Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [357,2,Mod(16,357)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(357, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("357.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 357 = 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 357.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.85065935216\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 16.14 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.14 |
$q$-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 \(\left(\mathbb{Z}/357\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(190\) | \(239\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.113439 | − | 0.196482i | 0.0802134 | − | 0.138934i | −0.823128 | − | 0.567856i | \(-0.807773\pi\) |
0.903342 | + | 0.428922i | \(0.141106\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.974263 | + | 1.68747i | 0.487132 | + | 0.843737i | ||||
\(5\) | −0.103638 | − | 0.0598352i | −0.0463481 | − | 0.0267591i | 0.476647 | − | 0.879095i | \(-0.341852\pi\) |
−0.522995 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(6\) | − | 0.226878i | − | 0.0926224i | ||||||
\(7\) | −2.28748 | + | 1.32945i | −0.864585 | + | 0.502487i | ||||
\(8\) | 0.895833 | 0.316725 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.0235130 | + | 0.0135753i | −0.00743548 | + | 0.00429288i | ||||
\(11\) | 3.73272 | − | 2.15509i | 1.12546 | − | 0.649784i | 0.182670 | − | 0.983174i | \(-0.441526\pi\) |
0.942789 | + | 0.333390i | \(0.108193\pi\) | |||||||
\(12\) | 1.68747 | + | 0.974263i | 0.487132 | + | 0.281246i | ||||
\(13\) | 5.22378 | 1.44882 | 0.724409 | − | 0.689371i | \(-0.242113\pi\) | ||||
0.724409 | + | 0.689371i | \(0.242113\pi\) | |||||||
\(14\) | 0.00172503 | + | 0.600260i | 0.000461033 | + | 0.160426i | ||||
\(15\) | −0.119670 | −0.0308987 | ||||||||
\(16\) | −1.84690 | + | 3.19893i | −0.461726 | + | 0.799733i | ||||
\(17\) | 0.947524 | + | 4.01275i | 0.229808 | + | 0.973236i | ||||
\(18\) | −0.113439 | − | 0.196482i | −0.0267378 | − | 0.0463112i | ||||
\(19\) | −1.79673 | + | 3.11203i | −0.412198 | + | 0.713948i | −0.995130 | − | 0.0985733i | \(-0.968572\pi\) |
0.582932 | + | 0.812521i | \(0.301905\pi\) | |||||||
\(20\) | − | 0.233181i | − | 0.0521408i | ||||||
\(21\) | −1.31629 | + | 2.29508i | −0.287237 | + | 0.500828i | ||||
\(22\) | − | 0.977884i | − | 0.208485i | ||||||
\(23\) | 1.22544 | + | 0.707507i | 0.255521 | + | 0.147525i | 0.622290 | − | 0.782787i | \(-0.286203\pi\) |
−0.366768 | + | 0.930312i | \(0.619536\pi\) | |||||||
\(24\) | 0.775814 | − | 0.447916i | 0.158362 | − | 0.0914305i | ||||
\(25\) | −2.49284 | − | 4.31772i | −0.498568 | − | 0.863545i | ||||
\(26\) | 0.592580 | − | 1.02638i | 0.116215 | − | 0.201289i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −4.47202 | − | 2.56482i | −0.845133 | − | 0.484705i | ||||
\(29\) | − | 9.62870i | − | 1.78801i | −0.448062 | − | 0.894003i | \(-0.647885\pi\) | ||
0.448062 | − | 0.894003i | \(-0.352115\pi\) | |||||||
\(30\) | −0.0135753 | + | 0.0235130i | −0.00247849 | + | 0.00429288i | ||||
\(31\) | −5.32463 | + | 3.07418i | −0.956332 | + | 0.552139i | −0.895042 | − | 0.445981i | \(-0.852855\pi\) |
−0.0612899 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(32\) | 1.31485 | + | 2.27739i | 0.232436 | + | 0.402590i | ||||
\(33\) | 2.15509 | − | 3.73272i | 0.375153 | − | 0.649784i | ||||
\(34\) | 0.895920 | + | 0.269031i | 0.153649 | + | 0.0461384i | ||||
\(35\) | 0.316617 | 0.000909894i | 0.0535180 | 0.000153800i | ||||||
\(36\) | 1.94853 | 0.324754 | ||||||||
\(37\) | −2.45201 | − | 1.41567i | −0.403109 | − | 0.232735i | 0.284716 | − | 0.958612i | \(-0.408101\pi\) |
−0.687824 | + | 0.725877i | \(0.741434\pi\) | |||||||
\(38\) | 0.407638 | + | 0.706049i | 0.0661276 | + | 0.114536i | ||||
\(39\) | 4.52393 | − | 2.61189i | 0.724409 | − | 0.418237i | ||||
\(40\) | −0.0928419 | − | 0.0536023i | −0.0146796 | − | 0.00847527i | ||||
\(41\) | 8.26223i | 1.29034i | 0.764038 | + | 0.645172i | \(0.223214\pi\) | ||||
−0.764038 | + | 0.645172i | \(0.776786\pi\) | |||||||
\(42\) | 0.301624 | + | 0.518977i | 0.0465415 | + | 0.0800800i | ||||
\(43\) | −4.00310 | −0.610467 | −0.305234 | − | 0.952277i | \(-0.598735\pi\) | ||||
−0.305234 | + | 0.952277i | \(0.598735\pi\) | |||||||
\(44\) | 7.27331 | + | 4.19925i | 1.09649 | + | 0.633061i | ||||
\(45\) | −0.103638 | + | 0.0598352i | −0.0154494 | + | 0.00891970i | ||||
\(46\) | 0.278025 | − | 0.160518i | 0.0409925 | − | 0.0236670i | ||||
\(47\) | 2.75198 | − | 4.76657i | 0.401418 | − | 0.695276i | −0.592479 | − | 0.805586i | \(-0.701851\pi\) |
0.993897 | + | 0.110309i | \(0.0351841\pi\) | |||||||
\(48\) | 3.69381i | 0.533155i | ||||||||
\(49\) | 3.46510 | − | 6.08219i | 0.495014 | − | 0.868885i | ||||
\(50\) | −1.13114 | −0.159967 | ||||||||
\(51\) | 2.82696 | + | 3.00139i | 0.395853 | + | 0.420278i | ||||
\(52\) | 5.08934 | + | 8.81500i | 0.705765 | + | 1.22242i | ||||
\(53\) | −4.71623 | − | 8.16874i | −0.647823 | − | 1.12206i | −0.983642 | − | 0.180136i | \(-0.942346\pi\) |
0.335818 | − | 0.941927i | \(-0.390987\pi\) | |||||||
\(54\) | −0.196482 | − | 0.113439i | −0.0267378 | − | 0.0154371i | ||||
\(55\) | −0.515801 | −0.0695505 | ||||||||
\(56\) | −2.04920 | + | 1.19097i | −0.273835 | + | 0.159150i | ||||
\(57\) | 3.59346i | 0.475965i | ||||||||
\(58\) | −1.89187 | − | 1.09227i | −0.248414 | − | 0.143422i | ||||
\(59\) | −4.76861 | − | 8.25948i | −0.620821 | − | 1.07529i | −0.989333 | − | 0.145670i | \(-0.953466\pi\) |
0.368513 | − | 0.929623i | \(-0.379867\pi\) | |||||||
\(60\) | −0.116590 | − | 0.201940i | −0.0150518 | − | 0.0260704i | ||||
\(61\) | −7.84116 | − | 4.52710i | −1.00396 | − | 0.579635i | −0.0945411 | − | 0.995521i | \(-0.530138\pi\) |
−0.909417 | + | 0.415885i | \(0.863472\pi\) | |||||||
\(62\) | 1.39492i | 0.177156i | ||||||||
\(63\) | 0.00760334 | + | 2.64574i | 0.000957931 | + | 0.333332i | ||||
\(64\) | −6.79099 | −0.848874 | ||||||||
\(65\) | −0.541380 | − | 0.312566i | −0.0671499 | − | 0.0387690i | ||||
\(66\) | −0.488942 | − | 0.846872i | −0.0601846 | − | 0.104243i | ||||
\(67\) | −2.66902 | − | 4.62287i | −0.326072 | − | 0.564774i | 0.655656 | − | 0.755059i | \(-0.272392\pi\) |
−0.981729 | + | 0.190285i | \(0.939059\pi\) | |||||||
\(68\) | −5.84828 | + | 5.50840i | −0.709208 | + | 0.667992i | ||||
\(69\) | 1.41501 | 0.170348 | ||||||||
\(70\) | 0.0357378 | − | 0.0623126i | 0.00427149 | − | 0.00744778i | ||||
\(71\) | 2.27301i | 0.269756i | 0.990862 | + | 0.134878i | \(0.0430643\pi\) | ||||
−0.990862 | + | 0.134878i | \(0.956936\pi\) | |||||||
\(72\) | 0.447916 | − | 0.775814i | 0.0527874 | − | 0.0914305i | ||||
\(73\) | 8.55939 | − | 4.94177i | 1.00180 | − | 0.578390i | 0.0930201 | − | 0.995664i | \(-0.470348\pi\) |
0.908781 | + | 0.417274i | \(0.137015\pi\) | |||||||
\(74\) | −0.556307 | + | 0.321184i | −0.0646694 | + | 0.0373369i | ||||
\(75\) | −4.31772 | − | 2.49284i | −0.498568 | − | 0.287848i | ||||
\(76\) | −7.00195 | −0.803179 | ||||||||
\(77\) | −5.67343 | + | 9.89221i | −0.646547 | + | 1.12732i | ||||
\(78\) | − | 1.18516i | − | 0.134193i | ||||||
\(79\) | 2.63292 | + | 1.52012i | 0.296227 | + | 0.171027i | 0.640747 | − | 0.767752i | \(-0.278625\pi\) |
−0.344520 | + | 0.938779i | \(0.611958\pi\) | |||||||
\(80\) | 0.382817 | − | 0.221020i | 0.0428003 | − | 0.0247107i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.62338 | + | 0.937258i | 0.179272 | + | 0.103503i | ||||
\(83\) | 1.58106 | 0.173544 | 0.0867718 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867718 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(84\) | −5.15530 | + | 0.0148153i | −0.562489 | + | 0.00161648i | ||||
\(85\) | 0.141905 | − | 0.472567i | 0.0153917 | − | 0.0512571i | ||||
\(86\) | −0.454107 | + | 0.786537i | −0.0489677 | + | 0.0848145i | ||||
\(87\) | −4.81435 | − | 8.33870i | −0.516153 | − | 0.894003i | ||||
\(88\) | 3.34390 | − | 1.93060i | 0.356461 | − | 0.205803i | ||||
\(89\) | 2.13643 | − | 3.70041i | 0.226461 | − | 0.392242i | −0.730296 | − | 0.683131i | \(-0.760618\pi\) |
0.956757 | + | 0.290889i | \(0.0939510\pi\) | |||||||
\(90\) | 0.0271505i | 0.00286192i | ||||||||
\(91\) | −11.9493 | + | 6.94479i | −1.25263 | + | 0.728011i | ||||
\(92\) | 2.75719i | 0.287457i | ||||||||
\(93\) | −3.07418 | + | 5.32463i | −0.318777 | + | 0.552139i | ||||
\(94\) | −0.624364 | − | 1.08143i | −0.0643982 | − | 0.111541i | ||||
\(95\) | 0.372417 | − | 0.215015i | 0.0382092 | − | 0.0220601i | ||||
\(96\) | 2.27739 | + | 1.31485i | 0.232436 | + | 0.134197i | ||||
\(97\) | 13.0140i | 1.32137i | 0.750662 | + | 0.660687i | \(0.229735\pi\) | ||||
−0.750662 | + | 0.660687i | \(0.770265\pi\) | |||||||
\(98\) | −0.801964 | − | 1.37079i | −0.0810106 | − | 0.138470i | ||||
\(99\) | − | 4.31018i | − | 0.433189i | ||||||
\(100\) | 4.85736 | − | 8.41320i | 0.485736 | − | 0.841320i | ||||
\(101\) | −5.18235 | − | 8.97609i | −0.515663 | − | 0.893154i | −0.999835 | − | 0.0181812i | \(-0.994212\pi\) |
0.484172 | − | 0.874973i | \(-0.339121\pi\) | |||||||
\(102\) | 0.910405 | − | 0.214972i | 0.0901435 | − | 0.0212854i | ||||
\(103\) | −8.58152 | + | 14.8636i | −0.845563 | + | 1.46456i | 0.0395688 | + | 0.999217i | \(0.487402\pi\) |
−0.885132 | + | 0.465341i | \(0.845932\pi\) | |||||||
\(104\) | 4.67964 | 0.458876 | ||||||||
\(105\) | 0.273743 | − | 0.159096i | 0.0267146 | − | 0.0155262i | ||||
\(106\) | −2.14001 | −0.207856 | ||||||||
\(107\) | −1.38873 | − | 0.801783i | −0.134253 | − | 0.0775113i | 0.431369 | − | 0.902176i | \(-0.358031\pi\) |
−0.565622 | + | 0.824664i | \(0.691364\pi\) | |||||||
\(108\) | 1.68747 | − | 0.974263i | 0.162377 | − | 0.0937485i | ||||
\(109\) | −3.19828 | + | 1.84653i | −0.306340 | + | 0.176866i | −0.645288 | − | 0.763940i | \(-0.723262\pi\) |
0.338947 | + | 0.940805i | \(0.389929\pi\) | |||||||
\(110\) | −0.0585118 | + | 0.101345i | −0.00557888 | + | 0.00966291i | ||||
\(111\) | −2.83134 | −0.268739 | ||||||||
\(112\) | −0.0280853 | − | 9.77286i | −0.00265381 | − | 0.923448i | ||||
\(113\) | 9.27139i | 0.872179i | 0.899903 | + | 0.436090i | \(0.143637\pi\) | ||||
−0.899903 | + | 0.436090i | \(0.856363\pi\) | |||||||
\(114\) | 0.706049 | + | 0.407638i | 0.0661276 | + | 0.0381788i | ||||
\(115\) | −0.0846676 | − | 0.146649i | −0.00789529 | − | 0.0136750i | ||||
\(116\) | 16.2482 | − | 9.38089i | 1.50861 | − | 0.870994i | ||||
\(117\) | 2.61189 | − | 4.52393i | 0.241470 | − | 0.418237i | ||||
\(118\) | −2.16378 | −0.199192 | ||||||||
\(119\) | −7.50222 | − | 7.91939i | −0.687727 | − | 0.725969i | ||||
\(120\) | −0.107205 | −0.00978639 | ||||||||
\(121\) | 3.78882 | − | 6.56243i | 0.344438 | − | 0.596585i | ||||
\(122\) | −1.77899 | + | 1.02710i | −0.161062 | + | 0.0929890i | ||||
\(123\) | 4.13112 | + | 7.15530i | 0.372490 | + | 0.645172i | ||||
\(124\) | −10.3752 | − | 5.99012i | −0.931719 | − | 0.537928i | ||||
\(125\) | 1.19499i | 0.106883i | ||||||||
\(126\) | 0.520703 | + | 0.298636i | 0.0463879 | + | 0.0266046i | ||||
\(127\) | 12.4278 | 1.10279 | 0.551395 | − | 0.834244i | \(-0.314096\pi\) | ||||
0.551395 | + | 0.834244i | \(0.314096\pi\) | |||||||
\(128\) | −3.40007 | + | 5.88910i | −0.300527 | + | 0.520527i | ||||
\(129\) | −3.46679 | + | 2.00155i | −0.305234 | + | 0.176227i | ||||
\(130\) | −0.122827 | + | 0.0709142i | −0.0107726 | + | 0.00621959i | ||||
\(131\) | −4.86357 | − | 2.80798i | −0.424932 | − | 0.245335i | 0.272253 | − | 0.962226i | \(-0.412231\pi\) |
−0.697185 | + | 0.716891i | \(0.745565\pi\) | |||||||
\(132\) | 8.39850 | 0.730995 | ||||||||
\(133\) | −0.0273223 | − | 9.50736i | −0.00236914 | − | 0.824392i | ||||
\(134\) | −1.21108 | −0.104621 | ||||||||
\(135\) | −0.0598352 | + | 0.103638i | −0.00514979 | + | 0.00891970i | ||||
\(136\) | 0.848823 | + | 3.59476i | 0.0727860 | + | 0.308248i | ||||
\(137\) | 8.70427 | + | 15.0762i | 0.743656 | + | 1.28805i | 0.950820 | + | 0.309744i | \(0.100243\pi\) |
−0.207164 | + | 0.978306i | \(0.566423\pi\) | |||||||
\(138\) | 0.160518 | − | 0.278025i | 0.0136642 | − | 0.0236670i | ||||
\(139\) | 17.1547i | 1.45504i | 0.686087 | + | 0.727520i | \(0.259327\pi\) | ||||
−0.686087 | + | 0.727520i | \(0.740673\pi\) | |||||||
\(140\) | 0.310003 | + | 0.533396i | 0.0262001 | + | 0.0450802i | ||||
\(141\) | − | 5.50397i | − | 0.463518i | ||||||
\(142\) | 0.446605 | + | 0.257847i | 0.0374782 | + | 0.0216381i | ||||
\(143\) | 19.4989 | − | 11.2577i | 1.63058 | − | 0.941418i | ||||
\(144\) | 1.84690 | + | 3.19893i | 0.153909 | + | 0.266578i | ||||
\(145\) | −0.576135 | + | 0.997895i | −0.0478454 | + | 0.0828707i | ||||
\(146\) | − | 2.24235i | − | 0.185578i | ||||||
\(147\) | −0.0402329 | − | 6.99988i | −0.00331836 | − | 0.577341i | ||||
\(148\) | − | 5.51695i | − | 0.453490i | ||||||
\(149\) | 11.6019 | − | 20.0951i | 0.950466 | − | 1.64626i | 0.206048 | − | 0.978542i | \(-0.433940\pi\) |
0.744418 | − | 0.667714i | \(-0.232727\pi\) | |||||||
\(150\) | −0.979596 | + | 0.565570i | −0.0799836 | + | 0.0461786i | ||||
\(151\) | −6.96011 | − | 12.0553i | −0.566406 | − | 0.981044i | −0.996917 | − | 0.0784587i | \(-0.975000\pi\) |
0.430511 | − | 0.902585i | \(-0.358333\pi\) | |||||||
\(152\) | −1.60957 | + | 2.78785i | −0.130553 | + | 0.226125i | ||||
\(153\) | 3.94891 | + | 1.18580i | 0.319250 | + | 0.0958660i | ||||
\(154\) | 1.30005 | + | 2.23689i | 0.104761 | + | 0.180253i | ||||
\(155\) | 0.735776 | 0.0590989 | ||||||||
\(156\) | 8.81500 | + | 5.08934i | 0.705765 | + | 0.407473i | ||||
\(157\) | 6.38886 | + | 11.0658i | 0.509887 | + | 0.883150i | 0.999934 | + | 0.0114541i | \(0.00364605\pi\) |
−0.490048 | + | 0.871696i | \(0.663021\pi\) | |||||||
\(158\) | 0.597352 | − | 0.344881i | 0.0475228 | − | 0.0274373i | ||||
\(159\) | −8.16874 | − | 4.71623i | −0.647823 | − | 0.374021i | ||||
\(160\) | − | 0.314698i | − | 0.0248791i | ||||||
\(161\) | −3.74376 | + | 0.0107588i | −0.295050 | + | 0.000847915i | ||||
\(162\) | −0.226878 | −0.0178252 | ||||||||
\(163\) | 17.8882 | + | 10.3278i | 1.40111 | + | 0.808932i | 0.994507 | − | 0.104672i | \(-0.0333792\pi\) |
0.406605 | + | 0.913604i | \(0.366713\pi\) | |||||||
\(164\) | −13.9423 | + | 8.04959i | −1.08871 | + | 0.628567i | ||||
\(165\) | −0.446696 | + | 0.257900i | −0.0347753 | + | 0.0200775i | ||||
\(166\) | 0.179353 | − | 0.310649i | 0.0139205 | − | 0.0241110i | ||||
\(167\) | 4.63395i | 0.358586i | 0.983796 | + | 0.179293i | \(0.0573810\pi\) | ||||
−0.983796 | + | 0.179293i | \(0.942619\pi\) | |||||||
\(168\) | −1.17917 | + | 2.05601i | −0.0909751 | + | 0.158624i | ||||
\(169\) | 14.2879 | 1.09907 | ||||||||
\(170\) | −0.0767534 | − | 0.0814892i | −0.00588672 | − | 0.00624994i | ||||
\(171\) | 1.79673 | + | 3.11203i | 0.137399 | + | 0.237983i | ||||
\(172\) | −3.90008 | − | 6.75513i | −0.297378 | − | 0.515074i | ||||
\(173\) | −18.7206 | − | 10.8084i | −1.42330 | − | 0.821744i | −0.426723 | − | 0.904382i | \(-0.640332\pi\) |
−0.996580 | + | 0.0826382i | \(0.973665\pi\) | |||||||
\(174\) | −2.18454 | −0.165609 | ||||||||
\(175\) | 11.4425 | + | 6.56258i | 0.864974 | + | 0.496084i | ||||
\(176\) | 15.9210i | 1.20009i | ||||||||
\(177\) | −8.25948 | − | 4.76861i | −0.620821 | − | 0.358431i | ||||
\(178\) | −0.484708 | − | 0.839540i | −0.0363304 | − | 0.0629261i | ||||
\(179\) | 1.47478 | + | 2.55439i | 0.110230 | + | 0.190924i | 0.915863 | − | 0.401491i | \(-0.131508\pi\) |
−0.805633 | + | 0.592415i | \(0.798175\pi\) | |||||||
\(180\) | −0.201940 | − | 0.116590i | −0.0150518 | − | 0.00869013i | ||||
\(181\) | 1.25305i | 0.0931383i | 0.998915 | + | 0.0465691i | \(0.0148288\pi\) | ||||
−0.998915 | + | 0.0465691i | \(0.985171\pi\) | |||||||
\(182\) | 0.00901118 | + | 3.13563i | 0.000667953 | + | 0.232428i | ||||
\(183\) | −9.05420 | −0.669305 | ||||||||
\(184\) | 1.09779 | + | 0.633808i | 0.0809299 | + | 0.0467249i | ||||
\(185\) | 0.169414 | + | 0.293433i | 0.0124556 | + | 0.0215736i | ||||
\(186\) | 0.697462 | + | 1.20804i | 0.0511404 | + | 0.0885778i | ||||
\(187\) | 12.1847 | + | 12.9365i | 0.891033 | + | 0.946011i | ||||
\(188\) | 10.7246 | 0.782174 | ||||||||
\(189\) | 1.32945 | + | 2.28748i | 0.0967036 | + | 0.166389i | ||||
\(190\) | − | 0.0975643i | − | 0.00707806i | ||||||
\(191\) | −12.5310 | + | 21.7043i | −0.906712 | + | 1.57047i | −0.0881093 | + | 0.996111i | \(0.528082\pi\) |
−0.818603 | + | 0.574360i | \(0.805251\pi\) | |||||||
\(192\) | −5.88117 | + | 3.39550i | −0.424437 | + | 0.245049i | ||||
\(193\) | 15.5498 | − | 8.97767i | 1.11930 | − | 0.646227i | 0.178076 | − | 0.984017i | \(-0.443013\pi\) |
0.941222 | + | 0.337790i | \(0.109679\pi\) | |||||||
\(194\) | 2.55702 | + | 1.47630i | 0.183583 | + | 0.105992i | ||||
\(195\) | −0.625132 | −0.0447666 | ||||||||
\(196\) | 13.6395 | − | 0.0783949i | 0.974247 | − | 0.00559964i | ||||
\(197\) | − | 23.8247i | − | 1.69744i | −0.528843 | − | 0.848720i | \(-0.677374\pi\) | ||
0.528843 | − | 0.848720i | \(-0.322626\pi\) | |||||||
\(198\) | −0.846872 | − | 0.488942i | −0.0601846 | − | 0.0347476i | ||||
\(199\) | 9.20203 | − | 5.31279i | 0.652314 | − | 0.376614i | −0.137028 | − | 0.990567i | \(-0.543755\pi\) |
0.789342 | + | 0.613953i | \(0.210422\pi\) | |||||||
\(200\) | −2.23317 | − | 3.86796i | −0.157909 | − | 0.273506i | ||||
\(201\) | −4.62287 | − | 2.66902i | −0.326072 | − | 0.188258i | ||||
\(202\) | −2.35152 | −0.165452 | ||||||||
\(203\) | 12.8009 | + | 22.0254i | 0.898449 | + | 1.54588i | ||||
\(204\) | −2.31056 | + | 7.69455i | −0.161771 | + | 0.538727i | ||||
\(205\) | 0.494372 | − | 0.856277i | 0.0345284 | − | 0.0598050i | ||||
\(206\) | 1.94696 | + | 3.37223i | 0.135651 | + | 0.234954i | ||||
\(207\) | 1.22544 | − | 0.707507i | 0.0851738 | − | 0.0491751i | ||||
\(208\) | −9.64783 | + | 16.7105i | −0.668957 | + | 1.15867i | ||||
\(209\) | 15.4884i | 1.07136i | ||||||||
\(210\) | −0.000206435 | − | 0.0718332i | −1.42453e−5 | − | 0.00495696i | ||||
\(211\) | − | 4.88194i | − | 0.336087i | −0.985780 | − | 0.168043i | \(-0.946255\pi\) | ||
0.985780 | − | 0.168043i | \(-0.0537448\pi\) | |||||||
\(212\) | 9.18969 | − | 15.9170i | 0.631151 | − | 1.09318i | ||||
\(213\) | 1.13650 | + | 1.96848i | 0.0778719 | + | 0.134878i | ||||
\(214\) | −0.315072 | + | 0.181907i | −0.0215378 | + | 0.0124349i | ||||
\(215\) | 0.414872 | + | 0.239526i | 0.0282940 | + | 0.0163356i | ||||
\(216\) | − | 0.895833i | − | 0.0609537i | ||||||
\(217\) | 8.09299 | − | 14.1110i | 0.549388 | − | 0.957915i | ||||
\(218\) | 0.837873i | 0.0567479i | ||||||||
\(219\) | 4.94177 | − | 8.55939i | 0.333934 | − | 0.578390i | ||||
\(220\) | −0.502525 | − | 0.870400i | −0.0338803 | − | 0.0586823i | ||||
\(221\) | 4.94966 | + | 20.9618i | 0.332950 | + | 1.41004i | ||||
\(222\) | −0.321184 | + | 0.556307i | −0.0215565 | + | 0.0373369i | ||||
\(223\) | 1.97588 | 0.132315 | 0.0661574 | − | 0.997809i | \(-0.478926\pi\) | ||||
0.0661574 | + | 0.997809i | \(0.478926\pi\) | |||||||
\(224\) | −6.03539 | − | 3.46145i | −0.403257 | − | 0.231278i | ||||
\(225\) | −4.98568 | −0.332379 | ||||||||
\(226\) | 1.82166 | + | 1.05174i | 0.121175 | + | 0.0699604i | ||||
\(227\) | 8.28358 | − | 4.78253i | 0.549800 | − | 0.317427i | −0.199241 | − | 0.979951i | \(-0.563848\pi\) |
0.749042 | + | 0.662523i | \(0.230514\pi\) | |||||||
\(228\) | −6.06386 | + | 3.50097i | −0.401589 | + | 0.231858i | ||||
\(229\) | 3.82356 | − | 6.62260i | 0.252668 | − | 0.437634i | −0.711592 | − | 0.702593i | \(-0.752025\pi\) |
0.964260 | + | 0.264960i | \(0.0853586\pi\) | |||||||
\(230\) | −0.0384184 | −0.00253323 | ||||||||
\(231\) | 0.0327718 | + | 11.4036i | 0.00215622 | + | 0.750303i | ||||
\(232\) | − | 8.62571i | − | 0.566305i | ||||||
\(233\) | −5.57572 | − | 3.21914i | −0.365277 | − | 0.210893i | 0.306116 | − | 0.951994i | \(-0.400970\pi\) |
−0.671393 | + | 0.741101i | \(0.734304\pi\) | |||||||
\(234\) | −0.592580 | − | 1.02638i | −0.0387382 | − | 0.0670965i | ||||
\(235\) | −0.570417 | + | 0.329331i | −0.0372099 | + | 0.0214832i | ||||
\(236\) | 9.29177 | − | 16.0938i | 0.604843 | − | 1.04762i | ||||
\(237\) | 3.04024 | 0.197485 | ||||||||
\(238\) | −2.40706 | + | 0.575683i | −0.156026 | + | 0.0373160i | ||||
\(239\) | −23.0422 | −1.49048 | −0.745239 | − | 0.666797i | \(-0.767665\pi\) | ||||
−0.745239 | + | 0.666797i | \(0.767665\pi\) | |||||||
\(240\) | 0.221020 | − | 0.382817i | 0.0142668 | − | 0.0247107i | ||||
\(241\) | 11.7978 | − | 6.81145i | 0.759961 | − | 0.438764i | −0.0693205 | − | 0.997594i | \(-0.522083\pi\) |
0.829282 | + | 0.558831i | \(0.188750\pi\) | |||||||
\(242\) | −0.859600 | − | 1.48887i | −0.0552572 | − | 0.0957082i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 17.6423i | − | 1.12944i | ||||||
\(245\) | −0.723043 | + | 0.423009i | −0.0461935 | + | 0.0270250i | ||||
\(246\) | 1.87452 | 0.119515 | ||||||||
\(247\) | −9.38572 | + | 16.2566i | −0.597199 | + | 1.03438i | ||||
\(248\) | −4.76998 | + | 2.75395i | −0.302894 | + | 0.174876i | ||||
\(249\) | 1.36924 | − | 0.790529i | 0.0867718 | − | 0.0500977i | ||||
\(250\) | 0.234794 | + | 0.135558i | 0.0148497 | + | 0.00857345i | ||||
\(251\) | −22.0330 | −1.39071 | −0.695356 | − | 0.718666i | \(-0.744753\pi\) | ||||
−0.695356 | + | 0.718666i | \(0.744753\pi\) | |||||||
\(252\) | −4.45721 | + | 2.59048i | −0.280778 | + | 0.163185i | ||||
\(253\) | 6.09896 | 0.383438 | ||||||||
\(254\) | 1.40980 | − | 2.44184i | 0.0884586 | − | 0.153215i | ||||
\(255\) | −0.113391 | − | 0.480208i | −0.00710079 | − | 0.0300718i | ||||
\(256\) | −6.01959 | − | 10.4262i | −0.376225 | − | 0.651640i | ||||
\(257\) | 4.99662 | − | 8.65440i | 0.311680 | − | 0.539846i | −0.667046 | − | 0.745017i | \(-0.732441\pi\) |
0.978726 | + | 0.205170i | \(0.0657748\pi\) | |||||||
\(258\) | 0.908215i | 0.0565430i | ||||||||
\(259\) | 7.49100 | − | 0.0215277i | 0.465468 | − | 0.00133766i | ||||
\(260\) | − | 1.21809i | − | 0.0755425i | ||||||
\(261\) | −8.33870 | − | 4.81435i | −0.516153 | − | 0.298001i | ||||
\(262\) | −1.10344 | + | 0.637069i | −0.0681705 | + | 0.0393583i | ||||
\(263\) | 4.54049 | + | 7.86436i | 0.279979 | + | 0.484937i | 0.971379 | − | 0.237535i | \(-0.0763393\pi\) |
−0.691400 | + | 0.722472i | \(0.743006\pi\) | |||||||
\(264\) | 1.93060 | − | 3.34390i | 0.118820 | − | 0.205803i | ||||
\(265\) | 1.12878i | 0.0693407i | ||||||||
\(266\) | −1.87112 | − | 1.07314i | −0.114726 | − | 0.0657981i | ||||
\(267\) | − | 4.27286i | − | 0.261495i | ||||||
\(268\) | 5.20065 | − | 9.00779i | 0.317680 | − | 0.550238i | ||||
\(269\) | 1.69737 | − | 0.979976i | 0.103490 | − | 0.0597502i | −0.447361 | − | 0.894353i | \(-0.647636\pi\) |
0.550852 | + | 0.834603i | \(0.314303\pi\) | |||||||
\(270\) | 0.0135753 | + | 0.0235130i | 0.000826164 | + | 0.00143096i | ||||
\(271\) | −1.96090 | + | 3.39638i | −0.119116 | + | 0.206315i | −0.919418 | − | 0.393283i | \(-0.871339\pi\) |
0.800302 | + | 0.599598i | \(0.204673\pi\) | |||||||
\(272\) | −14.5865 | − | 4.38011i | −0.884437 | − | 0.265583i | ||||
\(273\) | −6.87599 | + | 11.9890i | −0.416154 | + | 0.725607i | ||||
\(274\) | 3.94961 | 0.238605 | ||||||||
\(275\) | −18.6102 | − | 10.7446i | −1.12224 | − | 0.647923i | ||||
\(276\) | 1.37860 | + | 2.38780i | 0.0829817 | + | 0.143729i | ||||
\(277\) | −5.86738 | + | 3.38753i | −0.352537 | + | 0.203537i | −0.665802 | − | 0.746129i | \(-0.731910\pi\) |
0.313265 | + | 0.949666i | \(0.398577\pi\) | |||||||
\(278\) | 3.37058 | + | 1.94600i | 0.202154 | + | 0.116714i | ||||
\(279\) | 6.14836i | 0.368092i | ||||||||
\(280\) | 0.283635 | 0.000815113i | 0.0169505 | 4.87123e-5i | ||||||
\(281\) | 15.3118 | 0.913425 | 0.456712 | − | 0.889614i | \(-0.349027\pi\) | ||||
0.456712 | + | 0.889614i | \(0.349027\pi\) | |||||||
\(282\) | −1.08143 | − | 0.624364i | −0.0643982 | − | 0.0371803i | ||||
\(283\) | 9.83031 | − | 5.67553i | 0.584351 | − | 0.337375i | −0.178509 | − | 0.983938i | \(-0.557128\pi\) |
0.762861 | + | 0.646563i | \(0.223794\pi\) | |||||||
\(284\) | −3.83564 | + | 2.21451i | −0.227603 | + | 0.131407i | ||||
\(285\) | 0.215015 | − | 0.372417i | 0.0127364 | − | 0.0220601i | ||||
\(286\) | − | 5.10825i | − | 0.302057i | ||||||
\(287\) | −10.9843 | − | 18.8997i | −0.648381 | − | 1.11561i | ||||
\(288\) | 2.62971 | 0.154957 | ||||||||
\(289\) | −15.2044 | + | 7.60436i | −0.894376 | + | 0.447316i | ||||
\(290\) | 0.130712 | + | 0.226400i | 0.00767568 | + | 0.0132947i | ||||
\(291\) | 6.50701 | + | 11.2705i | 0.381448 | + | 0.660687i | ||||
\(292\) | 16.6782 | + | 9.62916i | 0.976018 | + | 0.563504i | ||||
\(293\) | 18.4766 | 1.07941 | 0.539707 | − | 0.841853i | \(-0.318535\pi\) | ||||
0.539707 | + | 0.841853i | \(0.318535\pi\) | |||||||
\(294\) | −1.37991 | − | 0.786154i | −0.0804782 | − | 0.0458494i | ||||
\(295\) | 1.14132i | 0.0664504i | ||||||||
\(296\) | −2.19659 | − | 1.26820i | −0.127674 | − | 0.0737129i | ||||
\(297\) | −2.15509 | − | 3.73272i | −0.125051 | − | 0.216595i | ||||
\(298\) | −2.63222 | − | 4.55913i | −0.152480 | − | 0.264103i | ||||
\(299\) | 6.40142 | + | 3.69586i | 0.370204 | + | 0.213737i | ||||
\(300\) | − | 9.71473i | − | 0.560880i | ||||||
\(301\) | 9.15700 | − | 5.32194i | 0.527801 | − | 0.306752i | ||||
\(302\) | −3.15819 | −0.181733 | ||||||||
\(303\) | −8.97609 | − | 5.18235i | −0.515663 | − | 0.297718i | ||||
\(304\) | −6.63677 | − | 11.4952i | −0.380645 | − | 0.659297i | ||||
\(305\) | 0.541759 | + | 0.938354i | 0.0310210 | + | 0.0537300i | ||||
\(306\) | 0.680947 | − | 0.641374i | 0.0389272 | − | 0.0366649i | ||||
\(307\) | 2.97735 | 0.169926 | 0.0849631 | − | 0.996384i | \(-0.472923\pi\) | ||||
0.0849631 | + | 0.996384i | \(0.472923\pi\) | |||||||
\(308\) | −22.2202 | + | 0.0638566i | −1.26612 | + | 0.00363857i | ||||
\(309\) | 17.1630i | 0.976372i | ||||||||
\(310\) | 0.0834655 | − | 0.144567i | 0.00474052 | − | 0.00821083i | ||||
\(311\) | −29.0675 | + | 16.7822i | −1.64827 | + | 0.951629i | −0.670509 | + | 0.741901i | \(0.733924\pi\) |
−0.977760 | + | 0.209728i | \(0.932742\pi\) | |||||||
\(312\) | 4.05268 | − | 2.33982i | 0.229438 | − | 0.132466i | ||||
\(313\) | 21.1646 | + | 12.2194i | 1.19629 | + | 0.690681i | 0.959727 | − | 0.280934i | \(-0.0906443\pi\) |
0.236567 | + | 0.971615i | \(0.423978\pi\) | |||||||
\(314\) | 2.89898 | 0.163599 | ||||||||
\(315\) | 0.157520 | − | 0.274653i | 0.00887526 | − | 0.0154749i | ||||
\(316\) | 5.92399i | 0.333250i | ||||||||
\(317\) | 15.5925 | + | 9.00232i | 0.875760 | + | 0.505620i | 0.869258 | − | 0.494358i | \(-0.164597\pi\) |
0.00650207 | + | 0.999979i | \(0.497930\pi\) | |||||||
\(318\) | −1.85331 | + | 1.07001i | −0.103928 | + | 0.0600030i | ||||
\(319\) | −20.7507 | − | 35.9413i | −1.16182 | − | 2.01233i | ||||
\(320\) | 0.703802 | + | 0.406340i | 0.0393437 | + | 0.0227151i | ||||
\(321\) | −1.60357 | −0.0895023 | ||||||||
\(322\) | −0.422574 | + | 0.736801i | −0.0235491 | + | 0.0410603i | ||||
\(323\) | −14.1902 | − | 4.26111i | −0.789566 | − | 0.237095i | ||||
\(324\) | 0.974263 | − | 1.68747i | 0.0541257 | − | 0.0937485i | ||||
\(325\) | −13.0221 | − | 22.5549i | −0.722334 | − | 1.25112i | ||||
\(326\) | 4.05843 | − | 2.34314i | 0.224776 | − | 0.129774i | ||||
\(327\) | −1.84653 | + | 3.19828i | −0.102113 | + | 0.176866i | ||||
\(328\) | 7.40158i | 0.408684i | ||||||||
\(329\) | 0.0418485 | + | 14.5621i | 0.00230718 | + | 0.802833i | ||||
\(330\) | 0.117024i | 0.00644194i | ||||||||
\(331\) | −11.3004 | + | 19.5728i | −0.621125 | + | 1.07582i | 0.368152 | + | 0.929766i | \(0.379991\pi\) |
−0.989277 | + | 0.146054i | \(0.953343\pi\) | |||||||
\(332\) | 1.54037 | + | 2.66799i | 0.0845386 | + | 0.146425i | ||||
\(333\) | −2.45201 | + | 1.41567i | −0.134370 | + | 0.0775783i | ||||
\(334\) | 0.910488 | + | 0.525671i | 0.0498197 | + | 0.0287634i | ||||
\(335\) | 0.638804i | 0.0349016i | ||||||||
\(336\) | −4.91075 | − | 8.44950i | −0.267903 | − | 0.460958i | ||||
\(337\) | 17.3246i | 0.943731i | 0.881670 | + | 0.471866i | \(0.156419\pi\) | ||||
−0.881670 | + | 0.471866i | \(0.843581\pi\) | |||||||
\(338\) | 1.62081 | − | 2.80732i | 0.0881602 | − | 0.152698i | ||||
\(339\) | 4.63570 | + | 8.02926i | 0.251776 | + | 0.436090i | ||||
\(340\) | 0.935697 | − | 0.220944i | 0.0507453 | − | 0.0119824i | ||||
\(341\) | −13.2503 | + | 22.9501i | −0.717542 | + | 1.24282i | ||||
\(342\) | 0.815276 | 0.0440851 | ||||||||
\(343\) | 0.159668 | + | 18.5196i | 0.00862128 | + | 0.999963i | ||||
\(344\) | −3.58611 | −0.193350 | ||||||||
\(345\) | −0.146649 | − | 0.0846676i | −0.00789529 | − | 0.00455835i | ||||
\(346\) | −4.24729 | + | 2.45218i | −0.228336 | + | 0.131830i | ||||
\(347\) | −4.22355 | + | 2.43847i | −0.226732 | + | 0.130904i | −0.609063 | − | 0.793121i | \(-0.708455\pi\) |
0.382332 | + | 0.924025i | \(0.375121\pi\) | |||||||
\(348\) | 9.38089 | − | 16.2482i | 0.502869 | − | 0.870994i | ||||
\(349\) | −18.7547 | −1.00392 | −0.501958 | − | 0.864892i | \(-0.667387\pi\) | ||||
−0.501958 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(350\) | 2.58746 | − | 1.50380i | 0.138305 | − | 0.0803814i | ||||
\(351\) | − | 5.22378i | − | 0.278825i | ||||||
\(352\) | 9.81598 | + | 5.66726i | 0.523193 | + | 0.302066i | ||||
\(353\) | −3.36366 | − | 5.82603i | −0.179030 | − | 0.310088i | 0.762519 | − | 0.646966i | \(-0.223962\pi\) |
−0.941548 | + | 0.336878i | \(0.890629\pi\) | |||||||
\(354\) | −1.87389 | + | 1.08189i | −0.0995962 | + | 0.0575019i | ||||
\(355\) | 0.136006 | − | 0.235569i | 0.00721843 | − | 0.0125027i | ||||
\(356\) | 8.32578 | 0.441266 | ||||||||
\(357\) | −10.4568 | − | 3.10729i | −0.553433 | − | 0.164455i | ||||
\(358\) | 0.669189 | 0.0353677 | ||||||||
\(359\) | 8.26314 | − | 14.3122i | 0.436112 | − | 0.755368i | −0.561274 | − | 0.827630i | \(-0.689688\pi\) |
0.997386 | + | 0.0722622i | \(0.0230218\pi\) | |||||||
\(360\) | −0.0928419 | + | 0.0536023i | −0.00489320 | + | 0.00282509i | ||||
\(361\) | 3.04353 | + | 5.27155i | 0.160186 | + | 0.277450i | ||||
\(362\) | 0.246201 | + | 0.142144i | 0.0129400 | + | 0.00747094i | ||||
\(363\) | − | 7.57765i | − | 0.397723i | ||||||
\(364\) | −23.3609 | − | 13.3981i | −1.22444 | − | 0.702249i | ||||
\(365\) | −1.18277 | −0.0619088 | ||||||||
\(366\) | −1.02710 | + | 1.77899i | −0.0536873 | + | 0.0929890i | ||||
\(367\) | −18.8930 | + | 10.9079i | −0.986207 | + | 0.569387i | −0.904138 | − | 0.427240i | \(-0.859486\pi\) |
−0.0820689 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(368\) | −4.52653 | + | 2.61339i | −0.235962 | + | 0.136233i | ||||
\(369\) | 7.15530 | + | 4.13112i | 0.372490 | + | 0.215057i | ||||
\(370\) | 0.0768724 | 0.00399641 | ||||||||
\(371\) | 21.6482 | + | 12.4158i | 1.12392 | + | 0.644596i | ||||
\(372\) | −11.9802 | −0.621146 | ||||||||
\(373\) | −2.04680 | + | 3.54516i | −0.105979 | + | 0.183561i | −0.914138 | − | 0.405404i | \(-0.867131\pi\) |
0.808159 | + | 0.588965i | \(0.200464\pi\) | |||||||
\(374\) | 3.92401 | − | 0.926568i | 0.202906 | − | 0.0479117i | ||||
\(375\) | 0.597495 | + | 1.03489i | 0.0308545 | + | 0.0534415i | ||||
\(376\) | 2.46532 | − | 4.27005i | 0.127139 | − | 0.220211i | ||||
\(377\) | − | 50.2983i | − | 2.59049i | ||||||
\(378\) | 0.600260 | − | 0.00172503i | 0.0308740 | − | 8.87259e-5i | ||||
\(379\) | − | 30.0701i | − | 1.54460i | −0.635258 | − | 0.772300i | \(-0.719106\pi\) | ||
0.635258 | − | 0.772300i | \(-0.280894\pi\) | |||||||
\(380\) | 0.725665 | + | 0.418963i | 0.0372258 | + | 0.0214923i | ||||
\(381\) | 10.7628 | − | 6.21391i | 0.551395 | − | 0.318348i | ||||
\(382\) | 2.84301 | + | 4.92423i | 0.145461 | + | 0.251946i | ||||
\(383\) | −5.81446 | + | 10.0709i | −0.297105 | + | 0.514601i | −0.975472 | − | 0.220122i | \(-0.929355\pi\) |
0.678367 | + | 0.734723i | \(0.262688\pi\) | |||||||
\(384\) | 6.80014i | 0.347018i | ||||||||
\(385\) | 1.17988 | − | 0.685733i | 0.0601323 | − | 0.0349482i | ||||
\(386\) | − | 4.07367i | − | 0.207344i | ||||||
\(387\) | −2.00155 | + | 3.46679i | −0.101745 | + | 0.176227i | ||||
\(388\) | −21.9608 | + | 12.6791i | −1.11489 | + | 0.643683i | ||||
\(389\) | −6.92068 | − | 11.9870i | −0.350893 | − | 0.607764i | 0.635514 | − | 0.772090i | \(-0.280788\pi\) |
−0.986406 | + | 0.164326i | \(0.947455\pi\) | |||||||
\(390\) | −0.0709142 | + | 0.122827i | −0.00359088 | + | 0.00621959i | ||||
\(391\) | −1.67792 | + | 5.58776i | −0.0848560 | + | 0.282585i | ||||
\(392\) | 3.10415 | − | 5.44863i | 0.156783 | − | 0.275197i | ||||
\(393\) | −5.61597 | −0.283288 | ||||||||
\(394\) | −4.68112 | − | 2.70265i | −0.235831 | − | 0.136157i | ||||
\(395\) | −0.181913 | − | 0.315083i | −0.00915304 | − | 0.0158535i | ||||
\(396\) | 7.27331 | − | 4.19925i | 0.365498 | − | 0.211020i | ||||
\(397\) | −1.84608 | − | 1.06584i | −0.0926523 | − | 0.0534928i | 0.452958 | − | 0.891532i | \(-0.350369\pi\) |
−0.545610 | + | 0.838039i | \(0.683702\pi\) | |||||||
\(398\) | − | 2.41071i | − | 0.120838i | ||||||
\(399\) | −4.77734 | − | 8.21995i | −0.239166 | − | 0.411512i | ||||
\(400\) | 18.4161 | 0.920807 | ||||||||
\(401\) | −13.7407 | − | 7.93322i | −0.686180 | − | 0.396166i | 0.116000 | − | 0.993249i | \(-0.462993\pi\) |
−0.802179 | + | 0.597083i | \(0.796326\pi\) | |||||||
\(402\) | −1.04883 | + | 0.605541i | −0.0523107 | + | 0.0302016i | ||||
\(403\) | −27.8147 | + | 16.0588i | −1.38555 | + | 0.799948i | ||||
\(404\) | 10.0979 | − | 17.4901i | 0.502391 | − | 0.870167i | ||||
\(405\) | 0.119670i | 0.00594647i | ||||||||
\(406\) | 5.77972 | − | 0.0166098i | 0.286843 | − | 0.000824330i | ||||
\(407\) | −12.2036 | −0.604910 | ||||||||
\(408\) | 2.53248 | + | 2.68874i | 0.125376 | + | 0.133112i | ||||
\(409\) | 3.86442 | + | 6.69338i | 0.191083 | + | 0.330966i | 0.945610 | − | 0.325304i | \(-0.105467\pi\) |
−0.754526 | + | 0.656270i | \(0.772133\pi\) | |||||||
\(410\) | −0.112162 | − | 0.194270i | −0.00553928 | − | 0.00959432i | ||||
\(411\) | 15.0762 | + | 8.70427i | 0.743656 | + | 0.429350i | ||||
\(412\) | −33.4427 | −1.64760 | ||||||||
\(413\) | 21.8887 | + | 12.5537i | 1.07707 | + | 0.617728i | ||||
\(414\) | − | 0.321035i | − | 0.0157780i | ||||||
\(415\) | −0.163857 | − | 0.0946028i | −0.00804342 | − | 0.00464387i | ||||
\(416\) | 6.86851 | + | 11.8966i | 0.336757 | + | 0.583280i | ||||
\(417\) | 8.57733 | + | 14.8564i | 0.420034 | + | 0.727520i | ||||
\(418\) | 3.04320 | + | 1.75699i | 0.148848 | + | 0.0859373i | ||||
\(419\) | 9.50944i | 0.464567i | 0.972648 | + | 0.232283i | \(0.0746196\pi\) | ||||
−0.972648 | + | 0.232283i | \(0.925380\pi\) | |||||||
\(420\) | 0.535169 | + | 0.306932i | 0.0261136 | + | 0.0149768i | ||||
\(421\) | 10.9082 | 0.531632 | 0.265816 | − | 0.964024i | \(-0.414359\pi\) | ||||
0.265816 | + | 0.964024i | \(0.414359\pi\) | |||||||
\(422\) | −0.959213 | − | 0.553802i | −0.0466937 | − | 0.0269586i | ||||
\(423\) | −2.75198 | − | 4.76657i | −0.133806 | − | 0.231759i | ||||
\(424\) | −4.22495 | − | 7.31783i | −0.205182 | − | 0.355385i | ||||
\(425\) | 14.9639 | − | 14.0943i | 0.725858 | − | 0.683674i | ||||
\(426\) | 0.515695 | 0.0249855 | ||||||||
\(427\) | 23.9551 | − | 0.0688421i | 1.15927 | − | 0.00333150i | ||||
\(428\) | − | 3.12459i | − | 0.151033i | ||||||
\(429\) | 11.2577 | − | 19.4989i | 0.543528 | − | 0.941418i | ||||
\(430\) | 0.0941251 | − | 0.0543432i | 0.00453912 | − | 0.00262066i | ||||
\(431\) | 14.2889 | − | 8.24968i | 0.688270 | − | 0.397373i | −0.114694 | − | 0.993401i | \(-0.536589\pi\) |
0.802964 | + | 0.596028i | \(0.203255\pi\) | |||||||
\(432\) | 3.19893 | + | 1.84690i | 0.153909 | + | 0.0888592i | ||||
\(433\) | −7.53820 | −0.362263 | −0.181131 | − | 0.983459i | \(-0.557976\pi\) | ||||
−0.181131 | + | 0.983459i | \(0.557976\pi\) | |||||||
\(434\) | −1.85449 | − | 3.19086i | −0.0890184 | − | 0.153166i | ||||
\(435\) | 1.15227i | 0.0552471i | ||||||||
\(436\) | −6.23194 | − | 3.59801i | −0.298456 | − | 0.172314i | ||||
\(437\) | −4.40356 | + | 2.54240i | −0.210651 | + | 0.121619i | ||||
\(438\) | −1.12118 | − | 1.94193i | −0.0535719 | − | 0.0927892i | ||||
\(439\) | −13.2208 | − | 7.63302i | −0.630993 | − | 0.364304i | 0.150143 | − | 0.988664i | \(-0.452026\pi\) |
−0.781137 | + | 0.624360i | \(0.785360\pi\) | |||||||
\(440\) | −0.462071 | −0.0220284 | ||||||||
\(441\) | −3.53478 | − | 6.04196i | −0.168323 | − | 0.287712i | ||||
\(442\) | 4.68009 | + | 1.40536i | 0.222609 | + | 0.0668461i | ||||
\(443\) | −12.9711 | + | 22.4667i | −0.616277 | + | 1.06742i | 0.373882 | + | 0.927476i | \(0.378027\pi\) |
−0.990159 | + | 0.139947i | \(0.955307\pi\) | |||||||
\(444\) | −2.75847 | − | 4.77782i | −0.130911 | − | 0.226745i | ||||
\(445\) | −0.442829 | + | 0.255667i | −0.0209921 | + | 0.0121198i | ||||
\(446\) | 0.224142 | − | 0.388225i | 0.0106134 | − | 0.0183830i | ||||
\(447\) | − | 23.2038i | − | 1.09750i | ||||||
\(448\) | 15.5342 | − | 9.02832i | 0.733924 | − | 0.426548i | ||||
\(449\) | 5.54961i | 0.261902i | 0.991389 | + | 0.130951i | \(0.0418031\pi\) | ||||
−0.991389 | + | 0.130951i | \(0.958197\pi\) | |||||||
\(450\) | −0.565570 | + | 0.979596i | −0.0266612 | + | 0.0461786i | ||||
\(451\) | 17.8058 | + | 30.8406i | 0.838445 | + | 1.45223i | ||||
\(452\) | −15.6452 | + | 9.03278i | −0.735889 | + | 0.424866i | ||||
\(453\) | −12.0553 | − | 6.96011i | −0.566406 | − | 0.327015i | ||||
\(454\) | − | 2.17010i | − | 0.101848i | ||||||
\(455\) | 1.65394 | − | 0.00475309i | 0.0775377 | − | 0.000222828i | ||||
\(456\) | 3.21914i | 0.150750i | ||||||||
\(457\) | −4.89863 | + | 8.48467i | −0.229148 | + | 0.396896i | −0.957556 | − | 0.288248i | \(-0.906927\pi\) |
0.728408 | + | 0.685144i | \(0.240261\pi\) | |||||||
\(458\) | −0.867481 | − | 1.50252i | −0.0405347 | − | 0.0702082i | ||||
\(459\) | 4.01275 | − | 0.947524i | 0.187299 | − | 0.0442266i | ||||
\(460\) | 0.164977 | − | 0.285749i | 0.00769209 | − | 0.0133231i | ||||
\(461\) | 24.3852 | 1.13573 | 0.567865 | − | 0.823122i | \(-0.307769\pi\) | ||||
0.567865 | + | 0.823122i | \(0.307769\pi\) | |||||||
\(462\) | 2.24432 | + | 1.28717i | 0.104415 | + | 0.0598848i | ||||
\(463\) | 27.2282 | 1.26540 | 0.632701 | − | 0.774396i | \(-0.281946\pi\) | ||||
0.632701 | + | 0.774396i | \(0.281946\pi\) | |||||||
\(464\) | 30.8016 | + | 17.7833i | 1.42993 | + | 0.825569i | ||||
\(465\) | 0.637200 | − | 0.367888i | 0.0295495 | − | 0.0170604i | ||||
\(466\) | −1.26501 | + | 0.730351i | −0.0586003 | + | 0.0338329i | ||||
\(467\) | −0.807533 | + | 1.39869i | −0.0373682 | + | 0.0647236i | −0.884105 | − | 0.467289i | \(-0.845231\pi\) |
0.846736 | + | 0.532013i | \(0.178564\pi\) | |||||||
\(468\) | 10.1787 | 0.470510 | ||||||||
\(469\) | 12.2512 | + | 7.02638i | 0.565709 | + | 0.324448i | ||||
\(470\) | 0.149436i | 0.00689295i | ||||||||
\(471\) | 11.0658 | + | 6.38886i | 0.509887 | + | 0.294383i | ||||
\(472\) | −4.27188 | − | 7.39911i | −0.196629 | − | 0.340572i | ||||
\(473\) | −14.9425 | + | 8.62705i | −0.687056 | + | 0.396672i | ||||
\(474\) | 0.344881 | − | 0.597352i | 0.0158409 | − | 0.0274373i | ||||
\(475\) | 17.9158 | 0.822035 | ||||||||
\(476\) | 6.05463 | − | 20.3754i | 0.277514 | − | 0.933903i | ||||
\(477\) | −9.43245 | −0.431882 | ||||||||
\(478\) | −2.61389 | + | 4.52738i | −0.119556 | + | 0.207078i | ||||
\(479\) | 1.27988 | − | 0.738941i | 0.0584794 | − | 0.0337631i | −0.470475 | − | 0.882413i | \(-0.655918\pi\) |
0.528955 | + | 0.848650i | \(0.322584\pi\) | |||||||
\(480\) | −0.157349 | − | 0.272536i | −0.00718197 | − | 0.0124395i | ||||
\(481\) | −12.8088 | − | 7.39516i | −0.584031 | − | 0.337190i | ||||
\(482\) | − | 3.09073i | − | 0.140779i | ||||||
\(483\) | −3.23681 | + | 1.88120i | −0.147280 | + | 0.0855974i | ||||
\(484\) | 14.7652 | 0.671147 | ||||||||
\(485\) | 0.778696 | − | 1.34874i | 0.0353588 | − | 0.0612432i | ||||
\(486\) | −0.196482 | + | 0.113439i | −0.00891260 | + | 0.00514569i | ||||
\(487\) | −34.0547 | + | 19.6615i | −1.54317 | + | 0.890948i | −0.544532 | + | 0.838740i | \(0.683293\pi\) |
−0.998636 | + | 0.0522082i | \(0.983374\pi\) | |||||||
\(488\) | −7.02437 | − | 4.05552i | −0.317978 | − | 0.183585i | ||||
\(489\) | 20.6555 | 0.934075 | ||||||||
\(490\) | 0.00109235 | + | 0.190051i | 4.93471e−5 | + | 0.00858561i | ||||
\(491\) | 4.73990 | 0.213909 | 0.106954 | − | 0.994264i | \(-0.465890\pi\) | ||||
0.106954 | + | 0.994264i | \(0.465890\pi\) | |||||||
\(492\) | −8.04959 | + | 13.9423i | −0.362903 | + | 0.628567i | ||||
\(493\) | 38.6376 | − | 9.12343i | 1.74015 | − | 0.410899i | ||||
\(494\) | 2.12941 | + | 3.68825i | 0.0958068 | + | 0.165942i | ||||
\(495\) | −0.257900 | + | 0.446696i | −0.0115918 | + | 0.0200775i | ||||
\(496\) | − | 22.7108i | − | 1.01975i | ||||||
\(497\) | −3.02186 | − | 5.19945i | −0.135549 | − | 0.233227i | ||||
\(498\) | − | 0.358707i | − | 0.0160740i | ||||||
\(499\) | −29.7378 | − | 17.1691i | −1.33125 | − | 0.768595i | −0.345755 | − | 0.938325i | \(-0.612377\pi\) |
−0.985491 | + | 0.169730i | \(0.945710\pi\) | |||||||
\(500\) | −2.01651 | + | 1.16423i | −0.0901812 | + | 0.0520661i | ||||
\(501\) | 2.31698 | + | 4.01312i | 0.103515 | + | 0.179293i | ||||
\(502\) | −2.49940 | + | 4.32909i | −0.111554 | + | 0.193217i | ||||
\(503\) | 3.02700i | 0.134967i | 0.997720 | + | 0.0674836i | \(0.0214970\pi\) | ||||
−0.997720 | + | 0.0674836i | \(0.978503\pi\) | |||||||
\(504\) | 0.00681132 | + | 2.37014i | 0.000303400 | + | 0.105574i | ||||
\(505\) | 1.24035i | 0.0551947i | ||||||||
\(506\) | 0.691859 | − | 1.19834i | 0.0307569 | − | 0.0532725i | ||||
\(507\) | 12.3737 | − | 7.14396i | 0.549535 | − | 0.317274i | ||||
\(508\) | 12.1080 | + | 20.9716i | 0.537204 | + | 0.930465i | ||||
\(509\) | 2.28760 | − | 3.96223i | 0.101396 | − | 0.175623i | −0.810864 | − | 0.585235i | \(-0.801002\pi\) |
0.912260 | + | 0.409612i | \(0.134336\pi\) | |||||||
\(510\) | −0.107215 | − | 0.0321950i | −0.00474756 | − | 0.00142562i | ||||
\(511\) | −13.0095 | + | 22.6835i | −0.575509 | + | 1.00346i | ||||
\(512\) | −16.3317 | −0.721766 | ||||||||
\(513\) | 3.11203 | + | 1.79673i | 0.137399 | + | 0.0793275i | ||||
\(514\) | −1.13362 | − | 1.96349i | −0.0500019 | − | 0.0866058i | ||||
\(515\) | 1.77874 | − | 1.02695i | 0.0783805 | − | 0.0452530i | ||||
\(516\) | −6.75513 | − | 3.90008i | −0.297378 | − | 0.171691i | ||||
\(517\) | − | 23.7231i | − | 1.04334i | ||||||
\(518\) | 0.845540 | − | 1.47429i | 0.0371509 | − | 0.0647765i | ||||
\(519\) | −21.6167 | −0.948868 | ||||||||
\(520\) | −0.484986 | − | 0.280007i | −0.0212680 | − | 0.0122791i | ||||
\(521\) | 31.2918 | − | 18.0663i | 1.37092 | − | 0.791500i | 0.379874 | − | 0.925038i | \(-0.375967\pi\) |
0.991044 | + | 0.133538i | \(0.0426340\pi\) | |||||||
\(522\) | −1.89187 | + | 1.09227i | −0.0828047 | + | 0.0478073i | ||||
\(523\) | −0.871285 | + | 1.50911i | −0.0380986 | + | 0.0659887i | −0.884446 | − | 0.466643i | \(-0.845463\pi\) |
0.846347 | + | 0.532631i | \(0.178797\pi\) | |||||||
\(524\) | − | 10.9429i | − | 0.478041i | ||||||
\(525\) | 13.1908 | − | 0.0379078i | 0.575694 | − | 0.00165443i | ||||
\(526\) | 2.06027 | 0.0898321 | ||||||||
\(527\) | −17.3811 | − | 18.4536i | −0.757134 | − | 0.803851i | ||||
\(528\) | 7.96049 | + | 13.7880i | 0.346436 | + | 0.600044i | ||||
\(529\) | −10.4989 | − | 18.1846i | −0.456473 | − | 0.790634i | ||||
\(530\) | 0.221786 | + | 0.128048i | 0.00963375 | + | 0.00556205i | ||||
\(531\) | −9.53723 | −0.413880 | ||||||||
\(532\) | 16.0168 | − | 9.30877i | 0.694416 | − | 0.403587i | ||||
\(533\) | 43.1601i | 1.86947i | ||||||||
\(534\) | −0.839540 | − | 0.484708i | −0.0363304 | − | 0.0209754i | ||||
\(535\) | 0.0959496 | + | 0.166190i | 0.00414826 | + | 0.00718500i | ||||
\(536\) | −2.39099 | − | 4.14132i | −0.103275 | − | 0.178878i | ||||
\(537\) | 2.55439 | + | 1.47478i | 0.110230 | + | 0.0636414i | ||||
\(538\) | − | 0.444670i | − | 0.0191711i | ||||||
\(539\) | −0.173411 | − | 30.1708i | −0.00746935 | − | 1.29955i | ||||
\(540\) | −0.233181 | −0.0100345 | ||||||||
\(541\) | 17.9757 | + | 10.3782i | 0.772834 | + | 0.446196i | 0.833885 | − | 0.551939i | \(-0.186112\pi\) |
−0.0610509 | + | 0.998135i | \(0.519445\pi\) | |||||||
\(542\) | 0.444884 | + | 0.770562i | 0.0191094 | + | 0.0330985i | ||||
\(543\) | 0.626524 | + | 1.08517i | 0.0268867 | + | 0.0465691i | ||||
\(544\) | −7.89277 | + | 7.43407i | −0.338400 | + | 0.318733i | ||||
\(545\) | 0.441950 | 0.0189310 | ||||||||
\(546\) | 1.57562 | + | 2.71103i | 0.0674302 | + | 0.116021i | ||||
\(547\) | 26.0552i | 1.11404i | 0.830499 | + | 0.557020i | \(0.188055\pi\) | ||||
−0.830499 | + | 0.557020i | \(0.811945\pi\) | |||||||
\(548\) | −16.9605 | + | 29.3765i | −0.724517 | + | 1.25490i | ||||
\(549\) | −7.84116 | + | 4.52710i | −0.334653 | + | 0.193212i | ||||
\(550\) | −4.22223 | + | 2.43771i | −0.180037 | + | 0.103944i | ||||
\(551\) | 29.9648 | + | 17.3002i | 1.27654 | + | 0.737012i | ||||
\(552\) | 1.26762 | 0.0539533 | ||||||||
\(553\) | −8.04368 | + | 0.0231160i | −0.342052 | + | 0.000982991i | ||||
\(554\) | 1.53711i | 0.0653056i | ||||||||
\(555\) | 0.293433 | + | 0.169414i | 0.0124556 | + | 0.00719122i | ||||
\(556\) | −28.9480 | + | 16.7132i | −1.22767 | + | 0.708796i | ||||
\(557\) | 9.48337 | + | 16.4257i | 0.401823 | + | 0.695978i | 0.993946 | − | 0.109870i | \(-0.0350433\pi\) |
−0.592123 | + | 0.805848i | \(0.701710\pi\) | |||||||
\(558\) | 1.20804 | + | 0.697462i | 0.0511404 | + | 0.0295259i | ||||
\(559\) | −20.9113 | −0.884456 | ||||||||
\(560\) | −0.581850 | + | 1.01452i | −0.0245876 | + | 0.0428711i | ||||
\(561\) | 17.0205 | + | 5.11100i | 0.718606 | + | 0.215787i | ||||
\(562\) | 1.73695 | − | 3.00849i | 0.0732689 | − | 0.126905i | ||||
\(563\) | 12.7116 | + | 22.0171i | 0.535730 | + | 0.927911i | 0.999128 | + | 0.0417606i | \(0.0132967\pi\) |
−0.463398 | + | 0.886150i | \(0.653370\pi\) | |||||||
\(564\) | 9.28780 | − | 5.36231i | 0.391087 | − | 0.225794i | ||||
\(565\) | 0.554755 | − | 0.960864i | 0.0233387 | − | 0.0404239i | ||||
\(566\) | − | 2.57530i | − | 0.108248i | ||||||
\(567\) | 2.29508 | + | 1.31629i | 0.0963843 | + | 0.0552788i | ||||
\(568\) | 2.03623i | 0.0854385i | ||||||||
\(569\) | −1.50866 | + | 2.61307i | −0.0632462 | + | 0.109546i | −0.895915 | − | 0.444226i | \(-0.853479\pi\) |
0.832668 | + | 0.553772i | \(0.186812\pi\) | |||||||
\(570\) | −0.0487821 | − | 0.0844931i | −0.00204326 | − | 0.00353903i | ||||
\(571\) | −16.8672 | + | 9.73830i | −0.705872 | + | 0.407535i | −0.809531 | − | 0.587078i | \(-0.800278\pi\) |
0.103659 | + | 0.994613i | \(0.466945\pi\) | |||||||
\(572\) | 37.9942 | + | 21.9360i | 1.58862 | + | 0.917189i | ||||
\(573\) | 25.0620i | 1.04698i | ||||||||
\(574\) | −4.95948 | + | 0.0142526i | −0.207005 | + | 0.000594891i | ||||
\(575\) | − | 7.05480i | − | 0.294206i | ||||||
\(576\) | −3.39550 | + | 5.88117i | −0.141479 | + | 0.245049i | ||||
\(577\) | 6.51749 | + | 11.2886i | 0.271326 | + | 0.469951i | 0.969202 | − | 0.246268i | \(-0.0792044\pi\) |
−0.697875 | + | 0.716219i | \(0.745871\pi\) | |||||||
\(578\) | −0.230650 | + | 3.85002i | −0.00959376 | + | 0.160140i | ||||
\(579\) | 8.97767 | − | 15.5498i | 0.373099 | − | 0.646227i | ||||
\(580\) | −2.24523 | −0.0932280 | ||||||||
\(581\) | −3.61663 | + | 2.10194i | −0.150043 | + | 0.0872034i | ||||
\(582\) | 2.95259 | 0.122389 | ||||||||
\(583\) | −35.2087 | − | 20.3278i | −1.45820 | − | 0.841891i | ||||
\(584\) | 7.66778 | − | 4.42700i | 0.317295 | − | 0.183190i | ||||
\(585\) | −0.541380 | + | 0.312566i | −0.0223833 | + | 0.0129230i | ||||
\(586\) | 2.09596 | − | 3.63031i | 0.0865834 | − | 0.149967i | ||||
\(587\) | 21.2227 | 0.875954 | 0.437977 | − | 0.898986i | \(-0.355695\pi\) | ||||
0.437977 | + | 0.898986i | \(0.355695\pi\) | |||||||
\(588\) | 11.7729 | − | 6.88762i | 0.485507 | − | 0.284041i | ||||
\(589\) | − | 22.0939i | − | 0.910362i | ||||||
\(590\) | 0.224249 | + | 0.129470i | 0.00923220 | + | 0.00533021i | ||||
\(591\) | −11.9123 | − | 20.6328i | −0.490009 | − | 0.848720i | ||||
\(592\) | 9.05727 | − | 5.22922i | 0.372252 | − | 0.214920i | ||||
\(593\) | 8.12508 | − | 14.0731i | 0.333657 | − | 0.577911i | −0.649569 | − | 0.760303i | \(-0.725051\pi\) |
0.983226 | + | 0.182392i | \(0.0583839\pi\) | |||||||
\(594\) | −0.977884 | −0.0401231 | ||||||||
\(595\) | 0.303653 | + | 1.26964i | 0.0124486 | + | 0.0520503i | ||||
\(596\) | 45.2133 | 1.85201 | ||||||||
\(597\) | 5.31279 | − | 9.20203i | 0.217438 | − | 0.376614i | ||||
\(598\) | 1.45234 | − | 0.838509i | 0.0593906 | − | 0.0342892i | ||||
\(599\) | 16.0131 | + | 27.7356i | 0.654280 | + | 1.13325i | 0.982074 | + | 0.188496i | \(0.0603614\pi\) |
−0.327794 | + | 0.944749i | \(0.606305\pi\) | |||||||
\(600\) | −3.86796 | − | 2.23317i | −0.157909 | − | 0.0911687i | ||||
\(601\) | − | 19.0735i | − | 0.778026i | −0.921232 | − | 0.389013i | \(-0.872816\pi\) | ||
0.921232 | − | 0.389013i | \(-0.127184\pi\) | |||||||
\(602\) | −0.00690547 | − | 2.40290i | −0.000281446 | − | 0.0979349i | ||||
\(603\) | −5.33803 | −0.217382 | ||||||||
\(604\) | 13.5620 | − | 23.4900i | 0.551828 | − | 0.955795i | ||||
\(605\) | −0.785329 | + | 0.453410i | −0.0319281 | + | 0.0184337i | ||||
\(606\) | −2.03647 | + | 1.17576i | −0.0827261 | + | 0.0477619i | ||||
\(607\) | 19.4216 | + | 11.2131i | 0.788298 | + | 0.455124i | 0.839363 | − | 0.543571i | \(-0.182928\pi\) |
−0.0510652 | + | 0.998695i | \(0.516262\pi\) | |||||||
\(608\) | −9.44975 | −0.383238 | ||||||||
\(609\) | 22.0986 | + | 12.6741i | 0.895482 | + | 0.513581i | ||||
\(610\) | 0.245826 | 0.00995321 | ||||||||
\(611\) | 14.3758 | − | 24.8996i | 0.581581 | − | 1.00733i | ||||
\(612\) | 1.84628 | + | 7.81896i | 0.0746313 | + | 0.316063i | ||||
\(613\) | −3.67217 | − | 6.36038i | −0.148317 | − | 0.256893i | 0.782288 | − | 0.622917i | \(-0.214052\pi\) |
−0.930606 | + | 0.366023i | \(0.880719\pi\) | |||||||
\(614\) | 0.337747 | − | 0.584995i | 0.0136304 | − | 0.0236085i | ||||
\(615\) | − | 0.988744i | − | 0.0398700i | ||||||
\(616\) | −5.08244 | + | 8.86176i | −0.204777 | + | 0.357051i | ||||
\(617\) | 42.4010i | 1.70700i | 0.521094 | + | 0.853499i | \(0.325524\pi\) | ||||
−0.521094 | + | 0.853499i | \(0.674476\pi\) | |||||||
\(618\) | 3.37223 | + | 1.94696i | 0.135651 | + | 0.0783181i | ||||
\(619\) | −13.5723 | + | 7.83595i | −0.545516 | + | 0.314954i | −0.747311 | − | 0.664474i | \(-0.768656\pi\) |
0.201796 | + | 0.979428i | \(0.435322\pi\) | |||||||
\(620\) | 0.716839 | + | 1.24160i | 0.0287890 | + | 0.0498639i | ||||
\(621\) | 0.707507 | − | 1.22544i | 0.0283913 | − | 0.0491751i | ||||
\(622\) | 7.61499i | 0.305333i | ||||||||
\(623\) | 0.0324880 | + | 11.3049i | 0.00130160 | + | 0.452920i | ||||
\(624\) | 19.2957i | 0.772445i | ||||||||
\(625\) | −12.3927 | + | 21.4648i | −0.495708 | + | 0.858591i | ||||
\(626\) | 4.80178 | − | 2.77231i | 0.191918 | − | 0.110804i | ||||
\(627\) | 7.74422 | + | 13.4134i | 0.309275 | + | 0.535679i | ||||
\(628\) | −12.4489 | + | 21.5621i | −0.496764 | + | 0.860420i | ||||
\(629\) | 3.35740 | − | 11.1807i | 0.133868 | − | 0.445804i | ||||
\(630\) | −0.0360954 | − | 0.0621062i | −0.00143808 | − | 0.00247437i | ||||
\(631\) | 0.246131 | 0.00979830 | 0.00489915 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489915 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(632\) | 2.35866 | + | 1.36177i | 0.0938224 | + | 0.0541684i | ||||
\(633\) | −2.44097 | − | 4.22788i | −0.0970198 | − | 0.168043i | ||||
\(634\) | 3.53758 | − | 2.04242i | 0.140495 | − | 0.0811150i | ||||
\(635\) | −1.28799 | − | 0.743621i | −0.0511123 | − | 0.0295097i | ||||
\(636\) | − | 18.3794i | − | 0.728790i | ||||||
\(637\) | 18.1009 | − | 31.7721i | 0.717185 | − | 1.25886i | ||||
\(638\) | −9.41575 | −0.372773 | ||||||||
\(639\) | 1.96848 | + | 1.13650i | 0.0778719 | + | 0.0449594i | ||||
\(640\) | 0.704750 | − | 0.406888i | 0.0278577 | − | 0.0160836i | ||||
\(641\) | −3.82475 | + | 2.20822i | −0.151069 | + | 0.0872195i | −0.573629 | − | 0.819115i | \(-0.694465\pi\) |
0.422560 | + | 0.906335i | \(0.361131\pi\) | |||||||
\(642\) | −0.181907 | + | 0.315072i | −0.00717928 | + | 0.0124349i | ||||
\(643\) | − | 12.4711i | − | 0.491811i | −0.969294 | − | 0.245906i | \(-0.920915\pi\) | ||
0.969294 | − | 0.245906i | \(-0.0790853\pi\) | |||||||
\(644\) | −3.66556 | − | 6.30701i | −0.144443 | − | 0.248531i | ||||
\(645\) | 0.479053 | 0.0188627 | ||||||||
\(646\) | −2.44696 | + | 2.30475i | −0.0962742 | + | 0.0906791i | ||||
\(647\) | −12.9174 | − | 22.3736i | −0.507836 | − | 0.879597i | −0.999959 | − | 0.00907170i | \(-0.997112\pi\) |
0.492123 | − | 0.870526i | \(-0.336221\pi\) | |||||||
\(648\) | −0.447916 | − | 0.775814i | −0.0175958 | − | 0.0304768i | ||||
\(649\) | −35.5998 | − | 20.5536i | −1.39742 | − | 0.806799i | ||||
\(650\) | −5.90883 | −0.231763 | ||||||||
\(651\) | −0.0467480 | − | 16.2670i | −0.00183220 | − | 0.637552i | ||||
\(652\) | 40.2478i | 1.57623i | ||||||||
\(653\) | 4.05208 | + | 2.33947i | 0.158570 | + | 0.0915505i | 0.577185 | − | 0.816613i | \(-0.304151\pi\) |
−0.418615 | + | 0.908164i | \(0.637484\pi\) | |||||||
\(654\) | 0.418937 | + | 0.725619i | 0.0163817 | + | 0.0283740i | ||||
\(655\) | 0.336032 | + | 0.582025i | 0.0131299 | + | 0.0227416i | ||||
\(656\) | −26.4303 | − | 15.2595i | −1.03193 | − | 0.595785i | ||||
\(657\) | − | 9.88353i | − | 0.385593i | ||||||
\(658\) | 2.86593 | + | 1.64368i | 0.111726 | + | 0.0640774i | ||||
\(659\) | 32.2523 | 1.25637 | 0.628186 | − | 0.778063i | \(-0.283798\pi\) | ||||
0.628186 | + | 0.778063i | \(0.283798\pi\) | |||||||
\(660\) | −0.870400 | − | 0.502525i | −0.0338803 | − | 0.0195608i | ||||
\(661\) | −2.00869 | − | 3.47915i | −0.0781289 | − | 0.135323i | 0.824314 | − | 0.566133i | \(-0.191561\pi\) |
−0.902443 | + | 0.430810i | \(0.858228\pi\) | |||||||
\(662\) | 2.56380 | + | 4.44064i | 0.0996450 | + | 0.172590i | ||||
\(663\) | 14.7674 | + | 15.6786i | 0.573519 | + | 0.608906i | ||||
\(664\) | 1.41636 | 0.0549655 | ||||||||
\(665\) | −0.566043 | + | 0.986954i | −0.0219502 | + | 0.0382724i | ||||
\(666\) | 0.642369i | 0.0248913i | ||||||||
\(667\) | 6.81237 | − | 11.7994i | 0.263776 | − | 0.456874i | ||||
\(668\) | −7.81968 | + | 4.51469i | −0.302552 | + | 0.174679i | ||||
\(669\) | 1.71116 | − | 0.987940i | 0.0661574 | − | 0.0381960i | ||||
\(670\) | 0.125513 | + | 0.0724652i | 0.00484901 | + | 0.00279958i | ||||
\(671\) | −39.0252 | −1.50655 | ||||||||
\(672\) | −6.95753 | + | 0.0199946i | −0.268392 | + | 0.000771307i | ||||
\(673\) | − | 36.5941i | − | 1.41060i | −0.708910 | − | 0.705299i | \(-0.750813\pi\) | ||
0.708910 | − | 0.705299i | \(-0.249187\pi\) | |||||||
\(674\) | 3.40397 | + | 1.96528i | 0.131116 | + | 0.0756999i | ||||
\(675\) | −4.31772 | + | 2.49284i | −0.166189 | + | 0.0959494i | ||||
\(676\) | 13.9202 | + | 24.1105i | 0.535392 | + | 0.927326i | ||||
\(677\) | −31.0298 | − | 17.9151i | −1.19257 | − | 0.688532i | −0.233683 | − | 0.972313i | \(-0.575078\pi\) |
−0.958889 | + | 0.283781i | \(0.908411\pi\) | |||||||
\(678\) | 2.10347 | 0.0807834 | ||||||||
\(679\) | −17.3016 | − | 29.7693i | −0.663973 | − | 1.14244i | ||||
\(680\) | 0.127123 | − | 0.423341i | 0.00487494 | − | 0.0162344i | ||||
\(681\) | 4.78253 | − | 8.28358i | 0.183267 | − | 0.317427i | ||||
\(682\) | 3.00619 | + | 5.20687i | 0.115113 | + | 0.199381i | ||||
\(683\) | 32.7458 | − | 18.9058i | 1.25298 | − | 0.723409i | 0.281281 | − | 0.959625i | \(-0.409241\pi\) |
0.971701 | + | 0.236216i | \(0.0759073\pi\) | |||||||
\(684\) | −3.50097 | + | 6.06386i | −0.133863 | + | 0.231858i | ||||
\(685\) | − | 2.08329i | − | 0.0795983i | ||||||
\(686\) | 3.65687 | + | 2.06947i | 0.139620 | + | 0.0790126i | ||||
\(687\) | − | 7.64712i | − | 0.291756i | ||||||
\(688\) | 7.39335 | − | 12.8057i | 0.281869 | − | 0.488211i | ||||
\(689\) | −24.6365 | − | 42.6718i | −0.938578 | − | 1.62566i | ||||
\(690\) | −0.0332713 | + | 0.0192092i | −0.00126662 | + | 0.000731281i | ||||
\(691\) | 10.1330 | + | 5.85028i | 0.385477 | + | 0.222555i | 0.680199 | − | 0.733028i | \(-0.261894\pi\) |
−0.294722 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(692\) | − | 42.1207i | − | 1.60119i | ||||||
\(693\) | 5.73019 | + | 9.85943i | 0.217672 | + | 0.374529i | ||||
\(694\) | 1.10647i | 0.0420009i | ||||||||
\(695\) | 1.02645 | − | 1.77787i | 0.0389355 | − | 0.0674383i | ||||
\(696\) | −4.31285 | − | 7.47008i | −0.163478 | − | 0.283153i | ||||
\(697\) | −33.1543 | + | 7.82866i | −1.25581 | + | 0.296532i | ||||
\(698\) | −2.12751 | + | 3.68496i | −0.0805275 | + | 0.139478i | ||||
\(699\) | −6.43828 | −0.243518 | ||||||||
\(700\) | 0.0738644 | + | 25.7026i | 0.00279181 | + | 0.971469i | ||||
\(701\) | −23.8211 | −0.899711 | −0.449856 | − | 0.893101i | \(-0.648525\pi\) | ||||
−0.449856 | + | 0.893101i | \(0.648525\pi\) | |||||||
\(702\) | −1.02638 | − | 0.592580i | −0.0387382 | − | 0.0223655i | ||||
\(703\) | 8.81121 | − | 5.08716i | 0.332321 | − | 0.191866i | ||||
\(704\) | −25.3489 | + | 14.6352i | −0.955373 | + | 0.551585i | ||||
\(705\) | −0.329331 | + | 0.570417i | −0.0124033 | + | 0.0214832i | ||||
\(706\) | −1.52628 | −0.0574423 | ||||||||
\(707\) | 23.7878 | + | 13.6429i | 0.894632 | + | 0.513094i | ||||
\(708\) | − | 18.5835i | − | 0.698412i | ||||||
\(709\) | 12.5730 | + | 7.25905i | 0.472191 | + | 0.272619i | 0.717156 | − | 0.696912i | \(-0.245443\pi\) |
−0.244966 | + | 0.969532i | \(0.578777\pi\) | |||||||
\(710\) | −0.0308567 | − | 0.0534453i | −0.00115803 | − | 0.00200577i | ||||
\(711\) | 2.63292 | − | 1.52012i | 0.0987424 | − | 0.0570089i | ||||
\(712\) | 1.91388 | − | 3.31494i | 0.0717258 | − | 0.124233i | ||||
\(713\) | −8.70001 | −0.325818 | ||||||||
\(714\) | −1.79673 | + | 1.70209i | −0.0672411 | + | 0.0636990i | ||||
\(715\) | −2.69443 | −0.100766 | ||||||||
\(716\) | −2.87365 | + | 4.97730i | −0.107393 | + | 0.186010i | ||||
\(717\) | −19.9552 | + | 11.5211i | −0.745239 | + | 0.430264i | ||||
\(718\) | −1.87472 | − | 3.24712i | −0.0699640 | − | 0.121181i | ||||
\(719\) | 23.9018 | + | 13.7997i | 0.891387 | + | 0.514643i | 0.874396 | − | 0.485213i | \(-0.161258\pi\) |
0.0169913 | + | 0.999856i | \(0.494591\pi\) | |||||||
\(720\) | − | 0.442039i | − | 0.0164738i | ||||||
\(721\) | −0.130497 | − | 45.4090i | −0.00485994 | − | 1.69112i | ||||
\(722\) | 1.38102 | 0.0513962 | ||||||||
\(723\) | 6.81145 | − | 11.7978i | 0.253320 | − | 0.438764i | ||||
\(724\) | −2.11448 | + | 1.22080i | −0.0785842 | + | 0.0453706i | ||||
\(725\) | −41.5741 | + | 24.0028i | −1.54402 | + | 0.891442i | ||||
\(726\) | −1.48887 | − | 0.859600i | −0.0552572 | − | 0.0319027i | ||||
\(727\) | 22.8158 | 0.846190 | 0.423095 | − | 0.906085i | \(-0.360944\pi\) | ||||
0.423095 | + | 0.906085i | \(0.360944\pi\) | |||||||
\(728\) | −10.7046 | + | 6.22137i | −0.396737 | + | 0.230579i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.134172 | + | 0.232392i | −0.00496591 | + | 0.00860121i | ||||
\(731\) | −3.79304 | − | 16.0635i | −0.140291 | − | 0.594129i | ||||
\(732\) | −8.82117 | − | 15.2787i | −0.326040 | − | 0.564718i | ||||
\(733\) | −16.8696 | + | 29.2189i | −0.623091 | + | 1.07923i | 0.365815 | + | 0.930687i | \(0.380790\pi\) |
−0.988907 | + | 0.148538i | \(0.952543\pi\) | |||||||
\(734\) | 4.94951i | 0.182690i | ||||||||
\(735\) | −0.414670 | + | 0.727858i | −0.0152953 | + | 0.0268474i | ||||
\(736\) | 3.72107i | 0.137161i | ||||||||
\(737\) | −19.9254 | − | 11.5039i | −0.733962 | − | 0.423753i | ||||
\(738\) | 1.62338 | − | 0.937258i | 0.0597574 | − | 0.0345009i | ||||
\(739\) | −7.19971 | − | 12.4703i | −0.264846 | − | 0.458726i | 0.702677 | − | 0.711509i | \(-0.251988\pi\) |
−0.967523 | + | 0.252782i | \(0.918654\pi\) | |||||||
\(740\) | −0.330107 | + | 0.571763i | −0.0121350 | + | 0.0210184i | ||||
\(741\) | 18.7714i | 0.689586i | ||||||||
\(742\) | 4.89523 | − | 2.84505i | 0.179710 | − | 0.104445i | ||||
\(743\) | − | 29.7992i | − | 1.09323i | −0.837385 | − | 0.546613i | \(-0.815917\pi\) | ||
0.837385 | − | 0.546613i | \(-0.184083\pi\) | |||||||
\(744\) | −2.75395 | + | 4.76998i | −0.100965 | + | 0.174876i | ||||
\(745\) | −2.40479 | + | 1.38841i | −0.0881046 | + | 0.0508672i | ||||
\(746\) | 0.464373 | + | 0.804317i | 0.0170019 | + | 0.0294482i | ||||
\(747\) | 0.790529 | − | 1.36924i | 0.0289239 | − | 0.0500977i | ||||
\(748\) | −9.95892 | + | 33.1649i | −0.364134 | + | 1.21263i | ||||
\(749\) | 4.24262 | − | 0.0121925i | 0.155022 | − | 0.000445503i | ||||
\(750\) | 0.271116 | 0.00989977 | ||||||||
\(751\) | 16.2013 | + | 9.35385i | 0.591196 | + | 0.341327i | 0.765570 | − | 0.643352i | \(-0.222457\pi\) |
−0.174374 | + | 0.984679i | \(0.555790\pi\) | |||||||
\(752\) | 10.1653 | + | 17.6068i | 0.370690 | + | 0.642054i | ||||
\(753\) | −19.0812 | + | 11.0165i | −0.695356 | + | 0.401464i | ||||
\(754\) | −9.88270 | − | 5.70578i | −0.359907 | − | 0.207792i | ||||
\(755\) | 1.66584i | 0.0606260i | ||||||||
\(756\) | −2.56482 | + | 4.47202i | −0.0932815 | + | 0.162646i | ||||
\(757\) | −35.3576 | −1.28509 | −0.642546 | − | 0.766247i | \(-0.722122\pi\) | ||||
−0.642546 | + | 0.766247i | \(0.722122\pi\) | |||||||
\(758\) | −5.90824 | − | 3.41112i | −0.214597 | − | 0.123898i | ||||
\(759\) | 5.28186 | − | 3.04948i | 0.191719 | − | 0.110689i | ||||
\(760\) | 0.333623 | − | 0.192618i | 0.0121018 | − | 0.00698697i | ||||
\(761\) | −11.4051 | + | 19.7541i | −0.413433 | + | 0.716087i | −0.995263 | − | 0.0972239i | \(-0.969004\pi\) |
0.581830 | + | 0.813311i | \(0.302337\pi\) | |||||||
\(762\) | − | 2.81960i | − | 0.102143i | ||||||
\(763\) | 4.86112 | − | 8.47587i | 0.175984 | − | 0.306847i | ||||
\(764\) | −48.8340 | −1.76675 | ||||||||
\(765\) | −0.338303 | − | 0.359177i | −0.0122314 | − | 0.0129861i | ||||
\(766\) | 1.31917 | + | 2.28487i | 0.0476636 | + | 0.0825558i | ||||
\(767\) | −24.9102 | − | 43.1457i | −0.899455 | − | 1.55790i | ||||
\(768\) | −10.4262 | − | 6.01959i | −0.376225 | − | 0.217213i | ||||
\(769\) | 11.7968 | 0.425404 | 0.212702 | − | 0.977117i | \(-0.431774\pi\) | ||||
0.212702 | + | 0.977117i | \(0.431774\pi\) | |||||||
\(770\) | −0.000889771 | − | 0.309614i | −3.20651e−5 | − | 0.0111577i | ||||
\(771\) | − | 9.99323i | − | 0.359898i | ||||||
\(772\) | 30.2992 | + | 17.4932i | 1.09049 | + | 0.629595i | ||||
\(773\) | 5.66039 | + | 9.80409i | 0.203590 | + | 0.352629i | 0.949683 | − | 0.313214i | \(-0.101406\pi\) |
−0.746092 | + | 0.665842i | \(0.768072\pi\) | |||||||
\(774\) | 0.454107 | + | 0.786537i | 0.0163226 | + | 0.0282715i | ||||
\(775\) | 26.5469 | + | 15.3269i | 0.953593 | + | 0.550557i | ||||
\(776\) | 11.6584i | 0.418512i | ||||||||
\(777\) | 6.47663 | − | 3.76414i | 0.232348 | − | 0.135038i | ||||
\(778\) | −3.14030 | −0.112585 | ||||||||
\(779\) | −25.7123 | − | 14.8450i | −0.921238 | − | 0.531877i | ||||
\(780\) | −0.609043 | − | 1.05489i | −0.0218072 | − | 0.0377712i | ||||
\(781\) | 4.89853 | + | 8.48451i | 0.175283 | + | 0.303600i | ||||
\(782\) | 0.907552 | + | 0.963550i | 0.0324540 | + | 0.0344565i | ||||
\(783\) | −9.62870 | −0.344102 | ||||||||
\(784\) | 13.0568 | + | 22.3178i | 0.466315 | + | 0.797066i | ||||
\(785\) | − | 1.52911i | − | 0.0545764i | ||||||
\(786\) | −0.637069 | + | 1.10344i | −0.0227235 | + | 0.0393583i | ||||
\(787\) | −22.7112 | + | 13.1123i | −0.809566 | + | 0.467403i | −0.846805 | − | 0.531903i | \(-0.821477\pi\) |
0.0372393 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(788\) | 40.2035 | − | 23.2115i | 1.43219 | − | 0.826876i | ||||
\(789\) | 7.86436 | + | 4.54049i | 0.279979 | + | 0.161646i | ||||
\(790\) | −0.0825441 | −0.00293679 | ||||||||
\(791\) | −12.3259 | − | 21.2081i | −0.438258 | − | 0.754073i | ||||
\(792\) | − | 3.86120i | − | 0.137202i | ||||||
\(793\) | −40.9605 | − | 23.6486i | −1.45455 | − | 0.839786i | ||||
\(794\) | −0.418835 | + | 0.241815i | −0.0148639 | + | 0.00858168i | ||||
\(795\) | 0.564392 | + | 0.977556i | 0.0200169 | + | 0.0346703i | ||||
\(796\) | 17.9304 | + | 10.3521i | 0.635526 | + | 0.366921i | ||||
\(797\) | −42.7086 | −1.51281 | −0.756407 | − | 0.654101i | \(-0.773047\pi\) | ||||
−0.756407 | + | 0.654101i | \(0.773047\pi\) | |||||||
\(798\) | −2.15701 | + | 0.00619882i | −0.0763572 | + | 0.000219436i | ||||
\(799\) | 21.7347 | + | 6.52659i | 0.768917 | + | 0.230894i | ||||
\(800\) | 6.55544 | − | 11.3544i | 0.231770 | − | 0.401437i | ||||
\(801\) | −2.13643 | − | 3.70041i | −0.0754870 | − | 0.130747i | ||||
\(802\) | −3.11747 | + | 1.79987i | −0.110082 | + | 0.0635556i | ||||
\(803\) | 21.2999 | − | 36.8925i | 0.751657 | − | 1.30191i | ||||
\(804\) | − | 10.4013i | − | 0.366826i | ||||||
\(805\) | 0.388638 | + | 0.222893i | 0.0136977 | + | 0.00785596i | ||||
\(806\) | 7.28679i | 0.256666i | ||||||||
\(807\) | 0.979976 | − | 1.69737i | 0.0344968 | − | 0.0597502i | ||||
\(808\) | −4.64252 | − | 8.04107i | −0.163323 | − | 0.282884i | ||||
\(809\) | 13.1203 | − | 7.57498i | 0.461284 | − | 0.266322i | −0.251300 | − | 0.967909i | \(-0.580858\pi\) |
0.712584 | + | 0.701587i | \(0.247525\pi\) | |||||||
\(810\) | 0.0235130 | + | 0.0135753i | 0.000826164 | + | 0.000476986i | ||||
\(811\) | − | 2.92328i | − | 0.102650i | −0.998682 | − | 0.0513251i | \(-0.983656\pi\) | ||
0.998682 | − | 0.0513251i | \(-0.0163445\pi\) | |||||||
\(812\) | −24.6959 | + | 43.0598i | −0.866655 | + | 1.51110i | ||||
\(813\) | 3.92180i | 0.137543i | ||||||||
\(814\) | −1.38436 | + | 2.39778i | −0.0485219 | + | 0.0840423i | ||||
\(815\) | −1.23593 | − | 2.14069i | −0.0432926 | − | 0.0749850i | ||||
\(816\) | −14.8223 | + | 3.49997i | −0.518886 | + | 0.122524i | ||||
\(817\) | 7.19249 | − | 12.4578i | 0.251633 | − | 0.435842i | ||||
\(818\) | 1.75350 | 0.0613098 | ||||||||
\(819\) | 0.0397182 | + | 13.8208i | 0.00138787 | + | 0.482937i | ||||
\(820\) | 1.92659 | 0.0672796 | ||||||||
\(821\) | 40.4388 | + | 23.3474i | 1.41132 | + | 0.814828i | 0.995513 | − | 0.0946227i | \(-0.0301645\pi\) |
0.415811 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(822\) | 3.42046 | − | 1.97481i | 0.119302 | − | 0.0688792i | ||||
\(823\) | −21.8508 | + | 12.6156i | −0.761673 | + | 0.439752i | −0.829896 | − | 0.557918i | \(-0.811600\pi\) |
0.0682234 | + | 0.997670i | \(0.478267\pi\) | |||||||
\(824\) | −7.68761 | + | 13.3153i | −0.267811 | + | 0.463862i | ||||
\(825\) | −21.4892 | −0.748157 | ||||||||
\(826\) | 4.94961 | − | 2.87665i | 0.172219 | − | 0.100092i | ||||
\(827\) | 4.10089i | 0.142602i | 0.997455 | + | 0.0713010i | \(0.0227151\pi\) | ||||
−0.997455 | + | 0.0713010i | \(0.977285\pi\) | |||||||
\(828\) | 2.38780 | + | 1.37860i | 0.0829817 | + | 0.0479095i | ||||
\(829\) | −2.70159 | − | 4.67929i | −0.0938301 | − | 0.162518i | 0.815290 | − | 0.579053i | \(-0.196578\pi\) |
−0.909120 | + | 0.416535i | \(0.863244\pi\) | |||||||
\(830\) | −0.0371755 | + | 0.0214633i | −0.00129038 | + | 0.000745001i | ||||
\(831\) | −3.38753 | + | 5.86738i | −0.117512 | + | 0.203537i | ||||
\(832\) | −35.4747 | −1.22986 | ||||||||
\(833\) | 27.6896 | + | 8.14157i | 0.959388 | + | 0.282089i | ||||
\(834\) | 3.89201 | 0.134769 | ||||||||
\(835\) | 0.277273 | − | 0.480252i | 0.00959544 | − | 0.0166198i | ||||
\(836\) | −26.1363 | + | 15.0898i | −0.903944 | + | 0.521893i | ||||
\(837\) | 3.07418 | + | 5.32463i | 0.106259 | + | 0.184046i | ||||
\(838\) | 1.86843 | + | 1.07874i | 0.0645439 | + | 0.0372645i | ||||
\(839\) | 9.31077i | 0.321443i | 0.987000 | + | 0.160722i | \(0.0513822\pi\) | ||||
−0.987000 | + | 0.160722i | \(0.948618\pi\) | |||||||
\(840\) | 0.245228 | − | 0.142524i | 0.00846117 | − | 0.00491753i | ||||
\(841\) | −63.7119 | −2.19696 | ||||||||
\(842\) | 1.23741 | − | 2.14326i | 0.0426440 | − | 0.0738616i | ||||
\(843\) | 13.2604 | − | 7.65589i | 0.456712 | − | 0.263683i | ||||
\(844\) | 8.23814 | − | 4.75629i | 0.283569 | − | 0.163718i | ||||
\(845\) | −1.48076 | − | 0.854920i | −0.0509399 | − | 0.0294101i | ||||
\(846\) | −1.24873 | −0.0429321 | ||||||||
\(847\) | 0.0576154 | + | 20.0485i | 0.00197969 | + | 0.688874i | ||||
\(848\) | 34.8417 | 1.19647 | ||||||||
\(849\) | 5.67553 | − | 9.83031i | 0.194784 | − | 0.337375i | ||||
\(850\) | −1.07178 | − | 4.53898i | −0.0367618 | − | 0.155686i | ||||
\(851\) | −2.00319 | − | 3.46963i | −0.0686686 | − | 0.118938i | ||||
\(852\) | −2.21451 | + | 3.83564i | −0.0758678 | + | 0.131407i | ||||
\(853\) | 7.55700i | 0.258747i | 0.991596 | + | 0.129373i | \(0.0412966\pi\) | ||||
−0.991596 | + | 0.129373i | \(0.958703\pi\) | |||||||
\(854\) | 2.70391 | − | 4.71454i | 0.0925258 | − | 0.161328i | ||||
\(855\) | − | 0.430030i | − | 0.0147067i | ||||||
\(856\) | −1.24407 | − | 0.718263i | −0.0425214 | − | 0.0245497i | ||||
\(857\) | −0.391745 | + | 0.226174i | −0.0133818 | + | 0.00772596i | −0.506676 | − | 0.862137i | \(-0.669126\pi\) |
0.493294 | + | 0.869863i | \(0.335793\pi\) | |||||||
\(858\) | −2.55413 | − | 4.42388i | −0.0871964 | − | 0.151029i | ||||
\(859\) | 13.4600 | − | 23.3134i | 0.459250 | − | 0.795444i | −0.539672 | − | 0.841875i | \(-0.681452\pi\) |
0.998921 | + | 0.0464318i | \(0.0147850\pi\) | |||||||
\(860\) | 0.933447i | 0.0318303i | ||||||||
\(861\) | −18.9625 | − | 10.8755i | −0.646240 | − | 0.370634i | ||||
\(862\) | − | 3.74334i | − | 0.127499i | ||||||
\(863\) | 9.49552 | − | 16.4467i | 0.323231 | − | 0.559853i | −0.657921 | − | 0.753087i | \(-0.728564\pi\) |
0.981153 | + | 0.193233i | \(0.0618975\pi\) | |||||||
\(864\) | 2.27739 | − | 1.31485i | 0.0774785 | − | 0.0447322i | ||||
\(865\) | 1.29344 | + | 2.24030i | 0.0439783 | + | 0.0761726i | ||||
\(866\) | −0.855125 | + | 1.48112i | −0.0290583 | + | 0.0503305i | ||||
\(867\) | −9.36521 | + | 14.1878i | −0.318059 | + | 0.481842i | ||||
\(868\) | 31.6966 | − | 0.0910898i | 1.07585 | − | 0.00309179i | ||||
\(869\) | 13.1040 | 0.444522 | ||||||||
\(870\) | 0.226400 | + | 0.130712i | 0.00767568 | + | 0.00443156i | ||||
\(871\) | −13.9424 | − | 24.1489i | −0.472419 | − | 0.818254i | ||||
\(872\) | −2.86513 | + | 1.65418i | −0.0970255 | + | 0.0560177i | ||||
\(873\) | 11.2705 | + | 6.50701i | 0.381448 | + | 0.220229i | ||||
\(874\) | 1.15363i | 0.0390220i | ||||||||
\(875\) | −1.58868 | − | 2.73351i | −0.0537073 | − | 0.0924095i | ||||
\(876\) | 19.2583 | 0.650678 | ||||||||
\(877\) | 11.7115 | + | 6.76161i | 0.395468 | + | 0.228324i | 0.684527 | − | 0.728988i | \(-0.260009\pi\) |
−0.289059 | + | 0.957311i | \(0.593342\pi\) | |||||||
\(878\) | −2.99950 | + | 1.73176i | −0.101228 | + | 0.0584441i | ||||
\(879\) | 16.0012 | − | 9.23829i | 0.539707 | − | 0.311600i | ||||
\(880\) | 0.952634 | − | 1.65001i | 0.0321133 | − | 0.0556219i | ||||
\(881\) | 2.52287i | 0.0849976i | 0.999097 | + | 0.0424988i | \(0.0135319\pi\) | ||||
−0.999097 | + | 0.0424988i | \(0.986468\pi\) | |||||||
\(882\) | −1.58812 | + | 0.00912796i | −0.0534747 | + | 0.000307354i | ||||
\(883\) | −22.9238 | −0.771446 | −0.385723 | − | 0.922615i | \(-0.626048\pi\) | ||||
−0.385723 | + | 0.922615i | \(0.626048\pi\) | |||||||
\(884\) | −30.5501 | + | 28.7747i | −1.02751 | + | 0.967798i | ||||
\(885\) | 0.570661 | + | 0.988415i | 0.0191826 | + | 0.0332252i | ||||
\(886\) | 2.94286 | + | 5.09718i | 0.0988673 | + | 0.171243i | ||||
\(887\) | −16.5305 | − | 9.54388i | −0.555039 | − | 0.320452i | 0.196113 | − | 0.980581i | \(-0.437168\pi\) |
−0.751152 | + | 0.660129i | \(0.770501\pi\) | |||||||
\(888\) | −2.53641 | −0.0851163 | ||||||||
\(889\) | −28.4284 | + | 16.5222i | −0.953456 | + | 0.554138i | ||||
\(890\) | 0.116010i | 0.00388868i | ||||||||
\(891\) | −3.73272 | − | 2.15509i | −0.125051 | − | 0.0721982i | ||||
\(892\) | 1.92503 | + | 3.33425i | 0.0644547 | + | 0.111639i | ||||
\(893\) | 9.88914 | + | 17.1285i | 0.330927 | + | 0.573183i | ||||
\(894\) | −4.55913 | − | 2.63222i | −0.152480 | − | 0.0880345i | ||||
\(895\) | − | 0.352975i | − | 0.0117986i | ||||||
\(896\) | −0.0517038 | − | 17.9914i | −0.00172730 | − | 0.601051i | ||||
\(897\) | 7.39173 | 0.246803 | ||||||||
\(898\) | 1.09040 | + | 0.629541i | 0.0363870 | + | 0.0210081i | ||||
\(899\) | 29.6003 | + | 51.2693i | 0.987227 | + | 1.70993i | ||||
\(900\) | −4.85736 | − | 8.41320i | −0.161912 | − | 0.280440i | ||||
\(901\) | 28.3104 | − | 26.6651i | 0.943157 | − | 0.888345i | ||||
\(902\) | 8.07950 | 0.269018 | ||||||||
\(903\) | 5.26923 | − | 9.18744i | 0.175349 | − | 0.305739i | ||||
\(904\) | 8.30561i | 0.276241i | ||||||||
\(905\) | 0.0749763 | − | 0.129863i | 0.00249230 | − | 0.00431678i | ||||
\(906\) | −2.73507 | + | 1.57909i | −0.0908667 | + | 0.0524619i | ||||
\(907\) | 42.5740 | − | 24.5801i | 1.41365 | − | 0.816170i | 0.417917 | − | 0.908485i | \(-0.362760\pi\) |
0.995730 | + | 0.0923154i | \(0.0294268\pi\) | |||||||
\(908\) | 16.1408 | + | 9.31888i | 0.535650 | + | 0.309258i | ||||
\(909\) | −10.3647 | −0.343775 | ||||||||
\(910\) | 0.186687 | − | 0.325508i | 0.00618861 | − | 0.0107905i | ||||
\(911\) | − | 37.3460i | − | 1.23733i | −0.785656 | − | 0.618664i | \(-0.787674\pi\) | ||
0.785656 | − | 0.618664i | \(-0.212326\pi\) | |||||||
\(912\) | −11.4952 | − | 6.63677i | −0.380645 | − | 0.219766i | ||||
\(913\) | 5.90165 | − | 3.40732i | 0.195316 | − | 0.112766i | ||||
\(914\) | 1.11139 | + | 1.92498i | 0.0367615 | + | 0.0636728i | ||||
\(915\) | 0.938354 | + | 0.541759i | 0.0310210 | + | 0.0179100i | ||||
\(916\) | 14.9006 | 0.492330 | ||||||||
\(917\) | 14.8584 | − | 0.0427001i | 0.490667 | − | 0.00141008i | ||||
\(918\) | 0.269031 | − | 0.895920i | 0.00887934 | − | 0.0295698i | ||||
\(919\) | −10.2671 | + | 17.7831i | −0.338679 | + | 0.586609i | −0.984185 | − | 0.177146i | \(-0.943313\pi\) |
0.645506 | + | 0.763756i | \(0.276647\pi\) | |||||||
\(920\) | −0.0758480 | − | 0.131373i | −0.00250063 | − | 0.00433122i | ||||
\(921\) | 2.57846 | − | 1.48867i | 0.0849631 | − | 0.0490535i | ||||
\(922\) | 2.76623 | − | 4.79124i | 0.0911008 | − | 0.157791i | ||||
\(923\) | 11.8737i | 0.390828i | ||||||||
\(924\) | −19.2114 | + | 11.1654i | −0.632008 | + | 0.367316i | ||||
\(925\) | 14.1162i | 0.464137i | ||||||||
\(926\) | 3.08874 | − | 5.34985i | 0.101502 | − | 0.175807i | ||||
\(927\) | 8.58152 | + | 14.8636i | 0.281854 | + | 0.488186i | ||||
\(928\) | 21.9284 | − | 12.6603i | 0.719833 | − | 0.415596i | ||||
\(929\) | 30.4443 | + | 17.5770i | 0.998844 | + | 0.576683i | 0.907906 | − | 0.419174i | \(-0.137680\pi\) |
0.0909380 | + | 0.995857i | \(0.471013\pi\) | |||||||
\(930\) | − | 0.166931i | − | 0.00547389i | ||||||
\(931\) | 12.7021 | + | 21.7115i | 0.416295 | + | 0.711567i | ||||
\(932\) | − | 12.5452i | − | 0.410931i | ||||||
\(933\) | −16.7822 | + | 29.0675i | −0.549423 | + | 0.951629i | ||||
\(934\) | 0.183211 | + | 0.317331i | 0.00599486 | + | 0.0103834i | ||||
\(935\) | −0.488734 | − | 2.06978i | −0.0159833 | − | 0.0676891i | ||||
\(936\) | 2.33982 | − | 4.05268i | 0.0764794 | − | 0.132466i | ||||
\(937\) | 27.0553 | 0.883859 | 0.441930 | − | 0.897050i | \(-0.354294\pi\) | ||||
0.441930 | + | 0.897050i | \(0.354294\pi\) | |||||||
\(938\) | 2.77032 | − | 1.61008i | 0.0904542 | − | 0.0525709i | ||||
\(939\) | 24.4388 | 0.797529 | ||||||||
\(940\) | −1.11147 | − | 0.641710i | −0.0362523 | − | 0.0209303i | ||||
\(941\) | −40.4807 | + | 23.3715i | −1.31963 | + | 0.761891i | −0.983669 | − | 0.179984i | \(-0.942395\pi\) |
−0.335964 | + | 0.941875i | \(0.609062\pi\) | |||||||
\(942\) | 2.51059 | − | 1.44949i | 0.0817995 | − | 0.0472270i | ||||
\(943\) | −5.84558 | + | 10.1248i | −0.190358 | + | 0.329710i | ||||
\(944\) | 35.2287 | 1.14660 | ||||||||
\(945\) | −0.000909894 | − | 0.316617i | −2.95989e−5 | − | 0.0102995i | ||||
\(946\) | 3.91457i | 0.127274i | ||||||||
\(947\) | −19.4130 | − | 11.2081i | −0.630838 | − | 0.364214i | 0.150239 | − | 0.988650i | \(-0.451996\pi\) |
−0.781076 | + | 0.624436i | \(0.785329\pi\) | |||||||
\(948\) | 2.96199 | + | 5.13032i | 0.0962011 | + | 0.166625i | ||||
\(949\) | 44.7124 | − | 25.8147i | 1.45143 | − | 0.837981i | ||||
\(950\) | 2.03235 | − | 3.52014i | 0.0659382 | − | 0.114208i | ||||
\(951\) | 18.0046 | 0.583840 | ||||||||
\(952\) | −6.72073 | − | 7.09445i | −0.217820 | − | 0.229932i | ||||
\(953\) | −18.6418 | −0.603867 | −0.301934 | − | 0.953329i | \(-0.597632\pi\) | ||||
−0.301934 | + | 0.953329i | \(0.597632\pi\) | |||||||
\(954\) | −1.07001 | + | 1.85331i | −0.0346427 | + | 0.0600030i | ||||
\(955\) | 2.59737 | − | 1.49959i | 0.0840488 | − | 0.0485256i | ||||
\(956\) | −22.4492 | − | 38.8832i | −0.726059 | − | 1.25757i | ||||
\(957\) | −35.9413 | − | 20.7507i | −1.16182 | − | 0.670776i | ||||
\(958\) | − | 0.335299i | − | 0.0108330i | ||||||
\(959\) | −39.9540 | − | 22.9146i | −1.29018 | − | 0.739951i | ||||
\(960\) | 0.812680 | 0.0262291 | ||||||||
\(961\) | 3.40114 | − | 5.89095i | 0.109714 | − | 0.190031i | ||||
\(962\) | −2.90603 | + | 1.67780i | −0.0936942 | + | 0.0540944i | ||||
\(963\) | −1.38873 | + | 0.801783i | −0.0447512 | + | 0.0258371i | ||||
\(964\) | 22.9883 | + | 13.2723i | 0.740402 | + | 0.427472i | ||||
\(965\) | −2.14872 | −0.0691698 | ||||||||
\(966\) | 0.00244094 | + | 0.849375i | 7.85359e−5 | + | 0.0273282i | ||||
\(967\) | 18.6151 | 0.598620 | 0.299310 | − | 0.954156i | \(-0.403244\pi\) | ||||
0.299310 | + | 0.954156i | \(0.403244\pi\) | |||||||
\(968\) | 3.39415 | − | 5.87884i | 0.109092 | − | 0.188953i | ||||
\(969\) | −14.4197 | + | 3.40489i | −0.463226 | + | 0.109381i | ||||
\(970\) | −0.176669 | − | 0.305999i | −0.00567249 | − | 0.00982505i | ||||
\(971\) | 0.948979 | − | 1.64368i | 0.0304542 | − | 0.0527482i | −0.850397 | − | 0.526142i | \(-0.823638\pi\) |
0.880851 | + | 0.473394i | \(0.156971\pi\) | |||||||
\(972\) | − | 1.94853i | − | 0.0624990i | ||||||
\(973\) | −22.8063 | − | 39.2409i | −0.731138 | − | 1.25800i | ||||
\(974\) | 8.92152i | 0.285864i | ||||||||
\(975\) | −22.5549 | − | 13.0221i | −0.722334 | − | 0.417040i | ||||
\(976\) | 28.9638 | − | 16.7222i | 0.927107 | − | 0.535266i | ||||
\(977\) | 11.7732 | + | 20.3918i | 0.376659 | + | 0.652392i | 0.990574 | − | 0.136980i | \(-0.0437395\pi\) |
−0.613915 | + | 0.789372i | \(0.710406\pi\) | |||||||
\(978\) | 2.34314 | − | 4.05843i | 0.0749253 | − | 0.129774i | ||||
\(979\) | − | 18.4168i | − | 0.588603i | ||||||
\(980\) | −1.41825 | − | 0.807995i | −0.0453044 | − | 0.0258104i | ||||
\(981\) | 3.69306i | 0.117910i | ||||||||
\(982\) | 0.537689 | − | 0.931304i | 0.0171583 | − | 0.0297191i | ||||
\(983\) | −10.7557 | + | 6.20979i | −0.343052 | + | 0.198061i | −0.661621 | − | 0.749838i | \(-0.730131\pi\) |
0.318569 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(984\) | 3.70079 | + | 6.40995i | 0.117977 | + | 0.204342i | ||||
\(985\) | −1.42555 | + | 2.46913i | −0.0454219 | + | 0.0786731i | ||||
\(986\) | 2.59042 | − | 8.62654i | 0.0824958 | − | 0.274725i | ||||
\(987\) | 7.31727 | + | 12.5902i | 0.232911 | + | 0.400750i | ||||
\(988\) | −36.5767 | −1.16366 | ||||||||
\(989\) | −4.90555 | − | 2.83222i | −0.155988 | − | 0.0900594i | ||||
\(990\) | 0.0585118 | + | 0.101345i | 0.00185963 | + | 0.00322097i | ||||
\(991\) | 27.9571 | − | 16.1410i | 0.888087 | − | 0.512737i | 0.0147704 | − | 0.999891i | \(-0.495298\pi\) |
0.873316 | + | 0.487154i | \(0.161965\pi\) | |||||||
\(992\) | −14.0022 | − | 8.08419i | −0.444571 | − | 0.256673i | ||||
\(993\) | 22.6007i | 0.717213i | ||||||||
\(994\) | −1.36439 | + | 0.00392100i | −0.0432760 | + | 0.000124367i | ||||
\(995\) | −1.27157 | −0.0403114 | ||||||||
\(996\) | 2.66799 | + | 1.54037i | 0.0845386 | + | 0.0488084i | ||||
\(997\) | 40.4862 | − | 23.3747i | 1.28221 | − | 0.740285i | 0.304959 | − | 0.952366i | \(-0.401357\pi\) |
0.977252 | + | 0.212081i | \(0.0680239\pi\) | |||||||
\(998\) | −6.74684 | + | 3.89529i | −0.213567 | + | 0.123303i | ||||
\(999\) | −1.41567 | + | 2.45201i | −0.0447899 | + | 0.0775783i |
(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 | 357.2.p.a.16.14 | yes | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.13 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.13 | ✓ | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.14 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.13 | ✓ | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.16.14 | yes | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.67.13 | yes | 48 | 7.4 | even | 3 | inner | |
357.2.p.a.67.14 | yes | 48 | 119.67 | even | 6 | inner |