Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.3 | ||
Root | \(0.756174 - 1.30973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.g.170.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.425563 | − | 0.737096i | −0.300918 | − | 0.521206i | 0.675426 | − | 0.737428i | \(-0.263960\pi\) |
−0.976344 | + | 0.216222i | \(0.930626\pi\) | |||||||
\(3\) | −0.330612 | + | 0.572636i | −0.190879 | + | 0.330612i | −0.945542 | − | 0.325501i | \(-0.894467\pi\) |
0.754663 | + | 0.656113i | \(0.227800\pi\) | |||||||
\(4\) | 0.637793 | − | 1.10469i | 0.318896 | − | 0.552345i | ||||
\(5\) | 1.72074 | + | 2.98041i | 0.769538 | + | 1.33288i | 0.937814 | + | 0.347139i | \(0.112847\pi\) |
−0.168276 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(6\) | 0.562784 | 0.229756 | ||||||||
\(7\) | −0.751763 | + | 2.53670i | −0.284140 | + | 0.958783i | ||||
\(8\) | −2.78793 | −0.985684 | ||||||||
\(9\) | 1.28139 | + | 2.21944i | 0.427131 | + | 0.739812i | ||||
\(10\) | 1.46456 | − | 2.53670i | 0.463136 | − | 0.802175i | ||||
\(11\) | −0.448993 | + | 0.777679i | −0.135377 | + | 0.234479i | −0.925741 | − | 0.378158i | \(-0.876558\pi\) |
0.790365 | + | 0.612637i | \(0.209891\pi\) | |||||||
\(12\) | 0.421723 | + | 0.730446i | 0.121741 | + | 0.210862i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.18972 | − | 0.525403i | 0.585226 | − | 0.140420i | ||||
\(15\) | −2.27559 | −0.587554 | ||||||||
\(16\) | −0.0891447 | − | 0.154403i | −0.0222862 | − | 0.0386008i | ||||
\(17\) | −0.968404 | + | 1.67733i | −0.234873 | + | 0.406811i | −0.959236 | − | 0.282607i | \(-0.908801\pi\) |
0.724363 | + | 0.689419i | \(0.242134\pi\) | |||||||
\(18\) | 1.09063 | − | 1.88902i | 0.257063 | − | 0.445246i | ||||
\(19\) | 0.519020 | + | 0.898968i | 0.119071 | + | 0.206237i | 0.919400 | − | 0.393324i | \(-0.128675\pi\) |
−0.800329 | + | 0.599562i | \(0.795342\pi\) | |||||||
\(20\) | 4.38990 | 0.981612 | ||||||||
\(21\) | −1.20406 | − | 1.26915i | −0.262748 | − | 0.276951i | ||||
\(22\) | 0.764299 | 0.162949 | ||||||||
\(23\) | −2.82506 | − | 4.89315i | −0.589067 | − | 1.02029i | −0.994355 | − | 0.106104i | \(-0.966162\pi\) |
0.405288 | − | 0.914189i | \(-0.367171\pi\) | |||||||
\(24\) | 0.921723 | − | 1.59647i | 0.188146 | − | 0.325878i | ||||
\(25\) | −3.42189 | + | 5.92688i | −0.684378 | + | 1.18538i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67824 | −0.707878 | ||||||||
\(28\) | 2.32280 | + | 2.44835i | 0.438967 | + | 0.462696i | ||||
\(29\) | −1.83594 | −0.340925 | −0.170463 | − | 0.985364i | \(-0.554526\pi\) | ||||
−0.170463 | + | 0.985364i | \(0.554526\pi\) | |||||||
\(30\) | 0.968404 | + | 1.67733i | 0.176806 | + | 0.306236i | ||||
\(31\) | −4.56692 | + | 7.91014i | −0.820244 | + | 1.42070i | 0.0852573 | + | 0.996359i | \(0.472829\pi\) |
−0.905501 | + | 0.424345i | \(0.860505\pi\) | |||||||
\(32\) | −2.86381 | + | 4.96026i | −0.506254 | + | 0.876858i | ||||
\(33\) | −0.296885 | − | 0.514219i | −0.0516810 | − | 0.0895141i | ||||
\(34\) | 1.64847 | 0.282710 | ||||||||
\(35\) | −8.85399 | + | 2.12444i | −1.49660 | + | 0.359096i | ||||
\(36\) | 3.26905 | 0.544842 | ||||||||
\(37\) | −5.30001 | − | 9.17989i | −0.871316 | − | 1.50916i | −0.860636 | − | 0.509221i | \(-0.829933\pi\) |
−0.0106808 | − | 0.999943i | \(-0.503400\pi\) | |||||||
\(38\) | 0.441751 | − | 0.765135i | 0.0716614 | − | 0.124121i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.79731 | − | 8.30918i | −0.758521 | − | 1.31380i | ||||
\(41\) | 5.33143 | 0.832629 | 0.416314 | − | 0.909221i | \(-0.363322\pi\) | ||||
0.416314 | + | 0.909221i | \(0.363322\pi\) | |||||||
\(42\) | −0.423080 | + | 1.42761i | −0.0652827 | + | 0.220286i | ||||
\(43\) | −3.91465 | −0.596978 | −0.298489 | − | 0.954413i | \(-0.596483\pi\) | ||||
−0.298489 | + | 0.954413i | \(0.596483\pi\) | |||||||
\(44\) | 0.572729 | + | 0.991996i | 0.0863422 | + | 0.149549i | ||||
\(45\) | −4.40988 | + | 7.63814i | −0.657387 | + | 1.13863i | ||||
\(46\) | −2.40448 | + | 4.16469i | −0.354522 | + | 0.614050i | ||||
\(47\) | 3.59565 | + | 6.22784i | 0.524479 | + | 0.908424i | 0.999594 | + | 0.0285004i | \(0.00907317\pi\) |
−0.475115 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(48\) | 0.117889 | 0.0170158 | ||||||||
\(49\) | −5.86970 | − | 3.81400i | −0.838529 | − | 0.544857i | ||||
\(50\) | 5.82491 | 0.823767 | ||||||||
\(51\) | −0.640331 | − | 1.10909i | −0.0896643 | − | 0.155303i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.69324 | − | 8.12893i | 0.644666 | − | 1.11659i | −0.339712 | − | 0.940529i | \(-0.610330\pi\) |
0.984378 | − | 0.176065i | \(-0.0563370\pi\) | |||||||
\(54\) | 1.56532 | + | 2.71122i | 0.213013 | + | 0.368950i | ||||
\(55\) | −3.09040 | −0.416710 | ||||||||
\(56\) | 2.09587 | − | 7.07216i | 0.280072 | − | 0.945056i | ||||
\(57\) | −0.686375 | −0.0909127 | ||||||||
\(58\) | 0.781307 | + | 1.35326i | 0.102591 | + | 0.177692i | ||||
\(59\) | −0.255259 | + | 0.442121i | −0.0332318 | + | 0.0575592i | −0.882163 | − | 0.470944i | \(-0.843913\pi\) |
0.848931 | + | 0.528503i | \(0.177247\pi\) | |||||||
\(60\) | −1.45135 | + | 2.51382i | −0.187369 | + | 0.324532i | ||||
\(61\) | −0.718095 | − | 1.24378i | −0.0919426 | − | 0.159249i | 0.816386 | − | 0.577507i | \(-0.195974\pi\) |
−0.908328 | + | 0.418258i | \(0.862641\pi\) | |||||||
\(62\) | 7.77405 | 0.987305 | ||||||||
\(63\) | −6.59335 | + | 1.58202i | −0.830684 | + | 0.199315i | ||||
\(64\) | 4.51834 | 0.564792 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.252686 | + | 0.437665i | −0.0311035 | + | 0.0538729i | ||||
\(67\) | −4.22466 | + | 7.31732i | −0.516124 | + | 0.893953i | 0.483701 | + | 0.875233i | \(0.339292\pi\) |
−0.999825 | + | 0.0187197i | \(0.994041\pi\) | |||||||
\(68\) | 1.23528 | + | 2.13957i | 0.149800 | + | 0.259461i | ||||
\(69\) | 3.73600 | 0.449761 | ||||||||
\(70\) | 5.33385 | + | 5.62216i | 0.637516 | + | 0.671977i | ||||
\(71\) | 3.44837 | 0.409247 | 0.204623 | − | 0.978841i | \(-0.434403\pi\) | ||||
0.204623 | + | 0.978841i | \(0.434403\pi\) | |||||||
\(72\) | −3.57244 | − | 6.18764i | −0.421016 | − | 0.729221i | ||||
\(73\) | 5.45026 | − | 9.44013i | 0.637905 | − | 1.10488i | −0.347987 | − | 0.937499i | \(-0.613135\pi\) |
0.985892 | − | 0.167384i | \(-0.0535320\pi\) | |||||||
\(74\) | −4.51097 | + | 7.81324i | −0.524390 | + | 0.908270i | ||||
\(75\) | −2.26263 | − | 3.91899i | −0.261266 | − | 0.452526i | ||||
\(76\) | 1.32411 | 0.151886 | ||||||||
\(77\) | −1.63520 | − | 1.72359i | −0.186349 | − | 0.196422i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.04589 | + | 10.4718i | 0.680216 | + | 1.17817i | 0.974915 | + | 0.222578i | \(0.0714472\pi\) |
−0.294699 | + | 0.955590i | \(0.595219\pi\) | |||||||
\(80\) | 0.306789 | − | 0.531375i | 0.0343001 | − | 0.0594095i | ||||
\(81\) | −2.62811 | + | 4.55201i | −0.292012 | + | 0.505779i | ||||
\(82\) | −2.26886 | − | 3.92977i | −0.250553 | − | 0.433971i | ||||
\(83\) | −1.51669 | −0.166479 | −0.0832393 | − | 0.996530i | \(-0.526527\pi\) | ||||
−0.0832393 | + | 0.996530i | \(0.526527\pi\) | |||||||
\(84\) | −2.16996 | + | 0.520663i | −0.236762 | + | 0.0568090i | ||||
\(85\) | −6.66549 | −0.722973 | ||||||||
\(86\) | 1.66593 | + | 2.88547i | 0.179642 | + | 0.311148i | ||||
\(87\) | 0.606982 | − | 1.05132i | 0.0650754 | − | 0.112714i | ||||
\(88\) | 1.25176 | − | 2.16812i | 0.133438 | − | 0.231122i | ||||
\(89\) | 6.80391 | + | 11.7847i | 0.721213 | + | 1.24918i | 0.960514 | + | 0.278232i | \(0.0897484\pi\) |
−0.239301 | + | 0.970945i | \(0.576918\pi\) | |||||||
\(90\) | 7.50673 | 0.791279 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.20722 | −0.751405 | ||||||||
\(93\) | −3.01976 | − | 5.23037i | −0.313134 | − | 0.542364i | ||||
\(94\) | 3.06035 | − | 5.30067i | 0.315651 | − | 0.546723i | ||||
\(95\) | −1.78619 | + | 3.09378i | −0.183260 | + | 0.317415i | ||||
\(96\) | −1.89362 | − | 3.27984i | −0.193266 | − | 0.334747i | ||||
\(97\) | −0.506241 | −0.0514010 | −0.0257005 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257005 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(98\) | −0.313356 | + | 5.94963i | −0.0316538 | + | 0.601004i | ||||
\(99\) | −2.30134 | −0.231294 | ||||||||
\(100\) | 4.36491 | + | 7.56025i | 0.436491 | + | 0.756025i | ||||
\(101\) | 2.99327 | − | 5.18450i | 0.297842 | − | 0.515877i | −0.677800 | − | 0.735246i | \(-0.737067\pi\) |
0.975642 | + | 0.219369i | \(0.0703999\pi\) | |||||||
\(102\) | −0.545002 | + | 0.943972i | −0.0539633 | + | 0.0934671i | ||||
\(103\) | 2.06651 | + | 3.57930i | 0.203619 | + | 0.352679i | 0.949692 | − | 0.313186i | \(-0.101396\pi\) |
−0.746073 | + | 0.665865i | \(0.768063\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.71070 | − | 5.77248i | 0.166947 | − | 0.563336i | ||||
\(106\) | −7.98908 | −0.775968 | ||||||||
\(107\) | 7.06169 | + | 12.2312i | 0.682679 | + | 1.18243i | 0.974160 | + | 0.225858i | \(0.0725186\pi\) |
−0.291481 | + | 0.956577i | \(0.594148\pi\) | |||||||
\(108\) | −2.34596 | + | 4.06331i | −0.225740 | + | 0.390993i | ||||
\(109\) | −2.10119 | + | 3.63936i | −0.201257 | + | 0.348588i | −0.948934 | − | 0.315475i | \(-0.897836\pi\) |
0.747677 | + | 0.664063i | \(0.231169\pi\) | |||||||
\(110\) | 1.31516 | + | 2.27792i | 0.125396 | + | 0.217191i | ||||
\(111\) | 7.00898 | 0.665263 | ||||||||
\(112\) | 0.458690 | − | 0.110059i | 0.0433421 | − | 0.0103996i | ||||
\(113\) | 13.7694 | 1.29532 | 0.647660 | − | 0.761929i | \(-0.275748\pi\) | ||||
0.647660 | + | 0.761929i | \(0.275748\pi\) | |||||||
\(114\) | 0.292096 | + | 0.505925i | 0.0273573 | + | 0.0473842i | ||||
\(115\) | 9.72240 | − | 16.8397i | 0.906618 | − | 1.57031i | ||||
\(116\) | −1.17095 | + | 2.02814i | −0.108720 | + | 0.188308i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.434514 | 0.0400003 | ||||||||
\(119\) | −3.52686 | − | 3.71750i | −0.323307 | − | 0.340783i | ||||
\(120\) | 6.34418 | 0.579142 | ||||||||
\(121\) | 5.09681 | + | 8.82793i | 0.463346 | + | 0.802539i | ||||
\(122\) | −0.611189 | + | 1.05861i | −0.0553344 | + | 0.0958420i | ||||
\(123\) | −1.76263 | + | 3.05297i | −0.158931 | + | 0.275277i | ||||
\(124\) | 5.82550 | + | 10.0901i | 0.523145 | + | 0.906114i | ||||
\(125\) | −6.34531 | −0.567542 | ||||||||
\(126\) | 3.97198 | + | 4.18669i | 0.353852 | + | 0.372980i | ||||
\(127\) | 1.94496 | 0.172588 | 0.0862938 | − | 0.996270i | \(-0.472498\pi\) | ||||
0.0862938 | + | 0.996270i | \(0.472498\pi\) | |||||||
\(128\) | 3.80478 | + | 6.59007i | 0.336298 | + | 0.582485i | ||||
\(129\) | 1.29423 | − | 2.24167i | 0.113950 | − | 0.197368i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.01770 | + | 10.4230i | 0.525769 | + | 0.910659i | 0.999549 | + | 0.0300158i | \(0.00955576\pi\) |
−0.473780 | + | 0.880643i | \(0.657111\pi\) | |||||||
\(132\) | −0.757404 | −0.0659235 | ||||||||
\(133\) | −2.67059 | + | 0.640786i | −0.231570 | + | 0.0555632i | ||||
\(134\) | 7.19143 | 0.621245 | ||||||||
\(135\) | −6.32930 | − | 10.9627i | −0.544739 | − | 0.943516i | ||||
\(136\) | 2.69985 | − | 4.67627i | 0.231510 | − | 0.400987i | ||||
\(137\) | 4.35857 | − | 7.54927i | 0.372378 | − | 0.644978i | −0.617553 | − | 0.786529i | \(-0.711876\pi\) |
0.989931 | + | 0.141552i | \(0.0452092\pi\) | |||||||
\(138\) | −1.58990 | − | 2.75379i | −0.135341 | − | 0.234418i | ||||
\(139\) | 4.21250 | 0.357299 | 0.178650 | − | 0.983913i | \(-0.442827\pi\) | ||||
0.178650 | + | 0.983913i | \(0.442827\pi\) | |||||||
\(140\) | −3.30017 | + | 11.1359i | −0.278915 | + | 0.941152i | ||||
\(141\) | −4.75505 | −0.400447 | ||||||||
\(142\) | −1.46750 | − | 2.54178i | −0.123150 | − | 0.213302i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.228459 | − | 0.395702i | 0.0190382 | − | 0.0329751i | ||||
\(145\) | −3.15917 | − | 5.47184i | −0.262355 | − | 0.454412i | ||||
\(146\) | −9.27771 | −0.767829 | ||||||||
\(147\) | 4.12462 | − | 2.10025i | 0.340193 | − | 0.173226i | ||||
\(148\) | −13.5212 | −1.11144 | ||||||||
\(149\) | 2.93242 | + | 5.07910i | 0.240233 | + | 0.416096i | 0.960781 | − | 0.277310i | \(-0.0894428\pi\) |
−0.720548 | + | 0.693406i | \(0.756109\pi\) | |||||||
\(150\) | −1.92578 | + | 3.33555i | −0.157240 | + | 0.272347i | ||||
\(151\) | −8.42840 | + | 14.5984i | −0.685893 | + | 1.18800i | 0.287262 | + | 0.957852i | \(0.407255\pi\) |
−0.973155 | + | 0.230150i | \(0.926078\pi\) | |||||||
\(152\) | −1.44699 | − | 2.50626i | −0.117367 | − | 0.203285i | ||||
\(153\) | −4.96362 | −0.401285 | ||||||||
\(154\) | −0.574572 | + | 1.93880i | −0.0463003 | + | 0.156233i | ||||
\(155\) | −31.4339 | −2.52483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.969500 | − | 1.67922i | 0.0773746 | − | 0.134017i | −0.824742 | − | 0.565509i | \(-0.808680\pi\) |
0.902116 | + | 0.431493i | \(0.142013\pi\) | |||||||
\(158\) | 5.14581 | − | 8.91280i | 0.409379 | − | 0.709065i | ||||
\(159\) | 3.10328 | + | 5.37504i | 0.246106 | + | 0.426268i | ||||
\(160\) | −19.7115 | −1.55833 | ||||||||
\(161\) | 14.5362 | − | 3.48785i | 1.14562 | − | 0.274881i | ||||
\(162\) | 4.47370 | 0.351487 | ||||||||
\(163\) | −5.94797 | − | 10.3022i | −0.465881 | − | 0.806929i | 0.533360 | − | 0.845888i | \(-0.320929\pi\) |
−0.999241 | + | 0.0389590i | \(0.987596\pi\) | |||||||
\(164\) | 3.40035 | − | 5.88957i | 0.265522 | − | 0.459898i | ||||
\(165\) | 1.02172 | − | 1.76968i | 0.0795410 | − | 0.137769i | ||||
\(166\) | 0.645448 | + | 1.11795i | 0.0500965 | + | 0.0867696i | ||||
\(167\) | −16.5760 | −1.28269 | −0.641346 | − | 0.767252i | \(-0.721624\pi\) | ||||
−0.641346 | + | 0.767252i | \(0.721624\pi\) | |||||||
\(168\) | 3.35685 | + | 3.53831i | 0.258987 | + | 0.272986i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.83658 | + | 4.91310i | 0.217556 | + | 0.376818i | ||||
\(171\) | −1.33013 | + | 2.30386i | −0.101718 | + | 0.176181i | ||||
\(172\) | −2.49673 | + | 4.32447i | −0.190374 | + | 0.329738i | ||||
\(173\) | 4.99328 | + | 8.64862i | 0.379632 | + | 0.657542i | 0.991009 | − | 0.133798i | \(-0.0427172\pi\) |
−0.611377 | + | 0.791340i | \(0.709384\pi\) | |||||||
\(174\) | −1.03324 | −0.0783295 | ||||||||
\(175\) | −12.4623 | − | 13.1359i | −0.942060 | − | 0.992982i | ||||
\(176\) | 0.160101 | 0.0120681 | ||||||||
\(177\) | −0.168783 | − | 0.292341i | −0.0126865 | − | 0.0219737i | ||||
\(178\) | 5.79098 | − | 10.0303i | 0.434052 | − | 0.751801i | ||||
\(179\) | −4.58829 | + | 7.94715i | −0.342945 | + | 0.593998i | −0.984978 | − | 0.172679i | \(-0.944758\pi\) |
0.642033 | + | 0.766677i | \(0.278091\pi\) | |||||||
\(180\) | 5.62518 | + | 9.74310i | 0.419276 | + | 0.726208i | ||||
\(181\) | 6.00489 | 0.446340 | 0.223170 | − | 0.974780i | \(-0.428360\pi\) | ||||
0.223170 | + | 0.974780i | \(0.428360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.949642 | 0.0701995 | ||||||||
\(184\) | 7.87609 | + | 13.6418i | 0.580633 | + | 1.00569i | ||||
\(185\) | 18.2399 | − | 31.5924i | 1.34102 | − | 2.32272i | ||||
\(186\) | −2.57019 | + | 4.45170i | −0.188456 | + | 0.326415i | ||||
\(187\) | −0.869614 | − | 1.50622i | −0.0635925 | − | 0.110145i | ||||
\(188\) | 9.17311 | 0.669018 | ||||||||
\(189\) | 2.76517 | − | 9.33060i | 0.201136 | − | 0.678701i | ||||
\(190\) | 3.04055 | 0.220585 | ||||||||
\(191\) | −0.658061 | − | 1.13980i | −0.0476156 | − | 0.0824727i | 0.841235 | − | 0.540669i | \(-0.181829\pi\) |
−0.888851 | + | 0.458197i | \(0.848496\pi\) | |||||||
\(192\) | −1.49382 | + | 2.58736i | −0.107807 | + | 0.186727i | ||||
\(193\) | −8.21270 | + | 14.2248i | −0.591163 | + | 1.02392i | 0.402913 | + | 0.915238i | \(0.367998\pi\) |
−0.994076 | + | 0.108686i | \(0.965336\pi\) | |||||||
\(194\) | 0.215437 | + | 0.373148i | 0.0154675 | + | 0.0267905i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.95694 | + | 4.05166i | −0.568353 | + | 0.289404i | ||||
\(197\) | 25.5875 | 1.82303 | 0.911517 | − | 0.411262i | \(-0.134912\pi\) | ||||
0.911517 | + | 0.411262i | \(0.134912\pi\) | |||||||
\(198\) | 0.979367 | + | 1.69631i | 0.0696006 | + | 0.120552i | ||||
\(199\) | 12.6894 | − | 21.9787i | 0.899528 | − | 1.55803i | 0.0714284 | − | 0.997446i | \(-0.477244\pi\) |
0.828099 | − | 0.560582i | \(-0.189422\pi\) | |||||||
\(200\) | 9.54000 | − | 16.5238i | 0.674580 | − | 1.16841i | ||||
\(201\) | −2.79344 | − | 4.83838i | −0.197034 | − | 0.341273i | ||||
\(202\) | −5.09530 | −0.358504 | ||||||||
\(203\) | 1.38019 | − | 4.65723i | 0.0968704 | − | 0.326873i | ||||
\(204\) | −1.63359 | −0.114375 | ||||||||
\(205\) | 9.17399 | + | 15.8898i | 0.640740 | + | 1.10979i | ||||
\(206\) | 1.75886 | − | 3.04643i | 0.122546 | − | 0.212255i | ||||
\(207\) | 7.24003 | − | 12.5401i | 0.503217 | − | 0.871597i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.932145 | −0.0644778 | ||||||||
\(210\) | −4.98288 | + | 1.19560i | −0.343852 | + | 0.0825043i | ||||
\(211\) | −5.69648 | −0.392162 | −0.196081 | − | 0.980588i | \(-0.562822\pi\) | ||||
−0.196081 | + | 0.980588i | \(0.562822\pi\) | |||||||
\(212\) | −5.98663 | − | 10.3691i | −0.411164 | − | 0.712156i | ||||
\(213\) | −1.14007 | + | 1.97466i | −0.0781165 | + | 0.135302i | ||||
\(214\) | 6.01038 | − | 10.4103i | 0.410861 | − | 0.711633i | ||||
\(215\) | −6.73608 | − | 11.6672i | −0.459397 | − | 0.795699i | ||||
\(216\) | 10.2547 | 0.697744 | ||||||||
\(217\) | −16.6324 | − | 17.5315i | −1.12908 | − | 1.19011i | ||||
\(218\) | 3.57675 | 0.242248 | ||||||||
\(219\) | 3.60384 | + | 6.24203i | 0.243525 | + | 0.421797i | ||||
\(220\) | −1.97104 | + | 3.41393i | −0.132887 | + | 0.230167i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.98276 | − | 5.16629i | −0.200190 | − | 0.346739i | ||||
\(223\) | −2.35812 | −0.157912 | −0.0789558 | − | 0.996878i | \(-0.525159\pi\) | ||||
−0.0789558 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(224\) | −10.4298 | − | 10.9936i | −0.696870 | − | 0.734538i | ||||
\(225\) | −17.5391 | −1.16927 | ||||||||
\(226\) | −5.85976 | − | 10.1494i | −0.389786 | − | 0.675129i | ||||
\(227\) | 13.1463 | − | 22.7701i | 0.872551 | − | 1.51130i | 0.0132022 | − | 0.999913i | \(-0.495797\pi\) |
0.859349 | − | 0.511390i | \(-0.170869\pi\) | |||||||
\(228\) | −0.437765 | + | 0.758232i | −0.0289917 | + | 0.0502151i | ||||
\(229\) | 0.0342777 | + | 0.0593708i | 0.00226514 | + | 0.00392333i | 0.867156 | − | 0.498037i | \(-0.165946\pi\) |
−0.864891 | + | 0.501960i | \(0.832612\pi\) | |||||||
\(230\) | −16.5500 | −1.09127 | ||||||||
\(231\) | 1.52761 | − | 0.366536i | 0.100509 | − | 0.0241163i | ||||
\(232\) | 5.11847 | 0.336044 | ||||||||
\(233\) | −7.33514 | − | 12.7048i | −0.480541 | − | 0.832322i | 0.519210 | − | 0.854647i | \(-0.326226\pi\) |
−0.999751 | + | 0.0223253i | \(0.992893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.3743 | + | 21.4330i | −0.807213 | + | 1.39813i | ||||
\(236\) | 0.325604 | + | 0.563963i | 0.0211950 | + | 0.0367109i | ||||
\(237\) | −7.99536 | −0.519355 | ||||||||
\(238\) | −1.23926 | + | 4.18167i | −0.0803291 | + | 0.271057i | ||||
\(239\) | −3.35434 | −0.216974 | −0.108487 | − | 0.994098i | \(-0.534601\pi\) | ||||
−0.108487 | + | 0.994098i | \(0.534601\pi\) | |||||||
\(240\) | 0.202856 | + | 0.351357i | 0.0130943 | + | 0.0226800i | ||||
\(241\) | −4.28989 | + | 7.43031i | −0.276336 | + | 0.478628i | −0.970471 | − | 0.241216i | \(-0.922454\pi\) |
0.694135 | + | 0.719845i | \(0.255787\pi\) | |||||||
\(242\) | 4.33802 | − | 7.51368i | 0.278859 | − | 0.482998i | ||||
\(243\) | −7.25513 | − | 12.5662i | −0.465417 | − | 0.806125i | ||||
\(244\) | −1.83198 | −0.117281 | ||||||||
\(245\) | 1.26704 | − | 24.0570i | 0.0809482 | − | 1.53695i | ||||
\(246\) | 3.00044 | 0.191301 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.7323 | − | 22.0530i | 0.808501 | − | 1.40036i | ||||
\(249\) | 0.501436 | − | 0.868513i | 0.0317772 | − | 0.0550398i | ||||
\(250\) | 2.70033 | + | 4.67711i | 0.170784 | + | 0.295806i | ||||
\(251\) | 21.5151 | 1.35802 | 0.679010 | − | 0.734129i | \(-0.262409\pi\) | ||||
0.679010 | + | 0.734129i | \(0.262409\pi\) | |||||||
\(252\) | −2.45755 | + | 8.29260i | −0.154811 | + | 0.522385i | ||||
\(253\) | 5.07374 | 0.318983 | ||||||||
\(254\) | −0.827704 | − | 1.43363i | −0.0519348 | − | 0.0899537i | ||||
\(255\) | 2.20369 | − | 3.81690i | 0.138000 | − | 0.239023i | ||||
\(256\) | 7.75668 | − | 13.4350i | 0.484793 | − | 0.839686i | ||||
\(257\) | −2.46896 | − | 4.27636i | −0.154010 | − | 0.266752i | 0.778688 | − | 0.627411i | \(-0.215885\pi\) |
−0.932698 | + | 0.360659i | \(0.882552\pi\) | |||||||
\(258\) | −2.20310 | −0.137159 | ||||||||
\(259\) | 27.2710 | − | 6.54344i | 1.69454 | − | 0.406590i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.35256 | − | 4.07475i | −0.145620 | − | 0.252221i | ||||
\(262\) | 5.12182 | − | 8.87125i | 0.316427 | − | 0.548068i | ||||
\(263\) | 4.47719 | − | 7.75473i | 0.276076 | − | 0.478177i | −0.694330 | − | 0.719656i | \(-0.744299\pi\) |
0.970406 | + | 0.241480i | \(0.0776327\pi\) | |||||||
\(264\) | 0.827695 | + | 1.43361i | 0.0509411 | + | 0.0882326i | ||||
\(265\) | 32.3034 | 1.98438 | ||||||||
\(266\) | 1.60883 | + | 1.69579i | 0.0986434 | + | 0.103976i | ||||
\(267\) | −8.99780 | −0.550657 | ||||||||
\(268\) | 5.38891 | + | 9.33387i | 0.329180 | + | 0.570157i | ||||
\(269\) | 2.41172 | − | 4.17723i | 0.147045 | − | 0.254690i | −0.783089 | − | 0.621910i | \(-0.786357\pi\) |
0.930134 | + | 0.367220i | \(0.119690\pi\) | |||||||
\(270\) | −5.38702 | + | 9.33060i | −0.327844 | + | 0.567842i | ||||
\(271\) | −3.71072 | − | 6.42715i | −0.225410 | − | 0.390422i | 0.731032 | − | 0.682343i | \(-0.239039\pi\) |
−0.956442 | + | 0.291921i | \(0.905706\pi\) | |||||||
\(272\) | 0.345312 | 0.0209376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.41938 | −0.448221 | ||||||||
\(275\) | −3.07281 | − | 5.32226i | −0.185297 | − | 0.320944i | ||||
\(276\) | 2.38279 | − | 4.12712i | 0.143427 | − | 0.248423i | ||||
\(277\) | −1.90816 | + | 3.30503i | −0.114650 | + | 0.198580i | −0.917640 | − | 0.397413i | \(-0.869908\pi\) |
0.802990 | + | 0.595993i | \(0.203241\pi\) | |||||||
\(278\) | −1.79268 | − | 3.10502i | −0.107518 | − | 0.186226i | ||||
\(279\) | −23.4081 | −1.40140 | ||||||||
\(280\) | 24.6843 | − | 5.92280i | 1.47517 | − | 0.353955i | ||||
\(281\) | −8.54978 | −0.510037 | −0.255019 | − | 0.966936i | \(-0.582082\pi\) | ||||
−0.255019 | + | 0.966936i | \(0.582082\pi\) | |||||||
\(282\) | 2.02357 | + | 3.50493i | 0.120502 | + | 0.208715i | ||||
\(283\) | −7.63217 | + | 13.2193i | −0.453686 | + | 0.785807i | −0.998612 | − | 0.0526775i | \(-0.983224\pi\) |
0.544926 | + | 0.838484i | \(0.316558\pi\) | |||||||
\(284\) | 2.19935 | − | 3.80938i | 0.130507 | − | 0.226045i | ||||
\(285\) | −1.18107 | − | 2.04568i | −0.0699607 | − | 0.121176i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00797 | + | 13.5242i | −0.236583 | + | 0.798310i | ||||
\(288\) | −14.6786 | −0.864947 | ||||||||
\(289\) | 6.62439 | + | 11.4738i | 0.389670 | + | 0.674928i | ||||
\(290\) | −2.68885 | + | 4.65723i | −0.157895 | + | 0.273482i | ||||
\(291\) | 0.167369 | − | 0.289892i | 0.00981135 | − | 0.0169938i | ||||
\(292\) | −6.95227 | − | 12.0417i | −0.406851 | − | 0.704687i | ||||
\(293\) | 5.93964 | 0.346997 | 0.173499 | − | 0.984834i | \(-0.444493\pi\) | ||||
0.173499 | + | 0.984834i | \(0.444493\pi\) | |||||||
\(294\) | −3.30337 | − | 2.14646i | −0.192657 | − | 0.125184i | ||||
\(295\) | −1.75693 | −0.102293 | ||||||||
\(296\) | 14.7761 | + | 25.5929i | 0.858842 | + | 1.48756i | ||||
\(297\) | 1.65151 | − | 2.86049i | 0.0958301 | − | 0.165983i | ||||
\(298\) | 2.49586 | − | 4.32295i | 0.144581 | − | 0.250422i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.77236 | −0.333267 | ||||||||
\(301\) | 2.94289 | − | 9.93028i | 0.169625 | − | 0.572372i | ||||
\(302\) | 14.3472 | 0.825591 | ||||||||
\(303\) | 1.97922 | + | 3.42811i | 0.113703 | + | 0.196940i | ||||
\(304\) | 0.0925356 | − | 0.160276i | 0.00530728 | − | 0.00919248i | ||||
\(305\) | 2.47131 | − | 4.28043i | 0.141507 | − | 0.245097i | ||||
\(306\) | 2.11233 | + | 3.65867i | 0.120754 | + | 0.209152i | ||||
\(307\) | −22.2133 | −1.26778 | −0.633891 | − | 0.773422i | \(-0.718543\pi\) | ||||
−0.633891 | + | 0.773422i | \(0.718543\pi\) | |||||||
\(308\) | −2.94695 | + | 0.707096i | −0.167918 | + | 0.0402906i | ||||
\(309\) | −2.73285 | −0.155466 | ||||||||
\(310\) | 13.3771 | + | 23.1698i | 0.759769 | + | 1.31596i | ||||
\(311\) | −4.92130 | + | 8.52394i | −0.279061 | + | 0.483348i | −0.971152 | − | 0.238463i | \(-0.923357\pi\) |
0.692091 | + | 0.721811i | \(0.256690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4563 | + | 18.1108i | 0.591023 | + | 1.02368i | 0.994095 | + | 0.108513i | \(0.0346090\pi\) |
−0.403072 | + | 0.915168i | \(0.632058\pi\) | |||||||
\(314\) | −1.65033 | −0.0931337 | ||||||||
\(315\) | −16.0605 | − | 16.9286i | −0.904906 | − | 0.953820i | ||||
\(316\) | 15.4241 | 0.867673 | ||||||||
\(317\) | −12.6801 | − | 21.9626i | −0.712188 | − | 1.23355i | −0.964034 | − | 0.265778i | \(-0.914371\pi\) |
0.251847 | − | 0.967767i | \(-0.418962\pi\) | |||||||
\(318\) | 2.64128 | − | 4.57483i | 0.148116 | − | 0.256544i | ||||
\(319\) | 0.824324 | − | 1.42777i | 0.0461533 | − | 0.0799398i | ||||
\(320\) | 7.77489 | + | 13.4665i | 0.434629 | + | 0.752800i | ||||
\(321\) | −9.33870 | −0.521236 | ||||||||
\(322\) | −8.75697 | − | 9.23032i | −0.488007 | − | 0.514385i | ||||
\(323\) | −2.01048 | −0.111866 | ||||||||
\(324\) | 3.35237 | + | 5.80648i | 0.186243 | + | 0.322582i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.06247 | + | 8.76845i | −0.280384 | + | 0.485640i | ||||
\(327\) | −1.38935 | − | 2.40643i | −0.0768314 | − | 0.133076i | ||||
\(328\) | −14.8637 | −0.820709 | ||||||||
\(329\) | −18.5012 | + | 4.43922i | −1.02001 | + | 0.244742i | ||||
\(330\) | −1.73923 | −0.0957413 | ||||||||
\(331\) | 0.891417 | + | 1.54398i | 0.0489967 | + | 0.0848648i | 0.889484 | − | 0.456967i | \(-0.151064\pi\) |
−0.840487 | + | 0.541832i | \(0.817731\pi\) | |||||||
\(332\) | −0.967335 | + | 1.67547i | −0.0530894 | + | 0.0919536i | ||||
\(333\) | 13.5828 | − | 23.5261i | 0.744332 | − | 1.28922i | ||||
\(334\) | 7.05414 | + | 12.2181i | 0.385985 | + | 0.668546i | ||||
\(335\) | −29.0781 | −1.58871 | ||||||||
\(336\) | −0.0886247 | + | 0.299049i | −0.00483487 | + | 0.0163145i | ||||
\(337\) | 9.56149 | 0.520848 | 0.260424 | − | 0.965494i | \(-0.416138\pi\) | ||||
0.260424 | + | 0.965494i | \(0.416138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.55234 | + | 7.88488i | −0.247249 | + | 0.428248i | ||||
\(340\) | −4.25120 | + | 7.36329i | −0.230554 | + | 0.399331i | ||||
\(341\) | −4.10103 | − | 7.10320i | −0.222083 | − | 0.384660i | ||||
\(342\) | 2.26422 | 0.122435 | ||||||||
\(343\) | 14.0876 | − | 12.0225i | 0.760659 | − | 0.649152i | ||||
\(344\) | 10.9138 | 0.588431 | ||||||||
\(345\) | 6.42867 | + | 11.1348i | 0.346108 | + | 0.599477i | ||||
\(346\) | 4.24991 | − | 7.36106i | 0.228477 | − | 0.395733i | ||||
\(347\) | −0.316694 | + | 0.548531i | −0.0170010 | + | 0.0294467i | −0.874401 | − | 0.485204i | \(-0.838745\pi\) |
0.857400 | + | 0.514651i | \(0.172079\pi\) | |||||||
\(348\) | −0.774258 | − | 1.34105i | −0.0415046 | − | 0.0718881i | ||||
\(349\) | −30.5989 | −1.63792 | −0.818960 | − | 0.573850i | \(-0.805449\pi\) | ||||
−0.818960 | + | 0.573850i | \(0.805449\pi\) | |||||||
\(350\) | −4.37895 | + | 14.7761i | −0.234065 | + | 0.789813i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.57166 | − | 4.45425i | −0.137070 | − | 0.237412i | ||||
\(353\) | −0.550173 | + | 0.952928i | −0.0292828 | + | 0.0507192i | −0.880295 | − | 0.474426i | \(-0.842656\pi\) |
0.851013 | + | 0.525145i | \(0.175989\pi\) | |||||||
\(354\) | −0.143655 | + | 0.248819i | −0.00763520 | + | 0.0132246i | ||||
\(355\) | 5.93375 | + | 10.2776i | 0.314931 | + | 0.545476i | ||||
\(356\) | 17.3579 | 0.919969 | ||||||||
\(357\) | 3.29480 | − | 0.790559i | 0.174379 | − | 0.0418408i | ||||
\(358\) | 7.81042 | 0.412793 | ||||||||
\(359\) | −4.88693 | − | 8.46441i | −0.257922 | − | 0.446734i | 0.707763 | − | 0.706450i | \(-0.249705\pi\) |
−0.965685 | + | 0.259716i | \(0.916371\pi\) | |||||||
\(360\) | 12.2945 | − | 21.2946i | 0.647975 | − | 1.12233i | ||||
\(361\) | 8.96124 | − | 15.5213i | 0.471644 | − | 0.816912i | ||||
\(362\) | −2.55546 | − | 4.42618i | −0.134312 | − | 0.232635i | ||||
\(363\) | −6.74026 | −0.353772 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.5139 | 1.96357 | ||||||||
\(366\) | −0.404132 | − | 0.699977i | −0.0211243 | − | 0.0365884i | ||||
\(367\) | 5.57363 | − | 9.65381i | 0.290941 | − | 0.503925i | −0.683092 | − | 0.730333i | \(-0.739365\pi\) |
0.974033 | + | 0.226408i | \(0.0726983\pi\) | |||||||
\(368\) | −0.503679 | + | 0.872397i | −0.0262561 | + | 0.0454769i | ||||
\(369\) | 6.83165 | + | 11.8328i | 0.355641 | + | 0.615989i | ||||
\(370\) | −31.0488 | −1.61415 | ||||||||
\(371\) | 17.0925 | + | 18.0164i | 0.887397 | + | 0.935364i | ||||
\(372\) | −7.70391 | −0.399429 | ||||||||
\(373\) | 15.3651 | + | 26.6131i | 0.795573 | + | 1.37797i | 0.922475 | + | 0.386057i | \(0.126163\pi\) |
−0.126902 | + | 0.991915i | \(0.540504\pi\) | |||||||
\(374\) | −0.740150 | + | 1.28198i | −0.0382723 | + | 0.0662895i | ||||
\(375\) | 2.09783 | − | 3.63355i | 0.108332 | − | 0.187636i | ||||
\(376\) | −10.0244 | − | 17.3628i | −0.516970 | − | 0.895419i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8.05430 | + | 1.93256i | −0.414269 | + | 0.0994002i | ||||
\(379\) | −22.6572 | −1.16382 | −0.581912 | − | 0.813252i | \(-0.697695\pi\) | ||||
−0.581912 | + | 0.813252i | \(0.697695\pi\) | |||||||
\(380\) | 2.27844 | + | 3.94638i | 0.116882 | + | 0.202445i | ||||
\(381\) | −0.643028 | + | 1.11376i | −0.0329433 | + | 0.0570595i | ||||
\(382\) | −0.560093 | + | 0.970109i | −0.0286568 | + | 0.0496351i | ||||
\(383\) | −0.294631 | − | 0.510317i | −0.0150550 | − | 0.0260760i | 0.858400 | − | 0.512981i | \(-0.171459\pi\) |
−0.873455 | + | 0.486905i | \(0.838126\pi\) | |||||||
\(384\) | −5.03161 | −0.256769 | ||||||||
\(385\) | 2.32325 | − | 7.83942i | 0.118404 | − | 0.399534i | ||||
\(386\) | 13.9801 | 0.711567 | ||||||||
\(387\) | −5.01619 | − | 8.68830i | −0.254988 | − | 0.441651i | ||||
\(388\) | −0.322877 | + | 0.559239i | −0.0163916 | + | 0.0283910i | ||||
\(389\) | −2.84973 | + | 4.93587i | −0.144487 | + | 0.250259i | −0.929181 | − | 0.369624i | \(-0.879486\pi\) |
0.784695 | + | 0.619883i | \(0.212820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.9432 | 0.553422 | ||||||||
\(392\) | 16.3643 | + | 10.6332i | 0.826524 | + | 0.537056i | ||||
\(393\) | −7.95809 | −0.401433 | ||||||||
\(394\) | −10.8891 | − | 18.8605i | −0.548584 | − | 0.950176i | ||||
\(395\) | −20.8068 | + | 36.0384i | −1.04690 | + | 1.81329i | ||||
\(396\) | −1.46778 | + | 2.54227i | −0.0737588 | + | 0.127754i | ||||
\(397\) | −12.7641 | − | 22.1082i | −0.640614 | − | 1.10958i | −0.985296 | − | 0.170857i | \(-0.945346\pi\) |
0.344682 | − | 0.938720i | \(-0.387987\pi\) | |||||||
\(398\) | −21.6005 | −1.08274 | ||||||||
\(399\) | 0.515992 | − | 1.74113i | 0.0258319 | − | 0.0871655i | ||||
\(400\) | 1.22017 | 0.0610086 | ||||||||
\(401\) | 12.7506 | + | 22.0846i | 0.636733 | + | 1.10285i | 0.986145 | + | 0.165884i | \(0.0530478\pi\) |
−0.349413 | + | 0.936969i | \(0.613619\pi\) | |||||||
\(402\) | −2.37757 | + | 4.11807i | −0.118582 | + | 0.205391i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.81817 | − | 6.61327i | −0.189961 | − | 0.329022i | ||||
\(405\) | −18.0891 | −0.898857 | ||||||||
\(406\) | −4.02018 | + | 0.964608i | −0.199518 | + | 0.0478727i | ||||
\(407\) | 9.51867 | 0.471823 | ||||||||
\(408\) | 1.78520 | + | 3.09206i | 0.0883807 | + | 0.153080i | ||||
\(409\) | 0.0734938 | − | 0.127295i | 0.00363403 | − | 0.00629433i | −0.864203 | − | 0.503144i | \(-0.832177\pi\) |
0.867837 | + | 0.496850i | \(0.165510\pi\) | |||||||
\(410\) | 7.80822 | − | 13.5242i | 0.385621 | − | 0.667914i | ||||
\(411\) | 2.88199 | + | 4.99175i | 0.142158 | + | 0.246225i | ||||
\(412\) | 5.27202 | 0.259734 | ||||||||
\(413\) | −0.929635 | − | 0.979885i | −0.0457443 | − | 0.0482170i | ||||
\(414\) | −12.3243 | −0.605709 | ||||||||
\(415\) | −2.60983 | − | 4.52036i | −0.128112 | − | 0.221896i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.39270 | + | 2.41223i | −0.0682008 | + | 0.118127i | ||||
\(418\) | 0.396686 | + | 0.687080i | 0.0194026 | + | 0.0336062i | ||||
\(419\) | 13.6959 | 0.669088 | 0.334544 | − | 0.942380i | \(-0.391418\pi\) | ||||
0.334544 | + | 0.942380i | \(0.391418\pi\) | |||||||
\(420\) | −5.28572 | − | 5.57144i | −0.257917 | − | 0.271858i | ||||
\(421\) | −3.44169 | −0.167738 | −0.0838688 | − | 0.996477i | \(-0.526728\pi\) | ||||
−0.0838688 | + | 0.996477i | \(0.526728\pi\) | |||||||
\(422\) | 2.42421 | + | 4.19885i | 0.118009 | + | 0.204397i | ||||
\(423\) | −9.21486 | + | 15.9606i | −0.448042 | + | 0.776032i | ||||
\(424\) | −13.0844 | + | 22.6629i | −0.635437 | + | 1.10061i | ||||
\(425\) | −6.62754 | − | 11.4792i | −0.321483 | − | 0.556825i | ||||
\(426\) | 1.94069 | 0.0940267 | ||||||||
\(427\) | 3.69493 | − | 0.886566i | 0.178810 | − | 0.0429039i | ||||
\(428\) | 18.0156 | 0.870816 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.73325 | + | 9.93028i | −0.276482 | + | 0.478881i | ||||
\(431\) | 11.1455 | − | 19.3046i | 0.536861 | − | 0.929870i | −0.462210 | − | 0.886771i | \(-0.652943\pi\) |
0.999071 | − | 0.0430997i | \(-0.0137233\pi\) | |||||||
\(432\) | 0.327896 | + | 0.567932i | 0.0157759 | + | 0.0273246i | ||||
\(433\) | −25.8963 | −1.24449 | −0.622247 | − | 0.782821i | \(-0.713780\pi\) | ||||
−0.622247 | + | 0.782821i | \(0.713780\pi\) | |||||||
\(434\) | −5.84424 | + | 19.7204i | −0.280533 | + | 0.946611i | ||||
\(435\) | 4.17783 | 0.200312 | ||||||||
\(436\) | 2.68024 | + | 4.64232i | 0.128360 | + | 0.222327i | ||||
\(437\) | 2.93253 | − | 5.07929i | 0.140282 | − | 0.242975i | ||||
\(438\) | 3.06732 | − | 5.31275i | 0.146562 | − | 0.253853i | ||||
\(439\) | 13.9919 | + | 24.2347i | 0.667798 | + | 1.15666i | 0.978519 | + | 0.206159i | \(0.0660963\pi\) |
−0.310721 | + | 0.950501i | \(0.600570\pi\) | |||||||
\(440\) | 8.61583 | 0.410744 | ||||||||
\(441\) | 0.943533 | − | 17.9147i | 0.0449301 | − | 0.853079i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.6044 | − | 28.7597i | −0.788900 | − | 1.36642i | −0.926641 | − | 0.375947i | \(-0.877317\pi\) |
0.137741 | − | 0.990468i | \(-0.456016\pi\) | |||||||
\(444\) | 4.47028 | − | 7.74275i | 0.212150 | − | 0.367454i | ||||
\(445\) | −23.4155 | + | 40.5568i | −1.11000 | + | 1.92258i | ||||
\(446\) | 1.00353 | + | 1.73816i | 0.0475185 | + | 0.0823044i | ||||
\(447\) | −3.87796 | −0.183421 | ||||||||
\(448\) | −3.39672 | + | 11.4617i | −0.160480 | + | 0.541513i | ||||
\(449\) | −19.6864 | −0.929059 | −0.464529 | − | 0.885558i | \(-0.653777\pi\) | ||||
−0.464529 | + | 0.885558i | \(0.653777\pi\) | |||||||
\(450\) | 7.46399 | + | 12.9280i | 0.351856 | + | 0.609433i | ||||
\(451\) | −2.39377 | + | 4.14614i | −0.112718 | + | 0.195234i | ||||
\(452\) | 8.78205 | − | 15.2110i | 0.413073 | − | 0.715464i | ||||
\(453\) | −5.57305 | − | 9.65281i | −0.261845 | − | 0.453528i | ||||
\(454\) | −22.3783 | −1.05027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.91357 | 0.0896111 | ||||||||
\(457\) | −0.373471 | − | 0.646871i | −0.0174702 | − | 0.0302593i | 0.857158 | − | 0.515053i | \(-0.172228\pi\) |
−0.874628 | + | 0.484794i | \(0.838895\pi\) | |||||||
\(458\) | 0.0291746 | − | 0.0505320i | 0.00136324 | − | 0.00236120i | ||||
\(459\) | 3.56203 | − | 6.16961i | 0.166261 | − | 0.287973i | ||||
\(460\) | −12.4017 | − | 21.4805i | −0.578235 | − | 1.00153i | ||||
\(461\) | 33.1710 | 1.54493 | 0.772464 | − | 0.635058i | \(-0.219024\pi\) | ||||
0.772464 | + | 0.635058i | \(0.219024\pi\) | |||||||
\(462\) | −0.920266 | − | 0.970010i | −0.0428146 | − | 0.0451289i | ||||
\(463\) | 30.7521 | 1.42917 | 0.714586 | − | 0.699548i | \(-0.246615\pi\) | ||||
0.714586 | + | 0.699548i | \(0.246615\pi\) | |||||||
\(464\) | 0.163664 | + | 0.283475i | 0.00759792 | + | 0.0131600i | ||||
\(465\) | 10.3924 | − | 18.0002i | 0.481937 | − | 0.834740i | ||||
\(466\) | −6.24313 | + | 10.8134i | −0.289207 | + | 0.500922i | ||||
\(467\) | 14.8033 | + | 25.6400i | 0.685013 | + | 1.18648i | 0.973433 | + | 0.228973i | \(0.0735367\pi\) |
−0.288420 | + | 0.957504i | \(0.593130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.3859 | − | 16.2176i | −0.710456 | − | 0.748859i | ||||
\(470\) | 21.0642 | 0.971621 | ||||||||
\(471\) | 0.641056 | + | 1.11034i | 0.0295383 | + | 0.0511618i | ||||
\(472\) | 0.711644 | − | 1.23260i | 0.0327561 | − | 0.0567352i | ||||
\(473\) | 1.75765 | − | 3.04434i | 0.0808168 | − | 0.139979i | ||||
\(474\) | 3.40253 | + | 5.89335i | 0.156283 | + | 0.270691i | ||||
\(475\) | −7.10411 | −0.325959 | ||||||||
\(476\) | −6.35609 | + | 1.52509i | −0.291331 | + | 0.0699024i | ||||
\(477\) | 24.0555 | 1.10143 | ||||||||
\(478\) | 1.42748 | + | 2.47247i | 0.0652915 | + | 0.113088i | ||||
\(479\) | 7.04527 | − | 12.2028i | 0.321907 | − | 0.557559i | −0.658975 | − | 0.752165i | \(-0.729010\pi\) |
0.980881 | + | 0.194606i | \(0.0623429\pi\) | |||||||
\(480\) | 6.51684 | − | 11.2875i | 0.297452 | − | 0.515201i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.30247 | 0.332618 | ||||||||
\(483\) | −2.80858 | + | 9.47710i | −0.127795 | + | 0.431223i | ||||
\(484\) | 13.0028 | 0.591038 | ||||||||
\(485\) | −0.871108 | − | 1.50880i | −0.0395550 | − | 0.0685112i | ||||
\(486\) | −6.17502 | + | 10.6955i | −0.280105 | + | 0.485156i | ||||
\(487\) | −8.39773 | + | 14.5453i | −0.380537 | + | 0.659110i | −0.991139 | − | 0.132828i | \(-0.957594\pi\) |
0.610602 | + | 0.791938i | \(0.290928\pi\) | |||||||
\(488\) | 2.00200 | + | 3.46757i | 0.0906263 | + | 0.156969i | ||||
\(489\) | 7.86587 | 0.355707 | ||||||||
\(490\) | −18.2715 | + | 9.30384i | −0.825424 | + | 0.420304i | ||||
\(491\) | 21.6690 | 0.977908 | 0.488954 | − | 0.872310i | \(-0.337379\pi\) | ||||
0.488954 | + | 0.872310i | \(0.337379\pi\) | |||||||
\(492\) | 2.24839 | + | 3.89432i | 0.101365 | + | 0.175570i | ||||
\(493\) | 1.77793 | − | 3.07947i | 0.0800740 | − | 0.138692i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.96001 | − | 6.85895i | −0.177989 | − | 0.308287i | ||||
\(496\) | 1.62847 | 0.0731203 | ||||||||
\(497\) | −2.59236 | + | 8.74749i | −0.116283 | + | 0.392379i | ||||
\(498\) | −0.853570 | −0.0382494 | ||||||||
\(499\) | −11.6524 | − | 20.1825i | −0.521633 | − | 0.903495i | −0.999683 | − | 0.0251622i | \(-0.991990\pi\) |
0.478051 | − | 0.878332i | \(-0.341344\pi\) | |||||||
\(500\) | −4.04699 | + | 7.00960i | −0.180987 | + | 0.313479i | ||||
\(501\) | 5.48023 | − | 9.49203i | 0.244838 | − | 0.424073i | ||||
\(502\) | −9.15601 | − | 15.8587i | −0.408653 | − | 0.707807i | ||||
\(503\) | −43.8829 | −1.95664 | −0.978322 | − | 0.207090i | \(-0.933601\pi\) | ||||
−0.978322 | + | 0.207090i | \(0.933601\pi\) | |||||||
\(504\) | 18.3818 | − | 4.41056i | 0.818791 | − | 0.196462i | ||||
\(505\) | 20.6026 | 0.916802 | ||||||||
\(506\) | −2.15919 | − | 3.73983i | −0.0959879 | − | 0.166256i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.24048 | − | 2.14858i | 0.0550376 | − | 0.0953279i | ||||
\(509\) | 9.96210 | + | 17.2549i | 0.441563 | + | 0.764809i | 0.997806 | − | 0.0662109i | \(-0.0210910\pi\) |
−0.556243 | + | 0.831020i | \(0.687758\pi\) | |||||||
\(510\) | −3.75123 | −0.166107 | ||||||||
\(511\) | 19.8495 | + | 20.9224i | 0.878089 | + | 0.925553i | ||||
\(512\) | 2.01529 | 0.0890641 | ||||||||
\(513\) | −1.90908 | − | 3.30662i | −0.0842879 | − | 0.145991i | ||||
\(514\) | −2.10139 | + | 3.63972i | −0.0926886 | + | 0.160541i | ||||
\(515\) | −7.11185 | + | 12.3181i | −0.313386 | + | 0.542800i | ||||
\(516\) | −1.65090 | − | 2.85944i | −0.0726767 | − | 0.125880i | ||||
\(517\) | −6.45768 | −0.284009 | ||||||||
\(518\) | −16.4287 | − | 17.3167i | −0.721834 | − | 0.760852i | ||||
\(519\) | −6.60335 | −0.289855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.26204 | − | 14.3103i | 0.361967 | − | 0.626944i | −0.626318 | − | 0.779568i | \(-0.715439\pi\) |
0.988284 | + | 0.152623i | \(0.0487721\pi\) | |||||||
\(522\) | −2.00232 | + | 3.46812i | −0.0876392 | + | 0.151796i | ||||
\(523\) | 5.99809 | + | 10.3890i | 0.262278 | + | 0.454279i | 0.966847 | − | 0.255357i | \(-0.0821929\pi\) |
−0.704569 | + | 0.709636i | \(0.748860\pi\) | |||||||
\(524\) | 15.3522 | 0.670664 | ||||||||
\(525\) | 11.6423 | − | 2.79346i | 0.508111 | − | 0.121917i | ||||
\(526\) | −7.62131 | −0.332305 | ||||||||
\(527\) | −8.84526 | − | 15.3204i | −0.385305 | − | 0.667369i | ||||
\(528\) | −0.0529314 | + | 0.0916798i | −0.00230354 | + | 0.00398985i | ||||
\(529\) | −4.46197 | + | 7.72837i | −0.193999 | + | 0.336016i | ||||
\(530\) | −13.7471 | − | 23.8107i | −0.597137 | − | 1.03427i | ||||
\(531\) | −1.30835 | −0.0567774 | ||||||||
\(532\) | −0.995416 | + | 3.35886i | −0.0431567 | + | 0.145625i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.82913 | + | 6.63225i | 0.165703 | + | 0.287005i | ||||
\(535\) | −24.3026 | + | 42.0934i | −1.05070 | + | 1.81986i | ||||
\(536\) | 11.7781 | − | 20.4002i | 0.508735 | − | 0.881155i | ||||
\(537\) | −3.03388 | − | 5.25484i | −0.130922 | − | 0.226763i | ||||
\(538\) | −4.10536 | −0.176995 | ||||||||
\(539\) | 5.60152 | − | 2.85229i | 0.241275 | − | 0.122857i | ||||
\(540\) | −16.1471 | −0.694861 | ||||||||
\(541\) | 18.1158 | + | 31.3775i | 0.778860 | + | 1.34903i | 0.932599 | + | 0.360914i | \(0.117535\pi\) |
−0.153739 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(542\) | −3.15829 | + | 5.47031i | −0.135660 | + | 0.234970i | ||||
\(543\) | −1.98529 | + | 3.43862i | −0.0851968 | + | 0.147565i | ||||
\(544\) | −5.54665 | − | 9.60707i | −0.237811 | − | 0.411900i | ||||
\(545\) | −14.4624 | −0.619500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34857 | −0.314202 | −0.157101 | − | 0.987583i | \(-0.550215\pi\) | ||||
−0.157101 | + | 0.987583i | \(0.550215\pi\) | |||||||
\(548\) | −5.55973 | − | 9.62974i | −0.237500 | − | 0.411362i | ||||
\(549\) | 1.84032 | − | 3.18753i | 0.0785430 | − | 0.136040i | ||||
\(550\) | −2.61535 | + | 4.52991i | −0.111519 | + | 0.193156i | ||||
\(551\) | −0.952888 | − | 1.65045i | −0.0405944 | − | 0.0703115i | ||||
\(552\) | −10.4157 | −0.443322 | ||||||||
\(553\) | −31.1089 | + | 7.46431i | −1.32288 | + | 0.317415i | ||||
\(554\) | 3.24816 | 0.138001 | ||||||||
\(555\) | 12.0606 | + | 20.8896i | 0.511945 | + | 0.886715i | ||||
\(556\) | 2.68670 | − | 4.65350i | 0.113941 | − | 0.197352i | ||||
\(557\) | 5.41399 | − | 9.37731i | 0.229398 | − | 0.397329i | −0.728232 | − | 0.685331i | \(-0.759658\pi\) |
0.957630 | + | 0.288002i | \(0.0929909\pi\) | |||||||
\(558\) | 9.96160 | + | 17.2540i | 0.421708 | + | 0.730420i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.11731 | + | 1.17770i | 0.0472148 | + | 0.0497670i | ||||
\(561\) | 1.15002 | 0.0485538 | ||||||||
\(562\) | 3.63847 | + | 6.30201i | 0.153480 | + | 0.265834i | ||||
\(563\) | 6.92997 | − | 12.0031i | 0.292064 | − | 0.505869i | −0.682234 | − | 0.731134i | \(-0.738991\pi\) |
0.974298 | + | 0.225265i | \(0.0723248\pi\) | |||||||
\(564\) | −3.03274 | + | 5.25285i | −0.127701 | + | 0.221185i | ||||
\(565\) | 23.6936 | + | 41.0386i | 0.996798 | + | 1.72651i | ||||
\(566\) | 12.9919 | 0.546089 | ||||||||
\(567\) | −9.57138 | − | 10.0888i | −0.401960 | − | 0.423688i | ||||
\(568\) | −9.61384 | −0.403388 | ||||||||
\(569\) | −13.7060 | − | 23.7395i | −0.574586 | − | 0.995212i | −0.996086 | − | 0.0883842i | \(-0.971830\pi\) |
0.421500 | − | 0.906828i | \(-0.361504\pi\) | |||||||
\(570\) | −1.00524 | + | 1.74113i | −0.0421049 | + | 0.0729279i | ||||
\(571\) | 0.103879 | − | 0.179923i | 0.00434719 | − | 0.00752956i | −0.863844 | − | 0.503760i | \(-0.831950\pi\) |
0.868191 | + | 0.496230i | \(0.165283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.870251 | 0.0363552 | ||||||||
\(574\) | 11.6743 | − | 2.80115i | 0.487276 | − | 0.116918i | ||||
\(575\) | 38.6682 | 1.61258 | ||||||||
\(576\) | 5.78976 | + | 10.0282i | 0.241240 | + | 0.417840i | ||||
\(577\) | −1.66328 | + | 2.88089i | −0.0692434 | + | 0.119933i | −0.898568 | − | 0.438833i | \(-0.855392\pi\) |
0.829325 | + | 0.558766i | \(0.188725\pi\) | |||||||
\(578\) | 5.63818 | − | 9.76562i | 0.234518 | − | 0.406196i | ||||
\(579\) | −5.43043 | − | 9.40577i | −0.225681 | − | 0.390891i | ||||
\(580\) | −8.05959 | −0.334656 | ||||||||
\(581\) | 1.14019 | − | 3.84739i | 0.0473032 | − | 0.159617i | ||||
\(582\) | −0.284904 | −0.0118097 | ||||||||
\(583\) | 4.21447 | + | 7.29967i | 0.174545 | + | 0.302321i | ||||
\(584\) | −15.1950 | + | 26.3185i | −0.628772 | + | 1.08907i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.52769 | − | 4.37809i | −0.104418 | − | 0.180857i | ||||
\(587\) | 15.0810 | 0.622461 | 0.311230 | − | 0.950335i | \(-0.399259\pi\) | ||||
0.311230 | + | 0.950335i | \(0.399259\pi\) | |||||||
\(588\) | 0.310529 | − | 5.89596i | 0.0128060 | − | 0.243145i | ||||
\(589\) | −9.48129 | −0.390670 | ||||||||
\(590\) | 0.747686 | + | 1.29503i | 0.0307817 | + | 0.0533155i | ||||
\(591\) | −8.45953 | + | 14.6523i | −0.347978 | + | 0.602716i | ||||
\(592\) | −0.944935 | + | 1.63668i | −0.0388366 | + | 0.0672670i | ||||
\(593\) | 12.9245 | + | 22.3859i | 0.530747 | + | 0.919281i | 0.999356 | + | 0.0358751i | \(0.0114218\pi\) |
−0.468609 | + | 0.883405i | \(0.655245\pi\) | |||||||
\(594\) | −2.81128 | −0.115348 | ||||||||
\(595\) | 5.01087 | − | 16.9083i | 0.205426 | − | 0.693175i | ||||
\(596\) | 7.48110 | 0.306438 | ||||||||
\(597\) | 8.39052 | + | 14.5328i | 0.343401 | + | 0.594788i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.7734 | − | 30.7845i | 0.726203 | − | 1.25782i | −0.232274 | − | 0.972650i | \(-0.574617\pi\) |
0.958477 | − | 0.285170i | \(-0.0920501\pi\) | |||||||
\(600\) | 6.30807 | + | 10.9259i | 0.257526 | + | 0.446048i | ||||
\(601\) | −27.2947 | −1.11338 | −0.556688 | − | 0.830722i | \(-0.687928\pi\) | ||||
−0.556688 | + | 0.830722i | \(0.687928\pi\) | |||||||
\(602\) | −8.57196 | + | 2.05677i | −0.349367 | + | 0.0838276i | ||||
\(603\) | −21.6538 | −0.881810 | ||||||||
\(604\) | 10.7511 | + | 18.6215i | 0.437458 | + | 0.757699i | ||||
\(605\) | −17.5406 | + | 30.3811i | −0.713125 | + | 1.23517i | ||||
\(606\) | 1.68456 | − | 2.91775i | 0.0684308 | − | 0.118526i | ||||
\(607\) | 19.4629 | + | 33.7108i | 0.789976 | + | 1.36828i | 0.925981 | + | 0.377570i | \(0.123240\pi\) |
−0.136006 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(608\) | −5.94549 | −0.241121 | ||||||||
\(609\) | 2.21059 | + | 2.33008i | 0.0895776 | + | 0.0944196i | ||||
\(610\) | −4.20679 | −0.170328 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.16576 | + | 5.48326i | −0.127968 | + | 0.221648i | ||||
\(613\) | 0.443322 | − | 0.767857i | 0.0179056 | − | 0.0310135i | −0.856934 | − | 0.515427i | \(-0.827633\pi\) |
0.874839 | + | 0.484413i | \(0.160967\pi\) | |||||||
\(614\) | 9.45317 | + | 16.3734i | 0.381499 | + | 0.660775i | ||||
\(615\) | −12.1321 | −0.489214 | ||||||||
\(616\) | 4.55884 | + | 4.80526i | 0.183681 | + | 0.193609i | ||||
\(617\) | −34.7888 | −1.40054 | −0.700272 | − | 0.713876i | \(-0.746938\pi\) | ||||
−0.700272 | + | 0.713876i | \(0.746938\pi\) | |||||||
\(618\) | 1.16300 | + | 2.01437i | 0.0467827 | + | 0.0810300i | ||||
\(619\) | 1.02781 | − | 1.78021i | 0.0413111 | − | 0.0715529i | −0.844631 | − | 0.535350i | \(-0.820180\pi\) |
0.885942 | + | 0.463797i | \(0.153513\pi\) | |||||||
\(620\) | −20.0483 | + | 34.7247i | −0.805161 | + | 1.39458i | ||||
\(621\) | 10.3913 | + | 17.9982i | 0.416987 | + | 0.722243i | ||||
\(622\) | 8.37728 | 0.335898 | ||||||||
\(623\) | −35.0092 | + | 8.40016i | −1.40262 | + | 0.336545i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.19081 | + | 10.7228i | 0.247632 | + | 0.428912i | ||||
\(626\) | 8.89959 | − | 15.4145i | 0.355699 | − | 0.616089i | ||||
\(627\) | 0.308178 | − | 0.533780i | 0.0123074 | − | 0.0213171i | ||||
\(628\) | −1.23668 | − | 2.14199i | −0.0493489 | − | 0.0854749i | ||||
\(629\) | 20.5302 | 0.818593 | ||||||||
\(630\) | −5.64328 | + | 19.0423i | −0.224834 | + | 0.758664i | ||||
\(631\) | 45.2337 | 1.80073 | 0.900363 | − | 0.435139i | \(-0.143301\pi\) | ||||
0.900363 | + | 0.435139i | \(0.143301\pi\) | |||||||
\(632\) | −16.8555 | − | 29.1946i | −0.670477 | − | 1.16130i | ||||
\(633\) | 1.88332 | − | 3.26201i | 0.0748554 | − | 0.129653i | ||||
\(634\) | −10.7924 | + | 18.6930i | −0.428621 | + | 0.742393i | ||||
\(635\) | 3.34678 | + | 5.79679i | 0.132813 | + | 0.230038i | ||||
\(636\) | 7.91700 | 0.313929 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.40321 | −0.0555534 | ||||||||
\(639\) | 4.41872 | + | 7.65345i | 0.174802 | + | 0.302766i | ||||
\(640\) | −13.0941 | + | 22.6796i | −0.517588 | + | 0.896489i | ||||
\(641\) | 9.53097 | − | 16.5081i | 0.376451 | − | 0.652032i | −0.614092 | − | 0.789234i | \(-0.710478\pi\) |
0.990543 | + | 0.137202i | \(0.0438111\pi\) | |||||||
\(642\) | 3.97420 | + | 6.88352i | 0.156849 | + | 0.271671i | ||||
\(643\) | 10.5351 | 0.415464 | 0.207732 | − | 0.978186i | \(-0.433392\pi\) | ||||
0.207732 | + | 0.978186i | \(0.433392\pi\) | |||||||
\(644\) | 5.41813 | − | 18.2826i | 0.213504 | − | 0.720434i | ||||
\(645\) | 8.90811 | 0.350756 | ||||||||
\(646\) | 0.855587 | + | 1.48192i | 0.0336626 | + | 0.0583053i | ||||
\(647\) | 12.0804 | − | 20.9239i | 0.474930 | − | 0.822603i | −0.524658 | − | 0.851313i | \(-0.675807\pi\) |
0.999588 | + | 0.0287105i | \(0.00914011\pi\) | |||||||
\(648\) | 7.32699 | − | 12.6907i | 0.287831 | − | 0.498538i | ||||
\(649\) | −0.229219 | − | 0.397019i | −0.00899762 | − | 0.0155843i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.5380 | − | 3.72822i | 0.608983 | − | 0.146120i | ||||
\(652\) | −15.1743 | −0.594271 | ||||||||
\(653\) | 16.8445 | + | 29.1755i | 0.659176 | + | 1.14173i | 0.980829 | + | 0.194869i | \(0.0624282\pi\) |
−0.321653 | + | 0.946858i | \(0.604238\pi\) | |||||||
\(654\) | −1.18251 | + | 2.04817i | −0.0462400 | + | 0.0800900i | ||||
\(655\) | −20.7098 | + | 35.8704i | −0.809199 | + | 1.40157i | ||||
\(656\) | −0.475268 | − | 0.823189i | −0.0185561 | − | 0.0321401i | ||||
\(657\) | 27.9357 | 1.08987 | ||||||||
\(658\) | 11.1456 | + | 11.7480i | 0.434500 | + | 0.457986i | ||||
\(659\) | −4.20059 | −0.163632 | −0.0818159 | − | 0.996647i | \(-0.526072\pi\) | ||||
−0.0818159 | + | 0.996647i | \(0.526072\pi\) | |||||||
\(660\) | −1.30329 | − | 2.25737i | −0.0507307 | − | 0.0878681i | ||||
\(661\) | 8.83631 | − | 15.3049i | 0.343693 | − | 0.595293i | −0.641423 | − | 0.767188i | \(-0.721655\pi\) |
0.985115 | + | 0.171894i | \(0.0549888\pi\) | |||||||
\(662\) | 0.758708 | − | 1.31412i | 0.0294880 | − | 0.0510748i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.22844 | 0.164095 | ||||||||
\(665\) | −6.50520 | − | 6.85683i | −0.252261 | − | 0.265897i | ||||
\(666\) | −23.1213 | −0.895932 | ||||||||
\(667\) | 5.18664 | + | 8.98353i | 0.200828 | + | 0.347844i | ||||
\(668\) | −10.5721 | + | 18.3114i | −0.409046 | + | 0.708488i | ||||
\(669\) | 0.779623 | − | 1.35035i | 0.0301420 | − | 0.0522074i | ||||
\(670\) | 12.3746 | + | 21.4334i | 0.478071 | + | 0.828044i | ||||
\(671\) | 1.28968 | 0.0497875 | ||||||||
\(672\) | 9.74352 | − | 2.33787i | 0.375865 | − | 0.0901855i | ||||
\(673\) | −20.6103 | −0.794469 | −0.397235 | − | 0.917717i | \(-0.630030\pi\) | ||||
−0.397235 | + | 0.917717i | \(0.630030\pi\) | |||||||
\(674\) | −4.06901 | − | 7.04774i | −0.156733 | − | 0.271469i | ||||
\(675\) | 12.5865 | − | 21.8005i | 0.484456 | − | 0.839102i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6537 | + | 18.4527i | 0.409455 | + | 0.709196i | 0.994829 | − | 0.101567i | \(-0.0323857\pi\) |
−0.585374 | + | 0.810763i | \(0.699052\pi\) | |||||||
\(678\) | 7.74922 | 0.297607 | ||||||||
\(679\) | 0.380573 | − | 1.28418i | 0.0146051 | − | 0.0492824i | ||||
\(680\) | 18.5829 | 0.712623 | ||||||||
\(681\) | 8.69264 | + | 15.0561i | 0.333103 | + | 0.576951i | ||||
\(682\) | −3.49049 | + | 6.04571i | −0.133658 | + | 0.231502i | ||||
\(683\) | −3.34878 | + | 5.80026i | −0.128138 | + | 0.221941i | −0.922955 | − | 0.384908i | \(-0.874233\pi\) |
0.794817 | + | 0.606849i | \(0.207567\pi\) | |||||||
\(684\) | 1.69670 | + | 2.93877i | 0.0648750 | + | 0.112367i | ||||
\(685\) | 29.9999 | 1.14624 | ||||||||
\(686\) | −14.8569 | − | 5.26761i | −0.567238 | − | 0.201118i | ||||
\(687\) | −0.0453305 | −0.00172946 | ||||||||
\(688\) | 0.348970 | + | 0.604433i | 0.0133043 | + | 0.0230438i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.47161 | − | 9.47710i | 0.208301 | − | 0.360787i | ||||
\(691\) | −12.4632 | − | 21.5868i | −0.474121 | − | 0.821202i | 0.525440 | − | 0.850831i | \(-0.323901\pi\) |
−0.999561 | + | 0.0296291i | \(0.990567\pi\) | |||||||
\(692\) | 12.7387 | 0.484253 | ||||||||
\(693\) | 1.73007 | − | 5.83782i | 0.0657198 | − | 0.221761i | ||||
\(694\) | 0.539093 | 0.0204637 | ||||||||
\(695\) | 7.24861 | + | 12.5550i | 0.274955 | + | 0.476237i | ||||
\(696\) | −1.69223 | + | 2.93102i | −0.0641437 | + | 0.111100i | ||||
\(697\) | −5.16298 | + | 8.94254i | −0.195562 | + | 0.338723i | ||||
\(698\) | 13.0217 | + | 22.5543i | 0.492880 | + | 0.853694i | ||||
\(699\) | 9.70033 | 0.366900 | ||||||||
\(700\) | −22.4595 | + | 5.38896i | −0.848888 | + | 0.203683i | ||||
\(701\) | −4.94583 | −0.186801 | −0.0934007 | − | 0.995629i | \(-0.529774\pi\) | ||||
−0.0934007 | + | 0.995629i | \(0.529774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.50162 | − | 9.52908i | 0.207497 | − | 0.359396i | ||||
\(704\) | −2.02870 | + | 3.51382i | −0.0764597 | + | 0.132432i | ||||
\(705\) | −8.18220 | − | 14.1720i | −0.308160 | − | 0.533748i | ||||
\(706\) | 0.936533 | 0.0352469 | ||||||||
\(707\) | 10.9013 | + | 11.4905i | 0.409985 | + | 0.432147i | ||||
\(708\) | −0.430594 | −0.0161827 | ||||||||
\(709\) | −2.32249 | − | 4.02267i | −0.0872228 | − | 0.151074i | 0.819113 | − | 0.573632i | \(-0.194466\pi\) |
−0.906336 | + | 0.422557i | \(0.861133\pi\) | |||||||
\(710\) | 5.05037 | − | 8.74749i | 0.189537 | − | 0.328288i | ||||
\(711\) | −15.4943 | + | 26.8369i | −0.581082 | + | 1.00646i | ||||
\(712\) | −18.9688 | − | 32.8550i | −0.710888 | − | 1.23129i | ||||
\(713\) | 51.6074 | 1.93271 | ||||||||
\(714\) | −1.98486 | − | 2.09215i | −0.0742816 | − | 0.0782968i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.85275 | + | 10.1373i | 0.218728 | + | 0.378847i | ||||
\(717\) | 1.10898 | − | 1.92082i | 0.0414157 | − | 0.0717342i | ||||
\(718\) | −4.15939 | + | 7.20427i | −0.155227 | + | 0.268861i | ||||
\(719\) | −15.8706 | − | 27.4887i | −0.591875 | − | 1.02516i | −0.993980 | − | 0.109564i | \(-0.965055\pi\) |
0.402105 | − | 0.915594i | \(-0.368279\pi\) | |||||||
\(720\) | 1.57247 | 0.0586025 | ||||||||
\(721\) | −10.6331 | + | 2.55133i | −0.395999 | + | 0.0950165i | ||||
\(722\) | −15.2543 | −0.567705 | ||||||||
\(723\) | −2.83658 | − | 4.91309i | −0.105493 | − | 0.182720i | ||||
\(724\) | 3.82987 | − | 6.63354i | 0.142336 | − | 0.246533i | ||||
\(725\) | 6.28237 | − | 10.8814i | 0.233322 | − | 0.404125i | ||||
\(726\) | 2.86840 | + | 4.96822i | 0.106456 | + | 0.184388i | ||||
\(727\) | 47.8755 | 1.77560 | 0.887801 | − | 0.460227i | \(-0.152232\pi\) | ||||
0.887801 | + | 0.460227i | \(0.152232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.17412 | −0.228671 | ||||||||
\(730\) | −15.9645 | − | 27.6514i | −0.590873 | − | 1.02342i | ||||
\(731\) | 3.79096 | − | 6.56613i | 0.140214 | − | 0.242857i | ||||
\(732\) | 0.605675 | − | 1.04906i | 0.0223864 | − | 0.0387743i | ||||
\(733\) | −3.80104 | − | 6.58359i | −0.140395 | − | 0.243171i | 0.787251 | − | 0.616633i | \(-0.211504\pi\) |
−0.927645 | + | 0.373463i | \(0.878170\pi\) | |||||||
\(734\) | −9.48771 | −0.350198 | ||||||||
\(735\) | 13.3570 | + | 8.67908i | 0.492681 | + | 0.320133i | ||||
\(736\) | 32.3618 | 1.19287 | ||||||||
\(737\) | −3.79368 | − | 6.57086i | −0.139742 | − | 0.242041i | ||||
\(738\) | 5.81459 | − | 10.0712i | 0.214038 | − | 0.370725i | ||||
\(739\) | −16.7118 | + | 28.9457i | −0.614754 | + | 1.06479i | 0.375673 | + | 0.926752i | \(0.377411\pi\) |
−0.990428 | + | 0.138033i | \(0.955922\pi\) | |||||||
\(740\) | −23.2665 | − | 40.2988i | −0.855294 | − | 1.48141i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00589 | − | 20.2659i | 0.220483 | − | 0.743984i | ||||
\(743\) | 2.93823 | 0.107793 | 0.0538966 | − | 0.998547i | \(-0.482836\pi\) | ||||
0.0538966 | + | 0.998547i | \(0.482836\pi\) | |||||||
\(744\) | 8.41888 | + | 14.5819i | 0.308651 | + | 0.534599i | ||||
\(745\) | −10.0919 | + | 17.4796i | −0.369737 | + | 0.640403i | ||||
\(746\) | 13.0776 | − | 22.6511i | 0.478805 | − | 0.829314i | ||||
\(747\) | −1.94348 | − | 3.36620i | −0.0711081 | − | 0.123163i | ||||
\(748\) | −2.21853 | −0.0811176 | ||||||||
\(749\) | −36.3356 | + | 8.71842i | −1.32767 | + | 0.318564i | ||||
\(750\) | −3.57104 | −0.130396 | ||||||||
\(751\) | −0.598389 | − | 1.03644i | −0.0218355 | − | 0.0378202i | 0.854901 | − | 0.518791i | \(-0.173618\pi\) |
−0.876737 | + | 0.480971i | \(0.840284\pi\) | |||||||
\(752\) | 0.641065 | − | 1.11036i | 0.0233773 | − | 0.0404906i | ||||
\(753\) | −7.11313 | + | 12.3203i | −0.259217 | + | 0.448977i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58.0123 | −2.11128 | ||||||||
\(756\) | −8.54381 | − | 9.00564i | −0.310735 | − | 0.327532i | ||||
\(757\) | 11.5464 | 0.419662 | 0.209831 | − | 0.977738i | \(-0.432709\pi\) | ||||
0.209831 | + | 0.977738i | \(0.432709\pi\) | |||||||
\(758\) | 9.64207 | + | 16.7006i | 0.350216 | + | 0.606592i | ||||
\(759\) | −1.67744 | + | 2.90541i | −0.0608871 | + | 0.105460i | ||||
\(760\) | 4.97979 | − | 8.62525i | 0.180636 | − | 0.312871i | ||||
\(761\) | 17.3249 | + | 30.0075i | 0.628026 | + | 1.08777i | 0.987947 | + | 0.154790i | \(0.0494702\pi\) |
−0.359921 | + | 0.932983i | \(0.617197\pi\) | |||||||
\(762\) | 1.09459 | 0.0396530 | ||||||||
\(763\) | −7.65238 | − | 8.06602i | −0.277035 | − | 0.292010i | ||||
\(764\) | −1.67883 | −0.0607378 | ||||||||
\(765\) | −8.54110 | − | 14.7936i | −0.308804 | − | 0.534864i | ||||
\(766\) | −0.250768 | + | 0.434344i | −0.00906063 | + | 0.0156935i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.12890 | + | 8.88351i | 0.185073 | + | 0.320556i | ||||
\(769\) | 6.54874 | 0.236154 | 0.118077 | − | 0.993004i | \(-0.462327\pi\) | ||||
0.118077 | + | 0.993004i | \(0.462327\pi\) | |||||||
\(770\) | −6.76710 | + | 1.62371i | −0.243869 | + | 0.0585143i | ||||
\(771\) | 3.26507 | 0.117589 | ||||||||
\(772\) | 10.4760 | + | 18.1450i | 0.377039 | + | 0.653051i | ||||
\(773\) | 16.9637 | − | 29.3821i | 0.610143 | − | 1.05680i | −0.381073 | − | 0.924545i | \(-0.624445\pi\) |
0.991216 | − | 0.132254i | \(-0.0422214\pi\) | |||||||
\(774\) | −4.26941 | + | 7.39484i | −0.153461 | + | 0.265802i | ||||
\(775\) | −31.2550 | − | 54.1352i | −1.12271 | − | 1.94459i | ||||
\(776\) | 1.41137 | 0.0506651 | ||||||||
\(777\) | −5.26909 | + | 17.7797i | −0.189028 | + | 0.637843i | ||||
\(778\) | 4.85095 | 0.173915 | ||||||||
\(779\) | 2.76711 | + | 4.79278i | 0.0991422 | + | 0.171719i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.54830 | + | 2.68173i | −0.0554024 | + | 0.0959598i | ||||
\(782\) | −4.65703 | − | 8.06620i | −0.166535 | − | 0.288447i | ||||
\(783\) | 6.75302 | 0.241333 | ||||||||
\(784\) | −0.0656403 | + | 1.24630i | −0.00234430 | + | 0.0445106i | ||||
\(785\) | 6.67303 | 0.238171 | ||||||||
\(786\) | 3.38667 | + | 5.86588i | 0.120798 | + | 0.209229i | ||||
\(787\) | 6.48717 | − | 11.2361i | 0.231243 | − | 0.400524i | −0.726932 | − | 0.686710i | \(-0.759054\pi\) |
0.958174 | + | 0.286186i | \(0.0923876\pi\) | |||||||
\(788\) | 16.3195 | − | 28.2662i | 0.581359 | − | 1.00694i | ||||
\(789\) | 2.96042 | + | 5.12760i | 0.105394 | + | 0.182548i | ||||
\(790\) | 35.4184 | 1.26013 | ||||||||
\(791\) | −10.3514 | + | 34.9290i | −0.368052 | + | 1.24193i | ||||
\(792\) | 6.41600 | 0.227983 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.8639 | + | 18.8168i | −0.385545 | + | 0.667784i | ||||
\(795\) | −10.6799 | + | 18.4981i | −0.378776 | + | 0.656059i | ||||
\(796\) | −16.1864 | − | 28.0357i | −0.573712 | − | 0.993699i | ||||
\(797\) | 4.41913 | 0.156533 | 0.0782667 | − | 0.996932i | \(-0.475061\pi\) | ||||
0.0782667 | + | 0.996932i | \(0.475061\pi\) | |||||||
\(798\) | −1.50297 | + | 0.360624i | −0.0532044 | + | 0.0127660i | ||||
\(799\) | −13.9282 | −0.492743 | ||||||||
\(800\) | −19.5993 | − | 33.9469i | −0.692938 | − | 1.20020i | ||||
\(801\) | −17.4369 | + | 30.2017i | −0.616104 | + | 1.06712i | ||||
\(802\) | 10.8523 | − | 18.7968i | 0.383209 | − | 0.663737i | ||||
\(803\) | 4.89426 | + | 8.47711i | 0.172715 | + | 0.299151i | ||||
\(804\) | −7.12655 | −0.251334 | ||||||||
\(805\) | 35.4083 | + | 37.3223i | 1.24798 | + | 1.31544i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.59469 | + | 2.76208i | 0.0561356 | + | 0.0972298i | ||||
\(808\) | −8.34504 | + | 14.4540i | −0.293578 | + | 0.508491i | ||||
\(809\) | −5.73580 | + | 9.93470i | −0.201660 | + | 0.349285i | −0.949063 | − | 0.315085i | \(-0.897967\pi\) |
0.747403 | + | 0.664371i | \(0.231300\pi\) | |||||||
\(810\) | 7.69807 | + | 13.3334i | 0.270482 | + | 0.468489i | ||||
\(811\) | −23.8664 | −0.838063 | −0.419032 | − | 0.907972i | \(-0.637630\pi\) | ||||
−0.419032 | + | 0.907972i | \(0.637630\pi\) | |||||||
\(812\) | −4.26451 | − | 4.49503i | −0.149655 | − | 0.157745i | ||||
\(813\) | 4.90723 | 0.172104 | ||||||||
\(814\) | −4.05079 | − | 7.01618i | −0.141980 | − | 0.245917i | ||||
\(815\) | 20.4698 | − | 35.4548i | 0.717026 | − | 1.24193i | ||||
\(816\) | −0.114164 | + | 0.197738i | −0.00399655 | + | 0.00692223i | ||||
\(817\) | −2.03178 | − | 3.51914i | −0.0710829 | − | 0.123119i | ||||
\(818\) | −0.125105 | −0.00437419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.4044 | 0.817318 | ||||||||
\(821\) | 15.4847 | + | 26.8203i | 0.540420 | + | 0.936035i | 0.998880 | + | 0.0473197i | \(0.0150679\pi\) |
−0.458460 | + | 0.888715i | \(0.651599\pi\) | |||||||
\(822\) | 2.45293 | − | 4.24861i | 0.0855559 | − | 0.148187i | ||||
\(823\) | 4.30678 | − | 7.45957i | 0.150125 | − | 0.260024i | −0.781148 | − | 0.624346i | \(-0.785366\pi\) |
0.931273 | + | 0.364321i | \(0.118699\pi\) | |||||||
\(824\) | −5.76129 | − | 9.97885i | −0.200704 | − | 0.347630i | ||||
\(825\) | 4.06362 | 0.141477 | ||||||||
\(826\) | −0.326652 | + | 1.10223i | −0.0113657 | + | 0.0383516i | ||||
\(827\) | −22.9128 | −0.796756 | −0.398378 | − | 0.917221i | \(-0.630427\pi\) | ||||
−0.398378 | + | 0.917221i | \(0.630427\pi\) | |||||||
\(828\) | −9.23528 | − | 15.9960i | −0.320948 | − | 0.555898i | ||||
\(829\) | 21.2806 | − | 36.8590i | 0.739104 | − | 1.28017i | −0.213795 | − | 0.976879i | \(-0.568582\pi\) |
0.952899 | − | 0.303287i | \(-0.0980842\pi\) | |||||||
\(830\) | −2.22129 | + | 3.84739i | −0.0771022 | + | 0.133545i | ||||
\(831\) | −1.26172 | − | 2.18536i | −0.0437685 | − | 0.0758093i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0816 | − | 6.15191i | 0.418601 | − | 0.213151i | ||||
\(834\) | 2.37073 | 0.0820915 | ||||||||
\(835\) | −28.5230 | − | 49.4033i | −0.987080 | − | 1.70967i | ||||
\(836\) | −0.594515 | + | 1.02973i | −0.0205617 | + | 0.0356140i | ||||
\(837\) | 16.7982 | − | 29.0954i | 0.580632 | − | 1.00568i | ||||
\(838\) | −5.82846 | − | 10.0952i | −0.201341 | − | 0.348733i | ||||
\(839\) | −1.84105 | −0.0635601 | −0.0317800 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317800 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(840\) | −4.76932 | + | 16.0933i | −0.164557 | + | 0.555271i | ||||
\(841\) | −25.6293 | −0.883770 | ||||||||
\(842\) | 1.46465 | + | 2.53686i | 0.0504753 | + | 0.0874258i | ||||
\(843\) | 2.82666 | − | 4.89591i | 0.0973553 | − | 0.168624i | ||||
\(844\) | −3.63317 | + | 6.29284i | −0.125059 | + | 0.216609i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.6860 | 0.539296 | ||||||||
\(847\) | −26.2254 | + | 6.29257i | −0.901116 | + | 0.216215i | ||||
\(848\) | −1.67351 | −0.0574686 | ||||||||
\(849\) | −5.04657 | − | 8.74092i | −0.173198 | − | 0.299988i | ||||
\(850\) | −5.64087 | + | 9.77027i | −0.193480 | + | 0.335118i | ||||
\(851\) | −29.9457 | + | 51.8675i | −1.02653 | + | 1.77800i | ||||
\(852\) | 1.45426 | + | 2.51885i | 0.0498221 | + | 0.0862944i | ||||
\(853\) | 27.0293 | 0.925466 | 0.462733 | − | 0.886498i | \(-0.346869\pi\) | ||||
0.462733 | + | 0.886498i | \(0.346869\pi\) | |||||||
\(854\) | −2.22591 | − | 2.34623i | −0.0761690 | − | 0.0802862i | ||||
\(855\) | −9.15526 | −0.313103 | ||||||||
\(856\) | −19.6875 | − | 34.0998i | −0.672906 | − | 1.16551i | ||||
\(857\) | −8.39268 | + | 14.5365i | −0.286688 | + | 0.496559i | −0.973017 | − | 0.230732i | \(-0.925888\pi\) |
0.686329 | + | 0.727291i | \(0.259221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.8058 | − | 44.6969i | −0.880482 | − | 1.52504i | −0.850806 | − | 0.525481i | \(-0.823886\pi\) |
−0.0296769 | − | 0.999560i | \(-0.509448\pi\) | |||||||
\(860\) | −17.1849 | −0.586000 | ||||||||
\(861\) | −6.41938 | − | 6.76638i | −0.218772 | − | 0.230598i | ||||
\(862\) | −18.9725 | −0.646205 | ||||||||
\(863\) | 10.9807 | + | 19.0191i | 0.373787 | + | 0.647417i | 0.990145 | − | 0.140049i | \(-0.0447259\pi\) |
−0.616358 | + | 0.787466i | \(0.711393\pi\) | |||||||
\(864\) | 10.5338 | − | 18.2450i | 0.358366 | − | 0.620709i | ||||
\(865\) | −17.1843 | + | 29.7640i | −0.584283 | + | 1.01201i | ||||
\(866\) | 11.0205 | + | 19.0880i | 0.374491 | + | 0.648638i | ||||
\(867\) | −8.76040 | −0.297519 | ||||||||
\(868\) | −29.9749 | + | 7.19221i | −1.01741 | + | 0.244120i | ||||
\(869\) | −10.8583 | −0.368341 | ||||||||
\(870\) | −1.77793 | − | 3.07947i | −0.0602775 | − | 0.104404i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.85797 | − | 10.1463i | 0.198376 | − | 0.343597i | ||||
\(873\) | −0.648693 | − | 1.12357i | −0.0219549 | − | 0.0380270i | ||||
\(874\) | −4.99190 | −0.168853 | ||||||||
\(875\) | 4.77017 | − | 16.0962i | 0.161261 | − | 0.544150i | ||||
\(876\) | 9.19401 | 0.310637 | ||||||||
\(877\) | −4.80873 | − | 8.32896i | −0.162379 | − | 0.281249i | 0.773342 | − | 0.633989i | \(-0.218583\pi\) |
−0.935721 | + | 0.352740i | \(0.885250\pi\) | |||||||
\(878\) | 11.9089 | − | 20.6268i | 0.401905 | − | 0.696120i | ||||
\(879\) | −1.96371 | + | 3.40125i | −0.0662344 | + | 0.114721i | ||||
\(880\) | 0.275493 | + | 0.477167i | 0.00928686 | + | 0.0160853i | ||||
\(881\) | 28.9726 | 0.976110 | 0.488055 | − | 0.872813i | \(-0.337707\pi\) | ||||
0.488055 | + | 0.872813i | \(0.337707\pi\) | |||||||
\(882\) | −13.6064 | + | 6.92834i | −0.458150 | + | 0.233289i | ||||
\(883\) | 6.60727 | 0.222352 | 0.111176 | − | 0.993801i | \(-0.464538\pi\) | ||||
0.111176 | + | 0.993801i | \(0.464538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.580863 | − | 1.00608i | 0.0195255 | − | 0.0338191i | ||||
\(886\) | −14.1325 | + | 24.4781i | −0.474789 | + | 0.822359i | ||||
\(887\) | 15.7072 | + | 27.2057i | 0.527397 | + | 0.913478i | 0.999490 | + | 0.0319293i | \(0.0101651\pi\) |
−0.472094 | + | 0.881548i | \(0.656502\pi\) | |||||||
\(888\) | −19.5406 | −0.655739 | ||||||||
\(889\) | −1.46215 | + | 4.93379i | −0.0490390 | + | 0.165474i | ||||
\(890\) | 39.8591 | 1.33608 | ||||||||
\(891\) | −2.36000 | − | 4.08765i | −0.0790631 | − | 0.136941i | ||||
\(892\) | −1.50399 | + | 2.60499i | −0.0503574 | + | 0.0872216i | ||||
\(893\) | −3.73242 | + | 6.46474i | −0.124901 | + | 0.216334i | ||||
\(894\) | 1.65032 | + | 2.85843i | 0.0551949 | + | 0.0956003i | ||||
\(895\) | −31.5810 | −1.05564 | ||||||||
\(896\) | −19.5773 | + | 4.69741i | −0.654033 | + | 0.156930i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.37780 | + | 14.5108i | 0.279571 | + | 0.484231i | ||||
\(899\) | 8.38459 | − | 14.5225i | 0.279642 | − | 0.484354i | ||||
\(900\) | −11.1863 | + | 19.3753i | −0.372877 | + | 0.645843i | ||||
\(901\) | 9.08991 | + | 15.7442i | 0.302829 | + | 0.524515i | ||||
\(902\) | 4.07480 | 0.135676 | ||||||||
\(903\) | 4.71349 | + | 4.96827i | 0.156855 | + | 0.165334i | ||||
\(904\) | −38.3883 | −1.27678 | ||||||||
\(905\) | 10.3328 | + | 17.8970i | 0.343475 | + | 0.594917i | ||||
\(906\) | −4.74337 | + | 8.21575i | −0.157588 | + | 0.272950i | ||||
\(907\) | −4.86821 | + | 8.43198i | −0.161646 | + | 0.279979i | −0.935459 | − | 0.353435i | \(-0.885014\pi\) |
0.773813 | + | 0.633414i | \(0.218347\pi\) | |||||||
\(908\) | −16.7692 | − | 29.0452i | −0.556507 | − | 0.963898i | ||||
\(909\) | 15.3422 | 0.508869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4372 | −1.27348 | −0.636740 | − | 0.771078i | \(-0.719718\pi\) | ||||
−0.636740 | + | 0.771078i | \(0.719718\pi\) | |||||||
\(912\) | 0.0611867 | + | 0.105979i | 0.00202609 | + | 0.00350930i | ||||
\(913\) | 0.680984 | − | 1.17950i | 0.0225373 | − | 0.0390357i | ||||
\(914\) | −0.317871 | + | 0.550568i | −0.0105142 | + | 0.0182112i | ||||
\(915\) | 1.63409 | + | 2.83032i | 0.0540212 | + | 0.0935675i | ||||
\(916\) | 0.0874483 | 0.00288937 | ||||||||
\(917\) | −30.9638 | + | 7.42951i | −1.02252 | + | 0.245344i | ||||
\(918\) | −6.06346 | −0.200124 | ||||||||
\(919\) | −27.1402 | − | 47.0082i | −0.895273 | − | 1.55066i | −0.833467 | − | 0.552569i | \(-0.813647\pi\) |
−0.0618056 | − | 0.998088i | \(-0.519686\pi\) | |||||||
\(920\) | −27.1054 | + | 46.9479i | −0.893639 | + | 1.54783i | ||||
\(921\) | 7.34398 | − | 12.7202i | 0.241993 | − | 0.419143i | ||||
\(922\) | −14.1164 | − | 24.4502i | −0.464897 | − | 0.805226i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.569388 | − | 1.92131i | 0.0187315 | − | 0.0632063i | ||||
\(925\) | 72.5442 | 2.38524 | ||||||||
\(926\) | −13.0869 | − | 22.6673i | −0.430064 | − | 0.744892i | ||||
\(927\) | −5.29602 | + | 9.17297i | −0.173944 | + | 0.301280i | ||||
\(928\) | 5.25777 | − | 9.10673i | 0.172595 | − | 0.298943i | ||||
\(929\) | −19.0960 | − | 33.0752i | −0.626519 | − | 1.08516i | −0.988245 | − | 0.152878i | \(-0.951146\pi\) |
0.361726 | − | 0.932284i | \(-0.382188\pi\) | |||||||
\(930\) | −17.6905 | −0.580095 | ||||||||
\(931\) | 0.382172 | − | 7.25622i | 0.0125252 | − | 0.237813i | ||||
\(932\) | −18.7132 | −0.612971 | ||||||||
\(933\) | −3.25408 | − | 5.63622i | −0.106534 | − | 0.184522i | ||||
\(934\) | 12.5994 | − | 21.8228i | 0.412266 | − | 0.714065i | ||||
\(935\) | 2.99276 | − | 5.18361i | 0.0978736 | − | 0.169522i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0376 | −0.621931 | −0.310966 | − | 0.950421i | \(-0.600652\pi\) | ||||
−0.310966 | + | 0.950421i | \(0.600652\pi\) | |||||||
\(938\) | −5.40625 | + | 18.2425i | −0.176520 | + | 0.595639i | ||||
\(939\) | −13.8278 | −0.451255 | ||||||||
\(940\) | 15.7845 | + | 27.3396i | 0.514835 | + | 0.891720i | ||||
\(941\) | 23.0811 | − | 39.9776i | 0.752422 | − | 1.30323i | −0.194224 | − | 0.980957i | \(-0.562219\pi\) |
0.946646 | − | 0.322275i | \(-0.104448\pi\) | |||||||
\(942\) | 0.545619 | − | 0.945040i | 0.0177772 | − | 0.0307911i | ||||
\(943\) | −15.0616 | − | 26.0875i | −0.490474 | − | 0.849526i | ||||
\(944\) | 0.0910198 | 0.00296244 | ||||||||
\(945\) | 32.5671 | − | 7.81420i | 1.05941 | − | 0.254196i | ||||
\(946\) | −2.99196 | −0.0972770 | ||||||||
\(947\) | −4.59687 | − | 7.96201i | −0.149378 | − | 0.258730i | 0.781620 | − | 0.623755i | \(-0.214394\pi\) |
−0.930998 | + | 0.365025i | \(0.881060\pi\) | |||||||
\(948\) | −5.09938 | + | 8.83239i | −0.165620 | + | 0.286863i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.02324 | + | 5.23641i | 0.0980869 | + | 0.169892i | ||||
\(951\) | 16.7688 | 0.543766 | ||||||||
\(952\) | 9.83266 | + | 10.3642i | 0.318678 | + | 0.335904i | ||||
\(953\) | −44.6463 | −1.44624 | −0.723118 | − | 0.690725i | \(-0.757292\pi\) | ||||
−0.723118 | + | 0.690725i | \(0.757292\pi\) | |||||||
\(954\) | −10.2371 | − | 17.7312i | −0.331440 | − | 0.574070i | ||||
\(955\) | 2.26470 | − | 3.92258i | 0.0732841 | − | 0.126932i | ||||
\(956\) | −2.13937 | + | 3.70550i | −0.0691923 | + | 0.119844i | ||||
\(957\) | 0.545062 | + | 0.944075i | 0.0176194 | + | 0.0305176i | ||||
\(958\) | −11.9928 | −0.387470 | ||||||||
\(959\) | 15.8736 | + | 16.7317i | 0.512586 | + | 0.540293i | ||||
\(960\) | −10.2819 | −0.331846 | ||||||||
\(961\) | −26.2136 | − | 45.4032i | −0.845599 | − | 1.46462i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0976 | + | 31.3459i | −0.583186 | + | 1.01011i | ||||
\(964\) | 5.47212 | + | 9.47799i | 0.176245 | + | 0.305266i | ||||
\(965\) | −56.5276 | −1.81969 | ||||||||
\(966\) | 8.18077 | − | 1.96290i | 0.263212 | − | 0.0631554i | ||||
\(967\) | −13.8268 | −0.444639 | −0.222320 | − | 0.974974i | \(-0.571363\pi\) | ||||
−0.222320 | + | 0.974974i | \(0.571363\pi\) | |||||||
\(968\) | −14.2096 | − | 24.6117i | −0.456713 | − | 0.791050i | ||||
\(969\) | 0.664689 | − | 1.15128i | 0.0213529 | − | 0.0369843i | ||||
\(970\) | −0.741422 | + | 1.28418i | −0.0238056 | + | 0.0412326i | ||||
\(971\) | −3.63437 | − | 6.29491i | −0.116632 | − | 0.202013i | 0.801799 | − | 0.597594i | \(-0.203877\pi\) |
−0.918431 | + | 0.395581i | \(0.870543\pi\) | |||||||
\(972\) | −18.5091 | −0.593679 | ||||||||
\(973\) | −3.16680 | + | 10.6858i | −0.101523 | + | 0.342572i | ||||
\(974\) | 14.2950 | 0.458043 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.128029 | + | 0.221752i | −0.00409810 | + | 0.00709811i | ||||
\(977\) | 21.4050 | − | 37.0746i | 0.684808 | − | 1.18612i | −0.288689 | − | 0.957423i | \(-0.593219\pi\) |
0.973497 | − | 0.228699i | \(-0.0734473\pi\) | |||||||
\(978\) | −3.34742 | − | 5.79790i | −0.107039 | − | 0.185397i | ||||
\(979\) | −12.2196 | −0.390541 | ||||||||
\(980\) | −25.7674 | − | 16.7431i | −0.823110 | − | 0.534838i | ||||
\(981\) | −10.7698 | −0.343852 | ||||||||
\(982\) | −9.22152 | − | 15.9721i | −0.294270 | − | 0.509691i | ||||
\(983\) | −23.1544 | + | 40.1046i | −0.738511 | + | 1.27914i | 0.214655 | + | 0.976690i | \(0.431137\pi\) |
−0.953166 | + | 0.302448i | \(0.902196\pi\) | |||||||
\(984\) | 4.91410 | − | 8.51147i | 0.156656 | − | 0.271336i | ||||
\(985\) | 44.0294 | + | 76.2612i | 1.40289 | + | 2.42988i | ||||
\(986\) | −3.02648 | −0.0963829 | ||||||||
\(987\) | 3.57467 | − | 12.0621i | 0.113783 | − | 0.383942i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0591 | + | 19.1550i | 0.351660 | + | 0.609092i | ||||
\(990\) | −3.37047 | + | 5.83782i | −0.107121 | + | 0.185538i | ||||
\(991\) | 29.1162 | − | 50.4307i | 0.924907 | − | 1.60199i | 0.133195 | − | 0.991090i | \(-0.457476\pi\) |
0.791711 | − | 0.610896i | \(-0.209190\pi\) | |||||||
\(992\) | −26.1576 | − | 45.3062i | −0.830504 | − | 1.43847i | ||||
\(993\) | −1.17885 | −0.0374097 | ||||||||
\(994\) | 7.55096 | − | 1.81179i | 0.239502 | − | 0.0574664i | ||||
\(995\) | 87.3406 | 2.76888 | ||||||||
\(996\) | −0.639625 | − | 1.10786i | −0.0202673 | − | 0.0351040i | ||||
\(997\) | 2.24739 | − | 3.89260i | 0.0711757 | − | 0.123280i | −0.828241 | − | 0.560372i | \(-0.810658\pi\) |
0.899417 | + | 0.437092i | \(0.143992\pi\) | |||||||
\(998\) | −9.91765 | + | 17.1779i | −0.313938 | + | 0.543756i | ||||
\(999\) | 19.4947 | + | 33.7658i | 0.616786 | + | 1.06830i |
(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 | 1183.2.e.g.508.3 | 12 | ||
7.2 | even | 3 | inner | 1183.2.e.g.170.3 | 12 | ||
7.3 | odd | 6 | 8281.2.a.cf.1.4 | 6 | |||
7.4 | even | 3 | 8281.2.a.ce.1.4 | 6 | |||
13.4 | even | 6 | 91.2.g.b.81.4 | yes | 12 | ||
13.10 | even | 6 | 91.2.h.b.74.3 | yes | 12 | ||
13.12 | even | 2 | 1183.2.e.h.508.4 | 12 | |||
39.17 | odd | 6 | 819.2.n.d.172.3 | 12 | |||
39.23 | odd | 6 | 819.2.s.d.802.4 | 12 | |||
91.4 | even | 6 | 637.2.f.k.393.4 | 12 | |||
91.10 | odd | 6 | 637.2.f.j.295.4 | 12 | |||
91.17 | odd | 6 | 637.2.f.j.393.4 | 12 | |||
91.23 | even | 6 | 91.2.g.b.9.4 | ✓ | 12 | ||
91.25 | even | 6 | 8281.2.a.bz.1.3 | 6 | |||
91.30 | even | 6 | 91.2.h.b.16.3 | yes | 12 | ||
91.38 | odd | 6 | 8281.2.a.ca.1.3 | 6 | |||
91.51 | even | 6 | 1183.2.e.h.170.4 | 12 | |||
91.62 | odd | 6 | 637.2.h.l.165.3 | 12 | |||
91.69 | odd | 6 | 637.2.g.l.263.4 | 12 | |||
91.75 | odd | 6 | 637.2.g.l.373.4 | 12 | |||
91.82 | odd | 6 | 637.2.h.l.471.3 | 12 | |||
91.88 | even | 6 | 637.2.f.k.295.4 | 12 | |||
273.23 | odd | 6 | 819.2.n.d.100.3 | 12 | |||
273.212 | odd | 6 | 819.2.s.d.289.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.4 | ✓ | 12 | 91.23 | even | 6 | ||
91.2.g.b.81.4 | yes | 12 | 13.4 | even | 6 | ||
91.2.h.b.16.3 | yes | 12 | 91.30 | even | 6 | ||
91.2.h.b.74.3 | yes | 12 | 13.10 | even | 6 | ||
637.2.f.j.295.4 | 12 | 91.10 | odd | 6 | |||
637.2.f.j.393.4 | 12 | 91.17 | odd | 6 | |||
637.2.f.k.295.4 | 12 | 91.88 | even | 6 | |||
637.2.f.k.393.4 | 12 | 91.4 | even | 6 | |||
637.2.g.l.263.4 | 12 | 91.69 | odd | 6 | |||
637.2.g.l.373.4 | 12 | 91.75 | odd | 6 | |||
637.2.h.l.165.3 | 12 | 91.62 | odd | 6 | |||
637.2.h.l.471.3 | 12 | 91.82 | odd | 6 | |||
819.2.n.d.100.3 | 12 | 273.23 | odd | 6 | |||
819.2.n.d.172.3 | 12 | 39.17 | odd | 6 | |||
819.2.s.d.289.4 | 12 | 273.212 | odd | 6 | |||
819.2.s.d.802.4 | 12 | 39.23 | odd | 6 | |||
1183.2.e.g.170.3 | 12 | 7.2 | even | 3 | inner | ||
1183.2.e.g.508.3 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.h.170.4 | 12 | 91.51 | even | 6 | |||
1183.2.e.h.508.4 | 12 | 13.12 | even | 2 | |||
8281.2.a.bz.1.3 | 6 | 91.25 | even | 6 | |||
8281.2.a.ca.1.3 | 6 | 91.38 | odd | 6 | |||
8281.2.a.ce.1.4 | 6 | 7.4 | even | 3 | |||
8281.2.a.cf.1.4 | 6 | 7.3 | odd | 6 |