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 | 16.13 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.13 |
$q$-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 | 0.522995 | − | 0.852336i | \(-0.324815\pi\) |
−0.476647 | + | 0.879095i | \(0.658148\pi\) | |||||||
\(6\) | 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 | −0.942789 | − | 0.333390i | \(-0.891807\pi\) |
−0.182670 | + | 0.983174i | \(0.558474\pi\) | |||||||
\(12\) | −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 | ||||
\(17\) | 3.00139 | + | 2.82696i | 0.727943 | + | 0.685638i | ||||
\(18\) | −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 | 0.366768 | − | 0.930312i | \(-0.380464\pi\) |
−0.622290 | + | 0.782787i | \(0.713797\pi\) | |||||||
\(24\) | −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 | \(0.352115\pi\) | ||||
−0.448062 | + | 0.894003i | \(0.647885\pi\) | |||||||
\(30\) | −0.0135753 | + | 0.0235130i | −0.00247849 | + | 0.00429288i | ||||
\(31\) | 5.32463 | − | 3.07418i | 0.956332 | − | 0.552139i | 0.0612899 | − | 0.998120i | \(-0.480479\pi\) |
0.895042 | + | 0.445981i | \(0.147145\pi\) | |||||||
\(32\) | 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 | 0.687824 | − | 0.725877i | \(-0.258566\pi\) |
−0.284716 | + | 0.958612i | \(0.591899\pi\) | |||||||
\(38\) | 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 | \(-0.776786\pi\) | ||
0.764038 | − | 0.645172i | \(-0.223214\pi\) | |||||||
\(42\) | 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 | ||||||||
\(51\) | −4.01275 | − | 0.947524i | −0.561898 | − | 0.132680i | ||||
\(52\) | 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 | 0.909417 | − | 0.415885i | \(-0.136528\pi\) |
0.0945411 | + | 0.995521i | \(0.469862\pi\) | |||||||
\(62\) | − | 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 | \(0.939059\pi\) | |||||||
\(68\) | −1.84628 | + | 7.81896i | −0.223894 | + | 0.948188i | ||||
\(69\) | 1.41501 | 0.170348 | ||||||||
\(70\) | 0.0357378 | − | 0.0623126i | 0.00427149 | − | 0.00744778i | ||||
\(71\) | − | 2.27301i | − | 0.269756i | −0.990862 | − | 0.134878i | \(-0.956936\pi\) | ||
0.990862 | − | 0.134878i | \(-0.0430643\pi\) | |||||||
\(72\) | 0.447916 | − | 0.775814i | 0.0527874 | − | 0.0914305i | ||||
\(73\) | −8.55939 | + | 4.94177i | −1.00180 | + | 0.578390i | −0.908781 | − | 0.417274i | \(-0.862985\pi\) |
−0.0930201 | + | 0.995664i | \(0.529652\pi\) | |||||||
\(74\) | 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 | 0.344520 | − | 0.938779i | \(-0.388042\pi\) |
−0.640747 | + | 0.767752i | \(0.721375\pi\) | |||||||
\(80\) | −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 | \(-0.770265\pi\) | ||
0.750662 | − | 0.660687i | \(-0.229735\pi\) | |||||||
\(98\) | −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 | \(-0.339121\pi\) | |||||||
\(102\) | −0.641374 | + | 0.680947i | −0.0635055 | + | 0.0674238i | ||||
\(103\) | −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 | 0.565622 | − | 0.824664i | \(-0.308636\pi\) |
−0.431369 | + | 0.902176i | \(0.641969\pi\) | |||||||
\(108\) | −1.68747 | + | 0.974263i | −0.162377 | + | 0.0937485i | ||||
\(109\) | 3.19828 | − | 1.84653i | 0.306340 | − | 0.176866i | −0.338947 | − | 0.940805i | \(-0.610071\pi\) |
0.645288 | + | 0.763940i | \(0.276738\pi\) | |||||||
\(110\) | −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 | \(-0.856363\pi\) | ||
0.899903 | − | 0.436090i | \(-0.143637\pi\) | |||||||
\(114\) | −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 | ||||||||
\(119\) | 10.6239 | + | 2.47639i | 0.973892 | + | 0.227011i | ||||
\(120\) | −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 | 0.697185 | − | 0.716891i | \(-0.254435\pi\) |
−0.272253 | + | 0.962226i | \(0.587769\pi\) | |||||||
\(132\) | 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 | ||||
\(136\) | 2.68874 | + | 2.53248i | 0.230557 | + | 0.217158i | ||||
\(137\) | 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 | \(-0.740673\pi\) | ||
0.686087 | − | 0.727520i | \(-0.259327\pi\) | |||||||
\(140\) | 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 | −0.406605 | − | 0.913604i | \(-0.633287\pi\) |
−0.994507 | + | 0.104672i | \(0.966621\pi\) | |||||||
\(164\) | 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 | \(-0.942619\pi\) | ||
0.983796 | − | 0.179293i | \(-0.0573810\pi\) | |||||||
\(168\) | −1.17917 | + | 2.05601i | −0.0909751 | + | 0.158624i | ||||
\(169\) | 14.2879 | 1.09907 | ||||||||
\(170\) | 0.108948 | + | 0.0257258i | 0.00835596 | + | 0.00197308i | ||||
\(171\) | 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 | 0.996580 | − | 0.0826382i | \(-0.0263346\pi\) |
0.426723 | + | 0.904382i | \(0.359668\pi\) | |||||||
\(174\) | −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 | \(-0.985171\pi\) | ||
0.998915 | − | 0.0465691i | \(-0.0148288\pi\) | |||||||
\(182\) | −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 | ||||
\(187\) | −17.2957 | − | 4.08400i | −1.26479 | − | 0.298652i | ||||
\(188\) | 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 | −0.941222 | − | 0.337790i | \(-0.890321\pi\) |
−0.178076 | + | 0.984017i | \(0.556987\pi\) | |||||||
\(194\) | −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 | \(0.322626\pi\) | ||||
−0.528843 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(198\) | 0.846872 | + | 0.488942i | 0.0601846 | + | 0.0347476i | ||||
\(199\) | −9.20203 | + | 5.31279i | −0.652314 | + | 0.376614i | −0.789342 | − | 0.613953i | \(-0.789578\pi\) |
0.137028 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(200\) | −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 | \(0.0537448\pi\) | ||||
−0.985780 | + | 0.168043i | \(0.946255\pi\) | |||||||
\(212\) | 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 | ||||
\(221\) | 15.6786 | + | 14.7674i | 1.05466 | + | 0.993364i | ||||
\(222\) | −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 | −0.749042 | − | 0.662523i | \(-0.769486\pi\) |
0.199241 | + | 0.979951i | \(0.436152\pi\) | |||||||
\(228\) | 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 | 0.671393 | − | 0.741101i | \(-0.265696\pi\) |
−0.306116 | + | 0.951994i | \(0.599030\pi\) | |||||||
\(234\) | −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 | ||||||||
\(238\) | 1.69173 | − | 1.80649i | 0.109659 | − | 0.117097i | ||||
\(239\) | −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 | −0.829282 | − | 0.558831i | \(-0.811250\pi\) |
0.0693205 | + | 0.997594i | \(0.477917\pi\) | |||||||
\(242\) | −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 | ||||
\(255\) | −0.359177 | − | 0.338303i | −0.0224925 | − | 0.0211853i | ||||
\(256\) | −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 | −0.550852 | − | 0.834603i | \(-0.685697\pi\) |
0.447361 | + | 0.894353i | \(0.352364\pi\) | |||||||
\(270\) | 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 | −0.313265 | − | 0.949666i | \(-0.601423\pi\) |
0.665802 | + | 0.746129i | \(0.268090\pi\) | |||||||
\(278\) | −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 | −0.762861 | − | 0.646563i | \(-0.776206\pi\) |
0.178509 | + | 0.983938i | \(0.442872\pi\) | |||||||
\(284\) | 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 | ||||||||
\(289\) | 1.01662 | + | 16.9696i | 0.0598015 | + | 0.998210i | ||||
\(290\) | 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 | ||||
\(306\) | 0.214972 | − | 0.910405i | 0.0122891 | − | 0.0520444i | ||||
\(307\) | 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 | \(-0.266076\pi\) |
0.977760 | − | 0.209728i | \(-0.0672578\pi\) | |||||||
\(312\) | −4.05268 | + | 2.33982i | −0.229438 | + | 0.132466i | ||||
\(313\) | −21.1646 | − | 12.2194i | −1.19629 | − | 0.690681i | −0.236567 | − | 0.971615i | \(-0.576022\pi\) |
−0.959727 | + | 0.280934i | \(0.909356\pi\) | |||||||
\(314\) | 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 | −0.00650207 | − | 0.999979i | \(-0.502070\pi\) |
−0.869258 | + | 0.494358i | \(0.835403\pi\) | |||||||
\(318\) | 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 | \(-0.843581\pi\) | ||
0.881670 | − | 0.471866i | \(-0.156419\pi\) | |||||||
\(338\) | 1.62081 | − | 2.80732i | 0.0881602 | − | 0.152698i | ||||
\(339\) | 4.63570 | + | 8.02926i | 0.251776 | + | 0.436090i | ||||
\(340\) | −0.659192 | + | 0.699865i | −0.0357497 | + | 0.0379555i | ||||
\(341\) | −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 | −0.382332 | − | 0.924025i | \(-0.624879\pi\) |
0.609063 | + | 0.793121i | \(0.291545\pi\) | |||||||
\(348\) | 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 | ||||||||
\(357\) | −10.4388 | + | 3.16734i | −0.552478 | + | 0.167633i | ||||
\(358\) | 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 | 0.0820689 | − | 0.996627i | \(-0.473847\pi\) |
0.904138 | + | 0.427240i | \(0.140514\pi\) | |||||||
\(368\) | 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 | \(0.200464\pi\) | |||||||
\(374\) | −2.76444 | + | 2.93501i | −0.142946 | + | 0.151766i | ||||
\(375\) | 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 | \(0.280894\pi\) | ||||
−0.635258 | + | 0.772300i | \(0.719106\pi\) | |||||||
\(380\) | −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 | 0.545610 | − | 0.838039i | \(-0.316298\pi\) |
−0.452958 | + | 0.891532i | \(0.649631\pi\) | |||||||
\(398\) | 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 | 0.802179 | − | 0.597083i | \(-0.203674\pi\) |
−0.116000 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(402\) | 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 | ||||||||
\(408\) | −3.59476 | − | 0.848823i | −0.177967 | − | 0.0420230i | ||||
\(409\) | 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 | \(-0.925380\pi\) | ||
0.972648 | − | 0.232283i | \(-0.0746196\pi\) | |||||||
\(420\) | −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 | ||||
\(425\) | 4.72405 | − | 20.0063i | 0.229150 | − | 0.970448i | ||||
\(426\) | 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 | −0.802964 | − | 0.596028i | \(-0.796745\pi\) |
0.114694 | + | 0.993401i | \(0.463411\pi\) | |||||||
\(432\) | −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 | 0.781137 | − | 0.624360i | \(-0.214640\pi\) |
−0.150143 | + | 0.988664i | \(0.547974\pi\) | |||||||
\(440\) | −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 | \(-0.958197\pi\) | ||
0.991389 | − | 0.130951i | \(-0.0418031\pi\) | |||||||
\(450\) | −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 | ||||
\(459\) | −2.82696 | + | 3.00139i | −0.131951 | + | 0.140093i | ||||
\(460\) | 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 | ||||||||
\(476\) | 6.17164 | + | 20.3402i | 0.282877 | + | 0.932293i | ||||
\(477\) | −9.43245 | −0.431882 | ||||||||
\(478\) | −2.61389 | + | 4.52738i | −0.119556 | + | 0.207078i | ||||
\(479\) | −1.27988 | + | 0.738941i | −0.0584794 | + | 0.0337631i | −0.528955 | − | 0.848650i | \(-0.677416\pi\) |
0.470475 | + | 0.882413i | \(0.344082\pi\) | |||||||
\(480\) | −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 | \(-0.316707\pi\) |
0.998636 | − | 0.0522082i | \(-0.0166259\pi\) | |||||||
\(488\) | 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 | ||||
\(493\) | −27.2199 | + | 28.8994i | −1.22592 | + | 1.30157i | ||||
\(494\) | 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 | 0.985491 | − | 0.169730i | \(-0.0542895\pi\) |
0.345755 | + | 0.938325i | \(0.387623\pi\) | |||||||
\(500\) | 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 | \(-0.978503\pi\) | ||
0.997720 | − | 0.0674836i | \(-0.0214970\pi\) | |||||||
\(504\) | −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 | −0.991044 | − | 0.133538i | \(-0.957366\pi\) |
−0.379874 | + | 0.925038i | \(0.624033\pi\) | |||||||
\(522\) | 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 | ||||||||
\(527\) | 24.6718 | + | 5.82572i | 1.07472 | + | 0.253772i | ||||
\(528\) | 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 | 0.0610509 | − | 0.998135i | \(-0.480555\pi\) |
−0.833885 | + | 0.551939i | \(0.813888\pi\) | |||||||
\(542\) | 0.444884 | + | 0.770562i | 0.0191094 | + | 0.0330985i | ||||
\(543\) | 0.626524 | + | 1.08517i | 0.0268867 | + | 0.0465691i | ||||
\(544\) | −2.49171 | + | 10.5524i | −0.106831 | + | 0.452429i | ||||
\(545\) | 0.441950 | 0.0189310 | ||||||||
\(546\) | 1.57562 | + | 2.71103i | 0.0674302 | + | 0.116021i | ||||
\(547\) | − | 26.0552i | − | 1.11404i | −0.830499 | − | 0.557020i | \(-0.811945\pi\) | ||
0.830499 | − | 0.557020i | \(-0.188055\pi\) | |||||||
\(548\) | −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 | −0.103659 | − | 0.994613i | \(-0.533055\pi\) |
0.809531 | + | 0.587078i | \(0.199722\pi\) | |||||||
\(572\) | −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 | \(0.745871\pi\) | |||||||
\(578\) | 3.44954 | + | 1.72526i | 0.143482 | + | 0.0717614i | ||||
\(579\) | 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 | ||||||||
\(595\) | 0.952861 | + | 0.892331i | 0.0390635 | + | 0.0365820i | ||||
\(596\) | 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 | \(0.127184\pi\) | ||||
−0.921232 | + | 0.389013i | \(0.872816\pi\) | |||||||
\(602\) | 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 | 0.0510652 | − | 0.998695i | \(-0.483738\pi\) |
−0.839363 | + | 0.543571i | \(0.817072\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 5.84828 | + | 5.50840i | 0.236403 | + | 0.222664i | ||||
\(613\) | −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 | \(-0.674476\pi\) | ||
0.521094 | − | 0.853499i | \(-0.325524\pi\) | |||||||
\(618\) | −3.37223 | − | 1.94696i | −0.135651 | − | 0.0783181i | ||||
\(619\) | 13.5723 | − | 7.83595i | 0.545516 | − | 0.314954i | −0.201796 | − | 0.979428i | \(-0.564678\pi\) |
0.747311 | + | 0.664474i | \(0.231344\pi\) | |||||||
\(620\) | 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 | −0.422560 | − | 0.906335i | \(-0.638869\pi\) |
0.573629 | + | 0.819115i | \(0.305535\pi\) | |||||||
\(642\) | −0.181907 | + | 0.315072i | −0.00717928 | + | 0.0124349i | ||||
\(643\) | 12.4711i | 0.491811i | 0.969294 | + | 0.245906i | \(0.0790853\pi\) | ||||
−0.969294 | + | 0.245906i | \(0.920915\pi\) | |||||||
\(644\) | −3.66556 | − | 6.30701i | −0.144443 | − | 0.248531i | ||||
\(645\) | 0.479053 | 0.0188627 | ||||||||
\(646\) | −0.772493 | + | 3.27150i | −0.0303933 | + | 0.128715i | ||||
\(647\) | −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 | 0.418615 | − | 0.908164i | \(-0.362516\pi\) |
−0.577185 | + | 0.816613i | \(0.695849\pi\) | |||||||
\(654\) | 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 | ||||
\(663\) | −20.9618 | − | 4.94966i | −0.814087 | − | 0.192229i | ||||
\(664\) | 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 | \(0.249187\pi\) | ||||
−0.708910 | + | 0.705299i | \(0.750813\pi\) | |||||||
\(674\) | −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 | 0.958889 | − | 0.283781i | \(-0.0915888\pi\) |
0.233683 | + | 0.972313i | \(0.424922\pi\) | |||||||
\(678\) | 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 | −0.971701 | − | 0.236216i | \(-0.924093\pi\) |
−0.281281 | + | 0.959625i | \(0.590759\pi\) | |||||||
\(684\) | −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 | 0.294722 | − | 0.955583i | \(-0.404773\pi\) |
−0.680199 | + | 0.733028i | \(0.738106\pi\) | |||||||
\(692\) | 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 | ||||
\(697\) | 23.3570 | − | 24.7981i | 0.884708 | − | 0.939296i | ||||
\(698\) | −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 | 0.244966 | − | 0.969532i | \(-0.421223\pi\) |
−0.717156 | + | 0.696912i | \(0.754557\pi\) | |||||||
\(710\) | −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 | ||||||||
\(714\) | −0.561838 | + | 2.41033i | −0.0210263 | + | 0.0902043i | ||||
\(715\) | −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 | −0.0169913 | − | 0.999856i | \(-0.505409\pi\) |
−0.874396 | + | 0.485213i | \(0.838742\pi\) | |||||||
\(720\) | 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 | ||||
\(731\) | −12.0149 | − | 11.3166i | −0.444385 | − | 0.418560i | ||||
\(732\) | −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 | \(0.184083\pi\) | ||||
−0.837385 | + | 0.546613i | \(0.815917\pi\) | |||||||
\(744\) | −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 | 0.174374 | − | 0.984679i | \(-0.444210\pi\) |
−0.765570 | + | 0.643352i | \(0.777543\pi\) | |||||||
\(752\) | 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 | ||||||||
\(765\) | 0.480208 | + | 0.113391i | 0.0173619 | + | 0.00409964i | ||||
\(766\) | 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 | ||||
\(782\) | −1.28823 | − | 0.304189i | −0.0460672 | − | 0.0108778i | ||||
\(783\) | −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 | −0.0372393 | − | 0.999306i | \(-0.511856\pi\) |
0.846805 | + | 0.531903i | \(0.178523\pi\) | |||||||
\(788\) | −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 | −0.712584 | − | 0.701587i | \(-0.752475\pi\) |
0.251300 | + | 0.967909i | \(0.419142\pi\) | |||||||
\(810\) | −0.0235130 | − | 0.0135753i | −0.000826164 | − | 0.000476986i | ||||
\(811\) | 2.92328i | 0.102650i | 0.998682 | + | 0.0513251i | \(0.0163445\pi\) | ||||
−0.998682 | + | 0.0513251i | \(0.983656\pi\) | |||||||
\(812\) | −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 | ||||
\(816\) | 10.4422 | − | 11.0865i | 0.365551 | − | 0.388107i | ||||
\(817\) | 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 | −0.415811 | − | 0.909451i | \(-0.636502\pi\) |
−0.995513 | + | 0.0946227i | \(0.969836\pi\) | |||||||
\(822\) | −3.42046 | + | 1.97481i | −0.119302 | + | 0.0688792i | ||||
\(823\) | 21.8508 | − | 12.6156i | 0.761673 | − | 0.439752i | −0.0682234 | − | 0.997670i | \(-0.521733\pi\) |
0.829896 | + | 0.557918i | \(0.188400\pi\) | |||||||
\(824\) | −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 | \(-0.977285\pi\) | ||
0.997455 | − | 0.0713010i | \(-0.0227151\pi\) | |||||||
\(828\) | −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 | ||||||||
\(833\) | 27.5942 | − | 8.45932i | 0.956082 | − | 0.293098i | ||||
\(834\) | 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 | \(-0.948618\pi\) | ||
0.987000 | − | 0.160722i | \(-0.0513822\pi\) | |||||||
\(840\) | −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 | ||||
\(850\) | −3.39499 | − | 3.19768i | −0.116447 | − | 0.109680i | ||||
\(851\) | −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 | \(-0.958703\pi\) | ||
0.991596 | − | 0.129373i | \(-0.0412966\pi\) | |||||||
\(854\) | 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 | −0.493294 | − | 0.869863i | \(-0.664207\pi\) |
0.506676 | + | 0.862137i | \(0.330874\pi\) | |||||||
\(858\) | −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 | 0.289059 | − | 0.957311i | \(-0.406658\pi\) |
−0.684527 | + | 0.728988i | \(0.739991\pi\) | |||||||
\(878\) | 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 | \(-0.986468\pi\) | ||
0.999097 | − | 0.0424988i | \(-0.0135319\pi\) | |||||||
\(882\) | −1.58812 | + | 0.00912796i | −0.0534747 | + | 0.000307354i | ||||
\(883\) | −22.9238 | −0.771446 | −0.385723 | − | 0.922615i | \(-0.626048\pi\) | ||||
−0.385723 | + | 0.922615i | \(0.626048\pi\) | |||||||
\(884\) | −9.64455 | + | 40.8446i | −0.324381 | + | 1.37375i | ||||
\(885\) | 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 | 0.751152 | − | 0.660129i | \(-0.229499\pi\) |
−0.196113 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(888\) | −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 | ||||
\(901\) | 8.93748 | − | 37.8501i | 0.297751 | − | 1.26097i | ||||
\(902\) | 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 | −0.995730 | − | 0.0923154i | \(-0.970573\pi\) |
−0.417917 | + | 0.908485i | \(0.637240\pi\) | |||||||
\(908\) | −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 | \(0.212326\pi\) | ||||
−0.785656 | + | 0.618664i | \(0.787674\pi\) | |||||||
\(912\) | 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 | −0.0909380 | − | 0.995857i | \(-0.528987\pi\) |
−0.907906 | + | 0.419174i | \(0.862320\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | −1.54812 | − | 1.45815i | −0.0506288 | − | 0.0476865i | ||||
\(936\) | 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 | 0.335964 | − | 0.941875i | \(-0.390938\pi\) |
0.983669 | + | 0.179984i | \(0.0576047\pi\) | |||||||
\(942\) | −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 | 0.781076 | − | 0.624436i | \(-0.214671\pi\) |
−0.150239 | + | 0.988650i | \(0.548004\pi\) | |||||||
\(948\) | 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 | ||||||||
\(952\) | 9.51725 | + | 2.21843i | 0.308456 | + | 0.0718998i | ||||
\(953\) | −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 | ||||
\(969\) | 10.1586 | − | 10.7854i | 0.326340 | − | 0.346475i | ||||
\(970\) | −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 | −0.318569 | − | 0.947900i | \(-0.603202\pi\) |
0.661621 | + | 0.749838i | \(0.269869\pi\) | |||||||
\(984\) | 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 | −0.873316 | − | 0.487154i | \(-0.838035\pi\) |
−0.0147704 | + | 0.999891i | \(0.504702\pi\) | |||||||
\(992\) | 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 | −0.977252 | − | 0.212081i | \(-0.931976\pi\) |
−0.304959 | + | 0.952366i | \(0.598643\pi\) | |||||||
\(998\) | 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.16.13 | ✓ | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.14 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.14 | yes | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.13 | ✓ | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.16.14 | yes | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.67.13 | yes | 48 | 119.67 | even | 6 | inner | |
357.2.p.a.67.14 | yes | 48 | 7.4 | even | 3 | inner |