Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(166,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.166");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Character | \(\chi\) | \(=\) | 429.199 |
Dual form | 429.2.s.b.166.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.945010 | − | 0.545602i | −0.668223 | − | 0.385799i | 0.127180 | − | 0.991880i | \(-0.459407\pi\) |
−0.795403 | + | 0.606081i | \(0.792741\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.404638 | − | 0.700853i | −0.202319 | − | 0.350427i | ||||
\(5\) | − | 1.08345i | − | 0.484531i | −0.970210 | − | 0.242266i | \(-0.922109\pi\) | ||
0.970210 | − | 0.242266i | \(-0.0778906\pi\) | |||||||
\(6\) | 0.945010 | − | 0.545602i | 0.385799 | − | 0.222741i | ||||
\(7\) | −2.79805 | + | 1.61546i | −1.05757 | + | 0.610585i | −0.924758 | − | 0.380556i | \(-0.875732\pi\) |
−0.132807 | + | 0.991142i | \(0.542399\pi\) | |||||||
\(8\) | 3.06549i | 1.08381i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.591129 | + | 1.02387i | −0.186932 | + | 0.323775i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | ||||
\(12\) | 0.809275 | 0.233618 | ||||||||
\(13\) | 3.52518 | − | 0.757049i | 0.977708 | − | 0.209968i | ||||
\(14\) | 3.52558 | 0.942252 | ||||||||
\(15\) | 0.938291 | + | 0.541723i | 0.242266 | + | 0.139872i | ||||
\(16\) | 0.863261 | − | 1.49521i | 0.215815 | − | 0.373803i | ||||
\(17\) | 2.05655 | + | 3.56204i | 0.498786 | + | 0.863922i | 0.999999 | − | 0.00140167i | \(-0.000446167\pi\) |
−0.501213 | + | 0.865324i | \(0.667113\pi\) | |||||||
\(18\) | 1.09120i | 0.257199i | ||||||||
\(19\) | 3.45345 | − | 1.99385i | 0.792275 | − | 0.457420i | −0.0484880 | − | 0.998824i | \(-0.515440\pi\) |
0.840763 | + | 0.541404i | \(0.182107\pi\) | |||||||
\(20\) | −0.759336 | + | 0.438403i | −0.169793 | + | 0.0980298i | ||||
\(21\) | − | 3.23091i | − | 0.705043i | ||||||
\(22\) | −0.545602 | − | 0.945010i | −0.116323 | − | 0.201477i | ||||
\(23\) | −1.43078 | + | 2.47818i | −0.298338 | + | 0.516737i | −0.975756 | − | 0.218862i | \(-0.929766\pi\) |
0.677418 | + | 0.735598i | \(0.263099\pi\) | |||||||
\(24\) | −2.65479 | − | 1.53275i | −0.541907 | − | 0.312870i | ||||
\(25\) | 3.82615 | 0.765229 | ||||||||
\(26\) | −3.74437 | − | 1.20792i | −0.734332 | − | 0.236893i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.26440 | + | 1.30735i | 0.427931 | + | 0.247066i | ||||
\(29\) | −2.58685 | + | 4.48056i | −0.480366 | + | 0.832018i | −0.999746 | − | 0.0225248i | \(-0.992830\pi\) |
0.519380 | + | 0.854543i | \(0.326163\pi\) | |||||||
\(30\) | −0.591129 | − | 1.02387i | −0.107925 | − | 0.186932i | ||||
\(31\) | − | 8.59681i | − | 1.54403i | −0.635602 | − | 0.772017i | \(-0.719248\pi\) | ||
0.635602 | − | 0.772017i | \(-0.280752\pi\) | |||||||
\(32\) | 3.67800 | − | 2.12350i | 0.650186 | − | 0.375385i | ||||
\(33\) | −0.866025 | + | 0.500000i | −0.150756 | + | 0.0870388i | ||||
\(34\) | − | 4.48822i | − | 0.769723i | ||||||
\(35\) | 1.75026 | + | 3.03154i | 0.295848 | + | 0.512423i | ||||
\(36\) | −0.404638 | + | 0.700853i | −0.0674396 | + | 0.116809i | ||||
\(37\) | 8.26769 | + | 4.77336i | 1.35920 | + | 0.784735i | 0.989516 | − | 0.144423i | \(-0.0461325\pi\) |
0.369684 | + | 0.929157i | \(0.379466\pi\) | |||||||
\(38\) | −4.35139 | −0.705888 | ||||||||
\(39\) | −1.10697 | + | 3.43142i | −0.177256 | + | 0.549467i | ||||
\(40\) | 3.32129 | 0.525142 | ||||||||
\(41\) | 5.76211 | + | 3.32675i | 0.899890 | + | 0.519552i | 0.877164 | − | 0.480190i | \(-0.159432\pi\) |
0.0227253 | + | 0.999742i | \(0.492766\pi\) | |||||||
\(42\) | −1.76279 | + | 3.05325i | −0.272005 | + | 0.471126i | ||||
\(43\) | 1.21027 | + | 2.09625i | 0.184564 | + | 0.319675i | 0.943430 | − | 0.331573i | \(-0.107579\pi\) |
−0.758865 | + | 0.651248i | \(0.774246\pi\) | |||||||
\(44\) | − | 0.809275i | − | 0.122003i | ||||||
\(45\) | −0.938291 | + | 0.541723i | −0.139872 | + | 0.0807552i | ||||
\(46\) | 2.70420 | − | 1.56127i | 0.398712 | − | 0.230197i | ||||
\(47\) | 5.83737i | 0.851468i | 0.904848 | + | 0.425734i | \(0.139984\pi\) | ||||
−0.904848 | + | 0.425734i | \(0.860016\pi\) | |||||||
\(48\) | 0.863261 | + | 1.49521i | 0.124601 | + | 0.215815i | ||||
\(49\) | 1.71940 | − | 2.97810i | 0.245629 | − | 0.425442i | ||||
\(50\) | −3.61575 | − | 2.08755i | −0.511344 | − | 0.295224i | ||||
\(51\) | −4.11309 | −0.575948 | ||||||||
\(52\) | −1.95700 | − | 2.16430i | −0.271387 | − | 0.300135i | ||||
\(53\) | 13.3492 | 1.83366 | 0.916829 | − | 0.399280i | \(-0.130740\pi\) | ||||
0.916829 | + | 0.399280i | \(0.130740\pi\) | |||||||
\(54\) | −0.945010 | − | 0.545602i | −0.128600 | − | 0.0742470i | ||||
\(55\) | 0.541723 | − | 0.938291i | 0.0730459 | − | 0.126519i | ||||
\(56\) | −4.95217 | − | 8.57741i | −0.661761 | − | 1.14620i | ||||
\(57\) | 3.98770i | 0.528183i | ||||||||
\(58\) | 4.88920 | − | 2.82278i | 0.641983 | − | 0.370649i | ||||
\(59\) | −11.7925 | + | 6.80838i | −1.53525 | + | 0.886376i | −0.536140 | + | 0.844129i | \(0.680118\pi\) |
−0.999107 | + | 0.0422468i | \(0.986548\pi\) | |||||||
\(60\) | − | 0.876806i | − | 0.113195i | ||||||
\(61\) | 5.66826 | + | 9.81771i | 0.725746 | + | 1.25703i | 0.958666 | + | 0.284533i | \(0.0918386\pi\) |
−0.232920 | + | 0.972496i | \(0.574828\pi\) | |||||||
\(62\) | −4.69044 | + | 8.12407i | −0.595686 | + | 1.03176i | ||||
\(63\) | 2.79805 | + | 1.61546i | 0.352522 | + | 0.203528i | ||||
\(64\) | −8.08738 | −1.01092 | ||||||||
\(65\) | −0.820221 | − | 3.81934i | −0.101736 | − | 0.473730i | ||||
\(66\) | 1.09120 | 0.134318 | ||||||||
\(67\) | −11.5015 | − | 6.64039i | −1.40513 | − | 0.811252i | −0.410217 | − | 0.911988i | \(-0.634547\pi\) |
−0.994913 | + | 0.100735i | \(0.967880\pi\) | |||||||
\(68\) | 1.66431 | − | 2.88267i | 0.201827 | − | 0.349575i | ||||
\(69\) | −1.43078 | − | 2.47818i | −0.172246 | − | 0.298338i | ||||
\(70\) | − | 3.81978i | − | 0.456551i | ||||||
\(71\) | 0.489486 | − | 0.282605i | 0.0580913 | − | 0.0335390i | −0.470673 | − | 0.882308i | \(-0.655989\pi\) |
0.528764 | + | 0.848769i | \(0.322656\pi\) | |||||||
\(72\) | 2.65479 | − | 1.53275i | 0.312870 | − | 0.180636i | ||||
\(73\) | − | 12.7075i | − | 1.48730i | −0.668569 | − | 0.743650i | \(-0.733093\pi\) | ||
0.668569 | − | 0.743650i | \(-0.266907\pi\) | |||||||
\(74\) | −5.20870 | − | 9.02173i | −0.605499 | − | 1.04876i | ||||
\(75\) | −1.91307 | + | 3.31354i | −0.220903 | + | 0.382615i | ||||
\(76\) | −2.79479 | − | 1.61357i | −0.320584 | − | 0.185089i | ||||
\(77\) | −3.23091 | −0.368197 | ||||||||
\(78\) | 2.91828 | − | 2.63876i | 0.330430 | − | 0.298781i | ||||
\(79\) | 1.87008 | 0.210401 | 0.105200 | − | 0.994451i | \(-0.466452\pi\) | ||||
0.105200 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(80\) | −1.61998 | − | 0.935296i | −0.181119 | − | 0.104569i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.63016 | − | 6.28763i | −0.400885 | − | 0.694352i | ||||
\(83\) | 2.40039i | 0.263477i | 0.991285 | + | 0.131738i | \(0.0420559\pi\) | ||||
−0.991285 | + | 0.131738i | \(0.957944\pi\) | |||||||
\(84\) | −2.26440 | + | 1.30735i | −0.247066 | + | 0.142644i | ||||
\(85\) | 3.85928 | − | 2.22815i | 0.418597 | − | 0.241677i | ||||
\(86\) | − | 2.64130i | − | 0.284819i | ||||||
\(87\) | −2.58685 | − | 4.48056i | −0.277339 | − | 0.480366i | ||||
\(88\) | −1.53275 | + | 2.65479i | −0.163391 | + | 0.283002i | ||||
\(89\) | −12.1719 | − | 7.02744i | −1.29022 | − | 0.744907i | −0.311524 | − | 0.950238i | \(-0.600840\pi\) |
−0.978693 | + | 0.205331i | \(0.934173\pi\) | |||||||
\(90\) | 1.18226 | 0.124621 | ||||||||
\(91\) | −8.64066 | + | 7.81304i | −0.905787 | + | 0.819029i | ||||
\(92\) | 2.31579 | 0.241438 | ||||||||
\(93\) | 7.44506 | + | 4.29841i | 0.772017 | + | 0.445724i | ||||
\(94\) | 3.18488 | − | 5.51637i | 0.328495 | − | 0.568970i | ||||
\(95\) | −2.16022 | − | 3.74162i | −0.221634 | − | 0.383882i | ||||
\(96\) | 4.24699i | 0.433457i | ||||||||
\(97\) | −15.0115 | + | 8.66687i | −1.52418 | + | 0.879987i | −0.524592 | + | 0.851354i | \(0.675782\pi\) |
−0.999590 | + | 0.0286332i | \(0.990885\pi\) | |||||||
\(98\) | −3.24971 | + | 1.87622i | −0.328270 | + | 0.189527i | ||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | −1.54820 | − | 2.68157i | −0.154820 | − | 0.268157i | ||||
\(101\) | 3.86014 | − | 6.68596i | 0.384098 | − | 0.665278i | −0.607545 | − | 0.794285i | \(-0.707846\pi\) |
0.991644 | + | 0.129007i | \(0.0411791\pi\) | |||||||
\(102\) | 3.88691 | + | 2.24411i | 0.384862 | + | 0.222200i | ||||
\(103\) | 9.08848 | 0.895515 | 0.447757 | − | 0.894155i | \(-0.352223\pi\) | ||||
0.447757 | + | 0.894155i | \(0.352223\pi\) | |||||||
\(104\) | 2.32073 | + | 10.8064i | 0.227566 | + | 1.05965i | ||||
\(105\) | −3.50052 | −0.341616 | ||||||||
\(106\) | −12.6152 | − | 7.28336i | −1.22529 | − | 0.707423i | ||||
\(107\) | −3.21702 | + | 5.57204i | −0.311001 | + | 0.538669i | −0.978579 | − | 0.205870i | \(-0.933997\pi\) |
0.667579 | + | 0.744539i | \(0.267331\pi\) | |||||||
\(108\) | −0.404638 | − | 0.700853i | −0.0389363 | − | 0.0674396i | ||||
\(109\) | 8.47732i | 0.811980i | 0.913878 | + | 0.405990i | \(0.133073\pi\) | ||||
−0.913878 | + | 0.405990i | \(0.866927\pi\) | |||||||
\(110\) | −1.02387 | + | 0.591129i | −0.0976218 | + | 0.0563620i | ||||
\(111\) | −8.26769 | + | 4.77336i | −0.784735 | + | 0.453067i | ||||
\(112\) | 5.57825i | 0.527095i | ||||||||
\(113\) | 2.86486 | + | 4.96208i | 0.269503 | + | 0.466793i | 0.968734 | − | 0.248103i | \(-0.0798072\pi\) |
−0.699230 | + | 0.714896i | \(0.746474\pi\) | |||||||
\(114\) | 2.17569 | − | 3.76841i | 0.203772 | − | 0.352944i | ||||
\(115\) | 2.68497 | + | 1.55017i | 0.250375 | + | 0.144554i | ||||
\(116\) | 4.18695 | 0.388748 | ||||||||
\(117\) | −2.41821 | − | 2.67437i | −0.223564 | − | 0.247245i | ||||
\(118\) | 14.8587 | 1.36785 | ||||||||
\(119\) | −11.5087 | − | 6.64452i | −1.05500 | − | 0.609102i | ||||
\(120\) | −1.66065 | + | 2.87632i | −0.151595 | + | 0.262571i | ||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | − | 12.3704i | − | 1.11997i | ||||||
\(123\) | −5.76211 | + | 3.32675i | −0.519552 | + | 0.299963i | ||||
\(124\) | −6.02510 | + | 3.47859i | −0.541070 | + | 0.312387i | ||||
\(125\) | − | 9.56265i | − | 0.855309i | ||||||
\(126\) | −1.76279 | − | 3.05325i | −0.157042 | − | 0.272005i | ||||
\(127\) | −0.674770 | + | 1.16874i | −0.0598762 | + | 0.103709i | −0.894410 | − | 0.447249i | \(-0.852404\pi\) |
0.834534 | + | 0.550957i | \(0.185737\pi\) | |||||||
\(128\) | 0.286642 | + | 0.165493i | 0.0253358 | + | 0.0146277i | ||||
\(129\) | −2.42054 | −0.213116 | ||||||||
\(130\) | −1.30872 | + | 4.05682i | −0.114782 | + | 0.355807i | ||||
\(131\) | 11.4747 | 1.00255 | 0.501273 | − | 0.865289i | \(-0.332865\pi\) | ||||
0.501273 | + | 0.865289i | \(0.332865\pi\) | |||||||
\(132\) | 0.700853 | + | 0.404638i | 0.0610014 | + | 0.0352192i | ||||
\(133\) | −6.44195 | + | 11.1578i | −0.558588 | + | 0.967503i | ||||
\(134\) | 7.24601 | + | 12.5505i | 0.625960 | + | 1.08419i | ||||
\(135\) | − | 1.08345i | − | 0.0932481i | ||||||
\(136\) | −10.9194 | + | 6.30432i | −0.936331 | + | 0.540591i | ||||
\(137\) | −9.09749 | + | 5.25244i | −0.777251 | + | 0.448746i | −0.835455 | − | 0.549559i | \(-0.814796\pi\) |
0.0582043 | + | 0.998305i | \(0.481463\pi\) | |||||||
\(138\) | 3.12254i | 0.265808i | ||||||||
\(139\) | 4.85985 | + | 8.41750i | 0.412207 | + | 0.713963i | 0.995131 | − | 0.0985634i | \(-0.0314247\pi\) |
−0.582924 | + | 0.812527i | \(0.698091\pi\) | |||||||
\(140\) | 1.41644 | − | 2.45335i | 0.119711 | − | 0.207346i | ||||
\(141\) | −5.05531 | − | 2.91868i | −0.425734 | − | 0.245798i | ||||
\(142\) | −0.616759 | −0.0517573 | ||||||||
\(143\) | 3.43142 | + | 1.10697i | 0.286950 | + | 0.0925691i | ||||
\(144\) | −1.72652 | −0.143877 | ||||||||
\(145\) | 4.85444 | + | 2.80271i | 0.403139 | + | 0.232752i | ||||
\(146\) | −6.93323 | + | 12.0087i | −0.573798 | + | 0.993848i | ||||
\(147\) | 1.71940 | + | 2.97810i | 0.141814 | + | 0.245629i | ||||
\(148\) | − | 7.72592i | − | 0.635067i | ||||||
\(149\) | 10.2722 | − | 5.93067i | 0.841534 | − | 0.485860i | −0.0162514 | − | 0.999868i | \(-0.505173\pi\) |
0.857785 | + | 0.514008i | \(0.171840\pi\) | |||||||
\(150\) | 3.61575 | − | 2.08755i | 0.295224 | − | 0.170448i | ||||
\(151\) | − | 22.2043i | − | 1.80696i | −0.428632 | − | 0.903479i | \(-0.641004\pi\) | ||
0.428632 | − | 0.903479i | \(-0.358996\pi\) | |||||||
\(152\) | 6.11212 | + | 10.5865i | 0.495759 | + | 0.858679i | ||||
\(153\) | 2.05655 | − | 3.56204i | 0.166262 | − | 0.287974i | ||||
\(154\) | 3.05325 | + | 1.76279i | 0.246038 | + | 0.142050i | ||||
\(155\) | −9.31418 | −0.748133 | ||||||||
\(156\) | 2.85284 | − | 0.612661i | 0.228410 | − | 0.0490521i | ||||
\(157\) | −3.02291 | −0.241255 | −0.120627 | − | 0.992698i | \(-0.538491\pi\) | ||||
−0.120627 | + | 0.992698i | \(0.538491\pi\) | |||||||
\(158\) | −1.76725 | − | 1.02032i | −0.140595 | − | 0.0811723i | ||||
\(159\) | −6.67461 | + | 11.5608i | −0.529331 | + | 0.916829i | ||||
\(160\) | −2.30069 | − | 3.98492i | −0.181886 | − | 0.315035i | ||||
\(161\) | − | 9.24545i | − | 0.728643i | ||||||
\(162\) | 0.945010 | − | 0.545602i | 0.0742470 | − | 0.0428665i | ||||
\(163\) | 10.1290 | − | 5.84800i | 0.793368 | − | 0.458051i | −0.0477791 | − | 0.998858i | \(-0.515214\pi\) |
0.841147 | + | 0.540807i | \(0.181881\pi\) | |||||||
\(164\) | − | 5.38452i | − | 0.420460i | ||||||
\(165\) | 0.541723 | + | 0.938291i | 0.0421730 | + | 0.0730459i | ||||
\(166\) | 1.30966 | − | 2.26839i | 0.101649 | − | 0.176061i | ||||
\(167\) | 18.8995 | + | 10.9116i | 1.46249 | + | 0.844368i | 0.999126 | − | 0.0418003i | \(-0.0133093\pi\) |
0.463363 | + | 0.886169i | \(0.346643\pi\) | |||||||
\(168\) | 9.90434 | 0.764136 | ||||||||
\(169\) | 11.8538 | − | 5.33746i | 0.911827 | − | 0.410574i | ||||
\(170\) | −4.86274 | −0.372955 | ||||||||
\(171\) | −3.45345 | − | 1.99385i | −0.264092 | − | 0.152473i | ||||
\(172\) | 0.979441 | − | 1.69644i | 0.0746817 | − | 0.129352i | ||||
\(173\) | −2.83167 | − | 4.90460i | −0.215288 | − | 0.372890i | 0.738074 | − | 0.674720i | \(-0.235736\pi\) |
−0.953362 | + | 0.301830i | \(0.902402\pi\) | |||||||
\(174\) | 5.64556i | 0.427989i | ||||||||
\(175\) | −10.7058 | + | 6.18098i | −0.809280 | + | 0.467238i | ||||
\(176\) | 1.49521 | − | 0.863261i | 0.112706 | − | 0.0650708i | ||||
\(177\) | − | 13.6168i | − | 1.02350i | ||||||
\(178\) | 7.66836 | + | 13.2820i | 0.574768 | + | 0.995528i | ||||
\(179\) | 0.920989 | − | 1.59520i | 0.0688379 | − | 0.119231i | −0.829552 | − | 0.558429i | \(-0.811404\pi\) |
0.898390 | + | 0.439199i | \(0.144738\pi\) | |||||||
\(180\) | 0.759336 | + | 0.438403i | 0.0565976 | + | 0.0326766i | ||||
\(181\) | 3.75761 | 0.279301 | 0.139651 | − | 0.990201i | \(-0.455402\pi\) | ||||
0.139651 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(182\) | 12.4283 | − | 2.66904i | 0.921248 | − | 0.197842i | ||||
\(183\) | −11.3365 | −0.838019 | ||||||||
\(184\) | −7.59684 | − | 4.38604i | −0.560047 | − | 0.323343i | ||||
\(185\) | 5.17167 | − | 8.95759i | 0.380229 | − | 0.658575i | ||||
\(186\) | −4.69044 | − | 8.12407i | −0.343919 | − | 0.595686i | ||||
\(187\) | 4.11309i | 0.300779i | ||||||||
\(188\) | 4.09114 | − | 2.36202i | 0.298377 | − | 0.172268i | ||||
\(189\) | −2.79805 | + | 1.61546i | −0.203528 | + | 0.117507i | ||||
\(190\) | 4.71449i | 0.342025i | ||||||||
\(191\) | −5.69417 | − | 9.86259i | −0.412015 | − | 0.713632i | 0.583095 | − | 0.812404i | \(-0.301842\pi\) |
−0.995110 | + | 0.0987726i | \(0.968508\pi\) | |||||||
\(192\) | 4.04369 | − | 7.00388i | 0.291828 | − | 0.505461i | ||||
\(193\) | 11.1931 | + | 6.46237i | 0.805700 | + | 0.465171i | 0.845461 | − | 0.534038i | \(-0.179326\pi\) |
−0.0397602 | + | 0.999209i | \(0.512659\pi\) | |||||||
\(194\) | 18.9146 | 1.35799 | ||||||||
\(195\) | 3.71775 | + | 1.19934i | 0.266234 | + | 0.0858862i | ||||
\(196\) | −2.78294 | −0.198782 | ||||||||
\(197\) | −13.8372 | − | 7.98893i | −0.985861 | − | 0.569187i | −0.0818268 | − | 0.996647i | \(-0.526075\pi\) |
−0.904035 | + | 0.427459i | \(0.859409\pi\) | |||||||
\(198\) | −0.545602 | + | 0.945010i | −0.0387742 | + | 0.0671589i | ||||
\(199\) | 2.49054 | + | 4.31374i | 0.176550 | + | 0.305793i | 0.940696 | − | 0.339249i | \(-0.110173\pi\) |
−0.764147 | + | 0.645042i | \(0.776840\pi\) | |||||||
\(200\) | 11.7290i | 0.829367i | ||||||||
\(201\) | 11.5015 | − | 6.64039i | 0.811252 | − | 0.468377i | ||||
\(202\) | −7.29574 | + | 4.21220i | −0.513326 | + | 0.296369i | ||||
\(203\) | − | 16.7158i | − | 1.17322i | ||||||
\(204\) | 1.66431 | + | 2.88267i | 0.116525 | + | 0.201827i | ||||
\(205\) | 3.60435 | − | 6.24293i | 0.251739 | − | 0.436025i | ||||
\(206\) | −8.58871 | − | 4.95869i | −0.598403 | − | 0.345488i | ||||
\(207\) | 2.86156 | 0.198892 | ||||||||
\(208\) | 1.91120 | − | 5.92442i | 0.132518 | − | 0.410785i | ||||
\(209\) | 3.98770 | 0.275835 | ||||||||
\(210\) | 3.30802 | + | 1.90989i | 0.228275 | + | 0.131795i | ||||
\(211\) | −8.53766 | + | 14.7877i | −0.587757 | + | 1.01802i | 0.406769 | + | 0.913531i | \(0.366655\pi\) |
−0.994526 | + | 0.104493i | \(0.966678\pi\) | |||||||
\(212\) | −5.40160 | − | 9.35585i | −0.370984 | − | 0.642562i | ||||
\(213\) | 0.565210i | 0.0387275i | ||||||||
\(214\) | 6.08022 | − | 3.51042i | 0.415636 | − | 0.239967i | ||||
\(215\) | 2.27117 | − | 1.31126i | 0.154892 | − | 0.0894272i | ||||
\(216\) | 3.06549i | 0.208580i | ||||||||
\(217\) | 13.8878 | + | 24.0543i | 0.942764 | + | 1.63292i | ||||
\(218\) | 4.62524 | − | 8.01115i | 0.313261 | − | 0.542584i | ||||
\(219\) | 11.0050 | + | 6.35375i | 0.743650 | + | 0.429347i | ||||
\(220\) | −0.876806 | −0.0591142 | ||||||||
\(221\) | 9.94633 | + | 10.9999i | 0.669062 | + | 0.739935i | ||||
\(222\) | 10.4174 | 0.699170 | ||||||||
\(223\) | 14.8828 | + | 8.59260i | 0.996628 | + | 0.575403i | 0.907249 | − | 0.420595i | \(-0.138178\pi\) |
0.0893788 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(224\) | −6.86084 | + | 11.8833i | −0.458409 | + | 0.793988i | ||||
\(225\) | −1.91307 | − | 3.31354i | −0.127538 | − | 0.220903i | ||||
\(226\) | − | 6.25228i | − | 0.415896i | ||||||
\(227\) | 8.31947 | − | 4.80325i | 0.552183 | − | 0.318803i | −0.197819 | − | 0.980239i | \(-0.563386\pi\) |
0.750002 | + | 0.661436i | \(0.230053\pi\) | |||||||
\(228\) | 2.79479 | − | 1.61357i | 0.185089 | − | 0.106861i | ||||
\(229\) | − | 4.61591i | − | 0.305028i | −0.988301 | − | 0.152514i | \(-0.951263\pi\) | ||
0.988301 | − | 0.152514i | \(-0.0487369\pi\) | |||||||
\(230\) | −1.69155 | − | 2.92985i | −0.111538 | − | 0.193189i | ||||
\(231\) | 1.61546 | − | 2.79805i | 0.106289 | − | 0.184098i | ||||
\(232\) | −13.7351 | − | 7.92997i | −0.901754 | − | 0.520628i | ||||
\(233\) | 1.75451 | 0.114942 | 0.0574709 | − | 0.998347i | \(-0.481696\pi\) | ||||
0.0574709 | + | 0.998347i | \(0.481696\pi\) | |||||||
\(234\) | 0.826094 | + | 3.84669i | 0.0540035 | + | 0.251466i | ||||
\(235\) | 6.32447 | 0.412563 | ||||||||
\(236\) | 9.54335 | + | 5.50985i | 0.621219 | + | 0.358661i | ||||
\(237\) | −0.935041 | + | 1.61954i | −0.0607374 | + | 0.105200i | ||||
\(238\) | 7.25053 | + | 12.5583i | 0.469982 | + | 0.814032i | ||||
\(239\) | 28.3540i | 1.83407i | 0.398807 | + | 0.917035i | \(0.369424\pi\) | ||||
−0.398807 | + | 0.917035i | \(0.630576\pi\) | |||||||
\(240\) | 1.61998 | − | 0.935296i | 0.104569 | − | 0.0603731i | ||||
\(241\) | −6.10023 | + | 3.52197i | −0.392951 | + | 0.226870i | −0.683438 | − | 0.730009i | \(-0.739516\pi\) |
0.290487 | + | 0.956879i | \(0.406183\pi\) | |||||||
\(242\) | − | 1.09120i | − | 0.0701452i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.58718 | − | 7.94523i | 0.293664 | − | 0.508641i | ||||
\(245\) | −3.22660 | − | 1.86288i | −0.206140 | − | 0.119015i | ||||
\(246\) | 7.26033 | 0.462902 | ||||||||
\(247\) | 10.6646 | − | 9.64309i | 0.678570 | − | 0.613575i | ||||
\(248\) | 26.3535 | 1.67345 | ||||||||
\(249\) | −2.07880 | − | 1.20019i | −0.131738 | − | 0.0760593i | ||||
\(250\) | −5.21740 | + | 9.03679i | −0.329977 | + | 0.571537i | ||||
\(251\) | −7.80186 | − | 13.5132i | −0.492449 | − | 0.852947i | 0.507513 | − | 0.861644i | \(-0.330565\pi\) |
−0.999962 | + | 0.00869727i | \(0.997232\pi\) | |||||||
\(252\) | − | 2.61470i | − | 0.164711i | ||||||
\(253\) | −2.47818 | + | 1.43078i | −0.155802 | + | 0.0899523i | ||||
\(254\) | 1.27533 | − | 0.736312i | 0.0800213 | − | 0.0462003i | ||||
\(255\) | 4.45631i | 0.279065i | ||||||||
\(256\) | 7.90679 | + | 13.6950i | 0.494175 | + | 0.855935i | ||||
\(257\) | −1.24846 | + | 2.16240i | −0.0778769 | + | 0.134887i | −0.902334 | − | 0.431038i | \(-0.858147\pi\) |
0.824457 | + | 0.565925i | \(0.191481\pi\) | |||||||
\(258\) | 2.28743 | + | 1.32065i | 0.142409 | + | 0.0822200i | ||||
\(259\) | −30.8446 | −1.91659 | ||||||||
\(260\) | −2.34490 | + | 2.12030i | −0.145425 | + | 0.131496i | ||||
\(261\) | 5.17370 | 0.320244 | ||||||||
\(262\) | −10.8437 | − | 6.26059i | −0.669924 | − | 0.386781i | ||||
\(263\) | 3.33075 | − | 5.76902i | 0.205383 | − | 0.355733i | −0.744872 | − | 0.667207i | \(-0.767489\pi\) |
0.950255 | + | 0.311474i | \(0.100823\pi\) | |||||||
\(264\) | −1.53275 | − | 2.65479i | −0.0943339 | − | 0.163391i | ||||
\(265\) | − | 14.4632i | − | 0.888465i | ||||||
\(266\) | 12.1754 | − | 7.02948i | 0.746523 | − | 0.431005i | ||||
\(267\) | 12.1719 | − | 7.02744i | 0.744907 | − | 0.430072i | ||||
\(268\) | 10.7478i | 0.656527i | ||||||||
\(269\) | −9.47612 | − | 16.4131i | −0.577769 | − | 1.00073i | −0.995735 | − | 0.0922627i | \(-0.970590\pi\) |
0.417966 | − | 0.908463i | \(-0.362743\pi\) | |||||||
\(270\) | −0.591129 | + | 1.02387i | −0.0359750 | + | 0.0623105i | ||||
\(271\) | −5.34468 | − | 3.08575i | −0.324666 | − | 0.187446i | 0.328804 | − | 0.944398i | \(-0.393354\pi\) |
−0.653471 | + | 0.756952i | \(0.726688\pi\) | |||||||
\(272\) | 7.10135 | 0.430582 | ||||||||
\(273\) | −2.44596 | − | 11.3895i | −0.148036 | − | 0.689327i | ||||
\(274\) | 11.4630 | 0.692502 | ||||||||
\(275\) | 3.31354 | + | 1.91307i | 0.199814 | + | 0.115363i | ||||
\(276\) | −1.15789 | + | 2.00553i | −0.0696970 | + | 0.120719i | ||||
\(277\) | −0.446788 | − | 0.773859i | −0.0268449 | − | 0.0464967i | 0.852291 | − | 0.523068i | \(-0.175213\pi\) |
−0.879136 | + | 0.476571i | \(0.841879\pi\) | |||||||
\(278\) | − | 10.6062i | − | 0.636116i | ||||||
\(279\) | −7.44506 | + | 4.29841i | −0.445724 | + | 0.257339i | ||||
\(280\) | −9.29315 | + | 5.36540i | −0.555372 | + | 0.320644i | ||||
\(281\) | 6.13506i | 0.365987i | 0.983114 | + | 0.182993i | \(0.0585787\pi\) | ||||
−0.983114 | + | 0.182993i | \(0.941421\pi\) | |||||||
\(282\) | 3.18488 | + | 5.51637i | 0.189657 | + | 0.328495i | ||||
\(283\) | −7.61927 | + | 13.1970i | −0.452918 | + | 0.784478i | −0.998566 | − | 0.0535370i | \(-0.982950\pi\) |
0.545647 | + | 0.838015i | \(0.316284\pi\) | |||||||
\(284\) | −0.396129 | − | 0.228705i | −0.0235059 | − | 0.0135712i | ||||
\(285\) | 4.32045 | 0.255921 | ||||||||
\(286\) | −2.63876 | − | 2.91828i | −0.156033 | − | 0.172562i | ||||
\(287\) | −21.4969 | −1.26892 | ||||||||
\(288\) | −3.67800 | − | 2.12350i | −0.216729 | − | 0.125128i | ||||
\(289\) | 0.0412387 | − | 0.0714275i | 0.00242580 | − | 0.00420162i | ||||
\(290\) | −3.05833 | − | 5.29718i | −0.179591 | − | 0.311061i | ||||
\(291\) | − | 17.3337i | − | 1.01612i | ||||||
\(292\) | −8.90609 | + | 5.14193i | −0.521190 | + | 0.300909i | ||||
\(293\) | −5.61984 | + | 3.24461i | −0.328314 | + | 0.189552i | −0.655092 | − | 0.755549i | \(-0.727370\pi\) |
0.326778 | + | 0.945101i | \(0.394037\pi\) | |||||||
\(294\) | − | 3.75244i | − | 0.218847i | ||||||
\(295\) | 7.37651 | + | 12.7765i | 0.429477 | + | 0.743876i | ||||
\(296\) | −14.6327 | + | 25.3445i | −0.850507 | + | 1.47312i | ||||
\(297\) | 0.866025 | + | 0.500000i | 0.0502519 | + | 0.0290129i | ||||
\(298\) | −12.9431 | −0.749776 | ||||||||
\(299\) | −3.16764 | + | 9.81920i | −0.183190 | + | 0.567859i | ||||
\(300\) | 3.09641 | 0.178771 | ||||||||
\(301\) | −6.77280 | − | 3.91028i | −0.390377 | − | 0.225385i | ||||
\(302\) | −12.1147 | + | 20.9833i | −0.697122 | + | 1.20745i | ||||
\(303\) | 3.86014 | + | 6.68596i | 0.221759 | + | 0.384098i | ||||
\(304\) | − | 6.88485i | − | 0.394873i | ||||||
\(305\) | 10.6370 | − | 6.14125i | 0.609070 | − | 0.351647i | ||||
\(306\) | −3.88691 | + | 2.24411i | −0.222200 | + | 0.128287i | ||||
\(307\) | − | 13.3662i | − | 0.762850i | −0.924400 | − | 0.381425i | \(-0.875433\pi\) | ||
0.924400 | − | 0.381425i | \(-0.124567\pi\) | |||||||
\(308\) | 1.30735 | + | 2.26440i | 0.0744932 | + | 0.129026i | ||||
\(309\) | −4.54424 | + | 7.87086i | −0.258513 | + | 0.447757i | ||||
\(310\) | 8.80199 | + | 5.08183i | 0.499919 | + | 0.288629i | ||||
\(311\) | 21.8817 | 1.24080 | 0.620398 | − | 0.784287i | \(-0.286971\pi\) | ||||
0.620398 | + | 0.784287i | \(0.286971\pi\) | |||||||
\(312\) | −10.5190 | − | 3.39339i | −0.595520 | − | 0.192113i | ||||
\(313\) | −18.9378 | −1.07043 | −0.535214 | − | 0.844717i | \(-0.679769\pi\) | ||||
−0.535214 | + | 0.844717i | \(0.679769\pi\) | |||||||
\(314\) | 2.85668 | + | 1.64931i | 0.161212 | + | 0.0930757i | ||||
\(315\) | 1.75026 | − | 3.03154i | 0.0986159 | − | 0.170808i | ||||
\(316\) | −0.756706 | − | 1.31065i | −0.0425680 | − | 0.0737300i | ||||
\(317\) | − | 15.1134i | − | 0.848852i | −0.905463 | − | 0.424426i | \(-0.860476\pi\) | ||
0.905463 | − | 0.424426i | \(-0.139524\pi\) | |||||||
\(318\) | 12.6152 | − | 7.28336i | 0.707423 | − | 0.408431i | ||||
\(319\) | −4.48056 | + | 2.58685i | −0.250863 | + | 0.144836i | ||||
\(320\) | 8.76223i | 0.489824i | ||||||||
\(321\) | −3.21702 | − | 5.57204i | −0.179556 | − | 0.311001i | ||||
\(322\) | −5.04433 | + | 8.73704i | −0.281110 | + | 0.486896i | ||||
\(323\) | 14.2043 | + | 8.20088i | 0.790351 | + | 0.456309i | ||||
\(324\) | 0.809275 | 0.0449597 | ||||||||
\(325\) | 13.4878 | − | 2.89658i | 0.748171 | − | 0.160673i | ||||
\(326\) | −12.7627 | −0.706862 | ||||||||
\(327\) | −7.34157 | − | 4.23866i | −0.405990 | − | 0.234398i | ||||
\(328\) | −10.1981 | + | 17.6637i | −0.563098 | + | 0.975314i | ||||
\(329\) | −9.43002 | − | 16.3333i | −0.519894 | − | 0.900482i | ||||
\(330\) | − | 1.18226i | − | 0.0650812i | ||||||
\(331\) | −10.3752 | + | 5.99012i | −0.570272 | + | 0.329247i | −0.757258 | − | 0.653116i | \(-0.773461\pi\) |
0.186986 | + | 0.982363i | \(0.440128\pi\) | |||||||
\(332\) | 1.68232 | − | 0.971288i | 0.0923293 | − | 0.0533064i | ||||
\(333\) | − | 9.54671i | − | 0.523157i | ||||||
\(334\) | −11.9068 | − | 20.6232i | −0.651512 | − | 1.12845i | ||||
\(335\) | −7.19450 | + | 12.4612i | −0.393077 | + | 0.680830i | ||||
\(336\) | −4.83090 | − | 2.78912i | −0.263547 | − | 0.152159i | ||||
\(337\) | 1.33145 | 0.0725285 | 0.0362643 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362643 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(338\) | −14.1140 | − | 1.42347i | −0.767703 | − | 0.0774267i | ||||
\(339\) | −5.72972 | −0.311195 | ||||||||
\(340\) | −3.12322 | − | 1.80319i | −0.169380 | − | 0.0977917i | ||||
\(341\) | 4.29841 | − | 7.44506i | 0.232772 | − | 0.403173i | ||||
\(342\) | 2.17569 | + | 3.76841i | 0.117648 | + | 0.203772i | ||||
\(343\) | − | 11.5059i | − | 0.621261i | ||||||
\(344\) | −6.42603 | + | 3.71007i | −0.346468 | + | 0.200033i | ||||
\(345\) | −2.68497 | + | 1.55017i | −0.144554 | + | 0.0834584i | ||||
\(346\) | 6.17986i | 0.332231i | ||||||||
\(347\) | 17.7364 | + | 30.7204i | 0.952141 | + | 1.64916i | 0.740779 | + | 0.671749i | \(0.234457\pi\) |
0.211363 | + | 0.977408i | \(0.432210\pi\) | |||||||
\(348\) | −2.09347 | + | 3.62600i | −0.112222 | + | 0.194374i | ||||
\(349\) | −4.49438 | − | 2.59483i | −0.240579 | − | 0.138898i | 0.374864 | − | 0.927080i | \(-0.377689\pi\) |
−0.615443 | + | 0.788182i | \(0.711023\pi\) | |||||||
\(350\) | 13.4894 | 0.721039 | ||||||||
\(351\) | 3.52518 | − | 0.757049i | 0.188160 | − | 0.0404083i | ||||
\(352\) | 4.24699 | 0.226366 | ||||||||
\(353\) | 6.65401 | + | 3.84169i | 0.354157 | + | 0.204473i | 0.666515 | − | 0.745492i | \(-0.267785\pi\) |
−0.312358 | + | 0.949965i | \(0.601119\pi\) | |||||||
\(354\) | −7.42933 | + | 12.8680i | −0.394864 | + | 0.683925i | ||||
\(355\) | −0.306187 | − | 0.530331i | −0.0162507 | − | 0.0281471i | ||||
\(356\) | 11.3743i | 0.602835i | ||||||||
\(357\) | 11.5087 | − | 6.64452i | 0.609102 | − | 0.351665i | ||||
\(358\) | −1.74069 | + | 1.00499i | −0.0919981 | + | 0.0531151i | ||||
\(359\) | − | 3.37413i | − | 0.178080i | −0.996028 | − | 0.0890400i | \(-0.971620\pi\) | ||
0.996028 | − | 0.0890400i | \(-0.0283799\pi\) | |||||||
\(360\) | −1.66065 | − | 2.87632i | −0.0875237 | − | 0.151595i | ||||
\(361\) | −1.54914 | + | 2.68319i | −0.0815338 | + | 0.141221i | ||||
\(362\) | −3.55098 | − | 2.05016i | −0.186635 | − | 0.107754i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 8.97213 | + | 2.89438i | 0.470267 | + | 0.151707i | ||||
\(365\) | −13.7679 | −0.720644 | ||||||||
\(366\) | 10.7131 | + | 6.18522i | 0.559984 | + | 0.323307i | ||||
\(367\) | 13.1719 | − | 22.8143i | 0.687566 | − | 1.19090i | −0.285058 | − | 0.958510i | \(-0.592013\pi\) |
0.972623 | − | 0.232388i | \(-0.0746539\pi\) | |||||||
\(368\) | 2.47027 | + | 4.27864i | 0.128772 | + | 0.223039i | ||||
\(369\) | − | 6.65351i | − | 0.346368i | ||||||
\(370\) | −9.77455 | + | 5.64334i | −0.508155 | + | 0.293383i | ||||
\(371\) | −37.3519 | + | 21.5651i | −1.93921 | + | 1.11960i | ||||
\(372\) | − | 6.95719i | − | 0.360713i | ||||||
\(373\) | −7.68103 | − | 13.3039i | −0.397708 | − | 0.688851i | 0.595734 | − | 0.803182i | \(-0.296861\pi\) |
−0.993443 | + | 0.114330i | \(0.963528\pi\) | |||||||
\(374\) | 2.24411 | − | 3.88691i | 0.116040 | − | 0.200987i | ||||
\(375\) | 8.28149 | + | 4.78132i | 0.427655 | + | 0.246906i | ||||
\(376\) | −17.8944 | −0.922833 | ||||||||
\(377\) | −5.72711 | + | 17.7531i | −0.294961 | + | 0.914333i | ||||
\(378\) | 3.52558 | 0.181336 | ||||||||
\(379\) | −12.1978 | − | 7.04243i | −0.626561 | − | 0.361745i | 0.152858 | − | 0.988248i | \(-0.451152\pi\) |
−0.779419 | + | 0.626503i | \(0.784486\pi\) | |||||||
\(380\) | −1.74822 | + | 3.02800i | −0.0896816 | + | 0.155333i | ||||
\(381\) | −0.674770 | − | 1.16874i | −0.0345695 | − | 0.0598762i | ||||
\(382\) | 12.4270i | 0.635820i | ||||||||
\(383\) | 11.6525 | − | 6.72757i | 0.595414 | − | 0.343763i | −0.171821 | − | 0.985128i | \(-0.554965\pi\) |
0.767235 | + | 0.641366i | \(0.221632\pi\) | |||||||
\(384\) | −0.286642 | + | 0.165493i | −0.0146277 | + | 0.00844528i | ||||
\(385\) | 3.50052i | 0.178403i | ||||||||
\(386\) | −7.05176 | − | 12.2140i | −0.358925 | − | 0.621676i | ||||
\(387\) | 1.21027 | − | 2.09625i | 0.0615214 | − | 0.106558i | ||||
\(388\) | 12.1484 | + | 7.01388i | 0.616742 | + | 0.356076i | ||||
\(389\) | −5.93346 | −0.300838 | −0.150419 | − | 0.988622i | \(-0.548062\pi\) | ||||
−0.150419 | + | 0.988622i | \(0.548062\pi\) | |||||||
\(390\) | −2.85895 | − | 3.16180i | −0.144769 | − | 0.160104i | ||||
\(391\) | −11.7698 | −0.595227 | ||||||||
\(392\) | 9.12932 | + | 5.27082i | 0.461100 | + | 0.266216i | ||||
\(393\) | −5.73733 | + | 9.93734i | −0.289410 | + | 0.501273i | ||||
\(394\) | 8.71754 | + | 15.0992i | 0.439183 | + | 0.760688i | ||||
\(395\) | − | 2.02613i | − | 0.101946i | ||||||
\(396\) | −0.700853 | + | 0.404638i | −0.0352192 | + | 0.0203338i | ||||
\(397\) | 28.0879 | − | 16.2165i | 1.40969 | − | 0.813884i | 0.414331 | − | 0.910126i | \(-0.364016\pi\) |
0.995358 | + | 0.0962421i | \(0.0306823\pi\) | |||||||
\(398\) | − | 5.43537i | − | 0.272450i | ||||||
\(399\) | −6.44195 | − | 11.1578i | −0.322501 | − | 0.558588i | ||||
\(400\) | 3.30296 | − | 5.72090i | 0.165148 | − | 0.286045i | ||||
\(401\) | −17.2287 | − | 9.94698i | −0.860359 | − | 0.496729i | 0.00377329 | − | 0.999993i | \(-0.498799\pi\) |
−0.864133 | + | 0.503264i | \(0.832132\pi\) | |||||||
\(402\) | −14.4920 | −0.722797 | ||||||||
\(403\) | −6.50821 | − | 30.3053i | −0.324197 | − | 1.50961i | ||||
\(404\) | −6.24783 | −0.310841 | ||||||||
\(405\) | 0.938291 | + | 0.541723i | 0.0466241 | + | 0.0269184i | ||||
\(406\) | −9.12016 | + | 15.7966i | −0.452626 | + | 0.783971i | ||||
\(407\) | 4.77336 | + | 8.26769i | 0.236606 | + | 0.409814i | ||||
\(408\) | − | 12.6086i | − | 0.624221i | ||||||
\(409\) | 16.3827 | − | 9.45857i | 0.810073 | − | 0.467696i | −0.0369081 | − | 0.999319i | \(-0.511751\pi\) |
0.846981 | + | 0.531623i | \(0.178418\pi\) | |||||||
\(410\) | −6.81230 | + | 3.93308i | −0.336436 | + | 0.194241i | ||||
\(411\) | − | 10.5049i | − | 0.518167i | ||||||
\(412\) | −3.67754 | − | 6.36969i | −0.181180 | − | 0.313812i | ||||
\(413\) | 21.9973 | − | 38.1004i | 1.08242 | − | 1.87480i | ||||
\(414\) | −2.70420 | − | 1.56127i | −0.132904 | − | 0.0767323i | ||||
\(415\) | 2.60069 | 0.127663 | ||||||||
\(416\) | 11.3580 | − | 10.2701i | 0.556873 | − | 0.503535i | ||||
\(417\) | −9.71970 | −0.475976 | ||||||||
\(418\) | −3.76841 | − | 2.17569i | −0.184319 | − | 0.106417i | ||||
\(419\) | 13.1214 | − | 22.7270i | 0.641023 | − | 1.11028i | −0.344181 | − | 0.938903i | \(-0.611844\pi\) |
0.985205 | − | 0.171382i | \(-0.0548232\pi\) | |||||||
\(420\) | 1.41644 | + | 2.45335i | 0.0691153 | + | 0.119711i | ||||
\(421\) | − | 2.62866i | − | 0.128113i | −0.997946 | − | 0.0640565i | \(-0.979596\pi\) | ||
0.997946 | − | 0.0640565i | \(-0.0204038\pi\) | |||||||
\(422\) | 16.1363 | − | 9.31632i | 0.785505 | − | 0.453511i | ||||
\(423\) | 5.05531 | − | 2.91868i | 0.245798 | − | 0.141911i | ||||
\(424\) | 40.9219i | 1.98734i | ||||||||
\(425\) | 7.86865 | + | 13.6289i | 0.381685 | + | 0.661098i | ||||
\(426\) | 0.308379 | − | 0.534129i | 0.0149410 | − | 0.0258786i | ||||
\(427\) | −31.7202 | − | 18.3137i | −1.53505 | − | 0.886260i | ||||
\(428\) | 5.20690 | 0.251685 | ||||||||
\(429\) | −2.67437 | + | 2.41821i | −0.129120 | + | 0.116752i | ||||
\(430\) | −2.86170 | −0.138004 | ||||||||
\(431\) | −25.4067 | − | 14.6686i | −1.22380 | − | 0.706559i | −0.258072 | − | 0.966126i | \(-0.583087\pi\) |
−0.965725 | + | 0.259566i | \(0.916420\pi\) | |||||||
\(432\) | 0.863261 | − | 1.49521i | 0.0415337 | − | 0.0719384i | ||||
\(433\) | 7.62347 | + | 13.2042i | 0.366361 | + | 0.634556i | 0.988994 | − | 0.147959i | \(-0.0472703\pi\) |
−0.622633 | + | 0.782514i | \(0.713937\pi\) | |||||||
\(434\) | − | 30.3088i | − | 1.45487i | ||||||
\(435\) | −4.85444 | + | 2.80271i | −0.232752 | + | 0.134380i | ||||
\(436\) | 5.94136 | − | 3.43024i | 0.284539 | − | 0.164279i | ||||
\(437\) | 11.4110i | 0.545863i | ||||||||
\(438\) | −6.93323 | − | 12.0087i | −0.331283 | − | 0.573798i | ||||
\(439\) | −12.4511 | + | 21.5659i | −0.594258 | + | 1.02928i | 0.399394 | + | 0.916780i | \(0.369221\pi\) |
−0.993651 | + | 0.112505i | \(0.964113\pi\) | |||||||
\(440\) | 2.87632 | + | 1.66065i | 0.137123 | + | 0.0791682i | ||||
\(441\) | −3.43881 | −0.163753 | ||||||||
\(442\) | −3.39780 | − | 15.8218i | −0.161617 | − | 0.752565i | ||||
\(443\) | −18.5762 | −0.882580 | −0.441290 | − | 0.897364i | \(-0.645479\pi\) | ||||
−0.441290 | + | 0.897364i | \(0.645479\pi\) | |||||||
\(444\) | 6.69084 | + | 3.86296i | 0.317533 | + | 0.183328i | ||||
\(445\) | −7.61384 | + | 13.1876i | −0.360931 | + | 0.625151i | ||||
\(446\) | −9.37628 | − | 16.2402i | −0.443979 | − | 0.768995i | ||||
\(447\) | 11.8613i | 0.561023i | ||||||||
\(448\) | 22.6289 | − | 13.0648i | 1.06912 | − | 0.617254i | ||||
\(449\) | −0.904836 | + | 0.522408i | −0.0427019 | + | 0.0246539i | −0.521199 | − | 0.853435i | \(-0.674515\pi\) |
0.478497 | + | 0.878089i | \(0.341182\pi\) | |||||||
\(450\) | 4.17510i | 0.196816i | ||||||||
\(451\) | 3.32675 | + | 5.76211i | 0.156651 | + | 0.271327i | ||||
\(452\) | 2.31846 | − | 4.01569i | 0.109051 | − | 0.188882i | ||||
\(453\) | 19.2295 | + | 11.1021i | 0.903479 | + | 0.521624i | ||||
\(454\) | −10.4826 | −0.491975 | ||||||||
\(455\) | 8.46500 | + | 9.36168i | 0.396845 | + | 0.438882i | ||||
\(456\) | −12.2242 | −0.572453 | ||||||||
\(457\) | −22.6264 | − | 13.0634i | −1.05842 | − | 0.611079i | −0.133425 | − | 0.991059i | \(-0.542597\pi\) |
−0.924995 | + | 0.379980i | \(0.875931\pi\) | |||||||
\(458\) | −2.51845 | + | 4.36208i | −0.117679 | + | 0.203826i | ||||
\(459\) | 2.05655 | + | 3.56204i | 0.0959913 | + | 0.166262i | ||||
\(460\) | − | 2.50903i | − | 0.116984i | ||||||
\(461\) | −11.5901 | + | 6.69153i | −0.539804 | + | 0.311656i | −0.744999 | − | 0.667065i | \(-0.767550\pi\) |
0.205196 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(462\) | −3.05325 | + | 1.76279i | −0.142050 | + | 0.0820125i | ||||
\(463\) | 23.7960i | 1.10589i | 0.833216 | + | 0.552947i | \(0.186497\pi\) | ||||
−0.833216 | + | 0.552947i | \(0.813503\pi\) | |||||||
\(464\) | 4.46626 | + | 7.73578i | 0.207341 | + | 0.359125i | ||||
\(465\) | 4.65709 | − | 8.06631i | 0.215967 | − | 0.374066i | ||||
\(466\) | −1.65803 | − | 0.957263i | −0.0768067 | − | 0.0443444i | ||||
\(467\) | −24.1995 | −1.11982 | −0.559911 | − | 0.828553i | \(-0.689165\pi\) | ||||
−0.559911 | + | 0.828553i | \(0.689165\pi\) | |||||||
\(468\) | −0.895840 | + | 2.77696i | −0.0414102 | + | 0.128365i | ||||
\(469\) | 42.9091 | 1.98136 | ||||||||
\(470\) | −5.97668 | − | 3.45064i | −0.275684 | − | 0.159166i | ||||
\(471\) | 1.51146 | − | 2.61792i | 0.0696442 | − | 0.120627i | ||||
\(472\) | −20.8710 | − | 36.1497i | −0.960667 | − | 1.66392i | ||||
\(473\) | 2.42054i | 0.111296i | ||||||||
\(474\) | 1.76725 | − | 1.02032i | 0.0811723 | − | 0.0468648i | ||||
\(475\) | 13.2134 | − | 7.62875i | 0.606272 | − | 0.350031i | ||||
\(476\) | 10.7545i | 0.492932i | ||||||||
\(477\) | −6.67461 | − | 11.5608i | −0.305610 | − | 0.529331i | ||||
\(478\) | 15.4700 | − | 26.7948i | 0.707582 | − | 1.22557i | ||||
\(479\) | −5.08360 | − | 2.93502i | −0.232276 | − | 0.134104i | 0.379346 | − | 0.925255i | \(-0.376149\pi\) |
−0.611621 | + | 0.791151i | \(0.709482\pi\) | |||||||
\(480\) | 4.60139 | 0.210024 | ||||||||
\(481\) | 32.7588 | + | 10.5679i | 1.49367 | + | 0.481854i | ||||
\(482\) | 7.68637 | 0.350105 | ||||||||
\(483\) | 8.00679 | + | 4.62272i | 0.364322 | + | 0.210341i | ||||
\(484\) | 0.404638 | − | 0.700853i | 0.0183926 | − | 0.0318570i | ||||
\(485\) | 9.39007 | + | 16.2641i | 0.426381 | + | 0.738514i | ||||
\(486\) | 1.09120i | 0.0494980i | ||||||||
\(487\) | 21.1621 | − | 12.2179i | 0.958945 | − | 0.553647i | 0.0630971 | − | 0.998007i | \(-0.479902\pi\) |
0.895848 | + | 0.444360i | \(0.146569\pi\) | |||||||
\(488\) | −30.0961 | + | 17.3760i | −1.36239 | + | 0.786574i | ||||
\(489\) | 11.6960i | 0.528912i | ||||||||
\(490\) | 2.03278 | + | 3.52088i | 0.0918317 | + | 0.159057i | ||||
\(491\) | −5.95863 | + | 10.3206i | −0.268909 | + | 0.465764i | −0.968580 | − | 0.248701i | \(-0.919996\pi\) |
0.699671 | + | 0.714465i | \(0.253330\pi\) | |||||||
\(492\) | 4.66313 | + | 2.69226i | 0.210230 | + | 0.121376i | ||||
\(493\) | −21.2799 | −0.958399 | ||||||||
\(494\) | −15.3394 | + | 3.29421i | −0.690153 | + | 0.148214i | ||||
\(495\) | −1.08345 | −0.0486972 | ||||||||
\(496\) | −12.8541 | − | 7.42130i | −0.577164 | − | 0.333226i | ||||
\(497\) | −0.913072 | + | 1.58149i | −0.0409569 | + | 0.0709394i | ||||
\(498\) | 1.30966 | + | 2.26839i | 0.0586871 | + | 0.101649i | ||||
\(499\) | − | 17.6126i | − | 0.788446i | −0.919015 | − | 0.394223i | \(-0.871014\pi\) | ||
0.919015 | − | 0.394223i | \(-0.128986\pi\) | |||||||
\(500\) | −6.70201 | + | 3.86941i | −0.299723 | + | 0.173045i | ||||
\(501\) | −18.8995 | + | 10.9116i | −0.844368 | + | 0.487496i | ||||
\(502\) | 17.0268i | 0.759945i | ||||||||
\(503\) | −6.91415 | − | 11.9757i | −0.308287 | − | 0.533968i | 0.669701 | − | 0.742631i | \(-0.266422\pi\) |
−0.977988 | + | 0.208663i | \(0.933089\pi\) | |||||||
\(504\) | −4.95217 | + | 8.57741i | −0.220587 | + | 0.382068i | ||||
\(505\) | −7.24387 | − | 4.18225i | −0.322348 | − | 0.186108i | ||||
\(506\) | 3.12254 | 0.138814 | ||||||||
\(507\) | −1.30450 | + | 12.9344i | −0.0579348 | + | 0.574436i | ||||
\(508\) | 1.09215 | 0.0484563 | ||||||||
\(509\) | −15.9091 | − | 9.18515i | −0.705160 | − | 0.407124i | 0.104106 | − | 0.994566i | \(-0.466802\pi\) |
−0.809266 | + | 0.587442i | \(0.800135\pi\) | |||||||
\(510\) | 2.43137 | − | 4.21126i | 0.107663 | − | 0.186478i | ||||
\(511\) | 20.5284 | + | 35.5563i | 0.908124 | + | 1.57292i | ||||
\(512\) | − | 17.9178i | − | 0.791863i | ||||||
\(513\) | 3.45345 | − | 1.99385i | 0.152473 | − | 0.0880305i | ||||
\(514\) | 2.35962 | − | 1.36233i | 0.104078 | − | 0.0600896i | ||||
\(515\) | − | 9.84687i | − | 0.433905i | ||||||
\(516\) | 0.979441 | + | 1.69644i | 0.0431175 | + | 0.0746817i | ||||
\(517\) | −2.91868 | + | 5.05531i | −0.128364 | + | 0.222332i | ||||
\(518\) | 29.1485 | + | 16.8289i | 1.28071 | + | 0.739418i | ||||
\(519\) | 5.66334 | 0.248593 | ||||||||
\(520\) | 11.7081 | − | 2.51438i | 0.513436 | − | 0.110263i | ||||
\(521\) | 29.1227 | 1.27589 | 0.637945 | − | 0.770082i | \(-0.279785\pi\) | ||||
0.637945 | + | 0.770082i | \(0.279785\pi\) | |||||||
\(522\) | −4.88920 | − | 2.82278i | −0.213994 | − | 0.123550i | ||||
\(523\) | −7.21022 | + | 12.4885i | −0.315281 | + | 0.546082i | −0.979497 | − | 0.201458i | \(-0.935432\pi\) |
0.664216 | + | 0.747540i | \(0.268765\pi\) | |||||||
\(524\) | −4.64308 | − | 8.04205i | −0.202834 | − | 0.351318i | ||||
\(525\) | − | 12.3620i | − | 0.539520i | ||||||
\(526\) | −6.29518 | + | 3.63452i | −0.274483 | + | 0.158473i | ||||
\(527\) | 30.6222 | − | 17.6797i | 1.33392 | − | 0.770142i | ||||
\(528\) | 1.72652i | 0.0751372i | ||||||||
\(529\) | 7.40574 | + | 12.8271i | 0.321989 | + | 0.557701i | ||||
\(530\) | −7.89112 | + | 13.6678i | −0.342768 | + | 0.593692i | ||||
\(531\) | 11.7925 | + | 6.80838i | 0.511749 | + | 0.295459i | ||||
\(532\) | 10.4266 | 0.452052 | ||||||||
\(533\) | 22.8310 | + | 7.36520i | 0.988919 | + | 0.319022i | ||||
\(534\) | −15.3367 | −0.663685 | ||||||||
\(535\) | 6.03700 | + | 3.48546i | 0.261002 | + | 0.150690i | ||||
\(536\) | 20.3560 | − | 35.2577i | 0.879247 | − | 1.52290i | ||||
\(537\) | 0.920989 | + | 1.59520i | 0.0397436 | + | 0.0688379i | ||||
\(538\) | 20.6807i | 0.891610i | ||||||||
\(539\) | 2.97810 | − | 1.71940i | 0.128276 | − | 0.0740600i | ||||
\(540\) | −0.759336 | + | 0.438403i | −0.0326766 | + | 0.0188659i | ||||
\(541\) | − | 14.9509i | − | 0.642789i | −0.946945 | − | 0.321395i | \(-0.895848\pi\) | ||
0.946945 | − | 0.321395i | \(-0.104152\pi\) | |||||||
\(542\) | 3.36718 | + | 5.83213i | 0.144633 | + | 0.250512i | ||||
\(543\) | −1.87881 | + | 3.25419i | −0.0806273 | + | 0.139651i | ||||
\(544\) | 15.1280 | + | 8.73414i | 0.648606 | + | 0.374473i | ||||
\(545\) | 9.18471 | 0.393430 | ||||||||
\(546\) | −3.90270 | + | 12.0978i | −0.167020 | + | 0.517736i | ||||
\(547\) | −27.9053 | −1.19314 | −0.596572 | − | 0.802560i | \(-0.703471\pi\) | ||||
−0.596572 | + | 0.802560i | \(0.703471\pi\) | |||||||
\(548\) | 7.36237 | + | 4.25067i | 0.314505 | + | 0.181580i | ||||
\(549\) | 5.66826 | − | 9.81771i | 0.241915 | − | 0.419010i | ||||
\(550\) | −2.08755 | − | 3.61575i | −0.0890135 | − | 0.154176i | ||||
\(551\) | 20.6311i | 0.878916i | ||||||||
\(552\) | 7.59684 | − | 4.38604i | 0.323343 | − | 0.186682i | ||||
\(553\) | −5.23259 | + | 3.02104i | −0.222512 | + | 0.128468i | ||||
\(554\) | 0.975073i | 0.0414269i | ||||||||
\(555\) | 5.17167 | + | 8.95759i | 0.219525 | + | 0.380229i | ||||
\(556\) | 3.93296 | − | 6.81208i | 0.166794 | − | 0.288897i | ||||
\(557\) | −28.0832 | − | 16.2138i | −1.18992 | − | 0.687002i | −0.231633 | − | 0.972803i | \(-0.574407\pi\) |
−0.958289 | + | 0.285801i | \(0.907740\pi\) | |||||||
\(558\) | 9.38087 | 0.397124 | ||||||||
\(559\) | 5.85337 | + | 6.47341i | 0.247571 | + | 0.273796i | ||||
\(560\) | 6.04372 | 0.255394 | ||||||||
\(561\) | −3.56204 | − | 2.05655i | −0.150390 | − | 0.0868274i | ||||
\(562\) | 3.34730 | − | 5.79769i | 0.141197 | − | 0.244561i | ||||
\(563\) | −10.0899 | − | 17.4762i | −0.425238 | − | 0.736534i | 0.571205 | − | 0.820808i | \(-0.306476\pi\) |
−0.996443 | + | 0.0842739i | \(0.973143\pi\) | |||||||
\(564\) | 4.72404i | 0.198918i | ||||||||
\(565\) | 5.37614 | − | 3.10392i | 0.226176 | − | 0.130583i | ||||
\(566\) | 14.4006 | − | 8.31417i | 0.605301 | − | 0.349471i | ||||
\(567\) | − | 3.23091i | − | 0.135686i | ||||||
\(568\) | 0.866323 | + | 1.50052i | 0.0363501 | + | 0.0629602i | ||||
\(569\) | −9.12870 | + | 15.8114i | −0.382695 | + | 0.662848i | −0.991447 | − | 0.130514i | \(-0.958337\pi\) |
0.608751 | + | 0.793361i | \(0.291671\pi\) | |||||||
\(570\) | −4.08287 | − | 2.35724i | −0.171012 | − | 0.0987341i | ||||
\(571\) | 2.44991 | 0.102525 | 0.0512627 | − | 0.998685i | \(-0.483675\pi\) | ||||
0.0512627 | + | 0.998685i | \(0.483675\pi\) | |||||||
\(572\) | −0.612661 | − | 2.85284i | −0.0256166 | − | 0.119283i | ||||
\(573\) | 11.3883 | 0.475754 | ||||||||
\(574\) | 20.3148 | + | 11.7288i | 0.847923 | + | 0.489549i | ||||
\(575\) | −5.47437 | + | 9.48189i | −0.228297 | + | 0.395422i | ||||
\(576\) | 4.04369 | + | 7.00388i | 0.168487 | + | 0.291828i | ||||
\(577\) | 20.4700i | 0.852176i | 0.904682 | + | 0.426088i | \(0.140109\pi\) | ||||
−0.904682 | + | 0.426088i | \(0.859891\pi\) | |||||||
\(578\) | −0.0779419 | + | 0.0449998i | −0.00324195 | + | 0.00187174i | ||||
\(579\) | −11.1931 | + | 6.46237i | −0.465171 | + | 0.268567i | ||||
\(580\) | − | 4.53633i | − | 0.188361i | ||||||
\(581\) | −3.87773 | − | 6.71642i | −0.160875 | − | 0.278644i | ||||
\(582\) | −9.45731 | + | 16.3805i | −0.392018 | + | 0.678995i | ||||
\(583\) | 11.5608 | + | 6.67461i | 0.478798 | + | 0.276434i | ||||
\(584\) | 38.9547 | 1.61196 | ||||||||
\(585\) | −2.89753 | + | 2.62000i | −0.119798 | + | 0.108324i | ||||
\(586\) | 7.08107 | 0.292516 | ||||||||
\(587\) | −22.3926 | − | 12.9284i | −0.924240 | − | 0.533610i | −0.0392548 | − | 0.999229i | \(-0.512498\pi\) |
−0.884985 | + | 0.465619i | \(0.845832\pi\) | |||||||
\(588\) | 1.39147 | − | 2.41010i | 0.0573833 | − | 0.0993908i | ||||
\(589\) | −17.1407 | − | 29.6886i | −0.706272 | − | 1.22330i | ||||
\(590\) | − | 16.0985i | − | 0.662766i | ||||||
\(591\) | 13.8372 | − | 7.98893i | 0.569187 | − | 0.328620i | ||||
\(592\) | 14.2744 | − | 8.24131i | 0.586673 | − | 0.338716i | ||||
\(593\) | 3.99700i | 0.164137i | 0.996627 | + | 0.0820686i | \(0.0261527\pi\) | ||||
−0.996627 | + | 0.0820686i | \(0.973847\pi\) | |||||||
\(594\) | −0.545602 | − | 0.945010i | −0.0223863 | − | 0.0387742i | ||||
\(595\) | −7.19898 | + | 12.4690i | −0.295129 | + | 0.511179i | ||||
\(596\) | −8.31306 | − | 4.79955i | −0.340516 | − | 0.196597i | ||||
\(597\) | −4.98108 | −0.203862 | ||||||||
\(598\) | 8.35083 | − | 7.55097i | 0.341491 | − | 0.308782i | ||||
\(599\) | −41.2173 | −1.68409 | −0.842047 | − | 0.539404i | \(-0.818650\pi\) | ||||
−0.842047 | + | 0.539404i | \(0.818650\pi\) | |||||||
\(600\) | −10.1576 | − | 5.86451i | −0.414683 | − | 0.239418i | ||||
\(601\) | 17.1849 | − | 29.7652i | 0.700988 | − | 1.21415i | −0.267131 | − | 0.963660i | \(-0.586076\pi\) |
0.968120 | − | 0.250488i | \(-0.0805909\pi\) | |||||||
\(602\) | 4.26691 | + | 7.39050i | 0.173906 | + | 0.301214i | ||||
\(603\) | 13.2808i | 0.540835i | ||||||||
\(604\) | −15.5619 | + | 8.98469i | −0.633206 | + | 0.365582i | ||||
\(605\) | 0.938291 | − | 0.541723i | 0.0381470 | − | 0.0220242i | ||||
\(606\) | − | 8.42439i | − | 0.342218i | ||||||
\(607\) | 22.0492 | + | 38.1904i | 0.894951 | + | 1.55010i | 0.833865 | + | 0.551968i | \(0.186123\pi\) |
0.0610857 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(608\) | 8.46786 | − | 14.6668i | 0.343417 | − | 0.594816i | ||||
\(609\) | 14.4763 | + | 8.35789i | 0.586609 | + | 0.338679i | ||||
\(610\) | −13.4027 | −0.542659 | ||||||||
\(611\) | 4.41917 | + | 20.5778i | 0.178781 | + | 0.832487i | ||||
\(612\) | −3.32862 | −0.134552 | ||||||||
\(613\) | −17.4807 | − | 10.0925i | −0.706039 | − | 0.407632i | 0.103554 | − | 0.994624i | \(-0.466979\pi\) |
−0.809593 | + | 0.586992i | \(0.800312\pi\) | |||||||
\(614\) | −7.29263 | + | 12.6312i | −0.294307 | + | 0.509754i | ||||
\(615\) | 3.60435 | + | 6.24293i | 0.145342 | + | 0.251739i | ||||
\(616\) | − | 9.90434i | − | 0.399057i | ||||||
\(617\) | −21.0976 | + | 12.1807i | −0.849359 | + | 0.490377i | −0.860434 | − | 0.509561i | \(-0.829808\pi\) |
0.0110758 | + | 0.999939i | \(0.496474\pi\) | |||||||
\(618\) | 8.58871 | − | 4.95869i | 0.345488 | − | 0.199468i | ||||
\(619\) | 1.80436i | 0.0725232i | 0.999342 | + | 0.0362616i | \(0.0115450\pi\) | ||||
−0.999342 | + | 0.0362616i | \(0.988455\pi\) | |||||||
\(620\) | 3.76887 | + | 6.52787i | 0.151361 | + | 0.262166i | ||||
\(621\) | −1.43078 | + | 2.47818i | −0.0574152 | + | 0.0994460i | ||||
\(622\) | −20.6784 | − | 11.9387i | −0.829128 | − | 0.478697i | ||||
\(623\) | 45.4101 | 1.81932 | ||||||||
\(624\) | 4.17510 | + | 4.61736i | 0.167138 | + | 0.184842i | ||||
\(625\) | 8.77013 | 0.350805 | ||||||||
\(626\) | 17.8964 | + | 10.3325i | 0.715284 | + | 0.412970i | ||||
\(627\) | −1.99385 | + | 3.45345i | −0.0796266 | + | 0.137917i | ||||
\(628\) | 1.22318 | + | 2.11862i | 0.0488104 | + | 0.0845420i | ||||
\(629\) | 39.2665i | 1.56566i | ||||||||
\(630\) | −3.30802 | + | 1.90989i | −0.131795 | + | 0.0760918i | ||||
\(631\) | 6.92607 | − | 3.99877i | 0.275722 | − | 0.159188i | −0.355763 | − | 0.934576i | \(-0.615779\pi\) |
0.631485 | + | 0.775388i | \(0.282446\pi\) | |||||||
\(632\) | 5.73272i | 0.228035i | ||||||||
\(633\) | −8.53766 | − | 14.7877i | −0.339342 | − | 0.587757i | ||||
\(634\) | −8.24589 | + | 14.2823i | −0.327486 | + | 0.567222i | ||||
\(635\) | 1.26626 | + | 0.731077i | 0.0502501 | + | 0.0290119i | ||||
\(636\) | 10.8032 | 0.428375 | ||||||||
\(637\) | 3.80664 | − | 11.8000i | 0.150825 | − | 0.467533i | ||||
\(638\) | 5.64556 | 0.223510 | ||||||||
\(639\) | −0.489486 | − | 0.282605i | −0.0193638 | − | 0.0111797i | ||||
\(640\) | 0.179303 | − | 0.310561i | 0.00708756 | − | 0.0122760i | ||||
\(641\) | −23.4892 | − | 40.6844i | −0.927766 | − | 1.60694i | −0.787051 | − | 0.616887i | \(-0.788393\pi\) |
−0.140715 | − | 0.990050i | \(-0.544940\pi\) | |||||||
\(642\) | 7.02084i | 0.277090i | ||||||||
\(643\) | −21.7416 | + | 12.5525i | −0.857404 | + | 0.495023i | −0.863142 | − | 0.504961i | \(-0.831507\pi\) |
0.00573777 | + | 0.999984i | \(0.498174\pi\) | |||||||
\(644\) | −6.47970 | + | 3.74106i | −0.255336 | + | 0.147418i | ||||
\(645\) | 2.62252i | 0.103262i | ||||||||
\(646\) | −8.94883 | − | 15.4998i | −0.352087 | − | 0.609832i | ||||
\(647\) | −5.06789 | + | 8.77784i | −0.199239 | + | 0.345093i | −0.948282 | − | 0.317429i | \(-0.897180\pi\) |
0.749043 | + | 0.662522i | \(0.230514\pi\) | |||||||
\(648\) | −2.65479 | − | 1.53275i | −0.104290 | − | 0.0602119i | ||||
\(649\) | −13.6168 | −0.534505 | ||||||||
\(650\) | −14.3265 | − | 4.62170i | −0.561933 | − | 0.181278i | ||||
\(651\) | −27.7756 | −1.08861 | ||||||||
\(652\) | −8.19718 | − | 4.73265i | −0.321027 | − | 0.185345i | ||||
\(653\) | −9.06830 | + | 15.7068i | −0.354870 | + | 0.614653i | −0.987096 | − | 0.160132i | \(-0.948808\pi\) |
0.632226 | + | 0.774784i | \(0.282141\pi\) | |||||||
\(654\) | 4.62524 | + | 8.01115i | 0.180861 | + | 0.313261i | ||||
\(655\) | − | 12.4322i | − | 0.485765i | ||||||
\(656\) | 9.94841 | − | 5.74371i | 0.388420 | − | 0.224254i | ||||
\(657\) | −11.0050 | + | 6.35375i | −0.429347 | + | 0.247883i | ||||
\(658\) | 20.5801i | 0.802297i | ||||||||
\(659\) | −4.52144 | − | 7.83137i | −0.176130 | − | 0.305067i | 0.764421 | − | 0.644717i | \(-0.223025\pi\) |
−0.940552 | + | 0.339650i | \(0.889691\pi\) | |||||||
\(660\) | 0.438403 | − | 0.759336i | 0.0170648 | − | 0.0295571i | ||||
\(661\) | 7.51960 | + | 4.34144i | 0.292478 | + | 0.168862i | 0.639059 | − | 0.769158i | \(-0.279324\pi\) |
−0.346581 | + | 0.938020i | \(0.612657\pi\) | |||||||
\(662\) | 13.0729 | 0.508092 | ||||||||
\(663\) | −14.4994 | + | 3.11381i | −0.563109 | + | 0.120930i | ||||
\(664\) | −7.35837 | −0.285560 | ||||||||
\(665\) | 12.0889 | + | 6.97950i | 0.468786 | + | 0.270653i | ||||
\(666\) | −5.20870 | + | 9.02173i | −0.201833 | + | 0.349585i | ||||
\(667\) | −7.40242 | − | 12.8214i | −0.286623 | − | 0.496445i | ||||
\(668\) | − | 17.6610i | − | 0.683327i | ||||||
\(669\) | −14.8828 | + | 8.59260i | −0.575403 | + | 0.332209i | ||||
\(670\) | 13.5977 | − | 7.85066i | 0.525326 | − | 0.303297i | ||||
\(671\) | 11.3365i | 0.437641i | ||||||||
\(672\) | −6.86084 | − | 11.8833i | −0.264663 | − | 0.458409i | ||||
\(673\) | 9.82195 | − | 17.0121i | 0.378608 | − | 0.655769i | −0.612252 | − | 0.790663i | \(-0.709736\pi\) |
0.990860 | + | 0.134894i | \(0.0430694\pi\) | |||||||
\(674\) | −1.25823 | − | 0.726440i | −0.0484652 | − | 0.0279814i | ||||
\(675\) | 3.82615 | 0.147268 | ||||||||
\(676\) | −8.53725 | − | 6.14800i | −0.328356 | − | 0.236462i | ||||
\(677\) | 12.4044 | 0.476741 | 0.238371 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238371 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(678\) | 5.41464 | + | 3.12614i | 0.207948 | + | 0.120059i | ||||
\(679\) | 28.0019 | − | 48.5007i | 1.07461 | − | 1.86129i | ||||
\(680\) | 6.83039 | + | 11.8306i | 0.261933 | + | 0.453682i | ||||
\(681\) | 9.60650i | 0.368122i | ||||||||
\(682\) | −8.12407 | + | 4.69044i | −0.311087 | + | 0.179606i | ||||
\(683\) | 19.0470 | − | 10.9968i | 0.728815 | − | 0.420781i | −0.0891737 | − | 0.996016i | \(-0.528423\pi\) |
0.817988 | + | 0.575235i | \(0.195089\pi\) | |||||||
\(684\) | 3.22714i | 0.123393i | ||||||||
\(685\) | 5.69073 | + | 9.85663i | 0.217432 | + | 0.376602i | ||||
\(686\) | −6.27764 | + | 10.8732i | −0.239681 | + | 0.415140i | ||||
\(687\) | 3.99749 | + | 2.30795i | 0.152514 | + | 0.0880539i | ||||
\(688\) | 4.17911 | 0.159327 | ||||||||
\(689\) | 47.0584 | − | 10.1060i | 1.79278 | − | 0.385009i | ||||
\(690\) | 3.38310 | 0.128792 | ||||||||
\(691\) | 21.0345 | + | 12.1443i | 0.800189 | + | 0.461989i | 0.843537 | − | 0.537071i | \(-0.180469\pi\) |
−0.0433481 | + | 0.999060i | \(0.513802\pi\) | |||||||
\(692\) | −2.29160 | + | 3.96917i | −0.0871136 | + | 0.150885i | ||||
\(693\) | 1.61546 | + | 2.79805i | 0.0613661 | + | 0.106289i | ||||
\(694\) | − | 38.7081i | − | 1.46934i | ||||||
\(695\) | 9.11990 | − | 5.26538i | 0.345938 | − | 0.199727i | ||||
\(696\) | 13.7351 | − | 7.92997i | 0.520628 | − | 0.300585i | ||||
\(697\) | 27.3665i | 1.03658i | ||||||||
\(698\) | 2.83149 | + | 4.90429i | 0.107173 | + | 0.185630i | ||||
\(699\) | −0.877254 | + | 1.51945i | −0.0331808 | + | 0.0574709i | ||||
\(700\) | 8.66391 | + | 5.00211i | 0.327465 | + | 0.189062i | ||||
\(701\) | −36.4133 | −1.37531 | −0.687657 | − | 0.726036i | \(-0.741361\pi\) | ||||
−0.687657 | + | 0.726036i | \(0.741361\pi\) | |||||||
\(702\) | −3.74437 | − | 1.20792i | −0.141322 | − | 0.0455902i | ||||
\(703\) | 38.0694 | 1.43581 | ||||||||
\(704\) | −7.00388 | − | 4.04369i | −0.263968 | − | 0.152402i | ||||
\(705\) | −3.16223 | + | 5.47715i | −0.119097 | + | 0.206281i | ||||
\(706\) | −4.19207 | − | 7.26088i | −0.157771 | − | 0.273267i | ||||
\(707\) | 24.9436i | 0.938099i | ||||||||
\(708\) | −9.54335 | + | 5.50985i | −0.358661 | + | 0.207073i | ||||
\(709\) | 38.8080 | − | 22.4058i | 1.45746 | − | 0.841467i | 0.458578 | − | 0.888654i | \(-0.348359\pi\) |
0.998886 | + | 0.0471869i | \(0.0150256\pi\) | |||||||
\(710\) | 0.668224i | 0.0250780i | ||||||||
\(711\) | −0.935041 | − | 1.61954i | −0.0350668 | − | 0.0607374i | ||||
\(712\) | 21.5425 | − | 37.3128i | 0.807341 | − | 1.39836i | ||||
\(713\) | 21.3045 | + | 12.3001i | 0.797858 | + | 0.460644i | ||||
\(714\) | −14.5011 | −0.542688 | ||||||||
\(715\) | 1.19934 | − | 3.71775i | 0.0448526 | − | 0.139036i | ||||
\(716\) | −1.49067 | −0.0557088 | ||||||||
\(717\) | −24.5553 | − | 14.1770i | −0.917035 | − | 0.529450i | ||||
\(718\) | −1.84093 | + | 3.18859i | −0.0687030 | + | 0.118997i | ||||
\(719\) | −10.6646 | − | 18.4716i | −0.397721 | − | 0.688874i | 0.595723 | − | 0.803190i | \(-0.296866\pi\) |
−0.993444 | + | 0.114316i | \(0.963532\pi\) | |||||||
\(720\) | 1.87059i | 0.0697129i | ||||||||
\(721\) | −25.4301 | + | 14.6821i | −0.947065 | + | 0.546788i | ||||
\(722\) | 2.92791 | − | 1.69043i | 0.108965 | − | 0.0629113i | ||||
\(723\) | − | 7.04394i | − | 0.261967i | ||||||
\(724\) | −1.52047 | − | 2.63353i | −0.0565079 | − | 0.0978745i | ||||
\(725\) | −9.89767 | + | 17.1433i | −0.367590 | + | 0.636685i | ||||
\(726\) | 0.945010 | + | 0.545602i | 0.0350726 | + | 0.0202492i | ||||
\(727\) | 42.5295 | 1.57733 | 0.788667 | − | 0.614821i | \(-0.210772\pi\) | ||||
0.788667 | + | 0.614821i | \(0.210772\pi\) | |||||||
\(728\) | −23.9508 | − | 26.4879i | −0.887675 | − | 0.981705i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.0108 | + | 7.51178i | 0.481551 | + | 0.278023i | ||||
\(731\) | −4.97795 | + | 8.62206i | −0.184116 | + | 0.318898i | ||||
\(732\) | 4.58718 | + | 7.94523i | 0.169547 | + | 0.293664i | ||||
\(733\) | 44.3019i | 1.63633i | 0.574985 | + | 0.818164i | \(0.305008\pi\) | ||||
−0.574985 | + | 0.818164i | \(0.694992\pi\) | |||||||
\(734\) | −24.8951 | + | 14.3732i | −0.918894 | + | 0.530524i | ||||
\(735\) | 3.22660 | − | 1.86288i | 0.119015 | − | 0.0687134i | ||||
\(736\) | 12.1530i | 0.447966i | ||||||||
\(737\) | −6.64039 | − | 11.5015i | −0.244602 | − | 0.423663i | ||||
\(738\) | −3.63016 | + | 6.28763i | −0.133628 | + | 0.231451i | ||||
\(739\) | −13.6402 | − | 7.87517i | −0.501762 | − | 0.289693i | 0.227679 | − | 0.973736i | \(-0.426886\pi\) |
−0.729441 | + | 0.684044i | \(0.760220\pi\) | |||||||
\(740\) | −8.37061 | −0.307710 | ||||||||
\(741\) | 3.01888 | + | 14.0573i | 0.110901 | + | 0.516409i | ||||
\(742\) | 47.0638 | 1.72777 | ||||||||
\(743\) | 29.4252 | + | 16.9886i | 1.07951 | + | 0.623253i | 0.930763 | − | 0.365623i | \(-0.119144\pi\) |
0.148743 | + | 0.988876i | \(0.452477\pi\) | |||||||
\(744\) | −13.1767 | + | 22.8228i | −0.483082 | + | 0.836723i | ||||
\(745\) | −6.42556 | − | 11.1294i | −0.235414 | − | 0.407750i | ||||
\(746\) | 16.7631i | 0.613742i | ||||||||
\(747\) | 2.07880 | − | 1.20019i | 0.0760593 | − | 0.0439128i | ||||
\(748\) | 2.88267 | − | 1.66431i | 0.105401 | − | 0.0608533i | ||||
\(749\) | − | 20.7878i | − | 0.759570i | ||||||
\(750\) | −5.21740 | − | 9.03679i | −0.190512 | − | 0.329977i | ||||
\(751\) | 13.3092 | − | 23.0523i | 0.485661 | − | 0.841189i | −0.514203 | − | 0.857668i | \(-0.671912\pi\) |
0.999864 | + | 0.0164790i | \(0.00524567\pi\) | |||||||
\(752\) | 8.72811 | + | 5.03917i | 0.318281 | + | 0.183760i | ||||
\(753\) | 15.6037 | 0.568631 | ||||||||
\(754\) | 15.0983 | − | 13.6522i | 0.549848 | − | 0.497182i | ||||
\(755\) | −24.0571 | −0.875528 | ||||||||
\(756\) | 2.26440 | + | 1.30735i | 0.0823553 | + | 0.0475479i | ||||
\(757\) | −2.72942 | + | 4.72749i | −0.0992024 | + | 0.171824i | −0.911355 | − | 0.411622i | \(-0.864962\pi\) |
0.812152 | + | 0.583445i | \(0.198296\pi\) | |||||||
\(758\) | 7.68472 | + | 13.3103i | 0.279122 | + | 0.483453i | ||||
\(759\) | − | 2.86156i | − | 0.103868i | ||||||
\(760\) | 11.4699 | − | 6.62215i | 0.416057 | − | 0.240211i | ||||
\(761\) | 26.6966 | − | 15.4133i | 0.967752 | − | 0.558732i | 0.0692016 | − | 0.997603i | \(-0.477955\pi\) |
0.898550 | + | 0.438871i | \(0.144621\pi\) | |||||||
\(762\) | 1.47262i | 0.0533475i | ||||||||
\(763\) | −13.6947 | − | 23.7200i | −0.495783 | − | 0.858722i | ||||
\(764\) | −4.60815 | + | 7.98155i | −0.166717 | + | 0.288762i | ||||
\(765\) | −3.85928 | − | 2.22815i | −0.139532 | − | 0.0805591i | ||||
\(766\) | −14.6823 | −0.530493 | ||||||||
\(767\) | −36.4162 | + | 32.9282i | −1.31491 | + | 1.18897i | ||||
\(768\) | −15.8136 | −0.570624 | ||||||||
\(769\) | −16.4285 | − | 9.48498i | −0.592426 | − | 0.342037i | 0.173630 | − | 0.984811i | \(-0.444450\pi\) |
−0.766056 | + | 0.642774i | \(0.777784\pi\) | |||||||
\(770\) | 1.90989 | − | 3.30802i | 0.0688276 | − | 0.119213i | ||||
\(771\) | −1.24846 | − | 2.16240i | −0.0449623 | − | 0.0778769i | ||||
\(772\) | − | 10.4597i | − | 0.376452i | ||||||
\(773\) | 29.1506 | − | 16.8301i | 1.04848 | − | 0.605338i | 0.126254 | − | 0.991998i | \(-0.459705\pi\) |
0.922222 | + | 0.386660i | \(0.126371\pi\) | |||||||
\(774\) | −2.28743 | + | 1.32065i | −0.0822200 | + | 0.0474698i | ||||
\(775\) | − | 32.8927i | − | 1.18154i | ||||||
\(776\) | −26.5682 | − | 46.0175i | −0.953743 | − | 1.65193i | ||||
\(777\) | 15.4223 | − | 26.7122i | 0.553272 | − | 0.958295i | ||||
\(778\) | 5.60718 | + | 3.23731i | 0.201027 | + | 0.116063i | ||||
\(779\) | 26.5322 | 0.950613 | ||||||||
\(780\) | −0.663785 | − | 3.09090i | −0.0237673 | − | 0.110672i | ||||
\(781\) | 0.565210 | 0.0202248 | ||||||||
\(782\) | 11.1226 | + | 6.42165i | 0.397744 | + | 0.229638i | ||||
\(783\) | −2.58685 | + | 4.48056i | −0.0924465 | + | 0.160122i | ||||
\(784\) | −2.96859 | − | 5.14175i | −0.106021 | − | 0.183634i | ||||
\(785\) | 3.27516i | 0.116895i | ||||||||
\(786\) | 10.8437 | − | 6.26059i | 0.386781 | − | 0.223308i | ||||
\(787\) | −4.64159 | + | 2.67982i | −0.165455 | + | 0.0955254i | −0.580441 | − | 0.814302i | \(-0.697120\pi\) |
0.414986 | + | 0.909828i | \(0.363786\pi\) | |||||||
\(788\) | 12.9305i | 0.460629i | ||||||||
\(789\) | 3.33075 | + | 5.76902i | 0.118578 | + | 0.205383i | ||||
\(790\) | −1.10546 | + | 1.91471i | −0.0393305 | + | 0.0681225i | ||||
\(791\) | −16.0321 | − | 9.25611i | −0.570034 | − | 0.329109i | ||||
\(792\) | 3.06549 | 0.108927 | ||||||||
\(793\) | 27.4141 | + | 30.3180i | 0.973503 | + | 1.07662i | ||||
\(794\) | −35.3911 | −1.25598 | ||||||||
\(795\) | 12.5255 | + | 7.23158i | 0.444232 | + | 0.256478i | ||||
\(796\) | 2.01553 | − | 3.49100i | 0.0714386 | − | 0.123735i | ||||
\(797\) | −2.96256 | − | 5.13131i | −0.104939 | − | 0.181760i | 0.808774 | − | 0.588119i | \(-0.200132\pi\) |
−0.913713 | + | 0.406359i | \(0.866798\pi\) | |||||||
\(798\) | 14.0590i | 0.497682i | ||||||||
\(799\) | −20.7930 | + | 12.0048i | −0.735602 | + | 0.424700i | ||||
\(800\) | 14.0726 | − | 8.12481i | 0.497541 | − | 0.287255i | ||||
\(801\) | 14.0549i | 0.496605i | ||||||||
\(802\) | 10.8542 | + | 18.8000i | 0.383274 | + | 0.663851i | ||||
\(803\) | 6.35375 | − | 11.0050i | 0.224219 | − | 0.388359i | ||||
\(804\) | −9.30787 | − | 5.37390i | −0.328263 | − | 0.189523i | ||||
\(805\) | −10.0169 | −0.353051 | ||||||||
\(806\) | −10.3843 | + | 32.1897i | −0.365771 | + | 1.13383i | ||||
\(807\) | 18.9522 | 0.667150 | ||||||||
\(808\) | 20.4957 | + | 11.8332i | 0.721037 | + | 0.416291i | ||||
\(809\) | 23.7269 | − | 41.0962i | 0.834194 | − | 1.44487i | −0.0604908 | − | 0.998169i | \(-0.519267\pi\) |
0.894685 | − | 0.446698i | \(-0.147400\pi\) | |||||||
\(810\) | −0.591129 | − | 1.02387i | −0.0207702 | − | 0.0359750i | ||||
\(811\) | 14.9271i | 0.524161i | 0.965046 | + | 0.262081i | \(0.0844086\pi\) | ||||
−0.965046 | + | 0.262081i | \(0.915591\pi\) | |||||||
\(812\) | −11.7153 | + | 6.76384i | −0.411127 | + | 0.237364i | ||||
\(813\) | 5.34468 | − | 3.08575i | 0.187446 | − | 0.108222i | ||||
\(814\) | − | 10.4174i | − | 0.365130i | ||||||
\(815\) | −6.33599 | − | 10.9743i | −0.221940 | − | 0.384412i | ||||
\(816\) | −3.55067 | + | 6.14995i | −0.124298 | + | 0.215291i | ||||
\(817\) | 8.35920 | + | 4.82618i | 0.292451 | + | 0.168847i | ||||
\(818\) | −20.6424 | −0.721746 | ||||||||
\(819\) | 11.0866 | + | 3.57651i | 0.387398 | + | 0.124973i | ||||
\(820\) | −5.83383 | −0.203726 | ||||||||
\(821\) | −36.8360 | − | 21.2673i | −1.28558 | − | 0.742232i | −0.307721 | − | 0.951477i | \(-0.599566\pi\) |
−0.977863 | + | 0.209244i | \(0.932900\pi\) | |||||||
\(822\) | −5.73148 | + | 9.92721i | −0.199908 | + | 0.346251i | ||||
\(823\) | −14.6807 | − | 25.4277i | −0.511736 | − | 0.886352i | −0.999907 | − | 0.0136047i | \(-0.995669\pi\) |
0.488172 | − | 0.872748i | \(-0.337664\pi\) | |||||||
\(824\) | 27.8607i | 0.970572i | ||||||||
\(825\) | −3.31354 | + | 1.91307i | −0.115363 | + | 0.0666047i | ||||
\(826\) | −41.5753 | + | 24.0035i | −1.44659 | + | 0.835189i | ||||
\(827\) | 1.84784i | 0.0642556i | 0.999484 | + | 0.0321278i | \(0.0102284\pi\) | ||||
−0.999484 | + | 0.0321278i | \(0.989772\pi\) | |||||||
\(828\) | −1.15789 | − | 2.00553i | −0.0402396 | − | 0.0696970i | ||||
\(829\) | 15.1977 | − | 26.3232i | 0.527839 | − | 0.914244i | −0.471634 | − | 0.881794i | \(-0.656336\pi\) |
0.999473 | − | 0.0324499i | \(-0.0103309\pi\) | |||||||
\(830\) | −2.45768 | − | 1.41894i | −0.0853072 | − | 0.0492522i | ||||
\(831\) | 0.893576 | 0.0309978 | ||||||||
\(832\) | −28.5094 | + | 6.12254i | −0.988387 | + | 0.212261i | ||||
\(833\) | 14.1441 | 0.490065 | ||||||||
\(834\) | 9.18521 | + | 5.30308i | 0.318058 | + | 0.183631i | ||||
\(835\) | 11.8222 | − | 20.4766i | 0.409123 | − | 0.708622i | ||||
\(836\) | −1.61357 | − | 2.79479i | −0.0558066 | − | 0.0966598i | ||||
\(837\) | − | 8.59681i | − | 0.297149i | ||||||
\(838\) | −24.7997 | + | 14.3181i | −0.856693 | + | 0.494612i | ||||
\(839\) | −13.9637 | + | 8.06193i | −0.482079 | + | 0.278329i | −0.721283 | − | 0.692641i | \(-0.756447\pi\) |
0.239203 | + | 0.970970i | \(0.423114\pi\) | |||||||
\(840\) | − | 10.7308i | − | 0.370248i | ||||||
\(841\) | 1.11641 | + | 1.93368i | 0.0384969 | + | 0.0666786i | ||||
\(842\) | −1.43420 | + | 2.48411i | −0.0494258 | + | 0.0856081i | ||||
\(843\) | −5.31312 | − | 3.06753i | −0.182993 | − | 0.105651i | ||||
\(844\) | 13.8186 | 0.475657 | ||||||||
\(845\) | −5.78285 | − | 12.8429i | −0.198936 | − | 0.441809i | ||||
\(846\) | −6.36976 | −0.218997 | ||||||||
\(847\) | −2.79805 | − | 1.61546i | −0.0961423 | − | 0.0555078i | ||||
\(848\) | 11.5239 | − | 19.9599i | 0.395731 | − | 0.685427i | ||||
\(849\) | −7.61927 | − | 13.1970i | −0.261493 | − | 0.452918i | ||||
\(850\) | − | 17.1726i | − | 0.589015i | ||||||
\(851\) | −23.6585 | + | 13.6592i | −0.811002 | + | 0.468232i | ||||
\(852\) | 0.396129 | − | 0.228705i | 0.0135712 | − | 0.00783531i | ||||
\(853\) | 55.1988i | 1.88997i | 0.327112 | + | 0.944986i | \(0.393925\pi\) | ||||
−0.327112 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(854\) | 19.9839 | + | 34.6132i | 0.683836 | + | 1.18444i | ||||
\(855\) | −2.16022 | + | 3.74162i | −0.0738781 | + | 0.127961i | ||||
\(856\) | −17.0810 | − | 9.86173i | −0.583817 | − | 0.337067i | ||||
\(857\) | −4.48302 | −0.153137 | −0.0765686 | − | 0.997064i | \(-0.524396\pi\) | ||||
−0.0765686 | + | 0.997064i | \(0.524396\pi\) | |||||||
\(858\) | 3.84669 | − | 0.826094i | 0.131324 | − | 0.0282024i | ||||
\(859\) | −3.35158 | −0.114355 | −0.0571773 | − | 0.998364i | \(-0.518210\pi\) | ||||
−0.0571773 | + | 0.998364i | \(0.518210\pi\) | |||||||
\(860\) | −1.83800 | − | 1.06117i | −0.0626753 | − | 0.0361856i | ||||
\(861\) | 10.7485 | − | 18.6169i | 0.366306 | − | 0.634461i | ||||
\(862\) | 16.0064 | + | 27.7239i | 0.545179 | + | 0.944278i | ||||
\(863\) | 28.5494i | 0.971832i | 0.874006 | + | 0.485916i | \(0.161514\pi\) | ||||
−0.874006 | + | 0.485916i | \(0.838486\pi\) | |||||||
\(864\) | 3.67800 | − | 2.12350i | 0.125128 | − | 0.0722428i | ||||
\(865\) | −5.31386 | + | 3.06796i | −0.180677 | + | 0.104314i | ||||
\(866\) | − | 16.6375i | − | 0.565366i | ||||||
\(867\) | 0.0412387 | + | 0.0714275i | 0.00140054 | + | 0.00242580i | ||||
\(868\) | 11.2390 | − | 19.4666i | 0.381478 | − | 0.660739i | ||||
\(869\) | 1.61954 | + | 0.935041i | 0.0549391 | + | 0.0317191i | ||||
\(870\) | 6.11665 | 0.207374 | ||||||||
\(871\) | −45.5719 | − | 14.7014i | −1.54414 | − | 0.498137i | ||||
\(872\) | −25.9871 | −0.880036 | ||||||||
\(873\) | 15.0115 | + | 8.66687i | 0.508061 | + | 0.293329i | ||||
\(874\) | 6.22587 | − | 10.7835i | 0.210593 | − | 0.364758i | ||||
\(875\) | 15.4480 | + | 26.7568i | 0.522239 | + | 0.904545i | ||||
\(876\) | − | 10.2839i | − | 0.347460i | ||||||
\(877\) | −24.1954 | + | 13.9692i | −0.817022 | + | 0.471708i | −0.849388 | − | 0.527768i | \(-0.823029\pi\) |
0.0323664 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(878\) | 23.5328 | − | 13.5867i | 0.794193 | − | 0.458527i | ||||
\(879\) | − | 6.48923i | − | 0.218876i | ||||||
\(880\) | −0.935296 | − | 1.61998i | −0.0315288 | − | 0.0546095i | ||||
\(881\) | −20.6746 | + | 35.8095i | −0.696546 | + | 1.20645i | 0.273111 | + | 0.961983i | \(0.411947\pi\) |
−0.969657 | + | 0.244470i | \(0.921386\pi\) | |||||||
\(882\) | 3.24971 | + | 1.87622i | 0.109423 | + | 0.0631756i | ||||
\(883\) | −37.9003 | −1.27545 | −0.637723 | − | 0.770266i | \(-0.720124\pi\) | ||||
−0.637723 | + | 0.770266i | \(0.720124\pi\) | |||||||
\(884\) | 3.68467 | − | 11.4219i | 0.123929 | − | 0.384160i | ||||
\(885\) | −14.7530 | −0.495917 | ||||||||
\(886\) | 17.5547 | + | 10.1352i | 0.589760 | + | 0.340498i | ||||
\(887\) | 11.2642 | − | 19.5102i | 0.378216 | − | 0.655089i | −0.612587 | − | 0.790403i | \(-0.709871\pi\) |
0.990803 | + | 0.135314i | \(0.0432044\pi\) | |||||||
\(888\) | −14.6327 | − | 25.3445i | −0.491040 | − | 0.850507i | ||||
\(889\) | − | 4.36025i | − | 0.146238i | ||||||
\(890\) | 14.3903 | − | 8.30825i | 0.482364 | − | 0.278493i | ||||
\(891\) | −0.866025 | + | 0.500000i | −0.0290129 | + | 0.0167506i | ||||
\(892\) | − | 13.9076i | − | 0.465660i | ||||||
\(893\) | 11.6388 | + | 20.1590i | 0.389478 | + | 0.674596i | ||||
\(894\) | 6.47157 | − | 11.2091i | 0.216442 | − | 0.374888i | ||||
\(895\) | −1.72831 | − | 0.997841i | −0.0577710 | − | 0.0333541i | ||||
\(896\) | −1.06939 | −0.0357257 | ||||||||
\(897\) | −6.91985 | − | 7.65286i | −0.231047 | − | 0.255522i | ||||
\(898\) | 1.14011 | 0.0380458 | ||||||||
\(899\) | 38.5185 | + | 22.2387i | 1.28466 | + | 0.741701i | ||||
\(900\) | −1.54820 | + | 2.68157i | −0.0516068 | + | 0.0893856i | ||||
\(901\) | 27.4533 | + | 47.5505i | 0.914602 | + | 1.58414i | ||||
\(902\) | − | 7.26033i | − | 0.241742i | ||||||
\(903\) | 6.77280 | − | 3.91028i | 0.225385 | − | 0.130126i | ||||
\(904\) | −15.2112 | + | 8.78220i | −0.505917 | + | 0.292091i | ||||
\(905\) | − | 4.07117i | − | 0.135330i | ||||||
\(906\) | −12.1147 | − | 20.9833i | −0.402484 | − | 0.697122i | ||||
\(907\) | −16.6527 | + | 28.8433i | −0.552943 | + | 0.957725i | 0.445118 | + | 0.895472i | \(0.353162\pi\) |
−0.998060 | + | 0.0622526i | \(0.980172\pi\) | |||||||
\(908\) | −6.73275 | − | 3.88715i | −0.223434 | − | 0.129000i | ||||
\(909\) | −7.72028 | −0.256065 | ||||||||
\(910\) | −2.89176 | − | 13.4654i | −0.0958608 | − | 0.446373i | ||||
\(911\) | 17.5218 | 0.580524 | 0.290262 | − | 0.956947i | \(-0.406258\pi\) | ||||
0.290262 | + | 0.956947i | \(0.406258\pi\) | |||||||
\(912\) | 5.96245 | + | 3.44242i | 0.197436 | + | 0.113990i | ||||
\(913\) | −1.20019 | + | 2.07880i | −0.0397206 | + | 0.0687982i | ||||
\(914\) | 14.2548 | + | 24.6900i | 0.471507 | + | 0.816673i | ||||
\(915\) | 12.2825i | 0.406047i | ||||||||
\(916\) | −3.23507 | + | 1.86777i | −0.106890 | + | 0.0617128i | ||||
\(917\) | −32.1067 | + | 18.5368i | −1.06026 | + | 0.612140i | ||||
\(918\) | − | 4.48822i | − | 0.148133i | ||||||
\(919\) | −27.3561 | − | 47.3821i | −0.902393 | − | 1.56299i | −0.824379 | − | 0.566039i | \(-0.808475\pi\) |
−0.0780145 | − | 0.996952i | \(-0.524858\pi\) | |||||||
\(920\) | −4.75203 | + | 8.23076i | −0.156670 | + | 0.271360i | ||||
\(921\) | 11.5755 | + | 6.68311i | 0.381425 | + | 0.220216i | ||||
\(922\) | 14.6036 | 0.480946 | ||||||||
\(923\) | 1.51158 | − | 1.36680i | 0.0497543 | − | 0.0449887i | ||||
\(924\) | −2.61470 | −0.0860173 | ||||||||
\(925\) | 31.6334 | + | 18.2636i | 1.04010 | + | 0.600502i | ||||
\(926\) | 12.9831 | − | 22.4875i | 0.426653 | − | 0.738984i | ||||
\(927\) | −4.54424 | − | 7.87086i | −0.149252 | − | 0.258513i | ||||
\(928\) | 21.9727i | 0.721288i | ||||||||
\(929\) | 6.67428 | − | 3.85340i | 0.218976 | − | 0.126426i | −0.386500 | − | 0.922289i | \(-0.626316\pi\) |
0.605476 | + | 0.795863i | \(0.292983\pi\) | |||||||
\(930\) | −8.80199 | + | 5.08183i | −0.288629 | + | 0.166640i | ||||
\(931\) | − | 13.7129i | − | 0.449423i | ||||||
\(932\) | −0.709940 | − | 1.22965i | −0.0232549 | − | 0.0402786i | ||||
\(933\) | −10.9408 | + | 18.9501i | −0.358187 | + | 0.620398i | ||||
\(934\) | 22.8688 | + | 13.2033i | 0.748290 | + | 0.432025i | ||||
\(935\) | 4.45631 | 0.145737 | ||||||||
\(936\) | 8.19825 | − | 7.41301i | 0.267968 | − | 0.242302i | ||||
\(937\) | −40.3770 | −1.31906 | −0.659530 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659530 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(938\) | −40.5495 | − | 23.4112i | −1.32399 | − | 0.764404i | ||||
\(939\) | 9.46890 | − | 16.4006i | 0.309006 | − | 0.535214i | ||||
\(940\) | −2.55912 | − | 4.43252i | −0.0834692 | − | 0.144573i | ||||
\(941\) | 16.4105i | 0.534966i | 0.963563 | + | 0.267483i | \(0.0861919\pi\) | ||||
−0.963563 | + | 0.267483i | \(0.913808\pi\) | |||||||
\(942\) | −2.85668 | + | 1.64931i | −0.0930757 | + | 0.0537373i | ||||
\(943\) | −16.4886 | + | 9.51970i | −0.536943 | + | 0.310004i | ||||
\(944\) | 23.5096i | 0.765174i | ||||||||
\(945\) | 1.75026 | + | 3.03154i | 0.0569359 | + | 0.0986159i | ||||
\(946\) | 1.32065 | − | 2.28743i | 0.0429380 | − | 0.0743708i | ||||
\(947\) | −22.2938 | − | 12.8713i | −0.724451 | − | 0.418262i | 0.0919380 | − | 0.995765i | \(-0.470694\pi\) |
−0.816389 | + | 0.577503i | \(0.804027\pi\) | |||||||
\(948\) | 1.51341 | 0.0491533 | ||||||||
\(949\) | −9.62020 | − | 44.7962i | −0.312285 | − | 1.45415i | ||||
\(950\) | −16.6490 | −0.540166 | ||||||||
\(951\) | 13.0886 | + | 7.55669i | 0.424426 | + | 0.245043i | ||||
\(952\) | 20.3687 | − | 35.2797i | 0.660154 | − | 1.14342i | ||||
\(953\) | 12.2543 | + | 21.2250i | 0.396955 | + | 0.687547i | 0.993349 | − | 0.115146i | \(-0.0367335\pi\) |
−0.596393 | + | 0.802692i | \(0.703400\pi\) | |||||||
\(954\) | 14.5667i | 0.471615i | ||||||||
\(955\) | −10.6856 | + | 6.16932i | −0.345777 | + | 0.199634i | ||||
\(956\) | 19.8720 | − | 11.4731i | 0.642707 | − | 0.371067i | ||||
\(957\) | − | 5.17370i | − | 0.167242i | ||||||
\(958\) | 3.20270 | + | 5.54724i | 0.103475 | + | 0.179223i | ||||
\(959\) | 16.9702 | − | 29.3932i | 0.547996 | − | 0.949156i | ||||
\(960\) | −7.58831 | − | 4.38112i | −0.244912 | − | 0.141400i | ||||
\(961\) | −42.9052 | −1.38404 | ||||||||
\(962\) | −25.1915 | − | 27.8600i | −0.812206 | − | 0.898242i | ||||
\(963\) | 6.43403 | 0.207334 | ||||||||
\(964\) | 4.93677 | + | 2.85024i | 0.159003 | + | 0.0918002i | ||||
\(965\) | 7.00162 | − | 12.1272i | 0.225390 | − | 0.390387i | ||||
\(966\) | −5.04433 | − | 8.73704i | −0.162299 | − | 0.281110i | ||||
\(967\) | − | 15.1247i | − | 0.486379i | −0.969979 | − | 0.243189i | \(-0.921806\pi\) | ||
0.969979 | − | 0.243189i | \(-0.0781936\pi\) | |||||||
\(968\) | −2.65479 | + | 1.53275i | −0.0853283 | + | 0.0492643i | ||||
\(969\) | −14.2043 | + | 8.20088i | −0.456309 | + | 0.263450i | ||||
\(970\) | − | 20.4930i | − | 0.657989i | ||||||
\(971\) | −19.7020 | − | 34.1249i | −0.632269 | − | 1.09512i | −0.987087 | − | 0.160186i | \(-0.948791\pi\) |
0.354818 | − | 0.934935i | \(-0.384543\pi\) | |||||||
\(972\) | −0.404638 | + | 0.700853i | −0.0129788 | + | 0.0224799i | ||||
\(973\) | −27.1962 | − | 15.7018i | −0.871871 | − | 0.503375i | ||||
\(974\) | −26.6645 | −0.854386 | ||||||||
\(975\) | −4.23541 | + | 13.1291i | −0.135642 | + | 0.420468i | ||||
\(976\) | 19.5728 | 0.626509 | ||||||||
\(977\) | 38.0554 | + | 21.9713i | 1.21750 | + | 0.702924i | 0.964383 | − | 0.264511i | \(-0.0852105\pi\) |
0.253118 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(978\) | 6.38136 | − | 11.0528i | 0.204053 | − | 0.353431i | ||||
\(979\) | −7.02744 | − | 12.1719i | −0.224598 | − | 0.389015i | ||||
\(980\) | 3.01517i | 0.0963160i | ||||||||
\(981\) | 7.34157 | − | 4.23866i | 0.234398 | − | 0.135330i | ||||
\(982\) | 11.2619 | − | 6.50208i | 0.359383 | − | 0.207490i | ||||
\(983\) | 26.1389i | 0.833703i | 0.908975 | + | 0.416851i | \(0.136866\pi\) | ||||
−0.908975 | + | 0.416851i | \(0.863134\pi\) | |||||||
\(984\) | −10.1981 | − | 17.6637i | −0.325105 | − | 0.563098i | ||||
\(985\) | −8.65556 | + | 14.9919i | −0.275789 | + | 0.477681i | ||||
\(986\) | 20.1097 | + | 11.6104i | 0.640424 | + | 0.369749i | ||||
\(987\) | 18.8600 | 0.600322 | ||||||||
\(988\) | −11.0737 | − | 3.57234i | −0.352301 | − | 0.113651i | ||||
\(989\) | −6.92651 | −0.220250 | ||||||||
\(990\) | 1.02387 | + | 0.591129i | 0.0325406 | + | 0.0187873i | ||||
\(991\) | −10.3362 | + | 17.9028i | −0.328339 | + | 0.568700i | −0.982182 | − | 0.187930i | \(-0.939822\pi\) |
0.653843 | + | 0.756630i | \(0.273155\pi\) | |||||||
\(992\) | −18.2553 | − | 31.6191i | −0.579607 | − | 1.00391i | ||||
\(993\) | − | 11.9802i | − | 0.380181i | ||||||
\(994\) | 1.72572 | − | 0.996348i | 0.0547367 | − | 0.0316022i | ||||
\(995\) | 4.67370 | − | 2.69836i | 0.148166 | − | 0.0855438i | ||||
\(996\) | 1.94258i | 0.0615529i | ||||||||
\(997\) | 6.18669 | + | 10.7157i | 0.195935 | + | 0.339369i | 0.947206 | − | 0.320624i | \(-0.103893\pi\) |
−0.751272 | + | 0.659993i | \(0.770559\pi\) | |||||||
\(998\) | −9.60944 | + | 16.6440i | −0.304181 | + | 0.526858i | ||||
\(999\) | 8.26769 | + | 4.77336i | 0.261578 | + | 0.151022i |
(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 | 429.2.s.b.199.5 | yes | 28 | |
13.6 | odd | 12 | 5577.2.a.bg.1.8 | 14 | |||
13.7 | odd | 12 | 5577.2.a.bf.1.7 | 14 | |||
13.10 | even | 6 | inner | 429.2.s.b.166.5 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.s.b.166.5 | ✓ | 28 | 13.10 | even | 6 | inner | |
429.2.s.b.199.5 | yes | 28 | 1.1 | even | 1 | trivial | |
5577.2.a.bf.1.7 | 14 | 13.7 | odd | 12 | |||
5577.2.a.bg.1.8 | 14 | 13.6 | odd | 12 |