Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.b (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: | \(1.83655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.11574317056.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 45x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.6 | ||
Root | \(-0.386289 - 0.386289i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.2.b.b.139.3 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.44270i | − | 0.832944i | −0.909149 | − | 0.416472i | \(-0.863266\pi\) | ||
0.909149 | − | 0.416472i | \(-0.136734\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.386289 | + | 2.20245i | −0.172754 | + | 0.984965i | ||||
\(6\) | 1.44270 | 0.588980 | ||||||||
\(7\) | 3.25886i | 1.23173i | 0.787850 | + | 0.615867i | \(0.211194\pi\) | ||||
−0.787850 | + | 0.615867i | \(0.788806\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.918614 | 0.306205 | ||||||||
\(10\) | −2.20245 | − | 0.386289i | −0.696475 | − | 0.122155i | ||||
\(11\) | 1.32988 | 0.400973 | 0.200486 | − | 0.979696i | \(-0.435748\pi\) | ||||
0.200486 | + | 0.979696i | \(0.435748\pi\) | |||||||
\(12\) | 1.44270i | 0.416472i | ||||||||
\(13\) | 1.25886i | 0.349145i | 0.984644 | + | 0.174573i | \(0.0558544\pi\) | ||||
−0.984644 | + | 0.174573i | \(0.944146\pi\) | |||||||
\(14\) | −3.25886 | −0.870967 | ||||||||
\(15\) | 3.17748 | + | 0.557299i | 0.820421 | + | 0.143894i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.62018i | 1.12056i | 0.828304 | + | 0.560279i | \(0.189306\pi\) | ||||
−0.828304 | + | 0.560279i | \(0.810694\pi\) | |||||||
\(18\) | 0.918614i | 0.216519i | ||||||||
\(19\) | 3.37169 | 0.773518 | 0.386759 | − | 0.922181i | \(-0.373595\pi\) | ||||
0.386759 | + | 0.922181i | \(0.373595\pi\) | |||||||
\(20\) | 0.386289 | − | 2.20245i | 0.0863768 | − | 0.492483i | ||||
\(21\) | 4.70156 | 1.02596 | ||||||||
\(22\) | 1.32988i | 0.283531i | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | −1.44270 | −0.294490 | ||||||||
\(25\) | −4.70156 | − | 1.70156i | −0.940312 | − | 0.340312i | ||||
\(26\) | −1.25886 | −0.246883 | ||||||||
\(27\) | − | 5.65339i | − | 1.08800i | ||||||
\(28\) | − | 3.25886i | − | 0.615867i | ||||||
\(29\) | −4.29207 | −0.797018 | −0.398509 | − | 0.917164i | \(-0.630472\pi\) | ||||
−0.398509 | + | 0.917164i | \(0.630472\pi\) | |||||||
\(30\) | −0.557299 | + | 3.17748i | −0.101748 | + | 0.580125i | ||||
\(31\) | 2.37346 | 0.426286 | 0.213143 | − | 0.977021i | \(-0.431630\pi\) | ||||
0.213143 | + | 0.977021i | \(0.431630\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 1.91861i | − | 0.333988i | ||||||
\(34\) | −4.62018 | −0.792354 | ||||||||
\(35\) | −7.17748 | − | 1.25886i | −1.21321 | − | 0.212786i | ||||
\(36\) | −0.918614 | −0.153102 | ||||||||
\(37\) | − | 5.74514i | − | 0.944496i | −0.881466 | − | 0.472248i | \(-0.843443\pi\) | ||
0.881466 | − | 0.472248i | \(-0.156557\pi\) | |||||||
\(38\) | 3.37169i | 0.546960i | ||||||||
\(39\) | 1.81616 | 0.290818 | ||||||||
\(40\) | 2.20245 | + | 0.386289i | 0.348238 | + | 0.0610776i | ||||
\(41\) | −5.13790 | −0.802405 | −0.401202 | − | 0.915989i | \(-0.631408\pi\) | ||||
−0.401202 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(42\) | 4.70156i | 0.725467i | ||||||||
\(43\) | − | 10.4678i | − | 1.59632i | −0.602445 | − | 0.798160i | \(-0.705807\pi\) | ||
0.602445 | − | 0.798160i | \(-0.294193\pi\) | |||||||
\(44\) | −1.32988 | −0.200486 | ||||||||
\(45\) | −0.354850 | + | 2.02320i | −0.0528979 | + | 0.301601i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − | 6.06288i | − | 0.884362i | −0.896926 | − | 0.442181i | \(-0.854205\pi\) | ||
0.896926 | − | 0.442181i | \(-0.145795\pi\) | |||||||
\(48\) | − | 1.44270i | − | 0.208236i | ||||||
\(49\) | −3.62018 | −0.517168 | ||||||||
\(50\) | 1.70156 | − | 4.70156i | 0.240637 | − | 0.664901i | ||||
\(51\) | 6.66553 | 0.933361 | ||||||||
\(52\) | − | 1.25886i | − | 0.174573i | ||||||
\(53\) | 11.1275i | 1.52848i | 0.644930 | + | 0.764242i | \(0.276887\pi\) | ||||
−0.644930 | + | 0.764242i | \(0.723113\pi\) | |||||||
\(54\) | 5.65339 | 0.769329 | ||||||||
\(55\) | −0.513716 | + | 2.92898i | −0.0692695 | + | 0.394944i | ||||
\(56\) | 3.25886 | 0.435484 | ||||||||
\(57\) | − | 4.86433i | − | 0.644297i | ||||||
\(58\) | − | 4.29207i | − | 0.563577i | ||||||
\(59\) | 2.72263 | 0.354456 | 0.177228 | − | 0.984170i | \(-0.443287\pi\) | ||||
0.177228 | + | 0.984170i | \(0.443287\pi\) | |||||||
\(60\) | −3.17748 | − | 0.557299i | −0.410210 | − | 0.0719470i | ||||
\(61\) | 12.3653 | 1.58322 | 0.791609 | − | 0.611029i | \(-0.209244\pi\) | ||||
0.791609 | + | 0.611029i | \(0.209244\pi\) | |||||||
\(62\) | 2.37346i | 0.301430i | ||||||||
\(63\) | 2.99364i | 0.377163i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.77258 | − | 0.486284i | −0.343896 | − | 0.0603161i | ||||
\(66\) | 1.91861 | 0.236165 | ||||||||
\(67\) | − | 6.60981i | − | 0.807516i | −0.914866 | − | 0.403758i | \(-0.867704\pi\) | ||
0.914866 | − | 0.403758i | \(-0.132296\pi\) | |||||||
\(68\) | − | 4.62018i | − | 0.560279i | ||||||
\(69\) | −1.44270 | −0.173681 | ||||||||
\(70\) | 1.25886 | − | 7.17748i | 0.150463 | − | 0.857872i | ||||
\(71\) | 0.265226 | 0.0314765 | 0.0157383 | − | 0.999876i | \(-0.494990\pi\) | ||||
0.0157383 | + | 0.999876i | \(0.494990\pi\) | |||||||
\(72\) | − | 0.918614i | − | 0.108260i | ||||||
\(73\) | − | 5.26464i | − | 0.616180i | −0.951357 | − | 0.308090i | \(-0.900310\pi\) | ||
0.951357 | − | 0.308090i | \(-0.0996897\pi\) | |||||||
\(74\) | 5.74514 | 0.667860 | ||||||||
\(75\) | −2.45485 | + | 6.78295i | −0.283461 | + | 0.783227i | ||||
\(76\) | −3.37169 | −0.386759 | ||||||||
\(77\) | 4.33388i | 0.493892i | ||||||||
\(78\) | 1.81616i | 0.205640i | ||||||||
\(79\) | 15.3275 | 1.72448 | 0.862240 | − | 0.506500i | \(-0.169061\pi\) | ||||
0.862240 | + | 0.506500i | \(0.169061\pi\) | |||||||
\(80\) | −0.386289 | + | 2.20245i | −0.0431884 | + | 0.246241i | ||||
\(81\) | −5.40031 | −0.600034 | ||||||||
\(82\) | − | 5.13790i | − | 0.567386i | ||||||
\(83\) | 2.02566i | 0.222345i | 0.993801 | + | 0.111172i | \(0.0354606\pi\) | ||||
−0.993801 | + | 0.111172i | \(0.964539\pi\) | |||||||
\(84\) | −4.70156 | −0.512982 | ||||||||
\(85\) | −10.1757 | − | 1.78472i | −1.10371 | − | 0.193580i | ||||
\(86\) | 10.4678 | 1.12877 | ||||||||
\(87\) | 6.19218i | 0.663871i | ||||||||
\(88\) | − | 1.32988i | − | 0.141765i | ||||||
\(89\) | −16.1500 | −1.71190 | −0.855951 | − | 0.517058i | \(-0.827027\pi\) | ||||
−0.855951 | + | 0.517058i | \(0.827027\pi\) | |||||||
\(90\) | −2.02320 | − | 0.354850i | −0.213264 | − | 0.0374045i | ||||
\(91\) | −4.10245 | −0.430054 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | − | 3.42419i | − | 0.355072i | ||||||
\(94\) | 6.06288 | 0.625338 | ||||||||
\(95\) | −1.30244 | + | 7.42597i | −0.133628 | + | 0.761888i | ||||
\(96\) | 1.44270 | 0.147245 | ||||||||
\(97\) | − | 8.62018i | − | 0.875246i | −0.899158 | − | 0.437623i | \(-0.855820\pi\) | ||
0.899158 | − | 0.437623i | \(-0.144180\pi\) | |||||||
\(98\) | − | 3.62018i | − | 0.365693i | ||||||
\(99\) | 1.22164 | 0.122780 | ||||||||
\(100\) | 4.70156 | + | 1.70156i | 0.470156 | + | 0.170156i | ||||
\(101\) | 14.4934 | 1.44215 | 0.721075 | − | 0.692857i | \(-0.243648\pi\) | ||||
0.721075 | + | 0.692857i | \(0.243648\pi\) | |||||||
\(102\) | 6.66553i | 0.659986i | ||||||||
\(103\) | 18.5410i | 1.82690i | 0.406950 | + | 0.913451i | \(0.366592\pi\) | ||||
−0.406950 | + | 0.913451i | \(0.633408\pi\) | |||||||
\(104\) | 1.25886 | 0.123441 | ||||||||
\(105\) | −1.81616 | + | 10.3550i | −0.177239 | + | 1.01054i | ||||
\(106\) | −11.1275 | −1.08080 | ||||||||
\(107\) | − | 4.48050i | − | 0.433147i | −0.976266 | − | 0.216573i | \(-0.930512\pi\) | ||
0.976266 | − | 0.216573i | \(-0.0694880\pi\) | |||||||
\(108\) | 5.65339i | 0.543998i | ||||||||
\(109\) | −17.1298 | −1.64073 | −0.820367 | − | 0.571838i | \(-0.806231\pi\) | ||||
−0.820367 | + | 0.571838i | \(0.806231\pi\) | |||||||
\(110\) | −2.92898 | − | 0.513716i | −0.279268 | − | 0.0489809i | ||||
\(111\) | −8.28853 | −0.786712 | ||||||||
\(112\) | 3.25886i | 0.307933i | ||||||||
\(113\) | 9.77435i | 0.919494i | 0.888050 | + | 0.459747i | \(0.152060\pi\) | ||||
−0.888050 | + | 0.459747i | \(0.847940\pi\) | |||||||
\(114\) | 4.86433 | 0.455587 | ||||||||
\(115\) | 2.20245 | + | 0.386289i | 0.205379 | + | 0.0360216i | ||||
\(116\) | 4.29207 | 0.398509 | ||||||||
\(117\) | 1.15641i | 0.106910i | ||||||||
\(118\) | 2.72263i | 0.250638i | ||||||||
\(119\) | −15.0565 | −1.38023 | ||||||||
\(120\) | 0.557299 | − | 3.17748i | 0.0508742 | − | 0.290062i | ||||
\(121\) | −9.23143 | −0.839221 | ||||||||
\(122\) | 12.3653i | 1.11950i | ||||||||
\(123\) | 7.41245i | 0.668358i | ||||||||
\(124\) | −2.37346 | −0.213143 | ||||||||
\(125\) | 5.56376 | − | 9.69766i | 0.497638 | − | 0.867385i | ||||
\(126\) | −2.99364 | −0.266694 | ||||||||
\(127\) | 1.02743i | 0.0911699i | 0.998960 | + | 0.0455849i | \(0.0145152\pi\) | ||||
−0.998960 | + | 0.0455849i | \(0.985485\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −15.1019 | −1.32965 | ||||||||
\(130\) | 0.486284 | − | 2.77258i | 0.0426499 | − | 0.243171i | ||||
\(131\) | 12.2885 | 1.07365 | 0.536827 | − | 0.843692i | \(-0.319623\pi\) | ||||
0.536827 | + | 0.843692i | \(0.319623\pi\) | |||||||
\(132\) | 1.91861i | 0.166994i | ||||||||
\(133\) | 10.9879i | 0.952768i | ||||||||
\(134\) | 6.60981 | 0.571000 | ||||||||
\(135\) | 12.4513 | + | 2.18384i | 1.07164 | + | 0.187955i | ||||
\(136\) | 4.62018 | 0.396177 | ||||||||
\(137\) | − | 8.82830i | − | 0.754253i | −0.926162 | − | 0.377126i | \(-0.876912\pi\) | ||
0.926162 | − | 0.377126i | \(-0.123088\pi\) | |||||||
\(138\) | − | 1.44270i | − | 0.122811i | ||||||
\(139\) | 11.5532 | 0.979927 | 0.489963 | − | 0.871743i | \(-0.337010\pi\) | ||||
0.489963 | + | 0.871743i | \(0.337010\pi\) | |||||||
\(140\) | 7.17748 | + | 1.25886i | 0.606607 | + | 0.106393i | ||||
\(141\) | −8.74692 | −0.736623 | ||||||||
\(142\) | 0.265226i | 0.0222573i | ||||||||
\(143\) | 1.67413i | 0.139998i | ||||||||
\(144\) | 0.918614 | 0.0765512 | ||||||||
\(145\) | 1.65798 | − | 9.45307i | 0.137688 | − | 0.785035i | ||||
\(146\) | 5.26464 | 0.435705 | ||||||||
\(147\) | 5.22283i | 0.430772i | ||||||||
\(148\) | 5.74514i | 0.472248i | ||||||||
\(149\) | 11.1333 | 0.912076 | 0.456038 | − | 0.889960i | \(-0.349268\pi\) | ||||
0.456038 | + | 0.889960i | \(0.349268\pi\) | |||||||
\(150\) | −6.78295 | − | 2.45485i | −0.553825 | − | 0.200437i | ||||
\(151\) | −3.23779 | −0.263488 | −0.131744 | − | 0.991284i | \(-0.542058\pi\) | ||||
−0.131744 | + | 0.991284i | \(0.542058\pi\) | |||||||
\(152\) | − | 3.37169i | − | 0.273480i | ||||||
\(153\) | 4.24416i | 0.343120i | ||||||||
\(154\) | −4.33388 | −0.349234 | ||||||||
\(155\) | −0.916840 | + | 5.22742i | −0.0736424 | + | 0.419877i | ||||
\(156\) | −1.81616 | −0.145409 | ||||||||
\(157\) | − | 17.6452i | − | 1.40824i | −0.710079 | − | 0.704122i | \(-0.751341\pi\) | ||
0.710079 | − | 0.704122i | \(-0.248659\pi\) | |||||||
\(158\) | 15.3275i | 1.21939i | ||||||||
\(159\) | 16.0537 | 1.27314 | ||||||||
\(160\) | −2.20245 | − | 0.386289i | −0.174119 | − | 0.0305388i | ||||
\(161\) | 3.25886 | 0.256834 | ||||||||
\(162\) | − | 5.40031i | − | 0.424288i | ||||||
\(163\) | − | 12.2107i | − | 0.956415i | −0.878247 | − | 0.478207i | \(-0.841287\pi\) | ||
0.878247 | − | 0.478207i | \(-0.158713\pi\) | |||||||
\(164\) | 5.13790 | 0.401202 | ||||||||
\(165\) | 4.22565 | + | 0.741139i | 0.328966 | + | 0.0576976i | ||||
\(166\) | −2.02566 | −0.157222 | ||||||||
\(167\) | 2.06288i | 0.159630i | 0.996810 | + | 0.0798151i | \(0.0254330\pi\) | ||||
−0.996810 | + | 0.0798151i | \(0.974567\pi\) | |||||||
\(168\) | − | 4.70156i | − | 0.362733i | ||||||
\(169\) | 11.4153 | 0.878098 | ||||||||
\(170\) | 1.78472 | − | 10.1757i | 0.136882 | − | 0.780441i | ||||
\(171\) | 3.09728 | 0.236855 | ||||||||
\(172\) | 10.4678i | 0.798160i | ||||||||
\(173\) | 2.10245i | 0.159847i | 0.996801 | + | 0.0799233i | \(0.0254675\pi\) | ||||
−0.996801 | + | 0.0799233i | \(0.974532\pi\) | |||||||
\(174\) | −6.19218 | −0.469428 | ||||||||
\(175\) | 5.54515 | − | 15.3217i | 0.419174 | − | 1.15821i | ||||
\(176\) | 1.32988 | 0.100243 | ||||||||
\(177\) | − | 3.92794i | − | 0.295242i | ||||||
\(178\) | − | 16.1500i | − | 1.21050i | ||||||
\(179\) | −20.4421 | −1.52792 | −0.763958 | − | 0.645266i | \(-0.776746\pi\) | ||||
−0.763958 | + | 0.645266i | \(0.776746\pi\) | |||||||
\(180\) | 0.354850 | − | 2.02320i | 0.0264490 | − | 0.150800i | ||||
\(181\) | −7.12175 | −0.529355 | −0.264678 | − | 0.964337i | \(-0.585266\pi\) | ||||
−0.264678 | + | 0.964337i | \(0.585266\pi\) | |||||||
\(182\) | − | 4.10245i | − | 0.304094i | ||||||
\(183\) | − | 17.8395i | − | 1.31873i | ||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 12.6534 | + | 2.21928i | 0.930296 | + | 0.163165i | ||||
\(186\) | 3.42419 | 0.251074 | ||||||||
\(187\) | 6.14426i | 0.449313i | ||||||||
\(188\) | 6.06288i | 0.442181i | ||||||||
\(189\) | 18.4236 | 1.34012 | ||||||||
\(190\) | −7.42597 | − | 1.30244i | −0.538736 | − | 0.0944892i | ||||
\(191\) | −16.7191 | −1.20975 | −0.604875 | − | 0.796320i | \(-0.706777\pi\) | ||||
−0.604875 | + | 0.796320i | \(0.706777\pi\) | |||||||
\(192\) | 1.44270i | 0.104118i | ||||||||
\(193\) | 6.51772i | 0.469156i | 0.972097 | + | 0.234578i | \(0.0753708\pi\) | ||||
−0.972097 | + | 0.234578i | \(0.924629\pi\) | |||||||
\(194\) | 8.62018 | 0.618893 | ||||||||
\(195\) | −0.701562 | + | 4.00000i | −0.0502399 | + | 0.286446i | ||||
\(196\) | 3.62018 | 0.258584 | ||||||||
\(197\) | 17.8184i | 1.26951i | 0.772714 | + | 0.634754i | \(0.218899\pi\) | ||||
−0.772714 | + | 0.634754i | \(0.781101\pi\) | |||||||
\(198\) | 1.22164i | 0.0868184i | ||||||||
\(199\) | 3.77435 | 0.267557 | 0.133778 | − | 0.991011i | \(-0.457289\pi\) | ||||
0.133778 | + | 0.991011i | \(0.457289\pi\) | |||||||
\(200\) | −1.70156 | + | 4.70156i | −0.120319 | + | 0.332451i | ||||
\(201\) | −9.53597 | −0.672616 | ||||||||
\(202\) | 14.4934i | 1.01975i | ||||||||
\(203\) | − | 13.9873i | − | 0.981714i | ||||||
\(204\) | −6.66553 | −0.466681 | ||||||||
\(205\) | 1.98471 | − | 11.3160i | 0.138618 | − | 0.790341i | ||||
\(206\) | −18.5410 | −1.29181 | ||||||||
\(207\) | − | 0.918614i | − | 0.0638481i | ||||||
\(208\) | 1.25886i | 0.0872863i | ||||||||
\(209\) | 4.48393 | 0.310160 | ||||||||
\(210\) | −10.3550 | − | 1.81616i | −0.714559 | − | 0.125327i | ||||
\(211\) | −23.9630 | −1.64968 | −0.824840 | − | 0.565366i | \(-0.808735\pi\) | ||||
−0.824840 | + | 0.565366i | \(0.808735\pi\) | |||||||
\(212\) | − | 11.1275i | − | 0.764242i | ||||||
\(213\) | − | 0.382642i | − | 0.0262182i | ||||||
\(214\) | 4.48050 | 0.306281 | ||||||||
\(215\) | 23.0547 | + | 4.04358i | 1.57232 | + | 0.275770i | ||||
\(216\) | −5.65339 | −0.384664 | ||||||||
\(217\) | 7.73477i | 0.525071i | ||||||||
\(218\) | − | 17.1298i | − | 1.16017i | ||||||
\(219\) | −7.59530 | −0.513243 | ||||||||
\(220\) | 0.513716 | − | 2.92898i | 0.0346347 | − | 0.197472i | ||||
\(221\) | −5.81616 | −0.391237 | ||||||||
\(222\) | − | 8.28853i | − | 0.556289i | ||||||
\(223\) | − | 20.2094i | − | 1.35332i | −0.736296 | − | 0.676660i | \(-0.763427\pi\) | ||
0.736296 | − | 0.676660i | \(-0.236573\pi\) | |||||||
\(224\) | −3.25886 | −0.217742 | ||||||||
\(225\) | −4.31892 | − | 1.56308i | −0.287928 | − | 0.104205i | ||||
\(226\) | −9.77435 | −0.650180 | ||||||||
\(227\) | − | 1.60666i | − | 0.106638i | −0.998578 | − | 0.0533189i | \(-0.983020\pi\) | ||
0.998578 | − | 0.0533189i | \(-0.0169800\pi\) | |||||||
\(228\) | 4.86433i | 0.322148i | ||||||||
\(229\) | 18.9019 | 1.24907 | 0.624536 | − | 0.780996i | \(-0.285288\pi\) | ||||
0.624536 | + | 0.780996i | \(0.285288\pi\) | |||||||
\(230\) | −0.386289 | + | 2.20245i | −0.0254711 | + | 0.145225i | ||||
\(231\) | 6.25250 | 0.411384 | ||||||||
\(232\) | 4.29207i | 0.281788i | ||||||||
\(233\) | 19.0112i | 1.24546i | 0.782436 | + | 0.622731i | \(0.213977\pi\) | ||||
−0.782436 | + | 0.622731i | \(0.786023\pi\) | |||||||
\(234\) | −1.15641 | −0.0755967 | ||||||||
\(235\) | 13.3532 | + | 2.34202i | 0.871065 | + | 0.152777i | ||||
\(236\) | −2.72263 | −0.177228 | ||||||||
\(237\) | − | 22.1130i | − | 1.43640i | ||||||
\(238\) | − | 15.0565i | − | 0.975969i | ||||||
\(239\) | −28.3387 | −1.83308 | −0.916538 | − | 0.399947i | \(-0.869028\pi\) | ||||
−0.916538 | + | 0.399947i | \(0.869028\pi\) | |||||||
\(240\) | 3.17748 | + | 0.557299i | 0.205105 | + | 0.0359735i | ||||
\(241\) | 6.35140 | 0.409130 | 0.204565 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204565 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(242\) | − | 9.23143i | − | 0.593419i | ||||||
\(243\) | − | 9.16914i | − | 0.588200i | ||||||
\(244\) | −12.3653 | −0.791609 | ||||||||
\(245\) | 1.39843 | − | 7.97325i | 0.0893426 | − | 0.509392i | ||||
\(246\) | −7.41245 | −0.472601 | ||||||||
\(247\) | 4.24448i | 0.270070i | ||||||||
\(248\) | − | 2.37346i | − | 0.150715i | ||||||
\(249\) | 2.92242 | 0.185201 | ||||||||
\(250\) | 9.69766 | + | 5.56376i | 0.613334 | + | 0.351883i | ||||
\(251\) | 19.7231 | 1.24491 | 0.622455 | − | 0.782655i | \(-0.286135\pi\) | ||||
0.622455 | + | 0.782655i | \(0.286135\pi\) | |||||||
\(252\) | − | 2.99364i | − | 0.188581i | ||||||
\(253\) | − | 1.32988i | − | 0.0836086i | ||||||
\(254\) | −1.02743 | −0.0644668 | ||||||||
\(255\) | −2.57482 | + | 14.6805i | −0.161241 | + | 0.919328i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.18102i | 0.0736701i | 0.999321 | + | 0.0368351i | \(0.0117276\pi\) | ||||
−0.999321 | + | 0.0368351i | \(0.988272\pi\) | |||||||
\(258\) | − | 15.1019i | − | 0.940201i | ||||||
\(259\) | 18.7226 | 1.16337 | ||||||||
\(260\) | 2.77258 | + | 0.486284i | 0.171948 | + | 0.0301580i | ||||
\(261\) | −3.94276 | −0.244051 | ||||||||
\(262\) | 12.2885i | 0.759188i | ||||||||
\(263\) | − | 24.3189i | − | 1.49957i | −0.661682 | − | 0.749784i | \(-0.730157\pi\) | ||
0.661682 | − | 0.749784i | \(-0.269843\pi\) | |||||||
\(264\) | −1.91861 | −0.118083 | ||||||||
\(265\) | −24.5078 | − | 4.29844i | −1.50550 | − | 0.264051i | ||||
\(266\) | −10.9879 | −0.673709 | ||||||||
\(267\) | 23.2997i | 1.42592i | ||||||||
\(268\) | 6.60981i | 0.403758i | ||||||||
\(269\) | −7.91283 | −0.482454 | −0.241227 | − | 0.970469i | \(-0.577550\pi\) | ||||
−0.241227 | + | 0.970469i | \(0.577550\pi\) | |||||||
\(270\) | −2.18384 | + | 12.4513i | −0.132904 | + | 0.757762i | ||||
\(271\) | −18.2979 | −1.11152 | −0.555758 | − | 0.831344i | \(-0.687572\pi\) | ||||
−0.555758 | + | 0.831344i | \(0.687572\pi\) | |||||||
\(272\) | 4.62018i | 0.280139i | ||||||||
\(273\) | 5.91861i | 0.358211i | ||||||||
\(274\) | 8.82830 | 0.533337 | ||||||||
\(275\) | −6.25250 | − | 2.26287i | −0.377040 | − | 0.136456i | ||||
\(276\) | 1.44270 | 0.0868404 | ||||||||
\(277\) | 28.6550i | 1.72171i | 0.508847 | + | 0.860857i | \(0.330072\pi\) | ||||
−0.508847 | + | 0.860857i | \(0.669928\pi\) | |||||||
\(278\) | 11.5532i | 0.692913i | ||||||||
\(279\) | 2.18029 | 0.130531 | ||||||||
\(280\) | −1.25886 | + | 7.17748i | −0.0752313 | + | 0.428936i | ||||
\(281\) | 2.74692 | 0.163867 | 0.0819337 | − | 0.996638i | \(-0.473890\pi\) | ||||
0.0819337 | + | 0.996638i | \(0.473890\pi\) | |||||||
\(282\) | − | 8.74692i | − | 0.520871i | ||||||
\(283\) | 5.45307i | 0.324151i | 0.986778 | + | 0.162076i | \(0.0518189\pi\) | ||||
−0.986778 | + | 0.162076i | \(0.948181\pi\) | |||||||
\(284\) | −0.265226 | −0.0157383 | ||||||||
\(285\) | 10.7134 | + | 1.87904i | 0.634610 | + | 0.111305i | ||||
\(286\) | −1.67413 | −0.0989934 | ||||||||
\(287\) | − | 16.7437i | − | 0.988349i | ||||||
\(288\) | 0.918614i | 0.0541298i | ||||||||
\(289\) | −4.34603 | −0.255649 | ||||||||
\(290\) | 9.45307 | + | 1.65798i | 0.555103 | + | 0.0973599i | ||||
\(291\) | −12.4363 | −0.729031 | ||||||||
\(292\) | 5.26464i | 0.308090i | ||||||||
\(293\) | − | 18.3806i | − | 1.07381i | −0.843644 | − | 0.536903i | \(-0.819594\pi\) | ||
0.843644 | − | 0.536903i | \(-0.180406\pi\) | |||||||
\(294\) | −5.22283 | −0.304602 | ||||||||
\(295\) | −1.05172 | + | 5.99645i | −0.0612336 | + | 0.349127i | ||||
\(296\) | −5.74514 | −0.333930 | ||||||||
\(297\) | − | 7.51831i | − | 0.436256i | ||||||
\(298\) | 11.1333i | 0.644935i | ||||||||
\(299\) | 1.25886 | 0.0728018 | ||||||||
\(300\) | 2.45485 | − | 6.78295i | 0.141731 | − | 0.391614i | ||||
\(301\) | 34.1130 | 1.96624 | ||||||||
\(302\) | − | 3.23779i | − | 0.186314i | ||||||
\(303\) | − | 20.9097i | − | 1.20123i | ||||||
\(304\) | 3.37169 | 0.193379 | ||||||||
\(305\) | −4.77658 | + | 27.2340i | −0.273506 | + | 1.55941i | ||||
\(306\) | −4.24416 | −0.242622 | ||||||||
\(307\) | − | 15.9234i | − | 0.908797i | −0.890799 | − | 0.454398i | \(-0.849854\pi\) | ||
0.890799 | − | 0.454398i | \(-0.150146\pi\) | |||||||
\(308\) | − | 4.33388i | − | 0.246946i | ||||||
\(309\) | 26.7492 | 1.52171 | ||||||||
\(310\) | −5.22742 | − | 0.916840i | −0.296898 | − | 0.0520730i | ||||
\(311\) | −11.3518 | −0.643702 | −0.321851 | − | 0.946790i | \(-0.604305\pi\) | ||||
−0.321851 | + | 0.946790i | \(0.604305\pi\) | |||||||
\(312\) | − | 1.81616i | − | 0.102820i | ||||||
\(313\) | 28.7913i | 1.62738i | 0.581299 | + | 0.813690i | \(0.302545\pi\) | ||||
−0.581299 | + | 0.813690i | \(0.697455\pi\) | |||||||
\(314\) | 17.6452 | 0.995779 | ||||||||
\(315\) | −6.59333 | − | 1.15641i | −0.371492 | − | 0.0651562i | ||||
\(316\) | −15.3275 | −0.862240 | ||||||||
\(317\) | − | 31.2299i | − | 1.75404i | −0.480451 | − | 0.877022i | \(-0.659527\pi\) | ||
0.480451 | − | 0.877022i | \(-0.340473\pi\) | |||||||
\(318\) | 16.0537i | 0.900246i | ||||||||
\(319\) | −5.70793 | −0.319583 | ||||||||
\(320\) | 0.386289 | − | 2.20245i | 0.0215942 | − | 0.123121i | ||||
\(321\) | −6.46403 | −0.360787 | ||||||||
\(322\) | 3.25886i | 0.181609i | ||||||||
\(323\) | 15.5778i | 0.866771i | ||||||||
\(324\) | 5.40031 | 0.300017 | ||||||||
\(325\) | 2.14203 | − | 5.91861i | 0.118818 | − | 0.328306i | ||||
\(326\) | 12.2107 | 0.676287 | ||||||||
\(327\) | 24.7131i | 1.36664i | ||||||||
\(328\) | 5.13790i | 0.283693i | ||||||||
\(329\) | 19.7581 | 1.08930 | ||||||||
\(330\) | −0.741139 | + | 4.22565i | −0.0407984 | + | 0.232614i | ||||
\(331\) | 17.6917 | 0.972421 | 0.486211 | − | 0.873842i | \(-0.338379\pi\) | ||||
0.486211 | + | 0.873842i | \(0.338379\pi\) | |||||||
\(332\) | − | 2.02566i | − | 0.111172i | ||||||
\(333\) | − | 5.27757i | − | 0.289209i | ||||||
\(334\) | −2.06288 | −0.112876 | ||||||||
\(335\) | 14.5578 | + | 2.55329i | 0.795375 | + | 0.139501i | ||||
\(336\) | 4.70156 | 0.256491 | ||||||||
\(337\) | − | 1.33801i | − | 0.0728863i | −0.999336 | − | 0.0364431i | \(-0.988397\pi\) | ||
0.999336 | − | 0.0364431i | \(-0.0116028\pi\) | |||||||
\(338\) | 11.4153i | 0.620909i | ||||||||
\(339\) | 14.1015 | 0.765886 | ||||||||
\(340\) | 10.1757 | + | 1.78472i | 0.551855 | + | 0.0967901i | ||||
\(341\) | 3.15641 | 0.170929 | ||||||||
\(342\) | 3.09728i | 0.167482i | ||||||||
\(343\) | 11.0144i | 0.594720i | ||||||||
\(344\) | −10.4678 | −0.564385 | ||||||||
\(345\) | 0.557299 | − | 3.17748i | 0.0300040 | − | 0.171070i | ||||
\(346\) | −2.10245 | −0.113029 | ||||||||
\(347\) | − | 5.36355i | − | 0.287930i | −0.989583 | − | 0.143965i | \(-0.954015\pi\) | ||
0.989583 | − | 0.143965i | \(-0.0459853\pi\) | |||||||
\(348\) | − | 6.19218i | − | 0.331936i | ||||||
\(349\) | 18.4306 | 0.986565 | 0.493283 | − | 0.869869i | \(-0.335797\pi\) | ||||
0.493283 | + | 0.869869i | \(0.335797\pi\) | |||||||
\(350\) | 15.3217 | + | 5.54515i | 0.818981 | + | 0.296401i | ||||
\(351\) | 7.11683 | 0.379868 | ||||||||
\(352\) | 1.32988i | 0.0708826i | ||||||||
\(353\) | − | 6.76477i | − | 0.360052i | −0.983662 | − | 0.180026i | \(-0.942382\pi\) | ||
0.983662 | − | 0.180026i | \(-0.0576182\pi\) | |||||||
\(354\) | 3.92794 | 0.208768 | ||||||||
\(355\) | −0.102454 | + | 0.584146i | −0.00543768 | + | 0.0310033i | ||||
\(356\) | 16.1500 | 0.855951 | ||||||||
\(357\) | 21.7220i | 1.14965i | ||||||||
\(358\) | − | 20.4421i | − | 1.08040i | ||||||
\(359\) | −27.5324 | −1.45311 | −0.726553 | − | 0.687111i | \(-0.758879\pi\) | ||||
−0.726553 | + | 0.687111i | \(0.758879\pi\) | |||||||
\(360\) | 2.02320 | + | 0.354850i | 0.106632 | + | 0.0187022i | ||||
\(361\) | −7.63174 | −0.401670 | ||||||||
\(362\) | − | 7.12175i | − | 0.374311i | ||||||
\(363\) | 13.3182i | 0.699024i | ||||||||
\(364\) | 4.10245 | 0.215027 | ||||||||
\(365\) | 11.5951 | + | 2.03367i | 0.606915 | + | 0.106447i | ||||
\(366\) | 17.8395 | 0.932484 | ||||||||
\(367\) | 24.0744i | 1.25668i | 0.777941 | + | 0.628338i | \(0.216264\pi\) | ||||
−0.777941 | + | 0.628338i | \(0.783736\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | −4.71975 | −0.245700 | ||||||||
\(370\) | −2.21928 | + | 12.6534i | −0.115375 | + | 0.657818i | ||||
\(371\) | −36.2631 | −1.88268 | ||||||||
\(372\) | 3.42419i | 0.177536i | ||||||||
\(373\) | 1.31459i | 0.0680668i | 0.999421 | + | 0.0340334i | \(0.0108353\pi\) | ||||
−0.999421 | + | 0.0340334i | \(0.989165\pi\) | |||||||
\(374\) | −6.14426 | −0.317712 | ||||||||
\(375\) | −13.9908 | − | 8.02685i | −0.722483 | − | 0.414505i | ||||
\(376\) | −6.06288 | −0.312669 | ||||||||
\(377\) | − | 5.40312i | − | 0.278275i | ||||||
\(378\) | 18.4236i | 0.947608i | ||||||||
\(379\) | −8.38961 | −0.430945 | −0.215473 | − | 0.976510i | \(-0.569129\pi\) | ||||
−0.215473 | + | 0.976510i | \(0.569129\pi\) | |||||||
\(380\) | 1.30244 | − | 7.42597i | 0.0668140 | − | 0.380944i | ||||
\(381\) | 1.48228 | 0.0759394 | ||||||||
\(382\) | − | 16.7191i | − | 0.855423i | ||||||
\(383\) | 24.1258i | 1.23277i | 0.787446 | + | 0.616384i | \(0.211403\pi\) | ||||
−0.787446 | + | 0.616384i | \(0.788597\pi\) | |||||||
\(384\) | −1.44270 | −0.0736225 | ||||||||
\(385\) | −9.54515 | − | 1.67413i | −0.486466 | − | 0.0853216i | ||||
\(386\) | −6.51772 | −0.331743 | ||||||||
\(387\) | − | 9.61584i | − | 0.488801i | ||||||
\(388\) | 8.62018i | 0.437623i | ||||||||
\(389\) | −12.5702 | −0.637336 | −0.318668 | − | 0.947866i | \(-0.603235\pi\) | ||||
−0.318668 | + | 0.947866i | \(0.603235\pi\) | |||||||
\(390\) | −4.00000 | − | 0.701562i | −0.202548 | − | 0.0355250i | ||||
\(391\) | 4.62018 | 0.233652 | ||||||||
\(392\) | 3.62018i | 0.182847i | ||||||||
\(393\) | − | 17.7287i | − | 0.894293i | ||||||
\(394\) | −17.8184 | −0.897678 | ||||||||
\(395\) | −5.92085 | + | 33.7581i | −0.297910 | + | 1.69855i | ||||
\(396\) | −1.22164 | −0.0613899 | ||||||||
\(397\) | 28.5318i | 1.43197i | 0.698115 | + | 0.715986i | \(0.254023\pi\) | ||||
−0.698115 | + | 0.715986i | \(0.745977\pi\) | |||||||
\(398\) | 3.77435i | 0.189191i | ||||||||
\(399\) | 15.8522 | 0.793602 | ||||||||
\(400\) | −4.70156 | − | 1.70156i | −0.235078 | − | 0.0850781i | ||||
\(401\) | −19.7130 | −0.984422 | −0.492211 | − | 0.870476i | \(-0.663811\pi\) | ||||
−0.492211 | + | 0.870476i | \(0.663811\pi\) | |||||||
\(402\) | − | 9.53597i | − | 0.475611i | ||||||
\(403\) | 2.98786i | 0.148836i | ||||||||
\(404\) | −14.4934 | −0.721075 | ||||||||
\(405\) | 2.08608 | − | 11.8939i | 0.103658 | − | 0.591013i | ||||
\(406\) | 13.9873 | 0.694177 | ||||||||
\(407\) | − | 7.64033i | − | 0.378717i | ||||||
\(408\) | − | 6.66553i | − | 0.329993i | ||||||
\(409\) | −20.3400 | −1.00575 | −0.502874 | − | 0.864360i | \(-0.667724\pi\) | ||||
−0.502874 | + | 0.864360i | \(0.667724\pi\) | |||||||
\(410\) | 11.3160 | + | 1.98471i | 0.558855 | + | 0.0980179i | ||||
\(411\) | −12.7366 | −0.628250 | ||||||||
\(412\) | − | 18.5410i | − | 0.913451i | ||||||
\(413\) | 8.87267i | 0.436596i | ||||||||
\(414\) | 0.918614 | 0.0451474 | ||||||||
\(415\) | −4.46141 | − | 0.782489i | −0.219002 | − | 0.0384109i | ||||
\(416\) | −1.25886 | −0.0617207 | ||||||||
\(417\) | − | 16.6678i | − | 0.816224i | ||||||
\(418\) | 4.48393i | 0.219316i | ||||||||
\(419\) | −9.91146 | −0.484207 | −0.242103 | − | 0.970250i | \(-0.577837\pi\) | ||||
−0.242103 | + | 0.970250i | \(0.577837\pi\) | |||||||
\(420\) | 1.81616 | − | 10.3550i | 0.0886195 | − | 0.505270i | ||||
\(421\) | −28.7927 | −1.40327 | −0.701634 | − | 0.712537i | \(-0.747546\pi\) | ||||
−0.701634 | + | 0.712537i | \(0.747546\pi\) | |||||||
\(422\) | − | 23.9630i | − | 1.16650i | ||||||
\(423\) | − | 5.56944i | − | 0.270796i | ||||||
\(424\) | 11.1275 | 0.540401 | ||||||||
\(425\) | 7.86152 | − | 21.7220i | 0.381340 | − | 1.05367i | ||||
\(426\) | 0.382642 | 0.0185390 | ||||||||
\(427\) | 40.2969i | 1.95010i | ||||||||
\(428\) | 4.48050i | 0.216573i | ||||||||
\(429\) | 2.41527 | 0.116610 | ||||||||
\(430\) | −4.04358 | + | 23.0547i | −0.194999 | + | 1.11180i | ||||
\(431\) | 36.6821 | 1.76691 | 0.883456 | − | 0.468513i | \(-0.155210\pi\) | ||||
0.883456 | + | 0.468513i | \(0.155210\pi\) | |||||||
\(432\) | − | 5.65339i | − | 0.271999i | ||||||
\(433\) | 29.6894i | 1.42678i | 0.700766 | + | 0.713391i | \(0.252842\pi\) | ||||
−0.700766 | + | 0.713391i | \(0.747158\pi\) | |||||||
\(434\) | −7.73477 | −0.371281 | ||||||||
\(435\) | −13.6380 | − | 2.39197i | −0.653890 | − | 0.114686i | ||||
\(436\) | 17.1298 | 0.820367 | ||||||||
\(437\) | − | 3.37169i | − | 0.161290i | ||||||
\(438\) | − | 7.59530i | − | 0.362918i | ||||||
\(439\) | −34.5378 | −1.64840 | −0.824200 | − | 0.566299i | \(-0.808375\pi\) | ||||
−0.824200 | + | 0.566299i | \(0.808375\pi\) | |||||||
\(440\) | 2.92898 | + | 0.513716i | 0.139634 | + | 0.0244905i | ||||
\(441\) | −3.32554 | −0.158359 | ||||||||
\(442\) | − | 5.81616i | − | 0.276647i | ||||||
\(443\) | − | 36.6735i | − | 1.74241i | −0.490917 | − | 0.871206i | \(-0.663338\pi\) | ||
0.490917 | − | 0.871206i | \(-0.336662\pi\) | |||||||
\(444\) | 8.28853 | 0.393356 | ||||||||
\(445\) | 6.23858 | − | 35.5696i | 0.295737 | − | 1.68616i | ||||
\(446\) | 20.2094 | 0.956942 | ||||||||
\(447\) | − | 16.0620i | − | 0.759708i | ||||||
\(448\) | − | 3.25886i | − | 0.153967i | ||||||
\(449\) | 13.2138 | 0.623599 | 0.311800 | − | 0.950148i | \(-0.399068\pi\) | ||||
0.311800 | + | 0.950148i | \(0.399068\pi\) | |||||||
\(450\) | 1.56308 | − | 4.31892i | 0.0736842 | − | 0.203596i | ||||
\(451\) | −6.83277 | −0.321743 | ||||||||
\(452\) | − | 9.77435i | − | 0.459747i | ||||||
\(453\) | 4.67117i | 0.219471i | ||||||||
\(454\) | 1.60666 | 0.0754044 | ||||||||
\(455\) | 1.58473 | − | 9.03544i | 0.0742934 | − | 0.423588i | ||||
\(456\) | −4.86433 | −0.227793 | ||||||||
\(457\) | − | 12.2292i | − | 0.572058i | −0.958221 | − | 0.286029i | \(-0.907665\pi\) | ||
0.958221 | − | 0.286029i | \(-0.0923353\pi\) | |||||||
\(458\) | 18.9019i | 0.883227i | ||||||||
\(459\) | 26.1196 | 1.21916 | ||||||||
\(460\) | −2.20245 | − | 0.386289i | −0.102690 | − | 0.0180108i | ||||
\(461\) | 24.0872 | 1.12185 | 0.560926 | − | 0.827866i | \(-0.310445\pi\) | ||||
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(462\) | 6.25250i | 0.290892i | ||||||||
\(463\) | − | 15.9173i | − | 0.739740i | −0.929084 | − | 0.369870i | \(-0.879402\pi\) | ||
0.929084 | − | 0.369870i | \(-0.120598\pi\) | |||||||
\(464\) | −4.29207 | −0.199254 | ||||||||
\(465\) | 7.54161 | + | 1.32273i | 0.349734 | + | 0.0613400i | ||||
\(466\) | −19.0112 | −0.880675 | ||||||||
\(467\) | 9.70011i | 0.448868i | 0.974489 | + | 0.224434i | \(0.0720533\pi\) | ||||
−0.974489 | + | 0.224434i | \(0.927947\pi\) | |||||||
\(468\) | − | 1.15641i | − | 0.0534550i | ||||||
\(469\) | 21.5404 | 0.994645 | ||||||||
\(470\) | −2.34202 | + | 13.3532i | −0.108029 | + | 0.615936i | ||||
\(471\) | −25.4568 | −1.17299 | ||||||||
\(472\) | − | 2.72263i | − | 0.125319i | ||||||
\(473\) | − | 13.9208i | − | 0.640081i | ||||||
\(474\) | 22.1130 | 1.01568 | ||||||||
\(475\) | −15.8522 | − | 5.73713i | −0.727348 | − | 0.263238i | ||||
\(476\) | 15.0565 | 0.690114 | ||||||||
\(477\) | 10.2219i | 0.468029i | ||||||||
\(478\) | − | 28.3387i | − | 1.29618i | ||||||
\(479\) | −14.1385 | −0.646004 | −0.323002 | − | 0.946398i | \(-0.604692\pi\) | ||||
−0.323002 | + | 0.946398i | \(0.604692\pi\) | |||||||
\(480\) | −0.557299 | + | 3.17748i | −0.0254371 | + | 0.145031i | ||||
\(481\) | 7.23234 | 0.329766 | ||||||||
\(482\) | 6.35140i | 0.289298i | ||||||||
\(483\) | − | 4.70156i | − | 0.213928i | ||||||
\(484\) | 9.23143 | 0.419610 | ||||||||
\(485\) | 18.9855 | + | 3.32988i | 0.862087 | + | 0.151202i | ||||
\(486\) | 9.16914 | 0.415920 | ||||||||
\(487\) | 3.75006i | 0.169932i | 0.996384 | + | 0.0849658i | \(0.0270781\pi\) | ||||
−0.996384 | + | 0.0849658i | \(0.972922\pi\) | |||||||
\(488\) | − | 12.3653i | − | 0.559752i | ||||||
\(489\) | −17.6164 | −0.796640 | ||||||||
\(490\) | 7.97325 | + | 1.39843i | 0.360195 | + | 0.0631748i | ||||
\(491\) | −3.19020 | −0.143972 | −0.0719860 | − | 0.997406i | \(-0.522934\pi\) | ||||
−0.0719860 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(492\) | − | 7.41245i | − | 0.334179i | ||||||
\(493\) | − | 19.8301i | − | 0.893104i | ||||||
\(494\) | −4.24448 | −0.190968 | ||||||||
\(495\) | −0.471907 | + | 2.69061i | −0.0212106 | + | 0.120934i | ||||
\(496\) | 2.37346 | 0.106571 | ||||||||
\(497\) | 0.864334i | 0.0387707i | ||||||||
\(498\) | 2.92242i | 0.130957i | ||||||||
\(499\) | −12.9355 | −0.579075 | −0.289537 | − | 0.957167i | \(-0.593501\pi\) | ||||
−0.289537 | + | 0.957167i | \(0.593501\pi\) | |||||||
\(500\) | −5.56376 | + | 9.69766i | −0.248819 | + | 0.433692i | ||||
\(501\) | 2.97611 | 0.132963 | ||||||||
\(502\) | 19.7231i | 0.880285i | ||||||||
\(503\) | − | 15.8845i | − | 0.708254i | −0.935197 | − | 0.354127i | \(-0.884778\pi\) | ||
0.935197 | − | 0.354127i | \(-0.115222\pi\) | |||||||
\(504\) | 2.99364 | 0.133347 | ||||||||
\(505\) | −5.59865 | + | 31.9210i | −0.249137 | + | 1.42047i | ||||
\(506\) | 1.32988 | 0.0591202 | ||||||||
\(507\) | − | 16.4688i | − | 0.731406i | ||||||
\(508\) | − | 1.02743i | − | 0.0455849i | ||||||
\(509\) | −22.6470 | −1.00381 | −0.501906 | − | 0.864922i | \(-0.667368\pi\) | ||||
−0.501906 | + | 0.864922i | \(0.667368\pi\) | |||||||
\(510\) | −14.6805 | − | 2.57482i | −0.650063 | − | 0.114015i | ||||
\(511\) | 17.1567 | 0.758969 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 19.0614i | − | 0.841583i | ||||||
\(514\) | −1.18102 | −0.0520927 | ||||||||
\(515\) | −40.8357 | − | 7.16219i | −1.79943 | − | 0.315604i | ||||
\(516\) | 15.1019 | 0.664823 | ||||||||
\(517\) | − | 8.06288i | − | 0.354605i | ||||||
\(518\) | 18.7226i | 0.822625i | ||||||||
\(519\) | 3.03321 | 0.133143 | ||||||||
\(520\) | −0.486284 | + | 2.77258i | −0.0213250 | + | 0.121586i | ||||
\(521\) | 22.7728 | 0.997693 | 0.498847 | − | 0.866690i | \(-0.333757\pi\) | ||||
0.498847 | + | 0.866690i | \(0.333757\pi\) | |||||||
\(522\) | − | 3.94276i | − | 0.172570i | ||||||
\(523\) | − | 16.1920i | − | 0.708026i | −0.935241 | − | 0.354013i | \(-0.884817\pi\) | ||
0.935241 | − | 0.354013i | \(-0.115183\pi\) | |||||||
\(524\) | −12.2885 | −0.536827 | ||||||||
\(525\) | −22.1047 | − | 8.00000i | −0.964728 | − | 0.349149i | ||||
\(526\) | 24.3189 | 1.06036 | ||||||||
\(527\) | 10.9658i | 0.477678i | ||||||||
\(528\) | − | 1.91861i | − | 0.0834970i | ||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 4.29844 | − | 24.5078i | 0.186712 | − | 1.06455i | ||||
\(531\) | 2.50105 | 0.108536 | ||||||||
\(532\) | − | 10.9879i | − | 0.476384i | ||||||
\(533\) | − | 6.46790i | − | 0.280156i | ||||||
\(534\) | −23.2997 | −1.00828 | ||||||||
\(535\) | 9.86808 | + | 1.73077i | 0.426634 | + | 0.0748276i | ||||
\(536\) | −6.60981 | −0.285500 | ||||||||
\(537\) | 29.4919i | 1.27267i | ||||||||
\(538\) | − | 7.91283i | − | 0.341147i | ||||||
\(539\) | −4.81439 | −0.207370 | ||||||||
\(540\) | −12.4513 | − | 2.18384i | −0.535819 | − | 0.0939775i | ||||
\(541\) | 14.4350 | 0.620610 | 0.310305 | − | 0.950637i | \(-0.399569\pi\) | ||||
0.310305 | + | 0.950637i | \(0.399569\pi\) | |||||||
\(542\) | − | 18.2979i | − | 0.785960i | ||||||
\(543\) | 10.2746i | 0.440923i | ||||||||
\(544\) | −4.62018 | −0.198088 | ||||||||
\(545\) | 6.61703 | − | 37.7274i | 0.283443 | − | 1.61607i | ||||
\(546\) | −5.91861 | −0.253293 | ||||||||
\(547\) | − | 0.846151i | − | 0.0361788i | −0.999836 | − | 0.0180894i | \(-0.994242\pi\) | ||
0.999836 | − | 0.0180894i | \(-0.00575835\pi\) | |||||||
\(548\) | 8.82830i | 0.377126i | ||||||||
\(549\) | 11.3590 | 0.484788 | ||||||||
\(550\) | 2.26287 | − | 6.25250i | 0.0964890 | − | 0.266607i | ||||
\(551\) | −14.4715 | −0.616508 | ||||||||
\(552\) | 1.44270i | 0.0614054i | ||||||||
\(553\) | 49.9503i | 2.12410i | ||||||||
\(554\) | −28.6550 | −1.21744 | ||||||||
\(555\) | 3.20176 | − | 18.2551i | 0.135907 | − | 0.774884i | ||||
\(556\) | −11.5532 | −0.489963 | ||||||||
\(557\) | 19.3532i | 0.820020i | 0.912081 | + | 0.410010i | \(0.134475\pi\) | ||||
−0.912081 | + | 0.410010i | \(0.865525\pi\) | |||||||
\(558\) | 2.18029i | 0.0922992i | ||||||||
\(559\) | 13.1775 | 0.557348 | ||||||||
\(560\) | −7.17748 | − | 1.25886i | −0.303304 | − | 0.0531966i | ||||
\(561\) | 8.86433 | 0.374252 | ||||||||
\(562\) | 2.74692i | 0.115872i | ||||||||
\(563\) | 29.3647i | 1.23758i | 0.785558 | + | 0.618788i | \(0.212376\pi\) | ||||
−0.785558 | + | 0.618788i | \(0.787624\pi\) | |||||||
\(564\) | 8.74692 | 0.368312 | ||||||||
\(565\) | −21.5275 | − | 3.77572i | −0.905669 | − | 0.158846i | ||||
\(566\) | −5.45307 | −0.229210 | ||||||||
\(567\) | − | 17.5988i | − | 0.739082i | ||||||
\(568\) | − | 0.265226i | − | 0.0111286i | ||||||
\(569\) | −6.41900 | −0.269098 | −0.134549 | − | 0.990907i | \(-0.542959\pi\) | ||||
−0.134549 | + | 0.990907i | \(0.542959\pi\) | |||||||
\(570\) | −1.87904 | + | 10.7134i | −0.0787042 | + | 0.448737i | ||||
\(571\) | 35.3009 | 1.47730 | 0.738648 | − | 0.674092i | \(-0.235465\pi\) | ||||
0.738648 | + | 0.674092i | \(0.235465\pi\) | |||||||
\(572\) | − | 1.67413i | − | 0.0699989i | ||||||
\(573\) | 24.1206i | 1.00765i | ||||||||
\(574\) | 16.7437 | 0.698868 | ||||||||
\(575\) | −1.70156 | + | 4.70156i | −0.0709600 | + | 0.196069i | ||||
\(576\) | −0.918614 | −0.0382756 | ||||||||
\(577\) | − | 6.96339i | − | 0.289890i | −0.989440 | − | 0.144945i | \(-0.953700\pi\) | ||
0.989440 | − | 0.144945i | \(-0.0463004\pi\) | |||||||
\(578\) | − | 4.34603i | − | 0.180771i | ||||||
\(579\) | 9.40312 | 0.390781 | ||||||||
\(580\) | −1.65798 | + | 9.45307i | −0.0688438 | + | 0.392517i | ||||
\(581\) | −6.60134 | −0.273870 | ||||||||
\(582\) | − | 12.4363i | − | 0.515503i | ||||||
\(583\) | 14.7982i | 0.612880i | ||||||||
\(584\) | −5.26464 | −0.217852 | ||||||||
\(585\) | −2.54693 | − | 0.446707i | −0.105303 | − | 0.0184691i | ||||
\(586\) | 18.3806 | 0.759296 | ||||||||
\(587\) | 23.7392i | 0.979823i | 0.871772 | + | 0.489912i | \(0.162971\pi\) | ||||
−0.871772 | + | 0.489912i | \(0.837029\pi\) | |||||||
\(588\) | − | 5.22283i | − | 0.215386i | ||||||
\(589\) | 8.00256 | 0.329740 | ||||||||
\(590\) | −5.99645 | − | 1.05172i | −0.246870 | − | 0.0432987i | ||||
\(591\) | 25.7066 | 1.05743 | ||||||||
\(592\) | − | 5.74514i | − | 0.236124i | ||||||
\(593\) | − | 23.1612i | − | 0.951116i | −0.879684 | − | 0.475558i | \(-0.842246\pi\) | ||
0.879684 | − | 0.475558i | \(-0.157754\pi\) | |||||||
\(594\) | 7.51831 | 0.308480 | ||||||||
\(595\) | 5.81616 | − | 33.1612i | 0.238439 | − | 1.35948i | ||||
\(596\) | −11.1333 | −0.456038 | ||||||||
\(597\) | − | 5.44526i | − | 0.222860i | ||||||
\(598\) | 1.25886i | 0.0514787i | ||||||||
\(599\) | −33.1344 | −1.35383 | −0.676916 | − | 0.736060i | \(-0.736684\pi\) | ||||
−0.676916 | + | 0.736060i | \(0.736684\pi\) | |||||||
\(600\) | 6.78295 | + | 2.45485i | 0.276913 | + | 0.100219i | ||||
\(601\) | 40.0432 | 1.63340 | 0.816698 | − | 0.577065i | \(-0.195802\pi\) | ||||
0.816698 | + | 0.577065i | \(0.195802\pi\) | |||||||
\(602\) | 34.1130i | 1.39034i | ||||||||
\(603\) | − | 6.07186i | − | 0.247265i | ||||||
\(604\) | 3.23779 | 0.131744 | ||||||||
\(605\) | 3.56600 | − | 20.3317i | 0.144978 | − | 0.826603i | ||||
\(606\) | 20.9097 | 0.849398 | ||||||||
\(607\) | − | 1.81294i | − | 0.0735849i | −0.999323 | − | 0.0367925i | \(-0.988286\pi\) | ||
0.999323 | − | 0.0367925i | \(-0.0117140\pi\) | |||||||
\(608\) | 3.37169i | 0.136740i | ||||||||
\(609\) | −20.1794 | −0.817713 | ||||||||
\(610\) | −27.2340 | − | 4.77658i | −1.10267 | − | 0.193398i | ||||
\(611\) | 7.63232 | 0.308771 | ||||||||
\(612\) | − | 4.24416i | − | 0.171560i | ||||||
\(613\) | 11.9329i | 0.481964i | 0.970530 | + | 0.240982i | \(0.0774694\pi\) | ||||
−0.970530 | + | 0.240982i | \(0.922531\pi\) | |||||||
\(614\) | 15.9234 | 0.642616 | ||||||||
\(615\) | −16.3255 | − | 2.86335i | −0.658309 | − | 0.115461i | ||||
\(616\) | 4.33388 | 0.174617 | ||||||||
\(617\) | − | 16.5923i | − | 0.667982i | −0.942576 | − | 0.333991i | \(-0.891604\pi\) | ||
0.942576 | − | 0.333991i | \(-0.108396\pi\) | |||||||
\(618\) | 26.7492i | 1.07601i | ||||||||
\(619\) | 1.43811 | 0.0578025 | 0.0289013 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289013 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(620\) | 0.916840 | − | 5.22742i | 0.0368212 | − | 0.209938i | ||||
\(621\) | −5.65339 | −0.226863 | ||||||||
\(622\) | − | 11.3518i | − | 0.455166i | ||||||
\(623\) | − | 52.6307i | − | 2.10861i | ||||||
\(624\) | 1.81616 | 0.0727046 | ||||||||
\(625\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(626\) | −28.7913 | −1.15073 | ||||||||
\(627\) | − | 6.46896i | − | 0.258346i | ||||||
\(628\) | 17.6452i | 0.704122i | ||||||||
\(629\) | 26.5436 | 1.05836 | ||||||||
\(630\) | 1.15641 | − | 6.59333i | 0.0460724 | − | 0.262685i | ||||
\(631\) | 7.67446 | 0.305515 | 0.152758 | − | 0.988264i | \(-0.451185\pi\) | ||||
0.152758 | + | 0.988264i | \(0.451185\pi\) | |||||||
\(632\) | − | 15.3275i | − | 0.609696i | ||||||
\(633\) | 34.5714i | 1.37409i | ||||||||
\(634\) | 31.2299 | 1.24030 | ||||||||
\(635\) | −2.26287 | − | 0.396885i | −0.0897991 | − | 0.0157499i | ||||
\(636\) | −16.0537 | −0.636570 | ||||||||
\(637\) | − | 4.55730i | − | 0.180567i | ||||||
\(638\) | − | 5.70793i | − | 0.225979i | ||||||
\(639\) | 0.243640 | 0.00963826 | ||||||||
\(640\) | 2.20245 | + | 0.386289i | 0.0870594 | + | 0.0152694i | ||||
\(641\) | −23.0562 | −0.910665 | −0.455332 | − | 0.890322i | \(-0.650480\pi\) | ||||
−0.455332 | + | 0.890322i | \(0.650480\pi\) | |||||||
\(642\) | − | 6.46403i | − | 0.255115i | ||||||
\(643\) | 9.51595i | 0.375272i | 0.982239 | + | 0.187636i | \(0.0600826\pi\) | ||||
−0.982239 | + | 0.187636i | \(0.939917\pi\) | |||||||
\(644\) | −3.25886 | −0.128417 | ||||||||
\(645\) | 5.83368 | − | 33.2611i | 0.229701 | − | 1.30965i | ||||
\(646\) | −15.5778 | −0.612900 | ||||||||
\(647\) | 38.9857i | 1.53269i | 0.642432 | + | 0.766343i | \(0.277926\pi\) | ||||
−0.642432 | + | 0.766343i | \(0.722074\pi\) | |||||||
\(648\) | 5.40031i | 0.212144i | ||||||||
\(649\) | 3.62076 | 0.142127 | ||||||||
\(650\) | 5.91861 | + | 2.14203i | 0.232147 | + | 0.0840173i | ||||
\(651\) | 11.1590 | 0.437354 | ||||||||
\(652\) | 12.2107i | 0.478207i | ||||||||
\(653\) | − | 7.32529i | − | 0.286661i | −0.989675 | − | 0.143330i | \(-0.954219\pi\) | ||
0.989675 | − | 0.143330i | \(-0.0457811\pi\) | |||||||
\(654\) | −24.7131 | −0.966360 | ||||||||
\(655\) | −4.74692 | + | 27.0649i | −0.185477 | + | 1.05751i | ||||
\(656\) | −5.13790 | −0.200601 | ||||||||
\(657\) | − | 4.83617i | − | 0.188677i | ||||||
\(658\) | 19.7581i | 0.770250i | ||||||||
\(659\) | 20.7177 | 0.807048 | 0.403524 | − | 0.914969i | \(-0.367785\pi\) | ||||
0.403524 | + | 0.914969i | \(0.367785\pi\) | |||||||
\(660\) | −4.22565 | − | 0.741139i | −0.164483 | − | 0.0288488i | ||||
\(661\) | 12.9749 | 0.504666 | 0.252333 | − | 0.967640i | \(-0.418802\pi\) | ||||
0.252333 | + | 0.967640i | \(0.418802\pi\) | |||||||
\(662\) | 17.6917i | 0.687606i | ||||||||
\(663\) | 8.39098i | 0.325879i | ||||||||
\(664\) | 2.02566 | 0.0786108 | ||||||||
\(665\) | −24.2002 | − | 4.24448i | −0.938443 | − | 0.164594i | ||||
\(666\) | 5.27757 | 0.204502 | ||||||||
\(667\) | 4.29207i | 0.166190i | ||||||||
\(668\) | − | 2.06288i | − | 0.0798151i | ||||||
\(669\) | −29.1561 | −1.12724 | ||||||||
\(670\) | −2.55329 | + | 14.5578i | −0.0986423 | + | 0.562415i | ||||
\(671\) | 16.4443 | 0.634827 | ||||||||
\(672\) | 4.70156i | 0.181367i | ||||||||
\(673\) | 15.8660i | 0.611589i | 0.952098 | + | 0.305794i | \(0.0989220\pi\) | ||||
−0.952098 | + | 0.305794i | \(0.901078\pi\) | |||||||
\(674\) | 1.33801 | 0.0515384 | ||||||||
\(675\) | −9.61959 | + | 26.5798i | −0.370258 | + | 1.02306i | ||||
\(676\) | −11.4153 | −0.439049 | ||||||||
\(677\) | 23.2787i | 0.894675i | 0.894365 | + | 0.447337i | \(0.147628\pi\) | ||||
−0.894365 | + | 0.447337i | \(0.852372\pi\) | |||||||
\(678\) | 14.1015i | 0.541564i | ||||||||
\(679\) | 28.0920 | 1.07807 | ||||||||
\(680\) | −1.78472 | + | 10.1757i | −0.0684410 | + | 0.390220i | ||||
\(681\) | −2.31793 | −0.0888234 | ||||||||
\(682\) | 3.15641i | 0.120865i | ||||||||
\(683\) | 27.5797i | 1.05531i | 0.849460 | + | 0.527654i | \(0.176928\pi\) | ||||
−0.849460 | + | 0.527654i | \(0.823072\pi\) | |||||||
\(684\) | −3.09728 | −0.118427 | ||||||||
\(685\) | 19.4439 | + | 3.41027i | 0.742913 | + | 0.130300i | ||||
\(686\) | −11.0144 | −0.420531 | ||||||||
\(687\) | − | 27.2698i | − | 1.04041i | ||||||
\(688\) | − | 10.4678i | − | 0.399080i | ||||||
\(689\) | −14.0080 | −0.533663 | ||||||||
\(690\) | 3.17748 | + | 0.557299i | 0.120964 | + | 0.0212160i | ||||
\(691\) | 8.61472 | 0.327719 | 0.163860 | − | 0.986484i | \(-0.447606\pi\) | ||||
0.163860 | + | 0.986484i | \(0.447606\pi\) | |||||||
\(692\) | − | 2.10245i | − | 0.0799233i | ||||||
\(693\) | 3.98116i | 0.151232i | ||||||||
\(694\) | 5.36355 | 0.203597 | ||||||||
\(695\) | −4.46286 | + | 25.4453i | −0.169286 | + | 0.965194i | ||||
\(696\) | 6.19218 | 0.234714 | ||||||||
\(697\) | − | 23.7380i | − | 0.899141i | ||||||
\(698\) | 18.4306i | 0.697607i | ||||||||
\(699\) | 27.4274 | 1.03740 | ||||||||
\(700\) | −5.54515 | + | 15.3217i | −0.209587 | + | 0.579107i | ||||
\(701\) | 17.4254 | 0.658148 | 0.329074 | − | 0.944304i | \(-0.393264\pi\) | ||||
0.329074 | + | 0.944304i | \(0.393264\pi\) | |||||||
\(702\) | 7.11683i | 0.268607i | ||||||||
\(703\) | − | 19.3708i | − | 0.730584i | ||||||
\(704\) | −1.32988 | −0.0501216 | ||||||||
\(705\) | 3.37884 | − | 19.2646i | 0.127254 | − | 0.725548i | ||||
\(706\) | 6.76477 | 0.254595 | ||||||||
\(707\) | 47.2321i | 1.77635i | ||||||||
\(708\) | 3.92794i | 0.147621i | ||||||||
\(709\) | 6.42019 | 0.241115 | 0.120558 | − | 0.992706i | \(-0.461532\pi\) | ||||
0.120558 | + | 0.992706i | \(0.461532\pi\) | |||||||
\(710\) | −0.584146 | − | 0.102454i | −0.0219226 | − | 0.00384502i | ||||
\(711\) | 14.0801 | 0.528044 | ||||||||
\(712\) | 16.1500i | 0.605248i | ||||||||
\(713\) | − | 2.37346i | − | 0.0888867i | ||||||
\(714\) | −21.7220 | −0.812927 | ||||||||
\(715\) | −3.68719 | − | 0.646697i | −0.137893 | − | 0.0241851i | ||||
\(716\) | 20.4421 | 0.763958 | ||||||||
\(717\) | 40.8842i | 1.52685i | ||||||||
\(718\) | − | 27.5324i | − | 1.02750i | ||||||
\(719\) | −1.50079 | −0.0559699 | −0.0279849 | − | 0.999608i | \(-0.508909\pi\) | ||||
−0.0279849 | + | 0.999608i | \(0.508909\pi\) | |||||||
\(720\) | −0.354850 | + | 2.02320i | −0.0132245 | + | 0.0754002i | ||||
\(721\) | −60.4226 | −2.25026 | ||||||||
\(722\) | − | 7.63174i | − | 0.284024i | ||||||
\(723\) | − | 9.16318i | − | 0.340782i | ||||||
\(724\) | 7.12175 | 0.264678 | ||||||||
\(725\) | 20.1794 | + | 7.30323i | 0.749446 | + | 0.271235i | ||||
\(726\) | −13.3182 | −0.494284 | ||||||||
\(727\) | 6.97867i | 0.258825i | 0.991591 | + | 0.129412i | \(0.0413091\pi\) | ||||
−0.991591 | + | 0.129412i | \(0.958691\pi\) | |||||||
\(728\) | 4.10245i | 0.152047i | ||||||||
\(729\) | −29.4292 | −1.08997 | ||||||||
\(730\) | −2.03367 | + | 11.5951i | −0.0752695 | + | 0.429154i | ||||
\(731\) | 48.3630 | 1.78877 | ||||||||
\(732\) | 17.8395i | 0.659365i | ||||||||
\(733\) | 3.61138i | 0.133389i | 0.997773 | + | 0.0666947i | \(0.0212453\pi\) | ||||
−0.997773 | + | 0.0666947i | \(0.978755\pi\) | |||||||
\(734\) | −24.0744 | −0.888604 | ||||||||
\(735\) | −11.5030 | − | 2.01752i | −0.424295 | − | 0.0744174i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − | 8.79022i | − | 0.323792i | ||||||
\(738\) | − | 4.71975i | − | 0.173736i | ||||||
\(739\) | −5.24953 | −0.193107 | −0.0965536 | − | 0.995328i | \(-0.530782\pi\) | ||||
−0.0965536 | + | 0.995328i | \(0.530782\pi\) | |||||||
\(740\) | −12.6534 | − | 2.21928i | −0.465148 | − | 0.0815825i | ||||
\(741\) | 6.12352 | 0.224953 | ||||||||
\(742\) | − | 36.2631i | − | 1.33126i | ||||||
\(743\) | − | 2.72603i | − | 0.100008i | −0.998749 | − | 0.0500042i | \(-0.984077\pi\) | ||
0.998749 | − | 0.0500042i | \(-0.0159235\pi\) | |||||||
\(744\) | −3.42419 | −0.125537 | ||||||||
\(745\) | −4.30067 | + | 24.5205i | −0.157564 | + | 0.898363i | ||||
\(746\) | −1.31459 | −0.0481305 | ||||||||
\(747\) | 1.86080i | 0.0680831i | ||||||||
\(748\) | − | 6.14426i | − | 0.224657i | ||||||
\(749\) | 14.6013 | 0.533521 | ||||||||
\(750\) | 8.02685 | − | 13.9908i | 0.293099 | − | 0.510872i | ||||
\(751\) | −20.6729 | −0.754364 | −0.377182 | − | 0.926139i | \(-0.623107\pi\) | ||||
−0.377182 | + | 0.926139i | \(0.623107\pi\) | |||||||
\(752\) | − | 6.06288i | − | 0.221090i | ||||||
\(753\) | − | 28.4545i | − | 1.03694i | ||||||
\(754\) | 5.40312 | 0.196770 | ||||||||
\(755\) | 1.25072 | − | 7.13107i | 0.0455185 | − | 0.259526i | ||||
\(756\) | −18.4236 | −0.670060 | ||||||||
\(757\) | 8.87759i | 0.322661i | 0.986900 | + | 0.161331i | \(0.0515786\pi\) | ||||
−0.986900 | + | 0.161331i | \(0.948421\pi\) | |||||||
\(758\) | − | 8.38961i | − | 0.304724i | ||||||
\(759\) | −1.91861 | −0.0696413 | ||||||||
\(760\) | 7.42597 | + | 1.30244i | 0.269368 | + | 0.0472446i | ||||
\(761\) | 31.8816 | 1.15571 | 0.577853 | − | 0.816141i | \(-0.303891\pi\) | ||||
0.577853 | + | 0.816141i | \(0.303891\pi\) | |||||||
\(762\) | 1.48228i | 0.0536973i | ||||||||
\(763\) | − | 55.8235i | − | 2.02095i | ||||||
\(764\) | 16.7191 | 0.604875 | ||||||||
\(765\) | −9.34754 | − | 1.63947i | −0.337961 | − | 0.0592752i | ||||
\(766\) | −24.1258 | −0.871699 | ||||||||
\(767\) | 3.42741i | 0.123757i | ||||||||
\(768\) | − | 1.44270i | − | 0.0520590i | ||||||
\(769\) | −37.6697 | −1.35841 | −0.679203 | − | 0.733951i | \(-0.737674\pi\) | ||||
−0.679203 | + | 0.733951i | \(0.737674\pi\) | |||||||
\(770\) | 1.67413 | − | 9.54515i | 0.0603314 | − | 0.343983i | ||||
\(771\) | 1.70386 | 0.0613631 | ||||||||
\(772\) | − | 6.51772i | − | 0.234578i | ||||||
\(773\) | 6.14066i | 0.220864i | 0.993884 | + | 0.110432i | \(0.0352235\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(774\) | 9.61584 | 0.345634 | ||||||||
\(775\) | −11.1590 | − | 4.03859i | −0.400842 | − | 0.145070i | ||||
\(776\) | −8.62018 | −0.309446 | ||||||||
\(777\) | − | 27.0112i | − | 0.969020i | ||||||
\(778\) | − | 12.5702i | − | 0.450665i | ||||||
\(779\) | −17.3234 | −0.620674 | ||||||||
\(780\) | 0.701562 | − | 4.00000i | 0.0251200 | − | 0.143223i | ||||
\(781\) | 0.352718 | 0.0126212 | ||||||||
\(782\) | 4.62018i | 0.165217i | ||||||||
\(783\) | 24.2648i | 0.867152i | ||||||||
\(784\) | −3.62018 | −0.129292 | ||||||||
\(785\) | 38.8628 | + | 6.81616i | 1.38707 | + | 0.243279i | ||||
\(786\) | 17.7287 | 0.632361 | ||||||||
\(787\) | 17.9373i | 0.639397i | 0.947519 | + | 0.319698i | \(0.103582\pi\) | ||||
−0.947519 | + | 0.319698i | \(0.896418\pi\) | |||||||
\(788\) | − | 17.8184i | − | 0.634754i | ||||||
\(789\) | −35.0849 | −1.24906 | ||||||||
\(790\) | −33.7581 | − | 5.92085i | −1.20106 | − | 0.210654i | ||||
\(791\) | −31.8533 | −1.13257 | ||||||||
\(792\) | − | 1.22164i | − | 0.0434092i | ||||||
\(793\) | 15.5662i | 0.552773i | ||||||||
\(794\) | −28.5318 | −1.01256 | ||||||||
\(795\) | −6.20136 | + | 35.3574i | −0.219940 | + | 1.25400i | ||||
\(796\) | −3.77435 | −0.133778 | ||||||||
\(797\) | − | 6.03367i | − | 0.213724i | −0.994274 | − | 0.106862i | \(-0.965920\pi\) | ||
0.994274 | − | 0.106862i | \(-0.0340802\pi\) | |||||||
\(798\) | 15.8522i | 0.561161i | ||||||||
\(799\) | 28.0116 | 0.990978 | ||||||||
\(800\) | 1.70156 | − | 4.70156i | 0.0601593 | − | 0.166225i | ||||
\(801\) | −14.8357 | −0.524192 | ||||||||
\(802\) | − | 19.7130i | − | 0.696092i | ||||||
\(803\) | − | 7.00132i | − | 0.247071i | ||||||
\(804\) | 9.53597 | 0.336308 | ||||||||
\(805\) | −1.25886 | + | 7.17748i | −0.0443690 | + | 0.252973i | ||||
\(806\) | −2.98786 | −0.105243 | ||||||||
\(807\) | 11.4159i | 0.401857i | ||||||||
\(808\) | − | 14.4934i | − | 0.509877i | ||||||
\(809\) | 51.6850 | 1.81715 | 0.908574 | − | 0.417723i | \(-0.137172\pi\) | ||||
0.908574 | + | 0.417723i | \(0.137172\pi\) | |||||||
\(810\) | 11.8939 | + | 2.08608i | 0.417909 | + | 0.0732973i | ||||
\(811\) | 11.6368 | 0.408623 | 0.204311 | − | 0.978906i | \(-0.434504\pi\) | ||||
0.204311 | + | 0.978906i | \(0.434504\pi\) | |||||||
\(812\) | 13.9873i | 0.490857i | ||||||||
\(813\) | 26.3983i | 0.925830i | ||||||||
\(814\) | 7.64033 | 0.267794 | ||||||||
\(815\) | 26.8934 | + | 4.71685i | 0.942035 | + | 0.165224i | ||||
\(816\) | 6.66553 | 0.233340 | ||||||||
\(817\) | − | 35.2940i | − | 1.23478i | ||||||
\(818\) | − | 20.3400i | − | 0.711171i | ||||||
\(819\) | −3.76857 | −0.131685 | ||||||||
\(820\) | −1.98471 | + | 11.3160i | −0.0693091 | + | 0.395170i | ||||
\(821\) | 6.02312 | 0.210208 | 0.105104 | − | 0.994461i | \(-0.466482\pi\) | ||||
0.105104 | + | 0.994461i | \(0.466482\pi\) | |||||||
\(822\) | − | 12.7366i | − | 0.444240i | ||||||
\(823\) | 40.1839i | 1.40072i | 0.713788 | + | 0.700362i | \(0.246978\pi\) | ||||
−0.713788 | + | 0.700362i | \(0.753022\pi\) | |||||||
\(824\) | 18.5410 | 0.645907 | ||||||||
\(825\) | −3.26464 | + | 9.02048i | −0.113660 | + | 0.314053i | ||||
\(826\) | −8.87267 | −0.308720 | ||||||||
\(827\) | − | 30.5980i | − | 1.06400i | −0.846745 | − | 0.531998i | \(-0.821441\pi\) | ||
0.846745 | − | 0.531998i | \(-0.178559\pi\) | |||||||
\(828\) | 0.918614i | 0.0319240i | ||||||||
\(829\) | −54.9892 | −1.90986 | −0.954928 | − | 0.296838i | \(-0.904068\pi\) | ||||
−0.954928 | + | 0.296838i | \(0.904068\pi\) | |||||||
\(830\) | 0.782489 | − | 4.46141i | 0.0271606 | − | 0.154858i | ||||
\(831\) | 41.3406 | 1.43409 | ||||||||
\(832\) | − | 1.25886i | − | 0.0436432i | ||||||
\(833\) | − | 16.7259i | − | 0.579516i | ||||||
\(834\) | 16.6678 | 0.577158 | ||||||||
\(835\) | −4.54338 | − | 0.796866i | −0.157230 | − | 0.0275767i | ||||
\(836\) | −4.48393 | −0.155080 | ||||||||
\(837\) | − | 13.4181i | − | 0.463797i | ||||||
\(838\) | − | 9.91146i | − | 0.342386i | ||||||
\(839\) | 12.5121 | 0.431965 | 0.215983 | − | 0.976397i | \(-0.430705\pi\) | ||||
0.215983 | + | 0.976397i | \(0.430705\pi\) | |||||||
\(840\) | 10.3550 | + | 1.81616i | 0.357280 | + | 0.0626635i | ||||
\(841\) | −10.5781 | −0.364762 | ||||||||
\(842\) | − | 28.7927i | − | 0.992260i | ||||||
\(843\) | − | 3.96298i | − | 0.136492i | ||||||
\(844\) | 23.9630 | 0.824840 | ||||||||
\(845\) | −4.40959 | + | 25.1415i | −0.151694 | + | 0.864895i | ||||
\(846\) | 5.56944 | 0.191481 | ||||||||
\(847\) | − | 30.0839i | − | 1.03370i | ||||||
\(848\) | 11.1275i | 0.382121i | ||||||||
\(849\) | 7.86715 | 0.270000 | ||||||||
\(850\) | 21.7220 | + | 7.86152i | 0.745060 | + | 0.269648i | ||||
\(851\) | −5.74514 | −0.196941 | ||||||||
\(852\) | 0.382642i | 0.0131091i | ||||||||
\(853\) | − | 52.3308i | − | 1.79177i | −0.444283 | − | 0.895886i | \(-0.646542\pi\) | ||
0.444283 | − | 0.895886i | \(-0.353458\pi\) | |||||||
\(854\) | −40.2969 | −1.37893 | ||||||||
\(855\) | −1.19644 | + | 6.82160i | −0.0409175 | + | 0.233294i | ||||
\(856\) | −4.48050 | −0.153140 | ||||||||
\(857\) | − | 4.53557i | − | 0.154932i | −0.996995 | − | 0.0774660i | \(-0.975317\pi\) | ||
0.996995 | − | 0.0774660i | \(-0.0246829\pi\) | |||||||
\(858\) | 2.41527i | 0.0824559i | ||||||||
\(859\) | −10.1708 | −0.347023 | −0.173511 | − | 0.984832i | \(-0.555511\pi\) | ||||
−0.173511 | + | 0.984832i | \(0.555511\pi\) | |||||||
\(860\) | −23.0547 | − | 4.04358i | −0.786160 | − | 0.137885i | ||||
\(861\) | −24.1561 | −0.823239 | ||||||||
\(862\) | 36.6821i | 1.24940i | ||||||||
\(863\) | − | 0.861113i | − | 0.0293126i | −0.999893 | − | 0.0146563i | \(-0.995335\pi\) | ||
0.999893 | − | 0.0146563i | \(-0.00466542\pi\) | |||||||
\(864\) | 5.65339 | 0.192332 | ||||||||
\(865\) | −4.63055 | − | 0.812154i | −0.157443 | − | 0.0276141i | ||||
\(866\) | −29.6894 | −1.00889 | ||||||||
\(867\) | 6.27002i | 0.212941i | ||||||||
\(868\) | − | 7.73477i | − | 0.262535i | ||||||
\(869\) | 20.3837 | 0.691470 | ||||||||
\(870\) | 2.39197 | − | 13.6380i | 0.0810953 | − | 0.462370i | ||||
\(871\) | 8.32083 | 0.281940 | ||||||||
\(872\) | 17.1298i | 0.580087i | ||||||||
\(873\) | − | 7.91861i | − | 0.268004i | ||||||
\(874\) | 3.37169 | 0.114049 | ||||||||
\(875\) | 31.6033 | + | 18.1315i | 1.06839 | + | 0.612958i | ||||
\(876\) | 7.59530 | 0.256621 | ||||||||
\(877\) | − | 26.4746i | − | 0.893984i | −0.894538 | − | 0.446992i | \(-0.852495\pi\) | ||
0.894538 | − | 0.446992i | \(-0.147505\pi\) | |||||||
\(878\) | − | 34.5378i | − | 1.16559i | ||||||
\(879\) | −26.5177 | −0.894421 | ||||||||
\(880\) | −0.513716 | + | 2.92898i | −0.0173174 | + | 0.0987361i | ||||
\(881\) | 32.8670 | 1.10732 | 0.553659 | − | 0.832743i | \(-0.313231\pi\) | ||||
0.553659 | + | 0.832743i | \(0.313231\pi\) | |||||||
\(882\) | − | 3.32554i | − | 0.111977i | ||||||
\(883\) | − | 29.1507i | − | 0.980999i | −0.871441 | − | 0.490500i | \(-0.836814\pi\) | ||
0.871441 | − | 0.490500i | \(-0.163186\pi\) | |||||||
\(884\) | 5.81616 | 0.195619 | ||||||||
\(885\) | 8.65109 | + | 1.51732i | 0.290803 | + | 0.0510041i | ||||
\(886\) | 36.6735 | 1.23207 | ||||||||
\(887\) | − | 29.6697i | − | 0.996212i | −0.867116 | − | 0.498106i | \(-0.834029\pi\) | ||
0.867116 | − | 0.498106i | \(-0.165971\pi\) | |||||||
\(888\) | 8.28853i | 0.278145i | ||||||||
\(889\) | −3.34826 | −0.112297 | ||||||||
\(890\) | 35.5696 | + | 6.23858i | 1.19230 | + | 0.209118i | ||||
\(891\) | −7.18174 | −0.240597 | ||||||||
\(892\) | 20.2094i | 0.676660i | ||||||||
\(893\) | − | 20.4421i | − | 0.684069i | ||||||
\(894\) | 16.0620 | 0.537195 | ||||||||
\(895\) | 7.89656 | − | 45.0227i | 0.263953 | − | 1.50494i | ||||
\(896\) | 3.25886 | 0.108871 | ||||||||
\(897\) | − | 1.81616i | − | 0.0606398i | ||||||
\(898\) | 13.2138i | 0.440951i | ||||||||
\(899\) | −10.1871 | −0.339757 | ||||||||
\(900\) | 4.31892 | + | 1.56308i | 0.143964 | + | 0.0521026i | ||||
\(901\) | −51.4111 | −1.71275 | ||||||||
\(902\) | − | 6.83277i | − | 0.227506i | ||||||
\(903\) | − | 49.2149i | − | 1.63777i | ||||||
\(904\) | 9.77435 | 0.325090 | ||||||||
\(905\) | 2.75105 | − | 15.6853i | 0.0914480 | − | 0.521397i | ||||
\(906\) | −4.67117 | −0.155189 | ||||||||
\(907\) | − | 7.66153i | − | 0.254397i | −0.991877 | − | 0.127198i | \(-0.959402\pi\) | ||
0.991877 | − | 0.127198i | \(-0.0405985\pi\) | |||||||
\(908\) | 1.60666i | 0.0533189i | ||||||||
\(909\) | 13.3139 | 0.441593 | ||||||||
\(910\) | 9.03544 | + | 1.58473i | 0.299522 | + | 0.0525333i | ||||
\(911\) | 53.4450 | 1.77071 | 0.885356 | − | 0.464914i | \(-0.153915\pi\) | ||||
0.885356 | + | 0.464914i | \(0.153915\pi\) | |||||||
\(912\) | − | 4.86433i | − | 0.161074i | ||||||
\(913\) | 2.69388i | 0.0891543i | ||||||||
\(914\) | 12.2292 | 0.404506 | ||||||||
\(915\) | 39.2905 | + | 6.89118i | 1.29890 | + | 0.227815i | ||||
\(916\) | −18.9019 | −0.624536 | ||||||||
\(917\) | 40.0466i | 1.32246i | ||||||||
\(918\) | 26.1196i | 0.862077i | ||||||||
\(919\) | −22.7485 | −0.750403 | −0.375202 | − | 0.926943i | \(-0.622427\pi\) | ||||
−0.375202 | + | 0.926943i | \(0.622427\pi\) | |||||||
\(920\) | 0.386289 | − | 2.20245i | 0.0127356 | − | 0.0726126i | ||||
\(921\) | −22.9727 | −0.756977 | ||||||||
\(922\) | 24.0872i | 0.793269i | ||||||||
\(923\) | 0.333883i | 0.0109899i | ||||||||
\(924\) | −6.25250 | −0.205692 | ||||||||
\(925\) | −9.77572 | + | 27.0112i | −0.321424 | + | 0.888121i | ||||
\(926\) | 15.9173 | 0.523075 | ||||||||
\(927\) | 17.0320i | 0.559406i | ||||||||
\(928\) | − | 4.29207i | − | 0.140894i | ||||||
\(929\) | −23.1810 | −0.760545 | −0.380272 | − | 0.924875i | \(-0.624170\pi\) | ||||
−0.380272 | + | 0.924875i | \(0.624170\pi\) | |||||||
\(930\) | −1.32273 | + | 7.54161i | −0.0433739 | + | 0.247299i | ||||
\(931\) | −12.2061 | −0.400039 | ||||||||
\(932\) | − | 19.0112i | − | 0.622731i | ||||||
\(933\) | 16.3773i | 0.536167i | ||||||||
\(934\) | −9.70011 | −0.317397 | ||||||||
\(935\) | −13.5324 | − | 2.37346i | −0.442558 | − | 0.0776204i | ||||
\(936\) | 1.15641 | 0.0377984 | ||||||||
\(937\) | − | 12.6027i | − | 0.411711i | −0.978582 | − | 0.205855i | \(-0.934002\pi\) | ||
0.978582 | − | 0.205855i | \(-0.0659977\pi\) | |||||||
\(938\) | 21.5404i | 0.703320i | ||||||||
\(939\) | 41.5372 | 1.35552 | ||||||||
\(940\) | −13.3532 | − | 2.34202i | −0.435533 | − | 0.0763883i | ||||
\(941\) | −47.9093 | −1.56180 | −0.780899 | − | 0.624657i | \(-0.785239\pi\) | ||||
−0.780899 | + | 0.624657i | \(0.785239\pi\) | |||||||
\(942\) | − | 25.4568i | − | 0.829428i | ||||||
\(943\) | 5.13790i | 0.167313i | ||||||||
\(944\) | 2.72263 | 0.0886141 | ||||||||
\(945\) | −7.11683 | + | 40.5771i | −0.231511 | + | 1.31997i | ||||
\(946\) | 13.9208 | 0.452606 | ||||||||
\(947\) | − | 30.4073i | − | 0.988105i | −0.869432 | − | 0.494053i | \(-0.835515\pi\) | ||
0.869432 | − | 0.494053i | \(-0.164485\pi\) | |||||||
\(948\) | 22.1130i | 0.718198i | ||||||||
\(949\) | 6.62745 | 0.215136 | ||||||||
\(950\) | 5.73713 | − | 15.8522i | 0.186137 | − | 0.514313i | ||||
\(951\) | −45.0553 | −1.46102 | ||||||||
\(952\) | 15.0565i | 0.487984i | ||||||||
\(953\) | − | 45.8534i | − | 1.48534i | −0.669658 | − | 0.742669i | \(-0.733559\pi\) | ||
0.669658 | − | 0.742669i | \(-0.266441\pi\) | |||||||
\(954\) | −10.2219 | −0.330946 | ||||||||
\(955\) | 6.45839 | − | 36.8229i | 0.208989 | − | 1.19156i | ||||
\(956\) | 28.3387 | 0.916538 | ||||||||
\(957\) | 8.23483i | 0.266194i | ||||||||
\(958\) | − | 14.1385i | − | 0.456794i | ||||||
\(959\) | 28.7702 | 0.929039 | ||||||||
\(960\) | −3.17748 | − | 0.557299i | −0.102553 | − | 0.0179867i | ||||
\(961\) | −25.3667 | −0.818280 | ||||||||
\(962\) | 7.23234i | 0.233180i | ||||||||
\(963\) | − | 4.11585i | − | 0.132632i | ||||||
\(964\) | −6.35140 | −0.204565 | ||||||||
\(965\) | −14.3550 | − | 2.51772i | −0.462102 | − | 0.0810483i | ||||
\(966\) | 4.70156 | 0.151270 | ||||||||
\(967\) | − | 57.3471i | − | 1.84416i | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||
0.387002 | − | 0.922079i | \(-0.373511\pi\) | |||||||
\(968\) | 9.23143i | 0.296709i | ||||||||
\(969\) | 22.4741 | 0.721971 | ||||||||
\(970\) | −3.32988 | + | 18.9855i | −0.106916 | + | 0.609588i | ||||
\(971\) | −44.6948 | −1.43432 | −0.717162 | − | 0.696906i | \(-0.754559\pi\) | ||||
−0.717162 | + | 0.696906i | \(0.754559\pi\) | |||||||
\(972\) | 9.16914i | 0.294100i | ||||||||
\(973\) | 37.6502i | 1.20701i | ||||||||
\(974\) | −3.75006 | −0.120160 | ||||||||
\(975\) | −8.53879 | − | 3.09031i | −0.273460 | − | 0.0989691i | ||||
\(976\) | 12.3653 | 0.395804 | ||||||||
\(977\) | 10.7663i | 0.344446i | 0.985058 | + | 0.172223i | \(0.0550950\pi\) | ||||
−0.985058 | + | 0.172223i | \(0.944905\pi\) | |||||||
\(978\) | − | 17.6164i | − | 0.563309i | ||||||
\(979\) | −21.4776 | −0.686426 | ||||||||
\(980\) | −1.39843 | + | 7.97325i | −0.0446713 | + | 0.254696i | ||||
\(981\) | −15.7356 | −0.502400 | ||||||||
\(982\) | − | 3.19020i | − | 0.101804i | ||||||
\(983\) | 4.38626i | 0.139900i | 0.997550 | + | 0.0699500i | \(0.0222840\pi\) | ||||
−0.997550 | + | 0.0699500i | \(0.977716\pi\) | |||||||
\(984\) | 7.41245 | 0.236300 | ||||||||
\(985\) | −39.2441 | − | 6.88304i | −1.25042 | − | 0.219312i | ||||
\(986\) | 19.8301 | 0.631520 | ||||||||
\(987\) | − | 28.5050i | − | 0.907324i | ||||||
\(988\) | − | 4.24448i | − | 0.135035i | ||||||
\(989\) | −10.4678 | −0.332856 | ||||||||
\(990\) | −2.69061 | − | 0.471907i | −0.0855131 | − | 0.0149982i | ||||
\(991\) | −1.49757 | −0.0475717 | −0.0237859 | − | 0.999717i | \(-0.507572\pi\) | ||||
−0.0237859 | + | 0.999717i | \(0.507572\pi\) | |||||||
\(992\) | 2.37346i | 0.0753574i | ||||||||
\(993\) | − | 25.5238i | − | 0.809972i | ||||||
\(994\) | −0.864334 | −0.0274150 | ||||||||
\(995\) | −1.45799 | + | 8.31281i | −0.0462214 | + | 0.263534i | ||||
\(996\) | −2.92242 | −0.0926004 | ||||||||
\(997\) | − | 45.4135i | − | 1.43826i | −0.694875 | − | 0.719130i | \(-0.744540\pi\) | ||
0.694875 | − | 0.719130i | \(-0.255460\pi\) | |||||||
\(998\) | − | 12.9355i | − | 0.409468i | ||||||
\(999\) | −32.4795 | −1.02761 |
(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 | 230.2.b.b.139.6 | yes | 8 | |
3.2 | odd | 2 | 2070.2.d.f.829.3 | 8 | |||
4.3 | odd | 2 | 1840.2.e.e.369.6 | 8 | |||
5.2 | odd | 4 | 1150.2.a.r.1.2 | 4 | |||
5.3 | odd | 4 | 1150.2.a.s.1.3 | 4 | |||
5.4 | even | 2 | inner | 230.2.b.b.139.3 | ✓ | 8 | |
15.14 | odd | 2 | 2070.2.d.f.829.7 | 8 | |||
20.3 | even | 4 | 9200.2.a.cj.1.2 | 4 | |||
20.7 | even | 4 | 9200.2.a.cr.1.3 | 4 | |||
20.19 | odd | 2 | 1840.2.e.e.369.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.3 | ✓ | 8 | 5.4 | even | 2 | inner | |
230.2.b.b.139.6 | yes | 8 | 1.1 | even | 1 | trivial | |
1150.2.a.r.1.2 | 4 | 5.2 | odd | 4 | |||
1150.2.a.s.1.3 | 4 | 5.3 | odd | 4 | |||
1840.2.e.e.369.3 | 8 | 20.19 | odd | 2 | |||
1840.2.e.e.369.6 | 8 | 4.3 | odd | 2 | |||
2070.2.d.f.829.3 | 8 | 3.2 | odd | 2 | |||
2070.2.d.f.829.7 | 8 | 15.14 | odd | 2 | |||
9200.2.a.cj.1.2 | 4 | 20.3 | even | 4 | |||
9200.2.a.cr.1.3 | 4 | 20.7 | even | 4 |