Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\), 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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.3 | ||
Character | \(\chi\) | \(=\) | 171.106 |
Dual form | 171.2.g.c.121.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.978515 | − | 1.69484i | −0.691914 | − | 1.19843i | −0.971210 | − | 0.238226i | \(-0.923434\pi\) |
0.279295 | − | 0.960205i | \(-0.409899\pi\) | |||||||
\(3\) | −1.73022 | − | 0.0795352i | −0.998945 | − | 0.0459197i | ||||
\(4\) | −0.914982 | + | 1.58480i | −0.457491 | + | 0.792398i | ||||
\(5\) | −0.196235 | −0.0877587 | −0.0438794 | − | 0.999037i | \(-0.513972\pi\) | ||||
−0.0438794 | + | 0.999037i | \(0.513972\pi\) | |||||||
\(6\) | 1.55825 | + | 3.01027i | 0.636153 | + | 1.22894i | ||||
\(7\) | −2.23368 | + | 3.86885i | −0.844253 | + | 1.46229i | 0.0420154 | + | 0.999117i | \(0.486622\pi\) |
−0.886268 | + | 0.463172i | \(0.846711\pi\) | |||||||
\(8\) | −0.332766 | −0.117650 | ||||||||
\(9\) | 2.98735 | + | 0.275227i | 0.995783 | + | 0.0917424i | ||||
\(10\) | 0.192018 | + | 0.332586i | 0.0607215 | + | 0.105173i | ||||
\(11\) | 0.0755474 | − | 0.130852i | 0.0227784 | − | 0.0394534i | −0.854412 | − | 0.519597i | \(-0.826082\pi\) |
0.877190 | + | 0.480144i | \(0.159415\pi\) | |||||||
\(12\) | 1.70917 | − | 2.66928i | 0.493395 | − | 0.770554i | ||||
\(13\) | −0.234555 | + | 0.406262i | −0.0650539 | + | 0.112677i | −0.896718 | − | 0.442603i | \(-0.854055\pi\) |
0.831664 | + | 0.555279i | \(0.187389\pi\) | |||||||
\(14\) | 8.74277 | 2.33660 | ||||||||
\(15\) | 0.339530 | + | 0.0156075i | 0.0876662 | + | 0.00402985i | ||||
\(16\) | 2.15558 | + | 3.73357i | 0.538895 | + | 0.933394i | ||||
\(17\) | 0.441434 | − | 0.764587i | 0.107064 | − | 0.185440i | −0.807516 | − | 0.589846i | \(-0.799188\pi\) |
0.914579 | + | 0.404406i | \(0.132522\pi\) | |||||||
\(18\) | −2.45670 | − | 5.33238i | −0.579049 | − | 1.25685i | ||||
\(19\) | −0.132216 | + | 4.35689i | −0.0303325 | + | 0.999540i | ||||
\(20\) | 0.179551 | − | 0.310992i | 0.0401488 | − | 0.0695398i | ||||
\(21\) | 4.17248 | − | 6.51633i | 0.910510 | − | 1.42198i | ||||
\(22\) | −0.295697 | −0.0630428 | ||||||||
\(23\) | −2.57631 | + | 4.46230i | −0.537197 | + | 0.930453i | 0.461856 | + | 0.886955i | \(0.347184\pi\) |
−0.999054 | + | 0.0434982i | \(0.986150\pi\) | |||||||
\(24\) | 0.575759 | + | 0.0264666i | 0.117526 | + | 0.00540247i | ||||
\(25\) | −4.96149 | −0.992298 | ||||||||
\(26\) | 0.918063 | 0.180047 | ||||||||
\(27\) | −5.14689 | − | 0.713804i | −0.990520 | − | 0.137372i | ||||
\(28\) | −4.08756 | − | 7.07986i | −0.772476 | − | 1.33797i | ||||
\(29\) | −1.57810 | −0.293047 | −0.146523 | − | 0.989207i | \(-0.546808\pi\) | ||||
−0.146523 | + | 0.989207i | \(0.546808\pi\) | |||||||
\(30\) | −0.305782 | − | 0.590720i | −0.0558280 | − | 0.107850i | ||||
\(31\) | −1.37848 | − | 2.38759i | −0.247582 | − | 0.428824i | 0.715273 | − | 0.698845i | \(-0.246302\pi\) |
−0.962854 | + | 0.270022i | \(0.912969\pi\) | |||||||
\(32\) | 3.88577 | − | 6.73035i | 0.686913 | − | 1.18977i | ||||
\(33\) | −0.141121 | + | 0.220394i | −0.0245661 | + | 0.0383658i | ||||
\(34\) | −1.72780 | −0.296315 | ||||||||
\(35\) | 0.438326 | − | 0.759203i | 0.0740906 | − | 0.128329i | ||||
\(36\) | −3.16955 | + | 4.48251i | −0.528258 | + | 0.747085i | ||||
\(37\) | −1.36950 | −0.225145 | −0.112572 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112572 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(38\) | 7.51360 | − | 4.03920i | 1.21887 | − | 0.655245i | ||||
\(39\) | 0.438145 | − | 0.684268i | 0.0701594 | − | 0.109571i | ||||
\(40\) | 0.0653001 | 0.0103249 | ||||||||
\(41\) | −8.13338 | −1.27022 | −0.635110 | − | 0.772422i | \(-0.719045\pi\) | ||||
−0.635110 | + | 0.772422i | \(0.719045\pi\) | |||||||
\(42\) | −15.1269 | − | 0.695358i | −2.33414 | − | 0.107296i | ||||
\(43\) | 4.09593 | + | 7.09436i | 0.624623 | + | 1.08188i | 0.988614 | + | 0.150477i | \(0.0480808\pi\) |
−0.363990 | + | 0.931403i | \(0.618586\pi\) | |||||||
\(44\) | 0.138249 | + | 0.239454i | 0.0208418 | + | 0.0360991i | ||||
\(45\) | −0.586221 | − | 0.0540091i | −0.0873886 | − | 0.00805120i | ||||
\(46\) | 10.0838 | 1.48678 | ||||||||
\(47\) | −11.8802 | −1.73291 | −0.866453 | − | 0.499259i | \(-0.833606\pi\) | ||||
−0.866453 | + | 0.499259i | \(0.833606\pi\) | |||||||
\(48\) | −3.43269 | − | 6.63136i | −0.495465 | − | 0.957155i | ||||
\(49\) | −6.47868 | − | 11.2214i | −0.925526 | − | 1.60306i | ||||
\(50\) | 4.85489 | + | 8.40892i | 0.686586 | + | 1.18920i | ||||
\(51\) | −0.824592 | + | 1.28780i | −0.115466 | + | 0.180328i | ||||
\(52\) | −0.429228 | − | 0.743444i | −0.0595232 | − | 0.103097i | ||||
\(53\) | 5.86701 | + | 10.1620i | 0.805895 | + | 1.39585i | 0.915685 | + | 0.401897i | \(0.131649\pi\) |
−0.109790 | + | 0.993955i | \(0.535018\pi\) | |||||||
\(54\) | 3.82653 | + | 9.42161i | 0.520724 | + | 1.28212i | ||||
\(55\) | −0.0148250 | + | 0.0256777i | −0.00199900 | + | 0.00346238i | ||||
\(56\) | 0.743293 | − | 1.28742i | 0.0993267 | − | 0.172039i | ||||
\(57\) | 0.575290 | − | 7.52788i | 0.0761990 | − | 0.997093i | ||||
\(58\) | 1.54420 | + | 2.67463i | 0.202763 | + | 0.351196i | ||||
\(59\) | 1.58868 | 0.206829 | 0.103414 | − | 0.994638i | \(-0.467023\pi\) | ||||
0.103414 | + | 0.994638i | \(0.467023\pi\) | |||||||
\(60\) | −0.335398 | + | 0.523804i | −0.0432997 | + | 0.0676228i | ||||
\(61\) | 9.13530 | 1.16966 | 0.584828 | − | 0.811158i | \(-0.301162\pi\) | ||||
0.584828 | + | 0.811158i | \(0.301162\pi\) | |||||||
\(62\) | −2.69772 | + | 4.67258i | −0.342610 | + | 0.593419i | ||||
\(63\) | −7.73760 | + | 10.9428i | −0.974846 | + | 1.37867i | ||||
\(64\) | −6.58680 | −0.823350 | ||||||||
\(65\) | 0.0460278 | − | 0.0797226i | 0.00570905 | − | 0.00988837i | ||||
\(66\) | 0.511622 | + | 0.0235183i | 0.0629763 | + | 0.00289490i | ||||
\(67\) | 6.46880 | − | 11.2043i | 0.790289 | − | 1.36882i | −0.135499 | − | 0.990778i | \(-0.543264\pi\) |
0.925788 | − | 0.378044i | \(-0.123403\pi\) | |||||||
\(68\) | 0.807809 | + | 1.39917i | 0.0979612 | + | 0.169674i | ||||
\(69\) | 4.81250 | − | 7.51586i | 0.579357 | − | 0.904804i | ||||
\(70\) | −1.71563 | −0.205057 | ||||||||
\(71\) | 3.90988 | − | 6.77211i | 0.464017 | − | 0.803702i | −0.535139 | − | 0.844764i | \(-0.679741\pi\) |
0.999157 | + | 0.0410621i | \(0.0130742\pi\) | |||||||
\(72\) | −0.994087 | − | 0.0915862i | −0.117154 | − | 0.0107935i | ||||
\(73\) | 5.72527 | − | 9.91646i | 0.670092 | − | 1.16063i | −0.307785 | − | 0.951456i | \(-0.599588\pi\) |
0.977878 | − | 0.209178i | \(-0.0670788\pi\) | |||||||
\(74\) | 1.34008 | + | 2.32108i | 0.155781 | + | 0.269821i | ||||
\(75\) | 8.58449 | + | 0.394613i | 0.991252 | + | 0.0455660i | ||||
\(76\) | −6.78381 | − | 4.19601i | −0.778156 | − | 0.481316i | ||||
\(77\) | 0.337498 | + | 0.584564i | 0.0384615 | + | 0.0666172i | ||||
\(78\) | −1.58845 | − | 0.0730183i | −0.179857 | − | 0.00826769i | ||||
\(79\) | 0.964341 | + | 1.67029i | 0.108497 | + | 0.187922i | 0.915162 | − | 0.403087i | \(-0.132063\pi\) |
−0.806665 | + | 0.591009i | \(0.798730\pi\) | |||||||
\(80\) | −0.422999 | − | 0.732656i | −0.0472928 | − | 0.0819134i | ||||
\(81\) | 8.84850 | + | 1.64440i | 0.983167 | + | 0.182711i | ||||
\(82\) | 7.95863 | + | 13.7848i | 0.878884 | + | 1.52227i | ||||
\(83\) | −1.40773 | + | 2.43826i | −0.154518 | + | 0.267633i | −0.932884 | − | 0.360178i | \(-0.882716\pi\) |
0.778365 | + | 0.627812i | \(0.216049\pi\) | |||||||
\(84\) | 6.50930 | + | 12.5748i | 0.710222 | + | 1.37203i | ||||
\(85\) | −0.0866247 | + | 0.150038i | −0.00939576 | + | 0.0162739i | ||||
\(86\) | 8.01585 | − | 13.8839i | 0.864372 | − | 1.49714i | ||||
\(87\) | 2.73047 | + | 0.125515i | 0.292738 | + | 0.0134566i | ||||
\(88\) | −0.0251396 | + | 0.0435430i | −0.00267989 | + | 0.00464170i | ||||
\(89\) | 4.84774 | + | 8.39654i | 0.513860 | + | 0.890031i | 0.999871 | + | 0.0160786i | \(0.00511821\pi\) |
−0.486011 | + | 0.873953i | \(0.661548\pi\) | |||||||
\(90\) | 0.482089 | + | 1.04640i | 0.0508167 | + | 0.110300i | ||||
\(91\) | −1.04784 | − | 1.81492i | −0.109844 | − | 0.190255i | ||||
\(92\) | −4.71455 | − | 8.16584i | −0.491526 | − | 0.851348i | ||||
\(93\) | 2.19517 | + | 4.24070i | 0.227629 | + | 0.439740i | ||||
\(94\) | 11.6250 | + | 20.1350i | 1.19902 | + | 2.07677i | ||||
\(95\) | 0.0259454 | − | 0.854973i | 0.00266194 | − | 0.0877184i | ||||
\(96\) | −7.25855 | + | 11.3360i | −0.740822 | + | 1.15697i | ||||
\(97\) | −7.61343 | − | 13.1868i | −0.773026 | − | 1.33892i | −0.935897 | − | 0.352274i | \(-0.885409\pi\) |
0.162871 | − | 0.986647i | \(-0.447925\pi\) | |||||||
\(98\) | −12.6790 | + | 21.9606i | −1.28077 | + | 2.21836i | ||||
\(99\) | 0.261700 | − | 0.370108i | 0.0263019 | − | 0.0371972i | ||||
\(100\) | 4.53968 | − | 7.86295i | 0.453968 | − | 0.786295i | ||||
\(101\) | −14.6934 | −1.46204 | −0.731022 | − | 0.682354i | \(-0.760956\pi\) | ||||
−0.731022 | + | 0.682354i | \(0.760956\pi\) | |||||||
\(102\) | 2.98948 | + | 0.137421i | 0.296003 | + | 0.0136067i | ||||
\(103\) | 5.86742 | + | 10.1627i | 0.578134 | + | 1.00136i | 0.995693 | + | 0.0927076i | \(0.0295522\pi\) |
−0.417560 | + | 0.908650i | \(0.637114\pi\) | |||||||
\(104\) | 0.0780519 | − | 0.135190i | 0.00765362 | − | 0.0132565i | ||||
\(105\) | −0.818785 | + | 1.27873i | −0.0799052 | + | 0.124791i | ||||
\(106\) | 11.4819 | − | 19.8872i | 1.11522 | − | 1.93162i | ||||
\(107\) | −7.10478 | −0.686845 | −0.343422 | − | 0.939181i | \(-0.611586\pi\) | ||||
−0.343422 | + | 0.939181i | \(0.611586\pi\) | |||||||
\(108\) | 5.84055 | − | 7.50365i | 0.562007 | − | 0.722039i | ||||
\(109\) | −5.92520 | + | 10.2627i | −0.567531 | + | 0.982992i | 0.429278 | + | 0.903172i | \(0.358768\pi\) |
−0.996809 | + | 0.0798200i | \(0.974565\pi\) | |||||||
\(110\) | 0.0580260 | 0.00553256 | ||||||||
\(111\) | 2.36955 | + | 0.108924i | 0.224907 | + | 0.0103386i | ||||
\(112\) | −19.2595 | −1.81985 | ||||||||
\(113\) | −4.99898 | − | 8.65848i | −0.470264 | − | 0.814521i | 0.529158 | − | 0.848524i | \(-0.322508\pi\) |
−0.999422 | + | 0.0340022i | \(0.989175\pi\) | |||||||
\(114\) | −13.3215 | + | 6.39112i | −1.24767 | + | 0.598583i | ||||
\(115\) | 0.505561 | − | 0.875656i | 0.0471438 | − | 0.0816554i | ||||
\(116\) | 1.44394 | − | 2.50097i | 0.134066 | − | 0.232209i | ||||
\(117\) | −0.812513 | + | 1.14909i | −0.0751168 | + | 0.106233i | ||||
\(118\) | −1.55455 | − | 2.69255i | −0.143108 | − | 0.247870i | ||||
\(119\) | 1.97205 | + | 3.41569i | 0.180777 | + | 0.313116i | ||||
\(120\) | −0.112984 | − | 0.00519366i | −0.0103140 | − | 0.000474114i | ||||
\(121\) | 5.48859 | + | 9.50651i | 0.498962 | + | 0.864228i | ||||
\(122\) | −8.93903 | − | 15.4828i | −0.809301 | − | 1.40175i | ||||
\(123\) | 14.0726 | + | 0.646890i | 1.26888 | + | 0.0583281i | ||||
\(124\) | 5.04512 | 0.453065 | ||||||||
\(125\) | 1.95479 | 0.174842 | ||||||||
\(126\) | 26.1177 | + | 2.40625i | 2.32675 | + | 0.214366i | ||||
\(127\) | 1.43057 | + | 2.47782i | 0.126943 | + | 0.219871i | 0.922491 | − | 0.386020i | \(-0.126150\pi\) |
−0.795548 | + | 0.605891i | \(0.792817\pi\) | |||||||
\(128\) | −1.32625 | − | 2.29714i | −0.117225 | − | 0.203040i | ||||
\(129\) | −6.52262 | − | 12.6006i | −0.574285 | − | 1.10942i | ||||
\(130\) | −0.180156 | −0.0158007 | ||||||||
\(131\) | 2.70228 | 0.236100 | 0.118050 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118050 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(132\) | −0.220157 | − | 0.425305i | −0.0191622 | − | 0.0370181i | ||||
\(133\) | −16.5609 | − | 10.2434i | −1.43601 | − | 0.888219i | ||||
\(134\) | −25.3192 | −2.18725 | ||||||||
\(135\) | 1.01000 | + | 0.140073i | 0.0869268 | + | 0.0120556i | ||||
\(136\) | −0.146894 | + | 0.254428i | −0.0125961 | + | 0.0218170i | ||||
\(137\) | 15.8061 | 1.35041 | 0.675205 | − | 0.737630i | \(-0.264055\pi\) | ||||
0.675205 | + | 0.737630i | \(0.264055\pi\) | |||||||
\(138\) | −17.4473 | − | 0.802018i | −1.48521 | − | 0.0682723i | ||||
\(139\) | −1.23741 | + | 2.14325i | −0.104956 | + | 0.181788i | −0.913720 | − | 0.406344i | \(-0.866803\pi\) |
0.808765 | + | 0.588133i | \(0.200137\pi\) | |||||||
\(140\) | 0.802120 | + | 1.38931i | 0.0677915 | + | 0.117418i | ||||
\(141\) | 20.5554 | + | 0.944894i | 1.73108 | + | 0.0795744i | ||||
\(142\) | −15.3035 | −1.28424 | ||||||||
\(143\) | 0.0354401 | + | 0.0613840i | 0.00296365 | + | 0.00513319i | ||||
\(144\) | 5.41189 | + | 11.7468i | 0.450991 | + | 0.978897i | ||||
\(145\) | 0.309679 | 0.0257174 | ||||||||
\(146\) | −22.4090 | −1.85459 | ||||||||
\(147\) | 10.3171 | + | 19.9308i | 0.850938 | + | 1.64387i | ||||
\(148\) | 1.25307 | − | 2.17038i | 0.103002 | − | 0.178404i | ||||
\(149\) | 16.6974 | 1.36790 | 0.683952 | − | 0.729527i | \(-0.260260\pi\) | ||||
0.683952 | + | 0.729527i | \(0.260260\pi\) | |||||||
\(150\) | −7.73125 | − | 14.9354i | −0.631254 | − | 1.21947i | ||||
\(151\) | −5.32769 | + | 9.22783i | −0.433561 | + | 0.750950i | −0.997177 | − | 0.0750871i | \(-0.976077\pi\) |
0.563616 | + | 0.826037i | \(0.309410\pi\) | |||||||
\(152\) | 0.0439970 | − | 1.44982i | 0.00356863 | − | 0.117596i | ||||
\(153\) | 1.52915 | − | 2.16259i | 0.123625 | − | 0.174835i | ||||
\(154\) | 0.660494 | − | 1.14401i | 0.0532241 | − | 0.0921868i | ||||
\(155\) | 0.270504 | + | 0.468528i | 0.0217274 | + | 0.0376330i | ||||
\(156\) | 0.683530 | + | 1.32046i | 0.0547262 | + | 0.105722i | ||||
\(157\) | −8.73989 | −0.697519 | −0.348760 | − | 0.937212i | \(-0.613397\pi\) | ||||
−0.348760 | + | 0.937212i | \(0.613397\pi\) | |||||||
\(158\) | 1.88724 | − | 3.26880i | 0.150141 | − | 0.260052i | ||||
\(159\) | −9.34300 | − | 18.0491i | −0.740948 | − | 1.43139i | ||||
\(160\) | −0.762522 | + | 1.32073i | −0.0602826 | + | 0.104413i | ||||
\(161\) | −11.5093 | − | 19.9347i | −0.907061 | − | 1.57108i | ||||
\(162\) | −5.87140 | − | 16.6058i | −0.461301 | − | 1.30468i | ||||
\(163\) | −6.73838 | −0.527791 | −0.263895 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263895 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(164\) | 7.44190 | − | 12.8897i | 0.581114 | − | 1.00652i | ||||
\(165\) | 0.0276929 | − | 0.0432490i | 0.00215589 | − | 0.00336693i | ||||
\(166\) | 5.50993 | 0.427654 | ||||||||
\(167\) | −5.38887 | + | 9.33380i | −0.417004 | + | 0.722271i | −0.995636 | − | 0.0933167i | \(-0.970253\pi\) |
0.578633 | + | 0.815588i | \(0.303586\pi\) | |||||||
\(168\) | −1.38846 | + | 2.16841i | −0.107122 | + | 0.167296i | ||||
\(169\) | 6.38997 | + | 11.0677i | 0.491536 | + | 0.851365i | ||||
\(170\) | 0.339054 | 0.0260043 | ||||||||
\(171\) | −1.59411 | + | 12.9792i | −0.121905 | + | 0.992542i | ||||
\(172\) | −14.9908 | −1.14304 | ||||||||
\(173\) | 10.8789 | + | 18.8428i | 0.827109 | + | 1.43259i | 0.900297 | + | 0.435276i | \(0.143349\pi\) |
−0.0731880 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(174\) | −2.45908 | − | 4.75053i | −0.186422 | − | 0.360136i | ||||
\(175\) | 11.0824 | − | 19.1953i | 0.837751 | − | 1.45103i | ||||
\(176\) | 0.651394 | 0.0491007 | ||||||||
\(177\) | −2.74877 | − | 0.126356i | −0.206610 | − | 0.00949750i | ||||
\(178\) | 9.48718 | − | 16.4323i | 0.711094 | − | 1.23165i | ||||
\(179\) | −14.4126 | −1.07725 | −0.538623 | − | 0.842547i | \(-0.681055\pi\) | ||||
−0.538623 | + | 0.842547i | \(0.681055\pi\) | |||||||
\(180\) | 0.621975 | − | 0.879623i | 0.0463593 | − | 0.0655632i | ||||
\(181\) | 0.775446 | + | 1.34311i | 0.0576384 | + | 0.0998327i | 0.893405 | − | 0.449252i | \(-0.148310\pi\) |
−0.835766 | + | 0.549085i | \(0.814976\pi\) | |||||||
\(182\) | −2.05066 | + | 3.55185i | −0.152005 | + | 0.263281i | ||||
\(183\) | −15.8061 | − | 0.726578i | −1.16842 | − | 0.0537102i | ||||
\(184\) | 0.857307 | − | 1.48490i | 0.0632015 | − | 0.109468i | ||||
\(185\) | 0.268744 | 0.0197584 | ||||||||
\(186\) | 5.03929 | − | 7.87005i | 0.369499 | − | 0.577060i | ||||
\(187\) | −0.0666985 | − | 0.115525i | −0.00487747 | − | 0.00844803i | ||||
\(188\) | 10.8702 | − | 18.8277i | 0.792789 | − | 1.37315i | ||||
\(189\) | 14.2581 | − | 18.3182i | 1.03713 | − | 1.33245i | ||||
\(190\) | −1.47443 | + | 0.792630i | −0.106966 | + | 0.0575034i | ||||
\(191\) | 2.32553 | − | 4.02794i | 0.168270 | − | 0.291452i | −0.769542 | − | 0.638596i | \(-0.779515\pi\) |
0.937812 | + | 0.347145i | \(0.112849\pi\) | |||||||
\(192\) | 11.3966 | + | 0.523882i | 0.822482 | + | 0.0378080i | ||||
\(193\) | 9.20254 | 0.662413 | 0.331207 | − | 0.943558i | \(-0.392544\pi\) | ||||
0.331207 | + | 0.943558i | \(0.392544\pi\) | |||||||
\(194\) | −14.8997 | + | 25.8070i | −1.06974 | + | 1.85284i | ||||
\(195\) | −0.0859792 | + | 0.134277i | −0.00615710 | + | 0.00961578i | ||||
\(196\) | 23.7115 | 1.69368 | ||||||||
\(197\) | 22.3492 | 1.59232 | 0.796158 | − | 0.605089i | \(-0.206862\pi\) | ||||
0.796158 | + | 0.605089i | \(0.206862\pi\) | |||||||
\(198\) | −0.883350 | − | 0.0813839i | −0.0627770 | − | 0.00578370i | ||||
\(199\) | −9.48803 | − | 16.4337i | −0.672588 | − | 1.16496i | −0.977168 | − | 0.212470i | \(-0.931849\pi\) |
0.304579 | − | 0.952487i | \(-0.401484\pi\) | |||||||
\(200\) | 1.65101 | 0.116744 | ||||||||
\(201\) | −12.0836 | + | 18.8714i | −0.852311 | + | 1.33109i | ||||
\(202\) | 14.3777 | + | 24.9029i | 1.01161 | + | 1.75216i | ||||
\(203\) | 3.52499 | − | 6.10545i | 0.247406 | − | 0.428519i | ||||
\(204\) | −1.28641 | − | 2.48512i | −0.0900665 | − | 0.173993i | ||||
\(205\) | 1.59605 | 0.111473 | ||||||||
\(206\) | 11.4827 | − | 19.8886i | 0.800038 | − | 1.38571i | ||||
\(207\) | −8.92447 | + | 12.6214i | −0.620294 | + | 0.877245i | ||||
\(208\) | −2.02241 | −0.140229 | ||||||||
\(209\) | 0.560119 | + | 0.346453i | 0.0387443 | + | 0.0239646i | ||||
\(210\) | 2.96843 | + | 0.136453i | 0.204841 | + | 0.00941616i | ||||
\(211\) | 6.91716 | 0.476197 | 0.238099 | − | 0.971241i | \(-0.423476\pi\) | ||||
0.238099 | + | 0.971241i | \(0.423476\pi\) | |||||||
\(212\) | −21.4728 | −1.47476 | ||||||||
\(213\) | −7.30359 | + | 11.4063i | −0.500434 | + | 0.781546i | ||||
\(214\) | 6.95213 | + | 12.0414i | 0.475238 | + | 0.823136i | ||||
\(215\) | −0.803763 | − | 1.39216i | −0.0548162 | − | 0.0949444i | ||||
\(216\) | 1.71271 | + | 0.237530i | 0.116535 | + | 0.0161618i | ||||
\(217\) | 12.3163 | 0.836086 | ||||||||
\(218\) | 23.1916 | 1.57073 | ||||||||
\(219\) | −10.6947 | + | 16.7023i | −0.722681 | + | 1.12864i | ||||
\(220\) | −0.0271292 | − | 0.0469892i | −0.00182905 | − | 0.00316801i | ||||
\(221\) | 0.207082 | + | 0.358676i | 0.0139298 | + | 0.0241271i | ||||
\(222\) | −2.13403 | − | 4.12258i | −0.143227 | − | 0.276689i | ||||
\(223\) | −6.26352 | − | 10.8487i | −0.419436 | − | 0.726485i | 0.576446 | − | 0.817135i | \(-0.304439\pi\) |
−0.995883 | + | 0.0906498i | \(0.971106\pi\) | |||||||
\(224\) | 17.3591 | + | 30.0669i | 1.15986 | + | 2.00893i | ||||
\(225\) | −14.8217 | − | 1.36554i | −0.988114 | − | 0.0910359i | ||||
\(226\) | −9.78314 | + | 16.9449i | −0.650765 | + | 1.12716i | ||||
\(227\) | 2.70163 | − | 4.67937i | 0.179314 | − | 0.310581i | −0.762332 | − | 0.647186i | \(-0.775946\pi\) |
0.941646 | + | 0.336606i | \(0.109279\pi\) | |||||||
\(228\) | 11.4038 | + | 7.79959i | 0.755233 | + | 0.516541i | ||||
\(229\) | −4.76720 | − | 8.25703i | −0.315025 | − | 0.545640i | 0.664417 | − | 0.747362i | \(-0.268680\pi\) |
−0.979443 | + | 0.201722i | \(0.935346\pi\) | |||||||
\(230\) | −1.97879 | −0.130478 | ||||||||
\(231\) | −0.537454 | − | 1.03827i | −0.0353619 | − | 0.0683131i | ||||
\(232\) | 0.525139 | 0.0344771 | ||||||||
\(233\) | 0.398324 | − | 0.689917i | 0.0260951 | − | 0.0451980i | −0.852683 | − | 0.522429i | \(-0.825026\pi\) |
0.878778 | + | 0.477231i | \(0.158359\pi\) | |||||||
\(234\) | 2.74257 | + | 0.252676i | 0.179288 | + | 0.0165179i | ||||
\(235\) | 2.33131 | 0.152078 | ||||||||
\(236\) | −1.45361 | + | 2.51773i | −0.0946222 | + | 0.163890i | ||||
\(237\) | −1.53568 | − | 2.96667i | −0.0997531 | − | 0.192706i | ||||
\(238\) | 3.85936 | − | 6.68460i | 0.250165 | − | 0.433299i | ||||
\(239\) | 4.00503 | + | 6.93691i | 0.259064 | + | 0.448711i | 0.965991 | − | 0.258574i | \(-0.0832527\pi\) |
−0.706928 | + | 0.707286i | \(0.749919\pi\) | |||||||
\(240\) | 0.673611 | + | 1.30130i | 0.0434814 | + | 0.0839987i | ||||
\(241\) | −16.5909 | −1.06871 | −0.534356 | − | 0.845260i | \(-0.679446\pi\) | ||||
−0.534356 | + | 0.845260i | \(0.679446\pi\) | |||||||
\(242\) | 10.7413 | − | 18.6045i | 0.690478 | − | 1.19594i | ||||
\(243\) | −15.1791 | − | 3.54895i | −0.973740 | − | 0.227665i | ||||
\(244\) | −8.35864 | + | 14.4776i | −0.535107 | + | 0.926832i | ||||
\(245\) | 1.27134 | + | 2.20203i | 0.0812230 | + | 0.140682i | ||||
\(246\) | −12.6738 | − | 24.4837i | −0.808055 | − | 1.56102i | ||||
\(247\) | −1.73903 | − | 1.07565i | −0.110652 | − | 0.0684418i | ||||
\(248\) | 0.458709 | + | 0.794508i | 0.0291281 | + | 0.0504513i | ||||
\(249\) | 2.62961 | − | 4.10677i | 0.166645 | − | 0.260256i | ||||
\(250\) | −1.91279 | − | 3.31305i | −0.120975 | − | 0.209536i | ||||
\(251\) | 11.2878 | + | 19.5511i | 0.712480 | + | 1.23405i | 0.963923 | + | 0.266180i | \(0.0857615\pi\) |
−0.251443 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(252\) | −10.2624 | − | 22.2750i | −0.646470 | − | 1.40319i | ||||
\(253\) | 0.389267 | + | 0.674230i | 0.0244730 | + | 0.0423885i | ||||
\(254\) | 2.79967 | − | 4.84917i | 0.175667 | − | 0.304264i | ||||
\(255\) | 0.161813 | − | 0.252710i | 0.0101331 | − | 0.0158253i | ||||
\(256\) | −9.18232 | + | 15.9042i | −0.573895 | + | 0.994015i | ||||
\(257\) | −9.13747 | + | 15.8266i | −0.569980 | + | 0.987234i | 0.426587 | + | 0.904446i | \(0.359716\pi\) |
−0.996567 | + | 0.0827879i | \(0.973618\pi\) | |||||||
\(258\) | −14.9735 | + | 23.3846i | −0.932208 | + | 1.45586i | ||||
\(259\) | 3.05904 | − | 5.29841i | 0.190079 | − | 0.329227i | ||||
\(260\) | 0.0842293 | + | 0.145889i | 0.00522368 | + | 0.00904768i | ||||
\(261\) | −4.71435 | − | 0.434337i | −0.291811 | − | 0.0268848i | ||||
\(262\) | −2.64422 | − | 4.57993i | −0.163361 | − | 0.282949i | ||||
\(263\) | 6.87838 | + | 11.9137i | 0.424139 | + | 0.734631i | 0.996340 | − | 0.0854830i | \(-0.0272433\pi\) |
−0.572200 | + | 0.820114i | \(0.693910\pi\) | |||||||
\(264\) | 0.0469603 | − | 0.0733397i | 0.00289021 | − | 0.00451375i | ||||
\(265\) | −1.15131 | − | 1.99413i | −0.0707244 | − | 0.122498i | ||||
\(266\) | −1.15593 | + | 38.0913i | −0.0708749 | + | 2.33553i | ||||
\(267\) | −7.71986 | − | 14.9135i | −0.472448 | − | 0.912689i | ||||
\(268\) | 11.8377 | + | 20.5034i | 0.723100 | + | 1.25245i | ||||
\(269\) | −6.63512 | + | 11.4924i | −0.404551 | + | 0.700702i | −0.994269 | − | 0.106907i | \(-0.965905\pi\) |
0.589718 | + | 0.807609i | \(0.299239\pi\) | |||||||
\(270\) | −0.750897 | − | 1.84885i | −0.0456981 | − | 0.112517i | ||||
\(271\) | −11.4102 | + | 19.7630i | −0.693119 | + | 1.20052i | 0.277691 | + | 0.960670i | \(0.410431\pi\) |
−0.970811 | + | 0.239847i | \(0.922903\pi\) | |||||||
\(272\) | 3.80619 | 0.230784 | ||||||||
\(273\) | 1.66866 | + | 3.22356i | 0.100992 | + | 0.195099i | ||||
\(274\) | −15.4665 | − | 26.7888i | −0.934368 | − | 1.61837i | ||||
\(275\) | −0.374828 | + | 0.649221i | −0.0226030 | + | 0.0391495i | ||||
\(276\) | 7.50775 | + | 14.5037i | 0.451914 | + | 0.873020i | ||||
\(277\) | 2.60433 | − | 4.51083i | 0.156479 | − | 0.271030i | −0.777118 | − | 0.629355i | \(-0.783319\pi\) |
0.933597 | + | 0.358326i | \(0.116652\pi\) | |||||||
\(278\) | 4.84328 | 0.290481 | ||||||||
\(279\) | −3.46086 | − | 7.51196i | −0.207196 | − | 0.449729i | ||||
\(280\) | −0.145860 | + | 0.252637i | −0.00871679 | + | 0.0150979i | ||||
\(281\) | −9.52031 | −0.567934 | −0.283967 | − | 0.958834i | \(-0.591651\pi\) | ||||
−0.283967 | + | 0.958834i | \(0.591651\pi\) | |||||||
\(282\) | −18.5123 | − | 35.7627i | −1.10239 | − | 2.12964i | ||||
\(283\) | 10.5770 | 0.628737 | 0.314368 | − | 0.949301i | \(-0.398207\pi\) | ||||
0.314368 | + | 0.949301i | \(0.398207\pi\) | |||||||
\(284\) | 7.15494 | + | 12.3927i | 0.424568 | + | 0.735373i | ||||
\(285\) | −0.112892 | + | 1.47723i | −0.00668713 | + | 0.0875036i | ||||
\(286\) | 0.0693573 | − | 0.120130i | 0.00410118 | − | 0.00710346i | ||||
\(287\) | 18.1674 | − | 31.4669i | 1.07239 | − | 1.85743i | ||||
\(288\) | 13.4605 | − | 19.0364i | 0.793169 | − | 1.12173i | ||||
\(289\) | 8.11027 | + | 14.0474i | 0.477075 | + | 0.826318i | ||||
\(290\) | −0.303025 | − | 0.524855i | −0.0177942 | − | 0.0308205i | ||||
\(291\) | 12.1241 | + | 23.4217i | 0.710728 | + | 1.37301i | ||||
\(292\) | 10.4770 | + | 18.1468i | 0.613122 | + | 1.06196i | ||||
\(293\) | 7.26863 | + | 12.5896i | 0.424638 | + | 0.735494i | 0.996387 | − | 0.0849345i | \(-0.0270681\pi\) |
−0.571749 | + | 0.820429i | \(0.693735\pi\) | |||||||
\(294\) | 23.6841 | − | 36.9884i | 1.38128 | − | 2.15721i | ||||
\(295\) | −0.311754 | −0.0181510 | ||||||||
\(296\) | 0.455724 | 0.0264884 | ||||||||
\(297\) | −0.482237 | + | 0.619555i | −0.0279822 | + | 0.0359502i | ||||
\(298\) | −16.3386 | − | 28.2993i | −0.946472 | − | 1.63934i | ||||
\(299\) | −1.20857 | − | 2.09331i | −0.0698936 | − | 0.121059i | ||||
\(300\) | −8.48004 | + | 13.2436i | −0.489595 | + | 0.764619i | ||||
\(301\) | −36.5960 | −2.10936 | ||||||||
\(302\) | 20.8529 | 1.19995 | ||||||||
\(303\) | 25.4228 | + | 1.16864i | 1.46050 | + | 0.0671366i | ||||
\(304\) | −16.5518 | + | 8.89799i | −0.949310 | + | 0.510335i | ||||
\(305\) | −1.79266 | −0.102648 | ||||||||
\(306\) | −5.16154 | − | 0.475538i | −0.295066 | − | 0.0271847i | ||||
\(307\) | 11.2958 | − | 19.5649i | 0.644687 | − | 1.11663i | −0.339687 | − | 0.940539i | \(-0.610321\pi\) |
0.984374 | − | 0.176092i | \(-0.0563456\pi\) | |||||||
\(308\) | −1.23522 | −0.0703831 | ||||||||
\(309\) | −9.34366 | − | 18.0504i | −0.531542 | − | 1.02685i | ||||
\(310\) | 0.529385 | − | 0.916922i | 0.0300671 | − | 0.0520777i | ||||
\(311\) | −16.6494 | − | 28.8377i | −0.944103 | − | 1.63523i | −0.757538 | − | 0.652791i | \(-0.773598\pi\) |
−0.186564 | − | 0.982443i | \(-0.559735\pi\) | |||||||
\(312\) | −0.145800 | + | 0.227701i | −0.00825428 | + | 0.0128910i | ||||
\(313\) | 14.7578 | 0.834158 | 0.417079 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417079 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(314\) | 8.55211 | + | 14.8127i | 0.482623 | + | 0.835928i | ||||
\(315\) | 1.51839 | − | 2.14736i | 0.0855513 | − | 0.120990i | ||||
\(316\) | −3.52942 | −0.198545 | ||||||||
\(317\) | 7.61430 | 0.427662 | 0.213831 | − | 0.976871i | \(-0.431406\pi\) | ||||
0.213831 | + | 0.976871i | \(0.431406\pi\) | |||||||
\(318\) | −21.4480 | + | 33.4962i | −1.20274 | + | 1.87837i | ||||
\(319\) | −0.119222 | + | 0.206498i | −0.00667513 | + | 0.0115617i | ||||
\(320\) | 1.29256 | 0.0722562 | ||||||||
\(321\) | 12.2929 | + | 0.565080i | 0.686120 | + | 0.0315397i | ||||
\(322\) | −22.5241 | + | 39.0128i | −1.25522 | + | 2.17410i | ||||
\(323\) | 3.27286 | + | 2.02437i | 0.182107 | + | 0.112639i | ||||
\(324\) | −10.7023 | + | 12.5185i | −0.594570 | + | 0.695470i | ||||
\(325\) | 1.16374 | − | 2.01566i | 0.0645529 | − | 0.111809i | ||||
\(326\) | 6.59361 | + | 11.4205i | 0.365186 | + | 0.632521i | ||||
\(327\) | 11.0682 | − | 17.2856i | 0.612071 | − | 0.955894i | ||||
\(328\) | 2.70651 | 0.149442 | ||||||||
\(329\) | 26.5366 | − | 45.9628i | 1.46301 | − | 2.53401i | ||||
\(330\) | −0.100398 | − | 0.00461511i | −0.00552672 | − | 0.000254053i | ||||
\(331\) | −0.881101 | + | 1.52611i | −0.0484297 | + | 0.0838826i | −0.889224 | − | 0.457472i | \(-0.848755\pi\) |
0.840794 | + | 0.541355i | \(0.182088\pi\) | |||||||
\(332\) | −2.57609 | − | 4.46192i | −0.141381 | − | 0.244880i | ||||
\(333\) | −4.09118 | − | 0.376925i | −0.224195 | − | 0.0206553i | ||||
\(334\) | 21.0924 | 1.15412 | ||||||||
\(335\) | −1.26940 | + | 2.19867i | −0.0693548 | + | 0.120126i | ||||
\(336\) | 33.3233 | + | 1.53181i | 1.81794 | + | 0.0835671i | ||||
\(337\) | −14.8632 | −0.809652 | −0.404826 | − | 0.914394i | \(-0.632668\pi\) | ||||
−0.404826 | + | 0.914394i | \(0.632668\pi\) | |||||||
\(338\) | 12.5054 | − | 21.6599i | 0.680202 | − | 1.17814i | ||||
\(339\) | 7.96069 | + | 15.3787i | 0.432366 | + | 0.835256i | ||||
\(340\) | −0.158520 | − | 0.274565i | −0.00859695 | − | 0.0148904i | ||||
\(341\) | −0.416561 | −0.0225580 | ||||||||
\(342\) | 23.5574 | − | 9.99855i | 1.27384 | − | 0.540660i | ||||
\(343\) | 26.6137 | 1.43701 | ||||||||
\(344\) | −1.36298 | − | 2.36076i | −0.0734872 | − | 0.127284i | ||||
\(345\) | −0.944378 | + | 1.47487i | −0.0508436 | + | 0.0794044i | ||||
\(346\) | 21.2904 | − | 36.8760i | 1.14458 | − | 1.98247i | ||||
\(347\) | −17.8141 | −0.956310 | −0.478155 | − | 0.878275i | \(-0.658694\pi\) | ||||
−0.478155 | + | 0.878275i | \(0.658694\pi\) | |||||||
\(348\) | −2.69725 | + | 4.21240i | −0.144588 | + | 0.225808i | ||||
\(349\) | −8.22239 | + | 14.2416i | −0.440134 | + | 0.762335i | −0.997699 | − | 0.0677984i | \(-0.978403\pi\) |
0.557565 | + | 0.830134i | \(0.311736\pi\) | |||||||
\(350\) | −43.3772 | −2.31861 | ||||||||
\(351\) | 1.49722 | − | 1.92356i | 0.0799158 | − | 0.102672i | ||||
\(352\) | −0.587119 | − | 1.01692i | −0.0312936 | − | 0.0542021i | ||||
\(353\) | 5.08611 | − | 8.80940i | 0.270706 | − | 0.468877i | −0.698337 | − | 0.715770i | \(-0.746076\pi\) |
0.969043 | + | 0.246892i | \(0.0794094\pi\) | |||||||
\(354\) | 2.47556 | + | 4.78236i | 0.131575 | + | 0.254180i | ||||
\(355\) | −0.767254 | + | 1.32892i | −0.0407216 | + | 0.0705319i | ||||
\(356\) | −17.7424 | −0.940345 | ||||||||
\(357\) | −3.14042 | − | 6.06675i | −0.166209 | − | 0.321087i | ||||
\(358\) | 14.1029 | + | 24.4269i | 0.745362 | + | 1.29100i | ||||
\(359\) | 17.4994 | − | 30.3098i | 0.923580 | − | 1.59969i | 0.129752 | − | 0.991546i | \(-0.458582\pi\) |
0.793828 | − | 0.608142i | \(-0.208085\pi\) | |||||||
\(360\) | 0.195074 | + | 0.0179724i | 0.0102813 | + | 0.000947227i | ||||
\(361\) | −18.9650 | − | 1.15210i | −0.998160 | − | 0.0606370i | ||||
\(362\) | 1.51757 | − | 2.62851i | 0.0797617 | − | 0.138151i | ||||
\(363\) | −8.74038 | − | 16.8849i | −0.458751 | − | 0.886229i | ||||
\(364\) | 3.83503 | 0.201010 | ||||||||
\(365\) | −1.12350 | + | 1.94595i | −0.0588064 | + | 0.101856i | ||||
\(366\) | 14.2351 | + | 27.4998i | 0.744080 | + | 1.43744i | ||||
\(367\) | 1.71482 | 0.0895127 | 0.0447564 | − | 0.998998i | \(-0.485749\pi\) | ||||
0.0447564 | + | 0.998998i | \(0.485749\pi\) | |||||||
\(368\) | −22.2137 | −1.15797 | ||||||||
\(369\) | −24.2972 | − | 2.23853i | −1.26486 | − | 0.116533i | ||||
\(370\) | −0.262970 | − | 0.455477i | −0.0136711 | − | 0.0236791i | ||||
\(371\) | −52.4201 | −2.72152 | ||||||||
\(372\) | −8.72919 | − | 0.401265i | −0.452587 | − | 0.0208046i | ||||
\(373\) | 16.8990 | + | 29.2699i | 0.874996 | + | 1.51554i | 0.856767 | + | 0.515703i | \(0.172469\pi\) |
0.0182282 | + | 0.999834i | \(0.494197\pi\) | |||||||
\(374\) | −0.130531 | + | 0.226086i | −0.00674959 | + | 0.0116906i | ||||
\(375\) | −3.38222 | − | 0.155474i | −0.174657 | − | 0.00802867i | ||||
\(376\) | 3.95332 | 0.203877 | ||||||||
\(377\) | 0.370153 | − | 0.641123i | 0.0190638 | − | 0.0330195i | ||||
\(378\) | −44.9981 | − | 6.24062i | −2.31445 | − | 0.320983i | ||||
\(379\) | 16.5713 | 0.851211 | 0.425605 | − | 0.904909i | \(-0.360061\pi\) | ||||
0.425605 | + | 0.904909i | \(0.360061\pi\) | |||||||
\(380\) | 1.33122 | + | 0.823403i | 0.0682900 | + | 0.0422397i | ||||
\(381\) | −2.27813 | − | 4.40096i | −0.116712 | − | 0.225468i | ||||
\(382\) | −9.10227 | −0.465713 | ||||||||
\(383\) | −11.6835 | −0.597001 | −0.298501 | − | 0.954409i | \(-0.596487\pi\) | ||||
−0.298501 | + | 0.954409i | \(0.596487\pi\) | |||||||
\(384\) | 2.11201 | + | 4.08004i | 0.107778 | + | 0.208209i | ||||
\(385\) | −0.0662288 | − | 0.114712i | −0.00337533 | − | 0.00584624i | ||||
\(386\) | −9.00482 | − | 15.5968i | −0.458333 | − | 0.793856i | ||||
\(387\) | 10.2834 | + | 22.3206i | 0.522735 | + | 1.13462i | ||||
\(388\) | 27.8646 | 1.41461 | ||||||||
\(389\) | 25.6990 | 1.30299 | 0.651496 | − | 0.758652i | \(-0.274142\pi\) | ||||
0.651496 | + | 0.758652i | \(0.274142\pi\) | |||||||
\(390\) | 0.311710 | + | 0.0143287i | 0.0157840 | + | 0.000725563i | ||||
\(391\) | 2.27454 | + | 3.93962i | 0.115029 | + | 0.199235i | ||||
\(392\) | 2.15588 | + | 3.73410i | 0.108889 | + | 0.188601i | ||||
\(393\) | −4.67556 | − | 0.214927i | −0.235851 | − | 0.0108416i | ||||
\(394\) | −21.8690 | − | 37.8783i | −1.10175 | − | 1.90828i | ||||
\(395\) | −0.189237 | − | 0.327768i | −0.00952155 | − | 0.0164918i | ||||
\(396\) | 0.347094 | + | 0.753384i | 0.0174421 | + | 0.0378589i | ||||
\(397\) | 1.27823 | − | 2.21396i | 0.0641525 | − | 0.111115i | −0.832165 | − | 0.554528i | \(-0.812899\pi\) |
0.896318 | + | 0.443412i | \(0.146232\pi\) | |||||||
\(398\) | −18.5683 | + | 32.1613i | −0.930747 | + | 1.61210i | ||||
\(399\) | 27.8393 | + | 19.0406i | 1.39371 | + | 0.953223i | ||||
\(400\) | −10.6949 | − | 18.5241i | −0.534745 | − | 0.926205i | ||||
\(401\) | −22.4419 | −1.12069 | −0.560347 | − | 0.828258i | \(-0.689332\pi\) | ||||
−0.560347 | + | 0.828258i | \(0.689332\pi\) | |||||||
\(402\) | 43.8080 | + | 2.01377i | 2.18494 | + | 0.100438i | ||||
\(403\) | 1.29331 | 0.0644246 | ||||||||
\(404\) | 13.4442 | − | 23.2860i | 0.668872 | − | 1.15852i | ||||
\(405\) | −1.73638 | − | 0.322688i | −0.0862815 | − | 0.0160345i | ||||
\(406\) | −13.7970 | −0.684734 | ||||||||
\(407\) | −0.103462 | + | 0.179202i | −0.00512844 | + | 0.00888272i | ||||
\(408\) | 0.274396 | − | 0.428535i | 0.0135846 | − | 0.0212156i | ||||
\(409\) | −4.28942 | + | 7.42950i | −0.212098 | + | 0.367365i | −0.952371 | − | 0.304942i | \(-0.901363\pi\) |
0.740273 | + | 0.672307i | \(0.234696\pi\) | |||||||
\(410\) | −1.56176 | − | 2.70504i | −0.0771297 | − | 0.133593i | ||||
\(411\) | −27.3482 | − | 1.25714i | −1.34898 | − | 0.0620103i | ||||
\(412\) | −21.4743 | −1.05796 | ||||||||
\(413\) | −3.54861 | + | 6.14637i | −0.174616 | + | 0.302443i | ||||
\(414\) | 30.1239 | + | 2.77534i | 1.48051 | + | 0.136401i | ||||
\(415\) | 0.276245 | − | 0.478470i | 0.0135603 | − | 0.0234872i | ||||
\(416\) | 1.82285 | + | 3.15728i | 0.0893728 | + | 0.154798i | ||||
\(417\) | 2.31146 | − | 3.60989i | 0.113192 | − | 0.176777i | ||||
\(418\) | 0.0390959 | − | 1.28832i | 0.00191224 | − | 0.0630138i | ||||
\(419\) | −10.3066 | − | 17.8516i | −0.503511 | − | 0.872106i | −0.999992 | − | 0.00405866i | \(-0.998708\pi\) |
0.496481 | − | 0.868048i | \(-0.334625\pi\) | |||||||
\(420\) | −1.27735 | − | 2.46762i | −0.0623282 | − | 0.120408i | ||||
\(421\) | −3.56881 | − | 6.18136i | −0.173933 | − | 0.301261i | 0.765858 | − | 0.643009i | \(-0.222314\pi\) |
−0.939792 | + | 0.341748i | \(0.888981\pi\) | |||||||
\(422\) | −6.76854 | − | 11.7235i | −0.329488 | − | 0.570689i | ||||
\(423\) | −35.4903 | − | 3.26976i | −1.72560 | − | 0.158981i | ||||
\(424\) | −1.95234 | − | 3.38155i | −0.0948139 | − | 0.164223i | ||||
\(425\) | −2.19017 | + | 3.79349i | −0.106239 | + | 0.184011i | ||||
\(426\) | 26.4785 | + | 1.21717i | 1.28289 | + | 0.0589719i | ||||
\(427\) | −20.4054 | + | 35.3431i | −0.987485 | + | 1.71037i | ||||
\(428\) | 6.50074 | − | 11.2596i | 0.314225 | − | 0.544254i | ||||
\(429\) | −0.0564371 | − | 0.109027i | −0.00272481 | − | 0.00526387i | ||||
\(430\) | −1.57299 | + | 2.72449i | −0.0758562 | + | 0.131387i | ||||
\(431\) | 3.59358 | + | 6.22427i | 0.173097 | + | 0.299813i | 0.939501 | − | 0.342546i | \(-0.111289\pi\) |
−0.766404 | + | 0.642359i | \(0.777956\pi\) | |||||||
\(432\) | −8.42949 | − | 20.7550i | −0.405564 | − | 0.998573i | ||||
\(433\) | −12.0394 | − | 20.8529i | −0.578578 | − | 1.00213i | −0.995643 | − | 0.0932498i | \(-0.970274\pi\) |
0.417065 | − | 0.908877i | \(-0.363059\pi\) | |||||||
\(434\) | −12.0517 | − | 20.8741i | −0.578500 | − | 1.00199i | ||||
\(435\) | −0.535813 | − | 0.0246303i | −0.0256903 | − | 0.00118093i | ||||
\(436\) | −10.8429 | − | 18.7804i | −0.519280 | − | 0.899420i | ||||
\(437\) | −19.1011 | − | 11.8147i | −0.913730 | − | 0.565173i | ||||
\(438\) | 38.7727 | + | 1.78231i | 1.85263 | + | 0.0851619i | ||||
\(439\) | 7.12727 | + | 12.3448i | 0.340166 | + | 0.589184i | 0.984463 | − | 0.175591i | \(-0.0561835\pi\) |
−0.644297 | + | 0.764775i | \(0.722850\pi\) | |||||||
\(440\) | 0.00493326 | − | 0.00854465i | 0.000235184 | − | 0.000407350i | ||||
\(441\) | −16.2656 | − | 35.3054i | −0.774554 | − | 1.68121i | ||||
\(442\) | 0.405265 | − | 0.701939i | 0.0192765 | − | 0.0333878i | ||||
\(443\) | 11.9991 | 0.570093 | 0.285047 | − | 0.958514i | \(-0.407991\pi\) | ||||
0.285047 | + | 0.958514i | \(0.407991\pi\) | |||||||
\(444\) | −2.34071 | + | 3.65558i | −0.111085 | + | 0.173486i | ||||
\(445\) | −0.951295 | − | 1.64769i | −0.0450957 | − | 0.0781080i | ||||
\(446\) | −12.2579 | + | 21.2313i | −0.580428 | + | 1.00533i | ||||
\(447\) | −28.8902 | − | 1.32803i | −1.36646 | − | 0.0628136i | ||||
\(448\) | 14.7128 | − | 25.4834i | 0.695116 | − | 1.20398i | ||||
\(449\) | −16.5849 | −0.782689 | −0.391345 | − | 0.920244i | \(-0.627990\pi\) | ||||
−0.391345 | + | 0.920244i | \(0.627990\pi\) | |||||||
\(450\) | 12.1889 | + | 26.4566i | 0.574590 | + | 1.24717i | ||||
\(451\) | −0.614456 | + | 1.06427i | −0.0289336 | + | 0.0501145i | ||||
\(452\) | 18.2959 | 0.860566 | ||||||||
\(453\) | 9.95203 | − | 15.5425i | 0.467587 | − | 0.730249i | ||||
\(454\) | −10.5744 | −0.496279 | ||||||||
\(455\) | 0.205623 | + | 0.356150i | 0.00963977 | + | 0.0166966i | ||||
\(456\) | −0.191437 | + | 2.50502i | −0.00896484 | + | 0.117308i | ||||
\(457\) | −1.23271 | + | 2.13512i | −0.0576639 | + | 0.0998768i | −0.893416 | − | 0.449230i | \(-0.851699\pi\) |
0.835752 | + | 0.549106i | \(0.185032\pi\) | |||||||
\(458\) | −9.32955 | + | 16.1593i | −0.435941 | + | 0.755072i | ||||
\(459\) | −2.81778 | + | 3.62015i | −0.131523 | + | 0.168974i | ||||
\(460\) | 0.925157 | + | 1.60242i | 0.0431357 | + | 0.0747132i | ||||
\(461\) | 13.2340 | + | 22.9219i | 0.616368 | + | 1.06758i | 0.990143 | + | 0.140062i | \(0.0447300\pi\) |
−0.373775 | + | 0.927520i | \(0.621937\pi\) | |||||||
\(462\) | −1.23379 | + | 1.92686i | −0.0574011 | + | 0.0896455i | ||||
\(463\) | −7.78625 | − | 13.4862i | −0.361858 | − | 0.626756i | 0.626409 | − | 0.779495i | \(-0.284524\pi\) |
−0.988267 | + | 0.152739i | \(0.951191\pi\) | |||||||
\(464\) | −3.40173 | − | 5.89197i | −0.157921 | − | 0.273528i | ||||
\(465\) | −0.430769 | − | 0.832172i | −0.0199764 | − | 0.0385911i | ||||
\(466\) | −1.55906 | −0.0722222 | ||||||||
\(467\) | −0.796236 | −0.0368454 | −0.0184227 | − | 0.999830i | \(-0.505864\pi\) | ||||
−0.0184227 | + | 0.999830i | \(0.505864\pi\) | |||||||
\(468\) | −1.07764 | − | 2.33906i | −0.0498138 | − | 0.108123i | ||||
\(469\) | 28.8985 | + | 50.0536i | 1.33441 | + | 2.31126i | ||||
\(470\) | −2.28122 | − | 3.95118i | −0.105225 | − | 0.182255i | ||||
\(471\) | 15.1220 | + | 0.695129i | 0.696783 | + | 0.0320298i | ||||
\(472\) | −0.528658 | −0.0243335 | ||||||||
\(473\) | 1.23775 | 0.0569117 | ||||||||
\(474\) | −3.52534 | + | 5.50566i | −0.161924 | + | 0.252883i | ||||
\(475\) | 0.655989 | − | 21.6167i | 0.0300989 | − | 0.991842i | ||||
\(476\) | −7.21756 | −0.330816 | ||||||||
\(477\) | 14.7299 | + | 31.9720i | 0.674438 | + | 1.46390i | ||||
\(478\) | 7.83795 | − | 13.5757i | 0.358500 | − | 0.620940i | ||||
\(479\) | 10.0567 | 0.459503 | 0.229751 | − | 0.973249i | \(-0.426209\pi\) | ||||
0.229751 | + | 0.973249i | \(0.426209\pi\) | |||||||
\(480\) | 1.42438 | − | 2.22450i | 0.0650136 | − | 0.101534i | ||||
\(481\) | 0.321224 | − | 0.556376i | 0.0146466 | − | 0.0253686i | ||||
\(482\) | 16.2344 | + | 28.1188i | 0.739457 | + | 1.28078i | ||||
\(483\) | 18.3282 | + | 35.4069i | 0.833961 | + | 1.61107i | ||||
\(484\) | −20.0878 | −0.913083 | ||||||||
\(485\) | 1.49402 | + | 2.58771i | 0.0678398 | + | 0.117502i | ||||
\(486\) | 8.83808 | + | 29.1988i | 0.400904 | + | 1.32448i | ||||
\(487\) | −17.6239 | −0.798614 | −0.399307 | − | 0.916817i | \(-0.630749\pi\) | ||||
−0.399307 | + | 0.916817i | \(0.630749\pi\) | |||||||
\(488\) | −3.03992 | −0.137610 | ||||||||
\(489\) | 11.6589 | + | 0.535939i | 0.527234 | + | 0.0242360i | ||||
\(490\) | 2.48805 | − | 4.30943i | 0.112399 | − | 0.194680i | ||||
\(491\) | 16.3828 | 0.739346 | 0.369673 | − | 0.929162i | \(-0.379470\pi\) | ||||
0.369673 | + | 0.929162i | \(0.379470\pi\) | |||||||
\(492\) | −13.9013 | + | 21.7102i | −0.626720 | + | 0.978773i | ||||
\(493\) | −0.696630 | + | 1.20660i | −0.0313746 | + | 0.0543424i | ||||
\(494\) | −0.121383 | + | 3.99990i | −0.00546127 | + | 0.179964i | ||||
\(495\) | −0.0513547 | + | 0.0726279i | −0.00230822 | + | 0.00326438i | ||||
\(496\) | 5.94283 | − | 10.2933i | 0.266841 | − | 0.462182i | ||||
\(497\) | 17.4669 | + | 30.2535i | 0.783496 | + | 1.35706i | ||||
\(498\) | −9.53341 | − | 0.438233i | −0.427203 | − | 0.0196377i | ||||
\(499\) | 18.0196 | 0.806669 | 0.403334 | − | 0.915053i | \(-0.367851\pi\) | ||||
0.403334 | + | 0.915053i | \(0.367851\pi\) | |||||||
\(500\) | −1.78860 | + | 3.09794i | −0.0799885 | + | 0.138544i | ||||
\(501\) | 10.0663 | − | 15.7210i | 0.449730 | − | 0.702361i | ||||
\(502\) | 22.0906 | − | 38.2620i | 0.985950 | − | 1.70772i | ||||
\(503\) | 18.7382 | + | 32.4554i | 0.835493 | + | 1.44712i | 0.893628 | + | 0.448808i | \(0.148151\pi\) |
−0.0581348 | + | 0.998309i | \(0.518515\pi\) | |||||||
\(504\) | 2.57481 | − | 3.64140i | 0.114691 | − | 0.162201i | ||||
\(505\) | 2.88335 | 0.128307 | ||||||||
\(506\) | 0.761806 | − | 1.31949i | 0.0338664 | − | 0.0586584i | ||||
\(507\) | −10.1758 | − | 19.6579i | −0.451923 | − | 0.873038i | ||||
\(508\) | −5.23578 | −0.232300 | ||||||||
\(509\) | −18.8240 | + | 32.6042i | −0.834361 | + | 1.44516i | 0.0601885 | + | 0.998187i | \(0.480830\pi\) |
−0.894550 | + | 0.446969i | \(0.852504\pi\) | |||||||
\(510\) | −0.586639 | − | 0.0269667i | −0.0259768 | − | 0.00119411i | ||||
\(511\) | 25.5769 | + | 44.3005i | 1.13145 | + | 1.95974i | ||||
\(512\) | 30.6351 | 1.35389 | ||||||||
\(513\) | 3.79047 | − | 22.3301i | 0.167353 | − | 0.985897i | ||||
\(514\) | 35.7646 | 1.57751 | ||||||||
\(515\) | −1.15139 | − | 1.99427i | −0.0507363 | − | 0.0878778i | ||||
\(516\) | 25.9374 | + | 1.19230i | 1.14183 | + | 0.0524879i | ||||
\(517\) | −0.897519 | + | 1.55455i | −0.0394728 | + | 0.0683689i | ||||
\(518\) | −11.9732 | −0.526074 | ||||||||
\(519\) | −17.3243 | − | 33.4676i | −0.760452 | − | 1.46906i | ||||
\(520\) | −0.0153165 | + | 0.0265289i | −0.000671672 | + | 0.00116337i | ||||
\(521\) | −25.6456 | −1.12355 | −0.561776 | − | 0.827289i | \(-0.689882\pi\) | ||||
−0.561776 | + | 0.827289i | \(0.689882\pi\) | |||||||
\(522\) | 3.87693 | + | 8.41506i | 0.169689 | + | 0.368317i | ||||
\(523\) | 8.31030 | + | 14.3939i | 0.363384 | + | 0.629399i | 0.988515 | − | 0.151120i | \(-0.0482880\pi\) |
−0.625132 | + | 0.780519i | \(0.714955\pi\) | |||||||
\(524\) | −2.47254 | + | 4.28257i | −0.108013 | + | 0.187085i | ||||
\(525\) | −20.7017 | + | 32.3307i | −0.903498 | + | 1.41103i | ||||
\(526\) | 13.4612 | − | 23.3155i | 0.586936 | − | 1.01660i | ||||
\(527\) | −2.43403 | −0.106028 | ||||||||
\(528\) | −1.12706 | − | 0.0518087i | −0.0490489 | − | 0.00225469i | ||||
\(529\) | −1.77472 | − | 3.07391i | −0.0771618 | − | 0.133648i | ||||
\(530\) | −2.25315 | + | 3.90256i | −0.0978704 | + | 0.169516i | ||||
\(531\) | 4.74594 | + | 0.437248i | 0.205956 | + | 0.0189750i | ||||
\(532\) | 31.3866 | − | 16.8730i | 1.36078 | − | 0.731537i | ||||
\(533\) | 1.90773 | − | 3.30428i | 0.0826328 | − | 0.143124i | ||||
\(534\) | −17.7219 | + | 27.6769i | −0.766901 | + | 1.19770i | ||||
\(535\) | 1.39420 | 0.0602766 | ||||||||
\(536\) | −2.15259 | + | 3.72840i | −0.0929779 | + | 0.161042i | ||||
\(537\) | 24.9370 | + | 1.14631i | 1.07611 | + | 0.0494667i | ||||
\(538\) | 25.9703 | 1.11966 | ||||||||
\(539\) | −1.95779 | −0.0843280 | ||||||||
\(540\) | −1.14612 | + | 1.47248i | −0.0493210 | + | 0.0633652i | ||||
\(541\) | −10.5384 | − | 18.2531i | −0.453083 | − | 0.784763i | 0.545493 | − | 0.838116i | \(-0.316343\pi\) |
−0.998576 | + | 0.0533527i | \(0.983009\pi\) | |||||||
\(542\) | 44.6601 | 1.91832 | ||||||||
\(543\) | −1.23487 | − | 2.38556i | −0.0529934 | − | 0.102374i | ||||
\(544\) | −3.43062 | − | 5.94201i | −0.147087 | − | 0.254762i | ||||
\(545\) | 1.16273 | − | 2.01390i | 0.0498058 | − | 0.0862662i | ||||
\(546\) | 3.83060 | − | 5.98240i | 0.163935 | − | 0.256023i | ||||
\(547\) | 44.3793 | 1.89752 | 0.948761 | − | 0.315996i | \(-0.102339\pi\) | ||||
0.948761 | + | 0.315996i | \(0.102339\pi\) | |||||||
\(548\) | −14.4623 | + | 25.0495i | −0.617800 | + | 1.07006i | ||||
\(549\) | 27.2903 | + | 2.51428i | 1.16472 | + | 0.107307i | ||||
\(550\) | 1.46710 | 0.0625573 | ||||||||
\(551\) | 0.208651 | − | 6.87563i | 0.00888883 | − | 0.292912i | ||||
\(552\) | −1.60143 | + | 2.50102i | −0.0681616 | + | 0.106451i | ||||
\(553\) | −8.61613 | −0.366395 | ||||||||
\(554\) | −10.1935 | −0.433080 | ||||||||
\(555\) | −0.464987 | − | 0.0213746i | −0.0197376 | − | 0.000907300i | ||||
\(556\) | −2.26441 | − | 3.92207i | −0.0960324 | − | 0.166333i | ||||
\(557\) | −4.03714 | − | 6.99254i | −0.171059 | − | 0.296283i | 0.767731 | − | 0.640772i | \(-0.221386\pi\) |
−0.938790 | + | 0.344489i | \(0.888052\pi\) | |||||||
\(558\) | −9.34504 | + | 13.2161i | −0.395607 | + | 0.559484i | ||||
\(559\) | −3.84289 | −0.162537 | ||||||||
\(560\) | 3.77939 | 0.159708 | ||||||||
\(561\) | 0.106215 | + | 0.205189i | 0.00448440 | + | 0.00866309i | ||||
\(562\) | 9.31576 | + | 16.1354i | 0.392962 | + | 0.680629i | ||||
\(563\) | −2.37128 | − | 4.10718i | −0.0999376 | − | 0.173097i | 0.811721 | − | 0.584045i | \(-0.198531\pi\) |
−0.911659 | + | 0.410948i | \(0.865198\pi\) | |||||||
\(564\) | −20.3053 | + | 31.7115i | −0.855007 | + | 1.33530i | ||||
\(565\) | 0.980972 | + | 1.69909i | 0.0412698 | + | 0.0714814i | ||||
\(566\) | −10.3497 | − | 17.9263i | −0.435032 | − | 0.753497i | ||||
\(567\) | −26.1267 | + | 30.5605i | −1.09722 | + | 1.28342i | ||||
\(568\) | −1.30107 | + | 2.25353i | −0.0545919 | + | 0.0945559i | ||||
\(569\) | 8.96716 | − | 15.5316i | 0.375923 | − | 0.651118i | −0.614542 | − | 0.788884i | \(-0.710659\pi\) |
0.990465 | + | 0.137767i | \(0.0439924\pi\) | |||||||
\(570\) | 2.61413 | − | 1.25416i | 0.109494 | − | 0.0525309i | ||||
\(571\) | −16.8027 | − | 29.1031i | −0.703170 | − | 1.21793i | −0.967348 | − | 0.253453i | \(-0.918434\pi\) |
0.264178 | − | 0.964474i | \(-0.414900\pi\) | |||||||
\(572\) | −0.129708 | −0.00542337 | ||||||||
\(573\) | −4.34406 | + | 6.78428i | −0.181476 | + | 0.283417i | ||||
\(574\) | −71.1082 | −2.96800 | ||||||||
\(575\) | 12.7823 | − | 22.1396i | 0.533060 | − | 0.923287i | ||||
\(576\) | −19.6771 | − | 1.81287i | −0.819878 | − | 0.0755362i | ||||
\(577\) | −21.7618 | −0.905954 | −0.452977 | − | 0.891522i | \(-0.649638\pi\) | ||||
−0.452977 | + | 0.891522i | \(0.649638\pi\) | |||||||
\(578\) | 15.8720 | − | 27.4912i | 0.660190 | − | 1.14348i | ||||
\(579\) | −15.9224 | − | 0.731925i | −0.661714 | − | 0.0304178i | ||||
\(580\) | −0.283350 | + | 0.490777i | −0.0117655 | + | 0.0203784i | ||||
\(581\) | −6.28884 | − | 10.8926i | −0.260905 | − | 0.451901i | ||||
\(582\) | 27.8324 | − | 43.4669i | 1.15369 | − | 1.80176i | ||||
\(583\) | 1.77295 | 0.0734280 | ||||||||
\(584\) | −1.90517 | + | 3.29986i | −0.0788366 | + | 0.136549i | ||||
\(585\) | 0.159443 | − | 0.225491i | 0.00659216 | − | 0.00932290i | ||||
\(586\) | 14.2249 | − | 24.6383i | 0.587626 | − | 1.01780i | ||||
\(587\) | −21.9847 | − | 38.0786i | −0.907406 | − | 1.57167i | −0.817654 | − | 0.575710i | \(-0.804726\pi\) |
−0.0897523 | − | 0.995964i | \(-0.528608\pi\) | |||||||
\(588\) | −41.0262 | − | 1.88590i | −1.69189 | − | 0.0777732i | ||||
\(589\) | 10.5847 | − | 5.69019i | 0.436136 | − | 0.234460i | ||||
\(590\) | 0.305056 | + | 0.528372i | 0.0125589 | + | 0.0217527i | ||||
\(591\) | −38.6691 | − | 1.77755i | −1.59064 | − | 0.0731186i | ||||
\(592\) | −2.95207 | − | 5.11314i | −0.121329 | − | 0.210149i | ||||
\(593\) | −7.81848 | − | 13.5420i | −0.321066 | − | 0.556103i | 0.659642 | − | 0.751580i | \(-0.270708\pi\) |
−0.980708 | + | 0.195477i | \(0.937375\pi\) | |||||||
\(594\) | 1.52192 | + | 0.211070i | 0.0624451 | + | 0.00866030i | ||||
\(595\) | −0.386984 | − | 0.670276i | −0.0158648 | − | 0.0274786i | ||||
\(596\) | −15.2778 | + | 26.4619i | −0.625803 | + | 1.08392i | ||||
\(597\) | 15.1093 | + | 29.1887i | 0.618384 | + | 1.19461i | ||||
\(598\) | −2.36521 | + | 4.09667i | −0.0967207 | + | 0.167525i | ||||
\(599\) | 6.72485 | − | 11.6478i | 0.274770 | − | 0.475916i | −0.695307 | − | 0.718713i | \(-0.744732\pi\) |
0.970077 | + | 0.242797i | \(0.0780649\pi\) | |||||||
\(600\) | −2.85662 | − | 0.131314i | −0.116621 | − | 0.00536086i | ||||
\(601\) | 20.6960 | − | 35.8466i | 0.844208 | − | 1.46221i | −0.0420990 | − | 0.999113i | \(-0.513404\pi\) |
0.886307 | − | 0.463098i | \(-0.153262\pi\) | |||||||
\(602\) | 35.8098 | + | 62.0243i | 1.45950 | + | 2.52792i | ||||
\(603\) | 22.4083 | − | 31.6907i | 0.912535 | − | 1.29055i | ||||
\(604\) | −9.74948 | − | 16.8866i | −0.396701 | − | 0.687106i | ||||
\(605\) | −1.07705 | − | 1.86551i | −0.0437883 | − | 0.0758436i | ||||
\(606\) | −22.8959 | − | 44.2311i | −0.930084 | − | 1.79676i | ||||
\(607\) | 3.77674 | + | 6.54150i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784345\pi\) | |||||||
\(608\) | 28.8096 | + | 17.8197i | 1.16839 | + | 0.722686i | ||||
\(609\) | −6.58461 | + | 10.2834i | −0.266822 | + | 0.416706i | ||||
\(610\) | 1.75415 | + | 3.03827i | 0.0710233 | + | 0.123016i | ||||
\(611\) | 2.78656 | − | 4.82647i | 0.112732 | − | 0.195258i | ||||
\(612\) | 2.02812 | + | 4.40213i | 0.0819818 | + | 0.177945i | ||||
\(613\) | 2.01301 | − | 3.48663i | 0.0813047 | − | 0.140824i | −0.822506 | − | 0.568757i | \(-0.807425\pi\) |
0.903811 | + | 0.427933i | \(0.140758\pi\) | |||||||
\(614\) | −44.2125 | −1.78427 | ||||||||
\(615\) | −2.76152 | − | 0.126942i | −0.111355 | − | 0.00511880i | ||||
\(616\) | −0.112308 | − | 0.194523i | −0.00452501 | − | 0.00783755i | ||||
\(617\) | −12.1705 | + | 21.0800i | −0.489968 | + | 0.848649i | −0.999933 | − | 0.0115460i | \(-0.996325\pi\) |
0.509966 | + | 0.860195i | \(0.329658\pi\) | |||||||
\(618\) | −21.4495 | + | 33.4985i | −0.862825 | + | 1.34751i | ||||
\(619\) | −8.47222 | + | 14.6743i | −0.340527 | + | 0.589811i | −0.984531 | − | 0.175212i | \(-0.943939\pi\) |
0.644003 | + | 0.765023i | \(0.277272\pi\) | |||||||
\(620\) | −0.990027 | −0.0397604 | ||||||||
\(621\) | 16.4452 | − | 21.1280i | 0.659922 | − | 0.847836i | ||||
\(622\) | −32.5834 | + | 56.4361i | −1.30648 | + | 2.26288i | ||||
\(623\) | −43.3133 | −1.73531 | ||||||||
\(624\) | 3.49922 | + | 0.160853i | 0.140081 | + | 0.00643926i | ||||
\(625\) | 24.4239 | 0.976955 | ||||||||
\(626\) | −14.4407 | − | 25.0120i | −0.577166 | − | 0.999680i | ||||
\(627\) | −0.941577 | − | 0.643990i | −0.0376030 | − | 0.0257185i | ||||
\(628\) | 7.99684 | − | 13.8509i | 0.319109 | − | 0.552712i | ||||
\(629\) | −0.604546 | + | 1.04710i | −0.0241048 | + | 0.0417508i | ||||
\(630\) | −5.12519 | − | 0.472189i | −0.204193 | − | 0.0188125i | ||||
\(631\) | 5.70293 | + | 9.87777i | 0.227030 | + | 0.393228i | 0.956927 | − | 0.290330i | \(-0.0937651\pi\) |
−0.729896 | + | 0.683558i | \(0.760432\pi\) | |||||||
\(632\) | −0.320900 | − | 0.555815i | −0.0127647 | − | 0.0221091i | ||||
\(633\) | −11.9682 | − | 0.550158i | −0.475695 | − | 0.0218668i | ||||
\(634\) | −7.45070 | − | 12.9050i | −0.295905 | − | 0.512523i | ||||
\(635\) | −0.280727 | − | 0.486234i | −0.0111403 | − | 0.0192956i | ||||
\(636\) | 37.1528 | + | 1.70784i | 1.47320 | + | 0.0677204i | ||||
\(637\) | 6.07844 | 0.240836 | ||||||||
\(638\) | 0.466641 | 0.0184745 | ||||||||
\(639\) | 13.5440 | − | 19.1546i | 0.535794 | − | 0.757742i | ||||
\(640\) | 0.260256 | + | 0.450777i | 0.0102875 | + | 0.0178185i | ||||
\(641\) | 13.7058 | + | 23.7392i | 0.541348 | + | 0.937642i | 0.998827 | + | 0.0484213i | \(0.0154190\pi\) |
−0.457479 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(642\) | −11.0710 | − | 21.3873i | −0.436938 | − | 0.844090i | ||||
\(643\) | 6.05186 | 0.238662 | 0.119331 | − | 0.992855i | \(-0.461925\pi\) | ||||
0.119331 | + | 0.992855i | \(0.461925\pi\) | |||||||
\(644\) | 42.1232 | 1.65989 | ||||||||
\(645\) | 1.27996 | + | 2.47267i | 0.0503985 | + | 0.0973614i | ||||
\(646\) | 0.228443 | − | 7.52784i | 0.00898797 | − | 0.296179i | ||||
\(647\) | 24.3919 | 0.958945 | 0.479473 | − | 0.877557i | \(-0.340828\pi\) | ||||
0.479473 | + | 0.877557i | \(0.340828\pi\) | |||||||
\(648\) | −2.94448 | − | 0.547200i | −0.115670 | − | 0.0214960i | ||||
\(649\) | 0.120021 | − | 0.207882i | 0.00471122 | − | 0.00816008i | ||||
\(650\) | −4.55496 | −0.178660 | ||||||||
\(651\) | −21.3100 | − | 0.979580i | −0.835204 | − | 0.0383928i | ||||
\(652\) | 6.16550 | − | 10.6790i | 0.241460 | − | 0.418220i | ||||
\(653\) | 20.0350 | + | 34.7016i | 0.784029 | + | 1.35798i | 0.929578 | + | 0.368626i | \(0.120172\pi\) |
−0.145549 | + | 0.989351i | \(0.546495\pi\) | |||||||
\(654\) | −40.1266 | − | 1.84455i | −1.56907 | − | 0.0721274i | ||||
\(655\) | −0.530281 | −0.0207198 | ||||||||
\(656\) | −17.5322 | − | 30.3666i | −0.684515 | − | 1.18562i | ||||
\(657\) | 19.8327 | − | 28.0482i | 0.773746 | − | 1.09426i | ||||
\(658\) | −103.866 | −4.04911 | ||||||||
\(659\) | −20.1868 | −0.786368 | −0.393184 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393184 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(660\) | 0.0432024 | + | 0.0834596i | 0.00168165 | + | 0.00324866i | ||||
\(661\) | −10.2656 | + | 17.7805i | −0.399284 | + | 0.691581i | −0.993638 | − | 0.112623i | \(-0.964075\pi\) |
0.594353 | + | 0.804204i | \(0.297408\pi\) | |||||||
\(662\) | 3.44868 | 0.134037 | ||||||||
\(663\) | −0.329770 | − | 0.637059i | −0.0128072 | − | 0.0247413i | ||||
\(664\) | 0.468444 | − | 0.811368i | 0.0181791 | − | 0.0314872i | ||||
\(665\) | 3.24981 | + | 2.01012i | 0.126022 | + | 0.0779490i | ||||
\(666\) | 3.36446 | + | 7.30271i | 0.130370 | + | 0.282974i | ||||
\(667\) | 4.06568 | − | 7.04197i | 0.157424 | − | 0.272666i | ||||
\(668\) | −9.86144 | − | 17.0805i | −0.381551 | − | 0.660865i | ||||
\(669\) | 9.97444 | + | 19.2689i | 0.385634 | + | 0.744979i | ||||
\(670\) | 4.96851 | 0.191950 | ||||||||
\(671\) | 0.690148 | − | 1.19537i | 0.0266429 | − | 0.0461468i | ||||
\(672\) | −27.6438 | − | 53.4032i | −1.06638 | − | 2.06007i | ||||
\(673\) | −5.67978 | + | 9.83766i | −0.218939 | + | 0.379214i | −0.954484 | − | 0.298262i | \(-0.903593\pi\) |
0.735545 | + | 0.677476i | \(0.236926\pi\) | |||||||
\(674\) | 14.5439 | + | 25.1908i | 0.560210 | + | 0.970312i | ||||
\(675\) | 25.5363 | + | 3.54153i | 0.982891 | + | 0.136314i | ||||
\(676\) | −23.3868 | −0.899493 | ||||||||
\(677\) | 5.92995 | − | 10.2710i | 0.227907 | − | 0.394746i | −0.729281 | − | 0.684214i | \(-0.760145\pi\) |
0.957187 | + | 0.289469i | \(0.0934786\pi\) | |||||||
\(678\) | 18.2747 | − | 28.5404i | 0.701837 | − | 1.09609i | ||||
\(679\) | 68.0239 | 2.61052 | ||||||||
\(680\) | 0.0288257 | − | 0.0499276i | 0.00110542 | − | 0.00191464i | ||||
\(681\) | −5.04661 | + | 7.88148i | −0.193386 | + | 0.302019i | ||||
\(682\) | 0.407611 | + | 0.706003i | 0.0156082 | + | 0.0270343i | ||||
\(683\) | −27.7320 | −1.06114 | −0.530568 | − | 0.847642i | \(-0.678021\pi\) | ||||
−0.530568 | + | 0.847642i | \(0.678021\pi\) | |||||||
\(684\) | −19.1107 | − | 14.4020i | −0.730717 | − | 0.550676i | ||||
\(685\) | −3.10171 | −0.118510 | ||||||||
\(686\) | −26.0419 | − | 45.1059i | −0.994286 | − | 1.72215i | ||||
\(687\) | 7.59160 | + | 14.6657i | 0.289638 | + | 0.559530i | ||||
\(688\) | −17.6582 | + | 30.5849i | −0.673213 | + | 1.16604i | ||||
\(689\) | −5.50455 | −0.209707 | ||||||||
\(690\) | 3.42376 | + | 0.157384i | 0.130340 | + | 0.00599149i | ||||
\(691\) | 17.9088 | − | 31.0190i | 0.681284 | − | 1.18002i | −0.293306 | − | 0.956019i | \(-0.594755\pi\) |
0.974589 | − | 0.223999i | \(-0.0719113\pi\) | |||||||
\(692\) | −39.8161 | −1.51358 | ||||||||
\(693\) | 0.847336 | + | 1.83918i | 0.0321876 | + | 0.0698648i | ||||
\(694\) | 17.4313 | + | 30.1920i | 0.661685 | + | 1.14607i | ||||
\(695\) | 0.242822 | − | 0.420580i | 0.00921077 | − | 0.0159535i | ||||
\(696\) | −0.908608 | − | 0.0417670i | −0.0344407 | − | 0.00158318i | ||||
\(697\) | −3.59035 | + | 6.21867i | −0.135994 | + | 0.235549i | ||||
\(698\) | 32.1829 | 1.21814 | ||||||||
\(699\) | −0.744062 | + | 1.16203i | −0.0281430 | + | 0.0439520i | ||||
\(700\) | 20.2804 | + | 35.1267i | 0.766527 | + | 1.32766i | ||||
\(701\) | −16.9108 | + | 29.2903i | −0.638711 | + | 1.10628i | 0.347006 | + | 0.937863i | \(0.387199\pi\) |
−0.985716 | + | 0.168416i | \(0.946135\pi\) | |||||||
\(702\) | −4.72517 | − | 0.655317i | −0.178340 | − | 0.0247334i | ||||
\(703\) | 0.181070 | − | 5.96678i | 0.00682920 | − | 0.225041i | ||||
\(704\) | −0.497616 | + | 0.861896i | −0.0187546 | + | 0.0324839i | ||||
\(705\) | −4.03368 | − | 0.185421i | −0.151917 | − | 0.00698335i | ||||
\(706\) | −19.9073 | −0.749223 | ||||||||
\(707\) | 32.8203 | − | 56.8465i | 1.23434 | − | 2.13793i | ||||
\(708\) | 2.71533 | − | 4.24063i | 0.102048 | − | 0.159373i | ||||
\(709\) | −8.01078 | −0.300851 | −0.150426 | − | 0.988621i | \(-0.548064\pi\) | ||||
−0.150426 | + | 0.988621i | \(0.548064\pi\) | |||||||
\(710\) | 3.00308 | 0.112703 | ||||||||
\(711\) | 2.42111 | + | 5.25514i | 0.0907989 | + | 0.197083i | ||||
\(712\) | −1.61316 | − | 2.79408i | −0.0604558 | − | 0.104713i | ||||
\(713\) | 14.2055 | 0.532000 | ||||||||
\(714\) | −7.20921 | + | 11.2589i | −0.269798 | + | 0.421354i | ||||
\(715\) | −0.00695457 | − | 0.0120457i | −0.000260086 | − | 0.000450482i | ||||
\(716\) | 13.1872 | − | 22.8410i | 0.492830 | − | 0.853607i | ||||
\(717\) | −6.37786 | − | 12.3209i | −0.238186 | − | 0.460134i | ||||
\(718\) | −68.4935 | −2.55615 | ||||||||
\(719\) | −3.19388 | + | 5.53196i | −0.119112 | + | 0.206307i | −0.919416 | − | 0.393287i | \(-0.871338\pi\) |
0.800304 | + | 0.599594i | \(0.204671\pi\) | |||||||
\(720\) | −1.06200 | − | 2.30512i | −0.0395784 | − | 0.0859068i | ||||
\(721\) | −52.4238 | −1.95236 | ||||||||
\(722\) | 16.6049 | + | 33.2700i | 0.617972 | + | 1.23818i | ||||
\(723\) | 28.7059 | + | 1.31956i | 1.06758 | + | 0.0490749i | ||||
\(724\) | −2.83808 | −0.105476 | ||||||||
\(725\) | 7.82975 | 0.290790 | ||||||||
\(726\) | −20.0646 | + | 31.3357i | −0.744667 | + | 1.16298i | ||||
\(727\) | 5.78070 | + | 10.0125i | 0.214394 | + | 0.371342i | 0.953085 | − | 0.302703i | \(-0.0978889\pi\) |
−0.738691 | + | 0.674045i | \(0.764556\pi\) | |||||||
\(728\) | 0.348687 | + | 0.603943i | 0.0129232 | + | 0.0223836i | ||||
\(729\) | 25.9810 | + | 7.34774i | 0.962258 | + | 0.272139i | ||||
\(730\) | 4.39743 | 0.162756 | ||||||||
\(731\) | 7.23233 | 0.267498 | ||||||||
\(732\) | 15.6138 | − | 24.3847i | 0.577102 | − | 0.901283i | ||||
\(733\) | 9.39109 | + | 16.2658i | 0.346868 | + | 0.600792i | 0.985691 | − | 0.168561i | \(-0.0539120\pi\) |
−0.638824 | + | 0.769353i | \(0.720579\pi\) | |||||||
\(734\) | −1.67797 | − | 2.90634i | −0.0619351 | − | 0.107275i | ||||
\(735\) | −2.02457 | − | 3.91112i | −0.0746772 | − | 0.144264i | ||||
\(736\) | 20.0219 | + | 34.6789i | 0.738016 | + | 1.27828i | ||||
\(737\) | −0.977402 | − | 1.69291i | −0.0360031 | − | 0.0623591i | ||||
\(738\) | 19.9813 | + | 43.3703i | 0.735520 | + | 1.59648i | ||||
\(739\) | 4.38969 | − | 7.60316i | 0.161477 | − | 0.279687i | −0.773921 | − | 0.633282i | \(-0.781708\pi\) |
0.935399 | + | 0.353595i | \(0.115041\pi\) | |||||||
\(740\) | −0.245896 | + | 0.425904i | −0.00903930 | + | 0.0156565i | ||||
\(741\) | 2.92335 | + | 1.99942i | 0.107392 | + | 0.0734506i | ||||
\(742\) | 51.2939 | + | 88.8436i | 1.88306 | + | 3.26155i | ||||
\(743\) | 36.0307 | 1.32184 | 0.660918 | − | 0.750458i | \(-0.270167\pi\) | ||||
0.660918 | + | 0.750458i | \(0.270167\pi\) | |||||||
\(744\) | −0.730478 | − | 1.41116i | −0.0267806 | − | 0.0517356i | ||||
\(745\) | −3.27660 | −0.120045 | ||||||||
\(746\) | 33.0718 | − | 57.2820i | 1.21084 | − | 2.09724i | ||||
\(747\) | −4.87645 | + | 6.89648i | −0.178420 | + | 0.252329i | ||||
\(748\) | 0.244112 | 0.00892560 | ||||||||
\(749\) | 15.8698 | − | 27.4873i | 0.579871 | − | 1.00437i | ||||
\(750\) | 3.04605 | + | 5.88445i | 0.111226 | + | 0.214870i | ||||
\(751\) | −12.4311 | + | 21.5313i | −0.453617 | + | 0.785688i | −0.998608 | − | 0.0527544i | \(-0.983200\pi\) |
0.544990 | + | 0.838442i | \(0.316533\pi\) | |||||||
\(752\) | −25.6087 | − | 44.3556i | −0.933854 | − | 1.61748i | ||||
\(753\) | −17.9754 | − | 34.7255i | −0.655061 | − | 1.26547i | ||||
\(754\) | −1.44880 | −0.0527622 | ||||||||
\(755\) | 1.04548 | − | 1.81082i | 0.0380488 | − | 0.0659024i | ||||
\(756\) | 15.9846 | + | 39.3570i | 0.581354 | + | 1.43140i | ||||
\(757\) | 7.93827 | − | 13.7495i | 0.288521 | − | 0.499734i | −0.684936 | − | 0.728604i | \(-0.740170\pi\) |
0.973457 | + | 0.228870i | \(0.0735031\pi\) | |||||||
\(758\) | −16.2153 | − | 28.0857i | −0.588965 | − | 1.02012i | ||||
\(759\) | −0.619894 | − | 1.19753i | −0.0225007 | − | 0.0434675i | ||||
\(760\) | −0.00863373 | + | 0.284506i | −0.000313178 | + | 0.0103201i | ||||
\(761\) | 24.0436 | + | 41.6448i | 0.871581 | + | 1.50962i | 0.860361 | + | 0.509685i | \(0.170238\pi\) |
0.0112194 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(762\) | −5.22973 | + | 8.16747i | −0.189453 | + | 0.295876i | ||||
\(763\) | −26.4700 | − | 45.8474i | −0.958279 | − | 1.65979i | ||||
\(764\) | 4.25564 | + | 7.37099i | 0.153964 | + | 0.266673i | ||||
\(765\) | −0.300073 | + | 0.424375i | −0.0108492 | + | 0.0153433i | ||||
\(766\) | 11.4325 | + | 19.8017i | 0.413074 | + | 0.715465i | ||||
\(767\) | −0.372633 | + | 0.645420i | −0.0134550 | + | 0.0233048i | ||||
\(768\) | 17.1524 | − | 26.7876i | 0.618934 | − | 0.966613i | ||||
\(769\) | 0.639031 | − | 1.10683i | 0.0230441 | − | 0.0399135i | −0.854273 | − | 0.519824i | \(-0.825998\pi\) |
0.877317 | + | 0.479910i | \(0.159331\pi\) | |||||||
\(770\) | −0.129612 | + | 0.224494i | −0.00467088 | + | 0.00809020i | ||||
\(771\) | 17.0686 | − | 26.6568i | 0.614712 | − | 0.960020i | ||||
\(772\) | −8.42015 | + | 14.5841i | −0.303048 | + | 0.524895i | ||||
\(773\) | −7.15330 | − | 12.3899i | −0.257286 | − | 0.445633i | 0.708228 | − | 0.705984i | \(-0.249495\pi\) |
−0.965514 | + | 0.260351i | \(0.916162\pi\) | |||||||
\(774\) | 27.7674 | − | 39.2698i | 0.998077 | − | 1.41152i | ||||
\(775\) | 6.83929 | + | 11.8460i | 0.245675 | + | 0.425521i | ||||
\(776\) | 2.53349 | + | 4.38813i | 0.0909469 | + | 0.157525i | ||||
\(777\) | −5.71423 | + | 8.92413i | −0.204997 | + | 0.320151i | ||||
\(778\) | −25.1469 | − | 43.5556i | −0.901558 | − | 1.56155i | ||||
\(779\) | 1.07536 | − | 35.4363i | 0.0385289 | − | 1.26964i | ||||
\(780\) | −0.134132 | − | 0.259120i | −0.00480270 | − | 0.00927800i | ||||
\(781\) | −0.590763 | − | 1.02323i | −0.0211392 | − | 0.0366141i | ||||
\(782\) | 4.45134 | − | 7.70995i | 0.159180 | − | 0.275707i | ||||
\(783\) | 8.12233 | + | 1.12646i | 0.290268 | + | 0.0402563i | ||||
\(784\) | 27.9306 | − | 48.3773i | 0.997523 | − | 1.72776i | ||||
\(785\) | 1.71507 | 0.0612134 | ||||||||
\(786\) | 4.21083 | + | 8.13461i | 0.150195 | + | 0.290152i | ||||
\(787\) | −10.1038 | − | 17.5003i | −0.360161 | − | 0.623818i | 0.627826 | − | 0.778354i | \(-0.283945\pi\) |
−0.987987 | + | 0.154536i | \(0.950612\pi\) | |||||||
\(788\) | −20.4491 | + | 35.4189i | −0.728470 | + | 1.26175i | ||||
\(789\) | −10.9536 | − | 21.1605i | −0.389958 | − | 0.753332i | ||||
\(790\) | −0.370342 | + | 0.641452i | −0.0131762 | + | 0.0228218i | ||||
\(791\) | 44.6645 | 1.58809 | ||||||||
\(792\) | −0.0870849 | + | 0.123159i | −0.00309443 | + | 0.00437627i | ||||
\(793\) | −2.14273 | + | 3.71132i | −0.0760907 | + | 0.131793i | ||||
\(794\) | −5.00306 | −0.177552 | ||||||||
\(795\) | 1.83342 | + | 3.54185i | 0.0650247 | + | 0.125617i | ||||
\(796\) | 34.7255 | 1.23081 | ||||||||
\(797\) | 6.56225 | + | 11.3661i | 0.232447 | + | 0.402610i | 0.958528 | − | 0.285000i | \(-0.0919935\pi\) |
−0.726081 | + | 0.687609i | \(0.758660\pi\) | |||||||
\(798\) | 5.02962 | − | 65.8145i | 0.178047 | − | 2.32981i | ||||
\(799\) | −5.24433 | + | 9.08344i | −0.185531 | + | 0.321349i | ||||
\(800\) | −19.2792 | + | 33.3926i | −0.681623 | + | 1.18061i | ||||
\(801\) | 12.1709 | + | 26.4176i | 0.430039 | + | 0.933421i | ||||
\(802\) | 21.9597 | + | 38.0354i | 0.775425 | + | 1.34308i | ||||
\(803\) | −0.865059 | − | 1.49833i | −0.0305273 | − | 0.0528748i | ||||
\(804\) | −18.8511 | − | 36.4170i | −0.664826 | − | 1.28433i | ||||
\(805\) | 2.25852 | + | 3.91188i | 0.0796025 | + | 0.137876i | ||||
\(806\) | −1.26553 | − | 2.19196i | −0.0445763 | − | 0.0772084i | ||||
\(807\) | 12.3943 | − | 19.3566i | 0.436300 | − | 0.681386i | ||||
\(808\) | 4.88945 | 0.172010 | ||||||||
\(809\) | −36.7460 | −1.29192 | −0.645959 | − | 0.763372i | \(-0.723542\pi\) | ||||
−0.645959 | + | 0.763372i | \(0.723542\pi\) | |||||||
\(810\) | 1.15217 | + | 3.25864i | 0.0404832 | + | 0.114497i | ||||
\(811\) | 3.65981 | + | 6.33898i | 0.128513 | + | 0.222592i | 0.923101 | − | 0.384558i | \(-0.125646\pi\) |
−0.794587 | + | 0.607150i | \(0.792313\pi\) | |||||||
\(812\) | 6.45060 | + | 11.1728i | 0.226372 | + | 0.392087i | ||||
\(813\) | 21.3140 | − | 33.2869i | 0.747515 | − | 1.16742i | ||||
\(814\) | 0.404958 | 0.0141938 | ||||||||
\(815\) | 1.32230 | 0.0463183 | ||||||||
\(816\) | −6.58556 | − | 0.302726i | −0.230541 | − | 0.0105975i | ||||
\(817\) | −31.4509 | + | 16.9075i | −1.10033 | + | 0.591520i | ||||
\(818\) | 16.7891 | 0.587016 | ||||||||
\(819\) | −2.63076 | − | 5.71019i | −0.0919262 | − | 0.199530i | ||||
\(820\) | −1.46036 | + | 2.52941i | −0.0509979 | + | 0.0883309i | ||||
\(821\) | −24.8518 | −0.867335 | −0.433668 | − | 0.901073i | \(-0.642781\pi\) | ||||
−0.433668 | + | 0.901073i | \(0.642781\pi\) | |||||||
\(822\) | 24.6299 | + | 47.5808i | 0.859067 | + | 1.65957i | ||||
\(823\) | −17.9325 | + | 31.0599i | −0.625086 | + | 1.08268i | 0.363438 | + | 0.931618i | \(0.381603\pi\) |
−0.988524 | + | 0.151063i | \(0.951731\pi\) | |||||||
\(824\) | −1.95248 | − | 3.38179i | −0.0680177 | − | 0.117810i | ||||
\(825\) | 0.700172 | − | 1.09349i | 0.0243769 | − | 0.0380703i | ||||
\(826\) | 13.8895 | 0.483276 | ||||||||
\(827\) | 21.3388 | + | 36.9598i | 0.742022 | + | 1.28522i | 0.951573 | + | 0.307422i | \(0.0994663\pi\) |
−0.209552 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(828\) | −11.8365 | − | 25.6918i | −0.411348 | − | 0.892851i | ||||
\(829\) | 15.8631 | 0.550949 | 0.275475 | − | 0.961308i | \(-0.411165\pi\) | ||||
0.275475 | + | 0.961308i | \(0.411165\pi\) | |||||||
\(830\) | −1.08124 | −0.0375303 | ||||||||
\(831\) | −4.86484 | + | 7.59761i | −0.168760 | + | 0.263558i | ||||
\(832\) | 1.54497 | − | 2.67597i | 0.0535622 | − | 0.0927724i | ||||
\(833\) | −11.4397 | −0.396360 | ||||||||
\(834\) | −8.37997 | − | 0.385212i | −0.290175 | − | 0.0133388i | ||||
\(835\) | 1.05748 | − | 1.83161i | 0.0365957 | − | 0.0633856i | ||||
\(836\) | −1.06156 | + | 0.570677i | −0.0367147 | + | 0.0197373i | ||||
\(837\) | 5.39059 | + | 13.2726i | 0.186326 | + | 0.458769i | ||||
\(838\) | −20.1703 | + | 34.9360i | −0.696773 | + | 1.20685i | ||||
\(839\) | −6.99690 | − | 12.1190i | −0.241560 | − | 0.418394i | 0.719599 | − | 0.694390i | \(-0.244326\pi\) |
−0.961159 | + | 0.275996i | \(0.910992\pi\) | |||||||
\(840\) | 0.272464 | − | 0.425517i | 0.00940089 | − | 0.0146817i | ||||
\(841\) | −26.5096 | −0.914124 | ||||||||
\(842\) | −6.98427 | + | 12.0971i | −0.240694 | + | 0.416894i | ||||
\(843\) | 16.4723 | + | 0.757199i | 0.567335 | + | 0.0260793i | ||||
\(844\) | −6.32908 | + | 10.9623i | −0.217856 | + | 0.377337i | ||||
\(845\) | −1.25393 | − | 2.17187i | −0.0431366 | − | 0.0747148i | ||||
\(846\) | 29.1861 | + | 63.3498i | 1.00344 | + | 2.17801i | ||||
\(847\) | −49.0390 | −1.68500 | ||||||||
\(848\) | −25.2936 | + | 43.8098i | −0.868586 | + | 1.50443i | ||||
\(849\) | −18.3006 | − | 0.841243i | −0.628074 | − | 0.0288714i | ||||
\(850\) | 8.57247 | 0.294033 | ||||||||
\(851\) | 3.52826 | − | 6.11113i | 0.120947 | − | 0.209487i | ||||
\(852\) | −11.3940 | − | 22.0112i | −0.390352 | − | 0.754093i | ||||
\(853\) | 7.28354 | + | 12.6155i | 0.249384 | + | 0.431945i | 0.963355 | − | 0.268230i | \(-0.0864387\pi\) |
−0.713971 | + | 0.700175i | \(0.753105\pi\) | |||||||
\(854\) | 79.8678 | 2.73302 | ||||||||
\(855\) | 0.312820 | − | 2.54696i | 0.0106982 | − | 0.0871042i | ||||
\(856\) | 2.36423 | 0.0808076 | ||||||||
\(857\) | 13.2511 | + | 22.9515i | 0.452648 | + | 0.784009i | 0.998550 | − | 0.0538404i | \(-0.0171462\pi\) |
−0.545902 | + | 0.837849i | \(0.683813\pi\) | |||||||
\(858\) | −0.129558 | + | 0.202336i | −0.00442304 | + | 0.00690764i | ||||
\(859\) | −12.0706 | + | 20.9069i | −0.411845 | + | 0.713336i | −0.995092 | − | 0.0989591i | \(-0.968449\pi\) |
0.583247 | + | 0.812295i | \(0.301782\pi\) | |||||||
\(860\) | 2.94171 | 0.100312 | ||||||||
\(861\) | −33.9364 | + | 52.9997i | −1.15655 | + | 1.80623i | ||||
\(862\) | 7.03275 | − | 12.1811i | 0.239536 | − | 0.414889i | ||||
\(863\) | 10.0162 | 0.340956 | 0.170478 | − | 0.985361i | \(-0.445469\pi\) | ||||
0.170478 | + | 0.985361i | \(0.445469\pi\) | |||||||
\(864\) | −24.8038 | + | 31.8667i | −0.843841 | + | 1.08413i | ||||
\(865\) | −2.13482 | − | 3.69762i | −0.0725860 | − | 0.125723i | ||||
\(866\) | −23.5615 | + | 40.8097i | −0.800653 | + | 1.38677i | ||||
\(867\) | −12.9153 | − | 24.9502i | −0.438627 | − | 0.847353i | ||||
\(868\) | −11.2692 | + | 19.5188i | −0.382502 | + | 0.662512i | ||||
\(869\) | 0.291414 | 0.00988554 | ||||||||
\(870\) | 0.482557 | + | 0.932217i | 0.0163602 | + | 0.0316051i | ||||
\(871\) | 3.03458 | + | 5.25605i | 0.102823 | + | 0.178094i | ||||
\(872\) | 1.97170 | − | 3.41509i | 0.0667703 | − | 0.115649i | ||||
\(873\) | −19.1146 | − | 41.4891i | −0.646931 | − | 1.40419i | ||||
\(874\) | −1.33324 | + | 43.9341i | −0.0450976 | + | 1.48609i | ||||
\(875\) | −4.36638 | + | 7.56279i | −0.147611 | + | 0.255669i | ||||
\(876\) | −16.6843 | − | 32.2312i | −0.563711 | − | 1.08899i | ||||
\(877\) | −23.3105 | −0.787140 | −0.393570 | − | 0.919295i | \(-0.628760\pi\) | ||||
−0.393570 | + | 0.919295i | \(0.628760\pi\) | |||||||
\(878\) | 13.9483 | − | 24.1591i | 0.470731 | − | 0.815330i | ||||
\(879\) | −11.5750 | − | 22.3610i | −0.390416 | − | 0.754218i | ||||
\(880\) | −0.127826 | −0.00430901 | ||||||||
\(881\) | −5.49429 | −0.185107 | −0.0925537 | − | 0.995708i | \(-0.529503\pi\) | ||||
−0.0925537 | + | 0.995708i | \(0.529503\pi\) | |||||||
\(882\) | −43.9207 | + | 62.1144i | −1.47889 | + | 2.09150i | ||||
\(883\) | −17.4681 | − | 30.2556i | −0.587848 | − | 1.01818i | −0.994514 | − | 0.104606i | \(-0.966642\pi\) |
0.406665 | − | 0.913577i | \(-0.366692\pi\) | |||||||
\(884\) | −0.757903 | −0.0254910 | ||||||||
\(885\) | 0.539404 | + | 0.0247954i | 0.0181319 | + | 0.000833488i | ||||
\(886\) | −11.7413 | − | 20.3365i | −0.394456 | − | 0.683217i | ||||
\(887\) | −2.59381 | + | 4.49262i | −0.0870918 | + | 0.150847i | −0.906281 | − | 0.422676i | \(-0.861091\pi\) |
0.819189 | + | 0.573524i | \(0.194424\pi\) | |||||||
\(888\) | −0.788504 | − | 0.0362461i | −0.0264605 | − | 0.00121634i | ||||
\(889\) | −12.7818 | −0.428686 | ||||||||
\(890\) | −1.86171 | + | 3.22458i | −0.0624047 | + | 0.108088i | ||||
\(891\) | 0.883654 | − | 1.03361i | 0.0296035 | − | 0.0346274i | ||||
\(892\) | 22.9240 | 0.767553 | ||||||||
\(893\) | 1.57075 | − | 51.7608i | 0.0525633 | − | 1.73211i | ||||
\(894\) | 26.0187 | + | 50.2637i | 0.870196 | + | 1.68107i | ||||
\(895\) | 2.82824 | 0.0945377 | ||||||||
\(896\) | 11.8497 | 0.395871 | ||||||||
\(897\) | 1.92461 | + | 3.71802i | 0.0642609 | + | 0.124141i | ||||
\(898\) | 16.2286 | + | 28.1087i | 0.541554 | + | 0.937999i | ||||
\(899\) | 2.17538 | + | 3.76787i | 0.0725529 | + | 0.125665i | ||||
\(900\) | 15.7257 | − | 22.2399i | 0.524190 | − | 0.741331i | ||||
\(901\) | 10.3596 | 0.345128 | ||||||||
\(902\) | 2.40502 | 0.0800783 | ||||||||
\(903\) | 63.3193 | + | 2.91067i | 2.10714 | + | 0.0968611i | ||||
\(904\) | 1.66349 | + | 2.88125i | 0.0553268 | + | 0.0958288i | ||||
\(905\) | −0.152169 | − | 0.263565i | −0.00505828 | − | 0.00876119i | ||||
\(906\) | −36.0802 | − | 1.65854i | −1.19868 | − | 0.0551012i | ||||
\(907\) | −8.21282 | − | 14.2250i | −0.272702 | − | 0.472334i | 0.696851 | − | 0.717216i | \(-0.254584\pi\) |
−0.969553 | + | 0.244882i | \(0.921251\pi\) | |||||||
\(908\) | 4.94389 | + | 8.56307i | 0.164069 | + | 0.284176i | ||||
\(909\) | −43.8942 | − | 4.04402i | −1.45588 | − | 0.134132i | ||||
\(910\) | 0.402411 | − | 0.696996i | 0.0133398 | − | 0.0231052i | ||||
\(911\) | −11.4146 | + | 19.7707i | −0.378184 | + | 0.655033i | −0.990798 | − | 0.135349i | \(-0.956785\pi\) |
0.612614 | + | 0.790382i | \(0.290118\pi\) | |||||||
\(912\) | 29.3460 | − | 14.0791i | 0.971743 | − | 0.466205i | ||||
\(913\) | 0.212700 | + | 0.368408i | 0.00703936 | + | 0.0121925i | ||||
\(914\) | 4.82491 | 0.159594 | ||||||||
\(915\) | 3.10171 | + | 0.142580i | 0.102539 | + | 0.00471354i | ||||
\(916\) | 17.4476 | 0.576485 | ||||||||
\(917\) | −6.03605 | + | 10.4547i | −0.199328 | + | 0.345246i | ||||
\(918\) | 8.89280 | + | 1.23331i | 0.293506 | + | 0.0407053i | ||||
\(919\) | −20.1717 | −0.665404 | −0.332702 | − | 0.943032i | \(-0.607960\pi\) | ||||
−0.332702 | + | 0.943032i | \(0.607960\pi\) | |||||||
\(920\) | −0.168233 | + | 0.291388i | −0.00554648 | + | 0.00960679i | ||||
\(921\) | −21.1004 | + | 32.9533i | −0.695282 | + | 1.08585i | ||||
\(922\) | 25.8993 | − | 44.8589i | 0.852948 | − | 1.47735i | ||||
\(923\) | 1.83417 | + | 3.17687i | 0.0603723 | + | 0.104568i | ||||
\(924\) | 2.13720 | + | 0.0982433i | 0.0703089 | + | 0.00323197i | ||||
\(925\) | 6.79478 | 0.223411 | ||||||||
\(926\) | −15.2379 | + | 26.3928i | −0.500749 | + | 0.867322i | ||||
\(927\) | 14.7310 | + | 31.9743i | 0.483829 | + | 1.05017i | ||||
\(928\) | −6.13215 | + | 10.6212i | −0.201298 | + | 0.348658i | ||||
\(929\) | −1.40609 | − | 2.43541i | −0.0461322 | − | 0.0799033i | 0.842037 | − | 0.539419i | \(-0.181356\pi\) |
−0.888169 | + | 0.459516i | \(0.848023\pi\) | |||||||
\(930\) | −0.988882 | + | 1.54438i | −0.0324267 | + | 0.0506421i | ||||
\(931\) | 49.7471 | − | 26.7433i | 1.63039 | − | 0.876476i | ||||
\(932\) | 0.728918 | + | 1.26252i | 0.0238765 | + | 0.0413553i | ||||
\(933\) | 26.5136 | + | 51.2198i | 0.868017 | + | 1.67686i | ||||
\(934\) | 0.779129 | + | 1.34949i | 0.0254939 | + | 0.0441567i | ||||
\(935\) | 0.0130885 | + | 0.0226700i | 0.000428041 | + | 0.000741389i | ||||
\(936\) | 0.270376 | − | 0.382377i | 0.00883753 | − | 0.0124984i | ||||
\(937\) | −8.01674 | − | 13.8854i | −0.261896 | − | 0.453617i | 0.704850 | − | 0.709356i | \(-0.251014\pi\) |
−0.966746 | + | 0.255740i | \(0.917681\pi\) | |||||||
\(938\) | 56.5552 | − | 97.9564i | 1.84659 | − | 3.19839i | ||||
\(939\) | −25.5342 | − | 1.17376i | −0.833278 | − | 0.0383042i | ||||
\(940\) | −2.13310 | + | 3.69464i | −0.0695741 | + | 0.120506i | ||||
\(941\) | 5.51528 | − | 9.55275i | 0.179793 | − | 0.311411i | −0.762016 | − | 0.647558i | \(-0.775790\pi\) |
0.941810 | + | 0.336147i | \(0.109124\pi\) | |||||||
\(942\) | −13.6189 | − | 26.3095i | −0.443729 | − | 0.857208i | ||||
\(943\) | 20.9541 | − | 36.2935i | 0.682359 | − | 1.18188i | ||||
\(944\) | 3.42453 | + | 5.93146i | 0.111459 | + | 0.193052i | ||||
\(945\) | −2.79794 | + | 3.59465i | −0.0910169 | + | 0.116934i | ||||
\(946\) | −1.21115 | − | 2.09778i | −0.0393780 | − | 0.0682047i | ||||
\(947\) | −7.39281 | − | 12.8047i | −0.240234 | − | 0.416098i | 0.720547 | − | 0.693406i | \(-0.243891\pi\) |
−0.960781 | + | 0.277309i | \(0.910558\pi\) | |||||||
\(948\) | 6.10668 | + | 0.280713i | 0.198336 | + | 0.00911713i | ||||
\(949\) | 2.68578 | + | 4.65192i | 0.0871843 | + | 0.151008i | ||||
\(950\) | −37.2787 | + | 20.0405i | −1.20948 | + | 0.650198i | ||||
\(951\) | −13.1744 | − | 0.605605i | −0.427211 | − | 0.0196381i | ||||
\(952\) | −0.656230 | − | 1.13662i | −0.0212685 | − | 0.0368382i | ||||
\(953\) | 28.4287 | − | 49.2399i | 0.920895 | − | 1.59504i | 0.122862 | − | 0.992424i | \(-0.460793\pi\) |
0.798033 | − | 0.602613i | \(-0.205874\pi\) | |||||||
\(954\) | 39.7740 | − | 56.2500i | 1.28773 | − | 1.82116i | ||||
\(955\) | −0.456350 | + | 0.790421i | −0.0147671 | + | 0.0255774i | ||||
\(956\) | −14.6581 | −0.474077 | ||||||||
\(957\) | 0.222704 | − | 0.347806i | 0.00719900 | − | 0.0112430i | ||||
\(958\) | −9.84064 | − | 17.0445i | −0.317937 | − | 0.550682i | ||||
\(959\) | −35.3059 | + | 61.1516i | −1.14009 | + | 1.97469i | ||||
\(960\) | −2.23641 | − | 0.102804i | −0.0721800 | − | 0.00331798i | ||||
\(961\) | 11.6996 | − | 20.2643i | 0.377407 | − | 0.653688i | ||||
\(962\) | −1.25729 | −0.0405367 | ||||||||
\(963\) | −21.2244 | − | 1.95543i | −0.683948 | − | 0.0630128i | ||||
\(964\) | 15.1803 | − | 26.2931i | 0.488926 | − | 0.846845i | ||||
\(965\) | −1.80586 | −0.0581325 | ||||||||
\(966\) | 42.0746 | − | 65.7094i | 1.35373 | − | 2.11417i | ||||
\(967\) | −35.3323 | −1.13621 | −0.568105 | − | 0.822956i | \(-0.692323\pi\) | ||||
−0.568105 | + | 0.822956i | \(0.692323\pi\) | |||||||
\(968\) | −1.82641 | − | 3.16344i | −0.0587031 | − | 0.101677i | ||||
\(969\) | −5.50177 | − | 3.76293i | −0.176742 | − | 0.120883i | ||||
\(970\) | 2.92384 | − | 5.06423i | 0.0938787 | − | 0.162603i | ||||
\(971\) | −10.3147 | + | 17.8656i | −0.331015 | + | 0.573335i | −0.982711 | − | 0.185146i | \(-0.940724\pi\) |
0.651696 | + | 0.758480i | \(0.274058\pi\) | |||||||
\(972\) | 19.5130 | − | 20.8085i | 0.625878 | − | 0.667434i | ||||
\(973\) | −5.52795 | − | 9.57469i | −0.177218 | − | 0.306951i | ||||
\(974\) | 17.2452 | + | 29.8696i | 0.552572 | + | 0.957083i | ||||
\(975\) | −2.17385 | + | 3.39499i | −0.0696190 | + | 0.108727i | ||||
\(976\) | 19.6919 | + | 34.1073i | 0.630321 | + | 1.09175i | ||||
\(977\) | 25.5253 | + | 44.2111i | 0.816627 | + | 1.41444i | 0.908154 | + | 0.418637i | \(0.137492\pi\) |
−0.0915267 | + | 0.995803i | \(0.529175\pi\) | |||||||
\(978\) | −10.5001 | − | 20.2844i | −0.335756 | − | 0.648623i | ||||
\(979\) | 1.46494 | 0.0468196 | ||||||||
\(980\) | −4.65302 | −0.148635 | ||||||||
\(981\) | −20.5252 | + | 29.0276i | −0.655320 | + | 0.926780i | ||||
\(982\) | −16.0308 | − | 27.7662i | −0.511564 | − | 0.886056i | ||||
\(983\) | 4.48421 | + | 7.76688i | 0.143024 | + | 0.247725i | 0.928634 | − | 0.370997i | \(-0.120984\pi\) |
−0.785610 | + | 0.618722i | \(0.787651\pi\) | |||||||
\(984\) | −4.68287 | − | 0.215263i | −0.149284 | − | 0.00686233i | ||||
\(985\) | −4.38569 | −0.139740 | ||||||||
\(986\) | 2.72665 | 0.0868342 | ||||||||
\(987\) | −49.5699 | + | 77.4153i | −1.57783 | + | 2.46415i | ||||
\(988\) | 3.29586 | − | 1.77180i | 0.104855 | − | 0.0563686i | ||||
\(989\) | −42.2095 | −1.34218 | ||||||||
\(990\) | 0.173344 | + | 0.0159703i | 0.00550923 | + | 0.000507570i | ||||
\(991\) | 17.2725 | − | 29.9168i | 0.548678 | − | 0.950338i | −0.449687 | − | 0.893186i | \(-0.648465\pi\) |
0.998365 | − | 0.0571522i | \(-0.0182020\pi\) | |||||||
\(992\) | −21.4257 | −0.680268 | ||||||||
\(993\) | 1.64588 | − | 2.57044i | 0.0522304 | − | 0.0815703i | ||||
\(994\) | 34.1832 | − | 59.2070i | 1.08422 | − | 1.87793i | ||||
\(995\) | 1.86188 | + | 3.22487i | 0.0590255 | + | 0.102235i | ||||
\(996\) | 4.10234 | + | 7.92501i | 0.129987 | + | 0.251114i | ||||
\(997\) | 44.6627 | 1.41448 | 0.707241 | − | 0.706973i | \(-0.249940\pi\) | ||||
0.707241 | + | 0.706973i | \(0.249940\pi\) | |||||||
\(998\) | −17.6325 | − | 30.5403i | −0.558146 | − | 0.966737i | ||||
\(999\) | 7.04868 | + | 0.977557i | 0.223010 | + | 0.0309285i |
(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 | 171.2.g.c.106.3 | ✓ | 32 | |
3.2 | odd | 2 | 513.2.g.c.505.14 | 32 | |||
9.4 | even | 3 | 171.2.h.c.49.14 | yes | 32 | ||
9.5 | odd | 6 | 513.2.h.c.334.3 | 32 | |||
19.7 | even | 3 | 171.2.h.c.7.14 | yes | 32 | ||
57.26 | odd | 6 | 513.2.h.c.235.3 | 32 | |||
171.121 | even | 3 | inner | 171.2.g.c.121.3 | yes | 32 | |
171.140 | odd | 6 | 513.2.g.c.64.14 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
171.2.g.c.121.3 | yes | 32 | 171.121 | even | 3 | inner | |
171.2.h.c.7.14 | yes | 32 | 19.7 | even | 3 | ||
171.2.h.c.49.14 | yes | 32 | 9.4 | even | 3 | ||
513.2.g.c.64.14 | 32 | 171.140 | odd | 6 | |||
513.2.g.c.505.14 | 32 | 3.2 | odd | 2 | |||
513.2.h.c.235.3 | 32 | 57.26 | odd | 6 | |||
513.2.h.c.334.3 | 32 | 9.5 | odd | 6 |