Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(919,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.919");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} - 11968 x^{8} + 10368 x^{7} + 9344 x^{6} + 18176 x^{5} + 56320 x^{4} + 28160 x^{3} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.9 | ||
Root | \(-1.19457 - 0.320085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1189 |
Dual form | 1710.2.t.c.919.9 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.34502 | + | 1.78632i | 0.601509 | + | 0.798866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.03495i | 1.52507i | 0.646949 | + | 0.762533i | \(0.276045\pi\) | ||||
−0.646949 | + | 0.762533i | \(0.723955\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.271659 | + | 2.21950i | 0.0859061 | + | 0.701869i | ||||
\(11\) | 1.47054 | 0.443384 | 0.221692 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221692 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38320 | + | 2.53064i | −1.21568 | + | 0.701874i | −0.963991 | − | 0.265934i | \(-0.914320\pi\) |
−0.251690 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(14\) | −2.01747 | + | 3.49437i | −0.539192 | + | 0.933909i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.0812933 | + | 0.0469347i | 0.0197165 | + | 0.0113833i | 0.509826 | − | 0.860278i | \(-0.329710\pi\) |
−0.490109 | + | 0.871661i | \(0.663043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00172 | − | 1.72807i | −0.918058 | − | 0.396447i | ||||
\(20\) | −0.874489 | + | 2.05798i | −0.195542 | + | 0.460178i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.27352 | + | 0.735269i | 0.271516 | + | 0.156760i | ||||
\(23\) | 2.22178 | − | 1.28274i | 0.463273 | − | 0.267471i | −0.250147 | − | 0.968208i | \(-0.580479\pi\) |
0.713419 | + | 0.700737i | \(0.247145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.38186 | + | 4.80525i | −0.276373 | + | 0.961051i | ||||
\(26\) | −5.06128 | −0.992599 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.49437 | + | 2.01747i | −0.660373 | + | 0.381267i | ||||
\(29\) | −2.10491 | − | 3.64581i | −0.390872 | − | 0.677011i | 0.601693 | − | 0.798728i | \(-0.294493\pi\) |
−0.992565 | + | 0.121717i | \(0.961160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26558 | 0.766120 | 0.383060 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383060 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0469347 | + | 0.0812933i | 0.00804924 | + | 0.0139417i | ||||
\(35\) | −7.20770 | + | 5.42707i | −1.21832 | + | 0.917342i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53807i | 0.252858i | 0.991976 | + | 0.126429i | \(0.0403515\pi\) | ||||
−0.991976 | + | 0.126429i | \(0.959648\pi\) | |||||||
\(38\) | −2.60156 | − | 3.49741i | −0.422028 | − | 0.567356i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.78632 | + | 1.34502i | −0.282442 | + | 0.212666i | ||||
\(41\) | 3.88123 | − | 6.72248i | 0.606146 | − | 1.04987i | −0.385724 | − | 0.922614i | \(-0.626048\pi\) |
0.991869 | − | 0.127261i | \(-0.0406184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.97202 | − | 2.29325i | −0.605727 | − | 0.349717i | 0.165564 | − | 0.986199i | \(-0.447056\pi\) |
−0.771291 | + | 0.636482i | \(0.780389\pi\) | |||||||
\(44\) | 0.735269 | + | 1.27352i | 0.110846 | + | 0.191991i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.56549 | 0.378261 | ||||||||
\(47\) | −3.49530 | + | 2.01801i | −0.509842 | + | 0.294358i | −0.732769 | − | 0.680478i | \(-0.761772\pi\) |
0.222927 | + | 0.974835i | \(0.428439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.28080 | −1.32583 | ||||||||
\(50\) | −3.59936 | + | 3.47054i | −0.509026 | + | 0.490808i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.38320 | − | 2.53064i | −0.607840 | − | 0.350937i | ||||
\(53\) | 9.22964 | − | 5.32873i | 1.26779 | − | 0.731958i | 0.293219 | − | 0.956045i | \(-0.405273\pi\) |
0.974569 | + | 0.224087i | \(0.0719401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.97790 | + | 2.62685i | 0.266700 | + | 0.354204i | ||||
\(56\) | −4.03495 | −0.539192 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.20982i | − | 0.552777i | ||||||
\(59\) | 3.07599 | − | 5.32777i | 0.400460 | − | 0.693617i | −0.593321 | − | 0.804966i | \(-0.702184\pi\) |
0.993781 | + | 0.111349i | \(0.0355170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.653722 | + | 1.13228i | 0.0837005 | + | 0.144974i | 0.904837 | − | 0.425759i | \(-0.139993\pi\) |
−0.821136 | + | 0.570732i | \(0.806659\pi\) | |||||||
\(62\) | 3.69410 | + | 2.13279i | 0.469151 | + | 0.270864i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −10.4160 | − | 4.42603i | −1.29195 | − | 0.548982i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.31187 | − | 5.37621i | 1.13763 | − | 0.656808i | 0.191784 | − | 0.981437i | \(-0.438573\pi\) |
0.945842 | + | 0.324629i | \(0.105239\pi\) | |||||||
\(68\) | 0.0938694i | 0.0113833i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.95558 | + | 1.09613i | −1.07040 | + | 0.131013i | ||||
\(71\) | −4.33806 | + | 7.51373i | −0.514833 | + | 0.891716i | 0.485019 | + | 0.874503i | \(0.338813\pi\) |
−0.999852 | + | 0.0172126i | \(0.994521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0108 | + | 6.35711i | 1.28872 | + | 0.744044i | 0.978426 | − | 0.206596i | \(-0.0662386\pi\) |
0.310296 | + | 0.950640i | \(0.399572\pi\) | |||||||
\(74\) | −0.769037 | + | 1.33201i | −0.0893987 | + | 0.154843i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.504306 | − | 4.32963i | −0.0578479 | − | 0.496642i | ||||
\(77\) | 5.93355i | 0.676190i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.48112 | + | 11.2256i | −0.729183 | + | 1.26298i | 0.228046 | + | 0.973650i | \(0.426766\pi\) |
−0.957229 | + | 0.289332i | \(0.906567\pi\) | |||||||
\(80\) | −2.21950 | + | 0.271659i | −0.248148 | + | 0.0303724i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.72248 | − | 3.88123i | 0.742374 | − | 0.428610i | ||||
\(83\) | 2.06328i | 0.226475i | 0.993568 | + | 0.113237i | \(0.0361221\pi\) | ||||
−0.993568 | + | 0.113237i | \(0.963878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0255005 | + | 0.208344i | 0.00276592 | + | 0.0225980i | ||||
\(86\) | −2.29325 | − | 3.97202i | −0.247287 | − | 0.428314i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.47054i | 0.156760i | ||||||||
\(89\) | 0.813846 | + | 1.40962i | 0.0862675 | + | 0.149420i | 0.905931 | − | 0.423426i | \(-0.139173\pi\) |
−0.819663 | + | 0.572846i | \(0.805839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2110 | − | 17.6860i | −1.07040 | − | 1.85399i | ||||
\(92\) | 2.22178 | + | 1.28274i | 0.231636 | + | 0.133735i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.03603 | −0.416285 | ||||||||
\(95\) | −2.29549 | − | 9.47263i | −0.235513 | − | 0.971871i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3479 | + | 5.97438i | 1.05067 | + | 0.606607i | 0.922838 | − | 0.385188i | \(-0.125864\pi\) |
0.127836 | + | 0.991795i | \(0.459197\pi\) | |||||||
\(98\) | −8.03741 | − | 4.64040i | −0.811901 | − | 0.468751i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.85240 | + | 1.20590i | −0.485240 | + | 0.120590i | ||||
\(101\) | 0.252103 | + | 0.436656i | 0.0250852 | + | 0.0434489i | 0.878295 | − | 0.478118i | \(-0.158681\pi\) |
−0.853210 | + | 0.521567i | \(0.825348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.33797i | 0.525966i | 0.964800 | + | 0.262983i | \(0.0847063\pi\) | ||||
−0.964800 | + | 0.262983i | \(0.915294\pi\) | |||||||
\(104\) | −2.53064 | − | 4.38320i | −0.248150 | − | 0.429808i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6575 | 1.03514 | ||||||||
\(107\) | 17.9275i | 1.73312i | 0.499076 | + | 0.866558i | \(0.333673\pi\) | ||||
−0.499076 | + | 0.866558i | \(0.666327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.43631 | + | 7.68392i | −0.424922 | + | 0.735986i | −0.996413 | − | 0.0846222i | \(-0.973032\pi\) |
0.571492 | + | 0.820608i | \(0.306365\pi\) | |||||||
\(110\) | 0.399485 | + | 3.26387i | 0.0380894 | + | 0.311198i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.49437 | − | 2.01747i | −0.330187 | − | 0.190633i | ||||
\(113\) | 15.8667i | 1.49261i | 0.665603 | + | 0.746306i | \(0.268174\pi\) | ||||
−0.665603 | + | 0.746306i | \(0.731826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.27972 | + | 2.24349i | 0.492336 | + | 0.209207i | ||||
\(116\) | 2.10491 | − | 3.64581i | 0.195436 | − | 0.338505i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.32777 | − | 3.07599i | 0.490461 | − | 0.283168i | ||||
\(119\) | −0.189379 | + | 0.328014i | −0.0173604 | + | 0.0300690i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.83752 | −0.803410 | ||||||||
\(122\) | 1.30744i | 0.118370i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.13279 | + | 3.69410i | 0.191530 | + | 0.331740i | ||||
\(125\) | −10.4423 | + | 3.99469i | −0.933991 | + | 0.357296i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.77290 | − | 3.33298i | 0.512262 | − | 0.295755i | −0.221501 | − | 0.975160i | \(-0.571096\pi\) |
0.733763 | + | 0.679406i | \(0.237762\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.80751 | − | 9.04106i | −0.597058 | − | 0.792953i | ||||
\(131\) | 3.53784 | − | 6.12771i | 0.309102 | − | 0.535381i | −0.669064 | − | 0.743205i | \(-0.733305\pi\) |
0.978166 | + | 0.207824i | \(0.0666381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.97268 | − | 16.1467i | 0.604608 | − | 1.40010i | ||||
\(134\) | 10.7524 | 0.928867 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0469347 | + | 0.0812933i | −0.00402462 | + | 0.00697084i | ||||
\(137\) | −16.3302 | + | 9.42826i | −1.39519 | + | 0.805511i | −0.993883 | − | 0.110435i | \(-0.964775\pi\) |
−0.401302 | + | 0.915946i | \(0.631442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.99616 | − | 17.3139i | −0.847864 | − | 1.46854i | −0.883111 | − | 0.469164i | \(-0.844555\pi\) |
0.0352474 | − | 0.999379i | \(-0.488778\pi\) | |||||||
\(140\) | −8.30383 | − | 3.52852i | −0.701802 | − | 0.298214i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.51373 | + | 4.33806i | −0.630538 | + | 0.364042i | ||||
\(143\) | −6.44566 | + | 3.72141i | −0.539014 | + | 0.311200i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.68144 | − | 8.66372i | 0.305727 | − | 0.719483i | ||||
\(146\) | 6.35711 | + | 11.0108i | 0.526119 | + | 0.911264i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.33201 | + | 0.769037i | −0.109491 | + | 0.0632144i | ||||
\(149\) | −6.10397 | + | 10.5724i | −0.500056 | + | 0.866123i | 0.499944 | + | 0.866058i | \(0.333354\pi\) |
−1.00000 | 6.51503e-5i | \(0.999979\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.9109 | 1.62032 | 0.810161 | − | 0.586207i | \(-0.199380\pi\) | ||||
0.810161 | + | 0.586207i | \(0.199380\pi\) | |||||||
\(152\) | 1.72807 | − | 4.00172i | 0.140165 | − | 0.324582i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.96677 | + | 5.13860i | −0.239069 | + | 0.414080i | ||||
\(155\) | 5.73727 | + | 7.61968i | 0.460828 | + | 0.612027i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0594 | + | 8.11721i | 1.12206 | + | 0.647824i | 0.941927 | − | 0.335817i | \(-0.109012\pi\) |
0.180137 | + | 0.983641i | \(0.442346\pi\) | |||||||
\(158\) | −11.2256 | + | 6.48112i | −0.893063 | + | 0.515610i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.05798 | − | 0.874489i | −0.162697 | − | 0.0691344i | ||||
\(161\) | 5.17581 | + | 8.96476i | 0.407911 | + | 0.706522i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.05750i | − | 0.161156i | −0.996748 | − | 0.0805780i | \(-0.974323\pi\) | ||
0.996748 | − | 0.0805780i | \(-0.0256766\pi\) | |||||||
\(164\) | 7.76245 | 0.606146 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03164 | + | 1.78686i | −0.0800709 | + | 0.138687i | ||||
\(167\) | 18.8169 | − | 10.8639i | 1.45609 | − | 0.840676i | 0.457278 | − | 0.889324i | \(-0.348824\pi\) |
0.998816 | + | 0.0486476i | \(0.0154911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.30829 | − | 10.9263i | 0.485253 | − | 0.840483i | ||||
\(170\) | −0.0820878 | + | 0.193181i | −0.00629584 | + | 0.0148163i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 4.58649i | − | 0.349717i | ||||||
\(173\) | 20.0963 | + | 11.6026i | 1.52790 | + | 0.882132i | 0.999450 | + | 0.0331655i | \(0.0105588\pi\) |
0.528447 | + | 0.848966i | \(0.322774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.3889 | − | 5.57575i | −1.46567 | − | 0.421487i | ||||
\(176\) | −0.735269 | + | 1.27352i | −0.0554230 | + | 0.0959955i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.62769i | 0.122001i | ||||||||
\(179\) | 6.37559 | 0.476534 | 0.238267 | − | 0.971200i | \(-0.423421\pi\) | ||||
0.238267 | + | 0.971200i | \(0.423421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.39603 | + | 7.61415i | 0.326755 | + | 0.565955i | 0.981866 | − | 0.189577i | \(-0.0607116\pi\) |
−0.655111 | + | 0.755532i | \(0.727378\pi\) | |||||||
\(182\) | − | 20.4220i | − | 1.51378i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.28274 | + | 2.22178i | 0.0945652 | + | 0.163792i | ||||
\(185\) | −2.74749 | + | 2.06873i | −0.201999 | + | 0.152096i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.119545 | + | 0.0690193i | 0.00874200 | + | 0.00504719i | ||||
\(188\) | −3.49530 | − | 2.01801i | −0.254921 | − | 0.147179i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.74836 | − | 9.35128i | 0.199387 | − | 0.678413i | ||||
\(191\) | −12.9659 | −0.938177 | −0.469088 | − | 0.883151i | \(-0.655417\pi\) | ||||
−0.469088 | + | 0.883151i | \(0.655417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.29710 | − | 3.05828i | −0.381294 | − | 0.220140i | 0.297087 | − | 0.954850i | \(-0.403985\pi\) |
−0.678381 | + | 0.734710i | \(0.737318\pi\) | |||||||
\(194\) | 5.97438 | + | 10.3479i | 0.428936 | + | 0.742939i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.64040 | − | 8.03741i | −0.331457 | − | 0.574101i | ||||
\(197\) | − | 7.34941i | − | 0.523624i | −0.965119 | − | 0.261812i | \(-0.915680\pi\) | ||
0.965119 | − | 0.261812i | \(-0.0843200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.71780 | + | 2.97531i | 0.121771 | + | 0.210914i | 0.920466 | − | 0.390822i | \(-0.127809\pi\) |
−0.798695 | + | 0.601736i | \(0.794476\pi\) | |||||||
\(200\) | −4.80525 | − | 1.38186i | −0.339783 | − | 0.0977125i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.504207i | 0.0354759i | ||||||||
\(203\) | 14.7107 | − | 8.49321i | 1.03249 | − | 0.596106i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.2288 | − | 2.10874i | 1.20331 | − | 0.147281i | ||||
\(206\) | −2.66899 | + | 4.62282i | −0.185957 | + | 0.322087i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.06128i | − | 0.350937i | ||||||
\(209\) | −5.88469 | − | 2.54120i | −0.407052 | − | 0.175778i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.01970 | − | 3.49822i | 0.139042 | − | 0.240827i | −0.788092 | − | 0.615557i | \(-0.788931\pi\) |
0.927134 | + | 0.374730i | \(0.122264\pi\) | |||||||
\(212\) | 9.22964 | + | 5.32873i | 0.633894 | + | 0.365979i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.96375 | + | 15.5257i | −0.612749 | + | 1.06131i | ||||
\(215\) | −1.24596 | − | 10.1797i | −0.0849739 | − | 0.694253i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.2114i | 1.16838i | ||||||||
\(218\) | −7.68392 | + | 4.43631i | −0.520421 | + | 0.300465i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.28597 | + | 3.02634i | −0.0867001 | + | 0.204035i | ||||
\(221\) | −0.475100 | −0.0319587 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6334 | − | 9.02593i | −1.04689 | − | 0.604421i | −0.125111 | − | 0.992143i | \(-0.539929\pi\) |
−0.921776 | + | 0.387722i | \(0.873262\pi\) | |||||||
\(224\) | −2.01747 | − | 3.49437i | −0.134798 | − | 0.233477i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.93334 | + | 13.7409i | −0.527718 | + | 0.914034i | ||||
\(227\) | − | 26.8513i | − | 1.78219i | −0.453820 | − | 0.891093i | \(-0.649939\pi\) | ||
0.453820 | − | 0.891093i | \(-0.350061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7131 | 0.906190 | 0.453095 | − | 0.891462i | \(-0.350320\pi\) | ||||
0.453095 | + | 0.891462i | \(0.350320\pi\) | |||||||
\(230\) | 3.45062 | + | 4.58278i | 0.227527 | + | 0.302180i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.64581 | − | 2.10491i | 0.239359 | − | 0.138194i | ||||
\(233\) | 0.00572506 | + | 0.00330537i | 0.000375061 | + | 0.000216542i | 0.500188 | − | 0.865917i | \(-0.333264\pi\) |
−0.499812 | + | 0.866134i | \(0.666598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.30605 | − | 3.52946i | −0.541827 | − | 0.230237i | ||||
\(236\) | 6.15198 | 0.400460 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.328014 | + | 0.189379i | −0.0212620 | + | 0.0122756i | ||||
\(239\) | −4.67499 | −0.302400 | −0.151200 | − | 0.988503i | \(-0.548314\pi\) | ||||
−0.151200 | + | 0.988503i | \(0.548314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.9044 | + | 24.0831i | 0.895659 | + | 1.55133i | 0.832987 | + | 0.553292i | \(0.186629\pi\) |
0.0626717 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(242\) | −7.65351 | − | 4.41876i | −0.491986 | − | 0.284049i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.653722 | + | 1.13228i | −0.0418503 | + | 0.0724868i | ||||
\(245\) | −12.4828 | − | 16.5785i | −0.797498 | − | 1.05916i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.9135 | − | 2.55244i | 1.39432 | − | 0.162408i | ||||
\(248\) | 4.26558i | 0.270864i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0407 | − | 1.76166i | −0.698274 | − | 0.111417i | ||||
\(251\) | −3.03259 | − | 5.25259i | −0.191415 | − | 0.331541i | 0.754304 | − | 0.656525i | \(-0.227974\pi\) |
−0.945719 | + | 0.324984i | \(0.894641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.26721 | − | 1.88633i | 0.205408 | − | 0.118592i | ||||
\(254\) | 6.66597 | 0.418260 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.11707 | − | 0.644941i | 0.0696809 | − | 0.0402303i | −0.464755 | − | 0.885439i | \(-0.653858\pi\) |
0.534436 | + | 0.845209i | \(0.320524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.20604 | −0.385625 | ||||||||
\(260\) | −1.37494 | − | 11.2335i | −0.0852704 | − | 0.696675i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.12771 | − | 3.53784i | 0.378571 | − | 0.218568i | ||||
\(263\) | −24.4863 | − | 14.1372i | −1.50989 | − | 0.871737i | −0.999933 | − | 0.0115378i | \(-0.996327\pi\) |
−0.509959 | − | 0.860199i | \(-0.670339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.9328 | + | 9.31984i | 1.34732 | + | 0.572513i | ||||
\(266\) | 14.1119 | − | 10.4971i | 0.865255 | − | 0.643621i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.31187 | + | 5.37621i | 0.568813 | + | 0.328404i | ||||
\(269\) | 13.8782 | − | 24.0377i | 0.846169 | − | 1.46561i | −0.0384337 | − | 0.999261i | \(-0.512237\pi\) |
0.884602 | − | 0.466346i | \(-0.154430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.42826 | + | 9.40202i | −0.329743 | + | 0.571132i | −0.982461 | − | 0.186469i | \(-0.940296\pi\) |
0.652718 | + | 0.757601i | \(0.273629\pi\) | |||||||
\(272\) | −0.0812933 | + | 0.0469347i | −0.00492913 | + | 0.00284584i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.8565 | −1.13916 | ||||||||
\(275\) | −2.03208 | + | 7.06631i | −0.122539 | + | 0.426115i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5237i | 1.47349i | 0.676173 | + | 0.736743i | \(0.263637\pi\) | ||||
−0.676173 | + | 0.736743i | \(0.736363\pi\) | |||||||
\(278\) | − | 19.9923i | − | 1.19906i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.42707 | − | 7.20770i | −0.324329 | − | 0.430742i | ||||
\(281\) | −3.29709 | − | 5.71073i | −0.196688 | − | 0.340674i | 0.750765 | − | 0.660570i | \(-0.229685\pi\) |
−0.947453 | + | 0.319896i | \(0.896352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4709 | − | 11.8189i | −1.21687 | − | 0.702559i | −0.252621 | − | 0.967565i | \(-0.581293\pi\) |
−0.964247 | + | 0.265006i | \(0.914626\pi\) | |||||||
\(284\) | −8.67611 | −0.514833 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.44281 | −0.440103 | ||||||||
\(287\) | 27.1248 | + | 15.6605i | 1.60113 | + | 0.924412i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.49559 | − | 14.7148i | −0.499741 | − | 0.865577i | ||||
\(290\) | 7.52008 | − | 5.66228i | 0.441595 | − | 0.332501i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.7142i | 0.744044i | ||||||||
\(293\) | − | 23.0123i | − | 1.34439i | −0.740374 | − | 0.672195i | \(-0.765352\pi\) | ||
0.740374 | − | 0.672195i | \(-0.234648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6544 | − | 1.67124i | 0.794987 | − | 0.0973034i | ||||
\(296\) | −1.53807 | −0.0893987 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.5724 | + | 6.10397i | −0.612442 | + | 0.353593i | ||||
\(299\) | −6.49233 | + | 11.2451i | −0.375461 | + | 0.650318i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.25313 | − | 16.0269i | 0.533341 | − | 0.923774i | ||||
\(302\) | 17.2433 | + | 9.95543i | 0.992241 | + | 0.572870i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.49741 | − | 2.60156i | 0.200590 | − | 0.149209i | ||||
\(305\) | −1.14335 | + | 2.69069i | −0.0654678 | + | 0.154068i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0807 | − | 12.7483i | −1.26021 | − | 0.727584i | −0.287097 | − | 0.957902i | \(-0.592690\pi\) |
−0.973116 | + | 0.230318i | \(0.926023\pi\) | |||||||
\(308\) | −5.13860 | + | 2.96677i | −0.292799 | + | 0.169048i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.15878 | + | 9.46747i | 0.0658144 | + | 0.537716i | ||||
\(311\) | 30.3172 | 1.71913 | 0.859565 | − | 0.511027i | \(-0.170735\pi\) | ||||
0.859565 | + | 0.511027i | \(0.170735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.54063 | − | 3.77623i | 0.369698 | − | 0.213445i | −0.303628 | − | 0.952791i | \(-0.598198\pi\) |
0.673327 | + | 0.739345i | \(0.264865\pi\) | |||||||
\(314\) | 8.11721 | + | 14.0594i | 0.458081 | + | 0.793419i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.9622 | −0.729183 | ||||||||
\(317\) | 12.1344 | − | 7.00579i | 0.681535 | − | 0.393484i | −0.118898 | − | 0.992906i | \(-0.537936\pi\) |
0.800433 | + | 0.599422i | \(0.204603\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.09535 | − | 5.36131i | −0.173307 | − | 0.300176i | ||||
\(320\) | −1.34502 | − | 1.78632i | −0.0751887 | − | 0.0998582i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.3516i | 0.576873i | ||||||||
\(323\) | −0.244207 | − | 0.328300i | −0.0135880 | − | 0.0182671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.10339 | − | 24.5594i | −0.338555 | − | 1.36231i | ||||
\(326\) | 1.02875 | − | 1.78185i | 0.0569773 | − | 0.0986875i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.72248 | + | 3.88123i | 0.371187 | + | 0.214305i | ||||
\(329\) | −8.14258 | − | 14.1034i | −0.448915 | − | 0.777544i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.20541 | −0.121220 | −0.0606102 | − | 0.998162i | \(-0.519305\pi\) | ||||
−0.0606102 | + | 0.998162i | \(0.519305\pi\) | |||||||
\(332\) | −1.78686 | + | 1.03164i | −0.0980665 | + | 0.0566187i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.7279 | 1.18890 | ||||||||
\(335\) | 22.1282 | + | 9.40287i | 1.20899 | + | 0.513734i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.35026 | − | 1.93428i | −0.182500 | − | 0.105367i | 0.405966 | − | 0.913888i | \(-0.366935\pi\) |
−0.588467 | + | 0.808521i | \(0.700268\pi\) | |||||||
\(338\) | 10.9263 | − | 6.30829i | 0.594311 | − | 0.343126i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.167681 | + | 0.126256i | −0.00909376 | + | 0.00684719i | ||||
\(341\) | 6.27270 | 0.339685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.20290i | − | 0.496910i | ||||||
\(344\) | 2.29325 | − | 3.97202i | 0.123644 | − | 0.214157i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.6026 | + | 20.0963i | 0.623761 | + | 1.08039i | ||||
\(347\) | 10.6406 | + | 6.14337i | 0.571219 | + | 0.329793i | 0.757636 | − | 0.652677i | \(-0.226354\pi\) |
−0.186417 | + | 0.982471i | \(0.559688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1329 | 1.23828 | 0.619139 | − | 0.785282i | \(-0.287482\pi\) | ||||
0.619139 | + | 0.785282i | \(0.287482\pi\) | |||||||
\(350\) | −14.0034 | − | 14.5232i | −0.748515 | − | 0.776298i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.27352 | + | 0.735269i | −0.0678791 | + | 0.0391900i | ||||
\(353\) | 2.27216i | 0.120935i | 0.998170 | + | 0.0604674i | \(0.0192591\pi\) | ||||
−0.998170 | + | 0.0604674i | \(0.980741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.2567 | + | 2.35694i | −1.02204 | + | 0.125094i | ||||
\(356\) | −0.813846 | + | 1.40962i | −0.0431338 | + | 0.0747098i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.52142 | + | 3.18779i | 0.291816 | + | 0.168480i | ||||
\(359\) | 10.3404 | − | 17.9101i | 0.545746 | − | 0.945260i | −0.452813 | − | 0.891605i | \(-0.649580\pi\) |
0.998560 | − | 0.0536549i | \(-0.0170871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0275 | + | 13.8305i | 0.685660 | + | 0.727922i | ||||
\(362\) | 8.79207i | 0.462101i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.2110 | − | 17.6860i | 0.535202 | − | 0.926997i | ||||
\(365\) | 3.45394 | + | 28.2193i | 0.180787 | + | 1.47707i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.7744 | − | 18.3450i | 1.65861 | − | 0.957600i | 0.685255 | − | 0.728304i | \(-0.259691\pi\) |
0.973357 | − | 0.229296i | \(-0.0736424\pi\) | |||||||
\(368\) | 2.56549i | 0.133735i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.41376 | + | 0.417831i | −0.177473 | + | 0.0217220i | ||||
\(371\) | 21.5012 | + | 37.2411i | 1.11628 | + | 1.93346i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5380i | 1.01164i | 0.862640 | + | 0.505819i | \(0.168810\pi\) | ||||
−0.862640 | + | 0.505819i | \(0.831190\pi\) | |||||||
\(374\) | 0.0690193 | + | 0.119545i | 0.00356890 | + | 0.00618152i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.01801 | − | 3.49530i | −0.104071 | − | 0.180256i | ||||
\(377\) | 18.4525 | + | 10.6536i | 0.950352 | + | 0.548686i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.46802 | −0.178140 | −0.0890701 | − | 0.996025i | \(-0.528390\pi\) | ||||
−0.0890701 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(380\) | 7.05579 | − | 6.72427i | 0.361954 | − | 0.344948i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.2288 | − | 6.48293i | −0.574514 | − | 0.331696i | ||||
\(383\) | −21.7388 | − | 12.5509i | −1.11080 | − | 0.641322i | −0.171765 | − | 0.985138i | \(-0.554947\pi\) |
−0.939037 | + | 0.343816i | \(0.888280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5992 | + | 7.98072i | −0.540185 | + | 0.406735i | ||||
\(386\) | −3.05828 | − | 5.29710i | −0.155662 | − | 0.269615i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.9488i | 0.606607i | ||||||||
\(389\) | −7.02074 | − | 12.1603i | −0.355965 | − | 0.616550i | 0.631317 | − | 0.775525i | \(-0.282515\pi\) |
−0.987283 | + | 0.158974i | \(0.949181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.240821 | 0.0121788 | ||||||||
\(392\) | − | 9.28080i | − | 0.468751i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.67471 | − | 6.36478i | 0.185129 | − | 0.320653i | ||||
\(395\) | −28.7698 | + | 3.52131i | −1.44756 | + | 0.177176i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.6267 | + | 15.3729i | 1.33635 | + | 0.771544i | 0.986265 | − | 0.165172i | \(-0.0528179\pi\) |
0.350089 | + | 0.936716i | \(0.386151\pi\) | |||||||
\(398\) | 3.43559i | 0.172211i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47054 | − | 3.59936i | −0.173527 | − | 0.179968i | ||||
\(401\) | 19.3518 | − | 33.5183i | 0.966381 | − | 1.67382i | 0.260525 | − | 0.965467i | \(-0.416104\pi\) |
0.705857 | − | 0.708355i | \(-0.250562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6969 | + | 10.7946i | −0.931357 | + | 0.537719i | ||||
\(404\) | −0.252103 | + | 0.436656i | −0.0125426 | + | 0.0217244i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.9864 | 0.843022 | ||||||||
\(407\) | 2.26180i | 0.112113i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3920 | − | 17.9994i | −0.513850 | − | 0.890014i | −0.999871 | − | 0.0160671i | \(-0.994885\pi\) |
0.486021 | − | 0.873947i | \(-0.338448\pi\) | |||||||
\(410\) | 15.9749 | + | 6.78818i | 0.788946 | + | 0.335244i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.62282 | + | 2.66899i | −0.227750 | + | 0.131491i | ||||
\(413\) | 21.4973 | + | 12.4115i | 1.05781 | + | 0.610728i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.68568 | + | 2.77515i | −0.180923 | + | 0.136227i | ||||
\(416\) | 2.53064 | − | 4.38320i | 0.124075 | − | 0.214904i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.82569 | − | 5.14308i | −0.187121 | − | 0.251556i | ||||
\(419\) | −36.2672 | −1.77177 | −0.885883 | − | 0.463908i | \(-0.846447\pi\) | ||||
−0.885883 | + | 0.463908i | \(0.846447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7212 | − | 18.5697i | 0.522519 | − | 0.905030i | −0.477137 | − | 0.878829i | \(-0.658326\pi\) |
0.999657 | − | 0.0262013i | \(-0.00834109\pi\) | |||||||
\(422\) | 3.49822 | − | 2.01970i | 0.170291 | − | 0.0983174i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.32873 | + | 9.22964i | 0.258786 | + | 0.448231i | ||||
\(425\) | −0.337869 | + | 0.325778i | −0.0163891 | + | 0.0158025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.56869 | + | 2.63773i | −0.221094 | + | 0.127649i | ||||
\(428\) | −15.5257 | + | 8.96375i | −0.750461 | + | 0.433279i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.01084 | − | 9.43890i | 0.193420 | − | 0.455184i | ||||
\(431\) | −2.91216 | − | 5.04400i | −0.140274 | − | 0.242961i | 0.787326 | − | 0.616537i | \(-0.211465\pi\) |
−0.927600 | + | 0.373576i | \(0.878132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.3690 | + | 15.8015i | −1.31527 | + | 0.759371i | −0.982963 | − | 0.183801i | \(-0.941160\pi\) |
−0.332305 | + | 0.943172i | \(0.607826\pi\) | |||||||
\(434\) | −8.60569 | + | 14.9055i | −0.413086 | + | 0.715486i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.87262 | −0.424922 | ||||||||
\(437\) | −11.1076 | + | 1.29379i | −0.531349 | + | 0.0618904i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.932951 | + | 1.61592i | −0.0445273 | + | 0.0771236i | −0.887430 | − | 0.460942i | \(-0.847512\pi\) |
0.842903 | + | 0.538066i | \(0.180845\pi\) | |||||||
\(440\) | −2.62685 | + | 1.97790i | −0.125230 | + | 0.0942926i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.411448 | − | 0.237550i | −0.0195706 | − | 0.0112991i | ||||
\(443\) | −13.6368 | + | 7.87318i | −0.647902 | + | 0.374066i | −0.787652 | − | 0.616121i | \(-0.788703\pi\) |
0.139750 | + | 0.990187i | \(0.455370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.42340 | + | 3.34975i | −0.0674755 | + | 0.158794i | ||||
\(446\) | −9.02593 | − | 15.6334i | −0.427390 | − | 0.740262i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 4.03495i | − | 0.190633i | ||||||
\(449\) | 29.7436 | 1.40369 | 0.701845 | − | 0.712330i | \(-0.252360\pi\) | ||||
0.701845 | + | 0.712330i | \(0.252360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.70749 | − | 9.88567i | 0.268755 | − | 0.465498i | ||||
\(452\) | −13.7409 | + | 7.93334i | −0.646320 | + | 0.373153i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.4257 | − | 23.2539i | 0.630098 | − | 1.09136i | ||||
\(455\) | 17.8588 | − | 42.0280i | 0.837234 | − | 1.97030i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.7891i | − | 0.598250i | −0.954214 | − | 0.299125i | \(-0.903305\pi\) | ||
0.954214 | − | 0.299125i | \(-0.0966948\pi\) | |||||||
\(458\) | 11.8759 | + | 6.85657i | 0.554926 | + | 0.320387i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.696938 | + | 5.69412i | 0.0324949 | + | 0.265490i | ||||
\(461\) | −5.96303 | + | 10.3283i | −0.277726 | + | 0.481035i | −0.970819 | − | 0.239813i | \(-0.922914\pi\) |
0.693093 | + | 0.720848i | \(0.256247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 19.3208i | − | 0.897913i | −0.893554 | − | 0.448956i | \(-0.851796\pi\) | ||
0.893554 | − | 0.448956i | \(-0.148204\pi\) | |||||||
\(464\) | 4.20982 | 0.195436 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.00330537 | + | 0.00572506i | 0.000153118 | + | 0.000265208i | ||||
\(467\) | − | 26.7009i | − | 1.23557i | −0.786347 | − | 0.617785i | \(-0.788030\pi\) | ||
0.786347 | − | 0.617785i | \(-0.211970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.6927 | + | 37.5729i | 1.00168 | + | 1.73496i | ||||
\(470\) | −5.42852 | − | 7.20963i | −0.250399 | − | 0.332555i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.32777 | + | 3.07599i | 0.245231 | + | 0.141584i | ||||
\(473\) | −5.84101 | − | 3.37231i | −0.268570 | − | 0.155059i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8337 | − | 16.8413i | 0.634732 | − | 0.772733i | ||||
\(476\) | −0.378758 | −0.0173604 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.04866 | − | 2.33750i | −0.185182 | − | 0.106915i | ||||
\(479\) | 6.79124 | + | 11.7628i | 0.310299 | + | 0.537454i | 0.978427 | − | 0.206592i | \(-0.0662373\pi\) |
−0.668128 | + | 0.744047i | \(0.732904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.89231 | − | 6.74168i | −0.177474 | − | 0.307394i | ||||
\(482\) | 27.8087i | 1.26665i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.41876 | − | 7.65351i | −0.200853 | − | 0.347887i | ||||
\(485\) | 3.24599 | + | 26.5204i | 0.147393 | + | 1.20423i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.03640i | 0.364164i | 0.983283 | + | 0.182082i | \(0.0582837\pi\) | ||||
−0.983283 | + | 0.182082i | \(0.941716\pi\) | |||||||
\(488\) | −1.13228 | + | 0.653722i | −0.0512559 | + | 0.0295926i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.52121 | − | 20.5988i | −0.113897 | − | 0.930558i | ||||
\(491\) | −10.3390 | + | 17.9077i | −0.466593 | + | 0.808163i | −0.999272 | − | 0.0381546i | \(-0.987852\pi\) |
0.532679 | + | 0.846317i | \(0.321185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.395174i | − | 0.0177977i | ||||||
\(494\) | 20.2538 | + | 8.74626i | 0.911263 | + | 0.393513i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13279 | + | 3.69410i | −0.0957650 | + | 0.165870i | ||||
\(497\) | −30.3175 | − | 17.5038i | −1.35993 | − | 0.785154i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.551160 | + | 0.954638i | −0.0246733 | + | 0.0427355i | −0.878098 | − | 0.478480i | \(-0.841188\pi\) |
0.853425 | + | 0.521216i | \(0.174521\pi\) | |||||||
\(500\) | −8.68068 | − | 7.04598i | −0.388212 | − | 0.315106i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 6.06517i | − | 0.270702i | ||||||
\(503\) | 21.0518 | − | 12.1543i | 0.938653 | − | 0.541932i | 0.0491154 | − | 0.998793i | \(-0.484360\pi\) |
0.889538 | + | 0.456861i | \(0.151026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.440923 | + | 1.03765i | −0.0196208 | + | 0.0461746i | ||||
\(506\) | 3.77265 | 0.167715 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.77290 | + | 3.33298i | 0.256131 | + | 0.147877i | ||||
\(509\) | 4.96728 | + | 8.60358i | 0.220171 | + | 0.381347i | 0.954860 | − | 0.297057i | \(-0.0960052\pi\) |
−0.734689 | + | 0.678404i | \(0.762672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.6506 | + | 44.4282i | −1.13472 | + | 1.96539i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.28988 | 0.0568942 | ||||||||
\(515\) | −9.53531 | + | 7.17966i | −0.420176 | + | 0.316373i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.13998 | + | 2.96757i | −0.226056 | + | 0.130513i | ||||
\(518\) | −5.37459 | − | 3.10302i | −0.236146 | − | 0.136339i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.42603 | − | 10.4160i | 0.194094 | − | 0.456772i | ||||
\(521\) | 20.9057 | 0.915895 | 0.457947 | − | 0.888979i | \(-0.348585\pi\) | ||||
0.457947 | + | 0.888979i | \(0.348585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.3676 | + | 15.8007i | −1.19670 | + | 0.690916i | −0.959818 | − | 0.280622i | \(-0.909459\pi\) |
−0.236883 | + | 0.971538i | \(0.576126\pi\) | |||||||
\(524\) | 7.07568 | 0.309102 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.1372 | − | 24.4863i | −0.616411 | − | 1.06766i | ||||
\(527\) | 0.346763 | + | 0.200204i | 0.0151052 | + | 0.00872101i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.20913 | + | 14.2186i | −0.356919 | + | 0.618202i | ||||
\(530\) | 14.3345 | + | 19.0376i | 0.622649 | + | 0.826942i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.4698 | − | 2.03485i | 0.757413 | − | 0.0882218i | ||||
\(533\) | 39.2880i | 1.70175i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.0242 | + | 24.1128i | −1.38453 | + | 1.04249i | ||||
\(536\) | 5.37621 | + | 9.31187i | 0.232217 | + | 0.402211i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.0377 | − | 13.8782i | 1.03634 | − | 0.598332i | ||||
\(539\) | −13.6478 | −0.587851 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50615 | − | 4.34078i | −0.107748 | − | 0.186625i | 0.807110 | − | 0.590402i | \(-0.201031\pi\) |
−0.914858 | + | 0.403777i | \(0.867697\pi\) | |||||||
\(542\) | −9.40202 | + | 5.42826i | −0.403851 | + | 0.233164i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0938694 | −0.00402462 | ||||||||
\(545\) | −19.6928 | + | 2.41033i | −0.843548 | + | 0.103247i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.7554 | − | 17.7566i | 1.31500 | − | 0.759218i | 0.332084 | − | 0.943250i | \(-0.392248\pi\) |
0.982920 | + | 0.184032i | \(0.0589150\pi\) | |||||||
\(548\) | −16.3302 | − | 9.42826i | −0.697593 | − | 0.402755i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.29299 | + | 5.10356i | −0.225694 | + | 0.217617i | ||||
\(551\) | 2.12304 | + | 18.2270i | 0.0904445 | + | 0.776495i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.2948 | − | 26.1510i | −1.92613 | − | 1.11205i | ||||
\(554\) | −12.2618 | + | 21.2381i | −0.520956 | + | 0.902322i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.99616 | − | 17.3139i | 0.423932 | − | 0.734271i | ||||
\(557\) | −8.45640 | + | 4.88231i | −0.358309 | + | 0.206870i | −0.668339 | − | 0.743857i | \(-0.732994\pi\) |
0.310030 | + | 0.950727i | \(0.399661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.2135 | 0.981828 | ||||||||
\(560\) | −1.09613 | − | 8.95558i | −0.0463199 | − | 0.378443i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6.59418i | − | 0.278159i | ||||||
\(563\) | − | 11.5237i | − | 0.485665i | −0.970068 | − | 0.242833i | \(-0.921923\pi\) | ||
0.970068 | − | 0.242833i | \(-0.0780766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.3429 | + | 21.3409i | −1.19240 | + | 0.897820i | ||||
\(566\) | −11.8189 | − | 20.4709i | −0.496784 | − | 0.860456i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.51373 | − | 4.33806i | −0.315269 | − | 0.182021i | ||||
\(569\) | 1.93925 | 0.0812978 | 0.0406489 | − | 0.999173i | \(-0.487057\pi\) | ||||
0.0406489 | + | 0.999173i | \(0.487057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0052 | −1.59047 | −0.795235 | − | 0.606301i | \(-0.792652\pi\) | ||||
−0.795235 | + | 0.606301i | \(0.792652\pi\) | |||||||
\(572\) | −6.44566 | − | 3.72141i | −0.269507 | − | 0.155600i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.6605 | + | 27.1248i | 0.653658 | + | 1.13217i | ||||
\(575\) | 3.09372 | + | 12.4488i | 0.129017 | + | 0.519150i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.3094i | 1.17854i | 0.807938 | + | 0.589268i | \(0.200584\pi\) | ||||
−0.807938 | + | 0.589268i | \(0.799416\pi\) | |||||||
\(578\) | − | 16.9912i | − | 0.706740i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.34372 | − | 1.14364i | 0.387977 | − | 0.0474869i | ||||
\(581\) | −8.32524 | −0.345389 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5725 | − | 7.83611i | 0.562117 | − | 0.324539i | ||||
\(584\) | −6.35711 | + | 11.0108i | −0.263059 | + | 0.455632i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5061 | − | 19.9292i | 0.475314 | − | 0.823267i | ||||
\(587\) | 9.39980 | + | 5.42698i | 0.387971 | + | 0.223995i | 0.681281 | − | 0.732022i | \(-0.261423\pi\) |
−0.293309 | + | 0.956018i | \(0.594757\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0696 | − | 7.37122i | −0.703342 | − | 0.303726i | ||||
\(590\) | 12.6606 | + | 5.37984i | 0.521230 | + | 0.221484i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.33201 | − | 0.769037i | −0.0547453 | − | 0.0316072i | ||||
\(593\) | −24.0190 | + | 13.8674i | −0.986341 | + | 0.569464i | −0.904179 | − | 0.427155i | \(-0.859516\pi\) |
−0.0821625 | + | 0.996619i | \(0.526183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.840656 | + | 0.102893i | −0.0344635 | + | 0.00421821i | ||||
\(596\) | −12.2079 | −0.500056 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.2451 | + | 6.49233i | −0.459844 | + | 0.265491i | ||||
\(599\) | −15.6071 | − | 27.0323i | −0.637690 | − | 1.10451i | −0.985938 | − | 0.167109i | \(-0.946557\pi\) |
0.348248 | − | 0.937402i | \(-0.386777\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.3271 | 1.72656 | 0.863280 | − | 0.504726i | \(-0.168406\pi\) | ||||
0.863280 | + | 0.504726i | \(0.168406\pi\) | |||||||
\(602\) | 16.0269 | − | 9.25313i | 0.653207 | − | 0.377129i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.95543 | + | 17.2433i | 0.405081 | + | 0.701620i | ||||
\(605\) | −11.8866 | − | 15.7866i | −0.483259 | − | 0.641817i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9882i | 0.527176i | 0.964635 | + | 0.263588i | \(0.0849059\pi\) | ||||
−0.964635 | + | 0.263588i | \(0.915094\pi\) | |||||||
\(608\) | 4.32963 | − | 0.504306i | 0.175590 | − | 0.0204523i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.33551 | + | 1.75853i | −0.0945621 | + | 0.0712009i | ||||
\(611\) | 10.2137 | − | 17.6907i | 0.413204 | − | 0.715690i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2303 | + | 13.4120i | 0.938264 | + | 0.541707i | 0.889416 | − | 0.457099i | \(-0.151112\pi\) |
0.0488484 | + | 0.998806i | \(0.484445\pi\) | |||||||
\(614\) | −12.7483 | − | 22.0807i | −0.514480 | − | 0.891105i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.93355 | −0.239069 | ||||||||
\(617\) | 11.9663 | − | 6.90877i | 0.481747 | − | 0.278136i | −0.239398 | − | 0.970922i | \(-0.576950\pi\) |
0.721144 | + | 0.692785i | \(0.243617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.2091 | 1.45537 | 0.727684 | − | 0.685912i | \(-0.240597\pi\) | ||||
0.727684 | + | 0.685912i | \(0.240597\pi\) | |||||||
\(620\) | −3.73020 | + | 8.77846i | −0.149808 | + | 0.352551i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.2555 | + | 15.1586i | 1.05275 | + | 0.607804i | ||||
\(623\) | −5.68775 | + | 3.28383i | −0.227875 | + | 0.131564i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1809 | − | 13.2804i | −0.847236 | − | 0.531216i | ||||
\(626\) | 7.55247 | 0.301857 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.2344i | 0.647824i | ||||||||
\(629\) | −0.0721890 | + | 0.125035i | −0.00287837 | + | 0.00498547i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00438 | − | 1.73963i | −0.0399836 | − | 0.0692536i | 0.845341 | − | 0.534227i | \(-0.179397\pi\) |
−0.885325 | + | 0.464973i | \(0.846064\pi\) | |||||||
\(632\) | −11.2256 | − | 6.48112i | −0.446532 | − | 0.257805i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0116 | 0.556471 | ||||||||
\(635\) | 13.7184 | + | 5.82932i | 0.544399 | + | 0.231329i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.6796 | − | 23.4864i | 1.61178 | − | 0.930564i | ||||
\(638\) | − | 6.19071i | − | 0.245093i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.271659 | − | 2.21950i | −0.0107383 | − | 0.0877336i | ||||
\(641\) | 8.04795 | − | 13.9395i | 0.317875 | − | 0.550575i | −0.662170 | − | 0.749354i | \(-0.730364\pi\) |
0.980044 | + | 0.198779i | \(0.0636975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6016 | + | 19.9773i | 1.36455 | + | 0.787826i | 0.990226 | − | 0.139470i | \(-0.0445399\pi\) |
0.374328 | + | 0.927296i | \(0.377873\pi\) | |||||||
\(644\) | −5.17581 | + | 8.96476i | −0.203955 | + | 0.353261i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0473389 | − | 0.406420i | −0.00186252 | − | 0.0159904i | ||||
\(647\) | 32.2985i | 1.26979i | 0.772600 | + | 0.634893i | \(0.218956\pi\) | ||||
−0.772600 | + | 0.634893i | \(0.781044\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.52336 | − | 7.83470i | 0.177558 | − | 0.307539i | ||||
\(650\) | 6.99400 | − | 24.3207i | 0.274327 | − | 0.953938i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.78185 | − | 1.02875i | 0.0697826 | − | 0.0402890i | ||||
\(653\) | 25.3382i | 0.991559i | 0.868448 | + | 0.495780i | \(0.165118\pi\) | ||||
−0.868448 | + | 0.495780i | \(0.834882\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.7045 | − | 1.92217i | 0.613625 | − | 0.0751054i | ||||
\(656\) | 3.88123 | + | 6.72248i | 0.151536 | + | 0.262469i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 16.2852i | − | 0.634862i | ||||||
\(659\) | −2.44914 | − | 4.24204i | −0.0954051 | − | 0.165247i | 0.814372 | − | 0.580343i | \(-0.197081\pi\) |
−0.909778 | + | 0.415096i | \(0.863748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1271 | − | 41.7893i | −0.938435 | − | 1.62542i | −0.768391 | − | 0.639980i | \(-0.778942\pi\) |
−0.170044 | − | 0.985437i | \(-0.554391\pi\) | |||||||
\(662\) | −1.90994 | − | 1.10271i | −0.0742320 | − | 0.0428579i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.06328 | −0.0800709 | ||||||||
\(665\) | 38.2216 | − | 9.26219i | 1.48217 | − | 0.359172i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.35330 | − | 5.40013i | −0.362161 | − | 0.209094i | ||||
\(668\) | 18.8169 | + | 10.8639i | 0.728047 | + | 0.420338i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.4622 | + | 19.2072i | 0.558723 | + | 0.742040i | ||||
\(671\) | 0.961324 | + | 1.66506i | 0.0371115 | + | 0.0642790i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3374i | 0.437025i | 0.975834 | + | 0.218512i | \(0.0701204\pi\) | ||||
−0.975834 | + | 0.218512i | \(0.929880\pi\) | |||||||
\(674\) | −1.93428 | − | 3.35026i | −0.0745055 | − | 0.129047i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.6166 | 0.485253 | ||||||||
\(677\) | − | 30.8182i | − | 1.18444i | −0.805776 | − | 0.592220i | \(-0.798252\pi\) | ||
0.805776 | − | 0.592220i | \(-0.201748\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.1063 | + | 41.7534i | −0.925116 | + | 1.60235i | ||||
\(680\) | −0.208344 | + | 0.0255005i | −0.00798961 | + | 0.000977899i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.43231 | + | 3.13635i | 0.208014 | + | 0.120097i | ||||
\(683\) | 10.5683i | 0.404386i | 0.979346 | + | 0.202193i | \(0.0648069\pi\) | ||||
−0.979346 | + | 0.202193i | \(0.935193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.8063 | − | 16.4898i | −1.48271 | − | 0.630043i | ||||
\(686\) | 4.60145 | − | 7.96995i | 0.175684 | − | 0.304294i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.97202 | − | 2.29325i | 0.151432 | − | 0.0874292i | ||||
\(689\) | −26.9702 | + | 46.7138i | −1.02748 | + | 1.77965i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.570970 | −0.0217207 | −0.0108604 | − | 0.999941i | \(-0.503457\pi\) | ||||
−0.0108604 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(692\) | 23.2053i | 0.882132i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.14337 | + | 10.6406i | 0.233199 | + | 0.403913i | ||||
\(695\) | 17.4831 | − | 41.1438i | 0.663171 | − | 1.56067i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.631035 | − | 0.364328i | 0.0239022 | − | 0.0137999i | ||||
\(698\) | 20.0337 | + | 11.5665i | 0.758287 | + | 0.437797i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.86573 | − | 19.5792i | −0.183907 | − | 0.740024i | ||||
\(701\) | −3.36247 | + | 5.82398i | −0.126999 | + | 0.219969i | −0.922513 | − | 0.385967i | \(-0.873868\pi\) |
0.795514 | + | 0.605936i | \(0.207201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.65790 | − | 6.15494i | 0.100245 | − | 0.232138i | ||||
\(704\) | −1.47054 | −0.0554230 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.13608 | + | 1.96775i | −0.0427569 | + | 0.0740571i | ||||
\(707\) | −1.76188 | + | 1.01722i | −0.0662625 | + | 0.0382566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.4517 | − | 26.7632i | −0.580302 | − | 1.00511i | −0.995443 | − | 0.0953554i | \(-0.969601\pi\) |
0.415141 | − | 0.909757i | \(-0.363732\pi\) | |||||||
\(710\) | −17.8552 | − | 7.58716i | −0.670095 | − | 0.284741i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.40962 | + | 0.813846i | −0.0528278 | + | 0.0305002i | ||||
\(713\) | 9.47717 | − | 5.47164i | 0.354923 | − | 0.204915i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.3171 | − | 6.50866i | −0.572828 | − | 0.243410i | ||||
\(716\) | 3.18779 | + | 5.52142i | 0.119133 | + | 0.206345i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.9101 | − | 10.3404i | 0.668400 | − | 0.385901i | ||||
\(719\) | 11.7185 | − | 20.2970i | 0.437025 | − | 0.756949i | −0.560434 | − | 0.828199i | \(-0.689366\pi\) |
0.997458 | + | 0.0712504i | \(0.0226989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.5384 | −0.802133 | ||||||||
\(722\) | 4.36691 | + | 18.4914i | 0.162520 | + | 0.688177i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.39603 | + | 7.61415i | −0.163377 | + | 0.282978i | ||||
\(725\) | 20.4278 | − | 5.07661i | 0.758668 | − | 0.188541i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.0238 | − | 19.6436i | −1.26187 | − | 0.728543i | −0.288436 | − | 0.957499i | \(-0.593135\pi\) |
−0.973437 | + | 0.228957i | \(0.926469\pi\) | |||||||
\(728\) | 17.6860 | − | 10.2110i | 0.655486 | − | 0.378445i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.1184 | + | 26.1656i | −0.411512 | + | 0.968432i | ||||
\(731\) | −0.215266 | − | 0.372851i | −0.00796189 | − | 0.0137904i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.2875i | 1.67273i | 0.548171 | + | 0.836366i | \(0.315324\pi\) | ||||
−0.548171 | + | 0.836366i | \(0.684676\pi\) | |||||||
\(734\) | 36.6899 | 1.35425 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.28274 | + | 2.22178i | −0.0472826 | + | 0.0818959i | ||||
\(737\) | 13.6935 | − | 7.90592i | 0.504405 | − | 0.291218i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7422 | − | 27.2663i | 0.579086 | − | 1.00301i | −0.416499 | − | 0.909136i | \(-0.636743\pi\) |
0.995585 | − | 0.0938695i | \(-0.0299237\pi\) | |||||||
\(740\) | −3.16532 | − | 1.34503i | −0.116359 | − | 0.0494442i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 43.0023i | 1.57866i | ||||||||
\(743\) | −40.4415 | − | 23.3489i | −1.48365 | − | 0.856587i | −0.483826 | − | 0.875164i | \(-0.660753\pi\) |
−0.999827 | + | 0.0185770i | \(0.994086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0956 | + | 3.31640i | −0.992705 | + | 0.121503i | ||||
\(746\) | −9.76898 | + | 16.9204i | −0.357668 | + | 0.619499i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.138039i | 0.00504719i | ||||||||
\(749\) | −72.3365 | −2.64312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.8807 | − | 25.7741i | −0.543004 | − | 0.940510i | −0.998730 | − | 0.0503901i | \(-0.983954\pi\) |
0.455726 | − | 0.890120i | \(-0.349380\pi\) | |||||||
\(752\) | − | 4.03603i | − | 0.147179i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.6536 | + | 18.4525i | 0.387980 | + | 0.672000i | ||||
\(755\) | 26.7804 | + | 35.5671i | 0.974639 | + | 1.29442i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2784 | + | 6.51161i | 0.409922 | + | 0.236668i | 0.690756 | − | 0.723088i | \(-0.257278\pi\) |
−0.280834 | + | 0.959756i | \(0.590611\pi\) | |||||||
\(758\) | −3.00339 | − | 1.73401i | −0.109088 | − | 0.0629820i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.47263 | − | 2.29549i | 0.343608 | − | 0.0832662i | ||||
\(761\) | −43.4538 | −1.57520 | −0.787600 | − | 0.616187i | \(-0.788676\pi\) | ||||
−0.787600 | + | 0.616187i | \(0.788676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.0042 | − | 17.9003i | −1.12243 | − | 0.648034i | ||||
\(764\) | −6.48293 | − | 11.2288i | −0.234544 | − | 0.406242i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.5509 | − | 21.7388i | −0.453483 | − | 0.785456i | ||||
\(767\) | 31.1369i | 1.12429i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.6418 | − | 40.9487i | −0.852544 | − | 1.47665i | −0.878905 | − | 0.476996i | \(-0.841725\pi\) |
0.0263617 | − | 0.999652i | \(-0.491608\pi\) | |||||||
\(770\) | −13.1695 | + | 1.61190i | −0.474597 | + | 0.0580889i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 6.11656i | − | 0.220140i | ||||||
\(773\) | 11.4692 | − | 6.62172i | 0.412517 | − | 0.238167i | −0.279354 | − | 0.960188i | \(-0.590120\pi\) |
0.691871 | + | 0.722022i | \(0.256787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.89445 | + | 20.4972i | −0.211735 | + | 0.736280i | ||||
\(776\) | −5.97438 | + | 10.3479i | −0.214468 | + | 0.371469i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 14.0415i | − | 0.503411i | ||||||
\(779\) | −27.1485 | + | 20.1944i | −0.972696 | + | 0.723541i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.37928 | + | 11.0492i | −0.228269 | + | 0.395373i | ||||
\(782\) | 0.208557 | + | 0.120411i | 0.00745799 | + | 0.00430587i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.64040 | − | 8.03741i | 0.165729 | − | 0.287050i | ||||
\(785\) | 4.41023 | + | 36.0324i | 0.157408 | + | 1.28605i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.7913i | − | 0.776775i | −0.921496 | − | 0.388388i | \(-0.873032\pi\) | ||
0.921496 | − | 0.388388i | \(-0.126968\pi\) | |||||||
\(788\) | 6.36478 | − | 3.67471i | 0.226736 | − | 0.130906i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −26.6760 | − | 11.3353i | −0.949089 | − | 0.403293i | ||||
\(791\) | −64.0212 | −2.27633 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.73079 | − | 3.30867i | −0.203506 | − | 0.117494i | ||||
\(794\) | 15.3729 | + | 26.6267i | 0.545564 | + | 0.944945i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.71780 | + | 2.97531i | −0.0608857 | + | 0.105457i | ||||
\(797\) | − | 14.8524i | − | 0.526099i | −0.964782 | − | 0.263049i | \(-0.915272\pi\) | ||
0.964782 | − | 0.263049i | \(-0.0847283\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.378860 | −0.0134031 | ||||||||
\(800\) | −1.20590 | − | 4.85240i | −0.0426349 | − | 0.171558i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.5183 | − | 19.3518i | 1.18357 | − | 0.683335i | ||||
\(803\) | 16.1919 | + | 9.34838i | 0.571399 | + | 0.329897i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.05237 | + | 21.3034i | −0.319054 | + | 0.750846i | ||||
\(806\) | −21.5893 | −0.760450 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.436656 | + | 0.252103i | −0.0153615 | + | 0.00886897i | ||||
\(809\) | −0.338772 | −0.0119106 | −0.00595530 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595530 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.04652 | − | 3.54467i | −0.0718629 | − | 0.124470i | 0.827855 | − | 0.560942i | \(-0.189561\pi\) |
−0.899718 | + | 0.436472i | \(0.856228\pi\) | |||||||
\(812\) | 14.7107 | + | 8.49321i | 0.516243 | + | 0.298053i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.13090 | + | 1.95877i | −0.0396380 | + | 0.0686550i | ||||
\(815\) | 3.67535 | − | 2.76737i | 0.128742 | − | 0.0969369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9320 | + | 16.0409i | 0.417448 | + | 0.561199i | ||||
\(818\) | − | 20.7839i | − | 0.726694i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4406 | + | 13.8662i | 0.364602 | + | 0.484229i | ||||
\(821\) | −17.2054 | − | 29.8007i | −0.600474 | − | 1.04005i | −0.992749 | − | 0.120203i | \(-0.961645\pi\) |
0.392275 | − | 0.919848i | \(-0.371688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3009 | + | 5.94720i | −0.359065 | + | 0.207306i | −0.668671 | − | 0.743559i | \(-0.733136\pi\) |
0.309605 | + | 0.950865i | \(0.399803\pi\) | |||||||
\(824\) | −5.33797 | −0.185957 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.4115 | + | 21.4973i | 0.431850 | + | 0.747986i | ||||
\(827\) | −10.5632 | + | 6.09865i | −0.367318 | + | 0.212071i | −0.672286 | − | 0.740292i | \(-0.734687\pi\) |
0.304968 | + | 0.952363i | \(0.401354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.0048 | 1.14631 | 0.573153 | − | 0.819449i | \(-0.305720\pi\) | ||||
0.573153 | + | 0.819449i | \(0.305720\pi\) | |||||||
\(830\) | −4.57947 | + | 0.560510i | −0.158956 | + | 0.0194556i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.38320 | − | 2.53064i | 0.151960 | − | 0.0877342i | ||||
\(833\) | −0.754467 | − | 0.435592i | −0.0261407 | − | 0.0150924i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.7154 | + | 19.0008i | 1.54744 | + | 0.657549i | ||||
\(836\) | −0.741602 | − | 6.36689i | −0.0256488 | − | 0.220203i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.4083 | − | 18.1336i | −1.08498 | − | 0.626414i | ||||
\(839\) | 8.97119 | − | 15.5386i | 0.309720 | − | 0.536451i | −0.668581 | − | 0.743639i | \(-0.733098\pi\) |
0.978301 | + | 0.207189i | \(0.0664314\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.63869 | − | 9.76650i | 0.194438 | − | 0.336776i | ||||
\(842\) | 18.5697 | − | 10.7212i | 0.639953 | − | 0.369477i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.03940 | 0.139042 | ||||||||
\(845\) | 28.0026 | − | 3.42741i | 0.963317 | − | 0.117906i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 35.6589i | − | 1.22525i | ||||||
\(848\) | 10.6575i | 0.365979i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.455492 | + | 0.113197i | −0.0156233 | + | 0.00388262i | ||||
\(851\) | 1.97295 | + | 3.41726i | 0.0676320 | + | 0.117142i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4891 | − | 11.2520i | −0.667295 | − | 0.385263i | 0.127756 | − | 0.991806i | \(-0.459223\pi\) |
−0.795051 | + | 0.606543i | \(0.792556\pi\) | |||||||
\(854\) | −5.27547 | −0.180523 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.9275 | −0.612749 | ||||||||
\(857\) | −1.71631 | − | 0.990914i | −0.0586281 | − | 0.0338490i | 0.470399 | − | 0.882454i | \(-0.344110\pi\) |
−0.529028 | + | 0.848605i | \(0.677443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.4673 | − | 28.5223i | −0.561858 | − | 0.973167i | −0.997334 | − | 0.0729670i | \(-0.976753\pi\) |
0.435476 | − | 0.900200i | \(-0.356580\pi\) | |||||||
\(860\) | 8.19293 | − | 6.16891i | 0.279377 | − | 0.210358i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 5.82431i | − | 0.198377i | ||||||
\(863\) | 1.13901i | 0.0387723i | 0.999812 | + | 0.0193862i | \(0.00617119\pi\) | ||||
−0.999812 | + | 0.0193862i | \(0.993829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.30392 | + | 51.5042i | 0.214340 | + | 1.75120i | ||||
\(866\) | −31.6030 | −1.07391 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.9055 | + | 8.60569i | −0.505925 | + | 0.292096i | ||||
\(869\) | −9.53074 | + | 16.5077i | −0.323308 | + | 0.559986i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.2105 | + | 47.1300i | −0.921993 | + | 1.59694i | ||||
\(872\) | −7.68392 | − | 4.43631i | −0.260210 | − | 0.150232i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.2664 | − | 4.43335i | −0.347265 | − | 0.149960i | ||||
\(875\) | −16.1184 | − | 42.1343i | −0.544901 | − | 1.42440i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.9508 | − | 11.5186i | −0.673692 | − | 0.388956i | 0.123782 | − | 0.992309i | \(-0.460498\pi\) |
−0.797474 | + | 0.603353i | \(0.793831\pi\) | |||||||
\(878\) | −1.61592 | + | 0.932951i | −0.0545346 | + | 0.0314856i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.26387 | + | 0.399485i | −0.110025 | + | 0.0134666i | ||||
\(881\) | 6.22555 | 0.209744 | 0.104872 | − | 0.994486i | \(-0.466557\pi\) | ||||
0.104872 | + | 0.994486i | \(0.466557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2402 | − | 16.3045i | 0.950360 | − | 0.548691i | 0.0571672 | − | 0.998365i | \(-0.481793\pi\) |
0.893193 | + | 0.449674i | \(0.148460\pi\) | |||||||
\(884\) | −0.237550 | − | 0.411448i | −0.00798967 | − | 0.0138385i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.7464 | −0.529009 | ||||||||
\(887\) | −3.26261 | + | 1.88367i | −0.109548 | + | 0.0632474i | −0.553773 | − | 0.832668i | \(-0.686812\pi\) |
0.444225 | + | 0.895915i | \(0.353479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4484 | + | 23.2933i | 0.451045 | + | 0.781234i | ||||
\(890\) | −2.90758 | + | 2.18927i | −0.0974621 | + | 0.0733846i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 18.0519i | − | 0.604421i | ||||||
\(893\) | 17.4745 | − | 2.03539i | 0.584762 | − | 0.0681118i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.57527 | + | 11.3888i | 0.286640 | + | 0.380687i | ||||
\(896\) | 2.01747 | − | 3.49437i | 0.0673991 | − | 0.116739i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.7588 | + | 14.8718i | 0.859581 | + | 0.496279i | ||||
\(899\) | −8.97866 | − | 15.5515i | −0.299455 | − | 0.518671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00041 | 0.0333285 | ||||||||
\(902\) | 9.88567 | − | 5.70749i | 0.329157 | − | 0.190039i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.8667 | −0.527718 | ||||||||
\(905\) | −7.68856 | + | 18.0939i | −0.255576 | + | 0.601461i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.85151 | + | 5.11042i | 0.293910 | + | 0.169689i | 0.639704 | − | 0.768622i | \(-0.279057\pi\) |
−0.345794 | + | 0.938310i | \(0.612390\pi\) | |||||||
\(908\) | 23.2539 | − | 13.4257i | 0.771709 | − | 0.445547i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 36.4802 | − | 27.4679i | 1.20931 | − | 0.910553i | ||||
\(911\) | 18.6042 | 0.616383 | 0.308192 | − | 0.951324i | \(-0.400276\pi\) | ||||
0.308192 | + | 0.951324i | \(0.400276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.03414i | 0.100415i | ||||||||
\(914\) | 6.39456 | − | 11.0757i | 0.211513 | − | 0.366352i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.85657 | + | 11.8759i | 0.226548 | + | 0.392392i | ||||
\(917\) | 24.7250 | + | 14.2750i | 0.816492 | + | 0.471402i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.5145 | 1.17152 | 0.585758 | − | 0.810486i | \(-0.300797\pi\) | ||||
0.585758 | + | 0.810486i | \(0.300797\pi\) | |||||||
\(920\) | −2.24349 | + | 5.27972i | −0.0739657 | + | 0.174067i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.3283 | + | 5.96303i | −0.340143 | + | 0.196382i | ||||
\(923\) | − | 43.9123i | − | 1.44539i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.39083 | − | 2.12541i | −0.243009 | − | 0.0698830i | ||||
\(926\) | 9.66039 | − | 16.7323i | 0.317460 | − | 0.549857i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.64581 | + | 2.10491i | 0.119680 | + | 0.0690971i | ||||
\(929\) | −2.13612 | + | 3.69987i | −0.0700838 | + | 0.121389i | −0.898938 | − | 0.438076i | \(-0.855660\pi\) |
0.828854 | + | 0.559465i | \(0.188993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.1392 | + | 16.0379i | 1.21719 | + | 0.525621i | ||||
\(932\) | 0.00661073i | 0.000216542i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.3504 | − | 23.1237i | 0.436840 | − | 0.756629i | ||||
\(935\) | 0.0374995 | + | 0.306377i | 0.00122636 | + | 0.0100196i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.5676 | + | 25.7311i | −1.45596 | + | 0.840599i | −0.998809 | − | 0.0487891i | \(-0.984464\pi\) |
−0.457152 | + | 0.889389i | \(0.651130\pi\) | |||||||
\(938\) | 43.3854i | 1.41658i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.09642 | − | 8.95798i | −0.0357614 | − | 0.292177i | ||||
\(941\) | 30.2442 | + | 52.3845i | 0.985934 | + | 1.70769i | 0.637712 | + | 0.770275i | \(0.279881\pi\) |
0.348222 | + | 0.937412i | \(0.386786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.9145i | − | 0.648505i | ||||||
\(944\) | 3.07599 | + | 5.32777i | 0.100115 | + | 0.173404i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.37231 | − | 5.84101i | −0.109643 | − | 0.189908i | ||||
\(947\) | 10.0415 | + | 5.79749i | 0.326306 | + | 0.188393i | 0.654200 | − | 0.756322i | \(-0.273005\pi\) |
−0.327894 | + | 0.944715i | \(0.606339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.3503 | −2.08890 | ||||||||
\(950\) | 20.4010 | − | 7.66818i | 0.661894 | − | 0.248789i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.328014 | − | 0.189379i | −0.0106310 | − | 0.00613781i | ||||
\(953\) | −22.5443 | − | 13.0160i | −0.730282 | − | 0.421629i | 0.0882433 | − | 0.996099i | \(-0.471875\pi\) |
−0.818525 | + | 0.574470i | \(0.805208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.4393 | − | 23.1612i | −0.564322 | − | 0.749477i | ||||
\(956\) | −2.33750 | − | 4.04866i | −0.0756000 | − | 0.130943i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.5825i | 0.438830i | ||||||||
\(959\) | −38.0425 | − | 65.8916i | −1.22846 | − | 2.12775i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.8049 | −0.413060 | ||||||||
\(962\) | − | 7.78462i | − | 0.250986i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.9044 | + | 24.0831i | −0.447829 | + | 0.775663i | ||||
\(965\) | −1.66162 | − | 13.5757i | −0.0534894 | − | 0.437019i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9595 | − | 8.63685i | −0.481064 | − | 0.277743i | 0.239796 | − | 0.970823i | \(-0.422920\pi\) |
−0.720860 | + | 0.693081i | \(0.756253\pi\) | |||||||
\(968\) | − | 8.83752i | − | 0.284049i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.4491 | + | 24.5903i | −0.335499 | + | 0.789547i | ||||
\(971\) | −5.47052 | + | 9.47522i | −0.175557 | + | 0.304074i | −0.940354 | − | 0.340198i | \(-0.889506\pi\) |
0.764797 | + | 0.644272i | \(0.222839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.8605 | − | 40.3340i | 2.23963 | − | 1.29305i | ||||
\(974\) | −4.01820 | + | 6.95973i | −0.128752 | + | 0.223004i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.30744 | −0.0418503 | ||||||||
\(977\) | 9.01488i | 0.288412i | 0.989548 | + | 0.144206i | \(0.0460627\pi\) | ||||
−0.989548 | + | 0.144206i | \(0.953937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.19679 | + | 2.07290i | 0.0382496 | + | 0.0662503i | ||||
\(980\) | 8.11595 | − | 19.0997i | 0.259255 | − | 0.610117i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.9077 | + | 10.3390i | −0.571457 | + | 0.329931i | ||||
\(983\) | −12.8956 | − | 7.44527i | −0.411305 | − | 0.237467i | 0.280045 | − | 0.959987i | \(-0.409651\pi\) |
−0.691350 | + | 0.722520i | \(0.742984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1284 | − | 9.88508i | 0.418305 | − | 0.314965i | ||||
\(986\) | 0.197587 | − | 0.342231i | 0.00629245 | − | 0.0108988i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.1672 | + | 17.7014i | 0.418905 | + | 0.563157i | ||||
\(989\) | −11.7666 | −0.374156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1717 | + | 40.1346i | −0.736075 | + | 1.27492i | 0.218176 | + | 0.975910i | \(0.429989\pi\) |
−0.954250 | + | 0.299009i | \(0.903344\pi\) | |||||||
\(992\) | −3.69410 | + | 2.13279i | −0.117288 | + | 0.0677161i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.5038 | − | 30.3175i | −0.555188 | − | 0.961613i | ||||
\(995\) | −3.00439 | + | 7.07037i | −0.0952454 | + | 0.224146i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.1990 | + | 15.1260i | −0.829730 | + | 0.479045i | −0.853760 | − | 0.520667i | \(-0.825683\pi\) |
0.0240304 | + | 0.999711i | \(0.492350\pi\) | |||||||
\(998\) | −0.954638 | + | 0.551160i | −0.0302185 | + | 0.0174467i | ||||
\(999\) | 0 | 0 |
(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 | 1710.2.t.c.1189.9 | 20 | ||
3.2 | odd | 2 | 570.2.q.c.49.2 | ✓ | 20 | ||
5.4 | even | 2 | inner | 1710.2.t.c.1189.1 | 20 | ||
15.14 | odd | 2 | 570.2.q.c.49.10 | yes | 20 | ||
19.7 | even | 3 | inner | 1710.2.t.c.919.1 | 20 | ||
57.26 | odd | 6 | 570.2.q.c.349.10 | yes | 20 | ||
95.64 | even | 6 | inner | 1710.2.t.c.919.9 | 20 | ||
285.254 | odd | 6 | 570.2.q.c.349.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.2 | ✓ | 20 | 3.2 | odd | 2 | ||
570.2.q.c.49.10 | yes | 20 | 15.14 | odd | 2 | ||
570.2.q.c.349.2 | yes | 20 | 285.254 | odd | 6 | ||
570.2.q.c.349.10 | yes | 20 | 57.26 | odd | 6 | ||
1710.2.t.c.919.1 | 20 | 19.7 | even | 3 | inner | ||
1710.2.t.c.919.9 | 20 | 95.64 | even | 6 | inner | ||
1710.2.t.c.1189.1 | 20 | 5.4 | even | 2 | inner | ||
1710.2.t.c.1189.9 | 20 | 1.1 | even | 1 | trivial |