Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,2,Mod(3,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.3");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.c (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: | \(1.93237972891\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 242.27 |
Dual form | 242.2.c.b.9.1 |
$q$-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 \(\left(\mathbb{Z}/242\mathbb{Z}\right)^\times\).
\(n\) | \(123\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | 1.61803 | + | 1.17557i | 0.934172 | + | 0.678716i | 0.947011 | − | 0.321202i | \(-0.104087\pi\) |
−0.0128385 | + | 0.999918i | \(0.504087\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.927051 | + | 2.85317i | −0.414590 | + | 1.27598i | 0.498027 | + | 0.867161i | \(0.334058\pi\) |
−0.912617 | + | 0.408815i | \(0.865942\pi\) | |||||||
\(6\) | −0.618034 | + | 1.90211i | −0.252311 | + | 0.776534i | ||||
\(7\) | 1.61803 | − | 1.17557i | 0.611559 | − | 0.444324i | −0.238404 | − | 0.971166i | \(-0.576624\pi\) |
0.849963 | + | 0.526842i | \(0.176624\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | −1.54508 | − | 4.75528i | −0.428529 | − | 1.31888i | −0.899574 | − | 0.436769i | \(-0.856123\pi\) |
0.471044 | − | 0.882109i | \(-0.343877\pi\) | |||||||
\(14\) | 1.61803 | + | 1.17557i | 0.432438 | + | 0.314184i | ||||
\(15\) | −4.85410 | + | 3.52671i | −1.25332 | + | 0.910593i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −0.927051 | + | 2.85317i | −0.224843 | + | 0.691995i | 0.773465 | + | 0.633839i | \(0.218522\pi\) |
−0.998308 | + | 0.0581558i | \(0.981478\pi\) | |||||||
\(18\) | −0.809017 | + | 0.587785i | −0.190687 | + | 0.138542i | ||||
\(19\) | 1.61803 | + | 1.17557i | 0.371202 | + | 0.269694i | 0.757709 | − | 0.652592i | \(-0.226318\pi\) |
−0.386507 | + | 0.922287i | \(0.626318\pi\) | |||||||
\(20\) | −0.927051 | − | 2.85317i | −0.207295 | − | 0.637988i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −0.618034 | − | 1.90211i | −0.126156 | − | 0.388267i | ||||
\(25\) | −3.23607 | − | 2.35114i | −0.647214 | − | 0.470228i | ||||
\(26\) | 4.04508 | − | 2.93893i | 0.793306 | − | 0.576371i | ||||
\(27\) | 1.23607 | − | 3.80423i | 0.237881 | − | 0.732124i | ||||
\(28\) | −0.618034 | + | 1.90211i | −0.116797 | + | 0.359466i | ||||
\(29\) | −2.42705 | + | 1.76336i | −0.450692 | + | 0.327447i | −0.789869 | − | 0.613276i | \(-0.789851\pi\) |
0.339177 | + | 0.940723i | \(0.389851\pi\) | |||||||
\(30\) | −4.85410 | − | 3.52671i | −0.886234 | − | 0.643886i | ||||
\(31\) | 0.618034 | + | 1.90211i | 0.111002 | + | 0.341630i | 0.991092 | − | 0.133177i | \(-0.0425179\pi\) |
−0.880090 | + | 0.474807i | \(0.842518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 1.85410 | + | 5.70634i | 0.313400 | + | 0.964547i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | 5.66312 | − | 4.11450i | 0.931011 | − | 0.676419i | −0.0152291 | − | 0.999884i | \(-0.504848\pi\) |
0.946240 | + | 0.323465i | \(0.104848\pi\) | |||||||
\(38\) | −0.618034 | + | 1.90211i | −0.100258 | + | 0.308563i | ||||
\(39\) | 3.09017 | − | 9.51057i | 0.494823 | − | 1.52291i | ||||
\(40\) | 2.42705 | − | 1.76336i | 0.383750 | − | 0.278811i | ||||
\(41\) | 2.42705 | + | 1.76336i | 0.379042 | + | 0.275390i | 0.760950 | − | 0.648810i | \(-0.224733\pi\) |
−0.381909 | + | 0.924200i | \(0.624733\pi\) | |||||||
\(42\) | 1.23607 | + | 3.80423i | 0.190729 | + | 0.587005i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 1.85410 | + | 5.70634i | 0.273372 | + | 0.841354i | ||||
\(47\) | −4.85410 | − | 3.52671i | −0.708044 | − | 0.514424i | 0.174498 | − | 0.984657i | \(-0.444170\pi\) |
−0.882542 | + | 0.470234i | \(0.844170\pi\) | |||||||
\(48\) | 1.61803 | − | 1.17557i | 0.233543 | − | 0.169679i | ||||
\(49\) | −0.927051 | + | 2.85317i | −0.132436 | + | 0.407596i | ||||
\(50\) | 1.23607 | − | 3.80423i | 0.174806 | − | 0.537999i | ||||
\(51\) | −4.85410 | + | 3.52671i | −0.679710 | + | 0.493838i | ||||
\(52\) | 4.04508 | + | 2.93893i | 0.560952 | + | 0.407556i | ||||
\(53\) | −0.927051 | − | 2.85317i | −0.127340 | − | 0.391913i | 0.866980 | − | 0.498343i | \(-0.166058\pi\) |
−0.994320 | + | 0.106430i | \(0.966058\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 1.23607 | + | 3.80423i | 0.163721 | + | 0.503882i | ||||
\(58\) | −2.42705 | − | 1.76336i | −0.318687 | − | 0.231540i | ||||
\(59\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(60\) | 1.85410 | − | 5.70634i | 0.239364 | − | 0.736685i | ||||
\(61\) | 3.09017 | − | 9.51057i | 0.395656 | − | 1.21770i | −0.532794 | − | 0.846245i | \(-0.678858\pi\) |
0.928450 | − | 0.371458i | \(-0.121142\pi\) | |||||||
\(62\) | −1.61803 | + | 1.17557i | −0.205491 | + | 0.149298i | ||||
\(63\) | 1.61803 | + | 1.17557i | 0.203853 | + | 0.148108i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 15.0000 | 1.86052 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | −0.927051 | − | 2.85317i | −0.112421 | − | 0.345998i | ||||
\(69\) | 9.70820 | + | 7.05342i | 1.16873 | + | 0.849132i | ||||
\(70\) | −4.85410 | + | 3.52671i | −0.580176 | + | 0.421523i | ||||
\(71\) | 3.70820 | − | 11.4127i | 0.440083 | − | 1.35444i | −0.447704 | − | 0.894182i | \(-0.647758\pi\) |
0.887787 | − | 0.460254i | \(-0.152242\pi\) | |||||||
\(72\) | 0.309017 | − | 0.951057i | 0.0364180 | − | 0.112083i | ||||
\(73\) | 11.3262 | − | 8.22899i | 1.32564 | − | 0.963131i | 0.325792 | − | 0.945441i | \(-0.394369\pi\) |
0.999844 | − | 0.0176895i | \(-0.00563103\pi\) | |||||||
\(74\) | 5.66312 | + | 4.11450i | 0.658324 | + | 0.478301i | ||||
\(75\) | −2.47214 | − | 7.60845i | −0.285458 | − | 0.878548i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0000 | 1.13228 | ||||||||
\(79\) | −0.618034 | − | 1.90211i | −0.0695343 | − | 0.214004i | 0.910251 | − | 0.414057i | \(-0.135889\pi\) |
−0.979785 | + | 0.200053i | \(0.935889\pi\) | |||||||
\(80\) | 2.42705 | + | 1.76336i | 0.271353 | + | 0.197149i | ||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | −0.927051 | + | 2.85317i | −0.102376 | + | 0.315080i | ||||
\(83\) | −5.56231 | + | 17.1190i | −0.610542 | + | 1.87906i | −0.157639 | + | 0.987497i | \(0.550388\pi\) |
−0.452904 | + | 0.891559i | \(0.649612\pi\) | |||||||
\(84\) | −3.23607 | + | 2.35114i | −0.353084 | + | 0.256531i | ||||
\(85\) | −7.28115 | − | 5.29007i | −0.789752 | − | 0.573788i | ||||
\(86\) | −2.47214 | − | 7.60845i | −0.266577 | − | 0.820440i | ||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | −0.927051 | − | 2.85317i | −0.0977198 | − | 0.300750i | ||||
\(91\) | −8.09017 | − | 5.87785i | −0.848080 | − | 0.616166i | ||||
\(92\) | −4.85410 | + | 3.52671i | −0.506075 | + | 0.367685i | ||||
\(93\) | −1.23607 | + | 3.80423i | −0.128174 | + | 0.394480i | ||||
\(94\) | 1.85410 | − | 5.70634i | 0.191236 | − | 0.588564i | ||||
\(95\) | −4.85410 | + | 3.52671i | −0.498020 | + | 0.361833i | ||||
\(96\) | 1.61803 | + | 1.17557i | 0.165140 | + | 0.119981i | ||||
\(97\) | 3.39919 | + | 10.4616i | 0.345135 | + | 1.06222i | 0.961511 | + | 0.274765i | \(0.0886000\pi\) |
−0.616376 | + | 0.787452i | \(0.711400\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −1.85410 | − | 5.70634i | −0.184490 | − | 0.567802i | 0.815449 | − | 0.578829i | \(-0.196490\pi\) |
−0.999939 | + | 0.0110267i | \(0.996490\pi\) | |||||||
\(102\) | −4.85410 | − | 3.52671i | −0.480628 | − | 0.349196i | ||||
\(103\) | −6.47214 | + | 4.70228i | −0.637719 | + | 0.463330i | −0.859066 | − | 0.511865i | \(-0.828955\pi\) |
0.221347 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(104\) | −1.54508 | + | 4.75528i | −0.151508 | + | 0.466294i | ||||
\(105\) | −3.70820 | + | 11.4127i | −0.361884 | + | 1.11376i | ||||
\(106\) | 2.42705 | − | 1.76336i | 0.235736 | − | 0.171272i | ||||
\(107\) | −4.85410 | − | 3.52671i | −0.469264 | − | 0.340940i | 0.327891 | − | 0.944716i | \(-0.393662\pi\) |
−0.797154 | + | 0.603776i | \(0.793662\pi\) | |||||||
\(108\) | 1.23607 | + | 3.80423i | 0.118941 | + | 0.366062i | ||||
\(109\) | −17.0000 | −1.62830 | −0.814152 | − | 0.580651i | \(-0.802798\pi\) | ||||
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | −0.618034 | − | 1.90211i | −0.0583987 | − | 0.179733i | ||||
\(113\) | 7.28115 | + | 5.29007i | 0.684953 | + | 0.497648i | 0.874997 | − | 0.484128i | \(-0.160863\pi\) |
−0.190044 | + | 0.981776i | \(0.560863\pi\) | |||||||
\(114\) | −3.23607 | + | 2.35114i | −0.303086 | + | 0.220205i | ||||
\(115\) | −5.56231 | + | 17.1190i | −0.518688 | + | 1.59636i | ||||
\(116\) | 0.927051 | − | 2.85317i | 0.0860745 | − | 0.264910i | ||||
\(117\) | 4.04508 | − | 2.93893i | 0.373968 | − | 0.271704i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.85410 | + | 5.70634i | 0.169965 | + | 0.523099i | ||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 1.85410 | + | 5.70634i | 0.167179 | + | 0.514523i | ||||
\(124\) | −1.61803 | − | 1.17557i | −0.145304 | − | 0.105569i | ||||
\(125\) | −2.42705 | + | 1.76336i | −0.217082 | + | 0.157719i | ||||
\(126\) | −0.618034 | + | 1.90211i | −0.0550588 | + | 0.169454i | ||||
\(127\) | −2.47214 | + | 7.60845i | −0.219367 | + | 0.675141i | 0.779448 | + | 0.626467i | \(0.215500\pi\) |
−0.998815 | + | 0.0486742i | \(0.984500\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | −12.9443 | − | 9.40456i | −1.13968 | − | 0.828026i | ||||
\(130\) | 4.63525 | + | 14.2658i | 0.406539 | + | 1.25120i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | −3.09017 | − | 9.51057i | −0.266950 | − | 0.821588i | ||||
\(135\) | 9.70820 | + | 7.05342i | 0.835549 | + | 0.607062i | ||||
\(136\) | 2.42705 | − | 1.76336i | 0.208118 | − | 0.151207i | ||||
\(137\) | 1.85410 | − | 5.70634i | 0.158407 | − | 0.487525i | −0.840083 | − | 0.542457i | \(-0.817494\pi\) |
0.998490 | + | 0.0549317i | \(0.0174941\pi\) | |||||||
\(138\) | −3.70820 | + | 11.4127i | −0.315663 | + | 0.971512i | ||||
\(139\) | −17.7984 | + | 12.9313i | −1.50964 | + | 1.09682i | −0.543301 | + | 0.839538i | \(0.682826\pi\) |
−0.966337 | + | 0.257279i | \(0.917174\pi\) | |||||||
\(140\) | −4.85410 | − | 3.52671i | −0.410246 | − | 0.298062i | ||||
\(141\) | −3.70820 | − | 11.4127i | −0.312287 | − | 0.961121i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.78115 | − | 8.55951i | −0.230962 | − | 0.710829i | ||||
\(146\) | 11.3262 | + | 8.22899i | 0.937366 | + | 0.681036i | ||||
\(147\) | −4.85410 | + | 3.52671i | −0.400360 | + | 0.290878i | ||||
\(148\) | −2.16312 | + | 6.65740i | −0.177807 | + | 0.547235i | ||||
\(149\) | 0.927051 | − | 2.85317i | 0.0759470 | − | 0.233741i | −0.905875 | − | 0.423545i | \(-0.860785\pi\) |
0.981822 | + | 0.189805i | \(0.0607854\pi\) | |||||||
\(150\) | 6.47214 | − | 4.70228i | 0.528448 | − | 0.383940i | ||||
\(151\) | 6.47214 | + | 4.70228i | 0.526695 | + | 0.382666i | 0.819120 | − | 0.573622i | \(-0.194462\pi\) |
−0.292425 | + | 0.956288i | \(0.594462\pi\) | |||||||
\(152\) | −0.618034 | − | 1.90211i | −0.0501292 | − | 0.154282i | ||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 3.09017 | + | 9.51057i | 0.247412 | + | 0.761455i | ||||
\(157\) | −1.61803 | − | 1.17557i | −0.129133 | − | 0.0938207i | 0.521344 | − | 0.853347i | \(-0.325431\pi\) |
−0.650477 | + | 0.759526i | \(0.725431\pi\) | |||||||
\(158\) | 1.61803 | − | 1.17557i | 0.128724 | − | 0.0935234i | ||||
\(159\) | 1.85410 | − | 5.70634i | 0.147040 | − | 0.452542i | ||||
\(160\) | −0.927051 | + | 2.85317i | −0.0732898 | + | 0.225563i | ||||
\(161\) | 9.70820 | − | 7.05342i | 0.765114 | − | 0.555888i | ||||
\(162\) | 8.89919 | + | 6.46564i | 0.699186 | + | 0.507988i | ||||
\(163\) | −6.79837 | − | 20.9232i | −0.532490 | − | 1.63883i | −0.749011 | − | 0.662557i | \(-0.769471\pi\) |
0.216522 | − | 0.976278i | \(-0.430529\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0000 | −1.39707 | ||||||||
\(167\) | 3.70820 | + | 11.4127i | 0.286949 | + | 0.883140i | 0.985808 | + | 0.167879i | \(0.0536919\pi\) |
−0.698858 | + | 0.715260i | \(0.746308\pi\) | |||||||
\(168\) | −3.23607 | − | 2.35114i | −0.249668 | − | 0.181394i | ||||
\(169\) | −9.70820 | + | 7.05342i | −0.746785 | + | 0.542571i | ||||
\(170\) | 2.78115 | − | 8.55951i | 0.213305 | − | 0.656484i | ||||
\(171\) | −0.618034 | + | 1.90211i | −0.0472622 | + | 0.145458i | ||||
\(172\) | 6.47214 | − | 4.70228i | 0.493496 | − | 0.358546i | ||||
\(173\) | 4.85410 | + | 3.52671i | 0.369051 | + | 0.268131i | 0.756817 | − | 0.653627i | \(-0.226753\pi\) |
−0.387767 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(174\) | −1.85410 | − | 5.70634i | −0.140559 | − | 0.432596i | ||||
\(175\) | −8.00000 | −0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.78115 | − | 8.55951i | −0.208456 | − | 0.641562i | ||||
\(179\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(180\) | 2.42705 | − | 1.76336i | 0.180902 | − | 0.131433i | ||||
\(181\) | 1.54508 | − | 4.75528i | 0.114845 | − | 0.353457i | −0.877069 | − | 0.480364i | \(-0.840505\pi\) |
0.991915 | + | 0.126906i | \(0.0405047\pi\) | |||||||
\(182\) | 3.09017 | − | 9.51057i | 0.229059 | − | 0.704970i | ||||
\(183\) | 16.1803 | − | 11.7557i | 1.19609 | − | 0.869007i | ||||
\(184\) | −4.85410 | − | 3.52671i | −0.357849 | − | 0.259993i | ||||
\(185\) | 6.48936 | + | 19.9722i | 0.477107 | + | 1.46838i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | −2.47214 | − | 7.60845i | −0.179821 | − | 0.553433i | ||||
\(190\) | −4.85410 | − | 3.52671i | −0.352154 | − | 0.255855i | ||||
\(191\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(192\) | −0.618034 | + | 1.90211i | −0.0446028 | + | 0.137273i | ||||
\(193\) | 4.01722 | − | 12.3637i | 0.289166 | − | 0.889961i | −0.695953 | − | 0.718087i | \(-0.745018\pi\) |
0.985119 | − | 0.171874i | \(-0.0549821\pi\) | |||||||
\(194\) | −8.89919 | + | 6.46564i | −0.638924 | + | 0.464206i | ||||
\(195\) | 24.2705 | + | 17.6336i | 1.73805 | + | 1.26277i | ||||
\(196\) | −0.927051 | − | 2.85317i | −0.0662179 | − | 0.203798i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 1.23607 | + | 3.80423i | 0.0874032 | + | 0.268999i | ||||
\(201\) | −16.1803 | − | 11.7557i | −1.14127 | − | 0.829184i | ||||
\(202\) | 4.85410 | − | 3.52671i | 0.341533 | − | 0.248139i | ||||
\(203\) | −1.85410 | + | 5.70634i | −0.130132 | + | 0.400506i | ||||
\(204\) | 1.85410 | − | 5.70634i | 0.129813 | − | 0.399524i | ||||
\(205\) | −7.28115 | + | 5.29007i | −0.508538 | + | 0.369474i | ||||
\(206\) | −6.47214 | − | 4.70228i | −0.450935 | − | 0.327624i | ||||
\(207\) | 1.85410 | + | 5.70634i | 0.128869 | + | 0.396618i | ||||
\(208\) | −5.00000 | −0.346688 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −12.0000 | −0.828079 | ||||||||
\(211\) | 1.23607 | + | 3.80423i | 0.0850944 | + | 0.261894i | 0.984546 | − | 0.175127i | \(-0.0560336\pi\) |
−0.899451 | + | 0.437021i | \(0.856034\pi\) | |||||||
\(212\) | 2.42705 | + | 1.76336i | 0.166691 | + | 0.121108i | ||||
\(213\) | 19.4164 | − | 14.1068i | 1.33039 | − | 0.966585i | ||||
\(214\) | 1.85410 | − | 5.70634i | 0.126744 | − | 0.390077i | ||||
\(215\) | 7.41641 | − | 22.8254i | 0.505795 | − | 1.55668i | ||||
\(216\) | −3.23607 | + | 2.35114i | −0.220187 | + | 0.159975i | ||||
\(217\) | 3.23607 | + | 2.35114i | 0.219679 | + | 0.159606i | ||||
\(218\) | −5.25329 | − | 16.1680i | −0.355798 | − | 1.09503i | ||||
\(219\) | 28.0000 | 1.89206 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | 1.00901 | ||||||||
\(222\) | 4.32624 | + | 13.3148i | 0.290358 | + | 0.893630i | ||||
\(223\) | 3.23607 | + | 2.35114i | 0.216703 | + | 0.157444i | 0.690841 | − | 0.723006i | \(-0.257240\pi\) |
−0.474138 | + | 0.880450i | \(0.657240\pi\) | |||||||
\(224\) | 1.61803 | − | 1.17557i | 0.108109 | − | 0.0785461i | ||||
\(225\) | 1.23607 | − | 3.80423i | 0.0824045 | − | 0.253615i | ||||
\(226\) | −2.78115 | + | 8.55951i | −0.185000 | + | 0.569370i | ||||
\(227\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(228\) | −3.23607 | − | 2.35114i | −0.214314 | − | 0.155708i | ||||
\(229\) | 1.54508 | + | 4.75528i | 0.102102 | + | 0.314238i | 0.989039 | − | 0.147652i | \(-0.0471715\pi\) |
−0.886937 | + | 0.461890i | \(0.847172\pi\) | |||||||
\(230\) | −18.0000 | −1.18688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 6.48936 | + | 19.9722i | 0.425132 | + | 1.30842i | 0.902868 | + | 0.429918i | \(0.141458\pi\) |
−0.477736 | + | 0.878503i | \(0.658542\pi\) | |||||||
\(234\) | 4.04508 | + | 2.93893i | 0.264435 | + | 0.192124i | ||||
\(235\) | 14.5623 | − | 10.5801i | 0.949940 | − | 0.690172i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.23607 | − | 3.80423i | 0.0802912 | − | 0.247111i | ||||
\(238\) | −4.85410 | + | 3.52671i | −0.314645 | + | 0.228603i | ||||
\(239\) | −24.2705 | − | 17.6336i | −1.56993 | − | 1.14062i | −0.927225 | − | 0.374505i | \(-0.877812\pi\) |
−0.642704 | − | 0.766115i | \(-0.722188\pi\) | |||||||
\(240\) | 1.85410 | + | 5.70634i | 0.119682 | + | 0.368343i | ||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 3.09017 | + | 9.51057i | 0.197828 | + | 0.608852i | ||||
\(245\) | −7.28115 | − | 5.29007i | −0.465176 | − | 0.337970i | ||||
\(246\) | −4.85410 | + | 3.52671i | −0.309486 | + | 0.224855i | ||||
\(247\) | 3.09017 | − | 9.51057i | 0.196623 | − | 0.605143i | ||||
\(248\) | 0.618034 | − | 1.90211i | 0.0392452 | − | 0.120784i | ||||
\(249\) | −29.1246 | + | 21.1603i | −1.84570 | + | 1.34098i | ||||
\(250\) | −2.42705 | − | 1.76336i | −0.153500 | − | 0.111524i | ||||
\(251\) | 5.56231 | + | 17.1190i | 0.351090 | + | 1.08054i | 0.958242 | + | 0.285958i | \(0.0923116\pi\) |
−0.607153 | + | 0.794585i | \(0.707688\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | −5.56231 | − | 17.1190i | −0.348325 | − | 1.07203i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −2.42705 | + | 1.76336i | −0.151395 | + | 0.109995i | −0.660904 | − | 0.750470i | \(-0.729827\pi\) |
0.509509 | + | 0.860465i | \(0.329827\pi\) | |||||||
\(258\) | 4.94427 | − | 15.2169i | 0.307817 | − | 0.947363i | ||||
\(259\) | 4.32624 | − | 13.3148i | 0.268819 | − | 0.827341i | ||||
\(260\) | −12.1353 | + | 8.81678i | −0.752597 | + | 0.546793i | ||||
\(261\) | −2.42705 | − | 1.76336i | −0.150231 | − | 0.109149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 1.23607 | + | 3.80423i | 0.0757882 | + | 0.233252i | ||||
\(267\) | −14.5623 | − | 10.5801i | −0.891199 | − | 0.647494i | ||||
\(268\) | 8.09017 | − | 5.87785i | 0.494186 | − | 0.359047i | ||||
\(269\) | −0.927051 | + | 2.85317i | −0.0565233 | + | 0.173961i | −0.975332 | − | 0.220742i | \(-0.929152\pi\) |
0.918809 | + | 0.394702i | \(0.129152\pi\) | |||||||
\(270\) | −3.70820 | + | 11.4127i | −0.225674 | + | 0.694553i | ||||
\(271\) | 16.1803 | − | 11.7557i | 0.982886 | − | 0.714108i | 0.0245340 | − | 0.999699i | \(-0.492190\pi\) |
0.958352 | + | 0.285591i | \(0.0921898\pi\) | |||||||
\(272\) | 2.42705 | + | 1.76336i | 0.147162 | + | 0.106919i | ||||
\(273\) | −6.18034 | − | 19.0211i | −0.374051 | − | 1.15121i | ||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.0000 | −0.722315 | ||||||||
\(277\) | −1.54508 | − | 4.75528i | −0.0928352 | − | 0.285717i | 0.893848 | − | 0.448370i | \(-0.147995\pi\) |
−0.986683 | + | 0.162652i | \(0.947995\pi\) | |||||||
\(278\) | −17.7984 | − | 12.9313i | −1.06748 | − | 0.775566i | ||||
\(279\) | −1.61803 | + | 1.17557i | −0.0968692 | + | 0.0703796i | ||||
\(280\) | 1.85410 | − | 5.70634i | 0.110804 | − | 0.341019i | ||||
\(281\) | −1.85410 | + | 5.70634i | −0.110606 | + | 0.340412i | −0.991005 | − | 0.133822i | \(-0.957275\pi\) |
0.880399 | + | 0.474234i | \(0.157275\pi\) | |||||||
\(282\) | 9.70820 | − | 7.05342i | 0.578115 | − | 0.420025i | ||||
\(283\) | 16.1803 | + | 11.7557i | 0.961821 | + | 0.698804i | 0.953573 | − | 0.301162i | \(-0.0973744\pi\) |
0.00824833 | + | 0.999966i | \(0.497374\pi\) | |||||||
\(284\) | 3.70820 | + | 11.4127i | 0.220041 | + | 0.677218i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | 6.47214 | + | 4.70228i | 0.380714 | + | 0.276605i | ||||
\(290\) | 7.28115 | − | 5.29007i | 0.427564 | − | 0.310643i | ||||
\(291\) | −6.79837 | + | 20.9232i | −0.398528 | + | 1.22654i | ||||
\(292\) | −4.32624 | + | 13.3148i | −0.253174 | + | 0.779189i | ||||
\(293\) | 16.9894 | − | 12.3435i | 0.992529 | − | 0.721114i | 0.0320554 | − | 0.999486i | \(-0.489795\pi\) |
0.960473 | + | 0.278372i | \(0.0897947\pi\) | |||||||
\(294\) | −4.85410 | − | 3.52671i | −0.283097 | − | 0.205682i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.00000 | −0.406867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | 0.173785 | ||||||||
\(299\) | −9.27051 | − | 28.5317i | −0.536127 | − | 1.65003i | ||||
\(300\) | 6.47214 | + | 4.70228i | 0.373669 | + | 0.271486i | ||||
\(301\) | −12.9443 | + | 9.40456i | −0.746095 | + | 0.542070i | ||||
\(302\) | −2.47214 | + | 7.60845i | −0.142255 | + | 0.437817i | ||||
\(303\) | 3.70820 | − | 11.4127i | 0.213031 | − | 0.655641i | ||||
\(304\) | 1.61803 | − | 1.17557i | 0.0928006 | − | 0.0674236i | ||||
\(305\) | 24.2705 | + | 17.6336i | 1.38973 | + | 1.00969i | ||||
\(306\) | −0.927051 | − | 2.85317i | −0.0529960 | − | 0.163105i | ||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | −1.85410 | − | 5.70634i | −0.105306 | − | 0.324098i | ||||
\(311\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(312\) | −8.09017 | + | 5.87785i | −0.458016 | + | 0.332768i | ||||
\(313\) | −0.309017 | + | 0.951057i | −0.0174667 | + | 0.0537569i | −0.959410 | − | 0.282015i | \(-0.908997\pi\) |
0.941943 | + | 0.335772i | \(0.108997\pi\) | |||||||
\(314\) | 0.618034 | − | 1.90211i | 0.0348777 | − | 0.107342i | ||||
\(315\) | −4.85410 | + | 3.52671i | −0.273498 | + | 0.198708i | ||||
\(316\) | 1.61803 | + | 1.17557i | 0.0910215 | + | 0.0661310i | ||||
\(317\) | −5.56231 | − | 17.1190i | −0.312410 | − | 0.961500i | −0.976807 | − | 0.214120i | \(-0.931312\pi\) |
0.664397 | − | 0.747380i | \(-0.268688\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.00000 | −0.167705 | ||||||||
\(321\) | −3.70820 | − | 11.4127i | −0.206972 | − | 0.636994i | ||||
\(322\) | 9.70820 | + | 7.05342i | 0.541017 | + | 0.393072i | ||||
\(323\) | −4.85410 | + | 3.52671i | −0.270089 | + | 0.196231i | ||||
\(324\) | −3.39919 | + | 10.4616i | −0.188844 | + | 0.581201i | ||||
\(325\) | −6.18034 | + | 19.0211i | −0.342824 | + | 1.05510i | ||||
\(326\) | 17.7984 | − | 12.9313i | 0.985761 | − | 0.716197i | ||||
\(327\) | −27.5066 | − | 19.9847i | −1.52112 | − | 1.10516i | ||||
\(328\) | −0.927051 | − | 2.85317i | −0.0511878 | − | 0.157540i | ||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | −5.56231 | − | 17.1190i | −0.305271 | − | 0.939528i | ||||
\(333\) | 5.66312 | + | 4.11450i | 0.310337 | + | 0.225473i | ||||
\(334\) | −9.70820 | + | 7.05342i | −0.531209 | + | 0.385946i | ||||
\(335\) | 9.27051 | − | 28.5317i | 0.506502 | − | 1.55885i | ||||
\(336\) | 1.23607 | − | 3.80423i | 0.0674330 | − | 0.207538i | ||||
\(337\) | −10.5172 | + | 7.64121i | −0.572910 | + | 0.416243i | −0.836161 | − | 0.548484i | \(-0.815205\pi\) |
0.263251 | + | 0.964727i | \(0.415205\pi\) | |||||||
\(338\) | −9.70820 | − | 7.05342i | −0.528057 | − | 0.383656i | ||||
\(339\) | 5.56231 | + | 17.1190i | 0.302103 | + | 0.929777i | ||||
\(340\) | 9.00000 | 0.488094 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 6.18034 | + | 19.0211i | 0.333707 | + | 1.02704i | ||||
\(344\) | 6.47214 | + | 4.70228i | 0.348954 | + | 0.253530i | ||||
\(345\) | −29.1246 | + | 21.1603i | −1.56802 | + | 1.13923i | ||||
\(346\) | −1.85410 | + | 5.70634i | −0.0996771 | + | 0.306775i | ||||
\(347\) | −11.1246 | + | 34.2380i | −0.597200 | + | 1.83799i | −0.0537472 | + | 0.998555i | \(0.517117\pi\) |
−0.543453 | + | 0.839439i | \(0.682883\pi\) | |||||||
\(348\) | 4.85410 | − | 3.52671i | 0.260207 | − | 0.189052i | ||||
\(349\) | 13.7533 | + | 9.99235i | 0.736197 | + | 0.534878i | 0.891518 | − | 0.452986i | \(-0.149641\pi\) |
−0.155321 | + | 0.987864i | \(0.549641\pi\) | |||||||
\(350\) | −2.47214 | − | 7.60845i | −0.132141 | − | 0.406689i | ||||
\(351\) | −20.0000 | −1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | −0.479022 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.1246 | + | 21.1603i | 1.54577 | + | 1.12307i | ||||
\(356\) | 7.28115 | − | 5.29007i | 0.385900 | − | 0.280373i | ||||
\(357\) | −3.70820 | + | 11.4127i | −0.196259 | + | 0.604023i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5623 | − | 10.5801i | 0.768569 | − | 0.558398i | −0.132958 | − | 0.991122i | \(-0.542447\pi\) |
0.901527 | + | 0.432724i | \(0.142447\pi\) | |||||||
\(360\) | 2.42705 | + | 1.76336i | 0.127917 | + | 0.0929370i | ||||
\(361\) | −4.63525 | − | 14.2658i | −0.243961 | − | 0.750834i | ||||
\(362\) | 5.00000 | 0.262794 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.0000 | 0.524142 | ||||||||
\(365\) | 12.9787 | + | 39.9444i | 0.679337 | + | 2.09078i | ||||
\(366\) | 16.1803 | + | 11.7557i | 0.845760 | + | 0.614481i | ||||
\(367\) | 8.09017 | − | 5.87785i | 0.422303 | − | 0.306821i | −0.356261 | − | 0.934387i | \(-0.615948\pi\) |
0.778564 | + | 0.627565i | \(0.215948\pi\) | |||||||
\(368\) | 1.85410 | − | 5.70634i | 0.0966517 | − | 0.297463i | ||||
\(369\) | −0.927051 | + | 2.85317i | −0.0482603 | + | 0.148530i | ||||
\(370\) | −16.9894 | + | 12.3435i | −0.883235 | + | 0.641708i | ||||
\(371\) | −4.85410 | − | 3.52671i | −0.252012 | − | 0.183098i | ||||
\(372\) | −1.23607 | − | 3.80423i | −0.0640871 | − | 0.197240i | ||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | −0.309839 | ||||||||
\(376\) | 1.85410 | + | 5.70634i | 0.0956180 | + | 0.294282i | ||||
\(377\) | 12.1353 | + | 8.81678i | 0.624997 | + | 0.454087i | ||||
\(378\) | 6.47214 | − | 4.70228i | 0.332891 | − | 0.241859i | ||||
\(379\) | −4.94427 | + | 15.2169i | −0.253970 | + | 0.781640i | 0.740061 | + | 0.672540i | \(0.234797\pi\) |
−0.994031 | + | 0.109100i | \(0.965203\pi\) | |||||||
\(380\) | 1.85410 | − | 5.70634i | 0.0951134 | − | 0.292729i | ||||
\(381\) | −12.9443 | + | 9.40456i | −0.663155 | + | 0.481810i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.70820 | + | 11.4127i | 0.189480 | + | 0.583161i | 0.999997 | − | 0.00255538i | \(-0.000813402\pi\) |
−0.810516 | + | 0.585716i | \(0.800813\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.0000 | 0.661683 | ||||||||
\(387\) | −2.47214 | − | 7.60845i | −0.125666 | − | 0.386759i | ||||
\(388\) | −8.89919 | − | 6.46564i | −0.451788 | − | 0.328243i | ||||
\(389\) | −26.6976 | + | 19.3969i | −1.35362 | + | 0.983463i | −0.354798 | + | 0.934943i | \(0.615450\pi\) |
−0.998822 | + | 0.0485195i | \(0.984550\pi\) | |||||||
\(390\) | −9.27051 | + | 28.5317i | −0.469431 | + | 1.44476i | ||||
\(391\) | −5.56231 | + | 17.1190i | −0.281298 | + | 0.865746i | ||||
\(392\) | 2.42705 | − | 1.76336i | 0.122585 | − | 0.0890629i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.63525 | + | 14.2658i | 0.233521 | + | 0.718703i | ||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0000 | 0.853206 | 0.426603 | − | 0.904439i | \(-0.359710\pi\) | ||||
0.426603 | + | 0.904439i | \(0.359710\pi\) | |||||||
\(398\) | −4.94427 | − | 15.2169i | −0.247834 | − | 0.762754i | ||||
\(399\) | 6.47214 | + | 4.70228i | 0.324012 | + | 0.235409i | ||||
\(400\) | −3.23607 | + | 2.35114i | −0.161803 | + | 0.117557i | ||||
\(401\) | −10.1976 | + | 31.3849i | −0.509242 | + | 1.56729i | 0.284279 | + | 0.958742i | \(0.408246\pi\) |
−0.793520 | + | 0.608544i | \(0.791754\pi\) | |||||||
\(402\) | 6.18034 | − | 19.0211i | 0.308247 | − | 0.948688i | ||||
\(403\) | 8.09017 | − | 5.87785i | 0.403000 | − | 0.292797i | ||||
\(404\) | 4.85410 | + | 3.52671i | 0.241501 | + | 0.175460i | ||||
\(405\) | 10.1976 | + | 31.3849i | 0.506721 | + | 1.55953i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.00000 | 0.297044 | ||||||||
\(409\) | 4.01722 | + | 12.3637i | 0.198639 | + | 0.611347i | 0.999915 | + | 0.0130525i | \(0.00415485\pi\) |
−0.801276 | + | 0.598295i | \(0.795845\pi\) | |||||||
\(410\) | −7.28115 | − | 5.29007i | −0.359591 | − | 0.261258i | ||||
\(411\) | 9.70820 | − | 7.05342i | 0.478870 | − | 0.347920i | ||||
\(412\) | 2.47214 | − | 7.60845i | 0.121793 | − | 0.374842i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.85410 | + | 3.52671i | −0.238566 | + | 0.173328i | ||||
\(415\) | −43.6869 | − | 31.7404i | −2.14451 | − | 1.55808i | ||||
\(416\) | −1.54508 | − | 4.75528i | −0.0757540 | − | 0.233147i | ||||
\(417\) | −44.0000 | −2.15469 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | −3.70820 | − | 11.4127i | −0.180942 | − | 0.556882i | ||||
\(421\) | −13.7533 | − | 9.99235i | −0.670294 | − | 0.486997i | 0.199829 | − | 0.979831i | \(-0.435961\pi\) |
−0.870124 | + | 0.492833i | \(0.835961\pi\) | |||||||
\(422\) | −3.23607 | + | 2.35114i | −0.157529 | + | 0.114452i | ||||
\(423\) | 1.85410 | − | 5.70634i | 0.0901495 | − | 0.277452i | ||||
\(424\) | −0.927051 | + | 2.85317i | −0.0450216 | + | 0.138562i | ||||
\(425\) | 9.70820 | − | 7.05342i | 0.470917 | − | 0.342141i | ||||
\(426\) | 19.4164 | + | 14.1068i | 0.940728 | + | 0.683479i | ||||
\(427\) | −6.18034 | − | 19.0211i | −0.299088 | − | 0.920497i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.0000 | 1.15738 | ||||||||
\(431\) | −11.1246 | − | 34.2380i | −0.535854 | − | 1.64919i | −0.741797 | − | 0.670624i | \(-0.766026\pi\) |
0.205944 | − | 0.978564i | \(-0.433974\pi\) | |||||||
\(432\) | −3.23607 | − | 2.35114i | −0.155695 | − | 0.113119i | ||||
\(433\) | 29.9336 | − | 21.7481i | 1.43852 | − | 1.04514i | 0.450169 | − | 0.892943i | \(-0.351364\pi\) |
0.988350 | − | 0.152201i | \(-0.0486362\pi\) | |||||||
\(434\) | −1.23607 | + | 3.80423i | −0.0593332 | + | 0.182609i | ||||
\(435\) | 5.56231 | − | 17.1190i | 0.266692 | − | 0.820794i | ||||
\(436\) | 13.7533 | − | 9.99235i | 0.658663 | − | 0.478547i | ||||
\(437\) | 9.70820 | + | 7.05342i | 0.464406 | + | 0.337411i | ||||
\(438\) | 8.65248 | + | 26.6296i | 0.413431 | + | 1.27241i | ||||
\(439\) | 22.0000 | 1.05000 | 0.525001 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 4.63525 | + | 14.2658i | 0.220477 | + | 0.678557i | ||||
\(443\) | −29.1246 | − | 21.1603i | −1.38375 | − | 1.00535i | −0.996518 | − | 0.0833731i | \(-0.973431\pi\) |
−0.387234 | − | 0.921982i | \(-0.626569\pi\) | |||||||
\(444\) | −11.3262 | + | 8.22899i | −0.537519 | + | 0.390531i | ||||
\(445\) | 8.34346 | − | 25.6785i | 0.395518 | − | 1.21728i | ||||
\(446\) | −1.23607 | + | 3.80423i | −0.0585295 | + | 0.180135i | ||||
\(447\) | 4.85410 | − | 3.52671i | 0.229591 | − | 0.166808i | ||||
\(448\) | 1.61803 | + | 1.17557i | 0.0764449 | + | 0.0555405i | ||||
\(449\) | −6.48936 | − | 19.9722i | −0.306252 | − | 0.942546i | −0.979207 | − | 0.202863i | \(-0.934975\pi\) |
0.672955 | − | 0.739683i | \(-0.265025\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.00000 | −0.423324 | ||||||||
\(453\) | 4.94427 | + | 15.2169i | 0.232302 | + | 0.714953i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.2705 | − | 17.6336i | 1.13782 | − | 0.826674i | ||||
\(456\) | 1.23607 | − | 3.80423i | 0.0578842 | − | 0.178149i | ||||
\(457\) | 0.309017 | − | 0.951057i | 0.0144552 | − | 0.0444885i | −0.943569 | − | 0.331177i | \(-0.892554\pi\) |
0.958024 | + | 0.286688i | \(0.0925544\pi\) | |||||||
\(458\) | −4.04508 | + | 2.93893i | −0.189014 | + | 0.137327i | ||||
\(459\) | 9.70820 | + | 7.05342i | 0.453140 | + | 0.329226i | ||||
\(460\) | −5.56231 | − | 17.1190i | −0.259344 | − | 0.798178i | ||||
\(461\) | −21.0000 | −0.978068 | −0.489034 | − | 0.872265i | \(-0.662651\pi\) | ||||
−0.489034 | + | 0.872265i | \(0.662651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 0.927051 | + | 2.85317i | 0.0430373 | + | 0.132455i | ||||
\(465\) | −9.70820 | − | 7.05342i | −0.450207 | − | 0.327095i | ||||
\(466\) | −16.9894 | + | 12.3435i | −0.787017 | + | 0.571801i | ||||
\(467\) | −3.70820 | + | 11.4127i | −0.171595 | + | 0.528116i | −0.999462 | − | 0.0328096i | \(-0.989555\pi\) |
0.827866 | + | 0.560925i | \(0.189555\pi\) | |||||||
\(468\) | −1.54508 | + | 4.75528i | −0.0714216 | + | 0.219813i | ||||
\(469\) | −16.1803 | + | 11.7557i | −0.747139 | + | 0.542828i | ||||
\(470\) | 14.5623 | + | 10.5801i | 0.671709 | + | 0.488025i | ||||
\(471\) | −1.23607 | − | 3.80423i | −0.0569550 | − | 0.175289i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | −2.47214 | − | 7.60845i | −0.113429 | − | 0.349100i | ||||
\(476\) | −4.85410 | − | 3.52671i | −0.222487 | − | 0.161647i | ||||
\(477\) | 2.42705 | − | 1.76336i | 0.111127 | − | 0.0807385i | ||||
\(478\) | 9.27051 | − | 28.5317i | 0.424023 | − | 1.30501i | ||||
\(479\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(480\) | −4.85410 | + | 3.52671i | −0.221558 | + | 0.160972i | ||||
\(481\) | −28.3156 | − | 20.5725i | −1.29108 | − | 0.938025i | ||||
\(482\) | 3.09017 | + | 9.51057i | 0.140753 | + | 0.433194i | ||||
\(483\) | 24.0000 | 1.09204 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.0000 | −1.49845 | ||||||||
\(486\) | 3.09017 | + | 9.51057i | 0.140173 | + | 0.431408i | ||||
\(487\) | 27.5066 | + | 19.9847i | 1.24644 | + | 0.905593i | 0.998010 | − | 0.0630562i | \(-0.0200847\pi\) |
0.248432 | + | 0.968649i | \(0.420085\pi\) | |||||||
\(488\) | −8.09017 | + | 5.87785i | −0.366225 | + | 0.266078i | ||||
\(489\) | 13.5967 | − | 41.8465i | 0.614866 | − | 1.89236i | ||||
\(490\) | 2.78115 | − | 8.55951i | 0.125640 | − | 0.386679i | ||||
\(491\) | −24.2705 | + | 17.6336i | −1.09531 | + | 0.795791i | −0.980289 | − | 0.197571i | \(-0.936695\pi\) |
−0.115024 | + | 0.993363i | \(0.536695\pi\) | |||||||
\(492\) | −4.85410 | − | 3.52671i | −0.218840 | − | 0.158996i | ||||
\(493\) | −2.78115 | − | 8.55951i | −0.125257 | − | 0.385501i | ||||
\(494\) | 10.0000 | 0.449921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −7.41641 | − | 22.8254i | −0.332671 | − | 1.02386i | ||||
\(498\) | −29.1246 | − | 21.1603i | −1.30511 | − | 0.948214i | ||||
\(499\) | 12.9443 | − | 9.40456i | 0.579465 | − | 0.421006i | −0.259066 | − | 0.965860i | \(-0.583415\pi\) |
0.838531 | + | 0.544853i | \(0.183415\pi\) | |||||||
\(500\) | 0.927051 | − | 2.85317i | 0.0414590 | − | 0.127598i | ||||
\(501\) | −7.41641 | + | 22.8254i | −0.331341 | + | 1.01976i | ||||
\(502\) | −14.5623 | + | 10.5801i | −0.649948 | + | 0.472215i | ||||
\(503\) | 24.2705 | + | 17.6336i | 1.08217 | + | 0.786241i | 0.978060 | − | 0.208324i | \(-0.0668010\pi\) |
0.104109 | + | 0.994566i | \(0.466801\pi\) | |||||||
\(504\) | −0.618034 | − | 1.90211i | −0.0275294 | − | 0.0847268i | ||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0000 | −1.06588 | ||||||||
\(508\) | −2.47214 | − | 7.60845i | −0.109683 | − | 0.337570i | ||||
\(509\) | −4.85410 | − | 3.52671i | −0.215154 | − | 0.156319i | 0.474988 | − | 0.879992i | \(-0.342452\pi\) |
−0.690143 | + | 0.723673i | \(0.742452\pi\) | |||||||
\(510\) | 14.5623 | − | 10.5801i | 0.644830 | − | 0.468496i | ||||
\(511\) | 8.65248 | − | 26.6296i | 0.382763 | − | 1.17802i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | 6.47214 | − | 4.70228i | 0.285752 | − | 0.207611i | ||||
\(514\) | −2.42705 | − | 1.76336i | −0.107053 | − | 0.0777783i | ||||
\(515\) | −7.41641 | − | 22.8254i | −0.326806 | − | 1.00581i | ||||
\(516\) | 16.0000 | 0.704361 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 14.0000 | 0.615125 | ||||||||
\(519\) | 3.70820 | + | 11.4127i | 0.162772 | + | 0.500961i | ||||
\(520\) | −12.1353 | − | 8.81678i | −0.532166 | − | 0.386641i | ||||
\(521\) | 14.5623 | − | 10.5801i | 0.637986 | − | 0.463524i | −0.221172 | − | 0.975235i | \(-0.570988\pi\) |
0.859158 | + | 0.511711i | \(0.170988\pi\) | |||||||
\(522\) | 0.927051 | − | 2.85317i | 0.0405759 | − | 0.124880i | ||||
\(523\) | 4.94427 | − | 15.2169i | 0.216198 | − | 0.665389i | −0.782868 | − | 0.622187i | \(-0.786244\pi\) |
0.999066 | − | 0.0432015i | \(-0.0137558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9443 | − | 9.40456i | −0.564934 | − | 0.410449i | ||||
\(526\) | −1.85410 | − | 5.70634i | −0.0808427 | − | 0.248808i | ||||
\(527\) | −6.00000 | −0.261364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 2.78115 | + | 8.55951i | 0.120806 | + | 0.371801i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.23607 | + | 2.35114i | −0.140301 | + | 0.101935i | ||||
\(533\) | 4.63525 | − | 14.2658i | 0.200775 | − | 0.617922i | ||||
\(534\) | 5.56231 | − | 17.1190i | 0.240705 | − | 0.740812i | ||||
\(535\) | 14.5623 | − | 10.5801i | 0.629583 | − | 0.457419i | ||||
\(536\) | 8.09017 | + | 5.87785i | 0.349442 | + | 0.253885i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.00000 | −0.129339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.0000 | −0.516398 | ||||||||
\(541\) | −0.618034 | − | 1.90211i | −0.0265714 | − | 0.0817782i | 0.936891 | − | 0.349620i | \(-0.113689\pi\) |
−0.963463 | + | 0.267842i | \(0.913689\pi\) | |||||||
\(542\) | 16.1803 | + | 11.7557i | 0.695005 | + | 0.504951i | ||||
\(543\) | 8.09017 | − | 5.87785i | 0.347182 | − | 0.252243i | ||||
\(544\) | −0.927051 | + | 2.85317i | −0.0397470 | + | 0.122329i | ||||
\(545\) | 15.7599 | − | 48.5039i | 0.675079 | − | 2.07768i | ||||
\(546\) | 16.1803 | − | 11.7557i | 0.692455 | − | 0.503098i | ||||
\(547\) | 6.47214 | + | 4.70228i | 0.276729 | + | 0.201055i | 0.717489 | − | 0.696570i | \(-0.245291\pi\) |
−0.440761 | + | 0.897625i | \(0.645291\pi\) | |||||||
\(548\) | 1.85410 | + | 5.70634i | 0.0792033 | + | 0.243763i | ||||
\(549\) | 10.0000 | 0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −3.70820 | − | 11.4127i | −0.157832 | − | 0.485756i | ||||
\(553\) | −3.23607 | − | 2.35114i | −0.137612 | − | 0.0999807i | ||||
\(554\) | 4.04508 | − | 2.93893i | 0.171859 | − | 0.124863i | ||||
\(555\) | −12.9787 | + | 39.9444i | −0.550916 | + | 1.69554i | ||||
\(556\) | 6.79837 | − | 20.9232i | 0.288315 | − | 0.887343i | ||||
\(557\) | −14.5623 | + | 10.5801i | −0.617025 | + | 0.448295i | −0.851881 | − | 0.523735i | \(-0.824538\pi\) |
0.234856 | + | 0.972030i | \(0.424538\pi\) | |||||||
\(558\) | −1.61803 | − | 1.17557i | −0.0684968 | − | 0.0497659i | ||||
\(559\) | 12.3607 | + | 38.0423i | 0.522801 | + | 1.60902i | ||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | 12.9787 | + | 39.9444i | 0.546988 | + | 1.68345i | 0.716217 | + | 0.697878i | \(0.245872\pi\) |
−0.169229 | + | 0.985577i | \(0.554128\pi\) | |||||||
\(564\) | 9.70820 | + | 7.05342i | 0.408789 | + | 0.297003i | ||||
\(565\) | −21.8435 | + | 15.8702i | −0.918961 | + | 0.667664i | ||||
\(566\) | −6.18034 | + | 19.0211i | −0.259779 | + | 0.799518i | ||||
\(567\) | 6.79837 | − | 20.9232i | 0.285505 | − | 0.878694i | ||||
\(568\) | −9.70820 | + | 7.05342i | −0.407347 | + | 0.295955i | ||||
\(569\) | 4.85410 | + | 3.52671i | 0.203495 | + | 0.147847i | 0.684865 | − | 0.728670i | \(-0.259861\pi\) |
−0.481371 | + | 0.876517i | \(0.659861\pi\) | |||||||
\(570\) | −3.70820 | − | 11.4127i | −0.155320 | − | 0.478024i | ||||
\(571\) | 10.0000 | 0.418487 | 0.209243 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.85410 | + | 5.70634i | 0.0773887 | + | 0.238178i | ||||
\(575\) | −19.4164 | − | 14.1068i | −0.809720 | − | 0.588296i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 3.39919 | − | 10.4616i | 0.141510 | − | 0.435523i | −0.855036 | − | 0.518569i | \(-0.826465\pi\) |
0.996546 | + | 0.0830461i | \(0.0264649\pi\) | |||||||
\(578\) | −2.47214 | + | 7.60845i | −0.102827 | + | 0.316470i | ||||
\(579\) | 21.0344 | − | 15.2824i | 0.874162 | − | 0.635116i | ||||
\(580\) | 7.28115 | + | 5.29007i | 0.302333 | + | 0.219658i | ||||
\(581\) | 11.1246 | + | 34.2380i | 0.461527 | + | 1.42043i | ||||
\(582\) | −22.0000 | −0.911929 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 4.63525 | + | 14.2658i | 0.191644 | + | 0.589820i | ||||
\(586\) | 16.9894 | + | 12.3435i | 0.701824 | + | 0.509905i | ||||
\(587\) | 14.5623 | − | 10.5801i | 0.601051 | − | 0.436689i | −0.245201 | − | 0.969472i | \(-0.578854\pi\) |
0.846252 | + | 0.532783i | \(0.178854\pi\) | |||||||
\(588\) | 1.85410 | − | 5.70634i | 0.0764619 | − | 0.235325i | ||||
\(589\) | −1.23607 | + | 3.80423i | −0.0509313 | + | 0.156750i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.2705 | + | 17.6336i | 0.998355 | + | 0.725348i | ||||
\(592\) | −2.16312 | − | 6.65740i | −0.0889036 | − | 0.273617i | ||||
\(593\) | −27.0000 | −1.10876 | −0.554379 | − | 0.832265i | \(-0.687044\pi\) | ||||
−0.554379 | + | 0.832265i | \(0.687044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | −0.737928 | ||||||||
\(596\) | 0.927051 | + | 2.85317i | 0.0379735 | + | 0.116870i | ||||
\(597\) | −25.8885 | − | 18.8091i | −1.05955 | − | 0.769806i | ||||
\(598\) | 24.2705 | − | 17.6336i | 0.992495 | − | 0.721090i | ||||
\(599\) | −12.9787 | + | 39.9444i | −0.530296 | + | 1.63208i | 0.223304 | + | 0.974749i | \(0.428316\pi\) |
−0.753599 | + | 0.657334i | \(0.771684\pi\) | |||||||
\(600\) | −2.47214 | + | 7.60845i | −0.100925 | + | 0.310614i | ||||
\(601\) | −10.5172 | + | 7.64121i | −0.429006 | + | 0.311691i | −0.781251 | − | 0.624216i | \(-0.785418\pi\) |
0.352245 | + | 0.935908i | \(0.385418\pi\) | |||||||
\(602\) | −12.9443 | − | 9.40456i | −0.527569 | − | 0.383301i | ||||
\(603\) | −3.09017 | − | 9.51057i | −0.125841 | − | 0.387300i | ||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | 6.79837 | + | 20.9232i | 0.275937 | + | 0.849248i | 0.988970 | + | 0.148117i | \(0.0473213\pi\) |
−0.713032 | + | 0.701131i | \(0.752679\pi\) | |||||||
\(608\) | 1.61803 | + | 1.17557i | 0.0656199 | + | 0.0476757i | ||||
\(609\) | −9.70820 | + | 7.05342i | −0.393396 | + | 0.285819i | ||||
\(610\) | −9.27051 | + | 28.5317i | −0.375352 | + | 1.15521i | ||||
\(611\) | −9.27051 | + | 28.5317i | −0.375045 | + | 1.15427i | ||||
\(612\) | 2.42705 | − | 1.76336i | 0.0981077 | − | 0.0712794i | ||||
\(613\) | 4.04508 | + | 2.93893i | 0.163379 | + | 0.118702i | 0.666471 | − | 0.745531i | \(-0.267804\pi\) |
−0.503091 | + | 0.864233i | \(0.667804\pi\) | |||||||
\(614\) | 3.09017 | + | 9.51057i | 0.124709 | + | 0.383815i | ||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.0000 | 1.57008 | 0.785040 | − | 0.619445i | \(-0.212642\pi\) | ||||
0.785040 | + | 0.619445i | \(0.212642\pi\) | |||||||
\(618\) | −4.94427 | − | 15.2169i | −0.198888 | − | 0.612114i | ||||
\(619\) | 8.09017 | + | 5.87785i | 0.325171 | + | 0.236251i | 0.738379 | − | 0.674386i | \(-0.235592\pi\) |
−0.413208 | + | 0.910637i | \(0.635592\pi\) | |||||||
\(620\) | 4.85410 | − | 3.52671i | 0.194945 | − | 0.141636i | ||||
\(621\) | 7.41641 | − | 22.8254i | 0.297610 | − | 0.915950i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5623 | + | 10.5801i | −0.583426 | + | 0.423884i | ||||
\(624\) | −8.09017 | − | 5.87785i | −0.323866 | − | 0.235302i | ||||
\(625\) | −8.96149 | − | 27.5806i | −0.358460 | − | 1.10323i | ||||
\(626\) | −1.00000 | −0.0399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | 6.48936 | + | 19.9722i | 0.258748 | + | 0.796343i | ||||
\(630\) | −4.85410 | − | 3.52671i | −0.193392 | − | 0.140508i | ||||
\(631\) | −30.7426 | + | 22.3358i | −1.22385 | + | 0.889176i | −0.996413 | − | 0.0846182i | \(-0.973033\pi\) |
−0.227432 | + | 0.973794i | \(0.573033\pi\) | |||||||
\(632\) | −0.618034 | + | 1.90211i | −0.0245841 | + | 0.0756620i | ||||
\(633\) | −2.47214 | + | 7.60845i | −0.0982586 | + | 0.302409i | ||||
\(634\) | 14.5623 | − | 10.5801i | 0.578343 | − | 0.420191i | ||||
\(635\) | −19.4164 | − | 14.1068i | −0.770517 | − | 0.559813i | ||||
\(636\) | 1.85410 | + | 5.70634i | 0.0735199 | + | 0.226271i | ||||
\(637\) | 15.0000 | 0.594322 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | −0.927051 | − | 2.85317i | −0.0366449 | − | 0.112781i | ||||
\(641\) | 26.6976 | + | 19.3969i | 1.05449 | + | 0.766132i | 0.973061 | − | 0.230547i | \(-0.0740516\pi\) |
0.0814291 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(642\) | 9.70820 | − | 7.05342i | 0.383152 | − | 0.278376i | ||||
\(643\) | 0.618034 | − | 1.90211i | 0.0243729 | − | 0.0750120i | −0.938130 | − | 0.346283i | \(-0.887444\pi\) |
0.962503 | + | 0.271271i | \(0.0874438\pi\) | |||||||
\(644\) | −3.70820 | + | 11.4127i | −0.146124 | + | 0.449723i | ||||
\(645\) | 38.8328 | − | 28.2137i | 1.52904 | − | 1.11091i | ||||
\(646\) | −4.85410 | − | 3.52671i | −0.190982 | − | 0.138757i | ||||
\(647\) | −3.70820 | − | 11.4127i | −0.145785 | − | 0.448679i | 0.851327 | − | 0.524636i | \(-0.175799\pi\) |
−0.997111 | + | 0.0759575i | \(0.975799\pi\) | |||||||
\(648\) | −11.0000 | −0.432121 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −20.0000 | −0.784465 | ||||||||
\(651\) | 2.47214 | + | 7.60845i | 0.0968906 | + | 0.298199i | ||||
\(652\) | 17.7984 | + | 12.9313i | 0.697038 | + | 0.506428i | ||||
\(653\) | −14.5623 | + | 10.5801i | −0.569867 | + | 0.414033i | −0.835057 | − | 0.550164i | \(-0.814565\pi\) |
0.265190 | + | 0.964196i | \(0.414565\pi\) | |||||||
\(654\) | 10.5066 | − | 32.3359i | 0.410840 | − | 1.26443i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.42705 | − | 1.76336i | 0.0947604 | − | 0.0688475i | ||||
\(657\) | 11.3262 | + | 8.22899i | 0.441879 | + | 0.321044i | ||||
\(658\) | −3.70820 | − | 11.4127i | −0.144561 | − | 0.444913i | ||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | 0.661223 | 0.330612 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330612 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(662\) | 6.18034 | + | 19.0211i | 0.240206 | + | 0.739277i | ||||
\(663\) | 24.2705 | + | 17.6336i | 0.942588 | + | 0.684831i | ||||
\(664\) | 14.5623 | − | 10.5801i | 0.565127 | − | 0.410589i | ||||
\(665\) | −3.70820 | + | 11.4127i | −0.143798 | + | 0.442565i | ||||
\(666\) | −2.16312 | + | 6.65740i | −0.0838192 | + | 0.257969i | ||||
\(667\) | −14.5623 | + | 10.5801i | −0.563855 | + | 0.409664i | ||||
\(668\) | −9.70820 | − | 7.05342i | −0.375622 | − | 0.272905i | ||||
\(669\) | 2.47214 | + | 7.60845i | 0.0955783 | + | 0.294160i | ||||
\(670\) | 30.0000 | 1.15900 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.00000 | 0.154303 | ||||||||
\(673\) | −11.7426 | − | 36.1401i | −0.452646 | − | 1.39310i | −0.873877 | − | 0.486147i | \(-0.838402\pi\) |
0.421231 | − | 0.906953i | \(-0.361598\pi\) | |||||||
\(674\) | −10.5172 | − | 7.64121i | −0.405108 | − | 0.294328i | ||||
\(675\) | −12.9443 | + | 9.40456i | −0.498225 | + | 0.361982i | ||||
\(676\) | 3.70820 | − | 11.4127i | 0.142623 | − | 0.438949i | ||||
\(677\) | 4.63525 | − | 14.2658i | 0.178147 | − | 0.548281i | −0.821616 | − | 0.570042i | \(-0.806927\pi\) |
0.999763 | + | 0.0217604i | \(0.00692711\pi\) | |||||||
\(678\) | −14.5623 | + | 10.5801i | −0.559262 | + | 0.406328i | ||||
\(679\) | 17.7984 | + | 12.9313i | 0.683039 | + | 0.496257i | ||||
\(680\) | 2.78115 | + | 8.55951i | 0.106652 | + | 0.328242i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | 0.229584 | 0.114792 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(684\) | −0.618034 | − | 1.90211i | −0.0236311 | − | 0.0727291i | ||||
\(685\) | 14.5623 | + | 10.5801i | 0.556397 | + | 0.404246i | ||||
\(686\) | −16.1803 | + | 11.7557i | −0.617768 | + | 0.448835i | ||||
\(687\) | −3.09017 | + | 9.51057i | −0.117897 | + | 0.362851i | ||||
\(688\) | −2.47214 | + | 7.60845i | −0.0942493 | + | 0.290070i | ||||
\(689\) | −12.1353 | + | 8.81678i | −0.462316 | + | 0.335893i | ||||
\(690\) | −29.1246 | − | 21.1603i | −1.10876 | − | 0.805558i | ||||
\(691\) | −1.23607 | − | 3.80423i | −0.0470222 | − | 0.144720i | 0.924789 | − | 0.380481i | \(-0.124242\pi\) |
−0.971811 | + | 0.235762i | \(0.924242\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.0000 | −1.36654 | ||||||||
\(695\) | −20.3951 | − | 62.7697i | −0.773631 | − | 2.38099i | ||||
\(696\) | 4.85410 | + | 3.52671i | 0.183994 | + | 0.133680i | ||||
\(697\) | −7.28115 | + | 5.29007i | −0.275793 | + | 0.200376i | ||||
\(698\) | −5.25329 | + | 16.1680i | −0.198840 | + | 0.611966i | ||||
\(699\) | −12.9787 | + | 39.9444i | −0.490900 | + | 1.51083i | ||||
\(700\) | 6.47214 | − | 4.70228i | 0.244624 | − | 0.177730i | ||||
\(701\) | −21.8435 | − | 15.8702i | −0.825016 | − | 0.599409i | 0.0931288 | − | 0.995654i | \(-0.470313\pi\) |
−0.918145 | + | 0.396245i | \(0.870313\pi\) | |||||||
\(702\) | −6.18034 | − | 19.0211i | −0.233262 | − | 0.717906i | ||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.0000 | 1.35584 | ||||||||
\(706\) | −2.78115 | − | 8.55951i | −0.104670 | − | 0.322141i | ||||
\(707\) | −9.70820 | − | 7.05342i | −0.365115 | − | 0.265271i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.09017 | + | 9.51057i | −0.116054 | + | 0.357177i | −0.992165 | − | 0.124932i | \(-0.960129\pi\) |
0.876112 | + | 0.482108i | \(0.160129\pi\) | |||||||
\(710\) | −11.1246 | + | 34.2380i | −0.417499 | + | 1.28493i | ||||
\(711\) | 1.61803 | − | 1.17557i | 0.0606810 | − | 0.0440873i | ||||
\(712\) | 7.28115 | + | 5.29007i | 0.272873 | + | 0.198254i | ||||
\(713\) | 3.70820 | + | 11.4127i | 0.138873 | + | 0.427408i | ||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.5410 | − | 57.0634i | −0.692427 | − | 2.13107i | ||||
\(718\) | 14.5623 | + | 10.5801i | 0.543460 | + | 0.394847i | ||||
\(719\) | −14.5623 | + | 10.5801i | −0.543082 | + | 0.394572i | −0.825229 | − | 0.564799i | \(-0.808954\pi\) |
0.282146 | + | 0.959371i | \(0.408954\pi\) | |||||||
\(720\) | −0.927051 | + | 2.85317i | −0.0345492 | + | 0.106331i | ||||
\(721\) | −4.94427 | + | 15.2169i | −0.184134 | + | 0.566707i | ||||
\(722\) | 12.1353 | − | 8.81678i | 0.451627 | − | 0.328127i | ||||
\(723\) | 16.1803 | + | 11.7557i | 0.601753 | + | 0.437199i | ||||
\(724\) | 1.54508 | + | 4.75528i | 0.0574226 | + | 0.176729i | ||||
\(725\) | 12.0000 | 0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 3.09017 | + | 9.51057i | 0.114529 | + | 0.352485i | ||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | −33.9787 | + | 24.6870i | −1.25761 | + | 0.913706i | ||||
\(731\) | 7.41641 | − | 22.8254i | 0.274306 | − | 0.844226i | ||||
\(732\) | −6.18034 | + | 19.0211i | −0.228432 | + | 0.703041i | ||||
\(733\) | 4.04508 | − | 2.93893i | 0.149409 | − | 0.108552i | −0.510570 | − | 0.859836i | \(-0.670565\pi\) |
0.659978 | + | 0.751285i | \(0.270565\pi\) | |||||||
\(734\) | 8.09017 | + | 5.87785i | 0.298614 | + | 0.216955i | ||||
\(735\) | −5.56231 | − | 17.1190i | −0.205169 | − | 0.631444i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.00000 | −0.110432 | ||||||||
\(739\) | −8.03444 | − | 24.7275i | −0.295552 | − | 0.909615i | −0.983036 | − | 0.183415i | \(-0.941285\pi\) |
0.687484 | − | 0.726200i | \(-0.258715\pi\) | |||||||
\(740\) | −16.9894 | − | 12.3435i | −0.624541 | − | 0.453756i | ||||
\(741\) | 16.1803 | − | 11.7557i | 0.594400 | − | 0.431857i | ||||
\(742\) | 1.85410 | − | 5.70634i | 0.0680662 | − | 0.209486i | ||||
\(743\) | 5.56231 | − | 17.1190i | 0.204061 | − | 0.628036i | −0.795689 | − | 0.605705i | \(-0.792891\pi\) |
0.999751 | − | 0.0223310i | \(-0.00710877\pi\) | |||||||
\(744\) | 3.23607 | − | 2.35114i | 0.118640 | − | 0.0861970i | ||||
\(745\) | 7.28115 | + | 5.29007i | 0.266761 | + | 0.193813i | ||||
\(746\) | 3.09017 | + | 9.51057i | 0.113139 | + | 0.348207i | ||||
\(747\) | −18.0000 | −0.658586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −1.85410 | − | 5.70634i | −0.0677022 | − | 0.208366i | ||||
\(751\) | −35.5967 | − | 25.8626i | −1.29894 | − | 0.943738i | −0.298999 | − | 0.954253i | \(-0.596653\pi\) |
−0.999945 | + | 0.0105155i | \(0.996653\pi\) | |||||||
\(752\) | −4.85410 | + | 3.52671i | −0.177011 | + | 0.128606i | ||||
\(753\) | −11.1246 | + | 34.2380i | −0.405403 | + | 1.24770i | ||||
\(754\) | −4.63525 | + | 14.2658i | −0.168806 | + | 0.519532i | ||||
\(755\) | −19.4164 | + | 14.1068i | −0.706635 | + | 0.513401i | ||||
\(756\) | 6.47214 | + | 4.70228i | 0.235389 | + | 0.171020i | ||||
\(757\) | 12.6697 | + | 38.9933i | 0.460488 | + | 1.41724i | 0.864570 | + | 0.502513i | \(0.167591\pi\) |
−0.404082 | + | 0.914723i | \(0.632409\pi\) | |||||||
\(758\) | −16.0000 | −0.581146 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | 0.217643 | ||||||||
\(761\) | −0.927051 | − | 2.85317i | −0.0336056 | − | 0.103427i | 0.932847 | − | 0.360273i | \(-0.117317\pi\) |
−0.966452 | + | 0.256846i | \(0.917317\pi\) | |||||||
\(762\) | −12.9443 | − | 9.40456i | −0.468921 | − | 0.340691i | ||||
\(763\) | −27.5066 | + | 19.9847i | −0.995805 | + | 0.723495i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.78115 | − | 8.55951i | 0.100553 | − | 0.309470i | ||||
\(766\) | −9.70820 | + | 7.05342i | −0.350772 | + | 0.254851i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.618034 | − | 1.90211i | −0.0223014 | − | 0.0686366i | ||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 4.01722 | + | 12.3637i | 0.144583 | + | 0.444981i | ||||
\(773\) | 33.9787 | + | 24.6870i | 1.22213 | + | 0.887929i | 0.996275 | − | 0.0862321i | \(-0.0274827\pi\) |
0.225854 | + | 0.974161i | \(0.427483\pi\) | |||||||
\(774\) | 6.47214 | − | 4.70228i | 0.232636 | − | 0.169020i | ||||
\(775\) | 2.47214 | − | 7.60845i | 0.0888017 | − | 0.273304i | ||||
\(776\) | 3.39919 | − | 10.4616i | 0.122024 | − | 0.375550i | ||||
\(777\) | 22.6525 | − | 16.4580i | 0.812653 | − | 0.590427i | ||||
\(778\) | −26.6976 | − | 19.3969i | −0.957154 | − | 0.695413i | ||||
\(779\) | 1.85410 | + | 5.70634i | 0.0664301 | + | 0.204451i | ||||
\(780\) | −30.0000 | −1.07417 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 3.70820 | + | 11.4127i | 0.132520 | + | 0.407856i | ||||
\(784\) | 2.42705 | + | 1.76336i | 0.0866804 | + | 0.0629770i | ||||
\(785\) | 4.85410 | − | 3.52671i | 0.173250 | − | 0.125874i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.23607 | − | 3.80423i | 0.0440611 | − | 0.135606i | −0.926606 | − | 0.376034i | \(-0.877288\pi\) |
0.970667 | + | 0.240428i | \(0.0772877\pi\) | |||||||
\(788\) | −12.1353 | + | 8.81678i | −0.432301 | + | 0.314085i | ||||
\(789\) | −9.70820 | − | 7.05342i | −0.345621 | − | 0.251109i | ||||
\(790\) | 1.85410 | + | 5.70634i | 0.0659660 | + | 0.203022i | ||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.0000 | −1.77555 | ||||||||
\(794\) | 5.25329 | + | 16.1680i | 0.186432 | + | 0.573779i | ||||
\(795\) | 14.5623 | + | 10.5801i | 0.516472 | + | 0.375239i | ||||
\(796\) | 12.9443 | − | 9.40456i | 0.458798 | − | 0.333336i | ||||
\(797\) | −12.9787 | + | 39.9444i | −0.459730 | + | 1.41490i | 0.405762 | + | 0.913979i | \(0.367006\pi\) |
−0.865492 | + | 0.500924i | \(0.832994\pi\) | |||||||
\(798\) | −2.47214 | + | 7.60845i | −0.0875127 | + | 0.269336i | ||||
\(799\) | 14.5623 | − | 10.5801i | 0.515177 | − | 0.374298i | ||||
\(800\) | −3.23607 | − | 2.35114i | −0.114412 | − | 0.0831254i | ||||
\(801\) | −2.78115 | − | 8.55951i | −0.0982672 | − | 0.302435i | ||||
\(802\) | −33.0000 | −1.16527 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 20.0000 | 0.705346 | ||||||||
\(805\) | 11.1246 | + | 34.2380i | 0.392091 | + | 1.20673i | ||||
\(806\) | 8.09017 | + | 5.87785i | 0.284964 | + | 0.207039i | ||||
\(807\) | −4.85410 | + | 3.52671i | −0.170872 | + | 0.124146i | ||||
\(808\) | −1.85410 | + | 5.70634i | −0.0652271 | + | 0.200748i | ||||
\(809\) | −1.85410 | + | 5.70634i | −0.0651868 | + | 0.200624i | −0.978345 | − | 0.206981i | \(-0.933636\pi\) |
0.913158 | + | 0.407605i | \(0.133636\pi\) | |||||||
\(810\) | −26.6976 | + | 19.3969i | −0.938057 | + | 0.681538i | ||||
\(811\) | −22.6525 | − | 16.4580i | −0.795436 | − | 0.577918i | 0.114136 | − | 0.993465i | \(-0.463590\pi\) |
−0.909572 | + | 0.415547i | \(0.863590\pi\) | |||||||
\(812\) | −1.85410 | − | 5.70634i | −0.0650662 | − | 0.200253i | ||||
\(813\) | 40.0000 | 1.40286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.0000 | 2.31188 | ||||||||
\(816\) | 1.85410 | + | 5.70634i | 0.0649066 | + | 0.199762i | ||||
\(817\) | −12.9443 | − | 9.40456i | −0.452863 | − | 0.329024i | ||||
\(818\) | −10.5172 | + | 7.64121i | −0.367726 | + | 0.267169i | ||||
\(819\) | 3.09017 | − | 9.51057i | 0.107979 | − | 0.332326i | ||||
\(820\) | 2.78115 | − | 8.55951i | 0.0971221 | − | 0.298911i | ||||
\(821\) | 24.2705 | − | 17.6336i | 0.847047 | − | 0.615415i | −0.0772835 | − | 0.997009i | \(-0.524625\pi\) |
0.924330 | + | 0.381594i | \(0.124625\pi\) | |||||||
\(822\) | 9.70820 | + | 7.05342i | 0.338612 | + | 0.246016i | ||||
\(823\) | 9.88854 | + | 30.4338i | 0.344693 | + | 1.06086i | 0.961748 | + | 0.273936i | \(0.0883256\pi\) |
−0.617055 | + | 0.786920i | \(0.711674\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.56231 | − | 17.1190i | −0.193420 | − | 0.595287i | −0.999991 | − | 0.00414942i | \(-0.998679\pi\) |
0.806571 | − | 0.591137i | \(-0.201321\pi\) | |||||||
\(828\) | −4.85410 | − | 3.52671i | −0.168692 | − | 0.122562i | ||||
\(829\) | 34.7877 | − | 25.2748i | 1.20823 | − | 0.877829i | 0.213159 | − | 0.977017i | \(-0.431625\pi\) |
0.995069 | + | 0.0991886i | \(0.0316247\pi\) | |||||||
\(830\) | 16.6869 | − | 51.3571i | 0.579211 | − | 1.78263i | ||||
\(831\) | 3.09017 | − | 9.51057i | 0.107197 | − | 0.329918i | ||||
\(832\) | 4.04508 | − | 2.93893i | 0.140238 | − | 0.101889i | ||||
\(833\) | −7.28115 | − | 5.29007i | −0.252277 | − | 0.183290i | ||||
\(834\) | −13.5967 | − | 41.8465i | −0.470817 | − | 1.44903i | ||||
\(835\) | −36.0000 | −1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −5.56231 | − | 17.1190i | −0.192147 | − | 0.591367i | ||||
\(839\) | −14.5623 | − | 10.5801i | −0.502747 | − | 0.365267i | 0.307318 | − | 0.951607i | \(-0.400568\pi\) |
−0.810065 | + | 0.586340i | \(0.800568\pi\) | |||||||
\(840\) | 9.70820 | − | 7.05342i | 0.334965 | − | 0.243366i | ||||
\(841\) | −6.18034 | + | 19.0211i | −0.213115 | + | 0.655901i | ||||
\(842\) | 5.25329 | − | 16.1680i | 0.181040 | − | 0.557185i | ||||
\(843\) | −9.70820 | + | 7.05342i | −0.334368 | + | 0.242933i | ||||
\(844\) | −3.23607 | − | 2.35114i | −0.111390 | − | 0.0809296i | ||||
\(845\) | −11.1246 | − | 34.2380i | −0.382698 | − | 1.17782i | ||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 12.3607 | + | 38.0423i | 0.424217 | + | 1.30561i | ||||
\(850\) | 9.70820 | + | 7.05342i | 0.332989 | + | 0.241930i | ||||
\(851\) | 33.9787 | − | 24.6870i | 1.16478 | − | 0.846259i | ||||
\(852\) | −7.41641 | + | 22.8254i | −0.254082 | + | 0.781984i | ||||
\(853\) | −8.96149 | + | 27.5806i | −0.306836 | + | 0.944343i | 0.672150 | + | 0.740415i | \(0.265371\pi\) |
−0.978986 | + | 0.203928i | \(0.934629\pi\) | |||||||
\(854\) | 16.1803 | − | 11.7557i | 0.553680 | − | 0.402272i | ||||
\(855\) | −4.85410 | − | 3.52671i | −0.166007 | − | 0.120611i | ||||
\(856\) | 1.85410 | + | 5.70634i | 0.0633719 | + | 0.195039i | ||||
\(857\) | 54.0000 | 1.84460 | 0.922302 | − | 0.386469i | \(-0.126305\pi\) | ||||
0.922302 | + | 0.386469i | \(0.126305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000 | 1.09183 | 0.545913 | − | 0.837842i | \(-0.316183\pi\) | ||||
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(860\) | 7.41641 | + | 22.8254i | 0.252897 | + | 0.778338i | ||||
\(861\) | 9.70820 | + | 7.05342i | 0.330855 | + | 0.240380i | ||||
\(862\) | 29.1246 | − | 21.1603i | 0.991988 | − | 0.720722i | ||||
\(863\) | 1.85410 | − | 5.70634i | 0.0631144 | − | 0.194246i | −0.914527 | − | 0.404524i | \(-0.867437\pi\) |
0.977642 | + | 0.210278i | \(0.0674370\pi\) | |||||||
\(864\) | 1.23607 | − | 3.80423i | 0.0420519 | − | 0.129422i | ||||
\(865\) | −14.5623 | + | 10.5801i | −0.495133 | + | 0.359735i | ||||
\(866\) | 29.9336 | + | 21.7481i | 1.01719 | + | 0.739029i | ||||
\(867\) | 4.94427 | + | 15.2169i | 0.167916 | + | 0.516793i | ||||
\(868\) | −4.00000 | −0.135769 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | 15.4508 | + | 47.5528i | 0.523532 | + | 1.61127i | ||||
\(872\) | 13.7533 | + | 9.99235i | 0.465745 | + | 0.338384i | ||||
\(873\) | −8.89919 | + | 6.46564i | −0.301192 | + | 0.218829i | ||||
\(874\) | −3.70820 | + | 11.4127i | −0.125432 | + | 0.386040i | ||||
\(875\) | −1.85410 | + | 5.70634i | −0.0626801 | + | 0.192909i | ||||
\(876\) | −22.6525 | + | 16.4580i | −0.765356 | + | 0.556064i | ||||
\(877\) | 33.1697 | + | 24.0992i | 1.12006 | + | 0.813772i | 0.984218 | − | 0.176958i | \(-0.0566258\pi\) |
0.135843 | + | 0.990730i | \(0.456626\pi\) | |||||||
\(878\) | 6.79837 | + | 20.9232i | 0.229434 | + | 0.706125i | ||||
\(879\) | 42.0000 | 1.41662 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.0000 | −1.51609 | −0.758044 | − | 0.652203i | \(-0.773845\pi\) | ||||
−0.758044 | + | 0.652203i | \(0.773845\pi\) | |||||||
\(882\) | −0.927051 | − | 2.85317i | −0.0312154 | − | 0.0960712i | ||||
\(883\) | 3.23607 | + | 2.35114i | 0.108902 | + | 0.0791222i | 0.640904 | − | 0.767621i | \(-0.278560\pi\) |
−0.532001 | + | 0.846744i | \(0.678560\pi\) | |||||||
\(884\) | −12.1353 | + | 8.81678i | −0.408153 | + | 0.296540i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1246 | − | 34.2380i | 0.373739 | − | 1.15025i | ||||
\(887\) | −14.5623 | + | 10.5801i | −0.488954 | + | 0.355246i | −0.804782 | − | 0.593570i | \(-0.797718\pi\) |
0.315828 | + | 0.948817i | \(0.397718\pi\) | |||||||
\(888\) | −11.3262 | − | 8.22899i | −0.380084 | − | 0.276147i | ||||
\(889\) | 4.94427 | + | 15.2169i | 0.165826 | + | 0.510359i | ||||
\(890\) | 27.0000 | 0.905042 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | −3.70820 | − | 11.4127i | −0.124090 | − | 0.381911i | ||||
\(894\) | 4.85410 | + | 3.52671i | 0.162345 | + | 0.117951i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.618034 | + | 1.90211i | −0.0206471 | + | 0.0635451i | ||||
\(897\) | 18.5410 | − | 57.0634i | 0.619067 | − | 1.90529i | ||||
\(898\) | 16.9894 | − | 12.3435i | 0.566942 | − | 0.411908i | ||||
\(899\) | −4.85410 | − | 3.52671i | −0.161893 | − | 0.117622i | ||||
\(900\) | 1.23607 | + | 3.80423i | 0.0412023 | + | 0.126808i | ||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.0000 | −1.06489 | ||||||||
\(904\) | −2.78115 | − | 8.55951i | −0.0924998 | − | 0.284685i | ||||
\(905\) | 12.1353 | + | 8.81678i | 0.403390 | + | 0.293080i | ||||
\(906\) | −12.9443 | + | 9.40456i | −0.430045 | + | 0.312446i | ||||
\(907\) | 13.5967 | − | 41.8465i | 0.451473 | − | 1.38949i | −0.423754 | − | 0.905777i | \(-0.639288\pi\) |
0.875227 | − | 0.483713i | \(-0.160712\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.85410 | − | 3.52671i | 0.161000 | − | 0.116974i | ||||
\(910\) | 24.2705 | + | 17.6336i | 0.804560 | + | 0.584547i | ||||
\(911\) | −7.41641 | − | 22.8254i | −0.245717 | − | 0.756238i | −0.995518 | − | 0.0945746i | \(-0.969851\pi\) |
0.749801 | − | 0.661663i | \(-0.230149\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.00000 | 0.0330771 | ||||||||
\(915\) | 18.5410 | + | 57.0634i | 0.612947 | + | 1.88646i | ||||
\(916\) | −4.04508 | − | 2.93893i | −0.133653 | − | 0.0971049i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.70820 | + | 11.4127i | −0.122389 | + | 0.376675i | ||||
\(919\) | 8.65248 | − | 26.6296i | 0.285419 | − | 0.878429i | −0.700854 | − | 0.713305i | \(-0.747198\pi\) |
0.986273 | − | 0.165124i | \(-0.0528025\pi\) | |||||||
\(920\) | 14.5623 | − | 10.5801i | 0.480105 | − | 0.348817i | ||||
\(921\) | 16.1803 | + | 11.7557i | 0.533160 | + | 0.387364i | ||||
\(922\) | −6.48936 | − | 19.9722i | −0.213716 | − | 0.657749i | ||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.0000 | −0.920634 | ||||||||
\(926\) | −1.23607 | − | 3.80423i | −0.0406197 | − | 0.125015i | ||||
\(927\) | −6.47214 | − | 4.70228i | −0.212573 | − | 0.154443i | ||||
\(928\) | −2.42705 | + | 1.76336i | −0.0796719 | + | 0.0578850i | ||||
\(929\) | 15.7599 | − | 48.5039i | 0.517064 | − | 1.59136i | −0.262430 | − | 0.964951i | \(-0.584524\pi\) |
0.779494 | − | 0.626410i | \(-0.215476\pi\) | |||||||
\(930\) | 3.70820 | − | 11.4127i | 0.121597 | − | 0.374236i | ||||
\(931\) | −4.85410 | + | 3.52671i | −0.159087 | + | 0.115583i | ||||
\(932\) | −16.9894 | − | 12.3435i | −0.556505 | − | 0.404324i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.00000 | −0.163430 | ||||||||
\(937\) | −7.10739 | − | 21.8743i | −0.232188 | − | 0.714602i | −0.997482 | − | 0.0709209i | \(-0.977406\pi\) |
0.765294 | − | 0.643681i | \(-0.222594\pi\) | |||||||
\(938\) | −16.1803 | − | 11.7557i | −0.528307 | − | 0.383837i | ||||
\(939\) | −1.61803 | + | 1.17557i | −0.0528025 | + | 0.0383633i | ||||
\(940\) | −5.56231 | + | 17.1190i | −0.181422 | + | 0.558361i | ||||
\(941\) | 12.0517 | − | 37.0912i | 0.392873 | − | 1.20914i | −0.537733 | − | 0.843115i | \(-0.680719\pi\) |
0.930606 | − | 0.366023i | \(-0.119281\pi\) | |||||||
\(942\) | 3.23607 | − | 2.35114i | 0.105437 | − | 0.0766043i | ||||
\(943\) | 14.5623 | + | 10.5801i | 0.474214 | + | 0.344537i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.0000 | 0.780720 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.0000 | −0.974869 | −0.487435 | − | 0.873160i | \(-0.662067\pi\) | ||||
−0.487435 | + | 0.873160i | \(0.662067\pi\) | |||||||
\(948\) | 1.23607 | + | 3.80423i | 0.0401456 | + | 0.123556i | ||||
\(949\) | −56.6312 | − | 41.1450i | −1.83833 | − | 1.33562i | ||||
\(950\) | 6.47214 | − | 4.70228i | 0.209984 | − | 0.152562i | ||||
\(951\) | 11.1246 | − | 34.2380i | 0.360740 | − | 1.11024i | ||||
\(952\) | 1.85410 | − | 5.70634i | 0.0600918 | − | 0.184944i | ||||
\(953\) | 31.5517 | − | 22.9236i | 1.02206 | − | 0.742569i | 0.0553547 | − | 0.998467i | \(-0.482371\pi\) |
0.966704 | + | 0.255898i | \(0.0823710\pi\) | |||||||
\(954\) | 2.42705 | + | 1.76336i | 0.0785787 | + | 0.0570908i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30.0000 | 0.970269 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.70820 | − | 11.4127i | −0.119744 | − | 0.368535i | ||||
\(960\) | −4.85410 | − | 3.52671i | −0.156665 | − | 0.113824i | ||||
\(961\) | 21.8435 | − | 15.8702i | 0.704628 | − | 0.511942i | ||||
\(962\) | 10.8156 | − | 33.2870i | 0.348709 | − | 1.07322i | ||||
\(963\) | 1.85410 | − | 5.70634i | 0.0597476 | − | 0.183884i | ||||
\(964\) | −8.09017 | + | 5.87785i | −0.260567 | + | 0.189313i | ||||
\(965\) | 31.5517 | + | 22.9236i | 1.01568 | + | 0.737938i | ||||
\(966\) | 7.41641 | + | 22.8254i | 0.238619 | + | 0.734394i | ||||
\(967\) | −50.0000 | −1.60789 | −0.803946 | − | 0.594703i | \(-0.797270\pi\) | ||||
−0.803946 | + | 0.594703i | \(0.797270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | −10.1976 | − | 31.3849i | −0.327424 | − | 1.00771i | ||||
\(971\) | −4.85410 | − | 3.52671i | −0.155776 | − | 0.113178i | 0.507167 | − | 0.861848i | \(-0.330693\pi\) |
−0.662943 | + | 0.748670i | \(0.730693\pi\) | |||||||
\(972\) | −8.09017 | + | 5.87785i | −0.259492 | + | 0.188532i | ||||
\(973\) | −13.5967 | + | 41.8465i | −0.435892 | + | 1.34154i | ||||
\(974\) | −10.5066 | + | 32.3359i | −0.336652 | + | 1.03611i | ||||
\(975\) | −32.3607 | + | 23.5114i | −1.03637 | + | 0.752968i | ||||
\(976\) | −8.09017 | − | 5.87785i | −0.258960 | − | 0.188145i | ||||
\(977\) | −10.1976 | − | 31.3849i | −0.326249 | − | 1.00409i | −0.970874 | − | 0.239592i | \(-0.922986\pi\) |
0.644625 | − | 0.764499i | \(-0.277014\pi\) | |||||||
\(978\) | 44.0000 | 1.40696 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 9.00000 | 0.287494 | ||||||||
\(981\) | −5.25329 | − | 16.1680i | −0.167725 | − | 0.516203i | ||||
\(982\) | −24.2705 | − | 17.6336i | −0.774503 | − | 0.562709i | ||||
\(983\) | −48.5410 | + | 35.2671i | −1.54822 | + | 1.12485i | −0.603312 | + | 0.797505i | \(0.706153\pi\) |
−0.944906 | + | 0.327341i | \(0.893847\pi\) | |||||||
\(984\) | 1.85410 | − | 5.70634i | 0.0591066 | − | 0.181911i | ||||
\(985\) | −13.9058 | + | 42.7975i | −0.443075 | + | 1.36364i | ||||
\(986\) | 7.28115 | − | 5.29007i | 0.231879 | − | 0.168470i | ||||
\(987\) | −19.4164 | − | 14.1068i | −0.618031 | − | 0.449026i | ||||
\(988\) | 3.09017 | + | 9.51057i | 0.0983114 | + | 0.302571i | ||||
\(989\) | −48.0000 | −1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | 0.618034 | + | 1.90211i | 0.0196226 | + | 0.0603921i | ||||
\(993\) | 32.3607 | + | 23.5114i | 1.02694 | + | 0.746112i | ||||
\(994\) | 19.4164 | − | 14.1068i | 0.615851 | − | 0.447442i | ||||
\(995\) | 14.8328 | − | 45.6507i | 0.470232 | − | 1.44722i | ||||
\(996\) | 11.1246 | − | 34.2380i | 0.352497 | − | 1.08487i | ||||
\(997\) | −25.0795 | + | 18.2213i | −0.794277 | + | 0.577076i | −0.909230 | − | 0.416295i | \(-0.863328\pi\) |
0.114953 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(998\) | 12.9443 | + | 9.40456i | 0.409744 | + | 0.297696i | ||||
\(999\) | −8.65248 | − | 26.6296i | −0.273752 | − | 0.842523i |
(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 | 242.2.c.b.27.1 | 4 | ||
11.2 | odd | 10 | 242.2.c.e.9.1 | 4 | |||
11.3 | even | 5 | 242.2.a.b.1.1 | yes | 1 | ||
11.4 | even | 5 | inner | 242.2.c.b.3.1 | 4 | ||
11.5 | even | 5 | inner | 242.2.c.b.81.1 | 4 | ||
11.6 | odd | 10 | 242.2.c.e.81.1 | 4 | |||
11.7 | odd | 10 | 242.2.c.e.3.1 | 4 | |||
11.8 | odd | 10 | 242.2.a.a.1.1 | ✓ | 1 | ||
11.9 | even | 5 | inner | 242.2.c.b.9.1 | 4 | ||
11.10 | odd | 2 | 242.2.c.e.27.1 | 4 | |||
33.8 | even | 10 | 2178.2.a.l.1.1 | 1 | |||
33.14 | odd | 10 | 2178.2.a.f.1.1 | 1 | |||
44.3 | odd | 10 | 1936.2.a.k.1.1 | 1 | |||
44.19 | even | 10 | 1936.2.a.j.1.1 | 1 | |||
55.14 | even | 10 | 6050.2.a.s.1.1 | 1 | |||
55.19 | odd | 10 | 6050.2.a.bl.1.1 | 1 | |||
88.3 | odd | 10 | 7744.2.a.h.1.1 | 1 | |||
88.19 | even | 10 | 7744.2.a.g.1.1 | 1 | |||
88.69 | even | 10 | 7744.2.a.bh.1.1 | 1 | |||
88.85 | odd | 10 | 7744.2.a.bi.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
242.2.a.a.1.1 | ✓ | 1 | 11.8 | odd | 10 | ||
242.2.a.b.1.1 | yes | 1 | 11.3 | even | 5 | ||
242.2.c.b.3.1 | 4 | 11.4 | even | 5 | inner | ||
242.2.c.b.9.1 | 4 | 11.9 | even | 5 | inner | ||
242.2.c.b.27.1 | 4 | 1.1 | even | 1 | trivial | ||
242.2.c.b.81.1 | 4 | 11.5 | even | 5 | inner | ||
242.2.c.e.3.1 | 4 | 11.7 | odd | 10 | |||
242.2.c.e.9.1 | 4 | 11.2 | odd | 10 | |||
242.2.c.e.27.1 | 4 | 11.10 | odd | 2 | |||
242.2.c.e.81.1 | 4 | 11.6 | odd | 10 | |||
1936.2.a.j.1.1 | 1 | 44.19 | even | 10 | |||
1936.2.a.k.1.1 | 1 | 44.3 | odd | 10 | |||
2178.2.a.f.1.1 | 1 | 33.14 | odd | 10 | |||
2178.2.a.l.1.1 | 1 | 33.8 | even | 10 | |||
6050.2.a.s.1.1 | 1 | 55.14 | even | 10 | |||
6050.2.a.bl.1.1 | 1 | 55.19 | odd | 10 | |||
7744.2.a.g.1.1 | 1 | 88.19 | even | 10 | |||
7744.2.a.h.1.1 | 1 | 88.3 | odd | 10 | |||
7744.2.a.bh.1.1 | 1 | 88.69 | even | 10 | |||
7744.2.a.bi.1.1 | 1 | 88.85 | odd | 10 |