Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(26,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(-0.762262 + 2.34600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.26 |
Dual form | 275.2.h.b.201.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.04238 | + | 1.48388i | 1.44418 | + | 1.04926i | 0.987148 | + | 0.159812i | \(0.0510887\pi\) |
0.457035 | + | 0.889449i | \(0.348911\pi\) | |||||||
\(3\) | 0.762262 | − | 2.34600i | 0.440092 | − | 1.35446i | −0.447685 | − | 0.894191i | \(-0.647751\pi\) |
0.887777 | − | 0.460273i | \(-0.152249\pi\) | |||||||
\(4\) | 1.35140 | + | 4.15918i | 0.675700 | + | 2.07959i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.03801 | − | 3.66033i | 2.05676 | − | 1.49432i | ||||
\(7\) | −0.646930 | − | 1.99105i | −0.244517 | − | 0.752545i | −0.995716 | − | 0.0924689i | \(-0.970524\pi\) |
0.751199 | − | 0.660076i | \(-0.229476\pi\) | |||||||
\(8\) | −1.85140 | + | 5.69802i | −0.654569 | + | 2.01456i | ||||
\(9\) | −2.49563 | − | 1.81318i | −0.831876 | − | 0.604393i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64693 | + | 2.87882i | −0.496568 | + | 0.867998i | ||||
\(12\) | 10.7876 | 3.11410 | ||||||||
\(13\) | 1.04238 | + | 0.757336i | 0.289105 | + | 0.210047i | 0.722879 | − | 0.690975i | \(-0.242818\pi\) |
−0.433774 | + | 0.901022i | \(0.642818\pi\) | |||||||
\(14\) | 1.63319 | − | 5.02644i | 0.436489 | − | 1.34337i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.16042 | + | 3.74926i | −1.29010 | + | 0.937316i | ||||
\(17\) | −2.41998 | + | 1.75822i | −0.586931 | + | 0.426430i | −0.841216 | − | 0.540699i | \(-0.818160\pi\) |
0.254285 | + | 0.967129i | \(0.418160\pi\) | |||||||
\(18\) | −2.40649 | − | 7.40641i | −0.567215 | − | 1.74571i | ||||
\(19\) | 0.664789 | − | 2.04601i | 0.152513 | − | 0.469387i | −0.845387 | − | 0.534154i | \(-0.820630\pi\) |
0.997900 | + | 0.0647668i | \(0.0206304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.16413 | −1.12690 | ||||||||
\(22\) | −7.63548 | + | 3.43582i | −1.62789 | + | 0.732518i | ||||
\(23\) | −8.77882 | −1.83051 | −0.915255 | − | 0.402874i | \(-0.868011\pi\) | ||||
−0.915255 | + | 0.402874i | \(0.868011\pi\) | |||||||
\(24\) | 11.9563 | + | 8.68677i | 2.44057 | + | 1.77318i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00515 | + | 3.09354i | 0.197126 | + | 0.606693i | ||||
\(27\) | −0.169161 | + | 0.122903i | −0.0325550 | + | 0.0236526i | ||||
\(28\) | 7.40686 | − | 5.38140i | 1.39977 | − | 1.01699i | ||||
\(29\) | −0.189313 | − | 0.582646i | −0.0351545 | − | 0.108195i | 0.931939 | − | 0.362614i | \(-0.118116\pi\) |
−0.967094 | + | 0.254419i | \(0.918116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.94887 | + | 2.14248i | 0.529633 | + | 0.384801i | 0.820221 | − | 0.572047i | \(-0.193851\pi\) |
−0.290587 | + | 0.956848i | \(0.593851\pi\) | |||||||
\(32\) | −4.12048 | −0.728405 | ||||||||
\(33\) | 5.49833 | + | 6.05812i | 0.957136 | + | 1.05458i | ||||
\(34\) | −7.55150 | −1.29507 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.16875 | − | 12.8301i | 0.694792 | − | 2.13835i | ||||
\(37\) | 0.578100 | + | 1.77921i | 0.0950391 | + | 0.292500i | 0.987264 | − | 0.159091i | \(-0.0508564\pi\) |
−0.892225 | + | 0.451592i | \(0.850856\pi\) | |||||||
\(38\) | 4.39378 | − | 3.19227i | 0.712766 | − | 0.517855i | ||||
\(39\) | 2.57128 | − | 1.86814i | 0.411734 | − | 0.299142i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.57810 | + | 4.85689i | −0.246458 | + | 0.758519i | 0.748935 | + | 0.662643i | \(0.230565\pi\) |
−0.995393 | + | 0.0958763i | \(0.969435\pi\) | |||||||
\(42\) | −10.5471 | − | 7.66294i | −1.62746 | − | 1.18242i | ||||
\(43\) | −5.17287 | −0.788856 | −0.394428 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394428 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(44\) | −14.1992 | − | 2.95944i | −2.14061 | − | 0.446152i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.9297 | − | 13.0267i | −2.64359 | − | 1.92068i | ||||
\(47\) | 2.25789 | − | 6.94907i | 0.329347 | − | 1.01363i | −0.640093 | − | 0.768298i | \(-0.721104\pi\) |
0.969440 | − | 0.245329i | \(-0.0788959\pi\) | |||||||
\(48\) | 4.86218 | + | 14.9643i | 0.701796 | + | 2.15991i | ||||
\(49\) | 2.11737 | − | 1.53836i | 0.302482 | − | 0.219766i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.28012 | + | 7.01749i | 0.319281 | + | 0.982645i | ||||
\(52\) | −1.74122 | + | 5.35892i | −0.241464 | + | 0.743149i | ||||
\(53\) | −2.38030 | − | 1.72939i | −0.326959 | − | 0.237549i | 0.412180 | − | 0.911102i | \(-0.364767\pi\) |
−0.739139 | + | 0.673553i | \(0.764767\pi\) | |||||||
\(54\) | −0.527864 | −0.0718332 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.5428 | 1.67610 | ||||||||
\(57\) | −4.29320 | − | 3.11919i | −0.568648 | − | 0.413147i | ||||
\(58\) | 0.477925 | − | 1.47090i | 0.0627547 | − | 0.193139i | ||||
\(59\) | −2.00682 | − | 6.17636i | −0.261266 | − | 0.804094i | −0.992530 | − | 0.121999i | \(-0.961069\pi\) |
0.731264 | − | 0.682094i | \(-0.238931\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.406490 | − | 0.295332i | 0.0520457 | − | 0.0378134i | −0.561458 | − | 0.827505i | \(-0.689759\pi\) |
0.613504 | + | 0.789692i | \(0.289759\pi\) | |||||||
\(62\) | 2.84355 | + | 8.75154i | 0.361131 | + | 1.11145i | ||||
\(63\) | −1.99563 | + | 6.14191i | −0.251425 | + | 0.773808i | ||||
\(64\) | 1.90523 | + | 1.38423i | 0.238154 | + | 0.173029i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.24019 | + | 20.5318i | 0.275748 | + | 2.52730i | ||||
\(67\) | 7.80964 | 0.954099 | 0.477050 | − | 0.878876i | \(-0.341706\pi\) | ||||
0.477050 | + | 0.878876i | \(0.341706\pi\) | |||||||
\(68\) | −10.5831 | − | 7.68907i | −1.28339 | − | 0.932437i | ||||
\(69\) | −6.69176 | + | 20.5951i | −0.805594 | + | 2.47936i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.14526 | − | 6.64442i | 1.08534 | − | 0.788548i | 0.106736 | − | 0.994287i | \(-0.465960\pi\) |
0.978607 | + | 0.205740i | \(0.0659600\pi\) | |||||||
\(72\) | 14.9519 | − | 10.8632i | 1.76210 | − | 1.28024i | ||||
\(73\) | 3.43539 | + | 10.5730i | 0.402082 | + | 1.23748i | 0.923308 | + | 0.384061i | \(0.125475\pi\) |
−0.521226 | + | 0.853419i | \(0.674525\pi\) | |||||||
\(74\) | −1.45943 | + | 4.49166i | −0.169655 | + | 0.522145i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.40812 | 1.07919 | ||||||||
\(77\) | 6.79732 | + | 1.41672i | 0.774626 | + | 0.161450i | ||||
\(78\) | 8.02363 | 0.908498 | ||||||||
\(79\) | −4.33558 | − | 3.14998i | −0.487791 | − | 0.354401i | 0.316543 | − | 0.948578i | \(-0.397478\pi\) |
−0.804334 | + | 0.594177i | \(0.797478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.70035 | − | 8.31082i | −0.300039 | − | 0.923425i | ||||
\(82\) | −10.4301 | + | 7.57793i | −1.15181 | + | 0.836842i | ||||
\(83\) | 8.77408 | − | 6.37474i | 0.963080 | − | 0.699719i | 0.00921619 | − | 0.999958i | \(-0.497066\pi\) |
0.953864 | + | 0.300239i | \(0.0970664\pi\) | |||||||
\(84\) | −6.97880 | − | 21.4785i | −0.761450 | − | 2.34350i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.5650 | − | 7.67591i | −1.13925 | − | 0.827715i | ||||
\(87\) | −1.51119 | −0.162017 | ||||||||
\(88\) | −13.3545 | − | 14.7141i | −1.42359 | − | 1.56853i | ||||
\(89\) | −4.32336 | −0.458275 | −0.229137 | − | 0.973394i | \(-0.573591\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.833541 | − | 2.56538i | 0.0873788 | − | 0.268924i | ||||
\(92\) | −11.8637 | − | 36.5127i | −1.23688 | − | 3.80671i | ||||
\(93\) | 7.27408 | − | 5.28493i | 0.754287 | − | 0.548021i | ||||
\(94\) | 14.9230 | − | 10.8422i | 1.53920 | − | 1.11829i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.14089 | + | 9.66666i | −0.320566 | + | 0.986599i | ||||
\(97\) | −0.284493 | − | 0.206696i | −0.0288859 | − | 0.0209868i | 0.573249 | − | 0.819381i | \(-0.305683\pi\) |
−0.602135 | + | 0.798395i | \(0.705683\pi\) | |||||||
\(98\) | 6.60723 | 0.667431 | ||||||||
\(99\) | 9.32995 | − | 4.19829i | 0.937695 | − | 0.421944i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7011 | + | 9.22791i | 1.26381 | + | 0.918211i | 0.998938 | − | 0.0460722i | \(-0.0146704\pi\) |
0.264872 | + | 0.964284i | \(0.414670\pi\) | |||||||
\(102\) | −5.75622 | + | 17.7158i | −0.569951 | + | 1.75413i | ||||
\(103\) | −2.06420 | − | 6.35297i | −0.203392 | − | 0.625977i | −0.999776 | − | 0.0211846i | \(-0.993256\pi\) |
0.796383 | − | 0.604792i | \(-0.206744\pi\) | |||||||
\(104\) | −6.24518 | + | 4.53739i | −0.612391 | + | 0.444928i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.29528 | − | 7.06414i | −0.222937 | − | 0.686130i | ||||
\(107\) | −4.82313 | + | 14.8441i | −0.466269 | + | 1.43503i | 0.391110 | + | 0.920344i | \(0.372091\pi\) |
−0.857379 | + | 0.514685i | \(0.827909\pi\) | |||||||
\(108\) | −0.739779 | − | 0.537481i | −0.0711852 | − | 0.0517191i | ||||
\(109\) | 11.5070 | 1.10217 | 0.551087 | − | 0.834448i | \(-0.314213\pi\) | ||||
0.551087 | + | 0.834448i | \(0.314213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.61469 | 0.438007 | ||||||||
\(112\) | 10.8034 | + | 7.84912i | 1.02082 | + | 0.741672i | ||||
\(113\) | −2.79606 | + | 8.60538i | −0.263031 | + | 0.809526i | 0.729110 | + | 0.684397i | \(0.239934\pi\) |
−0.992140 | + | 0.125129i | \(0.960066\pi\) | |||||||
\(114\) | −4.13986 | − | 12.7412i | −0.387733 | − | 1.19332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.16749 | − | 1.57477i | 0.201246 | − | 0.146214i | ||||
\(117\) | −1.22821 | − | 3.78006i | −0.113548 | − | 0.349466i | ||||
\(118\) | 5.06627 | − | 15.5924i | 0.466388 | − | 1.43539i | ||||
\(119\) | 5.06625 | + | 3.68084i | 0.464422 | + | 0.337422i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.57524 | − | 9.48244i | −0.506840 | − | 0.862040i | ||||
\(122\) | 1.26845 | 0.114840 | ||||||||
\(123\) | 10.1914 | + | 7.40445i | 0.918923 | + | 0.667637i | ||||
\(124\) | −4.92586 | + | 15.1602i | −0.442356 | + | 1.36143i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.1897 | + | 9.58287i | −1.17503 | + | 0.853710i | ||||
\(127\) | 15.2371 | − | 11.0704i | 1.35207 | − | 0.982339i | 0.353169 | − | 0.935560i | \(-0.385104\pi\) |
0.998905 | − | 0.0467796i | \(-0.0148959\pi\) | |||||||
\(128\) | 4.38378 | + | 13.4919i | 0.387475 | + | 1.19252i | ||||
\(129\) | −3.94308 | + | 12.1356i | −0.347169 | + | 1.06848i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.0997 | −1.75612 | −0.878058 | − | 0.478555i | \(-0.841161\pi\) | ||||
−0.878058 | + | 0.478555i | \(0.841161\pi\) | |||||||
\(132\) | −17.7664 | + | 31.0555i | −1.54636 | + | 2.70303i | ||||
\(133\) | −4.50377 | −0.390527 | ||||||||
\(134\) | 15.9503 | + | 11.5886i | 1.37789 | + | 1.00110i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.53801 | − | 17.0442i | −0.474881 | − | 1.46153i | ||||
\(137\) | −14.5390 | + | 10.5632i | −1.24215 | + | 0.902478i | −0.997740 | − | 0.0671930i | \(-0.978596\pi\) |
−0.244414 | + | 0.969671i | \(0.578596\pi\) | |||||||
\(138\) | −44.2278 | + | 32.1334i | −3.76492 | + | 2.73537i | ||||
\(139\) | 5.21098 | + | 16.0377i | 0.441989 | + | 1.36030i | 0.885752 | + | 0.464159i | \(0.153643\pi\) |
−0.443762 | + | 0.896145i | \(0.646357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.5814 | − | 10.5940i | −1.22798 | − | 0.892178i | ||||
\(142\) | 28.5376 | 2.39482 | ||||||||
\(143\) | −3.89697 | + | 1.75356i | −0.325881 | + | 0.146640i | ||||
\(144\) | 19.6766 | 1.63971 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.67272 | + | 26.6919i | −0.717759 | + | 2.20904i | ||||
\(147\) | −1.99500 | − | 6.13999i | −0.164545 | − | 0.506418i | ||||
\(148\) | −6.61881 | + | 4.80885i | −0.544063 | + | 0.395285i | ||||
\(149\) | −1.88797 | + | 1.37169i | −0.154669 | + | 0.112373i | −0.662428 | − | 0.749126i | \(-0.730474\pi\) |
0.507759 | + | 0.861499i | \(0.330474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.21718 | + | 3.74609i | −0.0990525 | + | 0.304852i | −0.988289 | − | 0.152596i | \(-0.951237\pi\) |
0.889236 | + | 0.457448i | \(0.151237\pi\) | |||||||
\(152\) | 10.4274 | + | 7.57597i | 0.845776 | + | 0.614492i | ||||
\(153\) | 9.22732 | 0.745985 | ||||||||
\(154\) | 11.7805 | + | 12.9799i | 0.949299 | + | 1.04595i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.2448 | + | 8.16981i | 0.900302 | + | 0.654108i | ||||
\(157\) | 1.50834 | − | 4.64218i | 0.120378 | − | 0.370486i | −0.872652 | − | 0.488342i | \(-0.837602\pi\) |
0.993031 | + | 0.117856i | \(0.0376020\pi\) | |||||||
\(158\) | −4.18073 | − | 12.8669i | −0.332601 | − | 1.02364i | ||||
\(159\) | −5.87155 | + | 4.26593i | −0.465644 | + | 0.338310i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.67928 | + | 17.4790i | 0.447590 | + | 1.37754i | ||||
\(162\) | 6.81710 | − | 20.9809i | 0.535602 | − | 1.64841i | ||||
\(163\) | −5.69202 | − | 4.13549i | −0.445833 | − | 0.323917i | 0.342115 | − | 0.939658i | \(-0.388857\pi\) |
−0.787948 | + | 0.615741i | \(0.788857\pi\) | |||||||
\(164\) | −22.3333 | −1.74394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.3794 | 2.12505 | ||||||||
\(167\) | 8.67223 | + | 6.30075i | 0.671078 | + | 0.487566i | 0.870386 | − | 0.492370i | \(-0.163869\pi\) |
−0.199308 | + | 0.979937i | \(0.563869\pi\) | |||||||
\(168\) | 9.56086 | − | 29.4253i | 0.737637 | − | 2.27021i | ||||
\(169\) | −3.50422 | − | 10.7849i | −0.269555 | − | 0.829605i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.36885 | + | 3.90070i | −0.410566 | + | 0.298294i | ||||
\(172\) | −6.99062 | − | 21.5149i | −0.533030 | − | 1.64050i | ||||
\(173\) | −2.59940 | + | 8.00012i | −0.197628 | + | 0.608238i | 0.802307 | + | 0.596911i | \(0.203605\pi\) |
−0.999936 | + | 0.0113267i | \(0.996395\pi\) | |||||||
\(174\) | −3.08644 | − | 2.24243i | −0.233982 | − | 0.169998i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.29462 | − | 21.0307i | −0.172963 | − | 1.58525i | ||||
\(177\) | −16.0195 | −1.20410 | ||||||||
\(178\) | −8.82995 | − | 6.41533i | −0.661833 | − | 0.480850i | ||||
\(179\) | 6.50062 | − | 20.0069i | 0.485879 | − | 1.49538i | −0.344824 | − | 0.938667i | \(-0.612061\pi\) |
0.830703 | − | 0.556716i | \(-0.187939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41020 | − | 1.02457i | 0.104819 | − | 0.0761557i | −0.534141 | − | 0.845395i | \(-0.679365\pi\) |
0.638960 | + | 0.769240i | \(0.279365\pi\) | |||||||
\(182\) | 5.50911 | − | 4.00261i | 0.408363 | − | 0.296693i | ||||
\(183\) | −0.382998 | − | 1.17875i | −0.0283120 | − | 0.0871355i | ||||
\(184\) | 16.2531 | − | 50.0219i | 1.19820 | − | 3.68767i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 22.6986 | 1.66435 | ||||||||
\(187\) | −1.07606 | − | 9.86234i | −0.0786893 | − | 0.721206i | ||||
\(188\) | 31.9538 | 2.33047 | ||||||||
\(189\) | 0.354140 | + | 0.257298i | 0.0257599 | + | 0.0187157i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.00771200 | + | 0.0237351i | 0.000558021 | + | 0.00171741i | 0.951335 | − | 0.308158i | \(-0.0997126\pi\) |
−0.950777 | + | 0.309876i | \(0.899713\pi\) | |||||||
\(192\) | 4.69969 | − | 3.41452i | 0.339171 | − | 0.246422i | ||||
\(193\) | 1.17894 | − | 0.856548i | 0.0848618 | − | 0.0616557i | −0.544545 | − | 0.838731i | \(-0.683298\pi\) |
0.629407 | + | 0.777076i | \(0.283298\pi\) | |||||||
\(194\) | −0.274331 | − | 0.844306i | −0.0196959 | − | 0.0606176i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.25974 | + | 6.72759i | 0.661410 | + | 0.480542i | ||||
\(197\) | −22.7027 | −1.61750 | −0.808751 | − | 0.588151i | \(-0.799856\pi\) | ||||
−0.808751 | + | 0.588151i | \(0.799856\pi\) | |||||||
\(198\) | 25.2851 | + | 5.26999i | 1.79693 | + | 0.374522i | ||||
\(199\) | −6.62834 | −0.469870 | −0.234935 | − | 0.972011i | \(-0.575488\pi\) | ||||
−0.234935 | + | 0.972011i | \(0.575488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.95299 | − | 18.3214i | 0.419892 | − | 1.29229i | ||||
\(202\) | 12.2475 | + | 37.6939i | 0.861729 | + | 2.65213i | ||||
\(203\) | −1.03760 | + | 0.753862i | −0.0728254 | + | 0.0529107i | ||||
\(204\) | −26.1057 | + | 18.9669i | −1.82776 | + | 1.32795i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.21114 | − | 16.0382i | 0.363077 | − | 1.11744i | ||||
\(207\) | 21.9087 | + | 15.9176i | 1.52276 | + | 1.10635i | ||||
\(208\) | −8.21858 | −0.569856 | ||||||||
\(209\) | 4.79524 | + | 5.28345i | 0.331694 | + | 0.365464i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.57709 | − | 3.32545i | −0.315100 | − | 0.228934i | 0.418982 | − | 0.907995i | \(-0.362387\pi\) |
−0.734082 | + | 0.679061i | \(0.762387\pi\) | |||||||
\(212\) | 3.97610 | − | 12.2372i | 0.273080 | − | 0.840453i | ||||
\(213\) | −8.61673 | − | 26.5196i | −0.590409 | − | 1.81709i | ||||
\(214\) | −31.8774 | + | 23.1603i | −2.17910 | + | 1.58321i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.387117 | − | 1.19143i | −0.0263400 | − | 0.0810662i | ||||
\(217\) | 2.35807 | − | 7.25738i | 0.160076 | − | 0.492663i | ||||
\(218\) | 23.5018 | + | 17.0750i | 1.59174 | + | 1.15647i | ||||
\(219\) | 27.4230 | 1.85308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.85410 | −0.259255 | ||||||||
\(222\) | 9.42497 | + | 6.84764i | 0.632563 | + | 0.459584i | ||||
\(223\) | −2.43642 | + | 7.49852i | −0.163155 | + | 0.502138i | −0.998896 | − | 0.0469856i | \(-0.985039\pi\) |
0.835741 | + | 0.549124i | \(0.185039\pi\) | |||||||
\(224\) | 2.66566 | + | 8.20407i | 0.178107 | + | 0.548158i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.4800 | + | 13.4265i | −1.22927 | + | 0.893116i | ||||
\(227\) | 3.46451 | + | 10.6627i | 0.229948 | + | 0.707706i | 0.997752 | + | 0.0670213i | \(0.0213495\pi\) |
−0.767804 | + | 0.640685i | \(0.778650\pi\) | |||||||
\(228\) | 7.17145 | − | 22.0715i | 0.474941 | − | 1.46172i | ||||
\(229\) | −21.8360 | − | 15.8647i | −1.44296 | − | 1.04837i | −0.987413 | − | 0.158160i | \(-0.949444\pi\) |
−0.455547 | − | 0.890212i | \(-0.650556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.50496 | − | 14.8666i | 0.559585 | − | 0.978151i | ||||
\(232\) | 3.67042 | 0.240975 | ||||||||
\(233\) | −8.77845 | − | 6.37792i | −0.575095 | − | 0.417831i | 0.261857 | − | 0.965107i | \(-0.415665\pi\) |
−0.836953 | + | 0.547275i | \(0.815665\pi\) | |||||||
\(234\) | 3.10066 | − | 9.54284i | 0.202696 | − | 0.623835i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.9766 | − | 16.6935i | 1.49565 | − | 1.08665i | ||||
\(237\) | −10.6947 | + | 7.77017i | −0.694697 | + | 0.504727i | ||||
\(238\) | 4.88529 | + | 15.0354i | 0.316666 | + | 0.974599i | ||||
\(239\) | −3.54327 | + | 10.9051i | −0.229195 | + | 0.705391i | 0.768643 | + | 0.639678i | \(0.220932\pi\) |
−0.997839 | + | 0.0657129i | \(0.979068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7542 | 0.821572 | 0.410786 | − | 0.911732i | \(-0.365254\pi\) | ||||
0.410786 | + | 0.911732i | \(0.365254\pi\) | |||||||
\(242\) | 2.68401 | − | 27.6398i | 0.172534 | − | 1.77675i | ||||
\(243\) | −22.1829 | −1.42303 | ||||||||
\(244\) | 1.77767 | + | 1.29155i | 0.113804 | + | 0.0826833i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.82734 | + | 30.2455i | 0.626568 | + | 1.92838i | ||||
\(247\) | 2.24248 | − | 1.62926i | 0.142686 | − | 0.103667i | ||||
\(248\) | −17.6675 | + | 12.8362i | −1.12188 | + | 0.815097i | ||||
\(249\) | −8.26700 | − | 25.4432i | −0.523900 | − | 1.61240i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.87130 | + | 7.17192i | 0.623071 | + | 0.452687i | 0.853993 | − | 0.520285i | \(-0.174174\pi\) |
−0.230922 | + | 0.972972i | \(0.574174\pi\) | |||||||
\(252\) | −28.2422 | −1.77909 | ||||||||
\(253\) | 14.4581 | − | 25.2727i | 0.908973 | − | 1.58888i | ||||
\(254\) | 47.5471 | 2.98337 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.61149 | + | 29.5811i | −0.600718 | + | 1.84882i | ||||
\(257\) | 1.82198 | + | 5.60747i | 0.113652 | + | 0.349784i | 0.991663 | − | 0.128855i | \(-0.0411302\pi\) |
−0.878012 | + | 0.478639i | \(0.841130\pi\) | |||||||
\(258\) | −26.0610 | + | 18.9344i | −1.62249 | + | 1.17881i | ||||
\(259\) | 3.16850 | − | 2.30205i | 0.196881 | − | 0.143042i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.583986 | + | 1.79733i | −0.0361478 | + | 0.111252i | ||||
\(262\) | −41.0512 | − | 29.8254i | −2.53615 | − | 1.84262i | ||||
\(263\) | 21.7305 | 1.33996 | 0.669980 | − | 0.742379i | \(-0.266302\pi\) | ||||
0.669980 | + | 0.742379i | \(0.266302\pi\) | |||||||
\(264\) | −44.6989 | + | 20.1136i | −2.75103 | + | 1.23791i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.19843 | − | 6.68305i | −0.563992 | − | 0.409764i | ||||
\(267\) | −3.29553 | + | 10.1426i | −0.201683 | + | 0.620717i | ||||
\(268\) | 10.5539 | + | 32.4817i | 0.644685 | + | 1.98414i | ||||
\(269\) | 3.66042 | − | 2.65945i | 0.223180 | − | 0.162149i | −0.470577 | − | 0.882359i | \(-0.655954\pi\) |
0.693757 | + | 0.720209i | \(0.255954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.72447 | − | 20.6958i | −0.408482 | − | 1.25718i | −0.917952 | − | 0.396691i | \(-0.870159\pi\) |
0.509470 | − | 0.860488i | \(-0.329841\pi\) | |||||||
\(272\) | 5.89608 | − | 18.1463i | 0.357502 | − | 1.10028i | ||||
\(273\) | −5.38300 | − | 3.91098i | −0.325794 | − | 0.236703i | ||||
\(274\) | −45.3688 | −2.74083 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −94.7021 | −5.70040 | ||||||||
\(277\) | −10.5452 | − | 7.66154i | −0.633600 | − | 0.460337i | 0.224046 | − | 0.974579i | \(-0.428074\pi\) |
−0.857645 | + | 0.514241i | \(0.828074\pi\) | |||||||
\(278\) | −13.1552 | + | 40.4877i | −0.788999 | + | 2.42829i | ||||
\(279\) | −3.47459 | − | 10.6937i | −0.208018 | − | 0.640214i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.59310 | + | 5.51671i | −0.452966 | + | 0.329099i | −0.790766 | − | 0.612119i | \(-0.790317\pi\) |
0.337799 | + | 0.941218i | \(0.390317\pi\) | |||||||
\(282\) | −14.0606 | − | 43.2741i | −0.837297 | − | 2.57694i | ||||
\(283\) | −4.30760 | + | 13.2574i | −0.256060 | + | 0.788072i | 0.737559 | + | 0.675283i | \(0.235979\pi\) |
−0.993619 | + | 0.112789i | \(0.964021\pi\) | |||||||
\(284\) | 39.9943 | + | 29.0575i | 2.37322 | + | 1.72425i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.5612 | − | 2.20119i | −0.624495 | − | 0.130159i | ||||
\(287\) | 10.6912 | 0.631083 | ||||||||
\(288\) | 10.2832 | + | 7.47118i | 0.605943 | + | 0.440243i | ||||
\(289\) | −2.48832 | + | 7.65828i | −0.146372 | + | 0.450487i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.701768 | + | 0.509864i | −0.0411383 | + | 0.0298888i | ||||
\(292\) | −39.3326 | + | 28.5768i | −2.30176 | + | 1.67233i | ||||
\(293\) | −9.41576 | − | 28.9787i | −0.550075 | − | 1.69296i | −0.708608 | − | 0.705602i | \(-0.750677\pi\) |
0.158534 | − | 0.987354i | \(-0.449323\pi\) | |||||||
\(294\) | 5.03644 | − | 15.5006i | 0.293731 | − | 0.904011i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.2083 | −0.651468 | ||||||||
\(297\) | −0.0752186 | − | 0.689397i | −0.00436463 | − | 0.0400028i | ||||
\(298\) | −5.89138 | −0.341278 | ||||||||
\(299\) | −9.15089 | − | 6.64851i | −0.529210 | − | 0.384493i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.34649 | + | 10.2994i | 0.192888 | + | 0.593649i | ||||
\(302\) | −8.04468 | + | 5.84480i | −0.462919 | + | 0.336330i | ||||
\(303\) | 31.3303 | − | 22.7628i | 1.79988 | − | 1.30769i | ||||
\(304\) | 4.24044 | + | 13.0507i | 0.243206 | + | 0.748511i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.8457 | + | 13.6922i | 1.07734 | + | 0.782732i | ||||
\(307\) | −5.08609 | −0.290278 | −0.145139 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145139 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(308\) | 3.29351 | + | 30.1858i | 0.187665 | + | 1.72000i | ||||
\(309\) | −16.4775 | −0.937375 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.25249 | − | 13.0878i | 0.241136 | − | 0.742141i | −0.755112 | − | 0.655596i | \(-0.772417\pi\) |
0.996248 | − | 0.0865451i | \(-0.0275827\pi\) | |||||||
\(312\) | 5.88426 | + | 18.1099i | 0.333131 | + | 1.02527i | ||||
\(313\) | 12.9060 | − | 9.37676i | 0.729491 | − | 0.530006i | −0.159912 | − | 0.987131i | \(-0.551121\pi\) |
0.889402 | + | 0.457125i | \(0.151121\pi\) | |||||||
\(314\) | 9.96903 | − | 7.24292i | 0.562585 | − | 0.408742i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.24225 | − | 22.2894i | 0.407408 | − | 1.25387i | ||||
\(317\) | 8.66246 | + | 6.29364i | 0.486532 | + | 0.353486i | 0.803849 | − | 0.594833i | \(-0.202782\pi\) |
−0.317317 | + | 0.948320i | \(0.602782\pi\) | |||||||
\(318\) | −18.3221 | −1.02745 | ||||||||
\(319\) | 1.98912 | + | 0.414578i | 0.111369 | + | 0.0232119i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.1477 | + | 22.6301i | 1.73849 | + | 1.26309i | ||||
\(322\) | −14.3375 | + | 44.1263i | −0.798997 | + | 2.45906i | ||||
\(323\) | 1.98855 | + | 6.12014i | 0.110646 | + | 0.340534i | ||||
\(324\) | 30.9170 | − | 22.4625i | 1.71761 | − | 1.24792i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.48871 | − | 16.8925i | −0.303992 | − | 0.935590i | ||||
\(327\) | 8.77138 | − | 26.9955i | 0.485058 | − | 1.49286i | ||||
\(328\) | −24.7530 | − | 17.9841i | −1.36676 | − | 0.993006i | ||||
\(329\) | −15.2966 | −0.843330 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.84618 | −0.486230 | −0.243115 | − | 0.969997i | \(-0.578169\pi\) | ||||
−0.243115 | + | 0.969997i | \(0.578169\pi\) | |||||||
\(332\) | 38.3710 | + | 27.8782i | 2.10588 | + | 1.53001i | ||||
\(333\) | 1.78330 | − | 5.48845i | 0.0977245 | − | 0.300765i | ||||
\(334\) | 8.36248 | + | 25.7371i | 0.457575 | + | 1.40827i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 26.6491 | − | 19.3617i | 1.45382 | − | 1.05627i | ||||
\(337\) | 3.58143 | + | 11.0225i | 0.195093 | + | 0.600434i | 0.999976 | + | 0.00699978i | \(0.00222812\pi\) |
−0.804883 | + | 0.593434i | \(0.797772\pi\) | |||||||
\(338\) | 8.84648 | − | 27.2267i | 0.481185 | − | 1.48093i | ||||
\(339\) | 18.0569 | + | 13.1191i | 0.980716 | + | 0.712532i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0244 | + | 4.96077i | −0.597005 | + | 0.268641i | ||||
\(342\) | −16.7534 | −0.905920 | ||||||||
\(343\) | −16.2885 | − | 11.8343i | −0.879498 | − | 0.638993i | ||||
\(344\) | 9.57705 | − | 29.4751i | 0.516360 | − | 1.58919i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.1802 | + | 12.4821i | −0.923611 | + | 0.671043i | ||||
\(347\) | −3.95529 | + | 2.87368i | −0.212331 | + | 0.154267i | −0.688868 | − | 0.724887i | \(-0.741892\pi\) |
0.476537 | + | 0.879155i | \(0.341892\pi\) | |||||||
\(348\) | −2.04223 | − | 6.28533i | −0.109475 | − | 0.336929i | ||||
\(349\) | 0.294654 | − | 0.906853i | 0.0157725 | − | 0.0485427i | −0.942861 | − | 0.333188i | \(-0.891876\pi\) |
0.958633 | + | 0.284645i | \(0.0918757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.269409 | −0.0143800 | ||||||||
\(352\) | 6.78615 | − | 11.8621i | 0.361703 | − | 0.632254i | ||||
\(353\) | 15.5166 | 0.825865 | 0.412933 | − | 0.910762i | \(-0.364505\pi\) | ||||
0.412933 | + | 0.910762i | \(0.364505\pi\) | |||||||
\(354\) | −32.7179 | − | 23.7709i | −1.73894 | − | 1.26341i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.84258 | − | 17.9816i | −0.309656 | − | 0.953024i | ||||
\(357\) | 12.4971 | − | 9.07965i | 0.661415 | − | 0.480546i | ||||
\(358\) | 42.9645 | − | 31.2155i | 2.27074 | − | 1.64979i | ||||
\(359\) | 6.25915 | + | 19.2637i | 0.330345 | + | 1.01670i | 0.968970 | + | 0.247180i | \(0.0795038\pi\) |
−0.638624 | + | 0.769519i | \(0.720496\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6271 | + | 8.44759i | 0.611953 | + | 0.444610i | ||||
\(362\) | 4.40051 | 0.231286 | ||||||||
\(363\) | −26.4956 | + | 5.85142i | −1.39066 | + | 0.307120i | ||||
\(364\) | 11.7963 | 0.618295 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.966888 | − | 2.97578i | 0.0505400 | − | 0.155546i | ||||
\(367\) | −11.0180 | − | 33.9099i | −0.575135 | − | 1.77008i | −0.635719 | − | 0.771920i | \(-0.719296\pi\) |
0.0605844 | − | 0.998163i | \(-0.480704\pi\) | |||||||
\(368\) | 45.3024 | − | 32.9141i | 2.36155 | − | 1.71577i | ||||
\(369\) | 12.7448 | − | 9.25962i | 0.663466 | − | 0.482037i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.90340 | + | 5.85807i | −0.0988198 | + | 0.304136i | ||||
\(372\) | 31.8112 | + | 23.1122i | 1.64933 | + | 1.19831i | ||||
\(373\) | −12.1358 | −0.628370 | −0.314185 | − | 0.949362i | \(-0.601731\pi\) | ||||
−0.314185 | + | 0.949362i | \(0.601731\pi\) | |||||||
\(374\) | 12.4368 | − | 21.7394i | 0.643091 | − | 1.12412i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.4157 | + | 25.7310i | 1.82643 | + | 1.32698i | ||||
\(377\) | 0.243922 | − | 0.750713i | 0.0125626 | − | 0.0386637i | ||||
\(378\) | 0.341491 | + | 1.05100i | 0.0175644 | + | 0.0540577i | ||||
\(379\) | −5.77971 | + | 4.19921i | −0.296884 | + | 0.215699i | −0.726248 | − | 0.687433i | \(-0.758738\pi\) |
0.429364 | + | 0.903131i | \(0.358738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3565 | − | 44.1848i | −0.735506 | − | 2.26366i | ||||
\(382\) | −0.0194691 | + | 0.0599198i | −0.000996127 | + | 0.00306576i | ||||
\(383\) | 12.9143 | + | 9.38279i | 0.659890 | + | 0.479438i | 0.866626 | − | 0.498959i | \(-0.166284\pi\) |
−0.206736 | + | 0.978397i | \(0.566284\pi\) | |||||||
\(384\) | 34.9936 | 1.78576 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.67885 | 0.187249 | ||||||||
\(387\) | 12.9096 | + | 9.37935i | 0.656230 | + | 0.476779i | ||||
\(388\) | 0.475223 | − | 1.46259i | 0.0241258 | − | 0.0742516i | ||||
\(389\) | −7.75336 | − | 23.8624i | −0.393111 | − | 1.20987i | −0.930423 | − | 0.366488i | \(-0.880560\pi\) |
0.537312 | − | 0.843384i | \(-0.319440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2445 | − | 15.4351i | 1.07438 | − | 0.780585i | ||||
\(392\) | 4.84551 | + | 14.9130i | 0.244735 | + | 0.753218i | ||||
\(393\) | −15.3212 | + | 47.1538i | −0.772853 | + | 2.37860i | ||||
\(394\) | −46.3677 | − | 33.6881i | −2.33597 | − | 1.69718i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.0699 | + | 33.1314i | 1.51107 | + | 1.66491i | ||||
\(397\) | −3.57490 | −0.179419 | −0.0897094 | − | 0.995968i | \(-0.528594\pi\) | ||||
−0.0897094 | + | 0.995968i | \(0.528594\pi\) | |||||||
\(398\) | −13.5376 | − | 9.83564i | −0.678579 | − | 0.493016i | ||||
\(399\) | −3.43305 | + | 10.5659i | −0.171868 | + | 0.528954i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3675 | + | 16.9775i | −1.16692 | + | 0.847815i | −0.990637 | − | 0.136524i | \(-0.956407\pi\) |
−0.176281 | + | 0.984340i | \(0.556407\pi\) | |||||||
\(402\) | 39.3451 | − | 28.5859i | 1.96235 | − | 1.42573i | ||||
\(403\) | 1.45128 | + | 4.46657i | 0.0722933 | + | 0.222496i | ||||
\(404\) | −21.2162 | + | 65.2969i | −1.05555 | + | 3.24864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.23782 | −0.160690 | ||||||||
\(407\) | −6.07412 | − | 1.26599i | −0.301083 | − | 0.0627526i | ||||
\(408\) | −44.2072 | −2.18858 | ||||||||
\(409\) | −7.78197 | − | 5.65393i | −0.384794 | − | 0.279569i | 0.378525 | − | 0.925591i | \(-0.376431\pi\) |
−0.763319 | + | 0.646022i | \(0.776431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6988 | + | 42.1606i | 0.675712 | + | 2.07963i | ||||
\(412\) | 23.6336 | − | 17.1708i | 1.16434 | − | 0.845945i | ||||
\(413\) | −10.9991 | + | 7.99135i | −0.541233 | + | 0.393229i | ||||
\(414\) | 21.1261 | + | 65.0196i | 1.03829 | + | 3.19554i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.29512 | − | 3.12059i | −0.210586 | − | 0.152999i | ||||
\(417\) | 41.5967 | 2.03700 | ||||||||
\(418\) | 1.95373 | + | 17.9064i | 0.0955599 | + | 0.875829i | ||||
\(419\) | −30.6537 | −1.49753 | −0.748765 | − | 0.662836i | \(-0.769353\pi\) | ||||
−0.748765 | + | 0.662836i | \(0.769353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.14755 | + | 6.60949i | −0.104665 | + | 0.322127i | −0.989652 | − | 0.143490i | \(-0.954168\pi\) |
0.884986 | + | 0.465617i | \(0.154168\pi\) | |||||||
\(422\) | −4.41361 | − | 13.5837i | −0.214851 | − | 0.661244i | ||||
\(423\) | −18.2348 | + | 13.2483i | −0.886605 | + | 0.644156i | ||||
\(424\) | 14.2610 | − | 10.3612i | 0.692574 | − | 0.503184i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 21.7532 | − | 66.9493i | 1.05394 | − | 3.24371i | ||||
\(427\) | −0.850991 | − | 0.618281i | −0.0411823 | − | 0.0299207i | ||||
\(428\) | −68.2571 | −3.29933 | ||||||||
\(429\) | 1.14334 | + | 10.4790i | 0.0552009 | + | 0.505929i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.61636 | + | 1.90090i | 0.126026 | + | 0.0915631i | 0.649013 | − | 0.760778i | \(-0.275182\pi\) |
−0.522987 | + | 0.852341i | \(0.675182\pi\) | |||||||
\(432\) | 0.412147 | − | 1.26846i | 0.0198294 | − | 0.0610287i | ||||
\(433\) | 9.39161 | + | 28.9044i | 0.451332 | + | 1.38906i | 0.875388 | + | 0.483421i | \(0.160606\pi\) |
−0.424056 | + | 0.905636i | \(0.639394\pi\) | |||||||
\(434\) | 15.5851 | − | 11.3233i | 0.748110 | − | 0.543534i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.5506 | + | 47.8598i | 0.744739 | + | 2.29207i | ||||
\(437\) | −5.83606 | + | 17.9616i | −0.279177 | + | 0.859218i | ||||
\(438\) | 56.0083 | + | 40.6924i | 2.67618 | + | 1.94436i | ||||
\(439\) | 36.5311 | 1.74353 | 0.871767 | − | 0.489921i | \(-0.162974\pi\) | ||||
0.871767 | + | 0.489921i | \(0.162974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.07350 | −0.384452 | ||||||||
\(442\) | −7.87155 | − | 5.71902i | −0.374412 | − | 0.272026i | ||||
\(443\) | 0.667949 | − | 2.05574i | 0.0317352 | − | 0.0976710i | −0.933934 | − | 0.357445i | \(-0.883648\pi\) |
0.965669 | + | 0.259774i | \(0.0836480\pi\) | |||||||
\(444\) | 6.23630 | + | 19.1933i | 0.295962 | + | 0.910876i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.1030 | + | 11.6995i | −0.762499 | + | 0.553988i | ||||
\(447\) | 1.77886 | + | 5.47477i | 0.0841372 | + | 0.258948i | ||||
\(448\) | 1.52352 | − | 4.68890i | 0.0719793 | − | 0.221530i | ||||
\(449\) | 9.32124 | + | 6.77228i | 0.439897 | + | 0.319604i | 0.785594 | − | 0.618742i | \(-0.212358\pi\) |
−0.345697 | + | 0.938346i | \(0.612358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3831 | − | 12.5420i | −0.536010 | − | 0.590581i | ||||
\(452\) | −39.5699 | −1.86121 | ||||||||
\(453\) | 7.86051 | + | 5.71100i | 0.369319 | + | 0.268326i | ||||
\(454\) | −8.74624 | + | 26.9182i | −0.410482 | + | 1.26333i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 25.7217 | − | 18.6879i | 1.20453 | − | 0.875140i | ||||
\(457\) | −12.8888 | + | 9.36427i | −0.602913 | + | 0.438042i | −0.846912 | − | 0.531734i | \(-0.821541\pi\) |
0.243999 | + | 0.969776i | \(0.421541\pi\) | |||||||
\(458\) | −21.0560 | − | 64.8038i | −0.983883 | − | 3.02808i | ||||
\(459\) | 0.193276 | − | 0.594843i | 0.00902136 | − | 0.0277649i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52527 | 0.0710387 | 0.0355193 | − | 0.999369i | \(-0.488691\pi\) | ||||
0.0355193 | + | 0.999369i | \(0.488691\pi\) | |||||||
\(462\) | 39.4306 | − | 17.7430i | 1.83448 | − | 0.825478i | ||||
\(463\) | −14.2073 | −0.660268 | −0.330134 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330134 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(464\) | 3.16143 | + | 2.29691i | 0.146765 | + | 0.106631i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.46491 | − | 26.0523i | −0.392129 | − | 1.20685i | ||||
\(467\) | −4.90020 | + | 3.56020i | −0.226754 | + | 0.164746i | −0.695362 | − | 0.718660i | \(-0.744756\pi\) |
0.468608 | + | 0.883406i | \(0.344756\pi\) | |||||||
\(468\) | 14.0621 | − | 10.2167i | 0.650022 | − | 0.472269i | ||||
\(469\) | −5.05229 | − | 15.5494i | −0.233293 | − | 0.718002i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.74081 | − | 7.07711i | −0.448833 | − | 0.326096i | ||||
\(472\) | 38.9085 | 1.79091 | ||||||||
\(473\) | 8.51936 | − | 14.8918i | 0.391720 | − | 0.684725i | ||||
\(474\) | −33.3727 | −1.53286 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.46277 | + | 26.0457i | −0.387890 | + | 1.19380i | ||||
\(477\) | 2.80464 | + | 8.63181i | 0.128416 | + | 0.395223i | ||||
\(478\) | −23.4185 | + | 17.0146i | −1.07114 | + | 0.778227i | ||||
\(479\) | 14.2455 | − | 10.3500i | 0.650894 | − | 0.472902i | −0.212681 | − | 0.977122i | \(-0.568220\pi\) |
0.863576 | + | 0.504219i | \(0.168220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.744857 | + | 2.29243i | −0.0339626 | + | 0.104526i | ||||
\(482\) | 26.0490 | + | 18.9257i | 1.18650 | + | 0.862043i | ||||
\(483\) | 45.3350 | 2.06281 | ||||||||
\(484\) | 31.9048 | − | 36.0030i | 1.45022 | − | 1.63650i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −45.3059 | − | 32.9167i | −2.05512 | − | 1.49313i | ||||
\(487\) | −2.09619 | + | 6.45140i | −0.0949874 | + | 0.292341i | −0.987250 | − | 0.159175i | \(-0.949117\pi\) |
0.892263 | + | 0.451516i | \(0.149117\pi\) | |||||||
\(488\) | 0.930235 | + | 2.86297i | 0.0421097 | + | 0.129600i | ||||
\(489\) | −14.0407 | + | 10.2011i | −0.634941 | + | 0.461312i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.160261 | + | 0.493232i | 0.00723247 | + | 0.0222592i | 0.954608 | − | 0.297866i | \(-0.0962749\pi\) |
−0.947375 | + | 0.320125i | \(0.896275\pi\) | |||||||
\(492\) | −17.0239 | + | 52.3941i | −0.767495 | + | 2.36211i | ||||
\(493\) | 1.48255 | + | 1.07714i | 0.0667707 | + | 0.0485117i | ||||
\(494\) | 6.99762 | 0.314838 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.2501 | −1.04396 | ||||||||
\(497\) | −19.1457 | − | 13.9102i | −0.858802 | − | 0.623956i | ||||
\(498\) | 20.8703 | − | 64.2320i | 0.935218 | − | 2.87831i | ||||
\(499\) | 6.75534 | + | 20.7908i | 0.302411 | + | 0.930725i | 0.980631 | + | 0.195866i | \(0.0627516\pi\) |
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.3921 | − | 15.5423i | 0.955727 | − | 0.694377i | ||||
\(502\) | 9.51872 | + | 29.2956i | 0.424841 | + | 1.30753i | ||||
\(503\) | −0.932202 | + | 2.86902i | −0.0415649 | + | 0.127923i | −0.969686 | − | 0.244356i | \(-0.921424\pi\) |
0.928121 | + | 0.372279i | \(0.121424\pi\) | |||||||
\(504\) | −31.3020 | − | 22.7423i | −1.39430 | − | 1.01302i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 67.0306 | − | 30.1624i | 2.97987 | − | 1.34088i | ||||
\(507\) | −27.9724 | −1.24230 | ||||||||
\(508\) | 66.6352 | + | 48.4133i | 2.95646 | + | 2.14799i | ||||
\(509\) | −7.94418 | + | 24.4497i | −0.352119 | + | 1.08371i | 0.605542 | + | 0.795814i | \(0.292957\pi\) |
−0.957661 | + | 0.287898i | \(0.907043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8289 | − | 13.6800i | 0.832943 | − | 0.605169i | ||||
\(512\) | −40.5713 | + | 29.4768i | −1.79302 | + | 1.30270i | ||||
\(513\) | 0.139004 | + | 0.427809i | 0.00613716 | + | 0.0188882i | ||||
\(514\) | −4.59962 | + | 14.1562i | −0.202881 | + | 0.624403i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −55.8027 | −2.45658 | ||||||||
\(517\) | 16.2866 | + | 17.9447i | 0.716282 | + | 0.789207i | ||||
\(518\) | 9.88725 | 0.434421 | ||||||||
\(519\) | 16.7869 | + | 12.1964i | 0.736862 | + | 0.535361i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.44017 | + | 10.5877i | 0.150716 | + | 0.463858i | 0.997702 | − | 0.0677588i | \(-0.0215848\pi\) |
−0.846985 | + | 0.531616i | \(0.821585\pi\) | |||||||
\(522\) | −3.85974 | + | 2.80426i | −0.168936 | + | 0.122739i | ||||
\(523\) | −5.28968 | + | 3.84318i | −0.231302 | + | 0.168050i | −0.697399 | − | 0.716683i | \(-0.745660\pi\) |
0.466098 | + | 0.884733i | \(0.345660\pi\) | |||||||
\(524\) | −27.1627 | − | 83.5981i | −1.18661 | − | 3.65200i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.3820 | + | 32.2454i | 1.93515 | + | 1.40597i | ||||
\(527\) | −10.9032 | −0.474949 | ||||||||
\(528\) | −51.0871 | − | 10.6477i | −2.22328 | − | 0.463383i | ||||
\(529\) | 54.0677 | 2.35077 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.19057 | + | 19.0526i | −0.268648 | + | 0.826814i | ||||
\(532\) | −6.08640 | − | 18.7320i | −0.263879 | − | 0.812135i | ||||
\(533\) | −5.32328 | + | 3.86759i | −0.230577 | + | 0.167524i | ||||
\(534\) | −21.7811 | + | 15.8249i | −0.942561 | + | 0.684811i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.4588 | + | 44.4995i | −0.624524 | + | 1.92209i | ||||
\(537\) | −41.9809 | − | 30.5009i | −1.81161 | − | 1.31621i | ||||
\(538\) | 11.4223 | 0.492449 | ||||||||
\(539\) | 0.941505 | + | 8.62911i | 0.0405535 | + | 0.371682i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.7684 | − | 24.5342i | −1.45182 | − | 1.05481i | −0.985403 | − | 0.170239i | \(-0.945546\pi\) |
−0.466413 | − | 0.884567i | \(-0.654454\pi\) | |||||||
\(542\) | 16.9761 | − | 52.2470i | 0.729185 | − | 2.24420i | ||||
\(543\) | −1.32870 | − | 4.08932i | −0.0570201 | − | 0.175490i | ||||
\(544\) | 9.97147 | − | 7.24470i | 0.427523 | − | 0.310614i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.19073 | − | 15.9754i | −0.222143 | − | 0.683685i | ||||
\(547\) | 1.37703 | − | 4.23806i | 0.0588775 | − | 0.181206i | −0.917292 | − | 0.398215i | \(-0.869630\pi\) |
0.976170 | + | 0.217008i | \(0.0696299\pi\) | |||||||
\(548\) | −63.5825 | − | 46.1954i | −2.71611 | − | 1.97337i | ||||
\(549\) | −1.54994 | −0.0661498 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.31795 | −0.0561466 | ||||||||
\(552\) | −104.962 | − | 76.2596i | −4.46750 | − | 3.24583i | ||||
\(553\) | −3.46695 | + | 10.6702i | −0.147430 | + | 0.453742i | ||||
\(554\) | −10.1686 | − | 31.2956i | −0.432020 | − | 1.32962i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −59.6618 | + | 43.3468i | −2.53022 | + | 1.83831i | ||||
\(557\) | −5.98608 | − | 18.4233i | −0.253638 | − | 0.780619i | −0.994095 | − | 0.108514i | \(-0.965391\pi\) |
0.740456 | − | 0.672104i | \(-0.234609\pi\) | |||||||
\(558\) | 8.77167 | − | 26.9964i | 0.371335 | − | 1.14285i | ||||
\(559\) | −5.39211 | − | 3.91760i | −0.228062 | − | 0.165697i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.9573 | − | 4.99325i | −1.01148 | − | 0.210815i | ||||
\(562\) | −23.6941 | −0.999477 | ||||||||
\(563\) | 16.7816 | + | 12.1925i | 0.707259 | + | 0.513853i | 0.882288 | − | 0.470710i | \(-0.156002\pi\) |
−0.175030 | + | 0.984563i | \(0.556002\pi\) | |||||||
\(564\) | 24.3571 | − | 74.9636i | 1.02562 | − | 3.15654i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.4702 | + | 20.6848i | −1.19669 | + | 0.869447i | ||||
\(567\) | −14.8003 | + | 10.7530i | −0.621554 | + | 0.451585i | ||||
\(568\) | 20.9285 | + | 64.4114i | 0.878141 | + | 2.70264i | ||||
\(569\) | −13.0945 | + | 40.3007i | −0.548950 | + | 1.68949i | 0.162458 | + | 0.986716i | \(0.448058\pi\) |
−0.711408 | + | 0.702779i | \(0.751942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.03980 | −0.210909 | −0.105455 | − | 0.994424i | \(-0.533630\pi\) | ||||
−0.105455 | + | 0.994424i | \(0.533630\pi\) | |||||||
\(572\) | −12.5597 | − | 13.8384i | −0.525148 | − | 0.578614i | ||||
\(573\) | 0.0615611 | 0.00257175 | ||||||||
\(574\) | 21.8356 | + | 15.8645i | 0.911399 | + | 0.662170i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.24488 | − | 6.90905i | −0.0935369 | − | 0.287877i | ||||
\(577\) | 28.1877 | − | 20.4796i | 1.17347 | − | 0.852576i | 0.182050 | − | 0.983289i | \(-0.441727\pi\) |
0.991420 | + | 0.130713i | \(0.0417267\pi\) | |||||||
\(578\) | −16.4461 | + | 11.9488i | −0.684066 | + | 0.497003i | ||||
\(579\) | −1.11080 | − | 3.41870i | −0.0461634 | − | 0.142076i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.3686 | − | 13.3456i | −0.762059 | − | 0.553668i | ||||
\(582\) | −2.18985 | −0.0907724 | ||||||||
\(583\) | 8.89878 | − | 4.00427i | 0.368550 | − | 0.165840i | ||||
\(584\) | −66.6057 | −2.75616 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.7703 | − | 73.1575i | 0.981943 | − | 3.02211i | ||||
\(587\) | 4.25772 | + | 13.1039i | 0.175735 | + | 0.540857i | 0.999666 | − | 0.0258331i | \(-0.00822386\pi\) |
−0.823931 | + | 0.566690i | \(0.808224\pi\) | |||||||
\(588\) | 22.8413 | − | 16.5952i | 0.941959 | − | 0.684373i | ||||
\(589\) | 6.34392 | − | 4.60913i | 0.261397 | − | 0.189916i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.3054 | + | 53.2606i | −0.711850 | + | 2.19085i | ||||
\(592\) | −9.65397 | − | 7.01402i | −0.396776 | − | 0.288274i | ||||
\(593\) | 25.1595 | 1.03318 | 0.516588 | − | 0.856234i | \(-0.327202\pi\) | ||||
0.516588 | + | 0.856234i | \(0.327202\pi\) | |||||||
\(594\) | 0.869355 | − | 1.51963i | 0.0356701 | − | 0.0623511i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.25651 | − | 5.99871i | −0.338200 | − | 0.245717i | ||||
\(597\) | −5.05253 | + | 15.5501i | −0.206786 | + | 0.636423i | ||||
\(598\) | −8.82405 | − | 27.1576i | −0.360842 | − | 1.11056i | ||||
\(599\) | 13.3539 | − | 9.70216i | 0.545624 | − | 0.396419i | −0.280545 | − | 0.959841i | \(-0.590515\pi\) |
0.826170 | + | 0.563421i | \(0.190515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.2509 | + | 37.7045i | 0.499726 | + | 1.53800i | 0.809460 | + | 0.587175i | \(0.199760\pi\) |
−0.309734 | + | 0.950823i | \(0.600240\pi\) | |||||||
\(602\) | −8.44829 | + | 26.0011i | −0.344326 | + | 1.05973i | ||||
\(603\) | −19.4900 | − | 14.1603i | −0.793692 | − | 0.576651i | ||||
\(604\) | −17.2255 | −0.700897 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 97.7656 | 3.97146 | ||||||||
\(607\) | 11.4795 | + | 8.34036i | 0.465939 | + | 0.338525i | 0.795857 | − | 0.605485i | \(-0.207021\pi\) |
−0.329917 | + | 0.944010i | \(0.607021\pi\) | |||||||
\(608\) | −2.73925 | + | 8.43055i | −0.111091 | + | 0.341904i | ||||
\(609\) | 0.977637 | + | 3.00886i | 0.0396158 | + | 0.121925i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.61636 | − | 5.53361i | 0.308125 | − | 0.223866i | ||||
\(612\) | 12.4698 | + | 38.3781i | 0.504062 | + | 1.55134i | ||||
\(613\) | −9.31820 | + | 28.6785i | −0.376359 | + | 1.15831i | 0.566199 | + | 0.824269i | \(0.308414\pi\) |
−0.942557 | + | 0.334044i | \(0.891586\pi\) | |||||||
\(614\) | −10.3877 | − | 7.54714i | −0.419215 | − | 0.304578i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.6570 | + | 36.1084i | −0.832296 | + | 1.45485i | ||||
\(617\) | 31.3844 | 1.26349 | 0.631744 | − | 0.775177i | \(-0.282339\pi\) | ||||
0.631744 | + | 0.775177i | \(0.282339\pi\) | |||||||
\(618\) | −33.6534 | − | 24.4507i | −1.35374 | − | 0.983550i | ||||
\(619\) | 10.8876 | − | 33.5087i | 0.437611 | − | 1.34683i | −0.452775 | − | 0.891625i | \(-0.649566\pi\) |
0.890387 | − | 0.455205i | \(-0.150434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.48503 | − | 1.07894i | 0.0595924 | − | 0.0432964i | ||||
\(622\) | 28.1059 | − | 20.4201i | 1.12694 | − | 0.818773i | ||||
\(623\) | 2.79691 | + | 8.60800i | 0.112056 | + | 0.344872i | ||||
\(624\) | −6.26471 | + | 19.2808i | −0.250789 | + | 0.771850i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 40.2730 | 1.60963 | ||||||||
\(627\) | 16.0502 | − | 7.22227i | 0.640983 | − | 0.288430i | ||||
\(628\) | 21.3460 | 0.851799 | ||||||||
\(629\) | −4.52723 | − | 3.28922i | −0.180512 | − | 0.131150i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.77213 | + | 5.45404i | 0.0705472 | + | 0.217122i | 0.980114 | − | 0.198436i | \(-0.0635863\pi\) |
−0.909567 | + | 0.415558i | \(0.863586\pi\) | |||||||
\(632\) | 25.9756 | − | 18.8724i | 1.03325 | − | 0.750702i | ||||
\(633\) | −11.2905 | + | 8.20300i | −0.448755 | + | 0.326040i | ||||
\(634\) | 8.35306 | + | 25.7081i | 0.331742 | + | 1.02100i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −25.6776 | − | 18.6559i | −1.01818 | − | 0.739753i | ||||
\(637\) | 3.37217 | 0.133610 | ||||||||
\(638\) | 3.44736 | + | 3.79834i | 0.136482 | + | 0.150378i | ||||
\(639\) | −34.8707 | −1.37946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.20167 | + | 6.77605i | −0.0869608 | + | 0.267638i | −0.985075 | − | 0.172124i | \(-0.944937\pi\) |
0.898115 | + | 0.439762i | \(0.144937\pi\) | |||||||
\(642\) | 30.0352 | + | 92.4388i | 1.18539 | + | 3.64827i | ||||
\(643\) | −17.1427 | + | 12.4549i | −0.676042 | + | 0.491173i | −0.872042 | − | 0.489431i | \(-0.837205\pi\) |
0.196000 | + | 0.980604i | \(0.437205\pi\) | |||||||
\(644\) | −65.0235 | + | 47.2423i | −2.56229 | + | 1.86161i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.02015 | + | 15.4504i | −0.197515 | + | 0.607889i | ||||
\(647\) | −4.57074 | − | 3.32083i | −0.179694 | − | 0.130555i | 0.494302 | − | 0.869290i | \(-0.335424\pi\) |
−0.673996 | + | 0.738735i | \(0.735424\pi\) | |||||||
\(648\) | 52.3547 | 2.05669 | ||||||||
\(649\) | 21.0857 | + | 4.39475i | 0.827688 | + | 0.172509i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.2284 | − | 11.0640i | −0.596846 | − | 0.433634i | ||||
\(652\) | 9.50807 | − | 29.2628i | 0.372365 | − | 1.14602i | ||||
\(653\) | 4.85563 | + | 14.9441i | 0.190016 | + | 0.584808i | 0.999999 | − | 0.00164558i | \(-0.000523804\pi\) |
−0.809983 | + | 0.586453i | \(0.800524\pi\) | |||||||
\(654\) | 57.9726 | − | 42.1195i | 2.26691 | − | 1.64700i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.0661 | − | 30.9803i | −0.393016 | − | 1.20958i | ||||
\(657\) | 10.5974 | − | 32.6153i | 0.413442 | − | 1.27245i | ||||
\(658\) | −31.2416 | − | 22.6983i | −1.21792 | − | 0.884872i | ||||
\(659\) | −41.7884 | −1.62784 | −0.813922 | − | 0.580975i | \(-0.802671\pi\) | ||||
−0.813922 | + | 0.580975i | \(0.802671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.8742 | 0.617435 | 0.308717 | − | 0.951154i | \(-0.400100\pi\) | ||||
0.308717 | + | 0.951154i | \(0.400100\pi\) | |||||||
\(662\) | −18.0673 | − | 13.1266i | −0.702205 | − | 0.510182i | ||||
\(663\) | −2.93784 | + | 9.04173i | −0.114096 | + | 0.351152i | ||||
\(664\) | 20.0791 | + | 61.7971i | 0.779220 | + | 2.39819i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.7864 | − | 8.56330i | 0.456713 | − | 0.331821i | ||||
\(667\) | 1.66195 | + | 5.11494i | 0.0643508 | + | 0.198051i | ||||
\(668\) | −14.4863 | + | 44.5842i | −0.560491 | + | 1.72502i | ||||
\(669\) | 15.7344 | + | 11.4317i | 0.608325 | + | 0.441974i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.180749 | + | 1.65660i | 0.00697773 | + | 0.0639525i | ||||
\(672\) | 21.2787 | 0.820844 | ||||||||
\(673\) | 26.0864 | + | 18.9529i | 1.00556 | + | 0.730580i | 0.963273 | − | 0.268525i | \(-0.0865363\pi\) |
0.0422850 | + | 0.999106i | \(0.486536\pi\) | |||||||
\(674\) | −9.04140 | + | 27.8266i | −0.348262 | + | 1.07184i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 40.1206 | − | 29.1493i | 1.54310 | − | 1.12113i | ||||
\(677\) | 14.2084 | − | 10.3230i | 0.546073 | − | 0.396745i | −0.280263 | − | 0.959923i | \(-0.590422\pi\) |
0.826336 | + | 0.563178i | \(0.190422\pi\) | |||||||
\(678\) | 17.4120 | + | 53.5885i | 0.668702 | + | 2.05805i | ||||
\(679\) | −0.227495 | + | 0.700157i | −0.00873044 | + | 0.0268695i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.6555 | 1.05976 | ||||||||
\(682\) | −29.8772 | − | 6.22710i | −1.14406 | − | 0.238448i | ||||
\(683\) | 5.93856 | 0.227233 | 0.113616 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113616 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(684\) | −23.4792 | − | 17.0586i | −0.897749 | − | 0.652253i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7067 | − | 48.3404i | −0.599686 | − | 1.84565i | ||||
\(687\) | −53.8634 | + | 39.1341i | −2.05502 | + | 1.49306i | ||||
\(688\) | 26.6942 | − | 19.3945i | 1.01771 | − | 0.739407i | ||||
\(689\) | −1.17145 | − | 3.60537i | −0.0446289 | − | 0.137353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.7463 | − | 12.8934i | −0.675100 | − | 0.490489i | 0.196629 | − | 0.980478i | \(-0.437001\pi\) |
−0.871728 | + | 0.489989i | \(0.837001\pi\) | |||||||
\(692\) | −36.7868 | −1.39842 | ||||||||
\(693\) | −14.3948 | − | 15.8604i | −0.546814 | − | 0.602485i | ||||
\(694\) | −12.3424 | −0.468511 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.79782 | − | 8.61082i | 0.106051 | − | 0.326392i | ||||
\(697\) | −4.72050 | − | 14.5282i | −0.178802 | − | 0.550295i | ||||
\(698\) | 1.94746 | − | 1.41491i | 0.0737123 | − | 0.0535551i | ||||
\(699\) | −21.6541 | + | 15.7326i | −0.819033 | + | 0.595062i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0186 | − | 30.8341i | 0.378397 | − | 1.16459i | −0.562761 | − | 0.826620i | \(-0.690261\pi\) |
0.941158 | − | 0.337967i | \(-0.109739\pi\) | |||||||
\(702\) | −0.550236 | − | 0.399770i | −0.0207673 | − | 0.0150884i | ||||
\(703\) | 4.02460 | 0.151791 | ||||||||
\(704\) | −7.12273 | + | 3.20509i | −0.268448 | + | 0.120796i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.6908 | + | 23.0247i | 1.19270 | + | 0.866547i | ||||
\(707\) | 10.1565 | − | 31.2584i | 0.381973 | − | 1.17559i | ||||
\(708\) | −21.6487 | − | 66.6279i | −0.813609 | − | 2.50403i | ||||
\(709\) | 13.0256 | − | 9.46362i | 0.489185 | − | 0.355414i | −0.315686 | − | 0.948864i | \(-0.602235\pi\) |
0.804871 | + | 0.593450i | \(0.202235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.10851 | + | 15.7224i | 0.191584 | + | 0.589635i | ||||
\(712\) | 8.00426 | − | 24.6346i | 0.299972 | − | 0.923220i | ||||
\(713\) | −25.8876 | − | 18.8085i | −0.969499 | − | 0.704383i | ||||
\(714\) | 38.9969 | 1.45942 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 91.9971 | 3.43809 | ||||||||
\(717\) | 22.8824 | + | 16.6250i | 0.854559 | + | 0.620874i | ||||
\(718\) | −15.8014 | + | 48.6316i | −0.589702 | + | 1.81492i | ||||
\(719\) | −2.41409 | − | 7.42981i | −0.0900304 | − | 0.277085i | 0.895896 | − | 0.444263i | \(-0.146534\pi\) |
−0.985927 | + | 0.167178i | \(0.946534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3137 | + | 8.21985i | −0.421343 | + | 0.306123i | ||||
\(722\) | 11.2118 | + | 34.5064i | 0.417261 | + | 1.28420i | ||||
\(723\) | 9.72206 | − | 29.9214i | 0.361567 | − | 1.11279i | ||||
\(724\) | 6.16712 | + | 4.48068i | 0.229199 | + | 0.166523i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −62.7970 | − | 27.3654i | −2.33061 | − | 1.01563i | ||||
\(727\) | 49.1218 | 1.82183 | 0.910914 | − | 0.412597i | \(-0.135378\pi\) | ||||
0.910914 | + | 0.412597i | \(0.135378\pi\) | |||||||
\(728\) | 13.0744 | + | 9.49907i | 0.484568 | + | 0.352059i | ||||
\(729\) | −8.80810 | + | 27.1086i | −0.326226 | + | 1.00402i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.5182 | − | 9.09503i | 0.463003 | − | 0.336392i | ||||
\(732\) | 4.38504 | − | 3.18592i | 0.162076 | − | 0.117755i | ||||
\(733\) | 0.206407 | + | 0.635255i | 0.00762382 | + | 0.0234637i | 0.954796 | − | 0.297262i | \(-0.0960734\pi\) |
−0.947172 | + | 0.320725i | \(0.896073\pi\) | |||||||
\(734\) | 27.8152 | − | 85.6064i | 1.02668 | − | 3.15979i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.1730 | 1.33335 | ||||||||
\(737\) | −12.8619 | + | 22.4826i | −0.473775 | + | 0.828156i | ||||
\(738\) | 39.7699 | 1.46395 | ||||||||
\(739\) | −30.8186 | − | 22.3911i | −1.13368 | − | 0.823668i | −0.147456 | − | 0.989069i | \(-0.547108\pi\) |
−0.986227 | + | 0.165400i | \(0.947108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.11288 | − | 6.50278i | −0.0776187 | − | 0.238886i | ||||
\(742\) | −12.5801 | + | 9.14001i | −0.461832 | + | 0.335540i | ||||
\(743\) | −25.3511 | + | 18.4186i | −0.930041 | + | 0.675714i | −0.946003 | − | 0.324159i | \(-0.894919\pi\) |
0.0159622 | + | 0.999873i | \(0.494919\pi\) | |||||||
\(744\) | 16.6464 | + | 51.2324i | 0.610287 | + | 1.87827i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.7860 | − | 18.0081i | −0.907480 | − | 0.659323i | ||||
\(747\) | −33.4554 | −1.22407 | ||||||||
\(748\) | 39.5651 | − | 17.8035i | 1.44664 | − | 0.650960i | ||||
\(749\) | 32.6754 | 1.19393 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4915 | + | 35.3673i | −0.419332 | + | 1.29057i | 0.488986 | + | 0.872292i | \(0.337367\pi\) |
−0.908318 | + | 0.418280i | \(0.862633\pi\) | |||||||
\(752\) | 14.4022 | + | 44.3255i | 0.525196 | + | 1.61639i | ||||
\(753\) | 24.3498 | − | 17.6912i | 0.887358 | − | 0.644703i | ||||
\(754\) | 1.61215 | − | 1.17129i | 0.0587110 | − | 0.0426560i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.591564 | + | 1.82065i | −0.0215150 | + | 0.0662162i | ||||
\(757\) | 5.40478 | + | 3.92680i | 0.196440 | + | 0.142722i | 0.681657 | − | 0.731672i | \(-0.261259\pi\) |
−0.485217 | + | 0.874394i | \(0.661259\pi\) | |||||||
\(758\) | −18.0355 | −0.655079 | ||||||||
\(759\) | −48.2689 | − | 53.1831i | −1.75205 | − | 1.93043i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.5213 | + | 13.4565i | 0.671398 | + | 0.487799i | 0.870493 | − | 0.492181i | \(-0.163800\pi\) |
−0.199095 | + | 0.979980i | \(0.563800\pi\) | |||||||
\(762\) | 36.2434 | − | 111.546i | 1.31296 | − | 4.04087i | ||||
\(763\) | −7.44425 | − | 22.9110i | −0.269500 | − | 0.829435i | ||||
\(764\) | −0.0882966 | + | 0.0641512i | −0.00319446 | + | 0.00232091i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.4530 | + | 38.3265i | 0.449947 | + | 1.38479i | ||||
\(767\) | 2.58570 | − | 7.95797i | 0.0933643 | − | 0.287346i | ||||
\(768\) | 62.0709 | + | 45.0971i | 2.23979 | + | 1.62730i | ||||
\(769\) | −13.1946 | −0.475808 | −0.237904 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237904 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5440 | 0.523788 | ||||||||
\(772\) | 5.15575 | + | 3.74587i | 0.185560 | + | 0.134817i | ||||
\(773\) | 3.83827 | − | 11.8130i | 0.138053 | − | 0.424883i | −0.857999 | − | 0.513651i | \(-0.828293\pi\) |
0.996052 | + | 0.0887673i | \(0.0282928\pi\) | |||||||
\(774\) | 12.4485 | + | 38.3124i | 0.447451 | + | 1.37711i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.70447 | − | 1.23837i | 0.0611869 | − | 0.0444549i | ||||
\(777\) | −2.98538 | − | 9.18807i | −0.107100 | − | 0.329620i | ||||
\(778\) | 19.5735 | − | 60.2412i | 0.701746 | − | 2.15975i | ||||
\(779\) | 8.88815 | + | 6.45762i | 0.318451 | + | 0.231368i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.06650 | + | 37.2705i | 0.145511 | + | 1.33364i | ||||
\(782\) | 66.2932 | 2.37064 | ||||||||
\(783\) | 0.103633 | + | 0.0752938i | 0.00370354 | + | 0.00269078i | ||||
\(784\) | −5.15881 | + | 15.8772i | −0.184243 | + | 0.567042i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −101.262 | + | 73.5714i | −3.61191 | + | 2.62420i | ||||
\(787\) | 17.3818 | − | 12.6286i | 0.619595 | − | 0.450162i | −0.233185 | − | 0.972432i | \(-0.574915\pi\) |
0.852780 | + | 0.522270i | \(0.174915\pi\) | |||||||
\(788\) | −30.6805 | − | 94.4247i | −1.09295 | − | 3.36374i | ||||
\(789\) | 16.5643 | − | 50.9798i | 0.589706 | − | 1.81493i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.9426 | 0.673520 | ||||||||
\(792\) | 6.64849 | + | 60.9350i | 0.236244 | + | 2.16523i | ||||
\(793\) | 0.647384 | 0.0229893 | ||||||||
\(794\) | −7.30130 | − | 5.30471i | −0.259114 | − | 0.188257i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.95753 | − | 27.5685i | −0.317491 | − | 0.977138i | ||||
\(797\) | 1.72264 | − | 1.25157i | 0.0610191 | − | 0.0443330i | −0.556858 | − | 0.830608i | \(-0.687993\pi\) |
0.617877 | + | 0.786275i | \(0.287993\pi\) | |||||||
\(798\) | −22.6901 | + | 16.4853i | −0.803219 | + | 0.583573i | ||||
\(799\) | 6.75393 | + | 20.7864i | 0.238937 | + | 0.735372i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.7895 | + | 7.83902i | 0.381228 | + | 0.276978i | ||||
\(802\) | −72.9179 | −2.57482 | ||||||||
\(803\) | −36.0957 | − | 7.52318i | −1.27379 | − | 0.265487i | ||||
\(804\) | 84.2470 | 2.97116 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.66378 | + | 11.2760i | −0.129051 | + | 0.397179i | ||||
\(807\) | −3.44887 | − | 10.6145i | −0.121406 | − | 0.373649i | ||||
\(808\) | −76.0957 | + | 55.2868i | −2.67704 | + | 1.94498i | ||||
\(809\) | 4.33820 | − | 3.15189i | 0.152523 | − | 0.110815i | −0.508906 | − | 0.860822i | \(-0.669950\pi\) |
0.661430 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.05047 | − | 18.6214i | 0.212461 | − | 0.653887i | −0.786863 | − | 0.617127i | \(-0.788296\pi\) |
0.999324 | − | 0.0367600i | \(-0.0117037\pi\) | |||||||
\(812\) | −4.53766 | − | 3.29681i | −0.159241 | − | 0.115695i | ||||
\(813\) | −53.6781 | −1.88257 | ||||||||
\(814\) | −10.5271 | − | 11.5989i | −0.368975 | − | 0.406541i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −38.0768 | − | 27.6644i | −1.33295 | − | 0.968448i | ||||
\(817\) | −3.43887 | + | 10.5837i | −0.120311 | + | 0.370278i | ||||
\(818\) | −7.50402 | − | 23.0950i | −0.262372 | − | 0.807497i | ||||
\(819\) | −6.73170 | + | 4.89086i | −0.235224 | + | 0.170901i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.14095 | − | 15.8222i | −0.179420 | − | 0.552199i | 0.820387 | − | 0.571808i | \(-0.193758\pi\) |
−0.999808 | + | 0.0196092i | \(0.993758\pi\) | |||||||
\(822\) | −34.5829 | + | 106.435i | −1.20622 | + | 3.71236i | ||||
\(823\) | −14.7993 | − | 10.7523i | −0.515870 | − | 0.374801i | 0.299176 | − | 0.954198i | \(-0.403288\pi\) |
−0.815046 | + | 0.579397i | \(0.803288\pi\) | |||||||
\(824\) | 40.0210 | 1.39420 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.3227 | −1.19424 | ||||||||
\(827\) | −30.7575 | − | 22.3466i | −1.06954 | − | 0.777069i | −0.0937136 | − | 0.995599i | \(-0.529874\pi\) |
−0.975830 | + | 0.218530i | \(0.929874\pi\) | |||||||
\(828\) | −36.5967 | + | 112.633i | −1.27182 | + | 3.91427i | ||||
\(829\) | 15.9762 | + | 49.1698i | 0.554877 | + | 1.70774i | 0.696267 | + | 0.717783i | \(0.254843\pi\) |
−0.141389 | + | 0.989954i | \(0.545157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.0122 | + | 18.8990i | −0.902353 | + | 0.655598i | ||||
\(832\) | 0.937652 | + | 2.88580i | 0.0325072 | + | 0.100047i | ||||
\(833\) | −2.41922 | + | 7.44560i | −0.0838210 | + | 0.257975i | ||||
\(834\) | 84.9564 | + | 61.7244i | 2.94180 | + | 2.13734i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.4945 | + | 27.0843i | −0.535889 | + | 0.936731i | ||||
\(837\) | −0.762151 | −0.0263438 | ||||||||
\(838\) | −62.6065 | − | 45.4863i | −2.16271 | − | 1.57130i | ||||
\(839\) | 11.9288 | − | 36.7132i | 0.411829 | − | 1.26748i | −0.503227 | − | 0.864154i | \(-0.667854\pi\) |
0.915056 | − | 0.403326i | \(-0.132146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1579 | − | 16.8252i | 0.798547 | − | 0.580178i | ||||
\(842\) | −14.1938 | + | 10.3124i | −0.489151 | + | 0.355389i | ||||
\(843\) | 7.15428 | + | 22.0186i | 0.246406 | + | 0.758361i | ||||
\(844\) | 7.64568 | − | 23.5310i | 0.263175 | − | 0.809969i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −56.9013 | −1.95631 | ||||||||
\(847\) | −15.2732 | + | 17.2350i | −0.524793 | + | 0.592203i | ||||
\(848\) | 18.7672 | 0.644470 | ||||||||
\(849\) | 27.8184 | + | 20.2113i | 0.954726 | + | 0.693649i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07504 | − | 15.6194i | −0.173970 | − | 0.535425i | ||||
\(852\) | 98.6551 | − | 71.6771i | 3.37987 | − | 2.45562i | ||||
\(853\) | 27.4303 | − | 19.9293i | 0.939197 | − | 0.682366i | −0.00903033 | − | 0.999959i | \(-0.502874\pi\) |
0.948227 | + | 0.317593i | \(0.102874\pi\) | |||||||
\(854\) | −0.820596 | − | 2.52553i | −0.0280802 | − | 0.0864220i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −75.6523 | − | 54.9646i | −2.58574 | − | 1.87865i | ||||
\(857\) | 56.7117 | 1.93723 | 0.968617 | − | 0.248558i | \(-0.0799568\pi\) | ||||
0.968617 | + | 0.248558i | \(0.0799568\pi\) | |||||||
\(858\) | −13.2144 | + | 23.0986i | −0.451131 | + | 0.788574i | ||||
\(859\) | −25.7505 | −0.878597 | −0.439298 | − | 0.898341i | \(-0.644773\pi\) | ||||
−0.439298 | + | 0.898341i | \(0.644773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.14951 | − | 25.0816i | 0.277735 | − | 0.854779i | ||||
\(862\) | 2.52291 | + | 7.76473i | 0.0859308 | + | 0.264468i | ||||
\(863\) | 28.9345 | − | 21.0222i | 0.984942 | − | 0.715603i | 0.0261347 | − | 0.999658i | \(-0.491680\pi\) |
0.958808 | + | 0.284056i | \(0.0916801\pi\) | |||||||
\(864\) | 0.697025 | − | 0.506418i | 0.0237133 | − | 0.0172287i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7093 | + | 72.9698i | −0.805676 | + | 2.47962i | ||||
\(867\) | 16.0696 | + | 11.6752i | 0.545751 | + | 0.396511i | ||||
\(868\) | 33.3714 | 1.13270 | ||||||||
\(869\) | 16.2086 | − | 7.29357i | 0.549841 | − | 0.247417i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.14064 | + | 5.91452i | 0.275835 | + | 0.200406i | ||||
\(872\) | −21.3041 | + | 65.5674i | −0.721449 | + | 2.22039i | ||||
\(873\) | 0.335211 | + | 1.03167i | 0.0113452 | + | 0.0349169i | ||||
\(874\) | −38.5722 | + | 28.0244i | −1.30473 | + | 0.947938i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 37.0595 | + | 114.057i | 1.25212 | + | 3.85364i | ||||
\(877\) | −5.34913 | + | 16.4629i | −0.180627 | + | 0.555913i | −0.999846 | − | 0.0175682i | \(-0.994408\pi\) |
0.819218 | + | 0.573482i | \(0.194408\pi\) | |||||||
\(878\) | 74.6105 | + | 54.2077i | 2.51798 | + | 1.82942i | ||||
\(879\) | −75.1614 | −2.53513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.15822 | −0.140094 | −0.0700470 | − | 0.997544i | \(-0.522315\pi\) | ||||
−0.0700470 | + | 0.997544i | \(0.522315\pi\) | |||||||
\(882\) | −16.4892 | − | 11.9801i | −0.555219 | − | 0.403391i | ||||
\(883\) | 12.7533 | − | 39.2505i | 0.429182 | − | 1.32088i | −0.469751 | − | 0.882799i | \(-0.655656\pi\) |
0.898933 | − | 0.438086i | \(-0.144344\pi\) | |||||||
\(884\) | −5.20843 | − | 16.0299i | −0.175179 | − | 0.539144i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.41467 | − | 3.20744i | 0.148314 | − | 0.107756i | ||||
\(887\) | −9.41854 | − | 28.9873i | −0.316243 | − | 0.973297i | −0.975240 | − | 0.221151i | \(-0.929019\pi\) |
0.658996 | − | 0.752146i | \(-0.270981\pi\) | |||||||
\(888\) | −8.54364 | + | 26.2946i | −0.286706 | + | 0.882390i | ||||
\(889\) | −31.8990 | − | 23.1760i | −1.06986 | − | 0.777298i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.3727 | + | 5.91352i | 0.950520 | + | 0.198110i | ||||
\(892\) | −34.4803 | −1.15449 | ||||||||
\(893\) | −12.7168 | − | 9.23933i | −0.425553 | − | 0.309182i | ||||
\(894\) | −4.49077 | + | 13.8212i | −0.150194 | + | 0.462249i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.0270 | − | 17.4566i | 0.802684 | − | 0.583184i | ||||
\(897\) | −22.5728 | + | 16.4001i | −0.753684 | + | 0.547583i | ||||
\(898\) | 8.98831 | + | 27.6632i | 0.299944 | + | 0.923132i | ||||
\(899\) | 0.690047 | − | 2.12375i | 0.0230144 | − | 0.0708309i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.80090 | 0.293200 | ||||||||
\(902\) | −4.63783 | − | 42.5068i | −0.154423 | − | 1.41532i | ||||
\(903\) | 26.7134 | 0.888965 | ||||||||
\(904\) | −43.8570 | − | 31.8640i | −1.45866 | − | 1.05978i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.57976 | + | 23.3281i | 0.251821 | + | 0.775024i | ||||
\(907\) | 9.13337 | − | 6.63578i | 0.303269 | − | 0.220338i | −0.425734 | − | 0.904848i | \(-0.639984\pi\) |
0.729003 | + | 0.684511i | \(0.239984\pi\) | |||||||
\(908\) | −39.6660 | + | 28.8191i | −1.31636 | + | 0.956394i | ||||
\(909\) | −14.9654 | − | 46.0589i | −0.496372 | − | 1.52768i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.9417 | − | 29.7459i | −1.35646 | − | 0.985525i | −0.998661 | − | 0.0517251i | \(-0.983528\pi\) |
−0.357797 | − | 0.933799i | \(-0.616472\pi\) | |||||||
\(912\) | 33.8494 | 1.12086 | ||||||||
\(913\) | 3.90146 | + | 35.7578i | 0.129119 | + | 1.18341i | ||||
\(914\) | −40.2193 | −1.33034 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.4753 | − | 112.259i | 1.20518 | − | 3.70915i | ||||
\(917\) | 13.0031 | + | 40.0193i | 0.429399 | + | 1.32156i | ||||
\(918\) | 1.27742 | − | 0.928099i | 0.0421611 | − | 0.0306318i | ||||
\(919\) | 22.0198 | − | 15.9983i | 0.726366 | − | 0.527736i | −0.162046 | − | 0.986783i | \(-0.551809\pi\) |
0.888412 | + | 0.459048i | \(0.151809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.87693 | + | 11.9320i | −0.127749 | + | 0.393172i | ||||
\(922\) | 3.11518 | + | 2.26331i | 0.102593 | + | 0.0745381i | ||||
\(923\) | 14.5649 | 0.479410 | ||||||||
\(924\) | 73.3265 | + | 15.2829i | 2.41227 | + | 0.502771i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.0167 | − | 21.0819i | −0.953547 | − | 0.692793i | ||||
\(927\) | −6.36759 | + | 19.5974i | −0.209139 | + | 0.643664i | ||||
\(928\) | 0.780061 | + | 2.40078i | 0.0256068 | + | 0.0788095i | ||||
\(929\) | 18.7776 | − | 13.6427i | 0.616073 | − | 0.447603i | −0.235475 | − | 0.971880i | \(-0.575664\pi\) |
0.851548 | + | 0.524277i | \(0.175664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.73990 | − | 5.35485i | −0.0570228 | − | 0.175498i | ||||
\(932\) | 14.6637 | − | 45.1303i | 0.480326 | − | 1.47829i | ||||
\(933\) | −27.4625 | − | 19.9527i | −0.899082 | − | 0.653221i | ||||
\(934\) | −15.2910 | −0.500336 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.8128 | 0.778344 | ||||||||
\(937\) | −34.1500 | − | 24.8114i | −1.11563 | − | 0.810554i | −0.132090 | − | 0.991238i | \(-0.542169\pi\) |
−0.983541 | + | 0.180684i | \(0.942169\pi\) | |||||||
\(938\) | 12.7546 | − | 39.2547i | 0.416453 | − | 1.28171i | ||||
\(939\) | −12.1601 | − | 37.4251i | −0.396831 | − | 1.22132i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.6336 | − | 17.1708i | 0.770435 | − | 0.559754i | −0.131658 | − | 0.991295i | \(-0.542030\pi\) |
0.902093 | + | 0.431542i | \(0.142030\pi\) | |||||||
\(942\) | −9.39289 | − | 28.9083i | −0.306037 | − | 0.941885i | ||||
\(943\) | 13.8539 | − | 42.6378i | 0.451144 | − | 1.38848i | ||||
\(944\) | 33.5128 | + | 24.3485i | 1.09075 | + | 0.792476i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.4974 | − | 17.7730i | 1.28417 | − | 0.577851i | ||||
\(947\) | −9.63809 | −0.313196 | −0.156598 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156598 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(948\) | −46.7704 | − | 33.9807i | −1.51903 | − | 1.10364i | ||||
\(949\) | −4.42634 | + | 13.6229i | −0.143685 | + | 0.442218i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.3680 | − | 15.5247i | 0.692904 | − | 0.503424i | ||||
\(952\) | −30.3532 | + | 22.0529i | −0.983752 | + | 0.714738i | ||||
\(953\) | −1.61353 | − | 4.96593i | −0.0522673 | − | 0.160862i | 0.921516 | − | 0.388341i | \(-0.126952\pi\) |
−0.973783 | + | 0.227479i | \(0.926952\pi\) | |||||||
\(954\) | −7.08039 | + | 21.7912i | −0.229236 | + | 0.705517i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −50.1446 | −1.62179 | ||||||||
\(957\) | 2.48883 | − | 4.35046i | 0.0804525 | − | 0.140630i | ||||
\(958\) | 44.4529 | 1.43621 | ||||||||
\(959\) | 30.4376 | + | 22.1142i | 0.982882 | + | 0.714106i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.47390 | − | 16.8469i | −0.176577 | − | 0.543450i | ||||
\(962\) | −4.92298 | + | 3.57675i | −0.158723 | + | 0.115319i | ||||
\(963\) | 38.9517 | − | 28.3001i | 1.25520 | − | 0.911956i | ||||
\(964\) | 17.2361 | + | 53.0471i | 0.555136 | + | 1.70853i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 92.5913 | + | 67.2715i | 2.97908 | + | 2.16443i | ||||
\(967\) | −38.4583 | −1.23674 | −0.618368 | − | 0.785889i | \(-0.712206\pi\) | ||||
−0.618368 | + | 0.785889i | \(0.712206\pi\) | |||||||
\(968\) | 64.3532 | − | 14.2121i | 2.06839 | − | 0.456793i | ||||
\(969\) | 15.8737 | 0.509935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.4928 | − | 41.5267i | 0.433006 | − | 1.33265i | −0.462111 | − | 0.886822i | \(-0.652908\pi\) |
0.895116 | − | 0.445832i | \(-0.147092\pi\) | |||||||
\(972\) | −29.9779 | − | 92.2625i | −0.961542 | − | 2.95932i | ||||
\(973\) | 28.5608 | − | 20.7506i | 0.915616 | − | 0.665234i | ||||
\(974\) | −13.8543 | + | 10.0658i | −0.443921 | + | 0.322527i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.990380 | + | 3.04808i | −0.0317013 | + | 0.0975665i | ||||
\(977\) | −9.50330 | − | 6.90455i | −0.304038 | − | 0.220896i | 0.425296 | − | 0.905054i | \(-0.360170\pi\) |
−0.729334 | + | 0.684158i | \(0.760170\pi\) | |||||||
\(978\) | −43.8137 | −1.40101 | ||||||||
\(979\) | 7.12027 | − | 12.4462i | 0.227565 | − | 0.397782i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.7173 | − | 20.8643i | −0.916872 | − | 0.666147i | ||||
\(982\) | −0.404582 | + | 1.24518i | −0.0129107 | + | 0.0397351i | ||||
\(983\) | −2.88989 | − | 8.89417i | −0.0921733 | − | 0.283680i | 0.894333 | − | 0.447401i | \(-0.147650\pi\) |
−0.986507 | + | 0.163721i | \(0.947650\pi\) | |||||||
\(984\) | −61.0590 | + | 44.3620i | −1.94649 | + | 1.41421i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.42960 | + | 4.39985i | 0.0455276 | + | 0.140120i | ||||
\(987\) | −11.6600 | + | 35.8859i | −0.371143 | + | 1.14226i | ||||
\(988\) | 9.80687 | + | 7.12510i | 0.311998 | + | 0.226680i | ||||
\(989\) | 45.4117 | 1.44401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.3450 | −1.02747 | −0.513737 | − | 0.857948i | \(-0.671739\pi\) | ||||
−0.513737 | + | 0.857948i | \(0.671739\pi\) | |||||||
\(992\) | −12.1508 | − | 8.82806i | −0.385788 | − | 0.280291i | ||||
\(993\) | −6.74310 | + | 20.7531i | −0.213986 | + | 0.658581i | ||||
\(994\) | −18.4619 | − | 56.8197i | −0.585574 | − | 1.80221i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 94.6510 | − | 68.7679i | 2.99913 | − | 2.17900i | ||||
\(997\) | 8.99777 | + | 27.6923i | 0.284962 | + | 0.877023i | 0.986410 | + | 0.164302i | \(0.0525373\pi\) |
−0.701448 | + | 0.712721i | \(0.747463\pi\) | |||||||
\(998\) | −17.0540 | + | 52.4869i | −0.539836 | + | 1.66144i | ||||
\(999\) | −0.316462 | − | 0.229923i | −0.0100124 | − | 0.00727444i |
(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 | 275.2.h.b.26.2 | 8 | ||
5.2 | odd | 4 | 275.2.z.b.224.1 | 16 | |||
5.3 | odd | 4 | 275.2.z.b.224.4 | 16 | |||
5.4 | even | 2 | 55.2.g.a.26.1 | ✓ | 8 | ||
11.3 | even | 5 | inner | 275.2.h.b.201.2 | 8 | ||
11.5 | even | 5 | 3025.2.a.v.1.1 | 4 | |||
11.6 | odd | 10 | 3025.2.a.be.1.4 | 4 | |||
15.14 | odd | 2 | 495.2.n.f.136.2 | 8 | |||
20.19 | odd | 2 | 880.2.bo.e.81.2 | 8 | |||
55.3 | odd | 20 | 275.2.z.b.124.1 | 16 | |||
55.4 | even | 10 | 605.2.g.j.251.2 | 8 | |||
55.9 | even | 10 | 605.2.g.j.511.2 | 8 | |||
55.14 | even | 10 | 55.2.g.a.36.1 | yes | 8 | ||
55.19 | odd | 10 | 605.2.g.n.366.2 | 8 | |||
55.24 | odd | 10 | 605.2.g.g.511.1 | 8 | |||
55.29 | odd | 10 | 605.2.g.g.251.1 | 8 | |||
55.39 | odd | 10 | 605.2.a.i.1.1 | 4 | |||
55.47 | odd | 20 | 275.2.z.b.124.4 | 16 | |||
55.49 | even | 10 | 605.2.a.l.1.4 | 4 | |||
55.54 | odd | 2 | 605.2.g.n.81.2 | 8 | |||
165.14 | odd | 10 | 495.2.n.f.91.2 | 8 | |||
165.104 | odd | 10 | 5445.2.a.bg.1.1 | 4 | |||
165.149 | even | 10 | 5445.2.a.bu.1.4 | 4 | |||
220.39 | even | 10 | 9680.2.a.cv.1.4 | 4 | |||
220.159 | odd | 10 | 9680.2.a.cs.1.4 | 4 | |||
220.179 | odd | 10 | 880.2.bo.e.641.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.a.26.1 | ✓ | 8 | 5.4 | even | 2 | ||
55.2.g.a.36.1 | yes | 8 | 55.14 | even | 10 | ||
275.2.h.b.26.2 | 8 | 1.1 | even | 1 | trivial | ||
275.2.h.b.201.2 | 8 | 11.3 | even | 5 | inner | ||
275.2.z.b.124.1 | 16 | 55.3 | odd | 20 | |||
275.2.z.b.124.4 | 16 | 55.47 | odd | 20 | |||
275.2.z.b.224.1 | 16 | 5.2 | odd | 4 | |||
275.2.z.b.224.4 | 16 | 5.3 | odd | 4 | |||
495.2.n.f.91.2 | 8 | 165.14 | odd | 10 | |||
495.2.n.f.136.2 | 8 | 15.14 | odd | 2 | |||
605.2.a.i.1.1 | 4 | 55.39 | odd | 10 | |||
605.2.a.l.1.4 | 4 | 55.49 | even | 10 | |||
605.2.g.g.251.1 | 8 | 55.29 | odd | 10 | |||
605.2.g.g.511.1 | 8 | 55.24 | odd | 10 | |||
605.2.g.j.251.2 | 8 | 55.4 | even | 10 | |||
605.2.g.j.511.2 | 8 | 55.9 | even | 10 | |||
605.2.g.n.81.2 | 8 | 55.54 | odd | 2 | |||
605.2.g.n.366.2 | 8 | 55.19 | odd | 10 | |||
880.2.bo.e.81.2 | 8 | 20.19 | odd | 2 | |||
880.2.bo.e.641.2 | 8 | 220.179 | odd | 10 | |||
3025.2.a.v.1.1 | 4 | 11.5 | even | 5 | |||
3025.2.a.be.1.4 | 4 | 11.6 | odd | 10 | |||
5445.2.a.bg.1.1 | 4 | 165.104 | odd | 10 | |||
5445.2.a.bu.1.4 | 4 | 165.149 | even | 10 | |||
9680.2.a.cs.1.4 | 4 | 220.159 | odd | 10 | |||
9680.2.a.cv.1.4 | 4 | 220.39 | even | 10 |