Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.5 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.a.221.5 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.641070 | − | 1.60905i | −0.370122 | − | 0.928983i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | 1.71401 | + | 0.249340i | 0.699742 | + | 0.101793i | ||||
\(7\) | −2.43208 | −0.919238 | −0.459619 | − | 0.888116i | \(-0.652014\pi\) | ||||
−0.459619 | + | 0.888116i | \(0.652014\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.17806 | + | 2.06302i | −0.726019 | + | 0.687674i | ||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | 2.32454i | 0.700874i | 0.936586 | + | 0.350437i | \(0.113967\pi\) | ||||
−0.936586 | + | 0.350437i | \(0.886033\pi\) | |||||||
\(12\) | −1.07294 | + | 1.35971i | −0.309731 | + | 0.392513i | ||||
\(13\) | −0.190454 | + | 0.109959i | −0.0528224 | + | 0.0304970i | −0.526179 | − | 0.850374i | \(-0.676376\pi\) |
0.473356 | + | 0.880871i | \(0.343042\pi\) | |||||||
\(14\) | 1.21604 | − | 2.10624i | 0.325000 | − | 0.562916i | ||||
\(15\) | −0.249340 | + | 1.71401i | −0.0643792 | + | 0.442555i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.43932 | + | 2.56304i | 1.07669 | + | 0.621629i | 0.930002 | − | 0.367553i | \(-0.119804\pi\) |
0.146691 | + | 0.989182i | \(0.453138\pi\) | |||||||
\(18\) | −0.697602 | − | 2.91776i | −0.164426 | − | 0.687724i | ||||
\(19\) | −3.94445 | + | 1.85508i | −0.904918 | + | 0.425585i | ||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 1.55913 | + | 3.91332i | 0.340230 | + | 0.853957i | ||||
\(22\) | −2.01311 | − | 1.16227i | −0.429196 | − | 0.247796i | ||||
\(23\) | 7.51400 | − | 4.33821i | 1.56678 | − | 0.904580i | 0.570237 | − | 0.821480i | \(-0.306851\pi\) |
0.996541 | − | 0.0830996i | \(-0.0264820\pi\) | |||||||
\(24\) | −0.641070 | − | 1.60905i | −0.130858 | − | 0.328445i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | − | 0.219917i | − | 0.0431293i | ||||||
\(27\) | 4.71579 | + | 2.18205i | 0.907554 | + | 0.419936i | ||||
\(28\) | 1.21604 | + | 2.10624i | 0.229810 | + | 0.398042i | ||||
\(29\) | 3.98772 | + | 6.90694i | 0.740502 | + | 1.28259i | 0.952267 | + | 0.305266i | \(0.0987454\pi\) |
−0.211765 | + | 0.977321i | \(0.567921\pi\) | |||||||
\(30\) | −1.35971 | − | 1.07294i | −0.248247 | − | 0.195891i | ||||
\(31\) | 4.02893i | 0.723616i | 0.932253 | + | 0.361808i | \(0.117840\pi\) | ||||
−0.932253 | + | 0.361808i | \(0.882160\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 3.74029 | − | 1.49019i | 0.651100 | − | 0.259409i | ||||
\(34\) | −4.43932 | + | 2.56304i | −0.761337 | + | 0.439558i | ||||
\(35\) | 2.10624 | + | 1.21604i | 0.356019 | + | 0.205548i | ||||
\(36\) | 2.87566 | + | 0.854742i | 0.479277 | + | 0.142457i | ||||
\(37\) | − | 1.28133i | − | 0.210650i | −0.994438 | − | 0.105325i | \(-0.966412\pi\) | ||
0.994438 | − | 0.105325i | \(-0.0335883\pi\) | |||||||
\(38\) | 0.365675 | − | 4.34353i | 0.0593203 | − | 0.704614i | ||||
\(39\) | 0.299023 | + | 0.235958i | 0.0478820 | + | 0.0377835i | ||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | −1.19057 | + | 2.06213i | −0.185936 | + | 0.322050i | −0.943891 | − | 0.330256i | \(-0.892865\pi\) |
0.757956 | + | 0.652306i | \(0.226198\pi\) | |||||||
\(42\) | −4.16860 | − | 0.606413i | −0.643229 | − | 0.0935716i | ||||
\(43\) | −0.705429 | + | 1.22184i | −0.107577 | + | 0.186329i | −0.914788 | − | 0.403934i | \(-0.867643\pi\) |
0.807211 | + | 0.590263i | \(0.200976\pi\) | |||||||
\(44\) | 2.01311 | − | 1.16227i | 0.303487 | − | 0.175218i | ||||
\(45\) | 2.91776 | − | 0.697602i | 0.434955 | − | 0.103992i | ||||
\(46\) | 8.67642i | 1.27927i | ||||||||
\(47\) | −4.74957 | + | 2.74216i | −0.692795 | + | 0.399986i | −0.804658 | − | 0.593738i | \(-0.797652\pi\) |
0.111863 | + | 0.993724i | \(0.464318\pi\) | |||||||
\(48\) | 1.71401 | + | 0.249340i | 0.247396 | + | 0.0359891i | ||||
\(49\) | −1.08501 | −0.155001 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.27814 | − | 8.78616i | 0.178975 | − | 1.23031i | ||||
\(52\) | 0.190454 | + | 0.109959i | 0.0264112 | + | 0.0152485i | ||||
\(53\) | 2.04507 | + | 3.54217i | 0.280912 | + | 0.486555i | 0.971610 | − | 0.236589i | \(-0.0760296\pi\) |
−0.690697 | + | 0.723144i | \(0.742696\pi\) | |||||||
\(54\) | −4.24761 | + | 2.99297i | −0.578026 | + | 0.407291i | ||||
\(55\) | 1.16227 | − | 2.01311i | 0.156720 | − | 0.271447i | ||||
\(56\) | −2.43208 | −0.325000 | ||||||||
\(57\) | 5.51358 | + | 5.15756i | 0.730292 | + | 0.683135i | ||||
\(58\) | −7.97545 | −1.04723 | ||||||||
\(59\) | 0.478076 | − | 0.828051i | 0.0622402 | − | 0.107803i | −0.833226 | − | 0.552932i | \(-0.813509\pi\) |
0.895466 | + | 0.445129i | \(0.146842\pi\) | |||||||
\(60\) | 1.60905 | − | 0.641070i | 0.207727 | − | 0.0827618i | ||||
\(61\) | 4.12504 | + | 7.14478i | 0.528158 | + | 0.914796i | 0.999461 | + | 0.0328247i | \(0.0104503\pi\) |
−0.471304 | + | 0.881971i | \(0.656216\pi\) | |||||||
\(62\) | −3.48915 | − | 2.01446i | −0.443123 | − | 0.255837i | ||||
\(63\) | 5.29720 | − | 5.01743i | 0.667385 | − | 0.632137i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.219917 | 0.0272774 | ||||||||
\(66\) | −0.579599 | + | 3.98428i | −0.0713437 | + | 0.490431i | ||||
\(67\) | −6.63960 | + | 3.83338i | −0.811157 | + | 0.468322i | −0.847357 | − | 0.531023i | \(-0.821808\pi\) |
0.0362006 | + | 0.999345i | \(0.488474\pi\) | |||||||
\(68\) | − | 5.12609i | − | 0.621629i | ||||||
\(69\) | −11.7974 | − | 9.30928i | −1.42024 | − | 1.12071i | ||||
\(70\) | −2.10624 | + | 1.21604i | −0.251744 | + | 0.145344i | ||||
\(71\) | −5.05616 | + | 8.75753i | −0.600056 | + | 1.03933i | 0.392756 | + | 0.919643i | \(0.371522\pi\) |
−0.992812 | + | 0.119685i | \(0.961812\pi\) | |||||||
\(72\) | −2.17806 | + | 2.06302i | −0.256687 | + | 0.243130i | ||||
\(73\) | −1.78502 | + | 3.09174i | −0.208921 | + | 0.361861i | −0.951375 | − | 0.308036i | \(-0.900328\pi\) |
0.742454 | + | 0.669897i | \(0.233662\pi\) | |||||||
\(74\) | 1.10967 | + | 0.640666i | 0.128996 | + | 0.0744760i | ||||
\(75\) | 1.07294 | − | 1.35971i | 0.123892 | − | 0.157005i | ||||
\(76\) | 3.57877 | + | 2.48845i | 0.410513 | + | 0.285445i | ||||
\(77\) | − | 5.65345i | − | 0.644270i | ||||||
\(78\) | −0.353857 | + | 0.140982i | −0.0400664 | + | 0.0159631i | ||||
\(79\) | −13.0596 | − | 7.53998i | −1.46932 | − | 0.848313i | −0.469914 | − | 0.882712i | \(-0.655715\pi\) |
−0.999408 | + | 0.0343988i | \(0.989048\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 0.487870 | − | 8.98677i | 0.0542078 | − | 0.998530i | ||||
\(82\) | −1.19057 | − | 2.06213i | −0.131476 | − | 0.227724i | ||||
\(83\) | 4.36047i | 0.478623i | 0.970943 | + | 0.239312i | \(0.0769218\pi\) | ||||
−0.970943 | + | 0.239312i | \(0.923078\pi\) | |||||||
\(84\) | 2.60947 | − | 3.30691i | 0.284717 | − | 0.360813i | ||||
\(85\) | −2.56304 | − | 4.43932i | −0.278001 | − | 0.481512i | ||||
\(86\) | −0.705429 | − | 1.22184i | −0.0760684 | − | 0.131754i | ||||
\(87\) | 8.55717 | − | 10.8443i | 0.917425 | − | 1.16263i | ||||
\(88\) | 2.32454i | 0.247796i | ||||||||
\(89\) | 2.03041 | + | 3.51677i | 0.215223 | + | 0.372776i | 0.953341 | − | 0.301894i | \(-0.0976190\pi\) |
−0.738119 | + | 0.674671i | \(0.764286\pi\) | |||||||
\(90\) | −0.854742 | + | 2.87566i | −0.0900977 | + | 0.303121i | ||||
\(91\) | 0.463199 | − | 0.267428i | 0.0485564 | − | 0.0280341i | ||||
\(92\) | −7.51400 | − | 4.33821i | −0.783389 | − | 0.452290i | ||||
\(93\) | 6.48273 | − | 2.58282i | 0.672227 | − | 0.267826i | ||||
\(94\) | − | 5.48433i | − | 0.565665i | ||||||
\(95\) | 4.34353 | + | 0.365675i | 0.445637 | + | 0.0375175i | ||||
\(96\) | −1.07294 | + | 1.35971i | −0.109506 | + | 0.138774i | ||||
\(97\) | 6.10768 | + | 3.52627i | 0.620141 | + | 0.358038i | 0.776924 | − | 0.629595i | \(-0.216779\pi\) |
−0.156783 | + | 0.987633i | \(0.550112\pi\) | |||||||
\(98\) | 0.542503 | − | 0.939644i | 0.0548011 | − | 0.0949183i | ||||
\(99\) | −4.79557 | − | 5.06297i | −0.481973 | − | 0.508848i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −10.2389 | + | 5.91143i | −1.01881 | + | 0.588209i | −0.913759 | − | 0.406258i | \(-0.866834\pi\) |
−0.105050 | + | 0.994467i | \(0.533500\pi\) | |||||||
\(102\) | 6.96997 | + | 5.49998i | 0.690130 | + | 0.544579i | ||||
\(103\) | − | 17.5769i | − | 1.73190i | −0.500130 | − | 0.865950i | \(-0.666714\pi\) | ||
0.500130 | − | 0.865950i | \(-0.333286\pi\) | |||||||
\(104\) | −0.190454 | + | 0.109959i | −0.0186756 | + | 0.0107823i | ||||
\(105\) | 0.606413 | − | 4.16860i | 0.0591799 | − | 0.406814i | ||||
\(106\) | −4.09015 | −0.397270 | ||||||||
\(107\) | −2.80439 | −0.271111 | −0.135555 | − | 0.990770i | \(-0.543282\pi\) | ||||
−0.135555 | + | 0.990770i | \(0.543282\pi\) | |||||||
\(108\) | −0.468182 | − | 5.17502i | −0.0450508 | − | 0.497966i | ||||
\(109\) | 13.8072 | + | 7.97161i | 1.32249 | + | 0.763542i | 0.984126 | − | 0.177472i | \(-0.0567919\pi\) |
0.338368 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(110\) | 1.16227 | + | 2.01311i | 0.110818 | + | 0.191942i | ||||
\(111\) | −2.06172 | + | 0.821425i | −0.195690 | + | 0.0779662i | ||||
\(112\) | 1.21604 | − | 2.10624i | 0.114905 | − | 0.199021i | ||||
\(113\) | −12.1749 | −1.14532 | −0.572659 | − | 0.819794i | \(-0.694088\pi\) | ||||
−0.572659 | + | 0.819794i | \(0.694088\pi\) | |||||||
\(114\) | −7.22337 | + | 2.19612i | −0.676530 | + | 0.205686i | ||||
\(115\) | −8.67642 | −0.809081 | ||||||||
\(116\) | 3.98772 | − | 6.90694i | 0.370251 | − | 0.641293i | ||||
\(117\) | 0.187972 | − | 0.632407i | 0.0173781 | − | 0.0584661i | ||||
\(118\) | 0.478076 | + | 0.828051i | 0.0440104 | + | 0.0762283i | ||||
\(119\) | −10.7968 | − | 6.23351i | −0.989738 | − | 0.571425i | ||||
\(120\) | −0.249340 | + | 1.71401i | −0.0227615 | + | 0.156467i | ||||
\(121\) | 5.59653 | 0.508776 | ||||||||
\(122\) | −8.25009 | −0.746928 | ||||||||
\(123\) | 4.08129 | + | 0.593712i | 0.367998 | + | 0.0535332i | ||||
\(124\) | 3.48915 | − | 2.01446i | 0.313335 | − | 0.180904i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.69662 | + | 7.09623i | 0.151147 | + | 0.632182i | ||||
\(127\) | 2.43948 | − | 1.40844i | 0.216469 | − | 0.124979i | −0.387845 | − | 0.921725i | \(-0.626780\pi\) |
0.604314 | + | 0.796746i | \(0.293447\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.41822 | + | 0.351783i | 0.212913 | + | 0.0309728i | ||||
\(130\) | −0.109959 | + | 0.190454i | −0.00964401 | + | 0.0167039i | ||||
\(131\) | −7.22873 | − | 4.17351i | −0.631577 | − | 0.364641i | 0.149785 | − | 0.988719i | \(-0.452142\pi\) |
−0.781363 | + | 0.624077i | \(0.785475\pi\) | |||||||
\(132\) | −3.16069 | − | 2.49409i | −0.275102 | − | 0.217082i | ||||
\(133\) | 9.59320 | − | 4.51170i | 0.831836 | − | 0.391214i | ||||
\(134\) | − | 7.66675i | − | 0.662307i | ||||||
\(135\) | −2.99297 | − | 4.24761i | −0.257593 | − | 0.365576i | ||||
\(136\) | 4.43932 | + | 2.56304i | 0.380669 | + | 0.219779i | ||||
\(137\) | 12.6626 | − | 7.31076i | 1.08184 | − | 0.624600i | 0.150448 | − | 0.988618i | \(-0.451929\pi\) |
0.931392 | + | 0.364018i | \(0.118595\pi\) | |||||||
\(138\) | 13.9608 | − | 5.56220i | 1.18842 | − | 0.473486i | ||||
\(139\) | 5.51342 | + | 9.54952i | 0.467642 | + | 0.809979i | 0.999316 | − | 0.0369693i | \(-0.0117704\pi\) |
−0.531675 | + | 0.846949i | \(0.678437\pi\) | |||||||
\(140\) | − | 2.43208i | − | 0.205548i | ||||||
\(141\) | 7.45707 | + | 5.88435i | 0.627999 | + | 0.495552i | ||||
\(142\) | −5.05616 | − | 8.75753i | −0.424304 | − | 0.734916i | ||||
\(143\) | −0.255603 | − | 0.442717i | −0.0213746 | − | 0.0370219i | ||||
\(144\) | −0.697602 | − | 2.91776i | −0.0581335 | − | 0.243147i | ||||
\(145\) | − | 7.97545i | − | 0.662325i | ||||||
\(146\) | −1.78502 | − | 3.09174i | −0.147729 | − | 0.255874i | ||||
\(147\) | 0.695566 | + | 1.74583i | 0.0573693 | + | 0.143993i | ||||
\(148\) | −1.10967 | + | 0.640666i | −0.0912141 | + | 0.0526625i | ||||
\(149\) | 18.2772 | + | 10.5523i | 1.49732 | + | 0.864480i | 0.999995 | − | 0.00308349i | \(-0.000981508\pi\) |
0.497327 | + | 0.867563i | \(0.334315\pi\) | |||||||
\(150\) | 0.641070 | + | 1.60905i | 0.0523432 | + | 0.131378i | ||||
\(151\) | − | 24.2149i | − | 1.97058i | −0.170899 | − | 0.985289i | \(-0.554667\pi\) | ||
0.170899 | − | 0.985289i | \(-0.445333\pi\) | |||||||
\(152\) | −3.94445 | + | 1.85508i | −0.319937 | + | 0.150467i | ||||
\(153\) | −14.9567 | + | 3.57597i | −1.20918 | + | 0.289100i | ||||
\(154\) | 4.89603 | + | 2.82672i | 0.394533 | + | 0.227784i | ||||
\(155\) | 2.01446 | − | 3.48915i | 0.161806 | − | 0.280255i | ||||
\(156\) | 0.0548341 | − | 0.376940i | 0.00439024 | − | 0.0301794i | ||||
\(157\) | −6.46343 | + | 11.1950i | −0.515837 | + | 0.893457i | 0.483993 | + | 0.875072i | \(0.339186\pi\) |
−0.999831 | + | 0.0183851i | \(0.994147\pi\) | |||||||
\(158\) | 13.0596 | − | 7.53998i | 1.03897 | − | 0.599848i | ||||
\(159\) | 4.38848 | − | 5.56140i | 0.348029 | − | 0.441048i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −18.2746 | + | 10.5509i | −1.44024 | + | 0.831524i | ||||
\(162\) | 7.53883 | + | 4.91589i | 0.592307 | + | 0.386229i | ||||
\(163\) | 13.6212 | 1.06690 | 0.533449 | − | 0.845832i | \(-0.320896\pi\) | ||||
0.533449 | + | 0.845832i | \(0.320896\pi\) | |||||||
\(164\) | 2.38114 | 0.185936 | ||||||||
\(165\) | −3.98428 | − | 0.579599i | −0.310176 | − | 0.0451217i | ||||
\(166\) | −3.77627 | − | 2.18023i | −0.293096 | − | 0.169219i | ||||
\(167\) | 5.43020 | + | 9.40538i | 0.420202 | + | 0.727810i | 0.995959 | − | 0.0898102i | \(-0.0286260\pi\) |
−0.575757 | + | 0.817621i | \(0.695293\pi\) | |||||||
\(168\) | 1.55913 | + | 3.91332i | 0.120290 | + | 0.301919i | ||||
\(169\) | −6.47582 | + | 11.2164i | −0.498140 | + | 0.862804i | ||||
\(170\) | 5.12609 | 0.393153 | ||||||||
\(171\) | 4.76416 | − | 12.1780i | 0.364324 | − | 0.931272i | ||||
\(172\) | 1.41086 | 0.107577 | ||||||||
\(173\) | 6.04765 | − | 10.4748i | 0.459794 | − | 0.796387i | −0.539156 | − | 0.842206i | \(-0.681257\pi\) |
0.998950 | + | 0.0458193i | \(0.0145899\pi\) | |||||||
\(174\) | 5.11282 | + | 12.8329i | 0.387602 | + | 0.972857i | ||||
\(175\) | −1.21604 | − | 2.10624i | −0.0919238 | − | 0.159217i | ||||
\(176\) | −2.01311 | − | 1.16227i | −0.151744 | − | 0.0876092i | ||||
\(177\) | −1.63885 | − | 0.238407i | −0.123184 | − | 0.0179197i | ||||
\(178\) | −4.06081 | −0.304371 | ||||||||
\(179\) | 9.17378 | 0.685681 | 0.342840 | − | 0.939394i | \(-0.388611\pi\) | ||||
0.342840 | + | 0.939394i | \(0.388611\pi\) | |||||||
\(180\) | −2.06302 | − | 2.17806i | −0.153769 | − | 0.162343i | ||||
\(181\) | −8.37372 | + | 4.83457i | −0.622414 | + | 0.359351i | −0.777808 | − | 0.628502i | \(-0.783668\pi\) |
0.155395 | + | 0.987852i | \(0.450335\pi\) | |||||||
\(182\) | 0.534856i | 0.0396461i | ||||||||
\(183\) | 8.85184 | − | 11.2177i | 0.654347 | − | 0.829236i | ||||
\(184\) | 7.51400 | − | 4.33821i | 0.553940 | − | 0.319817i | ||||
\(185\) | −0.640666 | + | 1.10967i | −0.0471027 | + | 0.0815843i | ||||
\(186\) | −1.00457 | + | 6.90562i | −0.0736587 | + | 0.506344i | ||||
\(187\) | −5.95789 | + | 10.3194i | −0.435684 | + | 0.754626i | ||||
\(188\) | 4.74957 | + | 2.74216i | 0.346398 | + | 0.199993i | ||||
\(189\) | −11.4692 | − | 5.30692i | −0.834258 | − | 0.386021i | ||||
\(190\) | −2.48845 | + | 3.57877i | −0.180531 | + | 0.259631i | ||||
\(191\) | − | 18.7213i | − | 1.35463i | −0.735695 | − | 0.677313i | \(-0.763144\pi\) | ||
0.735695 | − | 0.677313i | \(-0.236856\pi\) | |||||||
\(192\) | −0.641070 | − | 1.60905i | −0.0462653 | − | 0.116123i | ||||
\(193\) | −21.1958 | − | 12.2374i | −1.52571 | − | 0.880867i | −0.999535 | − | 0.0304886i | \(-0.990294\pi\) |
−0.526171 | − | 0.850379i | \(-0.676373\pi\) | |||||||
\(194\) | −6.10768 | + | 3.52627i | −0.438506 | + | 0.253171i | ||||
\(195\) | −0.140982 | − | 0.353857i | −0.0100960 | − | 0.0253402i | ||||
\(196\) | 0.542503 | + | 0.939644i | 0.0387502 | + | 0.0671174i | ||||
\(197\) | 4.97845i | 0.354700i | 0.984148 | + | 0.177350i | \(0.0567524\pi\) | ||||
−0.984148 | + | 0.177350i | \(0.943248\pi\) | |||||||
\(198\) | 6.78245 | − | 1.62160i | 0.482008 | − | 0.115242i | ||||
\(199\) | 9.08451 | + | 15.7348i | 0.643984 | + | 1.11541i | 0.984535 | + | 0.175187i | \(0.0560530\pi\) |
−0.340551 | + | 0.940226i | \(0.610614\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 10.4245 | + | 8.22596i | 0.735290 | + | 0.580215i | ||||
\(202\) | − | 11.8229i | − | 0.831854i | ||||||
\(203\) | −9.69845 | − | 16.7982i | −0.680698 | − | 1.17900i | ||||
\(204\) | −8.24811 | + | 3.28618i | −0.577483 | + | 0.230079i | ||||
\(205\) | 2.06213 | − | 1.19057i | 0.144025 | − | 0.0831529i | ||||
\(206\) | 15.2220 | + | 8.78844i | 1.06057 | + | 0.612319i | ||||
\(207\) | −7.41610 | + | 24.9504i | −0.515455 | + | 1.73418i | ||||
\(208\) | − | 0.219917i | − | 0.0152485i | ||||||
\(209\) | −4.31221 | − | 9.16901i | −0.298282 | − | 0.634234i | ||||
\(210\) | 3.30691 | + | 2.60947i | 0.228198 | + | 0.180071i | ||||
\(211\) | −2.49731 | − | 1.44183i | −0.171922 | − | 0.0992593i | 0.411570 | − | 0.911378i | \(-0.364981\pi\) |
−0.583492 | + | 0.812119i | \(0.698314\pi\) | |||||||
\(212\) | 2.04507 | − | 3.54217i | 0.140456 | − | 0.243277i | ||||
\(213\) | 17.3326 | + | 2.52141i | 1.18761 | + | 0.172764i | ||||
\(214\) | 1.40220 | − | 2.42868i | 0.0958522 | − | 0.166021i | ||||
\(215\) | 1.22184 | − | 0.705429i | 0.0833287 | − | 0.0481099i | ||||
\(216\) | 4.71579 | + | 2.18205i | 0.320869 | + | 0.148470i | ||||
\(217\) | − | 9.79865i | − | 0.665176i | ||||||
\(218\) | −13.8072 | + | 7.97161i | −0.935144 | + | 0.539906i | ||||
\(219\) | 6.11908 | + | 0.890152i | 0.413489 | + | 0.0601509i | ||||
\(220\) | −2.32454 | −0.156720 | ||||||||
\(221\) | −1.12732 | −0.0758314 | ||||||||
\(222\) | 0.319487 | − | 2.19622i | 0.0214426 | − | 0.147400i | ||||
\(223\) | −12.7294 | − | 7.34931i | −0.852422 | − | 0.492146i | 0.00904511 | − | 0.999959i | \(-0.497121\pi\) |
−0.861467 | + | 0.507813i | \(0.830454\pi\) | |||||||
\(224\) | 1.21604 | + | 2.10624i | 0.0812500 | + | 0.140729i | ||||
\(225\) | −2.87566 | − | 0.854742i | −0.191711 | − | 0.0569828i | ||||
\(226\) | 6.08745 | − | 10.5438i | 0.404931 | − | 0.701361i | ||||
\(227\) | −11.0675 | −0.734576 | −0.367288 | − | 0.930107i | \(-0.619714\pi\) | ||||
−0.367288 | + | 0.930107i | \(0.619714\pi\) | |||||||
\(228\) | 1.70979 | − | 7.35368i | 0.113233 | − | 0.487009i | ||||
\(229\) | 3.19538 | 0.211157 | 0.105578 | − | 0.994411i | \(-0.466331\pi\) | ||||
0.105578 | + | 0.994411i | \(0.466331\pi\) | |||||||
\(230\) | 4.33821 | − | 7.51400i | 0.286053 | − | 0.495459i | ||||
\(231\) | −9.09666 | + | 3.62426i | −0.598516 | + | 0.238459i | ||||
\(232\) | 3.98772 | + | 6.90694i | 0.261807 | + | 0.453463i | ||||
\(233\) | −6.96020 | − | 4.01848i | −0.455978 | − | 0.263259i | 0.254374 | − | 0.967106i | \(-0.418131\pi\) |
−0.710352 | + | 0.703847i | \(0.751464\pi\) | |||||||
\(234\) | 0.453695 | + | 0.478993i | 0.0296589 | + | 0.0313127i | ||||
\(235\) | 5.48433 | 0.357758 | ||||||||
\(236\) | −0.956151 | −0.0622402 | ||||||||
\(237\) | −3.76003 | + | 25.8472i | −0.244240 | + | 1.67895i | ||||
\(238\) | 10.7968 | − | 6.23351i | 0.699850 | − | 0.404059i | ||||
\(239\) | 5.17399i | 0.334678i | 0.985899 | + | 0.167339i | \(0.0535174\pi\) | ||||
−0.985899 | + | 0.167339i | \(0.946483\pi\) | |||||||
\(240\) | −1.35971 | − | 1.07294i | −0.0877687 | − | 0.0692579i | ||||
\(241\) | −25.4528 | + | 14.6952i | −1.63956 | + | 0.946601i | −0.658576 | + | 0.752514i | \(0.728841\pi\) |
−0.980984 | + | 0.194086i | \(0.937826\pi\) | |||||||
\(242\) | −2.79827 | + | 4.84674i | −0.179879 | + | 0.311560i | ||||
\(243\) | −14.7729 | + | 4.97615i | −0.947681 | + | 0.319220i | ||||
\(244\) | 4.12504 | − | 7.14478i | 0.264079 | − | 0.457398i | ||||
\(245\) | 0.939644 | + | 0.542503i | 0.0600316 | + | 0.0346593i | ||||
\(246\) | −2.55482 | + | 3.23765i | −0.162889 | + | 0.206425i | ||||
\(247\) | 0.547253 | − | 0.787034i | 0.0348209 | − | 0.0500778i | ||||
\(248\) | 4.02893i | 0.255837i | ||||||||
\(249\) | 7.01619 | − | 2.79537i | 0.444633 | − | 0.177149i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | −21.7086 | + | 12.5335i | −1.37024 | + | 0.791107i | −0.990958 | − | 0.134176i | \(-0.957161\pi\) |
−0.379279 | + | 0.925282i | \(0.623828\pi\) | |||||||
\(252\) | −6.99382 | − | 2.07880i | −0.440569 | − | 0.130952i | ||||
\(253\) | 10.0843 | + | 17.4666i | 0.633996 | + | 1.09811i | ||||
\(254\) | 2.81687i | 0.176746i | ||||||||
\(255\) | −5.49998 | + | 6.96997i | −0.344422 | + | 0.436476i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.30955 | − | 4.00025i | −0.144066 | − | 0.249529i | 0.784958 | − | 0.619548i | \(-0.212684\pi\) |
−0.929024 | + | 0.370020i | \(0.879351\pi\) | |||||||
\(258\) | −1.51377 | + | 1.91835i | −0.0942429 | + | 0.119431i | ||||
\(259\) | 3.11630i | 0.193637i | ||||||||
\(260\) | −0.109959 | − | 0.190454i | −0.00681935 | − | 0.0118115i | ||||
\(261\) | −22.9347 | − | 6.81695i | −1.41962 | − | 0.421958i | ||||
\(262\) | 7.22873 | − | 4.17351i | 0.446593 | − | 0.257840i | ||||
\(263\) | 24.7674 | + | 14.2995i | 1.52723 | + | 0.881744i | 0.999477 | + | 0.0323436i | \(0.0102971\pi\) |
0.527749 | + | 0.849401i | \(0.323036\pi\) | |||||||
\(264\) | 3.74029 | − | 1.49019i | 0.230199 | − | 0.0917149i | ||||
\(265\) | − | 4.09015i | − | 0.251256i | ||||||
\(266\) | −0.889349 | + | 10.5638i | −0.0545295 | + | 0.647708i | ||||
\(267\) | 4.35700 | − | 5.52151i | 0.266644 | − | 0.337911i | ||||
\(268\) | 6.63960 | + | 3.83338i | 0.405578 | + | 0.234161i | ||||
\(269\) | 1.62587 | − | 2.81609i | 0.0991312 | − | 0.171700i | −0.812194 | − | 0.583387i | \(-0.801727\pi\) |
0.911325 | + | 0.411687i | \(0.135060\pi\) | |||||||
\(270\) | 5.17502 | − | 0.468182i | 0.314942 | − | 0.0284926i | ||||
\(271\) | −3.17133 | + | 5.49291i | −0.192645 | + | 0.333670i | −0.946126 | − | 0.323799i | \(-0.895040\pi\) |
0.753481 | + | 0.657469i | \(0.228373\pi\) | |||||||
\(272\) | −4.43932 | + | 2.56304i | −0.269173 | + | 0.155407i | ||||
\(273\) | −0.727247 | − | 0.573868i | −0.0440150 | − | 0.0347321i | ||||
\(274\) | 14.6215i | 0.883318i | ||||||||
\(275\) | −2.01311 | + | 1.16227i | −0.121395 | + | 0.0700874i | ||||
\(276\) | −2.16338 | + | 14.8715i | −0.130220 | + | 0.895158i | ||||
\(277\) | 22.1670 | 1.33189 | 0.665943 | − | 0.746002i | \(-0.268029\pi\) | ||||
0.665943 | + | 0.746002i | \(0.268029\pi\) | |||||||
\(278\) | −11.0268 | −0.661345 | ||||||||
\(279\) | −8.31177 | − | 8.77523i | −0.497613 | − | 0.525359i | ||||
\(280\) | 2.10624 | + | 1.21604i | 0.125872 | + | 0.0726722i | ||||
\(281\) | 7.85570 | + | 13.6065i | 0.468632 | + | 0.811694i | 0.999357 | − | 0.0358495i | \(-0.0114137\pi\) |
−0.530725 | + | 0.847544i | \(0.678080\pi\) | |||||||
\(282\) | −8.82453 | + | 3.51584i | −0.525493 | + | 0.209365i | ||||
\(283\) | −10.1514 | + | 17.5827i | −0.603435 | + | 1.04518i | 0.388861 | + | 0.921296i | \(0.372869\pi\) |
−0.992297 | + | 0.123884i | \(0.960465\pi\) | |||||||
\(284\) | 10.1123 | 0.600056 | ||||||||
\(285\) | −2.19612 | − | 7.22337i | −0.130087 | − | 0.427875i | ||||
\(286\) | 0.511206 | 0.0302282 | ||||||||
\(287\) | 2.89555 | − | 5.01525i | 0.170919 | − | 0.296041i | ||||
\(288\) | 2.87566 | + | 0.854742i | 0.169450 | + | 0.0503661i | ||||
\(289\) | 4.63838 | + | 8.03390i | 0.272846 | + | 0.472583i | ||||
\(290\) | 6.90694 | + | 3.98772i | 0.405590 | + | 0.234167i | ||||
\(291\) | 1.75848 | − | 12.0881i | 0.103084 | − | 0.708618i | ||||
\(292\) | 3.57004 | 0.208921 | ||||||||
\(293\) | −16.1085 | −0.941067 | −0.470533 | − | 0.882382i | \(-0.655938\pi\) | ||||
−0.470533 | + | 0.882382i | \(0.655938\pi\) | |||||||
\(294\) | −1.85971 | − | 0.270535i | −0.108461 | − | 0.0157779i | ||||
\(295\) | −0.828051 | + | 0.478076i | −0.0482110 | + | 0.0278346i | ||||
\(296\) | − | 1.28133i | − | 0.0744760i | ||||||
\(297\) | −5.07226 | + | 10.9620i | −0.294322 | + | 0.636081i | ||||
\(298\) | −18.2772 | + | 10.5523i | −1.05877 | + | 0.611279i | ||||
\(299\) | −0.954048 | + | 1.65246i | −0.0551740 | + | 0.0955642i | ||||
\(300\) | −1.71401 | − | 0.249340i | −0.0989584 | − | 0.0143956i | ||||
\(301\) | 1.71566 | − | 2.97160i | 0.0988888 | − | 0.171280i | ||||
\(302\) | 20.9707 | + | 12.1074i | 1.20673 | + | 0.696704i | ||||
\(303\) | 16.0756 | + | 12.6852i | 0.923520 | + | 0.728747i | ||||
\(304\) | 0.365675 | − | 4.34353i | 0.0209729 | − | 0.249119i | ||||
\(305\) | − | 8.25009i | − | 0.472399i | ||||||
\(306\) | 4.38148 | − | 14.7409i | 0.250472 | − | 0.842680i | ||||
\(307\) | 6.95957 | + | 4.01811i | 0.397204 | + | 0.229326i | 0.685277 | − | 0.728283i | \(-0.259681\pi\) |
−0.288073 | + | 0.957608i | \(0.593015\pi\) | |||||||
\(308\) | −4.89603 | + | 2.82672i | −0.278977 | + | 0.161068i | ||||
\(309\) | −28.2820 | + | 11.2680i | −1.60891 | + | 0.641015i | ||||
\(310\) | 2.01446 | + | 3.48915i | 0.114414 | + | 0.198171i | ||||
\(311\) | − | 20.2592i | − | 1.14879i | −0.818577 | − | 0.574396i | \(-0.805237\pi\) | ||
0.818577 | − | 0.574396i | \(-0.194763\pi\) | |||||||
\(312\) | 0.299023 | + | 0.235958i | 0.0169288 | + | 0.0133585i | ||||
\(313\) | −12.0239 | − | 20.8260i | −0.679631 | − | 1.17716i | −0.975092 | − | 0.221801i | \(-0.928807\pi\) |
0.295461 | − | 0.955355i | \(-0.404527\pi\) | |||||||
\(314\) | −6.46343 | − | 11.1950i | −0.364752 | − | 0.631769i | ||||
\(315\) | −7.09623 | + | 1.69662i | −0.399827 | + | 0.0955937i | ||||
\(316\) | 15.0800i | 0.848313i | ||||||||
\(317\) | 6.26988 | + | 10.8598i | 0.352152 | + | 0.609944i | 0.986626 | − | 0.162999i | \(-0.0521168\pi\) |
−0.634475 | + | 0.772944i | \(0.718783\pi\) | |||||||
\(318\) | 2.62207 | + | 6.58124i | 0.147039 | + | 0.369057i | ||||
\(319\) | −16.0554 | + | 9.26961i | −0.898932 | + | 0.518998i | ||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 1.79781 | + | 4.51240i | 0.100344 | + | 0.251858i | ||||
\(322\) | − | 21.1017i | − | 1.17595i | ||||||
\(323\) | −22.2653 | − | 1.87448i | −1.23888 | − | 0.104299i | ||||
\(324\) | −8.02670 | + | 4.07088i | −0.445928 | + | 0.226160i | ||||
\(325\) | −0.190454 | − | 0.109959i | −0.0105645 | − | 0.00609941i | ||||
\(326\) | −6.81062 | + | 11.7963i | −0.377205 | + | 0.653339i | ||||
\(327\) | 3.97528 | − | 27.3268i | 0.219833 | − | 1.51118i | ||||
\(328\) | −1.19057 | + | 2.06213i | −0.0657382 | + | 0.113862i | ||||
\(329\) | 11.5513 | − | 6.66915i | 0.636844 | − | 0.367682i | ||||
\(330\) | 2.49409 | − | 3.16069i | 0.137295 | − | 0.173990i | ||||
\(331\) | 5.06995i | 0.278670i | 0.990245 | + | 0.139335i | \(0.0444965\pi\) | ||||
−0.990245 | + | 0.139335i | \(0.955504\pi\) | |||||||
\(332\) | 3.77627 | − | 2.18023i | 0.207250 | − | 0.119656i | ||||
\(333\) | 2.64342 | + | 2.79082i | 0.144858 | + | 0.152936i | ||||
\(334\) | −10.8604 | −0.594255 | ||||||||
\(335\) | 7.66675 | 0.418880 | ||||||||
\(336\) | −4.16860 | − | 0.606413i | −0.227416 | − | 0.0330826i | ||||
\(337\) | 3.52448 | + | 2.03486i | 0.191991 | + | 0.110846i | 0.592914 | − | 0.805266i | \(-0.297977\pi\) |
−0.400923 | + | 0.916112i | \(0.631311\pi\) | |||||||
\(338\) | −6.47582 | − | 11.2164i | −0.352238 | − | 0.610094i | ||||
\(339\) | 7.80496 | + | 19.5900i | 0.423907 | + | 1.06398i | ||||
\(340\) | −2.56304 | + | 4.43932i | −0.139001 | + | 0.240756i | ||||
\(341\) | −9.36538 | −0.507164 | ||||||||
\(342\) | 8.16435 | + | 10.2149i | 0.441477 | + | 0.552356i | ||||
\(343\) | 19.6634 | 1.06172 | ||||||||
\(344\) | −0.705429 | + | 1.22184i | −0.0380342 | + | 0.0658771i | ||||
\(345\) | 5.56220 | + | 13.9608i | 0.299459 | + | 0.751622i | ||||
\(346\) | 6.04765 | + | 10.4748i | 0.325124 | + | 0.563131i | ||||
\(347\) | 4.31415 | + | 2.49077i | 0.231596 | + | 0.133712i | 0.611308 | − | 0.791393i | \(-0.290644\pi\) |
−0.379712 | + | 0.925105i | \(0.623977\pi\) | |||||||
\(348\) | −13.6700 | − | 1.98860i | −0.732789 | − | 0.106600i | ||||
\(349\) | 17.2329 | 0.922458 | 0.461229 | − | 0.887281i | \(-0.347409\pi\) | ||||
0.461229 | + | 0.887281i | \(0.347409\pi\) | |||||||
\(350\) | 2.43208 | 0.130000 | ||||||||
\(351\) | −1.13808 | + | 0.102961i | −0.0607460 | + | 0.00549566i | ||||
\(352\) | 2.01311 | − | 1.16227i | 0.107299 | − | 0.0619491i | ||||
\(353\) | 26.6382i | 1.41781i | 0.705306 | + | 0.708903i | \(0.250810\pi\) | ||||
−0.705306 | + | 0.708903i | \(0.749190\pi\) | |||||||
\(354\) | 1.02589 | − | 1.30009i | 0.0545256 | − | 0.0690987i | ||||
\(355\) | 8.75753 | − | 5.05616i | 0.464802 | − | 0.268353i | ||||
\(356\) | 2.03041 | − | 3.51677i | 0.107611 | − | 0.186388i | ||||
\(357\) | −3.10853 | + | 21.3686i | −0.164521 | + | 1.13095i | ||||
\(358\) | −4.58689 | + | 7.94473i | −0.242425 | + | 0.419892i | ||||
\(359\) | 25.0199 | + | 14.4453i | 1.32050 | + | 0.762392i | 0.983809 | − | 0.179222i | \(-0.0573580\pi\) |
0.336694 | + | 0.941614i | \(0.390691\pi\) | |||||||
\(360\) | 2.91776 | − | 0.697602i | 0.153780 | − | 0.0367668i | ||||
\(361\) | 12.1173 | − | 14.6346i | 0.637754 | − | 0.770240i | ||||
\(362\) | − | 9.66914i | − | 0.508199i | ||||||
\(363\) | −3.58777 | − | 9.00508i | −0.188309 | − | 0.472644i | ||||
\(364\) | −0.463199 | − | 0.267428i | −0.0242782 | − | 0.0140170i | ||||
\(365\) | 3.09174 | − | 1.78502i | 0.161829 | − | 0.0934321i | ||||
\(366\) | 5.28889 | + | 13.2748i | 0.276454 | + | 0.693883i | ||||
\(367\) | −10.1670 | − | 17.6098i | −0.530713 | − | 0.919222i | −0.999358 | − | 0.0358355i | \(-0.988591\pi\) |
0.468644 | − | 0.883387i | \(-0.344743\pi\) | |||||||
\(368\) | 8.67642i | 0.452290i | ||||||||
\(369\) | −1.66109 | − | 6.94760i | −0.0864727 | − | 0.361678i | ||||
\(370\) | −0.640666 | − | 1.10967i | −0.0333067 | − | 0.0576888i | ||||
\(371\) | −4.97377 | − | 8.61483i | −0.258226 | − | 0.447260i | ||||
\(372\) | −5.47816 | − | 4.32279i | −0.284029 | − | 0.224126i | ||||
\(373\) | − | 12.2252i | − | 0.632997i | −0.948593 | − | 0.316499i | \(-0.897493\pi\) | ||
0.948593 | − | 0.316499i | \(-0.102507\pi\) | |||||||
\(374\) | −5.95789 | − | 10.3194i | −0.308075 | − | 0.533601i | ||||
\(375\) | −1.60905 | + | 0.641070i | −0.0830908 | + | 0.0331047i | ||||
\(376\) | −4.74957 | + | 2.74216i | −0.244940 | + | 0.141416i | ||||
\(377\) | −1.51896 | − | 0.876970i | −0.0782302 | − | 0.0451662i | ||||
\(378\) | 10.3305 | − | 7.27912i | 0.531344 | − | 0.374398i | ||||
\(379\) | − | 37.1799i | − | 1.90980i | −0.296925 | − | 0.954901i | \(-0.595961\pi\) | ||
0.296925 | − | 0.954901i | \(-0.404039\pi\) | |||||||
\(380\) | −1.85508 | − | 3.94445i | −0.0951637 | − | 0.202346i | ||||
\(381\) | −3.83012 | − | 3.02234i | −0.196223 | − | 0.154839i | ||||
\(382\) | 16.2131 | + | 9.36065i | 0.829536 | + | 0.478933i | ||||
\(383\) | −2.24543 | + | 3.88919i | −0.114736 | + | 0.198728i | −0.917674 | − | 0.397334i | \(-0.869936\pi\) |
0.802938 | + | 0.596062i | \(0.203269\pi\) | |||||||
\(384\) | 1.71401 | + | 0.249340i | 0.0874677 | + | 0.0127241i | ||||
\(385\) | −2.82672 | + | 4.89603i | −0.144063 | + | 0.249525i | ||||
\(386\) | 21.1958 | − | 12.2374i | 1.07884 | − | 0.622867i | ||||
\(387\) | −0.984217 | − | 4.11655i | −0.0500306 | − | 0.209256i | ||||
\(388\) | − | 7.05254i | − | 0.358038i | ||||||
\(389\) | 23.0418 | − | 13.3032i | 1.16827 | − | 0.674499i | 0.214996 | − | 0.976615i | \(-0.431026\pi\) |
0.953271 | + | 0.302116i | \(0.0976930\pi\) | |||||||
\(390\) | 0.376940 | + | 0.0548341i | 0.0190871 | + | 0.00277663i | ||||
\(391\) | 44.4761 | 2.24925 | ||||||||
\(392\) | −1.08501 | −0.0548011 | ||||||||
\(393\) | −2.08124 | + | 14.3069i | −0.104985 | + | 0.721686i | ||||
\(394\) | −4.31146 | − | 2.48922i | −0.217208 | − | 0.125405i | ||||
\(395\) | 7.53998 | + | 13.0596i | 0.379377 | + | 0.657101i | ||||
\(396\) | −1.98688 | + | 6.68457i | −0.0998444 | + | 0.335912i | ||||
\(397\) | −10.5922 | + | 18.3462i | −0.531606 | + | 0.920769i | 0.467713 | + | 0.883880i | \(0.345078\pi\) |
−0.999319 | + | 0.0368887i | \(0.988255\pi\) | |||||||
\(398\) | −18.1690 | −0.910731 | ||||||||
\(399\) | −13.4094 | − | 12.5436i | −0.671312 | − | 0.627964i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 11.5551 | − | 20.0141i | 0.577036 | − | 0.999456i | −0.418781 | − | 0.908087i | \(-0.637542\pi\) |
0.995817 | − | 0.0913687i | \(-0.0291242\pi\) | |||||||
\(402\) | −12.3362 | + | 4.91493i | −0.615272 | + | 0.245134i | ||||
\(403\) | −0.443015 | − | 0.767325i | −0.0220682 | − | 0.0382232i | ||||
\(404\) | 10.2389 | + | 5.91143i | 0.509404 | + | 0.294105i | ||||
\(405\) | −4.91589 | + | 7.53883i | −0.244273 | + | 0.374608i | ||||
\(406\) | 19.3969 | 0.962652 | ||||||||
\(407\) | 2.97850 | 0.147639 | ||||||||
\(408\) | 1.27814 | − | 8.78616i | 0.0632772 | − | 0.434980i | ||||
\(409\) | 8.26190 | − | 4.77001i | 0.408525 | − | 0.235862i | −0.281631 | − | 0.959523i | \(-0.590875\pi\) |
0.690156 | + | 0.723661i | \(0.257542\pi\) | |||||||
\(410\) | 2.38114i | 0.117596i | ||||||||
\(411\) | −19.8810 | − | 15.6880i | −0.980656 | − | 0.773832i | ||||
\(412\) | −15.2220 | + | 8.78844i | −0.749935 | + | 0.432975i | ||||
\(413\) | −1.16272 | + | 2.01388i | −0.0572135 | + | 0.0990967i | ||||
\(414\) | −17.8997 | − | 18.8978i | −0.879721 | − | 0.928774i | ||||
\(415\) | 2.18023 | − | 3.77627i | 0.107023 | − | 0.185370i | ||||
\(416\) | 0.190454 | + | 0.109959i | 0.00933778 | + | 0.00539117i | ||||
\(417\) | 11.8311 | − | 14.9933i | 0.579373 | − | 0.734223i | ||||
\(418\) | 10.0967 | + | 0.850025i | 0.493846 | + | 0.0415761i | ||||
\(419\) | 0.961723i | 0.0469832i | 0.999724 | + | 0.0234916i | \(0.00747830\pi\) | ||||
−0.999724 | + | 0.0234916i | \(0.992522\pi\) | |||||||
\(420\) | −3.91332 | + | 1.55913i | −0.190951 | + | 0.0760778i | ||||
\(421\) | −14.4170 | − | 8.32365i | −0.702641 | − | 0.405670i | 0.105689 | − | 0.994399i | \(-0.466295\pi\) |
−0.808330 | + | 0.588729i | \(0.799628\pi\) | |||||||
\(422\) | 2.49731 | − | 1.44183i | 0.121567 | − | 0.0701870i | ||||
\(423\) | 4.68768 | − | 15.7711i | 0.227923 | − | 0.766815i | ||||
\(424\) | 2.04507 | + | 3.54217i | 0.0993176 | + | 0.172023i | ||||
\(425\) | 5.12609i | 0.248652i | ||||||||
\(426\) | −10.8499 | + | 13.7498i | −0.525680 | + | 0.666180i | ||||
\(427\) | −10.0324 | − | 17.3767i | −0.485503 | − | 0.840915i | ||||
\(428\) | 1.40220 | + | 2.42868i | 0.0677777 | + | 0.117394i | ||||
\(429\) | −0.548493 | + | 0.695090i | −0.0264815 | + | 0.0335592i | ||||
\(430\) | 1.41086i | 0.0680376i | ||||||||
\(431\) | 5.03639 | + | 8.72328i | 0.242594 | + | 0.420185i | 0.961452 | − | 0.274971i | \(-0.0886683\pi\) |
−0.718858 | + | 0.695157i | \(0.755335\pi\) | |||||||
\(432\) | −4.24761 | + | 2.99297i | −0.204363 | + | 0.143999i | ||||
\(433\) | 5.91643 | − | 3.41585i | 0.284326 | − | 0.164155i | −0.351054 | − | 0.936355i | \(-0.614177\pi\) |
0.635380 | + | 0.772200i | \(0.280843\pi\) | |||||||
\(434\) | 8.48588 | + | 4.89933i | 0.407335 | + | 0.235175i | ||||
\(435\) | −12.8329 | + | 5.11282i | −0.615289 | + | 0.245141i | ||||
\(436\) | − | 15.9432i | − | 0.763542i | ||||||
\(437\) | −21.5909 | + | 31.0510i | −1.03283 | + | 1.48537i | ||||
\(438\) | −3.83043 | + | 4.85420i | −0.183025 | + | 0.231943i | ||||
\(439\) | 9.27371 | + | 5.35418i | 0.442610 | + | 0.255541i | 0.704704 | − | 0.709501i | \(-0.251080\pi\) |
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(440\) | 1.16227 | − | 2.01311i | 0.0554090 | − | 0.0959711i | ||||
\(441\) | 2.36321 | − | 2.23839i | 0.112534 | − | 0.106590i | ||||
\(442\) | 0.563658 | − | 0.976283i | 0.0268105 | − | 0.0464371i | ||||
\(443\) | −6.87406 | + | 3.96874i | −0.326596 | + | 0.188560i | −0.654329 | − | 0.756210i | \(-0.727049\pi\) |
0.327733 | + | 0.944771i | \(0.393715\pi\) | |||||||
\(444\) | 1.74224 | + | 1.37479i | 0.0826829 | + | 0.0652448i | ||||
\(445\) | − | 4.06081i | − | 0.192501i | ||||||
\(446\) | 12.7294 | − | 7.34931i | 0.602754 | − | 0.348000i | ||||
\(447\) | 5.26222 | − | 36.1736i | 0.248895 | − | 1.71095i | ||||
\(448\) | −2.43208 | −0.114905 | ||||||||
\(449\) | 16.3905 | 0.773515 | 0.386757 | − | 0.922181i | \(-0.373595\pi\) | ||||
0.386757 | + | 0.922181i | \(0.373595\pi\) | |||||||
\(450\) | 2.17806 | − | 2.06302i | 0.102675 | − | 0.0972519i | ||||
\(451\) | −4.79348 | − | 2.76752i | −0.225716 | − | 0.130317i | ||||
\(452\) | 6.08745 | + | 10.5438i | 0.286329 | + | 0.495937i | ||||
\(453\) | −38.9628 | + | 15.5234i | −1.83063 | + | 0.729354i | ||||
\(454\) | 5.53375 | − | 9.58473i | 0.259712 | − | 0.449834i | ||||
\(455\) | −0.534856 | −0.0250744 | ||||||||
\(456\) | 5.51358 | + | 5.15756i | 0.258197 | + | 0.241525i | ||||
\(457\) | −19.8202 | −0.927152 | −0.463576 | − | 0.886057i | \(-0.653434\pi\) | ||||
−0.463576 | + | 0.886057i | \(0.653434\pi\) | |||||||
\(458\) | −1.59769 | + | 2.76728i | −0.0746553 | + | 0.129307i | ||||
\(459\) | 15.3422 | + | 21.7736i | 0.716113 | + | 1.01630i | ||||
\(460\) | 4.33821 | + | 7.51400i | 0.202270 | + | 0.350342i | ||||
\(461\) | 35.9630 | + | 20.7632i | 1.67496 | + | 0.967040i | 0.964793 | + | 0.263010i | \(0.0847152\pi\) |
0.710170 | + | 0.704030i | \(0.248618\pi\) | |||||||
\(462\) | 1.40963 | − | 9.69007i | 0.0655819 | − | 0.450823i | ||||
\(463\) | 20.2445 | 0.940843 | 0.470422 | − | 0.882442i | \(-0.344102\pi\) | ||||
0.470422 | + | 0.882442i | \(0.344102\pi\) | |||||||
\(464\) | −7.97545 | −0.370251 | ||||||||
\(465\) | −6.90562 | − | 1.00457i | −0.320240 | − | 0.0465859i | ||||
\(466\) | 6.96020 | − | 4.01848i | 0.322425 | − | 0.186152i | ||||
\(467\) | − | 10.1496i | − | 0.469667i | −0.972036 | − | 0.234833i | \(-0.924546\pi\) | ||
0.972036 | − | 0.234833i | \(-0.0754544\pi\) | |||||||
\(468\) | −0.641667 | + | 0.153415i | −0.0296611 | + | 0.00709160i | ||||
\(469\) | 16.1480 | − | 9.32306i | 0.745646 | − | 0.430499i | ||||
\(470\) | −2.74216 | + | 4.74957i | −0.126487 | + | 0.219081i | ||||
\(471\) | 22.1567 | + | 3.22318i | 1.02093 | + | 0.148516i | ||||
\(472\) | 0.478076 | − | 0.828051i | 0.0220052 | − | 0.0381142i | ||||
\(473\) | −2.84021 | − | 1.63980i | −0.130593 | − | 0.0753979i | ||||
\(474\) | −20.5043 | − | 16.1799i | −0.941794 | − | 0.743166i | ||||
\(475\) | −3.57877 | − | 2.48845i | −0.164205 | − | 0.114178i | ||||
\(476\) | 12.4670i | 0.571425i | ||||||||
\(477\) | −11.7619 | − | 3.49602i | −0.538539 | − | 0.160072i | ||||
\(478\) | −4.48081 | − | 2.58700i | −0.204947 | − | 0.118326i | ||||
\(479\) | 35.2374 | − | 20.3443i | 1.61004 | − | 0.929555i | 0.620676 | − | 0.784067i | \(-0.286858\pi\) |
0.989360 | − | 0.145488i | \(-0.0464751\pi\) | |||||||
\(480\) | 1.60905 | − | 0.641070i | 0.0734426 | − | 0.0292607i | ||||
\(481\) | 0.140894 | + | 0.244035i | 0.00642420 | + | 0.0111270i | ||||
\(482\) | − | 29.3904i | − | 1.33870i | ||||||
\(483\) | 28.6921 | + | 22.6409i | 1.30554 | + | 1.03020i | ||||
\(484\) | −2.79827 | − | 4.84674i | −0.127194 | − | 0.220306i | ||||
\(485\) | −3.52627 | − | 6.10768i | −0.160120 | − | 0.277335i | ||||
\(486\) | 3.07697 | − | 15.2818i | 0.139574 | − | 0.693195i | ||||
\(487\) | 14.4557i | 0.655048i | 0.944843 | + | 0.327524i | \(0.106214\pi\) | ||||
−0.944843 | + | 0.327524i | \(0.893786\pi\) | |||||||
\(488\) | 4.12504 | + | 7.14478i | 0.186732 | + | 0.323429i | ||||
\(489\) | −8.73217 | − | 21.9172i | −0.394883 | − | 0.991130i | ||||
\(490\) | −0.939644 | + | 0.542503i | −0.0424488 | + | 0.0245078i | ||||
\(491\) | −13.6141 | − | 7.86008i | −0.614394 | − | 0.354721i | 0.160289 | − | 0.987070i | \(-0.448757\pi\) |
−0.774683 | + | 0.632350i | \(0.782091\pi\) | |||||||
\(492\) | −1.52648 | − | 3.83136i | −0.0688189 | − | 0.172731i | ||||
\(493\) | 40.8828i | 1.84127i | ||||||||
\(494\) | 0.407965 | + | 0.867452i | 0.0183552 | + | 0.0390285i | ||||
\(495\) | 1.62160 | + | 6.78245i | 0.0728855 | + | 0.304848i | ||||
\(496\) | −3.48915 | − | 2.01446i | −0.156668 | − | 0.0904521i | ||||
\(497\) | 12.2970 | − | 21.2990i | 0.551595 | − | 0.955390i | ||||
\(498\) | −1.08724 | + | 7.47388i | −0.0487203 | + | 0.334913i | ||||
\(499\) | −16.7701 | + | 29.0466i | −0.750731 | + | 1.30030i | 0.196738 | + | 0.980456i | \(0.436965\pi\) |
−0.947469 | + | 0.319848i | \(0.896368\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | 11.6526 | − | 14.7670i | 0.520598 | − | 0.659739i | ||||
\(502\) | − | 25.0670i | − | 1.11879i | ||||||
\(503\) | −7.23726 | + | 4.17843i | −0.322694 | + | 0.186307i | −0.652593 | − | 0.757709i | \(-0.726319\pi\) |
0.329899 | + | 0.944016i | \(0.392985\pi\) | |||||||
\(504\) | 5.29720 | − | 5.01743i | 0.235956 | − | 0.223494i | ||||
\(505\) | 11.8229 | 0.526110 | ||||||||
\(506\) | −20.1687 | −0.896606 | ||||||||
\(507\) | 22.1992 | + | 3.22936i | 0.985903 | + | 0.143421i | ||||
\(508\) | −2.43948 | − | 1.40844i | −0.108235 | − | 0.0624893i | ||||
\(509\) | −14.3398 | − | 24.8373i | −0.635602 | − | 1.10090i | −0.986387 | − | 0.164440i | \(-0.947418\pi\) |
0.350785 | − | 0.936456i | \(-0.385915\pi\) | |||||||
\(510\) | −3.28618 | − | 8.24811i | −0.145515 | − | 0.365232i | ||||
\(511\) | 4.34130 | − | 7.51935i | 0.192048 | − | 0.332636i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −22.6491 | + | 0.141188i | −0.999981 | + | 0.00623360i | ||||
\(514\) | 4.61909 | 0.203739 | ||||||||
\(515\) | −8.78844 | + | 15.2220i | −0.387265 | + | 0.670762i | ||||
\(516\) | −0.904459 | − | 2.27014i | −0.0398166 | − | 0.0999371i | ||||
\(517\) | −6.37426 | − | 11.0405i | −0.280340 | − | 0.485562i | ||||
\(518\) | −2.69879 | − | 1.55815i | −0.118578 | − | 0.0684612i | ||||
\(519\) | −20.7315 | − | 3.01584i | −0.910010 | − | 0.132381i | ||||
\(520\) | 0.219917 | 0.00964401 | ||||||||
\(521\) | 22.1970 | 0.972468 | 0.486234 | − | 0.873829i | \(-0.338370\pi\) | ||||
0.486234 | + | 0.873829i | \(0.338370\pi\) | |||||||
\(522\) | 17.3710 | − | 16.4535i | 0.760307 | − | 0.720152i | ||||
\(523\) | 22.4245 | − | 12.9468i | 0.980554 | − | 0.566123i | 0.0781167 | − | 0.996944i | \(-0.475109\pi\) |
0.902437 | + | 0.430821i | \(0.141776\pi\) | |||||||
\(524\) | 8.34702i | 0.364641i | ||||||||
\(525\) | −2.60947 | + | 3.30691i | −0.113887 | + | 0.144325i | ||||
\(526\) | −24.7674 | + | 14.2995i | −1.07991 | + | 0.623487i | ||||
\(527\) | −10.3263 | + | 17.8857i | −0.449821 | + | 0.779113i | ||||
\(528\) | −0.579599 | + | 3.98428i | −0.0252238 | + | 0.173393i | ||||
\(529\) | 26.1402 | − | 45.2761i | 1.13653 | − | 1.96853i | ||||
\(530\) | 3.54217 | + | 2.04507i | 0.153862 | + | 0.0888323i | ||||
\(531\) | 0.667013 | + | 2.78983i | 0.0289459 | + | 0.121068i | ||||
\(532\) | −8.70385 | − | 6.05210i | −0.377360 | − | 0.262392i | ||||
\(533\) | − | 0.523653i | − | 0.0226819i | ||||||
\(534\) | 2.60327 | + | 6.53403i | 0.112654 | + | 0.282755i | ||||
\(535\) | 2.42868 | + | 1.40220i | 0.105001 | + | 0.0606223i | ||||
\(536\) | −6.63960 | + | 3.83338i | −0.286787 | + | 0.165577i | ||||
\(537\) | −5.88104 | − | 14.7610i | −0.253786 | − | 0.636986i | ||||
\(538\) | 1.62587 | + | 2.81609i | 0.0700963 | + | 0.121410i | ||||
\(539\) | − | 2.52214i | − | 0.108636i | ||||||
\(540\) | −2.18205 | + | 4.71579i | −0.0939006 | + | 0.202935i | ||||
\(541\) | −5.15671 | − | 8.93169i | −0.221704 | − | 0.384003i | 0.733621 | − | 0.679559i | \(-0.237829\pi\) |
−0.955326 | + | 0.295555i | \(0.904495\pi\) | |||||||
\(542\) | −3.17133 | − | 5.49291i | −0.136220 | − | 0.235940i | ||||
\(543\) | 13.1472 | + | 10.3744i | 0.564200 | + | 0.445208i | ||||
\(544\) | − | 5.12609i | − | 0.219779i | ||||||
\(545\) | −7.97161 | − | 13.8072i | −0.341466 | − | 0.591437i | ||||
\(546\) | 0.860607 | − | 0.342880i | 0.0368306 | − | 0.0146739i | ||||
\(547\) | −6.35260 | + | 3.66767i | −0.271618 | + | 0.156818i | −0.629622 | − | 0.776901i | \(-0.716790\pi\) |
0.358005 | + | 0.933720i | \(0.383457\pi\) | |||||||
\(548\) | −12.6626 | − | 7.31076i | −0.540920 | − | 0.312300i | ||||
\(549\) | −23.7244 | − | 7.05169i | −1.01253 | − | 0.300959i | ||||
\(550\) | − | 2.32454i | − | 0.0991185i | ||||||
\(551\) | −28.5423 | − | 19.8465i | −1.21594 | − | 0.845490i | ||||
\(552\) | −11.7974 | − | 9.30928i | −0.502130 | − | 0.396229i | ||||
\(553\) | 31.7620 | + | 18.3378i | 1.35066 | + | 0.779802i | ||||
\(554\) | −11.0835 | + | 19.1972i | −0.470893 | + | 0.815611i | ||||
\(555\) | 2.19622 | + | 0.319487i | 0.0932242 | + | 0.0135615i | ||||
\(556\) | 5.51342 | − | 9.54952i | 0.233821 | − | 0.404990i | ||||
\(557\) | −12.9817 | + | 7.49498i | −0.550051 | + | 0.317572i | −0.749143 | − | 0.662409i | \(-0.769534\pi\) |
0.199091 | + | 0.979981i | \(0.436201\pi\) | |||||||
\(558\) | 11.7555 | − | 2.81059i | 0.497648 | − | 0.118982i | ||||
\(559\) | − | 0.310272i | − | 0.0131231i | ||||||
\(560\) | −2.10624 | + | 1.21604i | −0.0890049 | + | 0.0513870i | ||||
\(561\) | 20.4237 | + | 2.97108i | 0.862291 | + | 0.125439i | ||||
\(562\) | −15.7114 | −0.662746 | ||||||||
\(563\) | −19.5385 | −0.823450 | −0.411725 | − | 0.911308i | \(-0.635074\pi\) | ||||
−0.411725 | + | 0.911308i | \(0.635074\pi\) | |||||||
\(564\) | 1.36746 | − | 9.40019i | 0.0575805 | − | 0.395819i | ||||
\(565\) | 10.5438 | + | 6.08745i | 0.443580 | + | 0.256101i | ||||
\(566\) | −10.1514 | − | 17.5827i | −0.426693 | − | 0.739054i | ||||
\(567\) | −1.18654 | + | 21.8565i | −0.0498298 | + | 0.917887i | ||||
\(568\) | −5.05616 | + | 8.75753i | −0.212152 | + | 0.367458i | ||||
\(569\) | −43.9934 | −1.84430 | −0.922149 | − | 0.386835i | \(-0.873568\pi\) | ||||
−0.922149 | + | 0.386835i | \(0.873568\pi\) | |||||||
\(570\) | 7.35368 | + | 1.70979i | 0.308012 | + | 0.0716151i | ||||
\(571\) | −17.0307 | −0.712711 | −0.356356 | − | 0.934350i | \(-0.615981\pi\) | ||||
−0.356356 | + | 0.934350i | \(0.615981\pi\) | |||||||
\(572\) | −0.255603 | + | 0.442717i | −0.0106873 | + | 0.0185109i | ||||
\(573\) | −30.1234 | + | 12.0017i | −1.25842 | + | 0.501377i | ||||
\(574\) | 2.89555 | + | 5.01525i | 0.120858 | + | 0.209332i | ||||
\(575\) | 7.51400 | + | 4.33821i | 0.313356 | + | 0.180916i | ||||
\(576\) | −2.17806 | + | 2.06302i | −0.0907524 | + | 0.0859593i | ||||
\(577\) | −13.3602 | −0.556192 | −0.278096 | − | 0.960553i | \(-0.589703\pi\) | ||||
−0.278096 | + | 0.960553i | \(0.589703\pi\) | |||||||
\(578\) | −9.27675 | −0.385862 | ||||||||
\(579\) | −6.10254 | + | 41.9500i | −0.253613 | + | 1.74338i | ||||
\(580\) | −6.90694 | + | 3.98772i | −0.286795 | + | 0.165581i | ||||
\(581\) | − | 10.6050i | − | 0.439969i | ||||||
\(582\) | 9.58938 | + | 7.56695i | 0.397493 | + | 0.313660i | ||||
\(583\) | −8.23391 | + | 4.75385i | −0.341014 | + | 0.196884i | ||||
\(584\) | −1.78502 | + | 3.09174i | −0.0738646 | + | 0.127937i | ||||
\(585\) | −0.478993 | + | 0.453695i | −0.0198039 | + | 0.0187580i | ||||
\(586\) | 8.05424 | − | 13.9503i | 0.332717 | − | 0.576283i | ||||
\(587\) | −23.1836 | − | 13.3851i | −0.956891 | − | 0.552461i | −0.0616763 | − | 0.998096i | \(-0.519645\pi\) |
−0.895215 | + | 0.445635i | \(0.852978\pi\) | |||||||
\(588\) | 1.16415 | − | 1.47529i | 0.0480086 | − | 0.0608400i | ||||
\(589\) | −7.47399 | − | 15.8919i | −0.307960 | − | 0.654814i | ||||
\(590\) | − | 0.956151i | − | 0.0393641i | ||||||
\(591\) | 8.01055 | − | 3.19153i | 0.329510 | − | 0.131282i | ||||
\(592\) | 1.10967 | + | 0.640666i | 0.0456070 | + | 0.0263312i | ||||
\(593\) | −8.48127 | + | 4.89666i | −0.348284 | + | 0.201082i | −0.663929 | − | 0.747795i | \(-0.731112\pi\) |
0.315645 | + | 0.948877i | \(0.397779\pi\) | |||||||
\(594\) | −6.95726 | − | 9.87371i | −0.285460 | − | 0.405123i | ||||
\(595\) | 6.23351 | + | 10.7968i | 0.255549 | + | 0.442624i | ||||
\(596\) | − | 21.1046i | − | 0.864480i | ||||||
\(597\) | 19.4943 | − | 24.7045i | 0.797847 | − | 1.01109i | ||||
\(598\) | −0.954048 | − | 1.65246i | −0.0390139 | − | 0.0675741i | ||||
\(599\) | 13.4316 | + | 23.2641i | 0.548799 | + | 0.950547i | 0.998357 | + | 0.0572961i | \(0.0182479\pi\) |
−0.449559 | + | 0.893251i | \(0.648419\pi\) | |||||||
\(600\) | 1.07294 | − | 1.35971i | 0.0438026 | − | 0.0555098i | ||||
\(601\) | − | 26.9483i | − | 1.09925i | −0.835413 | − | 0.549623i | \(-0.814771\pi\) | ||
0.835413 | − | 0.549623i | \(-0.185229\pi\) | |||||||
\(602\) | 1.71566 | + | 2.97160i | 0.0699250 | + | 0.121114i | ||||
\(603\) | 6.55309 | − | 22.0470i | 0.266863 | − | 0.897822i | ||||
\(604\) | −20.9707 | + | 12.1074i | −0.853285 | + | 0.492644i | ||||
\(605\) | −4.84674 | − | 2.79827i | −0.197048 | − | 0.113766i | ||||
\(606\) | −19.0235 | + | 7.57929i | −0.772778 | + | 0.307887i | ||||
\(607\) | − | 24.9777i | − | 1.01381i | −0.862001 | − | 0.506906i | \(-0.830789\pi\) | ||
0.862001 | − | 0.506906i | \(-0.169211\pi\) | |||||||
\(608\) | 3.57877 | + | 2.48845i | 0.145138 | + | 0.100920i | ||||
\(609\) | −20.8117 | + | 26.3741i | −0.843332 | + | 1.06873i | ||||
\(610\) | 7.14478 | + | 4.12504i | 0.289284 | + | 0.167018i | ||||
\(611\) | 0.603049 | − | 1.04451i | 0.0243968 | − | 0.0422564i | ||||
\(612\) | 10.5752 | + | 11.1649i | 0.427479 | + | 0.451315i | ||||
\(613\) | 5.51510 | − | 9.55243i | 0.222753 | − | 0.385819i | −0.732890 | − | 0.680347i | \(-0.761829\pi\) |
0.955643 | + | 0.294528i | \(0.0951624\pi\) | |||||||
\(614\) | −6.95957 | + | 4.01811i | −0.280865 | + | 0.162158i | ||||
\(615\) | −3.23765 | − | 2.55482i | −0.130555 | − | 0.103020i | ||||
\(616\) | − | 5.65345i | − | 0.227784i | ||||||
\(617\) | 16.4524 | − | 9.49880i | 0.662349 | − | 0.382407i | −0.130823 | − | 0.991406i | \(-0.541762\pi\) |
0.793171 | + | 0.608999i | \(0.208429\pi\) | |||||||
\(618\) | 4.38261 | − | 30.1269i | 0.176295 | − | 1.21188i | ||||
\(619\) | −39.2407 | −1.57722 | −0.788608 | − | 0.614896i | \(-0.789198\pi\) | ||||
−0.788608 | + | 0.614896i | \(0.789198\pi\) | |||||||
\(620\) | −4.02893 | −0.161806 | ||||||||
\(621\) | 44.9007 | − | 4.06214i | 1.80180 | − | 0.163008i | ||||
\(622\) | 17.5450 | + | 10.1296i | 0.703489 | + | 0.406159i | ||||
\(623\) | −4.93810 | − | 8.55304i | −0.197841 | − | 0.342670i | ||||
\(624\) | −0.353857 | + | 0.140982i | −0.0141656 | + | 0.00564382i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 24.0478 | 0.961144 | ||||||||
\(627\) | −11.9889 | + | 12.8165i | −0.478792 | + | 0.511843i | ||||
\(628\) | 12.9269 | 0.515837 | ||||||||
\(629\) | 3.28411 | − | 5.68825i | 0.130946 | − | 0.226805i | ||||
\(630\) | 2.07880 | − | 6.99382i | 0.0828212 | − | 0.278641i | ||||
\(631\) | 9.58134 | + | 16.5954i | 0.381427 | + | 0.660651i | 0.991266 | − | 0.131874i | \(-0.0420994\pi\) |
−0.609840 | + | 0.792525i | \(0.708766\pi\) | |||||||
\(632\) | −13.0596 | − | 7.53998i | −0.519484 | − | 0.299924i | ||||
\(633\) | −0.719009 | + | 4.94261i | −0.0285780 | + | 0.196451i | ||||
\(634\) | −12.5398 | −0.498017 | ||||||||
\(635\) | −2.81687 | −0.111784 | ||||||||
\(636\) | −7.01055 | − | 1.01984i | −0.277987 | − | 0.0404391i | ||||
\(637\) | 0.206644 | − | 0.119306i | 0.00818753 | − | 0.00472707i | ||||
\(638\) | − | 18.5392i | − | 0.733975i | ||||||
\(639\) | −7.05438 | − | 29.5054i | −0.279067 | − | 1.16722i | ||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | 15.7483 | − | 27.2768i | 0.622020 | − | 1.07737i | −0.367090 | − | 0.930186i | \(-0.619646\pi\) |
0.989109 | − | 0.147184i | \(-0.0470209\pi\) | |||||||
\(642\) | −4.80676 | − | 0.699247i | −0.189708 | − | 0.0275971i | ||||
\(643\) | 4.48834 | − | 7.77403i | 0.177003 | − | 0.306578i | −0.763850 | − | 0.645394i | \(-0.776693\pi\) |
0.940853 | + | 0.338816i | \(0.110027\pi\) | |||||||
\(644\) | 18.2746 | + | 10.5509i | 0.720121 | + | 0.415762i | ||||
\(645\) | −1.91835 | − | 1.51377i | −0.0755350 | − | 0.0596044i | ||||
\(646\) | 12.7560 | − | 18.3451i | 0.501879 | − | 0.721778i | ||||
\(647\) | 4.22420i | 0.166071i | 0.996547 | + | 0.0830353i | \(0.0264614\pi\) | ||||
−0.996547 | + | 0.0830353i | \(0.973539\pi\) | |||||||
\(648\) | 0.487870 | − | 8.98677i | 0.0191653 | − | 0.353034i | ||||
\(649\) | 1.92484 | + | 1.11130i | 0.0755564 | + | 0.0436225i | ||||
\(650\) | 0.190454 | − | 0.109959i | 0.00747022 | − | 0.00431293i | ||||
\(651\) | −15.7665 | + | 6.28163i | −0.617937 | + | 0.246196i | ||||
\(652\) | −6.81062 | − | 11.7963i | −0.266724 | − | 0.461980i | ||||
\(653\) | − | 20.4175i | − | 0.798999i | −0.916733 | − | 0.399499i | \(-0.869184\pi\) | ||
0.916733 | − | 0.399499i | \(-0.130816\pi\) | |||||||
\(654\) | 21.6781 | + | 17.1061i | 0.847681 | + | 0.668902i | ||||
\(655\) | 4.17351 | + | 7.22873i | 0.163073 | + | 0.282450i | ||||
\(656\) | −1.19057 | − | 2.06213i | −0.0464839 | − | 0.0805125i | ||||
\(657\) | −2.49046 | − | 10.4165i | −0.0971622 | − | 0.406387i | ||||
\(658\) | 13.3383i | 0.519981i | ||||||||
\(659\) | 20.4046 | + | 35.3417i | 0.794849 | + | 1.37672i | 0.922935 | + | 0.384955i | \(0.125783\pi\) |
−0.128086 | + | 0.991763i | \(0.540883\pi\) | |||||||
\(660\) | 1.49019 | + | 3.74029i | 0.0580056 | + | 0.145590i | ||||
\(661\) | −6.66358 | + | 3.84722i | −0.259183 | + | 0.149640i | −0.623962 | − | 0.781455i | \(-0.714478\pi\) |
0.364779 | + | 0.931094i | \(0.381145\pi\) | |||||||
\(662\) | −4.39071 | − | 2.53498i | −0.170650 | − | 0.0985247i | ||||
\(663\) | 0.722688 | + | 1.81390i | 0.0280669 | + | 0.0704461i | ||||
\(664\) | 4.36047i | 0.169219i | ||||||||
\(665\) | −10.5638 | − | 0.889349i | −0.409647 | − | 0.0344875i | ||||
\(666\) | −3.73863 | + | 0.893860i | −0.144869 | + | 0.0346364i | ||||
\(667\) | 59.9276 | + | 34.5992i | 2.32040 | + | 1.33969i | ||||
\(668\) | 5.43020 | − | 9.40538i | 0.210101 | − | 0.363905i | ||||
\(669\) | −3.66495 | + | 25.1936i | −0.141695 | + | 0.974040i | ||||
\(670\) | −3.83338 | + | 6.63960i | −0.148096 | + | 0.256510i | ||||
\(671\) | −16.6083 | + | 9.58881i | −0.641157 | + | 0.370172i | ||||
\(672\) | 2.60947 | − | 3.30691i | 0.100662 | − | 0.127567i | ||||
\(673\) | − | 10.6822i | − | 0.411770i | −0.978576 | − | 0.205885i | \(-0.933993\pi\) | ||
0.978576 | − | 0.205885i | \(-0.0660073\pi\) | |||||||
\(674\) | −3.52448 | + | 2.03486i | −0.135758 | + | 0.0783798i | ||||
\(675\) | 0.468182 | + | 5.17502i | 0.0180203 | + | 0.199187i | ||||
\(676\) | 12.9516 | 0.498140 | ||||||||
\(677\) | 12.9215 | 0.496612 | 0.248306 | − | 0.968682i | \(-0.420126\pi\) | ||||
0.248306 | + | 0.968682i | \(0.420126\pi\) | |||||||
\(678\) | −20.8679 | − | 3.03568i | −0.801426 | − | 0.116585i | ||||
\(679\) | −14.8543 | − | 8.57615i | −0.570057 | − | 0.329123i | ||||
\(680\) | −2.56304 | − | 4.43932i | −0.0982882 | − | 0.170240i | ||||
\(681\) | 7.09504 | + | 17.8081i | 0.271883 | + | 0.682408i | ||||
\(682\) | 4.68269 | − | 8.11066i | 0.179310 | − | 0.310573i | ||||
\(683\) | −39.7388 | −1.52056 | −0.760282 | − | 0.649593i | \(-0.774939\pi\) | ||||
−0.760282 | + | 0.649593i | \(0.774939\pi\) | |||||||
\(684\) | −12.9285 | + | 1.96310i | −0.494334 | + | 0.0750611i | ||||
\(685\) | −14.6215 | −0.558660 | ||||||||
\(686\) | −9.83168 | + | 17.0290i | −0.375375 | + | 0.650169i | ||||
\(687\) | −2.04847 | − | 5.14152i | −0.0781539 | − | 0.196161i | ||||
\(688\) | −0.705429 | − | 1.22184i | −0.0268942 | − | 0.0465822i | ||||
\(689\) | −0.778985 | − | 0.449747i | −0.0296770 | − | 0.0171340i | ||||
\(690\) | −14.8715 | − | 2.16338i | −0.566147 | − | 0.0823584i | ||||
\(691\) | −9.39689 | −0.357474 | −0.178737 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178737 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(692\) | −12.0953 | −0.459794 | ||||||||
\(693\) | 11.6632 | + | 12.3135i | 0.443048 | + | 0.467753i | ||||
\(694\) | −4.31415 | + | 2.49077i | −0.163763 | + | 0.0945485i | ||||
\(695\) | − | 11.0268i | − | 0.418272i | ||||||
\(696\) | 8.55717 | − | 10.8443i | 0.324359 | − | 0.411051i | ||||
\(697\) | −10.5706 | + | 6.10296i | −0.400391 | + | 0.231166i | ||||
\(698\) | −8.61647 | + | 14.9242i | −0.326138 | + | 0.564888i | ||||
\(699\) | −2.00393 | + | 13.7754i | −0.0757956 | + | 0.521034i | ||||
\(700\) | −1.21604 | + | 2.10624i | −0.0459619 | + | 0.0796084i | ||||
\(701\) | 21.4383 | + | 12.3774i | 0.809713 | + | 0.467488i | 0.846856 | − | 0.531822i | \(-0.178492\pi\) |
−0.0371431 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(702\) | 0.479871 | − | 1.03708i | 0.0181116 | − | 0.0391422i | ||||
\(703\) | 2.37698 | + | 5.05415i | 0.0896494 | + | 0.190621i | ||||
\(704\) | 2.32454i | 0.0876092i | ||||||||
\(705\) | −3.51584 | − | 8.82453i | −0.132414 | − | 0.332351i | ||||
\(706\) | −23.0693 | − | 13.3191i | −0.868226 | − | 0.501270i | ||||
\(707\) | 24.9018 | − | 14.3770i | 0.936528 | − | 0.540705i | ||||
\(708\) | 0.612960 | + | 1.53849i | 0.0230365 | + | 0.0578201i | ||||
\(709\) | 6.84044 | + | 11.8480i | 0.256898 | + | 0.444960i | 0.965409 | − | 0.260739i | \(-0.0839662\pi\) |
−0.708511 | + | 0.705699i | \(0.750633\pi\) | |||||||
\(710\) | 10.1123i | 0.379509i | ||||||||
\(711\) | 43.9997 | − | 10.5198i | 1.65012 | − | 0.394523i | ||||
\(712\) | 2.03041 | + | 3.51677i | 0.0760927 | + | 0.131796i | ||||
\(713\) | 17.4783 | + | 30.2734i | 0.654569 | + | 1.13375i | ||||
\(714\) | −16.9515 | − | 13.3764i | −0.634394 | − | 0.500598i | ||||
\(715\) | 0.511206i | 0.0191180i | ||||||||
\(716\) | −4.58689 | − | 7.94473i | −0.171420 | − | 0.296908i | ||||
\(717\) | 8.32519 | − | 3.31689i | 0.310910 | − | 0.123872i | ||||
\(718\) | −25.0199 | + | 14.4453i | −0.933736 | + | 0.539093i | ||||
\(719\) | 16.2403 | + | 9.37635i | 0.605661 | + | 0.349679i | 0.771265 | − | 0.636514i | \(-0.219624\pi\) |
−0.165604 | + | 0.986192i | \(0.552957\pi\) | |||||||
\(720\) | −0.854742 | + | 2.87566i | −0.0318543 | + | 0.107169i | ||||
\(721\) | 42.7483i | 1.59203i | ||||||||
\(722\) | 6.61523 | + | 17.8112i | 0.246193 | + | 0.662864i | ||||
\(723\) | 39.9623 | + | 31.5341i | 1.48621 | + | 1.17277i | ||||
\(724\) | 8.37372 | + | 4.83457i | 0.311207 | + | 0.179675i | ||||
\(725\) | −3.98772 | + | 6.90694i | −0.148100 | + | 0.256517i | ||||
\(726\) | 9.59251 | + | 1.39544i | 0.356011 | + | 0.0517896i | ||||
\(727\) | 24.9453 | − | 43.2065i | 0.925170 | − | 1.60244i | 0.133883 | − | 0.990997i | \(-0.457255\pi\) |
0.791287 | − | 0.611445i | \(-0.209411\pi\) | |||||||
\(728\) | 0.463199 | − | 0.267428i | 0.0171673 | − | 0.00991153i | ||||
\(729\) | 17.4773 | + | 20.5802i | 0.647307 | + | 0.762229i | ||||
\(730\) | 3.57004i | 0.132133i | ||||||||
\(731\) | −6.26325 | + | 3.61609i | −0.231655 | + | 0.133746i | ||||
\(732\) | −14.1407 | − | 2.05707i | −0.522656 | − | 0.0760317i | ||||
\(733\) | 28.7958 | 1.06360 | 0.531799 | − | 0.846870i | \(-0.321516\pi\) | ||||
0.531799 | + | 0.846870i | \(0.321516\pi\) | |||||||
\(734\) | 20.3340 | 0.750542 | ||||||||
\(735\) | 0.270535 | − | 1.85971i | 0.00997885 | − | 0.0685965i | ||||
\(736\) | −7.51400 | − | 4.33821i | −0.276970 | − | 0.159909i | ||||
\(737\) | −8.91082 | − | 15.4340i | −0.328234 | − | 0.568519i | ||||
\(738\) | 6.84734 | + | 2.03526i | 0.252054 | + | 0.0749188i | ||||
\(739\) | −11.8821 | + | 20.5805i | −0.437092 | + | 0.757065i | −0.997464 | − | 0.0711761i | \(-0.977325\pi\) |
0.560372 | + | 0.828241i | \(0.310658\pi\) | |||||||
\(740\) | 1.28133 | 0.0471027 | ||||||||
\(741\) | −1.61720 | − | 0.376012i | −0.0594094 | − | 0.0138131i | ||||
\(742\) | 9.94755 | 0.365186 | ||||||||
\(743\) | −3.44798 | + | 5.97208i | −0.126494 | + | 0.219094i | −0.922316 | − | 0.386437i | \(-0.873706\pi\) |
0.795822 | + | 0.605531i | \(0.207039\pi\) | |||||||
\(744\) | 6.48273 | − | 2.58282i | 0.237668 | − | 0.0946910i | ||||
\(745\) | −10.5523 | − | 18.2772i | −0.386607 | − | 0.669623i | ||||
\(746\) | 10.5873 | + | 6.11260i | 0.387630 | + | 0.223798i | ||||
\(747\) | −8.99574 | − | 9.49735i | −0.329137 | − | 0.347490i | ||||
\(748\) | 11.9158 | 0.435684 | ||||||||
\(749\) | 6.82050 | 0.249216 | ||||||||
\(750\) | 0.249340 | − | 1.71401i | 0.00910460 | − | 0.0625868i | ||||
\(751\) | −36.8595 | + | 21.2808i | −1.34502 | + | 0.776548i | −0.987539 | − | 0.157372i | \(-0.949698\pi\) |
−0.357482 | + | 0.933920i | \(0.616365\pi\) | |||||||
\(752\) | − | 5.48433i | − | 0.199993i | ||||||
\(753\) | 34.0837 | + | 26.8953i | 1.24208 | + | 0.980121i | ||||
\(754\) | 1.51896 | − | 0.876970i | 0.0553171 | − | 0.0319373i | ||||
\(755\) | −12.1074 | + | 20.9707i | −0.440634 | + | 0.763201i | ||||
\(756\) | 1.13865 | + | 12.5860i | 0.0414124 | + | 0.457750i | ||||
\(757\) | −15.7761 | + | 27.3249i | −0.573391 | + | 0.993142i | 0.422824 | + | 0.906212i | \(0.361039\pi\) |
−0.996214 | + | 0.0869297i | \(0.972294\pi\) | |||||||
\(758\) | 32.1987 | + | 18.5899i | 1.16951 | + | 0.675217i | ||||
\(759\) | 21.6398 | − | 27.4235i | 0.785473 | − | 0.995408i | ||||
\(760\) | 4.34353 | + | 0.365675i | 0.157557 | + | 0.0132644i | ||||
\(761\) | 22.6385i | 0.820646i | 0.911940 | + | 0.410323i | \(0.134584\pi\) | ||||
−0.911940 | + | 0.410323i | \(0.865416\pi\) | |||||||
\(762\) | 4.53248 | − | 1.80581i | 0.164194 | − | 0.0654177i | ||||
\(763\) | −33.5803 | − | 19.3876i | −1.21569 | − | 0.701877i | ||||
\(764\) | −16.2131 | + | 9.36065i | −0.586570 | + | 0.338656i | ||||
\(765\) | 14.7409 | + | 4.38148i | 0.532958 | + | 0.158413i | ||||
\(766\) | −2.24543 | − | 3.88919i | −0.0811305 | − | 0.140522i | ||||
\(767\) | 0.210274i | 0.00759256i | ||||||||
\(768\) | −1.07294 | + | 1.35971i | −0.0387164 | + | 0.0490642i | ||||
\(769\) | 0.580659 | + | 1.00573i | 0.0209391 | + | 0.0362676i | 0.876305 | − | 0.481757i | \(-0.160001\pi\) |
−0.855366 | + | 0.518024i | \(0.826668\pi\) | |||||||
\(770\) | −2.82672 | − | 4.89603i | −0.101868 | − | 0.176441i | ||||
\(771\) | −4.95601 | + | 6.28061i | −0.178486 | + | 0.226191i | ||||
\(772\) | 24.4748i | 0.880867i | ||||||||
\(773\) | −7.13678 | − | 12.3613i | −0.256692 | − | 0.444604i | 0.708661 | − | 0.705549i | \(-0.249299\pi\) |
−0.965354 | + | 0.260945i | \(0.915966\pi\) | |||||||
\(774\) | 4.05715 | + | 1.20592i | 0.145831 | + | 0.0433459i | ||||
\(775\) | −3.48915 | + | 2.01446i | −0.125334 | + | 0.0723616i | ||||
\(776\) | 6.10768 | + | 3.52627i | 0.219253 | + | 0.126586i | ||||
\(777\) | 5.01427 | − | 1.99777i | 0.179886 | − | 0.0716695i | ||||
\(778\) | 26.6064i | 0.953886i | ||||||||
\(779\) | 0.870722 | − | 10.3425i | 0.0311969 | − | 0.370560i | ||||
\(780\) | −0.235958 | + | 0.299023i | −0.00844865 | + | 0.0107067i | ||||
\(781\) | −20.3572 | − | 11.7532i | −0.728438 | − | 0.420564i | ||||
\(782\) | −22.2380 | + | 38.5174i | −0.795231 | + | 1.37738i | ||||
\(783\) | 3.73396 | + | 41.2731i | 0.133441 | + | 1.47498i | ||||
\(784\) | 0.542503 | − | 0.939644i | 0.0193751 | − | 0.0335587i | ||||
\(785\) | 11.1950 | − | 6.46343i | 0.399566 | − | 0.230690i | ||||
\(786\) | −11.3495 | − | 8.95585i | −0.404823 | − | 0.319445i | ||||
\(787\) | 35.6942i | 1.27236i | 0.771540 | + | 0.636181i | \(0.219487\pi\) | ||||
−0.771540 | + | 0.636181i | \(0.780513\pi\) | |||||||
\(788\) | 4.31146 | − | 2.48922i | 0.153589 | − | 0.0886749i | ||||
\(789\) | 7.13086 | − | 49.0189i | 0.253865 | − | 1.74512i | ||||
\(790\) | −15.0800 | −0.536521 | ||||||||
\(791\) | 29.6103 | 1.05282 | ||||||||
\(792\) | −4.79557 | − | 5.06297i | −0.170403 | − | 0.179905i | ||||
\(793\) | −1.57126 | − | 0.907168i | −0.0557971 | − | 0.0322145i | ||||
\(794\) | −10.5922 | − | 18.3462i | −0.375902 | − | 0.651082i | ||||
\(795\) | −6.58124 | + | 2.62207i | −0.233412 | + | 0.0929953i | ||||
\(796\) | 9.08451 | − | 15.7348i | 0.321992 | − | 0.557707i | ||||
\(797\) | 33.7963 | 1.19713 | 0.598563 | − | 0.801076i | \(-0.295739\pi\) | ||||
0.598563 | + | 0.801076i | \(0.295739\pi\) | |||||||
\(798\) | 17.5678 | − | 5.34114i | 0.621893 | − | 0.189074i | ||||
\(799\) | −28.1131 | −0.994571 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −11.6775 | − | 3.47094i | −0.412605 | − | 0.122640i | ||||
\(802\) | 11.5551 | + | 20.0141i | 0.408026 | + | 0.706722i | ||||
\(803\) | −7.18686 | − | 4.14934i | −0.253619 | − | 0.146427i | ||||
\(804\) | 1.91163 | − | 13.1409i | 0.0674179 | − | 0.463444i | ||||
\(805\) | 21.1017 | 0.743738 | ||||||||
\(806\) | 0.886031 | 0.0312091 | ||||||||
\(807\) | −5.57352 | − | 0.810789i | −0.196197 | − | 0.0285411i | ||||
\(808\) | −10.2389 | + | 5.91143i | −0.360203 | + | 0.207963i | ||||
\(809\) | − | 9.95048i | − | 0.349840i | −0.984583 | − | 0.174920i | \(-0.944033\pi\) | ||
0.984583 | − | 0.174920i | \(-0.0559667\pi\) | |||||||
\(810\) | −4.07088 | − | 8.02670i | −0.143036 | − | 0.282030i | ||||
\(811\) | 12.1319 | − | 7.00436i | 0.426009 | − | 0.245956i | −0.271636 | − | 0.962400i | \(-0.587565\pi\) |
0.697645 | + | 0.716444i | \(0.254231\pi\) | |||||||
\(812\) | −9.69845 | + | 16.7982i | −0.340349 | + | 0.589501i | ||||
\(813\) | 10.8714 | + | 1.58148i | 0.381276 | + | 0.0554648i | ||||
\(814\) | −1.48925 | + | 2.57946i | −0.0521983 | + | 0.0904100i | ||||
\(815\) | −11.7963 | − | 6.81062i | −0.413208 | − | 0.238566i | ||||
\(816\) | 6.96997 | + | 5.49998i | 0.243998 | + | 0.192538i | ||||
\(817\) | 0.515915 | − | 6.12811i | 0.0180496 | − | 0.214395i | ||||
\(818\) | 9.54002i | 0.333559i | ||||||||
\(819\) | −0.457163 | + | 1.53806i | −0.0159746 | + | 0.0537443i | ||||
\(820\) | −2.06213 | − | 1.19057i | −0.0720125 | − | 0.0415765i | ||||
\(821\) | 18.2129 | − | 10.5152i | 0.635634 | − | 0.366984i | −0.147297 | − | 0.989092i | \(-0.547057\pi\) |
0.782931 | + | 0.622109i | \(0.213724\pi\) | |||||||
\(822\) | 23.5267 | − | 9.37342i | 0.820588 | − | 0.326936i | ||||
\(823\) | −13.6408 | − | 23.6265i | −0.475488 | − | 0.823569i | 0.524118 | − | 0.851646i | \(-0.324395\pi\) |
−0.999606 | + | 0.0280769i | \(0.991062\pi\) | |||||||
\(824\) | − | 17.5769i | − | 0.612319i | ||||||
\(825\) | 3.16069 | + | 2.49409i | 0.110041 | + | 0.0868329i | ||||
\(826\) | −1.16272 | − | 2.01388i | −0.0404561 | − | 0.0700720i | ||||
\(827\) | −22.4340 | − | 38.8568i | −0.780105 | − | 1.35118i | −0.931880 | − | 0.362767i | \(-0.881832\pi\) |
0.151775 | − | 0.988415i | \(-0.451501\pi\) | |||||||
\(828\) | 25.3158 | − | 6.05269i | 0.879784 | − | 0.210345i | ||||
\(829\) | − | 9.02419i | − | 0.313423i | −0.987644 | − | 0.156711i | \(-0.949911\pi\) | ||
0.987644 | − | 0.156711i | \(-0.0500893\pi\) | |||||||
\(830\) | 2.18023 | + | 3.77627i | 0.0756770 | + | 0.131076i | ||||
\(831\) | −14.2106 | − | 35.6677i | −0.492961 | − | 1.23730i | ||||
\(832\) | −0.190454 | + | 0.109959i | −0.00660280 | + | 0.00381213i | ||||
\(833\) | −4.81669 | − | 2.78092i | −0.166889 | − | 0.0963531i | ||||
\(834\) | 7.06898 | + | 17.7427i | 0.244779 | + | 0.614379i | ||||
\(835\) | − | 10.8604i | − | 0.375840i | ||||||
\(836\) | −5.78449 | + | 8.31899i | −0.200061 | + | 0.287718i | ||||
\(837\) | −8.79132 | + | 18.9996i | −0.303873 | + | 0.656721i | ||||
\(838\) | −0.832876 | − | 0.480861i | −0.0287712 | − | 0.0166111i | ||||
\(839\) | −9.31551 | + | 16.1349i | −0.321607 | + | 0.557040i | −0.980820 | − | 0.194917i | \(-0.937556\pi\) |
0.659213 | + | 0.751957i | \(0.270890\pi\) | |||||||
\(840\) | 0.606413 | − | 4.16860i | 0.0209232 | − | 0.143830i | ||||
\(841\) | −17.3039 | + | 29.9712i | −0.596686 | + | 1.03349i | ||||
\(842\) | 14.4170 | − | 8.32365i | 0.496842 | − | 0.286852i | ||||
\(843\) | 16.8574 | − | 21.3629i | 0.580599 | − | 0.735777i | ||||
\(844\) | 2.88365i | 0.0992593i | ||||||||
\(845\) | 11.2164 | − | 6.47582i | 0.385857 | − | 0.222775i | ||||
\(846\) | 11.3143 | + | 11.9452i | 0.388993 | + | 0.410684i | ||||
\(847\) | −13.6112 | −0.467686 | ||||||||
\(848\) | −4.09015 | −0.140456 | ||||||||
\(849\) | 34.7990 | + | 5.06227i | 1.19430 | + | 0.173737i | ||||
\(850\) | −4.43932 | − | 2.56304i | −0.152267 | − | 0.0879116i | ||||
\(851\) | −5.55869 | − | 9.62794i | −0.190550 | − | 0.330042i | ||||
\(852\) | −6.48271 | − | 16.2712i | −0.222094 | − | 0.557442i | ||||
\(853\) | −7.15637 | + | 12.3952i | −0.245029 | + | 0.424403i | −0.962140 | − | 0.272556i | \(-0.912131\pi\) |
0.717111 | + | 0.696959i | \(0.245464\pi\) | |||||||
\(854\) | 20.0648 | 0.686604 | ||||||||
\(855\) | −10.2149 | + | 8.16435i | −0.349341 | + | 0.279215i | ||||
\(856\) | −2.80439 | −0.0958522 | ||||||||
\(857\) | 23.2696 | − | 40.3041i | 0.794873 | − | 1.37676i | −0.128046 | − | 0.991768i | \(-0.540871\pi\) |
0.922920 | − | 0.384993i | \(-0.125796\pi\) | |||||||
\(858\) | −0.327719 | − | 0.822554i | −0.0111881 | − | 0.0280815i | ||||
\(859\) | −11.8783 | − | 20.5737i | −0.405281 | − | 0.701967i | 0.589073 | − | 0.808080i | \(-0.299493\pi\) |
−0.994354 | + | 0.106113i | \(0.966160\pi\) | |||||||
\(860\) | −1.22184 | − | 0.705429i | −0.0416644 | − | 0.0240549i | ||||
\(861\) | −9.92601 | − | 1.44395i | −0.338278 | − | 0.0492098i | ||||
\(862\) | −10.0728 | −0.343080 | ||||||||
\(863\) | −8.13980 | −0.277082 | −0.138541 | − | 0.990357i | \(-0.544241\pi\) | ||||
−0.138541 | + | 0.990357i | \(0.544241\pi\) | |||||||
\(864\) | −0.468182 | − | 5.17502i | −0.0159279 | − | 0.176058i | ||||
\(865\) | −10.4748 | + | 6.04765i | −0.356155 | + | 0.205626i | ||||
\(866\) | 6.83171i | 0.232151i | ||||||||
\(867\) | 9.95340 | − | 12.6137i | 0.338035 | − | 0.428382i | ||||
\(868\) | −8.48588 | + | 4.89933i | −0.288030 | + | 0.166294i | ||||
\(869\) | 17.5269 | − | 30.3576i | 0.594561 | − | 1.02981i | ||||
\(870\) | 1.98860 | − | 13.6700i | 0.0674197 | − | 0.463456i | ||||
\(871\) | 0.843026 | − | 1.46016i | 0.0285649 | − | 0.0494758i | ||||
\(872\) | 13.8072 | + | 7.97161i | 0.467572 | + | 0.269953i | ||||
\(873\) | −20.5776 | + | 4.91986i | −0.696448 | + | 0.166512i | ||||
\(874\) | −16.0955 | − | 34.2237i | −0.544438 | − | 1.15763i | ||||
\(875\) | 2.43208i | 0.0822192i | ||||||||
\(876\) | −2.28864 | − | 5.74435i | −0.0773261 | − | 0.194084i | ||||
\(877\) | −31.6447 | − | 18.2701i | −1.06857 | − | 0.616937i | −0.140777 | − | 0.990041i | \(-0.544960\pi\) |
−0.927789 | + | 0.373104i | \(0.878293\pi\) | |||||||
\(878\) | −9.27371 | + | 5.35418i | −0.312973 | + | 0.180695i | ||||
\(879\) | 10.3267 | + | 25.9193i | 0.348310 | + | 0.874235i | ||||
\(880\) | 1.16227 | + | 2.01311i | 0.0391800 | + | 0.0678618i | ||||
\(881\) | − | 29.6144i | − | 0.997735i | −0.866678 | − | 0.498868i | \(-0.833749\pi\) | ||
0.866678 | − | 0.498868i | \(-0.166251\pi\) | |||||||
\(882\) | 0.756903 | + | 3.16580i | 0.0254862 | + | 0.106598i | ||||
\(883\) | 17.6785 | + | 30.6200i | 0.594928 | + | 1.03045i | 0.993557 | + | 0.113334i | \(0.0361529\pi\) |
−0.398629 | + | 0.917112i | \(0.630514\pi\) | |||||||
\(884\) | 0.563658 | + | 0.976283i | 0.0189579 | + | 0.0328360i | ||||
\(885\) | 1.30009 | + | 1.02589i | 0.0437019 | + | 0.0344850i | ||||
\(886\) | − | 7.93748i | − | 0.266665i | ||||||
\(887\) | 27.9372 | + | 48.3886i | 0.938039 | + | 1.62473i | 0.769123 | + | 0.639101i | \(0.220693\pi\) |
0.168916 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(888\) | −2.06172 | + | 0.821425i | −0.0691869 | + | 0.0275652i | ||||
\(889\) | −5.93301 | + | 3.42543i | −0.198987 | + | 0.114885i | ||||
\(890\) | 3.51677 | + | 2.03041i | 0.117882 | + | 0.0680593i | ||||
\(891\) | 20.8901 | + | 1.13407i | 0.699843 | + | 0.0379928i | ||||
\(892\) | 14.6986i | 0.492146i | ||||||||
\(893\) | 13.6475 | − | 19.6272i | 0.456695 | − | 0.656798i | ||||
\(894\) | 28.6961 | + | 22.6440i | 0.959741 | + | 0.757329i | ||||
\(895\) | −7.94473 | − | 4.58689i | −0.265563 | − | 0.153323i | ||||
\(896\) | 1.21604 | − | 2.10624i | 0.0406250 | − | 0.0703645i | ||||
\(897\) | 3.27050 | + | 0.475764i | 0.109199 | + | 0.0158853i | ||||
\(898\) | −8.19524 | + | 14.1946i | −0.273479 | + | 0.473679i | ||||
\(899\) | −27.8275 | + | 16.0662i | −0.928101 | + | 0.535839i | ||||
\(900\) | 0.697602 | + | 2.91776i | 0.0232534 | + | 0.0972588i | ||||
\(901\) | 20.9664i | 0.698494i | ||||||||
\(902\) | 4.79348 | − | 2.76752i | 0.159606 | − | 0.0921483i | ||||
\(903\) | −5.88131 | − | 0.855563i | −0.195718 | − | 0.0284713i | ||||
\(904\) | −12.1749 | −0.404931 | ||||||||
\(905\) | 9.66914 | 0.321413 | ||||||||
\(906\) | 6.03773 | − | 41.5045i | 0.200590 | − | 1.37889i | ||||
\(907\) | 37.7050 | + | 21.7690i | 1.25197 | + | 0.722828i | 0.971501 | − | 0.237034i | \(-0.0761754\pi\) |
0.280473 | + | 0.959862i | \(0.409509\pi\) | |||||||
\(908\) | 5.53375 | + | 9.58473i | 0.183644 | + | 0.318081i | ||||
\(909\) | 10.1055 | − | 33.9985i | 0.335178 | − | 1.12766i | ||||
\(910\) | 0.267428 | − | 0.463199i | 0.00886515 | − | 0.0153549i | ||||
\(911\) | 34.1334 | 1.13089 | 0.565444 | − | 0.824786i | \(-0.308705\pi\) | ||||
0.565444 | + | 0.824786i | \(0.308705\pi\) | |||||||
\(912\) | −7.22337 | + | 2.19612i | −0.239190 | + | 0.0727209i | ||||
\(913\) | −10.1361 | −0.335455 | ||||||||
\(914\) | 9.91012 | − | 17.1648i | 0.327798 | − | 0.567762i | ||||
\(915\) | −13.2748 | + | 5.28889i | −0.438850 | + | 0.174845i | ||||
\(916\) | −1.59769 | − | 2.76728i | −0.0527892 | − | 0.0914336i | ||||
\(917\) | 17.5808 | + | 10.1503i | 0.580570 | + | 0.335192i | ||||
\(918\) | −26.5276 | + | 2.39994i | −0.875541 | + | 0.0792098i | ||||
\(919\) | −6.05120 | −0.199611 | −0.0998053 | − | 0.995007i | \(-0.531822\pi\) | ||||
−0.0998053 | + | 0.995007i | \(0.531822\pi\) | |||||||
\(920\) | −8.67642 | −0.286053 | ||||||||
\(921\) | 2.00375 | − | 13.7742i | 0.0660258 | − | 0.453874i | ||||
\(922\) | −35.9630 | + | 20.7632i | −1.18438 | + | 0.683801i | ||||
\(923\) | − | 2.22388i | − | 0.0731998i | ||||||
\(924\) | 7.68703 | + | 6.06581i | 0.252885 | + | 0.199550i | ||||
\(925\) | 1.10967 | − | 0.640666i | 0.0364856 | − | 0.0210650i | ||||
\(926\) | −10.1223 | + | 17.5323i | −0.332638 | + | 0.576147i | ||||
\(927\) | 36.2615 | + | 38.2834i | 1.19098 | + | 1.25739i | ||||
\(928\) | 3.98772 | − | 6.90694i | 0.130903 | − | 0.226731i | ||||
\(929\) | −14.4587 | − | 8.34775i | −0.474376 | − | 0.273881i | 0.243694 | − | 0.969852i | \(-0.421641\pi\) |
−0.718070 | + | 0.695971i | \(0.754974\pi\) | |||||||
\(930\) | 4.32279 | − | 5.47816i | 0.141750 | − | 0.179636i | ||||
\(931\) | 4.27975 | − | 2.01278i | 0.140263 | − | 0.0659661i | ||||
\(932\) | 8.03695i | 0.263259i | ||||||||
\(933\) | −32.5979 | + | 12.9876i | −1.06721 | + | 0.425193i | ||||
\(934\) | 8.78980 | + | 5.07479i | 0.287611 | + | 0.166052i | ||||
\(935\) | 10.3194 | − | 5.95789i | 0.337479 | − | 0.194844i | ||||
\(936\) | 0.187972 | − | 0.632407i | 0.00614407 | − | 0.0206709i | ||||
\(937\) | 18.3641 | + | 31.8076i | 0.599930 | + | 1.03911i | 0.992831 | + | 0.119529i | \(0.0381383\pi\) |
−0.392901 | + | 0.919581i | \(0.628528\pi\) | |||||||
\(938\) | 18.6461i | 0.608818i | ||||||||
\(939\) | −25.8018 | + | 32.6979i | −0.842011 | + | 1.06706i | ||||
\(940\) | −2.74216 | − | 4.74957i | −0.0894395 | − | 0.154914i | ||||
\(941\) | −19.7858 | − | 34.2699i | −0.644997 | − | 1.11717i | −0.984302 | − | 0.176491i | \(-0.943525\pi\) |
0.339305 | − | 0.940676i | \(-0.389808\pi\) | |||||||
\(942\) | −13.8697 | + | 17.5767i | −0.451900 | + | 0.572680i | ||||
\(943\) | 20.6598i | 0.672774i | ||||||||
\(944\) | 0.478076 | + | 0.828051i | 0.0155600 | + | 0.0269508i | ||||
\(945\) | 7.27912 | + | 10.3305i | 0.236790 | + | 0.336051i | ||||
\(946\) | 2.84021 | − | 1.63980i | 0.0923431 | − | 0.0533143i | ||||
\(947\) | −38.8622 | − | 22.4371i | −1.26285 | − | 0.729108i | −0.289227 | − | 0.957261i | \(-0.593398\pi\) |
−0.973625 | + | 0.228153i | \(0.926731\pi\) | |||||||
\(948\) | 24.2643 | − | 9.66731i | 0.788069 | − | 0.313980i | ||||
\(949\) | − | 0.785113i | − | 0.0254858i | ||||||
\(950\) | 3.94445 | − | 1.85508i | 0.127975 | − | 0.0601868i | ||||
\(951\) | 13.4544 | − | 17.0504i | 0.436289 | − | 0.552897i | ||||
\(952\) | −10.7968 | − | 6.23351i | −0.349925 | − | 0.202029i | ||||
\(953\) | 5.60620 | − | 9.71022i | 0.181603 | − | 0.314545i | −0.760824 | − | 0.648958i | \(-0.775205\pi\) |
0.942426 | + | 0.334414i | \(0.108538\pi\) | |||||||
\(954\) | 8.90858 | − | 8.43807i | 0.288426 | − | 0.273193i | ||||
\(955\) | −9.36065 | + | 16.2131i | −0.302904 | + | 0.524644i | ||||
\(956\) | 4.48081 | − | 2.58700i | 0.144920 | − | 0.0836695i | ||||
\(957\) | 25.2079 | + | 19.8915i | 0.814855 | + | 0.642999i | ||||
\(958\) | 40.6886i | 1.31459i | ||||||||
\(959\) | −30.7964 | + | 17.7803i | −0.994468 | + | 0.574157i | ||||
\(960\) | −0.249340 | + | 1.71401i | −0.00804741 | + | 0.0553194i | ||||
\(961\) | 14.7678 | 0.476379 | ||||||||
\(962\) | −0.281787 | −0.00908519 | ||||||||
\(963\) | 6.10813 | − | 5.78553i | 0.196832 | − | 0.186436i | ||||
\(964\) | 25.4528 | + | 14.6952i | 0.819780 | + | 0.473300i | ||||
\(965\) | 12.2374 | + | 21.1958i | 0.393936 | + | 0.682317i | ||||
\(966\) | −33.9536 | + | 13.5277i | −1.09244 | + | 0.435246i | ||||
\(967\) | −10.2650 | + | 17.7795i | −0.330101 | + | 0.571751i | −0.982531 | − | 0.186097i | \(-0.940416\pi\) |
0.652431 | + | 0.757848i | \(0.273749\pi\) | |||||||
\(968\) | 5.59653 | 0.179879 | ||||||||
\(969\) | 11.2575 | + | 37.0276i | 0.361643 | + | 1.18950i | ||||
\(970\) | 7.05254 | 0.226443 | ||||||||
\(971\) | −18.9504 | + | 32.8230i | −0.608147 | + | 1.05334i | 0.383399 | + | 0.923583i | \(0.374754\pi\) |
−0.991546 | + | 0.129759i | \(0.958580\pi\) | |||||||
\(972\) | 11.6959 | + | 10.3056i | 0.375146 | + | 0.330553i | ||||
\(973\) | −13.4090 | − | 23.2252i | −0.429874 | − | 0.744564i | ||||
\(974\) | −12.5190 | − | 7.22783i | −0.401134 | − | 0.231595i | ||||
\(975\) | −0.0548341 | + | 0.376940i | −0.00175610 | + | 0.0120718i | ||||
\(976\) | −8.25009 | −0.264079 | ||||||||
\(977\) | −46.2229 | −1.47880 | −0.739400 | − | 0.673266i | \(-0.764891\pi\) | ||||
−0.739400 | + | 0.673266i | \(0.764891\pi\) | |||||||
\(978\) | 23.3469 | + | 3.39632i | 0.746553 | + | 0.108602i | ||||
\(979\) | −8.17485 | + | 4.71975i | −0.261269 | + | 0.150844i | ||||
\(980\) | − | 1.08501i | − | 0.0346593i | ||||||
\(981\) | −46.5186 | + | 11.1220i | −1.48522 | + | 0.355099i | ||||
\(982\) | 13.6141 | − | 7.86008i | 0.434442 | − | 0.250825i | ||||
\(983\) | −1.93851 | + | 3.35759i | −0.0618287 | + | 0.107091i | −0.895283 | − | 0.445498i | \(-0.853027\pi\) |
0.833454 | + | 0.552589i | \(0.186360\pi\) | |||||||
\(984\) | 4.08129 | + | 0.593712i | 0.130107 | + | 0.0189269i | ||||
\(985\) | 2.48922 | − | 4.31146i | 0.0793132 | − | 0.137375i | ||||
\(986\) | −35.4056 | − | 20.4414i | −1.12754 | − | 0.650987i | ||||
\(987\) | −18.1362 | − | 14.3112i | −0.577281 | − | 0.455530i | ||||
\(988\) | −0.955218 | − | 0.0804183i | −0.0303895 | − | 0.00255845i | ||||
\(989\) | 12.2412i | 0.389248i | ||||||||
\(990\) | −6.68457 | − | 1.98688i | −0.212450 | − | 0.0631471i | ||||
\(991\) | −4.36664 | − | 2.52108i | −0.138711 | − | 0.0800848i | 0.429039 | − | 0.903286i | \(-0.358852\pi\) |
−0.567750 | + | 0.823201i | \(0.692186\pi\) | |||||||
\(992\) | 3.48915 | − | 2.01446i | 0.110781 | − | 0.0639593i | ||||
\(993\) | 8.15779 | − | 3.25020i | 0.258880 | − | 0.103142i | ||||
\(994\) | 12.2970 | + | 21.2990i | 0.390036 | + | 0.675563i | ||||
\(995\) | − | 18.1690i | − | 0.575997i | ||||||
\(996\) | −5.92895 | − | 4.67852i | −0.187866 | − | 0.148244i | ||||
\(997\) | −20.3710 | − | 35.2836i | −0.645156 | − | 1.11744i | −0.984266 | − | 0.176696i | \(-0.943459\pi\) |
0.339110 | − | 0.940747i | \(-0.389874\pi\) | |||||||
\(998\) | −16.7701 | − | 29.0466i | −0.530847 | − | 0.919454i | ||||
\(999\) | 2.79593 | − | 6.04249i | 0.0884595 | − | 0.191176i |
(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 | 570.2.s.a.521.5 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.b.521.1 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.b.221.1 | yes | 24 | ||
57.50 | even | 6 | inner | 570.2.s.a.221.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.5 | ✓ | 24 | 57.50 | even | 6 | inner | |
570.2.s.a.521.5 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.221.1 | yes | 24 | 19.12 | odd | 6 | ||
570.2.s.b.521.1 | yes | 24 | 3.2 | odd | 2 |