Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(107,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.107");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.8 | ||
Character | \(\chi\) | \(=\) | 300.107 |
Dual form | 300.3.l.g.143.8 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.837725 | + | 1.81610i | −0.418863 | + | 0.908050i | ||||
\(3\) | −1.32197 | + | 2.69303i | −0.440657 | + | 0.897676i | ||||
\(4\) | −2.59643 | − | 3.04278i | −0.649108 | − | 0.760696i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.78336 | − | 4.65685i | −0.630559 | − | 0.776141i | ||||
\(7\) | 3.54241 | − | 3.54241i | 0.506059 | − | 0.506059i | −0.407256 | − | 0.913314i | \(-0.633514\pi\) |
0.913314 | + | 0.407256i | \(0.133514\pi\) | |||||||
\(8\) | 7.70110 | − | 2.16636i | 0.962637 | − | 0.270795i | ||||
\(9\) | −5.50478 | − | 7.12021i | −0.611643 | − | 0.791134i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.8337 | 1.53034 | 0.765168 | − | 0.643831i | \(-0.222656\pi\) | ||||
0.765168 | + | 0.643831i | \(0.222656\pi\) | |||||||
\(12\) | 11.6267 | − | 2.96979i | 0.968892 | − | 0.247483i | ||||
\(13\) | 8.64592 | − | 8.64592i | 0.665071 | − | 0.665071i | −0.291500 | − | 0.956571i | \(-0.594154\pi\) |
0.956571 | + | 0.291500i | \(0.0941543\pi\) | |||||||
\(14\) | 3.46580 | + | 9.40093i | 0.247557 | + | 0.671495i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.51707 | + | 15.8008i | −0.157317 | + | 0.987548i | ||||
\(17\) | −9.72710 | + | 9.72710i | −0.572182 | + | 0.572182i | −0.932738 | − | 0.360556i | \(-0.882587\pi\) |
0.360556 | + | 0.932738i | \(0.382587\pi\) | |||||||
\(18\) | 17.5425 | − | 4.03246i | 0.974583 | − | 0.224025i | ||||
\(19\) | 4.78419 | 0.251800 | 0.125900 | − | 0.992043i | \(-0.459818\pi\) | ||||
0.125900 | + | 0.992043i | \(0.459818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.85684 | + | 14.2228i | 0.231278 | + | 0.677275i | ||||
\(22\) | −14.1020 | + | 30.5716i | −0.641000 | + | 1.38962i | ||||
\(23\) | 13.5716 | − | 13.5716i | 0.590070 | − | 0.590070i | −0.347580 | − | 0.937650i | \(-0.612997\pi\) |
0.937650 | + | 0.347580i | \(0.112997\pi\) | |||||||
\(24\) | −4.34655 | + | 23.6031i | −0.181106 | + | 0.983464i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.45895 | + | 22.9448i | 0.325344 | + | 0.882491i | ||||
\(27\) | 26.4521 | − | 5.41182i | 0.979706 | − | 0.200438i | ||||
\(28\) | −19.9764 | − | 1.58116i | −0.713444 | − | 0.0564699i | ||||
\(29\) | −14.8741 | −0.512899 | −0.256449 | − | 0.966558i | \(-0.582553\pi\) | ||||
−0.256449 | + | 0.966558i | \(0.582553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 14.0641i | − | 0.453680i | −0.973932 | − | 0.226840i | \(-0.927161\pi\) | ||
0.973932 | − | 0.226840i | \(-0.0728395\pi\) | |||||||
\(32\) | −26.5872 | − | 17.8080i | −0.830849 | − | 0.556498i | ||||
\(33\) | −22.2536 | + | 45.3336i | −0.674353 | + | 1.37374i | ||||
\(34\) | −9.51674 | − | 25.8140i | −0.279904 | − | 0.759235i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.37245 | + | 35.2370i | −0.204790 | + | 0.978806i | ||||
\(37\) | 10.1182 | + | 10.1182i | 0.273465 | + | 0.273465i | 0.830493 | − | 0.557029i | \(-0.188059\pi\) |
−0.557029 | + | 0.830493i | \(0.688059\pi\) | |||||||
\(38\) | −4.00784 | + | 8.68857i | −0.105469 | + | 0.228647i | ||||
\(39\) | 11.8540 | + | 34.7134i | 0.303950 | + | 0.890086i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.08509i | − | 0.148417i | −0.997243 | − | 0.0742084i | \(-0.976357\pi\) | ||
0.997243 | − | 0.0742084i | \(-0.0236430\pi\) | |||||||
\(42\) | −29.8987 | − | 3.09427i | −0.711873 | − | 0.0736730i | ||||
\(43\) | 57.2366 | + | 57.2366i | 1.33108 | + | 1.33108i | 0.904401 | + | 0.426683i | \(0.140318\pi\) |
0.426683 | + | 0.904401i | \(0.359682\pi\) | |||||||
\(44\) | −43.7075 | − | 51.2213i | −0.993353 | − | 1.16412i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.2781 | + | 36.0167i | 0.288654 | + | 0.782971i | ||||
\(47\) | 17.6247 | + | 17.6247i | 0.374993 | + | 0.374993i | 0.869292 | − | 0.494299i | \(-0.164575\pi\) |
−0.494299 | + | 0.869292i | \(0.664575\pi\) | |||||||
\(48\) | −39.2244 | − | 27.6667i | −0.817175 | − | 0.576390i | ||||
\(49\) | 23.9027i | 0.487809i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.3364 | − | 39.0543i | −0.261498 | − | 0.765770i | ||||
\(52\) | −48.7562 | − | 3.85911i | −0.937620 | − | 0.0742137i | ||||
\(53\) | −16.2015 | − | 16.2015i | −0.305688 | − | 0.305688i | 0.537546 | − | 0.843234i | \(-0.319351\pi\) |
−0.843234 | + | 0.537546i | \(0.819351\pi\) | |||||||
\(54\) | −12.3312 | + | 52.5732i | −0.228355 | + | 0.973578i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.6063 | − | 34.9546i | 0.350112 | − | 0.624189i | ||||
\(57\) | −6.32456 | + | 12.8840i | −0.110957 | + | 0.226034i | ||||
\(58\) | 12.4604 | − | 27.0128i | 0.214834 | − | 0.465738i | ||||
\(59\) | − | 4.37150i | − | 0.0740931i | −0.999314 | − | 0.0370466i | \(-0.988205\pi\) | ||
0.999314 | − | 0.0370466i | \(-0.0117950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.52269 | 0.139716 | 0.0698582 | − | 0.997557i | \(-0.477745\pi\) | ||||
0.0698582 | + | 0.997557i | \(0.477745\pi\) | |||||||
\(62\) | 25.5418 | + | 11.7818i | 0.411964 | + | 0.190030i | ||||
\(63\) | −44.7229 | − | 5.72249i | −0.709887 | − | 0.0908332i | ||||
\(64\) | 54.6137 | − | 33.3667i | 0.853340 | − | 0.521355i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −63.6878 | − | 78.3919i | −0.964967 | − | 1.18776i | ||||
\(67\) | 53.9714 | − | 53.9714i | 0.805543 | − | 0.805543i | −0.178413 | − | 0.983956i | \(-0.557096\pi\) |
0.983956 | + | 0.178413i | \(0.0570963\pi\) | |||||||
\(68\) | 54.8532 | + | 4.34170i | 0.806665 | + | 0.0638485i | ||||
\(69\) | 18.6074 | + | 54.4900i | 0.269673 | + | 0.789710i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.6679 | 0.516449 | 0.258225 | − | 0.966085i | \(-0.416863\pi\) | ||||
0.258225 | + | 0.966085i | \(0.416863\pi\) | |||||||
\(72\) | −57.8178 | − | 42.9080i | −0.803025 | − | 0.595945i | ||||
\(73\) | 12.6800 | − | 12.6800i | 0.173699 | − | 0.173699i | −0.614903 | − | 0.788602i | \(-0.710805\pi\) |
0.788602 | + | 0.614903i | \(0.210805\pi\) | |||||||
\(74\) | −26.8519 | + | 9.89937i | −0.362863 | + | 0.133775i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.4218 | − | 14.5573i | −0.163445 | − | 0.191543i | ||||
\(77\) | 59.6318 | − | 59.6318i | 0.774439 | − | 0.774439i | ||||
\(78\) | −72.9733 | − | 7.55214i | −0.935555 | − | 0.0968223i | ||||
\(79\) | 88.4346 | 1.11943 | 0.559713 | − | 0.828687i | \(-0.310912\pi\) | ||||
0.559713 | + | 0.828687i | \(0.310912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −20.3947 | + | 78.3904i | −0.251786 | + | 0.967783i | ||||
\(82\) | 11.0511 | + | 5.09763i | 0.134770 | + | 0.0621663i | ||||
\(83\) | −63.7372 | + | 63.7372i | −0.767918 | + | 0.767918i | −0.977740 | − | 0.209822i | \(-0.932712\pi\) |
0.209822 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(84\) | 30.6663 | − | 51.7068i | 0.365076 | − | 0.615557i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −151.896 | + | 55.9988i | −1.76623 | + | 0.651149i | ||||
\(87\) | 19.6631 | − | 40.0563i | 0.226013 | − | 0.460417i | ||||
\(88\) | 129.638 | − | 36.4679i | 1.47316 | − | 0.414408i | ||||
\(89\) | 115.022 | 1.29238 | 0.646190 | − | 0.763177i | \(-0.276361\pi\) | ||||
0.646190 | + | 0.763177i | \(0.276361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 61.2548i | − | 0.673130i | ||||||
\(92\) | −76.5332 | − | 6.05770i | −0.831883 | − | 0.0658445i | ||||
\(93\) | 37.8749 | + | 18.5923i | 0.407258 | + | 0.199917i | ||||
\(94\) | −46.7728 | + | 17.2435i | −0.497583 | + | 0.183442i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 83.1047 | − | 48.0583i | 0.865674 | − | 0.500607i | ||||
\(97\) | 85.3544 | + | 85.3544i | 0.879942 | + | 0.879942i | 0.993528 | − | 0.113586i | \(-0.0362338\pi\) |
−0.113586 | + | 0.993528i | \(0.536234\pi\) | |||||||
\(98\) | −43.4096 | − | 20.0239i | −0.442955 | − | 0.204325i | ||||
\(99\) | −92.6658 | − | 119.859i | −0.936018 | − | 1.21070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 158.917i | − | 1.57343i | −0.617313 | − | 0.786717i | \(-0.711779\pi\) | ||
0.617313 | − | 0.786717i | \(-0.288221\pi\) | |||||||
\(102\) | 82.0987 | + | 8.49654i | 0.804889 | + | 0.0832994i | ||||
\(103\) | −28.6266 | − | 28.6266i | −0.277928 | − | 0.277928i | 0.554353 | − | 0.832282i | \(-0.312966\pi\) |
−0.832282 | + | 0.554353i | \(0.812966\pi\) | |||||||
\(104\) | 47.8529 | − | 85.3133i | 0.460124 | − | 0.820320i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 42.9959 | − | 15.8511i | 0.405622 | − | 0.149539i | ||||
\(107\) | −28.1808 | − | 28.1808i | −0.263372 | − | 0.263372i | 0.563050 | − | 0.826423i | \(-0.309628\pi\) |
−0.826423 | + | 0.563050i | \(0.809628\pi\) | |||||||
\(108\) | −85.1480 | − | 66.4365i | −0.788408 | − | 0.615153i | ||||
\(109\) | − | 159.944i | − | 1.46737i | −0.679489 | − | 0.733686i | \(-0.737798\pi\) | ||
0.679489 | − | 0.733686i | \(-0.262202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −40.6245 | + | 13.8726i | −0.365986 | + | 0.124978i | ||||
\(112\) | 47.0563 | + | 64.8893i | 0.420146 | + | 0.579369i | ||||
\(113\) | −101.260 | − | 101.260i | −0.896110 | − | 0.896110i | 0.0989792 | − | 0.995089i | \(-0.468442\pi\) |
−0.995089 | + | 0.0989792i | \(0.968442\pi\) | |||||||
\(114\) | −18.1003 | − | 22.2793i | −0.158775 | − | 0.195432i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 38.6195 | + | 45.2586i | 0.332927 | + | 0.390160i | ||||
\(117\) | −109.155 | − | 13.9668i | −0.932946 | − | 0.119375i | ||||
\(118\) | 7.93907 | + | 3.66211i | 0.0672803 | + | 0.0310348i | ||||
\(119\) | 68.9147i | 0.579115i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 162.373 | 1.34193 | ||||||||
\(122\) | −7.13968 | + | 15.4781i | −0.0585219 | + | 0.126869i | ||||
\(123\) | 16.3873 | + | 8.04432i | 0.133230 | + | 0.0654009i | ||||
\(124\) | −42.7940 | + | 36.5165i | −0.345113 | + | 0.294488i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 47.8581 | − | 76.4273i | 0.379826 | − | 0.606566i | ||||
\(127\) | −94.0845 | + | 94.0845i | −0.740823 | + | 0.740823i | −0.972736 | − | 0.231914i | \(-0.925501\pi\) |
0.231914 | + | 0.972736i | \(0.425501\pi\) | |||||||
\(128\) | 14.8460 | + | 127.136i | 0.115985 | + | 0.993251i | ||||
\(129\) | −229.805 | + | 78.4746i | −1.78143 | + | 0.608330i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −145.148 | −1.10800 | −0.554002 | − | 0.832515i | \(-0.686900\pi\) | ||||
−0.554002 | + | 0.832515i | \(0.686900\pi\) | |||||||
\(132\) | 195.720 | − | 49.9925i | 1.48273 | − | 0.378731i | ||||
\(133\) | 16.9476 | − | 16.9476i | 0.127425 | − | 0.127425i | ||||
\(134\) | 52.8042 | + | 143.231i | 0.394061 | + | 1.06888i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −53.8369 | + | 95.9817i | −0.395859 | + | 0.705748i | ||||
\(137\) | −60.1022 | + | 60.1022i | −0.438702 | + | 0.438702i | −0.891575 | − | 0.452873i | \(-0.850399\pi\) |
0.452873 | + | 0.891575i | \(0.350399\pi\) | |||||||
\(138\) | −114.547 | − | 11.8547i | −0.830051 | − | 0.0859035i | ||||
\(139\) | −12.5985 | −0.0906366 | −0.0453183 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453183 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70.7630 | + | 24.1644i | −0.501865 | + | 0.171379i | ||||
\(142\) | −30.7176 | + | 66.5925i | −0.216321 | + | 0.468961i | ||||
\(143\) | 145.543 | − | 145.543i | 1.01778 | − | 1.01778i | ||||
\(144\) | 126.361 | − | 69.0578i | 0.877505 | − | 0.479568i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.4058 | + | 33.6506i | 0.0849713 | + | 0.230483i | ||||
\(147\) | −64.3705 | − | 31.5986i | −0.437895 | − | 0.214957i | ||||
\(148\) | 4.51626 | − | 57.0587i | 0.0305153 | − | 0.385531i | ||||
\(149\) | 25.9233 | 0.173982 | 0.0869911 | − | 0.996209i | \(-0.472275\pi\) | ||||
0.0869911 | + | 0.996209i | \(0.472275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 200.379i | 1.32701i | 0.748171 | + | 0.663506i | \(0.230932\pi\) | ||||
−0.748171 | + | 0.663506i | \(0.769068\pi\) | |||||||
\(152\) | 36.8435 | − | 10.3643i | 0.242392 | − | 0.0681862i | ||||
\(153\) | 122.805 | + | 15.7134i | 0.802644 | + | 0.102702i | ||||
\(154\) | 58.3422 | + | 158.252i | 0.378846 | + | 1.02761i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 74.8470 | − | 126.200i | 0.479789 | − | 0.808976i | ||||
\(157\) | −139.992 | − | 139.992i | −0.891666 | − | 0.891666i | 0.103014 | − | 0.994680i | \(-0.467151\pi\) |
−0.994680 | + | 0.103014i | \(0.967151\pi\) | |||||||
\(158\) | −74.0839 | + | 160.606i | −0.468885 | + | 1.01649i | ||||
\(159\) | 65.0489 | − | 22.2131i | 0.409113 | − | 0.139705i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 96.1524i | − | 0.597220i | ||||||
\(162\) | −125.280 | − | 102.708i | −0.773331 | − | 0.634003i | ||||
\(163\) | −58.6324 | − | 58.6324i | −0.359708 | − | 0.359708i | 0.503997 | − | 0.863705i | \(-0.331862\pi\) |
−0.863705 | + | 0.503997i | \(0.831862\pi\) | |||||||
\(164\) | −18.5156 | + | 15.7995i | −0.112900 | + | 0.0963386i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −62.3588 | − | 169.147i | −0.375655 | − | 1.01896i | ||||
\(167\) | 84.2556 | + | 84.2556i | 0.504524 | + | 0.504524i | 0.912841 | − | 0.408316i | \(-0.133884\pi\) |
−0.408316 | + | 0.912841i | \(0.633884\pi\) | |||||||
\(168\) | 68.2147 | + | 99.0092i | 0.406040 | + | 0.589341i | ||||
\(169\) | 19.4961i | 0.115361i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.3359 | − | 34.0644i | −0.154011 | − | 0.199207i | ||||
\(172\) | 25.5476 | − | 322.770i | 0.148533 | − | 1.87657i | ||||
\(173\) | 51.2341 | + | 51.2341i | 0.296151 | + | 0.296151i | 0.839504 | − | 0.543353i | \(-0.182846\pi\) |
−0.543353 | + | 0.839504i | \(0.682846\pi\) | |||||||
\(174\) | 56.2739 | + | 69.2663i | 0.323413 | + | 0.398082i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −42.3716 | + | 265.985i | −0.240747 | + | 1.51128i | ||||
\(177\) | 11.7726 | + | 5.77899i | 0.0665116 | + | 0.0326497i | ||||
\(178\) | −96.3566 | + | 208.891i | −0.541329 | + | 1.17354i | ||||
\(179\) | 27.2276i | 0.152109i | 0.997104 | + | 0.0760547i | \(0.0242324\pi\) | ||||
−0.997104 | + | 0.0760547i | \(0.975768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −276.624 | −1.52831 | −0.764155 | − | 0.645033i | \(-0.776844\pi\) | ||||
−0.764155 | + | 0.645033i | \(0.776844\pi\) | |||||||
\(182\) | 111.245 | + | 51.3147i | 0.611235 | + | 0.281949i | ||||
\(183\) | −11.2668 | + | 22.9518i | −0.0615670 | + | 0.125420i | ||||
\(184\) | 75.1152 | − | 133.917i | 0.408235 | − | 0.727811i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −65.4943 | + | 53.2094i | −0.352120 | + | 0.286072i | ||||
\(187\) | −163.743 | + | 163.743i | −0.875630 | + | 0.875630i | ||||
\(188\) | 7.86679 | − | 99.3894i | 0.0418446 | − | 0.528667i | ||||
\(189\) | 74.5332 | − | 112.875i | 0.394356 | − | 0.597222i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 340.010 | 1.78016 | 0.890078 | − | 0.455807i | \(-0.150649\pi\) | ||||
0.890078 | + | 0.455807i | \(0.150649\pi\) | |||||||
\(192\) | 17.6597 | + | 191.186i | 0.0919779 | + | 0.995761i | ||||
\(193\) | −100.981 | + | 100.981i | −0.523220 | + | 0.523220i | −0.918542 | − | 0.395322i | \(-0.870633\pi\) |
0.395322 | + | 0.918542i | \(0.370633\pi\) | |||||||
\(194\) | −226.515 | + | 83.5085i | −1.16761 | + | 0.430456i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.7306 | − | 62.0617i | 0.371075 | − | 0.316641i | ||||
\(197\) | 225.584 | − | 225.584i | 1.14510 | − | 1.14510i | 0.157595 | − | 0.987504i | \(-0.449626\pi\) |
0.987504 | − | 0.157595i | \(-0.0503741\pi\) | |||||||
\(198\) | 295.305 | − | 67.8811i | 1.49144 | − | 0.342834i | ||||
\(199\) | −286.672 | −1.44056 | −0.720281 | − | 0.693682i | \(-0.755987\pi\) | ||||
−0.720281 | + | 0.693682i | \(0.755987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 73.9977 | + | 216.695i | 0.368148 | + | 1.07808i | ||||
\(202\) | 288.609 | + | 133.129i | 1.42876 | + | 0.659053i | ||||
\(203\) | −52.6900 | + | 52.6900i | −0.259557 | + | 0.259557i | ||||
\(204\) | −84.2067 | + | 141.982i | −0.412778 | + | 0.695988i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 75.9701 | − | 28.0076i | 0.368787 | − | 0.135959i | ||||
\(207\) | −171.341 | − | 21.9239i | −0.827736 | − | 0.105912i | ||||
\(208\) | 114.850 | + | 158.375i | 0.552163 | + | 0.761416i | ||||
\(209\) | 80.5356 | 0.385338 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 183.842i | 0.871288i | 0.900119 | + | 0.435644i | \(0.143479\pi\) | ||||
−0.900119 | + | 0.435644i | \(0.856521\pi\) | |||||||
\(212\) | −7.23155 | + | 91.3637i | −0.0341111 | + | 0.430961i | ||||
\(213\) | −48.4739 | + | 98.7476i | −0.227577 | + | 0.463604i | ||||
\(214\) | 74.7870 | − | 27.5714i | 0.349472 | − | 0.128838i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 191.986 | − | 98.9818i | 0.888824 | − | 0.458249i | ||||
\(217\) | −49.8207 | − | 49.8207i | −0.229589 | − | 0.229589i | ||||
\(218\) | 290.473 | + | 133.989i | 1.33245 | + | 0.614627i | ||||
\(219\) | 17.3850 | + | 50.9103i | 0.0793836 | + | 0.232467i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 168.199i | 0.761083i | ||||||||
\(222\) | 8.83816 | − | 85.3995i | 0.0398115 | − | 0.384683i | ||||
\(223\) | −7.02165 | − | 7.02165i | −0.0314872 | − | 0.0314872i | 0.691188 | − | 0.722675i | \(-0.257088\pi\) |
−0.722675 | + | 0.691188i | \(0.757088\pi\) | |||||||
\(224\) | −157.266 | + | 31.0995i | −0.702079 | + | 0.138837i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 268.727 | − | 99.0706i | 1.18906 | − | 0.438366i | ||||
\(227\) | −36.6684 | − | 36.6684i | −0.161535 | − | 0.161535i | 0.621711 | − | 0.783246i | \(-0.286438\pi\) |
−0.783246 | + | 0.621711i | \(0.786438\pi\) | |||||||
\(228\) | 55.6244 | − | 14.2081i | 0.243967 | − | 0.0623160i | ||||
\(229\) | 270.126i | 1.17959i | 0.807554 | + | 0.589794i | \(0.200791\pi\) | ||||
−0.807554 | + | 0.589794i | \(0.799209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 81.7585 | + | 239.422i | 0.353933 | + | 1.03646i | ||||
\(232\) | −114.547 | + | 32.2226i | −0.493735 | + | 0.138891i | ||||
\(233\) | −55.2135 | − | 55.2135i | −0.236968 | − | 0.236968i | 0.578625 | − | 0.815593i | \(-0.303589\pi\) |
−0.815593 | + | 0.578625i | \(0.803589\pi\) | |||||||
\(234\) | 116.807 | − | 186.535i | 0.499174 | − | 0.797160i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.3015 | + | 11.3503i | −0.0563624 | + | 0.0480945i | ||||
\(237\) | −116.908 | + | 238.157i | −0.493283 | + | 1.00488i | ||||
\(238\) | −125.156 | − | 57.7316i | −0.525865 | − | 0.242570i | ||||
\(239\) | 46.1374i | 0.193044i | 0.995331 | + | 0.0965218i | \(0.0307718\pi\) | ||||
−0.995331 | + | 0.0965218i | \(0.969228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −212.165 | −0.880351 | −0.440176 | − | 0.897912i | \(-0.645084\pi\) | ||||
−0.440176 | + | 0.897912i | \(0.645084\pi\) | |||||||
\(242\) | −136.024 | + | 294.885i | −0.562082 | + | 1.21853i | ||||
\(243\) | −184.146 | − | 158.553i | −0.757803 | − | 0.652483i | ||||
\(244\) | −22.1286 | − | 25.9327i | −0.0906910 | − | 0.106282i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.3373 | + | 23.0221i | −0.115192 | + | 0.0935856i | ||||
\(247\) | 41.3638 | − | 41.3638i | 0.167465 | − | 0.167465i | ||||
\(248\) | −30.4679 | − | 108.309i | −0.122855 | − | 0.436729i | ||||
\(249\) | −87.3872 | − | 255.905i | −0.350953 | − | 1.02773i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −159.687 | −0.636203 | −0.318101 | − | 0.948057i | \(-0.603045\pi\) | ||||
−0.318101 | + | 0.948057i | \(0.603045\pi\) | |||||||
\(252\) | 98.7077 | + | 150.940i | 0.391697 | + | 0.598969i | ||||
\(253\) | 228.460 | − | 228.460i | 0.903004 | − | 0.903004i | ||||
\(254\) | −92.0498 | − | 249.684i | −0.362401 | − | 0.983007i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −243.329 | − | 79.5433i | −0.950503 | − | 0.310716i | ||||
\(257\) | −98.0877 | + | 98.0877i | −0.381664 | + | 0.381664i | −0.871701 | − | 0.490037i | \(-0.836983\pi\) |
0.490037 | + | 0.871701i | \(0.336983\pi\) | |||||||
\(258\) | 49.9957 | − | 483.089i | 0.193782 | − | 1.87244i | ||||
\(259\) | 71.6855 | 0.276778 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 81.8785 | + | 105.906i | 0.313711 | + | 0.405772i | ||||
\(262\) | 121.595 | − | 263.604i | 0.464101 | − | 1.00612i | ||||
\(263\) | 141.919 | − | 141.919i | 0.539614 | − | 0.539614i | −0.383802 | − | 0.923416i | \(-0.625385\pi\) |
0.923416 | + | 0.383802i | \(0.125385\pi\) | |||||||
\(264\) | −73.1685 | + | 397.328i | −0.277153 | + | 1.50503i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.5811 | + | 44.9759i | 0.0623348 | + | 0.169082i | ||||
\(267\) | −152.055 | + | 309.757i | −0.569496 | + | 1.16014i | ||||
\(268\) | −304.356 | − | 24.0902i | −1.13566 | − | 0.0898887i | ||||
\(269\) | 0.543377 | 0.00201999 | 0.00100999 | − | 0.999999i | \(-0.499679\pi\) | ||||
0.00100999 | + | 0.999999i | \(0.499679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 362.830i | − | 1.33886i | −0.742877 | − | 0.669428i | \(-0.766539\pi\) | ||
0.742877 | − | 0.669428i | \(-0.233461\pi\) | |||||||
\(272\) | −129.212 | − | 178.179i | −0.475044 | − | 0.655071i | ||||
\(273\) | 164.961 | + | 80.9771i | 0.604252 | + | 0.296619i | ||||
\(274\) | −58.8025 | − | 159.501i | −0.214608 | − | 0.582120i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 117.488 | − | 198.098i | 0.425682 | − | 0.717746i | ||||
\(277\) | 79.2266 | + | 79.2266i | 0.286016 | + | 0.286016i | 0.835503 | − | 0.549486i | \(-0.185177\pi\) |
−0.549486 | + | 0.835503i | \(0.685177\pi\) | |||||||
\(278\) | 10.5541 | − | 22.8801i | 0.0379643 | − | 0.0823025i | ||||
\(279\) | −100.139 | + | 77.4197i | −0.358922 | + | 0.277490i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 318.753i | − | 1.13435i | −0.823597 | − | 0.567176i | \(-0.808036\pi\) | ||
0.823597 | − | 0.567176i | \(-0.191964\pi\) | |||||||
\(282\) | 15.3950 | − | 148.756i | 0.0545922 | − | 0.527503i | ||||
\(283\) | −223.036 | − | 223.036i | −0.788112 | − | 0.788112i | 0.193072 | − | 0.981185i | \(-0.438155\pi\) |
−0.981185 | + | 0.193072i | \(0.938155\pi\) | |||||||
\(284\) | −95.2057 | − | 111.572i | −0.335231 | − | 0.392861i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 142.395 | + | 386.245i | 0.497885 | + | 1.35051i | ||||
\(287\) | −21.5559 | − | 21.5559i | −0.0751076 | − | 0.0751076i | ||||
\(288\) | 19.5603 | + | 287.335i | 0.0679176 | + | 0.997691i | ||||
\(289\) | 99.7672i | 0.345215i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −342.698 | + | 117.026i | −1.17765 | + | 0.402150i | ||||
\(292\) | −71.5054 | − | 5.65974i | −0.244881 | − | 0.0193827i | ||||
\(293\) | 75.3066 | + | 75.3066i | 0.257019 | + | 0.257019i | 0.823841 | − | 0.566822i | \(-0.191827\pi\) |
−0.566822 | + | 0.823841i | \(0.691827\pi\) | |||||||
\(294\) | 111.311 | − | 90.4323i | 0.378609 | − | 0.307593i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 99.8408 | + | 56.0015i | 0.337300 | + | 0.189194i | ||||
\(297\) | 445.286 | − | 91.1009i | 1.49928 | − | 0.306737i | ||||
\(298\) | −21.7166 | + | 47.0794i | −0.0728746 | + | 0.157984i | ||||
\(299\) | − | 234.678i | − | 0.784876i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 405.511 | 1.34721 | ||||||||
\(302\) | −363.908 | − | 167.862i | −1.20499 | − | 0.555836i | ||||
\(303\) | 427.967 | + | 210.084i | 1.41243 | + | 0.693345i | ||||
\(304\) | −12.0421 | + | 75.5939i | −0.0396123 | + | 0.248664i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −131.413 | + | 209.862i | −0.429456 | + | 0.685823i | ||||
\(307\) | 330.497 | − | 330.497i | 1.07654 | − | 1.07654i | 0.0797218 | − | 0.996817i | \(-0.474597\pi\) |
0.996817 | − | 0.0797218i | \(-0.0254032\pi\) | |||||||
\(308\) | −336.277 | − | 26.6167i | −1.09181 | − | 0.0864179i | ||||
\(309\) | 114.936 | − | 39.2487i | 0.371961 | − | 0.127018i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.5302 | −0.0853063 | −0.0426531 | − | 0.999090i | \(-0.513581\pi\) | ||||
−0.0426531 | + | 0.999090i | \(0.513581\pi\) | |||||||
\(312\) | 166.491 | + | 241.651i | 0.533624 | + | 0.774522i | ||||
\(313\) | −131.851 | + | 131.851i | −0.421248 | + | 0.421248i | −0.885633 | − | 0.464385i | \(-0.846275\pi\) |
0.464385 | + | 0.885633i | \(0.346275\pi\) | |||||||
\(314\) | 371.513 | − | 136.964i | 1.18316 | − | 0.436191i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −229.614 | − | 269.087i | −0.726628 | − | 0.851542i | ||||
\(317\) | −66.6091 | + | 66.6091i | −0.210123 | + | 0.210123i | −0.804320 | − | 0.594197i | \(-0.797470\pi\) |
0.594197 | + | 0.804320i | \(0.297470\pi\) | |||||||
\(318\) | −14.1519 | + | 136.744i | −0.0445027 | + | 0.430012i | ||||
\(319\) | −250.385 | −0.784907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 113.146 | − | 38.6375i | 0.352480 | − | 0.120366i | ||||
\(322\) | 174.622 | + | 80.5492i | 0.542305 | + | 0.250153i | ||||
\(323\) | −46.5363 | + | 46.5363i | −0.144075 | + | 0.144075i | ||||
\(324\) | 291.479 | − | 141.479i | 0.899625 | − | 0.436663i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 155.600 | − | 57.3644i | 0.477301 | − | 0.175965i | ||||
\(327\) | 430.732 | + | 211.441i | 1.31722 | + | 0.646608i | ||||
\(328\) | −13.1825 | − | 46.8619i | −0.0401906 | − | 0.142872i | ||||
\(329\) | 124.868 | 0.379537 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 284.948i | − | 0.860871i | −0.902621 | − | 0.430436i | \(-0.858360\pi\) | ||
0.902621 | − | 0.430436i | \(-0.141640\pi\) | |||||||
\(332\) | 359.428 | + | 28.4491i | 1.08261 | + | 0.0856902i | ||||
\(333\) | 16.3452 | − | 127.742i | 0.0490845 | − | 0.383610i | ||||
\(334\) | −223.599 | + | 82.4335i | −0.669460 | + | 0.246807i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −236.956 | + | 40.9421i | −0.705225 | + | 0.121852i | ||||
\(337\) | −294.164 | − | 294.164i | −0.872889 | − | 0.872889i | 0.119897 | − | 0.992786i | \(-0.461744\pi\) |
−0.992786 | + | 0.119897i | \(0.961744\pi\) | |||||||
\(338\) | −35.4068 | − | 16.3324i | −0.104754 | − | 0.0483206i | ||||
\(339\) | 406.561 | − | 138.834i | 1.19929 | − | 0.409539i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 236.750i | − | 0.694283i | ||||||
\(342\) | 83.9267 | − | 19.2921i | 0.245400 | − | 0.0564095i | ||||
\(343\) | 258.251 | + | 258.251i | 0.752919 | + | 0.752919i | ||||
\(344\) | 564.780 | + | 316.789i | 1.64180 | + | 0.920899i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −135.966 | + | 50.1262i | −0.392966 | + | 0.144873i | ||||
\(347\) | −274.053 | − | 274.053i | −0.789779 | − | 0.789779i | 0.191679 | − | 0.981458i | \(-0.438607\pi\) |
−0.981458 | + | 0.191679i | \(0.938607\pi\) | |||||||
\(348\) | −172.936 | + | 44.1729i | −0.496944 | + | 0.126934i | ||||
\(349\) | − | 129.175i | − | 0.370128i | −0.982726 | − | 0.185064i | \(-0.940751\pi\) | ||
0.982726 | − | 0.185064i | \(-0.0592492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 181.912 | − | 275.493i | 0.518269 | − | 0.784880i | ||||
\(352\) | −447.560 | − | 299.773i | −1.27148 | − | 0.851629i | ||||
\(353\) | −381.746 | − | 381.746i | −1.08143 | − | 1.08143i | −0.996376 | − | 0.0850569i | \(-0.972893\pi\) |
−0.0850569 | − | 0.996376i | \(-0.527107\pi\) | |||||||
\(354\) | −20.3574 | + | 16.5389i | −0.0575067 | + | 0.0467201i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −298.646 | − | 349.986i | −0.838894 | − | 0.983108i | ||||
\(357\) | −185.589 | − | 91.1033i | −0.519858 | − | 0.255191i | ||||
\(358\) | −49.4480 | − | 22.8092i | −0.138123 | − | 0.0637129i | ||||
\(359\) | 209.720i | 0.584178i | 0.956391 | + | 0.292089i | \(0.0943503\pi\) | ||||
−0.956391 | + | 0.292089i | \(0.905650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −338.112 | −0.936597 | ||||||||
\(362\) | 231.735 | − | 502.377i | 0.640151 | − | 1.38778i | ||||
\(363\) | −214.652 | + | 437.275i | −0.591329 | + | 1.20461i | ||||
\(364\) | −186.385 | + | 159.044i | −0.512047 | + | 0.436934i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −32.2444 | − | 39.6889i | −0.0880994 | − | 0.108440i | ||||
\(367\) | 4.27652 | − | 4.27652i | 0.0116527 | − | 0.0116527i | −0.701256 | − | 0.712909i | \(-0.747377\pi\) |
0.712909 | + | 0.701256i | \(0.247377\pi\) | |||||||
\(368\) | 180.281 | + | 248.602i | 0.489894 | + | 0.675550i | ||||
\(369\) | −43.3271 | + | 33.4971i | −0.117418 | + | 0.0907781i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −114.785 | −0.309393 | ||||||||
\(372\) | −41.7674 | − | 163.519i | −0.112278 | − | 0.439567i | ||||
\(373\) | −363.822 | + | 363.822i | −0.975394 | + | 0.975394i | −0.999704 | − | 0.0243109i | \(-0.992261\pi\) |
0.0243109 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(374\) | −160.202 | − | 434.545i | −0.428347 | − | 1.16188i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 173.911 | + | 97.5478i | 0.462529 | + | 0.259436i | ||||
\(377\) | −128.600 | + | 128.600i | −0.341114 | + | 0.341114i | ||||
\(378\) | 142.554 | + | 229.918i | 0.377127 | + | 0.608248i | ||||
\(379\) | 732.379 | 1.93240 | 0.966199 | − | 0.257796i | \(-0.0829962\pi\) | ||||
0.966199 | + | 0.257796i | \(0.0829962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −128.995 | − | 377.749i | −0.338570 | − | 0.991467i | ||||
\(382\) | −284.835 | + | 617.492i | −0.745641 | + | 1.61647i | ||||
\(383\) | −343.246 | + | 343.246i | −0.896203 | + | 0.896203i | −0.995098 | − | 0.0988948i | \(-0.968469\pi\) |
0.0988948 | + | 0.995098i | \(0.468469\pi\) | |||||||
\(384\) | −362.007 | − | 128.090i | −0.942727 | − | 0.333567i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −98.7977 | − | 267.987i | −0.255952 | − | 0.694267i | ||||
\(387\) | 92.4613 | − | 722.612i | 0.238918 | − | 1.86721i | ||||
\(388\) | 38.0980 | − | 481.332i | 0.0981907 | − | 1.24055i | ||||
\(389\) | −600.575 | −1.54389 | −0.771947 | − | 0.635687i | \(-0.780717\pi\) | ||||
−0.771947 | + | 0.635687i | \(0.780717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 264.025i | 0.675255i | ||||||||
\(392\) | 51.7819 | + | 184.077i | 0.132097 | + | 0.469583i | ||||
\(393\) | 191.882 | − | 390.889i | 0.488250 | − | 0.994628i | ||||
\(394\) | 220.706 | + | 598.662i | 0.560168 | + | 1.51945i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −124.105 | + | 593.169i | −0.313398 | + | 1.49790i | ||||
\(397\) | 295.285 | + | 295.285i | 0.743792 | + | 0.743792i | 0.973306 | − | 0.229513i | \(-0.0737135\pi\) |
−0.229513 | + | 0.973306i | \(0.573713\pi\) | |||||||
\(398\) | 240.152 | − | 520.625i | 0.603398 | − | 1.30810i | ||||
\(399\) | 23.2361 | + | 68.0445i | 0.0582357 | + | 0.170537i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 300.412i | 0.749157i | 0.927195 | + | 0.374578i | \(0.122213\pi\) | ||||
−0.927195 | + | 0.374578i | \(0.877787\pi\) | |||||||
\(402\) | −455.529 | − | 47.1436i | −1.13316 | − | 0.117273i | ||||
\(403\) | −121.597 | − | 121.597i | −0.301729 | − | 0.301729i | ||||
\(404\) | −483.550 | + | 412.617i | −1.19691 | + | 1.02133i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −51.5506 | − | 139.830i | −0.126972 | − | 0.344409i | ||||
\(407\) | 170.326 | + | 170.326i | 0.418492 | + | 0.418492i | ||||
\(408\) | −187.311 | − | 271.869i | −0.459094 | − | 0.666346i | ||||
\(409\) | 53.8159i | 0.131579i | 0.997834 | + | 0.0657896i | \(0.0209566\pi\) | ||||
−0.997834 | + | 0.0657896i | \(0.979043\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −82.4035 | − | 241.310i | −0.200495 | − | 0.587130i | ||||
\(412\) | −12.7775 | + | 161.432i | −0.0310134 | + | 0.391825i | ||||
\(413\) | −15.4856 | − | 15.4856i | −0.0374955 | − | 0.0374955i | ||||
\(414\) | 183.353 | − | 292.807i | 0.442881 | − | 0.707263i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −383.837 | + | 75.9043i | −0.922684 | + | 0.182462i | ||||
\(417\) | 16.6548 | − | 33.9281i | 0.0399397 | − | 0.0813623i | ||||
\(418\) | −67.4667 | + | 146.261i | −0.161404 | + | 0.349906i | ||||
\(419\) | − | 582.593i | − | 1.39044i | −0.718799 | − | 0.695218i | \(-0.755308\pi\) | ||
0.718799 | − | 0.695218i | \(-0.244692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 486.678 | 1.15600 | 0.578002 | − | 0.816035i | \(-0.303833\pi\) | ||||
0.578002 | + | 0.816035i | \(0.303833\pi\) | |||||||
\(422\) | −333.875 | − | 154.009i | −0.791173 | − | 0.364950i | ||||
\(423\) | 28.4713 | − | 222.511i | 0.0673080 | − | 0.526032i | ||||
\(424\) | −159.868 | − | 89.6709i | −0.377046 | − | 0.211488i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −138.728 | − | 170.757i | −0.325652 | − | 0.400837i | ||||
\(427\) | 30.1909 | − | 30.1909i | 0.0707046 | − | 0.0707046i | ||||
\(428\) | −12.5785 | + | 158.918i | −0.0293891 | + | 0.371304i | ||||
\(429\) | 199.547 | + | 584.354i | 0.465145 | + | 1.36213i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 554.639 | 1.28686 | 0.643432 | − | 0.765503i | \(-0.277510\pi\) | ||||
0.643432 | + | 0.765503i | \(0.277510\pi\) | |||||||
\(432\) | 18.9292 | + | 431.585i | 0.0438177 | + | 0.999040i | ||||
\(433\) | −152.907 | + | 152.907i | −0.353135 | + | 0.353135i | −0.861275 | − | 0.508140i | \(-0.830333\pi\) |
0.508140 | + | 0.861275i | \(0.330333\pi\) | |||||||
\(434\) | 132.216 | − | 48.7433i | 0.304644 | − | 0.112312i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −486.674 | + | 415.283i | −1.11622 | + | 0.952483i | ||||
\(437\) | 64.9292 | − | 64.9292i | 0.148579 | − | 0.148579i | ||||
\(438\) | −107.022 | − | 11.0759i | −0.244342 | − | 0.0252874i | ||||
\(439\) | −218.824 | −0.498461 | −0.249231 | − | 0.968444i | \(-0.580178\pi\) | ||||
−0.249231 | + | 0.968444i | \(0.580178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 170.192 | − | 131.579i | 0.385923 | − | 0.298365i | ||||
\(442\) | −305.467 | − | 140.905i | −0.691101 | − | 0.318789i | ||||
\(443\) | 39.9964 | − | 39.9964i | 0.0902853 | − | 0.0902853i | −0.660522 | − | 0.750807i | \(-0.729665\pi\) |
0.750807 | + | 0.660522i | \(0.229665\pi\) | |||||||
\(444\) | 147.690 | + | 87.5923i | 0.332635 | + | 0.197280i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.6342 | − | 6.86980i | 0.0417808 | − | 0.0154031i | ||||
\(447\) | −34.2699 | + | 69.8122i | −0.0766665 | + | 0.156180i | ||||
\(448\) | 75.2655 | − | 311.663i | 0.168003 | − | 0.695676i | ||||
\(449\) | 236.471 | 0.526660 | 0.263330 | − | 0.964706i | \(-0.415179\pi\) | ||||
0.263330 | + | 0.964706i | \(0.415179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 102.435i | − | 0.227128i | ||||||
\(452\) | −45.1977 | + | 571.030i | −0.0999949 | + | 1.26334i | ||||
\(453\) | −539.626 | − | 264.895i | −1.19123 | − | 0.584757i | ||||
\(454\) | 97.3115 | − | 35.8754i | 0.214343 | − | 0.0790208i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.7947 | + | 112.922i | −0.0456025 | + | 0.247636i | ||||
\(457\) | 242.806 | + | 242.806i | 0.531304 | + | 0.531304i | 0.920960 | − | 0.389657i | \(-0.127406\pi\) |
−0.389657 | + | 0.920960i | \(0.627406\pi\) | |||||||
\(458\) | −490.575 | − | 226.291i | −1.07112 | − | 0.494085i | ||||
\(459\) | −204.661 | + | 309.943i | −0.445884 | + | 0.675257i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 640.776i | 1.38997i | 0.719024 | + | 0.694985i | \(0.244589\pi\) | ||||
−0.719024 | + | 0.694985i | \(0.755411\pi\) | |||||||
\(462\) | −503.305 | − | 52.0879i | −1.08940 | − | 0.112744i | ||||
\(463\) | 162.780 | + | 162.780i | 0.351577 | + | 0.351577i | 0.860696 | − | 0.509119i | \(-0.170029\pi\) |
−0.509119 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(464\) | 37.4391 | − | 235.022i | 0.0806876 | − | 0.506512i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 146.527 | − | 54.0195i | 0.314436 | − | 0.115922i | ||||
\(467\) | 424.962 | + | 424.962i | 0.909984 | + | 0.909984i | 0.996270 | − | 0.0862867i | \(-0.0275001\pi\) |
−0.0862867 | + | 0.996270i | \(0.527500\pi\) | |||||||
\(468\) | 240.915 | + | 368.398i | 0.514775 | + | 0.787175i | ||||
\(469\) | − | 382.377i | − | 0.815304i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 562.066 | − | 191.936i | 1.19335 | − | 0.407508i | ||||
\(472\) | −9.47025 | − | 33.6653i | −0.0200641 | − | 0.0713248i | ||||
\(473\) | 963.503 | + | 963.503i | 2.03700 | + | 2.03700i | ||||
\(474\) | −334.579 | − | 411.826i | −0.705864 | − | 0.868832i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 209.693 | − | 178.932i | 0.440531 | − | 0.375909i | ||||
\(477\) | −26.1723 | + | 204.544i | −0.0548685 | + | 0.428813i | ||||
\(478\) | −83.7902 | − | 38.6505i | −0.175293 | − | 0.0808588i | ||||
\(479\) | 439.071i | 0.916641i | 0.888787 | + | 0.458321i | \(0.151549\pi\) | ||||
−0.888787 | + | 0.458321i | \(0.848451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 174.962 | 0.363747 | ||||||||
\(482\) | 177.736 | − | 385.312i | 0.368746 | − | 0.799403i | ||||
\(483\) | 258.941 | + | 127.111i | 0.536109 | + | 0.263169i | ||||
\(484\) | −421.591 | − | 494.066i | −0.871055 | − | 1.02080i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 442.213 | − | 201.604i | 0.909902 | − | 0.414823i | ||||
\(487\) | 308.231 | − | 308.231i | 0.632918 | − | 0.632918i | −0.315881 | − | 0.948799i | \(-0.602300\pi\) |
0.948799 | + | 0.315881i | \(0.102300\pi\) | |||||||
\(488\) | 65.6341 | − | 18.4633i | 0.134496 | − | 0.0378345i | ||||
\(489\) | 235.409 | − | 80.3883i | 0.481409 | − | 0.164393i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −751.660 | −1.53088 | −0.765438 | − | 0.643509i | \(-0.777478\pi\) | ||||
−0.765438 | + | 0.643509i | \(0.777478\pi\) | |||||||
\(492\) | −18.0714 | − | 70.7496i | −0.0367306 | − | 0.143800i | ||||
\(493\) | 144.681 | − | 144.681i | 0.293472 | − | 0.293472i | ||||
\(494\) | 40.4692 | + | 109.772i | 0.0819215 | + | 0.222211i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 222.223 | + | 35.4003i | 0.448031 | + | 0.0713715i | ||||
\(497\) | 129.893 | − | 129.893i | 0.261353 | − | 0.261353i | ||||
\(498\) | 537.955 | + | 55.6739i | 1.08023 | + | 0.111795i | ||||
\(499\) | −304.485 | −0.610191 | −0.305096 | − | 0.952322i | \(-0.598688\pi\) | ||||
−0.305096 | + | 0.952322i | \(0.598688\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −338.286 | + | 115.519i | −0.675221 | + | 0.230577i | ||||
\(502\) | 133.774 | − | 290.007i | 0.266481 | − | 0.577704i | ||||
\(503\) | 230.058 | − | 230.058i | 0.457372 | − | 0.457372i | −0.440420 | − | 0.897792i | \(-0.645170\pi\) |
0.897792 | + | 0.440420i | \(0.145170\pi\) | |||||||
\(504\) | −356.812 | + | 52.8166i | −0.707961 | + | 0.104795i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 223.519 | + | 606.293i | 0.441738 | + | 1.19821i | ||||
\(507\) | −52.5035 | − | 25.7733i | −0.103557 | − | 0.0508348i | ||||
\(508\) | 530.563 | + | 41.9947i | 1.04442 | + | 0.0826667i | ||||
\(509\) | 98.9386 | 0.194378 | 0.0971892 | − | 0.995266i | \(-0.469015\pi\) | ||||
0.0971892 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 89.8357i | − | 0.175804i | ||||||
\(512\) | 348.301 | − | 375.274i | 0.680276 | − | 0.732956i | ||||
\(513\) | 126.552 | − | 25.8912i | 0.246690 | − | 0.0504702i | ||||
\(514\) | −95.9665 | − | 260.307i | −0.186705 | − | 0.506435i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 835.454 | + | 495.493i | 1.61910 | + | 0.960257i | ||||
\(517\) | 296.688 | + | 296.688i | 0.573865 | + | 0.573865i | ||||
\(518\) | −60.0528 | + | 130.188i | −0.115932 | + | 0.251328i | ||||
\(519\) | −205.705 | + | 70.2448i | −0.396349 | + | 0.135346i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 485.997i | 0.932816i | 0.884570 | + | 0.466408i | \(0.154452\pi\) | ||||
−0.884570 | + | 0.466408i | \(0.845548\pi\) | |||||||
\(522\) | −260.928 | + | 59.9791i | −0.499863 | + | 0.114902i | ||||
\(523\) | 303.922 | + | 303.922i | 0.581112 | + | 0.581112i | 0.935209 | − | 0.354096i | \(-0.115212\pi\) |
−0.354096 | + | 0.935209i | \(0.615212\pi\) | |||||||
\(524\) | 376.868 | + | 441.655i | 0.719214 | + | 0.842854i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 138.849 | + | 376.627i | 0.263972 | + | 0.716021i | ||||
\(527\) | 136.803 | + | 136.803i | 0.259588 | + | 0.259588i | ||||
\(528\) | −660.291 | − | 465.733i | −1.25055 | − | 0.882069i | ||||
\(529\) | 160.623i | 0.303636i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.1260 | + | 24.0641i | −0.0586176 | + | 0.0453185i | ||||
\(532\) | −95.5710 | − | 7.56456i | −0.179645 | − | 0.0142191i | ||||
\(533\) | −52.6112 | − | 52.6112i | −0.0987077 | − | 0.0987077i | ||||
\(534\) | −435.168 | − | 535.639i | −0.814922 | − | 1.00307i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 298.717 | − | 532.560i | 0.557308 | − | 0.993583i | ||||
\(537\) | −73.3246 | − | 35.9941i | −0.136545 | − | 0.0670281i | ||||
\(538\) | −0.455200 | + | 0.986826i | −0.000846097 | + | 0.00183425i | ||||
\(539\) | 402.370i | 0.746512i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −388.275 | −0.717700 | −0.358850 | − | 0.933395i | \(-0.616831\pi\) | ||||
−0.358850 | + | 0.933395i | \(0.616831\pi\) | |||||||
\(542\) | 658.936 | + | 303.952i | 1.21575 | + | 0.560797i | ||||
\(543\) | 365.689 | − | 744.956i | 0.673460 | − | 1.37193i | ||||
\(544\) | 431.835 | − | 85.3962i | 0.793815 | − | 0.156978i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −285.254 | + | 231.749i | −0.522444 | + | 0.424448i | ||||
\(547\) | −169.325 | + | 169.325i | −0.309551 | + | 0.309551i | −0.844735 | − | 0.535184i | \(-0.820242\pi\) |
0.535184 | + | 0.844735i | \(0.320242\pi\) | |||||||
\(548\) | 338.929 | + | 26.8267i | 0.618484 | + | 0.0489538i | ||||
\(549\) | −46.9156 | − | 60.6834i | −0.0854565 | − | 0.110534i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −71.1604 | −0.129148 | ||||||||
\(552\) | 261.343 | + | 379.322i | 0.473447 | + | 0.687177i | ||||
\(553\) | 313.272 | − | 313.272i | 0.566495 | − | 0.566495i | ||||
\(554\) | −210.253 | + | 77.5132i | −0.379519 | + | 0.139916i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.7111 | + | 38.3345i | 0.0588330 | + | 0.0689469i | ||||
\(557\) | −310.481 | + | 310.481i | −0.557417 | + | 0.557417i | −0.928571 | − | 0.371155i | \(-0.878962\pi\) |
0.371155 | + | 0.928571i | \(0.378962\pi\) | |||||||
\(558\) | −56.7128 | − | 246.719i | −0.101636 | − | 0.442149i | ||||
\(559\) | 989.727 | 1.77053 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −224.501 | − | 657.427i | −0.400179 | − | 1.17188i | ||||
\(562\) | 578.887 | + | 267.027i | 1.03005 | + | 0.475137i | ||||
\(563\) | −234.187 | + | 234.187i | −0.415962 | + | 0.415962i | −0.883809 | − | 0.467847i | \(-0.845030\pi\) |
0.467847 | + | 0.883809i | \(0.345030\pi\) | |||||||
\(564\) | 257.259 | + | 152.575i | 0.456132 | + | 0.270524i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 591.898 | − | 218.212i | 1.04576 | − | 0.385534i | ||||
\(567\) | 205.445 | + | 349.937i | 0.362336 | + | 0.617173i | ||||
\(568\) | 282.383 | − | 79.4360i | 0.497153 | − | 0.139852i | ||||
\(569\) | −386.708 | −0.679627 | −0.339813 | − | 0.940493i | \(-0.610364\pi\) | ||||
−0.339813 | + | 0.940493i | \(0.610364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 556.152i | − | 0.973996i | −0.873403 | − | 0.486998i | \(-0.838092\pi\) | ||
0.873403 | − | 0.486998i | \(-0.161908\pi\) | |||||||
\(572\) | −820.747 | − | 64.9631i | −1.43487 | − | 0.113572i | ||||
\(573\) | −449.483 | + | 915.656i | −0.784439 | + | 1.59800i | ||||
\(574\) | 57.2055 | − | 21.0897i | 0.0996612 | − | 0.0367417i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −538.215 | − | 205.184i | −0.934401 | − | 0.356223i | ||||
\(577\) | −695.792 | − | 695.792i | −1.20588 | − | 1.20588i | −0.972350 | − | 0.233530i | \(-0.924972\pi\) |
−0.233530 | − | 0.972350i | \(-0.575028\pi\) | |||||||
\(578\) | −181.187 | − | 83.5775i | −0.313473 | − | 0.144598i | ||||
\(579\) | −138.451 | − | 405.440i | −0.239121 | − | 0.700242i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 451.566i | 0.777223i | ||||||||
\(582\) | 74.5563 | − | 720.408i | 0.128104 | − | 1.23781i | ||||
\(583\) | −272.731 | − | 272.731i | −0.467806 | − | 0.467806i | ||||
\(584\) | 70.1805 | − | 125.120i | 0.120172 | − | 0.214246i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −199.850 | + | 73.6780i | −0.341042 | + | 0.125730i | ||||
\(587\) | −241.691 | − | 241.691i | −0.411740 | − | 0.411740i | 0.470604 | − | 0.882344i | \(-0.344036\pi\) |
−0.882344 | + | 0.470604i | \(0.844036\pi\) | |||||||
\(588\) | 70.9859 | + | 277.909i | 0.120724 | + | 0.472635i | ||||
\(589\) | − | 67.2853i | − | 0.114236i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 309.289 | + | 905.721i | 0.523331 | + | 1.53252i | ||||
\(592\) | −185.343 | + | 134.407i | −0.313080 | + | 0.227039i | ||||
\(593\) | 109.471 | + | 109.471i | 0.184605 | + | 0.184605i | 0.793359 | − | 0.608754i | \(-0.208330\pi\) |
−0.608754 | + | 0.793359i | \(0.708330\pi\) | |||||||
\(594\) | −207.579 | + | 885.001i | −0.349459 | + | 1.48990i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −67.3082 | − | 78.8791i | −0.112933 | − | 0.132348i | ||||
\(597\) | 378.972 | − | 772.015i | 0.634794 | − | 1.29316i | ||||
\(598\) | 426.199 | + | 196.596i | 0.712707 | + | 0.328755i | ||||
\(599\) | 527.412i | 0.880487i | 0.897878 | + | 0.440243i | \(0.145108\pi\) | ||||
−0.897878 | + | 0.440243i | \(0.854892\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −133.338 | −0.221861 | −0.110930 | − | 0.993828i | \(-0.535383\pi\) | ||||
−0.110930 | + | 0.993828i | \(0.535383\pi\) | |||||||
\(602\) | −339.707 | + | 736.448i | −0.564297 | + | 1.22334i | ||||
\(603\) | −681.388 | − | 87.1866i | −1.13000 | − | 0.144588i | ||||
\(604\) | 609.710 | − | 520.270i | 1.00945 | − | 0.861375i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −740.052 | + | 601.239i | −1.22121 | + | 0.992144i | ||||
\(607\) | −401.515 | + | 401.515i | −0.661475 | + | 0.661475i | −0.955728 | − | 0.294253i | \(-0.904929\pi\) |
0.294253 | + | 0.955728i | \(0.404929\pi\) | |||||||
\(608\) | −127.198 | − | 85.1967i | −0.209207 | − | 0.140126i | ||||
\(609\) | −72.2410 | − | 211.550i | −0.118622 | − | 0.347373i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 304.763 | 0.498794 | ||||||||
\(612\) | −271.041 | − | 414.466i | −0.442878 | − | 0.677233i | ||||
\(613\) | 604.618 | − | 604.618i | 0.986326 | − | 0.986326i | −0.0135821 | − | 0.999908i | \(-0.504323\pi\) |
0.999908 | + | 0.0135821i | \(0.00432346\pi\) | |||||||
\(614\) | 323.350 | + | 877.082i | 0.526629 | + | 1.42847i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 330.046 | − | 588.414i | 0.535789 | − | 0.955218i | ||||
\(617\) | −51.5846 | + | 51.5846i | −0.0836055 | + | 0.0836055i | −0.747673 | − | 0.664067i | \(-0.768829\pi\) |
0.664067 | + | 0.747673i | \(0.268829\pi\) | |||||||
\(618\) | −25.0051 | + | 241.615i | −0.0404614 | + | 0.390962i | ||||
\(619\) | −1063.63 | −1.71831 | −0.859155 | − | 0.511716i | \(-0.829010\pi\) | ||||
−0.859155 | + | 0.511716i | \(0.829010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 285.550 | − | 432.444i | 0.459823 | − | 0.696367i | ||||
\(622\) | 22.2251 | − | 48.1816i | 0.0357316 | − | 0.0774623i | ||||
\(623\) | 407.454 | − | 407.454i | 0.654020 | − | 0.654020i | ||||
\(624\) | −578.335 | + | 99.9270i | −0.926819 | + | 0.160139i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −128.999 | − | 349.908i | −0.206069 | − | 0.558959i | ||||
\(627\) | −106.466 | + | 216.884i | −0.169802 | + | 0.345908i | ||||
\(628\) | −62.4854 | + | 789.443i | −0.0994990 | + | 1.25707i | ||||
\(629\) | −196.841 | −0.312943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 834.260i | 1.32212i | 0.750331 | + | 0.661062i | \(0.229894\pi\) | ||||
−0.750331 | + | 0.661062i | \(0.770106\pi\) | |||||||
\(632\) | 681.043 | − | 191.581i | 1.07760 | − | 0.303135i | ||||
\(633\) | −495.091 | − | 243.034i | −0.782134 | − | 0.383939i | ||||
\(634\) | −65.1686 | − | 176.769i | −0.102790 | − | 0.278815i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −236.485 | − | 140.255i | −0.371832 | − | 0.220527i | ||||
\(637\) | 206.661 | + | 206.661i | 0.324428 | + | 0.324428i | ||||
\(638\) | 209.754 | − | 454.725i | 0.328768 | − | 0.712735i | ||||
\(639\) | −201.849 | − | 261.083i | −0.315882 | − | 0.408581i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 104.566i | − | 0.163130i | −0.996668 | − | 0.0815648i | \(-0.974008\pi\) | ||
0.996668 | − | 0.0815648i | \(-0.0259918\pi\) | |||||||
\(642\) | −24.6157 | + | 237.852i | −0.0383423 | + | 0.370486i | ||||
\(643\) | 357.160 | + | 357.160i | 0.555459 | + | 0.555459i | 0.928011 | − | 0.372552i | \(-0.121517\pi\) |
−0.372552 | + | 0.928011i | \(0.621517\pi\) | |||||||
\(644\) | −292.571 | + | 249.653i | −0.454303 | + | 0.387660i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −45.5299 | − | 123.499i | −0.0704797 | − | 0.191175i | ||||
\(647\) | −428.808 | − | 428.808i | −0.662764 | − | 0.662764i | 0.293266 | − | 0.956031i | \(-0.405258\pi\) |
−0.956031 | + | 0.293266i | \(0.905258\pi\) | |||||||
\(648\) | 12.7606 | + | 647.874i | 0.0196923 | + | 0.999806i | ||||
\(649\) | − | 73.5884i | − | 0.113387i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 200.030 | − | 68.3070i | 0.307266 | − | 0.104926i | ||||
\(652\) | −26.1706 | + | 330.641i | −0.0401390 | + | 0.507118i | ||||
\(653\) | −216.356 | − | 216.356i | −0.331327 | − | 0.331327i | 0.521763 | − | 0.853090i | \(-0.325274\pi\) |
−0.853090 | + | 0.521763i | \(0.825274\pi\) | |||||||
\(654\) | −744.833 | + | 605.123i | −1.13889 | + | 0.925265i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 96.1491 | + | 15.3166i | 0.146569 | + | 0.0233485i | ||||
\(657\) | −160.085 | − | 20.4836i | −0.243661 | − | 0.0311775i | ||||
\(658\) | −104.605 | + | 226.772i | −0.158974 | + | 0.344638i | ||||
\(659\) | − | 862.678i | − | 1.30907i | −0.756031 | − | 0.654535i | \(-0.772864\pi\) | ||
0.756031 | − | 0.654535i | \(-0.227136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 56.1770 | 0.0849879 | 0.0424939 | − | 0.999097i | \(-0.486470\pi\) | ||||
0.0424939 | + | 0.999097i | \(0.486470\pi\) | |||||||
\(662\) | 517.494 | + | 238.708i | 0.781714 | + | 0.360587i | ||||
\(663\) | −452.966 | − | 222.355i | −0.683206 | − | 0.335377i | ||||
\(664\) | −352.768 | + | 628.924i | −0.531277 | + | 0.947175i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 218.299 | + | 136.697i | 0.327777 | + | 0.205251i | ||||
\(667\) | −201.865 | + | 201.865i | −0.302646 | + | 0.302646i | ||||
\(668\) | 37.6075 | − | 475.135i | 0.0562987 | − | 0.711281i | ||||
\(669\) | 28.1919 | − | 9.62707i | 0.0421404 | − | 0.0143902i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 143.468 | 0.213813 | ||||||||
\(672\) | 124.149 | − | 464.633i | 0.184745 | − | 0.691419i | ||||
\(673\) | −236.472 | + | 236.472i | −0.351371 | + | 0.351371i | −0.860619 | − | 0.509249i | \(-0.829923\pi\) |
0.509249 | + | 0.860619i | \(0.329923\pi\) | |||||||
\(674\) | 780.659 | − | 287.802i | 1.15825 | − | 0.427006i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 59.3223 | − | 50.6203i | 0.0877550 | − | 0.0748820i | ||||
\(677\) | −754.987 | + | 754.987i | −1.11520 | + | 1.11520i | −0.122759 | + | 0.992437i | \(0.539174\pi\) |
−0.992437 | + | 0.122759i | \(0.960826\pi\) | |||||||
\(678\) | −88.4502 | + | 854.659i | −0.130458 | + | 1.26056i | ||||
\(679\) | 604.720 | 0.890604 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 147.224 | − | 50.2744i | 0.216187 | − | 0.0738244i | ||||
\(682\) | 429.962 | + | 198.332i | 0.630443 | + | 0.290809i | ||||
\(683\) | −848.561 | + | 848.561i | −1.24240 | + | 1.24240i | −0.283401 | + | 0.959002i | \(0.591463\pi\) |
−0.959002 | + | 0.283401i | \(0.908537\pi\) | |||||||
\(684\) | −35.2712 | + | 168.581i | −0.0515661 | + | 0.246463i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −685.353 | + | 252.666i | −0.999057 | + | 0.368318i | ||||
\(687\) | −727.455 | − | 357.098i | −1.05889 | − | 0.519794i | ||||
\(688\) | −1048.45 | + | 760.314i | −1.52391 | + | 1.10511i | ||||
\(689\) | −280.154 | −0.406609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 973.366i | 1.40863i | 0.709886 | + | 0.704317i | \(0.248747\pi\) | ||||
−0.709886 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(692\) | 22.8684 | − | 288.920i | 0.0330468 | − | 0.417515i | ||||
\(693\) | −752.851 | − | 96.3306i | −1.08637 | − | 0.139005i | ||||
\(694\) | 727.289 | − | 268.127i | 1.04797 | − | 0.386350i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 64.6509 | − | 351.074i | 0.0928892 | − | 0.504417i | ||||
\(697\) | 59.1903 | + | 59.1903i | 0.0849215 | + | 0.0849215i | ||||
\(698\) | 234.594 | + | 108.213i | 0.336094 | + | 0.155033i | ||||
\(699\) | 221.682 | − | 75.7008i | 0.317142 | − | 0.108299i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.02635i | 0.0114499i | 0.999984 | + | 0.00572493i | \(0.00182231\pi\) | ||||
−0.999984 | + | 0.00572493i | \(0.998178\pi\) | |||||||
\(702\) | 347.930 | + | 561.158i | 0.495626 | + | 0.799371i | ||||
\(703\) | 48.4074 | + | 48.4074i | 0.0688583 | + | 0.0688583i | ||||
\(704\) | 919.350 | − | 561.685i | 1.30590 | − | 0.797848i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1013.09 | − | 373.490i | 1.43497 | − | 0.529023i | ||||
\(707\) | −562.949 | − | 562.949i | −0.796250 | − | 0.796250i | ||||
\(708\) | −12.9824 | − | 50.8261i | −0.0183368 | − | 0.0717883i | ||||
\(709\) | 378.225i | 0.533463i | 0.963771 | + | 0.266731i | \(0.0859437\pi\) | ||||
−0.963771 | + | 0.266731i | \(0.914056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −486.813 | − | 629.673i | −0.684688 | − | 0.885615i | ||||
\(712\) | 885.794 | − | 249.179i | 1.24409 | − | 0.349970i | ||||
\(713\) | −190.872 | − | 190.872i | −0.267703 | − | 0.267703i | ||||
\(714\) | 320.925 | − | 260.729i | 0.449475 | − | 0.365166i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 82.8476 | − | 70.6946i | 0.115709 | − | 0.0987354i | ||||
\(717\) | −124.249 | − | 60.9924i | −0.173291 | − | 0.0850660i | ||||
\(718\) | −380.872 | − | 175.688i | −0.530463 | − | 0.244690i | ||||
\(719\) | − | 901.949i | − | 1.25445i | −0.778838 | − | 0.627225i | \(-0.784191\pi\) | ||
0.778838 | − | 0.627225i | \(-0.215809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −202.815 | −0.281296 | ||||||||
\(722\) | 283.245 | − | 614.044i | 0.392305 | − | 0.850477i | ||||
\(723\) | 280.476 | − | 571.365i | 0.387933 | − | 0.790270i | ||||
\(724\) | 718.236 | + | 841.707i | 0.992038 | + | 1.16258i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −614.315 | − | 756.146i | −0.846163 | − | 1.04152i | ||||
\(727\) | −647.476 | + | 647.476i | −0.890613 | + | 0.890613i | −0.994581 | − | 0.103967i | \(-0.966846\pi\) |
0.103967 | + | 0.994581i | \(0.466846\pi\) | |||||||
\(728\) | −132.700 | − | 471.729i | −0.182280 | − | 0.647979i | ||||
\(729\) | 670.424 | − | 286.308i | 0.919649 | − | 0.392740i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1113.49 | −1.52325 | ||||||||
\(732\) | 99.0909 | − | 25.3106i | 0.135370 | − | 0.0345773i | ||||
\(733\) | 664.993 | − | 664.993i | 0.907221 | − | 0.907221i | −0.0888262 | − | 0.996047i | \(-0.528312\pi\) |
0.996047 | + | 0.0888262i | \(0.0283116\pi\) | |||||||
\(734\) | 4.18404 | + | 11.3491i | 0.00570033 | + | 0.0154620i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −602.513 | + | 119.148i | −0.818631 | + | 0.161886i | ||||
\(737\) | 908.537 | − | 908.537i | 1.23275 | − | 1.23275i | ||||
\(738\) | −24.5379 | − | 106.748i | −0.0332492 | − | 0.144645i | ||||
\(739\) | −605.307 | −0.819090 | −0.409545 | − | 0.912290i | \(-0.634313\pi\) | ||||
−0.409545 | + | 0.912290i | \(0.634313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 56.7120 | + | 166.075i | 0.0765344 | + | 0.224123i | ||||
\(742\) | 96.1580 | − | 208.460i | 0.129593 | − | 0.280944i | ||||
\(743\) | 149.548 | − | 149.548i | 0.201275 | − | 0.201275i | −0.599271 | − | 0.800546i | \(-0.704543\pi\) |
0.800546 | + | 0.599271i | \(0.204543\pi\) | |||||||
\(744\) | 331.956 | + | 61.1303i | 0.446178 | + | 0.0821643i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −355.954 | − | 965.519i | −0.477150 | − | 1.29426i | ||||
\(747\) | 804.681 | + | 102.963i | 1.07722 | + | 0.137835i | ||||
\(748\) | 923.382 | + | 73.0868i | 1.23447 | + | 0.0977096i | ||||
\(749\) | −199.656 | −0.266564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 988.027i | 1.31562i | 0.753186 | + | 0.657808i | \(0.228516\pi\) | ||||
−0.753186 | + | 0.657808i | \(0.771484\pi\) | |||||||
\(752\) | −322.846 | + | 234.121i | −0.429316 | + | 0.311331i | ||||
\(753\) | 211.101 | − | 430.041i | 0.280347 | − | 0.571103i | ||||
\(754\) | −125.819 | − | 341.282i | −0.166869 | − | 0.452629i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −536.975 | + | 66.2839i | −0.710284 | + | 0.0876771i | ||||
\(757\) | −590.607 | − | 590.607i | −0.780195 | − | 0.780195i | 0.199669 | − | 0.979863i | \(-0.436013\pi\) |
−0.979863 | + | 0.199669i | \(0.936013\pi\) | |||||||
\(758\) | −613.532 | + | 1330.07i | −0.809410 | + | 1.75471i | ||||
\(759\) | 313.231 | + | 917.267i | 0.412690 | + | 1.20852i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 354.692i | − | 0.466087i | −0.972466 | − | 0.233043i | \(-0.925132\pi\) | ||
0.972466 | − | 0.233043i | \(-0.0748684\pi\) | |||||||
\(762\) | 794.092 | + | 82.1820i | 1.04212 | + | 0.107850i | ||||
\(763\) | −566.586 | − | 566.586i | −0.742576 | − | 0.742576i | ||||
\(764\) | −882.813 | − | 1034.58i | −1.15551 | − | 1.35416i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −335.823 | − | 910.914i | −0.438411 | − | 1.18918i | ||||
\(767\) | −37.7956 | − | 37.7956i | −0.0492772 | − | 0.0492772i | ||||
\(768\) | 535.886 | − | 550.137i | 0.697768 | − | 0.716324i | ||||
\(769\) | − | 262.078i | − | 0.340804i | −0.985375 | − | 0.170402i | \(-0.945493\pi\) | ||
0.985375 | − | 0.170402i | \(-0.0545067\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −134.484 | − | 393.822i | −0.174428 | − | 0.510794i | ||||
\(772\) | 569.456 | + | 45.0732i | 0.737638 | + | 0.0583849i | ||||
\(773\) | 616.984 | + | 616.984i | 0.798168 | + | 0.798168i | 0.982806 | − | 0.184639i | \(-0.0591115\pi\) |
−0.184639 | + | 0.982806i | \(0.559112\pi\) | |||||||
\(774\) | 1234.88 | + | 773.269i | 1.59545 | + | 0.999056i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 842.231 | + | 472.413i | 1.08535 | + | 0.608780i | ||||
\(777\) | −94.7662 | + | 193.051i | −0.121964 | + | 0.248457i | ||||
\(778\) | 503.117 | − | 1090.70i | 0.646679 | − | 1.40193i | ||||
\(779\) | − | 29.1122i | − | 0.0373713i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 617.256 | 0.790340 | ||||||||
\(782\) | −479.495 | − | 221.180i | −0.613165 | − | 0.282839i | ||||
\(783\) | −393.450 | + | 80.4958i | −0.502490 | + | 0.102804i | ||||
\(784\) | −377.681 | − | 60.1647i | −0.481735 | − | 0.0767407i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 549.148 | + | 675.934i | 0.698662 | + | 0.859967i | ||||
\(787\) | −471.258 | + | 471.258i | −0.598803 | + | 0.598803i | −0.939994 | − | 0.341191i | \(-0.889170\pi\) |
0.341191 | + | 0.939994i | \(0.389170\pi\) | |||||||
\(788\) | −1272.12 | − | 100.690i | −1.61437 | − | 0.127779i | ||||
\(789\) | 194.578 | + | 569.802i | 0.246614 | + | 0.722183i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −717.412 | −0.906969 | ||||||||
\(792\) | −973.287 | − | 722.300i | −1.22890 | − | 0.911995i | ||||
\(793\) | 73.6865 | − | 73.6865i | 0.0929212 | − | 0.0929212i | ||||
\(794\) | −783.636 | + | 288.900i | −0.986947 | + | 0.363853i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 744.324 | + | 872.281i | 0.935081 | + | 1.09583i | ||||
\(797\) | 485.701 | − | 485.701i | 0.609411 | − | 0.609411i | −0.333381 | − | 0.942792i | \(-0.608189\pi\) |
0.942792 | + | 0.333381i | \(0.108189\pi\) | |||||||
\(798\) | −143.041 | − | 14.8036i | −0.179249 | − | 0.0185508i | ||||
\(799\) | −342.874 | −0.429129 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −633.170 | − | 818.979i | −0.790474 | − | 1.02245i | ||||
\(802\) | −545.578 | − | 251.663i | −0.680271 | − | 0.313794i | ||||
\(803\) | 213.451 | − | 213.451i | 0.265818 | − | 0.265818i | ||||
\(804\) | 467.226 | − | 787.793i | 0.581127 | − | 0.979842i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 322.697 | − | 118.967i | 0.400368 | − | 0.147602i | ||||
\(807\) | −0.718328 | + | 1.46333i | −0.000890122 | + | 0.00181329i | ||||
\(808\) | −344.272 | − | 1223.83i | −0.426079 | − | 1.51465i | ||||
\(809\) | −183.688 | −0.227056 | −0.113528 | − | 0.993535i | \(-0.536215\pi\) | ||||
−0.113528 | + | 0.993535i | \(0.536215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1332.68i | − | 1.64325i | −0.570027 | − | 0.821626i | \(-0.693067\pi\) | ||
0.570027 | − | 0.821626i | \(-0.306933\pi\) | |||||||
\(812\) | 297.131 | + | 23.5182i | 0.365924 | + | 0.0289634i | ||||
\(813\) | 977.111 | + | 479.651i | 1.20186 | + | 0.589977i | ||||
\(814\) | −452.016 | + | 166.643i | −0.555303 | + | 0.204721i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 650.656 | − | 112.423i | 0.797373 | − | 0.137773i | ||||
\(817\) | 273.831 | + | 273.831i | 0.335166 | + | 0.335166i | ||||
\(818\) | −97.7350 | − | 45.0829i | −0.119480 | − | 0.0551136i | ||||
\(819\) | −436.147 | + | 337.194i | −0.532536 | + | 0.411715i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1157.86i | − | 1.41030i | −0.709057 | − | 0.705152i | \(-0.750879\pi\) | ||
0.709057 | − | 0.705152i | \(-0.249121\pi\) | |||||||
\(822\) | 507.275 | + | 52.4988i | 0.617123 | + | 0.0638672i | ||||
\(823\) | −420.085 | − | 420.085i | −0.510432 | − | 0.510432i | 0.404227 | − | 0.914659i | \(-0.367541\pi\) |
−0.914659 | + | 0.404227i | \(0.867541\pi\) | |||||||
\(824\) | −282.472 | − | 158.441i | −0.342806 | − | 0.192282i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41.0961 | − | 15.1507i | 0.0497532 | − | 0.0183423i | ||||
\(827\) | 450.627 | + | 450.627i | 0.544893 | + | 0.544893i | 0.924959 | − | 0.380066i | \(-0.124099\pi\) |
−0.380066 | + | 0.924959i | \(0.624099\pi\) | |||||||
\(828\) | 378.167 | + | 578.279i | 0.456723 | + | 0.698404i | ||||
\(829\) | − | 1059.56i | − | 1.27812i | −0.769155 | − | 0.639062i | \(-0.779323\pi\) | ||
0.769155 | − | 0.639062i | \(-0.220677\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −318.094 | + | 108.624i | −0.382785 | + | 0.130715i | ||||
\(832\) | 183.700 | − | 760.672i | 0.220793 | − | 0.914270i | ||||
\(833\) | −232.504 | − | 232.504i | −0.279116 | − | 0.279116i | ||||
\(834\) | 47.6646 | + | 58.6692i | 0.0571517 | + | 0.0703468i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −209.105 | − | 245.052i | −0.250126 | − | 0.293125i | ||||
\(837\) | −76.1123 | − | 372.024i | −0.0909346 | − | 0.444473i | ||||
\(838\) | 1058.05 | + | 488.053i | 1.26259 | + | 0.582402i | ||||
\(839\) | − | 425.692i | − | 0.507380i | −0.967286 | − | 0.253690i | \(-0.918356\pi\) | ||
0.967286 | − | 0.253690i | \(-0.0816443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −619.762 | −0.736935 | ||||||||
\(842\) | −407.702 | + | 883.855i | −0.484207 | + | 1.04971i | ||||
\(843\) | 858.410 | + | 421.382i | 1.01828 | + | 0.499860i | ||||
\(844\) | 559.391 | − | 477.333i | 0.662786 | − | 0.565560i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 380.252 | + | 238.110i | 0.449470 | + | 0.281454i | ||||
\(847\) | 575.192 | − | 575.192i | 0.679093 | − | 0.679093i | ||||
\(848\) | 296.776 | − | 215.216i | 0.349972 | − | 0.253792i | ||||
\(849\) | 895.488 | − | 305.794i | 1.05476 | − | 0.360182i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 274.640 | 0.322726 | ||||||||
\(852\) | 426.327 | − | 108.896i | 0.500384 | − | 0.127812i | ||||
\(853\) | −533.860 | + | 533.860i | −0.625861 | + | 0.625861i | −0.947024 | − | 0.321163i | \(-0.895926\pi\) |
0.321163 | + | 0.947024i | \(0.395926\pi\) | |||||||
\(854\) | 29.5380 | + | 80.1213i | 0.0345878 | + | 0.0938188i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −278.073 | − | 155.973i | −0.324852 | − | 0.182212i | ||||
\(857\) | −575.339 | + | 575.339i | −0.671340 | + | 0.671340i | −0.958025 | − | 0.286685i | \(-0.907447\pi\) |
0.286685 | + | 0.958025i | \(0.407447\pi\) | |||||||
\(858\) | −1228.41 | − | 127.130i | −1.43171 | − | 0.148171i | ||||
\(859\) | 730.948 | 0.850929 | 0.425465 | − | 0.904975i | \(-0.360111\pi\) | ||||
0.425465 | + | 0.904975i | \(0.360111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 86.5468 | − | 29.5543i | 0.100519 | − | 0.0343256i | ||||
\(862\) | −464.635 | + | 1007.28i | −0.539019 | + | 1.16854i | ||||
\(863\) | 503.710 | − | 503.710i | 0.583673 | − | 0.583673i | −0.352238 | − | 0.935911i | \(-0.614579\pi\) |
0.935911 | + | 0.352238i | \(0.114579\pi\) | |||||||
\(864\) | −799.659 | − | 327.172i | −0.925531 | − | 0.378672i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −149.601 | − | 405.789i | −0.172749 | − | 0.468579i | ||||
\(867\) | −268.676 | − | 131.889i | −0.309891 | − | 0.152122i | ||||
\(868\) | −22.2375 | + | 280.950i | −0.0256193 | + | 0.323675i | ||||
\(869\) | 1488.68 | 1.71310 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 933.264i | − | 1.07149i | ||||||
\(872\) | −346.496 | − | 1231.74i | −0.397358 | − | 1.41255i | ||||
\(873\) | 137.883 | − | 1077.60i | 0.157942 | − | 1.23436i | ||||
\(874\) | 63.5250 | + | 172.311i | 0.0726831 | + | 0.197152i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 109.770 | − | 185.084i | 0.125308 | − | 0.211283i | ||||
\(877\) | 1002.77 | + | 1002.77i | 1.14341 | + | 1.14341i | 0.987822 | + | 0.155586i | \(0.0497266\pi\) |
0.155586 | + | 0.987822i | \(0.450273\pi\) | |||||||
\(878\) | 183.315 | − | 397.407i | 0.208787 | − | 0.452627i | ||||
\(879\) | −302.356 | + | 103.249i | −0.343977 | + | 0.117462i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1337.17i | 1.51779i | 0.651213 | + | 0.758895i | \(0.274261\pi\) | ||||
−0.651213 | + | 0.758895i | \(0.725739\pi\) | |||||||
\(882\) | 96.3865 | + | 419.312i | 0.109282 | + | 0.475411i | ||||
\(883\) | 29.5709 | + | 29.5709i | 0.0334891 | + | 0.0334891i | 0.723653 | − | 0.690164i | \(-0.242462\pi\) |
−0.690164 | + | 0.723653i | \(0.742462\pi\) | |||||||
\(884\) | 511.795 | − | 436.719i | 0.578953 | − | 0.494026i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1314 | + | 106.143i | 0.0441664 | + | 0.119801i | ||||
\(887\) | 815.068 | + | 815.068i | 0.918904 | + | 0.918904i | 0.996950 | − | 0.0780457i | \(-0.0248680\pi\) |
−0.0780457 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(888\) | −282.800 | + | 194.842i | −0.318469 | + | 0.219416i | ||||
\(889\) | 666.572i | 0.749799i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −343.318 | + | 1319.60i | −0.385318 | + | 1.48103i | ||||
\(892\) | −3.13412 | + | 39.5966i | −0.00351359 | + | 0.0443908i | ||||
\(893\) | 84.3198 | + | 84.3198i | 0.0944231 | + | 0.0944231i | ||||
\(894\) | −98.0772 | − | 120.721i | −0.109706 | − | 0.135035i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 502.959 | + | 397.778i | 0.561338 | + | 0.443948i | ||||
\(897\) | 631.994 | + | 310.238i | 0.704564 | + | 0.345861i | ||||
\(898\) | −198.097 | + | 429.454i | −0.220598 | + | 0.478234i | ||||
\(899\) | 209.190i | 0.232692i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 315.187 | 0.349819 | ||||||||
\(902\) | 186.031 | + | 85.8120i | 0.206243 | + | 0.0951352i | ||||
\(903\) | −536.074 | + | 1092.05i | −0.593659 | + | 1.20936i | ||||
\(904\) | −999.183 | − | 560.449i | −1.10529 | − | 0.619966i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 933.134 | − | 758.104i | 1.02995 | − | 0.836760i | ||||
\(907\) | 551.789 | − | 551.789i | 0.608367 | − | 0.608367i | −0.334152 | − | 0.942519i | \(-0.608450\pi\) |
0.942519 | + | 0.334152i | \(0.108450\pi\) | |||||||
\(908\) | −16.3670 | + | 206.781i | −0.0180253 | + | 0.227733i | ||||
\(909\) | −1131.52 | + | 874.803i | −1.24480 | + | 0.962380i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1547.30 | 1.69846 | 0.849231 | − | 0.528022i | \(-0.177066\pi\) | ||||
0.849231 | + | 0.528022i | \(0.177066\pi\) | |||||||
\(912\) | −187.657 | − | 132.363i | −0.205764 | − | 0.145135i | ||||
\(913\) | −1072.93 | + | 1072.93i | −1.17517 | + | 1.17517i | ||||
\(914\) | −644.364 | + | 237.555i | −0.704993 | + | 0.259907i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 821.934 | − | 701.363i | 0.897307 | − | 0.765680i | ||||
\(917\) | −514.175 | + | 514.175i | −0.560715 | + | 0.560715i | ||||
\(918\) | −391.438 | − | 631.331i | −0.426403 | − | 0.687725i | ||||
\(919\) | −1012.94 | −1.10222 | −0.551109 | − | 0.834433i | \(-0.685795\pi\) | ||||
−0.551109 | + | 0.834433i | \(0.685795\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 453.130 | + | 1326.95i | 0.491998 | + | 1.44077i | ||||
\(922\) | −1163.71 | − | 536.794i | −1.26216 | − | 0.582207i | ||||
\(923\) | 317.028 | − | 317.028i | 0.343475 | − | 0.343475i | ||||
\(924\) | 516.228 | − | 870.416i | 0.558688 | − | 0.942008i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −431.990 | + | 159.260i | −0.466512 | + | 0.171987i | ||||
\(927\) | −46.2441 | + | 361.411i | −0.0498858 | + | 0.389872i | ||||
\(928\) | 395.459 | + | 264.877i | 0.426141 | + | 0.285427i | ||||
\(929\) | −1529.05 | −1.64591 | −0.822955 | − | 0.568106i | \(-0.807676\pi\) | ||||
−0.822955 | + | 0.568106i | \(0.807676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 114.355i | 0.122830i | ||||||||
\(932\) | −24.6446 | + | 311.361i | −0.0264427 | + | 0.334079i | ||||
\(933\) | 35.0722 | − | 71.4467i | 0.0375908 | − | 0.0765773i | ||||
\(934\) | −1127.78 | + | 415.772i | −1.20747 | + | 0.445152i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −870.868 | + | 128.909i | −0.930414 | + | 0.137723i | ||||
\(937\) | −662.561 | − | 662.561i | −0.707109 | − | 0.707109i | 0.258818 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258818i | \(0.916667\pi\) | |||||||
\(938\) | 694.435 | + | 320.327i | 0.740336 | + | 0.341500i | ||||
\(939\) | −180.774 | − | 529.380i | −0.192518 | − | 0.563769i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 961.186i | 1.02145i | 0.859744 | + | 0.510726i | \(0.170623\pi\) | ||||
−0.859744 | + | 0.510726i | \(0.829377\pi\) | |||||||
\(942\) | −122.281 | + | 1181.56i | −0.129811 | + | 1.25431i | ||||
\(943\) | −82.5844 | − | 82.5844i | −0.0875763 | − | 0.0875763i | ||||
\(944\) | 69.0730 | + | 11.0034i | 0.0731706 | + | 0.0116561i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2556.97 | + | 942.667i | −2.70293 | + | 0.996476i | ||||
\(947\) | −1259.29 | − | 1259.29i | −1.32977 | − | 1.32977i | −0.905568 | − | 0.424202i | \(-0.860555\pi\) |
−0.424202 | − | 0.905568i | \(-0.639445\pi\) | |||||||
\(948\) | 1028.20 | − | 262.632i | 1.08460 | − | 0.277038i | ||||
\(949\) | − | 219.261i | − | 0.231044i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −91.3247 | − | 267.435i | −0.0960302 | − | 0.281215i | ||||
\(952\) | 149.294 | + | 530.719i | 0.156822 | + | 0.557478i | ||||
\(953\) | 62.1880 | + | 62.1880i | 0.0652550 | + | 0.0652550i | 0.738981 | − | 0.673726i | \(-0.235307\pi\) |
−0.673726 | + | 0.738981i | \(0.735307\pi\) | |||||||
\(954\) | −349.546 | − | 218.883i | −0.366401 | − | 0.229437i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 140.386 | − | 119.793i | 0.146848 | − | 0.125306i | ||||
\(957\) | 331.002 | − | 674.295i | 0.345875 | − | 0.704592i | ||||
\(958\) | −797.397 | − | 367.821i | −0.832356 | − | 0.383947i | ||||
\(959\) | 425.813i | 0.444018i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 763.202 | 0.794174 | ||||||||
\(962\) | −146.570 | + | 317.749i | −0.152360 | + | 0.330300i | ||||
\(963\) | −45.5240 | + | 355.783i | −0.0472731 | + | 0.369453i | ||||
\(964\) | 550.871 | + | 645.571i | 0.571443 | + | 0.669680i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −447.767 | + | 363.779i | −0.463527 | + | 0.376582i | ||||
\(967\) | −1.17333 | + | 1.17333i | −0.00121337 | + | 0.00121337i | −0.707713 | − | 0.706500i | \(-0.750273\pi\) |
0.706500 | + | 0.707713i | \(0.250273\pi\) | |||||||
\(968\) | 1250.45 | − | 351.759i | 1.29179 | − | 0.363387i | ||||
\(969\) | −63.8038 | − | 186.843i | −0.0658450 | − | 0.192821i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 570.125 | 0.587153 | 0.293576 | − | 0.955936i | \(-0.405154\pi\) | ||||
0.293576 | + | 0.955936i | \(0.405154\pi\) | |||||||
\(972\) | −4.32014 | + | 971.990i | −0.00444459 | + | 0.999990i | ||||
\(973\) | −44.6290 | + | 44.6290i | −0.0458674 | + | 0.0458674i | ||||
\(974\) | 301.565 | + | 817.991i | 0.309615 | + | 0.839827i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.4522 | + | 134.665i | −0.0219797 | + | 0.137977i | ||||
\(977\) | 430.216 | − | 430.216i | 0.440344 | − | 0.440344i | −0.451784 | − | 0.892128i | \(-0.649212\pi\) |
0.892128 | + | 0.451784i | \(0.149212\pi\) | |||||||
\(978\) | −51.2149 | + | 494.869i | −0.0523670 | + | 0.506001i | ||||
\(979\) | 1936.24 | 1.97777 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1138.83 | + | 880.455i | −1.16089 | + | 0.897507i | ||||
\(982\) | 629.685 | − | 1365.09i | 0.641227 | − | 1.39011i | ||||
\(983\) | −876.585 | + | 876.585i | −0.891745 | + | 0.891745i | −0.994687 | − | 0.102942i | \(-0.967174\pi\) |
0.102942 | + | 0.994687i | \(0.467174\pi\) | |||||||
\(984\) | 143.627 | + | 26.4492i | 0.145963 | + | 0.0268792i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 141.553 | + | 383.959i | 0.143563 | + | 0.389411i | ||||
\(987\) | −165.071 | + | 336.272i | −0.167246 | + | 0.340701i | ||||
\(988\) | −233.259 | − | 18.4627i | −0.236092 | − | 0.0186870i | ||||
\(989\) | 1553.59 | 1.57086 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 183.991i | − | 0.185662i | −0.995682 | − | 0.0928310i | \(-0.970408\pi\) | ||
0.995682 | − | 0.0928310i | \(-0.0295916\pi\) | |||||||
\(992\) | −250.453 | + | 373.924i | −0.252472 | + | 0.376939i | ||||
\(993\) | 767.373 | + | 376.693i | 0.772783 | + | 0.379349i | ||||
\(994\) | 127.084 | + | 344.712i | 0.127851 | + | 0.346793i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −551.768 | + | 930.340i | −0.553983 | + | 0.934076i | ||||
\(997\) | −276.341 | − | 276.341i | −0.277172 | − | 0.277172i | 0.554807 | − | 0.831979i | \(-0.312792\pi\) |
−0.831979 | + | 0.554807i | \(0.812792\pi\) | |||||||
\(998\) | 255.075 | − | 552.976i | 0.255586 | − | 0.554084i | ||||
\(999\) | 322.405 | + | 212.889i | 0.322728 | + | 0.213102i |
(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 | 300.3.l.g.107.8 | 40 | ||
3.2 | odd | 2 | inner | 300.3.l.g.107.13 | 40 | ||
4.3 | odd | 2 | inner | 300.3.l.g.107.3 | 40 | ||
5.2 | odd | 4 | 60.3.l.a.23.3 | ✓ | 40 | ||
5.3 | odd | 4 | inner | 300.3.l.g.143.18 | 40 | ||
5.4 | even | 2 | 60.3.l.a.47.13 | yes | 40 | ||
12.11 | even | 2 | inner | 300.3.l.g.107.18 | 40 | ||
15.2 | even | 4 | 60.3.l.a.23.18 | yes | 40 | ||
15.8 | even | 4 | inner | 300.3.l.g.143.3 | 40 | ||
15.14 | odd | 2 | 60.3.l.a.47.8 | yes | 40 | ||
20.3 | even | 4 | inner | 300.3.l.g.143.13 | 40 | ||
20.7 | even | 4 | 60.3.l.a.23.8 | yes | 40 | ||
20.19 | odd | 2 | 60.3.l.a.47.18 | yes | 40 | ||
60.23 | odd | 4 | inner | 300.3.l.g.143.8 | 40 | ||
60.47 | odd | 4 | 60.3.l.a.23.13 | yes | 40 | ||
60.59 | even | 2 | 60.3.l.a.47.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.l.a.23.3 | ✓ | 40 | 5.2 | odd | 4 | ||
60.3.l.a.23.8 | yes | 40 | 20.7 | even | 4 | ||
60.3.l.a.23.13 | yes | 40 | 60.47 | odd | 4 | ||
60.3.l.a.23.18 | yes | 40 | 15.2 | even | 4 | ||
60.3.l.a.47.3 | yes | 40 | 60.59 | even | 2 | ||
60.3.l.a.47.8 | yes | 40 | 15.14 | odd | 2 | ||
60.3.l.a.47.13 | yes | 40 | 5.4 | even | 2 | ||
60.3.l.a.47.18 | yes | 40 | 20.19 | odd | 2 | ||
300.3.l.g.107.3 | 40 | 4.3 | odd | 2 | inner | ||
300.3.l.g.107.8 | 40 | 1.1 | even | 1 | trivial | ||
300.3.l.g.107.13 | 40 | 3.2 | odd | 2 | inner | ||
300.3.l.g.107.18 | 40 | 12.11 | even | 2 | inner | ||
300.3.l.g.143.3 | 40 | 15.8 | even | 4 | inner | ||
300.3.l.g.143.8 | 40 | 60.23 | odd | 4 | inner | ||
300.3.l.g.143.13 | 40 | 20.3 | even | 4 | inner | ||
300.3.l.g.143.18 | 40 | 5.3 | odd | 4 | inner |