Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.11 | ||
Root | \(0.131596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.c.419.10 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.131596i | 0.0930521i | 0.998917 | + | 0.0465261i | \(0.0148151\pi\) | ||||
−0.998917 | + | 0.0465261i | \(0.985185\pi\) | |||||||
\(3\) | − | 1.44045i | − | 0.831644i | −0.909446 | − | 0.415822i | \(-0.863494\pi\) | ||
0.909446 | − | 0.415822i | \(-0.136506\pi\) | |||||||
\(4\) | 1.98268 | 0.991341 | ||||||||
\(5\) | −2.22416 | + | 0.230433i | −0.994676 | + | 0.103053i | ||||
\(6\) | 0.189557 | 0.0773863 | ||||||||
\(7\) | 0.456875i | 0.172683i | 0.996266 | + | 0.0863413i | \(0.0275175\pi\) | ||||
−0.996266 | + | 0.0863413i | \(0.972482\pi\) | |||||||
\(8\) | 0.524103i | 0.185299i | ||||||||
\(9\) | 0.925103 | 0.308368 | ||||||||
\(10\) | −0.0303239 | − | 0.292690i | −0.00958927 | − | 0.0925567i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 2.85596i | − | 0.824443i | ||||||
\(13\) | 5.24500i | 1.45470i | 0.686266 | + | 0.727351i | \(0.259249\pi\) | ||||
−0.686266 | + | 0.727351i | \(0.740751\pi\) | |||||||
\(14\) | −0.0601227 | −0.0160685 | ||||||||
\(15\) | 0.331927 | + | 3.20380i | 0.0857032 | + | 0.827217i | ||||
\(16\) | 3.89640 | 0.974099 | ||||||||
\(17\) | 6.95508i | 1.68685i | 0.537243 | + | 0.843427i | \(0.319466\pi\) | ||||
−0.537243 | + | 0.843427i | \(0.680534\pi\) | |||||||
\(18\) | 0.121739i | 0.0286943i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.40981 | + | 0.456875i | −0.986063 | + | 0.102160i | ||||
\(21\) | 0.658106 | 0.143610 | ||||||||
\(22\) | 0.131596i | 0.0280563i | ||||||||
\(23\) | − | 3.13721i | − | 0.654154i | −0.944998 | − | 0.327077i | \(-0.893936\pi\) | ||
0.944998 | − | 0.327077i | \(-0.106064\pi\) | |||||||
\(24\) | 0.754945 | 0.154102 | ||||||||
\(25\) | 4.89380 | − | 1.02504i | 0.978760 | − | 0.205008i | ||||
\(26\) | −0.690219 | −0.135363 | ||||||||
\(27\) | − | 5.65392i | − | 1.08810i | ||||||
\(28\) | 0.905838i | 0.171187i | ||||||||
\(29\) | 4.35289 | 0.808312 | 0.404156 | − | 0.914690i | \(-0.367565\pi\) | ||||
0.404156 | + | 0.914690i | \(0.367565\pi\) | |||||||
\(30\) | −0.421605 | + | 0.0436801i | −0.0769743 | + | 0.00797486i | ||||
\(31\) | 2.59338 | 0.465785 | 0.232892 | − | 0.972502i | \(-0.425181\pi\) | ||||
0.232892 | + | 0.972502i | \(0.425181\pi\) | |||||||
\(32\) | 1.56096i | 0.275941i | ||||||||
\(33\) | − | 1.44045i | − | 0.250750i | ||||||
\(34\) | −0.915258 | −0.156965 | ||||||||
\(35\) | −0.105279 | − | 1.01616i | −0.0177954 | − | 0.171763i | ||||
\(36\) | 1.83419 | 0.305698 | ||||||||
\(37\) | 0.922846i | 0.151715i | 0.997119 | + | 0.0758575i | \(0.0241694\pi\) | ||||
−0.997119 | + | 0.0758575i | \(0.975831\pi\) | |||||||
\(38\) | 0.131596i | 0.0213476i | ||||||||
\(39\) | 7.55516 | 1.20979 | ||||||||
\(40\) | −0.120771 | − | 1.16569i | −0.0190955 | − | 0.184312i | ||||
\(41\) | −3.30790 | −0.516607 | −0.258304 | − | 0.966064i | \(-0.583164\pi\) | ||||
−0.258304 | + | 0.966064i | \(0.583164\pi\) | |||||||
\(42\) | 0.0866038i | 0.0133633i | ||||||||
\(43\) | − | 0.870374i | − | 0.132731i | −0.997795 | − | 0.0663654i | \(-0.978860\pi\) | ||
0.997795 | − | 0.0663654i | \(-0.0211403\pi\) | |||||||
\(44\) | 1.98268 | 0.298901 | ||||||||
\(45\) | −2.05758 | + | 0.213174i | −0.306726 | + | 0.0317781i | ||||
\(46\) | 0.412843 | 0.0608704 | ||||||||
\(47\) | − | 10.3842i | − | 1.51469i | −0.653014 | − | 0.757346i | \(-0.726496\pi\) | ||
0.653014 | − | 0.757346i | \(-0.273504\pi\) | |||||||
\(48\) | − | 5.61256i | − | 0.810104i | ||||||
\(49\) | 6.79127 | 0.970181 | ||||||||
\(50\) | 0.134891 | + | 0.644003i | 0.0190764 | + | 0.0910757i | ||||
\(51\) | 10.0184 | 1.40286 | ||||||||
\(52\) | 10.3992i | 1.44211i | ||||||||
\(53\) | 8.75191i | 1.20217i | 0.799186 | + | 0.601084i | \(0.205264\pi\) | ||||
−0.799186 | + | 0.601084i | \(0.794736\pi\) | |||||||
\(54\) | 0.744030 | 0.101250 | ||||||||
\(55\) | −2.22416 | + | 0.230433i | −0.299906 | + | 0.0310716i | ||||
\(56\) | −0.239450 | −0.0319978 | ||||||||
\(57\) | − | 1.44045i | − | 0.190792i | ||||||
\(58\) | 0.572821i | 0.0752151i | ||||||||
\(59\) | −13.2528 | −1.72537 | −0.862686 | − | 0.505739i | \(-0.831220\pi\) | ||||
−0.862686 | + | 0.505739i | \(0.831220\pi\) | |||||||
\(60\) | 0.658106 | + | 6.35211i | 0.0849611 | + | 0.820054i | ||||
\(61\) | 3.21550 | 0.411702 | 0.205851 | − | 0.978583i | \(-0.434004\pi\) | ||||
0.205851 | + | 0.978583i | \(0.434004\pi\) | |||||||
\(62\) | 0.341277i | 0.0433423i | ||||||||
\(63\) | 0.422657i | 0.0532497i | ||||||||
\(64\) | 7.58738 | 0.948422 | ||||||||
\(65\) | −1.20862 | − | 11.6657i | −0.149911 | − | 1.44696i | ||||
\(66\) | 0.189557 | 0.0233328 | ||||||||
\(67\) | − | 1.23632i | − | 0.151040i | −0.997144 | − | 0.0755202i | \(-0.975938\pi\) | ||
0.997144 | − | 0.0755202i | \(-0.0240617\pi\) | |||||||
\(68\) | 13.7897i | 1.67225i | ||||||||
\(69\) | −4.51900 | −0.544024 | ||||||||
\(70\) | 0.133723 | − | 0.0138543i | 0.0159829 | − | 0.00165590i | ||||
\(71\) | 8.08829 | 0.959903 | 0.479951 | − | 0.877295i | \(-0.340654\pi\) | ||||
0.479951 | + | 0.877295i | \(0.340654\pi\) | |||||||
\(72\) | 0.484850i | 0.0571401i | ||||||||
\(73\) | 2.75185i | 0.322079i | 0.986948 | + | 0.161040i | \(0.0514847\pi\) | ||||
−0.986948 | + | 0.161040i | \(0.948515\pi\) | |||||||
\(74\) | −0.121442 | −0.0141174 | ||||||||
\(75\) | −1.47652 | − | 7.04928i | −0.170494 | − | 0.813980i | ||||
\(76\) | 1.98268 | 0.227429 | ||||||||
\(77\) | 0.456875i | 0.0520658i | ||||||||
\(78\) | 0.994226i | 0.112574i | ||||||||
\(79\) | −3.24490 | −0.365080 | −0.182540 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182540 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(80\) | −8.66622 | + | 0.897857i | −0.968913 | + | 0.100384i | ||||
\(81\) | −5.36888 | −0.596542 | ||||||||
\(82\) | − | 0.435305i | − | 0.0480714i | ||||||
\(83\) | − | 4.84685i | − | 0.532011i | −0.963972 | − | 0.266005i | \(-0.914296\pi\) | ||
0.963972 | − | 0.266005i | \(-0.0857039\pi\) | |||||||
\(84\) | 1.30482 | 0.142367 | ||||||||
\(85\) | −1.60268 | − | 15.4692i | −0.173835 | − | 1.67787i | ||||
\(86\) | 0.114537 | 0.0123509 | ||||||||
\(87\) | − | 6.27012i | − | 0.672228i | ||||||
\(88\) | 0.524103i | 0.0558696i | ||||||||
\(89\) | 5.97606 | 0.633461 | 0.316731 | − | 0.948516i | \(-0.397415\pi\) | ||||
0.316731 | + | 0.948516i | \(0.397415\pi\) | |||||||
\(90\) | −0.0280528 | − | 0.270768i | −0.00295702 | − | 0.0285415i | ||||
\(91\) | −2.39631 | −0.251202 | ||||||||
\(92\) | − | 6.22010i | − | 0.648490i | ||||||
\(93\) | − | 3.73564i | − | 0.387367i | ||||||
\(94\) | 1.36652 | 0.140945 | ||||||||
\(95\) | −2.22416 | + | 0.230433i | −0.228194 | + | 0.0236419i | ||||
\(96\) | 2.24848 | 0.229484 | ||||||||
\(97\) | − | 9.50533i | − | 0.965120i | −0.875863 | − | 0.482560i | \(-0.839707\pi\) | ||
0.875863 | − | 0.482560i | \(-0.160293\pi\) | |||||||
\(98\) | 0.893700i | 0.0902774i | ||||||||
\(99\) | 0.925103 | 0.0929763 | ||||||||
\(100\) | 9.70285 | − | 2.03233i | 0.970285 | − | 0.203233i | ||||
\(101\) | −4.04218 | −0.402212 | −0.201106 | − | 0.979570i | \(-0.564453\pi\) | ||||
−0.201106 | + | 0.979570i | \(0.564453\pi\) | |||||||
\(102\) | 1.31838i | 0.130539i | ||||||||
\(103\) | 5.05269i | 0.497856i | 0.968522 | + | 0.248928i | \(0.0800783\pi\) | ||||
−0.968522 | + | 0.248928i | \(0.919922\pi\) | |||||||
\(104\) | −2.74892 | −0.269554 | ||||||||
\(105\) | −1.46373 | + | 0.151649i | −0.142846 | + | 0.0147994i | ||||
\(106\) | −1.15171 | −0.111864 | ||||||||
\(107\) | − | 5.66293i | − | 0.547456i | −0.961807 | − | 0.273728i | \(-0.911743\pi\) | ||
0.961807 | − | 0.273728i | \(-0.0882568\pi\) | |||||||
\(108\) | − | 11.2099i | − | 1.07868i | ||||||
\(109\) | 8.25596 | 0.790778 | 0.395389 | − | 0.918514i | \(-0.370610\pi\) | ||||
0.395389 | + | 0.918514i | \(0.370610\pi\) | |||||||
\(110\) | −0.0303239 | − | 0.292690i | −0.00289127 | − | 0.0279069i | ||||
\(111\) | 1.32931 | 0.126173 | ||||||||
\(112\) | 1.78017i | 0.168210i | ||||||||
\(113\) | 16.4508i | 1.54757i | 0.633451 | + | 0.773783i | \(0.281638\pi\) | ||||
−0.633451 | + | 0.773783i | \(0.718362\pi\) | |||||||
\(114\) | 0.189557 | 0.0177536 | ||||||||
\(115\) | 0.722917 | + | 6.97767i | 0.0674124 | + | 0.650672i | ||||
\(116\) | 8.63040 | 0.801313 | ||||||||
\(117\) | 4.85217i | 0.448583i | ||||||||
\(118\) | − | 1.74402i | − | 0.160550i | ||||||
\(119\) | −3.17760 | −0.291290 | ||||||||
\(120\) | −1.67912 | + | 0.173964i | −0.153282 | + | 0.0158807i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.423145i | 0.0383098i | ||||||||
\(123\) | 4.76487i | 0.429634i | ||||||||
\(124\) | 5.14185 | 0.461752 | ||||||||
\(125\) | −10.6484 | + | 3.40755i | −0.952423 | + | 0.304780i | ||||
\(126\) | −0.0556197 | −0.00495500 | ||||||||
\(127\) | 9.13274i | 0.810399i | 0.914228 | + | 0.405200i | \(0.132798\pi\) | ||||
−0.914228 | + | 0.405200i | \(0.867202\pi\) | |||||||
\(128\) | 4.12038i | 0.364193i | ||||||||
\(129\) | −1.25373 | −0.110385 | ||||||||
\(130\) | 1.53516 | − | 0.159049i | 0.134642 | − | 0.0139495i | ||||
\(131\) | −22.0116 | −1.92316 | −0.961580 | − | 0.274525i | \(-0.911480\pi\) | ||||
−0.961580 | + | 0.274525i | \(0.911480\pi\) | |||||||
\(132\) | − | 2.85596i | − | 0.248579i | ||||||
\(133\) | 0.456875i | 0.0396161i | ||||||||
\(134\) | 0.162694 | 0.0140546 | ||||||||
\(135\) | 1.30285 | + | 12.5752i | 0.112131 | + | 1.08230i | ||||
\(136\) | −3.64518 | −0.312572 | ||||||||
\(137\) | − | 10.1936i | − | 0.870897i | −0.900214 | − | 0.435448i | \(-0.856590\pi\) | ||
0.900214 | − | 0.435448i | \(-0.143410\pi\) | |||||||
\(138\) | − | 0.594680i | − | 0.0506226i | ||||||
\(139\) | 14.7543 | 1.25144 | 0.625720 | − | 0.780048i | \(-0.284805\pi\) | ||||
0.625720 | + | 0.780048i | \(0.284805\pi\) | |||||||
\(140\) | −0.208735 | − | 2.01473i | −0.0176413 | − | 0.170276i | ||||
\(141\) | −14.9579 | −1.25968 | ||||||||
\(142\) | 1.06438i | 0.0893210i | ||||||||
\(143\) | 5.24500i | 0.438609i | ||||||||
\(144\) | 3.60457 | 0.300381 | ||||||||
\(145\) | −9.68154 | + | 1.00305i | −0.804008 | + | 0.0832987i | ||||
\(146\) | −0.362131 | −0.0299702 | ||||||||
\(147\) | − | 9.78248i | − | 0.806845i | ||||||
\(148\) | 1.82971i | 0.150401i | ||||||||
\(149\) | 16.9982 | 1.39255 | 0.696275 | − | 0.717775i | \(-0.254839\pi\) | ||||
0.696275 | + | 0.717775i | \(0.254839\pi\) | |||||||
\(150\) | 0.927654 | − | 0.194303i | 0.0757426 | − | 0.0158648i | ||||
\(151\) | −16.2869 | −1.32541 | −0.662703 | − | 0.748882i | \(-0.730591\pi\) | ||||
−0.662703 | + | 0.748882i | \(0.730591\pi\) | |||||||
\(152\) | 0.524103i | 0.0425104i | ||||||||
\(153\) | 6.43417i | 0.520171i | ||||||||
\(154\) | −0.0601227 | −0.00484483 | ||||||||
\(155\) | −5.76810 | + | 0.597600i | −0.463305 | + | 0.0480004i | ||||
\(156\) | 14.9795 | 1.19932 | ||||||||
\(157\) | 18.8960i | 1.50807i | 0.656835 | + | 0.754034i | \(0.271895\pi\) | ||||
−0.656835 | + | 0.754034i | \(0.728105\pi\) | |||||||
\(158\) | − | 0.427015i | − | 0.0339715i | ||||||
\(159\) | 12.6067 | 0.999776 | ||||||||
\(160\) | −0.359695 | − | 3.47182i | −0.0284364 | − | 0.274471i | ||||
\(161\) | 1.43331 | 0.112961 | ||||||||
\(162\) | − | 0.706520i | − | 0.0555095i | ||||||
\(163\) | − | 0.640614i | − | 0.0501768i | −0.999685 | − | 0.0250884i | \(-0.992013\pi\) | ||
0.999685 | − | 0.0250884i | \(-0.00798672\pi\) | |||||||
\(164\) | −6.55852 | −0.512134 | ||||||||
\(165\) | 0.331927 | + | 3.20380i | 0.0258405 | + | 0.249415i | ||||
\(166\) | 0.637824 | 0.0495047 | ||||||||
\(167\) | − | 8.05621i | − | 0.623408i | −0.950179 | − | 0.311704i | \(-0.899100\pi\) | ||
0.950179 | − | 0.311704i | \(-0.100900\pi\) | |||||||
\(168\) | 0.344916i | 0.0266108i | ||||||||
\(169\) | −14.5100 | −1.11616 | ||||||||
\(170\) | 2.03568 | − | 0.210905i | 0.156130 | − | 0.0161757i | ||||
\(171\) | 0.925103 | 0.0707444 | ||||||||
\(172\) | − | 1.72567i | − | 0.131581i | ||||||
\(173\) | 16.5942i | 1.26163i | 0.775933 | + | 0.630815i | \(0.217279\pi\) | ||||
−0.775933 | + | 0.630815i | \(0.782721\pi\) | |||||||
\(174\) | 0.825121 | 0.0625522 | ||||||||
\(175\) | 0.468315 | + | 2.23586i | 0.0354013 | + | 0.169015i | ||||
\(176\) | 3.89640 | 0.293702 | ||||||||
\(177\) | 19.0901i | 1.43490i | ||||||||
\(178\) | 0.786423i | 0.0589449i | ||||||||
\(179\) | −17.6845 | −1.32180 | −0.660902 | − | 0.750472i | \(-0.729826\pi\) | ||||
−0.660902 | + | 0.750472i | \(0.729826\pi\) | |||||||
\(180\) | −4.07953 | + | 0.422657i | −0.304070 | + | 0.0315030i | ||||
\(181\) | 0.536073 | 0.0398460 | 0.0199230 | − | 0.999802i | \(-0.493658\pi\) | ||||
0.0199230 | + | 0.999802i | \(0.493658\pi\) | |||||||
\(182\) | − | 0.315344i | − | 0.0233748i | ||||||
\(183\) | − | 4.63176i | − | 0.342390i | ||||||
\(184\) | 1.64422 | 0.121214 | ||||||||
\(185\) | −0.212654 | − | 2.05256i | −0.0156346 | − | 0.150907i | ||||
\(186\) | 0.491593 | 0.0360454 | ||||||||
\(187\) | 6.95508i | 0.508606i | ||||||||
\(188\) | − | 20.5886i | − | 1.50158i | ||||||
\(189\) | 2.58313 | 0.187895 | ||||||||
\(190\) | −0.0303239 | − | 0.292690i | −0.00219993 | − | 0.0212340i | ||||
\(191\) | −11.5909 | −0.838686 | −0.419343 | − | 0.907828i | \(-0.637739\pi\) | ||||
−0.419343 | + | 0.907828i | \(0.637739\pi\) | |||||||
\(192\) | − | 10.9292i | − | 0.788750i | ||||||
\(193\) | − | 16.7746i | − | 1.20746i | −0.797189 | − | 0.603730i | \(-0.793681\pi\) | ||
0.797189 | − | 0.603730i | \(-0.206319\pi\) | |||||||
\(194\) | 1.25086 | 0.0898065 | ||||||||
\(195\) | −16.8039 | + | 1.74096i | −1.20335 | + | 0.124673i | ||||
\(196\) | 13.4649 | 0.961780 | ||||||||
\(197\) | − | 19.4422i | − | 1.38520i | −0.721323 | − | 0.692599i | \(-0.756465\pi\) | ||
0.721323 | − | 0.692599i | \(-0.243535\pi\) | |||||||
\(198\) | 0.121739i | 0.00865165i | ||||||||
\(199\) | 16.5303 | 1.17180 | 0.585901 | − | 0.810383i | \(-0.300741\pi\) | ||||
0.585901 | + | 0.810383i | \(0.300741\pi\) | |||||||
\(200\) | 0.537227 | + | 2.56486i | 0.0379877 | + | 0.181363i | ||||
\(201\) | −1.78086 | −0.125612 | ||||||||
\(202\) | − | 0.531933i | − | 0.0374266i | ||||||
\(203\) | 1.98873i | 0.139581i | ||||||||
\(204\) | 19.8634 | 1.39072 | ||||||||
\(205\) | 7.35731 | − | 0.762249i | 0.513857 | − | 0.0532378i | ||||
\(206\) | −0.664911 | −0.0463266 | ||||||||
\(207\) | − | 2.90225i | − | 0.201720i | ||||||
\(208\) | 20.4366i | 1.41702i | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | −0.0199564 | − | 0.192621i | −0.00137712 | − | 0.0132921i | ||||
\(211\) | −10.7883 | −0.742695 | −0.371348 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371348 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(212\) | 17.3523i | 1.19176i | ||||||||
\(213\) | − | 11.6508i | − | 0.798298i | ||||||
\(214\) | 0.745217 | 0.0509420 | ||||||||
\(215\) | 0.200563 | + | 1.93585i | 0.0136783 | + | 0.132024i | ||||
\(216\) | 2.96324 | 0.201623 | ||||||||
\(217\) | 1.18485i | 0.0804329i | ||||||||
\(218\) | 1.08645i | 0.0735836i | ||||||||
\(219\) | 3.96390 | 0.267855 | ||||||||
\(220\) | −4.40981 | + | 0.456875i | −0.297309 | + | 0.0308025i | ||||
\(221\) | −36.4794 | −2.45387 | ||||||||
\(222\) | 0.174932i | 0.0117407i | ||||||||
\(223\) | − | 17.3295i | − | 1.16047i | −0.814450 | − | 0.580233i | \(-0.802961\pi\) | ||
0.814450 | − | 0.580233i | \(-0.197039\pi\) | |||||||
\(224\) | −0.713162 | −0.0476501 | ||||||||
\(225\) | 4.52727 | − | 0.948268i | 0.301818 | − | 0.0632178i | ||||
\(226\) | −2.16486 | −0.144004 | ||||||||
\(227\) | 8.11839i | 0.538836i | 0.963023 | + | 0.269418i | \(0.0868314\pi\) | ||||
−0.963023 | + | 0.269418i | \(0.913169\pi\) | |||||||
\(228\) | − | 2.85596i | − | 0.189140i | ||||||
\(229\) | 0.532942 | 0.0352178 | 0.0176089 | − | 0.999845i | \(-0.494395\pi\) | ||||
0.0176089 | + | 0.999845i | \(0.494395\pi\) | |||||||
\(230\) | −0.918231 | + | 0.0951327i | −0.0605464 | + | 0.00627286i | ||||
\(231\) | 0.658106 | 0.0433002 | ||||||||
\(232\) | 2.28137i | 0.149779i | ||||||||
\(233\) | − | 14.4041i | − | 0.943646i | −0.881693 | − | 0.471823i | \(-0.843596\pi\) | ||
0.881693 | − | 0.471823i | \(-0.156404\pi\) | |||||||
\(234\) | −0.638524 | −0.0417416 | ||||||||
\(235\) | 2.39286 | + | 23.0962i | 0.156093 | + | 1.50663i | ||||
\(236\) | −26.2762 | −1.71043 | ||||||||
\(237\) | 4.67412i | 0.303617i | ||||||||
\(238\) | − | 0.418159i | − | 0.0271052i | ||||||
\(239\) | −15.5773 | −1.00761 | −0.503804 | − | 0.863818i | \(-0.668067\pi\) | ||||
−0.503804 | + | 0.863818i | \(0.668067\pi\) | |||||||
\(240\) | 1.29332 | + | 12.4833i | 0.0834834 | + | 0.805791i | ||||
\(241\) | −19.4978 | −1.25596 | −0.627980 | − | 0.778229i | \(-0.716118\pi\) | ||||
−0.627980 | + | 0.778229i | \(0.716118\pi\) | |||||||
\(242\) | 0.131596i | 0.00845928i | ||||||||
\(243\) | − | 9.22815i | − | 0.591986i | ||||||
\(244\) | 6.37531 | 0.408137 | ||||||||
\(245\) | −15.1049 | + | 1.56493i | −0.965015 | + | 0.0999797i | ||||
\(246\) | −0.627035 | −0.0399783 | ||||||||
\(247\) | 5.24500i | 0.333731i | ||||||||
\(248\) | 1.35920i | 0.0863093i | ||||||||
\(249\) | −6.98165 | −0.442444 | ||||||||
\(250\) | −0.448418 | − | 1.40128i | −0.0283605 | − | 0.0886250i | ||||
\(251\) | −17.8989 | −1.12977 | −0.564883 | − | 0.825171i | \(-0.691079\pi\) | ||||
−0.564883 | + | 0.825171i | \(0.691079\pi\) | |||||||
\(252\) | 0.837994i | 0.0527886i | ||||||||
\(253\) | − | 3.13721i | − | 0.197235i | ||||||
\(254\) | −1.20183 | −0.0754094 | ||||||||
\(255\) | −22.2827 | + | 2.30858i | −1.39539 | + | 0.144569i | ||||
\(256\) | 14.6325 | 0.914533 | ||||||||
\(257\) | − | 7.87295i | − | 0.491101i | −0.969384 | − | 0.245551i | \(-0.921031\pi\) | ||
0.969384 | − | 0.245551i | \(-0.0789688\pi\) | |||||||
\(258\) | − | 0.164985i | − | 0.0102715i | ||||||
\(259\) | −0.421625 | −0.0261985 | ||||||||
\(260\) | −2.39631 | − | 23.1295i | −0.148613 | − | 1.43443i | ||||
\(261\) | 4.02687 | 0.249257 | ||||||||
\(262\) | − | 2.89663i | − | 0.178954i | ||||||
\(263\) | − | 10.0759i | − | 0.621308i | −0.950523 | − | 0.310654i | \(-0.899452\pi\) | ||
0.950523 | − | 0.310654i | \(-0.100548\pi\) | |||||||
\(264\) | 0.754945 | 0.0464636 | ||||||||
\(265\) | −2.01673 | − | 19.4657i | −0.123887 | − | 1.19577i | ||||
\(266\) | −0.0601227 | −0.00368636 | ||||||||
\(267\) | − | 8.60822i | − | 0.526814i | ||||||
\(268\) | − | 2.45123i | − | 0.149733i | ||||||
\(269\) | −12.7561 | −0.777751 | −0.388876 | − | 0.921290i | \(-0.627136\pi\) | ||||
−0.388876 | + | 0.921290i | \(0.627136\pi\) | |||||||
\(270\) | −1.65484 | + | 0.171449i | −0.100711 | + | 0.0104341i | ||||
\(271\) | −7.76932 | −0.471953 | −0.235976 | − | 0.971759i | \(-0.575829\pi\) | ||||
−0.235976 | + | 0.971759i | \(0.575829\pi\) | |||||||
\(272\) | 27.0997i | 1.64316i | ||||||||
\(273\) | 3.45177i | 0.208910i | ||||||||
\(274\) | 1.34143 | 0.0810388 | ||||||||
\(275\) | 4.89380 | − | 1.02504i | 0.295107 | − | 0.0618123i | ||||
\(276\) | −8.95974 | −0.539313 | ||||||||
\(277\) | 25.3910i | 1.52559i | 0.646638 | + | 0.762797i | \(0.276175\pi\) | ||||
−0.646638 | + | 0.762797i | \(0.723825\pi\) | |||||||
\(278\) | 1.94159i | 0.116449i | ||||||||
\(279\) | 2.39914 | 0.143633 | ||||||||
\(280\) | 0.532575 | − | 0.0551771i | 0.0318275 | − | 0.00329746i | ||||
\(281\) | 10.4799 | 0.625181 | 0.312590 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312590 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(282\) | − | 1.96840i | − | 0.117216i | ||||||
\(283\) | − | 31.6855i | − | 1.88350i | −0.336307 | − | 0.941752i | \(-0.609178\pi\) | ||
0.336307 | − | 0.941752i | \(-0.390822\pi\) | |||||||
\(284\) | 16.0365 | 0.951591 | ||||||||
\(285\) | 0.331927 | + | 3.20380i | 0.0196617 | + | 0.189777i | ||||
\(286\) | −0.690219 | −0.0408135 | ||||||||
\(287\) | − | 1.51130i | − | 0.0892091i | ||||||
\(288\) | 1.44404i | 0.0850911i | ||||||||
\(289\) | −31.3731 | −1.84548 | ||||||||
\(290\) | −0.131997 | − | 1.27405i | −0.00775112 | − | 0.0748147i | ||||
\(291\) | −13.6920 | −0.802636 | ||||||||
\(292\) | 5.45604i | 0.319291i | ||||||||
\(293\) | 15.0863i | 0.881352i | 0.897666 | + | 0.440676i | \(0.145261\pi\) | ||||
−0.897666 | + | 0.440676i | \(0.854739\pi\) | |||||||
\(294\) | 1.28733 | 0.0750787 | ||||||||
\(295\) | 29.4765 | − | 3.05389i | 1.71619 | − | 0.177804i | ||||
\(296\) | −0.483667 | −0.0281126 | ||||||||
\(297\) | − | 5.65392i | − | 0.328073i | ||||||
\(298\) | 2.23689i | 0.129580i | ||||||||
\(299\) | 16.4547 | 0.951599 | ||||||||
\(300\) | −2.92747 | − | 13.9765i | −0.169018 | − | 0.806932i | ||||
\(301\) | 0.397652 | 0.0229203 | ||||||||
\(302\) | − | 2.14328i | − | 0.123332i | ||||||
\(303\) | 5.82255i | 0.334497i | ||||||||
\(304\) | 3.89640 | 0.223474 | ||||||||
\(305\) | −7.15179 | + | 0.740956i | −0.409510 | + | 0.0424270i | ||||
\(306\) | −0.846708 | −0.0484031 | ||||||||
\(307\) | 8.63283i | 0.492702i | 0.969181 | + | 0.246351i | \(0.0792315\pi\) | ||||
−0.969181 | + | 0.246351i | \(0.920768\pi\) | |||||||
\(308\) | 0.905838i | 0.0516149i | ||||||||
\(309\) | 7.27814 | 0.414039 | ||||||||
\(310\) | −0.0786415 | − | 0.759057i | −0.00446654 | − | 0.0431115i | ||||
\(311\) | −0.0886279 | −0.00502562 | −0.00251281 | − | 0.999997i | \(-0.500800\pi\) | ||||
−0.00251281 | + | 0.999997i | \(0.500800\pi\) | |||||||
\(312\) | 3.95969i | 0.224173i | ||||||||
\(313\) | − | 4.80502i | − | 0.271596i | −0.990737 | − | 0.135798i | \(-0.956640\pi\) | ||
0.990737 | − | 0.135798i | \(-0.0433598\pi\) | |||||||
\(314\) | −2.48664 | −0.140329 | ||||||||
\(315\) | −0.0973939 | − | 0.940057i | −0.00548753 | − | 0.0529662i | ||||
\(316\) | −6.43361 | −0.361919 | ||||||||
\(317\) | − | 11.4320i | − | 0.642083i | −0.947065 | − | 0.321042i | \(-0.895967\pi\) | ||
0.947065 | − | 0.321042i | \(-0.104033\pi\) | |||||||
\(318\) | 1.65899i | 0.0930313i | ||||||||
\(319\) | 4.35289 | 0.243715 | ||||||||
\(320\) | −16.8756 | + | 1.74838i | −0.943373 | + | 0.0977374i | ||||
\(321\) | −8.15717 | −0.455289 | ||||||||
\(322\) | 0.188618i | 0.0105113i | ||||||||
\(323\) | 6.95508i | 0.386991i | ||||||||
\(324\) | −10.6448 | −0.591376 | ||||||||
\(325\) | 5.37634 | + | 25.6680i | 0.298226 | + | 1.42380i | ||||
\(326\) | 0.0843020 | 0.00466906 | ||||||||
\(327\) | − | 11.8923i | − | 0.657646i | ||||||
\(328\) | − | 1.73368i | − | 0.0957266i | ||||||
\(329\) | 4.74428 | 0.261561 | ||||||||
\(330\) | −0.421605 | + | 0.0436801i | −0.0232086 | + | 0.00240451i | ||||
\(331\) | −14.2878 | −0.785331 | −0.392665 | − | 0.919681i | \(-0.628447\pi\) | ||||
−0.392665 | + | 0.919681i | \(0.628447\pi\) | |||||||
\(332\) | − | 9.60976i | − | 0.527404i | ||||||
\(333\) | 0.853728i | 0.0467840i | ||||||||
\(334\) | 1.06016 | 0.0580095 | ||||||||
\(335\) | 0.284888 | + | 2.74977i | 0.0155651 | + | 0.150236i | ||||
\(336\) | 2.56424 | 0.139891 | ||||||||
\(337\) | − | 20.8355i | − | 1.13498i | −0.823380 | − | 0.567490i | \(-0.807915\pi\) | ||
0.823380 | − | 0.567490i | \(-0.192085\pi\) | |||||||
\(338\) | − | 1.90946i | − | 0.103861i | ||||||
\(339\) | 23.6966 | 1.28702 | ||||||||
\(340\) | −3.17760 | − | 30.6706i | −0.172330 | − | 1.66335i | ||||
\(341\) | 2.59338 | 0.140439 | ||||||||
\(342\) | 0.121739i | 0.00658292i | ||||||||
\(343\) | 6.30089i | 0.340216i | ||||||||
\(344\) | 0.456166 | 0.0245948 | ||||||||
\(345\) | 10.0510 | − | 1.04133i | 0.541127 | − | 0.0560631i | ||||
\(346\) | −2.18372 | −0.117397 | ||||||||
\(347\) | 4.98017i | 0.267350i | 0.991025 | + | 0.133675i | \(0.0426778\pi\) | ||||
−0.991025 | + | 0.133675i | \(0.957322\pi\) | |||||||
\(348\) | − | 12.4317i | − | 0.666407i | ||||||
\(349\) | −8.50465 | −0.455244 | −0.227622 | − | 0.973750i | \(-0.573095\pi\) | ||||
−0.227622 | + | 0.973750i | \(0.573095\pi\) | |||||||
\(350\) | −0.294229 | + | 0.0616282i | −0.0157272 | + | 0.00329417i | ||||
\(351\) | 29.6548 | 1.58286 | ||||||||
\(352\) | 1.56096i | 0.0831992i | ||||||||
\(353\) | − | 34.6465i | − | 1.84405i | −0.387135 | − | 0.922023i | \(-0.626535\pi\) | ||
0.387135 | − | 0.922023i | \(-0.373465\pi\) | |||||||
\(354\) | −2.51217 | −0.133520 | ||||||||
\(355\) | −17.9897 | + | 1.86381i | −0.954792 | + | 0.0989206i | ||||
\(356\) | 11.8486 | 0.627976 | ||||||||
\(357\) | 4.57718i | 0.242250i | ||||||||
\(358\) | − | 2.32721i | − | 0.122997i | ||||||
\(359\) | 22.4347 | 1.18406 | 0.592030 | − | 0.805916i | \(-0.298327\pi\) | ||||
0.592030 | + | 0.805916i | \(0.298327\pi\) | |||||||
\(360\) | −0.111725 | − | 1.07838i | −0.00588844 | − | 0.0568359i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.0705448i | 0.00370775i | ||||||||
\(363\) | − | 1.44045i | − | 0.0756040i | ||||||
\(364\) | −4.75112 | −0.249027 | ||||||||
\(365\) | −0.634116 | − | 6.12056i | −0.0331911 | − | 0.320365i | ||||
\(366\) | 0.609520 | 0.0318601 | ||||||||
\(367\) | − | 5.40720i | − | 0.282253i | −0.989992 | − | 0.141127i | \(-0.954927\pi\) | ||
0.989992 | − | 0.141127i | \(-0.0450725\pi\) | |||||||
\(368\) | − | 12.2238i | − | 0.637211i | ||||||
\(369\) | −3.06015 | −0.159305 | ||||||||
\(370\) | 0.270108 | − | 0.0279843i | 0.0140422 | − | 0.00145484i | ||||
\(371\) | −3.99853 | −0.207593 | ||||||||
\(372\) | − | 7.40658i | − | 0.384013i | ||||||
\(373\) | 21.4126i | 1.10870i | 0.832283 | + | 0.554351i | \(0.187034\pi\) | ||||
−0.832283 | + | 0.554351i | \(0.812966\pi\) | |||||||
\(374\) | −0.915258 | −0.0473269 | ||||||||
\(375\) | 4.90840 | + | 15.3385i | 0.253469 | + | 0.792077i | ||||
\(376\) | 5.44240 | 0.280670 | ||||||||
\(377\) | 22.8309i | 1.17585i | ||||||||
\(378\) | 0.339929i | 0.0174841i | ||||||||
\(379\) | −3.74465 | −0.192350 | −0.0961749 | − | 0.995364i | \(-0.530661\pi\) | ||||
−0.0961749 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(380\) | −4.40981 | + | 0.456875i | −0.226218 | + | 0.0234372i | ||||
\(381\) | 13.1553 | 0.673964 | ||||||||
\(382\) | − | 1.52531i | − | 0.0780415i | ||||||
\(383\) | 18.2790i | 0.934014i | 0.884254 | + | 0.467007i | \(0.154668\pi\) | ||||
−0.884254 | + | 0.467007i | \(0.845332\pi\) | |||||||
\(384\) | 5.93520 | 0.302879 | ||||||||
\(385\) | −0.105279 | − | 1.01616i | −0.00536552 | − | 0.0517885i | ||||
\(386\) | 2.20746 | 0.112357 | ||||||||
\(387\) | − | 0.805185i | − | 0.0409299i | ||||||
\(388\) | − | 18.8460i | − | 0.956763i | ||||||
\(389\) | 6.32254 | 0.320565 | 0.160283 | − | 0.987071i | \(-0.448759\pi\) | ||||
0.160283 | + | 0.987071i | \(0.448759\pi\) | |||||||
\(390\) | −0.229102 | − | 2.21132i | −0.0116010 | − | 0.111975i | ||||
\(391\) | 21.8196 | 1.10346 | ||||||||
\(392\) | 3.55933i | 0.179773i | ||||||||
\(393\) | 31.7066i | 1.59939i | ||||||||
\(394\) | 2.55851 | 0.128896 | ||||||||
\(395\) | 7.21719 | − | 0.747732i | 0.363136 | − | 0.0376225i | ||||
\(396\) | 1.83419 | 0.0921713 | ||||||||
\(397\) | − | 27.6346i | − | 1.38694i | −0.720485 | − | 0.693470i | \(-0.756081\pi\) | ||
0.720485 | − | 0.693470i | \(-0.243919\pi\) | |||||||
\(398\) | 2.17531i | 0.109039i | ||||||||
\(399\) | 0.658106 | 0.0329465 | ||||||||
\(400\) | 19.0682 | − | 3.99396i | 0.953409 | − | 0.199698i | ||||
\(401\) | −27.5885 | −1.37770 | −0.688851 | − | 0.724903i | \(-0.741885\pi\) | ||||
−0.688851 | + | 0.724903i | \(0.741885\pi\) | |||||||
\(402\) | − | 0.234353i | − | 0.0116885i | ||||||
\(403\) | 13.6023i | 0.677578i | ||||||||
\(404\) | −8.01435 | −0.398729 | ||||||||
\(405\) | 11.9413 | − | 1.23717i | 0.593366 | − | 0.0614752i | ||||
\(406\) | −0.261708 | −0.0129883 | ||||||||
\(407\) | 0.922846i | 0.0457438i | ||||||||
\(408\) | 5.25070i | 0.259949i | ||||||||
\(409\) | −22.5074 | −1.11292 | −0.556459 | − | 0.830875i | \(-0.687840\pi\) | ||||
−0.556459 | + | 0.830875i | \(0.687840\pi\) | |||||||
\(410\) | 0.100309 | + | 0.968190i | 0.00495389 | + | 0.0478155i | ||||
\(411\) | −14.6834 | −0.724277 | ||||||||
\(412\) | 10.0179i | 0.493545i | ||||||||
\(413\) | − | 6.05489i | − | 0.297942i | ||||||
\(414\) | 0.381923 | 0.0187705 | ||||||||
\(415\) | 1.11687 | + | 10.7802i | 0.0548251 | + | 0.529178i | ||||
\(416\) | −8.18721 | −0.401411 | ||||||||
\(417\) | − | 21.2528i | − | 1.04075i | ||||||
\(418\) | 0.131596i | 0.00643655i | ||||||||
\(419\) | 25.6597 | 1.25356 | 0.626779 | − | 0.779197i | \(-0.284373\pi\) | ||||
0.626779 | + | 0.779197i | \(0.284373\pi\) | |||||||
\(420\) | −2.90212 | + | 0.300672i | −0.141609 | + | 0.0146713i | ||||
\(421\) | −24.6504 | −1.20139 | −0.600693 | − | 0.799480i | \(-0.705108\pi\) | ||||
−0.600693 | + | 0.799480i | \(0.705108\pi\) | |||||||
\(422\) | − | 1.41969i | − | 0.0691094i | ||||||
\(423\) | − | 9.60646i | − | 0.467082i | ||||||
\(424\) | −4.58691 | −0.222760 | ||||||||
\(425\) | 7.12924 | + | 34.0368i | 0.345819 | + | 1.65103i | ||||
\(426\) | 1.53319 | 0.0742833 | ||||||||
\(427\) | 1.46908i | 0.0710938i | ||||||||
\(428\) | − | 11.2278i | − | 0.542716i | ||||||
\(429\) | 7.55516 | 0.364767 | ||||||||
\(430\) | −0.254750 | + | 0.0263932i | −0.0122851 | + | 0.00127279i | ||||
\(431\) | 24.6399 | 1.18686 | 0.593431 | − | 0.804885i | \(-0.297773\pi\) | ||||
0.593431 | + | 0.804885i | \(0.297773\pi\) | |||||||
\(432\) | − | 22.0299i | − | 1.05991i | ||||||
\(433\) | 27.2031i | 1.30730i | 0.756798 | + | 0.653649i | \(0.226763\pi\) | ||||
−0.756798 | + | 0.653649i | \(0.773237\pi\) | |||||||
\(434\) | −0.155921 | −0.00748446 | ||||||||
\(435\) | 1.44484 | + | 13.9458i | 0.0692749 | + | 0.668649i | ||||
\(436\) | 16.3690 | 0.783931 | ||||||||
\(437\) | − | 3.13721i | − | 0.150073i | ||||||
\(438\) | 0.521632i | 0.0249245i | ||||||||
\(439\) | 22.7258 | 1.08464 | 0.542321 | − | 0.840172i | \(-0.317546\pi\) | ||||
0.542321 | + | 0.840172i | \(0.317546\pi\) | |||||||
\(440\) | −0.120771 | − | 1.16569i | −0.00575751 | − | 0.0555722i | ||||
\(441\) | 6.28262 | 0.299172 | ||||||||
\(442\) | − | 4.80053i | − | 0.228338i | ||||||
\(443\) | − | 32.9667i | − | 1.56629i | −0.621837 | − | 0.783146i | \(-0.713614\pi\) | ||
0.621837 | − | 0.783146i | \(-0.286386\pi\) | |||||||
\(444\) | 2.63561 | 0.125080 | ||||||||
\(445\) | −13.2917 | + | 1.37708i | −0.630089 | + | 0.0652799i | ||||
\(446\) | 2.28048 | 0.107984 | ||||||||
\(447\) | − | 24.4851i | − | 1.15811i | ||||||
\(448\) | 3.46648i | 0.163776i | ||||||||
\(449\) | 30.3903 | 1.43421 | 0.717103 | − | 0.696967i | \(-0.245468\pi\) | ||||
0.717103 | + | 0.696967i | \(0.245468\pi\) | |||||||
\(450\) | 0.124788 | + | 0.595769i | 0.00588256 | + | 0.0280848i | ||||
\(451\) | −3.30790 | −0.155763 | ||||||||
\(452\) | 32.6168i | 1.53417i | ||||||||
\(453\) | 23.4604i | 1.10227i | ||||||||
\(454\) | −1.06834 | −0.0501399 | ||||||||
\(455\) | 5.32978 | − | 0.552189i | 0.249864 | − | 0.0258870i | ||||
\(456\) | 0.754945 | 0.0353535 | ||||||||
\(457\) | − | 18.0322i | − | 0.843509i | −0.906710 | − | 0.421755i | \(-0.861414\pi\) | ||
0.906710 | − | 0.421755i | \(-0.138586\pi\) | |||||||
\(458\) | 0.0701328i | 0.00327709i | ||||||||
\(459\) | 39.3234 | 1.83546 | ||||||||
\(460\) | 1.43331 | + | 13.8345i | 0.0668287 | + | 0.645038i | ||||
\(461\) | 14.1522 | 0.659135 | 0.329568 | − | 0.944132i | \(-0.393097\pi\) | ||||
0.329568 | + | 0.944132i | \(0.393097\pi\) | |||||||
\(462\) | 0.0866038i | 0.00402917i | ||||||||
\(463\) | − | 7.97479i | − | 0.370620i | −0.982680 | − | 0.185310i | \(-0.940671\pi\) | ||
0.982680 | − | 0.185310i | \(-0.0593289\pi\) | |||||||
\(464\) | 16.9606 | 0.787375 | ||||||||
\(465\) | 0.860813 | + | 8.30866i | 0.0399193 | + | 0.385305i | ||||
\(466\) | 1.89552 | 0.0878083 | ||||||||
\(467\) | 18.6954i | 0.865121i | 0.901605 | + | 0.432561i | \(0.142390\pi\) | ||||
−0.901605 | + | 0.432561i | \(0.857610\pi\) | |||||||
\(468\) | 9.62030i | 0.444699i | ||||||||
\(469\) | 0.564843 | 0.0260820 | ||||||||
\(470\) | −3.03935 | + | 0.314890i | −0.140195 | + | 0.0145248i | ||||
\(471\) | 27.2188 | 1.25418 | ||||||||
\(472\) | − | 6.94586i | − | 0.319709i | ||||||
\(473\) | − | 0.870374i | − | 0.0400198i | ||||||
\(474\) | −0.615094 | −0.0282522 | ||||||||
\(475\) | 4.89380 | − | 1.02504i | 0.224543 | − | 0.0470321i | ||||
\(476\) | −6.30018 | −0.288768 | ||||||||
\(477\) | 8.09642i | 0.370710i | ||||||||
\(478\) | − | 2.04990i | − | 0.0937601i | ||||||
\(479\) | 19.3936 | 0.886115 | 0.443057 | − | 0.896493i | \(-0.353894\pi\) | ||||
0.443057 | + | 0.896493i | \(0.353894\pi\) | |||||||
\(480\) | −5.00098 | + | 0.518123i | −0.228263 | + | 0.0236490i | ||||
\(481\) | −4.84033 | −0.220700 | ||||||||
\(482\) | − | 2.56582i | − | 0.116870i | ||||||
\(483\) | − | 2.06462i | − | 0.0939434i | ||||||
\(484\) | 1.98268 | 0.0901219 | ||||||||
\(485\) | 2.19034 | + | 21.1414i | 0.0994582 | + | 0.959981i | ||||
\(486\) | 1.21438 | 0.0550856 | ||||||||
\(487\) | − | 24.0327i | − | 1.08903i | −0.838753 | − | 0.544513i | \(-0.816715\pi\) | ||
0.838753 | − | 0.544513i | \(-0.183285\pi\) | |||||||
\(488\) | 1.68525i | 0.0762878i | ||||||||
\(489\) | −0.922773 | −0.0417292 | ||||||||
\(490\) | −0.205938 | − | 1.98774i | −0.00930333 | − | 0.0897967i | ||||
\(491\) | 12.2443 | 0.552579 | 0.276290 | − | 0.961074i | \(-0.410895\pi\) | ||||
0.276290 | + | 0.961074i | \(0.410895\pi\) | |||||||
\(492\) | 9.44722i | 0.425914i | ||||||||
\(493\) | 30.2747i | 1.36350i | ||||||||
\(494\) | −0.690219 | −0.0310544 | ||||||||
\(495\) | −2.05758 | + | 0.213174i | −0.0924813 | + | 0.00958146i | ||||
\(496\) | 10.1048 | 0.453721 | ||||||||
\(497\) | 3.69534i | 0.165759i | ||||||||
\(498\) | − | 0.918754i | − | 0.0411703i | ||||||
\(499\) | −15.9356 | −0.713373 | −0.356687 | − | 0.934224i | \(-0.616094\pi\) | ||||
−0.356687 | + | 0.934224i | \(0.616094\pi\) | |||||||
\(500\) | −21.1124 | + | 6.75609i | −0.944176 | + | 0.302141i | ||||
\(501\) | −11.6046 | −0.518454 | ||||||||
\(502\) | − | 2.35541i | − | 0.105127i | ||||||
\(503\) | 15.2623i | 0.680514i | 0.940332 | + | 0.340257i | \(0.110514\pi\) | ||||
−0.940332 | + | 0.340257i | \(0.889486\pi\) | |||||||
\(504\) | −0.221516 | −0.00986709 | ||||||||
\(505\) | 8.99046 | − | 0.931450i | 0.400070 | − | 0.0414490i | ||||
\(506\) | 0.412843 | 0.0183531 | ||||||||
\(507\) | 20.9010i | 0.928245i | ||||||||
\(508\) | 18.1073i | 0.803382i | ||||||||
\(509\) | −6.35745 | −0.281789 | −0.140894 | − | 0.990025i | \(-0.544998\pi\) | ||||
−0.140894 | + | 0.990025i | \(0.544998\pi\) | |||||||
\(510\) | −0.303799 | − | 2.93230i | −0.0134524 | − | 0.129844i | ||||
\(511\) | −1.25725 | −0.0556175 | ||||||||
\(512\) | 10.1663i | 0.449292i | ||||||||
\(513\) | − | 5.65392i | − | 0.249626i | ||||||
\(514\) | 1.03605 | 0.0456980 | ||||||||
\(515\) | −1.16430 | − | 11.2380i | −0.0513054 | − | 0.495205i | ||||
\(516\) | −2.48575 | −0.109429 | ||||||||
\(517\) | − | 10.3842i | − | 0.456697i | ||||||
\(518\) | − | 0.0554840i | − | 0.00243783i | ||||||
\(519\) | 23.9031 | 1.04923 | ||||||||
\(520\) | 6.11405 | − | 0.633442i | 0.268119 | − | 0.0277783i | ||||
\(521\) | −9.47236 | −0.414992 | −0.207496 | − | 0.978236i | \(-0.566531\pi\) | ||||
−0.207496 | + | 0.978236i | \(0.566531\pi\) | |||||||
\(522\) | 0.529919i | 0.0231939i | ||||||||
\(523\) | − | 23.8569i | − | 1.04319i | −0.853193 | − | 0.521595i | \(-0.825337\pi\) | ||
0.853193 | − | 0.521595i | \(-0.174663\pi\) | |||||||
\(524\) | −43.6420 | −1.90651 | ||||||||
\(525\) | 3.22064 | − | 0.674585i | 0.140560 | − | 0.0294413i | ||||
\(526\) | 1.32595 | 0.0578140 | ||||||||
\(527\) | 18.0372i | 0.785712i | ||||||||
\(528\) | − | 5.61256i | − | 0.244255i | ||||||
\(529\) | 13.1579 | 0.572082 | ||||||||
\(530\) | 2.56160 | − | 0.265392i | 0.111269 | − | 0.0115279i | ||||
\(531\) | −12.2602 | −0.532049 | ||||||||
\(532\) | 0.905838i | 0.0392731i | ||||||||
\(533\) | − | 17.3499i | − | 0.751509i | ||||||
\(534\) | 1.13280 | 0.0490212 | ||||||||
\(535\) | 1.30493 | + | 12.5953i | 0.0564168 | + | 0.544541i | ||||
\(536\) | 0.647959 | 0.0279876 | ||||||||
\(537\) | 25.4737i | 1.09927i | ||||||||
\(538\) | − | 1.67864i | − | 0.0723714i | ||||||
\(539\) | 6.79127 | 0.292520 | ||||||||
\(540\) | 2.58313 | + | 24.9327i | 0.111160 | + | 1.07293i | ||||
\(541\) | −1.20982 | −0.0520142 | −0.0260071 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260071 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(542\) | − | 1.02241i | − | 0.0439162i | ||||||
\(543\) | − | 0.772186i | − | 0.0331377i | ||||||
\(544\) | −10.8566 | −0.465472 | ||||||||
\(545\) | −18.3626 | + | 1.90244i | −0.786568 | + | 0.0814918i | ||||
\(546\) | −0.454237 | −0.0194396 | ||||||||
\(547\) | − | 9.94790i | − | 0.425341i | −0.977124 | − | 0.212671i | \(-0.931784\pi\) | ||
0.977124 | − | 0.212671i | \(-0.0682162\pi\) | |||||||
\(548\) | − | 20.2106i | − | 0.863356i | ||||||
\(549\) | 2.97467 | 0.126956 | ||||||||
\(550\) | 0.134891 | + | 0.644003i | 0.00575176 | + | 0.0274604i | ||||
\(551\) | 4.35289 | 0.185439 | ||||||||
\(552\) | − | 2.36842i | − | 0.100807i | ||||||
\(553\) | − | 1.48252i | − | 0.0630430i | ||||||
\(554\) | −3.34134 | −0.141960 | ||||||||
\(555\) | −2.95661 | + | 0.306318i | −0.125501 | + | 0.0130025i | ||||
\(556\) | 29.2530 | 1.24060 | ||||||||
\(557\) | 31.0507i | 1.31566i | 0.753166 | + | 0.657831i | \(0.228526\pi\) | ||||
−0.753166 | + | 0.657831i | \(0.771474\pi\) | |||||||
\(558\) | 0.315717i | 0.0133654i | ||||||||
\(559\) | 4.56511 | 0.193084 | ||||||||
\(560\) | −0.410209 | − | 3.95938i | −0.0173345 | − | 0.167314i | ||||
\(561\) | 10.0184 | 0.422979 | ||||||||
\(562\) | 1.37911i | 0.0581744i | ||||||||
\(563\) | − | 44.8070i | − | 1.88839i | −0.329390 | − | 0.944194i | \(-0.606843\pi\) | ||
0.329390 | − | 0.944194i | \(-0.393157\pi\) | |||||||
\(564\) | −29.6568 | −1.24878 | ||||||||
\(565\) | −3.79081 | − | 36.5894i | −0.159481 | − | 1.53933i | ||||
\(566\) | 4.16967 | 0.175264 | ||||||||
\(567\) | − | 2.45291i | − | 0.103012i | ||||||
\(568\) | 4.23910i | 0.177869i | ||||||||
\(569\) | 35.6674 | 1.49526 | 0.747628 | − | 0.664118i | \(-0.231193\pi\) | ||||
0.747628 | + | 0.664118i | \(0.231193\pi\) | |||||||
\(570\) | −0.421605 | + | 0.0436801i | −0.0176591 | + | 0.00182956i | ||||
\(571\) | −21.6619 | −0.906524 | −0.453262 | − | 0.891377i | \(-0.649740\pi\) | ||||
−0.453262 | + | 0.891377i | \(0.649740\pi\) | |||||||
\(572\) | 10.3992i | 0.434811i | ||||||||
\(573\) | 16.6961i | 0.697488i | ||||||||
\(574\) | 0.198880 | 0.00830109 | ||||||||
\(575\) | −3.21577 | − | 15.3529i | −0.134107 | − | 0.640260i | ||||
\(576\) | 7.01910 | 0.292463 | ||||||||
\(577\) | 21.2075i | 0.882879i | 0.897291 | + | 0.441440i | \(0.145532\pi\) | ||||
−0.897291 | + | 0.441440i | \(0.854468\pi\) | |||||||
\(578\) | − | 4.12857i | − | 0.171726i | ||||||
\(579\) | −24.1629 | −1.00418 | ||||||||
\(580\) | −19.1954 | + | 1.98873i | −0.797046 | + | 0.0825774i | ||||
\(581\) | 2.21441 | 0.0918690 | ||||||||
\(582\) | − | 1.80180i | − | 0.0746870i | ||||||
\(583\) | 8.75191i | 0.362467i | ||||||||
\(584\) | −1.44225 | −0.0596808 | ||||||||
\(585\) | −1.11810 | − | 10.7920i | −0.0462277 | − | 0.446195i | ||||
\(586\) | −1.98529 | −0.0820117 | ||||||||
\(587\) | 47.6238i | 1.96565i | 0.184552 | + | 0.982823i | \(0.440916\pi\) | ||||
−0.184552 | + | 0.982823i | \(0.559084\pi\) | |||||||
\(588\) | − | 19.3956i | − | 0.799859i | ||||||
\(589\) | 2.59338 | 0.106858 | ||||||||
\(590\) | 0.401878 | + | 3.87897i | 0.0165451 | + | 0.159695i | ||||
\(591\) | −28.0055 | −1.15199 | ||||||||
\(592\) | 3.59577i | 0.147785i | ||||||||
\(593\) | 14.7406i | 0.605323i | 0.953098 | + | 0.302661i | \(0.0978751\pi\) | ||||
−0.953098 | + | 0.302661i | \(0.902125\pi\) | |||||||
\(594\) | 0.744030 | 0.0305279 | ||||||||
\(595\) | 7.06751 | − | 0.732224i | 0.289740 | − | 0.0300183i | ||||
\(596\) | 33.7021 | 1.38049 | ||||||||
\(597\) | − | 23.8111i | − | 0.974522i | ||||||
\(598\) | 2.16536i | 0.0885483i | ||||||||
\(599\) | −29.8502 | −1.21965 | −0.609823 | − | 0.792538i | \(-0.708759\pi\) | ||||
−0.609823 | + | 0.792538i | \(0.708759\pi\) | |||||||
\(600\) | 3.69455 | − | 0.773849i | 0.150829 | − | 0.0315923i | ||||
\(601\) | −9.23160 | −0.376565 | −0.188282 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188282 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(602\) | 0.0523292i | 0.00213278i | ||||||||
\(603\) | − | 1.14372i | − | 0.0465760i | ||||||
\(604\) | −32.2917 | −1.31393 | ||||||||
\(605\) | −2.22416 | + | 0.230433i | −0.0904251 | + | 0.00936843i | ||||
\(606\) | −0.766222 | −0.0311257 | ||||||||
\(607\) | 27.9086i | 1.13278i | 0.824138 | + | 0.566389i | \(0.191660\pi\) | ||||
−0.824138 | + | 0.566389i | \(0.808340\pi\) | |||||||
\(608\) | 1.56096i | 0.0633051i | ||||||||
\(609\) | 2.86466 | 0.116082 | ||||||||
\(610\) | −0.0975065 | − | 0.941144i | −0.00394792 | − | 0.0381058i | ||||
\(611\) | 54.4652 | 2.20342 | ||||||||
\(612\) | 12.7569i | 0.515667i | ||||||||
\(613\) | − | 44.6257i | − | 1.80241i | −0.433390 | − | 0.901207i | \(-0.642683\pi\) | ||
0.433390 | − | 0.901207i | \(-0.357317\pi\) | |||||||
\(614\) | −1.13604 | −0.0458469 | ||||||||
\(615\) | −1.09798 | − | 10.5978i | −0.0442749 | − | 0.427346i | ||||
\(616\) | −0.239450 | −0.00964771 | ||||||||
\(617\) | − | 46.6619i | − | 1.87854i | −0.343184 | − | 0.939268i | \(-0.611505\pi\) | ||
0.343184 | − | 0.939268i | \(-0.388495\pi\) | |||||||
\(618\) | 0.957772i | 0.0385272i | ||||||||
\(619\) | −16.6735 | −0.670165 | −0.335083 | − | 0.942189i | \(-0.608764\pi\) | ||||
−0.335083 | + | 0.942189i | \(0.608764\pi\) | |||||||
\(620\) | −11.4363 | + | 1.18485i | −0.459293 | + | 0.0475848i | ||||
\(621\) | −17.7375 | −0.711783 | ||||||||
\(622\) | − | 0.0116630i | − | 0.000467645i | ||||||
\(623\) | 2.73031i | 0.109388i | ||||||||
\(624\) | 29.4379 | 1.17846 | ||||||||
\(625\) | 22.8986 | − | 10.0327i | 0.915943 | − | 0.401307i | ||||
\(626\) | 0.632320 | 0.0252726 | ||||||||
\(627\) | − | 1.44045i | − | 0.0575260i | ||||||
\(628\) | 37.4649i | 1.49501i | ||||||||
\(629\) | −6.41847 | −0.255921 | ||||||||
\(630\) | 0.123707 | − | 0.0128166i | 0.00492862 | − | 0.000510626i | ||||
\(631\) | 18.2634 | 0.727053 | 0.363527 | − | 0.931584i | \(-0.381573\pi\) | ||||
0.363527 | + | 0.931584i | \(0.381573\pi\) | |||||||
\(632\) | − | 1.70067i | − | 0.0676488i | ||||||
\(633\) | 15.5400i | 0.617658i | ||||||||
\(634\) | 1.50440 | 0.0597472 | ||||||||
\(635\) | −2.10448 | − | 20.3127i | −0.0835138 | − | 0.806085i | ||||
\(636\) | 24.9951 | 0.991119 | ||||||||
\(637\) | 35.6202i | 1.41132i | ||||||||
\(638\) | 0.572821i | 0.0226782i | ||||||||
\(639\) | 7.48250 | 0.296003 | ||||||||
\(640\) | −0.949470 | − | 9.16439i | −0.0375311 | − | 0.362254i | ||||
\(641\) | 2.90244 | 0.114639 | 0.0573197 | − | 0.998356i | \(-0.481745\pi\) | ||||
0.0573197 | + | 0.998356i | \(0.481745\pi\) | |||||||
\(642\) | − | 1.07345i | − | 0.0423656i | ||||||
\(643\) | − | 37.5112i | − | 1.47930i | −0.672993 | − | 0.739648i | \(-0.734992\pi\) | ||
0.672993 | − | 0.739648i | \(-0.265008\pi\) | |||||||
\(644\) | 2.84181 | 0.111983 | ||||||||
\(645\) | 2.78850 | − | 0.288900i | 0.109797 | − | 0.0113754i | ||||
\(646\) | −0.915258 | −0.0360103 | ||||||||
\(647\) | 2.87727i | 0.113117i | 0.998399 | + | 0.0565585i | \(0.0180127\pi\) | ||||
−0.998399 | + | 0.0565585i | \(0.981987\pi\) | |||||||
\(648\) | − | 2.81385i | − | 0.110538i | ||||||
\(649\) | −13.2528 | −0.520219 | ||||||||
\(650\) | −3.37779 | + | 0.707502i | −0.132488 | + | 0.0277505i | ||||
\(651\) | 1.70672 | 0.0668916 | ||||||||
\(652\) | − | 1.27014i | − | 0.0497423i | ||||||
\(653\) | 7.45085i | 0.291574i | 0.989316 | + | 0.145787i | \(0.0465715\pi\) | ||||
−0.989316 | + | 0.145787i | \(0.953429\pi\) | |||||||
\(654\) | 1.56497 | 0.0611953 | ||||||||
\(655\) | 48.9573 | − | 5.07219i | 1.91292 | − | 0.198187i | ||||
\(656\) | −12.8889 | −0.503227 | ||||||||
\(657\) | 2.54574i | 0.0993189i | ||||||||
\(658\) | 0.624327i | 0.0243388i | ||||||||
\(659\) | −24.9272 | −0.971025 | −0.485512 | − | 0.874230i | \(-0.661367\pi\) | ||||
−0.485512 | + | 0.874230i | \(0.661367\pi\) | |||||||
\(660\) | 0.658106 | + | 6.35211i | 0.0256167 | + | 0.247256i | ||||
\(661\) | −6.76983 | −0.263316 | −0.131658 | − | 0.991295i | \(-0.542030\pi\) | ||||
−0.131658 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(662\) | − | 1.88022i | − | 0.0730767i | ||||||
\(663\) | 52.5468i | 2.04075i | ||||||||
\(664\) | 2.54025 | 0.0985808 | ||||||||
\(665\) | −0.105279 | − | 1.01616i | −0.00408255 | − | 0.0394052i | ||||
\(666\) | −0.112347 | −0.00435335 | ||||||||
\(667\) | − | 13.6560i | − | 0.528761i | ||||||
\(668\) | − | 15.9729i | − | 0.618010i | ||||||
\(669\) | −24.9622 | −0.965095 | ||||||||
\(670\) | −0.361858 | + | 0.0374901i | −0.0139798 | + | 0.00144837i | ||||
\(671\) | 3.21550 | 0.124133 | ||||||||
\(672\) | 1.02727i | 0.0396280i | ||||||||
\(673\) | − | 47.8457i | − | 1.84432i | −0.386812 | − | 0.922159i | \(-0.626424\pi\) | ||
0.386812 | − | 0.922159i | \(-0.373576\pi\) | |||||||
\(674\) | 2.74185 | 0.105612 | ||||||||
\(675\) | −5.79549 | − | 27.6691i | −0.223069 | − | 1.06499i | ||||
\(676\) | −28.7688 | −1.10649 | ||||||||
\(677\) | − | 29.3775i | − | 1.12907i | −0.825410 | − | 0.564534i | \(-0.809056\pi\) | ||
0.825410 | − | 0.564534i | \(-0.190944\pi\) | |||||||
\(678\) | 3.11837i | 0.119760i | ||||||||
\(679\) | 4.34275 | 0.166659 | ||||||||
\(680\) | 8.10748 | − | 0.839969i | 0.310908 | − | 0.0322114i | ||||
\(681\) | 11.6941 | 0.448120 | ||||||||
\(682\) | 0.341277i | 0.0130682i | ||||||||
\(683\) | − | 35.4637i | − | 1.35698i | −0.734610 | − | 0.678490i | \(-0.762635\pi\) | ||
0.734610 | − | 0.678490i | \(-0.237365\pi\) | |||||||
\(684\) | 1.83419 | 0.0701318 | ||||||||
\(685\) | 2.34894 | + | 22.6722i | 0.0897483 | + | 0.866260i | ||||
\(686\) | −0.829169 | −0.0316578 | ||||||||
\(687\) | − | 0.767677i | − | 0.0292887i | ||||||
\(688\) | − | 3.39132i | − | 0.129293i | ||||||
\(689\) | −45.9038 | −1.74880 | ||||||||
\(690\) | 0.137034 | + | 1.32267i | 0.00521679 | + | 0.0503530i | ||||
\(691\) | 37.1831 | 1.41451 | 0.707256 | − | 0.706957i | \(-0.249933\pi\) | ||||
0.707256 | + | 0.706957i | \(0.249933\pi\) | |||||||
\(692\) | 32.9009i | 1.25071i | ||||||||
\(693\) | 0.422657i | 0.0160554i | ||||||||
\(694\) | −0.655369 | −0.0248775 | ||||||||
\(695\) | −32.8159 | + | 3.39986i | −1.24478 | + | 0.128964i | ||||
\(696\) | 3.28619 | 0.124563 | ||||||||
\(697\) | − | 23.0067i | − | 0.871442i | ||||||
\(698\) | − | 1.11917i | − | 0.0423614i | ||||||
\(699\) | −20.7484 | −0.784778 | ||||||||
\(700\) | 0.928521 | + | 4.43299i | 0.0350948 | + | 0.167551i | ||||
\(701\) | 7.78088 | 0.293880 | 0.146940 | − | 0.989145i | \(-0.453058\pi\) | ||||
0.146940 | + | 0.989145i | \(0.453058\pi\) | |||||||
\(702\) | 3.90244i | 0.147288i | ||||||||
\(703\) | 0.922846i | 0.0348058i | ||||||||
\(704\) | 7.58738 | 0.285960 | ||||||||
\(705\) | 33.2689 | − | 3.44680i | 1.25298 | − | 0.129814i | ||||
\(706\) | 4.55932 | 0.171592 | ||||||||
\(707\) | − | 1.84677i | − | 0.0694549i | ||||||
\(708\) | 37.8495i | 1.42247i | ||||||||
\(709\) | 43.5495 | 1.63554 | 0.817769 | − | 0.575547i | \(-0.195211\pi\) | ||||
0.817769 | + | 0.575547i | \(0.195211\pi\) | |||||||
\(710\) | −0.245269 | − | 2.36736i | −0.00920477 | − | 0.0888455i | ||||
\(711\) | −3.00187 | −0.112579 | ||||||||
\(712\) | 3.13207i | 0.117379i | ||||||||
\(713\) | − | 8.13599i | − | 0.304695i | ||||||
\(714\) | −0.602337 | −0.0225419 | ||||||||
\(715\) | −1.20862 | − | 11.6657i | −0.0451998 | − | 0.436274i | ||||
\(716\) | −35.0628 | −1.31036 | ||||||||
\(717\) | 22.4383i | 0.837972i | ||||||||
\(718\) | 2.95231i | 0.110179i | ||||||||
\(719\) | 19.1645 | 0.714716 | 0.357358 | − | 0.933967i | \(-0.383678\pi\) | ||||
0.357358 | + | 0.933967i | \(0.383678\pi\) | |||||||
\(720\) | −8.01714 | + | 0.830610i | −0.298781 | + | 0.0309550i | ||||
\(721\) | −2.30845 | −0.0859711 | ||||||||
\(722\) | 0.131596i | 0.00489748i | ||||||||
\(723\) | 28.0856i | 1.04451i | ||||||||
\(724\) | 1.06286 | 0.0395010 | ||||||||
\(725\) | 21.3022 | − | 4.46189i | 0.791143 | − | 0.165710i | ||||
\(726\) | 0.189557 | 0.00703512 | ||||||||
\(727\) | 38.1779i | 1.41594i | 0.706243 | + | 0.707970i | \(0.250389\pi\) | ||||
−0.706243 | + | 0.707970i | \(0.749611\pi\) | |||||||
\(728\) | − | 1.25591i | − | 0.0465473i | ||||||
\(729\) | −29.3993 | −1.08886 | ||||||||
\(730\) | 0.805438 | − | 0.0834468i | 0.0298106 | − | 0.00308851i | ||||
\(731\) | 6.05352 | 0.223897 | ||||||||
\(732\) | − | 9.18332i | − | 0.339425i | ||||||
\(733\) | 29.5379i | 1.09101i | 0.838109 | + | 0.545503i | \(0.183662\pi\) | ||||
−0.838109 | + | 0.545503i | \(0.816338\pi\) | |||||||
\(734\) | 0.711563 | 0.0262643 | ||||||||
\(735\) | 2.25420 | + | 21.7578i | 0.0831476 | + | 0.802550i | ||||
\(736\) | 4.89705 | 0.180508 | ||||||||
\(737\) | − | 1.23632i | − | 0.0455404i | ||||||
\(738\) | − | 0.402702i | − | 0.0148237i | ||||||
\(739\) | 24.9966 | 0.919516 | 0.459758 | − | 0.888044i | \(-0.347936\pi\) | ||||
0.459758 | + | 0.888044i | \(0.347936\pi\) | |||||||
\(740\) | −0.421625 | − | 4.06957i | −0.0154993 | − | 0.149601i | ||||
\(741\) | 7.55516 | 0.277546 | ||||||||
\(742\) | − | 0.526189i | − | 0.0193170i | ||||||
\(743\) | 23.9140i | 0.877318i | 0.898653 | + | 0.438659i | \(0.144546\pi\) | ||||
−0.898653 | + | 0.438659i | \(0.855454\pi\) | |||||||
\(744\) | 1.95786 | 0.0717786 | ||||||||
\(745\) | −37.8069 | + | 3.91695i | −1.38514 | + | 0.143506i | ||||
\(746\) | −2.81780 | −0.103167 | ||||||||
\(747\) | − | 4.48383i | − | 0.164055i | ||||||
\(748\) | 13.7897i | 0.504202i | ||||||||
\(749\) | 2.58725 | 0.0945361 | ||||||||
\(750\) | −2.01848 | + | 0.645924i | −0.0737044 | + | 0.0235858i | ||||
\(751\) | 32.9159 | 1.20112 | 0.600560 | − | 0.799580i | \(-0.294944\pi\) | ||||
0.600560 | + | 0.799580i | \(0.294944\pi\) | |||||||
\(752\) | − | 40.4610i | − | 1.47546i | ||||||
\(753\) | 25.7824i | 0.939564i | ||||||||
\(754\) | −3.00445 | −0.109416 | ||||||||
\(755\) | 36.2246 | − | 3.75303i | 1.31835 | − | 0.136587i | ||||
\(756\) | 5.12153 | 0.186268 | ||||||||
\(757\) | − | 19.8968i | − | 0.723161i | −0.932341 | − | 0.361580i | \(-0.882237\pi\) | ||
0.932341 | − | 0.361580i | \(-0.117763\pi\) | |||||||
\(758\) | − | 0.492780i | − | 0.0178986i | ||||||
\(759\) | −4.51900 | −0.164029 | ||||||||
\(760\) | −0.120771 | − | 1.16569i | −0.00438081 | − | 0.0422841i | ||||
\(761\) | 28.8803 | 1.04691 | 0.523456 | − | 0.852053i | \(-0.324642\pi\) | ||||
0.523456 | + | 0.852053i | \(0.324642\pi\) | |||||||
\(762\) | 1.73117i | 0.0627138i | ||||||||
\(763\) | 3.77194i | 0.136554i | ||||||||
\(764\) | −22.9810 | −0.831424 | ||||||||
\(765\) | −1.48264 | − | 14.3106i | −0.0536051 | − | 0.517402i | ||||
\(766\) | −2.40544 | −0.0869120 | ||||||||
\(767\) | − | 69.5112i | − | 2.50990i | ||||||
\(768\) | − | 21.0774i | − | 0.760566i | ||||||
\(769\) | 17.5385 | 0.632455 | 0.316228 | − | 0.948683i | \(-0.397584\pi\) | ||||
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(770\) | 0.133723 | − | 0.0138543i | 0.00481903 | − | 0.000499273i | ||||
\(771\) | −11.3406 | −0.408422 | ||||||||
\(772\) | − | 33.2586i | − | 1.19700i | ||||||
\(773\) | − | 45.4884i | − | 1.63611i | −0.575143 | − | 0.818053i | \(-0.695054\pi\) | ||
0.575143 | − | 0.818053i | \(-0.304946\pi\) | |||||||
\(774\) | 0.105959 | 0.00380861 | ||||||||
\(775\) | 12.6915 | − | 2.65832i | 0.455892 | − | 0.0954897i | ||||
\(776\) | 4.98177 | 0.178835 | ||||||||
\(777\) | 0.607330i | 0.0217879i | ||||||||
\(778\) | 0.832018i | 0.0298293i | ||||||||
\(779\) | −3.30790 | −0.118518 | ||||||||
\(780\) | −33.3168 | + | 3.45177i | −1.19293 | + | 0.123593i | ||||
\(781\) | 8.08829 | 0.289422 | ||||||||
\(782\) | 2.87136i | 0.102680i | ||||||||
\(783\) | − | 24.6109i | − | 0.879521i | ||||||
\(784\) | 26.4615 | 0.945052 | ||||||||
\(785\) | −4.35427 | − | 42.0279i | −0.155411 | − | 1.50004i | ||||
\(786\) | −4.17245 | −0.148826 | ||||||||
\(787\) | − | 14.4706i | − | 0.515820i | −0.966169 | − | 0.257910i | \(-0.916966\pi\) | ||
0.966169 | − | 0.257910i | \(-0.0830337\pi\) | |||||||
\(788\) | − | 38.5477i | − | 1.37320i | ||||||
\(789\) | −14.5139 | −0.516707 | ||||||||
\(790\) | 0.0983983 | + | 0.949751i | 0.00350085 | + | 0.0337906i | ||||
\(791\) | −7.51598 | −0.267238 | ||||||||
\(792\) | 0.484850i | 0.0172284i | ||||||||
\(793\) | 16.8653i | 0.598904i | ||||||||
\(794\) | 3.63659 | 0.129058 | ||||||||
\(795\) | −28.0393 | + | 2.90500i | −0.994453 | + | 0.103030i | ||||
\(796\) | 32.7743 | 1.16165 | ||||||||
\(797\) | 16.3564i | 0.579374i | 0.957121 | + | 0.289687i | \(0.0935513\pi\) | ||||
−0.957121 | + | 0.289687i | \(0.906449\pi\) | |||||||
\(798\) | 0.0866038i | 0.00306574i | ||||||||
\(799\) | 72.2230 | 2.55507 | ||||||||
\(800\) | 1.60004 | + | 7.63901i | 0.0565700 | + | 0.270080i | ||||
\(801\) | 5.52847 | 0.195339 | ||||||||
\(802\) | − | 3.63052i | − | 0.128198i | ||||||
\(803\) | 2.75185i | 0.0971106i | ||||||||
\(804\) | −3.53087 | −0.124524 | ||||||||
\(805\) | −3.18793 | + | 0.330283i | −0.112360 | + | 0.0116409i | ||||
\(806\) | −1.79000 | −0.0630501 | ||||||||
\(807\) | 18.3745i | 0.646812i | ||||||||
\(808\) | − | 2.11852i | − | 0.0745292i | ||||||
\(809\) | −33.2546 | −1.16917 | −0.584585 | − | 0.811332i | \(-0.698743\pi\) | ||||
−0.584585 | + | 0.811332i | \(0.698743\pi\) | |||||||
\(810\) | 0.162805 | + | 1.57142i | 0.00572040 | + | 0.0552139i | ||||
\(811\) | −35.9446 | −1.26219 | −0.631094 | − | 0.775707i | \(-0.717394\pi\) | ||||
−0.631094 | + | 0.775707i | \(0.717394\pi\) | |||||||
\(812\) | 3.94302i | 0.138373i | ||||||||
\(813\) | 11.1913i | 0.392497i | ||||||||
\(814\) | −0.121442 | −0.00425656 | ||||||||
\(815\) | 0.147619 | + | 1.42483i | 0.00517085 | + | 0.0499096i | ||||
\(816\) | 39.0358 | 1.36653 | ||||||||
\(817\) | − | 0.870374i | − | 0.0304505i | ||||||
\(818\) | − | 2.96187i | − | 0.103559i | ||||||
\(819\) | −2.21683 | −0.0774624 | ||||||||
\(820\) | 14.5872 | − | 1.51130i | 0.509408 | − | 0.0527768i | ||||
\(821\) | −13.7687 | −0.480531 | −0.240266 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240266 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(822\) | − | 1.93226i | − | 0.0673955i | ||||||
\(823\) | 4.39908i | 0.153342i | 0.997056 | + | 0.0766712i | \(0.0244292\pi\) | ||||
−0.997056 | + | 0.0766712i | \(0.975571\pi\) | |||||||
\(824\) | −2.64813 | −0.0922520 | ||||||||
\(825\) | −1.47652 | − | 7.04928i | −0.0514058 | − | 0.245424i | ||||
\(826\) | 0.796797 | 0.0277241 | ||||||||
\(827\) | 12.4264i | 0.432108i | 0.976381 | + | 0.216054i | \(0.0693187\pi\) | ||||
−0.976381 | + | 0.216054i | \(0.930681\pi\) | |||||||
\(828\) | − | 5.75423i | − | 0.199973i | ||||||
\(829\) | −56.5829 | −1.96521 | −0.982603 | − | 0.185718i | \(-0.940539\pi\) | ||||
−0.982603 | + | 0.185718i | \(0.940539\pi\) | |||||||
\(830\) | −1.41862 | + | 0.146976i | −0.0492412 | + | 0.00510160i | ||||
\(831\) | 36.5744 | 1.26875 | ||||||||
\(832\) | 39.7958i | 1.37967i | ||||||||
\(833\) | 47.2338i | 1.63655i | ||||||||
\(834\) | 2.79677 | 0.0968443 | ||||||||
\(835\) | 1.85641 | + | 17.9183i | 0.0642439 | + | 0.620089i | ||||
\(836\) | 1.98268 | 0.0685725 | ||||||||
\(837\) | − | 14.6628i | − | 0.506819i | ||||||
\(838\) | 3.37670i | 0.116646i | ||||||||
\(839\) | −3.17520 | −0.109620 | −0.0548100 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548100 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(840\) | −0.0794799 | − | 0.767148i | −0.00274232 | − | 0.0264691i | ||||
\(841\) | −10.0523 | −0.346632 | ||||||||
\(842\) | − | 3.24388i | − | 0.111791i | ||||||
\(843\) | − | 15.0958i | − | 0.519928i | ||||||
\(844\) | −21.3897 | −0.736265 | ||||||||
\(845\) | 32.2727 | − | 3.34359i | 1.11021 | − | 0.115023i | ||||
\(846\) | 1.26417 | 0.0434630 | ||||||||
\(847\) | 0.456875i | 0.0156984i | ||||||||
\(848\) | 34.1009i | 1.17103i | ||||||||
\(849\) | −45.6413 | −1.56641 | ||||||||
\(850\) | −4.47909 | + | 0.938176i | −0.153632 | + | 0.0321792i | ||||
\(851\) | 2.89517 | 0.0992450 | ||||||||
\(852\) | − | 23.0998i | − | 0.791386i | ||||||
\(853\) | 5.63265i | 0.192858i | 0.995340 | + | 0.0964291i | \(0.0307421\pi\) | ||||
−0.995340 | + | 0.0964291i | \(0.969258\pi\) | |||||||
\(854\) | −0.193324 | −0.00661543 | ||||||||
\(855\) | −2.05758 | + | 0.213174i | −0.0703677 | + | 0.00729040i | ||||
\(856\) | 2.96796 | 0.101443 | ||||||||
\(857\) | − | 18.1582i | − | 0.620271i | −0.950692 | − | 0.310135i | \(-0.899626\pi\) | ||
0.950692 | − | 0.310135i | \(-0.100374\pi\) | |||||||
\(858\) | 0.994226i | 0.0339423i | ||||||||
\(859\) | 9.75939 | 0.332986 | 0.166493 | − | 0.986043i | \(-0.446756\pi\) | ||||
0.166493 | + | 0.986043i | \(0.446756\pi\) | |||||||
\(860\) | 0.397652 | + | 3.83818i | 0.0135598 | + | 0.130881i | ||||
\(861\) | −2.17695 | −0.0741902 | ||||||||
\(862\) | 3.24250i | 0.110440i | ||||||||
\(863\) | 44.8518i | 1.52677i | 0.645942 | + | 0.763386i | \(0.276465\pi\) | ||||
−0.645942 | + | 0.763386i | \(0.723535\pi\) | |||||||
\(864\) | 8.82551 | 0.300250 | ||||||||
\(865\) | −3.82384 | − | 36.9081i | −0.130014 | − | 1.25491i | ||||
\(866\) | −3.57981 | −0.121647 | ||||||||
\(867\) | 45.1915i | 1.53478i | ||||||||
\(868\) | 2.34918i | 0.0797365i | ||||||||
\(869\) | −3.24490 | −0.110076 | ||||||||
\(870\) | −1.83520 | + | 0.190135i | −0.0622192 | + | 0.00644618i | ||||
\(871\) | 6.48449 | 0.219719 | ||||||||
\(872\) | 4.32698i | 0.146530i | ||||||||
\(873\) | − | 8.79341i | − | 0.297612i | ||||||
\(874\) | 0.412843 | 0.0139646 | ||||||||
\(875\) | −1.55682 | − | 4.86499i | −0.0526303 | − | 0.164467i | ||||
\(876\) | 7.85915 | 0.265536 | ||||||||
\(877\) | − | 30.7975i | − | 1.03996i | −0.854179 | − | 0.519978i | \(-0.825940\pi\) | ||
0.854179 | − | 0.519978i | \(-0.174060\pi\) | |||||||
\(878\) | 2.99061i | 0.100928i | ||||||||
\(879\) | 21.7311 | 0.732972 | ||||||||
\(880\) | −8.66622 | + | 0.897857i | −0.292138 | + | 0.0302668i | ||||
\(881\) | 15.9941 | 0.538856 | 0.269428 | − | 0.963021i | \(-0.413165\pi\) | ||||
0.269428 | + | 0.963021i | \(0.413165\pi\) | |||||||
\(882\) | 0.826765i | 0.0278386i | ||||||||
\(883\) | 6.19800i | 0.208579i | 0.994547 | + | 0.104290i | \(0.0332569\pi\) | ||||
−0.994547 | + | 0.104290i | \(0.966743\pi\) | |||||||
\(884\) | −72.3271 | −2.43262 | ||||||||
\(885\) | −4.39898 | − | 42.4594i | −0.147870 | − | 1.42726i | ||||
\(886\) | 4.33827 | 0.145747 | ||||||||
\(887\) | − | 57.1613i | − | 1.91929i | −0.281218 | − | 0.959644i | \(-0.590738\pi\) | ||
0.281218 | − | 0.959644i | \(-0.409262\pi\) | |||||||
\(888\) | 0.696698i | 0.0233797i | ||||||||
\(889\) | −4.17252 | −0.139942 | ||||||||
\(890\) | −0.181218 | − | 1.74913i | −0.00607443 | − | 0.0586311i | ||||
\(891\) | −5.36888 | −0.179864 | ||||||||
\(892\) | − | 34.3588i | − | 1.15042i | ||||||
\(893\) | − | 10.3842i | − | 0.347494i | ||||||
\(894\) | 3.22213 | 0.107764 | ||||||||
\(895\) | 39.3333 | − | 4.07510i | 1.31477 | − | 0.136216i | ||||
\(896\) | −1.88250 | −0.0628898 | ||||||||
\(897\) | − | 23.7022i | − | 0.791392i | ||||||
\(898\) | 3.99923i | 0.133456i | ||||||||
\(899\) | 11.2887 | 0.376499 | ||||||||
\(900\) | 8.97614 | − | 1.88011i | 0.299205 | − | 0.0626705i | ||||
\(901\) | −60.8703 | −2.02788 | ||||||||
\(902\) | − | 0.435305i | − | 0.0144941i | ||||||
\(903\) | − | 0.572798i | − | 0.0190615i | ||||||
\(904\) | −8.62194 | −0.286762 | ||||||||
\(905\) | −1.19231 | + | 0.123529i | −0.0396338 | + | 0.00410623i | ||||
\(906\) | −3.08729 | −0.102568 | ||||||||
\(907\) | 58.6428i | 1.94720i | 0.228258 | + | 0.973601i | \(0.426697\pi\) | ||||
−0.228258 | + | 0.973601i | \(0.573303\pi\) | |||||||
\(908\) | 16.0962i | 0.534171i | ||||||||
\(909\) | −3.73943 | −0.124029 | ||||||||
\(910\) | 0.0726656 | + | 0.701376i | 0.00240884 | + | 0.0232504i | ||||
\(911\) | 29.8092 | 0.987623 | 0.493811 | − | 0.869569i | \(-0.335603\pi\) | ||||
0.493811 | + | 0.869569i | \(0.335603\pi\) | |||||||
\(912\) | − | 5.61256i | − | 0.185851i | ||||||
\(913\) | − | 4.84685i | − | 0.160407i | ||||||
\(914\) | 2.37295 | 0.0784903 | ||||||||
\(915\) | 1.06731 | + | 10.3018i | 0.0352842 | + | 0.340567i | ||||
\(916\) | 1.05665 | 0.0349129 | ||||||||
\(917\) | − | 10.0565i | − | 0.332096i | ||||||
\(918\) | 5.17479i | 0.170794i | ||||||||
\(919\) | −12.6160 | −0.416163 | −0.208082 | − | 0.978111i | \(-0.566722\pi\) | ||||
−0.208082 | + | 0.978111i | \(0.566722\pi\) | |||||||
\(920\) | −3.65702 | + | 0.378883i | −0.120568 | + | 0.0124914i | ||||
\(921\) | 12.4352 | 0.409753 | ||||||||
\(922\) | 1.86237i | 0.0613339i | ||||||||
\(923\) | 42.4231i | 1.39637i | ||||||||
\(924\) | 1.30482 | 0.0429253 | ||||||||
\(925\) | 0.945954 | + | 4.51623i | 0.0311028 | + | 0.148493i | ||||
\(926\) | 1.04945 | 0.0344870 | ||||||||
\(927\) | 4.67426i | 0.153523i | ||||||||
\(928\) | 6.79467i | 0.223046i | ||||||||
\(929\) | −15.4757 | −0.507740 | −0.253870 | − | 0.967238i | \(-0.581704\pi\) | ||||
−0.253870 | + | 0.967238i | \(0.581704\pi\) | |||||||
\(930\) | −1.09338 | + | 0.113279i | −0.0358535 | + | 0.00371457i | ||||
\(931\) | 6.79127 | 0.222575 | ||||||||
\(932\) | − | 28.5588i | − | 0.935476i | ||||||
\(933\) | 0.127664i | 0.00417953i | ||||||||
\(934\) | −2.46024 | −0.0805014 | ||||||||
\(935\) | −1.60268 | − | 15.4692i | −0.0524132 | − | 0.505898i | ||||
\(936\) | −2.54304 | −0.0831218 | ||||||||
\(937\) | − | 33.1867i | − | 1.08416i | −0.840326 | − | 0.542081i | \(-0.817637\pi\) | ||
0.840326 | − | 0.542081i | \(-0.182363\pi\) | |||||||
\(938\) | 0.0743309i | 0.00242699i | ||||||||
\(939\) | −6.92140 | −0.225871 | ||||||||
\(940\) | 4.74428 | + | 45.7924i | 0.154741 | + | 1.49358i | ||||
\(941\) | −53.3449 | −1.73899 | −0.869497 | − | 0.493937i | \(-0.835557\pi\) | ||||
−0.869497 | + | 0.493937i | \(0.835557\pi\) | |||||||
\(942\) | 3.58188i | 0.116704i | ||||||||
\(943\) | 10.3776i | 0.337941i | ||||||||
\(944\) | −51.6383 | −1.68068 | ||||||||
\(945\) | −5.74531 | + | 0.595239i | −0.186895 | + | 0.0193631i | ||||
\(946\) | 0.114537 | 0.00372393 | ||||||||
\(947\) | 27.4898i | 0.893300i | 0.894709 | + | 0.446650i | \(0.147383\pi\) | ||||
−0.894709 | + | 0.446650i | \(0.852617\pi\) | |||||||
\(948\) | 9.26730i | 0.300988i | ||||||||
\(949\) | −14.4334 | −0.468529 | ||||||||
\(950\) | 0.134891 | + | 0.644003i | 0.00437643 | + | 0.0208942i | ||||
\(951\) | −16.4672 | −0.533985 | ||||||||
\(952\) | − | 1.66539i | − | 0.0539757i | ||||||
\(953\) | − | 14.7424i | − | 0.477553i | −0.971075 | − | 0.238776i | \(-0.923254\pi\) | ||
0.971075 | − | 0.238776i | \(-0.0767463\pi\) | |||||||
\(954\) | −1.06545 | −0.0344953 | ||||||||
\(955\) | 25.7800 | − | 2.67092i | 0.834220 | − | 0.0864288i | ||||
\(956\) | −30.8847 | −0.998884 | ||||||||
\(957\) | − | 6.27012i | − | 0.202684i | ||||||
\(958\) | 2.55211i | 0.0824548i | ||||||||
\(959\) | 4.65720 | 0.150389 | ||||||||
\(960\) | 2.51846 | + | 24.3084i | 0.0812828 | + | 0.784550i | ||||
\(961\) | −24.2744 | −0.783044 | ||||||||
\(962\) | − | 0.636966i | − | 0.0205366i | ||||||
\(963\) | − | 5.23879i | − | 0.168818i | ||||||
\(964\) | −38.6579 | −1.24509 | ||||||||
\(965\) | 3.86541 | + | 37.3094i | 0.124432 | + | 1.20103i | ||||
\(966\) | 0.271695 | 0.00874163 | ||||||||
\(967\) | 14.1757i | 0.455860i | 0.973678 | + | 0.227930i | \(0.0731957\pi\) | ||||
−0.973678 | + | 0.227930i | \(0.926804\pi\) | |||||||
\(968\) | 0.524103i | 0.0168453i | ||||||||
\(969\) | 10.0184 | 0.321839 | ||||||||
\(970\) | −2.78211 | + | 0.288239i | −0.0893283 | + | 0.00925480i | ||||
\(971\) | 30.6648 | 0.984079 | 0.492040 | − | 0.870573i | \(-0.336252\pi\) | ||||
0.492040 | + | 0.870573i | \(0.336252\pi\) | |||||||
\(972\) | − | 18.2965i | − | 0.586860i | ||||||
\(973\) | 6.74085i | 0.216102i | ||||||||
\(974\) | 3.16260 | 0.101336 | ||||||||
\(975\) | 36.9735 | − | 7.74435i | 1.18410 | − | 0.248018i | ||||
\(976\) | 12.5288 | 0.401039 | ||||||||
\(977\) | 36.7937i | 1.17713i | 0.808448 | + | 0.588567i | \(0.200308\pi\) | ||||
−0.808448 | + | 0.588567i | \(0.799692\pi\) | |||||||
\(978\) | − | 0.121433i | − | 0.00388300i | ||||||
\(979\) | 5.97606 | 0.190996 | ||||||||
\(980\) | −29.9482 | + | 3.10276i | −0.956660 | + | 0.0991140i | ||||
\(981\) | 7.63761 | 0.243850 | ||||||||
\(982\) | 1.61130i | 0.0514187i | ||||||||
\(983\) | 41.0129i | 1.30811i | 0.756448 | + | 0.654054i | \(0.226933\pi\) | ||||
−0.756448 | + | 0.654054i | \(0.773067\pi\) | |||||||
\(984\) | −2.49728 | −0.0796105 | ||||||||
\(985\) | 4.48012 | + | 43.2426i | 0.142748 | + | 1.37782i | ||||
\(986\) | −3.98402 | −0.126877 | ||||||||
\(987\) | − | 6.83391i | − | 0.217526i | ||||||
\(988\) | 10.3992i | 0.330842i | ||||||||
\(989\) | −2.73055 | −0.0868264 | ||||||||
\(990\) | −0.0280528 | − | 0.270768i | −0.000891575 | − | 0.00860558i | ||||
\(991\) | −36.2674 | −1.15207 | −0.576035 | − | 0.817425i | \(-0.695401\pi\) | ||||
−0.576035 | + | 0.817425i | \(0.695401\pi\) | |||||||
\(992\) | 4.04815i | 0.128529i | ||||||||
\(993\) | 20.5809i | 0.653116i | ||||||||
\(994\) | −0.486290 | −0.0154242 | ||||||||
\(995\) | −36.7661 | + | 3.80912i | −1.16556 | + | 0.120757i | ||||
\(996\) | −13.8424 | −0.438613 | ||||||||
\(997\) | 7.41034i | 0.234688i | 0.993091 | + | 0.117344i | \(0.0374380\pi\) | ||||
−0.993091 | + | 0.117344i | \(0.962562\pi\) | |||||||
\(998\) | − | 2.09705i | − | 0.0663809i | ||||||
\(999\) | 5.21769 | 0.165081 |
(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 | 1045.2.b.c.419.11 | yes | 20 | |
5.2 | odd | 4 | 5225.2.a.ba.1.10 | 20 | |||
5.3 | odd | 4 | 5225.2.a.ba.1.11 | 20 | |||
5.4 | even | 2 | inner | 1045.2.b.c.419.10 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.c.419.10 | ✓ | 20 | 5.4 | even | 2 | inner | |
1045.2.b.c.419.11 | yes | 20 | 1.1 | even | 1 | trivial | |
5225.2.a.ba.1.10 | 20 | 5.2 | odd | 4 | |||
5225.2.a.ba.1.11 | 20 | 5.3 | odd | 4 |