Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.4 | ||
Root | \(0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.a.97.4 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.707107 | + | 2.12132i | 0.223607 | + | 0.670820i | ||||
\(11\) | 1.51594 | 0.457072 | 0.228536 | − | 0.973535i | \(-0.426606\pi\) | ||||
0.228536 | + | 0.973535i | \(0.426606\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −3.93015 | + | 3.93015i | −1.09003 | + | 1.09003i | −0.0945033 | + | 0.995525i | \(0.530126\pi\) |
−0.995525 | + | 0.0945033i | \(0.969874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.707107 | − | 2.12132i | −0.182574 | − | 0.547723i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.07193 | − | 3.07193i | −0.745052 | − | 0.745052i | 0.228493 | − | 0.973546i | \(-0.426620\pi\) |
−0.973546 | + | 0.228493i | \(0.926620\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | 2.00000 | + | 1.00000i | 0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.07193 | − | 1.07193i | 0.228536 | − | 0.228536i | ||||
\(23\) | −3.00000 | − | 3.00000i | −0.625543 | − | 0.625543i | 0.321400 | − | 0.946943i | \(-0.395847\pi\) |
−0.946943 | + | 0.321400i | \(0.895847\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 5.55807i | 1.09003i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24558i | 0.788385i | 0.919028 | + | 0.394193i | \(0.128976\pi\) | ||||
−0.919028 | + | 0.394193i | \(0.871024\pi\) | |||||||
\(30\) | −2.00000 | − | 1.00000i | −0.365148 | − | 0.182574i | ||||
\(31\) | − | 10.4882i | − | 1.88374i | −0.335977 | − | 0.941870i | \(-0.609066\pi\) | ||
0.335977 | − | 0.941870i | \(-0.390934\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −1.07193 | + | 1.07193i | −0.186599 | + | 0.186599i | ||||
\(34\) | −4.34436 | −0.745052 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.55599 | − | 1.55599i | 0.255804 | − | 0.255804i | −0.567541 | − | 0.823345i | \(-0.692105\pi\) |
0.823345 | + | 0.567541i | \(0.192105\pi\) | |||||||
\(38\) | 0.414214 | − | 0.414214i | 0.0671943 | − | 0.0671943i | ||||
\(39\) | − | 5.55807i | − | 0.890004i | ||||||
\(40\) | 2.12132 | − | 0.707107i | 0.335410 | − | 0.111803i | ||||
\(41\) | 6.68873i | 1.04460i | 0.852761 | + | 0.522302i | \(0.174927\pi\) | ||||
−0.852761 | + | 0.522302i | \(0.825073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83051 | − | 3.83051i | −0.584147 | − | 0.584147i | 0.351893 | − | 0.936040i | \(-0.385538\pi\) |
−0.936040 | + | 0.351893i | \(0.885538\pi\) | |||||||
\(44\) | − | 1.51594i | − | 0.228536i | ||||||
\(45\) | 2.00000 | + | 1.00000i | 0.298142 | + | 0.149071i | ||||
\(46\) | −4.24264 | −0.625543 | ||||||||
\(47\) | −3.97021 | − | 3.97021i | −0.579114 | − | 0.579114i | 0.355545 | − | 0.934659i | \(-0.384295\pi\) |
−0.934659 | + | 0.355545i | \(0.884295\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.94975 | − | 0.707107i | −0.700000 | − | 0.100000i | ||||
\(51\) | 4.34436 | 0.608333 | ||||||||
\(52\) | 3.93015 | + | 3.93015i | 0.545014 | + | 0.545014i | ||||
\(53\) | −7.02893 | − | 7.02893i | −0.965498 | − | 0.965498i | 0.0339262 | − | 0.999424i | \(-0.489199\pi\) |
−0.999424 | + | 0.0339262i | \(0.989199\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.51594 | + | 3.03188i | −0.204409 | + | 0.408818i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.414214 | + | 0.414214i | −0.0548639 | + | 0.0548639i | ||||
\(58\) | 3.00208 | + | 3.00208i | 0.394193 | + | 0.394193i | ||||
\(59\) | 0.729646 | 0.0949918 | 0.0474959 | − | 0.998871i | \(-0.484876\pi\) | ||||
0.0474959 | + | 0.998871i | \(0.484876\pi\) | |||||||
\(60\) | −2.12132 | + | 0.707107i | −0.273861 | + | 0.0912871i | ||||
\(61\) | 3.03188i | 0.388192i | 0.980983 | + | 0.194096i | \(0.0621773\pi\) | ||||
−0.980983 | + | 0.194096i | \(0.937823\pi\) | |||||||
\(62\) | −7.41629 | − | 7.41629i | −0.941870 | − | 0.941870i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.93015 | − | 11.7905i | −0.487475 | − | 1.46243i | ||||
\(66\) | 1.51594i | 0.186599i | ||||||||
\(67\) | −9.93223 | + | 9.93223i | −1.21342 | + | 1.21342i | −0.243519 | + | 0.969896i | \(0.578302\pi\) |
−0.969896 | + | 0.243519i | \(0.921698\pi\) | |||||||
\(68\) | −3.07193 | + | 3.07193i | −0.372526 | + | 0.372526i | ||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.70193 | −0.676695 | −0.338347 | − | 0.941021i | \(-0.609868\pi\) | ||||
−0.338347 | + | 0.941021i | \(0.609868\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.48822 | − | 6.48822i | 0.759389 | − | 0.759389i | −0.216822 | − | 0.976211i | \(-0.569569\pi\) |
0.976211 | + | 0.216822i | \(0.0695691\pi\) | |||||||
\(74\) | − | 2.20051i | − | 0.255804i | ||||||
\(75\) | 4.94975 | + | 0.707107i | 0.571548 | + | 0.0816497i | ||||
\(76\) | − | 0.585786i | − | 0.0671943i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.93015 | − | 3.93015i | −0.445002 | − | 0.445002i | ||||
\(79\) | 6.68873i | 0.752541i | 0.926510 | + | 0.376270i | \(0.122794\pi\) | ||||
−0.926510 | + | 0.376270i | \(0.877206\pi\) | |||||||
\(80\) | 1.00000 | − | 2.00000i | 0.111803 | − | 0.223607i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.72965 | + | 4.72965i | 0.522302 | + | 0.522302i | ||||
\(83\) | −10.1029 | + | 10.1029i | −1.10894 | + | 1.10894i | −0.115652 | + | 0.993290i | \(0.536896\pi\) |
−0.993290 | + | 0.115652i | \(0.963104\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.21579 | − | 3.07193i | 0.999593 | − | 0.333198i | ||||
\(86\) | −5.41716 | −0.584147 | ||||||||
\(87\) | −3.00208 | − | 3.00208i | −0.321857 | − | 0.321857i | ||||
\(88\) | −1.07193 | − | 1.07193i | −0.114268 | − | 0.114268i | ||||
\(89\) | −18.0042 | −1.90844 | −0.954219 | − | 0.299110i | \(-0.903310\pi\) | ||||
−0.954219 | + | 0.299110i | \(0.903310\pi\) | |||||||
\(90\) | 2.12132 | − | 0.707107i | 0.223607 | − | 0.0745356i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | + | 3.00000i | −0.312772 | + | 0.312772i | ||||
\(93\) | 7.41629 | + | 7.41629i | 0.769034 | + | 0.769034i | ||||
\(94\) | −5.61472 | −0.579114 | ||||||||
\(95\) | −0.585786 | + | 1.17157i | −0.0601004 | + | 0.120201i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −12.2848 | − | 12.2848i | −1.24733 | − | 1.24733i | −0.956895 | − | 0.290435i | \(-0.906200\pi\) |
−0.290435 | − | 0.956895i | \(-0.593800\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.51594i | − | 0.152357i | ||||||
\(100\) | −4.00000 | + | 3.00000i | −0.400000 | + | 0.300000i | ||||
\(101\) | − | 7.70193i | − | 0.766371i | −0.923671 | − | 0.383185i | \(-0.874827\pi\) | ||
0.923671 | − | 0.383185i | \(-0.125173\pi\) | |||||||
\(102\) | 3.07193 | − | 3.07193i | 0.304166 | − | 0.304166i | ||||
\(103\) | 3.17157 | − | 3.17157i | 0.312504 | − | 0.312504i | −0.533375 | − | 0.845879i | \(-0.679076\pi\) |
0.845879 | + | 0.533375i | \(0.179076\pi\) | |||||||
\(104\) | 5.55807 | 0.545014 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.94041 | −0.965498 | ||||||||
\(107\) | 0.687511 | − | 0.687511i | 0.0664642 | − | 0.0664642i | −0.673093 | − | 0.739558i | \(-0.735035\pi\) |
0.739558 | + | 0.673093i | \(0.235035\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 5.80071i | − | 0.555608i | −0.960638 | − | 0.277804i | \(-0.910393\pi\) | ||
0.960638 | − | 0.277804i | \(-0.0896065\pi\) | |||||||
\(110\) | 1.07193 | + | 3.21579i | 0.102204 | + | 0.306613i | ||||
\(111\) | 2.20051i | 0.208863i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00416 | + | 8.00416i | 0.752968 | + | 0.752968i | 0.975032 | − | 0.222064i | \(-0.0712794\pi\) |
−0.222064 | + | 0.975032i | \(0.571279\pi\) | |||||||
\(114\) | 0.585786i | 0.0548639i | ||||||||
\(115\) | 9.00000 | − | 3.00000i | 0.839254 | − | 0.279751i | ||||
\(116\) | 4.24558 | 0.394193 | ||||||||
\(117\) | 3.93015 | + | 3.93015i | 0.363343 | + | 0.363343i | ||||
\(118\) | 0.515938 | − | 0.515938i | 0.0474959 | − | 0.0474959i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 2.00000i | −0.0912871 | + | 0.182574i | ||||
\(121\) | −8.70193 | −0.791085 | ||||||||
\(122\) | 2.14386 | + | 2.14386i | 0.194096 | + | 0.194096i | ||||
\(123\) | −4.72965 | − | 4.72965i | −0.426458 | − | 0.426458i | ||||
\(124\) | −10.4882 | −0.941870 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7019 | − | 11.7019i | 1.03838 | − | 1.03838i | 0.0391451 | − | 0.999234i | \(-0.487537\pi\) |
0.999234 | − | 0.0391451i | \(-0.0124635\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 5.41716 | 0.476954 | ||||||||
\(130\) | −11.1161 | − | 5.55807i | −0.974951 | − | 0.487475i | ||||
\(131\) | 4.92721i | 0.430492i | 0.976560 | + | 0.215246i | \(0.0690554\pi\) | ||||
−0.976560 | + | 0.215246i | \(0.930945\pi\) | |||||||
\(132\) | 1.07193 | + | 1.07193i | 0.0932995 | + | 0.0932995i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.0463i | 1.21342i | ||||||||
\(135\) | −2.12132 | + | 0.707107i | −0.182574 | + | 0.0608581i | ||||
\(136\) | 4.34436i | 0.372526i | ||||||||
\(137\) | −8.21787 | + | 8.21787i | −0.702100 | + | 0.702100i | −0.964861 | − | 0.262761i | \(-0.915367\pi\) |
0.262761 | + | 0.964861i | \(0.415367\pi\) | |||||||
\(138\) | 3.00000 | − | 3.00000i | 0.255377 | − | 0.255377i | ||||
\(139\) | 18.0475 | 1.53077 | 0.765385 | − | 0.643572i | \(-0.222548\pi\) | ||||
0.765385 | + | 0.643572i | \(0.222548\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.61472 | 0.472845 | ||||||||
\(142\) | −4.03188 | + | 4.03188i | −0.338347 | + | 0.338347i | ||||
\(143\) | −5.95786 | + | 5.95786i | −0.498222 | + | 0.498222i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −8.49117 | − | 4.24558i | −0.705153 | − | 0.352577i | ||||
\(146\) | − | 9.17574i | − | 0.759389i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.55599 | − | 1.55599i | −0.127902 | − | 0.127902i | ||||
\(149\) | 3.20955i | 0.262936i | 0.991320 | + | 0.131468i | \(0.0419691\pi\) | ||||
−0.991320 | + | 0.131468i | \(0.958031\pi\) | |||||||
\(150\) | 4.00000 | − | 3.00000i | 0.326599 | − | 0.244949i | ||||
\(151\) | 12.4503 | 1.01319 | 0.506594 | − | 0.862185i | \(-0.330904\pi\) | ||||
0.506594 | + | 0.862185i | \(0.330904\pi\) | |||||||
\(152\) | −0.414214 | − | 0.414214i | −0.0335972 | − | 0.0335972i | ||||
\(153\) | −3.07193 | + | 3.07193i | −0.248351 | + | 0.248351i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.9764 | + | 10.4882i | 1.68487 | + | 0.842434i | ||||
\(156\) | −5.55807 | −0.445002 | ||||||||
\(157\) | 1.07107 | + | 1.07107i | 0.0854805 | + | 0.0854805i | 0.748554 | − | 0.663074i | \(-0.230748\pi\) |
−0.663074 | + | 0.748554i | \(0.730748\pi\) | |||||||
\(158\) | 4.72965 | + | 4.72965i | 0.376270 | + | 0.376270i | ||||
\(159\) | 9.94041 | 0.788326 | ||||||||
\(160\) | −0.707107 | − | 2.12132i | −0.0559017 | − | 0.167705i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 9.44523 | + | 9.44523i | 0.739807 | + | 0.739807i | 0.972541 | − | 0.232733i | \(-0.0747669\pi\) |
−0.232733 | + | 0.972541i | \(0.574767\pi\) | |||||||
\(164\) | 6.68873 | 0.522302 | ||||||||
\(165\) | −1.07193 | − | 3.21579i | −0.0834496 | − | 0.250349i | ||||
\(166\) | 14.2877i | 1.10894i | ||||||||
\(167\) | 7.59081 | + | 7.59081i | 0.587395 | + | 0.587395i | 0.936925 | − | 0.349530i | \(-0.113659\pi\) |
−0.349530 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 17.8922i | − | 1.37632i | ||||||
\(170\) | 4.34436 | − | 8.68873i | 0.333198 | − | 0.666395i | ||||
\(171\) | − | 0.585786i | − | 0.0447962i | ||||||
\(172\) | −3.83051 | + | 3.83051i | −0.292074 | + | 0.292074i | ||||
\(173\) | −15.7875 | + | 15.7875i | −1.20030 | + | 1.20030i | −0.226228 | + | 0.974074i | \(0.572639\pi\) |
−0.974074 | + | 0.226228i | \(0.927361\pi\) | |||||||
\(174\) | −4.24558 | −0.321857 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.51594 | −0.114268 | ||||||||
\(177\) | −0.515938 | + | 0.515938i | −0.0387803 | + | 0.0387803i | ||||
\(178\) | −12.7309 | + | 12.7309i | −0.954219 | + | 0.954219i | ||||
\(179\) | 8.42447i | 0.629675i | 0.949146 | + | 0.314837i | \(0.101950\pi\) | ||||
−0.949146 | + | 0.314837i | \(0.898050\pi\) | |||||||
\(180\) | 1.00000 | − | 2.00000i | 0.0745356 | − | 0.149071i | ||||
\(181\) | 8.42742i | 0.626405i | 0.949686 | + | 0.313202i | \(0.101402\pi\) | ||||
−0.949686 | + | 0.313202i | \(0.898598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14386 | − | 2.14386i | −0.158479 | − | 0.158479i | ||||
\(184\) | 4.24264i | 0.312772i | ||||||||
\(185\) | 1.55599 | + | 4.66798i | 0.114399 | + | 0.343196i | ||||
\(186\) | 10.4882 | 0.769034 | ||||||||
\(187\) | −4.65685 | − | 4.65685i | −0.340543 | − | 0.340543i | ||||
\(188\) | −3.97021 | + | 3.97021i | −0.289557 | + | 0.289557i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.414214 | + | 1.24264i | 0.0300502 | + | 0.0901506i | ||||
\(191\) | 22.1029 | 1.59931 | 0.799656 | − | 0.600458i | \(-0.205015\pi\) | ||||
0.799656 | + | 0.600458i | \(0.205015\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 6.55807 | + | 6.55807i | 0.472060 | + | 0.472060i | 0.902581 | − | 0.430520i | \(-0.141670\pi\) |
−0.430520 | + | 0.902581i | \(0.641670\pi\) | |||||||
\(194\) | −17.3733 | −1.24733 | ||||||||
\(195\) | 11.1161 | + | 5.55807i | 0.796044 | + | 0.398022i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.52620 | − | 6.52620i | 0.464972 | − | 0.464972i | −0.435309 | − | 0.900281i | \(-0.643361\pi\) |
0.900281 | + | 0.435309i | \(0.143361\pi\) | |||||||
\(198\) | −1.07193 | − | 1.07193i | −0.0761787 | − | 0.0761787i | ||||
\(199\) | −13.0373 | −0.924187 | −0.462093 | − | 0.886831i | \(-0.652901\pi\) | ||||
−0.462093 | + | 0.886831i | \(0.652901\pi\) | |||||||
\(200\) | −0.707107 | + | 4.94975i | −0.0500000 | + | 0.350000i | ||||
\(201\) | − | 14.0463i | − | 0.990749i | ||||||
\(202\) | −5.44609 | − | 5.44609i | −0.383185 | − | 0.383185i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 4.34436i | − | 0.304166i | ||||||
\(205\) | −13.3775 | − | 6.68873i | −0.934322 | − | 0.467161i | ||||
\(206\) | − | 4.48528i | − | 0.312504i | ||||||
\(207\) | −3.00000 | + | 3.00000i | −0.208514 | + | 0.208514i | ||||
\(208\) | 3.93015 | − | 3.93015i | 0.272507 | − | 0.272507i | ||||
\(209\) | 0.888016 | 0.0614253 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6669 | −1.62930 | −0.814648 | − | 0.579955i | \(-0.803070\pi\) | ||||
−0.814648 | + | 0.579955i | \(0.803070\pi\) | |||||||
\(212\) | −7.02893 | + | 7.02893i | −0.482749 | + | 0.482749i | ||||
\(213\) | 4.03188 | − | 4.03188i | 0.276260 | − | 0.276260i | ||||
\(214\) | − | 0.972287i | − | 0.0664642i | ||||||
\(215\) | 11.4915 | − | 3.83051i | 0.783715 | − | 0.261238i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.10172 | − | 4.10172i | −0.277804 | − | 0.277804i | ||||
\(219\) | 9.17574i | 0.620039i | ||||||||
\(220\) | 3.03188 | + | 1.51594i | 0.204409 | + | 0.102204i | ||||
\(221\) | 24.1463 | 1.62426 | ||||||||
\(222\) | 1.55599 | + | 1.55599i | 0.104431 | + | 0.104431i | ||||
\(223\) | 5.80366 | − | 5.80366i | 0.388642 | − | 0.388642i | −0.485561 | − | 0.874203i | \(-0.661385\pi\) |
0.874203 | + | 0.485561i | \(0.161385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | 11.3196 | 0.752968 | ||||||||
\(227\) | −3.07279 | − | 3.07279i | −0.203948 | − | 0.203948i | 0.597741 | − | 0.801689i | \(-0.296065\pi\) |
−0.801689 | + | 0.597741i | \(0.796065\pi\) | |||||||
\(228\) | 0.414214 | + | 0.414214i | 0.0274320 | + | 0.0274320i | ||||
\(229\) | 29.5172 | 1.95055 | 0.975274 | − | 0.220998i | \(-0.0709314\pi\) | ||||
0.975274 | + | 0.220998i | \(0.0709314\pi\) | |||||||
\(230\) | 4.24264 | − | 8.48528i | 0.279751 | − | 0.559503i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00208 | − | 3.00208i | 0.197096 | − | 0.197096i | ||||
\(233\) | −3.16985 | − | 3.16985i | −0.207664 | − | 0.207664i | 0.595610 | − | 0.803274i | \(-0.296910\pi\) |
−0.803274 | + | 0.595610i | \(0.796910\pi\) | |||||||
\(234\) | 5.55807 | 0.363343 | ||||||||
\(235\) | 11.9106 | − | 3.97021i | 0.776963 | − | 0.258988i | ||||
\(236\) | − | 0.729646i | − | 0.0474959i | ||||||
\(237\) | −4.72965 | − | 4.72965i | −0.307224 | − | 0.307224i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.0475i | 1.81424i | 0.420869 | + | 0.907122i | \(0.361725\pi\) | ||||
−0.420869 | + | 0.907122i | \(0.638275\pi\) | |||||||
\(240\) | 0.707107 | + | 2.12132i | 0.0456435 | + | 0.136931i | ||||
\(241\) | − | 16.7846i | − | 1.08119i | −0.841283 | − | 0.540595i | \(-0.818199\pi\) | ||
0.841283 | − | 0.540595i | \(-0.181801\pi\) | |||||||
\(242\) | −6.15320 | + | 6.15320i | −0.395542 | + | 0.395542i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 3.03188 | 0.194096 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.68873 | −0.426458 | ||||||||
\(247\) | −2.30223 | + | 2.30223i | −0.146487 | + | 0.146487i | ||||
\(248\) | −7.41629 | + | 7.41629i | −0.470935 | + | 0.470935i | ||||
\(249\) | − | 14.2877i | − | 0.905447i | ||||||
\(250\) | 6.36396 | − | 9.19239i | 0.402492 | − | 0.581378i | ||||
\(251\) | 1.99411i | 0.125867i | 0.998018 | + | 0.0629337i | \(0.0200457\pi\) | ||||
−0.998018 | + | 0.0629337i | \(0.979954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.54781 | − | 4.54781i | −0.285919 | − | 0.285919i | ||||
\(254\) | − | 16.5490i | − | 1.03838i | ||||||
\(255\) | −4.34436 | + | 8.68873i | −0.272055 | + | 0.544109i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.9335 | − | 20.9335i | −1.30579 | − | 1.30579i | −0.924422 | − | 0.381371i | \(-0.875452\pi\) |
−0.381371 | − | 0.924422i | \(-0.624548\pi\) | |||||||
\(258\) | 3.83051 | − | 3.83051i | 0.238477 | − | 0.238477i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.7905 | + | 3.93015i | −0.731213 | + | 0.243738i | ||||
\(261\) | 4.24558 | 0.262795 | ||||||||
\(262\) | 3.48406 | + | 3.48406i | 0.215246 | + | 0.215246i | ||||
\(263\) | 17.5304 | + | 17.5304i | 1.08097 | + | 1.08097i | 0.996419 | + | 0.0845490i | \(0.0269449\pi\) |
0.0845490 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(264\) | 1.51594 | 0.0932995 | ||||||||
\(265\) | 21.0868 | − | 7.02893i | 1.29535 | − | 0.431784i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7309 | − | 12.7309i | 0.779116 | − | 0.779116i | ||||
\(268\) | 9.93223 | + | 9.93223i | 0.606708 | + | 0.606708i | ||||
\(269\) | −5.39554 | −0.328972 | −0.164486 | − | 0.986379i | \(-0.552597\pi\) | ||||
−0.164486 | + | 0.986379i | \(0.552597\pi\) | |||||||
\(270\) | −1.00000 | + | 2.00000i | −0.0608581 | + | 0.121716i | ||||
\(271\) | − | 10.6875i | − | 0.649220i | −0.945848 | − | 0.324610i | \(-0.894767\pi\) | ||
0.945848 | − | 0.324610i | \(-0.105233\pi\) | |||||||
\(272\) | 3.07193 | + | 3.07193i | 0.186263 | + | 0.186263i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6218i | 0.702100i | ||||||||
\(275\) | −4.54781 | − | 6.06375i | −0.274243 | − | 0.365658i | ||||
\(276\) | − | 4.24264i | − | 0.255377i | ||||||
\(277\) | 11.6168 | − | 11.6168i | 0.697986 | − | 0.697986i | −0.265990 | − | 0.963976i | \(-0.585699\pi\) |
0.963976 | + | 0.265990i | \(0.0856988\pi\) | |||||||
\(278\) | 12.7615 | − | 12.7615i | 0.765385 | − | 0.765385i | ||||
\(279\) | −10.4882 | −0.627914 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.40101 | 0.143232 | 0.0716161 | − | 0.997432i | \(-0.477184\pi\) | ||||
0.0716161 | + | 0.997432i | \(0.477184\pi\) | |||||||
\(282\) | 3.97021 | − | 3.97021i | 0.236422 | − | 0.236422i | ||||
\(283\) | −8.66274 | + | 8.66274i | −0.514946 | + | 0.514946i | −0.916038 | − | 0.401092i | \(-0.868631\pi\) |
0.401092 | + | 0.916038i | \(0.368631\pi\) | |||||||
\(284\) | 5.70193i | 0.338347i | ||||||||
\(285\) | −0.414214 | − | 1.24264i | −0.0245359 | − | 0.0736077i | ||||
\(286\) | 8.42569i | 0.498222i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 1.87351i | 0.110206i | ||||||||
\(290\) | −9.00624 | + | 3.00208i | −0.528865 | + | 0.176288i | ||||
\(291\) | 17.3733 | 1.01844 | ||||||||
\(292\) | −6.48822 | − | 6.48822i | −0.379695 | − | 0.379695i | ||||
\(293\) | −13.9127 | + | 13.9127i | −0.812789 | + | 0.812789i | −0.985051 | − | 0.172263i | \(-0.944892\pi\) |
0.172263 | + | 0.985051i | \(0.444892\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.729646 | + | 1.45929i | −0.0424816 | + | 0.0849633i | ||||
\(296\) | −2.20051 | −0.127902 | ||||||||
\(297\) | 1.07193 | + | 1.07193i | 0.0621997 | + | 0.0621997i | ||||
\(298\) | 2.26949 | + | 2.26949i | 0.131468 | + | 0.131468i | ||||
\(299\) | 23.5809 | 1.36372 | ||||||||
\(300\) | 0.707107 | − | 4.94975i | 0.0408248 | − | 0.285774i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.80366 | − | 8.80366i | 0.506594 | − | 0.506594i | ||||
\(303\) | 5.44609 | + | 5.44609i | 0.312870 | + | 0.312870i | ||||
\(304\) | −0.585786 | −0.0335972 | ||||||||
\(305\) | −6.06375 | − | 3.03188i | −0.347209 | − | 0.173605i | ||||
\(306\) | 4.34436i | 0.248351i | ||||||||
\(307\) | −13.5172 | − | 13.5172i | −0.771465 | − | 0.771465i | 0.206898 | − | 0.978363i | \(-0.433663\pi\) |
−0.978363 | + | 0.206898i | \(0.933663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.48528i | 0.255159i | ||||||||
\(310\) | 22.2489 | − | 7.41629i | 1.26365 | − | 0.421217i | ||||
\(311\) | 23.5477i | 1.33527i | 0.744489 | + | 0.667635i | \(0.232693\pi\) | ||||
−0.744489 | + | 0.667635i | \(0.767307\pi\) | |||||||
\(312\) | −3.93015 | + | 3.93015i | −0.222501 | + | 0.222501i | ||||
\(313\) | 8.58995 | − | 8.58995i | 0.485533 | − | 0.485533i | −0.421361 | − | 0.906893i | \(-0.638447\pi\) |
0.906893 | + | 0.421361i | \(0.138447\pi\) | |||||||
\(314\) | 1.51472 | 0.0854805 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.68873 | 0.376270 | ||||||||
\(317\) | 13.4985 | − | 13.4985i | 0.758150 | − | 0.758150i | −0.217835 | − | 0.975986i | \(-0.569900\pi\) |
0.975986 | + | 0.217835i | \(0.0698995\pi\) | |||||||
\(318\) | 7.02893 | − | 7.02893i | 0.394163 | − | 0.394163i | ||||
\(319\) | 6.43604i | 0.360349i | ||||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | 0.972287i | 0.0542678i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.79949 | − | 1.79949i | −0.100127 | − | 0.100127i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 27.5111 | + | 3.93015i | 1.52604 | + | 0.218006i | ||||
\(326\) | 13.3576 | 0.739807 | ||||||||
\(327\) | 4.10172 | + | 4.10172i | 0.226826 | + | 0.226826i | ||||
\(328\) | 4.72965 | − | 4.72965i | 0.261151 | − | 0.261151i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.03188 | − | 1.51594i | −0.166899 | − | 0.0834496i | ||||
\(331\) | −4.42569 | −0.243258 | −0.121629 | − | 0.992576i | \(-0.538812\pi\) | ||||
−0.121629 | + | 0.992576i | \(0.538812\pi\) | |||||||
\(332\) | 10.1029 | + | 10.1029i | 0.554471 | + | 0.554471i | ||||
\(333\) | −1.55599 | − | 1.55599i | −0.0852678 | − | 0.0852678i | ||||
\(334\) | 10.7350 | 0.587395 | ||||||||
\(335\) | −9.93223 | − | 29.7967i | −0.542656 | − | 1.62797i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.75564 | + | 4.75564i | −0.259056 | + | 0.259056i | −0.824670 | − | 0.565614i | \(-0.808639\pi\) |
0.565614 | + | 0.824670i | \(0.308639\pi\) | |||||||
\(338\) | −12.6517 | − | 12.6517i | −0.688161 | − | 0.688161i | ||||
\(339\) | −11.3196 | −0.614796 | ||||||||
\(340\) | −3.07193 | − | 9.21579i | −0.166599 | − | 0.499796i | ||||
\(341\) | − | 15.8995i | − | 0.861006i | ||||||
\(342\) | −0.414214 | − | 0.414214i | −0.0223981 | − | 0.0223981i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.41716i | 0.292074i | ||||||||
\(345\) | −4.24264 | + | 8.48528i | −0.228416 | + | 0.456832i | ||||
\(346\) | 22.3269i | 1.20030i | ||||||||
\(347\) | −21.2600 | + | 21.2600i | −1.14130 | + | 1.14130i | −0.153084 | + | 0.988213i | \(0.548920\pi\) |
−0.988213 | + | 0.153084i | \(0.951080\pi\) | |||||||
\(348\) | −3.00208 | + | 3.00208i | −0.160928 | + | 0.160928i | ||||
\(349\) | 5.85442 | 0.313380 | 0.156690 | − | 0.987648i | \(-0.449918\pi\) | ||||
0.156690 | + | 0.987648i | \(0.449918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.55807 | −0.296668 | ||||||||
\(352\) | −1.07193 | + | 1.07193i | −0.0571341 | + | 0.0571341i | ||||
\(353\) | −23.0165 | + | 23.0165i | −1.22504 | + | 1.22504i | −0.259229 | + | 0.965816i | \(0.583468\pi\) |
−0.965816 | + | 0.259229i | \(0.916532\pi\) | |||||||
\(354\) | 0.729646i | 0.0387803i | ||||||||
\(355\) | 5.70193 | − | 11.4039i | 0.302627 | − | 0.605254i | ||||
\(356\) | 18.0042i | 0.954219i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.95700 | + | 5.95700i | 0.314837 | + | 0.314837i | ||||
\(359\) | 12.1872i | 0.643217i | 0.946873 | + | 0.321608i | \(0.104223\pi\) | ||||
−0.946873 | + | 0.321608i | \(0.895777\pi\) | |||||||
\(360\) | −0.707107 | − | 2.12132i | −0.0372678 | − | 0.111803i | ||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | 5.95908 | + | 5.95908i | 0.313202 | + | 0.313202i | ||||
\(363\) | 6.15320 | − | 6.15320i | 0.322959 | − | 0.322959i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.48822 | + | 19.4647i | 0.339609 | + | 1.01883i | ||||
\(366\) | −3.03188 | −0.158479 | ||||||||
\(367\) | −16.9693 | − | 16.9693i | −0.885793 | − | 0.885793i | 0.108323 | − | 0.994116i | \(-0.465452\pi\) |
−0.994116 | + | 0.108323i | \(0.965452\pi\) | |||||||
\(368\) | 3.00000 | + | 3.00000i | 0.156386 | + | 0.156386i | ||||
\(369\) | 6.68873 | 0.348201 | ||||||||
\(370\) | 4.40101 | + | 2.20051i | 0.228798 | + | 0.114399i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.41629 | − | 7.41629i | 0.384517 | − | 0.384517i | ||||
\(373\) | 0.300148 | + | 0.300148i | 0.0155411 | + | 0.0155411i | 0.714835 | − | 0.699294i | \(-0.246502\pi\) |
−0.699294 | + | 0.714835i | \(0.746502\pi\) | |||||||
\(374\) | −6.58579 | −0.340543 | ||||||||
\(375\) | −6.36396 | + | 9.19239i | −0.328634 | + | 0.474693i | ||||
\(376\) | 5.61472i | 0.289557i | ||||||||
\(377\) | −16.6858 | − | 16.6858i | −0.859362 | − | 0.859362i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.96985i | 0.152551i | 0.997087 | + | 0.0762754i | \(0.0243028\pi\) | ||||
−0.997087 | + | 0.0762754i | \(0.975697\pi\) | |||||||
\(380\) | 1.17157 | + | 0.585786i | 0.0601004 | + | 0.0300502i | ||||
\(381\) | 16.5490i | 0.847833i | ||||||||
\(382\) | 15.6291 | − | 15.6291i | 0.799656 | − | 0.799656i | ||||
\(383\) | −11.3815 | + | 11.3815i | −0.581566 | + | 0.581566i | −0.935333 | − | 0.353767i | \(-0.884901\pi\) |
0.353767 | + | 0.935333i | \(0.384901\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.27452 | 0.472060 | ||||||||
\(387\) | −3.83051 | + | 3.83051i | −0.194716 | + | 0.194716i | ||||
\(388\) | −12.2848 | + | 12.2848i | −0.623665 | + | 0.623665i | ||||
\(389\) | − | 29.3576i | − | 1.48849i | −0.667908 | − | 0.744244i | \(-0.732810\pi\) | ||
0.667908 | − | 0.744244i | \(-0.267190\pi\) | |||||||
\(390\) | 11.7905 | − | 3.93015i | 0.597033 | − | 0.199011i | ||||
\(391\) | 18.4316i | 0.932125i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.48406 | − | 3.48406i | −0.175748 | − | 0.175748i | ||||
\(394\) | − | 9.22944i | − | 0.464972i | ||||||
\(395\) | −13.3775 | − | 6.68873i | −0.673093 | − | 0.336547i | ||||
\(396\) | −1.51594 | −0.0761787 | ||||||||
\(397\) | 6.24264 | + | 6.24264i | 0.313309 | + | 0.313309i | 0.846190 | − | 0.532881i | \(-0.178891\pi\) |
−0.532881 | + | 0.846190i | \(0.678891\pi\) | |||||||
\(398\) | −9.21873 | + | 9.21873i | −0.462093 | + | 0.462093i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −7.19209 | −0.359156 | −0.179578 | − | 0.983744i | \(-0.557473\pi\) | ||||
−0.179578 | + | 0.983744i | \(0.557473\pi\) | |||||||
\(402\) | −9.93223 | − | 9.93223i | −0.495375 | − | 0.495375i | ||||
\(403\) | 41.2203 | + | 41.2203i | 2.05333 | + | 2.05333i | ||||
\(404\) | −7.70193 | −0.383185 | ||||||||
\(405\) | 1.00000 | − | 2.00000i | 0.0496904 | − | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.35879 | − | 2.35879i | 0.116921 | − | 0.116921i | ||||
\(408\) | −3.07193 | − | 3.07193i | −0.152083 | − | 0.152083i | ||||
\(409\) | 14.6424 | 0.724022 | 0.362011 | − | 0.932174i | \(-0.382090\pi\) | ||||
0.362011 | + | 0.932174i | \(0.382090\pi\) | |||||||
\(410\) | −14.1889 | + | 4.72965i | −0.700742 | + | 0.233581i | ||||
\(411\) | − | 11.6218i | − | 0.573262i | ||||||
\(412\) | −3.17157 | − | 3.17157i | −0.156252 | − | 0.156252i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.24264i | 0.208514i | ||||||||
\(415\) | −10.1029 | − | 30.3088i | −0.495934 | − | 1.48780i | ||||
\(416\) | − | 5.55807i | − | 0.272507i | ||||||
\(417\) | −12.7615 | + | 12.7615i | −0.624934 | + | 0.624934i | ||||
\(418\) | 0.627922 | − | 0.627922i | 0.0307127 | − | 0.0307127i | ||||
\(419\) | 13.6569 | 0.667181 | 0.333590 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333590 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.1497 | −0.982039 | −0.491019 | − | 0.871149i | \(-0.663376\pi\) | ||||
−0.491019 | + | 0.871149i | \(0.663376\pi\) | |||||||
\(422\) | −16.7350 | + | 16.7350i | −0.814648 | + | 0.814648i | ||||
\(423\) | −3.97021 | + | 3.97021i | −0.193038 | + | 0.193038i | ||||
\(424\) | 9.94041i | 0.482749i | ||||||||
\(425\) | −3.07193 | + | 21.5035i | −0.149010 | + | 1.04307i | ||||
\(426\) | − | 5.70193i | − | 0.276260i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.687511 | − | 0.687511i | −0.0332321 | − | 0.0332321i | ||||
\(429\) | − | 8.42569i | − | 0.406796i | ||||||
\(430\) | 5.41716 | − | 10.8343i | 0.261238 | − | 0.522477i | ||||
\(431\) | 22.7279 | 1.09477 | 0.547383 | − | 0.836882i | \(-0.315624\pi\) | ||||
0.547383 | + | 0.836882i | \(0.315624\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −10.6875 | + | 10.6875i | −0.513609 | + | 0.513609i | −0.915630 | − | 0.402021i | \(-0.868308\pi\) |
0.402021 | + | 0.915630i | \(0.368308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.00624 | − | 3.00208i | 0.431816 | − | 0.143939i | ||||
\(436\) | −5.80071 | −0.277804 | ||||||||
\(437\) | −1.75736 | − | 1.75736i | −0.0840659 | − | 0.0840659i | ||||
\(438\) | 6.48822 | + | 6.48822i | 0.310019 | + | 0.310019i | ||||
\(439\) | 27.2654 | 1.30131 | 0.650653 | − | 0.759375i | \(-0.274495\pi\) | ||||
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(440\) | 3.21579 | − | 1.07193i | 0.153307 | − | 0.0511022i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.0740 | − | 17.0740i | 0.812128 | − | 0.812128i | ||||
\(443\) | −12.1439 | − | 12.1439i | −0.576972 | − | 0.576972i | 0.357096 | − | 0.934068i | \(-0.383767\pi\) |
−0.934068 | + | 0.357096i | \(0.883767\pi\) | |||||||
\(444\) | 2.20051 | 0.104431 | ||||||||
\(445\) | 18.0042 | − | 36.0083i | 0.853479 | − | 1.70696i | ||||
\(446\) | − | 8.20761i | − | 0.388642i | ||||||
\(447\) | −2.26949 | − | 2.26949i | −0.107343 | − | 0.107343i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.8368i | − | 1.26650i | −0.773945 | − | 0.633252i | \(-0.781720\pi\) | ||
0.773945 | − | 0.633252i | \(-0.218280\pi\) | |||||||
\(450\) | −0.707107 | + | 4.94975i | −0.0333333 | + | 0.233333i | ||||
\(451\) | 10.1397i | 0.477460i | ||||||||
\(452\) | 8.00416 | − | 8.00416i | 0.376484 | − | 0.376484i | ||||
\(453\) | −8.80366 | + | 8.80366i | −0.413632 | + | 0.413632i | ||||
\(454\) | −4.34558 | −0.203948 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.585786 | 0.0274320 | ||||||||
\(457\) | −19.1889 | + | 19.1889i | −0.897621 | + | 0.897621i | −0.995225 | − | 0.0976046i | \(-0.968882\pi\) |
0.0976046 | + | 0.995225i | \(0.468882\pi\) | |||||||
\(458\) | 20.8718 | − | 20.8718i | 0.975274 | − | 0.975274i | ||||
\(459\) | − | 4.34436i | − | 0.202778i | ||||||
\(460\) | −3.00000 | − | 9.00000i | −0.139876 | − | 0.419627i | ||||
\(461\) | − | 32.7813i | − | 1.52678i | −0.645939 | − | 0.763389i | \(-0.723534\pi\) | ||
0.645939 | − | 0.763389i | \(-0.276466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1480 | + | 26.1480i | 1.21520 | + | 1.21520i | 0.969293 | + | 0.245909i | \(0.0790863\pi\) |
0.245909 | + | 0.969293i | \(0.420914\pi\) | |||||||
\(464\) | − | 4.24558i | − | 0.197096i | ||||||
\(465\) | −22.2489 | + | 7.41629i | −1.03177 | + | 0.343922i | ||||
\(466\) | −4.48284 | −0.207664 | ||||||||
\(467\) | −1.51299 | − | 1.51299i | −0.0700130 | − | 0.0700130i | 0.671233 | − | 0.741246i | \(-0.265765\pi\) |
−0.741246 | + | 0.671233i | \(0.765765\pi\) | |||||||
\(468\) | 3.93015 | − | 3.93015i | 0.181671 | − | 0.181671i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.61472 | − | 11.2294i | 0.258988 | − | 0.517975i | ||||
\(471\) | −1.51472 | −0.0697946 | ||||||||
\(472\) | −0.515938 | − | 0.515938i | −0.0237480 | − | 0.0237480i | ||||
\(473\) | −5.80681 | − | 5.80681i | −0.266997 | − | 0.266997i | ||||
\(474\) | −6.68873 | −0.307224 | ||||||||
\(475\) | −1.75736 | − | 2.34315i | −0.0806332 | − | 0.107511i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.02893 | + | 7.02893i | −0.321833 | + | 0.321833i | ||||
\(478\) | 19.8326 | + | 19.8326i | 0.907122 | + | 0.907122i | ||||
\(479\) | 8.54487 | 0.390425 | 0.195213 | − | 0.980761i | \(-0.437460\pi\) | ||||
0.195213 | + | 0.980761i | \(0.437460\pi\) | |||||||
\(480\) | 2.00000 | + | 1.00000i | 0.0912871 | + | 0.0456435i | ||||
\(481\) | 12.2306i | 0.557666i | ||||||||
\(482\) | −11.8685 | − | 11.8685i | −0.540595 | − | 0.540595i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.70193i | 0.395542i | ||||||||
\(485\) | 36.8543 | − | 12.2848i | 1.67347 | − | 0.557823i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −12.6929 | + | 12.6929i | −0.575170 | + | 0.575170i | −0.933569 | − | 0.358399i | \(-0.883323\pi\) |
0.358399 | + | 0.933569i | \(0.383323\pi\) | |||||||
\(488\) | 2.14386 | − | 2.14386i | 0.0970480 | − | 0.0970480i | ||||
\(489\) | −13.3576 | −0.604050 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.139193 | −0.00628167 | −0.00314084 | − | 0.999995i | \(-0.501000\pi\) | ||||
−0.00314084 | + | 0.999995i | \(0.501000\pi\) | |||||||
\(492\) | −4.72965 | + | 4.72965i | −0.213229 | + | 0.213229i | ||||
\(493\) | 13.0421 | − | 13.0421i | 0.587388 | − | 0.587388i | ||||
\(494\) | 3.25584i | 0.146487i | ||||||||
\(495\) | 3.03188 | + | 1.51594i | 0.136273 | + | 0.0681363i | ||||
\(496\) | 10.4882i | 0.470935i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.1029 | − | 10.1029i | −0.452724 | − | 0.452724i | ||||
\(499\) | − | 43.2683i | − | 1.93696i | −0.249098 | − | 0.968478i | \(-0.580134\pi\) | ||
0.249098 | − | 0.968478i | \(-0.419866\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | −10.7350 | −0.479606 | ||||||||
\(502\) | 1.41005 | + | 1.41005i | 0.0629337 | + | 0.0629337i | ||||
\(503\) | 8.51680 | − | 8.51680i | 0.379745 | − | 0.379745i | −0.491265 | − | 0.871010i | \(-0.663465\pi\) |
0.871010 | + | 0.491265i | \(0.163465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4039 | + | 7.70193i | 0.685463 | + | 0.342732i | ||||
\(506\) | −6.43158 | −0.285919 | ||||||||
\(507\) | 12.6517 | + | 12.6517i | 0.561881 | + | 0.561881i | ||||
\(508\) | −11.7019 | − | 11.7019i | −0.519189 | − | 0.519189i | ||||
\(509\) | −12.9373 | −0.573434 | −0.286717 | − | 0.958015i | \(-0.592564\pi\) | ||||
−0.286717 | + | 0.958015i | \(0.592564\pi\) | |||||||
\(510\) | 3.07193 | + | 9.21579i | 0.136027 | + | 0.408082i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.414214 | + | 0.414214i | 0.0182880 | + | 0.0182880i | ||||
\(514\) | −29.6044 | −1.30579 | ||||||||
\(515\) | 3.17157 | + | 9.51472i | 0.139756 | + | 0.419269i | ||||
\(516\) | − | 5.41716i | − | 0.238477i | ||||||
\(517\) | −6.01858 | − | 6.01858i | −0.264697 | − | 0.264697i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.3269i | − | 0.980043i | ||||||
\(520\) | −5.55807 | + | 11.1161i | −0.243738 | + | 0.487475i | ||||
\(521\) | 6.97817i | 0.305719i | 0.988248 | + | 0.152860i | \(0.0488482\pi\) | ||||
−0.988248 | + | 0.152860i | \(0.951152\pi\) | |||||||
\(522\) | 3.00208 | − | 3.00208i | 0.131398 | − | 0.131398i | ||||
\(523\) | 0.132380 | − | 0.132380i | 0.00578859 | − | 0.00578859i | −0.704207 | − | 0.709995i | \(-0.748697\pi\) |
0.709995 | + | 0.704207i | \(0.248697\pi\) | |||||||
\(524\) | 4.92721 | 0.215246 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7917 | 1.08097 | ||||||||
\(527\) | −32.2191 | + | 32.2191i | −1.40349 | + | 1.40349i | ||||
\(528\) | 1.07193 | − | 1.07193i | 0.0466498 | − | 0.0466498i | ||||
\(529\) | − | 5.00000i | − | 0.217391i | ||||||
\(530\) | 9.94041 | − | 19.8808i | 0.431784 | − | 0.863568i | ||||
\(531\) | − | 0.729646i | − | 0.0316639i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.2877 | − | 26.2877i | −1.13865 | − | 1.13865i | ||||
\(534\) | − | 18.0042i | − | 0.779116i | ||||||
\(535\) | 0.687511 | + | 2.06253i | 0.0297237 | + | 0.0891710i | ||||
\(536\) | 14.0463 | 0.606708 | ||||||||
\(537\) | −5.95700 | − | 5.95700i | −0.257064 | − | 0.257064i | ||||
\(538\) | −3.81522 | + | 3.81522i | −0.164486 | + | 0.164486i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.707107 | + | 2.12132i | 0.0304290 | + | 0.0912871i | ||||
\(541\) | 25.4412 | 1.09380 | 0.546902 | − | 0.837197i | \(-0.315807\pi\) | ||||
0.546902 | + | 0.837197i | \(0.315807\pi\) | |||||||
\(542\) | −7.55721 | − | 7.55721i | −0.324610 | − | 0.324610i | ||||
\(543\) | −5.95908 | − | 5.95908i | −0.255729 | − | 0.255729i | ||||
\(544\) | 4.34436 | 0.186263 | ||||||||
\(545\) | 11.6014 | + | 5.80071i | 0.496951 | + | 0.248475i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.7474 | + | 26.7474i | −1.14363 | + | 1.14363i | −0.155855 | + | 0.987780i | \(0.549813\pi\) |
−0.987780 | + | 0.155855i | \(0.950187\pi\) | |||||||
\(548\) | 8.21787 | + | 8.21787i | 0.351050 | + | 0.351050i | ||||
\(549\) | 3.03188 | 0.129397 | ||||||||
\(550\) | −7.50351 | − | 1.07193i | −0.319951 | − | 0.0457072i | ||||
\(551\) | 2.48701i | 0.105950i | ||||||||
\(552\) | −3.00000 | − | 3.00000i | −0.127688 | − | 0.127688i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 16.4286i | − | 0.697986i | ||||||
\(555\) | −4.40101 | − | 2.20051i | −0.186812 | − | 0.0934062i | ||||
\(556\) | − | 18.0475i | − | 0.765385i | ||||||
\(557\) | −18.7321 | + | 18.7321i | −0.793704 | + | 0.793704i | −0.982094 | − | 0.188390i | \(-0.939673\pi\) |
0.188390 | + | 0.982094i | \(0.439673\pi\) | |||||||
\(558\) | −7.41629 | + | 7.41629i | −0.313957 | + | 0.313957i | ||||
\(559\) | 30.1090 | 1.27347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.58579 | 0.278052 | ||||||||
\(562\) | 1.69777 | − | 1.69777i | 0.0716161 | − | 0.0716161i | ||||
\(563\) | 3.01320 | − | 3.01320i | 0.126991 | − | 0.126991i | −0.640754 | − | 0.767746i | \(-0.721378\pi\) |
0.767746 | + | 0.640754i | \(0.221378\pi\) | |||||||
\(564\) | − | 5.61472i | − | 0.236422i | ||||||
\(565\) | −24.0125 | + | 8.00416i | −1.01021 | + | 0.336738i | ||||
\(566\) | 12.2510i | 0.514946i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.03188 | + | 4.03188i | 0.169174 | + | 0.169174i | ||||
\(569\) | 17.0956i | 0.716686i | 0.933590 | + | 0.358343i | \(0.116658\pi\) | ||||
−0.933590 | + | 0.358343i | \(0.883342\pi\) | |||||||
\(570\) | −1.17157 | − | 0.585786i | −0.0490718 | − | 0.0245359i | ||||
\(571\) | −26.9442 | −1.12758 | −0.563789 | − | 0.825919i | \(-0.690657\pi\) | ||||
−0.563789 | + | 0.825919i | \(0.690657\pi\) | |||||||
\(572\) | 5.95786 | + | 5.95786i | 0.249111 | + | 0.249111i | ||||
\(573\) | −15.6291 | + | 15.6291i | −0.652917 | + | 0.652917i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | + | 21.0000i | −0.125109 | + | 0.875761i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 32.1914 | + | 32.1914i | 1.34014 | + | 1.34014i | 0.895911 | + | 0.444233i | \(0.146524\pi\) |
0.444233 | + | 0.895911i | \(0.353476\pi\) | |||||||
\(578\) | 1.32477 | + | 1.32477i | 0.0551031 | + | 0.0551031i | ||||
\(579\) | −9.27452 | −0.385436 | ||||||||
\(580\) | −4.24558 | + | 8.49117i | −0.176288 | + | 0.352577i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.2848 | − | 12.2848i | 0.509220 | − | 0.509220i | ||||
\(583\) | −10.6554 | − | 10.6554i | −0.441303 | − | 0.441303i | ||||
\(584\) | −9.17574 | −0.379695 | ||||||||
\(585\) | −11.7905 | + | 3.93015i | −0.487475 | + | 0.162492i | ||||
\(586\) | 19.6755i | 0.812789i | ||||||||
\(587\) | 1.07695 | + | 1.07695i | 0.0444507 | + | 0.0444507i | 0.728983 | − | 0.684532i | \(-0.239993\pi\) |
−0.684532 | + | 0.728983i | \(0.739993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.14386i | − | 0.253153i | ||||||
\(590\) | 0.515938 | + | 1.54781i | 0.0212408 | + | 0.0637225i | ||||
\(591\) | 9.22944i | 0.379648i | ||||||||
\(592\) | −1.55599 | + | 1.55599i | −0.0639509 | + | 0.0639509i | ||||
\(593\) | 10.0371 | − | 10.0371i | 0.412175 | − | 0.412175i | −0.470321 | − | 0.882496i | \(-0.655862\pi\) |
0.882496 | + | 0.470321i | \(0.155862\pi\) | |||||||
\(594\) | 1.51594 | 0.0621997 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.20955 | 0.131468 | ||||||||
\(597\) | 9.21873 | − | 9.21873i | 0.377298 | − | 0.377298i | ||||
\(598\) | 16.6742 | − | 16.6742i | 0.681860 | − | 0.681860i | ||||
\(599\) | − | 2.76021i | − | 0.112779i | −0.998409 | − | 0.0563897i | \(-0.982041\pi\) | ||
0.998409 | − | 0.0563897i | \(-0.0179589\pi\) | |||||||
\(600\) | −3.00000 | − | 4.00000i | −0.122474 | − | 0.163299i | ||||
\(601\) | 26.7656i | 1.09179i | 0.837853 | + | 0.545896i | \(0.183811\pi\) | ||||
−0.837853 | + | 0.545896i | \(0.816189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.93223 | + | 9.93223i | 0.404472 | + | 0.404472i | ||||
\(604\) | − | 12.4503i | − | 0.506594i | ||||||
\(605\) | 8.70193 | − | 17.4039i | 0.353784 | − | 0.707568i | ||||
\(606\) | 7.70193 | 0.312870 | ||||||||
\(607\) | −26.6858 | − | 26.6858i | −1.08314 | − | 1.08314i | −0.996215 | − | 0.0869281i | \(-0.972295\pi\) |
−0.0869281 | − | 0.996215i | \(-0.527705\pi\) | |||||||
\(608\) | −0.414214 | + | 0.414214i | −0.0167986 | + | 0.0167986i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.43158 | + | 2.14386i | −0.260407 | + | 0.0868023i | ||||
\(611\) | 31.2070 | 1.26250 | ||||||||
\(612\) | 3.07193 | + | 3.07193i | 0.124175 | + | 0.124175i | ||||
\(613\) | 1.98635 | + | 1.98635i | 0.0802280 | + | 0.0802280i | 0.746082 | − | 0.665854i | \(-0.231933\pi\) |
−0.665854 | + | 0.746082i | \(0.731933\pi\) | |||||||
\(614\) | −19.1161 | −0.771465 | ||||||||
\(615\) | 14.1889 | − | 4.72965i | 0.572153 | − | 0.190718i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.64243 | − | 5.64243i | 0.227156 | − | 0.227156i | −0.584348 | − | 0.811503i | \(-0.698650\pi\) |
0.811503 | + | 0.584348i | \(0.198650\pi\) | |||||||
\(618\) | 3.17157 | + | 3.17157i | 0.127579 | + | 0.127579i | ||||
\(619\) | −17.7393 | −0.713002 | −0.356501 | − | 0.934295i | \(-0.616030\pi\) | ||||
−0.356501 | + | 0.934295i | \(0.616030\pi\) | |||||||
\(620\) | 10.4882 | − | 20.9764i | 0.421217 | − | 0.842434i | ||||
\(621\) | − | 4.24264i | − | 0.170251i | ||||||
\(622\) | 16.6508 | + | 16.6508i | 0.667635 | + | 0.667635i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.55807i | 0.222501i | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | − | 12.1480i | − | 0.485533i | ||||||
\(627\) | −0.627922 | + | 0.627922i | −0.0250768 | + | 0.0250768i | ||||
\(628\) | 1.07107 | − | 1.07107i | 0.0427403 | − | 0.0427403i | ||||
\(629\) | −9.55980 | −0.381174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.5660 | −1.61491 | −0.807453 | − | 0.589932i | \(-0.799155\pi\) | ||||
−0.807453 | + | 0.589932i | \(0.799155\pi\) | |||||||
\(632\) | 4.72965 | − | 4.72965i | 0.188135 | − | 0.188135i | ||||
\(633\) | 16.7350 | − | 16.7350i | 0.665158 | − | 0.665158i | ||||
\(634\) | − | 19.0897i | − | 0.758150i | ||||||
\(635\) | 11.7019 | + | 35.1058i | 0.464377 | + | 1.39313i | ||||
\(636\) | − | 9.94041i | − | 0.394163i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.55097 | + | 4.55097i | 0.180175 | + | 0.180175i | ||||
\(639\) | 5.70193i | 0.225565i | ||||||||
\(640\) | −2.12132 | + | 0.707107i | −0.0838525 | + | 0.0279508i | ||||
\(641\) | −39.9529 | −1.57804 | −0.789022 | − | 0.614365i | \(-0.789412\pi\) | ||||
−0.789022 | + | 0.614365i | \(0.789412\pi\) | |||||||
\(642\) | 0.687511 | + | 0.687511i | 0.0271339 | + | 0.0271339i | ||||
\(643\) | 22.1612 | − | 22.1612i | 0.873953 | − | 0.873953i | −0.118947 | − | 0.992901i | \(-0.537952\pi\) |
0.992901 | + | 0.118947i | \(0.0379519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.41716 | + | 10.8343i | −0.213300 | + | 0.426601i | ||||
\(646\) | −2.54487 | −0.100127 | ||||||||
\(647\) | −10.1737 | − | 10.1737i | −0.399968 | − | 0.399968i | 0.478254 | − | 0.878222i | \(-0.341270\pi\) |
−0.878222 | + | 0.478254i | \(0.841270\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 1.10610 | 0.0434181 | ||||||||
\(650\) | 22.2323 | − | 16.6742i | 0.872022 | − | 0.654017i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.44523 | − | 9.44523i | 0.369904 | − | 0.369904i | ||||
\(653\) | −6.28478 | − | 6.28478i | −0.245942 | − | 0.245942i | 0.573361 | − | 0.819303i | \(-0.305639\pi\) |
−0.819303 | + | 0.573361i | \(0.805639\pi\) | |||||||
\(654\) | 5.80071 | 0.226826 | ||||||||
\(655\) | −9.85442 | − | 4.92721i | −0.385044 | − | 0.192522i | ||||
\(656\) | − | 6.68873i | − | 0.261151i | ||||||
\(657\) | −6.48822 | − | 6.48822i | −0.253130 | − | 0.253130i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 14.7801i | − | 0.575751i | −0.957668 | − | 0.287876i | \(-0.907051\pi\) | ||
0.957668 | − | 0.287876i | \(-0.0929490\pi\) | |||||||
\(660\) | −3.21579 | + | 1.07193i | −0.125174 | + | 0.0417248i | ||||
\(661\) | − | 20.4995i | − | 0.797338i | −0.917095 | − | 0.398669i | \(-0.869472\pi\) | ||
0.917095 | − | 0.398669i | \(-0.130528\pi\) | |||||||
\(662\) | −3.12944 | + | 3.12944i | −0.121629 | + | 0.121629i | ||||
\(663\) | −17.0740 | + | 17.0740i | −0.663100 | + | 0.663100i | ||||
\(664\) | 14.2877 | 0.554471 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.20051 | −0.0852678 | ||||||||
\(667\) | 12.7368 | − | 12.7368i | 0.493169 | − | 0.493169i | ||||
\(668\) | 7.59081 | − | 7.59081i | 0.293697 | − | 0.293697i | ||||
\(669\) | 8.20761i | 0.317325i | ||||||||
\(670\) | −28.0926 | − | 14.0463i | −1.08531 | − | 0.542656i | ||||
\(671\) | 4.59613i | 0.177432i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.5068 | − | 24.5068i | −0.944668 | − | 0.944668i | 0.0538794 | − | 0.998547i | \(-0.482841\pi\) |
−0.998547 | + | 0.0538794i | \(0.982841\pi\) | |||||||
\(674\) | 6.72548i | 0.259056i | ||||||||
\(675\) | 0.707107 | − | 4.94975i | 0.0272166 | − | 0.190516i | ||||
\(676\) | −17.8922 | −0.688161 | ||||||||
\(677\) | −2.75564 | − | 2.75564i | −0.105908 | − | 0.105908i | 0.652167 | − | 0.758075i | \(-0.273860\pi\) |
−0.758075 | + | 0.652167i | \(0.773860\pi\) | |||||||
\(678\) | −8.00416 | + | 8.00416i | −0.307398 | + | 0.307398i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.68873 | − | 4.34436i | −0.333198 | − | 0.166599i | ||||
\(681\) | 4.34558 | 0.166523 | ||||||||
\(682\) | −11.2426 | − | 11.2426i | −0.430503 | − | 0.430503i | ||||
\(683\) | −33.1782 | − | 33.1782i | −1.26953 | − | 1.26953i | −0.946332 | − | 0.323195i | \(-0.895243\pi\) |
−0.323195 | − | 0.946332i | \(-0.604757\pi\) | |||||||
\(684\) | −0.585786 | −0.0223981 | ||||||||
\(685\) | −8.21787 | − | 24.6536i | −0.313989 | − | 0.941966i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.8718 | + | 20.8718i | −0.796308 | + | 0.796308i | ||||
\(688\) | 3.83051 | + | 3.83051i | 0.146037 | + | 0.146037i | ||||
\(689\) | 55.2495 | 2.10484 | ||||||||
\(690\) | 3.00000 | + | 9.00000i | 0.114208 | + | 0.342624i | ||||
\(691\) | 29.1671i | 1.10957i | 0.831994 | + | 0.554785i | \(0.187199\pi\) | ||||
−0.831994 | + | 0.554785i | \(0.812801\pi\) | |||||||
\(692\) | 15.7875 | + | 15.7875i | 0.600151 | + | 0.600151i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.0662i | 1.14130i | ||||||||
\(695\) | −18.0475 | + | 36.0950i | −0.684581 | + | 1.36916i | ||||
\(696\) | 4.24558i | 0.160928i | ||||||||
\(697\) | 20.5473 | − | 20.5473i | 0.778285 | − | 0.778285i | ||||
\(698\) | 4.13970 | − | 4.13970i | 0.156690 | − | 0.156690i | ||||
\(699\) | 4.48284 | 0.169557 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.2203 | −1.93456 | −0.967282 | − | 0.253703i | \(-0.918351\pi\) | ||||
−0.967282 | + | 0.253703i | \(0.918351\pi\) | |||||||
\(702\) | −3.93015 | + | 3.93015i | −0.148334 | + | 0.148334i | ||||
\(703\) | 0.911479 | − | 0.911479i | 0.0343771 | − | 0.0343771i | ||||
\(704\) | 1.51594i | 0.0571341i | ||||||||
\(705\) | −5.61472 | + | 11.2294i | −0.211463 | + | 0.422925i | ||||
\(706\) | 32.5503i | 1.22504i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.515938 | + | 0.515938i | 0.0193901 | + | 0.0193901i | ||||
\(709\) | 21.4080i | 0.803995i | 0.915641 | + | 0.401998i | \(0.131684\pi\) | ||||
−0.915641 | + | 0.401998i | \(0.868316\pi\) | |||||||
\(710\) | −4.03188 | − | 12.0956i | −0.151314 | − | 0.453941i | ||||
\(711\) | 6.68873 | 0.250847 | ||||||||
\(712\) | 12.7309 | + | 12.7309i | 0.477109 | + | 0.477109i | ||||
\(713\) | −31.4647 | + | 31.4647i | −1.17836 | + | 1.17836i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.95786 | − | 17.8736i | −0.222811 | − | 0.668434i | ||||
\(716\) | 8.42447 | 0.314837 | ||||||||
\(717\) | −19.8326 | − | 19.8326i | −0.740662 | − | 0.740662i | ||||
\(718\) | 8.61766 | + | 8.61766i | 0.321608 | + | 0.321608i | ||||
\(719\) | 28.1380 | 1.04937 | 0.524685 | − | 0.851297i | \(-0.324183\pi\) | ||||
0.524685 | + | 0.851297i | \(0.324183\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.1924 | + | 13.1924i | −0.490970 | + | 0.490970i | ||||
\(723\) | 11.8685 | + | 11.8685i | 0.441394 | + | 0.441394i | ||||
\(724\) | 8.42742 | 0.313202 | ||||||||
\(725\) | 16.9823 | − | 12.7368i | 0.630708 | − | 0.473031i | ||||
\(726\) | − | 8.70193i | − | 0.322959i | ||||||
\(727\) | −14.1426 | − | 14.1426i | −0.524522 | − | 0.524522i | 0.394412 | − | 0.918934i | \(-0.370948\pi\) |
−0.918934 | + | 0.394412i | \(0.870948\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 18.3515 | + | 9.17574i | 0.679218 | + | 0.339609i | ||||
\(731\) | 23.5341i | 0.870440i | ||||||||
\(732\) | −2.14386 | + | 2.14386i | −0.0792393 | + | 0.0792393i | ||||
\(733\) | −34.2919 | + | 34.2919i | −1.26660 | + | 1.26660i | −0.318766 | + | 0.947833i | \(0.603268\pi\) |
−0.947833 | + | 0.318766i | \(0.896732\pi\) | |||||||
\(734\) | −23.9983 | −0.885793 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.24264 | 0.156386 | ||||||||
\(737\) | −15.0566 | + | 15.0566i | −0.554619 | + | 0.554619i | ||||
\(738\) | 4.72965 | − | 4.72965i | 0.174101 | − | 0.174101i | ||||
\(739\) | 12.9518i | 0.476438i | 0.971211 | + | 0.238219i | \(0.0765637\pi\) | ||||
−0.971211 | + | 0.238219i | \(0.923436\pi\) | |||||||
\(740\) | 4.66798 | − | 1.55599i | 0.171598 | − | 0.0571994i | ||||
\(741\) | − | 3.25584i | − | 0.119606i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.2558 | − | 11.2558i | −0.412937 | − | 0.412937i | 0.469824 | − | 0.882760i | \(-0.344318\pi\) |
−0.882760 | + | 0.469824i | \(0.844318\pi\) | |||||||
\(744\) | − | 10.4882i | − | 0.384517i | ||||||
\(745\) | −6.41909 | − | 3.20955i | −0.235177 | − | 0.117589i | ||||
\(746\) | 0.424474 | 0.0155411 | ||||||||
\(747\) | 10.1029 | + | 10.1029i | 0.369647 | + | 0.369647i | ||||
\(748\) | −4.65685 | + | 4.65685i | −0.170271 | + | 0.170271i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.00000 | + | 11.0000i | 0.0730297 | + | 0.401663i | ||||
\(751\) | 4.13351 | 0.150834 | 0.0754170 | − | 0.997152i | \(-0.475971\pi\) | ||||
0.0754170 | + | 0.997152i | \(0.475971\pi\) | |||||||
\(752\) | 3.97021 | + | 3.97021i | 0.144779 | + | 0.144779i | ||||
\(753\) | −1.41005 | − | 1.41005i | −0.0513851 | − | 0.0513851i | ||||
\(754\) | −23.5973 | −0.859362 | ||||||||
\(755\) | −12.4503 | + | 24.9005i | −0.453111 | + | 0.906222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.98341 | − | 3.98341i | 0.144779 | − | 0.144779i | −0.631002 | − | 0.775781i | \(-0.717356\pi\) |
0.775781 | + | 0.631002i | \(0.217356\pi\) | |||||||
\(758\) | 2.10000 | + | 2.10000i | 0.0762754 | + | 0.0762754i | ||||
\(759\) | 6.43158 | 0.233452 | ||||||||
\(760\) | 1.24264 | − | 0.414214i | 0.0450753 | − | 0.0150251i | ||||
\(761\) | − | 2.88974i | − | 0.104753i | −0.998627 | − | 0.0523765i | \(-0.983320\pi\) | ||
0.998627 | − | 0.0523765i | \(-0.0166796\pi\) | |||||||
\(762\) | 11.7019 | + | 11.7019i | 0.423916 | + | 0.423916i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 22.1029i | − | 0.799656i | ||||||
\(765\) | −3.07193 | − | 9.21579i | −0.111066 | − | 0.333198i | ||||
\(766\) | 16.0958i | 0.581566i | ||||||||
\(767\) | −2.86762 | + | 2.86762i | −0.103544 | + | 0.103544i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −18.3818 | −0.662866 | −0.331433 | − | 0.943479i | \(-0.607532\pi\) | ||||
−0.331433 | + | 0.943479i | \(0.607532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.6044 | 1.06618 | ||||||||
\(772\) | 6.55807 | − | 6.55807i | 0.236030 | − | 0.236030i | ||||
\(773\) | 13.6701 | − | 13.6701i | 0.491678 | − | 0.491678i | −0.417157 | − | 0.908835i | \(-0.636973\pi\) |
0.908835 | + | 0.417157i | \(0.136973\pi\) | |||||||
\(774\) | 5.41716i | 0.194716i | ||||||||
\(775\) | −41.9529 | + | 31.4647i | −1.50699 | + | 1.13024i | ||||
\(776\) | 17.3733i | 0.623665i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.7589 | − | 20.7589i | −0.744244 | − | 0.744244i | ||||
\(779\) | 3.91817i | 0.140383i | ||||||||
\(780\) | 5.55807 | − | 11.1161i | 0.199011 | − | 0.398022i | ||||
\(781\) | −8.64378 | −0.309299 | ||||||||
\(782\) | 13.0331 | + | 13.0331i | 0.466063 | + | 0.466063i | ||||
\(783\) | −3.00208 | + | 3.00208i | −0.107286 | + | 0.107286i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.21320 | + | 1.07107i | −0.114684 | + | 0.0382280i | ||||
\(786\) | −4.92721 | −0.175748 | ||||||||
\(787\) | 24.0083 | + | 24.0083i | 0.855804 | + | 0.855804i | 0.990841 | − | 0.135036i | \(-0.0431151\pi\) |
−0.135036 | + | 0.990841i | \(0.543115\pi\) | |||||||
\(788\) | −6.52620 | − | 6.52620i | −0.232486 | − | 0.232486i | ||||
\(789\) | −24.7917 | −0.882607 | ||||||||
\(790\) | −14.1889 | + | 4.72965i | −0.504820 | + | 0.168273i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.07193 | + | 1.07193i | −0.0380894 | + | 0.0380894i | ||||
\(793\) | −11.9157 | − | 11.9157i | −0.423140 | − | 0.423140i | ||||
\(794\) | 8.82843 | 0.313309 | ||||||||
\(795\) | −9.94041 | + | 19.8808i | −0.352550 | + | 0.705100i | ||||
\(796\) | 13.0373i | 0.462093i | ||||||||
\(797\) | 21.0825 | + | 21.0825i | 0.746782 | + | 0.746782i | 0.973873 | − | 0.227091i | \(-0.0729216\pi\) |
−0.227091 | + | 0.973873i | \(0.572922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.3924i | 0.862941i | ||||||||
\(800\) | 4.94975 | + | 0.707107i | 0.175000 | + | 0.0250000i | ||||
\(801\) | 18.0042i | 0.636146i | ||||||||
\(802\) | −5.08558 | + | 5.08558i | −0.179578 | + | 0.179578i | ||||
\(803\) | 9.83574 | − | 9.83574i | 0.347096 | − | 0.347096i | ||||
\(804\) | −14.0463 | −0.495375 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 58.2943 | 2.05333 | ||||||||
\(807\) | 3.81522 | − | 3.81522i | 0.134302 | − | 0.134302i | ||||
\(808\) | −5.44609 | + | 5.44609i | −0.191593 | + | 0.191593i | ||||
\(809\) | − | 34.3107i | − | 1.20630i | −0.797628 | − | 0.603150i | \(-0.793912\pi\) | ||
0.797628 | − | 0.603150i | \(-0.206088\pi\) | |||||||
\(810\) | −0.707107 | − | 2.12132i | −0.0248452 | − | 0.0745356i | ||||
\(811\) | 23.3563i | 0.820152i | 0.912051 | + | 0.410076i | \(0.134498\pi\) | ||||
−0.912051 | + | 0.410076i | \(0.865502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.55721 | + | 7.55721i | 0.265043 | + | 0.265043i | ||||
\(814\) | − | 3.33583i | − | 0.116921i | ||||||
\(815\) | −28.3357 | + | 9.44523i | −0.992556 | + | 0.330852i | ||||
\(816\) | −4.34436 | −0.152083 | ||||||||
\(817\) | −2.24386 | − | 2.24386i | −0.0785027 | − | 0.0785027i | ||||
\(818\) | 10.3538 | − | 10.3538i | 0.362011 | − | 0.362011i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.68873 | + | 13.3775i | −0.233581 | + | 0.467161i | ||||
\(821\) | 1.61472 | 0.0563541 | 0.0281770 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281770 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(822\) | −8.21787 | − | 8.21787i | −0.286631 | − | 0.286631i | ||||
\(823\) | 7.61350 | + | 7.61350i | 0.265390 | + | 0.265390i | 0.827239 | − | 0.561850i | \(-0.189910\pi\) |
−0.561850 | + | 0.827239i | \(0.689910\pi\) | |||||||
\(824\) | −4.48528 | −0.156252 | ||||||||
\(825\) | 7.50351 | + | 1.07193i | 0.261239 | + | 0.0373198i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.62376 | + | 2.62376i | −0.0912371 | + | 0.0912371i | −0.751252 | − | 0.660015i | \(-0.770550\pi\) |
0.660015 | + | 0.751252i | \(0.270550\pi\) | |||||||
\(828\) | 3.00000 | + | 3.00000i | 0.104257 | + | 0.104257i | ||||
\(829\) | 21.0548 | 0.731265 | 0.365632 | − | 0.930759i | \(-0.380853\pi\) | ||||
0.365632 | + | 0.930759i | \(0.380853\pi\) | |||||||
\(830\) | −28.5754 | − | 14.2877i | −0.991868 | − | 0.495934i | ||||
\(831\) | 16.4286i | 0.569903i | ||||||||
\(832\) | −3.93015 | − | 3.93015i | −0.136253 | − | 0.136253i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.0475i | 0.624934i | ||||||||
\(835\) | −22.7724 | + | 7.59081i | −0.788073 | + | 0.262691i | ||||
\(836\) | − | 0.888016i | − | 0.0307127i | ||||||
\(837\) | 7.41629 | − | 7.41629i | 0.256345 | − | 0.256345i | ||||
\(838\) | 9.65685 | − | 9.65685i | 0.333590 | − | 0.333590i | ||||
\(839\) | 8.08427 | 0.279100 | 0.139550 | − | 0.990215i | \(-0.455434\pi\) | ||||
0.139550 | + | 0.990215i | \(0.455434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9750 | 0.378449 | ||||||||
\(842\) | −14.2480 | + | 14.2480i | −0.491019 | + | 0.491019i | ||||
\(843\) | −1.69777 | + | 1.69777i | −0.0584743 | + | 0.0584743i | ||||
\(844\) | 23.6669i | 0.814648i | ||||||||
\(845\) | 35.7844 | + | 17.8922i | 1.23102 | + | 0.615510i | ||||
\(846\) | 5.61472i | 0.193038i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.02893 | + | 7.02893i | 0.241375 | + | 0.241375i | ||||
\(849\) | − | 12.2510i | − | 0.420452i | ||||||
\(850\) | 13.0331 | + | 17.3775i | 0.447031 | + | 0.596042i | ||||
\(851\) | −9.33595 | −0.320032 | ||||||||
\(852\) | −4.03188 | − | 4.03188i | −0.138130 | − | 0.138130i | ||||
\(853\) | 21.5189 | − | 21.5189i | 0.736792 | − | 0.736792i | −0.235163 | − | 0.971956i | \(-0.575563\pi\) |
0.971956 | + | 0.235163i | \(0.0755625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.17157 | + | 0.585786i | 0.0400669 | + | 0.0200335i | ||||
\(856\) | −0.972287 | −0.0332321 | ||||||||
\(857\) | −4.64157 | − | 4.64157i | −0.158553 | − | 0.158553i | 0.623372 | − | 0.781925i | \(-0.285762\pi\) |
−0.781925 | + | 0.623372i | \(0.785762\pi\) | |||||||
\(858\) | −5.95786 | − | 5.95786i | −0.203398 | − | 0.203398i | ||||
\(859\) | 14.6554 | 0.500037 | 0.250018 | − | 0.968241i | \(-0.419563\pi\) | ||||
0.250018 | + | 0.968241i | \(0.419563\pi\) | |||||||
\(860\) | −3.83051 | − | 11.4915i | −0.130619 | − | 0.391858i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0711 | − | 16.0711i | 0.547383 | − | 0.547383i | ||||
\(863\) | 10.9927 | + | 10.9927i | 0.374195 | + | 0.374195i | 0.869003 | − | 0.494807i | \(-0.164761\pi\) |
−0.494807 | + | 0.869003i | \(0.664761\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −15.7875 | − | 47.3625i | −0.536791 | − | 1.61037i | ||||
\(866\) | 15.1144i | 0.513609i | ||||||||
\(867\) | −1.32477 | − | 1.32477i | −0.0449915 | − | 0.0449915i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1397i | 0.343966i | ||||||||
\(870\) | 4.24558 | − | 8.49117i | 0.143939 | − | 0.287878i | ||||
\(871\) | − | 78.0704i | − | 2.64531i | ||||||
\(872\) | −4.10172 | + | 4.10172i | −0.138902 | + | 0.138902i | ||||
\(873\) | −12.2848 | + | 12.2848i | −0.415777 | + | 0.415777i | ||||
\(874\) | −2.48528 | −0.0840659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.17574 | 0.310019 | ||||||||
\(877\) | 25.1269 | − | 25.1269i | 0.848473 | − | 0.848473i | −0.141469 | − | 0.989943i | \(-0.545183\pi\) |
0.989943 | + | 0.141469i | \(0.0451826\pi\) | |||||||
\(878\) | 19.2795 | − | 19.2795i | 0.650653 | − | 0.650653i | ||||
\(879\) | − | 19.6755i | − | 0.663639i | ||||||
\(880\) | 1.51594 | − | 3.03188i | 0.0511022 | − | 0.102204i | ||||
\(881\) | − | 4.21981i | − | 0.142169i | −0.997470 | − | 0.0710844i | \(-0.977354\pi\) | ||
0.997470 | − | 0.0710844i | \(-0.0226460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.79426 | + | 9.79426i | 0.329603 | + | 0.329603i | 0.852435 | − | 0.522832i | \(-0.175125\pi\) |
−0.522832 | + | 0.852435i | \(0.675125\pi\) | |||||||
\(884\) | − | 24.1463i | − | 0.812128i | ||||||
\(885\) | −0.515938 | − | 1.54781i | −0.0173431 | − | 0.0520292i | ||||
\(886\) | −17.1740 | −0.576972 | ||||||||
\(887\) | 16.5513 | + | 16.5513i | 0.555739 | + | 0.555739i | 0.928091 | − | 0.372352i | \(-0.121449\pi\) |
−0.372352 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(888\) | 1.55599 | − | 1.55599i | 0.0522157 | − | 0.0522157i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.7309 | − | 38.1926i | −0.426740 | − | 1.28022i | ||||
\(891\) | −1.51594 | −0.0507858 | ||||||||
\(892\) | −5.80366 | − | 5.80366i | −0.194321 | − | 0.194321i | ||||
\(893\) | −2.32569 | − | 2.32569i | −0.0778263 | − | 0.0778263i | ||||
\(894\) | −3.20955 | −0.107343 | ||||||||
\(895\) | −16.8489 | − | 8.42447i | −0.563198 | − | 0.281599i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.6742 | + | 16.6742i | −0.556736 | + | 0.556736i | ||||
\(898\) | −18.9764 | − | 18.9764i | −0.633252 | − | 0.633252i | ||||
\(899\) | 44.5286 | 1.48511 | ||||||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | 43.1848i | 1.43869i | ||||||||
\(902\) | 7.16985 | + | 7.16985i | 0.238730 | + | 0.238730i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 11.3196i | − | 0.376484i | ||||||
\(905\) | −16.8548 | − | 8.42742i | −0.560274 | − | 0.280137i | ||||
\(906\) | 12.4503i | 0.413632i | ||||||||
\(907\) | −7.46747 | + | 7.46747i | −0.247953 | + | 0.247953i | −0.820130 | − | 0.572177i | \(-0.806099\pi\) |
0.572177 | + | 0.820130i | \(0.306099\pi\) | |||||||
\(908\) | −3.07279 | + | 3.07279i | −0.101974 | + | 0.101974i | ||||
\(909\) | −7.70193 | −0.255457 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8940 | 0.625987 | 0.312994 | − | 0.949755i | \(-0.398668\pi\) | ||||
0.312994 | + | 0.949755i | \(0.398668\pi\) | |||||||
\(912\) | 0.414214 | − | 0.414214i | 0.0137160 | − | 0.0137160i | ||||
\(913\) | −15.3154 | + | 15.3154i | −0.506867 | + | 0.506867i | ||||
\(914\) | 27.1373i | 0.897621i | ||||||||
\(915\) | 6.43158 | − | 2.14386i | 0.212621 | − | 0.0708738i | ||||
\(916\) | − | 29.5172i | − | 0.975274i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.07193 | − | 3.07193i | −0.101389 | − | 0.101389i | ||||
\(919\) | − | 7.16295i | − | 0.236284i | −0.992997 | − | 0.118142i | \(-0.962306\pi\) | ||
0.992997 | − | 0.118142i | \(-0.0376938\pi\) | |||||||
\(920\) | −8.48528 | − | 4.24264i | −0.279751 | − | 0.139876i | ||||
\(921\) | 19.1161 | 0.629898 | ||||||||
\(922\) | −23.1799 | − | 23.1799i | −0.763389 | − | 0.763389i | ||||
\(923\) | 22.4095 | − | 22.4095i | 0.737616 | − | 0.737616i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8919 | − | 1.55599i | −0.358125 | − | 0.0511607i | ||||
\(926\) | 36.9789 | 1.21520 | ||||||||
\(927\) | −3.17157 | − | 3.17157i | −0.104168 | − | 0.104168i | ||||
\(928\) | −3.00208 | − | 3.00208i | −0.0985481 | − | 0.0985481i | ||||
\(929\) | −3.95046 | −0.129610 | −0.0648052 | − | 0.997898i | \(-0.520643\pi\) | ||||
−0.0648052 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(930\) | −10.4882 | + | 20.9764i | −0.343922 | + | 0.687845i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.16985 | + | 3.16985i | −0.103832 | + | 0.103832i | ||||
\(933\) | −16.6508 | − | 16.6508i | −0.545121 | − | 0.545121i | ||||
\(934\) | −2.13970 | −0.0700130 | ||||||||
\(935\) | 13.9706 | − | 4.65685i | 0.456886 | − | 0.152295i | ||||
\(936\) | − | 5.55807i | − | 0.181671i | ||||||
\(937\) | 8.50152 | + | 8.50152i | 0.277732 | + | 0.277732i | 0.832203 | − | 0.554471i | \(-0.187079\pi\) |
−0.554471 | + | 0.832203i | \(0.687079\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.1480i | 0.396436i | ||||||||
\(940\) | −3.97021 | − | 11.9106i | −0.129494 | − | 0.388481i | ||||
\(941\) | 22.7015i | 0.740048i | 0.929022 | + | 0.370024i | \(0.120651\pi\) | ||||
−0.929022 | + | 0.370024i | \(0.879349\pi\) | |||||||
\(942\) | −1.07107 | + | 1.07107i | −0.0348973 | + | 0.0348973i | ||||
\(943\) | 20.0662 | − | 20.0662i | 0.653445 | − | 0.653445i | ||||
\(944\) | −0.729646 | −0.0237480 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.21207 | −0.266997 | ||||||||
\(947\) | −17.4593 | + | 17.4593i | −0.567351 | + | 0.567351i | −0.931385 | − | 0.364035i | \(-0.881399\pi\) |
0.364035 | + | 0.931385i | \(0.381399\pi\) | |||||||
\(948\) | −4.72965 | + | 4.72965i | −0.153612 | + | 0.153612i | ||||
\(949\) | 50.9994i | 1.65551i | ||||||||
\(950\) | −2.89949 | − | 0.414214i | −0.0940720 | − | 0.0134389i | ||||
\(951\) | 19.0897i | 0.619027i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.99390 | − | 9.99390i | −0.323734 | − | 0.323734i | 0.526463 | − | 0.850198i | \(-0.323518\pi\) |
−0.850198 | + | 0.526463i | \(0.823518\pi\) | |||||||
\(954\) | 9.94041i | 0.321833i | ||||||||
\(955\) | −22.1029 | + | 44.2059i | −0.715234 | + | 1.43047i | ||||
\(956\) | 28.0475 | 0.907122 | ||||||||
\(957\) | −4.55097 | − | 4.55097i | −0.147112 | − | 0.147112i | ||||
\(958\) | 6.04214 | − | 6.04214i | 0.195213 | − | 0.195213i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.12132 | − | 0.707107i | 0.0684653 | − | 0.0228218i | ||||
\(961\) | −79.0029 | −2.54848 | ||||||||
\(962\) | 8.64832 | + | 8.64832i | 0.278833 | + | 0.278833i | ||||
\(963\) | −0.687511 | − | 0.687511i | −0.0221547 | − | 0.0221547i | ||||
\(964\) | −16.7846 | −0.540595 | ||||||||
\(965\) | −19.6742 | + | 6.55807i | −0.633336 | + | 0.211112i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6946 | + | 14.6946i | −0.472547 | + | 0.472547i | −0.902738 | − | 0.430191i | \(-0.858446\pi\) |
0.430191 | + | 0.902738i | \(0.358446\pi\) | |||||||
\(968\) | 6.15320 | + | 6.15320i | 0.197771 | + | 0.197771i | ||||
\(969\) | 2.54487 | 0.0817530 | ||||||||
\(970\) | 17.3733 | − | 34.7466i | 0.557823 | − | 1.11565i | ||||
\(971\) | − | 15.4534i | − | 0.495923i | −0.968770 | − | 0.247962i | \(-0.920239\pi\) | ||
0.968770 | − | 0.247962i | \(-0.0797607\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17.9505i | 0.575170i | ||||||||
\(975\) | −22.2323 | + | 16.6742i | −0.712003 | + | 0.534002i | ||||
\(976\) | − | 3.03188i | − | 0.0970480i | ||||||
\(977\) | 42.9661 | − | 42.9661i | 1.37461 | − | 1.37461i | 0.521130 | − | 0.853477i | \(-0.325511\pi\) |
0.853477 | − | 0.521130i | \(-0.174489\pi\) | |||||||
\(978\) | −9.44523 | + | 9.44523i | −0.302025 | + | 0.302025i | ||||
\(979\) | −27.2932 | −0.872294 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.80071 | −0.185203 | ||||||||
\(982\) | −0.0984240 | + | 0.0984240i | −0.00314084 | + | 0.00314084i | ||||
\(983\) | 14.9541 | − | 14.9541i | 0.476960 | − | 0.476960i | −0.427198 | − | 0.904158i | \(-0.640499\pi\) |
0.904158 | + | 0.427198i | \(0.140499\pi\) | |||||||
\(984\) | 6.68873i | 0.213229i | ||||||||
\(985\) | 6.52620 | + | 19.5786i | 0.207942 | + | 0.623826i | ||||
\(986\) | − | 18.4444i | − | 0.587388i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.30223 | + | 2.30223i | 0.0732437 | + | 0.0732437i | ||||
\(989\) | 22.9830i | 0.730818i | ||||||||
\(990\) | 3.21579 | − | 1.07193i | 0.102204 | − | 0.0340682i | ||||
\(991\) | −55.6939 | −1.76918 | −0.884588 | − | 0.466374i | \(-0.845560\pi\) | ||||
−0.884588 | + | 0.466374i | \(0.845560\pi\) | |||||||
\(992\) | 7.41629 | + | 7.41629i | 0.235468 | + | 0.235468i | ||||
\(993\) | 3.12944 | − | 3.12944i | 0.0993097 | − | 0.0993097i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0373 | − | 26.0745i | 0.413309 | − | 0.826618i | ||||
\(996\) | −14.2877 | −0.452724 | ||||||||
\(997\) | −39.3443 | − | 39.3443i | −1.24605 | − | 1.24605i | −0.957451 | − | 0.288594i | \(-0.906812\pi\) |
−0.288594 | − | 0.957451i | \(-0.593188\pi\) | |||||||
\(998\) | −30.5953 | − | 30.5953i | −0.968478 | − | 0.968478i | ||||
\(999\) | 2.20051 | 0.0696209 |
(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 | 1470.2.m.a.1273.4 | yes | 8 | |
5.2 | odd | 4 | 1470.2.m.b.97.4 | yes | 8 | ||
7.6 | odd | 2 | 1470.2.m.b.1273.4 | yes | 8 | ||
35.27 | even | 4 | inner | 1470.2.m.a.97.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.a.97.4 | ✓ | 8 | 35.27 | even | 4 | inner | |
1470.2.m.a.1273.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1470.2.m.b.97.4 | yes | 8 | 5.2 | odd | 4 | ||
1470.2.m.b.1273.4 | yes | 8 | 7.6 | odd | 2 |