Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(101,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.y (of order \(8\), degree \(4\), 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: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 101.15 | ||
Character | \(\chi\) | \(=\) | 800.101 |
Dual form | 800.2.y.e.301.15 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37866 | − | 0.315126i | 0.974858 | − | 0.222827i | ||||
\(3\) | −1.29511 | − | 3.12667i | −0.747731 | − | 1.80518i | −0.571053 | − | 0.820913i | \(-0.693465\pi\) |
−0.176678 | − | 0.984269i | \(-0.556535\pi\) | |||||||
\(4\) | 1.80139 | − | 0.868900i | 0.900696 | − | 0.434450i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.77080 | − | 3.90248i | −1.13118 | − | 1.59318i | ||||
\(7\) | −1.02642 | − | 1.02642i | −0.387952 | − | 0.387952i | 0.486004 | − | 0.873956i | \(-0.338454\pi\) |
−0.873956 | + | 0.486004i | \(0.838454\pi\) | |||||||
\(8\) | 2.20969 | − | 1.76558i | 0.781243 | − | 0.624227i | ||||
\(9\) | −5.97742 | + | 5.97742i | −1.99247 | + | 1.99247i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.473788 | − | 1.14383i | 0.142853 | − | 0.344876i | −0.836218 | − | 0.548397i | \(-0.815238\pi\) |
0.979071 | + | 0.203520i | \(0.0652383\pi\) | |||||||
\(12\) | −5.04976 | − | 4.50703i | −1.45774 | − | 1.30107i | ||||
\(13\) | −5.17663 | + | 2.14423i | −1.43574 | + | 0.594703i | −0.958761 | − | 0.284212i | \(-0.908268\pi\) |
−0.476979 | + | 0.878915i | \(0.658268\pi\) | |||||||
\(14\) | −1.73854 | − | 1.09164i | −0.464645 | − | 0.291752i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49002 | − | 3.13046i | 0.622506 | − | 0.782615i | ||||
\(17\) | − | 4.22533i | − | 1.02479i | −0.858749 | − | 0.512396i | \(-0.828758\pi\) | ||
0.858749 | − | 0.512396i | \(-0.171242\pi\) | |||||||
\(18\) | −6.35718 | + | 10.1245i | −1.49840 | + | 2.38636i | ||||
\(19\) | −3.63519 | + | 1.50574i | −0.833969 | + | 0.345441i | −0.758473 | − | 0.651705i | \(-0.774054\pi\) |
−0.0754966 | + | 0.997146i | \(0.524054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.87996 | + | 4.53862i | −0.410240 | + | 0.990408i | ||||
\(22\) | 0.292743 | − | 1.72625i | 0.0624130 | − | 0.368037i | ||||
\(23\) | 5.53379 | − | 5.53379i | 1.15388 | − | 1.15388i | 0.168107 | − | 0.985769i | \(-0.446235\pi\) |
0.985769 | − | 0.168107i | \(-0.0537653\pi\) | |||||||
\(24\) | −8.38217 | − | 4.62234i | −1.71100 | − | 0.943532i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.46110 | + | 4.58745i | −1.26713 | + | 0.899673i | ||||
\(27\) | 17.0508 | + | 7.06268i | 3.28143 | + | 1.35921i | ||||
\(28\) | −2.74085 | − | 0.957132i | −0.517973 | − | 0.180881i | ||||
\(29\) | 0.848854 | + | 2.04932i | 0.157628 | + | 0.380548i | 0.982888 | − | 0.184205i | \(-0.0589711\pi\) |
−0.825259 | + | 0.564754i | \(0.808971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.964876 | −0.173297 | −0.0866484 | − | 0.996239i | \(-0.527616\pi\) | ||||
−0.0866484 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(32\) | 2.44640 | − | 5.10050i | 0.432467 | − | 0.901650i | ||||
\(33\) | −4.18997 | −0.729380 | ||||||||
\(34\) | −1.33151 | − | 5.82528i | −0.228352 | − | 0.999027i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.57389 | + | 15.9615i | −0.928982 | + | 2.66024i | ||||
\(37\) | −2.41056 | − | 0.998488i | −0.396294 | − | 0.164150i | 0.175631 | − | 0.984456i | \(-0.443803\pi\) |
−0.571925 | + | 0.820306i | \(0.693803\pi\) | |||||||
\(38\) | −4.53718 | + | 3.22145i | −0.736028 | + | 0.522588i | ||||
\(39\) | 13.4086 | + | 13.4086i | 2.14709 | + | 2.14709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62808 | − | 4.62808i | 0.722785 | − | 0.722785i | −0.246387 | − | 0.969172i | \(-0.579243\pi\) |
0.969172 | + | 0.246387i | \(0.0792434\pi\) | |||||||
\(42\) | −1.16158 | + | 6.84962i | −0.179236 | + | 1.05692i | ||||
\(43\) | −0.394030 | + | 0.951273i | −0.0600890 | + | 0.145068i | −0.951072 | − | 0.308968i | \(-0.900016\pi\) |
0.890983 | + | 0.454036i | \(0.150016\pi\) | |||||||
\(44\) | −0.140393 | − | 2.47215i | −0.0211650 | − | 0.372691i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.88536 | − | 9.37304i | 0.867750 | − | 1.38198i | ||||
\(47\) | − | 2.36232i | − | 0.344580i | −0.985046 | − | 0.172290i | \(-0.944883\pi\) | ||
0.985046 | − | 0.172290i | \(-0.0551166\pi\) | |||||||
\(48\) | −13.0128 | − | 3.73119i | −1.87823 | − | 0.538551i | ||||
\(49\) | − | 4.89290i | − | 0.698986i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.2112 | + | 5.47226i | −1.84994 | + | 0.766269i | ||||
\(52\) | −7.46202 | + | 8.36058i | −1.03480 | + | 1.15940i | ||||
\(53\) | −1.51295 | + | 3.65259i | −0.207820 | + | 0.501722i | −0.993079 | − | 0.117445i | \(-0.962530\pi\) |
0.785259 | + | 0.619167i | \(0.212530\pi\) | |||||||
\(54\) | 25.7329 | + | 4.36386i | 3.50180 | + | 0.593847i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.08032 | − | 0.455844i | −0.545255 | − | 0.0609147i | ||||
\(57\) | 9.41592 | + | 9.41592i | 1.24717 | + | 1.24717i | ||||
\(58\) | 1.81607 | + | 2.55781i | 0.238462 | + | 0.335857i | ||||
\(59\) | −0.648566 | − | 0.268645i | −0.0844361 | − | 0.0349746i | 0.340066 | − | 0.940402i | \(-0.389551\pi\) |
−0.424502 | + | 0.905427i | \(0.639551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01738 | + | 7.28461i | 0.386336 | + | 0.932698i | 0.990709 | + | 0.135997i | \(0.0434237\pi\) |
−0.604373 | + | 0.796701i | \(0.706576\pi\) | |||||||
\(62\) | −1.33023 | + | 0.304057i | −0.168940 | + | 0.0386153i | ||||
\(63\) | 12.2708 | 1.54597 | ||||||||
\(64\) | 1.76545 | − | 7.80277i | 0.220681 | − | 0.975346i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.77653 | + | 1.32037i | −0.711042 | + | 0.162526i | ||||
\(67\) | −0.684344 | − | 1.65215i | −0.0836059 | − | 0.201843i | 0.876548 | − | 0.481315i | \(-0.159841\pi\) |
−0.960154 | + | 0.279472i | \(0.909841\pi\) | |||||||
\(68\) | −3.67139 | − | 7.61147i | −0.445222 | − | 0.923027i | ||||
\(69\) | −24.4692 | − | 10.1355i | −2.94574 | − | 1.22017i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.24109 | + | 6.24109i | 0.740681 | + | 0.740681i | 0.972709 | − | 0.232028i | \(-0.0745362\pi\) |
−0.232028 | + | 0.972709i | \(0.574536\pi\) | |||||||
\(72\) | −2.65462 | + | 23.7619i | −0.312850 | + | 2.80036i | ||||
\(73\) | 5.70275 | − | 5.70275i | 0.667457 | − | 0.667457i | −0.289670 | − | 0.957127i | \(-0.593546\pi\) |
0.957127 | + | 0.289670i | \(0.0935455\pi\) | |||||||
\(74\) | −3.63799 | − | 0.616942i | −0.422908 | − | 0.0717181i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.24006 | + | 5.87105i | −0.601076 | + | 0.673456i | ||||
\(77\) | −1.66036 | + | 0.687743i | −0.189216 | + | 0.0783756i | ||||
\(78\) | 22.7113 | + | 14.2605i | 2.57154 | + | 1.61468i | ||||
\(79\) | − | 14.9022i | − | 1.67663i | −0.545186 | − | 0.838315i | \(-0.683541\pi\) | ||
0.545186 | − | 0.838315i | \(-0.316459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 37.0991i | − | 4.12212i | ||||||
\(82\) | 4.92211 | − | 7.83896i | 0.543556 | − | 0.865669i | ||||
\(83\) | −3.35516 | + | 1.38975i | −0.368277 | + | 0.152545i | −0.559144 | − | 0.829071i | \(-0.688870\pi\) |
0.190867 | + | 0.981616i | \(0.438870\pi\) | |||||||
\(84\) | 0.557068 | + | 9.80933i | 0.0607811 | + | 1.07029i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.243462 | + | 1.43565i | −0.0262532 | + | 0.154810i | ||||
\(87\) | 5.30817 | − | 5.30817i | 0.569096 | − | 0.569096i | ||||
\(88\) | −0.972592 | − | 3.36401i | −0.103679 | − | 0.358605i | ||||
\(89\) | −9.90375 | − | 9.90375i | −1.04980 | − | 1.04980i | −0.998693 | − | 0.0511025i | \(-0.983726\pi\) |
−0.0511025 | − | 0.998693i | \(-0.516274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.51432 | + | 3.11253i | 0.787715 | + | 0.326282i | ||||
\(92\) | 5.16021 | − | 14.7768i | 0.537989 | − | 1.54059i | ||||
\(93\) | 1.24962 | + | 3.01685i | 0.129579 | + | 0.312832i | ||||
\(94\) | −0.744427 | − | 3.25683i | −0.0767818 | − | 0.335916i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.1159 | − | 1.04338i | −1.95101 | − | 0.106490i | ||||
\(97\) | −13.1798 | −1.33820 | −0.669101 | − | 0.743171i | \(-0.733321\pi\) | ||||
−0.669101 | + | 0.743171i | \(0.733321\pi\) | |||||||
\(98\) | −1.54188 | − | 6.74564i | −0.155753 | − | 0.681412i | ||||
\(99\) | 4.00510 | + | 9.66916i | 0.402528 | + | 0.971787i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.67079 | + | 1.52049i | 0.365257 | + | 0.151295i | 0.557761 | − | 0.830002i | \(-0.311661\pi\) |
−0.192503 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(102\) | −16.4893 | + | 11.7076i | −1.63268 | + | 1.15922i | ||||
\(103\) | 5.18393 | + | 5.18393i | 0.510788 | + | 0.510788i | 0.914768 | − | 0.403980i | \(-0.132374\pi\) |
−0.403980 | + | 0.914768i | \(0.632374\pi\) | |||||||
\(104\) | −7.65294 | + | 13.8779i | −0.750432 | + | 1.36084i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.934818 | + | 5.51244i | −0.0907975 | + | 0.535415i | ||||
\(107\) | 4.27693 | − | 10.3254i | 0.413467 | − | 0.998197i | −0.570733 | − | 0.821136i | \(-0.693341\pi\) |
0.984200 | − | 0.177061i | \(-0.0566590\pi\) | |||||||
\(108\) | 36.8520 | − | 2.09281i | 3.54608 | − | 0.201381i | ||||
\(109\) | 12.7925 | − | 5.29882i | 1.22530 | − | 0.507534i | 0.326207 | − | 0.945298i | \(-0.394229\pi\) |
0.899090 | + | 0.437764i | \(0.144229\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.83018i | 0.838123i | ||||||||
\(112\) | −5.76901 | + | 0.657360i | −0.545120 | + | 0.0621146i | ||||
\(113\) | 6.33910i | 0.596332i | 0.954514 | + | 0.298166i | \(0.0963750\pi\) | ||||
−0.954514 | + | 0.298166i | \(0.903625\pi\) | |||||||
\(114\) | 15.9485 | + | 10.0141i | 1.49372 | + | 0.937909i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30977 | + | 2.95405i | 0.307305 | + | 0.274277i | ||||
\(117\) | 18.1259 | − | 43.7599i | 1.67574 | − | 4.04561i | ||||
\(118\) | −0.978807 | − | 0.165989i | −0.0901065 | − | 0.0152806i | ||||
\(119\) | −4.33698 | + | 4.33698i | −0.397571 | + | 0.397571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.69431 | + | 6.69431i | 0.608574 | + | 0.608574i | ||||
\(122\) | 6.45550 | + | 9.09212i | 0.584454 | + | 0.823162i | ||||
\(123\) | −20.4643 | − | 8.47660i | −1.84521 | − | 0.764310i | ||||
\(124\) | −1.73812 | + | 0.838381i | −0.156088 | + | 0.0752888i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 16.9172 | − | 3.86683i | 1.50710 | − | 0.344484i | ||||
\(127\) | 11.3243 | 1.00487 | 0.502435 | − | 0.864615i | \(-0.332438\pi\) | ||||
0.502435 | + | 0.864615i | \(0.332438\pi\) | |||||||
\(128\) | −0.0249011 | − | 11.3137i | −0.00220097 | − | 0.999998i | ||||
\(129\) | 3.48462 | 0.306804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.92584 | − | 7.06361i | −0.255632 | − | 0.617151i | 0.743008 | − | 0.669282i | \(-0.233398\pi\) |
−0.998640 | + | 0.0521319i | \(0.983398\pi\) | |||||||
\(132\) | −7.54778 | + | 3.64067i | −0.656950 | + | 0.316879i | ||||
\(133\) | 5.27678 | + | 2.18571i | 0.457555 | + | 0.189526i | ||||
\(134\) | −1.46411 | − | 2.06210i | −0.126480 | − | 0.178138i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.46016 | − | 9.33666i | −0.639703 | − | 0.800612i | ||||
\(137\) | −9.25823 | + | 9.25823i | −0.790984 | + | 0.790984i | −0.981654 | − | 0.190670i | \(-0.938934\pi\) |
0.190670 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(138\) | −36.9286 | − | 6.26247i | −3.14357 | − | 0.533097i | ||||
\(139\) | −0.956760 | + | 2.30982i | −0.0811513 | + | 0.195917i | −0.959247 | − | 0.282568i | \(-0.908814\pi\) |
0.878096 | + | 0.478485i | \(0.158814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.38619 | + | 3.05946i | −0.622029 | + | 0.257653i | ||||
\(142\) | 10.5710 | + | 6.63759i | 0.887102 | + | 0.557014i | ||||
\(143\) | 6.93708i | 0.580108i | ||||||||
\(144\) | 3.82816 | + | 33.5960i | 0.319013 | + | 2.79967i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.06506 | − | 9.65922i | 0.501948 | − | 0.799403i | ||||
\(147\) | −15.2985 | + | 6.33684i | −1.26180 | + | 0.522654i | ||||
\(148\) | −5.20996 | + | 0.295872i | −0.428256 | + | 0.0243205i | ||||
\(149\) | −7.06329 | + | 17.0523i | −0.578647 | + | 1.39698i | 0.315380 | + | 0.948965i | \(0.397868\pi\) |
−0.894027 | + | 0.448012i | \(0.852132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2469 | − | 13.2469i | 1.07802 | − | 1.07802i | 0.0813322 | − | 0.996687i | \(-0.474083\pi\) |
0.996687 | − | 0.0813322i | \(-0.0259175\pi\) | |||||||
\(152\) | −5.37412 | + | 9.74545i | −0.435899 | + | 0.790460i | ||||
\(153\) | 25.2566 | + | 25.2566i | 2.04187 | + | 2.04187i | ||||
\(154\) | −2.07234 | + | 1.47138i | −0.166994 | + | 0.118568i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 35.8049 | + | 12.5034i | 2.86668 | + | 1.00107i | ||||
\(157\) | −4.36271 | − | 10.5325i | −0.348182 | − | 0.840586i | −0.996835 | − | 0.0795017i | \(-0.974667\pi\) |
0.648652 | − | 0.761085i | \(-0.275333\pi\) | |||||||
\(158\) | −4.69607 | − | 20.5451i | −0.373599 | − | 1.63448i | ||||
\(159\) | 13.3799 | 1.06109 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3600 | −0.895297 | ||||||||
\(162\) | −11.6909 | − | 51.1469i | −0.918522 | − | 4.01848i | ||||
\(163\) | −4.95082 | − | 11.9523i | −0.387778 | − | 0.936179i | −0.990410 | − | 0.138160i | \(-0.955881\pi\) |
0.602632 | − | 0.798019i | \(-0.294119\pi\) | |||||||
\(164\) | 4.31564 | − | 12.3583i | 0.336995 | − | 0.965023i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.18767 | + | 2.97329i | −0.325026 | + | 0.230772i | ||||
\(167\) | −6.45942 | − | 6.45942i | −0.499845 | − | 0.499845i | 0.411545 | − | 0.911390i | \(-0.364989\pi\) |
−0.911390 | + | 0.411545i | \(0.864989\pi\) | |||||||
\(168\) | 3.85918 | + | 13.3482i | 0.297742 | + | 1.02983i | ||||
\(169\) | 13.0074 | − | 13.0074i | 1.00057 | − | 1.00057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.7286 | − | 30.7295i | 0.973379 | − | 2.34995i | ||||
\(172\) | 0.116759 | + | 2.05599i | 0.00890278 | + | 0.156768i | ||||
\(173\) | 11.6647 | − | 4.83167i | 0.886849 | − | 0.367345i | 0.107700 | − | 0.994183i | \(-0.465651\pi\) |
0.779149 | + | 0.626838i | \(0.215651\pi\) | |||||||
\(174\) | 5.64541 | − | 8.99089i | 0.427977 | − | 0.681598i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.40096 | − | 4.33133i | −0.180979 | − | 0.326486i | ||||
\(177\) | 2.37577i | 0.178574i | ||||||||
\(178\) | −16.7748 | − | 10.5330i | −1.25733 | − | 0.789478i | ||||
\(179\) | 1.39173 | − | 0.576474i | 0.104023 | − | 0.0430877i | −0.330065 | − | 0.943958i | \(-0.607071\pi\) |
0.434088 | + | 0.900870i | \(0.357071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.941575 | + | 2.27316i | −0.0699867 | + | 0.168963i | −0.955002 | − | 0.296599i | \(-0.904148\pi\) |
0.885016 | + | 0.465562i | \(0.154148\pi\) | |||||||
\(182\) | 11.3405 | + | 1.92316i | 0.840615 | + | 0.142554i | ||||
\(183\) | 18.8687 | − | 18.8687i | 1.39481 | − | 1.39481i | ||||
\(184\) | 2.45760 | − | 21.9983i | 0.181177 | − | 1.62174i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.67348 | + | 3.76541i | 0.196029 | + | 0.276093i | ||||
\(187\) | −4.83304 | − | 2.00191i | −0.353427 | − | 0.146394i | ||||
\(188\) | −2.05262 | − | 4.25546i | −0.149703 | − | 0.310362i | ||||
\(189\) | −10.2521 | − | 24.7507i | −0.745729 | − | 1.80035i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0923 | 1.09204 | 0.546020 | − | 0.837772i | \(-0.316142\pi\) | ||||
0.546020 | + | 0.837772i | \(0.316142\pi\) | |||||||
\(192\) | −26.6831 | + | 4.58545i | −1.92569 | + | 0.330926i | ||||
\(193\) | 2.95918 | 0.213007 | 0.106503 | − | 0.994312i | \(-0.466035\pi\) | ||||
0.106503 | + | 0.994312i | \(0.466035\pi\) | |||||||
\(194\) | −18.1704 | + | 4.15328i | −1.30456 | + | 0.298188i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.25145 | − | 8.81404i | −0.303675 | − | 0.629574i | ||||
\(197\) | 12.4136 | + | 5.14189i | 0.884433 | + | 0.366344i | 0.778215 | − | 0.627998i | \(-0.216126\pi\) |
0.106219 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(198\) | 8.56866 | + | 12.0684i | 0.608948 | + | 0.857660i | ||||
\(199\) | 7.68494 | + | 7.68494i | 0.544771 | + | 0.544771i | 0.924924 | − | 0.380153i | \(-0.124129\pi\) |
−0.380153 | + | 0.924924i | \(0.624129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.27943 | + | 4.27943i | −0.301848 | + | 0.301848i | ||||
\(202\) | 5.53991 | + | 0.939476i | 0.389787 | + | 0.0661013i | ||||
\(203\) | 1.23218 | − | 2.97475i | 0.0864823 | − | 0.208787i | ||||
\(204\) | −19.0437 | + | 21.3369i | −1.33333 | + | 1.49388i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.78045 | + | 5.51327i | 0.611763 | + | 0.384128i | ||||
\(207\) | 66.1556i | 4.59813i | ||||||||
\(208\) | −6.17751 | + | 21.5444i | −0.428333 | + | 1.49384i | ||||
\(209\) | 4.87143i | 0.336964i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.07097 | + | 1.27204i | −0.211414 | + | 0.0875707i | −0.485877 | − | 0.874027i | \(-0.661500\pi\) |
0.274463 | + | 0.961598i | \(0.411500\pi\) | |||||||
\(212\) | 0.448317 | + | 7.89435i | 0.0307906 | + | 0.542186i | ||||
\(213\) | 11.4309 | − | 27.5967i | 0.783234 | − | 1.89089i | ||||
\(214\) | 2.64262 | − | 15.5830i | 0.180646 | − | 1.06523i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 50.1467 | − | 14.4983i | 3.41205 | − | 0.986482i | ||||
\(217\) | 0.990373 | + | 0.990373i | 0.0672309 | + | 0.0672309i | ||||
\(218\) | 15.9666 | − | 11.3365i | 1.08140 | − | 0.767804i | ||||
\(219\) | −25.2163 | − | 10.4449i | −1.70396 | − | 0.705803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.06009 | + | 21.8730i | 0.609447 | + | 1.47134i | ||||
\(222\) | 2.78262 | + | 12.1738i | 0.186757 | + | 0.817051i | ||||
\(223\) | −23.3670 | −1.56477 | −0.782384 | − | 0.622796i | \(-0.785996\pi\) | ||||
−0.782384 | + | 0.622796i | \(0.785996\pi\) | |||||||
\(224\) | −7.74633 | + | 2.72423i | −0.517573 | + | 0.182021i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.99761 | + | 8.73945i | 0.132879 | + | 0.581339i | ||||
\(227\) | −4.22308 | − | 10.1954i | −0.280295 | − | 0.676693i | 0.719547 | − | 0.694444i | \(-0.244349\pi\) |
−0.999842 | + | 0.0177508i | \(0.994349\pi\) | |||||||
\(228\) | 25.1433 | + | 8.78027i | 1.66515 | + | 0.581487i | ||||
\(229\) | 16.7615 | + | 6.94283i | 1.10763 | + | 0.458795i | 0.860121 | − | 0.510090i | \(-0.170388\pi\) |
0.247509 | + | 0.968886i | \(0.420388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.30069 | + | 4.30069i | 0.282965 | + | 0.282965i | ||||
\(232\) | 5.49394 | + | 3.02963i | 0.360695 | + | 0.198905i | ||||
\(233\) | −19.1508 | + | 19.1508i | −1.25461 | + | 1.25461i | −0.300978 | + | 0.953631i | \(0.597313\pi\) |
−0.953631 | + | 0.300978i | \(0.902687\pi\) | |||||||
\(234\) | 11.1996 | − | 66.0419i | 0.732141 | − | 4.31729i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.40175 | + | 0.0796047i | −0.0912460 | + | 0.00518183i | ||||
\(237\) | −46.5943 | + | 19.3000i | −3.02662 | + | 1.25367i | ||||
\(238\) | −4.61252 | + | 7.34591i | −0.298985 | + | 0.476165i | ||||
\(239\) | 19.5640i | 1.26549i | 0.774360 | + | 0.632745i | \(0.218072\pi\) | ||||
−0.774360 | + | 0.632745i | \(0.781928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.63126i | 0.298325i | 0.988813 | + | 0.149163i | \(0.0476578\pi\) | ||||
−0.988813 | + | 0.149163i | \(0.952342\pi\) | |||||||
\(242\) | 11.3387 | + | 7.11961i | 0.728880 | + | 0.457666i | ||||
\(243\) | −64.8441 | + | 26.8593i | −4.15975 | + | 1.72302i | ||||
\(244\) | 11.7651 | + | 10.5006i | 0.753182 | + | 0.672233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.8845 | − | 5.23750i | −1.96912 | − | 0.333931i | ||||
\(247\) | 15.5894 | − | 15.5894i | 0.991928 | − | 0.991928i | ||||
\(248\) | −2.13208 | + | 1.70357i | −0.135387 | + | 0.108177i | ||||
\(249\) | 8.69060 | + | 8.69060i | 0.550744 | + | 0.550744i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7556 | + | 4.45513i | 0.678890 | + | 0.281205i | 0.695363 | − | 0.718659i | \(-0.255244\pi\) |
−0.0164729 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(252\) | 22.1044 | − | 10.6621i | 1.39245 | − | 0.671647i | ||||
\(253\) | −3.70785 | − | 8.95154i | −0.233111 | − | 0.562779i | ||||
\(254\) | 15.6123 | − | 3.56858i | 0.979605 | − | 0.223913i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.59956 | − | 15.5898i | −0.224973 | − | 0.974365i | ||||
\(257\) | −4.04829 | −0.252525 | −0.126263 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126263 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(258\) | 4.80410 | − | 1.09809i | 0.299090 | − | 0.0683644i | ||||
\(259\) | 1.44939 | + | 3.49914i | 0.0900607 | + | 0.217426i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.3236 | − | 7.17567i | −1.07230 | − | 0.444163i | ||||
\(262\) | −6.25966 | − | 8.81629i | −0.386723 | − | 0.544672i | ||||
\(263\) | 1.60540 | + | 1.60540i | 0.0989933 | + | 0.0989933i | 0.754869 | − | 0.655876i | \(-0.227700\pi\) |
−0.655876 | + | 0.754869i | \(0.727700\pi\) | |||||||
\(264\) | −9.25853 | + | 7.39773i | −0.569823 | + | 0.455299i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.96365 | + | 1.35050i | 0.488283 | + | 0.0828046i | ||||
\(267\) | −18.1393 | + | 43.7922i | −1.11011 | + | 2.68004i | ||||
\(268\) | −2.66833 | − | 2.38155i | −0.162994 | − | 0.145476i | ||||
\(269\) | 3.38365 | − | 1.40155i | 0.206305 | − | 0.0854542i | −0.277138 | − | 0.960830i | \(-0.589386\pi\) |
0.483443 | + | 0.875376i | \(0.339386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4256i | 1.36226i | 0.732165 | + | 0.681128i | \(0.238510\pi\) | ||||
−0.732165 | + | 0.681128i | \(0.761490\pi\) | |||||||
\(272\) | −13.2272 | − | 10.5212i | −0.802018 | − | 0.637940i | ||||
\(273\) | − | 27.5258i | − | 1.66594i | ||||||
\(274\) | −9.84642 | + | 15.6814i | −0.594844 | + | 0.947350i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −52.8853 | + | 3.00334i | −3.18332 | + | 0.180780i | ||||
\(277\) | −2.20449 | + | 5.32210i | −0.132455 | + | 0.319774i | −0.976167 | − | 0.217022i | \(-0.930366\pi\) |
0.843712 | + | 0.536796i | \(0.180366\pi\) | |||||||
\(278\) | −0.591160 | + | 3.48595i | −0.0354554 | + | 0.209074i | ||||
\(279\) | 5.76747 | − | 5.76747i | 0.345289 | − | 0.345289i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81582 | + | 1.81582i | 0.108323 | + | 0.108323i | 0.759191 | − | 0.650868i | \(-0.225595\pi\) |
−0.650868 | + | 0.759191i | \(0.725595\pi\) | |||||||
\(282\) | −9.21891 | + | 6.54552i | −0.548978 | + | 0.389780i | ||||
\(283\) | 15.2115 | + | 6.30082i | 0.904232 | + | 0.374545i | 0.785846 | − | 0.618423i | \(-0.212228\pi\) |
0.118386 | + | 0.992968i | \(0.462228\pi\) | |||||||
\(284\) | 16.6655 | + | 5.81976i | 0.988917 | + | 0.345339i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.18605 | + | 9.56386i | 0.129264 | + | 0.565523i | ||||
\(287\) | −9.50075 | −0.560812 | ||||||||
\(288\) | 15.8647 | + | 45.1110i | 0.934835 | + | 2.65819i | ||||
\(289\) | −0.853410 | −0.0502006 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.0692 | + | 41.2087i | 1.00062 | + | 2.41570i | ||||
\(292\) | 5.31777 | − | 15.2280i | 0.311199 | − | 0.891152i | ||||
\(293\) | −15.7830 | − | 6.53752i | −0.922051 | − | 0.381926i | −0.129394 | − | 0.991593i | \(-0.541303\pi\) |
−0.792658 | + | 0.609667i | \(0.791303\pi\) | |||||||
\(294\) | −19.0945 | + | 13.5573i | −1.11361 | + | 0.790676i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.08951 | + | 2.04970i | −0.412069 | + | 0.119136i | ||||
\(297\) | 16.1569 | − | 16.1569i | 0.937521 | − | 0.937521i | ||||
\(298\) | −4.36424 | + | 25.7351i | −0.252814 | + | 1.49079i | ||||
\(299\) | −16.7807 | + | 40.5122i | −0.970452 | + | 2.34288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38085 | − | 0.571968i | 0.0795910 | − | 0.0329677i | ||||
\(302\) | 14.0885 | − | 22.4374i | 0.810703 | − | 1.29113i | ||||
\(303\) | − | 13.4465i | − | 0.772484i | ||||||
\(304\) | −4.33803 | + | 15.1292i | −0.248803 | + | 0.867716i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 42.7792 | + | 26.8612i | 2.44552 | + | 1.53555i | ||||
\(307\) | −0.490845 | + | 0.203315i | −0.0280140 | + | 0.0116038i | −0.396646 | − | 0.917971i | \(-0.629826\pi\) |
0.368632 | + | 0.929575i | \(0.379826\pi\) | |||||||
\(308\) | −2.39338 | + | 2.68158i | −0.136375 | + | 0.152797i | ||||
\(309\) | 9.49467 | − | 22.9222i | 0.540133 | − | 1.30400i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.66343 | − | 2.66343i | 0.151029 | − | 0.151029i | −0.627548 | − | 0.778578i | \(-0.715942\pi\) |
0.778578 | + | 0.627548i | \(0.215942\pi\) | |||||||
\(312\) | 53.3028 | + | 5.95487i | 3.01768 | + | 0.337128i | ||||
\(313\) | 13.7553 | + | 13.7553i | 0.777493 | + | 0.777493i | 0.979404 | − | 0.201911i | \(-0.0647150\pi\) |
−0.201911 | + | 0.979404i | \(0.564715\pi\) | |||||||
\(314\) | −9.33375 | − | 13.1459i | −0.526734 | − | 0.741868i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.9485 | − | 26.8447i | −0.728413 | − | 1.51013i | ||||
\(317\) | 8.28931 | + | 20.0122i | 0.465574 | + | 1.12399i | 0.966076 | + | 0.258259i | \(0.0831489\pi\) |
−0.500502 | + | 0.865736i | \(0.666851\pi\) | |||||||
\(318\) | 18.4462 | − | 4.21634i | 1.03441 | − | 0.236440i | ||||
\(319\) | 2.74624 | 0.153760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.8233 | −2.11109 | ||||||||
\(322\) | −15.6616 | + | 3.57984i | −0.872787 | + | 0.199497i | ||||
\(323\) | 6.36227 | + | 15.3599i | 0.354006 | + | 0.854646i | ||||
\(324\) | −32.2354 | − | 66.8300i | −1.79086 | − | 3.71278i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.5920 | − | 14.9180i | −0.586635 | − | 0.826234i | ||||
\(327\) | −33.1353 | − | 33.1353i | −1.83238 | − | 1.83238i | ||||
\(328\) | 2.05537 | − | 18.3979i | 0.113489 | − | 1.01585i | ||||
\(329\) | −2.42474 | + | 2.42474i | −0.133680 | + | 0.133680i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.45036 | + | 8.32990i | −0.189649 | + | 0.457853i | −0.989892 | − | 0.141823i | \(-0.954704\pi\) |
0.800243 | + | 0.599675i | \(0.204704\pi\) | |||||||
\(332\) | −4.83641 | + | 5.41879i | −0.265432 | + | 0.297395i | ||||
\(333\) | 20.3773 | − | 8.44057i | 1.11667 | − | 0.462540i | ||||
\(334\) | −10.9409 | − | 6.86980i | −0.598657 | − | 0.375899i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.52683 | + | 17.1864i | 0.519731 | + | 0.937595i | ||||
\(337\) | 12.2658i | 0.668162i | 0.942544 | + | 0.334081i | \(0.108426\pi\) | ||||
−0.942544 | + | 0.334081i | \(0.891574\pi\) | |||||||
\(338\) | 13.8338 | − | 22.0318i | 0.752460 | − | 1.19837i | ||||
\(339\) | 19.8203 | − | 8.20982i | 1.07649 | − | 0.445896i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.457147 | + | 1.10365i | −0.0247559 | + | 0.0597660i | ||||
\(342\) | 7.86470 | − | 46.3766i | 0.425274 | − | 2.50776i | ||||
\(343\) | −12.2072 | + | 12.2072i | −0.659125 | + | 0.659125i | ||||
\(344\) | 0.808865 | + | 2.79771i | 0.0436111 | + | 0.150842i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.5590 | − | 10.3371i | 0.782698 | − | 0.555724i | ||||
\(347\) | 16.2433 | + | 6.72820i | 0.871987 | + | 0.361189i | 0.773384 | − | 0.633938i | \(-0.218563\pi\) |
0.0986033 | + | 0.995127i | \(0.468563\pi\) | |||||||
\(348\) | 4.94982 | − | 14.1744i | 0.265338 | − | 0.759826i | ||||
\(349\) | −10.6274 | − | 25.6568i | −0.568871 | − | 1.37338i | −0.902507 | − | 0.430675i | \(-0.858275\pi\) |
0.333636 | − | 0.942702i | \(-0.391725\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −103.410 | −5.51961 | ||||||||
\(352\) | −4.67501 | − | 5.21481i | −0.249179 | − | 0.277951i | ||||
\(353\) | 21.9232 | 1.16686 | 0.583428 | − | 0.812165i | \(-0.301711\pi\) | ||||
0.583428 | + | 0.812165i | \(0.301711\pi\) | |||||||
\(354\) | 0.748667 | + | 3.27538i | 0.0397912 | + | 0.174084i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.4459 | − | 9.23516i | −1.40163 | − | 0.489463i | ||||
\(357\) | 19.1772 | + | 7.94344i | 1.01496 | + | 0.420412i | ||||
\(358\) | 1.73706 | − | 1.23333i | 0.0918064 | − | 0.0651835i | ||||
\(359\) | 4.02137 | + | 4.02137i | 0.212240 | + | 0.212240i | 0.805218 | − | 0.592978i | \(-0.202048\pi\) |
−0.592978 | + | 0.805218i | \(0.702048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.48770 | + | 2.48770i | −0.130931 | + | 0.130931i | ||||
\(362\) | −0.581777 | + | 3.43063i | −0.0305775 | + | 0.180310i | ||||
\(363\) | 12.2610 | − | 29.6007i | 0.643537 | − | 1.55364i | ||||
\(364\) | 16.2407 | − | 0.922305i | 0.851245 | − | 0.0483419i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 20.0675 | − | 31.9595i | 1.04894 | − | 1.67055i | ||||
\(367\) | − | 28.1923i | − | 1.47163i | −0.677183 | − | 0.735814i | \(-0.736800\pi\) | ||
0.677183 | − | 0.735814i | \(-0.263200\pi\) | |||||||
\(368\) | −3.54404 | − | 31.1026i | −0.184746 | − | 1.62133i | ||||
\(369\) | 55.3280i | 2.88026i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.30204 | − | 2.19618i | 0.275268 | − | 0.114020i | ||||
\(372\) | 4.87239 | + | 4.34873i | 0.252622 | + | 0.225471i | ||||
\(373\) | −0.472600 | + | 1.14096i | −0.0244703 | + | 0.0590765i | −0.935642 | − | 0.352950i | \(-0.885179\pi\) |
0.911172 | + | 0.412026i | \(0.135179\pi\) | |||||||
\(374\) | −7.29396 | − | 1.23693i | −0.377162 | − | 0.0639604i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.17087 | − | 5.21999i | −0.215096 | − | 0.269201i | ||||
\(377\) | −8.78842 | − | 8.78842i | −0.452627 | − | 0.452627i | ||||
\(378\) | −21.9337 | − | 30.8920i | −1.12815 | − | 1.58891i | ||||
\(379\) | −6.22454 | − | 2.57829i | −0.319733 | − | 0.132438i | 0.217044 | − | 0.976162i | \(-0.430358\pi\) |
−0.536777 | + | 0.843724i | \(0.680358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6662 | − | 35.4073i | −0.751372 | − | 1.81397i | ||||
\(382\) | 20.8071 | − | 4.75597i | 1.06458 | − | 0.243337i | ||||
\(383\) | 6.12827 | 0.313140 | 0.156570 | − | 0.987667i | \(-0.449956\pi\) | ||||
0.156570 | + | 0.987667i | \(0.449956\pi\) | |||||||
\(384\) | −35.3419 | + | 14.7303i | −1.80353 | + | 0.751702i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.07970 | − | 0.932514i | 0.207651 | − | 0.0474637i | ||||
\(387\) | −3.33087 | − | 8.04144i | −0.169318 | − | 0.408769i | ||||
\(388\) | −23.7419 | + | 11.4519i | −1.20531 | + | 0.581382i | ||||
\(389\) | 15.9683 | + | 6.61427i | 0.809623 | + | 0.335357i | 0.748804 | − | 0.662792i | \(-0.230629\pi\) |
0.0608194 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.3821 | − | 23.3821i | −1.18248 | − | 1.18248i | ||||
\(392\) | −8.63882 | − | 10.8118i | −0.436326 | − | 0.546078i | ||||
\(393\) | −18.2963 | + | 18.2963i | −0.922925 | + | 0.922925i | ||||
\(394\) | 18.7345 | + | 3.17705i | 0.943828 | + | 0.160058i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.6163 | + | 13.9379i | 0.784748 | + | 0.700407i | ||||
\(397\) | −14.8241 | + | 6.14033i | −0.743999 | + | 0.308174i | −0.722290 | − | 0.691590i | \(-0.756911\pi\) |
−0.0217084 | + | 0.999764i | \(0.506911\pi\) | |||||||
\(398\) | 13.0166 | + | 8.17318i | 0.652464 | + | 0.409684i | ||||
\(399\) | − | 19.3295i | − | 0.967684i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.3193i | − | 1.36426i | −0.731230 | − | 0.682131i | \(-0.761053\pi\) | ||
0.731230 | − | 0.682131i | \(-0.238947\pi\) | |||||||
\(402\) | −4.55131 | + | 7.24843i | −0.226999 | + | 0.361519i | ||||
\(403\) | 4.99481 | − | 2.06892i | 0.248809 | − | 0.103060i | ||||
\(404\) | 7.93369 | − | 0.450551i | 0.394716 | − | 0.0224158i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.761338 | − | 4.48946i | 0.0377846 | − | 0.222808i | ||||
\(407\) | −2.28419 | + | 2.28419i | −0.113223 | + | 0.113223i | ||||
\(408\) | −19.5309 | + | 35.4174i | −0.966925 | + | 1.75342i | ||||
\(409\) | −2.23691 | − | 2.23691i | −0.110608 | − | 0.110608i | 0.649637 | − | 0.760245i | \(-0.274921\pi\) |
−0.760245 | + | 0.649637i | \(0.774921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.9378 | + | 16.9570i | 2.01931 | + | 0.836427i | ||||
\(412\) | 13.8426 | + | 4.83397i | 0.681976 | + | 0.238152i | ||||
\(413\) | 0.389961 | + | 0.941448i | 0.0191887 | + | 0.0463256i | ||||
\(414\) | 20.8473 | + | 91.2059i | 1.02459 | + | 4.48253i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.72747 | + | 31.6491i | −0.0846960 | + | 1.55172i | ||||
\(417\) | 8.46115 | 0.414344 | ||||||||
\(418\) | 1.53511 | + | 6.71603i | 0.0750848 | + | 0.328492i | ||||
\(419\) | 3.88329 | + | 9.37508i | 0.189711 | + | 0.458003i | 0.989904 | − | 0.141740i | \(-0.0452696\pi\) |
−0.800193 | + | 0.599743i | \(0.795270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.20171 | + | 1.32619i | 0.156042 | + | 0.0646347i | 0.459337 | − | 0.888262i | \(-0.348087\pi\) |
−0.303295 | + | 0.952897i | \(0.598087\pi\) | |||||||
\(422\) | −3.83296 | + | 2.72144i | −0.186586 | + | 0.132478i | ||||
\(423\) | 14.1206 | + | 14.1206i | 0.686566 | + | 0.686566i | ||||
\(424\) | 3.10579 | + | 10.7423i | 0.150830 | + | 0.521693i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.06290 | − | 41.6485i | 0.342199 | − | 2.01788i | ||||
\(427\) | 4.37998 | − | 10.5742i | 0.211962 | − | 0.511722i | ||||
\(428\) | −1.26734 | − | 22.3164i | −0.0612591 | − | 1.07870i | ||||
\(429\) | 21.6899 | − | 8.98427i | 1.04720 | − | 0.433765i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27.4030i | − | 1.31996i | −0.751285 | − | 0.659978i | \(-0.770566\pi\) | ||
0.751285 | − | 0.659978i | \(-0.229434\pi\) | |||||||
\(432\) | 64.5664 | − | 35.7907i | 3.10645 | − | 1.72198i | ||||
\(433\) | 31.7483i | 1.52573i | 0.646560 | + | 0.762864i | \(0.276207\pi\) | ||||
−0.646560 | + | 0.762864i | \(0.723793\pi\) | |||||||
\(434\) | 1.67748 | + | 1.05329i | 0.0805214 | + | 0.0505597i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.4401 | − | 20.6606i | 0.883121 | − | 0.989465i | ||||
\(437\) | −11.7839 | + | 28.4489i | −0.563701 | + | 1.36089i | ||||
\(438\) | −38.0561 | − | 6.45368i | −1.81839 | − | 0.308369i | ||||
\(439\) | 7.15702 | − | 7.15702i | 0.341586 | − | 0.341586i | −0.515377 | − | 0.856963i | \(-0.672348\pi\) |
0.856963 | + | 0.515377i | \(0.172348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.2469 | + | 29.2469i | 1.39271 | + | 1.39271i | ||||
\(442\) | 19.3835 | + | 27.3003i | 0.921979 | + | 1.29854i | ||||
\(443\) | 6.00467 | + | 2.48722i | 0.285290 | + | 0.118171i | 0.520740 | − | 0.853715i | \(-0.325656\pi\) |
−0.235449 | + | 0.971887i | \(0.575656\pi\) | |||||||
\(444\) | 7.67255 | + | 15.9066i | 0.364123 | + | 0.754894i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −32.2150 | + | 7.36353i | −1.52543 | + | 0.348673i | ||||
\(447\) | 62.4645 | 2.95447 | ||||||||
\(448\) | −9.82106 | + | 6.19685i | −0.464001 | + | 0.292774i | ||||
\(449\) | 8.48000 | 0.400196 | 0.200098 | − | 0.979776i | \(-0.435874\pi\) | ||||
0.200098 | + | 0.979776i | \(0.435874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.10099 | − | 7.48645i | −0.146020 | − | 0.352523i | ||||
\(452\) | 5.50805 | + | 11.4192i | 0.259077 | + | 0.537114i | ||||
\(453\) | −58.5749 | − | 24.2625i | −2.75209 | − | 1.13995i | ||||
\(454\) | −9.03501 | − | 12.7252i | −0.424034 | − | 0.597222i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 37.4308 | + | 4.18169i | 1.75286 | + | 0.195826i | ||||
\(457\) | 17.8416 | − | 17.8416i | 0.834593 | − | 0.834593i | −0.153548 | − | 0.988141i | \(-0.549070\pi\) |
0.988141 | + | 0.153548i | \(0.0490701\pi\) | |||||||
\(458\) | 25.2962 | + | 4.28981i | 1.18201 | + | 0.200450i | ||||
\(459\) | 29.8421 | − | 72.0453i | 1.39291 | − | 3.36279i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.54536 | + | 1.05432i | −0.118549 | + | 0.0491047i | −0.441170 | − | 0.897424i | \(-0.645436\pi\) |
0.322620 | + | 0.946528i | \(0.395436\pi\) | |||||||
\(462\) | 7.28443 | + | 4.57392i | 0.338903 | + | 0.212798i | ||||
\(463\) | − | 26.6297i | − | 1.23759i | −0.785554 | − | 0.618793i | \(-0.787622\pi\) | ||
0.785554 | − | 0.618793i | \(-0.212378\pi\) | |||||||
\(464\) | 8.52897 | + | 2.44554i | 0.395947 | + | 0.113531i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.3675 | + | 32.4373i | −0.943504 | + | 1.50263i | ||||
\(467\) | −5.82058 | + | 2.41096i | −0.269344 | + | 0.111566i | −0.513268 | − | 0.858228i | \(-0.671565\pi\) |
0.243924 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(468\) | −5.37107 | − | 94.5784i | −0.248278 | − | 4.37189i | ||||
\(469\) | −0.993383 | + | 2.39824i | −0.0458702 | + | 0.110740i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.2815 | + | 27.2815i | −1.25706 | + | 1.25706i | ||||
\(472\) | −1.90744 | + | 0.551474i | −0.0877972 | + | 0.0253836i | ||||
\(473\) | 0.901403 | + | 0.901403i | 0.0414466 | + | 0.0414466i | ||||
\(474\) | −58.1556 | + | 41.2911i | −2.67118 | + | 1.89656i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.04420 | + | 11.5810i | −0.185366 | + | 0.530815i | ||||
\(477\) | −12.7895 | − | 30.8766i | −0.585592 | − | 1.41374i | ||||
\(478\) | 6.16512 | + | 26.9721i | 0.281986 | + | 1.23367i | ||||
\(479\) | 8.91801 | 0.407474 | 0.203737 | − | 0.979026i | \(-0.434691\pi\) | ||||
0.203737 | + | 0.979026i | \(0.434691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6196 | 0.666596 | ||||||||
\(482\) | 1.45943 | + | 6.38492i | 0.0664751 | + | 0.290825i | ||||
\(483\) | 14.7125 | + | 35.5191i | 0.669441 | + | 1.61617i | ||||
\(484\) | 17.8758 | + | 6.24239i | 0.812535 | + | 0.283745i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −80.9337 | + | 57.4638i | −3.67123 | + | 2.60661i | ||||
\(487\) | 14.5675 | + | 14.5675i | 0.660115 | + | 0.660115i | 0.955407 | − | 0.295292i | \(-0.0954169\pi\) |
−0.295292 | + | 0.955407i | \(0.595417\pi\) | |||||||
\(488\) | 19.5290 | + | 10.7693i | 0.884038 | + | 0.487502i | ||||
\(489\) | −30.9591 | + | 30.9591i | −1.40002 | + | 1.40002i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1115 | − | 29.2397i | 0.546584 | − | 1.31957i | −0.373420 | − | 0.927662i | \(-0.621815\pi\) |
0.920004 | − | 0.391908i | \(-0.128185\pi\) | |||||||
\(492\) | −44.2296 | + | 2.51178i | −1.99402 | + | 0.113240i | ||||
\(493\) | 8.65904 | − | 3.58669i | 0.389983 | − | 0.161536i | ||||
\(494\) | 16.5798 | − | 26.4050i | 0.745960 | − | 1.18802i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.40256 | + | 3.02051i | −0.107878 | + | 0.135625i | ||||
\(497\) | − | 12.8120i | − | 0.574697i | ||||||
\(498\) | 14.7200 | + | 9.24273i | 0.659618 | + | 0.414176i | ||||
\(499\) | −10.0229 | + | 4.15164i | −0.448689 | + | 0.185853i | −0.595574 | − | 0.803301i | \(-0.703075\pi\) |
0.146885 | + | 0.989154i | \(0.453075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8308 | + | 28.5621i | −0.528562 | + | 1.27606i | ||||
\(502\) | 16.2323 | + | 2.75272i | 0.724481 | + | 0.122860i | ||||
\(503\) | −15.5986 | + | 15.5986i | −0.695505 | + | 0.695505i | −0.963438 | − | 0.267932i | \(-0.913660\pi\) |
0.267932 | + | 0.963438i | \(0.413660\pi\) | |||||||
\(504\) | 27.1145 | − | 21.6650i | 1.20778 | − | 0.965036i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.93271 | − | 11.1727i | −0.352652 | − | 0.496686i | ||||
\(507\) | −57.5159 | − | 23.8239i | −2.55437 | − | 1.05806i | ||||
\(508\) | 20.3995 | − | 9.83969i | 0.905082 | − | 0.436566i | ||||
\(509\) | 1.06698 | + | 2.57591i | 0.0472930 | + | 0.114175i | 0.945761 | − | 0.324864i | \(-0.105319\pi\) |
−0.898468 | + | 0.439040i | \(0.855319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7069 | −0.517883 | ||||||||
\(512\) | −9.87532 | − | 20.3587i | −0.436432 | − | 0.899737i | ||||
\(513\) | −72.6175 | −3.20614 | ||||||||
\(514\) | −5.58120 | + | 1.27572i | −0.246176 | + | 0.0562696i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.27717 | − | 3.02779i | 0.276337 | − | 0.133291i | ||||
\(517\) | −2.70208 | − | 1.11924i | −0.118837 | − | 0.0492241i | ||||
\(518\) | 3.10088 | + | 4.36737i | 0.136245 | + | 0.191891i | ||||
\(519\) | −30.2140 | − | 30.2140i | −1.32625 | − | 1.32625i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9781 | + | 11.9781i | −0.524771 | + | 0.524771i | −0.919009 | − | 0.394238i | \(-0.871009\pi\) |
0.394238 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(522\) | −26.1445 | − | 4.43368i | −1.14431 | − | 0.194057i | ||||
\(523\) | −4.43446 | + | 10.7057i | −0.193905 | + | 0.468129i | −0.990690 | − | 0.136134i | \(-0.956532\pi\) |
0.796785 | + | 0.604263i | \(0.206532\pi\) | |||||||
\(524\) | −11.4082 | − | 10.1821i | −0.498368 | − | 0.444805i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.71920 | + | 1.70739i | 0.118563 | + | 0.0744459i | ||||
\(527\) | 4.07692i | 0.177593i | ||||||||
\(528\) | −10.4331 | + | 13.1165i | −0.454043 | + | 0.570824i | ||||
\(529\) | − | 38.2457i | − | 1.66286i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.48256 | − | 2.27095i | 0.237923 | − | 0.0985508i | ||||
\(532\) | 11.4047 | − | 0.647670i | 0.494457 | − | 0.0280801i | ||||
\(533\) | −14.0342 | + | 33.8816i | −0.607889 | + | 1.46757i | ||||
\(534\) | −11.2079 | + | 66.0906i | −0.485011 | + | 2.86002i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.42920 | − | 2.44248i | −0.191312 | − | 0.105499i | ||||
\(537\) | −3.60488 | − | 3.60488i | −0.155562 | − | 0.155562i | ||||
\(538\) | 4.22323 | − | 2.99853i | 0.182076 | − | 0.129276i | ||||
\(539\) | −5.59663 | − | 2.31820i | −0.241064 | − | 0.0998519i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.28137 | + | 19.9930i | 0.356044 | + | 0.859566i | 0.995848 | + | 0.0910282i | \(0.0290153\pi\) |
−0.639804 | + | 0.768538i | \(0.720985\pi\) | |||||||
\(542\) | 7.06687 | + | 30.9172i | 0.303548 | + | 1.32801i | ||||
\(543\) | 8.32686 | 0.357340 | ||||||||
\(544\) | −21.5513 | − | 10.3369i | −0.924004 | − | 0.443189i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.67410 | − | 37.9487i | −0.371217 | − | 1.62405i | ||||
\(547\) | −12.1997 | − | 29.4527i | −0.521623 | − | 1.25931i | −0.936895 | − | 0.349611i | \(-0.886314\pi\) |
0.415272 | − | 0.909697i | \(-0.363686\pi\) | |||||||
\(548\) | −8.63322 | + | 24.7222i | −0.368793 | + | 1.05608i | ||||
\(549\) | −61.5793 | − | 25.5070i | −2.62814 | − | 1.08861i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.17149 | − | 6.17149i | −0.262914 | − | 0.262914i | ||||
\(552\) | −71.9643 | + | 20.8061i | −3.06300 | + | 0.885566i | ||||
\(553\) | −15.2960 | + | 15.2960i | −0.650453 | + | 0.650453i | ||||
\(554\) | −1.36210 | + | 8.03205i | −0.0578701 | + | 0.341249i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.283507 | + | 4.99222i | 0.0120234 | + | 0.211717i | ||||
\(557\) | −1.09724 | + | 0.454492i | −0.0464916 | + | 0.0192574i | −0.405808 | − | 0.913958i | \(-0.633010\pi\) |
0.359316 | + | 0.933216i | \(0.383010\pi\) | |||||||
\(558\) | 6.13389 | − | 9.76884i | 0.259668 | − | 0.413548i | ||||
\(559\) | − | 5.76928i | − | 0.244015i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.7040i | 0.747464i | ||||||||
\(562\) | 3.07561 | + | 1.93118i | 0.129737 | + | 0.0814621i | ||||
\(563\) | 39.1382 | − | 16.2116i | 1.64948 | − | 0.683236i | 0.652275 | − | 0.757982i | \(-0.273815\pi\) |
0.997203 | + | 0.0747465i | \(0.0238148\pi\) | |||||||
\(564\) | −10.6471 | + | 11.9291i | −0.448322 | + | 0.502308i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.9570 | + | 3.89313i | 0.964956 | + | 0.163641i | ||||
\(567\) | −38.0794 | + | 38.0794i | −1.59919 | + | 1.59919i | ||||
\(568\) | 24.8100 | + | 2.77172i | 1.04100 | + | 0.116299i | ||||
\(569\) | 4.33822 | + | 4.33822i | 0.181868 | + | 0.181868i | 0.792169 | − | 0.610301i | \(-0.208952\pi\) |
−0.610301 | + | 0.792169i | \(0.708952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.2465 | − | 15.4280i | −1.55872 | − | 0.645643i | −0.573853 | − | 0.818958i | \(-0.694552\pi\) |
−0.984866 | + | 0.173316i | \(0.944552\pi\) | |||||||
\(572\) | 6.02763 | + | 12.4964i | 0.252028 | + | 0.522501i | ||||
\(573\) | −19.5462 | − | 47.1886i | −0.816553 | − | 1.97133i | ||||
\(574\) | −13.0983 | + | 2.99393i | −0.546712 | + | 0.124964i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 36.0876 | + | 57.1933i | 1.50365 | + | 2.38305i | ||||
\(577\) | 4.17488 | 0.173802 | 0.0869012 | − | 0.996217i | \(-0.472304\pi\) | ||||
0.0869012 | + | 0.996217i | \(0.472304\pi\) | |||||||
\(578\) | −1.17656 | + | 0.268931i | −0.0489384 | + | 0.0111861i | ||||
\(579\) | −3.83246 | − | 9.25238i | −0.159272 | − | 0.384516i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.87030 | + | 2.01735i | 0.202054 | + | 0.0836936i | ||||
\(582\) | 36.5185 | + | 51.4338i | 1.51374 | + | 2.13200i | ||||
\(583\) | 3.46111 | + | 3.46111i | 0.143344 | + | 0.143344i | ||||
\(584\) | 2.53264 | − | 22.6700i | 0.104801 | − | 0.938090i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.8195 | − | 4.03938i | −0.983973 | − | 0.166865i | ||||
\(587\) | −7.20581 | + | 17.3964i | −0.297415 | + | 0.718024i | 0.702564 | + | 0.711621i | \(0.252038\pi\) |
−0.999979 | + | 0.00640387i | \(0.997962\pi\) | |||||||
\(588\) | −22.0525 | + | 24.7080i | −0.909429 | + | 1.01894i | ||||
\(589\) | 3.50751 | − | 1.45286i | 0.144524 | − | 0.0598639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 45.4725i | − | 1.87049i | ||||||
\(592\) | −9.12809 | + | 5.05991i | −0.375162 | + | 0.207961i | ||||
\(593\) | 9.27068i | 0.380701i | 0.981716 | + | 0.190351i | \(0.0609625\pi\) | ||||
−0.981716 | + | 0.190351i | \(0.939038\pi\) | |||||||
\(594\) | 17.1834 | − | 27.3664i | 0.705045 | − | 1.12286i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.09299 | + | 36.8551i | 0.0857322 | + | 1.50965i | ||||
\(597\) | 14.0754 | − | 33.9811i | 0.576069 | − | 1.39075i | ||||
\(598\) | −10.3684 | + | 61.1404i | −0.423995 | + | 2.50022i | ||||
\(599\) | 22.3629 | − | 22.3629i | 0.913723 | − | 0.913723i | −0.0828402 | − | 0.996563i | \(-0.526399\pi\) |
0.996563 | + | 0.0828402i | \(0.0263991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9624 | + | 25.9624i | 1.05903 | + | 1.05903i | 0.998145 | + | 0.0608851i | \(0.0193923\pi\) |
0.0608851 | + | 0.998145i | \(0.480608\pi\) | |||||||
\(602\) | 1.72348 | − | 1.22369i | 0.0702438 | − | 0.0498739i | ||||
\(603\) | 13.9662 | + | 5.78500i | 0.568749 | + | 0.235583i | ||||
\(604\) | 12.3526 | − | 35.3732i | 0.502622 | − | 1.43931i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.23735 | − | 18.5382i | −0.172131 | − | 0.753062i | ||||
\(607\) | 3.46490 | 0.140636 | 0.0703179 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703179 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(608\) | −1.21308 | + | 22.2249i | −0.0491968 | + | 0.901340i | ||||
\(609\) | −10.8969 | −0.441564 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.06536 | + | 12.2289i | 0.204923 | + | 0.494727i | ||||
\(612\) | 67.4424 | + | 23.5515i | 2.72620 | + | 0.952014i | ||||
\(613\) | 33.2177 | + | 13.7592i | 1.34165 | + | 0.555730i | 0.933956 | − | 0.357388i | \(-0.116333\pi\) |
0.407695 | + | 0.913118i | \(0.366333\pi\) | |||||||
\(614\) | −0.612638 | + | 0.434979i | −0.0247241 | + | 0.0175543i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.45461 | + | 4.45120i | −0.0988991 | + | 0.179344i | ||||
\(617\) | −30.4580 | + | 30.4580i | −1.22619 | + | 1.22619i | −0.260799 | + | 0.965393i | \(0.583986\pi\) |
−0.965393 | + | 0.260799i | \(0.916014\pi\) | |||||||
\(618\) | 5.86654 | − | 34.5938i | 0.235987 | − | 1.39157i | ||||
\(619\) | 4.97518 | − | 12.0112i | 0.199969 | − | 0.482769i | −0.791804 | − | 0.610775i | \(-0.790858\pi\) |
0.991773 | + | 0.128006i | \(0.0408578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 133.439 | − | 55.2723i | 5.35473 | − | 2.21800i | ||||
\(622\) | 2.83264 | − | 4.51127i | 0.113578 | − | 0.180885i | ||||
\(623\) | 20.3309i | 0.814541i | ||||||||
\(624\) | 75.3628 | − | 8.58735i | 3.01693 | − | 0.343769i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.2984 | + | 14.6292i | 0.931192 | + | 0.584699i | ||||
\(627\) | 15.2313 | − | 6.30902i | 0.608281 | − | 0.251958i | ||||
\(628\) | −17.0107 | − | 15.1824i | −0.678799 | − | 0.605845i | ||||
\(629\) | −4.21894 | + | 10.1854i | −0.168220 | + | 0.406119i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.07552 | + | 7.07552i | −0.281672 | + | 0.281672i | −0.833776 | − | 0.552103i | \(-0.813825\pi\) |
0.552103 | + | 0.833776i | \(0.313825\pi\) | |||||||
\(632\) | −26.3111 | − | 32.9293i | −1.04660 | − | 1.30986i | ||||
\(633\) | 7.95447 | + | 7.95447i | 0.316162 | + | 0.316162i | ||||
\(634\) | 17.7345 | + | 24.9777i | 0.704325 | + | 0.991993i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 24.1024 | − | 11.6258i | 0.955721 | − | 0.460992i | ||||
\(637\) | 10.4915 | + | 25.3288i | 0.415689 | + | 1.00356i | ||||
\(638\) | 3.78612 | − | 0.865410i | 0.149894 | − | 0.0342619i | ||||
\(639\) | −74.6112 | −2.95157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.8007 | −1.17706 | −0.588528 | − | 0.808477i | \(-0.700292\pi\) | ||||
−0.588528 | + | 0.808477i | \(0.700292\pi\) | |||||||
\(642\) | −52.1453 | + | 11.9191i | −2.05801 | + | 0.470409i | ||||
\(643\) | −5.62912 | − | 13.5899i | −0.221991 | − | 0.535933i | 0.773169 | − | 0.634200i | \(-0.218670\pi\) |
−0.995160 | + | 0.0982665i | \(0.968670\pi\) | |||||||
\(644\) | −20.4639 | + | 9.87075i | −0.806390 | + | 0.388962i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6117 | + | 19.1711i | 0.535544 | + | 0.754276i | ||||
\(647\) | 29.5002 | + | 29.5002i | 1.15977 | + | 1.15977i | 0.984525 | + | 0.175247i | \(0.0560723\pi\) |
0.175247 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(648\) | −65.5014 | − | 81.9775i | −2.57314 | − | 3.22038i | ||||
\(649\) | −0.614566 | + | 0.614566i | −0.0241238 | + | 0.0241238i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.81393 | − | 4.37921i | 0.0710934 | − | 0.171635i | ||||
\(652\) | −19.3037 | − | 17.2291i | −0.755993 | − | 0.674742i | ||||
\(653\) | −31.2680 | + | 12.9516i | −1.22361 | + | 0.506836i | −0.898556 | − | 0.438859i | \(-0.855383\pi\) |
−0.325054 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(654\) | −56.1239 | − | 35.2404i | −2.19462 | − | 1.37801i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.96399 | − | 26.0121i | −0.115724 | − | 1.01560i | ||||
\(657\) | 68.1755i | 2.65978i | ||||||||
\(658\) | −2.57879 | + | 4.10699i | −0.100532 | + | 0.160107i | ||||
\(659\) | −38.4825 | + | 15.9400i | −1.49907 | + | 0.620933i | −0.973267 | − | 0.229676i | \(-0.926233\pi\) |
−0.525799 | + | 0.850609i | \(0.676233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.78263 | − | 18.7889i | 0.302709 | − | 0.730805i | −0.697194 | − | 0.716883i | \(-0.745568\pi\) |
0.999903 | − | 0.0139222i | \(-0.00443172\pi\) | |||||||
\(662\) | −2.13189 | + | 12.5714i | −0.0828584 | + | 0.488600i | ||||
\(663\) | 56.6558 | − | 56.6558i | 2.20033 | − | 2.20033i | ||||
\(664\) | −4.96014 | + | 8.99474i | −0.192491 | + | 0.349063i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.4335 | − | 18.0581i | 0.985529 | − | 0.699736i | ||||
\(667\) | 16.0379 | + | 6.64311i | 0.620989 | + | 0.257222i | ||||
\(668\) | −17.2485 | − | 6.02335i | −0.667366 | − | 0.233051i | ||||
\(669\) | 30.2627 | + | 73.0607i | 1.17003 | + | 2.82469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.76192 | 0.376855 | ||||||||
\(672\) | 18.5501 | + | 20.6920i | 0.715586 | + | 0.798212i | ||||
\(673\) | 33.3993 | 1.28745 | 0.643725 | − | 0.765257i | \(-0.277388\pi\) | ||||
0.643725 | + | 0.765257i | \(0.277388\pi\) | |||||||
\(674\) | 3.86527 | + | 16.9104i | 0.148885 | + | 0.651363i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.1293 | − | 34.7336i | 0.466512 | − | 1.33591i | ||||
\(677\) | 1.90403 | + | 0.788676i | 0.0731779 | + | 0.0303113i | 0.418972 | − | 0.907999i | \(-0.362390\pi\) |
−0.345794 | + | 0.938310i | \(0.612390\pi\) | |||||||
\(678\) | 24.7382 | − | 17.5644i | 0.950065 | − | 0.674557i | ||||
\(679\) | 13.5280 | + | 13.5280i | 0.519158 | + | 0.519158i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.4083 | + | 26.4083i | −1.01197 | + | 1.01197i | ||||
\(682\) | −0.282460 | + | 1.66561i | −0.0108160 | + | 0.0637796i | ||||
\(683\) | −2.13897 | + | 5.16393i | −0.0818454 | + | 0.197592i | −0.959505 | − | 0.281693i | \(-0.909104\pi\) |
0.877659 | + | 0.479285i | \(0.159104\pi\) | |||||||
\(684\) | −3.77173 | − | 66.4158i | −0.144216 | − | 2.53947i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.9827 | + | 20.6763i | −0.495682 | + | 0.789425i | ||||
\(687\) | − | 61.3993i | − | 2.34253i | ||||||
\(688\) | 1.99678 | + | 3.60219i | 0.0761264 | + | 0.137332i | ||||
\(689\) | − | 22.1522i | − | 0.843933i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8310 | + | 9.04271i | −0.830492 | + | 0.344001i | −0.757097 | − | 0.653302i | \(-0.773383\pi\) |
−0.0733946 | + | 0.997303i | \(0.523383\pi\) | |||||||
\(692\) | 16.8144 | − | 18.8392i | 0.639188 | − | 0.716158i | ||||
\(693\) | 5.81374 | − | 14.0356i | 0.220846 | − | 0.533168i | ||||
\(694\) | 24.5142 | + | 4.15720i | 0.930546 | + | 0.157805i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.35740 | − | 21.1014i | 0.0893571 | − | 0.799847i | ||||
\(697\) | −19.5552 | − | 19.5552i | −0.740705 | − | 0.740705i | ||||
\(698\) | −22.7367 | − | 32.0230i | −0.860595 | − | 1.21209i | ||||
\(699\) | 84.6804 | + | 35.0758i | 3.20291 | + | 1.32669i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.38145 | − | 22.6488i | −0.354332 | − | 0.855434i | −0.996075 | − | 0.0885139i | \(-0.971788\pi\) |
0.641743 | − | 0.766920i | \(-0.278212\pi\) | |||||||
\(702\) | −142.567 | + | 32.5871i | −5.38084 | + | 1.22992i | ||||
\(703\) | 10.2663 | 0.387202 | ||||||||
\(704\) | −8.08856 | − | 5.71623i | −0.304849 | − | 0.215438i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.2246 | − | 6.90857i | 1.13752 | − | 0.260007i | ||||
\(707\) | −2.20712 | − | 5.32846i | −0.0830073 | − | 0.200397i | ||||
\(708\) | 2.06431 | + | 4.27970i | 0.0775816 | + | 0.160841i | ||||
\(709\) | 34.4885 | + | 14.2856i | 1.29524 | + | 0.536506i | 0.920543 | − | 0.390640i | \(-0.127746\pi\) |
0.374698 | + | 0.927147i | \(0.377746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 89.0769 | + | 89.0769i | 3.34064 | + | 3.34064i | ||||
\(712\) | −39.3701 | − | 4.39834i | −1.47546 | − | 0.164835i | ||||
\(713\) | −5.33942 | + | 5.33942i | −0.199963 | + | 0.199963i | ||||
\(714\) | 28.9419 | + | 4.90807i | 1.08312 | + | 0.183680i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.00615 | − | 2.24773i | 0.0749735 | − | 0.0840017i | ||||
\(717\) | 61.1701 | − | 25.3375i | 2.28444 | − | 0.946246i | ||||
\(718\) | 6.81133 | + | 4.27686i | 0.254197 | + | 0.159611i | ||||
\(719\) | − | 47.1132i | − | 1.75702i | −0.477719 | − | 0.878512i | \(-0.658536\pi\) | ||
0.477719 | − | 0.878512i | \(-0.341464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.6418i | − | 0.396322i | ||||||
\(722\) | −2.64575 | + | 4.21362i | −0.0984645 | + | 0.156815i | ||||
\(723\) | 14.4804 | − | 5.99798i | 0.538532 | − | 0.223067i | ||||
\(724\) | 0.279007 | + | 4.91299i | 0.0103692 | + | 0.182590i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.57580 | − | 44.6730i | 0.281164 | − | 1.65797i | ||||
\(727\) | 32.2735 | − | 32.2735i | 1.19696 | − | 1.19696i | 0.221885 | − | 0.975073i | \(-0.428779\pi\) |
0.975073 | − | 0.221885i | \(-0.0712210\pi\) | |||||||
\(728\) | 22.0997 | − | 6.38941i | 0.819071 | − | 0.236807i | ||||
\(729\) | 89.2611 | + | 89.2611i | 3.30597 | + | 3.30597i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.01944 | + | 1.66491i | 0.148664 | + | 0.0615788i | ||||
\(732\) | 17.5949 | − | 50.3849i | 0.650326 | − | 1.86228i | ||||
\(733\) | −16.0772 | − | 38.8138i | −0.593825 | − | 1.43362i | −0.879782 | − | 0.475378i | \(-0.842311\pi\) |
0.285956 | − | 0.958243i | \(-0.407689\pi\) | |||||||
\(734\) | −8.88413 | − | 38.8676i | −0.327919 | − | 1.43463i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.6872 | − | 41.7630i | −0.541379 | − | 1.53940i | ||||
\(737\) | −2.21401 | −0.0815541 | ||||||||
\(738\) | 17.4353 | + | 76.2783i | 0.641801 | + | 2.80784i | ||||
\(739\) | −3.96376 | − | 9.56937i | −0.145809 | − | 0.352015i | 0.834054 | − | 0.551682i | \(-0.186014\pi\) |
−0.979864 | + | 0.199667i | \(0.936014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −68.9327 | − | 28.5529i | −2.53231 | − | 1.04892i | ||||
\(742\) | 6.61762 | − | 4.69858i | 0.242941 | − | 0.172490i | ||||
\(743\) | 27.5088 | + | 27.5088i | 1.00920 | + | 1.00920i | 0.999957 | + | 0.00924260i | \(0.00294205\pi\) |
0.00924260 | + | 0.999957i | \(0.497058\pi\) | |||||||
\(744\) | 8.08775 | + | 4.45999i | 0.296511 | + | 0.163511i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.292008 | + | 1.72192i | −0.0106912 | + | 0.0630439i | ||||
\(747\) | 11.7481 | − | 28.3624i | 0.429840 | − | 1.03773i | ||||
\(748\) | −10.4457 | + | 0.593205i | −0.381931 | + | 0.0216897i | ||||
\(749\) | −14.9882 | + | 6.20833i | −0.547658 | + | 0.226847i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 29.6365i | − | 1.08145i | −0.841199 | − | 0.540726i | \(-0.818149\pi\) | ||
0.841199 | − | 0.540726i | \(-0.181851\pi\) | |||||||
\(752\) | −7.39515 | − | 5.88223i | −0.269673 | − | 0.214503i | ||||
\(753\) | − | 39.3992i | − | 1.43579i | ||||||
\(754\) | −14.8857 | − | 9.34676i | −0.542104 | − | 0.340389i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −39.9739 | − | 35.6777i | −1.45384 | − | 1.29758i | ||||
\(757\) | −20.0533 | + | 48.4128i | −0.728848 | + | 1.75959i | −0.0824488 | + | 0.996595i | \(0.526274\pi\) |
−0.646399 | + | 0.762999i | \(0.723726\pi\) | |||||||
\(758\) | −9.39399 | − | 1.59306i | −0.341205 | − | 0.0578627i | ||||
\(759\) | −23.1864 | + | 23.1864i | −0.841614 | + | 0.841614i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.0239 | − | 31.0239i | −1.12461 | − | 1.12461i | −0.991039 | − | 0.133576i | \(-0.957354\pi\) |
−0.133576 | − | 0.991039i | \(-0.542646\pi\) | |||||||
\(762\) | −31.3774 | − | 44.1929i | −1.13668 | − | 1.60094i | ||||
\(763\) | −18.5694 | − | 7.69168i | −0.672256 | − | 0.278457i | ||||
\(764\) | 27.1872 | − | 13.1137i | 0.983597 | − | 0.474437i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.44878 | − | 1.93118i | 0.305267 | − | 0.0697762i | ||||
\(767\) | 3.93343 | 0.142028 | ||||||||
\(768\) | −44.0824 | + | 31.4452i | −1.59069 | + | 1.13468i | ||||
\(769\) | −9.26292 | −0.334029 | −0.167015 | − | 0.985954i | \(-0.553413\pi\) | ||||
−0.167015 | + | 0.985954i | \(0.553413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.24297 | + | 12.6576i | 0.188821 | + | 0.455854i | ||||
\(772\) | 5.33065 | − | 2.57124i | 0.191854 | − | 0.0925408i | ||||
\(773\) | 20.4673 | + | 8.47782i | 0.736156 | + | 0.304926i | 0.719079 | − | 0.694928i | \(-0.244564\pi\) |
0.0170771 | + | 0.999854i | \(0.494564\pi\) | |||||||
\(774\) | −7.12620 | − | 10.0367i | −0.256146 | − | 0.360763i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29.1232 | + | 23.2699i | −1.04546 | + | 0.835342i | ||||
\(777\) | 9.06352 | − | 9.06352i | 0.325152 | − | 0.325152i | ||||
\(778\) | 24.0991 | + | 4.08680i | 0.863994 | + | 0.146519i | ||||
\(779\) | −9.85524 | + | 23.7927i | −0.353101 | + | 0.852460i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0957 | − | 4.18176i | 0.361251 | − | 0.149635i | ||||
\(782\) | −39.6042 | − | 24.8676i | −1.41624 | − | 0.889264i | ||||
\(783\) | 40.9377i | 1.46299i | ||||||||
\(784\) | −15.3170 | − | 12.1834i | −0.547037 | − | 0.435123i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.4587 | + | 30.9899i | −0.694068 | + | 1.10537i | ||||
\(787\) | 22.8472 | − | 9.46364i | 0.814416 | − | 0.337342i | 0.0637018 | − | 0.997969i | \(-0.479709\pi\) |
0.750715 | + | 0.660627i | \(0.229709\pi\) | |||||||
\(788\) | 26.8296 | − | 1.52364i | 0.955764 | − | 0.0542775i | ||||
\(789\) | 2.94039 | − | 7.09872i | 0.104681 | − | 0.252721i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.50661 | − | 6.50661i | 0.231348 | − | 0.231348i | ||||
\(792\) | 25.9217 | + | 14.2945i | 0.921088 | + | 0.507934i | ||||
\(793\) | −31.2398 | − | 31.2398i | −1.10936 | − | 1.10936i | ||||
\(794\) | −18.5023 | + | 13.1369i | −0.656623 | + | 0.466210i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5210 | + | 7.16614i | 0.727349 | + | 0.253997i | ||||
\(797\) | 10.7716 | + | 26.0050i | 0.381551 | + | 0.921145i | 0.991666 | + | 0.128833i | \(0.0411230\pi\) |
−0.610115 | + | 0.792313i | \(0.708877\pi\) | |||||||
\(798\) | −6.09121 | − | 26.6487i | −0.215627 | − | 0.943355i | ||||
\(799\) | −9.98158 | −0.353123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 118.398 | 4.18338 | ||||||||
\(802\) | −8.60902 | − | 37.6640i | −0.303995 | − | 1.32996i | ||||
\(803\) | −3.82106 | − | 9.22485i | −0.134842 | − | 0.325538i | ||||
\(804\) | −3.99053 | + | 11.4273i | −0.140735 | + | 0.403011i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.23416 | − | 4.42632i | 0.219589 | − | 0.155911i | ||||
\(807\) | −8.76438 | − | 8.76438i | −0.308521 | − | 0.308521i | ||||
\(808\) | 10.7959 | − | 3.12126i | 0.379797 | − | 0.109806i | ||||
\(809\) | −24.2885 | + | 24.2885i | −0.853938 | + | 0.853938i | −0.990616 | − | 0.136678i | \(-0.956357\pi\) |
0.136678 | + | 0.990616i | \(0.456357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8336 | − | 30.9831i | 0.450649 | − | 1.08796i | −0.521426 | − | 0.853296i | \(-0.674600\pi\) |
0.972076 | − | 0.234667i | \(-0.0754001\pi\) | |||||||
\(812\) | −0.365120 | − | 6.42934i | −0.0128132 | − | 0.225626i | ||||
\(813\) | 70.1173 | − | 29.0435i | 2.45912 | − | 1.01860i | ||||
\(814\) | −2.42931 | + | 3.86893i | −0.0851473 | + | 0.135606i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −15.7655 | + | 54.9832i | −0.551904 | + | 1.92480i | ||||
\(817\) | − | 4.05136i | − | 0.141739i | ||||||
\(818\) | −3.78885 | − | 2.37903i | −0.132474 | − | 0.0831808i | ||||
\(819\) | −63.5212 | + | 26.3113i | −2.21961 | + | 0.919393i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.76592 | + | 9.09173i | −0.131431 | + | 0.317304i | −0.975871 | − | 0.218347i | \(-0.929934\pi\) |
0.844440 | + | 0.535651i | \(0.179934\pi\) | |||||||
\(822\) | 61.7828 | + | 10.4773i | 2.15492 | + | 0.365439i | ||||
\(823\) | −9.16017 | + | 9.16017i | −0.319304 | + | 0.319304i | −0.848500 | − | 0.529196i | \(-0.822494\pi\) |
0.529196 | + | 0.848500i | \(0.322494\pi\) | |||||||
\(824\) | 20.6075 | + | 2.30223i | 0.717897 | + | 0.0802018i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.834296 | + | 1.17505i | 0.0290289 | + | 0.0408851i | ||||
\(827\) | −40.0605 | − | 16.5936i | −1.39304 | − | 0.577017i | −0.445106 | − | 0.895478i | \(-0.646834\pi\) |
−0.947936 | + | 0.318461i | \(0.896834\pi\) | |||||||
\(828\) | 57.4827 | + | 119.172i | 1.99766 | + | 4.14152i | ||||
\(829\) | 9.71946 | + | 23.4648i | 0.337571 | + | 0.814968i | 0.997948 | + | 0.0640336i | \(0.0203965\pi\) |
−0.660377 | + | 0.750934i | \(0.729604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.4955 | 0.676291 | ||||||||
\(832\) | 7.59186 | + | 44.1776i | 0.263200 | + | 1.53158i | ||||
\(833\) | −20.6741 | −0.716316 | ||||||||
\(834\) | 11.6650 | − | 2.66633i | 0.403927 | − | 0.0923273i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.23278 | + | 8.77535i | 0.146394 | + | 0.303502i | ||||
\(837\) | −16.4519 | − | 6.81461i | −0.568662 | − | 0.235547i | ||||
\(838\) | 8.30805 | + | 11.7013i | 0.286997 | + | 0.404215i | ||||
\(839\) | 32.2653 | + | 32.2653i | 1.11392 | + | 1.11392i | 0.992615 | + | 0.121307i | \(0.0387085\pi\) |
0.121307 | + | 0.992615i | \(0.461292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0270 | − | 17.0270i | 0.587136 | − | 0.587136i | ||||
\(842\) | 4.83198 | + | 0.819424i | 0.166521 | + | 0.0282392i | ||||
\(843\) | 3.32578 | − | 8.02915i | 0.114546 | − | 0.276539i | ||||
\(844\) | −4.42675 | + | 4.95980i | −0.152375 | + | 0.170723i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23.9172 | + | 15.0177i | 0.822290 | + | 0.516319i | ||||
\(847\) | − | 13.7424i | − | 0.472195i | ||||||
\(848\) | 7.66700 | + | 13.8313i | 0.263286 | + | 0.474968i | ||||
\(849\) | − | 55.7216i | − | 1.91236i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8650 | + | 7.81413i | −0.646683 | + | 0.267865i | ||||
\(852\) | −3.38721 | − | 59.6448i | −0.116044 | − | 2.04340i | ||||
\(853\) | 1.83040 | − | 4.41898i | 0.0626718 | − | 0.151303i | −0.889441 | − | 0.457050i | \(-0.848906\pi\) |
0.952113 | + | 0.305747i | \(0.0989061\pi\) | |||||||
\(854\) | 2.70629 | − | 15.9585i | 0.0926073 | − | 0.546087i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.77968 | − | 30.3673i | −0.300083 | − | 1.03793i | ||||
\(857\) | −13.7258 | − | 13.7258i | −0.468864 | − | 0.468864i | 0.432683 | − | 0.901546i | \(-0.357567\pi\) |
−0.901546 | + | 0.432683i | \(0.857567\pi\) | |||||||
\(858\) | 27.0718 | − | 19.2213i | 0.924217 | − | 0.656204i | ||||
\(859\) | −35.3096 | − | 14.6257i | −1.20475 | − | 0.499023i | −0.312217 | − | 0.950011i | \(-0.601072\pi\) |
−0.892530 | + | 0.450988i | \(0.851072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.3045 | + | 29.7057i | 0.419336 | + | 1.01237i | ||||
\(862\) | −8.63538 | − | 37.7793i | −0.294122 | − | 1.28677i | ||||
\(863\) | −52.6541 | −1.79237 | −0.896183 | − | 0.443685i | \(-0.853671\pi\) | ||||
−0.896183 | + | 0.443685i | \(0.853671\pi\) | |||||||
\(864\) | 77.7363 | − | 69.6896i | 2.64464 | − | 2.37089i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.0047 | + | 43.7701i | 0.339974 | + | 1.48737i | ||||
\(867\) | 1.10526 | + | 2.66833i | 0.0375365 | + | 0.0906212i | ||||
\(868\) | 2.64458 | + | 0.923514i | 0.0897630 | + | 0.0313461i | ||||
\(869\) | −17.0455 | − | 7.06050i | −0.578231 | − | 0.239511i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.08520 | + | 7.08520i | 0.240073 | + | 0.240073i | ||||
\(872\) | 18.9119 | − | 34.2949i | 0.640438 | − | 1.16137i | ||||
\(873\) | 78.7810 | − | 78.7810i | 2.66633 | − | 2.66633i | ||||
\(874\) | −7.28100 | + | 42.9346i | −0.246283 | + | 1.45229i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −54.5000 | + | 3.09504i | −1.84138 | + | 0.104572i | ||||
\(877\) | 29.5360 | − | 12.2342i | 0.997359 | − | 0.413120i | 0.176531 | − | 0.984295i | \(-0.443512\pi\) |
0.820828 | + | 0.571175i | \(0.193512\pi\) | |||||||
\(878\) | 7.61172 | − | 12.1224i | 0.256883 | − | 0.409113i | ||||
\(879\) | 57.8149i | 1.95005i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.17260i | 0.275342i | 0.990478 | + | 0.137671i | \(0.0439617\pi\) | ||||
−0.990478 | + | 0.137671i | \(0.956038\pi\) | |||||||
\(882\) | 49.5380 | + | 31.1051i | 1.66803 | + | 1.04736i | ||||
\(883\) | 11.6784 | − | 4.83737i | 0.393011 | − | 0.162790i | −0.177422 | − | 0.984135i | \(-0.556776\pi\) |
0.570432 | + | 0.821345i | \(0.306776\pi\) | |||||||
\(884\) | 35.3262 | + | 31.5295i | 1.18815 | + | 1.06045i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.06216 | + | 1.53679i | 0.304449 | + | 0.0516295i | ||||
\(887\) | −24.8109 | + | 24.8109i | −0.833067 | + | 0.833067i | −0.987935 | − | 0.154868i | \(-0.950505\pi\) |
0.154868 | + | 0.987935i | \(0.450505\pi\) | |||||||
\(888\) | 15.5904 | + | 19.5119i | 0.523179 | + | 0.654778i | ||||
\(889\) | −11.6236 | − | 11.6236i | −0.389841 | − | 0.389841i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.4349 | − | 17.5771i | −1.42162 | − | 0.588855i | ||||
\(892\) | −42.0931 | + | 20.3036i | −1.40938 | + | 0.679814i | ||||
\(893\) | 3.55705 | + | 8.58748i | 0.119032 | + | 0.287369i | ||||
\(894\) | 86.1172 | − | 19.6842i | 2.88019 | − | 0.658337i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.5871 | + | 11.6382i | −0.387097 | + | 0.388805i | ||||
\(897\) | 148.401 | 4.95496 | ||||||||
\(898\) | 11.6910 | − | 2.67227i | 0.390134 | − | 0.0891747i | ||||
\(899\) | −0.819039 | − | 1.97734i | −0.0273165 | − | 0.0659478i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4334 | + | 6.39272i | 0.514161 | + | 0.212972i | ||||
\(902\) | −6.63437 | − | 9.34405i | −0.220900 | − | 0.311123i | ||||
\(903\) | −3.57671 | − | 3.57671i | −0.119025 | − | 0.119025i | ||||
\(904\) | 11.1922 | + | 14.0074i | 0.372247 | + | 0.465881i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −88.4005 | − | 14.9912i | −2.93691 | − | 0.498051i | ||||
\(907\) | −13.3908 | + | 32.3281i | −0.444633 | + | 1.07344i | 0.529672 | + | 0.848203i | \(0.322315\pi\) |
−0.974304 | + | 0.225236i | \(0.927685\pi\) | |||||||
\(908\) | −16.4662 | − | 14.6965i | −0.546450 | − | 0.487720i | ||||
\(909\) | −31.0305 | + | 12.8533i | −1.02922 | + | 0.426315i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2045i | 0.636273i | 0.948045 | + | 0.318137i | \(0.103057\pi\) | ||||
−0.948045 | + | 0.318137i | \(0.896943\pi\) | |||||||
\(912\) | 52.9220 | − | 6.03030i | 1.75242 | − | 0.199683i | ||||
\(913\) | 4.49617i | 0.148802i | ||||||||
\(914\) | 18.9751 | − | 30.2197i | 0.627639 | − | 0.999579i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.2266 | − | 2.05730i | 1.19696 | − | 0.0679750i | ||||
\(917\) | −4.24711 | + | 10.2534i | −0.140252 | + | 0.338598i | ||||
\(918\) | 18.4388 | − | 108.730i | 0.608570 | − | 3.58862i | ||||
\(919\) | −7.47911 | + | 7.47911i | −0.246713 | + | 0.246713i | −0.819620 | − | 0.572907i | \(-0.805816\pi\) |
0.572907 | + | 0.819620i | \(0.305816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27140 | + | 1.27140i | 0.0418939 | + | 0.0418939i | ||||
\(922\) | −3.17693 | + | 2.25566i | −0.104627 | + | 0.0742861i | ||||
\(923\) | −45.6902 | − | 18.9255i | −1.50391 | − | 0.622940i | ||||
\(924\) | 11.4841 | + | 4.01036i | 0.377799 | + | 0.131931i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.39169 | − | 36.7132i | −0.275768 | − | 1.20647i | ||||
\(927\) | −61.9731 | −2.03546 | ||||||||
\(928\) | 12.5292 | + | 0.683866i | 0.411290 | + | 0.0224490i | ||||
\(929\) | 33.1810 | 1.08863 | 0.544317 | − | 0.838880i | \(-0.316789\pi\) | ||||
0.544317 | + | 0.838880i | \(0.316789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.36746 | + | 17.7866i | 0.241459 | + | 0.582933i | ||||
\(932\) | −17.8579 | + | 51.1382i | −0.584956 | + | 1.67509i | ||||
\(933\) | −11.7771 | − | 4.87822i | −0.385564 | − | 0.159706i | ||||
\(934\) | −7.26482 | + | 5.15810i | −0.237712 | + | 0.168778i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −37.2089 | − | 128.699i | −1.21621 | − | 4.20665i | ||||
\(937\) | −4.34060 | + | 4.34060i | −0.141801 | + | 0.141801i | −0.774444 | − | 0.632643i | \(-0.781970\pi\) |
0.632643 | + | 0.774444i | \(0.281970\pi\) | |||||||
\(938\) | −0.613788 | + | 3.61939i | −0.0200409 | + | 0.118177i | ||||
\(939\) | 25.1936 | − | 60.8227i | 0.822161 | − | 1.98487i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2850 | + | 10.8876i | −0.856866 | + | 0.354925i | −0.767481 | − | 0.641072i | \(-0.778490\pi\) |
−0.0893847 | + | 0.995997i | \(0.528490\pi\) | |||||||
\(942\) | −29.0147 | + | 46.2089i | −0.945351 | + | 1.50557i | ||||
\(943\) | − | 51.2217i | − | 1.66801i | ||||||
\(944\) | −2.45593 | + | 1.36138i | −0.0799336 | + | 0.0443091i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.52678 | + | 0.958671i | 0.0496400 | + | 0.0311691i | ||||
\(947\) | 35.7030 | − | 14.7887i | 1.16019 | − | 0.480567i | 0.282252 | − | 0.959340i | \(-0.408918\pi\) |
0.877939 | + | 0.478773i | \(0.158918\pi\) | |||||||
\(948\) | −67.1648 | + | 75.2526i | −2.18141 | + | 2.44409i | ||||
\(949\) | −17.2930 | + | 41.7491i | −0.561356 | + | 1.35523i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.8358 | − | 51.8358i | 1.68089 | − | 1.68089i | ||||
\(952\) | −1.92609 | + | 17.2407i | −0.0624250 | + | 0.558774i | ||||
\(953\) | −16.4270 | − | 16.4270i | −0.532122 | − | 0.532122i | 0.389081 | − | 0.921204i | \(-0.372793\pi\) |
−0.921204 | + | 0.389081i | \(0.872793\pi\) | |||||||
\(954\) | −27.3624 | − | 38.5380i | −0.885889 | − | 1.24771i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.9992 | + | 35.2424i | 0.549793 | + | 1.13982i | ||||
\(957\) | −3.55667 | − | 8.58657i | −0.114971 | − | 0.277564i | ||||
\(958\) | 12.2949 | − | 2.81029i | 0.397229 | − | 0.0907965i | ||||
\(959\) | 19.0058 | 0.613728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0690 | −0.969968 | ||||||||
\(962\) | 20.1554 | − | 4.60701i | 0.649837 | − | 0.148536i | ||||
\(963\) | 36.1544 | + | 87.2845i | 1.16506 | + | 2.81270i | ||||
\(964\) | 4.02410 | + | 8.34271i | 0.129608 | + | 0.268701i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 31.4764 | + | 44.3324i | 1.01274 | + | 1.42637i | ||||
\(967\) | 6.93584 | + | 6.93584i | 0.223042 | + | 0.223042i | 0.809778 | − | 0.586736i | \(-0.199588\pi\) |
−0.586736 | + | 0.809778i | \(0.699588\pi\) | |||||||
\(968\) | 26.6117 | + | 2.97300i | 0.855332 | + | 0.0955558i | ||||
\(969\) | 39.7854 | − | 39.7854i | 1.27809 | − | 1.27809i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.4706 | − | 34.9351i | 0.464383 | − | 1.12112i | −0.502197 | − | 0.864753i | \(-0.667475\pi\) |
0.966580 | − | 0.256366i | \(-0.0825253\pi\) | |||||||
\(972\) | −93.4715 | + | 104.727i | −2.99810 | + | 3.35913i | ||||
\(973\) | 3.35290 | − | 1.38882i | 0.107489 | − | 0.0445234i | ||||
\(974\) | 24.6741 | + | 15.4930i | 0.790610 | + | 0.496427i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.3175 | + | 8.69305i | 0.970440 | + | 0.278258i | ||||
\(977\) | 21.7591i | 0.696134i | 0.937470 | + | 0.348067i | \(0.113162\pi\) | ||||
−0.937470 | + | 0.348067i | \(0.886838\pi\) | |||||||
\(978\) | −32.9260 | + | 52.4380i | −1.05286 | + | 1.67678i | ||||
\(979\) | −16.0205 | + | 6.63589i | −0.512016 | + | 0.212084i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.7928 | + | 108.139i | −1.43012 | + | 3.45262i | ||||
\(982\) | 7.48341 | − | 44.1282i | 0.238805 | − | 1.40819i | ||||
\(983\) | −31.8111 | + | 31.8111i | −1.01462 | + | 1.01462i | −0.0147254 | + | 0.999892i | \(0.504687\pi\) |
−0.999892 | + | 0.0147254i | \(0.995313\pi\) | |||||||
\(984\) | −60.1859 | + | 17.4008i | −1.91866 | + | 0.554716i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.8076 | − | 7.67350i | 0.344184 | − | 0.244374i | ||||
\(987\) | 10.7217 | + | 4.44106i | 0.341275 | + | 0.141361i | ||||
\(988\) | 14.5370 | − | 41.6282i | 0.462482 | − | 1.32437i | ||||
\(989\) | 3.08366 | + | 7.44463i | 0.0980548 | + | 0.236725i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.60717 | −0.146352 | −0.0731758 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731758 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(992\) | −2.36047 | + | 4.92135i | −0.0749451 | + | 0.156253i | ||||
\(993\) | 30.5134 | 0.968313 | ||||||||
\(994\) | −4.03739 | − | 17.6634i | −0.128058 | − | 0.560248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.2064 | + | 8.10391i | 0.735324 | + | 0.256782i | ||||
\(997\) | −29.7932 | − | 12.3407i | −0.943559 | − | 0.390835i | −0.142752 | − | 0.989758i | \(-0.545595\pi\) |
−0.800806 | + | 0.598924i | \(0.795595\pi\) | |||||||
\(998\) | −12.5099 | + | 8.88218i | −0.395995 | + | 0.281160i | ||||
\(999\) | −34.0501 | − | 34.0501i | −1.07730 | − | 1.07730i |
(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 | 800.2.y.e.101.15 | yes | 64 | |
5.2 | odd | 4 | 800.2.ba.f.549.10 | 64 | |||
5.3 | odd | 4 | 800.2.ba.h.549.7 | 64 | |||
5.4 | even | 2 | 800.2.y.d.101.2 | ✓ | 64 | ||
32.13 | even | 8 | inner | 800.2.y.e.301.15 | yes | 64 | |
160.13 | odd | 8 | 800.2.ba.f.749.10 | 64 | |||
160.77 | odd | 8 | 800.2.ba.h.749.7 | 64 | |||
160.109 | even | 8 | 800.2.y.d.301.2 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.2.y.d.101.2 | ✓ | 64 | 5.4 | even | 2 | ||
800.2.y.d.301.2 | yes | 64 | 160.109 | even | 8 | ||
800.2.y.e.101.15 | yes | 64 | 1.1 | even | 1 | trivial | |
800.2.y.e.301.15 | yes | 64 | 32.13 | even | 8 | inner | |
800.2.ba.f.549.10 | 64 | 5.2 | odd | 4 | |||
800.2.ba.f.749.10 | 64 | 160.13 | odd | 8 | |||
800.2.ba.h.549.7 | 64 | 5.3 | odd | 4 | |||
800.2.ba.h.749.7 | 64 | 160.77 | odd | 8 |