | 0.233259 | ||||||||
\(55\) | 8.04270 | − | 9.67269i | 1.08448 | − | 1.30426i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.797333 | + | 0.797333i | −0.105609 | + | 0.105609i | ||||
\(58\) | 2.23093 | + | 2.23093i | 0.292936 | + | 0.292936i | ||||
\(59\) | 5.47845 | 0.713234 | 0.356617 | − | 0.934251i | \(-0.383930\pi\) | ||||
0.356617 | + | 0.934251i | \(0.383930\pi\) | |||||||
\(60\) | −0.645146 | + | 0.0593598i | −0.0832880 | + | 0.00766332i | ||||
\(61\) | 4.60924i | 0.590153i | 0.955474 | + | 0.295077i | \(0.0953451\pi\) | ||||
−0.955474 | + | 0.295077i | \(0.904655\pi\) | |||||||
\(62\) | −2.72127 | − | 2.72127i | −0.345602 | − | 0.345602i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.414214 | − | 4.50184i | −0.0513769 | − | 0.558384i | ||||
\(66\) | − | 1.62999i | − | 0.200638i | ||||||
\(67\) | 0.597494 | − | 0.597494i | 0.0729956 | − | 0.0729956i | −0.669666 | − | 0.742662i | \(-0.733563\pi\) |
0.742662 | + | 0.669666i | \(0.233563\pi\) | |||||||
\(68\) | −3.75384 | + | 3.75384i | −0.455220 | + | 0.455220i | ||||
\(69\) | −0.325641 | −0.0392026 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.77710 | 0.566937 | 0.283469 | − | 0.958982i | \(-0.408515\pi\) | ||||
0.283469 | + | 0.958982i | \(0.408515\pi\) | |||||||
\(72\) | 2.06196 | − | 2.06196i | 0.243004 | − | 0.243004i | ||||
\(73\) | −3.96848 | + | 3.96848i | −0.464475 | + | 0.464475i | −0.900119 | − | 0.435644i | \(-0.856521\pi\) |
0.435644 | + | 0.900119i | \(0.356521\pi\) | |||||||
\(74\) | 5.03997i | 0.585885i | ||||||||
\(75\) | −1.19410 | − | 0.820253i | −0.137883 | − | 0.0947147i | ||||
\(76\) | 3.89180i | 0.446420i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.414214 | − | 0.414214i | −0.0469005 | − | 0.0469005i | ||||
\(79\) | 6.24784i | 0.702937i | 0.936200 | + | 0.351469i | \(0.114318\pi\) | ||||
−0.936200 | + | 0.351469i | \(0.885682\pi\) | |||||||
\(80\) | −1.42962 | + | 1.71936i | −0.159836 | + | 0.192230i | ||||
\(81\) | −8.25152 | −0.916836 | ||||||||
\(82\) | 5.09860 | + | 5.09860i | 0.563046 | + | 0.563046i | ||||
\(83\) | −5.67281 | + | 5.67281i | −0.622672 | + | 0.622672i | −0.946214 | − | 0.323542i | \(-0.895126\pi\) |
0.323542 | + | 0.946214i | \(0.395126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8207 | + | 1.08763i | −1.28214 | + | 0.117970i | ||||
\(86\) | 2.62576 | 0.283143 | ||||||||
\(87\) | 0.646383 | + | 0.646383i | 0.0692996 | + | 0.0692996i | ||||
\(88\) | −3.97801 | − | 3.97801i | −0.424058 | − | 0.424058i | ||||
\(89\) | −11.9218 | −1.26371 | −0.631855 | − | 0.775087i | \(-0.717706\pi\) | ||||
−0.631855 | + | 0.775087i | \(0.717706\pi\) | |||||||
\(90\) | 6.49307 | − | 0.597426i | 0.684429 | − | 0.0629742i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.794732 | + | 0.794732i | −0.0828566 | + | 0.0828566i | ||||
\(93\) | −0.788454 | − | 0.788454i | −0.0817588 | − | 0.0817588i | ||||
\(94\) | 5.89564 | 0.608089 | ||||||||
\(95\) | −5.56380 | + | 6.69140i | −0.570834 | + | 0.686523i | ||||
\(96\) | 0.289737i | 0.0295711i | ||||||||
\(97\) | 6.63103 | + | 6.63103i | 0.673279 | + | 0.673279i | 0.958471 | − | 0.285191i | \(-0.0920572\pi\) |
−0.285191 | + | 0.958471i | \(0.592057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.4050i | 1.64877i | ||||||||
\(100\) | −4.91605 | + | 0.912375i | −0.491605 | + | 0.0912375i | ||||
\(101\) | 16.0992i | 1.60193i | 0.598711 | + | 0.800965i | \(0.295680\pi\) | ||||
−0.598711 | + | 0.800965i | \(0.704320\pi\) | |||||||
\(102\) | −1.08763 | + | 1.08763i | −0.107691 | + | 0.107691i | ||||
\(103\) | 13.9084 | − | 13.9084i | 1.37044 | − | 1.37044i | 0.510653 | − | 0.859787i | \(-0.329404\pi\) |
0.859787 | − | 0.510653i | \(-0.170596\pi\) | |||||||
\(104\) | −2.02179 | −0.198253 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.38312 | −0.134340 | ||||||||
\(107\) | 1.98061 | − | 1.98061i | 0.191473 | − | 0.191473i | −0.604859 | − | 0.796332i | \(-0.706771\pi\) |
0.796332 | + | 0.604859i | \(0.206771\pi\) | |||||||
\(108\) | 1.21205 | − | 1.21205i | 0.116630 | − | 0.116630i | ||||
\(109\) | 5.91085i | 0.566157i | 0.959097 | + | 0.283078i | \(0.0913557\pi\) | ||||
−0.959097 | + | 0.283078i | \(0.908644\pi\) | |||||||
\(110\) | −1.15258 | − | 12.5267i | −0.109894 | − | 1.19437i | ||||
\(111\) | 1.46027i | 0.138602i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5818 | − | 13.5818i | −1.27767 | − | 1.27767i | −0.941970 | − | 0.335697i | \(-0.891028\pi\) |
−0.335697 | − | 0.941970i | \(-0.608972\pi\) | |||||||
\(114\) | 1.12760i | 0.105609i | ||||||||
\(115\) | −2.50259 | + | 0.230263i | −0.233368 | + | 0.0214722i | ||||
\(116\) | 3.15502 | 0.292936 | ||||||||
\(117\) | 4.16885 | + | 4.16885i | 0.385410 | + | 0.385410i | ||||
\(118\) | 3.87385 | − | 3.87385i | 0.356617 | − | 0.356617i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.414214 | + | 0.498161i | −0.0378124 | + | 0.0454757i | ||||
\(121\) | 20.6492 | 1.87720 | ||||||||
\(122\) | 3.25923 | + | 3.25923i | 0.295077 | + | 0.295077i | ||||
\(123\) | 1.47725 | + | 1.47725i | 0.133199 | + | 0.133199i | ||||
\(124\) | −3.84846 | −0.345602 | ||||||||
\(125\) | −9.75680 | − | 5.45939i | −0.872674 | − | 0.488303i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.63487 | − | 4.63487i | 0.411278 | − | 0.411278i | −0.470906 | − | 0.882184i | \(-0.656073\pi\) |
0.882184 | + | 0.470906i | \(0.156073\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0.760780 | 0.0669829 | ||||||||
\(130\) | −3.47617 | − | 2.89039i | −0.304881 | − | 0.253504i | ||||
\(131\) | 7.69535i | 0.672346i | 0.941800 | + | 0.336173i | \(0.109133\pi\) | ||||
−0.941800 | + | 0.336173i | \(0.890867\pi\) | |||||||
\(132\) | −1.15258 | − | 1.15258i | −0.100319 | − | 0.100319i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.844985i | − | 0.0729956i | ||||||
\(135\) | 3.81672 | − | 0.351176i | 0.328491 | − | 0.0302244i | ||||
\(136\) | 5.30873i | 0.455220i | ||||||||
\(137\) | −6.24784 | + | 6.24784i | −0.533789 | + | 0.533789i | −0.921698 | − | 0.387909i | \(-0.873198\pi\) |
0.387909 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(138\) | −0.230263 | + | 0.230263i | −0.0196013 | + | 0.0196013i | ||||
\(139\) | −11.0631 | −0.938361 | −0.469180 | − | 0.883102i | \(-0.655451\pi\) | ||||
−0.469180 | + | 0.883102i | \(0.655451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.70818 | 0.143855 | ||||||||
\(142\) | 3.37792 | − | 3.37792i | 0.283469 | − | 0.283469i | ||||
\(143\) | 8.04270 | − | 8.04270i | 0.672564 | − | 0.672564i | ||||
\(144\) | − | 2.91605i | − | 0.243004i | ||||||
\(145\) | 5.42460 | + | 4.51047i | 0.450488 | + | 0.374574i | ||||
\(146\) | 5.61227i | 0.464475i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.56380 | + | 3.56380i | 0.292943 | + | 0.292943i | ||||
\(149\) | − | 5.04885i | − | 0.413618i | −0.978381 | − | 0.206809i | \(-0.933692\pi\) | ||
0.978381 | − | 0.206809i | \(-0.0663079\pi\) | |||||||
\(150\) | −1.42436 | + | 0.264349i | −0.116299 | + | 0.0215840i | ||||
\(151\) | 13.4428 | 1.09396 | 0.546981 | − | 0.837145i | \(-0.315777\pi\) | ||||
0.546981 | + | 0.837145i | \(0.315777\pi\) | |||||||
\(152\) | 2.75192 | + | 2.75192i | 0.223210 | + | 0.223210i | ||||
\(153\) | 10.9464 | − | 10.9464i | 0.884963 | − | 0.884963i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.61688 | − | 5.50184i | −0.531481 | − | 0.441918i | ||||
\(156\) | −0.585786 | −0.0469005 | ||||||||
\(157\) | −0.779844 | − | 0.779844i | −0.0622383 | − | 0.0622383i | 0.675303 | − | 0.737541i | \(-0.264013\pi\) |
−0.737541 | + | 0.675303i | \(0.764013\pi\) | |||||||
\(158\) | 4.41789 | + | 4.41789i | 0.351469 | + | 0.351469i | ||||
\(159\) | −0.400741 | −0.0317808 | ||||||||
\(160\) | 0.204875 | + | 2.22666i | 0.0161968 | + | 0.176033i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.83471 | + | 5.83471i | −0.458418 | + | 0.458418i | ||||
\(163\) | −9.36288 | − | 9.36288i | −0.733358 | − | 0.733358i | 0.237926 | − | 0.971283i | \(-0.423533\pi\) |
−0.971283 | + | 0.237926i | \(0.923533\pi\) | |||||||
\(164\) | 7.21050 | 0.563046 | ||||||||
\(165\) | −0.333944 | − | 3.62944i | −0.0259975 | − | 0.282551i | ||||
\(166\) | 8.02257i | 0.622672i | ||||||||
\(167\) | 4.70680 | + | 4.70680i | 0.364223 | + | 0.364223i | 0.865365 | − | 0.501142i | \(-0.167087\pi\) |
−0.501142 | + | 0.865365i | \(0.667087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.91237i | 0.685567i | ||||||||
\(170\) | −7.58946 | + | 9.12760i | −0.582085 | + | 0.700055i | ||||
\(171\) | − | 11.3487i | − | 0.867857i | ||||||
\(172\) | 1.85669 | − | 1.85669i | 0.141571 | − | 0.141571i | ||||
\(173\) | −4.98835 | + | 4.98835i | −0.379257 | + | 0.379257i | −0.870834 | − | 0.491577i | \(-0.836421\pi\) |
0.491577 | + | 0.870834i | \(0.336421\pi\) | |||||||
\(174\) | 0.914124 | 0.0692996 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.62576 | −0.424058 | ||||||||
\(177\) | 1.12240 | − | 1.12240i | 0.0843646 | − | 0.0843646i | ||||
\(178\) | −8.42999 | + | 8.42999i | −0.631855 | + | 0.631855i | ||||
\(179\) | − | 2.20635i | − | 0.164910i | −0.996595 | − | 0.0824550i | \(-0.973724\pi\) | ||
0.996595 | − | 0.0824550i | \(-0.0262761\pi\) | |||||||
\(180\) | 4.16885 | − | 5.01373i | 0.310727 | − | 0.373702i | ||||
\(181\) | − | 4.11867i | − | 0.306139i | −0.988215 | − | 0.153069i | \(-0.951084\pi\) | ||
0.988215 | − | 0.153069i | \(-0.0489158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.944318 | + | 0.944318i | 0.0698060 | + | 0.0698060i | ||||
\(184\) | 1.12392i | 0.0828566i | ||||||||
\(185\) | 1.03256 | + | 11.2223i | 0.0759156 | + | 0.825081i | ||||
\(186\) | −1.11504 | −0.0817588 | ||||||||
\(187\) | −21.1182 | − | 21.1182i | −1.54432 | − | 1.54432i | ||||
\(188\) | 4.16885 | − | 4.16885i | 0.304044 | − | 0.304044i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.797333 | + | 8.66573i | 0.0578446 | + | 0.628678i | ||||
\(191\) | −17.2023 | −1.24472 | −0.622359 | − | 0.782732i | \(-0.713826\pi\) | ||||
−0.622359 | + | 0.782732i | \(0.713826\pi\) | |||||||
\(192\) | 0.204875 | + | 0.204875i | 0.0147856 | + | 0.0147856i | ||||
\(193\) | −8.53293 | − | 8.53293i | −0.614214 | − | 0.614214i | 0.329827 | − | 0.944041i | \(-0.393009\pi\) |
−0.944041 | + | 0.329827i | \(0.893009\pi\) | |||||||
\(194\) | 9.37769 | 0.673279 | ||||||||
\(195\) | −1.00718 | − | 0.837452i | −0.0721254 | − | 0.0599712i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3135 | − | 14.3135i | 1.01979 | − | 1.01979i | 0.0199932 | − | 0.999800i | \(-0.493636\pi\) |
0.999800 | − | 0.0199932i | \(-0.00636444\pi\) | |||||||
\(198\) | 11.6001 | + | 11.6001i | 0.824383 | + | 0.824383i | ||||
\(199\) | −7.53307 | −0.534005 | −0.267002 | − | 0.963696i | \(-0.586033\pi\) | ||||
−0.267002 | + | 0.963696i | \(0.586033\pi\) | |||||||
\(200\) | −2.83103 | + | 4.12132i | −0.200184 | + | 0.291421i | ||||
\(201\) | − | 0.244823i | − | 0.0172685i | ||||||
\(202\) | 11.3839 | + | 11.3839i | 0.800965 | + | 0.800965i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.53813i | 0.107691i | ||||||||
\(205\) | 12.3974 | + | 10.3083i | 0.865874 | + | 0.719961i | ||||
\(206\) | − | 19.6695i | − | 1.37044i | ||||||
\(207\) | 2.31748 | − | 2.31748i | 0.161076 | − | 0.161076i | ||||
\(208\) | −1.42962 | + | 1.42962i | −0.0991263 | + | 0.0991263i | ||||
\(209\) | −21.8944 | −1.51446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5766 | 1.34771 | 0.673854 | − | 0.738865i | \(-0.264638\pi\) | ||||
0.673854 | + | 0.738865i | \(0.264638\pi\) | |||||||
\(212\) | −0.978013 | + | 0.978013i | −0.0671702 | + | 0.0671702i | ||||
\(213\) | 0.978707 | − | 0.978707i | 0.0670599 | − | 0.0670599i | ||||
\(214\) | − | 2.80101i | − | 0.191473i | ||||||
\(215\) | 5.84668 | − | 0.537952i | 0.398740 | − | 0.0366880i | ||||
\(216\) | − | 1.71410i | − | 0.116630i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.17960 | + | 4.17960i | 0.283078 | + | 0.283078i | ||||
\(219\) | 1.62608i | 0.109880i | ||||||||
\(220\) | −9.67269 | − | 8.04270i | −0.652132 | − | 0.542239i | ||||
\(221\) | −10.7331 | −0.721988 | ||||||||
\(222\) | 1.03256 | + | 1.03256i | 0.0693012 | + | 0.0693012i | ||||
\(223\) | −1.46027 | + | 1.46027i | −0.0977867 | + | 0.0977867i | −0.754308 | − | 0.656521i | \(-0.772027\pi\) |
0.656521 | + | 0.754308i | \(0.272027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3355 | − | 2.66053i | 0.955698 | − | 0.177369i | ||||
\(226\) | −19.2075 | −1.27767 | ||||||||
\(227\) | −13.1828 | − | 13.1828i | −0.874974 | − | 0.874974i | 0.118035 | − | 0.993009i | \(-0.462340\pi\) |
−0.993009 | + | 0.118035i | \(0.962340\pi\) | |||||||
\(228\) | 0.797333 | + | 0.797333i | 0.0528047 | + | 0.0528047i | ||||
\(229\) | −4.00767 | −0.264834 | −0.132417 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132417 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(230\) | −1.60678 | + | 1.93242i | −0.105948 | + | 0.127420i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.23093 | − | 2.23093i | 0.146468 | − | 0.146468i | ||||
\(233\) | −9.70971 | − | 9.70971i | −0.636104 | − | 0.636104i | 0.313488 | − | 0.949592i | \(-0.398502\pi\) |
−0.949592 | + | 0.313488i | \(0.898502\pi\) | |||||||
\(234\) | 5.89564 | 0.385410 | ||||||||
\(235\) | 13.1276 | − | 1.20787i | 0.856350 | − | 0.0787927i | ||||
\(236\) | − | 5.47845i | − | 0.356617i | ||||||
\(237\) | 1.28003 | + | 1.28003i | 0.0831466 | + | 0.0831466i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.6621i | − | 1.27183i | −0.771758 | − | 0.635916i | \(-0.780622\pi\) | ||
0.771758 | − | 0.635916i | \(-0.219378\pi\) | |||||||
\(240\) | 0.0593598 | + | 0.645146i | 0.00383166 | + | 0.0416440i | ||||
\(241\) | − | 5.88512i | − | 0.379094i | −0.981872 | − | 0.189547i | \(-0.939298\pi\) | ||
0.981872 | − | 0.189547i | \(-0.0607020\pi\) | |||||||
\(242\) | 14.6012 | − | 14.6012i | 0.938599 | − | 0.938599i | ||||
\(243\) | −5.32668 | + | 5.32668i | −0.341707 | + | 0.341707i | ||||
\(244\) | 4.60924 | 0.295077 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.08915 | 0.133199 | ||||||||
\(247\) | −5.56380 | + | 5.56380i | −0.354016 | + | 0.354016i | ||||
\(248\) | −2.72127 | + | 2.72127i | −0.172801 | + | 0.172801i | ||||
\(249\) | 2.32443i | 0.147305i | ||||||||
\(250\) | −10.7595 | + | 3.03873i | −0.680488 | + | 0.192186i | ||||
\(251\) | − | 7.09950i | − | 0.448116i | −0.974576 | − | 0.224058i | \(-0.928069\pi\) | ||
0.974576 | − | 0.224058i | \(-0.0719306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.47097 | − | 4.47097i | −0.281088 | − | 0.281088i | ||||
\(254\) | − | 6.55469i | − | 0.411278i | ||||||
\(255\) | −2.19895 | + | 2.64460i | −0.137703 | + | 0.165611i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.99107 | + | 6.99107i | 0.436091 | + | 0.436091i | 0.890694 | − | 0.454603i | \(-0.150219\pi\) |
−0.454603 | + | 0.890694i | \(0.650219\pi\) | |||||||
\(258\) | 0.537952 | − | 0.537952i | 0.0334915 | − | 0.0334915i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.50184 | + | 0.414214i | −0.279192 | + | 0.0256884i | ||||
\(261\) | −9.20019 | −0.569477 | ||||||||
\(262\) | 5.44144 | + | 5.44144i | 0.336173 | + | 0.336173i | ||||
\(263\) | 9.72142 | + | 9.72142i | 0.599448 | + | 0.599448i | 0.940166 | − | 0.340718i | \(-0.110670\pi\) |
−0.340718 | + | 0.940166i | \(0.610670\pi\) | |||||||
\(264\) | −1.62999 | −0.100319 | ||||||||
\(265\) | −3.07974 | + | 0.283366i | −0.189187 | + | 0.0174071i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.44248 | + | 2.44248i | −0.149477 | + | 0.149477i | ||||
\(268\) | −0.597494 | − | 0.597494i | −0.0364978 | − | 0.0364978i | ||||
\(269\) | −26.5020 | −1.61586 | −0.807928 | − | 0.589281i | \(-0.799411\pi\) | ||||
−0.807928 | + | 0.589281i | \(0.799411\pi\) | |||||||
\(270\) | 2.45051 | − | 2.94715i | 0.149133 | − | 0.179358i | ||||
\(271\) | 12.7969i | 0.777355i | 0.921374 | + | 0.388678i | \(0.127068\pi\) | ||||
−0.921374 | + | 0.388678i | \(0.872932\pi\) | |||||||
\(272\) | 3.75384 | + | 3.75384i | 0.227610 | + | 0.227610i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.83578i | 0.533789i | ||||||||
\(275\) | −5.13280 | − | 27.6565i | −0.309520 | − | 1.66775i | ||||
\(276\) | 0.325641i | 0.0196013i | ||||||||
\(277\) | 14.2152 | − | 14.2152i | 0.854110 | − | 0.854110i | −0.136526 | − | 0.990636i | \(-0.543594\pi\) |
0.990636 | + | 0.136526i | \(0.0435938\pi\) | |||||||
\(278\) | −7.82280 | + | 7.82280i | −0.469180 | + | 0.469180i | ||||
\(279\) | 11.2223 | 0.671863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1498 | −0.844107 | −0.422054 | − | 0.906571i | \(-0.638691\pi\) | ||||
−0.422054 | + | 0.906571i | \(0.638691\pi\) | |||||||
\(282\) | 1.20787 | − | 1.20787i | 0.0719275 | − | 0.0719275i | ||||
\(283\) | 19.1397 | − | 19.1397i | 1.13774 | − | 1.13774i | 0.148885 | − | 0.988854i | \(-0.452431\pi\) |
0.988854 | − | 0.148885i | \(-0.0475686\pi\) | |||||||
\(284\) | − | 4.77710i | − | 0.283469i | ||||||
\(285\) | 0.231017 | + | 2.51078i | 0.0136843 | + | 0.148726i | ||||
\(286\) | − | 11.3741i | − | 0.672564i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.06196 | − | 2.06196i | −0.121502 | − | 0.121502i | ||||
\(289\) | 11.1826i | 0.657800i | ||||||||
\(290\) | 7.02515 | − | 0.646383i | 0.412531 | − | 0.0379569i | ||||
\(291\) | 2.71706 | 0.159277 | ||||||||
\(292\) | 3.96848 | + | 3.96848i | 0.232237 | + | 0.232237i | ||||
\(293\) | −17.1191 | + | 17.1191i | −1.00011 | + | 1.00011i | −0.000106876 | 1.00000i | \(0.500034\pi\) | |
−1.00000 | 0.000106876i | \(0.999966\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.83211 | − | 9.41941i | 0.456003 | − | 0.548420i | ||||
\(296\) | 5.03997 | 0.292943 | ||||||||
\(297\) | 6.81871 | + | 6.81871i | 0.395661 | + | 0.395661i | ||||
\(298\) | −3.57008 | − | 3.57008i | −0.206809 | − | 0.206809i | ||||
\(299\) | −2.27233 | −0.131412 | ||||||||
\(300\) | −0.820253 | + | 1.19410i | −0.0473573 | + | 0.0689413i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.50552 | − | 9.50552i | 0.546981 | − | 0.546981i | ||||
\(303\) | 3.29832 | + | 3.29832i | 0.189484 | + | 0.189484i | ||||
\(304\) | 3.89180 | 0.223210 | ||||||||
\(305\) | 7.92493 | + | 6.58946i | 0.453780 | + | 0.377312i | ||||
\(306\) | − | 15.4805i | − | 0.884963i | ||||||
\(307\) | −17.2974 | − | 17.2974i | −0.987217 | − | 0.987217i | 0.0127019 | − | 0.999919i | \(-0.495957\pi\) |
−0.999919 | + | 0.0127019i | \(0.995957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.69898i | − | 0.324204i | ||||||
\(310\) | −8.56923 | + | 0.788454i | −0.486699 | + | 0.0447812i | ||||
\(311\) | − | 10.9823i | − | 0.622749i | −0.950287 | − | 0.311374i | \(-0.899211\pi\) | ||
0.950287 | − | 0.311374i | \(-0.100789\pi\) | |||||||
\(312\) | −0.414214 | + | 0.414214i | −0.0234502 | + | 0.0234502i | ||||
\(313\) | 20.7967 | − | 20.7967i | 1.17550 | − | 1.17550i | 0.194620 | − | 0.980879i | \(-0.437653\pi\) |
0.980879 | − | 0.194620i | \(-0.0623475\pi\) | |||||||
\(314\) | −1.10287 | −0.0622383 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.24784 | 0.351469 | ||||||||
\(317\) | 3.03630 | − | 3.03630i | 0.170535 | − | 0.170535i | −0.616679 | − | 0.787215i | \(-0.711522\pi\) |
0.787215 | + | 0.616679i | \(0.211522\pi\) | |||||||
\(318\) | −0.283366 | + | 0.283366i | −0.0158904 | + | 0.0158904i | ||||
\(319\) | 17.7494i | 0.993773i | ||||||||
\(320\) | 1.71936 | + | 1.42962i | 0.0961150 | + | 0.0799182i | ||||
\(321\) | − | 0.811556i | − | 0.0452966i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6092 | + | 14.6092i | 0.812878 | + | 0.812878i | ||||
\(324\) | 8.25152i | 0.458418i | ||||||||
\(325\) | −8.33243 | − | 5.72374i | −0.462200 | − | 0.317496i | ||||
\(326\) | −13.2411 | −0.733358 | ||||||||
\(327\) | 1.21099 | + | 1.21099i | 0.0669676 | + | 0.0669676i | ||||
\(328\) | 5.09860 | − | 5.09860i | 0.281523 | − | 0.281523i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.80253 | − | 2.33027i | −0.154274 | − | 0.128277i | ||||
\(331\) | 35.4499 | 1.94850 | 0.974250 | − | 0.225469i | \(-0.0723914\pi\) | ||||
0.974250 | + | 0.225469i | \(0.0723914\pi\) | |||||||
\(332\) | 5.67281 | + | 5.67281i | 0.311336 | + | 0.311336i | ||||
\(333\) | −10.3922 | − | 10.3922i | −0.569491 | − | 0.569491i | ||||
\(334\) | 6.65642 | 0.364223 | ||||||||
\(335\) | −0.173116 | − | 1.88150i | −0.00945835 | − | 0.102797i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1473 | + | 12.1473i | −0.661708 | + | 0.661708i | −0.955782 | − | 0.294075i | \(-0.904989\pi\) |
0.294075 | + | 0.955782i | \(0.404989\pi\) | |||||||
\(338\) | 6.30200 | + | 6.30200i | 0.342784 | + | 0.342784i | ||||
\(339\) | −5.56513 | −0.302257 | ||||||||
\(340\) | 1.08763 | + | 11.8207i | 0.0589848 | + | 0.641070i | ||||
\(341\) | − | 21.6505i | − | 1.17244i | ||||||
\(342\) | −8.02475 | − | 8.02475i | −0.433929 | − | 0.433929i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.62576i | − | 0.141571i | ||||||
\(345\) | −0.465543 | + | 0.559894i | −0.0250640 | + | 0.0301437i | ||||
\(346\) | 7.05459i | 0.379257i | ||||||||
\(347\) | 6.34718 | − | 6.34718i | 0.340734 | − | 0.340734i | −0.515909 | − | 0.856643i | \(-0.672546\pi\) |
0.856643 | + | 0.515909i | \(0.172546\pi\) | |||||||
\(348\) | 0.646383 | − | 0.646383i | 0.0346498 | − | 0.0346498i | ||||
\(349\) | 26.0251 | 1.39309 | 0.696546 | − | 0.717512i | \(-0.254719\pi\) | ||||
0.696546 | + | 0.717512i | \(0.254719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.46554 | 0.184977 | ||||||||
\(352\) | −3.97801 | + | 3.97801i | −0.212029 | + | 0.212029i | ||||
\(353\) | −7.04715 | + | 7.04715i | −0.375082 | + | 0.375082i | −0.869324 | − | 0.494242i | \(-0.835446\pi\) |
0.494242 | + | 0.869324i | \(0.335446\pi\) | |||||||
\(354\) | − | 1.58731i | − | 0.0843646i | ||||||
\(355\) | 6.82943 | − | 8.21353i | 0.362469 | − | 0.435929i | ||||
\(356\) | 11.9218i | 0.631855i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.56012 | − | 1.56012i | −0.0824550 | − | 0.0824550i | ||||
\(359\) | 11.5741i | 0.610858i | 0.952215 | + | 0.305429i | \(0.0987999\pi\) | ||||
−0.952215 | + | 0.305429i | \(0.901200\pi\) | |||||||
\(360\) | −0.597426 | − | 6.49307i | −0.0314871 | − | 0.342215i | ||||
\(361\) | −3.85386 | −0.202835 | ||||||||
\(362\) | −2.91234 | − | 2.91234i | −0.153069 | − | 0.153069i | ||||
\(363\) | 4.23050 | − | 4.23050i | 0.222044 | − | 0.222044i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.14981 | + | 12.4966i | 0.0601840 | + | 0.654104i | ||||
\(366\) | 1.33547 | 0.0698060 | ||||||||
\(367\) | 11.8047 | + | 11.8047i | 0.616202 | + | 0.616202i | 0.944555 | − | 0.328353i | \(-0.106494\pi\) |
−0.328353 | + | 0.944555i | \(0.606494\pi\) | |||||||
\(368\) | 0.794732 | + | 0.794732i | 0.0414283 | + | 0.0414283i | ||||
\(369\) | −21.0262 | −1.09458 | ||||||||
\(370\) | 8.66551 | + | 7.20525i | 0.450499 | + | 0.374583i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.788454 | + | 0.788454i | −0.0408794 | + | 0.0408794i | ||||
\(373\) | 2.24784 | + | 2.24784i | 0.116389 | + | 0.116389i | 0.762902 | − | 0.646514i | \(-0.223774\pi\) |
−0.646514 | + | 0.762902i | \(0.723774\pi\) | |||||||
\(374\) | −29.8656 | −1.54432 | ||||||||
\(375\) | −3.11741 | + | 0.880431i | −0.160983 | + | 0.0454653i | ||||
\(376\) | − | 5.89564i | − | 0.304044i | ||||||
\(377\) | 4.51047 | + | 4.51047i | 0.232301 | + | 0.232301i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.15349i | − | 0.367450i | −0.982978 | − | 0.183725i | \(-0.941184\pi\) | ||
0.982978 | − | 0.183725i | \(-0.0588156\pi\) | |||||||
\(380\) | 6.69140 | + | 5.56380i | 0.343262 | + | 0.285417i | ||||
\(381\) | − | 1.89914i | − | 0.0972957i | ||||||
\(382\) | −12.1639 | + | 12.1639i | −0.622359 | + | 0.622359i | ||||
\(383\) | −10.3191 | + | 10.3191i | −0.527280 | + | 0.527280i | −0.919760 | − | 0.392480i | \(-0.871617\pi\) |
0.392480 | + | 0.919760i | \(0.371617\pi\) | |||||||
\(384\) | 0.289737 | 0.0147856 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.0674 | −0.614214 | ||||||||
\(387\) | −5.41421 | + | 5.41421i | −0.275220 | + | 0.275220i | ||||
\(388\) | 6.63103 | − | 6.63103i | 0.336640 | − | 0.336640i | ||||
\(389\) | − | 6.19651i | − | 0.314176i | −0.987585 | − | 0.157088i | \(-0.949789\pi\) | ||
0.987585 | − | 0.157088i | \(-0.0502106\pi\) | |||||||
\(390\) | −1.30435 | + | 0.120013i | −0.0660483 | + | 0.00607709i | ||||
\(391\) | 5.96659i | 0.301744i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.57658 | + | 1.57658i | 0.0795282 | + | 0.0795282i | ||||
\(394\) | − | 20.2423i | − | 1.01979i | ||||||
\(395\) | 10.7423 | + | 8.93204i | 0.540502 | + | 0.449420i | ||||
\(396\) | 16.4050 | 0.824383 | ||||||||
\(397\) | −2.06184 | − | 2.06184i | −0.103481 | − | 0.103481i | 0.653471 | − | 0.756952i | \(-0.273312\pi\) |
−0.756952 | + | 0.653471i | \(0.773312\pi\) | |||||||
\(398\) | −5.32668 | + | 5.32668i | −0.267002 | + | 0.267002i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.912375 | + | 4.91605i | 0.0456187 | + | 0.245803i | ||||
\(401\) | −19.9706 | −0.997282 | −0.498641 | − | 0.866809i | \(-0.666167\pi\) | ||||
−0.498641 | + | 0.866809i | \(0.666167\pi\) | |||||||
\(402\) | −0.173116 | − | 0.173116i | −0.00863425 | − | 0.00863425i | ||||
\(403\) | −5.50184 | − | 5.50184i | −0.274066 | − | 0.274066i | ||||
\(404\) | 16.0992 | 0.800965 | ||||||||
\(405\) | −11.7965 | + | 14.1873i | −0.586175 | + | 0.704973i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0491 | + | 20.0491i | −0.993796 | + | 0.993796i | ||||
\(408\) | 1.08763 | + | 1.08763i | 0.0538455 | + | 0.0538455i | ||||
\(409\) | 34.3582 | 1.69890 | 0.849451 | − | 0.527668i | \(-0.176933\pi\) | ||||
0.849451 | + | 0.527668i | \(0.176933\pi\) | |||||||
\(410\) | 16.0554 | − | 1.47725i | 0.792918 | − | 0.0729562i | ||||
\(411\) | 2.56005i | 0.126278i | ||||||||
\(412\) | −13.9084 | − | 13.9084i | −0.685220 | − | 0.685220i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 3.27741i | − | 0.161076i | ||||||
\(415\) | 1.64362 | + | 17.8636i | 0.0806823 | + | 0.876887i | ||||
\(416\) | 2.02179i | 0.0991263i | ||||||||
\(417\) | −2.26655 | + | 2.26655i | −0.110994 | + | 0.110994i | ||||
\(418\) | −15.4816 | + | 15.4816i | −0.757232 | + | 0.757232i | ||||
\(419\) | 31.1360 | 1.52109 | 0.760547 | − | 0.649283i | \(-0.224931\pi\) | ||||
0.760547 | + | 0.649283i | \(0.224931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6728 | −1.64111 | −0.820555 | − | 0.571567i | \(-0.806336\pi\) | ||||
−0.820555 | + | 0.571567i | \(0.806336\pi\) | |||||||
\(422\) | 13.8427 | − | 13.8427i | 0.673854 | − | 0.673854i | ||||
\(423\) | −12.1566 | + | 12.1566i | −0.591073 | + | 0.591073i | ||||
\(424\) | 1.38312i | 0.0671702i | ||||||||
\(425\) | −15.0292 | + | 21.8790i | −0.729021 | + | 1.06129i | ||||
\(426\) | − | 1.38410i | − | 0.0670599i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.98061 | − | 1.98061i | −0.0957366 | − | 0.0957366i | ||||
\(429\) | − | 3.29549i | − | 0.159108i | ||||||
\(430\) | 3.75384 | − | 4.51462i | 0.181026 | − | 0.217714i | ||||
\(431\) | −14.7457 | −0.710274 | −0.355137 | − | 0.934814i | \(-0.615566\pi\) | ||||
−0.355137 | + | 0.934814i | \(0.615566\pi\) | |||||||
\(432\) | −1.21205 | − | 1.21205i | −0.0583148 | − | 0.0583148i | ||||
\(433\) | 9.98256 | − | 9.98256i | 0.479731 | − | 0.479731i | −0.425315 | − | 0.905046i | \(-0.639837\pi\) |
0.905046 | + | 0.425315i | \(0.139837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.03545 | − | 0.187281i | 0.0975922 | − | 0.00897944i | ||||
\(436\) | 5.91085 | 0.283078 | ||||||||
\(437\) | 3.09294 | + | 3.09294i | 0.147955 | + | 0.147955i | ||||
\(438\) | 1.14981 | + | 1.14981i | 0.0549402 | + | 0.0549402i | ||||
\(439\) | 38.4285 | 1.83409 | 0.917046 | − | 0.398782i | \(-0.130567\pi\) | ||||
0.917046 | + | 0.398782i | \(0.130567\pi\) | |||||||
\(440\) | −12.5267 | + | 1.15258i | −0.597186 | + | 0.0549470i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.58946 | + | 7.58946i | −0.360994 | + | 0.360994i | ||||
\(443\) | 4.05568 | + | 4.05568i | 0.192691 | + | 0.192691i | 0.796858 | − | 0.604167i | \(-0.206494\pi\) |
−0.604167 | + | 0.796858i | \(0.706494\pi\) | |||||||
\(444\) | 1.46027 | 0.0693012 | ||||||||
\(445\) | −17.0437 | + | 20.4978i | −0.807947 | + | 0.971691i | ||||
\(446\) | 2.06513i | 0.0977867i | ||||||||
\(447\) | −1.03438 | − | 1.03438i | −0.0489247 | − | 0.0489247i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.30267i | − | 0.344635i | −0.985042 | − | 0.172317i | \(-0.944875\pi\) | ||
0.985042 | − | 0.172317i | \(-0.0551254\pi\) | |||||||
\(450\) | 8.25543 | − | 12.0180i | 0.389165 | − | 0.566533i | ||||
\(451\) | 40.5646i | 1.91011i | ||||||||
\(452\) | −13.5818 | + | 13.5818i | −0.638833 | + | 0.638833i | ||||
\(453\) | 2.75410 | − | 2.75410i | 0.129399 | − | 0.129399i | ||||
\(454\) | −18.6433 | −0.874974 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.12760 | 0.0528047 | ||||||||
\(457\) | 3.63864 | − | 3.63864i | 0.170208 | − | 0.170208i | −0.616863 | − | 0.787071i | \(-0.711597\pi\) |
0.787071 | + | 0.616863i | \(0.211597\pi\) | |||||||
\(458\) | −2.83385 | + | 2.83385i | −0.132417 | + | 0.132417i | ||||
\(459\) | − | 9.09969i | − | 0.424737i | ||||||
\(460\) | 0.230263 | + | 2.50259i | 0.0107361 | + | 0.116684i | ||||
\(461\) | − | 29.4110i | − | 1.36981i | −0.728634 | − | 0.684903i | \(-0.759845\pi\) | ||
0.728634 | − | 0.684903i | \(-0.240155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.04625 | − | 4.04625i | −0.188045 | − | 0.188045i | 0.606805 | − | 0.794851i | \(-0.292451\pi\) |
−0.794851 | + | 0.606805i | \(0.792451\pi\) | |||||||
\(464\) | − | 3.15502i | − | 0.146468i | ||||||
\(465\) | −2.48282 | + | 0.228444i | −0.115138 | + | 0.0105938i | ||||
\(466\) | −13.7316 | −0.636104 | ||||||||
\(467\) | −11.7682 | − | 11.7682i | −0.544568 | − | 0.544568i | 0.380297 | − | 0.924865i | \(-0.375822\pi\) |
−0.924865 | + | 0.380297i | \(0.875822\pi\) | |||||||
\(468\) | 4.16885 | − | 4.16885i | 0.192705 | − | 0.192705i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.42852 | − | 10.1367i | 0.388779 | − | 0.467571i | ||||
\(471\) | −0.319541 | −0.0147237 | ||||||||
\(472\) | −3.87385 | − | 3.87385i | −0.178308 | − | 0.178308i | ||||
\(473\) | 10.4453 | + | 10.4453i | 0.480276 | + | 0.480276i | ||||
\(474\) | 1.81023 | 0.0831466 | ||||||||
\(475\) | 3.55078 | + | 19.1323i | 0.162921 | + | 0.877851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.85194 | − | 2.85194i | 0.130581 | − | 0.130581i | ||||
\(478\) | −13.9032 | − | 13.9032i | −0.635916 | − | 0.635916i | ||||
\(479\) | 15.3892 | 0.703150 | 0.351575 | − | 0.936160i | \(-0.385646\pi\) | ||||
0.351575 | + | 0.936160i | \(0.385646\pi\) | |||||||
\(480\) | 0.498161 | + | 0.414214i | 0.0227378 | + | 0.0189062i | ||||
\(481\) | 10.1898i | 0.464613i | ||||||||
\(482\) | −4.16141 | − | 4.16141i | −0.189547 | − | 0.189547i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 20.6492i | − | 0.938599i | ||||||
\(485\) | 20.8810 | − | 1.92125i | 0.948155 | − | 0.0872396i | ||||
\(486\) | 7.53307i | 0.341707i | ||||||||
\(487\) | −25.4502 | + | 25.4502i | −1.15326 | + | 1.15326i | −0.167363 | + | 0.985895i | \(0.553525\pi\) |
−0.985895 | + | 0.167363i | \(0.946475\pi\) | |||||||
\(488\) | 3.25923 | − | 3.25923i | 0.147538 | − | 0.147538i | ||||
\(489\) | −3.83644 | −0.173490 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2823 | −0.689680 | −0.344840 | − | 0.938661i | \(-0.612067\pi\) | ||||
−0.344840 | + | 0.938661i | \(0.612067\pi\) | |||||||
\(492\) | 1.47725 | − | 1.47725i | 0.0665996 | − | 0.0665996i | ||||
\(493\) | 11.8434 | − | 11.8434i | 0.533401 | − | 0.533401i | ||||
\(494\) | 7.86840i | 0.354016i | ||||||||
\(495\) | 28.2061 | + | 23.4529i | 1.26777 | + | 1.05413i | ||||
\(496\) | 3.84846i | 0.172801i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.64362 | + | 1.64362i | 0.0736525 | + | 0.0736525i | ||||
\(499\) | − | 31.5850i | − | 1.41394i | −0.707245 | − | 0.706969i | \(-0.750062\pi\) | ||
0.707245 | − | 0.706969i | \(-0.249938\pi\) | |||||||
\(500\) | −5.45939 | + | 9.75680i | −0.244151 | + | 0.436337i | ||||
\(501\) | 1.92861 | 0.0861639 | ||||||||
\(502\) | −5.02010 | − | 5.02010i | −0.224058 | − | 0.224058i | ||||
\(503\) | −16.9777 | + | 16.9777i | −0.756997 | + | 0.756997i | −0.975775 | − | 0.218778i | \(-0.929793\pi\) |
0.218778 | + | 0.975775i | \(0.429793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.6803 | + | 23.0157i | 1.23176 | + | 1.02419i | ||||
\(506\) | −6.32291 | −0.281088 | ||||||||
\(507\) | 1.82592 | + | 1.82592i | 0.0810920 | + | 0.0810920i | ||||
\(508\) | −4.63487 | − | 4.63487i | −0.205639 | − | 0.205639i | ||||
\(509\) | 21.5141 | 0.953597 | 0.476799 | − | 0.879013i | \(-0.341797\pi\) | ||||
0.476799 | + | 0.879013i | \(0.341797\pi\) | |||||||
\(510\) | 0.315125 | + | 3.42491i | 0.0139540 | + | 0.151657i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.71706 | − | 4.71706i | −0.208263 | − | 0.208263i | ||||
\(514\) | 9.88686 | 0.436091 | ||||||||
\(515\) | −4.02979 | − | 43.7974i | −0.177574 | − | 1.92994i | ||||
\(516\) | − | 0.760780i | − | 0.0334915i | ||||||
\(517\) | 23.4529 | + | 23.4529i | 1.03146 | + | 1.03146i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.04397i | 0.0897205i | ||||||||
\(520\) | −2.89039 | + | 3.47617i | −0.126752 | + | 0.152440i | ||||
\(521\) | 13.2395i | 0.580031i | 0.957022 | + | 0.290016i | \(0.0936605\pi\) | ||||
−0.957022 | + | 0.290016i | \(0.906340\pi\) | |||||||
\(522\) | −6.50552 | + | 6.50552i | −0.284739 | + | 0.284739i | ||||
\(523\) | −19.0426 | + | 19.0426i | −0.832673 | + | 0.832673i | −0.987882 | − | 0.155209i | \(-0.950395\pi\) |
0.155209 | + | 0.987882i | \(0.450395\pi\) | |||||||
\(524\) | 7.69535 | 0.336173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.7482 | 0.599448 | ||||||||
\(527\) | −14.4465 | + | 14.4465i | −0.629300 | + | 0.629300i | ||||
\(528\) | −1.15258 | + | 1.15258i | −0.0501595 | + | 0.0501595i | ||||
\(529\) | − | 21.7368i | − | 0.945078i | ||||||
\(530\) | −1.97733 | + | 2.37808i | −0.0858899 | + | 0.103297i | ||||
\(531\) | 15.9755i | 0.693276i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3083 | + | 10.3083i | 0.446501 | + | 0.446501i | ||||
\(534\) | 3.45419i | 0.149477i | ||||||||
\(535\) | −0.573857 | − | 6.23691i | −0.0248100 | − | 0.269645i | ||||
\(536\) | −0.844985 | −0.0364978 | ||||||||
\(537\) | −0.452025 | − | 0.452025i | −0.0195063 | − | 0.0195063i | ||||
\(538\) | −18.7398 | + | 18.7398i | −0.807928 | + | 0.807928i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.351176 | − | 3.81672i | −0.0151122 | − | 0.164245i | ||||
\(541\) | −11.3298 | −0.487107 | −0.243553 | − | 0.969888i | \(-0.578313\pi\) | ||||
−0.243553 | + | 0.969888i | \(0.578313\pi\) | |||||||
\(542\) | 9.04876 | + | 9.04876i | 0.388678 | + | 0.388678i | ||||
\(543\) | −0.843813 | − | 0.843813i | −0.0362115 | − | 0.0362115i | ||||
\(544\) | 5.30873 | 0.227610 | ||||||||
\(545\) | 10.1629 | + | 8.45027i | 0.435329 | + | 0.361970i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.9149 | + | 30.9149i | −1.32182 | + | 1.32182i | −0.409527 | + | 0.912298i | \(0.634306\pi\) |
−0.912298 | + | 0.409527i | \(0.865694\pi\) | |||||||
\(548\) | 6.24784 | + | 6.24784i | 0.266895 | + | 0.266895i | ||||
\(549\) | −13.4408 | −0.573639 | ||||||||
\(550\) | −23.1856 | − | 15.9267i | −0.988636 | − | 0.679116i | ||||
\(551\) | − | 12.2787i | − | 0.523090i | ||||||
\(552\) | 0.230263 | + | 0.230263i | 0.00980065 | + | 0.00980065i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 20.1034i | − | 0.854110i | ||||||
\(555\) | 2.51072 | + | 2.08763i | 0.106574 | + | 0.0886148i | ||||
\(556\) | 11.0631i | 0.469180i | ||||||||
\(557\) | −18.6675 | + | 18.6675i | −0.790967 | + | 0.790967i | −0.981651 | − | 0.190685i | \(-0.938929\pi\) |
0.190685 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(558\) | 7.93538 | − | 7.93538i | 0.335931 | − | 0.335931i | ||||
\(559\) | 5.30873 | 0.224535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.65318 | −0.365337 | ||||||||
\(562\) | −10.0054 | + | 10.0054i | −0.422054 | + | 0.422054i | ||||
\(563\) | −14.2790 | + | 14.2790i | −0.601788 | + | 0.601788i | −0.940787 | − | 0.338999i | \(-0.889912\pi\) |
0.338999 | + | 0.940787i | \(0.389912\pi\) | |||||||
\(564\) | − | 1.70818i | − | 0.0719275i | ||||||
\(565\) | −42.7687 | + | 3.93514i | −1.79929 | + | 0.165553i | ||||
\(566\) | − | 27.0677i | − | 1.13774i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.37792 | − | 3.37792i | −0.141734 | − | 0.141734i | ||||
\(569\) | 24.8134i | 1.04023i | 0.854096 | + | 0.520116i | \(0.174111\pi\) | ||||
−0.854096 | + | 0.520116i | \(0.825889\pi\) | |||||||
\(570\) | 1.93874 | + | 1.61204i | 0.0812051 | + | 0.0675208i | ||||
\(571\) | 4.58059 | 0.191692 | 0.0958458 | − | 0.995396i | \(-0.469444\pi\) | ||||
0.0958458 | + | 0.995396i | \(0.469444\pi\) | |||||||
\(572\) | −8.04270 | − | 8.04270i | −0.336282 | − | 0.336282i | ||||
\(573\) | −3.52433 | + | 3.52433i | −0.147231 | + | 0.147231i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.18185 | + | 4.63204i | −0.132692 | + | 0.193169i | ||||
\(576\) | −2.91605 | −0.121502 | ||||||||
\(577\) | −13.9869 | − | 13.9869i | −0.582284 | − | 0.582284i | 0.353247 | − | 0.935530i | \(-0.385078\pi\) |
−0.935530 | + | 0.353247i | \(0.885078\pi\) | |||||||
\(578\) | 7.90730 | + | 7.90730i | 0.328900 | + | 0.328900i | ||||
\(579\) | −3.49637 | −0.145304 | ||||||||
\(580\) | 4.51047 | − | 5.42460i | 0.187287 | − | 0.225244i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.92125 | − | 1.92125i | 0.0796385 | − | 0.0796385i | ||||
\(583\) | −5.50207 | − | 5.50207i | −0.227872 | − | 0.227872i | ||||
\(584\) | 5.61227 | 0.232237 | ||||||||
\(585\) | 13.1276 | − | 1.20787i | 0.542759 | − | 0.0499392i | ||||
\(586\) | 24.2100i | 1.00011i | ||||||||
\(587\) | −19.3782 | − | 19.3782i | −0.799824 | − | 0.799824i | 0.183244 | − | 0.983068i | \(-0.441340\pi\) |
−0.983068 | + | 0.183244i | \(0.941340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.9775i | 0.617136i | ||||||||
\(590\) | −1.12240 | − | 12.1987i | −0.0462084 | − | 0.502211i | ||||
\(591\) | − | 5.86495i | − | 0.241252i | ||||||
\(592\) | 3.56380 | − | 3.56380i | 0.146471 | − | 0.146471i | ||||
\(593\) | 2.28943 | − | 2.28943i | 0.0940155 | − | 0.0940155i | −0.658535 | − | 0.752550i | \(-0.728823\pi\) |
0.752550 | + | 0.658535i | \(0.228823\pi\) | |||||||
\(594\) | 9.64311 | 0.395661 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.04885 | −0.206809 | ||||||||
\(597\) | −1.54334 | + | 1.54334i | −0.0631645 | + | 0.0631645i | ||||
\(598\) | −1.60678 | + | 1.60678i | −0.0657061 | + | 0.0657061i | ||||
\(599\) | − | 7.80349i | − | 0.318842i | −0.987211 | − | 0.159421i | \(-0.949037\pi\) | ||
0.987211 | − | 0.159421i | \(-0.0509627\pi\) | |||||||
\(600\) | 0.264349 | + | 1.42436i | 0.0107920 | + | 0.0581493i | ||||
\(601\) | − | 31.7170i | − | 1.29377i | −0.762590 | − | 0.646883i | \(-0.776072\pi\) | ||
0.762590 | − | 0.646883i | \(-0.223928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.74233 | + | 1.74233i | 0.0709530 | + | 0.0709530i | ||||
\(604\) | − | 13.4428i | − | 0.546981i | ||||||
\(605\) | 29.5205 | − | 35.5033i | 1.20018 | − | 1.44341i | ||||
\(606\) | 4.66453 | 0.189484 | ||||||||
\(607\) | −0.544276 | − | 0.544276i | −0.0220915 | − | 0.0220915i | 0.695975 | − | 0.718066i | \(-0.254973\pi\) |
−0.718066 | + | 0.695975i | \(0.754973\pi\) | |||||||
\(608\) | 2.75192 | − | 2.75192i | 0.111605 | − | 0.111605i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2632 | − | 0.944318i | 0.415546 | − | 0.0382343i | ||||
\(611\) | 11.9197 | 0.482221 | ||||||||
\(612\) | −10.9464 | − | 10.9464i | −0.442482 | − | 0.442482i | ||||
\(613\) | 24.7496 | + | 24.7496i | 0.999626 | + | 0.999626i | 1.00000 | 0.000373538i | \(-0.000118901\pi\) | |
−0.000373538 | 1.00000i | \(0.500119\pi\) | ||||||||
\(614\) | −24.4623 | −0.987217 | ||||||||
\(615\) | 4.65183 | − | 0.428014i | 0.187580 | − | 0.0172592i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5403 | − | 21.5403i | 0.867179 | − | 0.867179i | −0.124980 | − | 0.992159i | \(-0.539887\pi\) |
0.992159 | + | 0.124980i | \(0.0398866\pi\) | |||||||
\(618\) | −4.02979 | − | 4.02979i | −0.162102 | − | 0.162102i | ||||
\(619\) | −43.3415 | −1.74204 | −0.871021 | − | 0.491247i | \(-0.836541\pi\) | ||||
−0.871021 | + | 0.491247i | \(0.836541\pi\) | |||||||
\(620\) | −5.50184 | + | 6.61688i | −0.220959 | + | 0.265740i | ||||
\(621\) | − | 1.92651i | − | 0.0773082i | ||||||
\(622\) | −7.76566 | − | 7.76566i | −0.311374 | − | 0.311374i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.585786i | 0.0234502i | ||||||||
\(625\) | −23.3351 | + | 8.97056i | −0.933406 | + | 0.358823i | ||||
\(626\) | − | 29.4110i | − | 1.17550i | ||||||
\(627\) | −4.48560 | + | 4.48560i | −0.179138 | + | 0.179138i | ||||
\(628\) | −0.779844 | + | 0.779844i | −0.0311192 | + | 0.0311192i | ||||
\(629\) | 26.7559 | 1.06683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.53463 | 0.299949 | 0.149974 | − | 0.988690i | \(-0.452081\pi\) | ||||
0.149974 | + | 0.988690i | \(0.452081\pi\) | |||||||
\(632\) | 4.41789 | − | 4.41789i | 0.175734 | − | 0.175734i | ||||
\(633\) | 4.01075 | − | 4.01075i | 0.159413 | − | 0.159413i | ||||
\(634\) | − | 4.29397i | − | 0.170535i | ||||||
\(635\) | −1.34289 | − | 14.5951i | −0.0532910 | − | 0.579188i | ||||
\(636\) | 0.400741i | 0.0158904i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.5507 | + | 12.5507i | 0.496887 | + | 0.496887i | ||||
\(639\) | 13.9303i | 0.551073i | ||||||||
\(640\) | 2.22666 | − | 0.204875i | 0.0880166 | − | 0.00809839i | ||||
\(641\) | 24.3315 | 0.961035 | 0.480518 | − | 0.876985i | \(-0.340449\pi\) | ||||
0.480518 | + | 0.876985i | \(0.340449\pi\) | |||||||
\(642\) | −0.573857 | − | 0.573857i | −0.0226483 | − | 0.0226483i | ||||
\(643\) | 6.21713 | − | 6.21713i | 0.245180 | − | 0.245180i | −0.573809 | − | 0.818989i | \(-0.694535\pi\) |
0.818989 | + | 0.573809i | \(0.194535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.08763 | − | 1.30805i | 0.0428252 | − | 0.0515045i | ||||
\(646\) | 20.6605 | 0.812878 | ||||||||
\(647\) | 14.5856 | + | 14.5856i | 0.573418 | + | 0.573418i | 0.933082 | − | 0.359664i | \(-0.117109\pi\) |
−0.359664 | + | 0.933082i | \(0.617109\pi\) | |||||||
\(648\) | 5.83471 | + | 5.83471i | 0.229209 | + | 0.229209i | ||||
\(649\) | 30.8205 | 1.20981 | ||||||||
\(650\) | −9.93921 | + | 1.84463i | −0.389848 | + | 0.0723523i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.36288 | + | 9.36288i | −0.366679 | + | 0.366679i | ||||
\(653\) | 18.4835 | + | 18.4835i | 0.723316 | + | 0.723316i | 0.969279 | − | 0.245963i | \(-0.0791041\pi\) |
−0.245963 | + | 0.969279i | \(0.579104\pi\) | |||||||
\(654\) | 1.71259 | 0.0669676 | ||||||||
\(655\) | 13.2311 | + | 11.0014i | 0.516980 | + | 0.429861i | ||||
\(656\) | − | 7.21050i | − | 0.281523i | ||||||
\(657\) | −11.5723 | − | 11.5723i | −0.451478 | − | 0.451478i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.2448i | − | 0.944443i | −0.881480 | − | 0.472222i | \(-0.843452\pi\) | ||
0.881480 | − | 0.472222i | \(-0.156548\pi\) | |||||||
\(660\) | −3.62944 | + | 0.333944i | −0.141276 | + | 0.0129988i | ||||
\(661\) | 17.9326i | 0.697497i | 0.937216 | + | 0.348749i | \(0.113393\pi\) | ||||
−0.937216 | + | 0.348749i | \(0.886607\pi\) | |||||||
\(662\) | 25.0668 | − | 25.0668i | 0.974250 | − | 0.974250i | ||||
\(663\) | −2.19895 | + | 2.19895i | −0.0854001 | + | 0.0854001i | ||||
\(664\) | 8.02257 | 0.311336 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.6968 | −0.569491 | ||||||||
\(667\) | 2.50739 | − | 2.50739i | 0.0970866 | − | 0.0970866i | ||||
\(668\) | 4.70680 | − | 4.70680i | 0.182112 | − | 0.182112i | ||||
\(669\) | 0.598344i | 0.0231333i | ||||||||
\(670\) | −1.45283 | − | 1.20801i | −0.0561277 | − | 0.0466694i | ||||
\(671\) | 25.9305i | 1.00104i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.85386 | − | 4.85386i | −0.187103 | − | 0.187103i | 0.607340 | − | 0.794442i | \(-0.292237\pi\) |
−0.794442 | + | 0.607340i | \(0.792237\pi\) | |||||||
\(674\) | 17.1789i | 0.661708i | ||||||||
\(675\) | 4.85266 | − | 7.06435i | 0.186779 | − | 0.271907i | ||||
\(676\) | 8.91237 | 0.342784 | ||||||||
\(677\) | 13.0676 | + | 13.0676i | 0.502227 | + | 0.502227i | 0.912129 | − | 0.409902i | \(-0.134437\pi\) |
−0.409902 | + | 0.912129i | \(0.634437\pi\) | |||||||
\(678\) | −3.93514 | + | 3.93514i | −0.151128 | + | 0.151128i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.12760 | + | 7.58946i | 0.350027 | + | 0.291043i | ||||
\(681\) | −5.40166 | −0.206992 | ||||||||
\(682\) | −15.3092 | − | 15.3092i | −0.586221 | − | 0.586221i | ||||
\(683\) | −18.9512 | − | 18.9512i | −0.725147 | − | 0.725147i | 0.244502 | − | 0.969649i | \(-0.421375\pi\) |
−0.969649 | + | 0.244502i | \(0.921375\pi\) | |||||||
\(684\) | −11.3487 | −0.433929 | ||||||||
\(685\) | 1.81023 | + | 19.6743i | 0.0691653 | + | 0.751717i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.821071 | + | 0.821071i | −0.0313258 | + | 0.0313258i | ||||
\(688\) | −1.85669 | − | 1.85669i | −0.0707857 | − | 0.0707857i | ||||
\(689\) | −2.79637 | −0.106533 | ||||||||
\(690\) | 0.0667157 | + | 0.725093i | 0.00253983 | + | 0.0276038i | ||||
\(691\) | − | 29.0722i | − | 1.10596i | −0.833194 | − | 0.552980i | \(-0.813491\pi\) | ||
0.833194 | − | 0.552980i | \(-0.186509\pi\) | |||||||
\(692\) | 4.98835 | + | 4.98835i | 0.189628 | + | 0.189628i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 8.97626i | − | 0.340734i | ||||||
\(695\) | −15.8160 | + | 19.0214i | −0.599937 | + | 0.721524i | ||||
\(696\) | − | 0.914124i | − | 0.0346498i | ||||||
\(697\) | 27.0671 | − | 27.0671i | 1.02524 | − | 1.02524i | ||||
\(698\) | 18.4025 | − | 18.4025i | 0.696546 | − | 0.696546i | ||||
\(699\) | −3.97855 | −0.150483 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4462 | 0.961089 | 0.480545 | − | 0.876970i | \(-0.340439\pi\) | ||||
0.480545 | + | 0.876970i | \(0.340439\pi\) | |||||||
\(702\) | 2.45051 | − | 2.45051i | 0.0924885 | − | 0.0924885i | ||||
\(703\) | 13.8696 | − | 13.8696i | 0.523102 | − | 0.523102i | ||||
\(704\) | 5.62576i | 0.212029i | ||||||||
\(705\) | 2.44205 | − | 2.93698i | 0.0919731 | − | 0.110613i | ||||
\(706\) | 9.96618i | 0.375082i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.12240 | − | 1.12240i | −0.0421823 | − | 0.0421823i | ||||
\(709\) | − | 31.4072i | − | 1.17952i | −0.807578 | − | 0.589760i | \(-0.799222\pi\) | ||
0.807578 | − | 0.589760i | \(-0.200778\pi\) | |||||||
\(710\) | −0.978707 | − | 10.6370i | −0.0367302 | − | 0.399199i | ||||
\(711\) | −18.2190 | −0.683267 | ||||||||
\(712\) | 8.42999 | + | 8.42999i | 0.315927 | + | 0.315927i | ||||
\(713\) | −3.05850 | + | 3.05850i | −0.114542 | + | 0.114542i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.33027 | − | 25.3263i | −0.0871470 | − | 0.947149i | ||||
\(716\) | −2.20635 | −0.0824550 | ||||||||
\(717\) | −4.02826 | − | 4.02826i | −0.150438 | − | 0.150438i | ||||
\(718\) | 8.18413 | + | 8.18413i | 0.305429 | + | 0.305429i | ||||
\(719\) | −10.8043 | −0.402932 | −0.201466 | − | 0.979496i | \(-0.564570\pi\) | ||||
−0.201466 | + | 0.979496i | \(0.564570\pi\) | |||||||
\(720\) | −5.01373 | − | 4.16885i | −0.186851 | − | 0.155364i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.72509 | + | 2.72509i | −0.101417 | + | 0.101417i | ||||
\(723\) | −1.20571 | − | 1.20571i | −0.0448410 | − | 0.0448410i | ||||
\(724\) | −4.11867 | −0.153069 | ||||||||
\(725\) | 15.5102 | − | 2.87856i | 0.576035 | − | 0.106907i | ||||
\(726\) | − | 5.98283i | − | 0.222044i | ||||||
\(727\) | −33.6108 | − | 33.6108i | −1.24656 | − | 1.24656i | −0.957231 | − | 0.289326i | \(-0.906569\pi\) |
−0.289326 | − | 0.957231i | \(-0.593431\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 22.5720i | − | 0.835998i | ||||||
\(730\) | 9.64950 | + | 8.02342i | 0.357144 | + | 0.296960i | ||||
\(731\) | − | 13.9394i | − | 0.515569i | ||||||
\(732\) | 0.944318 | − | 0.944318i | 0.0349030 | − | 0.0349030i | ||||
\(733\) | 18.2134 | − | 18.2134i | 0.672729 | − | 0.672729i | −0.285616 | − | 0.958344i | \(-0.592198\pi\) |
0.958344 | + | 0.285616i | \(0.0921981\pi\) | |||||||
\(734\) | 16.6944 | 0.616202 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.12392 | 0.0414283 | ||||||||
\(737\) | 3.36136 | − | 3.36136i | 0.123817 | − | 0.123817i | ||||
\(738\) | −14.8678 | + | 14.8678i | −0.547290 | + | 0.547290i | ||||
\(739\) | − | 12.1184i | − | 0.445782i | −0.974843 | − | 0.222891i | \(-0.928451\pi\) | ||
0.974843 | − | 0.222891i | \(-0.0715495\pi\) | |||||||
\(740\) | 11.2223 | − | 1.03256i | 0.412541 | − | 0.0379578i | ||||
\(741\) | 2.27977i | 0.0837493i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.2618 | + | 23.2618i | 0.853393 | + | 0.853393i | 0.990549 | − | 0.137157i | \(-0.0437964\pi\) |
−0.137157 | + | 0.990549i | \(0.543796\pi\) | |||||||
\(744\) | 1.11504i | 0.0408794i | ||||||||
\(745\) | −8.68078 | − | 7.21794i | −0.318039 | − | 0.264445i | ||||
\(746\) | 3.17893 | 0.116389 | ||||||||
\(747\) | −16.5422 | − | 16.5422i | −0.605248 | − | 0.605248i | ||||
\(748\) | −21.1182 | + | 21.1182i | −0.772158 | + | 0.772158i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.58179 | + | 2.82690i | −0.0577587 | + | 0.103224i | ||||
\(751\) | 13.9777 | 0.510055 | 0.255028 | − | 0.966934i | \(-0.417915\pi\) | ||||
0.255028 | + | 0.966934i | \(0.417915\pi\) | |||||||
\(752\) | −4.16885 | − | 4.16885i | −0.152022 | − | 0.152022i | ||||
\(753\) | −1.45451 | − | 1.45451i | −0.0530053 | − | 0.0530053i | ||||
\(754\) | 6.37877 | 0.232301 | ||||||||
\(755\) | 19.2181 | − | 23.1130i | 0.699420 | − | 0.841169i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5547 | − | 17.5547i | 0.638036 | − | 0.638036i | −0.312035 | − | 0.950071i | \(-0.601010\pi\) |
0.950071 | + | 0.312035i | \(0.101010\pi\) | |||||||
\(758\) | −5.05828 | − | 5.05828i | −0.183725 | − | 0.183725i | ||||
\(759\) | −1.83198 | −0.0664967 | ||||||||
\(760\) | 8.66573 | − | 0.797333i | 0.314339 | − | 0.0289223i | ||||
\(761\) | − | 21.8667i | − | 0.792669i | −0.918106 | − | 0.396334i | \(-0.870282\pi\) | ||
0.918106 | − | 0.396334i | \(-0.129718\pi\) | |||||||
\(762\) | −1.34289 | − | 1.34289i | −0.0486478 | − | 0.0486478i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.2023i | 0.622359i | ||||||||
\(765\) | −3.17157 | − | 34.4699i | −0.114668 | − | 1.24626i | ||||
\(766\) | 14.5934i | 0.527280i | ||||||||
\(767\) | 7.83211 | − | 7.83211i | 0.282801 | − | 0.282801i | ||||
\(768\) | 0.204875 | − | 0.204875i | 0.00739279 | − | 0.00739279i | ||||
\(769\) | −31.0506 | −1.11971 | −0.559857 | − | 0.828589i | \(-0.689144\pi\) | ||||
−0.559857 | + | 0.828589i | \(0.689144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.86459 | 0.103166 | ||||||||
\(772\) | −8.53293 | + | 8.53293i | −0.307107 | + | 0.307107i | ||||
\(773\) | 4.29108 | − | 4.29108i | 0.154340 | − | 0.154340i | −0.625713 | − | 0.780053i | \(-0.715192\pi\) |
0.780053 | + | 0.625713i | \(0.215192\pi\) | |||||||
\(774\) | 7.65685i | 0.275220i | ||||||||
\(775\) | −18.9192 | + | 3.51124i | −0.679599 | + | 0.126127i | ||||
\(776\) | − | 9.37769i | − | 0.336640i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.38160 | − | 4.38160i | −0.157088 | − | 0.157088i | ||||
\(779\) | − | 28.0619i | − | 1.00542i | ||||||
\(780\) | −0.837452 | + | 1.00718i | −0.0299856 | + | 0.0360627i | ||||
\(781\) | 26.8748 | 0.961656 | ||||||||
\(782\) | 4.21902 | + | 4.21902i | 0.150872 | + | 0.150872i | ||||
\(783\) | −3.82404 | + | 3.82404i | −0.136660 | + | 0.136660i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.45571 | + | 0.225950i | −0.0876481 | + | 0.00806449i | ||||
\(786\) | 2.22963 | 0.0795282 | ||||||||
\(787\) | −15.8118 | − | 15.8118i | −0.563630 | − | 0.563630i | 0.366707 | − | 0.930336i | \(-0.380485\pi\) |
−0.930336 | + | 0.366707i | \(0.880485\pi\) | |||||||
\(788\) | −14.3135 | − | 14.3135i | −0.509897 | − | 0.509897i | ||||
\(789\) | 3.98335 | 0.141811 | ||||||||
\(790\) | 13.9118 | − | 1.28003i | 0.494961 | − | 0.0455413i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.6001 | − | 11.6001i | 0.412191 | − | 0.412191i | ||||
\(793\) | 6.58946 | + | 6.58946i | 0.233999 | + | 0.233999i | ||||
\(794\) | −2.91588 | −0.103481 | ||||||||
\(795\) | −0.572907 | + | 0.689016i | −0.0203189 | + | 0.0244369i | ||||
\(796\) | 7.53307i | 0.267002i | ||||||||
\(797\) | −16.5528 | − | 16.5528i | −0.586330 | − | 0.586330i | 0.350305 | − | 0.936636i | \(-0.386078\pi\) |
−0.936636 | + | 0.350305i | \(0.886078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 31.2984i | − | 1.10726i | ||||||
\(800\) | 4.12132 | + | 2.83103i | 0.145711 | + | 0.100092i | ||||
\(801\) | − | 34.7646i | − | 1.22835i | ||||||
\(802\) | −14.1213 | + | 14.1213i | −0.498641 | + | 0.498641i | ||||
\(803\) | −22.3257 | + | 22.3257i | −0.787857 | + | 0.787857i | ||||
\(804\) | −0.244823 | −0.00863425 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.78078 | −0.274066 | ||||||||
\(807\) | −5.42960 | + | 5.42960i | −0.191131 | + | 0.191131i | ||||
\(808\) | 11.3839 | − | 11.3839i | 0.400483 | − | 0.400483i | ||||
\(809\) | − | 3.28096i | − | 0.115352i | −0.998335 | − | 0.0576762i | \(-0.981631\pi\) | ||
0.998335 | − | 0.0576762i | \(-0.0183691\pi\) | |||||||
\(810\) | 1.69053 | + | 18.3734i | 0.0593991 | + | 0.645574i | ||||
\(811\) | 17.8693i | 0.627476i | 0.949510 | + | 0.313738i | \(0.101581\pi\) | ||||
−0.949510 | + | 0.313738i | \(0.898419\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.62176 | + | 2.62176i | 0.0919491 | + | 0.0919491i | ||||
\(814\) | 28.3537i | 0.993796i | ||||||||
\(815\) | −29.4835 | + | 2.71277i | −1.03276 | + | 0.0950243i | ||||
\(816\) | 1.53813 | 0.0538455 | ||||||||
\(817\) | −7.22588 | − | 7.22588i | −0.252802 | − | 0.252802i | ||||
\(818\) | 24.2949 | − | 24.2949i | 0.849451 | − | 0.849451i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.3083 | − | 12.3974i | 0.359981 | − | 0.432937i | ||||
\(821\) | −11.8167 | −0.412407 | −0.206204 | − | 0.978509i | \(-0.566111\pi\) | ||||
−0.206204 | + | 0.978509i | \(0.566111\pi\) | |||||||
\(822\) | 1.81023 | + | 1.81023i | 0.0631390 | + | 0.0631390i | ||||
\(823\) | 24.9625 | + | 24.9625i | 0.870139 | + | 0.870139i | 0.992487 | − | 0.122348i | \(-0.0390424\pi\) |
−0.122348 | + | 0.992487i | \(0.539042\pi\) | |||||||
\(824\) | −19.6695 | −0.685220 | ||||||||
\(825\) | −6.71771 | − | 4.61455i | −0.233881 | − | 0.160658i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.2835 | + | 17.2835i | −0.601005 | + | 0.601005i | −0.940579 | − | 0.339574i | \(-0.889717\pi\) |
0.339574 | + | 0.940579i | \(0.389717\pi\) | |||||||
\(828\) | −2.31748 | − | 2.31748i | −0.0805380 | − | 0.0805380i | ||||
\(829\) | 34.5754 | 1.20085 | 0.600426 | − | 0.799680i | \(-0.294998\pi\) | ||||
0.600426 | + | 0.799680i | \(0.294998\pi\) | |||||||
\(830\) | 13.7937 | + | 11.4692i | 0.478785 | + | 0.398102i | ||||
\(831\) | − | 5.82469i | − | 0.202056i | ||||||
\(832\) | 1.42962 | + | 1.42962i | 0.0495631 | + | 0.0495631i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.20539i | 0.110994i | ||||||||
\(835\) | 14.8216 | − | 1.36373i | 0.512923 | − | 0.0471939i | ||||
\(836\) | 21.8944i | 0.757232i | ||||||||
\(837\) | 4.66453 | − | 4.66453i | 0.161230 | − | 0.161230i | ||||
\(838\) | 22.0165 | − | 22.0165i | 0.760547 | − | 0.760547i | ||||
\(839\) | 50.1328 | 1.73078 | 0.865388 | − | 0.501102i | \(-0.167072\pi\) | ||||
0.865388 | + | 0.501102i | \(0.167072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0459 | 0.656754 | ||||||||
\(842\) | −23.8102 | + | 23.8102i | −0.820555 | + | 0.820555i | ||||
\(843\) | −2.89894 | + | 2.89894i | −0.0998449 | + | 0.0998449i | ||||
\(844\) | − | 19.5766i | − | 0.673854i | ||||||
\(845\) | 15.3236 | + | 12.7413i | 0.527146 | + | 0.438314i | ||||
\(846\) | 17.1920i | 0.591073i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.978013 | + | 0.978013i | 0.0335851 | + | 0.0335851i | ||||
\(849\) | − | 7.84251i | − | 0.269154i | ||||||
\(850\) | 4.84355 | + | 26.0980i | 0.166132 | + | 0.895154i | ||||
\(851\) | 5.66453 | 0.194178 | ||||||||
\(852\) | −0.978707 | − | 0.978707i | −0.0335300 | − | 0.0335300i | ||||
\(853\) | 2.37500 | − | 2.37500i | 0.0813183 | − | 0.0813183i | −0.665278 | − | 0.746596i | \(-0.731687\pi\) |
0.746596 | + | 0.665278i | \(0.231687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.5125 | − | 16.2243i | −0.667312 | − | 0.554860i | ||||
\(856\) | −2.80101 | −0.0957366 | ||||||||
\(857\) | −29.6551 | − | 29.6551i | −1.01300 | − | 1.01300i | −0.999914 | − | 0.0130861i | \(-0.995834\pi\) |
−0.0130861 | − | 0.999914i | \(-0.504166\pi\) | |||||||
\(858\) | −2.33027 | − | 2.33027i | −0.0795540 | − | 0.0795540i | ||||
\(859\) | −2.35695 | −0.0804179 | −0.0402090 | − | 0.999191i | \(-0.512802\pi\) | ||||
−0.0402090 | + | 0.999191i | \(0.512802\pi\) | |||||||
\(860\) | −0.537952 | − | 5.84668i | −0.0183440 | − | 0.199370i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.4268 | + | 10.4268i | −0.355137 | + | 0.355137i | ||||
\(863\) | 34.1884 | + | 34.1884i | 1.16379 | + | 1.16379i | 0.983640 | + | 0.180146i | \(0.0576572\pi\) |
0.180146 | + | 0.983640i | \(0.442343\pi\) | |||||||
\(864\) | −1.71410 | −0.0583148 | ||||||||
\(865\) | 1.44531 | + | 15.7082i | 0.0491419 | + | 0.534094i | ||||
\(866\) | − | 14.1175i | − | 0.479731i | ||||||
\(867\) | 2.29104 | + | 2.29104i | 0.0778076 | + | 0.0778076i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.1489i | 1.19234i | ||||||||
\(870\) | 1.30685 | − | 1.57171i | 0.0443064 | − | 0.0532858i | ||||
\(871\) | − | 1.70838i | − | 0.0578862i | ||||||
\(872\) | 4.17960 | − | 4.17960i | 0.141539 | − | 0.141539i | ||||
\(873\) | −19.3364 | + | 19.3364i | −0.654439 | + | 0.654439i | ||||
\(874\) | 4.37408 | 0.147955 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.62608 | 0.0549402 | ||||||||
\(877\) | −9.74471 | + | 9.74471i | −0.329055 | + | 0.329055i | −0.852227 | − | 0.523172i | \(-0.824749\pi\) |
0.523172 | + | 0.852227i | \(0.324749\pi\) | |||||||
\(878\) | 27.1730 | − | 27.1730i | 0.917046 | − | 0.917046i | ||||
\(879\) | 7.01454i | 0.236594i | ||||||||
\(880\) | −8.04270 | + | 9.67269i | −0.271119 | + | 0.326066i | ||||
\(881\) | 3.32542i | 0.112036i | 0.998430 | + | 0.0560181i | \(0.0178405\pi\) | ||||
−0.998430 | + | 0.0560181i | \(0.982160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.8930 | − | 36.8930i | −1.24155 | − | 1.24155i | −0.959358 | − | 0.282191i | \(-0.908939\pi\) |
−0.282191 | − | 0.959358i | \(-0.591061\pi\) | |||||||
\(884\) | 10.7331i | 0.360994i | ||||||||
\(885\) | −0.325200 | − | 3.53440i | −0.0109315 | − | 0.118808i | ||||
\(886\) | 5.73560 | 0.192691 | ||||||||
\(887\) | 25.3290 | + | 25.3290i | 0.850465 | + | 0.850465i | 0.990190 | − | 0.139725i | \(-0.0446218\pi\) |
−0.139725 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(888\) | 1.03256 | − | 1.03256i | 0.0346506 | − | 0.0346506i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.44248 | + | 26.5458i | 0.0818721 | + | 0.889819i | ||||
\(891\) | −46.4211 | −1.55516 | ||||||||
\(892\) | 1.46027 | + | 1.46027i | 0.0488933 | + | 0.0488933i | ||||
\(893\) | −16.2243 | − | 16.2243i | −0.542927 | − | 0.542927i | ||||
\(894\) | −1.46284 | −0.0489247 | ||||||||
\(895\) | −3.79349 | − | 3.15423i | −0.126803 | − | 0.105434i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.465543 | + | 0.465543i | −0.0155440 | + | 0.0155440i | ||||
\(898\) | −5.16377 | − | 5.16377i | −0.172317 | − | 0.172317i | ||||
\(899\) | 12.1420 | 0.404957 | ||||||||
\(900\) | −2.66053 | − | 14.3355i | −0.0886844 | − | 0.477849i | ||||
\(901\) | 7.34261i | 0.244618i | ||||||||
\(902\) | 28.6835 | + | 28.6835i | 0.955055 | + | 0.955055i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2075i | 0.638833i | ||||||||
\(905\) | −7.08147 | − | 5.88814i | −0.235396 | − | 0.195728i | ||||
\(906\) | − | 3.89488i | − | 0.129399i | ||||||
\(907\) | −12.2030 | + | 12.2030i | −0.405195 | + | 0.405195i | −0.880059 | − | 0.474864i | \(-0.842497\pi\) |
0.474864 | + | 0.880059i | \(0.342497\pi\) | |||||||
\(908\) | −13.1828 | + | 13.1828i | −0.437487 | + | 0.437487i | ||||
\(909\) | −46.9461 | −1.55710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.56820 | 0.184483 | 0.0922414 | − | 0.995737i | \(-0.470597\pi\) | ||||
0.0922414 | + | 0.995737i | \(0.470597\pi\) | |||||||
\(912\) | 0.797333 | − | 0.797333i | 0.0264023 | − | 0.0264023i | ||||
\(913\) | −31.9139 | + | 31.9139i | −1.05620 | + | 1.05620i | ||||
\(914\) | − | 5.14581i | − | 0.170208i | ||||||
\(915\) | 2.97364 | − | 0.273604i | 0.0983054 | − | 0.00904506i | ||||
\(916\) | 4.00767i | 0.132417i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.43445 | − | 6.43445i | −0.212368 | − | 0.212368i | ||||
\(919\) | 6.21187i | 0.204911i | 0.994738 | + | 0.102455i | \(0.0326699\pi\) | ||||
−0.994738 | + | 0.102455i | \(0.967330\pi\) | |||||||
\(920\) | 1.93242 | + | 1.60678i | 0.0637100 | + | 0.0529740i | ||||
\(921\) | −7.08763 | −0.233545 | ||||||||
\(922\) | −20.7967 | − | 20.7967i | −0.684903 | − | 0.684903i | ||||
\(923\) | 6.82943 | − | 6.82943i | 0.224794 | − | 0.224794i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.7713 | + | 14.2683i | 0.682958 | + | 0.469139i | ||||
\(926\) | −5.72226 | −0.188045 | ||||||||
\(927\) | 40.5578 | + | 40.5578i | 1.33209 | + | 1.33209i | ||||
\(928\) | −2.23093 | − | 2.23093i | −0.0732340 | − | 0.0732340i | ||||
\(929\) | 0.189459 | 0.00621596 | 0.00310798 | − | 0.999995i | \(-0.499011\pi\) | ||||
0.00310798 | + | 0.999995i | \(0.499011\pi\) | |||||||
\(930\) | −1.59409 | + | 1.91715i | −0.0522721 | + | 0.0628660i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.70971 | + | 9.70971i | −0.318052 | + | 0.318052i | ||||
\(933\) | −2.25000 | − | 2.25000i | −0.0736616 | − | 0.0736616i | ||||
\(934\) | −16.6428 | −0.544568 | ||||||||
\(935\) | −66.5007 | + | 6.11872i | −2.17481 | + | 0.200104i | ||||
\(936\) | − | 5.89564i | − | 0.192705i | ||||||
\(937\) | 34.2022 | + | 34.2022i | 1.11734 | + | 1.11734i | 0.992131 | + | 0.125208i | \(0.0399598\pi\) |
0.125208 | + | 0.992131i | \(0.460040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8.52144i | − | 0.278087i | ||||||
\(940\) | −1.20787 | − | 13.1276i | −0.0393963 | − | 0.428175i | ||||
\(941\) | − | 18.9170i | − | 0.616677i | −0.951277 | − | 0.308339i | \(-0.900227\pi\) | ||
0.951277 | − | 0.308339i | \(-0.0997730\pi\) | |||||||
\(942\) | −0.225950 | + | 0.225950i | −0.00736184 | + | 0.00736184i | ||||
\(943\) | 5.73042 | − | 5.73042i | 0.186608 | − | 0.186608i | ||||
\(944\) | −5.47845 | −0.178308 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7719 | 0.480276 | ||||||||
\(947\) | 33.3401 | − | 33.3401i | 1.08341 | − | 1.08341i | 0.0872195 | − | 0.996189i | \(-0.472202\pi\) |
0.996189 | − | 0.0872195i | \(-0.0277981\pi\) | |||||||
\(948\) | 1.28003 | − | 1.28003i | 0.0415733 | − | 0.0415733i | ||||
\(949\) | 11.3468i | 0.368333i | ||||||||
\(950\) | 16.0394 | + | 11.0178i | 0.520386 | + | 0.357465i | ||||
\(951\) | − | 1.24412i | − | 0.0403434i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.8431 | + | 18.8431i | 0.610389 | + | 0.610389i | 0.943047 | − | 0.332658i | \(-0.107946\pi\) |
−0.332658 | + | 0.943047i | \(0.607946\pi\) | |||||||
\(954\) | − | 4.03325i | − | 0.130581i | ||||||
\(955\) | −24.5928 | + | 29.5770i | −0.795805 | + | 0.957088i | ||||
\(956\) | −19.6621 | −0.635916 | ||||||||
\(957\) | 3.63640 | + | 3.63640i | 0.117548 | + | 0.117548i | ||||
\(958\) | 10.8818 | − | 10.8818i | 0.351575 | − | 0.351575i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.645146 | − | 0.0593598i | 0.0208220 | − | 0.00191583i | ||||
\(961\) | 16.1893 | 0.522237 | ||||||||
\(962\) | 7.20525 | + | 7.20525i | 0.232306 | + | 0.232306i | ||||
\(963\) | 5.77557 | + | 5.77557i | 0.186115 | + | 0.186115i | ||||
\(964\) | −5.88512 | −0.189547 | ||||||||
\(965\) | −26.8700 | + | 2.47231i | −0.864976 | + | 0.0795863i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.3703 | − | 27.3703i | 0.880169 | − | 0.880169i | −0.113383 | − | 0.993551i | \(-0.536169\pi\) |
0.993551 | + | 0.113383i | \(0.0361687\pi\) | |||||||
\(968\) | −14.6012 | − | 14.6012i | −0.469299 | − | 0.469299i | ||||
\(969\) | 5.98612 | 0.192302 | ||||||||
\(970\) | 13.4065 | − | 16.1236i | 0.430458 | − | 0.517698i | ||||
\(971\) | 32.1872i | 1.03294i | 0.856306 | + | 0.516469i | \(0.172754\pi\) | ||||
−0.856306 | + | 0.516469i | \(0.827246\pi\) | |||||||
\(972\) | 5.32668 | + | 5.32668i | 0.170853 | + | 0.170853i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35.9920i | 1.15326i | ||||||||
\(975\) | −2.87976 | + | 0.534457i | −0.0922260 | + | 0.0171163i | ||||
\(976\) | − | 4.60924i | − | 0.147538i | ||||||
\(977\) | −16.4600 | + | 16.4600i | −0.526603 | + | 0.526603i | −0.919558 | − | 0.392955i | \(-0.871453\pi\) |
0.392955 | + | 0.919558i | \(0.371453\pi\) | |||||||
\(978\) | −2.71277 | + | 2.71277i | −0.0867449 | + | 0.0867449i | ||||
\(979\) | −67.0692 | −2.14354 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.2364 | −0.550314 | ||||||||
\(982\) | −10.8062 | + | 10.8062i | −0.344840 | + | 0.344840i | ||||
\(983\) | −40.3334 | + | 40.3334i | −1.28644 | + | 1.28644i | −0.349499 | + | 0.936937i | \(0.613648\pi\) |
−0.936937 | + | 0.349499i | \(0.886352\pi\) | |||||||
\(984\) | − | 2.08915i | − | 0.0665996i | ||||||
\(985\) | −4.14714 | − | 45.0728i | −0.132139 | − | 1.43614i | ||||
\(986\) | − | 16.7491i | − | 0.533401i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.56380 | + | 5.56380i | 0.177008 | + | 0.177008i | ||||
\(989\) | − | 2.95115i | − | 0.0938410i | ||||||
\(990\) | 36.5284 | − | 3.36098i | 1.16095 | − | 0.106819i | ||||
\(991\) | −57.5405 | −1.82784 | −0.913918 | − | 0.405900i | \(-0.866958\pi\) | ||||
−0.913918 | + | 0.405900i | \(0.866958\pi\) | |||||||
\(992\) | 2.72127 | + | 2.72127i | 0.0864005 | + | 0.0864005i | ||||
\(993\) | 7.26279 | − | 7.26279i | 0.230478 | − | 0.230478i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.7694 | + | 12.9520i | −0.341414 | + | 0.410607i | ||||
\(996\) | 2.32443 | 0.0736525 | ||||||||
\(997\) | 17.1508 | + | 17.1508i | 0.543171 | + | 0.543171i | 0.924457 | − | 0.381286i | \(-0.124519\pi\) |
−0.381286 | + | 0.924457i | \(0.624519\pi\) | |||||||
\(998\) | −22.3339 | − | 22.3339i | −0.706969 | − | 0.706969i | ||||
\(999\) | −8.63901 | −0.273326 |
(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 | 490.2.g.c.293.7 | 16 | ||
5.2 | odd | 4 | inner | 490.2.g.c.97.6 | 16 | ||
7.2 | even | 3 | 490.2.l.c.423.2 | 16 | |||
7.3 | odd | 6 | 490.2.l.c.313.4 | 16 | |||
7.4 | even | 3 | 70.2.k.a.33.3 | yes | 16 | ||
7.5 | odd | 6 | 70.2.k.a.3.1 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 490.2.g.c.293.6 | 16 | ||
21.5 | even | 6 | 630.2.bv.c.73.3 | 16 | |||
21.11 | odd | 6 | 630.2.bv.c.523.1 | 16 | |||
28.11 | odd | 6 | 560.2.ci.c.33.3 | 16 | |||
28.19 | even | 6 | 560.2.ci.c.353.3 | 16 | |||
35.2 | odd | 12 | 490.2.l.c.227.4 | 16 | |||
35.4 | even | 6 | 350.2.o.c.243.2 | 16 | |||
35.12 | even | 12 | 70.2.k.a.17.3 | yes | 16 | ||
35.17 | even | 12 | 490.2.l.c.117.2 | 16 | |||
35.18 | odd | 12 | 350.2.o.c.257.4 | 16 | |||
35.19 | odd | 6 | 350.2.o.c.143.4 | 16 | |||
35.27 | even | 4 | inner | 490.2.g.c.97.7 | 16 | ||
35.32 | odd | 12 | 70.2.k.a.47.1 | yes | 16 | ||
35.33 | even | 12 | 350.2.o.c.157.2 | 16 | |||
105.32 | even | 12 | 630.2.bv.c.397.3 | 16 | |||
105.47 | odd | 12 | 630.2.bv.c.577.1 | 16 | |||
140.47 | odd | 12 | 560.2.ci.c.17.3 | 16 | |||
140.67 | even | 12 | 560.2.ci.c.257.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.1 | ✓ | 16 | 7.5 | odd | 6 | ||
70.2.k.a.17.3 | yes | 16 | 35.12 | even | 12 | ||
70.2.k.a.33.3 | yes | 16 | 7.4 | even | 3 | ||
70.2.k.a.47.1 | yes | 16 | 35.32 | odd | 12 | ||
350.2.o.c.143.4 | 16 | 35.19 | odd | 6 | |||
350.2.o.c.157.2 | 16 | 35.33 | even | 12 | |||
350.2.o.c.243.2 | 16 | 35.4 | even | 6 | |||
350.2.o.c.257.4 | 16 | 35.18 | odd | 12 | |||
490.2.g.c.97.6 | 16 | 5.2 | odd | 4 | inner | ||
490.2.g.c.97.7 | 16 | 35.27 | even | 4 | inner | ||
490.2.g.c.293.6 | 16 | 7.6 | odd | 2 | inner | ||
490.2.g.c.293.7 | 16 | 1.1 | even | 1 | trivial | ||
490.2.l.c.117.2 | 16 | 35.17 | even | 12 | |||
490.2.l.c.227.4 | 16 | 35.2 | odd | 12 | |||
490.2.l.c.313.4 | 16 | 7.3 | odd | 6 | |||
490.2.l.c.423.2 | 16 | 7.2 | even | 3 | |||
560.2.ci.c.17.3 | 16 | 140.47 | odd | 12 | |||
560.2.ci.c.33.3 | 16 | 28.11 | odd | 6 | |||
560.2.ci.c.257.3 | 16 | 140.67 | even | 12 | |||
560.2.ci.c.353.3 | 16 | 28.19 | even | 6 | |||
630.2.bv.c.73.3 | 16 | 21.5 | even | 6 | |||
630.2.bv.c.397.3 | 16 | 105.32 | even | 12 | |||
630.2.bv.c.523.1 | 16 | 21.11 | odd | 6 | |||
630.2.bv.c.577.1 | 16 | 105.47 | odd | 12 |