Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,2,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.82670423155\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.41542366334681088.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.8 | ||
Root | \(-0.869925 + 1.49774i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.2.c.a.353.7 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.869925 | + | 1.49774i | 0.502252 | + | 0.864722i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.66014i | 0.742437i | 0.928546 | + | 0.371218i | \(0.121060\pi\) | ||||
−0.928546 | + | 0.371218i | \(0.878940\pi\) | |||||||
\(6\) | −0.869925 | − | 1.49774i | −0.355146 | − | 0.611450i | ||||
\(7\) | −3.57946 | −1.35291 | −0.676454 | − | 0.736485i | \(-0.736484\pi\) | ||||
−0.676454 | + | 0.736485i | \(0.736484\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.48646 | + | 2.60585i | −0.495487 | + | 0.868616i | ||||
\(10\) | − | 1.66014i | − | 0.524982i | ||||||
\(11\) | −4.82340 | −1.45431 | −0.727154 | − | 0.686474i | \(-0.759158\pi\) | ||||
−0.727154 | + | 0.686474i | \(0.759158\pi\) | |||||||
\(12\) | 0.869925 | + | 1.49774i | 0.251126 | + | 0.432361i | ||||
\(13\) | − | 0.418899i | − | 0.116182i | −0.998311 | − | 0.0580908i | \(-0.981499\pi\) | ||
0.998311 | − | 0.0580908i | \(-0.0185013\pi\) | |||||||
\(14\) | 3.57946 | 0.956651 | ||||||||
\(15\) | −2.48646 | + | 1.44420i | −0.642001 | + | 0.372890i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.742751i | − | 0.180143i | −0.995935 | − | 0.0900717i | \(-0.971290\pi\) | ||
0.995935 | − | 0.0900717i | \(-0.0287096\pi\) | |||||||
\(18\) | 1.48646 | − | 2.60585i | 0.350362 | − | 0.614204i | ||||
\(19\) | 1.24394 | 0.285379 | 0.142689 | − | 0.989768i | \(-0.454425\pi\) | ||||
0.142689 | + | 0.989768i | \(0.454425\pi\) | |||||||
\(20\) | 1.66014i | 0.371218i | ||||||||
\(21\) | −3.11386 | − | 5.36111i | −0.679500 | − | 1.16989i | ||||
\(22\) | 4.82340 | 1.02835 | ||||||||
\(23\) | 1.25480 | 0.261645 | 0.130822 | − | 0.991406i | \(-0.458238\pi\) | ||||
0.130822 | + | 0.991406i | \(0.458238\pi\) | |||||||
\(24\) | −0.869925 | − | 1.49774i | −0.177573 | − | 0.305725i | ||||
\(25\) | 2.24394 | 0.448787 | ||||||||
\(26\) | 0.418899i | 0.0821528i | ||||||||
\(27\) | −5.19599 | + | 0.0405586i | −0.999970 | + | 0.00780551i | ||||
\(28\) | −3.57946 | −0.676454 | ||||||||
\(29\) | − | 4.78075i | − | 0.887763i | −0.896085 | − | 0.443882i | \(-0.853601\pi\) | ||
0.896085 | − | 0.443882i | \(-0.146399\pi\) | |||||||
\(30\) | 2.48646 | − | 1.44420i | 0.453963 | − | 0.263673i | ||||
\(31\) | 10.4469i | 1.87632i | 0.346198 | + | 0.938161i | \(0.387472\pi\) | ||||
−0.346198 | + | 0.938161i | \(0.612528\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.19599 | − | 7.22420i | −0.730429 | − | 1.25757i | ||||
\(34\) | 0.742751i | 0.127381i | ||||||||
\(35\) | − | 5.94240i | − | 1.00445i | ||||||
\(36\) | −1.48646 | + | 2.60585i | −0.247743 | + | 0.434308i | ||||
\(37\) | 6.02199i | 0.990010i | 0.868890 | + | 0.495005i | \(0.164834\pi\) | ||||
−0.868890 | + | 0.495005i | \(0.835166\pi\) | |||||||
\(38\) | −1.24394 | −0.201793 | ||||||||
\(39\) | 0.627402 | − | 0.364411i | 0.100465 | − | 0.0583524i | ||||
\(40\) | − | 1.66014i | − | 0.262491i | ||||||
\(41\) | 9.24875i | 1.44441i | 0.691678 | + | 0.722206i | \(0.256872\pi\) | ||||
−0.691678 | + | 0.722206i | \(0.743128\pi\) | |||||||
\(42\) | 3.11386 | + | 5.36111i | 0.480479 | + | 0.827237i | ||||
\(43\) | − | 3.58258i | − | 0.546338i | −0.961966 | − | 0.273169i | \(-0.911928\pi\) | ||
0.961966 | − | 0.273169i | \(-0.0880719\pi\) | |||||||
\(44\) | −4.82340 | −0.727154 | ||||||||
\(45\) | −4.32607 | − | 2.46773i | −0.644892 | − | 0.367868i | ||||
\(46\) | −1.25480 | −0.185011 | ||||||||
\(47\) | −8.39199 | −1.22410 | −0.612049 | − | 0.790820i | \(-0.709654\pi\) | ||||
−0.612049 | + | 0.790820i | \(0.709654\pi\) | |||||||
\(48\) | 0.869925 | + | 1.49774i | 0.125563 | + | 0.216180i | ||||
\(49\) | 5.81253 | 0.830361 | ||||||||
\(50\) | −2.24394 | −0.317341 | ||||||||
\(51\) | 1.11245 | − | 0.646138i | 0.155774 | − | 0.0904774i | ||||
\(52\) | − | 0.418899i | − | 0.0580908i | ||||||
\(53\) | 9.66765i | 1.32795i | 0.747753 | + | 0.663977i | \(0.231133\pi\) | ||||
−0.747753 | + | 0.663977i | \(0.768867\pi\) | |||||||
\(54\) | 5.19599 | − | 0.0405586i | 0.707085 | − | 0.00551933i | ||||
\(55\) | − | 8.00751i | − | 1.07973i | ||||||
\(56\) | 3.57946 | 0.478325 | ||||||||
\(57\) | 1.08213 | + | 1.86310i | 0.143332 | + | 0.246773i | ||||
\(58\) | 4.78075i | 0.627744i | ||||||||
\(59\) | 5.47701 | − | 5.38539i | 0.713046 | − | 0.701118i | ||||
\(60\) | −2.48646 | + | 1.44420i | −0.321001 | + | 0.186445i | ||||
\(61\) | 9.08804i | 1.16360i | 0.813330 | + | 0.581802i | \(0.197652\pi\) | ||||
−0.813330 | + | 0.581802i | \(0.802348\pi\) | |||||||
\(62\) | − | 10.4469i | − | 1.32676i | ||||||
\(63\) | 5.32072 | − | 9.32752i | 0.670348 | − | 1.17516i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.695430 | 0.0862575 | ||||||||
\(66\) | 4.19599 | + | 7.22420i | 0.516491 | + | 0.889238i | ||||
\(67\) | 13.0941i | 1.59970i | 0.600203 | + | 0.799848i | \(0.295087\pi\) | ||||
−0.600203 | + | 0.799848i | \(0.704913\pi\) | |||||||
\(68\) | − | 0.742751i | − | 0.0900717i | ||||||
\(69\) | 1.09159 | + | 1.87937i | 0.131411 | + | 0.226250i | ||||
\(70\) | 5.94240i | 0.710253i | ||||||||
\(71\) | − | 4.01996i | − | 0.477082i | −0.971132 | − | 0.238541i | \(-0.923331\pi\) | ||
0.971132 | − | 0.238541i | \(-0.0766691\pi\) | |||||||
\(72\) | 1.48646 | − | 2.60585i | 0.175181 | − | 0.307102i | ||||
\(73\) | − | 10.6897i | − | 1.25113i | −0.780172 | − | 0.625565i | \(-0.784869\pi\) | ||
0.780172 | − | 0.625565i | \(-0.215131\pi\) | |||||||
\(74\) | − | 6.02199i | − | 0.700043i | ||||||
\(75\) | 1.95206 | + | 3.36084i | 0.225404 | + | 0.388076i | ||||
\(76\) | 1.24394 | 0.142689 | ||||||||
\(77\) | 17.2652 | 1.96755 | ||||||||
\(78\) | −0.627402 | + | 0.364411i | −0.0710393 | + | 0.0412614i | ||||
\(79\) | 3.55772 | 0.400275 | 0.200138 | − | 0.979768i | \(-0.435861\pi\) | ||||
0.200138 | + | 0.979768i | \(0.435861\pi\) | |||||||
\(80\) | 1.66014i | 0.185609i | ||||||||
\(81\) | −4.58087 | − | 7.74697i | −0.508986 | − | 0.860775i | ||||
\(82\) | − | 9.24875i | − | 1.02135i | ||||||
\(83\) | −2.87316 | −0.315370 | −0.157685 | − | 0.987489i | \(-0.550403\pi\) | ||||
−0.157685 | + | 0.987489i | \(0.550403\pi\) | |||||||
\(84\) | −3.11386 | − | 5.36111i | −0.339750 | − | 0.584945i | ||||
\(85\) | 1.23307 | 0.133745 | ||||||||
\(86\) | 3.58258i | 0.386320i | ||||||||
\(87\) | 7.16033 | − | 4.15890i | 0.767668 | − | 0.445881i | ||||
\(88\) | 4.82340 | 0.514176 | ||||||||
\(89\) | 16.0885 | 1.70538 | 0.852691 | − | 0.522415i | \(-0.174969\pi\) | ||||
0.852691 | + | 0.522415i | \(0.174969\pi\) | |||||||
\(90\) | 4.32607 | + | 2.46773i | 0.456008 | + | 0.260122i | ||||
\(91\) | 1.49943i | 0.157183i | ||||||||
\(92\) | 1.25480 | 0.130822 | ||||||||
\(93\) | −15.6468 | + | 9.08804i | −1.62250 | + | 0.942386i | ||||
\(94\) | 8.39199 | 0.865567 | ||||||||
\(95\) | 2.06511i | 0.211876i | ||||||||
\(96\) | −0.869925 | − | 1.49774i | −0.0887864 | − | 0.152863i | ||||
\(97\) | − | 11.5275i | − | 1.17044i | −0.810876 | − | 0.585218i | \(-0.801009\pi\) | ||
0.810876 | − | 0.585218i | \(-0.198991\pi\) | |||||||
\(98\) | −5.81253 | −0.587154 | ||||||||
\(99\) | 7.16979 | − | 12.5690i | 0.720591 | − | 1.26324i | ||||
\(100\) | 2.24394 | 0.224394 | ||||||||
\(101\) | 11.2652 | 1.12092 | 0.560462 | − | 0.828180i | \(-0.310624\pi\) | ||||
0.560462 | + | 0.828180i | \(0.310624\pi\) | |||||||
\(102\) | −1.11245 | + | 0.646138i | −0.110149 | + | 0.0639771i | ||||
\(103\) | 1.60162i | 0.157812i | 0.996882 | + | 0.0789059i | \(0.0251427\pi\) | ||||
−0.996882 | + | 0.0789059i | \(0.974857\pi\) | |||||||
\(104\) | 0.418899i | 0.0410764i | ||||||||
\(105\) | 8.90018 | − | 5.16945i | 0.868569 | − | 0.504486i | ||||
\(106\) | − | 9.66765i | − | 0.939005i | ||||||
\(107\) | 0.0585239i | 0.00565772i | 0.999996 | + | 0.00282886i | \(0.000900456\pi\) | ||||
−0.999996 | + | 0.00282886i | \(0.999100\pi\) | |||||||
\(108\) | −5.19599 | + | 0.0405586i | −0.499985 | + | 0.00390275i | ||||
\(109\) | 5.56810i | 0.533327i | 0.963790 | + | 0.266664i | \(0.0859212\pi\) | ||||
−0.963790 | + | 0.266664i | \(0.914079\pi\) | |||||||
\(110\) | 8.00751i | 0.763486i | ||||||||
\(111\) | −9.01939 | + | 5.23868i | −0.856083 | + | 0.497234i | ||||
\(112\) | −3.57946 | −0.338227 | ||||||||
\(113\) | −3.43798 | −0.323418 | −0.161709 | − | 0.986839i | \(-0.551701\pi\) | ||||
−0.161709 | + | 0.986839i | \(0.551701\pi\) | |||||||
\(114\) | −1.08213 | − | 1.86310i | −0.101351 | − | 0.174495i | ||||
\(115\) | 2.08315i | 0.194255i | ||||||||
\(116\) | − | 4.78075i | − | 0.443882i | ||||||
\(117\) | 1.09159 | + | 0.622676i | 0.100917 | + | 0.0575664i | ||||
\(118\) | −5.47701 | + | 5.38539i | −0.504199 | + | 0.495765i | ||||
\(119\) | 2.65865i | 0.243718i | ||||||||
\(120\) | 2.48646 | − | 1.44420i | 0.226982 | − | 0.131837i | ||||
\(121\) | 12.2652 | 1.11501 | ||||||||
\(122\) | − | 9.08804i | − | 0.822793i | ||||||
\(123\) | −13.8522 | + | 8.04572i | −1.24901 | + | 0.725458i | ||||
\(124\) | 10.4469i | 0.938161i | ||||||||
\(125\) | 12.0259i | 1.07563i | ||||||||
\(126\) | −5.32072 | + | 9.32752i | −0.474008 | + | 0.830962i | ||||
\(127\) | −22.0994 | −1.96101 | −0.980503 | − | 0.196505i | \(-0.937041\pi\) | ||||
−0.980503 | + | 0.196505i | \(0.937041\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.36578 | − | 3.11658i | 0.472431 | − | 0.274399i | ||||
\(130\) | −0.695430 | −0.0609933 | ||||||||
\(131\) | 13.6966 | 1.19667 | 0.598337 | − | 0.801245i | \(-0.295828\pi\) | ||||
0.598337 | + | 0.801245i | \(0.295828\pi\) | |||||||
\(132\) | −4.19599 | − | 7.22420i | −0.365214 | − | 0.628786i | ||||
\(133\) | −4.45262 | −0.386091 | ||||||||
\(134\) | − | 13.0941i | − | 1.13116i | ||||||
\(135\) | −0.0673329 | − | 8.62608i | −0.00579510 | − | 0.742414i | ||||
\(136\) | 0.742751i | 0.0636903i | ||||||||
\(137\) | 7.16560i | 0.612199i | 0.952000 | + | 0.306099i | \(0.0990240\pi\) | ||||
−0.952000 | + | 0.306099i | \(0.900976\pi\) | |||||||
\(138\) | −1.09159 | − | 1.87937i | −0.0929219 | − | 0.159983i | ||||
\(139\) | 5.20504 | 0.441486 | 0.220743 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220743 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(140\) | − | 5.94240i | − | 0.502225i | ||||||
\(141\) | −7.30040 | − | 12.5690i | −0.614805 | − | 1.05850i | ||||
\(142\) | 4.01996i | 0.337348i | ||||||||
\(143\) | 2.02051i | 0.168964i | ||||||||
\(144\) | −1.48646 | + | 2.60585i | −0.123872 | + | 0.217154i | ||||
\(145\) | 7.93672 | 0.659108 | ||||||||
\(146\) | 10.6897i | 0.884682i | ||||||||
\(147\) | 5.05647 | + | 8.70567i | 0.417050 | + | 0.718031i | ||||
\(148\) | 6.02199i | 0.495005i | ||||||||
\(149\) | −8.82075 | −0.722624 | −0.361312 | − | 0.932445i | \(-0.617671\pi\) | ||||
−0.361312 | + | 0.932445i | \(0.617671\pi\) | |||||||
\(150\) | −1.95206 | − | 3.36084i | −0.159385 | − | 0.274411i | ||||
\(151\) | 0.872794i | 0.0710270i | 0.999369 | + | 0.0355135i | \(0.0113067\pi\) | ||||
−0.999369 | + | 0.0355135i | \(0.988693\pi\) | |||||||
\(152\) | −1.24394 | −0.100897 | ||||||||
\(153\) | 1.93549 | + | 1.10407i | 0.156475 | + | 0.0892587i | ||||
\(154\) | −17.2652 | −1.39127 | ||||||||
\(155\) | −17.3434 | −1.39305 | ||||||||
\(156\) | 0.627402 | − | 0.364411i | 0.0502324 | − | 0.0291762i | ||||
\(157\) | − | 23.3287i | − | 1.86183i | −0.365231 | − | 0.930917i | \(-0.619010\pi\) | ||
0.365231 | − | 0.930917i | \(-0.380990\pi\) | |||||||
\(158\) | −3.55772 | −0.283037 | ||||||||
\(159\) | −14.4796 | + | 8.41013i | −1.14831 | + | 0.666967i | ||||
\(160\) | − | 1.66014i | − | 0.131246i | ||||||
\(161\) | −4.49152 | −0.353981 | ||||||||
\(162\) | 4.58087 | + | 7.74697i | 0.359907 | + | 0.608660i | ||||
\(163\) | 4.74255 | 0.371465 | 0.185732 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185732 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(164\) | 9.24875i | 0.722206i | ||||||||
\(165\) | 11.9932 | − | 6.96594i | 0.933668 | − | 0.542297i | ||||
\(166\) | 2.87316 | 0.223001 | ||||||||
\(167\) | − | 7.18517i | − | 0.556005i | −0.960580 | − | 0.278003i | \(-0.910328\pi\) | ||
0.960580 | − | 0.278003i | \(-0.0896724\pi\) | |||||||
\(168\) | 3.11386 | + | 5.36111i | 0.240240 | + | 0.413618i | ||||
\(169\) | 12.8245 | 0.986502 | ||||||||
\(170\) | −1.23307 | −0.0945721 | ||||||||
\(171\) | −1.84906 | + | 3.24151i | −0.141401 | + | 0.247884i | ||||
\(172\) | − | 3.58258i | − | 0.273169i | ||||||
\(173\) | 4.12797 | 0.313843 | 0.156922 | − | 0.987611i | \(-0.449843\pi\) | ||||
0.156922 | + | 0.987611i | \(0.449843\pi\) | |||||||
\(174\) | −7.16033 | + | 4.15890i | −0.542823 | + | 0.315285i | ||||
\(175\) | −8.03208 | −0.607168 | ||||||||
\(176\) | −4.82340 | −0.363577 | ||||||||
\(177\) | 12.8305 | + | 3.51826i | 0.964400 | + | 0.264448i | ||||
\(178\) | −16.0885 | −1.20589 | ||||||||
\(179\) | −12.7736 | −0.954746 | −0.477373 | − | 0.878701i | \(-0.658411\pi\) | ||||
−0.477373 | + | 0.878701i | \(0.658411\pi\) | |||||||
\(180\) | −4.32607 | − | 2.46773i | −0.322446 | − | 0.183934i | ||||
\(181\) | −6.91511 | −0.513996 | −0.256998 | − | 0.966412i | \(-0.582733\pi\) | ||||
−0.256998 | + | 0.966412i | \(0.582733\pi\) | |||||||
\(182\) | − | 1.49943i | − | 0.111145i | ||||||
\(183\) | −13.6115 | + | 7.90592i | −1.00619 | + | 0.584422i | ||||
\(184\) | −1.25480 | −0.0925054 | ||||||||
\(185\) | −9.99735 | −0.735020 | ||||||||
\(186\) | 15.6468 | − | 9.08804i | 1.14728 | − | 0.666368i | ||||
\(187\) | 3.58258i | 0.261984i | ||||||||
\(188\) | −8.39199 | −0.612049 | ||||||||
\(189\) | 18.5988 | − | 0.145178i | 1.35287 | − | 0.0105601i | ||||
\(190\) | − | 2.06511i | − | 0.149819i | ||||||
\(191\) | −3.69921 | −0.267665 | −0.133833 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133833 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(192\) | 0.869925 | + | 1.49774i | 0.0627814 | + | 0.108090i | ||||
\(193\) | −11.9714 | −0.861724 | −0.430862 | − | 0.902418i | \(-0.641790\pi\) | ||||
−0.430862 | + | 0.902418i | \(0.641790\pi\) | |||||||
\(194\) | 11.5275i | 0.827623i | ||||||||
\(195\) | 0.604972 | + | 1.04157i | 0.0433230 | + | 0.0745887i | ||||
\(196\) | 5.81253 | 0.415181 | ||||||||
\(197\) | 12.7702i | 0.909841i | 0.890532 | + | 0.454920i | \(0.150332\pi\) | ||||
−0.890532 | + | 0.454920i | \(0.849668\pi\) | |||||||
\(198\) | −7.16979 | + | 12.5690i | −0.509534 | + | 0.893242i | ||||
\(199\) | 7.63327 | 0.541108 | 0.270554 | − | 0.962705i | \(-0.412793\pi\) | ||||
0.270554 | + | 0.962705i | \(0.412793\pi\) | |||||||
\(200\) | −2.24394 | −0.158670 | ||||||||
\(201\) | −19.6115 | + | 11.3909i | −1.38329 | + | 0.803450i | ||||
\(202\) | −11.2652 | −0.792613 | ||||||||
\(203\) | 17.1125i | 1.20106i | ||||||||
\(204\) | 1.11245 | − | 0.646138i | 0.0778870 | − | 0.0452387i | ||||
\(205\) | −15.3542 | −1.07239 | ||||||||
\(206\) | − | 1.60162i | − | 0.111590i | ||||||
\(207\) | −1.86522 | + | 3.26983i | −0.129641 | + | 0.227269i | ||||
\(208\) | − | 0.418899i | − | 0.0290454i | ||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | −8.90018 | + | 5.16945i | −0.614171 | + | 0.356726i | ||||
\(211\) | 18.3522i | 1.26342i | 0.775204 | + | 0.631710i | \(0.217647\pi\) | ||||
−0.775204 | + | 0.631710i | \(0.782353\pi\) | |||||||
\(212\) | 9.66765i | 0.663977i | ||||||||
\(213\) | 6.02086 | − | 3.49707i | 0.412543 | − | 0.239615i | ||||
\(214\) | − | 0.0585239i | − | 0.00400061i | ||||||
\(215\) | 5.94758 | 0.405622 | ||||||||
\(216\) | 5.19599 | − | 0.0405586i | 0.353543 | − | 0.00275966i | ||||
\(217\) | − | 37.3943i | − | 2.53849i | ||||||
\(218\) | − | 5.56810i | − | 0.377119i | ||||||
\(219\) | 16.0103 | − | 9.29920i | 1.08188 | − | 0.628382i | ||||
\(220\) | − | 8.00751i | − | 0.539866i | ||||||
\(221\) | −0.311137 | −0.0209294 | ||||||||
\(222\) | 9.01939 | − | 5.23868i | 0.605342 | − | 0.351597i | ||||
\(223\) | −11.9108 | −0.797607 | −0.398804 | − | 0.917036i | \(-0.630574\pi\) | ||||
−0.398804 | + | 0.917036i | \(0.630574\pi\) | |||||||
\(224\) | 3.57946 | 0.239163 | ||||||||
\(225\) | −3.33552 | + | 5.84736i | −0.222368 | + | 0.389824i | ||||
\(226\) | 3.43798 | 0.228691 | ||||||||
\(227\) | 8.70313 | 0.577647 | 0.288823 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288823 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(228\) | 1.08213 | + | 1.86310i | 0.0716659 | + | 0.123387i | ||||
\(229\) | − | 17.0329i | − | 1.12557i | −0.826604 | − | 0.562783i | \(-0.809730\pi\) | ||
0.826604 | − | 0.562783i | \(-0.190270\pi\) | |||||||
\(230\) | − | 2.08315i | − | 0.137359i | ||||||
\(231\) | 15.0194 | + | 25.8587i | 0.988203 | + | 1.70138i | ||||
\(232\) | 4.78075i | 0.313872i | ||||||||
\(233\) | 9.87973 | 0.647243 | 0.323621 | − | 0.946187i | \(-0.395100\pi\) | ||||
0.323621 | + | 0.946187i | \(0.395100\pi\) | |||||||
\(234\) | −1.09159 | − | 0.622676i | −0.0713592 | − | 0.0407056i | ||||
\(235\) | − | 13.9319i | − | 0.908815i | ||||||
\(236\) | 5.47701 | − | 5.38539i | 0.356523 | − | 0.350559i | ||||
\(237\) | 3.09495 | + | 5.32855i | 0.201039 | + | 0.346127i | ||||
\(238\) | − | 2.65865i | − | 0.172334i | ||||||
\(239\) | 6.14770i | 0.397662i | 0.980034 | + | 0.198831i | \(0.0637145\pi\) | ||||
−0.980034 | + | 0.198831i | \(0.936286\pi\) | |||||||
\(240\) | −2.48646 | + | 1.44420i | −0.160500 | + | 0.0932225i | ||||
\(241\) | 16.4096 | 1.05703 | 0.528516 | − | 0.848923i | \(-0.322749\pi\) | ||||
0.528516 | + | 0.848923i | \(0.322749\pi\) | |||||||
\(242\) | −12.2652 | −0.788434 | ||||||||
\(243\) | 7.61795 | − | 13.6003i | 0.488692 | − | 0.872457i | ||||
\(244\) | 9.08804i | 0.581802i | ||||||||
\(245\) | 9.64961i | 0.616491i | ||||||||
\(246\) | 13.8522 | − | 8.04572i | 0.883187 | − | 0.512977i | ||||
\(247\) | − | 0.521083i | − | 0.0331557i | ||||||
\(248\) | − | 10.4469i | − | 0.663380i | ||||||
\(249\) | −2.49944 | − | 4.30325i | −0.158395 | − | 0.272708i | ||||
\(250\) | − | 12.0259i | − | 0.760588i | ||||||
\(251\) | 5.45388i | 0.344246i | 0.985075 | + | 0.172123i | \(0.0550626\pi\) | ||||
−0.985075 | + | 0.172123i | \(0.944937\pi\) | |||||||
\(252\) | 5.32072 | − | 9.32752i | 0.335174 | − | 0.587579i | ||||
\(253\) | −6.05242 | −0.380512 | ||||||||
\(254\) | 22.0994 | 1.38664 | ||||||||
\(255\) | 1.07268 | + | 1.84682i | 0.0671737 | + | 0.115652i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 20.1335i | − | 1.25589i | −0.778256 | − | 0.627947i | \(-0.783895\pi\) | ||
0.778256 | − | 0.627947i | \(-0.216105\pi\) | |||||||
\(258\) | −5.36578 | + | 3.11658i | −0.334059 | + | 0.194030i | ||||
\(259\) | − | 21.5555i | − | 1.33939i | ||||||
\(260\) | 0.695430 | 0.0431288 | ||||||||
\(261\) | 12.4579 | + | 7.10640i | 0.771125 | + | 0.439875i | ||||
\(262\) | −13.6966 | −0.846176 | ||||||||
\(263\) | − | 28.6271i | − | 1.76522i | −0.470102 | − | 0.882612i | \(-0.655783\pi\) | ||
0.470102 | − | 0.882612i | \(-0.344217\pi\) | |||||||
\(264\) | 4.19599 | + | 7.22420i | 0.258246 | + | 0.444619i | ||||
\(265\) | −16.0496 | −0.985922 | ||||||||
\(266\) | 4.45262 | 0.273008 | ||||||||
\(267\) | 13.9958 | + | 24.0965i | 0.856531 | + | 1.47468i | ||||
\(268\) | 13.0941i | 0.799848i | ||||||||
\(269\) | 5.51883 | 0.336489 | 0.168244 | − | 0.985745i | \(-0.446190\pi\) | ||||
0.168244 | + | 0.985745i | \(0.446190\pi\) | |||||||
\(270\) | 0.0673329 | + | 8.62608i | 0.00409775 | + | 0.524966i | ||||
\(271\) | −30.9726 | −1.88145 | −0.940725 | − | 0.339170i | \(-0.889854\pi\) | ||||
−0.940725 | + | 0.339170i | \(0.889854\pi\) | |||||||
\(272\) | − | 0.742751i | − | 0.0450359i | ||||||
\(273\) | −2.24576 | + | 1.30439i | −0.135920 | + | 0.0789454i | ||||
\(274\) | − | 7.16560i | − | 0.432890i | ||||||
\(275\) | −10.8234 | −0.652675 | ||||||||
\(276\) | 1.09159 | + | 1.87937i | 0.0657057 | + | 0.113125i | ||||
\(277\) | 19.9781 | 1.20037 | 0.600185 | − | 0.799861i | \(-0.295094\pi\) | ||||
0.600185 | + | 0.799861i | \(0.295094\pi\) | |||||||
\(278\) | −5.20504 | −0.312177 | ||||||||
\(279\) | −27.2231 | − | 15.5289i | −1.62980 | − | 0.929693i | ||||
\(280\) | 5.94240i | 0.355126i | ||||||||
\(281\) | − | 23.4938i | − | 1.40152i | −0.713395 | − | 0.700762i | \(-0.752844\pi\) | ||
0.713395 | − | 0.700762i | \(-0.247156\pi\) | |||||||
\(282\) | 7.30040 | + | 12.5690i | 0.434733 | + | 0.748475i | ||||
\(283\) | − | 13.7557i | − | 0.817692i | −0.912603 | − | 0.408846i | \(-0.865931\pi\) | ||
0.912603 | − | 0.408846i | \(-0.134069\pi\) | |||||||
\(284\) | − | 4.01996i | − | 0.238541i | ||||||
\(285\) | −3.09300 | + | 1.79649i | −0.183213 | + | 0.106415i | ||||
\(286\) | − | 2.02051i | − | 0.119476i | ||||||
\(287\) | − | 33.1055i | − | 1.95416i | ||||||
\(288\) | 1.48646 | − | 2.60585i | 0.0875905 | − | 0.153551i | ||||
\(289\) | 16.4483 | 0.967548 | ||||||||
\(290\) | −7.93672 | −0.466060 | ||||||||
\(291\) | 17.2652 | − | 10.0280i | 1.01210 | − | 0.587853i | ||||
\(292\) | − | 10.6897i | − | 0.625565i | ||||||
\(293\) | 19.3118i | 1.12821i | 0.825704 | + | 0.564103i | \(0.190778\pi\) | ||||
−0.825704 | + | 0.564103i | \(0.809222\pi\) | |||||||
\(294\) | −5.05647 | − | 8.70567i | −0.294899 | − | 0.507725i | ||||
\(295\) | 8.94049 | + | 9.09259i | 0.520536 | + | 0.529391i | ||||
\(296\) | − | 6.02199i | − | 0.350021i | ||||||
\(297\) | 25.0623 | − | 0.195630i | 1.45426 | − | 0.0113516i | ||||
\(298\) | 8.82075 | 0.510972 | ||||||||
\(299\) | − | 0.525636i | − | 0.0303983i | ||||||
\(300\) | 1.95206 | + | 3.36084i | 0.112702 | + | 0.194038i | ||||
\(301\) | 12.8237i | 0.739146i | ||||||||
\(302\) | − | 0.872794i | − | 0.0502237i | ||||||
\(303\) | 9.79984 | + | 16.8723i | 0.562986 | + | 0.969287i | ||||
\(304\) | 1.24394 | 0.0713447 | ||||||||
\(305\) | −15.0874 | −0.863903 | ||||||||
\(306\) | −1.93549 | − | 1.10407i | −0.110645 | − | 0.0631154i | ||||
\(307\) | −26.6117 | −1.51881 | −0.759404 | − | 0.650619i | \(-0.774509\pi\) | ||||
−0.759404 | + | 0.650619i | \(0.774509\pi\) | |||||||
\(308\) | 17.2652 | 0.983773 | ||||||||
\(309\) | −2.39881 | + | 1.39329i | −0.136463 | + | 0.0792613i | ||||
\(310\) | 17.3434 | 0.985036 | ||||||||
\(311\) | 13.4625i | 0.763389i | 0.924288 | + | 0.381695i | \(0.124659\pi\) | ||||
−0.924288 | + | 0.381695i | \(0.875341\pi\) | |||||||
\(312\) | −0.627402 | + | 0.364411i | −0.0355196 | + | 0.0206307i | ||||
\(313\) | 4.24421i | 0.239897i | 0.992780 | + | 0.119949i | \(0.0382730\pi\) | ||||
−0.992780 | + | 0.119949i | \(0.961727\pi\) | |||||||
\(314\) | 23.3287i | 1.31652i | ||||||||
\(315\) | 15.4850 | + | 8.83314i | 0.872480 | + | 0.497691i | ||||
\(316\) | 3.55772 | 0.200138 | ||||||||
\(317\) | 5.48243i | 0.307924i | 0.988077 | + | 0.153962i | \(0.0492033\pi\) | ||||
−0.988077 | + | 0.153962i | \(0.950797\pi\) | |||||||
\(318\) | 14.4796 | − | 8.41013i | 0.811978 | − | 0.471617i | ||||
\(319\) | 23.0595i | 1.29108i | ||||||||
\(320\) | 1.66014i | 0.0928046i | ||||||||
\(321\) | −0.0876537 | + | 0.0509114i | −0.00489235 | + | 0.00284160i | ||||
\(322\) | 4.49152 | 0.250303 | ||||||||
\(323\) | − | 0.923935i | − | 0.0514091i | ||||||
\(324\) | −4.58087 | − | 7.74697i | −0.254493 | − | 0.430387i | ||||
\(325\) | − | 0.939982i | − | 0.0521408i | ||||||
\(326\) | −4.74255 | −0.262665 | ||||||||
\(327\) | −8.33957 | + | 4.84383i | −0.461179 | + | 0.267864i | ||||
\(328\) | − | 9.24875i | − | 0.510677i | ||||||
\(329\) | 30.0388 | 1.65609 | ||||||||
\(330\) | −11.9932 | + | 6.96594i | −0.660203 | + | 0.383462i | ||||
\(331\) | 32.1662 | 1.76802 | 0.884008 | − | 0.467472i | \(-0.154835\pi\) | ||||
0.884008 | + | 0.467472i | \(0.154835\pi\) | |||||||
\(332\) | −2.87316 | −0.157685 | ||||||||
\(333\) | −15.6924 | − | 8.95145i | −0.859938 | − | 0.490537i | ||||
\(334\) | 7.18517i | 0.393155i | ||||||||
\(335\) | −21.7380 | −1.18767 | ||||||||
\(336\) | −3.11386 | − | 5.36111i | −0.169875 | − | 0.292472i | ||||
\(337\) | 17.9638i | 0.978550i | 0.872129 | + | 0.489275i | \(0.162739\pi\) | ||||
−0.872129 | + | 0.489275i | \(0.837261\pi\) | |||||||
\(338\) | −12.8245 | −0.697562 | ||||||||
\(339\) | −2.99078 | − | 5.14920i | −0.162437 | − | 0.279666i | ||||
\(340\) | 1.23307 | 0.0668726 | ||||||||
\(341\) | − | 50.3896i | − | 2.72875i | ||||||
\(342\) | 1.84906 | − | 3.24151i | 0.0999858 | − | 0.175281i | ||||
\(343\) | 4.25050 | 0.229506 | ||||||||
\(344\) | 3.58258i | 0.193160i | ||||||||
\(345\) | −3.12002 | + | 1.81218i | −0.167976 | + | 0.0975647i | ||||
\(346\) | −4.12797 | −0.221921 | ||||||||
\(347\) | 30.2193 | 1.62226 | 0.811129 | − | 0.584868i | \(-0.198854\pi\) | ||||
0.811129 | + | 0.584868i | \(0.198854\pi\) | |||||||
\(348\) | 7.16033 | − | 4.15890i | 0.383834 | − | 0.222940i | ||||
\(349\) | 27.1281i | 1.45214i | 0.687623 | + | 0.726068i | \(0.258654\pi\) | ||||
−0.687623 | + | 0.726068i | \(0.741346\pi\) | |||||||
\(350\) | 8.03208 | 0.429333 | ||||||||
\(351\) | 0.0169899 | + | 2.17660i | 0.000906856 | + | 0.116178i | ||||
\(352\) | 4.82340 | 0.257088 | ||||||||
\(353\) | −15.5292 | −0.826534 | −0.413267 | − | 0.910610i | \(-0.635612\pi\) | ||||
−0.413267 | + | 0.910610i | \(0.635612\pi\) | |||||||
\(354\) | −12.8305 | − | 3.51826i | −0.681934 | − | 0.186993i | ||||
\(355\) | 6.67370 | 0.354203 | ||||||||
\(356\) | 16.0885 | 0.852691 | ||||||||
\(357\) | −3.98196 | + | 2.31282i | −0.210748 | + | 0.122408i | ||||
\(358\) | 12.7736 | 0.675107 | ||||||||
\(359\) | 9.70378i | 0.512146i | 0.966657 | + | 0.256073i | \(0.0824287\pi\) | ||||
−0.966657 | + | 0.256073i | \(0.917571\pi\) | |||||||
\(360\) | 4.32607 | + | 2.46773i | 0.228004 | + | 0.130061i | ||||
\(361\) | −17.4526 | −0.918559 | ||||||||
\(362\) | 6.91511 | 0.363450 | ||||||||
\(363\) | 10.6698 | + | 18.3700i | 0.560017 | + | 0.964176i | ||||
\(364\) | 1.49943i | 0.0785915i | ||||||||
\(365\) | 17.7463 | 0.928885 | ||||||||
\(366\) | 13.6115 | − | 7.90592i | 0.711487 | − | 0.413249i | ||||
\(367\) | 21.1320i | 1.10308i | 0.834147 | + | 0.551541i | \(0.185960\pi\) | ||||
−0.834147 | + | 0.551541i | \(0.814040\pi\) | |||||||
\(368\) | 1.25480 | 0.0654112 | ||||||||
\(369\) | −24.1008 | − | 13.7479i | −1.25464 | − | 0.715687i | ||||
\(370\) | 9.99735 | 0.519737 | ||||||||
\(371\) | − | 34.6050i | − | 1.79660i | ||||||
\(372\) | −15.6468 | + | 9.08804i | −0.811248 | + | 0.471193i | ||||
\(373\) | −26.4779 | −1.37097 | −0.685486 | − | 0.728085i | \(-0.740410\pi\) | ||||
−0.685486 | + | 0.728085i | \(0.740410\pi\) | |||||||
\(374\) | − | 3.58258i | − | 0.185251i | ||||||
\(375\) | −18.0118 | + | 10.4617i | −0.930123 | + | 0.540239i | ||||
\(376\) | 8.39199 | 0.432784 | ||||||||
\(377\) | −2.00265 | −0.103142 | ||||||||
\(378\) | −18.5988 | + | 0.145178i | −0.956622 | + | 0.00746714i | ||||
\(379\) | 2.78409 | 0.143009 | 0.0715047 | − | 0.997440i | \(-0.477220\pi\) | ||||
0.0715047 | + | 0.997440i | \(0.477220\pi\) | |||||||
\(380\) | 2.06511i | 0.105938i | ||||||||
\(381\) | −19.2248 | − | 33.0992i | −0.984918 | − | 1.69572i | ||||
\(382\) | 3.69921 | 0.189268 | ||||||||
\(383\) | 35.3588i | 1.80675i | 0.428853 | + | 0.903374i | \(0.358918\pi\) | ||||
−0.428853 | + | 0.903374i | \(0.641082\pi\) | |||||||
\(384\) | −0.869925 | − | 1.49774i | −0.0443932 | − | 0.0764313i | ||||
\(385\) | 28.6626i | 1.46078i | ||||||||
\(386\) | 11.9714 | 0.609331 | ||||||||
\(387\) | 9.33565 | + | 5.32536i | 0.474558 | + | 0.270703i | ||||
\(388\) | − | 11.5275i | − | 0.585218i | ||||||
\(389\) | 12.5625i | 0.636943i | 0.947932 | + | 0.318472i | \(0.103170\pi\) | ||||
−0.947932 | + | 0.318472i | \(0.896830\pi\) | |||||||
\(390\) | −0.604972 | − | 1.04157i | −0.0306340 | − | 0.0527422i | ||||
\(391\) | − | 0.932006i | − | 0.0471336i | ||||||
\(392\) | −5.81253 | −0.293577 | ||||||||
\(393\) | 11.9150 | + | 20.5139i | 0.601031 | + | 1.03479i | ||||
\(394\) | − | 12.7702i | − | 0.643354i | ||||||
\(395\) | 5.90632i | 0.297179i | ||||||||
\(396\) | 7.16979 | − | 12.5690i | 0.360295 | − | 0.631618i | ||||
\(397\) | 32.5653i | 1.63440i | 0.576351 | + | 0.817202i | \(0.304476\pi\) | ||||
−0.576351 | + | 0.817202i | \(0.695524\pi\) | |||||||
\(398\) | −7.63327 | −0.382621 | ||||||||
\(399\) | −3.87345 | − | 6.66888i | −0.193915 | − | 0.333861i | ||||
\(400\) | 2.24394 | 0.112197 | ||||||||
\(401\) | −25.7353 | −1.28516 | −0.642581 | − | 0.766218i | \(-0.722136\pi\) | ||||
−0.642581 | + | 0.766218i | \(0.722136\pi\) | |||||||
\(402\) | 19.6115 | − | 11.3909i | 0.978135 | − | 0.568125i | ||||
\(403\) | 4.37620 | 0.217994 | ||||||||
\(404\) | 11.2652 | 0.560462 | ||||||||
\(405\) | 12.8611 | − | 7.60489i | 0.639071 | − | 0.377890i | ||||
\(406\) | − | 17.1125i | − | 0.849280i | ||||||
\(407\) | − | 29.0465i | − | 1.43978i | ||||||
\(408\) | −1.11245 | + | 0.646138i | −0.0550744 | + | 0.0319886i | ||||
\(409\) | − | 2.79568i | − | 0.138237i | −0.997608 | − | 0.0691186i | \(-0.977981\pi\) | ||
0.997608 | − | 0.0691186i | \(-0.0220187\pi\) | |||||||
\(410\) | 15.3542 | 0.758291 | ||||||||
\(411\) | −10.7322 | + | 6.23354i | −0.529381 | + | 0.307478i | ||||
\(412\) | 1.60162i | 0.0789059i | ||||||||
\(413\) | −19.6047 | + | 19.2768i | −0.964685 | + | 0.948548i | ||||
\(414\) | 1.86522 | − | 3.26983i | 0.0916704 | − | 0.160703i | ||||
\(415\) | − | 4.76985i | − | 0.234143i | ||||||
\(416\) | 0.418899i | 0.0205382i | ||||||||
\(417\) | 4.52799 | + | 7.79580i | 0.221737 | + | 0.381762i | ||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −26.4494 | −1.29214 | −0.646070 | − | 0.763278i | \(-0.723589\pi\) | ||||
−0.646070 | + | 0.763278i | \(0.723589\pi\) | |||||||
\(420\) | 8.90018 | − | 5.16945i | 0.434284 | − | 0.252243i | ||||
\(421\) | 11.9509i | 0.582452i | 0.956654 | + | 0.291226i | \(0.0940631\pi\) | ||||
−0.956654 | + | 0.291226i | \(0.905937\pi\) | |||||||
\(422\) | − | 18.3522i | − | 0.893374i | ||||||
\(423\) | 12.4744 | − | 21.8682i | 0.606524 | − | 1.06327i | ||||
\(424\) | − | 9.66765i | − | 0.469503i | ||||||
\(425\) | − | 1.66669i | − | 0.0808461i | ||||||
\(426\) | −6.02086 | + | 3.49707i | −0.291712 | + | 0.169433i | ||||
\(427\) | − | 32.5303i | − | 1.57425i | ||||||
\(428\) | 0.0585239i | 0.00282886i | ||||||||
\(429\) | −3.02621 | + | 1.75770i | −0.146107 | + | 0.0848624i | ||||
\(430\) | −5.94758 | −0.286818 | ||||||||
\(431\) | 11.5375 | 0.555742 | 0.277871 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277871 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(432\) | −5.19599 | + | 0.0405586i | −0.249992 | + | 0.00195138i | ||||
\(433\) | −36.2956 | −1.74425 | −0.872127 | − | 0.489279i | \(-0.837260\pi\) | ||||
−0.872127 | + | 0.489279i | \(0.837260\pi\) | |||||||
\(434\) | 37.3943i | 1.79499i | ||||||||
\(435\) | 6.90435 | + | 11.8872i | 0.331038 | + | 0.569945i | ||||
\(436\) | 5.56810i | 0.266664i | ||||||||
\(437\) | 1.56090 | 0.0746678 | ||||||||
\(438\) | −16.0103 | + | 9.29920i | −0.765004 | + | 0.444333i | ||||
\(439\) | 11.5445 | 0.550988 | 0.275494 | − | 0.961303i | \(-0.411159\pi\) | ||||
0.275494 | + | 0.961303i | \(0.411159\pi\) | |||||||
\(440\) | 8.00751i | 0.381743i | ||||||||
\(441\) | −8.64009 | + | 15.1466i | −0.411433 | + | 0.721265i | ||||
\(442\) | 0.311137 | 0.0147993 | ||||||||
\(443\) | 12.3499 | 0.586762 | 0.293381 | − | 0.955996i | \(-0.405220\pi\) | ||||
0.293381 | + | 0.955996i | \(0.405220\pi\) | |||||||
\(444\) | −9.01939 | + | 5.23868i | −0.428041 | + | 0.248617i | ||||
\(445\) | 26.7092i | 1.26614i | ||||||||
\(446\) | 11.9108 | 0.563993 | ||||||||
\(447\) | −7.67339 | − | 13.2112i | −0.362939 | − | 0.624868i | ||||
\(448\) | −3.57946 | −0.169114 | ||||||||
\(449\) | − | 28.4979i | − | 1.34490i | −0.740143 | − | 0.672450i | \(-0.765242\pi\) | ||
0.740143 | − | 0.672450i | \(-0.234758\pi\) | |||||||
\(450\) | 3.33552 | − | 5.84736i | 0.157238 | − | 0.275647i | ||||
\(451\) | − | 44.6104i | − | 2.10062i | ||||||
\(452\) | −3.43798 | −0.161709 | ||||||||
\(453\) | −1.30722 | + | 0.759266i | −0.0614186 | + | 0.0356734i | ||||
\(454\) | −8.70313 | −0.408458 | ||||||||
\(455\) | −2.48926 | −0.116699 | ||||||||
\(456\) | −1.08213 | − | 1.86310i | −0.0506755 | − | 0.0872475i | ||||
\(457\) | 22.4605i | 1.05066i | 0.850900 | + | 0.525328i | \(0.176057\pi\) | ||||
−0.850900 | + | 0.525328i | \(0.823943\pi\) | |||||||
\(458\) | 17.0329i | 0.795896i | ||||||||
\(459\) | 0.0301249 | + | 3.85933i | 0.00140611 | + | 0.180138i | ||||
\(460\) | 2.08315i | 0.0971274i | ||||||||
\(461\) | − | 6.76019i | − | 0.314854i | −0.987531 | − | 0.157427i | \(-0.949680\pi\) | ||
0.987531 | − | 0.157427i | \(-0.0503198\pi\) | |||||||
\(462\) | −15.0194 | − | 25.8587i | −0.698765 | − | 1.20306i | ||||
\(463\) | − | 32.1740i | − | 1.49525i | −0.664119 | − | 0.747627i | \(-0.731193\pi\) | ||
0.664119 | − | 0.747627i | \(-0.268807\pi\) | |||||||
\(464\) | − | 4.78075i | − | 0.221941i | ||||||
\(465\) | −15.0874 | − | 25.9759i | −0.699662 | − | 1.20460i | ||||
\(466\) | −9.87973 | −0.457670 | ||||||||
\(467\) | −29.7721 | −1.37769 | −0.688844 | − | 0.724909i | \(-0.741882\pi\) | ||||
−0.688844 | + | 0.724909i | \(0.741882\pi\) | |||||||
\(468\) | 1.09159 | + | 0.622676i | 0.0504586 | + | 0.0287832i | ||||
\(469\) | − | 46.8697i | − | 2.16424i | ||||||
\(470\) | 13.9319i | 0.642629i | ||||||||
\(471\) | 34.9404 | − | 20.2942i | 1.60997 | − | 0.935109i | ||||
\(472\) | −5.47701 | + | 5.38539i | −0.252100 | + | 0.247883i | ||||
\(473\) | 17.2802i | 0.794545i | ||||||||
\(474\) | −3.09495 | − | 5.32855i | −0.142156 | − | 0.244749i | ||||
\(475\) | 2.79132 | 0.128074 | ||||||||
\(476\) | 2.65865i | 0.121859i | ||||||||
\(477\) | −25.1924 | − | 14.3706i | −1.15348 | − | 0.657983i | ||||
\(478\) | − | 6.14770i | − | 0.281189i | ||||||
\(479\) | − | 11.4600i | − | 0.523623i | −0.965119 | − | 0.261811i | \(-0.915680\pi\) | ||
0.965119 | − | 0.261811i | \(-0.0843199\pi\) | |||||||
\(480\) | 2.48646 | − | 1.44420i | 0.113491 | − | 0.0659183i | ||||
\(481\) | 2.52261 | 0.115021 | ||||||||
\(482\) | −16.4096 | −0.747435 | ||||||||
\(483\) | −3.90729 | − | 6.72714i | −0.177788 | − | 0.306095i | ||||
\(484\) | 12.2652 | 0.557507 | ||||||||
\(485\) | 19.1372 | 0.868975 | ||||||||
\(486\) | −7.61795 | + | 13.6003i | −0.345557 | + | 0.616920i | ||||
\(487\) | 8.42054 | 0.381571 | 0.190786 | − | 0.981632i | \(-0.438896\pi\) | ||||
0.190786 | + | 0.981632i | \(0.438896\pi\) | |||||||
\(488\) | − | 9.08804i | − | 0.411396i | ||||||
\(489\) | 4.12566 | + | 7.10311i | 0.186569 | + | 0.321214i | ||||
\(490\) | − | 9.64961i | − | 0.435925i | ||||||
\(491\) | − | 7.10664i | − | 0.320718i | −0.987059 | − | 0.160359i | \(-0.948735\pi\) | ||
0.987059 | − | 0.160359i | \(-0.0512652\pi\) | |||||||
\(492\) | −13.8522 | + | 8.04572i | −0.624507 | + | 0.362729i | ||||
\(493\) | −3.55091 | −0.159925 | ||||||||
\(494\) | 0.521083i | 0.0234447i | ||||||||
\(495\) | 20.8663 | + | 11.9028i | 0.937872 | + | 0.534993i | ||||
\(496\) | 10.4469i | 0.469081i | ||||||||
\(497\) | 14.3893i | 0.645448i | ||||||||
\(498\) | 2.49944 | + | 4.30325i | 0.112002 | + | 0.192833i | ||||
\(499\) | 33.2330 | 1.48771 | 0.743856 | − | 0.668340i | \(-0.232995\pi\) | ||||
0.743856 | + | 0.668340i | \(0.232995\pi\) | |||||||
\(500\) | 12.0259i | 0.537817i | ||||||||
\(501\) | 10.7615 | − | 6.25056i | 0.480790 | − | 0.279254i | ||||
\(502\) | − | 5.45388i | − | 0.243419i | ||||||
\(503\) | −41.4063 | −1.84621 | −0.923107 | − | 0.384544i | \(-0.874359\pi\) | ||||
−0.923107 | + | 0.384544i | \(0.874359\pi\) | |||||||
\(504\) | −5.32072 | + | 9.32752i | −0.237004 | + | 0.415481i | ||||
\(505\) | 18.7017i | 0.832216i | ||||||||
\(506\) | 6.05242 | 0.269063 | ||||||||
\(507\) | 11.1564 | + | 19.2078i | 0.495472 | + | 0.853049i | ||||
\(508\) | −22.0994 | −0.980503 | ||||||||
\(509\) | 7.71730 | 0.342063 | 0.171032 | − | 0.985266i | \(-0.445290\pi\) | ||||
0.171032 | + | 0.985266i | \(0.445290\pi\) | |||||||
\(510\) | −1.07268 | − | 1.84682i | −0.0474990 | − | 0.0817786i | ||||
\(511\) | 38.2632i | 1.69266i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.46349 | + | 0.0504523i | −0.285370 | + | 0.00222753i | ||||
\(514\) | 20.1335i | 0.888052i | ||||||||
\(515\) | −2.65891 | −0.117165 | ||||||||
\(516\) | 5.36578 | − | 3.11658i | 0.236215 | − | 0.137200i | ||||
\(517\) | 40.4779 | 1.78022 | ||||||||
\(518\) | 21.5555i | 0.947093i | ||||||||
\(519\) | 3.59102 | + | 6.18263i | 0.157628 | + | 0.271387i | ||||
\(520\) | −0.695430 | −0.0304966 | ||||||||
\(521\) | 40.0700i | 1.75550i | 0.479122 | + | 0.877748i | \(0.340955\pi\) | ||||
−0.479122 | + | 0.877748i | \(0.659045\pi\) | |||||||
\(522\) | −12.4579 | − | 7.10640i | −0.545268 | − | 0.311039i | ||||
\(523\) | 1.42446 | 0.0622872 | 0.0311436 | − | 0.999515i | \(-0.490085\pi\) | ||||
0.0311436 | + | 0.999515i | \(0.490085\pi\) | |||||||
\(524\) | 13.6966 | 0.598337 | ||||||||
\(525\) | −6.98731 | − | 12.0300i | −0.304951 | − | 0.525031i | ||||
\(526\) | 28.6271i | 1.24820i | ||||||||
\(527\) | 7.75946 | 0.338007 | ||||||||
\(528\) | −4.19599 | − | 7.22420i | −0.182607 | − | 0.314393i | ||||
\(529\) | −21.4255 | −0.931542 | ||||||||
\(530\) | 16.0496 | 0.697152 | ||||||||
\(531\) | 5.89214 | + | 22.2774i | 0.255697 | + | 0.966757i | ||||
\(532\) | −4.45262 | −0.193046 | ||||||||
\(533\) | 3.87429 | 0.167814 | ||||||||
\(534\) | −13.9958 | − | 24.0965i | −0.605659 | − | 1.04276i | ||||
\(535\) | −0.0971579 | −0.00420050 | ||||||||
\(536\) | − | 13.0941i | − | 0.565578i | ||||||
\(537\) | −11.1121 | − | 19.1316i | −0.479523 | − | 0.825589i | ||||
\(538\) | −5.51883 | −0.237933 | ||||||||
\(539\) | −28.0361 | −1.20760 | ||||||||
\(540\) | −0.0673329 | − | 8.62608i | −0.00289755 | − | 0.371207i | ||||
\(541\) | − | 23.6082i | − | 1.01500i | −0.861653 | − | 0.507498i | \(-0.830571\pi\) | ||
0.861653 | − | 0.507498i | \(-0.169429\pi\) | |||||||
\(542\) | 30.9726 | 1.33039 | ||||||||
\(543\) | −6.01563 | − | 10.3571i | −0.258156 | − | 0.444464i | ||||
\(544\) | 0.742751i | 0.0318452i | ||||||||
\(545\) | −9.24382 | −0.395962 | ||||||||
\(546\) | 2.24576 | − | 1.30439i | 0.0961097 | − | 0.0558229i | ||||
\(547\) | 21.2284 | 0.907660 | 0.453830 | − | 0.891088i | \(-0.350057\pi\) | ||||
0.453830 | + | 0.891088i | \(0.350057\pi\) | |||||||
\(548\) | 7.16560i | 0.306099i | ||||||||
\(549\) | −23.6820 | − | 13.5090i | −1.01073 | − | 0.576551i | ||||
\(550\) | 10.8234 | 0.461511 | ||||||||
\(551\) | − | 5.94695i | − | 0.253349i | ||||||
\(552\) | −1.09159 | − | 1.87937i | −0.0464610 | − | 0.0799914i | ||||
\(553\) | −12.7347 | −0.541536 | ||||||||
\(554\) | −19.9781 | −0.848790 | ||||||||
\(555\) | −8.69695 | − | 14.9734i | −0.369165 | − | 0.635587i | ||||
\(556\) | 5.20504 | 0.220743 | ||||||||
\(557\) | 27.9493i | 1.18425i | 0.805846 | + | 0.592126i | \(0.201711\pi\) | ||||
−0.805846 | + | 0.592126i | \(0.798289\pi\) | |||||||
\(558\) | 27.2231 | + | 15.5289i | 1.15244 | + | 0.657392i | ||||
\(559\) | −1.50074 | −0.0634745 | ||||||||
\(560\) | − | 5.94240i | − | 0.251112i | ||||||
\(561\) | −5.36578 | + | 3.11658i | −0.226543 | + | 0.131582i | ||||
\(562\) | 23.4938i | 0.991027i | ||||||||
\(563\) | 39.1650 | 1.65061 | 0.825304 | − | 0.564689i | \(-0.191004\pi\) | ||||
0.825304 | + | 0.564689i | \(0.191004\pi\) | |||||||
\(564\) | −7.30040 | − | 12.5690i | −0.307402 | − | 0.529252i | ||||
\(565\) | − | 5.70752i | − | 0.240117i | ||||||
\(566\) | 13.7557i | 0.578196i | ||||||||
\(567\) | 16.3970 | + | 27.7300i | 0.688611 | + | 1.16455i | ||||
\(568\) | 4.01996i | 0.168674i | ||||||||
\(569\) | 7.87708 | 0.330224 | 0.165112 | − | 0.986275i | \(-0.447201\pi\) | ||||
0.165112 | + | 0.986275i | \(0.447201\pi\) | |||||||
\(570\) | 3.09300 | − | 1.79649i | 0.129551 | − | 0.0752467i | ||||
\(571\) | 21.5046i | 0.899939i | 0.893044 | + | 0.449969i | \(0.148565\pi\) | ||||
−0.893044 | + | 0.449969i | \(0.851435\pi\) | |||||||
\(572\) | 2.02051i | 0.0844819i | ||||||||
\(573\) | −3.21804 | − | 5.54046i | −0.134435 | − | 0.231456i | ||||
\(574\) | 33.1055i | 1.38180i | ||||||||
\(575\) | 2.81570 | 0.117423 | ||||||||
\(576\) | −1.48646 | + | 2.60585i | −0.0619358 | + | 0.108577i | ||||
\(577\) | 33.8946 | 1.41105 | 0.705526 | − | 0.708684i | \(-0.250711\pi\) | ||||
0.705526 | + | 0.708684i | \(0.250711\pi\) | |||||||
\(578\) | −16.4483 | −0.684160 | ||||||||
\(579\) | −10.4143 | − | 17.9301i | −0.432802 | − | 0.745151i | ||||
\(580\) | 7.93672 | 0.329554 | ||||||||
\(581\) | 10.2844 | 0.426667 | ||||||||
\(582\) | −17.2652 | + | 10.0280i | −0.715663 | + | 0.415675i | ||||
\(583\) | − | 46.6309i | − | 1.93125i | ||||||
\(584\) | 10.6897i | 0.442341i | ||||||||
\(585\) | −1.03373 | + | 1.81218i | −0.0427394 | + | 0.0749246i | ||||
\(586\) | − | 19.3118i | − | 0.797762i | ||||||
\(587\) | 7.95528 | 0.328349 | 0.164175 | − | 0.986431i | \(-0.447504\pi\) | ||||
0.164175 | + | 0.986431i | \(0.447504\pi\) | |||||||
\(588\) | 5.05647 | + | 8.70567i | 0.208525 | + | 0.359016i | ||||
\(589\) | 12.9953i | 0.535463i | ||||||||
\(590\) | −8.94049 | − | 9.09259i | −0.368074 | − | 0.374336i | ||||
\(591\) | −19.1265 | + | 11.1091i | −0.786759 | + | 0.456969i | ||||
\(592\) | 6.02199i | 0.247502i | ||||||||
\(593\) | − | 5.58810i | − | 0.229476i | −0.993396 | − | 0.114738i | \(-0.963397\pi\) | ||
0.993396 | − | 0.114738i | \(-0.0366028\pi\) | |||||||
\(594\) | −25.0623 | + | 0.195630i | −1.02832 | + | 0.00802680i | ||||
\(595\) | −4.41372 | −0.180945 | ||||||||
\(596\) | −8.82075 | −0.361312 | ||||||||
\(597\) | 6.64038 | + | 11.4327i | 0.271773 | + | 0.467908i | ||||
\(598\) | 0.525636i | 0.0214948i | ||||||||
\(599\) | 32.0609i | 1.30997i | 0.755640 | + | 0.654987i | \(0.227326\pi\) | ||||
−0.755640 | + | 0.654987i | \(0.772674\pi\) | |||||||
\(600\) | −1.95206 | − | 3.36084i | −0.0796924 | − | 0.137206i | ||||
\(601\) | − | 21.2151i | − | 0.865383i | −0.901542 | − | 0.432691i | \(-0.857564\pi\) | ||
0.901542 | − | 0.432691i | \(-0.142436\pi\) | |||||||
\(602\) | − | 12.8237i | − | 0.522655i | ||||||
\(603\) | −34.1211 | − | 19.4638i | −1.38952 | − | 0.792628i | ||||
\(604\) | 0.872794i | 0.0355135i | ||||||||
\(605\) | 20.3619i | 0.827827i | ||||||||
\(606\) | −9.79984 | − | 16.8723i | −0.398091 | − | 0.685390i | ||||
\(607\) | 21.2904 | 0.864151 | 0.432076 | − | 0.901837i | \(-0.357781\pi\) | ||||
0.432076 | + | 0.901837i | \(0.357781\pi\) | |||||||
\(608\) | −1.24394 | −0.0504483 | ||||||||
\(609\) | −25.6301 | + | 14.8866i | −1.03858 | + | 0.603236i | ||||
\(610\) | 15.0874 | 0.610872 | ||||||||
\(611\) | 3.51539i | 0.142218i | ||||||||
\(612\) | 1.93549 | + | 1.10407i | 0.0782377 | + | 0.0446293i | ||||
\(613\) | − | 9.86776i | − | 0.398555i | −0.979943 | − | 0.199277i | \(-0.936140\pi\) | ||
0.979943 | − | 0.199277i | \(-0.0638595\pi\) | |||||||
\(614\) | 26.6117 | 1.07396 | ||||||||
\(615\) | −13.3570 | − | 22.9967i | −0.538607 | − | 0.927314i | ||||
\(616\) | −17.2652 | −0.695633 | ||||||||
\(617\) | 26.3747i | 1.06181i | 0.847432 | + | 0.530904i | \(0.178147\pi\) | ||||
−0.847432 | + | 0.530904i | \(0.821853\pi\) | |||||||
\(618\) | 2.39881 | − | 1.39329i | 0.0964941 | − | 0.0560462i | ||||
\(619\) | 7.99178 | 0.321217 | 0.160608 | − | 0.987018i | \(-0.448654\pi\) | ||||
0.160608 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(620\) | −17.3434 | −0.696526 | ||||||||
\(621\) | −6.51995 | + | 0.0508931i | −0.261637 | + | 0.00204227i | ||||
\(622\) | − | 13.4625i | − | 0.539798i | ||||||
\(623\) | −57.5883 | −2.30723 | ||||||||
\(624\) | 0.627402 | − | 0.364411i | 0.0251162 | − | 0.0145881i | ||||
\(625\) | −8.74506 | −0.349803 | ||||||||
\(626\) | − | 4.24421i | − | 0.169633i | ||||||
\(627\) | −5.21955 | − | 8.98645i | −0.208449 | − | 0.358884i | ||||
\(628\) | − | 23.3287i | − | 0.930917i | ||||||
\(629\) | 4.47284 | 0.178344 | ||||||||
\(630\) | −15.4850 | − | 8.83314i | −0.616937 | − | 0.351921i | ||||
\(631\) | −25.0296 | −0.996411 | −0.498206 | − | 0.867059i | \(-0.666008\pi\) | ||||
−0.498206 | + | 0.867059i | \(0.666008\pi\) | |||||||
\(632\) | −3.55772 | −0.141519 | ||||||||
\(633\) | −27.4869 | + | 15.9651i | −1.09251 | + | 0.634555i | ||||
\(634\) | − | 5.48243i | − | 0.217735i | ||||||
\(635\) | − | 36.6881i | − | 1.45592i | ||||||
\(636\) | −14.4796 | + | 8.41013i | −0.574155 | + | 0.333483i | ||||
\(637\) | − | 2.43486i | − | 0.0964727i | ||||||
\(638\) | − | 23.0595i | − | 0.912933i | ||||||
\(639\) | 10.4754 | + | 5.97551i | 0.414400 | + | 0.236388i | ||||
\(640\) | − | 1.66014i | − | 0.0656228i | ||||||
\(641\) | − | 9.52542i | − | 0.376232i | −0.982147 | − | 0.188116i | \(-0.939762\pi\) | ||
0.982147 | − | 0.188116i | \(-0.0602380\pi\) | |||||||
\(642\) | 0.0876537 | − | 0.0509114i | 0.00345942 | − | 0.00200931i | ||||
\(643\) | 23.2413 | 0.916547 | 0.458273 | − | 0.888811i | \(-0.348468\pi\) | ||||
0.458273 | + | 0.888811i | \(0.348468\pi\) | |||||||
\(644\) | −4.49152 | −0.176991 | ||||||||
\(645\) | 5.17395 | + | 8.90794i | 0.203724 | + | 0.350750i | ||||
\(646\) | 0.923935i | 0.0363517i | ||||||||
\(647\) | 8.94338i | 0.351601i | 0.984426 | + | 0.175800i | \(0.0562513\pi\) | ||||
−0.984426 | + | 0.175800i | \(0.943749\pi\) | |||||||
\(648\) | 4.58087 | + | 7.74697i | 0.179954 | + | 0.304330i | ||||
\(649\) | −26.4178 | + | 25.9759i | −1.03699 | + | 1.01964i | ||||
\(650\) | 0.939982i | 0.0368691i | ||||||||
\(651\) | 56.0071 | − | 32.5303i | 2.19509 | − | 1.27496i | ||||
\(652\) | 4.74255 | 0.185732 | ||||||||
\(653\) | − | 16.9383i | − | 0.662846i | −0.943482 | − | 0.331423i | \(-0.892471\pi\) | ||
0.943482 | − | 0.331423i | \(-0.107529\pi\) | |||||||
\(654\) | 8.33957 | − | 4.84383i | 0.326103 | − | 0.189409i | ||||
\(655\) | 22.7382i | 0.888455i | ||||||||
\(656\) | 9.24875i | 0.361103i | ||||||||
\(657\) | 27.8556 | + | 15.8898i | 1.08675 | + | 0.619918i | ||||
\(658\) | −30.0388 | −1.17103 | ||||||||
\(659\) | 14.0859 | 0.548709 | 0.274354 | − | 0.961629i | \(-0.411536\pi\) | ||||
0.274354 | + | 0.961629i | \(0.411536\pi\) | |||||||
\(660\) | 11.9932 | − | 6.96594i | 0.466834 | − | 0.271149i | ||||
\(661\) | 0.840963 | 0.0327097 | 0.0163548 | − | 0.999866i | \(-0.494794\pi\) | ||||
0.0163548 | + | 0.999866i | \(0.494794\pi\) | |||||||
\(662\) | −32.1662 | −1.25018 | ||||||||
\(663\) | −0.270666 | − | 0.466003i | −0.0105118 | − | 0.0180981i | ||||
\(664\) | 2.87316 | 0.111500 | ||||||||
\(665\) | − | 7.39197i | − | 0.286648i | ||||||
\(666\) | 15.6924 | + | 8.95145i | 0.608068 | + | 0.346862i | ||||
\(667\) | − | 5.99891i | − | 0.232279i | ||||||
\(668\) | − | 7.18517i | − | 0.278003i | ||||||
\(669\) | −10.3615 | − | 17.8393i | −0.400599 | − | 0.689708i | ||||
\(670\) | 21.7380 | 0.839812 | ||||||||
\(671\) | − | 43.8352i | − | 1.69224i | ||||||
\(672\) | 3.11386 | + | 5.36111i | 0.120120 | + | 0.206809i | ||||
\(673\) | 26.8836i | 1.03629i | 0.855293 | + | 0.518144i | \(0.173377\pi\) | ||||
−0.855293 | + | 0.518144i | \(0.826623\pi\) | |||||||
\(674\) | − | 17.9638i | − | 0.691940i | ||||||
\(675\) | −11.6595 | + | 0.0910109i | −0.448774 | + | 0.00350301i | ||||
\(676\) | 12.8245 | 0.493251 | ||||||||
\(677\) | − | 9.79922i | − | 0.376615i | −0.982110 | − | 0.188307i | \(-0.939700\pi\) | ||
0.982110 | − | 0.188307i | \(-0.0603001\pi\) | |||||||
\(678\) | 2.99078 | + | 5.14920i | 0.114860 | + | 0.197754i | ||||
\(679\) | 41.2621i | 1.58349i | ||||||||
\(680\) | −1.23307 | −0.0472861 | ||||||||
\(681\) | 7.57107 | + | 13.0350i | 0.290124 | + | 0.499504i | ||||
\(682\) | 50.3896i | 1.92952i | ||||||||
\(683\) | 31.2678 | 1.19643 | 0.598215 | − | 0.801336i | \(-0.295877\pi\) | ||||
0.598215 | + | 0.801336i | \(0.295877\pi\) | |||||||
\(684\) | −1.84906 | + | 3.24151i | −0.0707007 | + | 0.123942i | ||||
\(685\) | −11.8959 | −0.454519 | ||||||||
\(686\) | −4.25050 | −0.162285 | ||||||||
\(687\) | 25.5109 | − | 14.8174i | 0.973302 | − | 0.565318i | ||||
\(688\) | − | 3.58258i | − | 0.136585i | ||||||
\(689\) | 4.04977 | 0.154284 | ||||||||
\(690\) | 3.12002 | − | 1.81218i | 0.118777 | − | 0.0689887i | ||||
\(691\) | − | 32.2762i | − | 1.22784i | −0.789366 | − | 0.613922i | \(-0.789591\pi\) | ||
0.789366 | − | 0.613922i | \(-0.210409\pi\) | |||||||
\(692\) | 4.12797 | 0.156922 | ||||||||
\(693\) | −25.6640 | + | 44.9903i | −0.974893 | + | 1.70904i | ||||
\(694\) | −30.2193 | −1.14711 | ||||||||
\(695\) | 8.64109i | 0.327775i | ||||||||
\(696\) | −7.16033 | + | 4.15890i | −0.271412 | + | 0.157643i | ||||
\(697\) | 6.86952 | 0.260201 | ||||||||
\(698\) | − | 27.1281i | − | 1.02681i | ||||||
\(699\) | 8.59463 | + | 14.7973i | 0.325079 | + | 0.559685i | ||||
\(700\) | −8.03208 | −0.303584 | ||||||||
\(701\) | 50.5534 | 1.90938 | 0.954688 | − | 0.297607i | \(-0.0961886\pi\) | ||||
0.954688 | + | 0.297607i | \(0.0961886\pi\) | |||||||
\(702\) | −0.0169899 | − | 2.17660i | −0.000641244 | − | 0.0821503i | ||||
\(703\) | 7.49098i | 0.282528i | ||||||||
\(704\) | −4.82340 | −0.181789 | ||||||||
\(705\) | 20.8663 | − | 12.1197i | 0.785872 | − | 0.456454i | ||||
\(706\) | 15.5292 | 0.584448 | ||||||||
\(707\) | −40.3231 | −1.51651 | ||||||||
\(708\) | 12.8305 | + | 3.51826i | 0.482200 | + | 0.132224i | ||||
\(709\) | 17.5937 | 0.660746 | 0.330373 | − | 0.943850i | \(-0.392825\pi\) | ||||
0.330373 | + | 0.943850i | \(0.392825\pi\) | |||||||
\(710\) | −6.67370 | −0.250459 | ||||||||
\(711\) | −5.28842 | + | 9.27089i | −0.198331 | + | 0.347685i | ||||
\(712\) | −16.0885 | −0.602944 | ||||||||
\(713\) | 13.1088i | 0.490930i | ||||||||
\(714\) | 3.98196 | − | 2.31282i | 0.149021 | − | 0.0865552i | ||||
\(715\) | −3.35434 | −0.125445 | ||||||||
\(716\) | −12.7736 | −0.477373 | ||||||||
\(717\) | −9.20767 | + | 5.34804i | −0.343867 | + | 0.199726i | ||||
\(718\) | − | 9.70378i | − | 0.362142i | ||||||
\(719\) | 51.0870 | 1.90522 | 0.952612 | − | 0.304187i | \(-0.0983849\pi\) | ||||
0.952612 | + | 0.304187i | \(0.0983849\pi\) | |||||||
\(720\) | −4.32607 | − | 2.46773i | −0.161223 | − | 0.0919669i | ||||
\(721\) | − | 5.73292i | − | 0.213505i | ||||||
\(722\) | 17.4526 | 0.649519 | ||||||||
\(723\) | 14.2751 | + | 24.5773i | 0.530896 | + | 0.914039i | ||||
\(724\) | −6.91511 | −0.256998 | ||||||||
\(725\) | − | 10.7277i | − | 0.398417i | ||||||
\(726\) | −10.6698 | − | 18.3700i | −0.395992 | − | 0.681776i | ||||
\(727\) | 27.9108 | 1.03515 | 0.517577 | − | 0.855636i | \(-0.326834\pi\) | ||||
0.517577 | + | 0.855636i | \(0.326834\pi\) | |||||||
\(728\) | − | 1.49943i | − | 0.0555726i | ||||||
\(729\) | 26.9967 | − | 0.421485i | 0.999878 | − | 0.0156105i | ||||
\(730\) | −17.7463 | −0.656821 | ||||||||
\(731\) | −2.66096 | −0.0984193 | ||||||||
\(732\) | −13.6115 | + | 7.90592i | −0.503097 | + | 0.292211i | ||||
\(733\) | 24.5303 | 0.906047 | 0.453024 | − | 0.891498i | \(-0.350345\pi\) | ||||
0.453024 | + | 0.891498i | \(0.350345\pi\) | |||||||
\(734\) | − | 21.1320i | − | 0.779997i | ||||||
\(735\) | −14.4526 | + | 8.39444i | −0.533093 | + | 0.309634i | ||||
\(736\) | −1.25480 | −0.0462527 | ||||||||
\(737\) | − | 63.1579i | − | 2.32645i | ||||||
\(738\) | 24.1008 | + | 13.7479i | 0.887164 | + | 0.506067i | ||||
\(739\) | − | 17.0899i | − | 0.628661i | −0.949314 | − | 0.314331i | \(-0.898220\pi\) | ||
0.949314 | − | 0.314331i | \(-0.101780\pi\) | |||||||
\(740\) | −9.99735 | −0.367510 | ||||||||
\(741\) | 0.780448 | − | 0.453304i | 0.0286705 | − | 0.0166525i | ||||
\(742\) | 34.6050i | 1.27039i | ||||||||
\(743\) | 1.24732i | 0.0457597i | 0.999738 | + | 0.0228798i | \(0.00728352\pi\) | ||||
−0.999738 | + | 0.0228798i | \(0.992716\pi\) | |||||||
\(744\) | 15.6468 | − | 9.08804i | 0.573639 | − | 0.333184i | ||||
\(745\) | − | 14.6437i | − | 0.536502i | ||||||
\(746\) | 26.4779 | 0.969424 | ||||||||
\(747\) | 4.27084 | − | 7.48702i | 0.156262 | − | 0.273936i | ||||
\(748\) | 3.58258i | 0.130992i | ||||||||
\(749\) | − | 0.209484i | − | 0.00765438i | ||||||
\(750\) | 18.0118 | − | 10.4617i | 0.657696 | − | 0.382006i | ||||
\(751\) | 42.5159i | 1.55143i | 0.631085 | + | 0.775714i | \(0.282610\pi\) | ||||
−0.631085 | + | 0.775714i | \(0.717390\pi\) | |||||||
\(752\) | −8.39199 | −0.306024 | ||||||||
\(753\) | −8.16850 | + | 4.74447i | −0.297677 | + | 0.172898i | ||||
\(754\) | 2.00265 | 0.0729322 | ||||||||
\(755\) | −1.44896 | −0.0527331 | ||||||||
\(756\) | 18.5988 | − | 0.145178i | 0.676434 | − | 0.00528007i | ||||
\(757\) | −15.0798 | −0.548086 | −0.274043 | − | 0.961717i | \(-0.588361\pi\) | ||||
−0.274043 | + | 0.961717i | \(0.588361\pi\) | |||||||
\(758\) | −2.78409 | −0.101123 | ||||||||
\(759\) | −5.26515 | − | 9.06496i | −0.191113 | − | 0.329037i | ||||
\(760\) | − | 2.06511i | − | 0.0749094i | ||||||
\(761\) | − | 19.8632i | − | 0.720039i | −0.932945 | − | 0.360019i | \(-0.882770\pi\) | ||
0.932945 | − | 0.360019i | \(-0.117230\pi\) | |||||||
\(762\) | 19.2248 | + | 33.0992i | 0.696442 | + | 1.19906i | ||||
\(763\) | − | 19.9308i | − | 0.721543i | ||||||
\(764\) | −3.69921 | −0.133833 | ||||||||
\(765\) | −1.83291 | + | 3.21319i | −0.0662690 | + | 0.116173i | ||||
\(766\) | − | 35.3588i | − | 1.27756i | ||||||
\(767\) | −2.25593 | − | 2.29431i | −0.0814570 | − | 0.0828428i | ||||
\(768\) | 0.869925 | + | 1.49774i | 0.0313907 | + | 0.0540451i | ||||
\(769\) | − | 34.3092i | − | 1.23722i | −0.785698 | − | 0.618610i | \(-0.787696\pi\) | ||
0.785698 | − | 0.618610i | \(-0.212304\pi\) | |||||||
\(770\) | − | 28.6626i | − | 1.03293i | ||||||
\(771\) | 30.1548 | − | 17.5147i | 1.08600 | − | 0.630775i | ||||
\(772\) | −11.9714 | −0.430862 | ||||||||
\(773\) | −1.83830 | −0.0661190 | −0.0330595 | − | 0.999453i | \(-0.510525\pi\) | ||||
−0.0330595 | + | 0.999453i | \(0.510525\pi\) | |||||||
\(774\) | −9.33565 | − | 5.32536i | −0.335563 | − | 0.191416i | ||||
\(775\) | 23.4422i | 0.842070i | ||||||||
\(776\) | 11.5275i | 0.413812i | ||||||||
\(777\) | 32.2845 | − | 18.7517i | 1.15820 | − | 0.672712i | ||||
\(778\) | − | 12.5625i | − | 0.450387i | ||||||
\(779\) | 11.5049i | 0.412204i | ||||||||
\(780\) | 0.604972 | + | 1.04157i | 0.0216615 | + | 0.0372944i | ||||
\(781\) | 19.3899i | 0.693824i | ||||||||
\(782\) | 0.932006i | 0.0333285i | ||||||||
\(783\) | 0.193901 | + | 24.8408i | 0.00692944 | + | 0.887736i | ||||
\(784\) | 5.81253 | 0.207590 | ||||||||
\(785\) | 38.7289 | 1.38229 | ||||||||
\(786\) | −11.9150 | − | 20.5139i | −0.424993 | − | 0.731707i | ||||
\(787\) | −13.2050 | −0.470709 | −0.235354 | − | 0.971910i | \(-0.575625\pi\) | ||||
−0.235354 | + | 0.971910i | \(0.575625\pi\) | |||||||
\(788\) | 12.7702i | 0.454920i | ||||||||
\(789\) | 42.8760 | − | 24.9035i | 1.52643 | − | 0.886586i | ||||
\(790\) | − | 5.90632i | − | 0.210137i | ||||||
\(791\) | 12.3061 | 0.437554 | ||||||||
\(792\) | −7.16979 | + | 12.5690i | −0.254767 | + | 0.446621i | ||||
\(793\) | 3.80697 | 0.135189 | ||||||||
\(794\) | − | 32.5653i | − | 1.15570i | ||||||
\(795\) | −13.9620 | − | 24.0382i | −0.495181 | − | 0.852548i | ||||
\(796\) | 7.63327 | 0.270554 | ||||||||
\(797\) | −25.7748 | −0.912989 | −0.456494 | − | 0.889726i | \(-0.650895\pi\) | ||||
−0.456494 | + | 0.889726i | \(0.650895\pi\) | |||||||
\(798\) | 3.87345 | + | 6.66888i | 0.137119 | + | 0.236076i | ||||
\(799\) | 6.23315i | 0.220513i | ||||||||
\(800\) | −2.24394 | −0.0793351 | ||||||||
\(801\) | −23.9150 | + | 41.9243i | −0.844994 | + | 1.48132i | ||||
\(802\) | 25.7353 | 0.908746 | ||||||||
\(803\) | 51.5605i | 1.81953i | ||||||||
\(804\) | −19.6115 | + | 11.3909i | −0.691646 | + | 0.401725i | ||||
\(805\) | − | 7.45655i | − | 0.262809i | ||||||
\(806\) | −4.37620 | −0.154145 | ||||||||
\(807\) | 4.80097 | + | 8.26578i | 0.169002 | + | 0.290969i | ||||
\(808\) | −11.2652 | −0.396307 | ||||||||
\(809\) | −29.8058 | −1.04792 | −0.523959 | − | 0.851744i | \(-0.675545\pi\) | ||||
−0.523959 | + | 0.851744i | \(0.675545\pi\) | |||||||
\(810\) | −12.8611 | + | 7.60489i | −0.451891 | + | 0.267209i | ||||
\(811\) | − | 17.7097i | − | 0.621872i | −0.950431 | − | 0.310936i | \(-0.899357\pi\) | ||
0.950431 | − | 0.310936i | \(-0.100643\pi\) | |||||||
\(812\) | 17.1125i | 0.600531i | ||||||||
\(813\) | −26.9438 | − | 46.3889i | −0.944961 | − | 1.62693i | ||||
\(814\) | 29.0465i | 1.01808i | ||||||||
\(815\) | 7.87329i | 0.275789i | ||||||||
\(816\) | 1.11245 | − | 0.646138i | 0.0389435 | − | 0.0226193i | ||||
\(817\) | − | 4.45650i | − | 0.155913i | ||||||
\(818\) | 2.79568i | 0.0977485i | ||||||||
\(819\) | −3.90729 | − | 2.22884i | −0.136532 | − | 0.0778821i | ||||
\(820\) | −15.3542 | −0.536193 | ||||||||
\(821\) | −14.4107 | −0.502936 | −0.251468 | − | 0.967866i | \(-0.580913\pi\) | ||||
−0.251468 | + | 0.967866i | \(0.580913\pi\) | |||||||
\(822\) | 10.7322 | − | 6.23354i | 0.374329 | − | 0.217420i | ||||
\(823\) | − | 35.1384i | − | 1.22485i | −0.790529 | − | 0.612425i | \(-0.790194\pi\) | ||
0.790529 | − | 0.612425i | \(-0.209806\pi\) | |||||||
\(824\) | − | 1.60162i | − | 0.0557949i | ||||||
\(825\) | −9.41555 | − | 16.2107i | −0.327807 | − | 0.564382i | ||||
\(826\) | 19.6047 | − | 19.2768i | 0.682136 | − | 0.670725i | ||||
\(827\) | 24.7747i | 0.861499i | 0.902471 | + | 0.430750i | \(0.141751\pi\) | ||||
−0.902471 | + | 0.430750i | \(0.858249\pi\) | |||||||
\(828\) | −1.86522 | + | 3.26983i | −0.0648207 | + | 0.113634i | ||||
\(829\) | 1.97335 | 0.0685372 | 0.0342686 | − | 0.999413i | \(-0.489090\pi\) | ||||
0.0342686 | + | 0.999413i | \(0.489090\pi\) | |||||||
\(830\) | 4.76985i | 0.165564i | ||||||||
\(831\) | 17.3795 | + | 29.9221i | 0.602888 | + | 1.03799i | ||||
\(832\) | − | 0.418899i | − | 0.0145227i | ||||||
\(833\) | − | 4.31726i | − | 0.149584i | ||||||
\(834\) | −4.52799 | − | 7.79580i | −0.156792 | − | 0.269947i | ||||
\(835\) | 11.9284 | 0.412799 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | −0.423713 | − | 54.2822i | −0.0146456 | − | 1.87627i | ||||
\(838\) | 26.4494 | 0.913681 | ||||||||
\(839\) | 3.80927 | 0.131511 | 0.0657553 | − | 0.997836i | \(-0.479054\pi\) | ||||
0.0657553 | + | 0.997836i | \(0.479054\pi\) | |||||||
\(840\) | −8.90018 | + | 5.16945i | −0.307085 | + | 0.178363i | ||||
\(841\) | 6.14441 | 0.211876 | ||||||||
\(842\) | − | 11.9509i | − | 0.411855i | ||||||
\(843\) | 35.1877 | − | 20.4379i | 1.21193 | − | 0.703917i | ||||
\(844\) | 18.3522i | 0.631710i | ||||||||
\(845\) | 21.2905i | 0.732415i | ||||||||
\(846\) | −12.4744 | + | 21.8682i | −0.428877 | + | 0.751845i | ||||
\(847\) | −43.9026 | −1.50851 | ||||||||
\(848\) | 9.66765i | 0.331988i | ||||||||
\(849\) | 20.6025 | − | 11.9664i | 0.707076 | − | 0.410687i | ||||
\(850\) | 1.66669i | 0.0571668i | ||||||||
\(851\) | 7.55642i | 0.259031i | ||||||||
\(852\) | 6.02086 | − | 3.49707i | 0.206271 | − | 0.119807i | ||||
\(853\) | −51.2486 | −1.75472 | −0.877359 | − | 0.479834i | \(-0.840697\pi\) | ||||
−0.877359 | + | 0.479834i | \(0.840697\pi\) | |||||||
\(854\) | 32.5303i | 1.11316i | ||||||||
\(855\) | −5.38136 | − | 3.06970i | −0.184039 | − | 0.104982i | ||||
\(856\) | − | 0.0585239i | − | 0.00200031i | ||||||
\(857\) | 0.987887 | 0.0337456 | 0.0168728 | − | 0.999858i | \(-0.494629\pi\) | ||||
0.0168728 | + | 0.999858i | \(0.494629\pi\) | |||||||
\(858\) | 3.02621 | − | 1.75770i | 0.103313 | − | 0.0600068i | ||||
\(859\) | 49.0308i | 1.67291i | 0.548037 | + | 0.836454i | \(0.315375\pi\) | ||||
−0.548037 | + | 0.836454i | \(0.684625\pi\) | |||||||
\(860\) | 5.94758 | 0.202811 | ||||||||
\(861\) | 49.5835 | − | 28.7993i | 1.68980 | − | 0.981479i | ||||
\(862\) | −11.5375 | −0.392969 | ||||||||
\(863\) | 17.2465 | 0.587077 | 0.293538 | − | 0.955947i | \(-0.405167\pi\) | ||||
0.293538 | + | 0.955947i | \(0.405167\pi\) | |||||||
\(864\) | 5.19599 | − | 0.0405586i | 0.176771 | − | 0.00137983i | ||||
\(865\) | 6.85300i | 0.233009i | ||||||||
\(866\) | 36.2956 | 1.23337 | ||||||||
\(867\) | 14.3088 | + | 24.6353i | 0.485953 | + | 0.836660i | ||||
\(868\) | − | 37.3943i | − | 1.26925i | ||||||
\(869\) | −17.1603 | −0.582124 | ||||||||
\(870\) | −6.90435 | − | 11.8872i | −0.234079 | − | 0.403012i | ||||
\(871\) | 5.48509 | 0.185855 | ||||||||
\(872\) | − | 5.56810i | − | 0.188560i | ||||||
\(873\) | 30.0388 | + | 17.1351i | 1.01666 | + | 0.579935i | ||||
\(874\) | −1.56090 | −0.0527981 | ||||||||
\(875\) | − | 43.0464i | − | 1.45523i | ||||||
\(876\) | 16.0103 | − | 9.29920i | 0.540939 | − | 0.314191i | ||||
\(877\) | 4.86999 | 0.164448 | 0.0822239 | − | 0.996614i | \(-0.473798\pi\) | ||||
0.0822239 | + | 0.996614i | \(0.473798\pi\) | |||||||
\(878\) | −11.5445 | −0.389607 | ||||||||
\(879\) | −28.9240 | + | 16.7998i | −0.975584 | + | 0.566643i | ||||
\(880\) | − | 8.00751i | − | 0.269933i | ||||||
\(881\) | −14.3475 | −0.483380 | −0.241690 | − | 0.970353i | \(-0.577702\pi\) | ||||
−0.241690 | + | 0.970353i | \(0.577702\pi\) | |||||||
\(882\) | 8.64009 | − | 15.1466i | 0.290927 | − | 0.510011i | ||||
\(883\) | 26.9717 | 0.907671 | 0.453835 | − | 0.891086i | \(-0.350055\pi\) | ||||
0.453835 | + | 0.891086i | \(0.350055\pi\) | |||||||
\(884\) | −0.311137 | −0.0104647 | ||||||||
\(885\) | −5.84080 | + | 21.3004i | −0.196336 | + | 0.716006i | ||||
\(886\) | −12.3499 | −0.414904 | ||||||||
\(887\) | 20.8782 | 0.701022 | 0.350511 | − | 0.936559i | \(-0.386008\pi\) | ||||
0.350511 | + | 0.936559i | \(0.386008\pi\) | |||||||
\(888\) | 9.01939 | − | 5.23868i | 0.302671 | − | 0.175799i | ||||
\(889\) | 79.1040 | 2.65306 | ||||||||
\(890\) | − | 26.7092i | − | 0.895295i | ||||||
\(891\) | 22.0954 | + | 37.3667i | 0.740223 | + | 1.25183i | ||||
\(892\) | −11.9108 | −0.398804 | ||||||||
\(893\) | −10.4391 | −0.349331 | ||||||||
\(894\) | 7.67339 | + | 13.2112i | 0.256637 | + | 0.441849i | ||||
\(895\) | − | 21.2060i | − | 0.708839i | ||||||
\(896\) | 3.57946 | 0.119581 | ||||||||
\(897\) | 0.787267 | − | 0.457264i | 0.0262861 | − | 0.0152676i | ||||
\(898\) | 28.4979i | 0.950988i | ||||||||
\(899\) | 49.9442 | 1.66573 | ||||||||
\(900\) | −3.33552 | + | 5.84736i | −0.111184 | + | 0.194912i | ||||
\(901\) | 7.18065 | 0.239222 | ||||||||
\(902\) | 44.6104i | 1.48536i | ||||||||
\(903\) | −19.2066 | + | 11.1557i | −0.639155 | + | 0.371237i | ||||
\(904\) | 3.43798 | 0.114345 | ||||||||
\(905\) | − | 11.4801i | − | 0.381610i | ||||||
\(906\) | 1.30722 | − | 0.759266i | 0.0434295 | − | 0.0252249i | ||||
\(907\) | −6.35574 | −0.211039 | −0.105519 | − | 0.994417i | \(-0.533651\pi\) | ||||
−0.105519 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(908\) | 8.70313 | 0.288823 | ||||||||
\(909\) | −16.7452 | + | 29.3553i | −0.555403 | + | 0.973652i | ||||
\(910\) | 2.48926 | 0.0825183 | ||||||||
\(911\) | − | 21.1718i | − | 0.701452i | −0.936478 | − | 0.350726i | \(-0.885935\pi\) | ||
0.936478 | − | 0.350726i | \(-0.114065\pi\) | |||||||
\(912\) | 1.08213 | + | 1.86310i | 0.0358330 | + | 0.0616933i | ||||
\(913\) | 13.8584 | 0.458646 | ||||||||
\(914\) | − | 22.4605i | − | 0.742926i | ||||||
\(915\) | −13.1249 | − | 22.5971i | −0.433897 | − | 0.747036i | ||||
\(916\) | − | 17.0329i | − | 0.562783i | ||||||
\(917\) | −49.0263 | −1.61899 | ||||||||
\(918\) | −0.0301249 | − | 3.85933i | −0.000994271 | − | 0.127377i | ||||
\(919\) | − | 21.0620i | − | 0.694772i | −0.937722 | − | 0.347386i | \(-0.887069\pi\) | ||
0.937722 | − | 0.347386i | \(-0.112931\pi\) | |||||||
\(920\) | − | 2.08315i | − | 0.0686794i | ||||||
\(921\) | −23.1502 | − | 39.8574i | −0.762824 | − | 1.31335i | ||||
\(922\) | 6.76019i | 0.222635i | ||||||||
\(923\) | −1.68396 | −0.0554281 | ||||||||
\(924\) | 15.0194 | + | 25.8587i | 0.494102 | + | 0.850690i | ||||
\(925\) | 13.5130i | 0.444304i | ||||||||
\(926\) | 32.1740i | 1.05730i | ||||||||
\(927\) | −4.17356 | − | 2.38074i | −0.137078 | − | 0.0781937i | ||||
\(928\) | 4.78075i | 0.156936i | ||||||||
\(929\) | −32.5664 | −1.06847 | −0.534235 | − | 0.845336i | \(-0.679400\pi\) | ||||
−0.534235 | + | 0.845336i | \(0.679400\pi\) | |||||||
\(930\) | 15.0874 | + | 25.9759i | 0.494736 | + | 0.851782i | ||||
\(931\) | 7.23042 | 0.236967 | ||||||||
\(932\) | 9.87973 | 0.323621 | ||||||||
\(933\) | −20.1634 | + | 11.7114i | −0.660119 | + | 0.383414i | ||||
\(934\) | 29.7721 | 0.974173 | ||||||||
\(935\) | −5.94758 | −0.194507 | ||||||||
\(936\) | −1.09159 | − | 0.622676i | −0.0356796 | − | 0.0203528i | ||||
\(937\) | − | 28.2471i | − | 0.922792i | −0.887194 | − | 0.461396i | \(-0.847349\pi\) | ||
0.887194 | − | 0.461396i | \(-0.152651\pi\) | |||||||
\(938\) | 46.8697i | 1.53035i | ||||||||
\(939\) | −6.35674 | + | 3.69215i | −0.207444 | + | 0.120489i | ||||
\(940\) | − | 13.9319i | − | 0.454408i | ||||||
\(941\) | −24.1748 | −0.788077 | −0.394039 | − | 0.919094i | \(-0.628922\pi\) | ||||
−0.394039 | + | 0.919094i | \(0.628922\pi\) | |||||||
\(942\) | −34.9404 | + | 20.2942i | −1.13842 | + | 0.661222i | ||||
\(943\) | 11.6054i | 0.377923i | ||||||||
\(944\) | 5.47701 | − | 5.38539i | 0.178261 | − | 0.175279i | ||||
\(945\) | 0.241016 | + | 30.8767i | 0.00784023 | + | 1.00442i | ||||
\(946\) | − | 17.2802i | − | 0.561828i | ||||||
\(947\) | − | 12.7052i | − | 0.412863i | −0.978461 | − | 0.206431i | \(-0.933815\pi\) | ||
0.978461 | − | 0.206431i | \(-0.0661850\pi\) | |||||||
\(948\) | 3.09495 | + | 5.32855i | 0.100519 | + | 0.173063i | ||||
\(949\) | −4.47788 | −0.145358 | ||||||||
\(950\) | −2.79132 | −0.0905622 | ||||||||
\(951\) | −8.21126 | + | 4.76930i | −0.266268 | + | 0.154655i | ||||
\(952\) | − | 2.65865i | − | 0.0861672i | ||||||
\(953\) | 19.7288i | 0.639078i | 0.947573 | + | 0.319539i | \(0.103528\pi\) | ||||
−0.947573 | + | 0.319539i | \(0.896472\pi\) | |||||||
\(954\) | 25.1924 | + | 14.3706i | 0.815634 | + | 0.465265i | ||||
\(955\) | − | 6.14120i | − | 0.198725i | ||||||
\(956\) | 6.14770i | 0.198831i | ||||||||
\(957\) | −34.5371 | + | 20.0600i | −1.11643 | + | 0.648448i | ||||
\(958\) | 11.4600i | 0.370257i | ||||||||
\(959\) | − | 25.6490i | − | 0.828249i | ||||||
\(960\) | −2.48646 | + | 1.44420i | −0.0802502 | + | 0.0466113i | ||||
\(961\) | −78.1382 | −2.52059 | ||||||||
\(962\) | −2.52261 | −0.0813321 | ||||||||
\(963\) | −0.152504 | − | 0.0869935i | −0.00491439 | − | 0.00280333i | ||||
\(964\) | 16.4096 | 0.528516 | ||||||||
\(965\) | − | 19.8743i | − | 0.639775i | ||||||
\(966\) | 3.90729 | + | 6.72714i | 0.125715 | + | 0.216442i | ||||
\(967\) | − | 43.7060i | − | 1.40549i | −0.711441 | − | 0.702745i | \(-0.751957\pi\) | ||
0.711441 | − | 0.702745i | \(-0.248043\pi\) | |||||||
\(968\) | −12.2652 | −0.394217 | ||||||||
\(969\) | 1.38382 | − | 0.803754i | 0.0444546 | − | 0.0258203i | ||||
\(970\) | −19.1372 | −0.614458 | ||||||||
\(971\) | 38.0875i | 1.22229i | 0.791521 | + | 0.611143i | \(0.209290\pi\) | ||||
−0.791521 | + | 0.611143i | \(0.790710\pi\) | |||||||
\(972\) | 7.61795 | − | 13.6003i | 0.244346 | − | 0.436228i | ||||
\(973\) | −18.6312 | −0.597290 | ||||||||
\(974\) | −8.42054 | −0.269812 | ||||||||
\(975\) | 1.40785 | − | 0.817714i | 0.0450873 | − | 0.0261878i | ||||
\(976\) | 9.08804i | 0.290901i | ||||||||
\(977\) | −6.63591 | −0.212302 | −0.106151 | − | 0.994350i | \(-0.533853\pi\) | ||||
−0.106151 | + | 0.994350i | \(0.533853\pi\) | |||||||
\(978\) | −4.12566 | − | 7.10311i | −0.131924 | − | 0.227132i | ||||
\(979\) | −77.6014 | −2.48015 | ||||||||
\(980\) | 9.64961i | 0.308245i | ||||||||
\(981\) | −14.5096 | − | 8.27675i | −0.463256 | − | 0.264256i | ||||
\(982\) | 7.10664i | 0.226782i | ||||||||
\(983\) | −39.0530 | −1.24560 | −0.622799 | − | 0.782382i | \(-0.714005\pi\) | ||||
−0.622799 | + | 0.782382i | \(0.714005\pi\) | |||||||
\(984\) | 13.8522 | − | 8.04572i | 0.441593 | − | 0.256488i | ||||
\(985\) | −21.2004 | −0.675499 | ||||||||
\(986\) | 3.55091 | 0.113084 | ||||||||
\(987\) | 26.1315 | + | 44.9903i | 0.831775 | + | 1.43206i | ||||
\(988\) | − | 0.521083i | − | 0.0165779i | ||||||
\(989\) | − | 4.49544i | − | 0.142947i | ||||||
\(990\) | −20.8663 | − | 11.9028i | −0.663176 | − | 0.378297i | ||||
\(991\) | 28.3842i | 0.901654i | 0.892611 | + | 0.450827i | \(0.148871\pi\) | ||||
−0.892611 | + | 0.450827i | \(0.851129\pi\) | |||||||
\(992\) | − | 10.4469i | − | 0.331690i | ||||||
\(993\) | 27.9822 | + | 48.1767i | 0.887989 | + | 1.52884i | ||||
\(994\) | − | 14.3893i | − | 0.456400i | ||||||
\(995\) | 12.6723i | 0.401739i | ||||||||
\(996\) | −2.49944 | − | 4.30325i | −0.0791977 | − | 0.136354i | ||||
\(997\) | −0.641094 | −0.0203037 | −0.0101518 | − | 0.999948i | \(-0.503231\pi\) | ||||
−0.0101518 | + | 0.999948i | \(0.503231\pi\) | |||||||
\(998\) | −33.2330 | −1.05197 | ||||||||
\(999\) | −0.244244 | − | 31.2902i | −0.00772753 | − | 0.989979i |
(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 | 354.2.c.a.353.8 | yes | 10 | |
3.2 | odd | 2 | 354.2.c.b.353.7 | yes | 10 | ||
59.58 | odd | 2 | 354.2.c.b.353.8 | yes | 10 | ||
177.176 | even | 2 | inner | 354.2.c.a.353.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.2.c.a.353.7 | ✓ | 10 | 177.176 | even | 2 | inner | |
354.2.c.a.353.8 | yes | 10 | 1.1 | even | 1 | trivial | |
354.2.c.b.353.7 | yes | 10 | 3.2 | odd | 2 | ||
354.2.c.b.353.8 | yes | 10 | 59.58 | odd | 2 |