Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, 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("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not 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: | \(4.83094932229\) |
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 | 81.2 | ||
Root | \(-0.762262 + 2.34600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.81 |
Dual form | 605.2.g.n.366.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 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 | \(0.352249\pi\) |
−0.887777 | + | 0.460273i | \(0.847751\pi\) | |||||||
\(4\) | 1.35140 | + | 4.15918i | 0.675700 | + | 2.07959i | ||||
\(5\) | −0.809017 | + | 0.587785i | −0.361803 | + | 0.262866i | ||||
\(6\) | −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 | ||||
\(10\) | −2.52452 | −0.798325 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −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 | ||||
\(15\) | −0.762262 | − | 2.34600i | −0.196815 | − | 0.605735i | ||||
\(16\) | −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 | −0.997900 | − | 0.0647668i | \(-0.979370\pi\) |
0.845387 | + | 0.534154i | \(0.179370\pi\) | |||||||
\(20\) | −3.53801 | − | 2.57052i | −0.791123 | − | 0.574785i | ||||
\(21\) | 5.16413 | 1.12690 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.77882 | 1.83051 | 0.915255 | − | 0.402874i | \(-0.131989\pi\) | ||||
0.915255 | + | 0.402874i | \(0.131989\pi\) | |||||||
\(24\) | −11.9563 | − | 8.68677i | −2.44057 | − | 1.77318i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 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 | 0.967094 | − | 0.254419i | \(-0.0818844\pi\) |
−0.931939 | + | 0.362614i | \(0.881884\pi\) | |||||||
\(30\) | 1.92435 | − | 5.92254i | 0.351336 | − | 1.08130i | ||||
\(31\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.55150 | −1.29507 | ||||||||
\(35\) | 1.69369 | + | 1.23053i | 0.286285 | + | 0.207998i | ||||
\(36\) | 4.16875 | − | 12.8301i | 0.694792 | − | 2.13835i | ||||
\(37\) | −0.578100 | − | 1.77921i | −0.0950391 | − | 0.292500i | 0.892225 | − | 0.451592i | \(-0.149144\pi\) |
−0.987264 | + | 0.159091i | \(0.949144\pi\) | |||||||
\(38\) | −4.39378 | + | 3.19227i | −0.712766 | + | 0.517855i | ||||
\(39\) | −2.57128 | + | 1.86814i | −0.411734 | + | 0.299142i | ||||
\(40\) | −1.85140 | − | 5.69802i | −0.292732 | − | 0.900937i | ||||
\(41\) | 1.57810 | − | 4.85689i | 0.246458 | − | 0.758519i | −0.748935 | − | 0.662643i | \(-0.769435\pi\) |
0.995393 | − | 0.0958763i | \(-0.0305653\pi\) | |||||||
\(42\) | 10.5471 | + | 7.66294i | 1.62746 | + | 1.18242i | ||||
\(43\) | −5.17287 | −0.788856 | −0.394428 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394428 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.08477 | 0.459850 | ||||||||
\(46\) | 17.9297 | + | 13.0267i | 2.64359 | + | 1.92068i | ||||
\(47\) | −2.25789 | + | 6.94907i | −0.329347 | + | 1.01363i | 0.640093 | + | 0.768298i | \(0.278896\pi\) |
−0.969440 | + | 0.245329i | \(0.921104\pi\) | |||||||
\(48\) | −4.86218 | − | 14.9643i | −0.701796 | − | 2.15991i | ||||
\(49\) | 2.11737 | − | 1.53836i | 0.302482 | − | 0.219766i | ||||
\(50\) | 2.04238 | − | 1.48388i | 0.288837 | − | 0.209852i | ||||
\(51\) | −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 | 0.739139 | − | 0.673553i | \(-0.235233\pi\) |
−0.412180 | + | 0.911102i | \(0.635233\pi\) | |||||||
\(54\) | 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 | \(-0.238931\pi\) | |||||||
\(60\) | 8.72732 | − | 6.34077i | 1.12669 | − | 0.818590i | ||||
\(61\) | −0.406490 | + | 0.295332i | −0.0520457 | + | 0.0378134i | −0.613504 | − | 0.789692i | \(-0.710241\pi\) |
0.561458 | + | 0.827505i | \(0.310241\pi\) | |||||||
\(62\) | 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 | ||||
\(65\) | −1.28846 | −0.159813 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.80964 | −0.954099 | −0.477050 | − | 0.878876i | \(-0.658294\pi\) | ||||
−0.477050 | + | 0.878876i | \(0.658294\pi\) | |||||||
\(68\) | −10.5831 | − | 7.68907i | −1.28339 | − | 0.932437i | ||||
\(69\) | −6.69176 | + | 20.5951i | −0.805594 | + | 2.47936i | ||||
\(70\) | 1.63319 | + | 5.02644i | 0.195204 | + | 0.600775i | ||||
\(71\) | 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 | ||||
\(75\) | 1.99563 | + | 1.44991i | 0.230435 | + | 0.167421i | ||||
\(76\) | −9.40812 | −1.07919 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.02363 | −0.908498 | ||||||||
\(79\) | 4.33558 | + | 3.14998i | 0.487791 | + | 0.354401i | 0.804334 | − | 0.594177i | \(-0.202522\pi\) |
−0.316543 | + | 0.948578i | \(0.602522\pi\) | |||||||
\(80\) | 1.97110 | − | 6.06643i | 0.220376 | − | 0.678248i | ||||
\(81\) | −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 | ||||
\(85\) | 0.924349 | − | 2.84485i | 0.100260 | − | 0.308568i | ||||
\(86\) | −10.5650 | − | 7.67591i | −1.13925 | − | 0.827715i | ||||
\(87\) | −1.51119 | −0.162017 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.32336 | −0.458275 | −0.229137 | − | 0.973394i | \(-0.573591\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573591\pi\) | |||||||
\(90\) | 6.30027 | + | 4.57742i | 0.664107 | + | 0.482502i | ||||
\(91\) | 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 | ||||
\(95\) | −0.664789 | − | 2.04601i | −0.0682059 | − | 0.209916i | ||||
\(96\) | 3.14089 | − | 9.66666i | 0.320566 | − | 0.986599i | ||||
\(97\) | 0.284493 | + | 0.206696i | 0.0288859 | + | 0.0209868i | 0.602135 | − | 0.798395i | \(-0.294317\pi\) |
−0.573249 | + | 0.819381i | \(0.694317\pi\) | |||||||
\(98\) | 6.60723 | 0.667431 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.37322 | 0.437322 | ||||||||
\(101\) | −12.7011 | − | 9.22791i | −1.26381 | − | 0.918211i | −0.264872 | − | 0.964284i | \(-0.585330\pi\) |
−0.998938 | + | 0.0460722i | \(0.985330\pi\) | |||||||
\(102\) | 5.75622 | − | 17.7158i | 0.569951 | − | 1.75413i | ||||
\(103\) | 2.06420 | + | 6.35297i | 0.203392 | + | 0.625977i | 0.999776 | + | 0.0211846i | \(0.00674378\pi\) |
−0.796383 | + | 0.604792i | \(0.793256\pi\) | |||||||
\(104\) | −6.24518 | + | 4.53739i | −0.612391 | + | 0.444928i | ||||
\(105\) | −4.17787 | + | 3.03540i | −0.407718 | + | 0.296225i | ||||
\(106\) | 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 | \(-0.685787\pi\) | ||||
−0.551087 | + | 0.834448i | \(0.685787\pi\) | |||||||
\(110\) | 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 | \(-0.760066\pi\) |
0.992140 | − | 0.125129i | \(-0.0399345\pi\) | |||||||
\(114\) | −4.13986 | − | 12.7412i | −0.387733 | − | 1.19332i | ||||
\(115\) | −7.10222 | + | 5.16006i | −0.662285 | + | 0.481178i | ||||
\(116\) | −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 | ||||
\(120\) | 14.7788 | 1.34912 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.26845 | −0.114840 | ||||||||
\(123\) | 10.1914 | + | 7.40445i | 0.918923 | + | 0.667637i | ||||
\(124\) | −4.92586 | + | 15.1602i | −0.442356 | + | 1.36143i | ||||
\(125\) | 0.309017 | + | 0.951057i | 0.0276393 | + | 0.0850651i | ||||
\(126\) | −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 | ||||
\(130\) | −2.63152 | − | 1.91191i | −0.230800 | − | 0.167686i | ||||
\(131\) | 20.0997 | 1.75612 | 0.878058 | − | 0.478555i | \(-0.158839\pi\) | ||||
0.878058 | + | 0.478555i | \(0.158839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50377 | 0.390527 | ||||||||
\(134\) | −15.9503 | − | 11.5886i | −1.37789 | − | 1.00110i | ||||
\(135\) | −0.0646137 | + | 0.198861i | −0.00556107 | + | 0.0171152i | ||||
\(136\) | −5.53801 | − | 17.0442i | −0.474881 | − | 1.46153i | ||||
\(137\) | 14.5390 | − | 10.5632i | 1.24215 | − | 0.902478i | 0.244414 | − | 0.969671i | \(-0.421404\pi\) |
0.997740 | + | 0.0671930i | \(0.0214043\pi\) | |||||||
\(138\) | −44.2278 | + | 32.1334i | −3.76492 | + | 2.73537i | ||||
\(139\) | −5.21098 | − | 16.0377i | −0.441989 | − | 1.36030i | −0.885752 | − | 0.464159i | \(-0.846357\pi\) |
0.443762 | − | 0.896145i | \(-0.353643\pi\) | |||||||
\(140\) | −2.82917 | + | 8.70729i | −0.239108 | + | 0.735900i | ||||
\(141\) | −14.5814 | − | 10.5940i | −1.22798 | − | 0.892178i | ||||
\(142\) | 28.5376 | 2.39482 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 19.6766 | 1.63971 | ||||||||
\(145\) | −0.495628 | − | 0.360095i | −0.0411597 | − | 0.0299042i | ||||
\(146\) | −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 | −0.507759 | − | 0.861499i | \(-0.669526\pi\) |
0.662428 | + | 0.749126i | \(0.269526\pi\) | |||||||
\(150\) | 1.92435 | + | 5.92254i | 0.157122 | + | 0.483573i | ||||
\(151\) | 1.21718 | − | 3.74609i | 0.0990525 | − | 0.304852i | −0.889236 | − | 0.457448i | \(-0.848763\pi\) |
0.988289 | + | 0.152596i | \(0.0487634\pi\) | |||||||
\(152\) | −10.4274 | − | 7.57597i | −0.845776 | − | 0.614492i | ||||
\(153\) | 9.22732 | 0.745985 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.64501 | −0.292774 | ||||||||
\(156\) | −11.2448 | − | 8.16981i | −0.900302 | − | 0.654108i | ||||
\(157\) | −1.50834 | + | 4.64218i | −0.120378 | + | 0.370486i | −0.993031 | − | 0.117856i | \(-0.962398\pi\) |
0.872652 | + | 0.488342i | \(0.162398\pi\) | |||||||
\(158\) | 4.18073 | + | 12.8669i | 0.332601 | + | 1.02364i | ||||
\(159\) | −5.87155 | + | 4.26593i | −0.465644 | + | 0.338310i | ||||
\(160\) | 3.33354 | − | 2.42196i | 0.263540 | − | 0.191473i | ||||
\(161\) | −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 | 0.787948 | − | 0.615741i | \(-0.211143\pi\) |
−0.342115 | + | 0.939658i | \(0.611143\pi\) | |||||||
\(164\) | 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 | ||||
\(170\) | 6.10929 | − | 4.43866i | 0.468561 | − | 0.340430i | ||||
\(171\) | 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 | ||||
\(175\) | −2.09351 | −0.158254 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 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 | \(-0.187939\pi\) | |||||||
\(180\) | 4.16875 | + | 12.8301i | 0.310720 | + | 0.956299i | ||||
\(181\) | 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 | ||||
\(185\) | 1.51349 | + | 1.09961i | 0.111274 | + | 0.0808451i | ||||
\(186\) | −22.6986 | −1.66435 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −31.9538 | −2.33047 | ||||||||
\(189\) | −0.354140 | − | 0.257298i | −0.0257599 | − | 0.0187157i | ||||
\(190\) | 1.67828 | − | 5.16520i | 0.121755 | − | 0.374723i | ||||
\(191\) | 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 | ||||
\(195\) | 0.982141 | − | 3.02272i | 0.0703326 | − | 0.216461i | ||||
\(196\) | 9.25974 | + | 6.72759i | 0.661410 | + | 0.480542i | ||||
\(197\) | −22.7027 | −1.61750 | −0.808751 | − | 0.588151i | \(-0.799856\pi\) | ||||
−0.808751 | + | 0.588151i | \(0.799856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.62834 | −0.469870 | −0.234935 | − | 0.972011i | \(-0.575488\pi\) | ||||
−0.234935 | + | 0.972011i | \(0.575488\pi\) | |||||||
\(200\) | 4.84703 | + | 3.52157i | 0.342737 | + | 0.249013i | ||||
\(201\) | 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 | ||||
\(205\) | 1.57810 | + | 4.85689i | 0.110219 | + | 0.339220i | ||||
\(206\) | −5.21114 | + | 16.0382i | −0.363077 | + | 1.11744i | ||||
\(207\) | −21.9087 | − | 15.9176i | −1.52276 | − | 1.10635i | ||||
\(208\) | −8.21858 | −0.569856 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −13.0370 | −0.899636 | ||||||||
\(211\) | 4.57709 | + | 3.32545i | 0.315100 | + | 0.228934i | 0.734082 | − | 0.679061i | \(-0.237613\pi\) |
−0.418982 | + | 0.907995i | \(0.637613\pi\) | |||||||
\(212\) | −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 | ||||
\(215\) | 4.18494 | − | 3.04054i | 0.285411 | − | 0.207363i | ||||
\(216\) | 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 | −0.835741 | − | 0.549124i | \(-0.814961\pi\) |
0.998896 | + | 0.0469856i | \(0.0149615\pi\) | |||||||
\(224\) | 2.66566 | + | 8.20407i | 0.178107 | + | 0.548158i | ||||
\(225\) | −2.49563 | + | 1.81318i | −0.166375 | + | 0.120879i | ||||
\(226\) | 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 | \(-0.650556\pi\) | |||||||
\(230\) | −22.1623 | −1.46134 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −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 | ||||
\(235\) | −2.25789 | − | 6.94907i | −0.147289 | − | 0.453307i | ||||
\(236\) | 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 | \(-0.779068\pi\) |
0.997839 | − | 0.0657129i | \(-0.0209322\pi\) | |||||||
\(240\) | 12.7294 | + | 9.24842i | 0.821677 | + | 0.596983i | ||||
\(241\) | −12.7542 | −0.821572 | −0.410786 | − | 0.911732i | \(-0.634746\pi\) | ||||
−0.410786 | + | 0.911732i | \(0.634746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1829 | 1.42303 | ||||||||
\(244\) | −1.77767 | − | 1.29155i | −0.113804 | − | 0.0826833i | ||||
\(245\) | −0.808764 | + | 2.48912i | −0.0516701 | + | 0.159024i | ||||
\(246\) | 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 | ||||
\(250\) | −0.780121 | + | 2.40097i | −0.0493392 | + | 0.151850i | ||||
\(251\) | 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 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 47.5471 | 2.98337 | ||||||||
\(255\) | 5.96943 | + | 4.33705i | 0.373820 | + | 0.271596i | ||||
\(256\) | −9.61149 | + | 29.5811i | −0.600718 | + | 1.84882i | ||||
\(257\) | −1.82198 | − | 5.60747i | −0.113652 | − | 0.349784i | 0.878012 | − | 0.478639i | \(-0.158870\pi\) |
−0.991663 | + | 0.128855i | \(0.958870\pi\) | |||||||
\(258\) | 26.0610 | − | 18.9344i | 1.62249 | − | 1.17881i | ||||
\(259\) | −3.16850 | + | 2.30205i | −0.196881 | + | 0.143042i | ||||
\(260\) | −1.74122 | − | 5.35892i | −0.107986 | − | 0.332346i | ||||
\(261\) | 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 | \(0.266302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.94221 | −0.180738 | ||||||||
\(266\) | 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 | \(0.255954\pi\) | |||||||
\(270\) | −0.427051 | + | 0.310271i | −0.0259895 | + | 0.0188825i | ||||
\(271\) | 6.72447 | + | 20.6958i | 0.408482 | + | 1.25718i | 0.917952 | + | 0.396691i | \(0.129841\pi\) |
−0.509470 | + | 0.860488i | \(0.670159\pi\) | |||||||
\(272\) | 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 | ||||
\(280\) | −10.1473 | + | 7.37245i | −0.606417 | + | 0.440588i | ||||
\(281\) | 7.59310 | − | 5.51671i | 0.452966 | − | 0.329099i | −0.337799 | − | 0.941218i | \(-0.609683\pi\) |
0.790766 | + | 0.612119i | \(0.209683\pi\) | |||||||
\(282\) | −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 | ||||
\(285\) | 5.30669 | 0.314341 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6912 | −0.631083 | ||||||||
\(288\) | 10.2832 | + | 7.47118i | 0.605943 | + | 0.440243i | ||||
\(289\) | −2.48832 | + | 7.65828i | −0.146372 | + | 0.450487i | ||||
\(290\) | −0.477925 | − | 1.47090i | −0.0280647 | − | 0.0863744i | ||||
\(291\) | −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 | ||||
\(295\) | 5.25393 | + | 3.81720i | 0.305895 | + | 0.222246i | ||||
\(296\) | 11.2083 | 0.651468 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.89138 | 0.341278 | ||||||||
\(299\) | 9.15089 | + | 6.64851i | 0.529210 | + | 0.384493i | ||||
\(300\) | −3.33354 | + | 10.2596i | −0.192462 | + | 0.592337i | ||||
\(301\) | 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 | ||||
\(305\) | 0.155265 | − | 0.477858i | 0.00889047 | − | 0.0273621i | ||||
\(306\) | 18.8457 | + | 13.6922i | 1.07734 | + | 0.782732i | ||||
\(307\) | −5.08609 | −0.290278 | −0.145139 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145139 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.4775 | −0.937375 | ||||||||
\(310\) | −7.44450 | − | 5.40875i | −0.422819 | − | 0.307196i | ||||
\(311\) | 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 | −0.889402 | − | 0.457125i | \(-0.848879\pi\) |
0.159912 | + | 0.987131i | \(0.448879\pi\) | |||||||
\(314\) | −9.96903 | + | 7.24292i | −0.562585 | + | 0.408742i | ||||
\(315\) | −1.99563 | − | 6.14191i | −0.112441 | − | 0.346057i | ||||
\(316\) | −7.24225 | + | 22.2894i | −0.407408 | + | 1.25387i | ||||
\(317\) | −8.66246 | − | 6.29364i | −0.486532 | − | 0.353486i | 0.317317 | − | 0.948320i | \(-0.397218\pi\) |
−0.803849 | + | 0.594833i | \(0.797218\pi\) | |||||||
\(318\) | −18.3221 | −1.02745 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.35499 | −0.131648 | ||||||||
\(321\) | −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 | ||||
\(325\) | 1.04238 | − | 0.757336i | 0.0578210 | − | 0.0420094i | ||||
\(326\) | 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 | ||||
\(335\) | 6.31813 | − | 4.59039i | 0.345196 | − | 0.250800i | ||||
\(336\) | −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 | ||||
\(340\) | 13.0814 | 0.709440 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 16.7534 | 0.905920 | ||||||||
\(343\) | −16.2885 | − | 11.8343i | −0.879498 | − | 0.638993i | ||||
\(344\) | 9.57705 | − | 29.4751i | 0.516360 | − | 1.58919i | ||||
\(345\) | −6.69176 | − | 20.5951i | −0.360272 | − | 1.10880i | ||||
\(346\) | −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 | −0.958633 | − | 0.284645i | \(-0.908124\pi\) |
0.942861 | + | 0.333188i | \(0.108124\pi\) | |||||||
\(350\) | −4.27575 | − | 3.10651i | −0.228548 | − | 0.166050i | ||||
\(351\) | 0.269409 | 0.0143800 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.5166 | −0.825865 | −0.412933 | − | 0.910762i | \(-0.635495\pi\) | ||||
−0.412933 | + | 0.910762i | \(0.635495\pi\) | |||||||
\(354\) | 32.7179 | + | 23.7709i | 1.73894 | + | 1.26341i | ||||
\(355\) | −3.49318 | + | 10.7509i | −0.185399 | + | 0.570598i | ||||
\(356\) | −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 | \(-0.920496\pi\) |
0.638624 | − | 0.769519i | \(-0.279504\pi\) | |||||||
\(360\) | −5.71114 | + | 17.5771i | −0.301003 | + | 0.926393i | ||||
\(361\) | 11.6271 | + | 8.44759i | 0.611953 | + | 0.444610i | ||||
\(362\) | 4.40051 | 0.231286 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.7963 | 0.618295 | ||||||||
\(365\) | −8.99396 | − | 6.53449i | −0.470765 | − | 0.342031i | ||||
\(366\) | 0.966888 | − | 2.97578i | 0.0505400 | − | 0.155546i | ||||
\(367\) | 11.0180 | + | 33.9099i | 0.575135 | + | 1.77008i | 0.635719 | + | 0.771920i | \(0.280704\pi\) |
−0.0605844 | + | 0.998163i | \(0.519296\pi\) | |||||||
\(368\) | −45.3024 | + | 32.9141i | −2.36155 | + | 1.71577i | ||||
\(369\) | −12.7448 | + | 9.25962i | −0.663466 | + | 0.482037i | ||||
\(370\) | 1.45943 | + | 4.49166i | 0.0758721 | + | 0.233510i | ||||
\(371\) | 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 | \(0.601731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.46673 | −0.127381 | ||||||||
\(376\) | −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 | \(0.358738\pi\) | |||||||
\(380\) | 7.61133 | − | 5.52996i | 0.390453 | − | 0.283681i | ||||
\(381\) | 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 | 0.206736 | − | 0.978397i | \(-0.433716\pi\) |
−0.866626 | + | 0.498959i | \(0.833716\pi\) | |||||||
\(384\) | −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 | \(-0.319440\pi\) | |||||||
\(390\) | 6.49126 | − | 4.71617i | 0.328698 | − | 0.238813i | ||||
\(391\) | −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 | ||||
\(395\) | −5.35907 | −0.269644 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.57490 | 0.179419 | 0.0897094 | − | 0.995968i | \(-0.471406\pi\) | ||||
0.0897094 | + | 0.995968i | \(0.471406\pi\) | |||||||
\(398\) | −13.5376 | − | 9.83564i | −0.678579 | − | 0.493016i | ||||
\(399\) | −3.43305 | + | 10.5659i | −0.171868 | + | 0.528954i | ||||
\(400\) | 1.97110 | + | 6.06643i | 0.0985552 | + | 0.303322i | ||||
\(401\) | −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 | ||||
\(405\) | 7.06961 | + | 5.13637i | 0.351292 | + | 0.255228i | ||||
\(406\) | 3.23782 | 0.160690 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 44.2072 | 2.18858 | ||||||||
\(409\) | 7.78197 | + | 5.65393i | 0.384794 | + | 0.279569i | 0.763319 | − | 0.646022i | \(-0.223569\pi\) |
−0.378525 | + | 0.925591i | \(0.623569\pi\) | |||||||
\(410\) | −3.98395 | + | 12.2613i | −0.196753 | + | 0.605545i | ||||
\(411\) | 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 | ||||
\(415\) | −3.35140 | + | 10.3145i | −0.164514 | + | 0.506321i | ||||
\(416\) | −4.29512 | − | 3.12059i | −0.210586 | − | 0.152999i | ||||
\(417\) | 41.5967 | 2.03700 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.6537 | −1.49753 | −0.748765 | − | 0.662836i | \(-0.769353\pi\) | ||||
−0.748765 | + | 0.662836i | \(0.769353\pi\) | |||||||
\(420\) | −18.2707 | − | 13.2745i | −0.891521 | − | 0.647728i | ||||
\(421\) | −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 | ||||
\(425\) | 0.924349 | + | 2.84485i | 0.0448375 | + | 0.137996i | ||||
\(426\) | −21.7532 | + | 66.9493i | −1.05394 | + | 3.24371i | ||||
\(427\) | 0.850991 | + | 0.618281i | 0.0411823 | + | 0.0299207i | ||||
\(428\) | −68.2571 | −3.29933 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.0590 | 0.629763 | ||||||||
\(431\) | −2.61636 | − | 1.90090i | −0.126026 | − | 0.0915631i | 0.522987 | − | 0.852341i | \(-0.324818\pi\) |
−0.649013 | + | 0.760778i | \(0.724818\pi\) | |||||||
\(432\) | −0.412147 | + | 1.26846i | −0.0198294 | + | 0.0610287i | ||||
\(433\) | −9.39161 | − | 28.9044i | −0.451332 | − | 1.38906i | −0.875388 | − | 0.483421i | \(-0.839394\pi\) |
0.424056 | − | 0.905636i | \(-0.360606\pi\) | |||||||
\(434\) | 15.5851 | − | 11.3233i | 0.748110 | − | 0.543534i | ||||
\(435\) | 1.22258 | − | 0.888257i | 0.0586183 | − | 0.0425887i | ||||
\(436\) | −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 | \(-0.837026\pi\) | ||||
−0.871767 | + | 0.489921i | \(0.837026\pi\) | |||||||
\(440\) | 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 | −0.965669 | − | 0.259774i | \(-0.916352\pi\) |
0.933934 | + | 0.357445i | \(0.116352\pi\) | |||||||
\(444\) | 6.23630 | + | 19.1933i | 0.295962 | + | 0.910876i | ||||
\(445\) | 3.49767 | − | 2.54120i | 0.165805 | − | 0.120465i | ||||
\(446\) | 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 | \(0.612358\pi\) | |||||||
\(450\) | −7.78757 | −0.367109 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 39.5699 | 1.86121 | ||||||||
\(453\) | 7.86051 | + | 5.71100i | 0.369319 | + | 0.268326i | ||||
\(454\) | −8.74624 | + | 26.9182i | −0.410482 | + | 1.26333i | ||||
\(455\) | 0.833541 | + | 2.56538i | 0.0390770 | + | 0.120267i | ||||
\(456\) | 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 | ||||
\(460\) | −31.0596 | − | 22.5661i | −1.44816 | − | 1.05215i | ||||
\(461\) | −1.52527 | −0.0710387 | −0.0355193 | − | 0.999369i | \(-0.511309\pi\) | ||||
−0.0355193 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2073 | 0.660268 | 0.330134 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330134 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(464\) | −3.16143 | − | 2.29691i | −0.146765 | − | 0.106631i | ||||
\(465\) | 2.77845 | − | 8.55119i | 0.128848 | − | 0.396552i | ||||
\(466\) | −8.46491 | − | 26.0523i | −0.392129 | − | 1.20685i | ||||
\(467\) | 4.90020 | − | 3.56020i | 0.226754 | − | 0.164746i | −0.468608 | − | 0.883406i | \(-0.655244\pi\) |
0.695362 | + | 0.718660i | \(0.255244\pi\) | |||||||
\(468\) | 14.0621 | − | 10.2167i | 0.650022 | − | 0.472269i | ||||
\(469\) | 5.05229 | + | 15.5494i | 0.233293 | + | 0.718002i | ||||
\(470\) | 5.70010 | − | 17.5431i | 0.262926 | − | 0.809203i | ||||
\(471\) | −9.74081 | − | 7.07711i | −0.448833 | − | 0.326096i | ||||
\(472\) | 38.9085 | 1.79091 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −33.3727 | −1.53286 | ||||||||
\(475\) | 1.74044 | + | 1.26450i | 0.0798569 | + | 0.0580194i | ||||
\(476\) | −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 | −0.863576 | − | 0.504219i | \(-0.831780\pi\) |
0.212681 | + | 0.977122i | \(0.431780\pi\) | |||||||
\(480\) | 3.14089 | + | 9.66666i | 0.143361 | + | 0.441221i | ||||
\(481\) | 0.744857 | − | 2.29243i | 0.0339626 | − | 0.104526i | ||||
\(482\) | −26.0490 | − | 18.9257i | −1.18650 | − | 0.862043i | ||||
\(483\) | 45.3350 | 2.06281 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.351653 | −0.0159677 | ||||||||
\(486\) | 45.3059 | + | 32.9167i | 2.05512 | + | 1.49313i | ||||
\(487\) | 2.09619 | − | 6.45140i | 0.0949874 | − | 0.292341i | −0.892263 | − | 0.451516i | \(-0.850883\pi\) |
0.987250 | + | 0.159175i | \(0.0508834\pi\) | |||||||
\(488\) | −0.930235 | − | 2.86297i | −0.0421097 | − | 0.129600i | ||||
\(489\) | −14.0407 | + | 10.2011i | −0.634941 | + | 0.461312i | ||||
\(490\) | −5.34536 | + | 3.88363i | −0.241479 | + | 0.175445i | ||||
\(491\) | −0.160261 | − | 0.493232i | −0.00723247 | − | 0.0222592i | 0.947375 | − | 0.320125i | \(-0.103725\pi\) |
−0.954608 | + | 0.297866i | \(0.903725\pi\) | |||||||
\(492\) | −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 | \(0.737248\pi\) | |||||||
\(500\) | −3.53801 | + | 2.57052i | −0.158225 | + | 0.114957i | ||||
\(501\) | −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 | ||||
\(505\) | 15.6995 | 0.698617 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 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 | \(0.907043\pi\) | |||||||
\(510\) | 5.75622 | + | 17.7158i | 0.254890 | + | 0.784470i | ||||
\(511\) | 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 | ||||
\(515\) | −5.40416 | − | 3.92635i | −0.238136 | − | 0.173016i | ||||
\(516\) | 55.8027 | 2.45658 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9.88725 | −0.434421 | ||||||||
\(519\) | −16.7869 | − | 12.1964i | −0.736862 | − | 0.535361i | ||||
\(520\) | 2.38545 | − | 7.34165i | 0.104609 | − | 0.321953i | ||||
\(521\) | 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 | ||||
\(525\) | 1.59580 | − | 4.91138i | 0.0696466 | − | 0.214350i | ||||
\(526\) | 44.3820 | + | 32.2454i | 1.93515 | + | 1.40597i | ||||
\(527\) | −10.9032 | −0.474949 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.0677 | 2.35077 | ||||||||
\(530\) | −6.00911 | − | 4.36588i | −0.261019 | − | 0.189642i | ||||
\(531\) | −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 | ||||
\(535\) | −4.82313 | − | 14.8441i | −0.208522 | − | 0.641765i | ||||
\(536\) | 14.4588 | − | 44.4995i | 0.624524 | − | 1.92209i | ||||
\(537\) | 41.9809 | + | 30.5009i | 1.81161 | + | 1.31621i | ||||
\(538\) | 11.4223 | 0.492449 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.914417 | −0.0393502 | ||||||||
\(541\) | 33.7684 | + | 24.5342i | 1.45182 | + | 1.05481i | 0.985403 | + | 0.170239i | \(0.0544538\pi\) |
0.466413 | + | 0.884567i | \(0.345546\pi\) | |||||||
\(542\) | −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 | ||||
\(545\) | 9.30939 | − | 6.76367i | 0.398770 | − | 0.289724i | ||||
\(546\) | 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 | ||||
\(555\) | −3.73337 | + | 2.71245i | −0.158473 | + | 0.115137i | ||||
\(556\) | 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 | ||||
\(560\) | −13.3537 | −0.564298 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||
\(565\) | 2.79606 | + | 8.60538i | 0.117631 | + | 0.362031i | ||||
\(566\) | −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 | \(-0.551942\pi\) |
0.711408 | − | 0.702779i | \(-0.248058\pi\) | |||||||
\(570\) | 10.8383 | + | 7.87447i | 0.453966 | + | 0.329825i | ||||
\(571\) | 5.03980 | 0.210909 | 0.105455 | − | 0.994424i | \(-0.466370\pi\) | ||||
0.105455 | + | 0.994424i | \(0.466370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.0615611 | −0.00257175 | ||||||||
\(574\) | −21.8356 | − | 15.8645i | −0.911399 | − | 0.662170i | ||||
\(575\) | 2.71281 | − | 8.34916i | 0.113132 | − | 0.348184i | ||||
\(576\) | −2.24488 | − | 6.90905i | −0.0935369 | − | 0.287877i | ||||
\(577\) | −28.1877 | + | 20.4796i | −1.17347 | + | 0.852576i | −0.991420 | − | 0.130713i | \(-0.958273\pi\) |
−0.182050 | + | 0.983289i | \(0.558273\pi\) | |||||||
\(578\) | −16.4461 | + | 11.9488i | −0.684066 | + | 0.497003i | ||||
\(579\) | 1.11080 | + | 3.41870i | 0.0461634 | + | 0.142076i | ||||
\(580\) | 0.827908 | − | 2.54804i | 0.0343770 | − | 0.105802i | ||||
\(581\) | −18.3686 | − | 13.3456i | −0.762059 | − | 0.553668i | ||||
\(582\) | −2.18985 | −0.0907724 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −66.6057 | −2.75616 | ||||||||
\(585\) | 3.21551 | + | 2.33620i | 0.132945 | + | 0.0965901i | ||||
\(586\) | 23.7703 | − | 73.1575i | 0.981943 | − | 3.02211i | ||||
\(587\) | −4.25772 | − | 13.1039i | −0.175735 | − | 0.540857i | 0.823931 | − | 0.566690i | \(-0.191776\pi\) |
−0.999666 | + | 0.0258331i | \(0.991776\pi\) | |||||||
\(588\) | −22.8413 | + | 16.5952i | −0.941959 | + | 0.684373i | ||||
\(589\) | −6.34392 | + | 4.60913i | −0.261397 | + | 0.189916i | ||||
\(590\) | 5.06627 | + | 15.5924i | 0.208575 | + | 0.641928i | ||||
\(591\) | 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 | 0 | ||||||||
\(595\) | −6.26222 | −0.256726 | ||||||||
\(596\) | 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 | \(0.190515\pi\) | |||||||
\(600\) | −11.9563 | + | 8.68677i | −0.488115 | + | 0.354636i | ||||
\(601\) | −12.2509 | − | 37.7045i | −0.499726 | − | 1.53800i | −0.809460 | − | 0.587175i | \(-0.800240\pi\) |
0.309734 | − | 0.950823i | \(-0.399760\pi\) | |||||||
\(602\) | −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 | ||||
\(610\) | 1.02619 | − | 0.745574i | 0.0415494 | − | 0.0301874i | ||||
\(611\) | −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 | ||||
\(615\) | −12.5972 | −0.507968 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3844 | −1.26349 | −0.631744 | − | 0.775177i | \(-0.717661\pi\) | ||||
−0.631744 | + | 0.775177i | \(0.717661\pi\) | |||||||
\(618\) | −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 | \(-0.150434\pi\) | |||||||
\(620\) | −4.92586 | − | 15.1602i | −0.197827 | − | 0.608850i | ||||
\(621\) | 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 | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | −40.2730 | −1.60963 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.3460 | −0.851799 | ||||||||
\(629\) | 4.52723 | + | 3.28922i | 0.180512 | + | 0.131150i | ||||
\(630\) | 5.03801 | − | 15.5054i | 0.200719 | − | 0.617750i | ||||
\(631\) | 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 | ||||
\(635\) | −5.82005 | + | 17.9123i | −0.230962 | + | 0.710827i | ||||
\(636\) | −25.6776 | − | 18.6559i | −1.01818 | − | 0.739753i | ||||
\(637\) | 3.37217 | 0.133610 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.8707 | −1.37946 | ||||||||
\(640\) | −11.4769 | − | 8.33844i | −0.453663 | − | 0.329606i | ||||
\(641\) | −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 | −0.196000 | − | 0.980604i | \(-0.562795\pi\) |
0.872042 | + | 0.489431i | \(0.162795\pi\) | |||||||
\(644\) | 65.0235 | − | 47.2423i | 2.56229 | − | 1.86161i | ||||
\(645\) | 3.94308 | + | 12.1356i | 0.155259 | + | 0.477837i | ||||
\(646\) | 5.02015 | − | 15.4504i | 0.197515 | − | 0.607889i | ||||
\(647\) | 4.57074 | + | 3.32083i | 0.179694 | + | 0.130555i | 0.673996 | − | 0.738735i | \(-0.264576\pi\) |
−0.494302 | + | 0.869290i | \(0.664576\pi\) | |||||||
\(648\) | 52.3547 | 2.05669 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.25274 | 0.127583 | ||||||||
\(651\) | 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 | 0.809983 | − | 0.586453i | \(-0.199476\pi\) |
−0.999999 | + | 0.00164558i | \(0.999476\pi\) | |||||||
\(654\) | 57.9726 | − | 42.1195i | 2.26691 | − | 1.64700i | ||||
\(655\) | −16.2610 | + | 11.8143i | −0.635368 | + | 0.461622i | ||||
\(656\) | 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 | \(-0.197329\pi\) | ||||
0.813922 | + | 0.580975i | \(0.197329\pi\) | |||||||
\(660\) | 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 | ||||
\(665\) | −3.64363 | + | 2.64725i | −0.141294 | + | 0.102656i | ||||
\(666\) | −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 | ||||
\(670\) | 19.7156 | 0.761681 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −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 | ||||
\(675\) | −0.0646137 | − | 0.198861i | −0.00248698 | − | 0.00765415i | ||||
\(676\) | 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 | ||||
\(680\) | 14.4987 | + | 10.5339i | 0.556000 | + | 0.403957i | ||||
\(681\) | −27.6555 | −1.05976 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.93856 | −0.227233 | −0.113616 | − | 0.993525i | \(-0.536243\pi\) | ||||
−0.113616 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(684\) | 23.4792 | + | 17.0586i | 0.897749 | + | 0.652253i | ||||
\(685\) | −5.55342 | + | 17.0917i | −0.212185 | + | 0.653039i | ||||
\(686\) | −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 | ||||
\(690\) | 16.8935 | − | 51.9929i | 0.643125 | − | 1.97934i | ||||
\(691\) | −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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.3424 | −0.468511 | ||||||||
\(695\) | 13.6425 | + | 9.91187i | 0.517490 | + | 0.375979i | ||||
\(696\) | 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 | ||||
\(700\) | −2.82917 | − | 8.70729i | −0.106933 | − | 0.329105i | ||||
\(701\) | −10.0186 | + | 30.8341i | −0.378397 | + | 1.16459i | 0.562761 | + | 0.826620i | \(0.309739\pi\) |
−0.941158 | + | 0.337967i | \(0.890261\pi\) | |||||||
\(702\) | 0.550236 | + | 0.399770i | 0.0207673 | + | 0.0150884i | ||||
\(703\) | 4.02460 | 0.151791 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0236 | 0.678809 | ||||||||
\(706\) | −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 | \(0.202235\pi\) | |||||||
\(710\) | −23.0874 | + | 16.7740i | −0.866456 | + | 0.629517i | ||||
\(711\) | −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 | \(0.946534\pi\) | |||||||
\(720\) | −15.9187 | + | 11.5656i | −0.593254 | + | 0.431024i | ||||
\(721\) | 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 | ||||
\(725\) | 0.612630 | 0.0227525 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.1218 | −1.82183 | −0.910914 | − | 0.412597i | \(-0.864622\pi\) | ||||
−0.910914 | + | 0.412597i | \(0.864622\pi\) | |||||||
\(728\) | 13.0744 | + | 9.49907i | 0.484568 | + | 0.352059i | ||||
\(729\) | −8.80810 | + | 27.1086i | −0.326226 | + | 1.00402i | ||||
\(730\) | −8.67272 | − | 26.6919i | −0.320992 | − | 0.987911i | ||||
\(731\) | 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 | ||||
\(735\) | −5.22299 | − | 3.79472i | −0.192653 | − | 0.139971i | ||||
\(736\) | −36.1730 | −1.33335 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −39.7699 | −1.46395 | ||||||||
\(739\) | 30.8186 | + | 22.3911i | 1.13368 | + | 0.823668i | 0.986227 | − | 0.165400i | \(-0.0528916\pi\) |
0.147456 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(740\) | −2.52816 | + | 7.78088i | −0.0929371 | + | 0.286031i | ||||
\(741\) | −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 | ||||
\(745\) | −0.721140 | + | 2.21944i | −0.0264205 | + | 0.0813140i | ||||
\(746\) | −24.7860 | − | 18.0081i | −0.907480 | − | 0.659323i | ||||
\(747\) | −33.4554 | −1.22407 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.6754 | 1.19393 | ||||||||
\(750\) | −5.03801 | − | 3.66033i | −0.183962 | − | 0.133656i | ||||
\(751\) | −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 | ||||
\(755\) | 1.21718 | + | 3.74609i | 0.0442976 | + | 0.136334i | ||||
\(756\) | 0.591564 | − | 1.82065i | 0.0215150 | − | 0.0662162i | ||||
\(757\) | −5.40478 | − | 3.92680i | −0.196440 | − | 0.142722i | 0.485217 | − | 0.874394i | \(-0.338741\pi\) |
−0.681657 | + | 0.731672i | \(0.738741\pi\) | |||||||
\(758\) | −18.0355 | −0.655079 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.8890 | 0.467533 | ||||||||
\(761\) | −18.5213 | − | 13.4565i | −0.671398 | − | 0.487799i | 0.199095 | − | 0.979980i | \(-0.436200\pi\) |
−0.870493 | + | 0.492181i | \(0.836200\pi\) | |||||||
\(762\) | −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 | ||||
\(765\) | −7.46506 | + | 5.42368i | −0.269900 | + | 0.196094i | ||||
\(766\) | −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 | \(-0.423540\pi\) | ||||
0.237904 | + | 0.971289i | \(0.423540\pi\) | |||||||
\(770\) | 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 | −0.996052 | − | 0.0887673i | \(-0.971707\pi\) |
0.857999 | + | 0.513651i | \(0.171707\pi\) | |||||||
\(774\) | 12.4485 | + | 38.3124i | 0.447451 | + | 1.37711i | ||||
\(775\) | 2.94887 | − | 2.14248i | 0.105927 | − | 0.0769602i | ||||
\(776\) | −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 | ||||
\(780\) | 13.8993 | 0.497675 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −66.2932 | −2.37064 | ||||||||
\(783\) | 0.103633 | + | 0.0752938i | 0.00370354 | + | 0.00269078i | ||||
\(784\) | −5.15881 | + | 15.8772i | −0.184243 | + | 0.567042i | ||||
\(785\) | −1.50834 | − | 4.64218i | −0.0538348 | − | 0.165686i | ||||
\(786\) | −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 | ||||
\(790\) | −10.9453 | − | 7.95221i | −0.389416 | − | 0.282927i | ||||
\(791\) | −18.9426 | −0.673520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.647384 | −0.0229893 | ||||||||
\(794\) | 7.30130 | + | 5.30471i | 0.259114 | + | 0.188257i | ||||
\(795\) | 2.24273 | − | 6.90242i | 0.0795416 | − | 0.244804i | ||||
\(796\) | −8.95753 | − | 27.5685i | −0.317491 | − | 0.977138i | ||||
\(797\) | −1.72264 | + | 1.25157i | −0.0610191 | + | 0.0443330i | −0.617877 | − | 0.786275i | \(-0.712007\pi\) |
0.556858 | + | 0.830608i | \(0.312007\pi\) | |||||||
\(798\) | −22.6901 | + | 16.4853i | −0.803219 | + | 0.583573i | ||||
\(799\) | −6.75393 | − | 20.7864i | −0.238937 | − | 0.735372i | ||||
\(800\) | −1.27330 | + | 3.91881i | −0.0450179 | + | 0.138551i | ||||
\(801\) | 10.7895 | + | 7.83902i | 0.381228 | + | 0.276978i | ||||
\(802\) | −72.9179 | −2.57482 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 84.2470 | 2.97116 | ||||||||
\(805\) | 14.8686 | + | 10.8026i | 0.524048 | + | 0.380743i | ||||
\(806\) | −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 | −0.661430 | − | 0.750007i | \(-0.730050\pi\) |
0.508906 | + | 0.860822i | \(0.330050\pi\) | |||||||
\(810\) | 6.81710 | + | 20.9809i | 0.239528 | + | 0.737193i | ||||
\(811\) | −6.05047 | + | 18.6214i | −0.212461 | + | 0.653887i | 0.786863 | + | 0.617127i | \(0.211704\pi\) |
−0.999324 | + | 0.0367600i | \(0.988296\pi\) | |||||||
\(812\) | 4.53766 | + | 3.29681i | 0.159241 | + | 0.115695i | ||||
\(813\) | −53.6781 | −1.88257 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.03572 | −0.246450 | ||||||||
\(816\) | 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 | ||||
\(820\) | −18.0681 | + | 13.1272i | −0.630964 | + | 0.458422i | ||||
\(821\) | 5.14095 | + | 15.8222i | 0.179420 | + | 0.552199i | 0.999808 | − | 0.0196092i | \(-0.00624219\pi\) |
−0.820387 | + | 0.571808i | \(0.806242\pi\) | |||||||
\(822\) | −34.5829 | + | 106.435i | −1.20622 | + | 3.71236i | ||||
\(823\) | 14.7993 | + | 10.7523i | 0.515870 | + | 0.374801i | 0.815046 | − | 0.579397i | \(-0.196712\pi\) |
−0.299176 | + | 0.954198i | \(0.596712\pi\) | |||||||
\(824\) | −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 | \(0.545157\pi\) | |||||||
\(830\) | −22.1504 | + | 16.0932i | −0.768851 | + | 0.558603i | ||||
\(831\) | 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 | ||||
\(835\) | −10.7195 | −0.370963 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 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 | \(-0.132146\pi\) | |||||||
\(840\) | −9.56086 | − | 29.4253i | −0.329881 | − | 1.01527i | ||||
\(841\) | 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 | ||||
\(845\) | 9.17416 | + | 6.66541i | 0.315601 | + | 0.229297i | ||||
\(846\) | 56.9013 | 1.95631 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.7672 | −0.644470 | ||||||||
\(849\) | −27.8184 | − | 20.2113i | −0.954726 | − | 0.693649i | ||||
\(850\) | −2.33354 | + | 7.18190i | −0.0800398 | + | 0.246337i | ||||
\(851\) | −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 | ||||
\(855\) | −2.05072 | + | 6.31146i | −0.0701331 | + | 0.215847i | ||||
\(856\) | −75.6523 | − | 54.9646i | −2.58574 | − | 1.87865i | ||||
\(857\) | 56.7117 | 1.93723 | 0.968617 | − | 0.248558i | \(-0.0799568\pi\) | ||||
0.968617 | + | 0.248558i | \(0.0799568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.7505 | −0.878597 | −0.439298 | − | 0.898341i | \(-0.644773\pi\) | ||||
−0.439298 | + | 0.898341i | \(0.644773\pi\) | |||||||
\(860\) | 18.3017 | + | 13.2969i | 0.624082 | + | 0.453422i | ||||
\(861\) | 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 | −0.958808 | − | 0.284056i | \(-0.908320\pi\) |
−0.0261347 | + | 0.999658i | \(0.508320\pi\) | |||||||
\(864\) | −0.697025 | + | 0.506418i | −0.0237133 | + | 0.0172287i | ||||
\(865\) | −2.59940 | − | 8.00012i | −0.0883821 | − | 0.272012i | ||||
\(866\) | 23.7093 | − | 72.9698i | 0.805676 | − | 2.47962i | ||||
\(867\) | −16.0696 | − | 11.6752i | −0.545751 | − | 0.396511i | ||||
\(868\) | 33.3714 | 1.13270 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.81504 | 0.129342 | ||||||||
\(871\) | −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 | ||||
\(875\) | 1.69369 | − | 1.23053i | 0.0572570 | − | 0.0415996i | ||||
\(876\) | −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 | \(0.344344\pi\) |
−0.898933 | + | 0.438086i | \(0.855656\pi\) | |||||||
\(884\) | −5.20843 | − | 16.0299i | −0.175179 | − | 0.539144i | ||||
\(885\) | −12.9600 | + | 9.41601i | −0.435647 | + | 0.316516i | ||||
\(886\) | −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 | ||||
\(890\) | 10.9144 | 0.365852 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 34.4803 | 1.15449 | ||||||||
\(893\) | −12.7168 | − | 9.23933i | −0.425553 | − | 0.309182i | ||||
\(894\) | −4.49077 | + | 13.8212i | −0.150194 | + | 0.462249i | ||||
\(895\) | 6.50062 | + | 20.0069i | 0.217292 | + | 0.668756i | ||||
\(896\) | 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 | ||||
\(900\) | −10.9139 | − | 7.92944i | −0.363798 | − | 0.264315i | ||||
\(901\) | −8.80090 | −0.293200 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.7134 | −0.888965 | ||||||||
\(904\) | 43.8570 | + | 31.8640i | 1.45866 | + | 1.05978i | ||||
\(905\) | −0.538649 | + | 1.65779i | −0.0179053 | + | 0.0551068i | ||||
\(906\) | 7.57976 | + | 23.3281i | 0.251821 | + | 0.775024i | ||||
\(907\) | −9.13337 | + | 6.63578i | −0.303269 | + | 0.220338i | −0.729003 | − | 0.684511i | \(-0.760016\pi\) |
0.425734 | + | 0.904848i | \(0.360016\pi\) | |||||||
\(908\) | −39.6660 | + | 28.8191i | −1.31636 | + | 0.956394i | ||||
\(909\) | 14.9654 | + | 46.0589i | 0.496372 | + | 1.52768i | ||||
\(910\) | −2.10429 | + | 6.47635i | −0.0697567 | + | 0.214689i | ||||
\(911\) | −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 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.2193 | −1.33034 | ||||||||
\(915\) | 1.00270 | + | 0.728506i | 0.0331483 | + | 0.0240837i | ||||
\(916\) | 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 | −0.888412 | − | 0.459048i | \(-0.848191\pi\) |
0.162046 | + | 0.986783i | \(0.448191\pi\) | |||||||
\(920\) | −16.2531 | − | 50.0219i | −0.535849 | − | 1.64917i | ||||
\(921\) | 3.87693 | − | 11.9320i | 0.127749 | − | 0.393172i | ||||
\(922\) | −3.11518 | − | 2.26331i | −0.102593 | − | 0.0745381i | ||||
\(923\) | 14.5649 | 0.479410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.87077 | −0.0615106 | ||||||||
\(926\) | 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 | \(0.175664\pi\) | |||||||
\(930\) | 18.3636 | − | 13.3419i | 0.602166 | − | 0.437499i | ||||
\(931\) | 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 | ||||
\(940\) | 25.8511 | − | 18.7819i | 0.843171 | − | 0.612600i | ||||
\(941\) | −23.6336 | + | 17.1708i | −0.770435 | + | 0.559754i | −0.902093 | − | 0.431542i | \(-0.857970\pi\) |
0.131658 | + | 0.991295i | \(0.457970\pi\) | |||||||
\(942\) | −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 | ||||
\(945\) | 0.437741 | 0.0142397 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.63809 | 0.313196 | 0.156598 | − | 0.987662i | \(-0.449947\pi\) | ||||
0.156598 | + | 0.987662i | \(0.449947\pi\) | |||||||
\(948\) | −46.7704 | − | 33.9807i | −1.51903 | − | 1.10364i | ||||
\(949\) | −4.42634 | + | 13.6229i | −0.143685 | + | 0.442218i | ||||
\(950\) | 1.67828 | + | 5.16520i | 0.0544505 | + | 0.167581i | ||||
\(951\) | 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 | ||||
\(955\) | −0.0201903 | − | 0.0146691i | −0.000653342 | − | 0.000474681i | ||||
\(956\) | 50.1446 | 1.62179 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.4529 | −1.43621 | ||||||||
\(959\) | −30.4376 | − | 22.1142i | −0.982882 | − | 0.714106i | ||||
\(960\) | 1.79512 | − | 5.52482i | 0.0579373 | − | 0.178313i | ||||
\(961\) | −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 | ||||
\(965\) | −0.450314 | + | 1.38592i | −0.0144961 | + | 0.0446145i | ||||
\(966\) | 92.5913 | + | 67.2715i | 2.97908 | + | 2.16443i | ||||
\(967\) | −38.4583 | −1.23674 | −0.618368 | − | 0.785889i | \(-0.712206\pi\) | ||||
−0.618368 | + | 0.785889i | \(0.712206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.8737 | 0.509935 | ||||||||
\(970\) | −0.718209 | − | 0.521810i | −0.0230603 | − | 0.0167543i | ||||
\(971\) | 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 | ||||
\(975\) | 0.982141 | + | 3.02272i | 0.0314537 | + | 0.0968045i | ||||
\(976\) | 0.990380 | − | 3.04808i | 0.0317013 | − | 0.0975665i | ||||
\(977\) | 9.50330 | + | 6.90455i | 0.304038 | + | 0.220896i | 0.729334 | − | 0.684158i | \(-0.239830\pi\) |
−0.425296 | + | 0.905054i | \(0.639830\pi\) | |||||||
\(978\) | −43.8137 | −1.40101 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −11.4457 | −0.365618 | ||||||||
\(981\) | 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 | 0.986507 | − | 0.163721i | \(-0.0523497\pi\) |
−0.894333 | + | 0.447401i | \(0.852350\pi\) | |||||||
\(984\) | −61.0590 | + | 44.3620i | −1.94649 | + | 1.41421i | ||||
\(985\) | 18.3669 | − | 13.3443i | 0.585218 | − | 0.425186i | ||||
\(986\) | −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 | ||||
\(995\) | 5.36244 | − | 3.89604i | 0.170001 | − | 0.123513i | ||||
\(996\) | −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 | 605.2.g.n.81.2 | 8 | ||
11.2 | odd | 10 | 605.2.g.j.511.2 | 8 | |||
11.3 | even | 5 | inner | 605.2.g.n.366.2 | 8 | ||
11.4 | even | 5 | 605.2.g.g.251.1 | 8 | |||
11.5 | even | 5 | 605.2.a.i.1.1 | 4 | |||
11.6 | odd | 10 | 605.2.a.l.1.4 | 4 | |||
11.7 | odd | 10 | 605.2.g.j.251.2 | 8 | |||
11.8 | odd | 10 | 55.2.g.a.36.1 | yes | 8 | ||
11.9 | even | 5 | 605.2.g.g.511.1 | 8 | |||
11.10 | odd | 2 | 55.2.g.a.26.1 | ✓ | 8 | ||
33.5 | odd | 10 | 5445.2.a.bu.1.4 | 4 | |||
33.8 | even | 10 | 495.2.n.f.91.2 | 8 | |||
33.17 | even | 10 | 5445.2.a.bg.1.1 | 4 | |||
33.32 | even | 2 | 495.2.n.f.136.2 | 8 | |||
44.19 | even | 10 | 880.2.bo.e.641.2 | 8 | |||
44.27 | odd | 10 | 9680.2.a.cv.1.4 | 4 | |||
44.39 | even | 10 | 9680.2.a.cs.1.4 | 4 | |||
44.43 | even | 2 | 880.2.bo.e.81.2 | 8 | |||
55.8 | even | 20 | 275.2.z.b.124.4 | 16 | |||
55.19 | odd | 10 | 275.2.h.b.201.2 | 8 | |||
55.32 | even | 4 | 275.2.z.b.224.4 | 16 | |||
55.39 | odd | 10 | 3025.2.a.v.1.1 | 4 | |||
55.43 | even | 4 | 275.2.z.b.224.1 | 16 | |||
55.49 | even | 10 | 3025.2.a.be.1.4 | 4 | |||
55.52 | even | 20 | 275.2.z.b.124.1 | 16 | |||
55.54 | odd | 2 | 275.2.h.b.26.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.a.26.1 | ✓ | 8 | 11.10 | odd | 2 | ||
55.2.g.a.36.1 | yes | 8 | 11.8 | odd | 10 | ||
275.2.h.b.26.2 | 8 | 55.54 | odd | 2 | |||
275.2.h.b.201.2 | 8 | 55.19 | odd | 10 | |||
275.2.z.b.124.1 | 16 | 55.52 | even | 20 | |||
275.2.z.b.124.4 | 16 | 55.8 | even | 20 | |||
275.2.z.b.224.1 | 16 | 55.43 | even | 4 | |||
275.2.z.b.224.4 | 16 | 55.32 | even | 4 | |||
495.2.n.f.91.2 | 8 | 33.8 | even | 10 | |||
495.2.n.f.136.2 | 8 | 33.32 | even | 2 | |||
605.2.a.i.1.1 | 4 | 11.5 | even | 5 | |||
605.2.a.l.1.4 | 4 | 11.6 | odd | 10 | |||
605.2.g.g.251.1 | 8 | 11.4 | even | 5 | |||
605.2.g.g.511.1 | 8 | 11.9 | even | 5 | |||
605.2.g.j.251.2 | 8 | 11.7 | odd | 10 | |||
605.2.g.j.511.2 | 8 | 11.2 | odd | 10 | |||
605.2.g.n.81.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.n.366.2 | 8 | 11.3 | even | 5 | inner | ||
880.2.bo.e.81.2 | 8 | 44.43 | even | 2 | |||
880.2.bo.e.641.2 | 8 | 44.19 | even | 10 | |||
3025.2.a.v.1.1 | 4 | 55.39 | odd | 10 | |||
3025.2.a.be.1.4 | 4 | 55.49 | even | 10 | |||
5445.2.a.bg.1.1 | 4 | 33.17 | even | 10 | |||
5445.2.a.bu.1.4 | 4 | 33.5 | odd | 10 | |||
9680.2.a.cs.1.4 | 4 | 44.39 | even | 10 | |||
9680.2.a.cv.1.4 | 4 | 44.27 | odd | 10 |