Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (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: | \(5.08647060876\) |
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 | 393.4 | ||
Root | \(0.756174 - 1.30973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.393 |
Dual form | 637.2.f.k.295.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0.976344 | − | 0.216222i | \(-0.0693735\pi\) |
−0.675426 | + | 0.737428i | \(0.736040\pi\) | |||||||
\(3\) | −0.330612 | − | 0.572636i | −0.190879 | − | 0.330612i | 0.754663 | − | 0.656113i | \(-0.227800\pi\) |
−0.945542 | + | 0.325501i | \(0.894467\pi\) | |||||||
\(4\) | 0.637793 | − | 1.10469i | 0.318896 | − | 0.552345i | ||||
\(5\) | 3.44148 | 1.53908 | 0.769538 | − | 0.638601i | \(-0.220487\pi\) | ||||
0.769538 | + | 0.638601i | \(0.220487\pi\) | |||||||
\(6\) | 0.281392 | − | 0.487385i | 0.114878 | − | 0.198974i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | \(-0.123442\pi\) |
−0.790365 | + | 0.612637i | \(0.790109\pi\) | |||||||
\(12\) | −0.843447 | −0.243482 | ||||||||
\(13\) | −3.07517 | + | 1.88237i | −0.852900 | + | 0.522075i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13779 | − | 1.97071i | −0.293777 | − | 0.508836i | ||||
\(16\) | −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 | \(0.242134\pi\) | |||||||
\(18\) | 2.18125 | 0.514126 | ||||||||
\(19\) | −0.519020 | + | 0.898968i | −0.119071 | + | 0.206237i | −0.919400 | − | 0.393324i | \(-0.871325\pi\) |
0.800329 | + | 0.599562i | \(0.204658\pi\) | |||||||
\(20\) | 2.19495 | − | 3.80177i | 0.490806 | − | 0.850101i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.382150 | + | 0.661902i | −0.0814745 | + | 0.141118i | ||||
\(23\) | −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 | ||||
\(25\) | 6.84378 | 1.36876 | ||||||||
\(26\) | −2.69617 | − | 1.46563i | −0.528762 | − | 0.287434i | ||||
\(27\) | −3.67824 | −0.707878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.917969 | + | 1.58997i | 0.170463 | + | 0.295250i | 0.938582 | − | 0.345057i | \(-0.112140\pi\) |
−0.768119 | + | 0.640307i | \(0.778807\pi\) | |||||||
\(30\) | 0.968404 | − | 1.67733i | 0.176806 | − | 0.306236i | ||||
\(31\) | −9.13385 | −1.64049 | −0.820244 | − | 0.572014i | \(-0.806162\pi\) | ||||
−0.820244 | + | 0.572014i | \(0.806162\pi\) | |||||||
\(32\) | 2.86381 | − | 4.96026i | 0.506254 | − | 0.876858i | ||||
\(33\) | 0.296885 | − | 0.514219i | 0.0516810 | − | 0.0895141i | ||||
\(34\) | −1.64847 | −0.282710 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.63452 | − | 2.83108i | −0.272421 | − | 0.471847i | ||||
\(37\) | 5.30001 | + | 9.17989i | 0.871316 | + | 1.50916i | 0.860636 | + | 0.509221i | \(0.170067\pi\) |
0.0106808 | + | 0.999943i | \(0.496600\pi\) | |||||||
\(38\) | −0.883501 | −0.143323 | ||||||||
\(39\) | 2.09460 | + | 1.13862i | 0.335404 | + | 0.182325i | ||||
\(40\) | 9.59462 | 1.51704 | ||||||||
\(41\) | 2.66571 | + | 4.61715i | 0.416314 | + | 0.721078i | 0.995565 | − | 0.0940715i | \(-0.0299882\pi\) |
−0.579251 | + | 0.815149i | \(0.696655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95732 | − | 3.39018i | 0.298489 | − | 0.516998i | −0.677302 | − | 0.735706i | \(-0.736851\pi\) |
0.975790 | + | 0.218708i | \(0.0701841\pi\) | |||||||
\(44\) | 1.14546 | 0.172684 | ||||||||
\(45\) | 4.40988 | − | 7.63814i | 0.657387 | − | 1.13863i | ||||
\(46\) | 2.40448 | − | 4.16469i | 0.354522 | − | 0.614050i | ||||
\(47\) | 7.19129 | 1.04896 | 0.524479 | − | 0.851423i | \(-0.324260\pi\) | ||||
0.524479 | + | 0.851423i | \(0.324260\pi\) | |||||||
\(48\) | −0.0589445 | + | 0.102095i | −0.00850791 | + | 0.0147361i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.91246 | + | 5.04452i | 0.411883 | + | 0.713403i | ||||
\(51\) | 1.28066 | 0.179329 | ||||||||
\(52\) | 0.118109 | + | 4.59767i | 0.0163788 | + | 0.637582i | ||||
\(53\) | −9.38648 | −1.28933 | −0.644666 | − | 0.764464i | \(-0.723004\pi\) | ||||
−0.644666 | + | 0.764464i | \(0.723004\pi\) | |||||||
\(54\) | −1.56532 | − | 2.71122i | −0.213013 | − | 0.368950i | ||||
\(55\) | 1.54520 | + | 2.67637i | 0.208355 | + | 0.360881i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.686375 | 0.0909127 | ||||||||
\(58\) | −0.781307 | + | 1.35326i | −0.102591 | + | 0.177692i | ||||
\(59\) | 0.255259 | − | 0.442121i | 0.0332318 | − | 0.0575592i | −0.848931 | − | 0.528503i | \(-0.822753\pi\) |
0.882163 | + | 0.470944i | \(0.156087\pi\) | |||||||
\(60\) | −2.90270 | −0.374737 | ||||||||
\(61\) | −0.718095 | + | 1.24378i | −0.0919426 | + | 0.159249i | −0.908328 | − | 0.418258i | \(-0.862641\pi\) |
0.816386 | + | 0.577507i | \(0.195974\pi\) | |||||||
\(62\) | −3.88702 | − | 6.73252i | −0.493653 | − | 0.855031i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.51834 | 0.564792 | ||||||||
\(65\) | −10.5831 | + | 6.47813i | −1.31268 | + | 0.803513i | ||||
\(66\) | 0.505372 | 0.0622070 | ||||||||
\(67\) | 4.22466 | + | 7.31732i | 0.516124 | + | 0.893953i | 0.999825 | + | 0.0187197i | \(0.00595900\pi\) |
−0.483701 | + | 0.875233i | \(0.660708\pi\) | |||||||
\(68\) | 1.23528 | + | 2.13957i | 0.149800 | + | 0.259461i | ||||
\(69\) | −1.86800 | + | 3.23547i | −0.224881 | + | 0.389504i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.72419 | − | 2.98638i | 0.204623 | − | 0.354418i | −0.745389 | − | 0.666629i | \(-0.767736\pi\) |
0.950013 | + | 0.312211i | \(0.101070\pi\) | |||||||
\(72\) | 3.57244 | − | 6.18764i | 0.421016 | − | 0.729221i | ||||
\(73\) | 10.9005 | 1.27581 | 0.637905 | − | 0.770115i | \(-0.279801\pi\) | ||||
0.637905 | + | 0.770115i | \(0.279801\pi\) | |||||||
\(74\) | −4.51097 | + | 7.81324i | −0.524390 | + | 0.908270i | ||||
\(75\) | −2.26263 | − | 3.91899i | −0.261266 | − | 0.452526i | ||||
\(76\) | 0.662054 | + | 1.14671i | 0.0759428 | + | 0.131537i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0521095 | + | 2.02848i | 0.00590024 | + | 0.229680i | ||||
\(79\) | −12.0918 | −1.36043 | −0.680216 | − | 0.733012i | \(-0.738114\pi\) | ||||
−0.680216 | + | 0.733012i | \(0.738114\pi\) | |||||||
\(80\) | −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 | \(-0.473473\pi\) | ||||
0.0832393 | + | 0.996530i | \(0.473473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.33274 | + | 5.77248i | −0.361487 | + | 0.626113i | ||||
\(86\) | 3.33185 | 0.359283 | ||||||||
\(87\) | 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 | \(-0.910252\pi\) |
0.239301 | − | 0.970945i | \(-0.423082\pi\) | |||||||
\(90\) | 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 | ||||
\(96\) | −3.78723 | −0.386533 | ||||||||
\(97\) | −0.253120 | + | 0.438417i | −0.0257005 | + | 0.0445145i | −0.878590 | − | 0.477578i | \(-0.841515\pi\) |
0.852889 | + | 0.522092i | \(0.174848\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.30134 | 0.231294 | ||||||||
\(100\) | 4.36491 | − | 7.56025i | 0.436491 | − | 0.756025i | ||||
\(101\) | 2.99327 | + | 5.18450i | 0.297842 | + | 0.515877i | 0.975642 | − | 0.219369i | \(-0.0703999\pi\) |
−0.677800 | + | 0.735246i | \(0.737067\pi\) | |||||||
\(102\) | 0.545002 | + | 0.943972i | 0.0539633 | + | 0.0934671i | ||||
\(103\) | −4.13302 | −0.407239 | −0.203619 | − | 0.979050i | \(-0.565270\pi\) | ||||
−0.203619 | + | 0.979050i | \(0.565270\pi\) | |||||||
\(104\) | −8.57338 | + | 5.24792i | −0.840689 | + | 0.514601i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.99454 | − | 6.91874i | −0.387984 | − | 0.672008i | ||||
\(107\) | 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 | ||||
\(109\) | −4.20237 | −0.402514 | −0.201257 | − | 0.979538i | \(-0.564503\pi\) | ||||
−0.201257 | + | 0.979538i | \(0.564503\pi\) | |||||||
\(110\) | −1.31516 | + | 2.27792i | −0.125396 | + | 0.217191i | ||||
\(111\) | 3.50449 | − | 6.06995i | 0.332631 | − | 0.576135i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.88472 | + | 11.9247i | −0.647660 | + | 1.12178i | 0.336020 | + | 0.941855i | \(0.390919\pi\) |
−0.983680 | + | 0.179926i | \(0.942414\pi\) | |||||||
\(114\) | 0.292096 | + | 0.505925i | 0.0273573 | + | 0.0473842i | ||||
\(115\) | −9.72240 | − | 16.8397i | −0.906618 | − | 1.57031i | ||||
\(116\) | 2.34190 | 0.217440 | ||||||||
\(117\) | 0.237294 | + | 9.23720i | 0.0219379 | + | 0.853980i | ||||
\(118\) | 0.434514 | 0.0400003 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.17209 | − | 5.49422i | −0.289571 | − | 0.501552i | ||||
\(121\) | 5.09681 | − | 8.82793i | 0.463346 | − | 0.802539i | ||||
\(122\) | −1.22238 | −0.110669 | ||||||||
\(123\) | 1.76263 | − | 3.05297i | 0.158931 | − | 0.275277i | ||||
\(124\) | −5.82550 | + | 10.0901i | −0.523145 | + | 0.906114i | ||||
\(125\) | 6.34531 | 0.567542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.972482 | − | 1.68439i | −0.0862938 | − | 0.149465i | 0.819648 | − | 0.572868i | \(-0.194169\pi\) |
−0.905942 | + | 0.423402i | \(0.860836\pi\) | |||||||
\(128\) | −3.80478 | − | 6.59007i | −0.336298 | − | 0.582485i | ||||
\(129\) | −2.58845 | −0.227901 | ||||||||
\(130\) | −9.27880 | − | 5.04394i | −0.813804 | − | 0.442383i | ||||
\(131\) | −12.0354 | −1.05154 | −0.525769 | − | 0.850627i | \(-0.676222\pi\) | ||||
−0.525769 | + | 0.850627i | \(0.676222\pi\) | |||||||
\(132\) | −0.378702 | − | 0.655931i | −0.0329618 | − | 0.0570914i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.59571 | + | 6.22796i | −0.310622 | + | 0.538014i | ||||
\(135\) | −12.6586 | −1.08948 | ||||||||
\(136\) | −2.69985 | + | 4.67627i | −0.231510 | + | 0.400987i | ||||
\(137\) | −4.35857 | + | 7.54927i | −0.372378 | + | 0.644978i | −0.989931 | − | 0.141552i | \(-0.954791\pi\) |
0.617553 | + | 0.786529i | \(0.288124\pi\) | |||||||
\(138\) | −3.17980 | −0.270683 | ||||||||
\(139\) | −2.10625 | + | 3.64813i | −0.178650 | + | 0.309430i | −0.941418 | − | 0.337241i | \(-0.890506\pi\) |
0.762769 | + | 0.646672i | \(0.223840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.37752 | − | 4.11799i | −0.200224 | − | 0.346798i | ||||
\(142\) | 2.93500 | 0.246300 | ||||||||
\(143\) | −2.84461 | − | 1.54633i | −0.237878 | − | 0.129310i | ||||
\(144\) | −0.456917 | −0.0380764 | ||||||||
\(145\) | 3.15917 | + | 5.47184i | 0.262355 | + | 0.454412i | ||||
\(146\) | 4.63885 | + | 8.03473i | 0.383914 | + | 0.664959i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.5212 | 1.11144 | ||||||||
\(149\) | −2.93242 | + | 5.07910i | −0.240233 | + | 0.416096i | −0.960781 | − | 0.277310i | \(-0.910557\pi\) |
0.720548 | + | 0.693406i | \(0.243891\pi\) | |||||||
\(150\) | 1.92578 | − | 3.33555i | 0.157240 | − | 0.272347i | ||||
\(151\) | −16.8568 | −1.37179 | −0.685893 | − | 0.727702i | \(-0.740588\pi\) | ||||
−0.685893 | + | 0.727702i | \(0.740588\pi\) | |||||||
\(152\) | −1.44699 | + | 2.50626i | −0.117367 | + | 0.203285i | ||||
\(153\) | 2.48181 | + | 4.29862i | 0.200643 | + | 0.347523i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.4339 | −2.52483 | ||||||||
\(156\) | 2.59374 | − | 1.58768i | 0.207666 | − | 0.127116i | ||||
\(157\) | −1.93900 | −0.154749 | −0.0773746 | − | 0.997002i | \(-0.524654\pi\) | ||||
−0.0773746 | + | 0.997002i | \(0.524654\pi\) | |||||||
\(158\) | −5.14581 | − | 8.91280i | −0.409379 | − | 0.709065i | ||||
\(159\) | 3.10328 | + | 5.37504i | 0.246106 | + | 0.426268i | ||||
\(160\) | 9.85573 | − | 17.0706i | 0.779164 | − | 1.34955i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.23685 | − | 3.87433i | 0.175743 | − | 0.304396i | ||||
\(163\) | 5.94797 | − | 10.3022i | 0.465881 | − | 0.806929i | −0.533360 | − | 0.845888i | \(-0.679071\pi\) |
0.999241 | + | 0.0389590i | \(0.0124042\pi\) | |||||||
\(164\) | 6.80069 | 0.531045 | ||||||||
\(165\) | 1.02172 | − | 1.76968i | 0.0795410 | − | 0.137769i | ||||
\(166\) | 0.645448 | + | 1.11795i | 0.0500965 | + | 0.0867696i | ||||
\(167\) | −8.28801 | − | 14.3553i | −0.641346 | − | 1.11084i | −0.985133 | − | 0.171796i | \(-0.945043\pi\) |
0.343787 | − | 0.939048i | \(-0.388290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.91338 | − | 11.5772i | 0.454875 | − | 0.890555i | ||||
\(170\) | −5.67316 | −0.435112 | ||||||||
\(171\) | 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 | −0.611377 | − | 0.791340i | \(-0.709384\pi\) |
0.991009 | + | 0.133798i | \(0.0427172\pi\) | |||||||
\(174\) | 1.03324 | 0.0783295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0800507 | − | 0.138652i | 0.00603405 | − | 0.0104513i | ||||
\(177\) | −0.337566 | −0.0253730 | ||||||||
\(178\) | 5.79098 | − | 10.0303i | 0.434052 | − | 0.751801i | ||||
\(179\) | −4.58829 | − | 7.94715i | −0.342945 | − | 0.593998i | 0.642033 | − | 0.766677i | \(-0.278091\pi\) |
−0.984978 | + | 0.172679i | \(0.944758\pi\) | |||||||
\(180\) | −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 | ||||
\(187\) | −1.73923 | −0.127185 | ||||||||
\(188\) | 4.58655 | − | 7.94415i | 0.334509 | − | 0.579386i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.04055 | −0.220585 | ||||||||
\(191\) | −0.658061 | + | 1.13980i | −0.0476156 | + | 0.0824727i | −0.888851 | − | 0.458197i | \(-0.848496\pi\) |
0.841235 | + | 0.540669i | \(0.181829\pi\) | |||||||
\(192\) | −1.49382 | − | 2.58736i | −0.107807 | − | 0.186727i | ||||
\(193\) | 8.21270 | + | 14.2248i | 0.591163 | + | 1.02392i | 0.994076 | + | 0.108686i | \(0.0346643\pi\) |
−0.402913 | + | 0.915238i | \(0.632002\pi\) | |||||||
\(194\) | −0.430874 | −0.0309350 | ||||||||
\(195\) | 7.20852 | + | 3.91854i | 0.516213 | + | 0.280613i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7938 | + | 22.1594i | 0.911517 | + | 1.57879i | 0.811922 | + | 0.583766i | \(0.198421\pi\) |
0.0995951 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(198\) | 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 | \(-0.189422\pi\) | |||||||
\(200\) | 19.0800 | 1.34916 | ||||||||
\(201\) | 2.79344 | − | 4.83838i | 0.197034 | − | 0.341273i | ||||
\(202\) | −2.54765 | + | 4.41266i | −0.179252 | + | 0.310473i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.816797 | − | 1.41473i | 0.0571873 | − | 0.0990512i | ||||
\(205\) | 9.17399 | + | 15.8898i | 0.640740 | + | 1.10979i | ||||
\(206\) | −1.75886 | − | 3.04643i | −0.122546 | − | 0.212255i | ||||
\(207\) | −14.4801 | −1.00643 | ||||||||
\(208\) | 0.564779 | + | 0.307013i | 0.0391604 | + | 0.0212875i | ||||
\(209\) | −0.932145 | −0.0644778 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.84824 | + | 4.93330i | 0.196081 | + | 0.339622i | 0.947254 | − | 0.320483i | \(-0.103845\pi\) |
−0.751173 | + | 0.660105i | \(0.770512\pi\) | |||||||
\(212\) | −5.98663 | + | 10.3691i | −0.411164 | + | 0.712156i | ||||
\(213\) | −2.28014 | −0.156233 | ||||||||
\(214\) | −6.01038 | + | 10.4103i | −0.410861 | + | 0.711633i | ||||
\(215\) | 6.73608 | − | 11.6672i | 0.459397 | − | 0.795699i | ||||
\(216\) | −10.2547 | −0.697744 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.78837 | − | 3.09755i | −0.121124 | − | 0.209793i | ||||
\(219\) | −3.60384 | − | 6.24203i | −0.243525 | − | 0.421797i | ||||
\(220\) | 3.94207 | 0.265774 | ||||||||
\(221\) | −0.179334 | − | 6.98096i | −0.0120633 | − | 0.469590i | ||||
\(222\) | 5.96552 | 0.400380 | ||||||||
\(223\) | −1.17906 | − | 2.04219i | −0.0789558 | − | 0.136755i | 0.823844 | − | 0.566817i | \(-0.191825\pi\) |
−0.902800 | + | 0.430061i | \(0.858492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.76956 | − | 15.1893i | 0.584637 | − | 1.01262i | ||||
\(226\) | −11.7195 | −0.779571 | ||||||||
\(227\) | −13.1463 | + | 22.7701i | −0.872551 | + | 1.51130i | −0.0132022 | + | 0.999913i | \(0.504203\pi\) |
−0.859349 | + | 0.511390i | \(0.829131\pi\) | |||||||
\(228\) | 0.437765 | − | 0.758232i | 0.0289917 | − | 0.0502151i | ||||
\(229\) | 0.0685555 | 0.00453027 | 0.00226514 | − | 0.999997i | \(-0.499279\pi\) | ||||
0.00226514 | + | 0.999997i | \(0.499279\pi\) | |||||||
\(230\) | 8.27498 | − | 14.3327i | 0.545636 | − | 0.945069i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.55924 | + | 4.43273i | 0.168022 | + | 0.291023i | ||||
\(233\) | 14.6703 | 0.961082 | 0.480541 | − | 0.876972i | \(-0.340440\pi\) | ||||
0.480541 | + | 0.876972i | \(0.340440\pi\) | |||||||
\(234\) | −6.70772 | + | 4.10592i | −0.438498 | + | 0.268412i | ||||
\(235\) | 24.7487 | 1.61443 | ||||||||
\(236\) | −0.325604 | − | 0.563963i | −0.0211950 | − | 0.0367109i | ||||
\(237\) | 3.99768 | + | 6.92419i | 0.259677 | + | 0.449774i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.35434 | 0.216974 | 0.108487 | − | 0.994098i | \(-0.465399\pi\) | ||||
0.108487 | + | 0.994098i | \(0.465399\pi\) | |||||||
\(240\) | −0.202856 | + | 0.351357i | −0.0130943 | + | 0.0226800i | ||||
\(241\) | 4.28989 | − | 7.43031i | 0.276336 | − | 0.478628i | −0.694135 | − | 0.719845i | \(-0.744213\pi\) |
0.970471 | + | 0.241216i | \(0.0775464\pi\) | |||||||
\(242\) | 8.67605 | 0.557718 | ||||||||
\(243\) | −7.25513 | + | 12.5662i | −0.465417 | + | 0.806125i | ||||
\(244\) | 0.915991 | + | 1.58654i | 0.0586403 | + | 0.101568i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.00044 | 0.191301 | ||||||||
\(247\) | −0.0961145 | − | 3.74147i | −0.00611562 | − | 0.238064i | ||||
\(248\) | −25.4646 | −1.61700 | ||||||||
\(249\) | −0.501436 | − | 0.868513i | −0.0317772 | − | 0.0550398i | ||||
\(250\) | 2.70033 | + | 4.67711i | 0.170784 | + | 0.295806i | ||||
\(251\) | −10.7575 | + | 18.6326i | −0.679010 | + | 1.17608i | 0.296270 | + | 0.955104i | \(0.404257\pi\) |
−0.975280 | + | 0.220975i | \(0.929076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.53687 | − | 4.39399i | 0.159492 | − | 0.276248i | ||||
\(254\) | 0.827704 | − | 1.43363i | 0.0519348 | − | 0.0899537i | ||||
\(255\) | 4.40737 | 0.276000 | ||||||||
\(256\) | 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 | \(0.882552\pi\) | |||||||
\(258\) | −1.10155 | − | 1.90794i | −0.0685795 | − | 0.118783i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.406471 | + | 15.8228i | 0.0252083 | + | 0.981288i | ||||
\(261\) | 4.70511 | 0.291239 | ||||||||
\(262\) | −5.12182 | − | 8.87125i | −0.316427 | − | 0.548068i | ||||
\(263\) | 4.47719 | + | 7.75473i | 0.276076 | + | 0.478177i | 0.970406 | − | 0.241480i | \(-0.0776327\pi\) |
−0.694330 | + | 0.719656i | \(0.744299\pi\) | |||||||
\(264\) | 0.827695 | − | 1.43361i | 0.0509411 | − | 0.0882326i | ||||
\(265\) | −32.3034 | −1.98438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.49890 | + | 7.79233i | −0.275328 | + | 0.476883i | ||||
\(268\) | 10.7778 | 0.658360 | ||||||||
\(269\) | 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 | 0.956442 | − | 0.291921i | \(-0.0942945\pi\) |
−0.731032 | + | 0.682343i | \(0.760961\pi\) | |||||||
\(272\) | 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 | \(0.203241\pi\) | |||||||
\(278\) | −3.58536 | −0.215036 | ||||||||
\(279\) | −11.7040 | + | 20.2720i | −0.700702 | + | 1.21365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.54978 | 0.510037 | 0.255019 | − | 0.966936i | \(-0.417918\pi\) | ||||
0.255019 | + | 0.966936i | \(0.417918\pi\) | |||||||
\(282\) | 2.02357 | − | 3.50493i | 0.120502 | − | 0.208715i | ||||
\(283\) | −7.63217 | − | 13.2193i | −0.453686 | − | 0.785807i | 0.544926 | − | 0.838484i | \(-0.316558\pi\) |
−0.998612 | + | 0.0526775i | \(0.983224\pi\) | |||||||
\(284\) | −2.19935 | − | 3.80938i | −0.130507 | − | 0.226045i | ||||
\(285\) | 2.36215 | 0.139921 | ||||||||
\(286\) | −0.0707683 | − | 2.75481i | −0.00418461 | − | 0.162895i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.33932 | − | 12.7121i | −0.432474 | − | 0.749066i | ||||
\(289\) | 6.62439 | + | 11.4738i | 0.389670 | + | 0.674928i | ||||
\(290\) | −2.68885 | + | 4.65723i | −0.157895 | + | 0.273482i | ||||
\(291\) | 0.334738 | 0.0196227 | ||||||||
\(292\) | 6.95227 | − | 12.0417i | 0.406851 | − | 0.704687i | ||||
\(293\) | 2.96982 | − | 5.14388i | 0.173499 | − | 0.300509i | −0.766142 | − | 0.642671i | \(-0.777826\pi\) |
0.939641 | + | 0.342163i | \(0.111159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.878467 | − | 1.52155i | 0.0511463 | − | 0.0885881i | ||||
\(296\) | 14.7761 | + | 25.5929i | 0.858842 | + | 1.48756i | ||||
\(297\) | −1.65151 | − | 2.86049i | −0.0958301 | − | 0.165983i | ||||
\(298\) | −4.99171 | −0.289162 | ||||||||
\(299\) | 17.8983 | + | 9.72949i | 1.03508 | + | 0.562671i | ||||
\(300\) | −5.77236 | −0.333267 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.17362 | − | 12.4251i | −0.412796 | − | 0.714983i | ||||
\(303\) | 1.97922 | − | 3.42811i | 0.113703 | − | 0.196940i | ||||
\(304\) | 0.185071 | 0.0106146 | ||||||||
\(305\) | −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 | \(-0.281457\pi\) | ||||
0.633891 | + | 0.773422i | \(0.281457\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36642 | + | 2.36672i | 0.0777332 | + | 0.134638i | ||||
\(310\) | −13.3771 | − | 23.1698i | −0.759769 | − | 1.31596i | ||||
\(311\) | 9.84259 | 0.558122 | 0.279061 | − | 0.960273i | \(-0.409977\pi\) | ||||
0.279061 | + | 0.960273i | \(0.409977\pi\) | |||||||
\(312\) | 5.83961 | + | 3.17440i | 0.330603 | + | 0.179715i | ||||
\(313\) | −20.9125 | −1.18205 | −0.591023 | − | 0.806655i | \(-0.701276\pi\) | ||||
−0.591023 | + | 0.806655i | \(0.701276\pi\) | |||||||
\(314\) | −0.825166 | − | 1.42923i | −0.0465668 | − | 0.0806561i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.71205 | + | 13.3577i | −0.433837 | + | 0.751427i | ||||
\(317\) | −25.3603 | −1.42438 | −0.712188 | − | 0.701989i | \(-0.752295\pi\) | ||||
−0.712188 | + | 0.701989i | \(0.752295\pi\) | |||||||
\(318\) | −2.64128 | + | 4.57483i | −0.148116 | + | 0.256544i | ||||
\(319\) | −0.824324 | + | 1.42777i | −0.0461533 | + | 0.0799398i | ||||
\(320\) | 15.5498 | 0.869259 | ||||||||
\(321\) | 4.66935 | − | 8.08755i | 0.260618 | − | 0.451403i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00524 | − | 1.74113i | −0.0559331 | − | 0.0968790i | ||||
\(324\) | −6.70475 | −0.372486 | ||||||||
\(325\) | −21.0458 | + | 12.8825i | −1.16741 | + | 0.714593i | ||||
\(326\) | 10.1249 | 0.560768 | ||||||||
\(327\) | 1.38935 | + | 2.40643i | 0.0768314 | + | 0.133076i | ||||
\(328\) | 7.43183 | + | 12.8723i | 0.410354 | + | 0.710755i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.73923 | 0.0957413 | ||||||||
\(331\) | −0.891417 | + | 1.54398i | −0.0489967 | + | 0.0848648i | −0.889484 | − | 0.456967i | \(-0.848936\pi\) |
0.840487 | + | 0.541832i | \(0.182269\pi\) | |||||||
\(332\) | 0.967335 | − | 1.67547i | 0.0530894 | − | 0.0919536i | ||||
\(333\) | 27.1656 | 1.48866 | ||||||||
\(334\) | 7.05414 | − | 12.2181i | 0.385985 | − | 0.668546i | ||||
\(335\) | 14.5391 | + | 25.1824i | 0.794354 | + | 1.37586i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.56149 | 0.520848 | 0.260424 | − | 0.965494i | \(-0.416138\pi\) | ||||
0.260424 | + | 0.965494i | \(0.416138\pi\) | |||||||
\(338\) | 11.0500 | − | 0.568103i | 0.601043 | − | 0.0309007i | ||||
\(339\) | 9.10468 | 0.494498 | ||||||||
\(340\) | 4.25120 | + | 7.36329i | 0.230554 | + | 0.399331i | ||||
\(341\) | −4.10103 | − | 7.10320i | −0.222083 | − | 0.384660i | ||||
\(342\) | −1.13211 | + | 1.96087i | −0.0612176 | + | 0.106032i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.45689 | − | 9.45160i | 0.294216 | − | 0.509596i | ||||
\(345\) | −6.42867 | + | 11.1348i | −0.346108 | + | 0.599477i | ||||
\(346\) | 8.49982 | 0.456953 | ||||||||
\(347\) | −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 | ||||
\(349\) | −15.2994 | − | 26.4994i | −0.818960 | − | 1.41848i | −0.906449 | − | 0.422315i | \(-0.861217\pi\) |
0.0874885 | − | 0.996166i | \(-0.472116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3112 | − | 6.92381i | 0.603749 | − | 0.369565i | ||||
\(352\) | 5.14332 | 0.274140 | ||||||||
\(353\) | 0.550173 | + | 0.952928i | 0.0292828 | + | 0.0507192i | 0.880295 | − | 0.474426i | \(-0.157344\pi\) |
−0.851013 | + | 0.525145i | \(0.824011\pi\) | |||||||
\(354\) | −0.143655 | − | 0.248819i | −0.00763520 | − | 0.0132246i | ||||
\(355\) | 5.93375 | − | 10.2776i | 0.314931 | − | 0.545476i | ||||
\(356\) | −17.3579 | −0.919969 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.90521 | − | 6.76402i | 0.206397 | − | 0.357489i | ||||
\(359\) | −9.77386 | −0.515845 | −0.257922 | − | 0.966166i | \(-0.583038\pi\) | ||||
−0.257922 | + | 0.966166i | \(0.583038\pi\) | |||||||
\(360\) | 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 | 0.974033 | − | 0.226408i | \(-0.0726983\pi\) |
−0.683092 | + | 0.730333i | \(0.739365\pi\) | |||||||
\(368\) | −0.503679 | + | 0.872397i | −0.0262561 | + | 0.0454769i | ||||
\(369\) | 13.6633 | 0.711283 | ||||||||
\(370\) | −15.5244 | + | 26.8891i | −0.807076 | + | 1.39790i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.70391 | 0.399429 | ||||||||
\(373\) | 15.3651 | − | 26.6131i | 0.795573 | − | 1.37797i | −0.126902 | − | 0.991915i | \(-0.540504\pi\) |
0.922475 | − | 0.386057i | \(-0.126163\pi\) | |||||||
\(374\) | −0.740150 | − | 1.28198i | −0.0382723 | − | 0.0662895i | ||||
\(375\) | −2.09783 | − | 3.63355i | −0.108332 | − | 0.187636i | ||||
\(376\) | 20.0489 | 1.03394 | ||||||||
\(377\) | −5.81582 | − | 3.16147i | −0.299530 | − | 0.162824i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3286 | − | 19.6217i | −0.581912 | − | 1.00790i | −0.995253 | − | 0.0973246i | \(-0.968972\pi\) |
0.413341 | − | 0.910576i | \(-0.364362\pi\) | |||||||
\(380\) | 2.27844 | + | 3.94638i | 0.116882 | + | 0.202445i | ||||
\(381\) | −0.643028 | + | 1.11376i | −0.0329433 | + | 0.0570595i | ||||
\(382\) | −1.12019 | −0.0573137 | ||||||||
\(383\) | 0.294631 | − | 0.510317i | 0.0150550 | − | 0.0260760i | −0.858400 | − | 0.512981i | \(-0.828541\pi\) |
0.873455 | + | 0.486905i | \(0.161874\pi\) | |||||||
\(384\) | −2.51581 | + | 4.35751i | −0.128384 | + | 0.222368i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.99004 | + | 12.1071i | −0.355783 | + | 0.616235i | ||||
\(387\) | −5.01619 | − | 8.68830i | −0.254988 | − | 0.441651i | ||||
\(388\) | 0.322877 | + | 0.559239i | 0.0163916 | + | 0.0283910i | ||||
\(389\) | 5.69945 | 0.288974 | 0.144487 | − | 0.989507i | \(-0.453847\pi\) | ||||
0.144487 | + | 0.989507i | \(0.453847\pi\) | |||||||
\(390\) | 0.179334 | + | 6.98096i | 0.00908091 | + | 0.353495i | ||||
\(391\) | 10.9432 | 0.553422 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.97904 | + | 6.89191i | 0.200716 | + | 0.347651i | ||||
\(394\) | −10.8891 | + | 18.8605i | −0.548584 | + | 0.950176i | ||||
\(395\) | −41.6136 | −2.09381 | ||||||||
\(396\) | 1.46778 | − | 2.54227i | 0.0737588 | − | 0.127754i | ||||
\(397\) | 12.7641 | − | 22.1082i | 0.640614 | − | 1.10958i | −0.344682 | − | 0.938720i | \(-0.612013\pi\) |
0.985296 | − | 0.170857i | \(-0.0546535\pi\) | |||||||
\(398\) | 21.6005 | 1.08274 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.610086 | − | 1.05670i | −0.0305043 | − | 0.0528350i | ||||
\(401\) | −12.7506 | − | 22.0846i | −0.636733 | − | 1.10285i | −0.986145 | − | 0.165884i | \(-0.946952\pi\) |
0.349413 | − | 0.936969i | \(-0.386381\pi\) | |||||||
\(402\) | 4.75514 | 0.237165 | ||||||||
\(403\) | 28.0882 | − | 17.1933i | 1.39917 | − | 0.856457i | ||||
\(404\) | 7.63635 | 0.379922 | ||||||||
\(405\) | −9.04457 | − | 15.6657i | −0.449428 | − | 0.778433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.75934 | + | 8.24341i | −0.235912 | + | 0.408611i | ||||
\(408\) | 3.57040 | 0.176761 | ||||||||
\(409\) | −0.0734938 | + | 0.127295i | −0.00363403 | + | 0.00629433i | −0.867837 | − | 0.496850i | \(-0.834490\pi\) |
0.864203 | + | 0.503144i | \(0.167823\pi\) | |||||||
\(410\) | −7.80822 | + | 13.5242i | −0.385621 | + | 0.667914i | ||||
\(411\) | 5.76398 | 0.284316 | ||||||||
\(412\) | −2.63601 | + | 4.56570i | −0.129867 | + | 0.224936i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.16217 | − | 10.6732i | −0.302854 | − | 0.524559i | ||||
\(415\) | 5.21966 | 0.256223 | ||||||||
\(416\) | 0.530333 | + | 20.6444i | 0.0260017 | + | 1.01217i | ||||
\(417\) | 2.78540 | 0.136402 | ||||||||
\(418\) | −0.396686 | − | 0.687080i | −0.0194026 | − | 0.0336062i | ||||
\(419\) | −6.84795 | − | 11.8610i | −0.334544 | − | 0.579447i | 0.648853 | − | 0.760914i | \(-0.275249\pi\) |
−0.983397 | + | 0.181466i | \(0.941916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.44169 | 0.167738 | 0.0838688 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838688 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(422\) | −2.42421 | + | 4.19885i | −0.118009 | + | 0.204397i | ||||
\(423\) | 9.21486 | − | 15.9606i | 0.448042 | − | 0.776032i | ||||
\(424\) | −26.1689 | −1.27087 | ||||||||
\(425\) | −6.62754 | + | 11.4792i | −0.321483 | + | 0.556825i | ||||
\(426\) | −0.970345 | − | 1.68069i | −0.0470134 | − | 0.0814295i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.0156 | 0.870816 | ||||||||
\(429\) | 0.0549785 | + | 2.14016i | 0.00265439 | + | 0.103328i | ||||
\(430\) | 11.4665 | 0.552964 | ||||||||
\(431\) | −11.1455 | − | 19.3046i | −0.536861 | − | 0.929870i | −0.999071 | − | 0.0430997i | \(-0.986277\pi\) |
0.462210 | − | 0.886771i | \(-0.347057\pi\) | |||||||
\(432\) | 0.327896 | + | 0.567932i | 0.0157759 | + | 0.0273246i | ||||
\(433\) | 12.9481 | − | 22.4268i | 0.622247 | − | 1.07776i | −0.366819 | − | 0.930292i | \(-0.619553\pi\) |
0.989066 | − | 0.147472i | \(-0.0471136\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.08892 | − | 3.61811i | 0.100156 | − | 0.173475i | ||||
\(436\) | −2.68024 | + | 4.64232i | −0.128360 | + | 0.222327i | ||||
\(437\) | 5.86505 | 0.280564 | ||||||||
\(438\) | 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 | \(0.600570\pi\) | |||||||
\(440\) | 4.30792 | + | 7.46153i | 0.205372 | + | 0.355715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.06932 | − | 3.10302i | 0.241123 | − | 0.147596i | ||||
\(443\) | 33.2089 | 1.57780 | 0.788900 | − | 0.614521i | \(-0.210651\pi\) | ||||
0.788900 | + | 0.614521i | \(0.210651\pi\) | |||||||
\(444\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.84320 | + | 17.0489i | −0.464529 | + | 0.804589i | −0.999180 | − | 0.0404845i | \(-0.987110\pi\) |
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(450\) | 14.9280 | 0.703712 | ||||||||
\(451\) | −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 | 0.874628 | − | 0.484794i | \(-0.161105\pi\) |
−0.857158 | + | 0.515053i | \(0.827772\pi\) | |||||||
\(458\) | 0.0291746 | + | 0.0505320i | 0.00136324 | + | 0.00236120i | ||||
\(459\) | 3.56203 | − | 6.16961i | 0.166261 | − | 0.287973i | ||||
\(460\) | −24.8035 | −1.15647 | ||||||||
\(461\) | 16.5855 | − | 28.7269i | 0.772464 | − | 1.33795i | −0.163744 | − | 0.986503i | \(-0.552357\pi\) |
0.936209 | − | 0.351445i | \(-0.114309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.7521 | −1.42917 | −0.714586 | − | 0.699548i | \(-0.753385\pi\) | ||||
−0.714586 | + | 0.699548i | \(0.753385\pi\) | |||||||
\(464\) | 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 | ||||
\(467\) | −29.6065 | −1.37003 | −0.685013 | − | 0.728531i | \(-0.740203\pi\) | ||||
−0.685013 | + | 0.728531i | \(0.740203\pi\) | |||||||
\(468\) | 10.3556 | + | 5.62928i | 0.478687 | + | 0.260214i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.5321 | + | 18.2422i | 0.485810 | + | 0.841448i | ||||
\(471\) | 0.641056 | + | 1.11034i | 0.0295383 | + | 0.0511618i | ||||
\(472\) | 0.711644 | − | 1.23260i | 0.0327561 | − | 0.0567352i | ||||
\(473\) | 3.51530 | 0.161634 | ||||||||
\(474\) | −3.40253 | + | 5.89335i | −0.156283 | + | 0.270691i | ||||
\(475\) | −3.55205 | + | 6.15234i | −0.162979 | + | 0.282289i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0278 | + | 20.8327i | −0.550714 | + | 0.953864i | ||||
\(478\) | 1.42748 | + | 2.47247i | 0.0652915 | + | 0.113088i | ||||
\(479\) | −7.04527 | − | 12.2028i | −0.321907 | − | 0.557559i | 0.658975 | − | 0.752165i | \(-0.270990\pi\) |
−0.980881 | + | 0.194606i | \(0.937657\pi\) | |||||||
\(480\) | −13.0337 | −0.594903 | ||||||||
\(481\) | −33.5784 | − | 18.2532i | −1.53104 | − | 0.832273i | ||||
\(482\) | 7.30247 | 0.332618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.50142 | − | 11.2608i | −0.295519 | − | 0.511854i | ||||
\(485\) | −0.871108 | + | 1.50880i | −0.0395550 | + | 0.0685112i | ||||
\(486\) | −12.3500 | −0.560210 | ||||||||
\(487\) | 8.39773 | − | 14.5453i | 0.380537 | − | 0.659110i | −0.610602 | − | 0.791938i | \(-0.709072\pi\) |
0.991139 | + | 0.132828i | \(0.0424057\pi\) | |||||||
\(488\) | −2.00200 | + | 3.46757i | −0.0906263 | + | 0.156969i | ||||
\(489\) | −7.86587 | −0.355707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8345 | − | 18.7659i | −0.488954 | − | 0.846893i | 0.510965 | − | 0.859601i | \(-0.329288\pi\) |
−0.999919 | + | 0.0127081i | \(0.995955\pi\) | |||||||
\(492\) | −2.24839 | − | 3.89432i | −0.101365 | − | 0.175570i | ||||
\(493\) | −3.55586 | −0.160148 | ||||||||
\(494\) | 2.71692 | − | 1.66308i | 0.122240 | − | 0.0748253i | ||||
\(495\) | 7.92003 | 0.355979 | ||||||||
\(496\) | 0.814234 | + | 1.41029i | 0.0365602 | + | 0.0633241i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.426785 | − | 0.739213i | 0.0191247 | − | 0.0331249i | ||||
\(499\) | −23.3048 | −1.04327 | −0.521633 | − | 0.853170i | \(-0.674677\pi\) | ||||
−0.521633 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(500\) | 4.04699 | − | 7.00960i | 0.180987 | − | 0.313479i | ||||
\(501\) | −5.48023 | + | 9.49203i | −0.244838 | + | 0.424073i | ||||
\(502\) | −18.3120 | −0.817306 | ||||||||
\(503\) | 21.9415 | − | 38.0037i | 0.978322 | − | 1.69450i | 0.309816 | − | 0.950796i | \(-0.399732\pi\) |
0.668506 | − | 0.743707i | \(-0.266934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3013 | + | 17.8423i | 0.458401 | + | 0.793974i | ||||
\(506\) | 4.31839 | 0.191976 | ||||||||
\(507\) | −8.58456 | + | 0.441349i | −0.381254 | + | 0.0196010i | ||||
\(508\) | −2.48097 | −0.110075 | ||||||||
\(509\) | −9.96210 | − | 17.2549i | −0.441563 | − | 0.764809i | 0.556243 | − | 0.831020i | \(-0.312242\pi\) |
−0.997806 | + | 0.0662109i | \(0.978909\pi\) | |||||||
\(510\) | 1.87561 | + | 3.24866i | 0.0830536 | + | 0.143853i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.01529 | −0.0890641 | ||||||||
\(513\) | 1.90908 | − | 3.30662i | 0.0842879 | − | 0.145991i | ||||
\(514\) | 2.10139 | − | 3.63972i | 0.0926886 | − | 0.160541i | ||||
\(515\) | −14.2237 | −0.626771 | ||||||||
\(516\) | −1.65090 | + | 2.85944i | −0.0726767 | + | 0.125880i | ||||
\(517\) | 3.22884 | + | 5.59252i | 0.142004 | + | 0.245959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.60335 | −0.289855 | ||||||||
\(520\) | −29.5051 | + | 18.0606i | −1.29388 | + | 0.792010i | ||||
\(521\) | −16.5241 | −0.723933 | −0.361967 | − | 0.932191i | \(-0.617895\pi\) | ||||
−0.361967 | + | 0.932191i | \(0.617895\pi\) | |||||||
\(522\) | 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 | \(0.748860\pi\) | |||||||
\(524\) | −7.67609 | + | 13.2954i | −0.335332 | + | 0.580812i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.81065 | + | 6.60024i | −0.166152 | + | 0.287784i | ||||
\(527\) | 8.84526 | − | 15.3204i | 0.385305 | − | 0.667369i | ||||
\(528\) | −0.105863 | −0.00460709 | ||||||||
\(529\) | −4.46197 | + | 7.72837i | −0.193999 | + | 0.336016i | ||||
\(530\) | −13.7471 | − | 23.8107i | −0.597137 | − | 1.03427i | ||||
\(531\) | −0.654173 | − | 1.13306i | −0.0283887 | − | 0.0491706i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.8887 | − | 9.18068i | −0.731531 | − | 0.397660i | ||||
\(534\) | −7.65826 | −0.331405 | ||||||||
\(535\) | 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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.07356 | + | 13.9838i | −0.347431 | + | 0.601767i | ||||
\(541\) | 36.2317 | 1.55772 | 0.778860 | − | 0.627197i | \(-0.215798\pi\) | ||||
0.778860 | + | 0.627197i | \(0.215798\pi\) | |||||||
\(542\) | −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 | ||||
\(551\) | −1.90578 | −0.0811888 | ||||||||
\(552\) | −5.20786 | + | 9.02027i | −0.221661 | + | 0.383928i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −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 | \(-0.240342\pi\) |
−0.957630 | + | 0.288002i | \(0.907009\pi\) | |||||||
\(558\) | −19.9232 | −0.843417 | ||||||||
\(559\) | 0.362466 | + | 14.1098i | 0.0153307 | + | 0.596781i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.575009 | + | 0.995945i | 0.0242769 | + | 0.0420488i | ||||
\(562\) | 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 | \(0.0723248\pi\) | |||||||
\(564\) | −6.06547 | −0.255402 | ||||||||
\(565\) | −23.6936 | + | 41.0386i | −0.996798 | + | 1.72651i | ||||
\(566\) | 6.49594 | − | 11.2513i | 0.273045 | − | 0.472927i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.80692 | − | 8.32583i | 0.201694 | − | 0.349344i | ||||
\(569\) | −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 | ||||
\(571\) | −0.207758 | −0.00869439 | −0.00434719 | − | 0.999991i | \(-0.501384\pi\) | ||||
−0.00434719 | + | 0.999991i | \(0.501384\pi\) | |||||||
\(572\) | −3.52248 | + | 2.15617i | −0.147282 | + | 0.0901542i | ||||
\(573\) | 0.870251 | 0.0363552 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.3341 | − | 33.4876i | −0.806288 | − | 1.39653i | ||||
\(576\) | 5.78976 | − | 10.0282i | 0.241240 | − | 0.417840i | ||||
\(577\) | −3.32656 | −0.138487 | −0.0692434 | − | 0.997600i | \(-0.522058\pi\) | ||||
−0.0692434 | + | 0.997600i | \(0.522058\pi\) | |||||||
\(578\) | −5.63818 | + | 9.76562i | −0.234518 | + | 0.406196i | ||||
\(579\) | 5.43043 | − | 9.40577i | 0.225681 | − | 0.390891i | ||||
\(580\) | 8.05959 | 0.334656 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.142452 | + | 0.246734i | 0.00590483 | + | 0.0102275i | ||||
\(583\) | −4.21447 | − | 7.29967i | −0.174545 | − | 0.302321i | ||||
\(584\) | 30.3899 | 1.25754 | ||||||||
\(585\) | 0.816643 | + | 31.7896i | 0.0337640 | + | 1.31434i | ||||
\(586\) | 5.05538 | 0.208836 | ||||||||
\(587\) | 7.54051 | + | 13.0606i | 0.311230 | + | 0.539067i | 0.978629 | − | 0.205634i | \(-0.0659256\pi\) |
−0.667399 | + | 0.744701i | \(0.732592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.74064 | − | 8.21104i | 0.195335 | − | 0.338330i | ||||
\(590\) | 1.49537 | 0.0615635 | ||||||||
\(591\) | 8.45953 | − | 14.6523i | 0.347978 | − | 0.602716i | ||||
\(592\) | 0.944935 | − | 1.63668i | 0.0388366 | − | 0.0672670i | ||||
\(593\) | 25.8491 | 1.06149 | 0.530747 | − | 0.847530i | \(-0.321911\pi\) | ||||
0.530747 | + | 0.847530i | \(0.321911\pi\) | |||||||
\(594\) | 1.40564 | − | 2.43464i | 0.0576740 | − | 0.0998944i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.74055 | + | 6.47882i | 0.153219 | + | 0.265383i | ||||
\(597\) | −16.7810 | −0.686803 | ||||||||
\(598\) | 0.445274 | + | 17.3333i | 0.0182086 | + | 0.708810i | ||||
\(599\) | −35.5469 | −1.45241 | −0.726203 | − | 0.687480i | \(-0.758717\pi\) | ||||
−0.726203 | + | 0.687480i | \(0.758717\pi\) | |||||||
\(600\) | −6.30807 | − | 10.9259i | −0.257526 | − | 0.446048i | ||||
\(601\) | 13.6474 | + | 23.6379i | 0.556688 | + | 0.964212i | 0.997770 | + | 0.0667449i | \(0.0212614\pi\) |
−0.441082 | + | 0.897467i | \(0.645405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.6538 | 0.881810 | ||||||||
\(604\) | −10.7511 | + | 18.6215i | −0.437458 | + | 0.757699i | ||||
\(605\) | 17.5406 | − | 30.3811i | 0.713125 | − | 1.23517i | ||||
\(606\) | 3.36913 | 0.136862 | ||||||||
\(607\) | 19.4629 | − | 33.7108i | 0.789976 | − | 1.36828i | −0.136006 | − | 0.990708i | \(-0.543426\pi\) |
0.925981 | − | 0.377570i | \(-0.123240\pi\) | |||||||
\(608\) | 2.97274 | + | 5.14894i | 0.120561 | + | 0.208817i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.20679 | −0.170328 | ||||||||
\(611\) | −22.1145 | + | 13.5367i | −0.894656 | + | 0.547635i | ||||
\(612\) | 6.33152 | 0.255937 | ||||||||
\(613\) | −0.443322 | − | 0.767857i | −0.0179056 | − | 0.0310135i | 0.856934 | − | 0.515427i | \(-0.172367\pi\) |
−0.874839 | + | 0.484413i | \(0.839033\pi\) | |||||||
\(614\) | 9.45317 | + | 16.3734i | 0.381499 | + | 0.660775i | ||||
\(615\) | 6.06606 | − | 10.5067i | 0.244607 | − | 0.423672i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3944 | + | 30.1280i | −0.700272 | + | 1.21291i | 0.268099 | + | 0.963391i | \(0.413605\pi\) |
−0.968371 | + | 0.249515i | \(0.919729\pi\) | |||||||
\(618\) | −1.16300 | + | 2.01437i | −0.0467827 | + | 0.0810300i | ||||
\(619\) | 2.05562 | 0.0826221 | 0.0413111 | − | 0.999146i | \(-0.486847\pi\) | ||||
0.0413111 | + | 0.999146i | \(0.486847\pi\) | |||||||
\(620\) | −20.0483 | + | 34.7247i | −0.805161 | + | 1.39458i | ||||
\(621\) | 10.3913 | + | 17.9982i | 0.416987 | + | 0.722243i | ||||
\(622\) | 4.18864 | + | 7.25494i | 0.167949 | + | 0.290897i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.0109156 | − | 0.424915i | −0.000436975 | − | 0.0170102i | ||||
\(625\) | −12.3816 | −0.495265 | ||||||||
\(626\) | −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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.6169 | − | 39.1736i | 0.900363 | − | 1.55947i | 0.0733401 | − | 0.997307i | \(-0.476634\pi\) |
0.827023 | − | 0.562168i | \(-0.190033\pi\) | |||||||
\(632\) | −33.7111 | −1.34095 | ||||||||
\(633\) | 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 | \(0.0438111\pi\) | |||||||
\(642\) | 7.94841 | 0.313699 | ||||||||
\(643\) | 5.26755 | − | 9.12367i | 0.207732 | − | 0.359802i | −0.743268 | − | 0.668994i | \(-0.766725\pi\) |
0.951000 | + | 0.309192i | \(0.100058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.90811 | −0.350756 | ||||||||
\(646\) | 0.855587 | − | 1.48192i | 0.0336626 | − | 0.0583053i | ||||
\(647\) | 12.0804 | + | 20.9239i | 0.474930 | + | 0.822603i | 0.999588 | − | 0.0287105i | \(-0.00914011\pi\) |
−0.524658 | + | 0.851313i | \(0.675807\pi\) | |||||||
\(648\) | −7.32699 | − | 12.6907i | −0.287831 | − | 0.498538i | ||||
\(649\) | 0.458438 | 0.0179952 | ||||||||
\(650\) | −18.4520 | − | 10.0305i | −0.723745 | − | 0.393427i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.58714 | − | 13.1413i | −0.297135 | − | 0.514654i | ||||
\(653\) | 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 | ||||
\(655\) | −41.4196 | −1.61840 | ||||||||
\(656\) | 0.475268 | − | 0.823189i | 0.0185561 | − | 0.0321401i | ||||
\(657\) | 13.9678 | − | 24.1930i | 0.544937 | − | 0.943859i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.10030 | − | 3.63782i | 0.0818159 | − | 0.141709i | −0.822214 | − | 0.569178i | \(-0.807261\pi\) |
0.904030 | + | 0.427469i | \(0.140595\pi\) | |||||||
\(660\) | −1.30329 | − | 2.25737i | −0.0507307 | − | 0.0878681i | ||||
\(661\) | −8.83631 | − | 15.3049i | −0.343693 | − | 0.595293i | 0.641423 | − | 0.767188i | \(-0.278345\pi\) |
−0.985115 | + | 0.171894i | \(0.945011\pi\) | |||||||
\(662\) | −1.51742 | −0.0589760 | ||||||||
\(663\) | −3.93826 | + | 2.41068i | −0.152949 | + | 0.0936230i | ||||
\(664\) | 4.22844 | 0.164095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.5607 | + | 20.0236i | 0.447966 | + | 0.775900i | ||||
\(667\) | 5.18664 | − | 8.98353i | 0.200828 | − | 0.347844i | ||||
\(668\) | −21.1441 | −0.818091 | ||||||||
\(669\) | −0.779623 | + | 1.35035i | −0.0301420 | + | 0.0522074i | ||||
\(670\) | −12.3746 | + | 21.4334i | −0.478071 | + | 0.828044i | ||||
\(671\) | −1.28968 | −0.0497875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3052 | + | 17.8491i | 0.397235 | + | 0.688031i | 0.993384 | − | 0.114843i | \(-0.0366366\pi\) |
−0.596149 | + | 0.802874i | \(0.703303\pi\) | |||||||
\(674\) | 4.06901 | + | 7.04774i | 0.156733 | + | 0.271469i | ||||
\(675\) | −25.1731 | −0.968911 | ||||||||
\(676\) | −9.01772 | − | 13.9163i | −0.346835 | − | 0.535243i | ||||
\(677\) | −21.3074 | −0.818909 | −0.409455 | − | 0.912330i | \(-0.634281\pi\) | ||||
−0.409455 | + | 0.912330i | \(0.634281\pi\) | |||||||
\(678\) | 3.87461 | + | 6.71102i | 0.148804 | + | 0.257735i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.29147 | + | 16.0933i | −0.356312 | + | 0.617150i | ||||
\(681\) | 17.3853 | 0.666206 | ||||||||
\(682\) | 3.49049 | − | 6.04571i | 0.133658 | − | 0.231502i | ||||
\(683\) | 3.34878 | − | 5.80026i | 0.128138 | − | 0.221941i | −0.794817 | − | 0.606849i | \(-0.792433\pi\) |
0.922955 | + | 0.384908i | \(0.125767\pi\) | |||||||
\(684\) | 3.39340 | 0.129750 | ||||||||
\(685\) | −14.9999 | + | 25.9806i | −0.573118 | + | 0.992670i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0226652 | − | 0.0392573i | −0.000864732 | − | 0.00149776i | ||||
\(688\) | −0.697939 | −0.0266087 | ||||||||
\(689\) | 28.8651 | − | 17.6688i | 1.09967 | − | 0.673128i | ||||
\(690\) | −10.9432 | −0.416601 | ||||||||
\(691\) | 12.4632 | + | 21.5868i | 0.474121 | + | 0.821202i | 0.999561 | − | 0.0296291i | \(-0.00943262\pi\) |
−0.525440 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(692\) | −6.36936 | − | 11.0321i | −0.242127 | − | 0.419376i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.539093 | −0.0204637 | ||||||||
\(695\) | −7.24861 | + | 12.5550i | −0.274955 | + | 0.476237i | ||||
\(696\) | 1.69223 | − | 2.93102i | 0.0641437 | − | 0.111100i | ||||
\(697\) | −10.3260 | −0.391123 | ||||||||
\(698\) | 13.0217 | − | 22.5543i | 0.492880 | − | 0.853694i | ||||
\(699\) | −4.85017 | − | 8.40073i | −0.183450 | − | 0.317745i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.94583 | −0.186801 | −0.0934007 | − | 0.995629i | \(-0.529774\pi\) | ||||
−0.0934007 | + | 0.995629i | \(0.529774\pi\) | |||||||
\(702\) | 9.91715 | + | 5.39095i | 0.374299 | + | 0.203468i | ||||
\(703\) | −11.0032 | −0.414995 | ||||||||
\(704\) | 2.02870 | + | 3.51382i | 0.0764597 | + | 0.132432i | ||||
\(705\) | −8.18220 | − | 14.1720i | −0.308160 | − | 0.533748i | ||||
\(706\) | −0.468266 | + | 0.811061i | −0.0176234 | + | 0.0305247i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.215297 | + | 0.372905i | −0.00809136 | + | 0.0140146i | ||||
\(709\) | 2.32249 | − | 4.02267i | 0.0872228 | − | 0.151074i | −0.819113 | − | 0.573632i | \(-0.805534\pi\) |
0.906336 | + | 0.422557i | \(0.138867\pi\) | |||||||
\(710\) | 10.1007 | 0.379074 | ||||||||
\(711\) | −15.4943 | + | 26.8369i | −0.581082 | + | 1.00646i | ||||
\(712\) | −18.9688 | − | 32.8550i | −0.710888 | − | 1.23129i | ||||
\(713\) | 25.8037 | + | 44.6933i | 0.966356 | + | 1.67378i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.78966 | − | 5.32165i | −0.366113 | − | 0.199018i | ||||
\(716\) | −11.7055 | −0.437455 | ||||||||
\(717\) | −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 | 0.402105 | + | 0.915594i | \(0.368279\pi\) |
−0.993980 | + | 0.109564i | \(0.965055\pi\) | |||||||
\(720\) | −1.57247 | −0.0586025 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.62714 | + | 13.2106i | −0.283853 | + | 0.491647i | ||||
\(723\) | −5.67315 | −0.210987 | ||||||||
\(724\) | 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 | ||||
\(733\) | −7.60208 | −0.280789 | −0.140395 | − | 0.990096i | \(-0.544837\pi\) | ||||
−0.140395 | + | 0.990096i | \(0.544837\pi\) | |||||||
\(734\) | −4.74386 | + | 8.21660i | −0.175099 | + | 0.303280i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | 0.990428 | + | 0.138033i | \(0.0440781\pi\) |
−0.375673 | + | 0.926752i | \(0.622589\pi\) | |||||||
\(740\) | 46.5330 | 1.71059 | ||||||||
\(741\) | −2.11072 | + | 1.29201i | −0.0775394 | + | 0.0474632i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.46912 | + | 2.54458i | 0.0538966 | + | 0.0933517i | 0.891715 | − | 0.452597i | \(-0.149503\pi\) |
−0.837818 | + | 0.545949i | \(0.816169\pi\) | |||||||
\(744\) | 8.41888 | + | 14.5819i | 0.308651 | + | 0.534599i | ||||
\(745\) | −10.0919 | + | 17.4796i | −0.369737 | + | 0.640403i | ||||
\(746\) | 26.1552 | 0.957609 | ||||||||
\(747\) | 1.94348 | − | 3.36620i | 0.0711081 | − | 0.123163i | ||||
\(748\) | −1.10927 | + | 1.92131i | −0.0405588 | + | 0.0702499i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.78552 | − | 3.09261i | 0.0651980 | − | 0.112926i | ||||
\(751\) | −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 | ||||
\(753\) | 14.2263 | 0.518434 | ||||||||
\(754\) | −0.144686 | − | 5.63223i | −0.00526916 | − | 0.205114i | ||||
\(755\) | −58.0123 | −2.11128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.77321 | − | 9.99950i | −0.209831 | − | 0.363438i | 0.741830 | − | 0.670588i | \(-0.233958\pi\) |
−0.951661 | + | 0.307150i | \(0.900625\pi\) | |||||||
\(758\) | 9.64207 | − | 16.7006i | 0.350216 | − | 0.606592i | ||||
\(759\) | −3.35487 | −0.121774 | ||||||||
\(760\) | −4.97979 | + | 8.62525i | −0.180636 | + | 0.312871i | ||||
\(761\) | −17.3249 | + | 30.0075i | −0.628026 | + | 1.08777i | 0.359921 | + | 0.932983i | \(0.382803\pi\) |
−0.987947 | + | 0.154790i | \(0.950530\pi\) | |||||||
\(762\) | −1.09459 | −0.0396530 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.839413 | + | 1.45391i | 0.0303689 | + | 0.0526005i | ||||
\(765\) | 8.54110 | + | 14.7936i | 0.308804 | + | 0.534864i | ||||
\(766\) | 0.501537 | 0.0181213 | ||||||||
\(767\) | 0.0472700 | + | 1.84009i | 0.00170682 | + | 0.0664418i | ||||
\(768\) | −10.2578 | −0.370146 | ||||||||
\(769\) | 3.27437 | + | 5.67138i | 0.118077 | + | 0.204515i | 0.919006 | − | 0.394245i | \(-0.128994\pi\) |
−0.800929 | + | 0.598760i | \(0.795660\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.63253 | + | 2.82763i | −0.0587943 | + | 0.101835i | ||||
\(772\) | 20.9520 | 0.754079 | ||||||||
\(773\) | −16.9637 | + | 29.3821i | −0.610143 | + | 1.05680i | 0.381073 | + | 0.924545i | \(0.375555\pi\) |
−0.991216 | + | 0.132254i | \(0.957779\pi\) | |||||||
\(774\) | 4.26941 | − | 7.39484i | 0.153461 | − | 0.265802i | ||||
\(775\) | −62.5100 | −2.24542 | ||||||||
\(776\) | −0.705683 | + | 1.22228i | −0.0253325 | + | 0.0438772i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.42547 | + | 4.20104i | 0.0869575 | + | 0.150615i | ||||
\(779\) | −5.53423 | −0.198284 | ||||||||
\(780\) | 8.92632 | − | 5.46396i | 0.319613 | − | 0.195641i | ||||
\(781\) | 3.09659 | 0.110805 | ||||||||
\(782\) | 4.65703 | + | 8.06620i | 0.166535 | + | 0.288447i | ||||
\(783\) | −3.37651 | − | 5.84829i | −0.120667 | − | 0.209001i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.67303 | −0.238171 | ||||||||
\(786\) | −3.38667 | + | 5.86588i | −0.120798 | + | 0.209229i | ||||
\(787\) | −6.48717 | + | 11.2361i | −0.231243 | + | 0.400524i | −0.958174 | − | 0.286186i | \(-0.907612\pi\) |
0.726932 | + | 0.686710i | \(0.240946\pi\) | |||||||
\(788\) | 32.6390 | 1.16272 | ||||||||
\(789\) | 2.96042 | − | 5.12760i | 0.105394 | − | 0.182548i | ||||
\(790\) | −17.7092 | − | 30.6732i | −0.630065 | − | 1.09130i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.41600 | 0.227983 | ||||||||
\(793\) | −0.132980 | − | 5.17655i | −0.00472226 | − | 0.183825i | ||||
\(794\) | 21.7278 | 0.771090 | ||||||||
\(795\) | 10.6799 | + | 18.4981i | 0.378776 | + | 0.656059i | ||||
\(796\) | −16.1864 | − | 28.0357i | −0.573712 | − | 0.993699i | ||||
\(797\) | −2.20956 | + | 3.82707i | −0.0782667 | + | 0.135562i | −0.902502 | − | 0.430685i | \(-0.858272\pi\) |
0.824235 | + | 0.566247i | \(0.191605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.96408 | + | 12.0621i | −0.246371 | + | 0.426728i | ||||
\(800\) | 19.5993 | − | 33.9469i | 0.692938 | − | 1.20020i | ||||
\(801\) | −34.8739 | −1.23221 | ||||||||
\(802\) | 10.8523 | − | 18.7968i | 0.383209 | − | 0.663737i | ||||
\(803\) | 4.89426 | + | 8.47711i | 0.172715 | + | 0.299151i | ||||
\(804\) | −3.56327 | − | 6.17177i | −0.125667 | − | 0.217662i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.6264 | + | 13.3869i | 0.867427 | + | 0.471532i | ||||
\(807\) | −3.18937 | −0.112271 | ||||||||
\(808\) | 8.34504 | + | 14.4540i | 0.293578 | + | 0.508491i | ||||
\(809\) | −5.73580 | − | 9.93470i | −0.201660 | − | 0.349285i | 0.747403 | − | 0.664371i | \(-0.231300\pi\) |
−0.949063 | + | 0.315085i | \(0.897967\pi\) | |||||||
\(810\) | 7.69807 | − | 13.3334i | 0.270482 | − | 0.468489i | ||||
\(811\) | 23.8664 | 0.838063 | 0.419032 | − | 0.907972i | \(-0.362370\pi\) | ||||
0.419032 | + | 0.907972i | \(0.362370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.45361 | − | 4.24978i | 0.0860520 | − | 0.149046i | ||||
\(814\) | −8.10159 | −0.283960 | ||||||||
\(815\) | 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 | \(-0.984932\pi\) |
0.458460 | − | 0.888715i | \(-0.348401\pi\) | |||||||
\(822\) | 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 | \(0.118699\pi\) | |||||||
\(824\) | −11.5226 | −0.401408 | ||||||||
\(825\) | 2.03181 | − | 3.51920i | 0.0707386 | − | 0.122523i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.9128 | 0.796756 | 0.398378 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398378 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(828\) | −9.23528 | + | 15.9960i | −0.320948 | + | 0.555898i | ||||
\(829\) | 21.2806 | + | 36.8590i | 0.739104 | + | 1.28017i | 0.952899 | + | 0.303287i | \(0.0980842\pi\) |
−0.213795 | + | 0.976879i | \(0.568582\pi\) | |||||||
\(830\) | 2.22129 | + | 3.84739i | 0.0771022 | + | 0.133545i | ||||
\(831\) | 2.52344 | 0.0875370 | ||||||||
\(832\) | −13.8947 | + | 8.50518i | −0.481711 | + | 0.294864i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.18536 | + | 2.05311i | 0.0410458 | + | 0.0710933i | ||||
\(835\) | −28.5230 | − | 49.4033i | −0.987080 | − | 1.70967i | ||||
\(836\) | −0.594515 | + | 1.02973i | −0.0205617 | + | 0.0356140i | ||||
\(837\) | 33.5965 | 1.16126 | ||||||||
\(838\) | 5.82846 | − | 10.0952i | 0.201341 | − | 0.348733i | ||||
\(839\) | −0.920524 | + | 1.59439i | −0.0317800 | + | 0.0550446i | −0.881478 | − | 0.472225i | \(-0.843451\pi\) |
0.849698 | + | 0.527270i | \(0.176784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8147 | − | 22.1957i | 0.441885 | − | 0.765367i | ||||
\(842\) | 1.46465 | + | 2.53686i | 0.0504753 | + | 0.0874258i | ||||
\(843\) | −2.82666 | − | 4.89591i | −0.0973553 | − | 0.168624i | ||||
\(844\) | 7.26635 | 0.250118 | ||||||||
\(845\) | 20.3508 | − | 39.8427i | 0.700088 | − | 1.37063i | ||||
\(846\) | 15.6860 | 0.539296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.836755 | + | 1.44930i | 0.0287343 | + | 0.0497692i | ||||
\(849\) | −5.04657 | + | 8.74092i | −0.173198 | + | 0.299988i | ||||
\(850\) | −11.2817 | −0.386960 | ||||||||
\(851\) | 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 | \(-0.653131\pi\) | ||||
−0.462733 | + | 0.886498i | \(0.653131\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.57763 | + | 7.92869i | 0.156552 | + | 0.271155i | ||||
\(856\) | 19.6875 | + | 34.0998i | 0.672906 | + | 1.16551i | ||||
\(857\) | 16.7854 | 0.573377 | 0.286688 | − | 0.958024i | \(-0.407446\pi\) | ||||
0.286688 | + | 0.958024i | \(0.407446\pi\) | |||||||
\(858\) | −1.55411 | + | 0.951297i | −0.0530563 | + | 0.0324767i | ||||
\(859\) | 51.6116 | 1.76096 | 0.880482 | − | 0.474079i | \(-0.157219\pi\) | ||||
0.880482 | + | 0.474079i | \(0.157219\pi\) | |||||||
\(860\) | −8.59245 | − | 14.8826i | −0.293000 | − | 0.507491i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.48624 | − | 16.4306i | 0.323102 | − | 0.559630i | ||||
\(863\) | 21.9614 | 0.747573 | 0.373787 | − | 0.927515i | \(-0.378059\pi\) | ||||
0.373787 | + | 0.927515i | \(0.378059\pi\) | |||||||
\(864\) | −10.5338 | + | 18.2450i | −0.358366 | + | 0.620709i | ||||
\(865\) | 17.1843 | − | 29.7640i | 0.584283 | − | 1.01201i | ||||
\(866\) | 22.0410 | 0.748983 | ||||||||
\(867\) | 4.38020 | − | 7.58673i | 0.148759 | − | 0.257659i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42913 | − | 9.40352i | −0.184170 | − | 0.318993i | ||||
\(870\) | 3.55586 | 0.120555 | ||||||||
\(871\) | −26.7654 | − | 14.5497i | −0.906913 | − | 0.492997i | ||||
\(872\) | −11.7159 | −0.396752 | ||||||||
\(873\) | 0.648693 | + | 1.12357i | 0.0219549 | + | 0.0380270i | ||||
\(874\) | 2.49595 | + | 4.32311i | 0.0844267 | + | 0.146231i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.19401 | −0.310637 | ||||||||
\(877\) | 4.80873 | − | 8.32896i | 0.162379 | − | 0.281249i | −0.773342 | − | 0.633989i | \(-0.781417\pi\) |
0.935721 | + | 0.352740i | \(0.114750\pi\) | |||||||
\(878\) | −11.9089 | + | 20.6268i | −0.401905 | + | 0.696120i | ||||
\(879\) | −3.92743 | −0.132469 | ||||||||
\(880\) | 0.275493 | − | 0.477167i | 0.00928686 | − | 0.0160853i | ||||
\(881\) | −14.4863 | − | 25.0910i | −0.488055 | − | 0.845336i | 0.511851 | − | 0.859075i | \(-0.328960\pi\) |
−0.999906 | + | 0.0137383i | \(0.995627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.60727 | 0.222352 | 0.111176 | − | 0.993801i | \(-0.464538\pi\) | ||||
0.111176 | + | 0.993801i | \(0.464538\pi\) | |||||||
\(884\) | −7.82617 | − | 4.25430i | −0.263223 | − | 0.143088i | ||||
\(885\) | −1.16173 | −0.0390510 | ||||||||
\(886\) | 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 | \(0.656502\pi\) | |||||||
\(888\) | 9.77029 | − | 16.9226i | 0.327869 | − | 0.567886i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 19.9295 | − | 34.5190i | 0.668039 | − | 1.15708i | ||||
\(891\) | 2.36000 | − | 4.08765i | 0.0790631 | − | 0.136941i | ||||
\(892\) | −3.00799 | −0.100715 | ||||||||
\(893\) | −3.73242 | + | 6.46474i | −0.124901 | + | 0.216334i | ||||
\(894\) | 1.65032 | + | 2.85843i | 0.0551949 | + | 0.0956003i | ||||
\(895\) | −15.7905 | − | 27.3499i | −0.527818 | − | 0.914208i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.345925 | − | 13.4659i | −0.0115501 | − | 0.449613i | ||||
\(898\) | −16.7556 | −0.559142 | ||||||||
\(899\) | −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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.1942 | + | 33.2453i | −0.638388 | + | 1.10572i | ||||
\(905\) | 20.6657 | 0.686951 | ||||||||
\(906\) | −4.74337 | + | 8.21575i | −0.157588 | + | 0.272950i | ||||
\(907\) | −4.86821 | − | 8.43198i | −0.161646 | − | 0.279979i | 0.773813 | − | 0.633414i | \(-0.218347\pi\) |
−0.935459 | + | 0.353435i | \(0.885014\pi\) | |||||||
\(908\) | 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 | ||||
\(915\) | 3.26817 | 0.108042 | ||||||||
\(916\) | 0.0437242 | − | 0.0757325i | 0.00144469 | − | 0.00250227i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.06346 | 0.200124 | ||||||||
\(919\) | −27.1402 | + | 47.0082i | −0.895273 | + | 1.55066i | −0.0618056 | + | 0.998088i | \(0.519686\pi\) |
−0.833467 | + | 0.552569i | \(0.813647\pi\) | |||||||
\(920\) | −27.1054 | − | 46.9479i | −0.893639 | − | 1.54783i | ||||
\(921\) | −7.34398 | − | 12.7202i | −0.241993 | − | 0.419143i | ||||
\(922\) | 28.2327 | 0.929795 | ||||||||
\(923\) | 0.319293 | + | 12.4292i | 0.0105097 | + | 0.409112i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2721 | + | 62.8251i | 1.19262 | + | 2.06568i | ||||
\(926\) | −13.0869 | − | 22.6673i | −0.430064 | − | 0.744892i | ||||
\(927\) | −5.29602 | + | 9.17297i | −0.173944 | + | 0.301280i | ||||
\(928\) | 10.5155 | 0.345190 | ||||||||
\(929\) | 19.0960 | − | 33.0752i | 0.626519 | − | 1.08516i | −0.361726 | − | 0.932284i | \(-0.617812\pi\) |
0.988245 | − | 0.152878i | \(-0.0488542\pi\) | |||||||
\(930\) | −8.84526 | + | 15.3204i | −0.290047 | + | 0.502377i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.35660 | − | 16.2061i | 0.306486 | − | 0.530849i | ||||
\(933\) | −3.25408 | − | 5.63622i | −0.106534 | − | 0.184522i | ||||
\(934\) | −12.5994 | − | 21.8228i | −0.412266 | − | 0.714065i | ||||
\(935\) | −5.98552 | −0.195747 | ||||||||
\(936\) | 0.661561 | + | 25.7527i | 0.0216238 | + | 0.841754i | ||||
\(937\) | −19.0376 | −0.621931 | −0.310966 | − | 0.950421i | \(-0.600652\pi\) | ||||
−0.310966 | + | 0.950421i | \(0.600652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.91392 | + | 11.9753i | 0.225627 | + | 0.390798i | ||||
\(940\) | 15.7845 | − | 27.3396i | 0.514835 | − | 0.891720i | ||||
\(941\) | 46.1622 | 1.50484 | 0.752422 | − | 0.658682i | \(-0.228886\pi\) | ||||
0.752422 | + | 0.658682i | \(0.228886\pi\) | |||||||
\(942\) | −0.545619 | + | 0.945040i | −0.0177772 | + | 0.0307911i | ||||
\(943\) | 15.0616 | − | 26.0875i | 0.490474 | − | 0.849526i | ||||
\(944\) | −0.0910198 | −0.00296244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.49598 | + | 2.59111i | 0.0486385 | + | 0.0842443i | ||||
\(947\) | 4.59687 | + | 7.96201i | 0.149378 | + | 0.258730i | 0.930998 | − | 0.365025i | \(-0.118940\pi\) |
−0.781620 | + | 0.623755i | \(0.785606\pi\) | |||||||
\(948\) | 10.1988 | 0.331241 | ||||||||
\(949\) | −33.5210 | + | 20.5188i | −1.08814 | + | 0.666068i | ||||
\(950\) | −6.04648 | −0.196174 | ||||||||
\(951\) | 8.38440 | + | 14.5222i | 0.271883 | + | 0.470915i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.3232 | − | 38.6648i | 0.723118 | − | 1.25248i | −0.236626 | − | 0.971601i | \(-0.576042\pi\) |
0.959744 | − | 0.280876i | \(-0.0906250\pi\) | |||||||
\(954\) | −20.4743 | −0.662879 | ||||||||
\(955\) | −2.26470 | + | 3.92258i | −0.0732841 | + | 0.126932i | ||||
\(956\) | 2.13937 | − | 3.70550i | 0.0691923 | − | 0.119844i | ||||
\(957\) | 1.09012 | 0.0352387 | ||||||||
\(958\) | 5.99641 | − | 10.3861i | 0.193735 | − | 0.335559i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.14093 | − | 8.90436i | −0.165923 | − | 0.287387i | ||||
\(961\) | 52.4271 | 1.69120 | ||||||||
\(962\) | −0.835363 | − | 32.5184i | −0.0269332 | − | 1.04843i | ||||
\(963\) | 36.1952 | 1.16637 | ||||||||
\(964\) | −5.47212 | − | 9.47799i | −0.176245 | − | 0.305266i | ||||
\(965\) | 28.2638 | + | 48.9544i | 0.909845 | + | 1.57590i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8268 | 0.444639 | 0.222320 | − | 0.974974i | \(-0.428637\pi\) | ||||
0.222320 | + | 0.974974i | \(0.428637\pi\) | |||||||
\(968\) | 14.2096 | − | 24.6117i | 0.456713 | − | 0.791050i | ||||
\(969\) | −0.664689 | + | 1.15128i | −0.0213529 | + | 0.0369843i | ||||
\(970\) | −1.48284 | −0.0476113 | ||||||||
\(971\) | −3.63437 | + | 6.29491i | −0.116632 | + | 0.202013i | −0.918431 | − | 0.395581i | \(-0.870543\pi\) |
0.801799 | + | 0.597594i | \(0.203877\pi\) | |||||||
\(972\) | 9.25454 | + | 16.0293i | 0.296839 | + | 0.514141i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.2950 | 0.458043 | ||||||||
\(975\) | 14.3350 | + | 7.79247i | 0.459086 | + | 0.249559i | ||||
\(976\) | 0.256057 | 0.00819619 | ||||||||
\(977\) | −21.4050 | − | 37.0746i | −0.684808 | − | 1.18612i | −0.973497 | − | 0.228699i | \(-0.926553\pi\) |
0.288689 | − | 0.957423i | \(-0.406781\pi\) | |||||||
\(978\) | −3.34742 | − | 5.79790i | −0.107039 | − | 0.185397i | ||||
\(979\) | 6.10982 | − | 10.5825i | 0.195271 | − | 0.338219i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.38489 | + | 9.32690i | −0.171926 | + | 0.297785i | ||||
\(982\) | 9.22152 | − | 15.9721i | 0.294270 | − | 0.509691i | ||||
\(983\) | −46.3088 | −1.47702 | −0.738511 | − | 0.674242i | \(-0.764471\pi\) | ||||
−0.738511 | + | 0.674242i | \(0.764471\pi\) | |||||||
\(984\) | 4.91410 | − | 8.51147i | 0.156656 | − | 0.271336i | ||||
\(985\) | 44.0294 | + | 76.2612i | 1.40289 | + | 2.42988i | ||||
\(986\) | −1.51324 | − | 2.62101i | −0.0481914 | − | 0.0834700i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.19446 | − | 2.28010i | −0.133444 | − | 0.0725398i | ||||
\(989\) | −22.1182 | −0.703319 | ||||||||
\(990\) | 3.37047 | + | 5.83782i | 0.107121 | + | 0.185538i | ||||
\(991\) | 29.1162 | + | 50.4307i | 0.924907 | + | 1.60199i | 0.791711 | + | 0.610896i | \(0.209190\pi\) |
0.133195 | + | 0.991090i | \(0.457476\pi\) | |||||||
\(992\) | −26.1576 | + | 45.3062i | −0.830504 | + | 1.43847i | ||||
\(993\) | 1.17885 | 0.0374097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.6703 | − | 75.6392i | 1.38444 | − | 2.39792i | ||||
\(996\) | −1.27925 | −0.0405346 | ||||||||
\(997\) | 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 | 637.2.f.k.393.4 | 12 | ||
7.2 | even | 3 | 91.2.g.b.81.4 | yes | 12 | ||
7.3 | odd | 6 | 637.2.h.l.471.3 | 12 | |||
7.4 | even | 3 | 91.2.h.b.16.3 | yes | 12 | ||
7.5 | odd | 6 | 637.2.g.l.263.4 | 12 | |||
7.6 | odd | 2 | 637.2.f.j.393.4 | 12 | |||
13.3 | even | 3 | 8281.2.a.bz.1.3 | 6 | |||
13.9 | even | 3 | inner | 637.2.f.k.295.4 | 12 | ||
13.10 | even | 6 | 8281.2.a.ce.1.4 | 6 | |||
21.2 | odd | 6 | 819.2.n.d.172.3 | 12 | |||
21.11 | odd | 6 | 819.2.s.d.289.4 | 12 | |||
91.9 | even | 3 | 91.2.h.b.74.3 | yes | 12 | ||
91.16 | even | 3 | 1183.2.e.h.508.4 | 12 | |||
91.23 | even | 6 | 1183.2.e.g.508.3 | 12 | |||
91.48 | odd | 6 | 637.2.f.j.295.4 | 12 | |||
91.55 | odd | 6 | 8281.2.a.ca.1.3 | 6 | |||
91.61 | odd | 6 | 637.2.h.l.165.3 | 12 | |||
91.62 | odd | 6 | 8281.2.a.cf.1.4 | 6 | |||
91.74 | even | 3 | 91.2.g.b.9.4 | ✓ | 12 | ||
91.81 | even | 3 | 1183.2.e.h.170.4 | 12 | |||
91.87 | odd | 6 | 637.2.g.l.373.4 | 12 | |||
91.88 | even | 6 | 1183.2.e.g.170.3 | 12 | |||
273.74 | odd | 6 | 819.2.n.d.100.3 | 12 | |||
273.191 | odd | 6 | 819.2.s.d.802.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.4 | ✓ | 12 | 91.74 | even | 3 | ||
91.2.g.b.81.4 | yes | 12 | 7.2 | even | 3 | ||
91.2.h.b.16.3 | yes | 12 | 7.4 | even | 3 | ||
91.2.h.b.74.3 | yes | 12 | 91.9 | even | 3 | ||
637.2.f.j.295.4 | 12 | 91.48 | odd | 6 | |||
637.2.f.j.393.4 | 12 | 7.6 | odd | 2 | |||
637.2.f.k.295.4 | 12 | 13.9 | even | 3 | inner | ||
637.2.f.k.393.4 | 12 | 1.1 | even | 1 | trivial | ||
637.2.g.l.263.4 | 12 | 7.5 | odd | 6 | |||
637.2.g.l.373.4 | 12 | 91.87 | odd | 6 | |||
637.2.h.l.165.3 | 12 | 91.61 | odd | 6 | |||
637.2.h.l.471.3 | 12 | 7.3 | odd | 6 | |||
819.2.n.d.100.3 | 12 | 273.74 | odd | 6 | |||
819.2.n.d.172.3 | 12 | 21.2 | odd | 6 | |||
819.2.s.d.289.4 | 12 | 21.11 | odd | 6 | |||
819.2.s.d.802.4 | 12 | 273.191 | odd | 6 | |||
1183.2.e.g.170.3 | 12 | 91.88 | even | 6 | |||
1183.2.e.g.508.3 | 12 | 91.23 | even | 6 | |||
1183.2.e.h.170.4 | 12 | 91.81 | even | 3 | |||
1183.2.e.h.508.4 | 12 | 91.16 | even | 3 | |||
8281.2.a.bz.1.3 | 6 | 13.3 | even | 3 | |||
8281.2.a.ca.1.3 | 6 | 91.55 | odd | 6 | |||
8281.2.a.ce.1.4 | 6 | 13.10 | even | 6 | |||
8281.2.a.cf.1.4 | 6 | 91.62 | odd | 6 |