Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(11,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.18 | ||
Character | \(\chi\) | \(=\) | 105.11 |
Dual form | 105.3.t.b.86.18 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.31814 | − | 1.91573i | 1.65907 | − | 0.957864i | 0.685923 | − | 0.727675i | \(-0.259399\pi\) |
0.973146 | − | 0.230189i | \(-0.0739345\pi\) | |||||||
\(3\) | −2.97174 | − | 0.410813i | −0.990580 | − | 0.136938i | ||||
\(4\) | 5.34002 | − | 9.24919i | 1.33501 | − | 2.31230i | ||||
\(5\) | 1.93649 | − | 1.11803i | 0.387298 | − | 0.223607i | ||||
\(6\) | −10.6476 | + | 4.32991i | −1.77461 | + | 0.721651i | ||||
\(7\) | −5.86414 | + | 3.82255i | −0.837734 | + | 0.546078i | ||||
\(8\) | − | 25.5943i | − | 3.19929i | ||||||
\(9\) | 8.66247 | + | 2.44166i | 0.962496 | + | 0.271295i | ||||
\(10\) | 4.28370 | − | 7.41958i | 0.428370 | − | 0.741958i | ||||
\(11\) | 9.48205 | + | 5.47446i | 0.862004 | + | 0.497679i | 0.864683 | − | 0.502318i | \(-0.167519\pi\) |
−0.00267854 | + | 0.999996i | \(0.500853\pi\) | |||||||
\(12\) | −19.6688 | + | 25.2924i | −1.63907 | + | 2.10770i | ||||
\(13\) | −3.75260 | −0.288662 | −0.144331 | − | 0.989529i | \(-0.546103\pi\) | ||||
−0.144331 | + | 0.989529i | \(0.546103\pi\) | |||||||
\(14\) | −12.1351 | + | 23.9178i | −0.866791 | + | 1.70842i | ||||
\(15\) | −6.21405 | + | 2.52697i | −0.414270 | + | 0.168465i | ||||
\(16\) | −27.6716 | − | 47.9286i | −1.72947 | − | 2.99554i | ||||
\(17\) | 12.6515 | + | 7.30435i | 0.744206 | + | 0.429668i | 0.823597 | − | 0.567176i | \(-0.191964\pi\) |
−0.0793904 | + | 0.996844i | \(0.525297\pi\) | |||||||
\(18\) | 33.4208 | − | 8.49316i | 1.85671 | − | 0.471842i | ||||
\(19\) | 5.54612 | + | 9.60616i | 0.291901 | + | 0.505587i | 0.974259 | − | 0.225431i | \(-0.0723789\pi\) |
−0.682358 | + | 0.731018i | \(0.739046\pi\) | |||||||
\(20\) | − | 23.8813i | − | 1.19407i | ||||||
\(21\) | 18.9970 | − | 8.95054i | 0.904621 | − | 0.426216i | ||||
\(22\) | 41.9503 | 1.90683 | ||||||||
\(23\) | −8.53608 | + | 4.92831i | −0.371134 | + | 0.214274i | −0.673954 | − | 0.738774i | \(-0.735405\pi\) |
0.302820 | + | 0.953048i | \(0.402072\pi\) | |||||||
\(24\) | −10.5145 | + | 76.0595i | −0.438103 | + | 3.16915i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | −12.4516 | + | 7.18896i | −0.478909 | + | 0.276499i | ||||
\(27\) | −24.7395 | − | 10.8146i | −0.916279 | − | 0.400542i | ||||
\(28\) | 4.04080 | + | 74.6510i | 0.144314 | + | 2.66611i | ||||
\(29\) | 10.0771i | 0.347485i | 0.984791 | + | 0.173743i | \(0.0555861\pi\) | ||||
−0.984791 | + | 0.173743i | \(0.944414\pi\) | |||||||
\(30\) | −15.7781 | + | 20.2893i | −0.525936 | + | 0.676309i | ||||
\(31\) | −12.0674 | + | 20.9013i | −0.389270 | + | 0.674236i | −0.992352 | − | 0.123444i | \(-0.960606\pi\) |
0.603081 | + | 0.797680i | \(0.293939\pi\) | |||||||
\(32\) | −94.9750 | − | 54.8338i | −2.96797 | − | 1.71356i | ||||
\(33\) | −25.9292 | − | 20.1640i | −0.785733 | − | 0.611031i | ||||
\(34\) | 55.9726 | 1.64625 | ||||||||
\(35\) | −7.08212 | + | 13.9586i | −0.202346 | + | 0.398818i | ||||
\(36\) | 68.8411 | − | 67.0823i | 1.91225 | − | 1.86340i | ||||
\(37\) | 19.1895 | + | 33.2372i | 0.518636 | + | 0.898303i | 0.999766 | + | 0.0216538i | \(0.00689317\pi\) |
−0.481130 | + | 0.876649i | \(0.659773\pi\) | |||||||
\(38\) | 36.8056 | + | 21.2497i | 0.968568 | + | 0.559203i | ||||
\(39\) | 11.1518 | + | 1.54162i | 0.285942 | + | 0.0395287i | ||||
\(40\) | −28.6153 | − | 49.5631i | −0.715382 | − | 1.23908i | ||||
\(41\) | − | 67.5044i | − | 1.64645i | −0.567716 | − | 0.823224i | \(-0.692173\pi\) | ||
0.567716 | − | 0.823224i | \(-0.307827\pi\) | |||||||
\(42\) | 45.8880 | − | 66.0923i | 1.09257 | − | 1.57363i | ||||
\(43\) | −77.4222 | −1.80052 | −0.900258 | − | 0.435356i | \(-0.856623\pi\) | ||||
−0.900258 | + | 0.435356i | \(0.856623\pi\) | |||||||
\(44\) | 101.269 | − | 58.4675i | 2.30156 | − | 1.32881i | ||||
\(45\) | 19.5046 | − | 4.95668i | 0.433437 | − | 0.110148i | ||||
\(46\) | −18.8826 | + | 32.7056i | −0.410491 | + | 0.710991i | ||||
\(47\) | 4.91770 | − | 2.83924i | 0.104632 | − | 0.0604093i | −0.446771 | − | 0.894648i | \(-0.647426\pi\) |
0.551403 | + | 0.834239i | \(0.314093\pi\) | |||||||
\(48\) | 62.5430 | + | 153.799i | 1.30298 | + | 3.20415i | ||||
\(49\) | 19.7763 | − | 44.8319i | 0.403598 | − | 0.914936i | ||||
\(50\) | − | 19.1573i | − | 0.383145i | ||||||
\(51\) | −34.5963 | − | 26.9040i | −0.678358 | − | 0.527530i | ||||
\(52\) | −20.0390 | + | 34.7085i | −0.385365 | + | 0.667472i | ||||
\(53\) | −59.9505 | − | 34.6124i | −1.13114 | − | 0.653065i | −0.186920 | − | 0.982375i | \(-0.559850\pi\) |
−0.944222 | + | 0.329310i | \(0.893184\pi\) | |||||||
\(54\) | −102.807 | + | 11.5098i | −1.90383 | + | 0.213144i | ||||
\(55\) | 24.4825 | 0.445137 | ||||||||
\(56\) | 97.8353 | + | 150.088i | 1.74706 | + | 2.68015i | ||||
\(57\) | −12.5353 | − | 30.8254i | −0.219917 | − | 0.540797i | ||||
\(58\) | 19.3049 | + | 33.4371i | 0.332844 | + | 0.576502i | ||||
\(59\) | −45.4375 | − | 26.2334i | −0.770128 | − | 0.444634i | 0.0627923 | − | 0.998027i | \(-0.479999\pi\) |
−0.832920 | + | 0.553393i | \(0.813333\pi\) | |||||||
\(60\) | −9.81075 | + | 70.9690i | −0.163513 | + | 1.18282i | ||||
\(61\) | 6.77556 | + | 11.7356i | 0.111075 | + | 0.192387i | 0.916204 | − | 0.400712i | \(-0.131237\pi\) |
−0.805129 | + | 0.593100i | \(0.797904\pi\) | |||||||
\(62\) | 92.4712i | 1.49147i | ||||||||
\(63\) | −60.1313 | + | 18.7944i | −0.954465 | + | 0.298324i | ||||
\(64\) | −198.814 | −3.10647 | ||||||||
\(65\) | −7.26688 | + | 4.19554i | −0.111798 | + | 0.0645467i | ||||
\(66\) | −124.665 | − | 17.2337i | −1.88887 | − | 0.261117i | ||||
\(67\) | −10.6264 | + | 18.4054i | −0.158603 | + | 0.274708i | −0.934365 | − | 0.356317i | \(-0.884032\pi\) |
0.775762 | + | 0.631025i | \(0.217366\pi\) | |||||||
\(68\) | 135.119 | − | 78.0108i | 1.98704 | − | 1.14722i | ||||
\(69\) | 27.3916 | − | 11.1389i | 0.396980 | − | 0.161433i | ||||
\(70\) | 3.24148 | + | 59.8841i | 0.0463069 | + | 0.855487i | ||||
\(71\) | 25.6835i | 0.361740i | 0.983507 | + | 0.180870i | \(0.0578913\pi\) | ||||
−0.983507 | + | 0.180870i | \(0.942109\pi\) | |||||||
\(72\) | 62.4925 | − | 221.710i | 0.867951 | − | 3.07930i | ||||
\(73\) | 12.4056 | − | 21.4871i | 0.169939 | − | 0.294344i | −0.768459 | − | 0.639899i | \(-0.778976\pi\) |
0.938398 | + | 0.345555i | \(0.112309\pi\) | |||||||
\(74\) | 127.347 | + | 73.5238i | 1.72090 | + | 0.993564i | ||||
\(75\) | −9.20822 | + | 11.8410i | −0.122776 | + | 0.157880i | ||||
\(76\) | 118.466 | 1.55876 | ||||||||
\(77\) | −76.5305 | + | 4.14254i | −0.993902 | + | 0.0537992i | ||||
\(78\) | 39.9564 | − | 16.2484i | 0.512261 | − | 0.208313i | ||||
\(79\) | 55.3563 | + | 95.8799i | 0.700713 | + | 1.21367i | 0.968217 | + | 0.250113i | \(0.0804679\pi\) |
−0.267504 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(80\) | −107.172 | − | 61.8755i | −1.33964 | − | 0.773444i | ||||
\(81\) | 69.0766 | + | 42.3016i | 0.852798 | + | 0.522241i | ||||
\(82\) | −129.320 | − | 223.989i | −1.57707 | − | 2.73157i | ||||
\(83\) | − | 102.155i | − | 1.23078i | −0.788222 | − | 0.615392i | \(-0.788998\pi\) | ||
0.788222 | − | 0.615392i | \(-0.211002\pi\) | |||||||
\(84\) | 18.6594 | − | 223.503i | 0.222136 | − | 2.66075i | ||||
\(85\) | 32.6661 | 0.384307 | ||||||||
\(86\) | −256.898 | + | 148.320i | −2.98718 | + | 1.72465i | ||||
\(87\) | 4.13979 | − | 29.9464i | 0.0475838 | − | 0.344212i | ||||
\(88\) | 140.115 | − | 242.686i | 1.59222 | − | 2.75780i | ||||
\(89\) | −62.5361 | + | 36.1052i | −0.702652 | + | 0.405677i | −0.808335 | − | 0.588723i | \(-0.799631\pi\) |
0.105682 | + | 0.994400i | \(0.466297\pi\) | |||||||
\(90\) | 55.2234 | − | 53.8125i | 0.613594 | − | 0.597917i | ||||
\(91\) | 22.0058 | − | 14.3445i | 0.241822 | − | 0.157632i | ||||
\(92\) | 105.269i | 1.14423i | ||||||||
\(93\) | 44.4476 | − | 57.1558i | 0.477932 | − | 0.614579i | ||||
\(94\) | 10.8784 | − | 18.8420i | 0.115728 | − | 0.200446i | ||||
\(95\) | 21.4800 | + | 12.4015i | 0.226106 | + | 0.130542i | ||||
\(96\) | 259.714 | + | 201.969i | 2.70536 | + | 2.10384i | ||||
\(97\) | −6.23399 | −0.0642680 | −0.0321340 | − | 0.999484i | \(-0.510230\pi\) | ||||
−0.0321340 | + | 0.999484i | \(0.510230\pi\) | |||||||
\(98\) | −20.2652 | − | 186.644i | −0.206788 | − | 1.90453i | ||||
\(99\) | 68.7712 | + | 70.5743i | 0.694658 | + | 0.712871i | ||||
\(100\) | −26.7001 | − | 46.2459i | −0.267001 | − | 0.462459i | ||||
\(101\) | 44.7681 | + | 25.8469i | 0.443249 | + | 0.255910i | 0.704975 | − | 0.709232i | \(-0.250958\pi\) |
−0.261726 | + | 0.965142i | \(0.584292\pi\) | |||||||
\(102\) | −166.336 | − | 22.9943i | −1.63074 | − | 0.225434i | ||||
\(103\) | 58.1765 | + | 100.765i | 0.564821 | + | 0.978298i | 0.997066 | + | 0.0765423i | \(0.0243880\pi\) |
−0.432246 | + | 0.901756i | \(0.642279\pi\) | |||||||
\(104\) | 96.0451i | 0.923511i | ||||||||
\(105\) | 26.7806 | − | 38.5720i | 0.255053 | − | 0.367352i | ||||
\(106\) | −265.232 | −2.50219 | ||||||||
\(107\) | 123.457 | − | 71.2779i | 1.15380 | − | 0.666148i | 0.203992 | − | 0.978973i | \(-0.434608\pi\) |
0.949811 | + | 0.312824i | \(0.101275\pi\) | |||||||
\(108\) | −232.136 | + | 171.070i | −2.14941 | + | 1.58398i | ||||
\(109\) | 40.3534 | − | 69.8941i | 0.370214 | − | 0.641230i | −0.619384 | − | 0.785088i | \(-0.712618\pi\) |
0.989598 | + | 0.143858i | \(0.0459509\pi\) | |||||||
\(110\) | 81.2364 | − | 46.9019i | 0.738513 | − | 0.426381i | ||||
\(111\) | −43.3720 | − | 106.656i | −0.390738 | − | 0.960862i | ||||
\(112\) | 345.479 | + | 175.284i | 3.08464 | + | 1.56504i | ||||
\(113\) | 78.3508i | 0.693370i | 0.937982 | + | 0.346685i | \(0.112693\pi\) | ||||
−0.937982 | + | 0.346685i | \(0.887307\pi\) | |||||||
\(114\) | −100.647 | − | 78.2688i | −0.882867 | − | 0.686568i | ||||
\(115\) | −11.0200 | + | 19.0872i | −0.0958263 | + | 0.165976i | ||||
\(116\) | 93.2048 | + | 53.8118i | 0.803490 | + | 0.463895i | ||||
\(117\) | −32.5068 | − | 9.16257i | −0.277836 | − | 0.0783126i | ||||
\(118\) | −201.024 | −1.70359 | ||||||||
\(119\) | −102.111 | + | 5.52722i | −0.858079 | + | 0.0464472i | ||||
\(120\) | 64.6760 | + | 159.044i | 0.538966 | + | 1.32537i | ||||
\(121\) | −0.560494 | − | 0.970804i | −0.00463218 | − | 0.00802317i | ||||
\(122\) | 44.9645 | + | 25.9603i | 0.368561 | + | 0.212789i | ||||
\(123\) | −27.7317 | + | 200.605i | −0.225461 | + | 1.63094i | ||||
\(124\) | 128.880 | + | 223.227i | 1.03936 | + | 1.80022i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −163.519 | + | 177.558i | −1.29777 | + | 1.40919i | ||||
\(127\) | −68.5186 | −0.539517 | −0.269758 | − | 0.962928i | \(-0.586944\pi\) | ||||
−0.269758 | + | 0.962928i | \(0.586944\pi\) | |||||||
\(128\) | −279.792 | + | 161.538i | −2.18588 | + | 1.26202i | ||||
\(129\) | 230.079 | + | 31.8061i | 1.78356 | + | 0.246559i | ||||
\(130\) | −16.0750 | + | 27.8427i | −0.123654 | + | 0.214175i | ||||
\(131\) | −16.0698 | + | 9.27792i | −0.122671 | + | 0.0708239i | −0.560080 | − | 0.828439i | \(-0.689229\pi\) |
0.437409 | + | 0.899263i | \(0.355896\pi\) | |||||||
\(132\) | −324.963 | + | 132.148i | −2.46184 | + | 1.00112i | ||||
\(133\) | −69.2432 | − | 35.1316i | −0.520626 | − | 0.264147i | ||||
\(134\) | 81.4290i | 0.607679i | ||||||||
\(135\) | −59.9990 | + | 6.71720i | −0.444437 | + | 0.0497570i | ||||
\(136\) | 186.950 | − | 323.806i | 1.37463 | − | 2.38093i | ||||
\(137\) | 116.043 | + | 66.9972i | 0.847027 | + | 0.489031i | 0.859646 | − | 0.510889i | \(-0.170684\pi\) |
−0.0126199 | + | 0.999920i | \(0.504017\pi\) | |||||||
\(138\) | 69.5500 | − | 89.4353i | 0.503985 | − | 0.648082i | ||||
\(139\) | 89.7025 | 0.645342 | 0.322671 | − | 0.946511i | \(-0.395419\pi\) | ||||
0.322671 | + | 0.946511i | \(0.395419\pi\) | |||||||
\(140\) | 91.2874 | + | 140.043i | 0.652053 | + | 1.00031i | ||||
\(141\) | −15.7805 | + | 6.41721i | −0.111919 | + | 0.0455122i | ||||
\(142\) | 49.2026 | + | 85.2214i | 0.346497 | + | 0.600151i | ||||
\(143\) | −35.5824 | − | 20.5435i | −0.248828 | − | 0.143661i | ||||
\(144\) | −122.679 | − | 482.744i | −0.851937 | − | 3.35239i | ||||
\(145\) | 11.2665 | + | 19.5142i | 0.0777001 | + | 0.134581i | ||||
\(146\) | − | 95.0628i | − | 0.651115i | ||||||
\(147\) | −77.1875 | + | 125.104i | −0.525085 | + | 0.851050i | ||||
\(148\) | 409.890 | 2.76953 | ||||||||
\(149\) | 100.678 | − | 58.1267i | 0.675693 | − | 0.390112i | −0.122537 | − | 0.992464i | \(-0.539103\pi\) |
0.798230 | + | 0.602352i | \(0.205770\pi\) | |||||||
\(150\) | −7.87006 | + | 56.9304i | −0.0524670 | + | 0.379536i | ||||
\(151\) | −8.06785 | + | 13.9739i | −0.0534295 | + | 0.0925425i | −0.891503 | − | 0.453015i | \(-0.850349\pi\) |
0.838074 | + | 0.545557i | \(0.183682\pi\) | |||||||
\(152\) | 245.863 | − | 141.949i | 1.61752 | − | 0.933875i | ||||
\(153\) | 91.7585 | + | 94.1643i | 0.599729 | + | 0.615453i | ||||
\(154\) | −246.003 | + | 160.357i | −1.59742 | + | 1.04128i | ||||
\(155\) | 53.9670i | 0.348174i | ||||||||
\(156\) | 73.8093 | − | 94.9124i | 0.473137 | − | 0.608413i | ||||
\(157\) | 96.1224 | − | 166.489i | 0.612245 | − | 1.06044i | −0.378617 | − | 0.925554i | \(-0.623600\pi\) |
0.990861 | − | 0.134885i | \(-0.0430666\pi\) | |||||||
\(158\) | 367.360 | + | 212.095i | 2.32506 | + | 1.34237i | ||||
\(159\) | 163.938 | + | 127.488i | 1.03106 | + | 0.801809i | ||||
\(160\) | −245.224 | −1.53265 | ||||||||
\(161\) | 31.2181 | − | 61.5298i | 0.193901 | − | 0.382173i | ||||
\(162\) | 310.244 | + | 8.03041i | 1.91509 | + | 0.0495705i | ||||
\(163\) | −138.563 | − | 239.999i | −0.850081 | − | 1.47238i | −0.881134 | − | 0.472866i | \(-0.843219\pi\) |
0.0310533 | − | 0.999518i | \(-0.490114\pi\) | |||||||
\(164\) | −624.361 | − | 360.475i | −3.80708 | − | 2.19802i | ||||
\(165\) | −72.7557 | − | 10.0577i | −0.440944 | − | 0.0609561i | ||||
\(166\) | −195.701 | − | 338.964i | −1.17892 | − | 2.04195i | ||||
\(167\) | − | 34.5337i | − | 0.206789i | −0.994640 | − | 0.103394i | \(-0.967030\pi\) | ||
0.994640 | − | 0.103394i | \(-0.0329704\pi\) | |||||||
\(168\) | −229.083 | − | 486.216i | −1.36359 | − | 2.89414i | ||||
\(169\) | −154.918 | −0.916674 | ||||||||
\(170\) | 108.390 | − | 62.5792i | 0.637591 | − | 0.368113i | ||||
\(171\) | 24.5881 | + | 96.7548i | 0.143790 | + | 0.565817i | ||||
\(172\) | −413.436 | + | 716.093i | −2.40370 | + | 4.16333i | ||||
\(173\) | −280.241 | + | 161.797i | −1.61989 | + | 0.935244i | −0.632943 | + | 0.774198i | \(0.718153\pi\) |
−0.986947 | + | 0.161046i | \(0.948513\pi\) | |||||||
\(174\) | −43.6328 | − | 107.297i | −0.250763 | − | 0.616650i | ||||
\(175\) | 1.89175 | + | 34.9488i | 0.0108100 | + | 0.199708i | ||||
\(176\) | − | 605.948i | − | 3.44289i | ||||||
\(177\) | 124.252 | + | 96.6251i | 0.701986 | + | 0.545904i | ||||
\(178\) | −138.335 | + | 239.604i | −0.777166 | + | 1.34609i | ||||
\(179\) | −5.71552 | − | 3.29986i | −0.0319303 | − | 0.0184350i | 0.483950 | − | 0.875096i | \(-0.339202\pi\) |
−0.515880 | + | 0.856661i | \(0.672535\pi\) | |||||||
\(180\) | 58.3100 | − | 206.871i | 0.323944 | − | 1.14928i | ||||
\(181\) | 225.761 | 1.24730 | 0.623649 | − | 0.781704i | \(-0.285649\pi\) | ||||
0.623649 | + | 0.781704i | \(0.285649\pi\) | |||||||
\(182\) | 45.5381 | − | 89.7541i | 0.250209 | − | 0.493154i | ||||
\(183\) | −15.3141 | − | 37.6587i | −0.0836834 | − | 0.205785i | ||||
\(184\) | 126.136 | + | 218.475i | 0.685524 | + | 1.18736i | ||||
\(185\) | 74.3207 | + | 42.9091i | 0.401733 | + | 0.231941i | ||||
\(186\) | 37.9884 | − | 274.800i | 0.204239 | − | 1.47742i | ||||
\(187\) | 79.9748 | + | 138.520i | 0.427673 | + | 0.740751i | ||||
\(188\) | − | 60.6463i | − | 0.322587i | ||||||
\(189\) | 186.415 | − | 31.1495i | 0.986325 | − | 0.164812i | ||||
\(190\) | 95.0316 | 0.500166 | ||||||||
\(191\) | 54.2635 | − | 31.3290i | 0.284102 | − | 0.164026i | −0.351177 | − | 0.936309i | \(-0.614218\pi\) |
0.635279 | + | 0.772283i | \(0.280885\pi\) | |||||||
\(192\) | 590.823 | + | 81.6754i | 3.07721 | + | 0.425393i | ||||
\(193\) | 4.92768 | − | 8.53500i | 0.0255320 | − | 0.0442228i | −0.852977 | − | 0.521948i | \(-0.825205\pi\) |
0.878509 | + | 0.477726i | \(0.158539\pi\) | |||||||
\(194\) | −20.6852 | + | 11.9426i | −0.106625 | + | 0.0615600i | ||||
\(195\) | 23.3189 | − | 9.48271i | 0.119584 | − | 0.0486293i | ||||
\(196\) | −309.053 | − | 422.318i | −1.57680 | − | 2.15468i | ||||
\(197\) | 89.3102i | 0.453351i | 0.973970 | + | 0.226676i | \(0.0727858\pi\) | ||||
−0.973970 | + | 0.226676i | \(0.927214\pi\) | |||||||
\(198\) | 363.393 | + | 102.428i | 1.83532 | + | 0.517315i | ||||
\(199\) | −51.3259 | + | 88.8991i | −0.257919 | + | 0.446729i | −0.965684 | − | 0.259719i | \(-0.916370\pi\) |
0.707765 | + | 0.706448i | \(0.249704\pi\) | |||||||
\(200\) | −110.827 | − | 63.9857i | −0.554133 | − | 0.319929i | ||||
\(201\) | 39.1400 | − | 50.3307i | 0.194727 | − | 0.250402i | ||||
\(202\) | 198.062 | 0.980507 | ||||||||
\(203\) | −38.5201 | − | 59.0934i | −0.189754 | − | 0.291101i | ||||
\(204\) | −433.585 | + | 176.319i | −2.12542 | + | 0.864310i | ||||
\(205\) | −75.4722 | − | 130.722i | −0.368157 | − | 0.637667i | ||||
\(206\) | 386.075 | + | 222.901i | 1.87415 | + | 1.08204i | ||||
\(207\) | −85.9767 | + | 21.8491i | −0.415346 | + | 0.105551i | ||||
\(208\) | 103.840 | + | 179.857i | 0.499233 | + | 0.864696i | ||||
\(209\) | 121.448i | 0.581091i | ||||||||
\(210\) | 14.9683 | − | 179.292i | 0.0712777 | − | 0.853769i | ||||
\(211\) | −236.900 | −1.12275 | −0.561374 | − | 0.827562i | \(-0.689727\pi\) | ||||
−0.561374 | + | 0.827562i | \(0.689727\pi\) | |||||||
\(212\) | −640.274 | + | 369.662i | −3.02016 | + | 1.74369i | ||||
\(213\) | 10.5511 | − | 76.3247i | 0.0495358 | − | 0.358332i | ||||
\(214\) | 273.098 | − | 473.019i | 1.27616 | − | 2.21037i | ||||
\(215\) | −149.928 | + | 86.5607i | −0.697337 | + | 0.402608i | ||||
\(216\) | −276.793 | + | 633.190i | −1.28145 | + | 2.93144i | ||||
\(217\) | −9.13141 | − | 168.696i | −0.0420802 | − | 0.777403i | ||||
\(218\) | − | 309.224i | − | 1.41846i | ||||||
\(219\) | −45.6933 | + | 58.7576i | −0.208645 | + | 0.268300i | ||||
\(220\) | 130.737 | − | 226.444i | 0.594261 | − | 1.02929i | ||||
\(221\) | −47.4761 | − | 27.4103i | −0.214824 | − | 0.124029i | ||||
\(222\) | −348.237 | − | 270.809i | −1.56864 | − | 1.21986i | ||||
\(223\) | 198.043 | 0.888084 | 0.444042 | − | 0.896006i | \(-0.353544\pi\) | ||||
0.444042 | + | 0.896006i | \(0.353544\pi\) | |||||||
\(224\) | 766.551 | − | 41.4929i | 3.42210 | − | 0.185236i | ||||
\(225\) | 32.2289 | − | 31.4054i | 0.143239 | − | 0.139580i | ||||
\(226\) | 150.099 | + | 259.979i | 0.664154 | + | 1.15035i | ||||
\(227\) | 20.9608 | + | 12.1017i | 0.0923382 | + | 0.0533115i | 0.545458 | − | 0.838138i | \(-0.316356\pi\) |
−0.453120 | + | 0.891450i | \(0.649689\pi\) | |||||||
\(228\) | −352.049 | − | 48.6672i | −1.54407 | − | 0.213453i | ||||
\(229\) | −92.0744 | − | 159.477i | −0.402071 | − | 0.696408i | 0.591904 | − | 0.806008i | \(-0.298376\pi\) |
−0.993976 | + | 0.109600i | \(0.965043\pi\) | |||||||
\(230\) | 84.4455i | 0.367154i | ||||||||
\(231\) | 229.130 | + | 19.1292i | 0.991906 | + | 0.0828103i | ||||
\(232\) | 257.916 | 1.11171 | ||||||||
\(233\) | −116.135 | + | 67.0507i | −0.498434 | + | 0.287771i | −0.728067 | − | 0.685506i | \(-0.759581\pi\) |
0.229633 | + | 0.973277i | \(0.426248\pi\) | |||||||
\(234\) | −125.415 | + | 31.8715i | −0.535961 | + | 0.136203i | ||||
\(235\) | 6.34873 | − | 10.9963i | 0.0270159 | − | 0.0467928i | ||||
\(236\) | −485.275 | + | 280.174i | −2.05625 | + | 1.18718i | ||||
\(237\) | −125.116 | − | 307.671i | −0.527915 | − | 1.29819i | ||||
\(238\) | −328.231 | + | 213.958i | −1.37912 | + | 0.898982i | ||||
\(239\) | − | 442.916i | − | 1.85321i | −0.376041 | − | 0.926603i | \(-0.622715\pi\) | ||
0.376041 | − | 0.926603i | \(-0.377285\pi\) | |||||||
\(240\) | 293.067 | + | 227.905i | 1.22111 | + | 0.949606i | ||||
\(241\) | −189.467 | + | 328.166i | −0.786168 | + | 1.36168i | 0.142130 | + | 0.989848i | \(0.454605\pi\) |
−0.928299 | + | 0.371836i | \(0.878729\pi\) | |||||||
\(242\) | −3.71959 | − | 2.14751i | −0.0153702 | − | 0.00887399i | ||||
\(243\) | −187.900 | − | 154.087i | −0.773250 | − | 0.634102i | ||||
\(244\) | 144.727 | 0.593142 | ||||||||
\(245\) | −11.8269 | − | 108.927i | −0.0482732 | − | 0.444601i | ||||
\(246\) | 292.288 | + | 718.763i | 1.18816 | + | 2.92180i | ||||
\(247\) | −20.8124 | − | 36.0481i | −0.0842606 | − | 0.145944i | ||||
\(248\) | 534.954 | + | 308.856i | 2.15707 | + | 1.24539i | ||||
\(249\) | −41.9666 | + | 303.578i | −0.168541 | + | 1.21919i | ||||
\(250\) | −21.4185 | − | 37.0979i | −0.0856739 | − | 0.148392i | ||||
\(251\) | − | 272.894i | − | 1.08723i | −0.839336 | − | 0.543614i | \(-0.817056\pi\) | ||
0.839336 | − | 0.543614i | \(-0.182944\pi\) | |||||||
\(252\) | −147.269 | + | 656.528i | −0.584401 | + | 2.60527i | ||||
\(253\) | −107.919 | −0.426559 | ||||||||
\(254\) | −227.354 | + | 131.263i | −0.895095 | + | 0.516783i | ||||
\(255\) | −97.0750 | − | 13.4196i | −0.380686 | − | 0.0526260i | ||||
\(256\) | −221.298 | + | 383.299i | −0.864445 | + | 1.49726i | ||||
\(257\) | 152.437 | − | 88.0093i | 0.593138 | − | 0.342448i | −0.173199 | − | 0.984887i | \(-0.555410\pi\) |
0.766337 | + | 0.642438i | \(0.222077\pi\) | |||||||
\(258\) | 824.364 | − | 335.231i | 3.19521 | − | 1.29935i | ||||
\(259\) | −239.581 | − | 121.555i | −0.925022 | − | 0.469324i | ||||
\(260\) | 89.6170i | 0.344681i | ||||||||
\(261\) | −24.6048 | + | 87.2923i | −0.0942712 | + | 0.334453i | ||||
\(262\) | −35.5479 | + | 61.5709i | −0.135679 | + | 0.235003i | ||||
\(263\) | −185.007 | − | 106.814i | −0.703450 | − | 0.406137i | 0.105181 | − | 0.994453i | \(-0.466458\pi\) |
−0.808631 | + | 0.588316i | \(0.799791\pi\) | |||||||
\(264\) | −516.084 | + | 663.639i | −1.95486 | + | 2.51378i | ||||
\(265\) | −154.792 | −0.584119 | ||||||||
\(266\) | −297.061 | + | 16.0797i | −1.11677 | + | 0.0604500i | ||||
\(267\) | 200.673 | − | 81.6046i | 0.751586 | − | 0.305635i | ||||
\(268\) | 113.490 | + | 196.571i | 0.423471 | + | 0.733474i | ||||
\(269\) | −121.886 | − | 70.3711i | −0.453109 | − | 0.261602i | 0.256034 | − | 0.966668i | \(-0.417584\pi\) |
−0.709142 | + | 0.705065i | \(0.750918\pi\) | |||||||
\(270\) | −186.217 | + | 137.230i | −0.689691 | + | 0.508260i | ||||
\(271\) | 59.6978 | + | 103.400i | 0.220287 | + | 0.381548i | 0.954895 | − | 0.296943i | \(-0.0959673\pi\) |
−0.734608 | + | 0.678492i | \(0.762634\pi\) | |||||||
\(272\) | − | 808.492i | − | 2.97240i | ||||||
\(273\) | −71.2883 | + | 33.5878i | −0.261129 | + | 0.123032i | ||||
\(274\) | 513.394 | 1.87370 | ||||||||
\(275\) | 47.4102 | − | 27.3723i | 0.172401 | − | 0.0995357i | ||||
\(276\) | 43.2459 | − | 312.832i | 0.156688 | − | 1.13345i | ||||
\(277\) | 68.8872 | − | 119.316i | 0.248690 | − | 0.430744i | −0.714472 | − | 0.699664i | \(-0.753333\pi\) |
0.963163 | + | 0.268920i | \(0.0866666\pi\) | |||||||
\(278\) | 297.645 | − | 171.846i | 1.07067 | − | 0.618150i | ||||
\(279\) | −155.567 | + | 151.593i | −0.557588 | + | 0.543342i | ||||
\(280\) | 357.261 | + | 181.262i | 1.27593 | + | 0.647364i | ||||
\(281\) | − | 131.474i | − | 0.467880i | −0.972251 | − | 0.233940i | \(-0.924838\pi\) | ||
0.972251 | − | 0.233940i | \(-0.0751619\pi\) | |||||||
\(282\) | −40.0683 | + | 51.5244i | −0.142086 | + | 0.182711i | ||||
\(283\) | 259.772 | − | 449.938i | 0.917922 | − | 1.58989i | 0.115355 | − | 0.993324i | \(-0.463199\pi\) |
0.802566 | − | 0.596563i | \(-0.203467\pi\) | |||||||
\(284\) | 237.552 | + | 137.151i | 0.836450 | + | 0.482925i | ||||
\(285\) | −58.7383 | − | 45.6783i | −0.206099 | − | 0.160275i | ||||
\(286\) | −157.423 | −0.550429 | ||||||||
\(287\) | 258.039 | + | 395.855i | 0.899089 | + | 1.37929i | ||||
\(288\) | −688.832 | − | 706.893i | −2.39178 | − | 2.45449i | ||||
\(289\) | −37.7929 | − | 65.4592i | −0.130771 | − | 0.226503i | ||||
\(290\) | 74.7677 | + | 43.1671i | 0.257820 | + | 0.148852i | ||||
\(291\) | 18.5258 | + | 2.56101i | 0.0636625 | + | 0.00880071i | ||||
\(292\) | −132.492 | − | 229.483i | −0.453740 | − | 0.785901i | ||||
\(293\) | 351.830i | 1.20078i | 0.799706 | + | 0.600392i | \(0.204989\pi\) | ||||
−0.799706 | + | 0.600392i | \(0.795011\pi\) | |||||||
\(294\) | −16.4530 | + | 562.983i | −0.0559625 | + | 1.91491i | ||||
\(295\) | −117.319 | −0.397692 | ||||||||
\(296\) | 850.683 | − | 491.142i | 2.87393 | − | 1.65926i | ||||
\(297\) | −175.377 | − | 237.980i | −0.590495 | − | 0.801281i | ||||
\(298\) | 222.710 | − | 385.744i | 0.747348 | − | 1.29444i | ||||
\(299\) | 32.0325 | − | 18.4940i | 0.107132 | − | 0.0618527i | ||||
\(300\) | 60.3473 | + | 148.400i | 0.201158 | + | 0.494665i | ||||
\(301\) | 454.015 | − | 295.950i | 1.50835 | − | 0.983223i | ||||
\(302\) | 61.8232i | 0.204713i | ||||||||
\(303\) | −122.421 | − | 95.2016i | −0.404030 | − | 0.314197i | ||||
\(304\) | 306.940 | − | 531.635i | 1.00967 | − | 1.74880i | ||||
\(305\) | 26.2416 | + | 15.1506i | 0.0860381 | + | 0.0496741i | ||||
\(306\) | 484.861 | + | 136.666i | 1.58451 | + | 0.446621i | ||||
\(307\) | −390.275 | −1.27126 | −0.635628 | − | 0.771996i | \(-0.719259\pi\) | ||||
−0.635628 | + | 0.771996i | \(0.719259\pi\) | |||||||
\(308\) | −370.359 | + | 729.966i | −1.20246 | + | 2.37002i | ||||
\(309\) | −131.490 | − | 323.346i | −0.425534 | − | 1.04643i | ||||
\(310\) | 103.386 | + | 179.070i | 0.333503 | + | 0.577644i | ||||
\(311\) | 62.8518 | + | 36.2875i | 0.202096 | + | 0.116680i | 0.597633 | − | 0.801770i | \(-0.296108\pi\) |
−0.395537 | + | 0.918450i | \(0.629441\pi\) | |||||||
\(312\) | 39.4566 | − | 285.421i | 0.126463 | − | 0.914811i | ||||
\(313\) | 247.662 | + | 428.963i | 0.791253 | + | 1.37049i | 0.925192 | + | 0.379500i | \(0.123904\pi\) |
−0.133939 | + | 0.990990i | \(0.542763\pi\) | |||||||
\(314\) | − | 736.577i | − | 2.34579i | ||||||
\(315\) | −95.4309 | + | 103.624i | −0.302955 | + | 0.328965i | ||||
\(316\) | 1182.42 | 3.74182 | ||||||||
\(317\) | 310.675 | − | 179.369i | 0.980048 | − | 0.565831i | 0.0777637 | − | 0.996972i | \(-0.475222\pi\) |
0.902285 | + | 0.431141i | \(0.141889\pi\) | |||||||
\(318\) | 788.200 | + | 108.961i | 2.47862 | + | 0.342644i | ||||
\(319\) | −55.1666 | + | 95.5513i | −0.172936 | + | 0.299534i | ||||
\(320\) | −385.002 | + | 222.281i | −1.20313 | + | 0.694628i | ||||
\(321\) | −396.163 | + | 161.102i | −1.23415 | + | 0.501874i | ||||
\(322\) | −14.2885 | − | 263.970i | −0.0443742 | − | 0.819782i | ||||
\(323\) | 162.043i | 0.501682i | ||||||||
\(324\) | 760.126 | − | 413.011i | 2.34607 | − | 1.27473i | ||||
\(325\) | −9.38150 | + | 16.2492i | −0.0288662 | + | 0.0499977i | ||||
\(326\) | −919.543 | − | 530.899i | −2.82069 | − | 1.62852i | ||||
\(327\) | −148.633 | + | 191.129i | −0.454535 | + | 0.584493i | ||||
\(328\) | −1727.73 | −5.26746 | ||||||||
\(329\) | −17.9850 | + | 35.4478i | −0.0546656 | + | 0.107744i | ||||
\(330\) | −260.681 | + | 106.007i | −0.789944 | + | 0.321234i | ||||
\(331\) | 157.641 | + | 273.042i | 0.476256 | + | 0.824899i | 0.999630 | − | 0.0272038i | \(-0.00866031\pi\) |
−0.523374 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(332\) | −944.851 | − | 545.510i | −2.84594 | − | 1.64310i | ||||
\(333\) | 85.0746 | + | 334.770i | 0.255479 | + | 1.00532i | ||||
\(334\) | −66.1572 | − | 114.588i | −0.198076 | − | 0.343077i | ||||
\(335\) | 47.5227i | 0.141859i | ||||||||
\(336\) | −954.665 | − | 662.826i | −2.84127 | − | 1.97270i | ||||
\(337\) | 104.826 | 0.311058 | 0.155529 | − | 0.987831i | \(-0.450292\pi\) | ||||
0.155529 | + | 0.987831i | \(0.450292\pi\) | |||||||
\(338\) | −514.039 | + | 296.781i | −1.52083 | + | 0.878049i | ||||
\(339\) | 32.1875 | − | 232.838i | 0.0949485 | − | 0.686838i | ||||
\(340\) | 174.437 | − | 302.135i | 0.513051 | − | 0.888631i | ||||
\(341\) | −228.847 | + | 132.125i | −0.671106 | + | 0.387463i | ||||
\(342\) | 266.942 | + | 273.941i | 0.780533 | + | 0.800998i | ||||
\(343\) | 55.4009 | + | 338.496i | 0.161519 | + | 0.986870i | ||||
\(344\) | 1981.57i | 5.76037i | ||||||||
\(345\) | 40.5899 | − | 52.1951i | 0.117652 | − | 0.151290i | ||||
\(346\) | −619.919 | + | 1073.73i | −1.79167 | + | 3.10327i | ||||
\(347\) | 377.205 | + | 217.779i | 1.08705 | + | 0.627606i | 0.932788 | − | 0.360424i | \(-0.117368\pi\) |
0.154258 | + | 0.988031i | \(0.450701\pi\) | |||||||
\(348\) | −254.874 | − | 198.204i | −0.732396 | − | 0.569553i | ||||
\(349\) | −372.478 | −1.06727 | −0.533636 | − | 0.845715i | \(-0.679175\pi\) | ||||
−0.533636 | + | 0.845715i | \(0.679175\pi\) | |||||||
\(350\) | 73.2295 | + | 112.341i | 0.209227 | + | 0.320974i | ||||
\(351\) | 92.8376 | + | 40.5830i | 0.264494 | + | 0.115621i | ||||
\(352\) | −600.372 | − | 1039.87i | −1.70560 | − | 2.95419i | ||||
\(353\) | −44.5982 | − | 25.7488i | −0.126341 | − | 0.0729428i | 0.435498 | − | 0.900190i | \(-0.356572\pi\) |
−0.561838 | + | 0.827247i | \(0.689906\pi\) | |||||||
\(354\) | 597.391 | + | 82.5833i | 1.68754 | + | 0.233286i | ||||
\(355\) | 28.7151 | + | 49.7359i | 0.0808875 | + | 0.140101i | ||||
\(356\) | 771.211i | 2.16632i | ||||||||
\(357\) | 305.719 | + | 25.5233i | 0.856356 | + | 0.0714937i | ||||
\(358\) | −25.2865 | −0.0706327 | ||||||||
\(359\) | −321.578 | + | 185.663i | −0.895759 | + | 0.517167i | −0.875822 | − | 0.482634i | \(-0.839680\pi\) |
−0.0199374 | + | 0.999801i | \(0.506347\pi\) | |||||||
\(360\) | −126.863 | − | 499.208i | −0.352396 | − | 1.38669i | ||||
\(361\) | 118.981 | − | 206.081i | 0.329588 | − | 0.570862i | ||||
\(362\) | 749.106 | − | 432.497i | 2.06935 | − | 1.19474i | ||||
\(363\) | 1.26682 | + | 3.11523i | 0.00348987 | + | 0.00858191i | ||||
\(364\) | −15.1635 | − | 280.136i | −0.0416580 | − | 0.769603i | ||||
\(365\) | − | 55.4794i | − | 0.151998i | ||||||
\(366\) | −122.958 | − | 95.6191i | −0.335951 | − | 0.261254i | ||||
\(367\) | −166.498 | + | 288.383i | −0.453672 | + | 0.785784i | −0.998611 | − | 0.0526924i | \(-0.983220\pi\) |
0.544938 | + | 0.838476i | \(0.316553\pi\) | |||||||
\(368\) | 472.413 | + | 272.748i | 1.28373 | + | 0.741163i | ||||
\(369\) | 164.823 | − | 584.754i | 0.446674 | − | 1.58470i | ||||
\(370\) | 328.808 | 0.888671 | ||||||||
\(371\) | 483.866 | − | 26.1913i | 1.30422 | − | 0.0705965i | ||||
\(372\) | −291.294 | − | 716.318i | −0.783047 | − | 1.92559i | ||||
\(373\) | 21.0920 | + | 36.5325i | 0.0565470 | + | 0.0979423i | 0.892913 | − | 0.450229i | \(-0.148658\pi\) |
−0.836366 | + | 0.548171i | \(0.815324\pi\) | |||||||
\(374\) | 530.735 | + | 306.420i | 1.41908 | + | 0.819304i | ||||
\(375\) | −4.59303 | + | 33.2251i | −0.0122481 | + | 0.0886001i | ||||
\(376\) | −72.6682 | − | 125.865i | −0.193267 | − | 0.334748i | ||||
\(377\) | − | 37.8153i | − | 0.100306i | ||||||
\(378\) | 558.878 | − | 460.479i | 1.47851 | − | 1.21820i | ||||
\(379\) | −404.220 | −1.06654 | −0.533272 | − | 0.845944i | \(-0.679038\pi\) | ||||
−0.533272 | + | 0.845944i | \(0.679038\pi\) | |||||||
\(380\) | 229.408 | − | 132.449i | 0.603704 | − | 0.348549i | ||||
\(381\) | 203.619 | + | 28.1483i | 0.534434 | + | 0.0738802i | ||||
\(382\) | 120.036 | − | 207.908i | 0.314230 | − | 0.544262i | ||||
\(383\) | 338.568 | − | 195.472i | 0.883989 | − | 0.510371i | 0.0120171 | − | 0.999928i | \(-0.496175\pi\) |
0.871971 | + | 0.489557i | \(0.162841\pi\) | |||||||
\(384\) | 897.831 | − | 365.107i | 2.33810 | − | 0.950799i | ||||
\(385\) | −143.569 | + | 93.5856i | −0.372907 | + | 0.243080i | ||||
\(386\) | − | 37.7604i | − | 0.0978249i | ||||||
\(387\) | −670.667 | − | 189.039i | −1.73299 | − | 0.488472i | ||||
\(388\) | −33.2897 | + | 57.6594i | −0.0857981 | + | 0.148607i | ||||
\(389\) | −327.986 | − | 189.363i | −0.843152 | − | 0.486794i | 0.0151826 | − | 0.999885i | \(-0.495167\pi\) |
−0.858334 | + | 0.513091i | \(0.828500\pi\) | |||||||
\(390\) | 59.2089 | − | 76.1375i | 0.151818 | − | 0.195224i | ||||
\(391\) | −143.992 | −0.368267 | ||||||||
\(392\) | −1147.44 | − | 506.160i | −2.92714 | − | 1.29122i | ||||
\(393\) | 51.5669 | − | 20.9699i | 0.131213 | − | 0.0533585i | ||||
\(394\) | 171.094 | + | 296.344i | 0.434249 | + | 0.752141i | ||||
\(395\) | 214.394 | + | 123.780i | 0.542770 | + | 0.313368i | ||||
\(396\) | 1019.99 | − | 259.209i | 2.57574 | − | 0.654569i | ||||
\(397\) | 127.529 | + | 220.886i | 0.321231 | + | 0.556388i | 0.980742 | − | 0.195306i | \(-0.0625701\pi\) |
−0.659511 | + | 0.751695i | \(0.729237\pi\) | |||||||
\(398\) | 393.306i | 0.988206i | ||||||||
\(399\) | 191.340 | + | 132.848i | 0.479549 | + | 0.332952i | ||||
\(400\) | −276.716 | −0.691789 | ||||||||
\(401\) | −185.343 | + | 107.008i | −0.462203 | + | 0.266853i | −0.712970 | − | 0.701194i | \(-0.752651\pi\) |
0.250767 | + | 0.968047i | \(0.419317\pi\) | |||||||
\(402\) | 33.4521 | − | 241.986i | 0.0832142 | − | 0.601955i | ||||
\(403\) | 45.2841 | − | 78.4343i | 0.112367 | − | 0.194626i | ||||
\(404\) | 478.126 | − | 276.046i | 1.18348 | − | 0.683282i | ||||
\(405\) | 181.061 | + | 4.68661i | 0.447064 | + | 0.0115719i | ||||
\(406\) | −241.022 | − | 122.286i | −0.593650 | − | 0.301197i | ||||
\(407\) | 420.209i | 1.03246i | ||||||||
\(408\) | −688.589 | + | 885.466i | −1.68772 | + | 2.17026i | ||||
\(409\) | −170.178 | + | 294.757i | −0.416083 | + | 0.720678i | −0.995542 | − | 0.0943244i | \(-0.969931\pi\) |
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(410\) | −500.854 | − | 289.168i | −1.22160 | − | 0.705288i | ||||
\(411\) | −317.325 | − | 246.770i | −0.772080 | − | 0.600414i | ||||
\(412\) | 1242.66 | 3.01616 | ||||||||
\(413\) | 366.730 | − | 19.8508i | 0.887967 | − | 0.0480650i | ||||
\(414\) | −243.426 | + | 237.206i | −0.587984 | + | 0.572962i | ||||
\(415\) | −114.213 | − | 197.822i | −0.275211 | − | 0.476680i | ||||
\(416\) | 356.403 | + | 205.770i | 0.856739 | + | 0.494638i | ||||
\(417\) | −266.573 | − | 36.8510i | −0.639263 | − | 0.0883716i | ||||
\(418\) | 232.661 | + | 402.981i | 0.556606 | + | 0.964071i | ||||
\(419\) | − | 586.646i | − | 1.40011i | −0.714088 | − | 0.700055i | \(-0.753159\pi\) | ||
0.714088 | − | 0.700055i | \(-0.246841\pi\) | |||||||
\(420\) | −213.751 | − | 453.674i | −0.508930 | − | 1.08018i | ||||
\(421\) | −216.123 | −0.513357 | −0.256678 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256678 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(422\) | −786.066 | + | 453.835i | −1.86271 | + | 1.07544i | ||||
\(423\) | 49.5319 | − | 12.5874i | 0.117097 | − | 0.0297575i | ||||
\(424\) | −885.881 | + | 1534.39i | −2.08934 | + | 3.61884i | ||||
\(425\) | 63.2575 | − | 36.5218i | 0.148841 | − | 0.0859335i | ||||
\(426\) | −111.207 | − | 273.469i | −0.261050 | − | 0.641946i | ||||
\(427\) | −84.5928 | − | 42.9194i | −0.198110 | − | 0.100514i | ||||
\(428\) | − | 1522.50i | − | 3.55725i | ||||||
\(429\) | 97.3019 | + | 75.6676i | 0.226811 | + | 0.176381i | ||||
\(430\) | −331.653 | + | 574.440i | −0.771287 | + | 1.33591i | ||||
\(431\) | 286.275 | + | 165.281i | 0.664211 | + | 0.383483i | 0.793880 | − | 0.608075i | \(-0.208058\pi\) |
−0.129668 | + | 0.991557i | \(0.541391\pi\) | |||||||
\(432\) | 166.252 | + | 1484.99i | 0.384843 | + | 3.43747i | ||||
\(433\) | 825.106 | 1.90556 | 0.952778 | − | 0.303668i | \(-0.0982112\pi\) | ||||
0.952778 | + | 0.303668i | \(0.0982112\pi\) | |||||||
\(434\) | −353.475 | − | 542.264i | −0.814460 | − | 1.24946i | ||||
\(435\) | −25.4645 | − | 62.6195i | −0.0585390 | − | 0.143953i | ||||
\(436\) | −430.976 | − | 746.472i | −0.988477 | − | 1.71209i | ||||
\(437\) | −94.6842 | − | 54.6659i | −0.216669 | − | 0.125094i | ||||
\(438\) | −39.0530 | + | 282.502i | −0.0891622 | + | 0.644981i | ||||
\(439\) | 363.096 | + | 628.901i | 0.827099 | + | 1.43258i | 0.900305 | + | 0.435260i | \(0.143344\pi\) |
−0.0732063 | + | 0.997317i | \(0.523323\pi\) | |||||||
\(440\) | − | 626.613i | − | 1.42412i | ||||||
\(441\) | 280.776 | − | 340.068i | 0.636679 | − | 0.771129i | ||||
\(442\) | −210.043 | −0.475210 | ||||||||
\(443\) | 620.467 | − | 358.227i | 1.40060 | − | 0.808638i | 0.406148 | − | 0.913807i | \(-0.366872\pi\) |
0.994454 | + | 0.105169i | \(0.0335383\pi\) | |||||||
\(444\) | −1218.09 | − | 168.388i | −2.74344 | − | 0.379252i | ||||
\(445\) | −80.7337 | + | 139.835i | −0.181424 | + | 0.314236i | ||||
\(446\) | 657.133 | − | 379.396i | 1.47339 | − | 0.850664i | ||||
\(447\) | −323.069 | + | 131.377i | −0.722749 | + | 0.293909i | ||||
\(448\) | 1165.87 | − | 759.976i | 2.60240 | − | 1.69637i | ||||
\(449\) | 564.847i | 1.25801i | 0.777401 | + | 0.629006i | \(0.216538\pi\) | ||||
−0.777401 | + | 0.629006i | \(0.783462\pi\) | |||||||
\(450\) | 46.7755 | − | 165.949i | 0.103946 | − | 0.368776i | ||||
\(451\) | 369.550 | − | 640.080i | 0.819402 | − | 1.41925i | ||||
\(452\) | 724.681 | + | 418.395i | 1.60328 | + | 0.925653i | ||||
\(453\) | 29.7162 | − | 38.2125i | 0.0655987 | − | 0.0843542i | ||||
\(454\) | 92.7343 | 0.204261 | ||||||||
\(455\) | 26.5764 | − | 52.3812i | 0.0584096 | − | 0.115124i | ||||
\(456\) | −788.955 | + | 320.832i | −1.73016 | + | 0.703578i | ||||
\(457\) | 426.738 | + | 739.133i | 0.933782 | + | 1.61736i | 0.776792 | + | 0.629758i | \(0.216846\pi\) |
0.156990 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(458\) | −611.031 | − | 352.779i | −1.33413 | − | 0.770259i | ||||
\(459\) | −233.998 | − | 317.527i | −0.509800 | − | 0.691781i | ||||
\(460\) | 117.694 | + | 203.853i | 0.255857 | + | 0.443158i | ||||
\(461\) | 891.718i | 1.93431i | 0.254185 | + | 0.967156i | \(0.418193\pi\) | ||||
−0.254185 | + | 0.967156i | \(0.581807\pi\) | |||||||
\(462\) | 796.932 | − | 375.478i | 1.72496 | − | 0.812723i | ||||
\(463\) | 750.155 | 1.62021 | 0.810103 | − | 0.586287i | \(-0.199411\pi\) | ||||
0.810103 | + | 0.586287i | \(0.199411\pi\) | |||||||
\(464\) | 482.980 | − | 278.849i | 1.04091 | − | 0.600967i | ||||
\(465\) | 22.1703 | − | 160.376i | 0.0476781 | − | 0.344894i | ||||
\(466\) | −256.902 | + | 444.967i | −0.551291 | + | 0.954864i | ||||
\(467\) | 84.6817 | − | 48.8910i | 0.181331 | − | 0.104692i | −0.406587 | − | 0.913612i | \(-0.633281\pi\) |
0.587918 | + | 0.808921i | \(0.299948\pi\) | |||||||
\(468\) | −258.333 | + | 251.733i | −0.551994 | + | 0.537891i | ||||
\(469\) | −8.04101 | − | 148.552i | −0.0171450 | − | 0.316742i | ||||
\(470\) | − | 48.6497i | − | 0.103510i | ||||||
\(471\) | −354.046 | + | 455.273i | −0.751691 | + | 0.966610i | ||||
\(472\) | −671.425 | + | 1162.94i | −1.42251 | + | 2.46386i | ||||
\(473\) | −734.121 | − | 423.845i | −1.55205 | − | 0.896079i | ||||
\(474\) | −1004.57 | − | 781.208i | −2.11934 | − | 1.64812i | ||||
\(475\) | 55.4612 | 0.116760 | ||||||||
\(476\) | −494.155 | + | 973.963i | −1.03814 | + | 2.04614i | ||||
\(477\) | −434.807 | − | 446.208i | −0.911546 | − | 0.935446i | ||||
\(478\) | −848.507 | − | 1469.66i | −1.77512 | − | 3.07460i | ||||
\(479\) | 0.948693 | + | 0.547728i | 0.00198057 | + | 0.00114348i | 0.500990 | − | 0.865453i | \(-0.332969\pi\) |
−0.499009 | + | 0.866597i | \(0.666303\pi\) | |||||||
\(480\) | 728.743 | + | 100.741i | 1.51821 | + | 0.209878i | ||||
\(481\) | −72.0106 | − | 124.726i | −0.149710 | − | 0.259306i | ||||
\(482\) | 1451.87i | 3.01217i | ||||||||
\(483\) | −118.049 | + | 170.026i | −0.244408 | + | 0.352020i | ||||
\(484\) | −11.9722 | −0.0247359 | ||||||||
\(485\) | −12.0721 | + | 6.96982i | −0.0248909 | + | 0.0143708i | ||||
\(486\) | −918.665 | − | 151.317i | −1.89026 | − | 0.311351i | ||||
\(487\) | 393.745 | − | 681.987i | 0.808512 | − | 1.40038i | −0.105383 | − | 0.994432i | \(-0.533607\pi\) |
0.913895 | − | 0.405952i | \(-0.133060\pi\) | |||||||
\(488\) | 300.365 | − | 173.416i | 0.615501 | − | 0.355360i | ||||
\(489\) | 313.179 | + | 770.137i | 0.640448 | + | 1.57492i | ||||
\(490\) | −247.918 | − | 338.778i | −0.505955 | − | 0.691384i | ||||
\(491\) | − | 294.128i | − | 0.599039i | −0.954090 | − | 0.299520i | \(-0.903174\pi\) | ||
0.954090 | − | 0.299520i | \(-0.0968264\pi\) | |||||||
\(492\) | 1707.35 | + | 1327.73i | 3.47022 | + | 2.69864i | ||||
\(493\) | −73.6065 | + | 127.490i | −0.149303 | + | 0.258601i | ||||
\(494\) | −138.117 | − | 79.7417i | −0.279588 | − | 0.161420i | ||||
\(495\) | 212.079 | + | 59.7780i | 0.428443 | + | 0.120764i | ||||
\(496\) | 1335.69 | 2.69293 | ||||||||
\(497\) | −98.1764 | − | 150.612i | −0.197538 | − | 0.303042i | ||||
\(498\) | 442.322 | + | 1087.71i | 0.888196 | + | 2.18416i | ||||
\(499\) | −248.981 | − | 431.248i | −0.498960 | − | 0.864225i | 0.501039 | − | 0.865425i | \(-0.332951\pi\) |
−0.999999 | + | 0.00119993i | \(0.999618\pi\) | |||||||
\(500\) | −103.409 | − | 59.7033i | −0.206818 | − | 0.119407i | ||||
\(501\) | −14.1869 | + | 102.625i | −0.0283172 | + | 0.204841i | ||||
\(502\) | −522.791 | − | 905.500i | −1.04142 | − | 1.80378i | ||||
\(503\) | 524.122i | 1.04199i | 0.853559 | + | 0.520996i | \(0.174439\pi\) | ||||
−0.853559 | + | 0.520996i | \(0.825561\pi\) | |||||||
\(504\) | 481.030 | + | 1539.02i | 0.954425 | + | 3.05360i | ||||
\(505\) | 115.591 | 0.228893 | ||||||||
\(506\) | −358.091 | + | 206.744i | −0.707690 | + | 0.408585i | ||||
\(507\) | 460.376 | + | 63.6423i | 0.908039 | + | 0.125527i | ||||
\(508\) | −365.891 | + | 633.742i | −0.720258 | + | 1.24752i | ||||
\(509\) | 19.3736 | − | 11.1854i | 0.0380621 | − | 0.0219752i | −0.480848 | − | 0.876804i | \(-0.659671\pi\) |
0.518910 | + | 0.854829i | \(0.326338\pi\) | |||||||
\(510\) | −347.816 | + | 141.441i | −0.681993 | + | 0.277335i | ||||
\(511\) | 9.38732 | + | 173.424i | 0.0183705 | + | 0.339382i | ||||
\(512\) | 403.481i | 0.788049i | ||||||||
\(513\) | −33.3213 | − | 297.631i | −0.0649538 | − | 0.580177i | ||||
\(514\) | 337.203 | − | 584.054i | 0.656038 | − | 1.13629i | ||||
\(515\) | 225.317 | + | 130.087i | 0.437508 | + | 0.252596i | ||||
\(516\) | 1522.81 | − | 1958.20i | 2.95117 | − | 3.79495i | ||||
\(517\) | 62.1732 | 0.120258 | ||||||||
\(518\) | −1027.83 | + | 55.6356i | −1.98422 | + | 0.107405i | ||||
\(519\) | 899.272 | − | 365.692i | 1.73270 | − | 0.704610i | ||||
\(520\) | 107.382 | + | 185.991i | 0.206503 | + | 0.357674i | ||||
\(521\) | −692.733 | − | 399.950i | −1.32962 | − | 0.767658i | −0.344382 | − | 0.938830i | \(-0.611911\pi\) |
−0.985241 | + | 0.171172i | \(0.945245\pi\) | |||||||
\(522\) | 85.5863 | + | 336.784i | 0.163958 | + | 0.645180i | ||||
\(523\) | 205.763 | + | 356.392i | 0.393429 | + | 0.681439i | 0.992899 | − | 0.118958i | \(-0.0379554\pi\) |
−0.599470 | + | 0.800397i | \(0.704622\pi\) | |||||||
\(524\) | 198.177i | 0.378201i | ||||||||
\(525\) | 8.73564 | − | 104.636i | 0.0166393 | − | 0.199307i | ||||
\(526\) | −818.506 | −1.55610 | ||||||||
\(527\) | −305.341 | + | 176.289i | −0.579395 | + | 0.334514i | ||||
\(528\) | −248.931 | + | 1800.72i | −0.471461 | + | 3.41045i | ||||
\(529\) | −215.924 | + | 373.991i | −0.408173 | + | 0.706977i | ||||
\(530\) | −513.619 | + | 296.538i | −0.969093 | + | 0.559506i | ||||
\(531\) | −329.548 | − | 338.189i | −0.620618 | − | 0.636890i | ||||
\(532\) | −694.699 | + | 452.840i | −1.30583 | + | 0.851203i | ||||
\(533\) | 253.317i | 0.475267i | ||||||||
\(534\) | 509.529 | − | 655.211i | 0.954175 | − | 1.22699i | ||||
\(535\) | 159.382 | − | 276.058i | 0.297911 | − | 0.515996i | ||||
\(536\) | 471.074 | + | 271.975i | 0.878870 | + | 0.507416i | ||||
\(537\) | 15.6294 | + | 12.1543i | 0.0291051 | + | 0.0226338i | ||||
\(538\) | −539.247 | −1.00232 | ||||||||
\(539\) | 432.950 | − | 316.834i | 0.803247 | − | 0.587817i | ||||
\(540\) | −258.267 | + | 590.812i | −0.478273 | + | 1.09410i | ||||
\(541\) | 325.969 | + | 564.595i | 0.602530 | + | 1.04361i | 0.992437 | + | 0.122759i | \(0.0391741\pi\) |
−0.389906 | + | 0.920855i | \(0.627493\pi\) | |||||||
\(542\) | 396.171 | + | 228.729i | 0.730943 | + | 0.422010i | ||||
\(543\) | −670.903 | − | 92.7456i | −1.23555 | − | 0.170802i | ||||
\(544\) | −801.051 | − | 1387.46i | −1.47252 | − | 2.55048i | ||||
\(545\) | − | 180.466i | − | 0.331130i | ||||||
\(546\) | −172.199 | + | 248.018i | −0.315384 | + | 0.454245i | ||||
\(547\) | −85.9480 | −0.157126 | −0.0785631 | − | 0.996909i | \(-0.525033\pi\) | ||||
−0.0785631 | + | 0.996909i | \(0.525033\pi\) | |||||||
\(548\) | 1239.34 | − | 715.534i | 2.26157 | − | 1.30572i | ||||
\(549\) | 30.0387 | + | 118.203i | 0.0547153 | + | 0.215306i | ||||
\(550\) | 104.876 | − | 181.650i | 0.190683 | − | 0.330273i | ||||
\(551\) | −96.8020 | + | 55.8887i | −0.175684 | + | 0.101431i | ||||
\(552\) | −285.092 | − | 701.068i | −0.516472 | − | 1.27005i | ||||
\(553\) | −691.123 | − | 350.651i | −1.24977 | − | 0.634090i | ||||
\(554\) | − | 527.876i | − | 0.952845i | ||||||
\(555\) | −203.234 | − | 158.046i | −0.366187 | − | 0.284768i | ||||
\(556\) | 479.013 | − | 829.676i | 0.861535 | − | 1.49222i | ||||
\(557\) | −858.157 | − | 495.457i | −1.54068 | − | 0.889510i | −0.998796 | − | 0.0490540i | \(-0.984379\pi\) |
−0.541880 | − | 0.840456i | \(-0.682287\pi\) | |||||||
\(558\) | −225.783 | + | 801.029i | −0.404629 | + | 1.43554i | ||||
\(559\) | 290.535 | 0.519740 | ||||||||
\(560\) | 864.991 | − | 46.8213i | 1.54463 | − | 0.0836095i | ||||
\(561\) | −180.758 | − | 444.501i | −0.322207 | − | 0.792337i | ||||
\(562\) | −251.869 | − | 436.249i | −0.448165 | − | 0.776245i | ||||
\(563\) | −208.613 | − | 120.443i | −0.370539 | − | 0.213931i | 0.303155 | − | 0.952941i | \(-0.401960\pi\) |
−0.673694 | + | 0.739011i | \(0.735293\pi\) | |||||||
\(564\) | −24.9143 | + | 180.225i | −0.0441743 | + | 0.319548i | ||||
\(565\) | 87.5989 | + | 151.726i | 0.155042 | + | 0.268541i | ||||
\(566\) | − | 1990.61i | − | 3.51698i | ||||||
\(567\) | −566.775 | + | 15.9862i | −0.999602 | + | 0.0281943i | ||||
\(568\) | 657.351 | 1.15731 | ||||||||
\(569\) | −100.616 | + | 58.0909i | −0.176830 | + | 0.102093i | −0.585803 | − | 0.810454i | \(-0.699221\pi\) |
0.408972 | + | 0.912547i | \(0.365887\pi\) | |||||||
\(570\) | −282.409 | − | 39.0402i | −0.495454 | − | 0.0684916i | ||||
\(571\) | 519.274 | − | 899.409i | 0.909412 | − | 1.57515i | 0.0945293 | − | 0.995522i | \(-0.469865\pi\) |
0.814883 | − | 0.579626i | \(-0.196801\pi\) | |||||||
\(572\) | −380.021 | + | 219.405i | −0.664373 | + | 0.383576i | ||||
\(573\) | −174.127 | + | 70.8096i | −0.303887 | + | 0.123577i | ||||
\(574\) | 1614.56 | + | 819.170i | 2.81282 | + | 1.42713i | ||||
\(575\) | 49.2831i | 0.0857097i | ||||||||
\(576\) | −1722.22 | − | 485.436i | −2.98996 | − | 0.842771i | ||||
\(577\) | 37.6724 | − | 65.2504i | 0.0652901 | − | 0.113086i | −0.831533 | − | 0.555476i | \(-0.812536\pi\) |
0.896823 | + | 0.442390i | \(0.145869\pi\) | |||||||
\(578\) | −250.804 | − | 144.802i | −0.433917 | − | 0.250522i | ||||
\(579\) | −18.1501 | + | 23.3394i | −0.0313473 | + | 0.0403099i | ||||
\(580\) | 240.654 | 0.414920 | ||||||||
\(581\) | 390.492 | + | 599.051i | 0.672103 | + | 1.03107i | ||||
\(582\) | 66.3773 | − | 26.9926i | 0.114050 | − | 0.0463791i | ||||
\(583\) | −378.969 | − | 656.394i | −0.650033 | − | 1.12589i | ||||
\(584\) | −549.947 | − | 317.512i | −0.941689 | − | 0.543685i | ||||
\(585\) | −73.1932 | + | 18.6004i | −0.125117 | + | 0.0317956i | ||||
\(586\) | 674.009 | + | 1167.42i | 1.15019 | + | 1.99218i | ||||
\(587\) | − | 34.4849i | − | 0.0587477i | −0.999568 | − | 0.0293739i | \(-0.990649\pi\) | ||
0.999568 | − | 0.0293739i | \(-0.00935134\pi\) | |||||||
\(588\) | 744.930 | + | 1381.98i | 1.26689 | + | 2.35031i | ||||
\(589\) | −267.709 | −0.454514 | ||||||||
\(590\) | −389.281 | + | 224.752i | −0.659799 | + | 0.380935i | ||||
\(591\) | 36.6898 | − | 265.407i | 0.0620809 | − | 0.449081i | ||||
\(592\) | 1062.01 | − | 1839.45i | 1.79393 | − | 3.10718i | ||||
\(593\) | 179.738 | − | 103.772i | 0.303099 | − | 0.174994i | −0.340735 | − | 0.940159i | \(-0.610676\pi\) |
0.643834 | + | 0.765165i | \(0.277343\pi\) | |||||||
\(594\) | −1037.83 | − | 453.677i | −1.74719 | − | 0.763766i | ||||
\(595\) | −191.558 | + | 124.867i | −0.321947 | + | 0.209861i | ||||
\(596\) | − | 1241.59i | − | 2.08321i | ||||||
\(597\) | 189.048 | − | 243.100i | 0.316664 | − | 0.407202i | ||||
\(598\) | 70.8588 | − | 122.731i | 0.118493 | − | 0.205236i | ||||
\(599\) | 99.0015 | + | 57.1586i | 0.165278 | + | 0.0954233i | 0.580357 | − | 0.814362i | \(-0.302913\pi\) |
−0.415079 | + | 0.909785i | \(0.636246\pi\) | |||||||
\(600\) | 303.061 | + | 235.678i | 0.505102 | + | 0.392796i | ||||
\(601\) | −705.812 | −1.17440 | −0.587198 | − | 0.809444i | \(-0.699769\pi\) | ||||
−0.587198 | + | 0.809444i | \(0.699769\pi\) | |||||||
\(602\) | 939.524 | − | 1851.77i | 1.56067 | − | 3.07603i | ||||
\(603\) | −136.991 | + | 133.491i | −0.227182 | + | 0.221377i | ||||
\(604\) | 86.1650 | + | 149.242i | 0.142657 | + | 0.247090i | ||||
\(605\) | −2.17078 | − | 1.25330i | −0.00358807 | − | 0.00207157i | ||||
\(606\) | −588.590 | − | 81.3666i | −0.971271 | − | 0.134268i | ||||
\(607\) | 301.545 | + | 522.291i | 0.496779 | + | 0.860446i | 0.999993 | − | 0.00371550i | \(-0.00118268\pi\) |
−0.503214 | + | 0.864162i | \(0.667849\pi\) | |||||||
\(608\) | − | 1216.46i | − | 2.00076i | ||||||
\(609\) | 90.1953 | + | 191.435i | 0.148104 | + | 0.314343i | ||||
\(610\) | 116.098 | 0.190324 | ||||||||
\(611\) | −18.4542 | + | 10.6545i | −0.0302032 | + | 0.0174378i | ||||
\(612\) | 1360.94 | − | 345.852i | 2.22375 | − | 0.565118i | ||||
\(613\) | −286.342 | + | 495.959i | −0.467116 | + | 0.809069i | −0.999294 | − | 0.0375638i | \(-0.988040\pi\) |
0.532178 | + | 0.846632i | \(0.321374\pi\) | |||||||
\(614\) | −1294.99 | + | 747.661i | −2.10910 | + | 1.21769i | ||||
\(615\) | 170.581 | + | 419.476i | 0.277368 | + | 0.682074i | ||||
\(616\) | 106.025 | + | 1958.74i | 0.172119 | + | 3.17978i | ||||
\(617\) | 30.2182i | 0.0489759i | 0.999700 | + | 0.0244880i | \(0.00779554\pi\) | ||||
−0.999700 | + | 0.0244880i | \(0.992204\pi\) | |||||||
\(618\) | −1055.74 | − | 821.008i | −1.70833 | − | 1.32849i | ||||
\(619\) | 92.6047 | − | 160.396i | 0.149604 | − | 0.259121i | −0.781477 | − | 0.623934i | \(-0.785534\pi\) |
0.931081 | + | 0.364812i | \(0.118867\pi\) | |||||||
\(620\) | 499.151 | + | 288.185i | 0.805082 | + | 0.464814i | ||||
\(621\) | 264.476 | − | 29.6095i | 0.425888 | − | 0.0476803i | ||||
\(622\) | 278.068 | 0.447054 | ||||||||
\(623\) | 228.706 | − | 450.773i | 0.367105 | − | 0.723552i | ||||
\(624\) | −234.699 | − | 577.147i | −0.376120 | − | 0.924915i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 1643.55 | + | 948.906i | 2.62548 | + | 1.51582i | ||||
\(627\) | 49.8925 | − | 360.912i | 0.0795733 | − | 0.575617i | ||||
\(628\) | −1026.59 | − | 1778.11i | −1.63470 | − | 2.83138i | ||||
\(629\) | 560.668i | 0.891364i | ||||||||
\(630\) | −118.137 | + | 526.658i | −0.187519 | + | 0.835966i | ||||
\(631\) | 451.153 | 0.714981 | 0.357491 | − | 0.933917i | \(-0.383632\pi\) | ||||
0.357491 | + | 0.933917i | \(0.383632\pi\) | |||||||
\(632\) | 2453.98 | − | 1416.81i | 3.88288 | − | 2.24178i | ||||
\(633\) | 704.004 | + | 97.3215i | 1.11217 | + | 0.153746i | ||||
\(634\) | 687.242 | − | 1190.34i | 1.08398 | − | 1.87751i | ||||
\(635\) | −132.686 | + | 76.6061i | −0.208954 | + | 0.120640i | ||||
\(636\) | 2054.59 | − | 835.507i | 3.23049 | − | 1.31369i | ||||
\(637\) | −74.2126 | + | 168.236i | −0.116503 | + | 0.264107i | ||||
\(638\) | 422.737i | 0.662597i | ||||||||
\(639\) | −62.7104 | + | 222.483i | −0.0981383 | + | 0.348173i | ||||
\(640\) | −361.210 | + | 625.634i | −0.564391 | + | 0.977554i | ||||
\(641\) | 240.850 | + | 139.055i | 0.375741 | + | 0.216934i | 0.675964 | − | 0.736935i | \(-0.263728\pi\) |
−0.300223 | + | 0.953869i | \(0.597061\pi\) | |||||||
\(642\) | −1005.90 | + | 1293.50i | −1.56682 | + | 2.01479i | ||||
\(643\) | 231.489 | 0.360014 | 0.180007 | − | 0.983665i | \(-0.442388\pi\) | ||||
0.180007 | + | 0.983665i | \(0.442388\pi\) | |||||||
\(644\) | −402.396 | − | 617.313i | −0.624838 | − | 0.958560i | ||||
\(645\) | 481.106 | − | 195.644i | 0.745900 | − | 0.303323i | ||||
\(646\) | 310.431 | + | 537.682i | 0.480543 | + | 0.832324i | ||||
\(647\) | 397.213 | + | 229.331i | 0.613930 | + | 0.354452i | 0.774502 | − | 0.632572i | \(-0.218001\pi\) |
−0.160572 | + | 0.987024i | \(0.551334\pi\) | |||||||
\(648\) | 1082.68 | − | 1767.97i | 1.67080 | − | 2.72834i | ||||
\(649\) | −287.227 | − | 497.492i | −0.442569 | − | 0.766552i | ||||
\(650\) | 71.8896i | 0.110599i | ||||||||
\(651\) | −42.1665 | + | 505.073i | −0.0647719 | + | 0.775842i | ||||
\(652\) | −2959.72 | −4.53945 | ||||||||
\(653\) | −5.08630 | + | 2.93658i | −0.00778913 | + | 0.00449706i | −0.503890 | − | 0.863768i | \(-0.668098\pi\) |
0.496100 | + | 0.868265i | \(0.334765\pi\) | |||||||
\(654\) | −127.033 | + | 918.934i | −0.194241 | + | 1.40510i | ||||
\(655\) | −20.7461 | + | 35.9332i | −0.0316734 | + | 0.0548599i | ||||
\(656\) | −3235.39 | + | 1867.95i | −4.93200 | + | 2.84749i | ||||
\(657\) | 159.927 | − | 155.841i | 0.243420 | − | 0.237201i | ||||
\(658\) | 8.23171 | + | 152.075i | 0.0125102 | + | 0.231117i | ||||
\(659\) | 425.682i | 0.645952i | 0.946407 | + | 0.322976i | \(0.104683\pi\) | ||||
−0.946407 | + | 0.322976i | \(0.895317\pi\) | |||||||
\(660\) | −481.543 | + | 619.223i | −0.729611 | + | 0.938217i | ||||
\(661\) | −516.635 | + | 894.838i | −0.781596 | + | 1.35376i | 0.149415 | + | 0.988775i | \(0.452261\pi\) |
−0.931012 | + | 0.364990i | \(0.881072\pi\) | |||||||
\(662\) | 1046.15 | + | 603.993i | 1.58028 | + | 0.912376i | ||||
\(663\) | 129.826 | + | 100.960i | 0.195816 | + | 0.152278i | ||||
\(664\) | −2614.58 | −3.93763 | ||||||||
\(665\) | −173.367 | + | 9.38424i | −0.260703 | + | 0.0141116i | ||||
\(666\) | 923.618 | + | 947.835i | 1.38681 | + | 1.42317i | ||||
\(667\) | −49.6629 | − | 86.0187i | −0.0744572 | − | 0.128964i | ||||
\(668\) | −319.409 | − | 184.411i | −0.478157 | − | 0.276064i | ||||
\(669\) | −588.532 | − | 81.3586i | −0.879718 | − | 0.121612i | ||||
\(670\) | 91.0404 | + | 157.687i | 0.135881 | + | 0.235353i | ||||
\(671\) | 148.370i | 0.221118i | ||||||||
\(672\) | −2295.04 | − | 191.603i | −3.41523 | − | 0.285124i | ||||
\(673\) | −726.867 | −1.08004 | −0.540020 | − | 0.841652i | \(-0.681583\pi\) | ||||
−0.540020 | + | 0.841652i | \(0.681583\pi\) | |||||||
\(674\) | 347.829 | − | 200.819i | 0.516066 | − | 0.297951i | ||||
\(675\) | −108.677 | + | 80.0887i | −0.161004 | + | 0.118650i | ||||
\(676\) | −827.265 | + | 1432.87i | −1.22377 | + | 2.11962i | ||||
\(677\) | 139.975 | − | 80.8146i | 0.206758 | − | 0.119372i | −0.393046 | − | 0.919519i | \(-0.628579\pi\) |
0.599804 | + | 0.800147i | \(0.295245\pi\) | |||||||
\(678\) | −339.252 | − | 834.251i | −0.500371 | − | 1.23046i | ||||
\(679\) | 36.5570 | − | 23.8297i | 0.0538395 | − | 0.0350953i | ||||
\(680\) | − | 836.064i | − | 1.22951i | ||||||
\(681\) | −57.3184 | − | 44.5741i | −0.0841680 | − | 0.0654539i | ||||
\(682\) | −506.230 | + | 876.817i | −0.742273 | + | 1.28566i | ||||
\(683\) | 245.110 | + | 141.515i | 0.358873 | + | 0.207195i | 0.668586 | − | 0.743635i | \(-0.266900\pi\) |
−0.309713 | + | 0.950830i | \(0.600233\pi\) | |||||||
\(684\) | 1026.20 | + | 289.252i | 1.50030 | + | 0.422884i | ||||
\(685\) | 299.621 | 0.437403 | ||||||||
\(686\) | 832.294 | + | 1017.04i | 1.21326 | + | 1.48257i | ||||
\(687\) | 208.106 | + | 511.751i | 0.302919 | + | 0.744906i | ||||
\(688\) | 2142.40 | + | 3710.74i | 3.11395 | + | 5.39351i | ||||
\(689\) | 224.970 | + | 129.887i | 0.326517 | + | 0.188515i | ||||
\(690\) | 34.6913 | − | 250.950i | 0.0502772 | − | 0.363695i | ||||
\(691\) | −380.317 | − | 658.729i | −0.550387 | − | 0.953298i | −0.998246 | − | 0.0591940i | \(-0.981147\pi\) |
0.447860 | − | 0.894104i | \(-0.352186\pi\) | |||||||
\(692\) | 3456.00i | 4.99422i | ||||||||
\(693\) | −673.057 | − | 150.977i | −0.971222 | − | 0.217859i | ||||
\(694\) | 1668.82 | 2.40465 | ||||||||
\(695\) | 173.708 | − | 100.290i | 0.249940 | − | 0.144303i | ||||
\(696\) | −766.458 | − | 105.955i | −1.10123 | − | 0.152234i | ||||
\(697\) | 493.076 | − | 854.032i | 0.707426 | − | 1.22530i | ||||
\(698\) | −1235.93 | + | 713.565i | −1.77068 | + | 1.02230i | ||||
\(699\) | 372.669 | − | 151.547i | 0.533145 | − | 0.216806i | ||||
\(700\) | 333.350 | + | 169.130i | 0.476215 | + | 0.241615i | ||||
\(701\) | − | 193.212i | − | 0.275624i | −0.990458 | − | 0.137812i | \(-0.955993\pi\) | ||
0.990458 | − | 0.137812i | \(-0.0440070\pi\) | |||||||
\(702\) | 385.794 | − | 43.1916i | 0.549564 | − | 0.0615265i | ||||
\(703\) | −212.855 | + | 368.675i | −0.302780 | + | 0.524431i | ||||
\(704\) | −1885.16 | − | 1088.40i | −2.67779 | − | 1.54602i | ||||
\(705\) | −23.3842 | + | 30.0700i | −0.0331691 | + | 0.0426525i | ||||
\(706\) | −197.311 | −0.279477 | ||||||||
\(707\) | −361.328 | + | 19.5584i | −0.511072 | + | 0.0276639i | ||||
\(708\) | 1557.21 | − | 633.246i | 2.19945 | − | 0.894415i | ||||
\(709\) | 163.509 | + | 283.205i | 0.230618 | + | 0.399443i | 0.957990 | − | 0.286801i | \(-0.0925917\pi\) |
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(710\) | 190.561 | + | 110.020i | 0.268396 | + | 0.154958i | ||||
\(711\) | 245.416 | + | 965.718i | 0.345170 | + | 1.35825i | ||||
\(712\) | 924.087 | + | 1600.57i | 1.29788 | + | 2.24799i | ||||
\(713\) | − | 237.887i | − | 0.333642i | ||||||
\(714\) | 1063.31 | − | 500.985i | 1.48923 | − | 0.701660i | ||||
\(715\) | −91.8732 | −0.128494 | ||||||||
\(716\) | −61.0420 | + | 35.2426i | −0.0852542 | + | 0.0492216i | ||||
\(717\) | −181.956 | + | 1316.23i | −0.253774 | + | 1.83575i | ||||
\(718\) | −711.359 | + | 1232.11i | −0.990751 | + | 1.71603i | ||||
\(719\) | 535.646 | − | 309.256i | 0.744988 | − | 0.430119i | −0.0788921 | − | 0.996883i | \(-0.525138\pi\) |
0.823880 | + | 0.566764i | \(0.191805\pi\) | |||||||
\(720\) | −777.291 | − | 797.671i | −1.07957 | − | 1.10788i | ||||
\(721\) | −726.333 | − | 368.516i | −1.00740 | − | 0.511118i | ||||
\(722\) | − | 911.741i | − | 1.26280i | ||||||
\(723\) | 697.860 | − | 897.388i | 0.965228 | − | 1.24120i | ||||
\(724\) | 1205.57 | − | 2088.11i | 1.66515 | − | 2.88413i | ||||
\(725\) | 43.6350 | + | 25.1927i | 0.0601862 | + | 0.0347485i | ||||
\(726\) | 10.1714 | + | 7.90988i | 0.0140102 | + | 0.0108952i | ||||
\(727\) | −944.743 | −1.29951 | −0.649755 | − | 0.760144i | \(-0.725128\pi\) | ||||
−0.649755 | + | 0.760144i | \(0.725128\pi\) | |||||||
\(728\) | −367.137 | − | 563.222i | −0.504309 | − | 0.773657i | ||||
\(729\) | 495.088 | + | 535.097i | 0.679133 | + | 0.734015i | ||||
\(730\) | −106.283 | − | 184.088i | −0.145594 | − | 0.252176i | ||||
\(731\) | −979.508 | − | 565.519i | −1.33996 | − | 0.773624i | ||||
\(732\) | −430.090 | − | 59.4556i | −0.587554 | − | 0.0812234i | ||||
\(733\) | −398.388 | − | 690.029i | −0.543504 | − | 0.941377i | −0.998699 | − | 0.0509850i | \(-0.983764\pi\) |
0.455195 | − | 0.890392i | \(-0.349569\pi\) | |||||||
\(734\) | 1275.86i | 1.73823i | ||||||||
\(735\) | −9.60210 | + | 328.562i | −0.0130641 | + | 0.447023i | ||||
\(736\) | 1080.95 | 1.46868 | ||||||||
\(737\) | −201.520 | + | 116.348i | −0.273433 | + | 0.157866i | ||||
\(738\) | −573.326 | − | 2256.05i | −0.776864 | − | 3.05698i | ||||
\(739\) | 526.190 | − | 911.387i | 0.712029 | − | 1.23327i | −0.252065 | − | 0.967710i | \(-0.581110\pi\) |
0.964094 | − | 0.265561i | \(-0.0855571\pi\) | |||||||
\(740\) | 793.748 | − | 458.271i | 1.07263 | − | 0.619285i | ||||
\(741\) | 47.0399 | + | 115.676i | 0.0634817 | + | 0.156107i | ||||
\(742\) | 1555.36 | − | 1013.86i | 2.09617 | − | 1.36639i | ||||
\(743\) | − | 923.243i | − | 1.24259i | −0.783577 | − | 0.621294i | \(-0.786607\pi\) | ||
0.783577 | − | 0.621294i | \(-0.213393\pi\) | |||||||
\(744\) | −1462.86 | − | 1137.61i | −1.96621 | − | 1.52904i | ||||
\(745\) | 129.975 | − | 225.124i | 0.174463 | − | 0.302179i | ||||
\(746\) | 139.972 | + | 80.8131i | 0.187631 | + | 0.108329i | ||||
\(747\) | 249.428 | − | 884.914i | 0.333906 | − | 1.18462i | ||||
\(748\) | 1708.27 | 2.28378 | ||||||||
\(749\) | −451.506 | + | 889.903i | −0.602811 | + | 1.18812i | ||||
\(750\) | 48.4098 | + | 119.044i | 0.0645465 | + | 0.158726i | ||||
\(751\) | 256.554 | + | 444.364i | 0.341616 | + | 0.591697i | 0.984733 | − | 0.174071i | \(-0.0556924\pi\) |
−0.643117 | + | 0.765768i | \(0.722359\pi\) | |||||||
\(752\) | −272.161 | − | 157.132i | −0.361916 | − | 0.208953i | ||||
\(753\) | −112.108 | + | 810.970i | −0.148882 | + | 1.07699i | ||||
\(754\) | −72.4437 | − | 125.476i | −0.0960792 | − | 0.166414i | ||||
\(755\) | 36.0805i | 0.0477888i | ||||||||
\(756\) | 707.355 | − | 1890.53i | 0.935655 | − | 2.50070i | ||||
\(757\) | −702.065 | −0.927430 | −0.463715 | − | 0.885984i | \(-0.653484\pi\) | ||||
−0.463715 | + | 0.885984i | \(0.653484\pi\) | |||||||
\(758\) | −1341.26 | + | 774.375i | −1.76947 | + | 1.02160i | ||||
\(759\) | 320.708 | + | 44.3347i | 0.422540 | + | 0.0584119i | ||||
\(760\) | 317.408 | − | 549.766i | 0.417641 | − | 0.723376i | ||||
\(761\) | 129.267 | − | 74.6326i | 0.169865 | − | 0.0980717i | −0.412657 | − | 0.910886i | \(-0.635399\pi\) |
0.582522 | + | 0.812815i | \(0.302066\pi\) | |||||||
\(762\) | 729.562 | − | 296.679i | 0.957430 | − | 0.389343i | ||||
\(763\) | 30.5355 | + | 564.121i | 0.0400203 | + | 0.739347i | ||||
\(764\) | − | 669.191i | − | 0.875905i | ||||||
\(765\) | 282.969 | + | 79.7593i | 0.369894 | + | 0.104261i | ||||
\(766\) | 748.942 | − | 1297.21i | 0.977732 | − | 1.69348i | ||||
\(767\) | 170.509 | + | 98.4434i | 0.222306 | + | 0.128349i | ||||
\(768\) | 815.104 | − | 1048.15i | 1.06133 | − | 1.36478i | ||||
\(769\) | 592.088 | 0.769945 | 0.384972 | − | 0.922928i | \(-0.374211\pi\) | ||||
0.384972 | + | 0.922928i | \(0.374211\pi\) | |||||||
\(770\) | −297.097 | + | 585.569i | −0.385841 | + | 0.760479i | ||||
\(771\) | −489.157 | + | 198.918i | −0.634445 | + | 0.258000i | ||||
\(772\) | −52.6279 | − | 91.1542i | −0.0681708 | − | 0.118075i | ||||
\(773\) | 750.282 | + | 433.175i | 0.970611 | + | 0.560382i | 0.899422 | − | 0.437081i | \(-0.143988\pi\) |
0.0711882 | + | 0.997463i | \(0.477321\pi\) | |||||||
\(774\) | −2587.51 | + | 657.560i | −3.34304 | + | 0.849560i | ||||
\(775\) | 60.3369 | + | 104.507i | 0.0778541 | + | 0.134847i | ||||
\(776\) | 159.555i | 0.205612i | ||||||||
\(777\) | 662.035 | + | 459.652i | 0.852040 | + | 0.591573i | ||||
\(778\) | −1451.07 | −1.86513 | ||||||||
\(779\) | 648.458 | − | 374.387i | 0.832424 | − | 0.480600i | ||||
\(780\) | 36.8158 | − | 266.318i | 0.0471998 | − | 0.341434i | ||||
\(781\) | −140.604 | + | 243.532i | −0.180030 | + | 0.311821i | ||||
\(782\) | −477.786 | + | 275.850i | −0.610980 | + | 0.352749i | ||||
\(783\) | 108.980 | − | 249.302i | 0.139182 | − | 0.318393i | ||||
\(784\) | −2695.97 | + | 292.719i | −3.43874 | + | 0.373367i | ||||
\(785\) | − | 429.872i | − | 0.547608i | ||||||
\(786\) | 130.933 | − | 168.369i | 0.166582 | − | 0.214210i | ||||
\(787\) | −155.487 | + | 269.312i | −0.197570 | + | 0.342201i | −0.947740 | − | 0.319044i | \(-0.896638\pi\) |
0.750170 | + | 0.661245i | \(0.229972\pi\) | |||||||
\(788\) | 826.047 | + | 476.919i | 1.04828 | + | 0.605227i | ||||
\(789\) | 505.913 | + | 393.427i | 0.641208 | + | 0.498640i | ||||
\(790\) | 948.519 | 1.20066 | ||||||||
\(791\) | −299.500 | − | 459.460i | −0.378634 | − | 0.580860i | ||||
\(792\) | 1806.30 | − | 1760.15i | 2.28068 | − | 2.22241i | ||||
\(793\) | −25.4260 | − | 44.0391i | −0.0320630 | − | 0.0555348i | ||||
\(794\) | 846.316 | + | 488.620i | 1.06589 | + | 0.615391i | ||||
\(795\) | 460.000 | + | 63.5904i | 0.578616 | + | 0.0799879i | ||||
\(796\) | 548.163 | + | 949.446i | 0.688647 | + | 1.19277i | ||||
\(797\) | − | 1327.14i | − | 1.66517i | −0.553899 | − | 0.832584i | \(-0.686861\pi\) | ||
0.553899 | − | 0.832584i | \(-0.313139\pi\) | |||||||
\(798\) | 889.393 | + | 74.2519i | 1.11453 | + | 0.0930475i | ||||
\(799\) | 82.9551 | 0.103824 | ||||||||
\(800\) | −474.875 | + | 274.169i | −0.593594 | + | 0.342711i | ||||
\(801\) | −629.873 | + | 160.068i | −0.786358 | + | 0.199836i | ||||
\(802\) | −409.997 | + | 710.135i | −0.511218 | + | 0.885455i | ||||
\(803\) | 235.261 | − | 135.828i | 0.292977 | − | 0.169150i | ||||
\(804\) | −256.510 | − | 630.781i | −0.319042 | − | 0.784553i | ||||
\(805\) | −8.33888 | − | 154.055i | −0.0103589 | − | 0.191372i | ||||
\(806\) | − | 347.008i | − | 0.430531i | ||||||
\(807\) | 333.305 | + | 259.197i | 0.413017 | + | 0.321186i | ||||
\(808\) | 661.533 | − | 1145.81i | 0.818729 | − | 1.41808i | ||||
\(809\) | −7.08815 | − | 4.09235i | −0.00876162 | − | 0.00505852i | 0.495613 | − | 0.868544i | \(-0.334944\pi\) |
−0.504374 | + | 0.863485i | \(0.668277\pi\) | |||||||
\(810\) | 609.763 | − | 331.312i | 0.752794 | − | 0.409028i | ||||
\(811\) | −1472.35 | −1.81547 | −0.907737 | − | 0.419539i | \(-0.862192\pi\) | ||||
−0.907737 | + | 0.419539i | \(0.862192\pi\) | |||||||
\(812\) | −752.264 | + | 40.7195i | −0.926434 | + | 0.0501472i | ||||
\(813\) | −134.928 | − | 331.801i | −0.165964 | − | 0.408120i | ||||
\(814\) | 805.006 | + | 1394.31i | 0.988951 | + | 1.71291i | ||||
\(815\) | −536.653 | − | 309.837i | −0.658470 | − | 0.380168i | ||||
\(816\) | −332.139 | + | 2402.63i | −0.407033 | + | 2.94440i | ||||
\(817\) | −429.393 | − | 743.730i | −0.525573 | − | 0.910319i | ||||
\(818\) | 1304.06i | 1.59420i | ||||||||
\(819\) | 225.649 | − | 70.5280i | 0.275517 | − | 0.0861148i | ||||
\(820\) | −1612.09 | −1.96597 | ||||||||
\(821\) | −738.622 | + | 426.444i | −0.899661 | + | 0.519420i | −0.877090 | − | 0.480326i | \(-0.840519\pi\) |
−0.0225710 | + | 0.999745i | \(0.507185\pi\) | |||||||
\(822\) | −1525.67 | − | 210.909i | −1.85605 | − | 0.256580i | ||||
\(823\) | −268.528 | + | 465.105i | −0.326280 | + | 0.565133i | −0.981771 | − | 0.190070i | \(-0.939128\pi\) |
0.655491 | + | 0.755203i | \(0.272462\pi\) | |||||||
\(824\) | 2579.00 | − | 1488.99i | 3.12986 | − | 1.80702i | ||||
\(825\) | −152.136 | + | 61.8666i | −0.184407 | + | 0.0749899i | ||||
\(826\) | 1178.83 | − | 768.423i | 1.42716 | − | 0.930295i | ||||
\(827\) | 1112.68i | 1.34545i | 0.739894 | + | 0.672724i | \(0.234876\pi\) | ||||
−0.739894 | + | 0.672724i | \(0.765124\pi\) | |||||||
\(828\) | −257.031 | + | 911.889i | −0.310424 | + | 1.10132i | ||||
\(829\) | −228.298 | + | 395.424i | −0.275390 | + | 0.476989i | −0.970233 | − | 0.242172i | \(-0.922140\pi\) |
0.694843 | + | 0.719161i | \(0.255474\pi\) | |||||||
\(830\) | −757.947 | − | 437.601i | −0.913189 | − | 0.527230i | ||||
\(831\) | −253.731 | + | 326.277i | −0.305333 | + | 0.392631i | ||||
\(832\) | 746.070 | 0.896719 | ||||||||
\(833\) | 577.668 | − | 422.738i | 0.693479 | − | 0.507489i | ||||
\(834\) | −955.121 | + | 388.404i | −1.14523 | + | 0.465712i | ||||
\(835\) | −38.6099 | − | 66.8743i | −0.0462394 | − | 0.0800890i | ||||
\(836\) | 1123.30 | + | 648.536i | 1.34366 | + | 0.775760i | ||||
\(837\) | 524.581 | − | 386.584i | 0.626740 | − | 0.461869i | ||||
\(838\) | −1123.85 | − | 1946.57i | −1.34112 | − | 2.32288i | ||||
\(839\) | − | 1354.69i | − | 1.61465i | −0.590106 | − | 0.807326i | \(-0.700914\pi\) | ||
0.590106 | − | 0.807326i | \(-0.299086\pi\) | |||||||
\(840\) | −987.223 | − | 685.431i | −1.17526 | − | 0.815989i | ||||
\(841\) | 739.453 | 0.879254 | ||||||||
\(842\) | −717.126 | + | 414.033i | −0.851694 | + | 0.491726i | ||||
\(843\) | −54.0113 | + | 390.707i | −0.0640704 | + | 0.463472i | ||||
\(844\) | −1265.05 | + | 2191.13i | −1.49887 | + | 2.59613i | ||||
\(845\) | −299.997 | + | 173.204i | −0.355026 | + | 0.204975i | ||||
\(846\) | 140.239 | − | 136.656i | 0.165768 | − | 0.161532i | ||||
\(847\) | 6.99775 | + | 3.55042i | 0.00826181 | + | 0.00419175i | ||||
\(848\) | 3831.12i | 4.51783i | ||||||||
\(849\) | −956.815 | + | 1230.38i | −1.12699 | + | 1.44921i | ||||
\(850\) | 139.931 | − | 242.368i | 0.164625 | − | 0.285139i | ||||
\(851\) | −327.606 | − | 189.144i | −0.384966 | − | 0.222260i | ||||
\(852\) | −649.599 | − | 505.165i | −0.762440 | − | 0.592917i | ||||
\(853\) | 1348.04 | 1.58035 | 0.790175 | − | 0.612881i | \(-0.209990\pi\) | ||||
0.790175 | + | 0.612881i | \(0.209990\pi\) | |||||||
\(854\) | −362.912 | + | 19.6442i | −0.424956 | + | 0.0230025i | ||||
\(855\) | 155.790 | + | 159.874i | 0.182210 | + | 0.186988i | ||||
\(856\) | −1824.31 | − | 3159.79i | −2.13120 | − | 3.69134i | ||||
\(857\) | −972.089 | − | 561.236i | −1.13429 | − | 0.654884i | −0.189282 | − | 0.981923i | \(-0.560616\pi\) |
−0.945011 | + | 0.327039i | \(0.893949\pi\) | |||||||
\(858\) | 467.820 | + | 64.6713i | 0.545244 | + | 0.0753745i | ||||
\(859\) | −173.759 | − | 300.960i | −0.202281 | − | 0.350361i | 0.746982 | − | 0.664844i | \(-0.231502\pi\) |
−0.949263 | + | 0.314483i | \(0.898169\pi\) | |||||||
\(860\) | 1848.94i | 2.14993i | ||||||||
\(861\) | −604.201 | − | 1282.38i | −0.701743 | − | 1.48941i | ||||
\(862\) | 1266.53 | 1.46930 | ||||||||
\(863\) | −25.2484 | + | 14.5771i | −0.0292565 | + | 0.0168913i | −0.514557 | − | 0.857456i | \(-0.672044\pi\) |
0.485300 | + | 0.874347i | \(0.338710\pi\) | |||||||
\(864\) | 1756.63 | + | 2383.68i | 2.03313 | + | 2.75889i | ||||
\(865\) | −361.790 | + | 626.638i | −0.418254 | + | 0.724437i | ||||
\(866\) | 2737.81 | − | 1580.68i | 3.16145 | − | 1.82526i | ||||
\(867\) | 85.4191 | + | 210.054i | 0.0985226 | + | 0.242276i | ||||
\(868\) | −1609.07 | − | 816.384i | −1.85376 | − | 0.940535i | ||||
\(869\) | 1212.18i | 1.39492i | ||||||||
\(870\) | −204.456 | − | 158.997i | −0.235007 | − | 0.182755i | ||||
\(871\) | 39.8766 | − | 69.0683i | 0.0457825 | − | 0.0792977i | ||||
\(872\) | −1788.89 | − | 1032.82i | −2.05148 | − | 1.18442i | ||||
\(873\) | −54.0017 | − | 15.2213i | −0.0618577 | − | 0.0174356i | ||||
\(874\) | −418.900 | −0.479291 | ||||||||
\(875\) | 42.7374 | + | 65.5631i | 0.0488427 | + | 0.0749292i | ||||
\(876\) | 299.457 | + | 736.393i | 0.341846 | + | 0.840632i | ||||
\(877\) | −274.688 | − | 475.773i | −0.313213 | − | 0.542500i | 0.665843 | − | 0.746092i | \(-0.268072\pi\) |
−0.979056 | + | 0.203591i | \(0.934739\pi\) | |||||||
\(878\) | 2409.61 | + | 1391.19i | 2.74443 | + | 1.58450i | ||||
\(879\) | 144.536 | − | 1045.55i | 0.164432 | − | 1.18947i | ||||
\(880\) | −677.471 | − | 1173.41i | −0.769853 | − | 1.33342i | ||||
\(881\) | − | 1340.63i | − | 1.52171i | −0.648919 | − | 0.760857i | \(-0.724779\pi\) | ||
0.648919 | − | 0.760857i | \(-0.275221\pi\) | |||||||
\(882\) | 280.175 | − | 1666.28i | 0.317659 | − | 1.88921i | ||||
\(883\) | −94.2575 | −0.106747 | −0.0533735 | − | 0.998575i | \(-0.516997\pi\) | ||||
−0.0533735 | + | 0.998575i | \(0.516997\pi\) | |||||||
\(884\) | −507.046 | + | 292.743i | −0.573582 | + | 0.331158i | ||||
\(885\) | 348.642 | + | 48.1963i | 0.393946 | + | 0.0544591i | ||||
\(886\) | 1372.53 | − | 2377.29i | 1.54913 | − | 2.68317i | ||||
\(887\) | −783.894 | + | 452.582i | −0.883759 | + | 0.510239i | −0.871896 | − | 0.489691i | \(-0.837110\pi\) |
−0.0118632 | + | 0.999930i | \(0.503776\pi\) | |||||||
\(888\) | −2729.77 | + | 1110.07i | −3.07407 | + | 1.25008i | ||||
\(889\) | 401.803 | − | 261.915i | 0.451972 | − | 0.294618i | ||||
\(890\) | 618.655i | 0.695118i | ||||||||
\(891\) | 423.409 | + | 779.263i | 0.475207 | + | 0.874594i | ||||
\(892\) | 1057.55 | − | 1831.74i | 1.18560 | − | 2.05352i | ||||
\(893\) | 54.5483 | + | 31.4935i | 0.0610844 | + | 0.0352671i | ||||
\(894\) | −820.304 | + | 1054.84i | −0.917566 | + | 1.17991i | ||||
\(895\) | −14.7574 | −0.0164887 | ||||||||
\(896\) | 1023.25 | − | 2016.80i | 1.14202 | − | 2.25089i | ||||
\(897\) | −102.790 | + | 41.7999i | −0.114593 | + | 0.0465996i | ||||
\(898\) | 1082.09 | + | 1874.24i | 1.20500 | + | 2.08713i | ||||
\(899\) | −210.624 | − | 121.604i | −0.234287 | − | 0.135266i | ||||
\(900\) | −118.372 | − | 465.796i | −0.131524 | − | 0.517552i | ||||
\(901\) | −505.643 | − | 875.799i | −0.561202 | − | 0.972030i | ||||
\(902\) | − | 2831.83i | − | 3.13950i | ||||||
\(903\) | −1470.79 | + | 692.971i | −1.62879 | + | 0.767410i | ||||
\(904\) | 2005.33 | 2.21829 | ||||||||
\(905\) | 437.184 | − | 252.409i | 0.483077 | − | 0.278905i | ||||
\(906\) | 25.3978 | − | 183.722i | 0.0280329 | − | 0.202784i | ||||
\(907\) | −142.777 | + | 247.298i | −0.157417 | + | 0.272655i | −0.933937 | − | 0.357439i | \(-0.883650\pi\) |
0.776519 | + | 0.630093i | \(0.216983\pi\) | |||||||
\(908\) | 223.862 | − | 129.247i | 0.246544 | − | 0.142342i | ||||
\(909\) | 324.693 | + | 333.206i | 0.357198 | + | 0.366564i | ||||
\(910\) | −12.1640 | − | 224.721i | −0.0133670 | − | 0.246946i | ||||
\(911\) | 362.812i | 0.398257i | 0.979973 | + | 0.199128i | \(0.0638111\pi\) | ||||
−0.979973 | + | 0.199128i | \(0.936189\pi\) | |||||||
\(912\) | −1130.55 | + | 1453.79i | −1.23964 | + | 1.59406i | ||||
\(913\) | 559.244 | − | 968.639i | 0.612534 | − | 1.06094i | ||||
\(914\) | 2831.95 | + | 1635.03i | 3.09842 | + | 1.78887i | ||||
\(915\) | −71.7592 | − | 55.8041i | −0.0784254 | − | 0.0609881i | ||||
\(916\) | −1966.72 | −2.14707 | ||||||||
\(917\) | 58.7705 | − | 115.835i | 0.0640900 | − | 0.126319i | ||||
\(918\) | −1384.73 | − | 605.322i | −1.50843 | − | 0.659393i | ||||
\(919\) | −55.3185 | − | 95.8145i | −0.0601942 | − | 0.104259i | 0.834358 | − | 0.551223i | \(-0.185839\pi\) |
−0.894552 | + | 0.446964i | \(0.852505\pi\) | |||||||
\(920\) | 488.524 | + | 282.050i | 0.531005 | + | 0.306576i | ||||
\(921\) | 1159.80 | + | 160.330i | 1.25928 | + | 0.174083i | ||||
\(922\) | 1708.29 | + | 2958.84i | 1.85281 | + | 3.20915i | ||||
\(923\) | − | 96.3800i | − | 0.104420i | ||||||
\(924\) | 1400.49 | − | 2017.12i | 1.51568 | − | 2.18303i | ||||
\(925\) | 191.895 | 0.207454 | ||||||||
\(926\) | 2489.12 | − | 1437.09i | 2.68803 | − | 1.55194i | ||||
\(927\) | 257.919 | + | 1014.92i | 0.278230 | + | 1.09484i | ||||
\(928\) | 552.565 | − | 957.070i | 0.595436 | − | 1.03133i | ||||
\(929\) | −956.341 | + | 552.144i | −1.02943 | + | 0.594342i | −0.916821 | − | 0.399298i | \(-0.869254\pi\) |
−0.112609 | + | 0.993639i | \(0.535921\pi\) | |||||||
\(930\) | −233.672 | − | 574.621i | −0.251260 | − | 0.617872i | ||||
\(931\) | 540.344 | − | 58.6687i | 0.580391 | − | 0.0630169i | ||||
\(932\) | 1432.21i | 1.53670i | ||||||||
\(933\) | −171.872 | − | 133.657i | −0.184214 | − | 0.143255i | ||||
\(934\) | 187.324 | − | 324.454i | 0.200561 | − | 0.347381i | ||||
\(935\) | 309.741 | + | 178.829i | 0.331274 | + | 0.191261i | ||||
\(936\) | −234.509 | + | 831.988i | −0.250544 | + | 0.888876i | ||||
\(937\) | 1747.24 | 1.86472 | 0.932359 | − | 0.361534i | \(-0.117747\pi\) | ||||
0.932359 | + | 0.361534i | \(0.117747\pi\) | |||||||
\(938\) | −311.266 | − | 477.511i | −0.331840 | − | 0.509074i | ||||
\(939\) | −559.763 | − | 1376.51i | −0.596127 | − | 1.46593i | ||||
\(940\) | −67.8047 | − | 117.441i | −0.0721326 | − | 0.124937i | ||||
\(941\) | −495.187 | − | 285.896i | −0.526235 | − | 0.303822i | 0.213247 | − | 0.976998i | \(-0.431596\pi\) |
−0.739482 | + | 0.673176i | \(0.764929\pi\) | |||||||
\(942\) | −302.596 | + | 2188.92i | −0.321227 | + | 2.32369i | ||||
\(943\) | 332.682 | + | 576.223i | 0.352791 | + | 0.611053i | ||||
\(944\) | 2903.68i | 3.07593i | ||||||||
\(945\) | 326.166 | − | 268.739i | 0.345149 | − | 0.284380i | ||||
\(946\) | −3247.89 | −3.43328 | ||||||||
\(947\) | −514.440 | + | 297.012i | −0.543232 | + | 0.313635i | −0.746388 | − | 0.665511i | \(-0.768213\pi\) |
0.203156 | + | 0.979146i | \(0.434880\pi\) | |||||||
\(948\) | −3513.83 | − | 485.752i | −3.70657 | − | 0.512396i | ||||
\(949\) | −46.5532 | + | 80.6325i | −0.0490550 | + | 0.0849657i | ||||
\(950\) | 184.028 | − | 106.249i | 0.193714 | − | 0.111841i | ||||
\(951\) | −996.933 | + | 405.407i | −1.04830 | + | 0.426295i | ||||
\(952\) | 141.465 | + | 2613.47i | 0.148598 | + | 2.74524i | ||||
\(953\) | 812.582i | 0.852657i | 0.904568 | + | 0.426328i | \(0.140193\pi\) | ||||
−0.904568 | + | 0.426328i | \(0.859807\pi\) | |||||||
\(954\) | −2297.56 | − | 647.606i | −2.40835 | − | 0.678832i | ||||
\(955\) | 70.0539 | − | 121.337i | 0.0733548 | − | 0.127054i | ||||
\(956\) | −4096.62 | − | 2365.18i | −4.28516 | − | 2.47404i | ||||
\(957\) | 203.194 | − | 261.291i | 0.212324 | − | 0.273031i | ||||
\(958\) | 4.19719 | 0.00438120 | ||||||||
\(959\) | −936.590 | + | 50.6969i | −0.976632 | + | 0.0528644i | ||||
\(960\) | 1235.44 | − | 502.397i | 1.28692 | − | 0.523330i | ||||
\(961\) | 189.257 | + | 327.802i | 0.196937 | + | 0.341105i | ||||
\(962\) | −477.882 | − | 275.905i | −0.496759 | − | 0.286804i | ||||
\(963\) | 1243.48 | − | 316.003i | 1.29125 | − | 0.328144i | ||||
\(964\) | 2023.51 | + | 3504.82i | 2.09908 | + | 3.63571i | ||||
\(965\) | − | 22.0373i | − | 0.0228366i | ||||||
\(966\) | −65.9805 | + | 790.319i | −0.0683028 | + | 0.818136i | ||||
\(967\) | 295.134 | 0.305206 | 0.152603 | − | 0.988288i | \(-0.451234\pi\) | ||||
0.152603 | + | 0.988288i | \(0.451234\pi\) | |||||||
\(968\) | −24.8470 | + | 14.3454i | −0.0256684 | + | 0.0148197i | ||||
\(969\) | 66.5695 | − | 481.550i | 0.0686991 | − | 0.496956i | ||||
\(970\) | −26.7045 | + | 46.2536i | −0.0275304 | + | 0.0476841i | ||||
\(971\) | −1247.69 | + | 720.356i | −1.28496 | + | 0.741870i | −0.977750 | − | 0.209773i | \(-0.932728\pi\) |
−0.307206 | + | 0.951643i | \(0.599394\pi\) | |||||||
\(972\) | −2428.57 | + | 915.093i | −2.49852 | + | 0.941453i | ||||
\(973\) | −526.028 | + | 342.892i | −0.540625 | + | 0.352407i | ||||
\(974\) | − | 3017.23i | − | 3.09778i | ||||||
\(975\) | 34.5548 | − | 44.4345i | 0.0354408 | − | 0.0455738i | ||||
\(976\) | 374.981 | − | 649.486i | 0.384202 | − | 0.665457i | ||||
\(977\) | −764.640 | − | 441.465i | −0.782641 | − | 0.451858i | 0.0547244 | − | 0.998501i | \(-0.482572\pi\) |
−0.837365 | + | 0.546643i | \(0.815905\pi\) | |||||||
\(978\) | 2514.54 | + | 1955.45i | 2.57111 | + | 1.99944i | ||||
\(979\) | −790.627 | −0.807586 | ||||||||
\(980\) | −1070.64 | − | 472.284i | −1.09249 | − | 0.481922i | ||||
\(981\) | 520.217 | − | 506.926i | 0.530293 | − | 0.516744i | ||||
\(982\) | −563.469 | − | 975.957i | −0.573798 | − | 0.993847i | ||||
\(983\) | −700.602 | − | 404.493i | −0.712718 | − | 0.411488i | 0.0993485 | − | 0.995053i | \(-0.468324\pi\) |
−0.812067 | + | 0.583565i | \(0.801657\pi\) | |||||||
\(984\) | 5134.35 | + | 709.772i | 5.21784 | + | 0.721313i | ||||
\(985\) | 99.8519 | + | 172.949i | 0.101372 | + | 0.175582i | ||||
\(986\) | 564.040i | 0.572049i | ||||||||
\(987\) | 68.0091 | − | 97.9532i | 0.0689049 | − | 0.0992434i | ||||
\(988\) | −444.554 | −0.449954 | ||||||||
\(989\) | 660.882 | − | 381.560i | 0.668233 | − | 0.385804i | ||||
\(990\) | 818.226 | − | 207.934i | 0.826491 | − | 0.210035i | ||||
\(991\) | 160.428 | − | 277.870i | 0.161885 | − | 0.280393i | −0.773660 | − | 0.633601i | \(-0.781576\pi\) |
0.935545 | + | 0.353208i | \(0.114909\pi\) | |||||||
\(992\) | 2292.20 | − | 1323.40i | 2.31068 | − | 1.33407i | ||||
\(993\) | −356.298 | − | 876.169i | −0.358809 | − | 0.882346i | ||||
\(994\) | −614.294 | − | 311.671i | −0.618002 | − | 0.313553i | ||||
\(995\) | 229.537i | 0.230690i | ||||||||
\(996\) | 2583.75 | + | 2009.27i | 2.59412 | + | 2.01734i | ||||
\(997\) | 95.8320 | − | 165.986i | 0.0961204 | − | 0.166485i | −0.813955 | − | 0.580928i | \(-0.802690\pi\) |
0.910076 | + | 0.414442i | \(0.136023\pi\) | |||||||
\(998\) | −1652.31 | − | 953.960i | −1.65562 | − | 0.955872i | ||||
\(999\) | −115.291 | − | 1029.80i | −0.115407 | − | 1.03083i |
(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 | 105.3.t.b.11.18 | yes | 36 | |
3.2 | odd | 2 | inner | 105.3.t.b.11.1 | ✓ | 36 | |
7.2 | even | 3 | inner | 105.3.t.b.86.1 | yes | 36 | |
21.2 | odd | 6 | inner | 105.3.t.b.86.18 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.t.b.11.1 | ✓ | 36 | 3.2 | odd | 2 | inner | |
105.3.t.b.11.18 | yes | 36 | 1.1 | even | 1 | trivial | |
105.3.t.b.86.1 | yes | 36 | 7.2 | even | 3 | inner | |
105.3.t.b.86.18 | yes | 36 | 21.2 | odd | 6 | inner |