Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(43,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.l (of order \(4\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-0.394902 - 0.394902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.127 |
Dual form | 210.3.l.b.43.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.93066 | + | 0.829843i | −0.986131 | + | 0.165969i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.267261 | + | 0.267261i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 5.76050 | + | 4.10081i | 0.576050 | + | 0.410081i | ||||
\(11\) | −5.74922 | −0.522656 | −0.261328 | − | 0.965250i | \(-0.584160\pi\) | ||||
−0.261328 | + | 0.965250i | \(0.584160\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 15.0034 | − | 15.0034i | 1.15411 | − | 1.15411i | 0.168391 | − | 0.985720i | \(-0.446143\pi\) |
0.985720 | − | 0.168391i | \(-0.0538571\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 5.02245 | − | 7.05514i | 0.334830 | − | 0.470343i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −4.78821 | − | 4.78821i | −0.281659 | − | 0.281659i | 0.552111 | − | 0.833771i | \(-0.313822\pi\) |
−0.833771 | + | 0.552111i | \(0.813822\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | − | 17.4017i | − | 0.915877i | −0.888984 | − | 0.457938i | \(-0.848588\pi\) | ||
0.888984 | − | 0.457938i | \(-0.151412\pi\) | |||||||
\(20\) | −1.65969 | − | 9.86131i | −0.0829843 | − | 0.493066i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 5.74922 | + | 5.74922i | 0.261328 | + | 0.261328i | ||||
\(23\) | 13.2261 | − | 13.2261i | 0.575048 | − | 0.575048i | −0.358487 | − | 0.933535i | \(-0.616707\pi\) |
0.933535 | + | 0.358487i | \(0.116707\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 23.6227 | − | 8.18334i | 0.944909 | − | 0.327333i | ||||
\(26\) | −30.0069 | −1.15411 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −3.74166 | + | 3.74166i | −0.133631 | + | 0.133631i | ||||
\(29\) | − | 37.7271i | − | 1.30093i | −0.759534 | − | 0.650467i | \(-0.774573\pi\) | ||
0.759534 | − | 0.650467i | \(-0.225427\pi\) | |||||||
\(30\) | −12.0776 | + | 2.03269i | −0.402586 | + | 0.0677564i | ||||
\(31\) | −27.0130 | −0.871386 | −0.435693 | − | 0.900095i | \(-0.643497\pi\) | ||||
−0.435693 | + | 0.900095i | \(0.643497\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 7.04132 | − | 7.04132i | 0.213373 | − | 0.213373i | ||||
\(34\) | 9.57642i | 0.281659i | ||||||||
\(35\) | −10.7769 | − | 7.67192i | −0.307912 | − | 0.219198i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 11.3640 | + | 11.3640i | 0.307136 | + | 0.307136i | 0.843798 | − | 0.536661i | \(-0.180315\pi\) |
−0.536661 | + | 0.843798i | \(0.680315\pi\) | |||||||
\(38\) | −17.4017 | + | 17.4017i | −0.457938 | + | 0.457938i | ||||
\(39\) | 36.7508i | 0.942328i | ||||||||
\(40\) | −8.20163 | + | 11.5210i | −0.205041 | + | 0.288025i | ||||
\(41\) | −53.0897 | −1.29487 | −0.647435 | − | 0.762121i | \(-0.724158\pi\) | ||||
−0.647435 | + | 0.762121i | \(0.724158\pi\) | |||||||
\(42\) | 4.58258 | + | 4.58258i | 0.109109 | + | 0.109109i | ||||
\(43\) | 37.1052 | − | 37.1052i | 0.862912 | − | 0.862912i | −0.128763 | − | 0.991675i | \(-0.541101\pi\) |
0.991675 | + | 0.128763i | \(0.0411007\pi\) | |||||||
\(44\) | − | 11.4984i | − | 0.261328i | ||||||
\(45\) | 2.48953 | + | 14.7920i | 0.0553228 | + | 0.328710i | ||||
\(46\) | −26.4522 | −0.575048 | ||||||||
\(47\) | −9.39190 | − | 9.39190i | −0.199828 | − | 0.199828i | 0.600098 | − | 0.799926i | \(-0.295128\pi\) |
−0.799926 | + | 0.600098i | \(0.795128\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −31.8061 | − | 15.4394i | −0.636121 | − | 0.308788i | ||||
\(51\) | 11.7287 | 0.229974 | ||||||||
\(52\) | 30.0069 | + | 30.0069i | 0.577056 | + | 0.577056i | ||||
\(53\) | 43.8996 | − | 43.8996i | 0.828294 | − | 0.828294i | −0.158987 | − | 0.987281i | \(-0.550823\pi\) |
0.987281 | + | 0.158987i | \(0.0508228\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 28.3474 | − | 4.77095i | 0.515407 | − | 0.0867445i | ||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 21.3126 | + | 21.3126i | 0.373905 | + | 0.373905i | ||||
\(58\) | −37.7271 | + | 37.7271i | −0.650467 | + | 0.650467i | ||||
\(59\) | 62.9694i | 1.06728i | 0.845713 | + | 0.533639i | \(0.179176\pi\) | ||||
−0.845713 | + | 0.533639i | \(0.820824\pi\) | |||||||
\(60\) | 14.1103 | + | 10.0449i | 0.235171 | + | 0.167415i | ||||
\(61\) | −1.67492 | −0.0274577 | −0.0137288 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137288 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(62\) | 27.0130 | + | 27.0130i | 0.435693 | + | 0.435693i | ||||
\(63\) | 5.61249 | − | 5.61249i | 0.0890871 | − | 0.0890871i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −61.5263 | + | 86.4273i | −0.946559 | + | 1.32965i | ||||
\(66\) | −14.0826 | −0.213373 | ||||||||
\(67\) | 28.4909 | + | 28.4909i | 0.425238 | + | 0.425238i | 0.887003 | − | 0.461765i | \(-0.152784\pi\) |
−0.461765 | + | 0.887003i | \(0.652784\pi\) | |||||||
\(68\) | 9.57642 | − | 9.57642i | 0.140830 | − | 0.140830i | ||||
\(69\) | 32.3972i | 0.469525i | ||||||||
\(70\) | 3.10499 | + | 18.4488i | 0.0443570 | + | 0.263555i | ||||
\(71\) | 47.2039 | 0.664844 | 0.332422 | − | 0.943131i | \(-0.392134\pi\) | ||||
0.332422 | + | 0.943131i | \(0.392134\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −31.2071 | + | 31.2071i | −0.427495 | + | 0.427495i | −0.887774 | − | 0.460279i | \(-0.847749\pi\) |
0.460279 | + | 0.887774i | \(0.347749\pi\) | |||||||
\(74\) | − | 22.7281i | − | 0.307136i | ||||||
\(75\) | −18.9093 | + | 38.9543i | −0.252124 | + | 0.519391i | ||||
\(76\) | 34.8033 | 0.457938 | ||||||||
\(77\) | −10.7558 | − | 10.7558i | −0.139686 | − | 0.139686i | ||||
\(78\) | 36.7508 | − | 36.7508i | 0.471164 | − | 0.471164i | ||||
\(79\) | 107.134i | 1.35612i | 0.735006 | + | 0.678061i | \(0.237179\pi\) | ||||
−0.735006 | + | 0.678061i | \(0.762821\pi\) | |||||||
\(80\) | 19.7226 | − | 3.31937i | 0.246533 | − | 0.0414921i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 53.0897 | + | 53.0897i | 0.647435 | + | 0.647435i | ||||
\(83\) | 18.2365 | − | 18.2365i | 0.219716 | − | 0.219716i | −0.588662 | − | 0.808379i | \(-0.700345\pi\) |
0.808379 | + | 0.588662i | \(0.200345\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | 27.5825 | + | 19.6356i | 0.324500 | + | 0.231007i | ||||
\(86\) | −74.2105 | −0.862912 | ||||||||
\(87\) | 46.2061 | + | 46.2061i | 0.531104 | + | 0.531104i | ||||
\(88\) | −11.4984 | + | 11.4984i | −0.130664 | + | 0.130664i | ||||
\(89\) | − | 174.675i | − | 1.96265i | −0.192368 | − | 0.981323i | \(-0.561617\pi\) | ||
0.192368 | − | 0.981323i | \(-0.438383\pi\) | |||||||
\(90\) | 12.3024 | − | 17.2815i | 0.136694 | − | 0.192017i | ||||
\(91\) | 56.1378 | 0.616898 | ||||||||
\(92\) | 26.4522 | + | 26.4522i | 0.287524 | + | 0.287524i | ||||
\(93\) | 33.0840 | − | 33.0840i | 0.355742 | − | 0.355742i | ||||
\(94\) | 18.7838i | 0.199828i | ||||||||
\(95\) | 14.4406 | + | 85.8016i | 0.152007 | + | 0.903175i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −91.5084 | − | 91.5084i | −0.943385 | − | 0.943385i | 0.0550959 | − | 0.998481i | \(-0.482454\pi\) |
−0.998481 | + | 0.0550959i | \(0.982454\pi\) | |||||||
\(98\) | 7.00000 | − | 7.00000i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 17.2477i | 0.174219i | ||||||||
\(100\) | 16.3667 | + | 47.2454i | 0.163667 | + | 0.472454i | ||||
\(101\) | −182.855 | −1.81045 | −0.905223 | − | 0.424937i | \(-0.860296\pi\) | ||||
−0.905223 | + | 0.424937i | \(0.860296\pi\) | |||||||
\(102\) | −11.7287 | − | 11.7287i | −0.114987 | − | 0.114987i | ||||
\(103\) | −46.6226 | + | 46.6226i | −0.452647 | + | 0.452647i | −0.896232 | − | 0.443586i | \(-0.853706\pi\) |
0.443586 | + | 0.896232i | \(0.353706\pi\) | |||||||
\(104\) | − | 60.0138i | − | 0.577056i | ||||||
\(105\) | 22.5951 | − | 3.80282i | 0.215191 | − | 0.0362173i | ||||
\(106\) | −87.7991 | −0.828294 | ||||||||
\(107\) | 57.5651 | + | 57.5651i | 0.537992 | + | 0.537992i | 0.922939 | − | 0.384947i | \(-0.125780\pi\) |
−0.384947 | + | 0.922939i | \(0.625780\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 205.254i | − | 1.88307i | −0.336920 | − | 0.941533i | \(-0.609385\pi\) | ||
0.336920 | − | 0.941533i | \(-0.390615\pi\) | |||||||
\(110\) | −33.1184 | − | 23.5765i | −0.301076 | − | 0.214331i | ||||
\(111\) | −27.8361 | −0.250776 | ||||||||
\(112\) | −7.48331 | − | 7.48331i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | 32.6037 | − | 32.6037i | 0.288528 | − | 0.288528i | −0.547970 | − | 0.836498i | \(-0.684599\pi\) |
0.836498 | + | 0.547970i | \(0.184599\pi\) | |||||||
\(114\) | − | 42.6252i | − | 0.373905i | ||||||
\(115\) | −54.2378 | + | 76.1890i | −0.471633 | + | 0.662513i | ||||
\(116\) | 75.4542 | 0.650467 | ||||||||
\(117\) | −45.0103 | − | 45.0103i | −0.384704 | − | 0.384704i | ||||
\(118\) | 62.9694 | − | 62.9694i | 0.533639 | − | 0.533639i | ||||
\(119\) | − | 17.9158i | − | 0.150553i | ||||||
\(120\) | −4.06538 | − | 24.1552i | −0.0338782 | − | 0.201293i | ||||
\(121\) | −87.9465 | −0.726831 | ||||||||
\(122\) | 1.67492 | + | 1.67492i | 0.0137288 | + | 0.0137288i | ||||
\(123\) | 65.0213 | − | 65.0213i | 0.528629 | − | 0.528629i | ||||
\(124\) | − | 54.0259i | − | 0.435693i | ||||||
\(125\) | −109.685 | + | 59.9524i | −0.877477 | + | 0.479619i | ||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | −103.735 | − | 103.735i | −0.816814 | − | 0.816814i | 0.168831 | − | 0.985645i | \(-0.446001\pi\) |
−0.985645 | + | 0.168831i | \(0.946001\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 90.8889i | 0.704565i | ||||||||
\(130\) | 147.954 | − | 24.9010i | 1.13810 | − | 0.191546i | ||||
\(131\) | 157.999 | 1.20610 | 0.603049 | − | 0.797704i | \(-0.293952\pi\) | ||||
0.603049 | + | 0.797704i | \(0.293952\pi\) | |||||||
\(132\) | 14.0826 | + | 14.0826i | 0.106687 | + | 0.106687i | ||||
\(133\) | 32.5555 | − | 32.5555i | 0.244778 | − | 0.244778i | ||||
\(134\) | − | 56.9819i | − | 0.425238i | ||||||
\(135\) | −21.1654 | − | 15.0673i | −0.156781 | − | 0.111610i | ||||
\(136\) | −19.1528 | −0.140830 | ||||||||
\(137\) | −36.9574 | − | 36.9574i | −0.269762 | − | 0.269762i | 0.559242 | − | 0.829004i | \(-0.311092\pi\) |
−0.829004 | + | 0.559242i | \(0.811092\pi\) | |||||||
\(138\) | 32.3972 | − | 32.3972i | 0.234762 | − | 0.234762i | ||||
\(139\) | − | 132.183i | − | 0.950960i | −0.879727 | − | 0.475480i | \(-0.842274\pi\) | ||
0.879727 | − | 0.475480i | \(-0.157726\pi\) | |||||||
\(140\) | 15.3438 | − | 21.5538i | 0.109599 | − | 0.153956i | ||||
\(141\) | 23.0054 | 0.163159 | ||||||||
\(142\) | −47.2039 | − | 47.2039i | −0.332422 | − | 0.332422i | ||||
\(143\) | −86.2581 | + | 86.2581i | −0.603203 | + | 0.603203i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 31.3076 | + | 186.019i | 0.215914 | + | 1.28289i | ||||
\(146\) | 62.4143 | 0.427495 | ||||||||
\(147\) | −8.57321 | − | 8.57321i | −0.0583212 | − | 0.0583212i | ||||
\(148\) | −22.7281 | + | 22.7281i | −0.153568 | + | 0.153568i | ||||
\(149\) | 255.329i | 1.71362i | 0.515634 | + | 0.856809i | \(0.327556\pi\) | ||||
−0.515634 | + | 0.856809i | \(0.672444\pi\) | |||||||
\(150\) | 57.8636 | − | 20.0450i | 0.385757 | − | 0.133633i | ||||
\(151\) | −210.524 | −1.39420 | −0.697098 | − | 0.716976i | \(-0.745526\pi\) | ||||
−0.697098 | + | 0.716976i | \(0.745526\pi\) | |||||||
\(152\) | −34.8033 | − | 34.8033i | −0.228969 | − | 0.228969i | ||||
\(153\) | −14.3646 | + | 14.3646i | −0.0938865 | + | 0.0938865i | ||||
\(154\) | 21.5116i | 0.139686i | ||||||||
\(155\) | 133.192 | − | 22.4165i | 0.859301 | − | 0.144623i | ||||
\(156\) | −73.5016 | −0.471164 | ||||||||
\(157\) | −181.671 | − | 181.671i | −1.15714 | − | 1.15714i | −0.985088 | − | 0.172052i | \(-0.944960\pi\) |
−0.172052 | − | 0.985088i | \(-0.555040\pi\) | |||||||
\(158\) | 107.134 | − | 107.134i | 0.678061 | − | 0.678061i | ||||
\(159\) | 107.532i | 0.676299i | ||||||||
\(160\) | −23.0420 | − | 16.4033i | −0.144012 | − | 0.102520i | ||||
\(161\) | 49.4876 | 0.307376 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 155.563 | − | 155.563i | 0.954376 | − | 0.954376i | −0.0446274 | − | 0.999004i | \(-0.514210\pi\) |
0.999004 | + | 0.0446274i | \(0.0142101\pi\) | |||||||
\(164\) | − | 106.179i | − | 0.647435i | ||||||
\(165\) | −28.8751 | + | 40.5615i | −0.175001 | + | 0.245827i | ||||
\(166\) | −36.4729 | −0.219716 | ||||||||
\(167\) | 76.0788 | + | 76.0788i | 0.455562 | + | 0.455562i | 0.897195 | − | 0.441634i | \(-0.145601\pi\) |
−0.441634 | + | 0.897195i | \(0.645601\pi\) | |||||||
\(168\) | −9.16515 | + | 9.16515i | −0.0545545 | + | 0.0545545i | ||||
\(169\) | − | 281.207i | − | 1.66395i | ||||||
\(170\) | −7.94692 | − | 47.2180i | −0.0467466 | − | 0.277753i | ||||
\(171\) | −52.2050 | −0.305292 | ||||||||
\(172\) | 74.2105 | + | 74.2105i | 0.431456 | + | 0.431456i | ||||
\(173\) | 28.9323 | − | 28.9323i | 0.167239 | − | 0.167239i | −0.618526 | − | 0.785765i | \(-0.712270\pi\) |
0.785765 | + | 0.618526i | \(0.212270\pi\) | |||||||
\(174\) | − | 92.4121i | − | 0.531104i | ||||||
\(175\) | 59.5037 | + | 28.8844i | 0.340021 | + | 0.165054i | ||||
\(176\) | 22.9969 | 0.130664 | ||||||||
\(177\) | −77.1214 | − | 77.1214i | −0.435714 | − | 0.435714i | ||||
\(178\) | −174.675 | + | 174.675i | −0.981323 | + | 0.981323i | ||||
\(179\) | − | 126.849i | − | 0.708653i | −0.935122 | − | 0.354327i | \(-0.884710\pi\) | ||
0.935122 | − | 0.354327i | \(-0.115290\pi\) | |||||||
\(180\) | −29.5839 | + | 4.97906i | −0.164355 | + | 0.0276614i | ||||
\(181\) | 307.681 | 1.69989 | 0.849947 | − | 0.526867i | \(-0.176634\pi\) | ||||
0.849947 | + | 0.526867i | \(0.176634\pi\) | |||||||
\(182\) | −56.1378 | − | 56.1378i | −0.308449 | − | 0.308449i | ||||
\(183\) | 2.05135 | − | 2.05135i | 0.0112096 | − | 0.0112096i | ||||
\(184\) | − | 52.9044i | − | 0.287524i | ||||||
\(185\) | −65.4626 | − | 46.6018i | −0.353852 | − | 0.251902i | ||||
\(186\) | −66.1680 | −0.355742 | ||||||||
\(187\) | 27.5285 | + | 27.5285i | 0.147211 | + | 0.147211i | ||||
\(188\) | 18.7838 | − | 18.7838i | 0.0999139 | − | 0.0999139i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 71.3609 | − | 100.242i | 0.375584 | − | 0.527591i | ||||
\(191\) | 71.4969 | 0.374329 | 0.187165 | − | 0.982329i | \(-0.440070\pi\) | ||||
0.187165 | + | 0.982329i | \(0.440070\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −155.347 | + | 155.347i | −0.804908 | + | 0.804908i | −0.983858 | − | 0.178950i | \(-0.942730\pi\) |
0.178950 | + | 0.983858i | \(0.442730\pi\) | |||||||
\(194\) | 183.017i | 0.943385i | ||||||||
\(195\) | −30.4974 | − | 181.205i | −0.156397 | − | 0.929259i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 190.520 | + | 190.520i | 0.967107 | + | 0.967107i | 0.999476 | − | 0.0323691i | \(-0.0103052\pi\) |
−0.0323691 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(198\) | 17.2477 | − | 17.2477i | 0.0871093 | − | 0.0871093i | ||||
\(199\) | 173.246i | 0.870582i | 0.900290 | + | 0.435291i | \(0.143354\pi\) | ||||
−0.900290 | + | 0.435291i | \(0.856646\pi\) | |||||||
\(200\) | 30.8788 | − | 63.6121i | 0.154394 | − | 0.318061i | ||||
\(201\) | −69.7883 | −0.347205 | ||||||||
\(202\) | 182.855 | + | 182.855i | 0.905223 | + | 0.905223i | ||||
\(203\) | 70.5809 | − | 70.5809i | 0.347689 | − | 0.347689i | ||||
\(204\) | 23.4573i | 0.114987i | ||||||||
\(205\) | 261.767 | − | 44.0561i | 1.27691 | − | 0.214908i | ||||
\(206\) | 93.2452 | 0.452647 | ||||||||
\(207\) | −39.6783 | − | 39.6783i | −0.191683 | − | 0.191683i | ||||
\(208\) | −60.0138 | + | 60.0138i | −0.288528 | + | 0.288528i | ||||
\(209\) | 100.046i | 0.478689i | ||||||||
\(210\) | −26.3979 | − | 18.7923i | −0.125704 | − | 0.0894871i | ||||
\(211\) | 53.9193 | 0.255542 | 0.127771 | − | 0.991804i | \(-0.459218\pi\) | ||||
0.127771 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(212\) | 87.7991 | + | 87.7991i | 0.414147 | + | 0.414147i | ||||
\(213\) | −57.8128 | + | 57.8128i | −0.271422 | + | 0.271422i | ||||
\(214\) | − | 115.130i | − | 0.537992i | ||||||
\(215\) | −152.162 | + | 213.745i | −0.707728 | + | 0.994161i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −50.5366 | − | 50.5366i | −0.232888 | − | 0.232888i | ||||
\(218\) | −205.254 | + | 205.254i | −0.941533 | + | 0.941533i | ||||
\(219\) | − | 76.4415i | − | 0.349048i | ||||||
\(220\) | 9.54189 | + | 56.6948i | 0.0433722 | + | 0.257704i | ||||
\(221\) | −143.679 | −0.650133 | ||||||||
\(222\) | 27.8361 | + | 27.8361i | 0.125388 | + | 0.125388i | ||||
\(223\) | −146.512 | + | 146.512i | −0.657006 | + | 0.657006i | −0.954671 | − | 0.297664i | \(-0.903792\pi\) |
0.297664 | + | 0.954671i | \(0.403792\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | −24.5500 | − | 70.8682i | −0.109111 | − | 0.314970i | ||||
\(226\) | −65.2073 | −0.288528 | ||||||||
\(227\) | 162.897 | + | 162.897i | 0.717607 | + | 0.717607i | 0.968115 | − | 0.250508i | \(-0.0805975\pi\) |
−0.250508 | + | 0.968115i | \(0.580598\pi\) | |||||||
\(228\) | −42.6252 | + | 42.6252i | −0.186953 | + | 0.186953i | ||||
\(229\) | 176.209i | 0.769470i | 0.923027 | + | 0.384735i | \(0.125707\pi\) | ||||
−0.923027 | + | 0.384735i | \(0.874293\pi\) | |||||||
\(230\) | 130.427 | − | 21.9512i | 0.567073 | − | 0.0954399i | ||||
\(231\) | 26.3462 | 0.114053 | ||||||||
\(232\) | −75.4542 | − | 75.4542i | −0.325234 | − | 0.325234i | ||||
\(233\) | −18.3615 | + | 18.3615i | −0.0788049 | + | 0.0788049i | −0.745411 | − | 0.666606i | \(-0.767747\pi\) |
0.666606 | + | 0.745411i | \(0.267747\pi\) | |||||||
\(234\) | 90.0207i | 0.384704i | ||||||||
\(235\) | 54.1020 | + | 38.5144i | 0.230221 | + | 0.163891i | ||||
\(236\) | −125.939 | −0.533639 | ||||||||
\(237\) | −131.211 | − | 131.211i | −0.553634 | − | 0.553634i | ||||
\(238\) | −17.9158 | + | 17.9158i | −0.0752767 | + | 0.0752767i | ||||
\(239\) | 275.093i | 1.15102i | 0.817795 | + | 0.575509i | \(0.195196\pi\) | ||||
−0.817795 | + | 0.575509i | \(0.804804\pi\) | |||||||
\(240\) | −20.0898 | + | 28.2206i | −0.0837075 | + | 0.117586i | ||||
\(241\) | 338.925 | 1.40633 | 0.703164 | − | 0.711028i | \(-0.251770\pi\) | ||||
0.703164 | + | 0.711028i | \(0.251770\pi\) | |||||||
\(242\) | 87.9465 | + | 87.9465i | 0.363415 | + | 0.363415i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 3.34984i | − | 0.0137288i | ||||||
\(245\) | −5.80890 | − | 34.5146i | −0.0237098 | − | 0.140876i | ||||
\(246\) | −130.043 | −0.528629 | ||||||||
\(247\) | −261.085 | − | 261.085i | −1.05702 | − | 1.05702i | ||||
\(248\) | −54.0259 | + | 54.0259i | −0.217846 | + | 0.217846i | ||||
\(249\) | 44.6700i | 0.179398i | ||||||||
\(250\) | 169.637 | + | 49.7323i | 0.678548 | + | 0.198929i | ||||
\(251\) | 72.1187 | 0.287326 | 0.143663 | − | 0.989627i | \(-0.454112\pi\) | ||||
0.143663 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(252\) | 11.2250 | + | 11.2250i | 0.0445435 | + | 0.0445435i | ||||
\(253\) | −76.0397 | + | 76.0397i | −0.300552 | + | 0.300552i | ||||
\(254\) | 207.471i | 0.816814i | ||||||||
\(255\) | −57.8301 | + | 9.73296i | −0.226785 | + | 0.0381685i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −12.2256 | − | 12.2256i | −0.0475703 | − | 0.0475703i | 0.682921 | − | 0.730492i | \(-0.260709\pi\) |
−0.730492 | + | 0.682921i | \(0.760709\pi\) | |||||||
\(258\) | 90.8889 | − | 90.8889i | 0.352282 | − | 0.352282i | ||||
\(259\) | 42.5204i | 0.164171i | ||||||||
\(260\) | −172.855 | − | 123.053i | −0.664826 | − | 0.473279i | ||||
\(261\) | −113.181 | −0.433645 | ||||||||
\(262\) | −157.999 | − | 157.999i | −0.603049 | − | 0.603049i | ||||
\(263\) | 275.733 | − | 275.733i | 1.04842 | − | 1.04842i | 0.0496495 | − | 0.998767i | \(-0.484190\pi\) |
0.998767 | − | 0.0496495i | \(-0.0158104\pi\) | |||||||
\(264\) | − | 28.1653i | − | 0.106687i | ||||||
\(265\) | −180.024 | + | 252.883i | −0.679335 | + | 0.954277i | ||||
\(266\) | −65.1110 | −0.244778 | ||||||||
\(267\) | 213.933 | + | 213.933i | 0.801247 | + | 0.801247i | ||||
\(268\) | −56.9819 | + | 56.9819i | −0.212619 | + | 0.212619i | ||||
\(269\) | − | 275.988i | − | 1.02598i | −0.858395 | − | 0.512989i | \(-0.828538\pi\) | ||
0.858395 | − | 0.512989i | \(-0.171462\pi\) | |||||||
\(270\) | 6.09807 | + | 36.2328i | 0.0225855 | + | 0.134195i | ||||
\(271\) | 295.698 | 1.09114 | 0.545568 | − | 0.838067i | \(-0.316314\pi\) | ||||
0.545568 | + | 0.838067i | \(0.316314\pi\) | |||||||
\(272\) | 19.1528 | + | 19.1528i | 0.0704149 | + | 0.0704149i | ||||
\(273\) | −68.7544 | + | 68.7544i | −0.251848 | + | 0.251848i | ||||
\(274\) | 73.9148i | 0.269762i | ||||||||
\(275\) | −135.812 | + | 47.0478i | −0.493862 | + | 0.171083i | ||||
\(276\) | −64.7944 | −0.234762 | ||||||||
\(277\) | −21.4676 | − | 21.4676i | −0.0775005 | − | 0.0775005i | 0.667294 | − | 0.744794i | \(-0.267452\pi\) |
−0.744794 | + | 0.667294i | \(0.767452\pi\) | |||||||
\(278\) | −132.183 | + | 132.183i | −0.475480 | + | 0.475480i | ||||
\(279\) | 81.0389i | 0.290462i | ||||||||
\(280\) | −36.8976 | + | 6.20997i | −0.131777 | + | 0.0221785i | ||||
\(281\) | 74.2011 | 0.264061 | 0.132030 | − | 0.991246i | \(-0.457850\pi\) | ||||
0.132030 | + | 0.991246i | \(0.457850\pi\) | |||||||
\(282\) | −23.0054 | − | 23.0054i | −0.0815793 | − | 0.0815793i | ||||
\(283\) | −322.473 | + | 322.473i | −1.13948 | + | 1.13948i | −0.150937 | + | 0.988543i | \(0.548229\pi\) |
−0.988543 | + | 0.150937i | \(0.951771\pi\) | |||||||
\(284\) | 94.4079i | 0.332422i | ||||||||
\(285\) | −122.771 | − | 87.3989i | −0.430776 | − | 0.306663i | ||||
\(286\) | 172.516 | 0.603203 | ||||||||
\(287\) | −99.3217 | − | 99.3217i | −0.346069 | − | 0.346069i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 243.146i | − | 0.841336i | ||||||
\(290\) | 154.712 | − | 217.327i | 0.533489 | − | 0.749403i | ||||
\(291\) | 224.149 | 0.770271 | ||||||||
\(292\) | −62.4143 | − | 62.4143i | −0.213747 | − | 0.213747i | ||||
\(293\) | −145.754 | + | 145.754i | −0.497456 | + | 0.497456i | −0.910645 | − | 0.413189i | \(-0.864415\pi\) |
0.413189 | + | 0.910645i | \(0.364415\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | −52.2547 | − | 310.480i | −0.177134 | − | 1.05248i | ||||
\(296\) | 45.4562 | 0.153568 | ||||||||
\(297\) | −21.1240 | − | 21.1240i | −0.0711245 | − | 0.0711245i | ||||
\(298\) | 255.329 | − | 255.329i | 0.856809 | − | 0.856809i | ||||
\(299\) | − | 396.874i | − | 1.32734i | ||||||
\(300\) | −77.9086 | − | 37.8186i | −0.259695 | − | 0.126062i | ||||
\(301\) | 138.835 | 0.461246 | ||||||||
\(302\) | 210.524 | + | 210.524i | 0.697098 | + | 0.697098i | ||||
\(303\) | 223.951 | − | 223.951i | 0.739111 | − | 0.739111i | ||||
\(304\) | 69.6066i | 0.228969i | ||||||||
\(305\) | 8.25845 | − | 1.38992i | 0.0270769 | − | 0.00455711i | ||||
\(306\) | 28.7293 | 0.0938865 | ||||||||
\(307\) | −308.104 | − | 308.104i | −1.00360 | − | 1.00360i | −0.999994 | − | 0.00360237i | \(-0.998853\pi\) |
−0.00360237 | − | 0.999994i | \(-0.501147\pi\) | |||||||
\(308\) | 21.5116 | − | 21.5116i | 0.0698429 | − | 0.0698429i | ||||
\(309\) | − | 114.202i | − | 0.369584i | ||||||
\(310\) | −155.608 | − | 110.775i | −0.501962 | − | 0.357339i | ||||
\(311\) | −29.1191 | −0.0936304 | −0.0468152 | − | 0.998904i | \(-0.514907\pi\) | ||||
−0.0468152 | + | 0.998904i | \(0.514907\pi\) | |||||||
\(312\) | 73.5016 | + | 73.5016i | 0.235582 | + | 0.235582i | ||||
\(313\) | 12.1714 | − | 12.1714i | 0.0388863 | − | 0.0388863i | −0.687396 | − | 0.726283i | \(-0.741246\pi\) |
0.726283 | + | 0.687396i | \(0.241246\pi\) | |||||||
\(314\) | 363.342i | 1.15714i | ||||||||
\(315\) | −23.0158 | + | 32.3307i | −0.0730659 | + | 0.102637i | ||||
\(316\) | −214.267 | −0.678061 | ||||||||
\(317\) | 219.192 | + | 219.192i | 0.691456 | + | 0.691456i | 0.962552 | − | 0.271096i | \(-0.0873862\pi\) |
−0.271096 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(318\) | 107.532 | − | 107.532i | 0.338150 | − | 0.338150i | ||||
\(319\) | 216.901i | 0.679941i | ||||||||
\(320\) | 6.63874 | + | 39.4452i | 0.0207461 | + | 0.123266i | ||||
\(321\) | −141.005 | −0.439269 | ||||||||
\(322\) | −49.4876 | − | 49.4876i | −0.153688 | − | 0.153688i | ||||
\(323\) | −83.3228 | + | 83.3228i | −0.257965 | + | 0.257965i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 231.644 | − | 477.201i | 0.712751 | − | 1.46831i | ||||
\(326\) | −311.127 | −0.954376 | ||||||||
\(327\) | 251.384 | + | 251.384i | 0.768759 | + | 0.768759i | ||||
\(328\) | −106.179 | + | 106.179i | −0.323718 | + | 0.323718i | ||||
\(329\) | − | 35.1413i | − | 0.106812i | ||||||
\(330\) | 69.4367 | − | 11.6864i | 0.210414 | − | 0.0354133i | ||||
\(331\) | 276.111 | 0.834171 | 0.417086 | − | 0.908867i | \(-0.363052\pi\) | ||||
0.417086 | + | 0.908867i | \(0.363052\pi\) | |||||||
\(332\) | 36.4729 | + | 36.4729i | 0.109858 | + | 0.109858i | ||||
\(333\) | 34.0921 | − | 34.0921i | 0.102379 | − | 0.102379i | ||||
\(334\) | − | 152.158i | − | 0.455562i | ||||||
\(335\) | −164.122 | − | 116.836i | −0.489916 | − | 0.348764i | ||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | 276.393 | + | 276.393i | 0.820157 | + | 0.820157i | 0.986130 | − | 0.165973i | \(-0.0530766\pi\) |
−0.165973 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(338\) | −281.207 | + | 281.207i | −0.831973 | + | 0.831973i | ||||
\(339\) | 79.8623i | 0.235582i | ||||||||
\(340\) | −39.2711 | + | 55.1650i | −0.115503 | + | 0.162250i | ||||
\(341\) | 155.303 | 0.455435 | ||||||||
\(342\) | 52.2050 | + | 52.2050i | 0.152646 | + | 0.152646i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 148.421i | − | 0.431456i | ||||||
\(345\) | −26.8846 | − | 159.739i | −0.0779263 | − | 0.463013i | ||||
\(346\) | −57.8647 | −0.167239 | ||||||||
\(347\) | −158.084 | − | 158.084i | −0.455573 | − | 0.455573i | 0.441626 | − | 0.897199i | \(-0.354402\pi\) |
−0.897199 | + | 0.441626i | \(0.854402\pi\) | |||||||
\(348\) | −92.4121 | + | 92.4121i | −0.265552 | + | 0.265552i | ||||
\(349\) | 452.412i | 1.29631i | 0.761508 | + | 0.648155i | \(0.224459\pi\) | ||||
−0.761508 | + | 0.648155i | \(0.775541\pi\) | |||||||
\(350\) | −30.6192 | − | 88.3881i | −0.0874835 | − | 0.252538i | ||||
\(351\) | 110.252 | 0.314109 | ||||||||
\(352\) | −22.9969 | − | 22.9969i | −0.0653320 | − | 0.0653320i | ||||
\(353\) | 481.681 | − | 481.681i | 1.36453 | − | 1.36453i | 0.496495 | − | 0.868039i | \(-0.334620\pi\) |
0.868039 | − | 0.496495i | \(-0.165380\pi\) | |||||||
\(354\) | 154.243i | 0.435714i | ||||||||
\(355\) | −232.746 | + | 39.1718i | −0.655624 | + | 0.110343i | ||||
\(356\) | 349.351 | 0.981323 | ||||||||
\(357\) | 21.9423 | + | 21.9423i | 0.0614631 | + | 0.0614631i | ||||
\(358\) | −126.849 | + | 126.849i | −0.354327 | + | 0.354327i | ||||
\(359\) | 485.514i | 1.35241i | 0.736716 | + | 0.676203i | \(0.236376\pi\) | ||||
−0.736716 | + | 0.676203i | \(0.763624\pi\) | |||||||
\(360\) | 34.5630 | + | 24.6049i | 0.0960083 | + | 0.0683469i | ||||
\(361\) | 58.1823 | 0.161170 | ||||||||
\(362\) | −307.681 | − | 307.681i | −0.849947 | − | 0.849947i | ||||
\(363\) | 107.712 | − | 107.712i | 0.296727 | − | 0.296727i | ||||
\(364\) | 112.276i | 0.308449i | ||||||||
\(365\) | 127.975 | − | 179.769i | 0.350615 | − | 0.492517i | ||||
\(366\) | −4.10270 | −0.0112096 | ||||||||
\(367\) | 205.331 | + | 205.331i | 0.559486 | + | 0.559486i | 0.929161 | − | 0.369675i | \(-0.120531\pi\) |
−0.369675 | + | 0.929161i | \(0.620531\pi\) | |||||||
\(368\) | −52.9044 | + | 52.9044i | −0.143762 | + | 0.143762i | ||||
\(369\) | 159.269i | 0.431623i | ||||||||
\(370\) | 18.8607 | + | 112.064i | 0.0509750 | + | 0.302877i | ||||
\(371\) | 164.257 | 0.442742 | ||||||||
\(372\) | 66.1680 | + | 66.1680i | 0.177871 | + | 0.177871i | ||||
\(373\) | −24.9803 | + | 24.9803i | −0.0669714 | + | 0.0669714i | −0.739799 | − | 0.672828i | \(-0.765079\pi\) |
0.672828 | + | 0.739799i | \(0.265079\pi\) | |||||||
\(374\) | − | 55.0569i | − | 0.147211i | ||||||
\(375\) | 60.9093 | − | 207.762i | 0.162425 | − | 0.554032i | ||||
\(376\) | −37.5676 | −0.0999139 | ||||||||
\(377\) | −566.037 | − | 566.037i | −1.50142 | − | 1.50142i | ||||
\(378\) | 13.7477 | − | 13.7477i | 0.0363696 | − | 0.0363696i | ||||
\(379\) | − | 356.423i | − | 0.940429i | −0.882552 | − | 0.470215i | \(-0.844177\pi\) | ||
0.882552 | − | 0.470215i | \(-0.155823\pi\) | |||||||
\(380\) | −171.603 | + | 28.8813i | −0.451587 | + | 0.0760034i | ||||
\(381\) | 254.099 | 0.666926 | ||||||||
\(382\) | −71.4969 | − | 71.4969i | −0.187165 | − | 0.187165i | ||||
\(383\) | 480.677 | − | 480.677i | 1.25503 | − | 1.25503i | 0.301596 | − | 0.953436i | \(-0.402481\pi\) |
0.953436 | − | 0.301596i | \(-0.0975194\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 61.9588 | + | 44.1075i | 0.160932 | + | 0.114565i | ||||
\(386\) | 310.695 | 0.804908 | ||||||||
\(387\) | −111.316 | − | 111.316i | −0.287637 | − | 0.287637i | ||||
\(388\) | 183.017 | − | 183.017i | 0.471693 | − | 0.471693i | ||||
\(389\) | − | 169.784i | − | 0.436461i | −0.975897 | − | 0.218231i | \(-0.929971\pi\) | ||
0.975897 | − | 0.218231i | \(-0.0700285\pi\) | |||||||
\(390\) | −150.708 | + | 211.703i | −0.386431 | + | 0.542828i | ||||
\(391\) | −126.659 | −0.323935 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | −193.508 | + | 193.508i | −0.492387 | + | 0.492387i | ||||
\(394\) | − | 381.040i | − | 0.967107i | ||||||
\(395\) | −88.9040 | − | 528.239i | −0.225073 | − | 1.33731i | ||||
\(396\) | −34.4953 | −0.0871093 | ||||||||
\(397\) | −66.1208 | − | 66.1208i | −0.166551 | − | 0.166551i | 0.618910 | − | 0.785462i | \(-0.287574\pi\) |
−0.785462 | + | 0.618910i | \(0.787574\pi\) | |||||||
\(398\) | 173.246 | − | 173.246i | 0.435291 | − | 0.435291i | ||||
\(399\) | 79.7444i | 0.199861i | ||||||||
\(400\) | −94.4909 | + | 32.7333i | −0.236227 | + | 0.0818334i | ||||
\(401\) | −213.860 | −0.533318 | −0.266659 | − | 0.963791i | \(-0.585920\pi\) | ||||
−0.266659 | + | 0.963791i | \(0.585920\pi\) | |||||||
\(402\) | 69.7883 | + | 69.7883i | 0.173603 | + | 0.173603i | ||||
\(403\) | −405.288 | + | 405.288i | −1.00568 | + | 1.00568i | ||||
\(404\) | − | 365.710i | − | 0.905223i | ||||||
\(405\) | 44.3759 | − | 7.46858i | 0.109570 | − | 0.0184409i | ||||
\(406\) | −141.162 | −0.347689 | ||||||||
\(407\) | −65.3344 | − | 65.3344i | −0.160527 | − | 0.160527i | ||||
\(408\) | 23.4573 | − | 23.4573i | 0.0574935 | − | 0.0574935i | ||||
\(409\) | − | 300.366i | − | 0.734391i | −0.930144 | − | 0.367196i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367196i | \(-0.119682\pi\) | |||||||
\(410\) | −305.823 | − | 217.711i | −0.745910 | − | 0.531002i | ||||
\(411\) | 90.5267 | 0.220260 | ||||||||
\(412\) | −93.2452 | − | 93.2452i | −0.226323 | − | 0.226323i | ||||
\(413\) | −117.805 | + | 117.805i | −0.285242 | + | 0.285242i | ||||
\(414\) | 79.3566i | 0.191683i | ||||||||
\(415\) | −74.7843 | + | 105.051i | −0.180203 | + | 0.253135i | ||||
\(416\) | 120.028 | 0.288528 | ||||||||
\(417\) | 161.891 | + | 161.891i | 0.388228 | + | 0.388228i | ||||
\(418\) | 100.046 | − | 100.046i | 0.239344 | − | 0.239344i | ||||
\(419\) | 696.907i | 1.66326i | 0.555328 | + | 0.831632i | \(0.312593\pi\) | ||||
−0.555328 | + | 0.831632i | \(0.687407\pi\) | |||||||
\(420\) | 7.60563 | + | 45.1902i | 0.0181087 | + | 0.107596i | ||||
\(421\) | −114.980 | −0.273111 | −0.136555 | − | 0.990632i | \(-0.543603\pi\) | ||||
−0.136555 | + | 0.990632i | \(0.543603\pi\) | |||||||
\(422\) | −53.9193 | − | 53.9193i | −0.127771 | − | 0.127771i | ||||
\(423\) | −28.1757 | + | 28.1757i | −0.0666092 | + | 0.0666092i | ||||
\(424\) | − | 175.598i | − | 0.414147i | ||||||
\(425\) | −152.294 | − | 73.9270i | −0.358339 | − | 0.173946i | ||||
\(426\) | 115.626 | 0.271422 | ||||||||
\(427\) | −3.13349 | − | 3.13349i | −0.00733838 | − | 0.00733838i | ||||
\(428\) | −115.130 | + | 115.130i | −0.268996 | + | 0.268996i | ||||
\(429\) | − | 211.288i | − | 0.492513i | ||||||
\(430\) | 365.906 | − | 61.5830i | 0.850945 | − | 0.143216i | ||||
\(431\) | −724.694 | −1.68143 | −0.840713 | − | 0.541481i | \(-0.817864\pi\) | ||||
−0.840713 | + | 0.541481i | \(0.817864\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 100.327 | − | 100.327i | 0.231703 | − | 0.231703i | −0.581700 | − | 0.813403i | \(-0.697612\pi\) |
0.813403 | + | 0.581700i | \(0.197612\pi\) | |||||||
\(434\) | 101.073i | 0.232888i | ||||||||
\(435\) | −266.170 | − | 189.482i | −0.611885 | − | 0.435592i | ||||
\(436\) | 410.509 | 0.941533 | ||||||||
\(437\) | −230.156 | − | 230.156i | −0.526673 | − | 0.526673i | ||||
\(438\) | −76.4415 | + | 76.4415i | −0.174524 | + | 0.174524i | ||||
\(439\) | 685.890i | 1.56239i | 0.624286 | + | 0.781195i | \(0.285390\pi\) | ||||
−0.624286 | + | 0.781195i | \(0.714610\pi\) | |||||||
\(440\) | 47.1529 | − | 66.2367i | 0.107166 | − | 0.150538i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | 143.679 | + | 143.679i | 0.325066 | + | 0.325066i | ||||
\(443\) | 339.752 | − | 339.752i | 0.766935 | − | 0.766935i | −0.210631 | − | 0.977566i | \(-0.567552\pi\) |
0.977566 | + | 0.210631i | \(0.0675517\pi\) | |||||||
\(444\) | − | 55.6722i | − | 0.125388i | ||||||
\(445\) | 144.953 | + | 861.264i | 0.325737 | + | 1.93543i | ||||
\(446\) | 293.025 | 0.657006 | ||||||||
\(447\) | −312.713 | − | 312.713i | −0.699581 | − | 0.699581i | ||||
\(448\) | 14.9666 | − | 14.9666i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 226.637i | 0.504758i | 0.967628 | + | 0.252379i | \(0.0812130\pi\) | ||||
−0.967628 | + | 0.252379i | \(0.918787\pi\) | |||||||
\(450\) | −46.3182 | + | 95.4182i | −0.102929 | + | 0.212040i | ||||
\(451\) | 305.224 | 0.676772 | ||||||||
\(452\) | 65.2073 | + | 65.2073i | 0.144264 | + | 0.144264i | ||||
\(453\) | 257.838 | − | 257.838i | 0.569178 | − | 0.569178i | ||||
\(454\) | − | 325.794i | − | 0.717607i | ||||||
\(455\) | −276.796 | + | 46.5855i | −0.608343 | + | 0.102386i | ||||
\(456\) | 85.2504 | 0.186953 | ||||||||
\(457\) | −266.282 | − | 266.282i | −0.582675 | − | 0.582675i | 0.352963 | − | 0.935637i | \(-0.385174\pi\) |
−0.935637 | + | 0.352963i | \(0.885174\pi\) | |||||||
\(458\) | 176.209 | − | 176.209i | 0.384735 | − | 0.384735i | ||||
\(459\) | − | 35.1860i | − | 0.0766580i | ||||||
\(460\) | −152.378 | − | 108.476i | −0.331256 | − | 0.235816i | ||||
\(461\) | −121.199 | −0.262905 | −0.131453 | − | 0.991322i | \(-0.541964\pi\) | ||||
−0.131453 | + | 0.991322i | \(0.541964\pi\) | |||||||
\(462\) | −26.3462 | − | 26.3462i | −0.0570265 | − | 0.0570265i | ||||
\(463\) | −565.604 | + | 565.604i | −1.22161 | + | 1.22161i | −0.254547 | + | 0.967061i | \(0.581926\pi\) |
−0.967061 | + | 0.254547i | \(0.918074\pi\) | |||||||
\(464\) | 150.908i | 0.325234i | ||||||||
\(465\) | −135.671 | + | 190.580i | −0.291766 | + | 0.409850i | ||||
\(466\) | 36.7231 | 0.0788049 | ||||||||
\(467\) | −279.536 | − | 279.536i | −0.598578 | − | 0.598578i | 0.341356 | − | 0.939934i | \(-0.389114\pi\) |
−0.939934 | + | 0.341356i | \(0.889114\pi\) | |||||||
\(468\) | 90.0207 | − | 90.0207i | 0.192352 | − | 0.192352i | ||||
\(469\) | 106.603i | 0.227299i | ||||||||
\(470\) | −15.5876 | − | 92.6165i | −0.0331651 | − | 0.197056i | ||||
\(471\) | 445.001 | 0.944801 | ||||||||
\(472\) | 125.939 | + | 125.939i | 0.266819 | + | 0.266819i | ||||
\(473\) | −213.326 | + | 213.326i | −0.451006 | + | 0.451006i | ||||
\(474\) | 262.423i | 0.553634i | ||||||||
\(475\) | −142.404 | − | 411.075i | −0.299797 | − | 0.865420i | ||||
\(476\) | 35.8317 | 0.0752767 | ||||||||
\(477\) | −131.699 | − | 131.699i | −0.276098 | − | 0.276098i | ||||
\(478\) | 275.093 | − | 275.093i | 0.575509 | − | 0.575509i | ||||
\(479\) | 101.987i | 0.212916i | 0.994317 | + | 0.106458i | \(0.0339510\pi\) | ||||
−0.994317 | + | 0.106458i | \(0.966049\pi\) | |||||||
\(480\) | 48.3104 | − | 8.13076i | 0.100647 | − | 0.0169391i | ||||
\(481\) | 341.000 | 0.708939 | ||||||||
\(482\) | −338.925 | − | 338.925i | −0.703164 | − | 0.703164i | ||||
\(483\) | −60.6096 | + | 60.6096i | −0.125486 | + | 0.125486i | ||||
\(484\) | − | 175.893i | − | 0.363415i | ||||||
\(485\) | 527.134 | + | 375.259i | 1.08687 | + | 0.773729i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 250.272 | + | 250.272i | 0.513907 | + | 0.513907i | 0.915721 | − | 0.401815i | \(-0.131620\pi\) |
−0.401815 | + | 0.915721i | \(0.631620\pi\) | |||||||
\(488\) | −3.34984 | + | 3.34984i | −0.00686442 | + | 0.00686442i | ||||
\(489\) | 381.051i | 0.779245i | ||||||||
\(490\) | −28.7057 | + | 40.3235i | −0.0585830 | + | 0.0822928i | ||||
\(491\) | −648.021 | −1.31980 | −0.659899 | − | 0.751355i | \(-0.729401\pi\) | ||||
−0.659899 | + | 0.751355i | \(0.729401\pi\) | |||||||
\(492\) | 130.043 | + | 130.043i | 0.264314 | + | 0.264314i | ||||
\(493\) | −180.645 | + | 180.645i | −0.366421 | + | 0.366421i | ||||
\(494\) | 522.170i | 1.05702i | ||||||||
\(495\) | −14.3128 | − | 85.0422i | −0.0289148 | − | 0.171802i | ||||
\(496\) | 108.052 | 0.217846 | ||||||||
\(497\) | 88.3105 | + | 88.3105i | 0.177687 | + | 0.177687i | ||||
\(498\) | 44.6700 | − | 44.6700i | 0.0896989 | − | 0.0896989i | ||||
\(499\) | 377.798i | 0.757110i | 0.925579 | + | 0.378555i | \(0.123579\pi\) | ||||
−0.925579 | + | 0.378555i | \(0.876421\pi\) | |||||||
\(500\) | −119.905 | − | 219.369i | −0.239809 | − | 0.438738i | ||||
\(501\) | −186.354 | −0.371965 | ||||||||
\(502\) | −72.1187 | − | 72.1187i | −0.143663 | − | 0.143663i | ||||
\(503\) | −221.145 | + | 221.145i | −0.439651 | + | 0.439651i | −0.891895 | − | 0.452243i | \(-0.850624\pi\) |
0.452243 | + | 0.891895i | \(0.350624\pi\) | |||||||
\(504\) | − | 22.4499i | − | 0.0445435i | ||||||
\(505\) | 901.595 | − | 151.741i | 1.78534 | − | 0.300477i | ||||
\(506\) | 152.079 | 0.300552 | ||||||||
\(507\) | 344.407 | + | 344.407i | 0.679303 | + | 0.679303i | ||||
\(508\) | 207.471 | − | 207.471i | 0.408407 | − | 0.408407i | ||||
\(509\) | − | 586.753i | − | 1.15276i | −0.817183 | − | 0.576378i | \(-0.804465\pi\) | ||
0.817183 | − | 0.576378i | \(-0.195535\pi\) | |||||||
\(510\) | 67.5630 | + | 48.0971i | 0.132476 | + | 0.0943080i | ||||
\(511\) | −116.766 | −0.228506 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 63.9378 | − | 63.9378i | 0.124635 | − | 0.124635i | ||||
\(514\) | 24.4511i | 0.0475703i | ||||||||
\(515\) | 191.191 | − | 268.569i | 0.371244 | − | 0.521494i | ||||
\(516\) | −181.778 | −0.352282 | ||||||||
\(517\) | 53.9961 | + | 53.9961i | 0.104441 | + | 0.104441i | ||||
\(518\) | 42.5204 | − | 42.5204i | 0.0820857 | − | 0.0820857i | ||||
\(519\) | 70.8694i | 0.136550i | ||||||||
\(520\) | 49.8020 | + | 295.907i | 0.0957731 | + | 0.569052i | ||||
\(521\) | −466.427 | −0.895253 | −0.447626 | − | 0.894221i | \(-0.647731\pi\) | ||||
−0.447626 | + | 0.894221i | \(0.647731\pi\) | |||||||
\(522\) | 113.181 | + | 113.181i | 0.216822 | + | 0.216822i | ||||
\(523\) | 303.656 | − | 303.656i | 0.580604 | − | 0.580604i | −0.354465 | − | 0.935069i | \(-0.615337\pi\) |
0.935069 | + | 0.354465i | \(0.115337\pi\) | |||||||
\(524\) | 315.998i | 0.603049i | ||||||||
\(525\) | −108.253 | + | 37.5008i | −0.206196 | + | 0.0714300i | ||||
\(526\) | −551.467 | −1.04842 | ||||||||
\(527\) | 129.344 | + | 129.344i | 0.245434 | + | 0.245434i | ||||
\(528\) | −28.1653 | + | 28.1653i | −0.0533434 | + | 0.0533434i | ||||
\(529\) | 179.140i | 0.338639i | ||||||||
\(530\) | 432.907 | − | 72.8595i | 0.816806 | − | 0.137471i | ||||
\(531\) | 188.908 | 0.355759 | ||||||||
\(532\) | 65.1110 | + | 65.1110i | 0.122389 | + | 0.122389i | ||||
\(533\) | −796.528 | + | 796.528i | −1.49442 | + | 1.49442i | ||||
\(534\) | − | 427.866i | − | 0.801247i | ||||||
\(535\) | −331.604 | − | 236.064i | −0.619820 | − | 0.441241i | ||||
\(536\) | 113.964 | 0.212619 | ||||||||
\(537\) | 155.358 | + | 155.358i | 0.289307 | + | 0.289307i | ||||
\(538\) | −275.988 | + | 275.988i | −0.512989 | + | 0.512989i | ||||
\(539\) | − | 40.2445i | − | 0.0746652i | ||||||
\(540\) | 30.1347 | − | 42.3308i | 0.0558050 | − | 0.0783904i | ||||
\(541\) | 465.245 | 0.859973 | 0.429986 | − | 0.902835i | \(-0.358518\pi\) | ||||
0.429986 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(542\) | −295.698 | − | 295.698i | −0.545568 | − | 0.545568i | ||||
\(543\) | −376.831 | + | 376.831i | −0.693979 | + | 0.693979i | ||||
\(544\) | − | 38.3057i | − | 0.0704149i | ||||||
\(545\) | 170.329 | + | 1012.04i | 0.312530 | + | 1.85695i | ||||
\(546\) | 137.509 | 0.251848 | ||||||||
\(547\) | 492.529 | + | 492.529i | 0.900419 | + | 0.900419i | 0.995472 | − | 0.0950533i | \(-0.0303021\pi\) |
−0.0950533 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(548\) | 73.9148 | − | 73.9148i | 0.134881 | − | 0.134881i | ||||
\(549\) | 5.02476i | 0.00915257i | ||||||||
\(550\) | 182.860 | + | 88.7644i | 0.332473 | + | 0.161390i | ||||
\(551\) | −656.514 | −1.19150 | ||||||||
\(552\) | 64.7944 | + | 64.7944i | 0.117381 | + | 0.117381i | ||||
\(553\) | −200.429 | + | 200.429i | −0.362439 | + | 0.362439i | ||||
\(554\) | 42.9353i | 0.0775005i | ||||||||
\(555\) | 137.250 | − | 23.0996i | 0.247298 | − | 0.0416209i | ||||
\(556\) | 264.367 | 0.475480 | ||||||||
\(557\) | 395.342 | + | 395.342i | 0.709771 | + | 0.709771i | 0.966487 | − | 0.256716i | \(-0.0826405\pi\) |
−0.256716 | + | 0.966487i | \(0.582641\pi\) | |||||||
\(558\) | 81.0389 | − | 81.0389i | 0.145231 | − | 0.145231i | ||||
\(559\) | − | 1113.41i | − | 1.99179i | ||||||
\(560\) | 43.1076 | + | 30.6877i | 0.0769779 | + | 0.0547994i | ||||
\(561\) | −67.4307 | −0.120197 | ||||||||
\(562\) | −74.2011 | − | 74.2011i | −0.132030 | − | 0.132030i | ||||
\(563\) | 447.005 | − | 447.005i | 0.793971 | − | 0.793971i | −0.188167 | − | 0.982137i | \(-0.560254\pi\) |
0.982137 | + | 0.188167i | \(0.0602545\pi\) | |||||||
\(564\) | 46.0107i | 0.0815793i | ||||||||
\(565\) | −133.701 | + | 187.813i | −0.236640 | + | 0.332413i | ||||
\(566\) | 644.946 | 1.13948 | ||||||||
\(567\) | −16.8375 | − | 16.8375i | −0.0296957 | − | 0.0296957i | ||||
\(568\) | 94.4079 | − | 94.4079i | 0.166211 | − | 0.166211i | ||||
\(569\) | − | 39.2969i | − | 0.0690631i | −0.999404 | − | 0.0345316i | \(-0.989006\pi\) | ||
0.999404 | − | 0.0345316i | \(-0.0109939\pi\) | |||||||
\(570\) | 35.3722 | + | 210.170i | 0.0620565 | + | 0.368719i | ||||
\(571\) | −824.326 | −1.44365 | −0.721826 | − | 0.692074i | \(-0.756697\pi\) | ||||
−0.721826 | + | 0.692074i | \(0.756697\pi\) | |||||||
\(572\) | −172.516 | − | 172.516i | −0.301602 | − | 0.301602i | ||||
\(573\) | −87.5654 | + | 87.5654i | −0.152819 | + | 0.152819i | ||||
\(574\) | 198.643i | 0.346069i | ||||||||
\(575\) | 204.203 | − | 420.670i | 0.355136 | − | 0.731600i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 645.287 | + | 645.287i | 1.11835 | + | 1.11835i | 0.991984 | + | 0.126365i | \(0.0403311\pi\) |
0.126365 | + | 0.991984i | \(0.459669\pi\) | |||||||
\(578\) | −243.146 | + | 243.146i | −0.420668 | + | 0.420668i | ||||
\(579\) | − | 380.522i | − | 0.657205i | ||||||
\(580\) | −372.039 | + | 62.6151i | −0.641446 | + | 0.107957i | ||||
\(581\) | 68.2346 | 0.117443 | ||||||||
\(582\) | −224.149 | − | 224.149i | −0.385135 | − | 0.385135i | ||||
\(583\) | −252.388 | + | 252.388i | −0.432913 | + | 0.432913i | ||||
\(584\) | 124.829i | 0.213747i | ||||||||
\(585\) | 259.282 | + | 184.579i | 0.443217 | + | 0.315520i | ||||
\(586\) | 291.509 | 0.497456 | ||||||||
\(587\) | 512.978 | + | 512.978i | 0.873898 | + | 0.873898i | 0.992895 | − | 0.118997i | \(-0.0379679\pi\) |
−0.118997 | + | 0.992895i | \(0.537968\pi\) | |||||||
\(588\) | 17.1464 | − | 17.1464i | 0.0291606 | − | 0.0291606i | ||||
\(589\) | 470.070i | 0.798082i | ||||||||
\(590\) | −258.226 | + | 362.735i | −0.437670 | + | 0.614805i | ||||
\(591\) | −466.677 | −0.789639 | ||||||||
\(592\) | −45.4562 | − | 45.4562i | −0.0767841 | − | 0.0767841i | ||||
\(593\) | −379.753 | + | 379.753i | −0.640393 | + | 0.640393i | −0.950652 | − | 0.310259i | \(-0.899584\pi\) |
0.310259 | + | 0.950652i | \(0.399584\pi\) | |||||||
\(594\) | 42.2479i | 0.0711245i | ||||||||
\(595\) | 14.8673 | + | 88.3369i | 0.0249871 | + | 0.148465i | ||||
\(596\) | −510.658 | −0.856809 | ||||||||
\(597\) | −212.182 | − | 212.182i | −0.355414 | − | 0.355414i | ||||
\(598\) | −396.874 | + | 396.874i | −0.663669 | + | 0.663669i | ||||
\(599\) | − | 167.160i | − | 0.279065i | −0.990218 | − | 0.139532i | \(-0.955440\pi\) | ||
0.990218 | − | 0.139532i | \(-0.0445599\pi\) | |||||||
\(600\) | 40.0900 | + | 115.727i | 0.0668167 | + | 0.192879i | ||||
\(601\) | 649.442 | 1.08060 | 0.540302 | − | 0.841472i | \(-0.318310\pi\) | ||||
0.540302 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(602\) | −138.835 | − | 138.835i | −0.230623 | − | 0.230623i | ||||
\(603\) | 85.4728 | − | 85.4728i | 0.141746 | − | 0.141746i | ||||
\(604\) | − | 421.047i | − | 0.697098i | ||||||
\(605\) | 433.634 | − | 72.9818i | 0.716750 | − | 0.120631i | ||||
\(606\) | −447.901 | −0.739111 | ||||||||
\(607\) | −342.997 | − | 342.997i | −0.565069 | − | 0.565069i | 0.365674 | − | 0.930743i | \(-0.380839\pi\) |
−0.930743 | + | 0.365674i | \(0.880839\pi\) | |||||||
\(608\) | 69.6066 | − | 69.6066i | 0.114485 | − | 0.114485i | ||||
\(609\) | 172.887i | 0.283887i | ||||||||
\(610\) | −9.64837 | − | 6.86853i | −0.0158170 | − | 0.0112599i | ||||
\(611\) | −281.822 | −0.461247 | ||||||||
\(612\) | −28.7293 | − | 28.7293i | −0.0469432 | − | 0.0469432i | ||||
\(613\) | −311.569 | + | 311.569i | −0.508270 | + | 0.508270i | −0.913995 | − | 0.405725i | \(-0.867019\pi\) |
0.405725 | + | 0.913995i | \(0.367019\pi\) | |||||||
\(614\) | 616.208i | 1.00360i | ||||||||
\(615\) | −266.640 | + | 374.555i | −0.433561 | + | 0.609033i | ||||
\(616\) | −43.0232 | −0.0698429 | ||||||||
\(617\) | 442.165 | + | 442.165i | 0.716636 | + | 0.716636i | 0.967915 | − | 0.251279i | \(-0.0808510\pi\) |
−0.251279 | + | 0.967915i | \(0.580851\pi\) | |||||||
\(618\) | −114.202 | + | 114.202i | −0.184792 | + | 0.184792i | ||||
\(619\) | − | 375.146i | − | 0.606052i | −0.952982 | − | 0.303026i | \(-0.902003\pi\) | ||
0.952982 | − | 0.303026i | \(-0.0979968\pi\) | |||||||
\(620\) | 44.8330 | + | 266.383i | 0.0723113 | + | 0.429650i | ||||
\(621\) | 97.1916 | 0.156508 | ||||||||
\(622\) | 29.1191 | + | 29.1191i | 0.0468152 | + | 0.0468152i | ||||
\(623\) | 326.788 | − | 326.788i | 0.524539 | − | 0.524539i | ||||
\(624\) | − | 147.003i | − | 0.235582i | ||||||
\(625\) | 491.066 | − | 386.625i | 0.785706 | − | 0.618601i | ||||
\(626\) | −24.3428 | −0.0388863 | ||||||||
\(627\) | −122.531 | − | 122.531i | −0.195424 | − | 0.195424i | ||||
\(628\) | 363.342 | − | 363.342i | 0.578570 | − | 0.578570i | ||||
\(629\) | − | 108.827i | − | 0.173016i | ||||||
\(630\) | 55.3465 | − | 9.31496i | 0.0878515 | − | 0.0147857i | ||||
\(631\) | −973.951 | −1.54350 | −0.771752 | − | 0.635924i | \(-0.780619\pi\) | ||||
−0.771752 | + | 0.635924i | \(0.780619\pi\) | |||||||
\(632\) | 214.267 | + | 214.267i | 0.339030 | + | 0.339030i | ||||
\(633\) | −66.0374 | + | 66.0374i | −0.104324 | + | 0.104324i | ||||
\(634\) | − | 438.383i | − | 0.691456i | ||||||
\(635\) | 597.568 | + | 425.400i | 0.941051 | + | 0.669921i | ||||
\(636\) | −215.063 | −0.338150 | ||||||||
\(637\) | 105.024 | + | 105.024i | 0.164873 | + | 0.164873i | ||||
\(638\) | 216.901 | − | 216.901i | 0.339971 | − | 0.339971i | ||||
\(639\) | − | 141.612i | − | 0.221615i | ||||||
\(640\) | 32.8065 | − | 46.0840i | 0.0512602 | − | 0.0720062i | ||||
\(641\) | 487.398 | 0.760371 | 0.380185 | − | 0.924910i | \(-0.375860\pi\) | ||||
0.380185 | + | 0.924910i | \(0.375860\pi\) | |||||||
\(642\) | 141.005 | + | 141.005i | 0.219634 | + | 0.219634i | ||||
\(643\) | 554.739 | − | 554.739i | 0.862736 | − | 0.862736i | −0.128919 | − | 0.991655i | \(-0.541151\pi\) |
0.991655 | + | 0.128919i | \(0.0411509\pi\) | |||||||
\(644\) | 98.9751i | 0.153688i | ||||||||
\(645\) | −75.4235 | − | 448.142i | −0.116936 | − | 0.694793i | ||||
\(646\) | 166.646 | 0.257965 | ||||||||
\(647\) | 337.971 | + | 337.971i | 0.522367 | + | 0.522367i | 0.918285 | − | 0.395919i | \(-0.129574\pi\) |
−0.395919 | + | 0.918285i | \(0.629574\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 362.025i | − | 0.557819i | ||||||
\(650\) | −708.845 | + | 245.557i | −1.09053 | + | 0.377779i | ||||
\(651\) | 123.789 | 0.190152 | ||||||||
\(652\) | 311.127 | + | 311.127i | 0.477188 | + | 0.477188i | ||||
\(653\) | 379.091 | − | 379.091i | 0.580537 | − | 0.580537i | −0.354514 | − | 0.935051i | \(-0.615354\pi\) |
0.935051 | + | 0.354514i | \(0.115354\pi\) | |||||||
\(654\) | − | 502.768i | − | 0.768759i | ||||||
\(655\) | −779.038 | + | 131.114i | −1.18937 | + | 0.200174i | ||||
\(656\) | 212.359 | 0.323718 | ||||||||
\(657\) | 93.6214 | + | 93.6214i | 0.142498 | + | 0.142498i | ||||
\(658\) | −35.1413 | + | 35.1413i | −0.0534062 | + | 0.0534062i | ||||
\(659\) | − | 932.566i | − | 1.41512i | −0.706652 | − | 0.707561i | \(-0.749795\pi\) | ||
0.706652 | − | 0.707561i | \(-0.250205\pi\) | |||||||
\(660\) | −81.1231 | − | 57.7503i | −0.122914 | − | 0.0875005i | ||||
\(661\) | 435.268 | 0.658500 | 0.329250 | − | 0.944243i | \(-0.393204\pi\) | ||||
0.329250 | + | 0.944243i | \(0.393204\pi\) | |||||||
\(662\) | −276.111 | − | 276.111i | −0.417086 | − | 0.417086i | ||||
\(663\) | 175.971 | − | 175.971i | 0.265416 | − | 0.265416i | ||||
\(664\) | − | 72.9459i | − | 0.109858i | ||||||
\(665\) | −133.504 | + | 187.536i | −0.200758 | + | 0.282009i | ||||
\(666\) | −68.1843 | −0.102379 | ||||||||
\(667\) | −498.983 | − | 498.983i | −0.748100 | − | 0.748100i | ||||
\(668\) | −152.158 | + | 152.158i | −0.227781 | + | 0.227781i | ||||
\(669\) | − | 358.881i | − | 0.536443i | ||||||
\(670\) | 47.2860 | + | 280.958i | 0.0705761 | + | 0.419340i | ||||
\(671\) | 9.62948 | 0.0143509 | ||||||||
\(672\) | −18.3303 | − | 18.3303i | −0.0272772 | − | 0.0272772i | ||||
\(673\) | 268.394 | − | 268.394i | 0.398803 | − | 0.398803i | −0.479008 | − | 0.877811i | \(-0.659003\pi\) |
0.877811 | + | 0.479008i | \(0.159003\pi\) | |||||||
\(674\) | − | 552.786i | − | 0.820157i | ||||||
\(675\) | 116.863 | + | 56.7279i | 0.173130 | + | 0.0840414i | ||||
\(676\) | 562.414 | 0.831973 | ||||||||
\(677\) | −317.565 | − | 317.565i | −0.469076 | − | 0.469076i | 0.432539 | − | 0.901615i | \(-0.357618\pi\) |
−0.901615 | + | 0.432539i | \(0.857618\pi\) | |||||||
\(678\) | 79.8623 | − | 79.8623i | 0.117791 | − | 0.117791i | ||||
\(679\) | − | 342.393i | − | 0.504261i | ||||||
\(680\) | 94.4361 | − | 15.8938i | 0.138877 | − | 0.0233733i | ||||
\(681\) | −399.014 | −0.585924 | ||||||||
\(682\) | −155.303 | − | 155.303i | −0.227718 | − | 0.227718i | ||||
\(683\) | 750.781 | − | 750.781i | 1.09924 | − | 1.09924i | 0.104741 | − | 0.994500i | \(-0.466599\pi\) |
0.994500 | − | 0.104741i | \(-0.0334012\pi\) | |||||||
\(684\) | − | 104.410i | − | 0.152646i | ||||||
\(685\) | 212.893 | + | 151.555i | 0.310793 | + | 0.221249i | ||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | −215.811 | − | 215.811i | −0.314135 | − | 0.314135i | ||||
\(688\) | −148.421 | + | 148.421i | −0.215728 | + | 0.215728i | ||||
\(689\) | − | 1317.29i | − | 1.91189i | ||||||
\(690\) | −132.855 | + | 186.624i | −0.192543 | + | 0.270470i | ||||
\(691\) | −630.352 | −0.912231 | −0.456116 | − | 0.889921i | \(-0.650760\pi\) | ||||
−0.456116 | + | 0.889921i | \(0.650760\pi\) | |||||||
\(692\) | 57.8647 | + | 57.8647i | 0.0836194 | + | 0.0836194i | ||||
\(693\) | −32.2674 | + | 32.2674i | −0.0465619 | + | 0.0465619i | ||||
\(694\) | 316.168i | 0.455573i | ||||||||
\(695\) | 109.691 | + | 651.751i | 0.157829 | + | 0.937771i | ||||
\(696\) | 184.824 | 0.265552 | ||||||||
\(697\) | 254.205 | + | 254.205i | 0.364712 | + | 0.364712i | ||||
\(698\) | 452.412 | − | 452.412i | 0.648155 | − | 0.648155i | ||||
\(699\) | − | 44.9764i | − | 0.0643440i | ||||||
\(700\) | −57.7689 | + | 119.007i | −0.0825270 | + | 0.170011i | ||||
\(701\) | −1143.23 | −1.63085 | −0.815425 | − | 0.578863i | \(-0.803497\pi\) | ||||
−0.815425 | + | 0.578863i | \(0.803497\pi\) | |||||||
\(702\) | −110.252 | − | 110.252i | −0.157055 | − | 0.157055i | ||||
\(703\) | 197.753 | − | 197.753i | 0.281299 | − | 0.281299i | ||||
\(704\) | 45.9937i | 0.0653320i | ||||||||
\(705\) | −113.432 | + | 19.0908i | −0.160896 | + | 0.0270792i | ||||
\(706\) | −963.362 | −1.36453 | ||||||||
\(707\) | −342.090 | − | 342.090i | −0.483862 | − | 0.483862i | ||||
\(708\) | 154.243 | − | 154.243i | 0.217857 | − | 0.217857i | ||||
\(709\) | 120.909i | 0.170535i | 0.996358 | + | 0.0852674i | \(0.0271745\pi\) | ||||
−0.996358 | + | 0.0852674i | \(0.972826\pi\) | |||||||
\(710\) | 271.918 | + | 193.575i | 0.382983 | + | 0.272640i | ||||
\(711\) | 321.401 | 0.452040 | ||||||||
\(712\) | −349.351 | − | 349.351i | −0.490661 | − | 0.490661i | ||||
\(713\) | −357.276 | + | 357.276i | −0.501089 | + | 0.501089i | ||||
\(714\) | − | 43.8847i | − | 0.0614631i | ||||||
\(715\) | 353.728 | − | 496.889i | 0.494725 | − | 0.694950i | ||||
\(716\) | 253.698 | 0.354327 | ||||||||
\(717\) | −336.919 | − | 336.919i | −0.469901 | − | 0.469901i | ||||
\(718\) | 485.514 | − | 485.514i | 0.676203 | − | 0.676203i | ||||
\(719\) | − | 157.658i | − | 0.219274i | −0.993972 | − | 0.109637i | \(-0.965031\pi\) | ||
0.993972 | − | 0.109637i | \(-0.0349688\pi\) | |||||||
\(720\) | −9.95811 | − | 59.1679i | −0.0138307 | − | 0.0821776i | ||||
\(721\) | −174.446 | −0.241950 | ||||||||
\(722\) | −58.1823 | − | 58.1823i | −0.0805849 | − | 0.0805849i | ||||
\(723\) | −415.097 | + | 415.097i | −0.574131 | + | 0.574131i | ||||
\(724\) | 615.362i | 0.849947i | ||||||||
\(725\) | −308.734 | − | 891.217i | −0.425839 | − | 1.22926i | ||||
\(726\) | −215.424 | −0.296727 | ||||||||
\(727\) | 45.5944 | + | 45.5944i | 0.0627159 | + | 0.0627159i | 0.737769 | − | 0.675053i | \(-0.235879\pi\) |
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(728\) | 112.276 | − | 112.276i | 0.154225 | − | 0.154225i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −307.743 | + | 51.7940i | −0.421566 | + | 0.0709507i | ||||
\(731\) | −355.335 | −0.486095 | ||||||||
\(732\) | 4.10270 | + | 4.10270i | 0.00560478 | + | 0.00560478i | ||||
\(733\) | 5.02444 | − | 5.02444i | 0.00685462 | − | 0.00685462i | −0.703671 | − | 0.710526i | \(-0.748457\pi\) |
0.710526 | + | 0.703671i | \(0.248457\pi\) | |||||||
\(734\) | − | 410.663i | − | 0.559486i | ||||||
\(735\) | 49.3860 | + | 35.1571i | 0.0671918 | + | 0.0478328i | ||||
\(736\) | 105.809 | 0.143762 | ||||||||
\(737\) | −163.801 | − | 163.801i | −0.222253 | − | 0.222253i | ||||
\(738\) | 159.269 | − | 159.269i | 0.215812 | − | 0.215812i | ||||
\(739\) | − | 1207.29i | − | 1.63368i | −0.576865 | − | 0.816839i | \(-0.695724\pi\) | ||
0.576865 | − | 0.816839i | \(-0.304276\pi\) | |||||||
\(740\) | 93.2037 | − | 130.925i | 0.125951 | − | 0.176926i | ||||
\(741\) | 639.525 | 0.863056 | ||||||||
\(742\) | −164.257 | − | 164.257i | −0.221371 | − | 0.221371i | ||||
\(743\) | −162.402 | + | 162.402i | −0.218577 | + | 0.218577i | −0.807898 | − | 0.589322i | \(-0.799395\pi\) |
0.589322 | + | 0.807898i | \(0.299395\pi\) | |||||||
\(744\) | − | 132.336i | − | 0.177871i | ||||||
\(745\) | −211.883 | − | 1258.94i | −0.284407 | − | 1.68985i | ||||
\(746\) | 49.9606 | 0.0669714 | ||||||||
\(747\) | −54.7094 | − | 54.7094i | −0.0732388 | − | 0.0732388i | ||||
\(748\) | −55.0569 | + | 55.0569i | −0.0736055 | + | 0.0736055i | ||||
\(749\) | 215.389i | 0.287569i | ||||||||
\(750\) | −268.671 | + | 146.853i | −0.358228 | + | 0.195804i | ||||
\(751\) | −1054.43 | −1.40404 | −0.702020 | − | 0.712157i | \(-0.747718\pi\) | ||||
−0.702020 | + | 0.712157i | \(0.747718\pi\) | |||||||
\(752\) | 37.5676 | + | 37.5676i | 0.0499569 | + | 0.0499569i | ||||
\(753\) | −88.3270 | + | 88.3270i | −0.117300 | + | 0.117300i | ||||
\(754\) | 1132.07i | 1.50142i | ||||||||
\(755\) | 1038.02 | − | 174.701i | 1.37486 | − | 0.231393i | ||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | 166.416 | + | 166.416i | 0.219836 | + | 0.219836i | 0.808429 | − | 0.588593i | \(-0.200318\pi\) |
−0.588593 | + | 0.808429i | \(0.700318\pi\) | |||||||
\(758\) | −356.423 | + | 356.423i | −0.470215 | + | 0.470215i | ||||
\(759\) | − | 186.259i | − | 0.245400i | ||||||
\(760\) | 200.484 | + | 142.722i | 0.263795 | + | 0.187792i | ||||
\(761\) | 1422.52 | 1.86928 | 0.934640 | − | 0.355596i | \(-0.115722\pi\) | ||||
0.934640 | + | 0.355596i | \(0.115722\pi\) | |||||||
\(762\) | −254.099 | − | 254.099i | −0.333463 | − | 0.333463i | ||||
\(763\) | 383.996 | − | 383.996i | 0.503271 | − | 0.503271i | ||||
\(764\) | 142.994i | 0.187165i | ||||||||
\(765\) | 58.9067 | − | 82.7474i | 0.0770022 | − | 0.108167i | ||||
\(766\) | −961.354 | −1.25503 | ||||||||
\(767\) | 944.758 | + | 944.758i | 1.23176 | + | 1.23176i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 502.250i | − | 0.653121i | −0.945176 | − | 0.326560i | \(-0.894110\pi\) | ||
0.945176 | − | 0.326560i | \(-0.105890\pi\) | |||||||
\(770\) | −17.8512 | − | 106.066i | −0.0231834 | − | 0.137748i | ||||
\(771\) | 29.9464 | 0.0388410 | ||||||||
\(772\) | −310.695 | − | 310.695i | −0.402454 | − | 0.402454i | ||||
\(773\) | −339.873 | + | 339.873i | −0.439681 | + | 0.439681i | −0.891904 | − | 0.452224i | \(-0.850631\pi\) |
0.452224 | + | 0.891904i | \(0.350631\pi\) | |||||||
\(774\) | 222.631i | 0.287637i | ||||||||
\(775\) | −638.120 | + | 221.056i | −0.823380 | + | 0.285234i | ||||
\(776\) | −366.033 | −0.471693 | ||||||||
\(777\) | −52.0766 | − | 52.0766i | −0.0670227 | − | 0.0670227i | ||||
\(778\) | −169.784 | + | 169.784i | −0.218231 | + | 0.218231i | ||||
\(779\) | 923.848i | 1.18594i | ||||||||
\(780\) | 362.411 | − | 60.9947i | 0.464629 | − | 0.0781984i | ||||
\(781\) | −271.386 | −0.347485 | ||||||||
\(782\) | 126.659 | + | 126.659i | 0.161968 | + | 0.161968i | ||||
\(783\) | 138.618 | − | 138.618i | 0.177035 | − | 0.177035i | ||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 1046.52 | + | 744.999i | 1.33314 | + | 0.949043i | ||||
\(786\) | 387.017 | 0.492387 | ||||||||
\(787\) | 752.550 | + | 752.550i | 0.956227 | + | 0.956227i | 0.999081 | − | 0.0428547i | \(-0.0136452\pi\) |
−0.0428547 | + | 0.999081i | \(0.513645\pi\) | |||||||
\(788\) | −381.040 | + | 381.040i | −0.483553 | + | 0.483553i | ||||
\(789\) | 675.406i | 0.856028i | ||||||||
\(790\) | −439.335 | + | 617.143i | −0.556120 | + | 0.781193i | ||||
\(791\) | 121.992 | 0.154225 | ||||||||
\(792\) | 34.4953 | + | 34.4953i | 0.0435547 | + | 0.0435547i | ||||
\(793\) | −25.1296 | + | 25.1296i | −0.0316892 | + | 0.0316892i | ||||
\(794\) | 132.242i | 0.166551i | ||||||||
\(795\) | −89.2343 | − | 530.201i | −0.112244 | − | 0.666919i | ||||
\(796\) | −346.492 | −0.435291 | ||||||||
\(797\) | −182.962 | − | 182.962i | −0.229564 | − | 0.229564i | 0.582947 | − | 0.812511i | \(-0.301900\pi\) |
−0.812511 | + | 0.582947i | \(0.801900\pi\) | |||||||
\(798\) | 79.7444 | − | 79.7444i | 0.0999303 | − | 0.0999303i | ||||
\(799\) | 89.9408i | 0.112567i | ||||||||
\(800\) | 127.224 | + | 61.7575i | 0.159030 | + | 0.0771969i | ||||
\(801\) | −524.026 | −0.654215 | ||||||||
\(802\) | 213.860 | + | 213.860i | 0.266659 | + | 0.266659i | ||||
\(803\) | 179.417 | − | 179.417i | 0.223433 | − | 0.223433i | ||||
\(804\) | − | 139.577i | − | 0.173603i | ||||||
\(805\) | −244.006 | + | 41.0669i | −0.303113 | + | 0.0510148i | ||||
\(806\) | 810.575 | 1.00568 | ||||||||
\(807\) | 338.015 | + | 338.015i | 0.418853 | + | 0.418853i | ||||
\(808\) | −365.710 | + | 365.710i | −0.452611 | + | 0.452611i | ||||
\(809\) | − | 508.611i | − | 0.628690i | −0.949309 | − | 0.314345i | \(-0.898215\pi\) | ||
0.949309 | − | 0.314345i | \(-0.101785\pi\) | |||||||
\(810\) | −51.8445 | − | 36.9073i | −0.0640055 | − | 0.0455646i | ||||
\(811\) | −768.233 | −0.947267 | −0.473633 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473633 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(812\) | 141.162 | + | 141.162i | 0.173845 | + | 0.173845i | ||||
\(813\) | −362.154 | + | 362.154i | −0.445454 | + | 0.445454i | ||||
\(814\) | 130.669i | 0.160527i | ||||||||
\(815\) | −637.936 | + | 896.122i | −0.782744 | + | 1.09954i | ||||
\(816\) | −46.9147 | −0.0574935 | ||||||||
\(817\) | −645.693 | − | 645.693i | −0.790321 | − | 0.790321i | ||||
\(818\) | −300.366 | + | 300.366i | −0.367196 | + | 0.367196i | ||||
\(819\) | − | 168.413i | − | 0.205633i | ||||||
\(820\) | 88.1122 | + | 523.534i | 0.107454 | + | 0.638456i | ||||
\(821\) | 103.940 | 0.126602 | 0.0633011 | − | 0.997994i | \(-0.479837\pi\) | ||||
0.0633011 | + | 0.997994i | \(0.479837\pi\) | |||||||
\(822\) | −90.5267 | − | 90.5267i | −0.110130 | − | 0.110130i | ||||
\(823\) | 353.698 | − | 353.698i | 0.429767 | − | 0.429767i | −0.458782 | − | 0.888549i | \(-0.651714\pi\) |
0.888549 | + | 0.458782i | \(0.151714\pi\) | |||||||
\(824\) | 186.490i | 0.226323i | ||||||||
\(825\) | 108.714 | − | 223.957i | 0.131774 | − | 0.271463i | ||||
\(826\) | 235.610 | 0.285242 | ||||||||
\(827\) | 57.1544 | + | 57.1544i | 0.0691105 | + | 0.0691105i | 0.740817 | − | 0.671707i | \(-0.234438\pi\) |
−0.671707 | + | 0.740817i | \(0.734438\pi\) | |||||||
\(828\) | 79.3566 | − | 79.3566i | 0.0958413 | − | 0.0958413i | ||||
\(829\) | − | 260.205i | − | 0.313878i | −0.987608 | − | 0.156939i | \(-0.949837\pi\) | ||
0.987608 | − | 0.156939i | \(-0.0501626\pi\) | |||||||
\(830\) | 179.835 | − | 30.2668i | 0.216669 | − | 0.0364660i | ||||
\(831\) | 52.5848 | 0.0632789 | ||||||||
\(832\) | −120.028 | − | 120.028i | −0.144264 | − | 0.144264i | ||||
\(833\) | 33.5175 | − | 33.5175i | 0.0402371 | − | 0.0402371i | ||||
\(834\) | − | 323.782i | − | 0.388228i | ||||||
\(835\) | −438.252 | − | 311.985i | −0.524852 | − | 0.373635i | ||||
\(836\) | −200.092 | −0.239344 | ||||||||
\(837\) | −99.2520 | − | 99.2520i | −0.118581 | − | 0.118581i | ||||
\(838\) | 696.907 | − | 696.907i | 0.831632 | − | 0.831632i | ||||
\(839\) | 742.004i | 0.884391i | 0.896919 | + | 0.442196i | \(0.145800\pi\) | ||||
−0.896919 | + | 0.442196i | \(0.854200\pi\) | |||||||
\(840\) | 37.5846 | − | 52.7958i | 0.0447435 | − | 0.0628522i | ||||
\(841\) | −582.334 | −0.692430 | ||||||||
\(842\) | 114.980 | + | 114.980i | 0.136555 | + | 0.136555i | ||||
\(843\) | −90.8774 | + | 90.8774i | −0.107802 | + | 0.107802i | ||||
\(844\) | 107.839i | 0.127771i | ||||||||
\(845\) | 233.357 | + | 1386.53i | 0.276163 | + | 1.64087i | ||||
\(846\) | 56.3514 | 0.0666092 | ||||||||
\(847\) | −164.533 | − | 164.533i | −0.194254 | − | 0.194254i | ||||
\(848\) | −175.598 | + | 175.598i | −0.207073 | + | 0.207073i | ||||
\(849\) | − | 789.894i | − | 0.930382i | ||||||
\(850\) | 78.3671 | + | 226.221i | 0.0921966 | + | 0.266143i | ||||
\(851\) | 300.604 | 0.353236 | ||||||||
\(852\) | −115.626 | − | 115.626i | −0.135711 | − | 0.135711i | ||||
\(853\) | 876.382 | − | 876.382i | 1.02741 | − | 1.02741i | 0.0277980 | − | 0.999614i | \(-0.491150\pi\) |
0.999614 | − | 0.0277980i | \(-0.00884953\pi\) | |||||||
\(854\) | 6.26698i | 0.00733838i | ||||||||
\(855\) | 257.405 | − | 43.3219i | 0.301058 | − | 0.0506689i | ||||
\(856\) | 230.261 | 0.268996 | ||||||||
\(857\) | 953.370 | + | 953.370i | 1.11245 | + | 1.11245i | 0.992818 | + | 0.119632i | \(0.0381716\pi\) |
0.119632 | + | 0.992818i | \(0.461828\pi\) | |||||||
\(858\) | −211.288 | + | 211.288i | −0.246257 | + | 0.246257i | ||||
\(859\) | 808.979i | 0.941768i | 0.882195 | + | 0.470884i | \(0.156065\pi\) | ||||
−0.882195 | + | 0.470884i | \(0.843935\pi\) | |||||||
\(860\) | −427.489 | − | 304.323i | −0.497080 | − | 0.353864i | ||||
\(861\) | 243.287 | 0.282564 | ||||||||
\(862\) | 724.694 | + | 724.694i | 0.840713 | + | 0.840713i | ||||
\(863\) | 315.788 | − | 315.788i | 0.365919 | − | 0.365919i | −0.500068 | − | 0.865986i | \(-0.666692\pi\) |
0.865986 | + | 0.500068i | \(0.166692\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −118.646 | + | 166.665i | −0.137163 | + | 0.192676i | ||||
\(866\) | −200.655 | −0.231703 | ||||||||
\(867\) | 297.792 | + | 297.792i | 0.343474 | + | 0.343474i | ||||
\(868\) | 101.073 | − | 101.073i | 0.116444 | − | 0.116444i | ||||
\(869\) | − | 615.934i | − | 0.708785i | ||||||
\(870\) | 76.6875 | + | 455.652i | 0.0881466 | + | 0.523738i | ||||
\(871\) | 854.925 | 0.981544 | ||||||||
\(872\) | −410.509 | − | 410.509i | −0.470767 | − | 0.470767i | ||||
\(873\) | −274.525 | + | 274.525i | −0.314462 | + | 0.314462i | ||||
\(874\) | 460.312i | 0.526673i | ||||||||
\(875\) | −317.362 | − | 93.0405i | −0.362699 | − | 0.106332i | ||||
\(876\) | 152.883 | 0.174524 | ||||||||
\(877\) | −291.014 | − | 291.014i | −0.331829 | − | 0.331829i | 0.521452 | − | 0.853281i | \(-0.325391\pi\) |
−0.853281 | + | 0.521452i | \(0.825391\pi\) | |||||||
\(878\) | 685.890 | − | 685.890i | 0.781195 | − | 0.781195i | ||||
\(879\) | − | 357.024i | − | 0.406171i | ||||||
\(880\) | −113.390 | + | 19.0838i | −0.128852 | + | 0.0216861i | ||||
\(881\) | 368.877 | 0.418702 | 0.209351 | − | 0.977841i | \(-0.432865\pi\) | ||||
0.209351 | + | 0.977841i | \(0.432865\pi\) | |||||||
\(882\) | −21.0000 | − | 21.0000i | −0.0238095 | − | 0.0238095i | ||||
\(883\) | 1221.90 | − | 1221.90i | 1.38380 | − | 1.38380i | 0.546042 | − | 0.837758i | \(-0.316134\pi\) |
0.837758 | − | 0.546042i | \(-0.183866\pi\) | |||||||
\(884\) | − | 287.359i | − | 0.325066i | ||||||
\(885\) | 444.258 | + | 316.260i | 0.501986 | + | 0.357356i | ||||
\(886\) | −679.505 | −0.766935 | ||||||||
\(887\) | 67.8606 | + | 67.8606i | 0.0765058 | + | 0.0765058i | 0.744324 | − | 0.667818i | \(-0.232772\pi\) |
−0.667818 | + | 0.744324i | \(0.732772\pi\) | |||||||
\(888\) | −55.6722 | + | 55.6722i | −0.0626940 | + | 0.0626940i | ||||
\(889\) | − | 388.142i | − | 0.436606i | ||||||
\(890\) | 716.311 | − | 1006.22i | 0.804844 | − | 1.13058i | ||||
\(891\) | 51.7430 | 0.0580729 | ||||||||
\(892\) | −293.025 | − | 293.025i | −0.328503 | − | 0.328503i | ||||
\(893\) | −163.435 | + | 163.435i | −0.183018 | + | 0.183018i | ||||
\(894\) | 625.426i | 0.699581i | ||||||||
\(895\) | 105.265 | + | 625.448i | 0.117614 | + | 0.698825i | ||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 486.070 | + | 486.070i | 0.541884 | + | 0.541884i | ||||
\(898\) | 226.637 | − | 226.637i | 0.252379 | − | 0.252379i | ||||
\(899\) | 1019.12i | 1.13362i | ||||||||
\(900\) | 141.736 | − | 49.1000i | 0.157485 | − | 0.0545556i | ||||
\(901\) | −420.401 | −0.466594 | ||||||||
\(902\) | −305.224 | − | 305.224i | −0.338386 | − | 0.338386i | ||||
\(903\) | −170.038 | + | 170.038i | −0.188303 | + | 0.188303i | ||||
\(904\) | − | 130.415i | − | 0.144264i | ||||||
\(905\) | −1517.07 | + | 255.327i | −1.67632 | + | 0.282129i | ||||
\(906\) | −515.675 | −0.569178 | ||||||||
\(907\) | −144.428 | − | 144.428i | −0.159237 | − | 0.159237i | 0.622991 | − | 0.782229i | \(-0.285917\pi\) |
−0.782229 | + | 0.622991i | \(0.785917\pi\) | |||||||
\(908\) | −325.794 | + | 325.794i | −0.358804 | + | 0.358804i | ||||
\(909\) | 548.565i | 0.603482i | ||||||||
\(910\) | 323.381 | + | 230.210i | 0.355364 | + | 0.252978i | ||||
\(911\) | 423.332 | 0.464689 | 0.232345 | − | 0.972634i | \(-0.425360\pi\) | ||||
0.232345 | + | 0.972634i | \(0.425360\pi\) | |||||||
\(912\) | −85.2504 | − | 85.2504i | −0.0934763 | − | 0.0934763i | ||||
\(913\) | −104.845 | + | 104.845i | −0.114836 | + | 0.114836i | ||||
\(914\) | 532.565i | 0.582675i | ||||||||
\(915\) | −8.41220 | + | 11.8168i | −0.00919366 | + | 0.0129145i | ||||
\(916\) | −352.417 | −0.384735 | ||||||||
\(917\) | 295.589 | + | 295.589i | 0.322343 | + | 0.322343i | ||||
\(918\) | −35.1860 | + | 35.1860i | −0.0383290 | + | 0.0383290i | ||||
\(919\) | 1289.08i | 1.40269i | 0.712820 | + | 0.701347i | \(0.247418\pi\) | ||||
−0.712820 | + | 0.701347i | \(0.752582\pi\) | |||||||
\(920\) | 43.9023 | + | 260.853i | 0.0477199 | + | 0.283536i | ||||
\(921\) | 754.697 | 0.819433 | ||||||||
\(922\) | 121.199 | + | 121.199i | 0.131453 | + | 0.131453i | ||||
\(923\) | 708.222 | − | 708.222i | 0.767304 | − | 0.767304i | ||||
\(924\) | 52.6924i | 0.0570265i | ||||||||
\(925\) | 361.446 | + | 175.454i | 0.390752 | + | 0.189680i | ||||
\(926\) | 1131.21 | 1.22161 | ||||||||
\(927\) | 139.868 | + | 139.868i | 0.150882 | + | 0.150882i | ||||
\(928\) | 150.908 | − | 150.908i | 0.162617 | − | 0.162617i | ||||
\(929\) | 749.538i | 0.806823i | 0.915019 | + | 0.403411i | \(0.132176\pi\) | ||||
−0.915019 | + | 0.403411i | \(0.867824\pi\) | |||||||
\(930\) | 326.251 | − | 54.9090i | 0.350808 | − | 0.0590419i | ||||
\(931\) | 121.812 | 0.130840 | ||||||||
\(932\) | −36.7231 | − | 36.7231i | −0.0394025 | − | 0.0394025i | ||||
\(933\) | 35.6634 | − | 35.6634i | 0.0382245 | − | 0.0382245i | ||||
\(934\) | 559.072i | 0.598578i | ||||||||
\(935\) | −158.578 | − | 112.889i | −0.169602 | − | 0.120737i | ||||
\(936\) | −180.041 | −0.192352 | ||||||||
\(937\) | −208.580 | − | 208.580i | −0.222605 | − | 0.222605i | 0.586990 | − | 0.809594i | \(-0.300313\pi\) |
−0.809594 | + | 0.586990i | \(0.800313\pi\) | |||||||
\(938\) | 106.603 | − | 106.603i | 0.113650 | − | 0.113650i | ||||
\(939\) | 29.8138i | 0.0317506i | ||||||||
\(940\) | −77.0289 | + | 108.204i | −0.0819456 | + | 0.115111i | ||||
\(941\) | −1017.80 | −1.08161 | −0.540807 | − | 0.841147i | \(-0.681881\pi\) | ||||
−0.540807 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(942\) | −445.001 | − | 445.001i | −0.472400 | − | 0.472400i | ||||
\(943\) | −702.170 | + | 702.170i | −0.744613 | + | 0.744613i | ||||
\(944\) | − | 251.877i | − | 0.266819i | ||||||
\(945\) | −11.4085 | − | 67.7853i | −0.0120724 | − | 0.0717305i | ||||
\(946\) | 426.652 | 0.451006 | ||||||||
\(947\) | 288.192 | + | 288.192i | 0.304321 | + | 0.304321i | 0.842702 | − | 0.538381i | \(-0.180964\pi\) |
−0.538381 | + | 0.842702i | \(0.680964\pi\) | |||||||
\(948\) | 262.423 | − | 262.423i | 0.276817 | − | 0.276817i | ||||
\(949\) | 936.429i | 0.986753i | ||||||||
\(950\) | −268.671 | + | 553.478i | −0.282811 | + | 0.582609i | ||||
\(951\) | −536.907 | −0.564571 | ||||||||
\(952\) | −35.8317 | − | 35.8317i | −0.0376383 | − | 0.0376383i | ||||
\(953\) | −450.504 | + | 450.504i | −0.472722 | + | 0.472722i | −0.902794 | − | 0.430072i | \(-0.858488\pi\) |
0.430072 | + | 0.902794i | \(0.358488\pi\) | |||||||
\(954\) | 263.397i | 0.276098i | ||||||||
\(955\) | −352.527 | + | 59.3312i | −0.369138 | + | 0.0621269i | ||||
\(956\) | −550.187 | −0.575509 | ||||||||
\(957\) | −265.649 | − | 265.649i | −0.277585 | − | 0.277585i | ||||
\(958\) | 101.987 | − | 101.987i | 0.106458 | − | 0.106458i | ||||
\(959\) | − | 138.282i | − | 0.144194i | ||||||
\(960\) | −56.4411 | − | 40.1796i | −0.0587928 | − | 0.0418537i | ||||
\(961\) | −231.300 | −0.240687 | ||||||||
\(962\) | −341.000 | − | 341.000i | −0.354470 | − | 0.354470i | ||||
\(963\) | 172.695 | − | 172.695i | 0.179331 | − | 0.179331i | ||||
\(964\) | 677.850i | 0.703164i | ||||||||
\(965\) | 637.050 | − | 894.878i | 0.660155 | − | 0.927334i | ||||
\(966\) | 121.219 | 0.125486 | ||||||||
\(967\) | 824.848 | + | 824.848i | 0.852997 | + | 0.852997i | 0.990501 | − | 0.137505i | \(-0.0439082\pi\) |
−0.137505 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(968\) | −175.893 | + | 175.893i | −0.181708 | + | 0.181708i | ||||
\(969\) | − | 204.098i | − | 0.210628i | ||||||
\(970\) | −151.875 | − | 902.392i | −0.156572 | − | 0.930301i | ||||
\(971\) | −770.810 | −0.793831 | −0.396916 | − | 0.917855i | \(-0.629919\pi\) | ||||
−0.396916 | + | 0.917855i | \(0.629919\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 247.293 | − | 247.293i | 0.254155 | − | 0.254155i | ||||
\(974\) | − | 500.545i | − | 0.513907i | ||||||
\(975\) | 300.744 | + | 868.154i | 0.308455 | + | 0.890414i | ||||
\(976\) | 6.69968 | 0.00686442 | ||||||||
\(977\) | 126.844 | + | 126.844i | 0.129830 | + | 0.129830i | 0.769036 | − | 0.639206i | \(-0.220737\pi\) |
−0.639206 | + | 0.769036i | \(0.720737\pi\) | |||||||
\(978\) | 381.051 | − | 381.051i | 0.389623 | − | 0.389623i | ||||
\(979\) | 1004.25i | 1.02579i | ||||||||
\(980\) | 69.0292 | − | 11.6178i | 0.0704379 | − | 0.0118549i | ||||
\(981\) | −615.763 | −0.627689 | ||||||||
\(982\) | 648.021 | + | 648.021i | 0.659899 | + | 0.659899i | ||||
\(983\) | −1168.93 | + | 1168.93i | −1.18914 | + | 1.18914i | −0.211839 | + | 0.977305i | \(0.567945\pi\) |
−0.977305 | + | 0.211839i | \(0.932055\pi\) | |||||||
\(984\) | − | 260.085i | − | 0.264314i | ||||||
\(985\) | −1097.49 | − | 781.287i | −1.11420 | − | 0.793185i | ||||
\(986\) | 361.291 | 0.366421 | ||||||||
\(987\) | 43.0391 | + | 43.0391i | 0.0436060 | + | 0.0436060i | ||||
\(988\) | 522.170 | − | 522.170i | 0.528512 | − | 0.528512i | ||||
\(989\) | − | 981.515i | − | 0.992432i | ||||||
\(990\) | −70.7294 | + | 99.3551i | −0.0714438 | + | 0.100359i | ||||
\(991\) | 1475.28 | 1.48868 | 0.744339 | − | 0.667802i | \(-0.232765\pi\) | ||||
0.744339 | + | 0.667802i | \(0.232765\pi\) | |||||||
\(992\) | −108.052 | − | 108.052i | −0.108923 | − | 0.108923i | ||||
\(993\) | −338.165 | + | 338.165i | −0.340549 | + | 0.340549i | ||||
\(994\) | − | 176.621i | − | 0.177687i | ||||||
\(995\) | −143.767 | − | 854.215i | −0.144489 | − | 0.858508i | ||||
\(996\) | −89.3401 | −0.0896989 | ||||||||
\(997\) | −997.648 | − | 997.648i | −1.00065 | − | 1.00065i | −1.00000 | 0.000649790i | \(-0.999793\pi\) | |
−0.000649790 | − | 1.00000i | \(-0.500207\pi\) | |||||||
\(998\) | 377.798 | − | 377.798i | 0.378555 | − | 0.378555i | ||||
\(999\) | 83.5084i | 0.0835919i |
(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 | 210.3.l.b.127.1 | yes | 16 | |
3.2 | odd | 2 | 630.3.o.f.127.8 | 16 | |||
5.2 | odd | 4 | 1050.3.l.h.43.6 | 16 | |||
5.3 | odd | 4 | inner | 210.3.l.b.43.1 | ✓ | 16 | |
5.4 | even | 2 | 1050.3.l.h.757.6 | 16 | |||
15.8 | even | 4 | 630.3.o.f.253.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.1 | ✓ | 16 | 5.3 | odd | 4 | inner | |
210.3.l.b.127.1 | yes | 16 | 1.1 | even | 1 | trivial | |
630.3.o.f.127.8 | 16 | 3.2 | odd | 2 | |||
630.3.o.f.253.8 | 16 | 15.8 | even | 4 | |||
1050.3.l.h.43.6 | 16 | 5.2 | odd | 4 | |||
1050.3.l.h.757.6 | 16 | 5.4 | even | 2 |