Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(200\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{22})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{22}]$ |
Embedding invariants
Embedding label | 5.15 | ||
Character | \(\chi\) | \(=\) | 804.5 |
Dual form | 804.2.s.b.161.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{22}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.650892 | + | 1.60510i | 0.375793 | + | 0.926704i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.966140 | + | 0.283684i | −0.432071 | + | 0.126867i | −0.490534 | − | 0.871422i | \(-0.663198\pi\) |
0.0584631 | + | 0.998290i | \(0.481380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.54930 | + | 1.34247i | 0.585579 | + | 0.507407i | 0.896509 | − | 0.443026i | \(-0.146095\pi\) |
−0.310930 | + | 0.950433i | \(0.600640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.15268 | + | 2.08949i | −0.717560 | + | 0.696497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.68695 | + | 0.788959i | −0.810145 | + | 0.237880i | −0.660467 | − | 0.750855i | \(-0.729642\pi\) |
−0.149678 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.303154 | + | 0.471717i | 0.0840798 | + | 0.130831i | 0.880746 | − | 0.473588i | \(-0.157042\pi\) |
−0.796666 | + | 0.604419i | \(0.793405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.08419 | − | 1.36610i | −0.279938 | − | 0.352726i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.99315 | − | 0.430350i | −0.725946 | − | 0.104375i | −0.230572 | − | 0.973055i | \(-0.574060\pi\) |
−0.495374 | + | 0.868680i | \(0.664969\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.48728 | + | 4.02453i | 0.800036 | + | 0.923291i | 0.998383 | − | 0.0568410i | \(-0.0181028\pi\) |
−0.198347 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.14638 | + | 3.36058i | −0.250160 | + | 0.733338i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.38260 | + | 0.631411i | −0.288292 | + | 0.131658i | −0.554312 | − | 0.832309i | \(-0.687018\pi\) |
0.266020 | + | 0.963967i | \(0.414291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.35332 | + | 2.15505i | −0.670664 | + | 0.431009i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.75500 | − | 2.09523i | −0.915100 | − | 0.403227i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.01679i | 0.188814i | 0.995534 | + | 0.0944069i | \(0.0300955\pi\) | ||||
−0.995534 | + | 0.0944069i | \(0.969905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77218 | − | 2.75757i | 0.318293 | − | 0.495274i | −0.644833 | − | 0.764323i | \(-0.723073\pi\) |
0.963126 | + | 0.269049i | \(0.0867095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.01527 | − | 3.79929i | −0.524891 | − | 0.661371i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.87767 | − | 0.857505i | −0.317385 | − | 0.144945i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.414150 | 0.0680858 | 0.0340429 | − | 0.999420i | \(-0.489162\pi\) | ||||
0.0340429 | + | 0.999420i | \(0.489162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.559831 | + | 0.793629i | −0.0896448 | + | 0.127082i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.649850 | + | 4.51980i | −0.101489 | + | 0.705875i | 0.874016 | + | 0.485898i | \(0.161507\pi\) |
−0.975505 | + | 0.219977i | \(0.929402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.863281 | + | 0.124121i | 0.131649 | + | 0.0189283i | 0.207824 | − | 0.978166i | \(-0.433362\pi\) |
−0.0761752 | + | 0.997094i | \(0.524271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.48703 | − | 2.62942i | 0.221674 | − | 0.391971i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.67750 | + | 0.766089i | −0.244689 | + | 0.111746i | −0.533985 | − | 0.845494i | \(-0.679306\pi\) |
0.289296 | + | 0.957240i | \(0.406579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.398118 | − | 2.76897i | −0.0568740 | − | 0.395568i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.25746 | − | 5.08441i | −0.176080 | − | 0.711960i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.21708 | + | 8.46498i | 0.167179 | + | 1.16275i | 0.884681 | + | 0.466197i | \(0.154376\pi\) |
−0.717502 | + | 0.696557i | \(0.754715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37215 | − | 1.52449i | 0.319861 | − | 0.205562i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.18993 | + | 8.21696i | −0.554969 | + | 1.08836i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.75024 | + | 2.72343i | −0.227862 | + | 0.354560i | −0.936293 | − | 0.351220i | \(-0.885767\pi\) |
0.708431 | + | 0.705780i | \(0.249403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.230536 | + | 0.785133i | −0.0295171 | + | 0.100526i | −0.972934 | − | 0.231083i | \(-0.925773\pi\) |
0.943417 | + | 0.331609i | \(0.107591\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.14022 | + | 0.347328i | −0.773595 | + | 0.0437593i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.426708 | − | 0.369744i | −0.0529266 | − | 0.0458612i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.16532 | − | 0.572263i | 0.997553 | − | 0.0699131i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.91340 | − | 1.80822i | −0.230346 | − | 0.217685i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.98320 | + | 0.428919i | −0.354040 | + | 0.0509033i | −0.317041 | − | 0.948412i | \(-0.602689\pi\) |
−0.0369996 | + | 0.999315i | \(0.511780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.06133 | − | 0.898887i | −0.358301 | − | 0.105207i | 0.0976275 | − | 0.995223i | \(-0.468875\pi\) |
−0.455929 | + | 0.890016i | \(0.650693\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.64171 | − | 3.97970i | −0.651449 | − | 0.459536i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.22203 | − | 2.38482i | −0.595106 | − | 0.271776i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0461512 | + | 0.0718126i | 0.00519241 | + | 0.00807955i | 0.843840 | − | 0.536595i | \(-0.180290\pi\) |
−0.838648 | + | 0.544674i | \(0.816653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.268052 | − | 8.99601i | 0.0297835 | − | 0.999556i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.01301 | − | 10.2614i | −0.330720 | − | 1.12633i | −0.942195 | − | 0.335066i | \(-0.891241\pi\) |
0.611474 | − | 0.791264i | \(-0.290577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.01389 | − | 0.433331i | 0.326902 | − | 0.0470014i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.63205 | + | 0.661823i | −0.174975 | + | 0.0709549i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.74397 | + | 3.99324i | 0.926859 | + | 0.423282i | 0.820890 | − | 0.571087i | \(-0.193478\pi\) |
0.105970 | + | 0.994369i | \(0.466205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.163592 | + | 1.13781i | −0.0171491 | + | 0.119274i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.57967 | + | 1.04965i | 0.578585 | + | 0.108843i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.51089 | − | 2.89897i | −0.462808 | − | 0.297428i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.47150i | 0.352477i | 0.984347 | + | 0.176239i | \(0.0563930\pi\) | ||||
−0.984347 | + | 0.176239i | \(0.943607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.13561 | − | 7.31273i | 0.415645 | − | 0.734957i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.21410 | + | 2.55520i | 0.220311 | + | 0.254252i | 0.855136 | − | 0.518403i | \(-0.173473\pi\) |
−0.634825 | + | 0.772656i | \(0.718928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.21404 | + | 5.27884i | 0.809354 | + | 0.520140i | 0.878656 | − | 0.477456i | \(-0.158441\pi\) |
−0.0693021 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.154216 | − | 3.57200i | 0.0150500 | − | 0.348591i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.90540 | − | 6.48919i | 0.184202 | − | 0.627334i | −0.814673 | − | 0.579920i | \(-0.803084\pi\) |
0.998875 | − | 0.0474140i | \(-0.0150980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.92724 | + | 12.3350i | 0.759292 | + | 1.18148i | 0.978589 | + | 0.205824i | \(0.0659873\pi\) |
−0.219297 | + | 0.975658i | \(0.570376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.269567 | + | 0.664751i | 0.0255861 | + | 0.0630953i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4656 | + | 3.66022i | 1.17266 | + | 0.344324i | 0.809340 | − | 0.587340i | \(-0.199825\pi\) |
0.363321 | + | 0.931664i | \(0.381643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.15666 | − | 1.00225i | 0.107859 | − | 0.0934606i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.63824 | − | 0.382017i | −0.151456 | − | 0.0353175i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.05954 | − | 4.68496i | −0.372138 | − | 0.429470i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65656 | + | 1.70727i | −0.241505 | + | 0.155206i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.67771 | + | 1.89883i | −0.692276 | + | 0.171212i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.92541 | − | 6.83828i | 0.529985 | − | 0.611635i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.39668 | + | 1.61186i | −0.123936 | + | 0.143029i | −0.814326 | − | 0.580408i | \(-0.802893\pi\) |
0.690391 | + | 0.723437i | \(0.257439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.362676 | + | 1.46644i | 0.0319319 | + | 0.129113i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30624 | − | 3.33665i | 0.638349 | − | 0.291524i | −0.0698282 | − | 0.997559i | \(-0.522245\pi\) |
0.708177 | + | 0.706035i | \(0.249518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9168i | 0.946604i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.18838 | + | 0.675363i | 0.446544 | + | 0.0581260i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.97149 | + | 15.2654i | 0.595615 | + | 1.30421i | 0.931989 | + | 0.362486i | \(0.118072\pi\) |
−0.336375 | + | 0.941728i | \(0.609201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.28442 | − | 7.78001i | −0.193762 | − | 0.659892i | −0.997859 | − | 0.0653948i | \(-0.979169\pi\) |
0.804098 | − | 0.594497i | \(-0.202649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.32152 | − | 2.19391i | −0.195507 | − | 0.184761i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.18672 | − | 1.02830i | −0.0992389 | − | 0.0859910i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.288448 | − | 0.982365i | −0.0239543 | − | 0.0815809i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.18534 | − | 2.44132i | 0.345201 | − | 0.201357i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1494 | − | 13.9935i | 1.32301 | − | 1.14640i | 0.344825 | − | 0.938667i | \(-0.387938\pi\) |
0.978187 | − | 0.207729i | \(-0.0666071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.189990 | − | 1.32141i | 0.0154611 | − | 0.107535i | −0.980629 | − | 0.195872i | \(-0.937246\pi\) |
0.996091 | + | 0.0883374i | \(0.0281554\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.34251 | − | 5.32776i | 0.593606 | − | 0.430724i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.929896 | + | 3.16694i | −0.0746911 | + | 0.254374i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.86174 | + | 19.4045i | 0.707244 | + | 1.54865i | 0.830961 | + | 0.556330i | \(0.187791\pi\) |
−0.123718 | + | 0.992317i | \(0.539482\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.7949 | + | 7.46332i | −1.01470 | + | 0.591880i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.98971 | − | 0.877857i | −0.235622 | − | 0.0691848i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.47744 | −0.115722 | −0.0578608 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578608 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.99097 | + | 2.81526i | 0.310697 | + | 0.219167i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.89688 | + | 1.64366i | −0.146785 | + | 0.127190i | −0.725158 | − | 0.688582i | \(-0.758233\pi\) |
0.578373 | + | 0.815773i | \(0.303688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.26978 | − | 11.5392i | 0.405368 | − | 0.887632i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.9162 | − | 1.37689i | −1.21714 | − | 0.105293i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.75608 | − | 10.5127i | 0.513655 | − | 0.799263i | −0.483444 | − | 0.875375i | \(-0.660614\pi\) |
0.997099 | + | 0.0761122i | \(0.0242507\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.08838 | − | 1.16293i | −0.611424 | − | 0.0879095i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.51059 | − | 1.03665i | −0.414201 | − | 0.0779194i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.58992 | − | 10.0505i | 0.343067 | − | 0.751212i | −0.656929 | − | 0.753952i | \(-0.728145\pi\) |
0.999996 | + | 0.00274020i | \(0.000872234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.387326 | + | 0.848125i | 0.0287897 | + | 0.0630406i | 0.923481 | − | 0.383645i | \(-0.125331\pi\) |
−0.894691 | + | 0.446686i | \(0.852604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41027 | + | 0.141004i | −0.104250 | + | 0.0104233i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.400126 | + | 0.117488i | −0.0294179 | + | 0.00863787i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.38197 | − | 1.20515i | 0.612950 | − | 0.0881289i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.55412 | − | 9.62959i | −0.331263 | − | 0.700449i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.97243 | + | 8.69841i | −0.287435 | + | 0.629395i | −0.997179 | − | 0.0750653i | \(-0.976083\pi\) |
0.709744 | + | 0.704460i | \(0.248811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1470 | + | 12.9477i | 1.45021 | + | 0.931994i | 0.999221 | + | 0.0394647i | \(0.0125653\pi\) |
0.450990 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.315735 | − | 0.925572i | 0.0226103 | − | 0.0662816i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.49850 | + | 10.4223i | 0.106764 | + | 0.742560i | 0.970932 | + | 0.239356i | \(0.0769363\pi\) |
−0.864168 | + | 0.503204i | \(0.832155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.29446 | + | 8.41826i | −0.517091 | + | 0.596755i | −0.952900 | − | 0.303284i | \(-0.901917\pi\) |
0.435809 | + | 0.900039i | \(0.356462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.23328 | + | 12.7337i | 0.439662 | + | 0.898163i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.36502 | + | 1.57531i | −0.0958055 | + | 0.110565i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.654351 | − | 4.55111i | −0.0457019 | − | 0.317864i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.65696 | − | 4.24815i | 0.115167 | − | 0.295267i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5453 | − | 8.06239i | −0.867778 | − | 0.557687i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.67188 | − | 12.4197i | 0.390468 | − | 0.855006i | −0.607680 | − | 0.794182i | \(-0.707900\pi\) |
0.998148 | − | 0.0608245i | \(-0.0193730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.63020 | − | 4.50914i | −0.180218 | − | 0.308961i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.869261 | + | 0.124981i | −0.0592831 | + | 0.00852362i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.44760 | − | 1.89319i | 0.437691 | − | 0.128518i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.549793 | − | 5.49881i | −0.0371515 | − | 0.371575i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.704383 | − | 1.54238i | −0.0473819 | − | 0.103752i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.86676 | − | 6.27733i | 0.191973 | − | 0.420361i | −0.789030 | − | 0.614354i | \(-0.789417\pi\) |
0.981003 | + | 0.193993i | \(0.0621439\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.71567 | − | 11.6459i | 0.181044 | − | 0.776390i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.5035 | + | 3.09174i | 1.42724 | + | 0.205206i | 0.812240 | − | 0.583324i | \(-0.198248\pi\) |
0.614997 | + | 0.788529i | \(0.289157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.34315 | − | 14.5382i | 0.617413 | − | 0.960713i | −0.381920 | − | 0.924195i | \(-0.624737\pi\) |
0.999333 | − | 0.0365175i | \(-0.0116265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.428893 | − | 9.93414i | 0.0282191 | − | 0.653618i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.77365 | − | 12.6425i | 0.378245 | − | 0.828240i | −0.620776 | − | 0.783988i | \(-0.713182\pi\) |
0.999020 | − | 0.0442520i | \(-0.0140905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.40337 | − | 1.21603i | 0.0915460 | − | 0.0793250i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0852269 | + | 0.120819i | −0.00553608 | + | 0.00784807i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.28691 | 0.212613 | 0.106306 | − | 0.994333i | \(-0.466098\pi\) | ||||
0.106306 | + | 0.994333i | \(0.466098\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.1310 | − | 7.08551i | −1.55442 | − | 0.456418i | −0.611999 | − | 0.790859i | \(-0.709634\pi\) |
−0.942417 | + | 0.334441i | \(0.891453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6139 | − | 5.42518i | 0.937485 | − | 0.348026i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.17015 | + | 2.56227i | 0.0747583 | + | 0.163698i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.841258 | + | 2.86506i | −0.0535279 | + | 0.182299i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.5093 | − | 11.5152i | 0.919492 | − | 0.729747i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.44108 | − | 10.0229i | 0.0909599 | − | 0.632640i | −0.892437 | − | 0.451172i | \(-0.851006\pi\) |
0.983397 | − | 0.181468i | \(-0.0580848\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21681 | − | 2.78738i | 0.202239 | − | 0.175241i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.65725 | + | 4.55553i | 0.166404 | + | 0.285278i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00280 | − | 10.2266i | −0.187310 | − | 0.637919i | −0.998581 | − | 0.0532489i | \(-0.983042\pi\) |
0.811271 | − | 0.584670i | \(-0.198776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.641641 | + | 0.555985i | 0.0398696 | + | 0.0345472i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.12458 | − | 2.18883i | −0.131508 | − | 0.135485i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.74612 | − | 19.5695i | −0.354321 | − | 1.20671i | −0.923211 | − | 0.384292i | \(-0.874445\pi\) |
0.568891 | − | 0.822413i | \(-0.307373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.57725 | − | 7.83308i | −0.219749 | − | 0.481182i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.718155 | + | 16.6341i | −0.0439504 | + | 1.01799i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.7758i | 1.14478i | 0.819980 | + | 0.572392i | \(0.193984\pi\) | ||||
−0.819980 | + | 0.572392i | \(0.806016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3459 | + | 4.72482i | −0.628470 | + | 0.287013i | −0.704075 | − | 0.710125i | \(-0.748638\pi\) |
0.0756055 | + | 0.997138i | \(0.475911\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.93277 | + | 0.478008i | −0.116977 | + | 0.0289304i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.30995 | − | 8.43613i | 0.440806 | − | 0.508718i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.83597 | + | 9.04319i | −0.470818 | + | 0.543353i | −0.940639 | − | 0.339409i | \(-0.889773\pi\) |
0.469821 | + | 0.882762i | \(0.344318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.94698 | + | 9.63912i | 0.116563 | + | 0.577079i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.01821 | + | 1.93968i | −0.180051 | + | 0.115712i | −0.627562 | − | 0.778567i | \(-0.715947\pi\) |
0.447511 | + | 0.894279i | \(0.352311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.46491 | − | 8.61497i | −0.443743 | − | 0.512107i | 0.489180 | − | 0.872183i | \(-0.337296\pi\) |
−0.932923 | + | 0.360076i | \(0.882751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.71703 | − | 9.12734i | 0.101708 | − | 0.540657i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.07452 | + | 6.13011i | −0.417596 | + | 0.361849i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.53763 | − | 2.21325i | −0.443390 | − | 0.130191i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.57209 | + | 2.25957i | −0.326642 | + | 0.132458i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.35113 | + | 8.32652i | 0.312616 | + | 0.486441i | 0.961635 | − | 0.274332i | \(-0.0884567\pi\) |
−0.649019 | + | 0.760772i | \(0.724820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.918384 | − | 3.12773i | 0.0534704 | − | 0.182103i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.4295 | + | 1.87826i | 0.837284 | + | 0.108988i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.716988 | − | 0.460780i | −0.0414645 | − | 0.0266476i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17085 | + | 1.35123i | 0.0674866 | + | 0.0778837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.66022 | + | 5.21701i | −0.152825 | + | 0.299709i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.823948i | − | 0.0471791i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.18062 | + | 3.32938i | 0.295674 | + | 0.190018i | 0.680064 | − | 0.733153i | \(-0.261952\pi\) |
−0.384390 | + | 0.923171i | \(0.625588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.12661 | + | 16.6203i | −0.177866 | + | 0.945496i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.81843 | + | 33.5129i | −0.273228 | + | 1.90034i | 0.140728 | + | 0.990048i | \(0.455056\pi\) |
−0.413957 | + | 0.910297i | \(0.635853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8275 | − | 9.96830i | −1.23377 | − | 0.563442i | −0.311591 | − | 0.950216i | \(-0.600862\pi\) |
−0.922174 | + | 0.386775i | \(0.873589\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.83378 | − | 2.07745i | 0.328696 | − | 0.117051i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.5268 | + | 2.80753i | −1.09673 | + | 0.157687i | −0.666846 | − | 0.745195i | \(-0.732356\pi\) |
−0.429888 | + | 0.902882i | \(0.641447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.802209 | − | 2.73207i | −0.0449151 | − | 0.152967i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6560 | − | 1.16541i | 0.650574 | − | 0.0650470i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.70599 | − | 13.5468i | −0.484414 | − | 0.753763i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.03314 | − | 0.928506i | −0.112779 | − | 0.0515042i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.6392 | + | 20.7528i | −0.809547 | + | 1.14763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.62740 | − | 1.06510i | −0.199985 | − | 0.0587209i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.36891 | + | 1.20327i | −0.459997 | + | 0.0661375i | −0.368418 | − | 0.929660i | \(-0.620100\pi\) |
−0.0915788 | + | 0.995798i | \(0.529191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.891531 | + | 0.865362i | −0.0488556 | + | 0.0474216i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.72650 | + | 2.86926i | −0.422144 | + | 0.156764i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.94419 | − | 2.55116i | −0.160380 | − | 0.138970i | 0.570974 | − | 0.820968i | \(-0.306566\pi\) |
−0.731354 | + | 0.681998i | \(0.761111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.23873 | + | 22.3908i | 0.121591 | + | 1.21610i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.58615 | + | 8.80762i | −0.140048 | + | 0.476959i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.8587 | − | 16.8965i | 0.586315 | − | 0.912325i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.36158 | + | 1.20420i | 0.127143 | + | 0.0648318i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.66034 | − | 6.20832i | 0.518594 | − | 0.333280i | −0.255022 | − | 0.966935i | \(-0.582083\pi\) |
0.773616 | + | 0.633655i | \(0.218446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.77161 | + | 33.1873i | 0.255418 | + | 1.77647i | 0.564494 | + | 0.825437i | \(0.309071\pi\) |
−0.309076 | + | 0.951037i | \(0.600020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.453144 | − | 2.87819i | −0.0241870 | − | 0.153626i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.418454 | + | 2.91041i | 0.0222721 | + | 0.154906i | 0.997923 | − | 0.0644256i | \(-0.0205215\pi\) |
−0.975650 | + | 0.219331i | \(0.929612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.76051 | − | 1.26068i | 0.146512 | − | 0.0669100i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.87750 | − | 9.56537i | 0.258145 | − | 0.506253i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.2740 | − | 5.21541i | −1.91447 | − | 0.275259i | −0.921016 | − | 0.389524i | \(-0.872640\pi\) |
−0.993450 | + | 0.114265i | \(0.963549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.33177 | + | 9.26270i | −0.0700934 | + | 0.487510i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.46946 | − | 3.15279i | −0.234586 | − | 0.165478i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.21267 | 0.168159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0174 | − | 6.85821i | −0.783901 | − | 0.357995i | −0.0170778 | − | 0.999854i | \(-0.505436\pi\) |
−0.766823 | + | 0.641859i | \(0.778164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.04517 | − | 11.0875i | −0.418815 | − | 0.577194i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.47838 | + | 14.7487i | −0.492093 | + | 0.765712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2146i | 1.25378i | 0.779106 | + | 0.626892i | \(0.215673\pi\) | ||||
−0.779106 | + | 0.626892i | \(0.784327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.8329 | + | 5.05987i | 0.765969 | + | 0.261291i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.479639 | + | 0.308245i | −0.0247027 | + | 0.0158754i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.71132 | − | 1.69490i | 0.190638 | − | 0.0870612i | −0.317809 | − | 0.948155i | \(-0.602947\pi\) |
0.508447 | + | 0.861093i | \(0.330220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.49628 | − | 1.19267i | −0.179120 | − | 0.0611022i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.71606 | − | 5.44262i | −0.240979 | − | 0.278105i | 0.622357 | − | 0.782733i | \(-0.286175\pi\) |
−0.863337 | + | 0.504628i | \(0.831630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.72175 | + | 0.822664i | 0.291607 | + | 0.0419268i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.11772 | + | 1.53663i | −0.107650 | + | 0.0781111i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.77788 | + | 13.6586i | 0.445056 | + | 0.692521i | 0.989217 | − | 0.146460i | \(-0.0467881\pi\) |
−0.544160 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41005 | − | 1.29491i | 0.223026 | − | 0.0654863i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1112 | + | 9.55543i | 0.510043 | + | 0.482008i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0649606 | − | 0.0562887i | −0.00326852 | − | 0.00283219i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.99947 | + | 1.76160i | −0.301105 | + | 0.0884123i | −0.428795 | − | 0.903402i | \(-0.641062\pi\) |
0.127690 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.5225 | + | 7.10564i | −0.877221 | + | 0.355727i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2313 | −1.01030 | −0.505152 | − | 0.863030i | \(-0.668564\pi\) | ||||
−0.505152 | + | 0.863030i | \(0.668564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.83804 | 0.0915591 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.29305 | + | 8.76744i | 0.113943 | + | 0.435658i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.11280 | + | 0.326747i | −0.0551594 | + | 0.0161963i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.00324140 | + | 0.00280869i | 0.000160277 | + | 0.000138881i | 0.654941 | − | 0.755680i | \(-0.272694\pi\) |
−0.654781 | + | 0.755819i | \(0.727239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.9648 | + | 21.1261i | −0.984792 | + | 1.04207i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.36777 | + | 1.86975i | −0.313338 | + | 0.0920042i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.82197 | + | 9.05916i | 0.285789 | + | 0.444697i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0008 | − | 8.73066i | 0.538710 | − | 0.427542i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.8438 | + | 3.28445i | 1.11600 | + | 0.160456i | 0.675543 | − | 0.737320i | \(-0.263909\pi\) |
0.440452 | + | 0.897776i | \(0.354818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.60373 | − | 4.15892i | −0.175635 | − | 0.202693i | 0.661106 | − | 0.750293i | \(-0.270087\pi\) |
−0.836741 | + | 0.547599i | \(0.815542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.01038 | − | 5.15427i | 0.0977482 | − | 0.250609i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.9644 | − | 5.00728i | 0.531852 | − | 0.242889i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.41119 | + | 0.906916i | −0.0682922 | + | 0.0438887i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.878097 | − | 2.57412i | 0.0423949 | − | 0.124280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0153i | 1.59029i | 0.606418 | + | 0.795146i | \(0.292606\pi\) | ||||
−0.606418 | + | 0.795146i | \(0.707394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.71980 | − | 8.90018i | 0.274876 | − | 0.427716i | −0.676179 | − | 0.736738i | \(-0.736365\pi\) |
0.951055 | + | 0.309022i | \(0.100002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.38904 | − | 1.10240i | 0.0665995 | − | 0.0528561i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.36264 | − | 3.36240i | −0.352203 | − | 0.160846i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.9237 | −1.38045 | −0.690226 | − | 0.723593i | \(-0.742489\pi\) | ||||
−0.690226 | + | 0.723593i | \(0.742489\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.64277 | + | 5.12885i | 0.316322 | + | 0.244231i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.62916 | − | 18.2862i | 0.124915 | − | 0.868803i | −0.826948 | − | 0.562279i | \(-0.809925\pi\) |
0.951863 | − | 0.306524i | \(-0.0991661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.58071 | − | 1.37750i | −0.454169 | − | 0.0652997i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.9725 | + | 16.8131i | 1.55955 | + | 0.795232i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.1989 | + | 7.39779i | −0.764473 | + | 0.349123i | −0.759195 | − | 0.650863i | \(-0.774407\pi\) |
−0.00527804 | + | 0.999986i | \(0.501680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81983 | − | 12.6572i | −0.0856924 | − | 0.596003i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.24465 | − | 0.555142i | 0.105463 | − | 0.0260828i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.164725 | − | 1.14569i | −0.00772243 | − | 0.0537107i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.4659 | + | 18.2939i | −1.33158 | + | 0.855754i | −0.996265 | − | 0.0863520i | \(-0.972479\pi\) |
−0.335315 | + | 0.942106i | \(0.608843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.3308 | + | 8.31764i | 0.622226 | + | 0.388234i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.94920 | + | 4.58905i | −0.137358 | + | 0.213733i | −0.903117 | − | 0.429394i | \(-0.858727\pi\) |
0.765759 | + | 0.643128i | \(0.222364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.34889 | − | 18.2166i | 0.248584 | − | 0.846599i | −0.736780 | − | 0.676133i | \(-0.763654\pi\) |
0.985364 | − | 0.170466i | \(-0.0545274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.68851 | + | 0.568759i | −0.263798 | + | 0.0263756i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.0193 | + | 12.1478i | 0.648736 | + | 0.562133i | 0.915844 | − | 0.401534i | \(-0.131523\pi\) |
−0.267108 | + | 0.963667i | \(0.586068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4188 | + | 10.0751i | 0.619621 | + | 0.465226i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.3781 | + | 26.8542i | −1.16936 | + | 1.23738i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.41752 | + | 0.347586i | −0.111158 | + | 0.0159820i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.3670 | − | 5.98029i | −0.934502 | − | 0.274395i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.3075 | − | 15.6793i | −0.929816 | − | 0.717906i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.8352 | + | 11.3419i | 1.13475 | + | 0.518222i | 0.892076 | − | 0.451886i | \(-0.149249\pi\) |
0.242673 | + | 0.970108i | \(0.421976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.125551 | + | 0.195361i | 0.00572464 | + | 0.00890771i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.536930 | − | 5.37016i | −0.0244312 | − | 0.244351i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.984809 | − | 3.35395i | −0.0447179 | − | 0.152295i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.5010 | − | 3.95405i | 1.24619 | − | 0.179175i | 0.512516 | − | 0.858678i | \(-0.328714\pi\) |
0.733673 | + | 0.679503i | \(0.237804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.961651 | − | 2.37143i | −0.0434874 | − | 0.107240i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.78595 | − | 1.27230i | −0.125728 | − | 0.0574182i | 0.351558 | − | 0.936166i | \(-0.385652\pi\) |
−0.477286 | + | 0.878748i | \(0.658379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.437577 | − | 3.04342i | 0.0197075 | − | 0.137069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.92107 | + | 8.23833i | −0.0863458 | + | 0.370285i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.19767 | − | 3.34034i | −0.233147 | − | 0.149835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.7775i | − | 1.51209i | −0.654521 | − | 0.756044i | \(-0.727130\pi\) | ||
0.654521 | − | 0.756044i | \(-0.272870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.87290 | − | 1.97484i | −0.173028 | − | 0.0882293i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.18125 | − | 9.44167i | −0.364784 | − | 0.420983i | 0.543453 | − | 0.839440i | \(-0.317117\pi\) |
−0.908237 | + | 0.418456i | \(0.862571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.86400 | − | 1.84058i | −0.127446 | − | 0.0819047i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.9516 | + | 0.947733i | 0.974906 | + | 0.0420903i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.15954 | + | 24.3831i | −0.317341 | + | 1.08076i | 0.634181 | + | 0.773184i | \(0.281337\pi\) |
−0.951522 | + | 0.307580i | \(0.900481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.53617 | − | 5.50239i | −0.156431 | − | 0.243411i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.14969 | − | 26.4433i | −0.359818 | − | 1.16750i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.43344 | − | 2.76991i | −0.415687 | − | 0.122057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.90295 | − | 3.38192i | 0.171651 | − | 0.148737i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.2713 | + | 4.00156i | 0.933708 | + | 0.175649i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.55265 | − | 9.87029i | −0.374699 | − | 0.432425i | 0.536812 | − | 0.843702i | \(-0.319628\pi\) |
−0.911511 | + | 0.411277i | \(0.865083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.5661 | − | 12.5744i | 0.855567 | − | 0.549840i | −0.0377395 | − | 0.999288i | \(-0.512016\pi\) |
0.893306 | + | 0.449448i | \(0.148379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.39804 | − | 13.7396i | −0.148303 | − | 0.599644i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.49113 | + | 7.49116i | −0.282758 | + | 0.326320i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5489 | + | 15.6363i | −0.589083 | + | 0.679838i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.92287 | − | 9.51978i | −0.0834456 | − | 0.413123i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.32907 | + | 1.06365i | −0.100883 | + | 0.0460719i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.81000i | 0.294422i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.1196 | + | 0.825465i | 0.825073 | + | 0.0356215i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.25433 | + | 7.12599i | 0.140174 | + | 0.306938i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6811 | − | 36.3766i | −0.459218 | − | 1.56395i | −0.785612 | − | 0.618720i | \(-0.787652\pi\) |
0.326393 | − | 0.945234i | \(-0.394167\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.10922 | + | 1.17373i | −0.0476010 | + | 0.0503697i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.1581 | − | 9.66853i | −0.477960 | − | 0.414154i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.93535 | + | 23.6196i | 0.296534 | + | 1.00990i | 0.964141 | + | 0.265389i | \(0.0855005\pi\) |
−0.667607 | + | 0.744514i | \(0.732681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.14426 | − | 2.17184i | −0.0488358 | − | 0.0926920i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.09212 | + | 3.54584i | −0.174330 | + | 0.151058i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0249047 | + | 0.173216i | −0.00105905 | + | 0.00736588i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.449018 | − | 0.565770i | −0.0190598 | − | 0.0240156i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.197657 | + | 0.673158i | −0.00837500 | + | 0.0285226i | −0.963574 | − | 0.267440i | \(-0.913822\pi\) |
0.955199 | + | 0.295963i | \(0.0956404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.203157 | + | 0.444852i | 0.00859263 | + | 0.0188152i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.39013 | + | 12.6695i | 0.312012 | + | 0.534905i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.72548 | + | 1.09390i | 0.157010 | + | 0.0461024i | 0.359293 | − | 0.933225i | \(-0.383018\pi\) |
−0.202283 | + | 0.979327i | \(0.564836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.0818 | −0.550356 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.4922 | − | 13.5776i | 0.524623 | − | 0.570207i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.8384 | + | 9.39154i | −0.454370 | + | 0.393714i | −0.851757 | − | 0.523937i | \(-0.824463\pi\) |
0.397387 | + | 0.917651i | \(0.369917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9314 | − | 23.9364i | 0.457464 | − | 1.00171i | −0.530594 | − | 0.847626i | \(-0.678031\pi\) |
0.988058 | − | 0.154081i | \(-0.0492416\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.5474 | − | 0.714413i | −0.691278 | − | 0.0298450i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.27557 | − | 5.09689i | 0.136601 | − | 0.212555i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.1561 | − | 5.48602i | −1.58846 | − | 0.228386i | −0.709297 | − | 0.704909i | \(-0.750988\pi\) |
−0.879162 | + | 0.476523i | \(0.841897\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.66878 | + | 40.7654i | −0.318703 | + | 1.69415i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.10755 | − | 19.9428i | 0.377845 | − | 0.827365i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.94875 | − | 21.7847i | −0.412035 | − | 0.902231i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.69114 | − | 0.0956613i | 0.0699202 | − | 0.00395511i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.3634 | − | 6.86013i | 0.964313 | − | 0.283148i | 0.238579 | − | 0.971123i | \(-0.423318\pi\) |
0.725734 | + | 0.687975i | \(0.241500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.2780 | − | 2.48420i | 0.711928 | − | 0.102360i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.7535 | + | 9.18905i | −0.648012 | + | 0.377987i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.35922 | − | 11.7351i | 0.220077 | − | 0.481901i | −0.767101 | − | 0.641526i | \(-0.778301\pi\) |
0.987178 | + | 0.159626i | \(0.0510287\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.25114 | + | 3.37470i | 0.215276 | + | 0.138349i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.2600 | − | 6.22895i | −0.747334 | − | 0.254934i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.00325 | + | 27.8432i | 0.163568 | + | 1.13764i | 0.891839 | + | 0.452353i | \(0.149415\pi\) |
−0.728271 | + | 0.685290i | \(0.759676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3336 | + | 18.8499i | −0.666260 | + | 0.768905i | −0.983786 | − | 0.179345i | \(-0.942602\pi\) |
0.317526 | + | 0.948249i | \(0.397148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.3816 | + | 18.2933i | −0.667110 | + | 0.744960i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.08228 | − | 2.40308i | 0.0846567 | − | 0.0976991i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.952491 | + | 6.62472i | 0.0386604 | + | 0.268889i | 0.999979 | − | 0.00655145i | \(-0.00208541\pi\) |
−0.961318 | + | 0.275440i | \(0.911176\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.41701 | − | 1.16563i | −0.138464 | − | 0.0472336i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.869919 | − | 0.559063i | −0.0351931 | − | 0.0226173i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.13198 | − | 11.2375i | 0.207279 | − | 0.453877i | −0.777229 | − | 0.629218i | \(-0.783375\pi\) |
0.984508 | + | 0.175340i | \(0.0561026\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.87907 | − | 4.01258i | 0.277391 | − | 0.161803i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.84688 | + | 0.840654i | −0.235386 | + | 0.0338435i | −0.258998 | − | 0.965878i | \(-0.583392\pi\) |
0.0236120 | + | 0.999721i | \(0.492483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.7054 | + | 11.6586i | −1.59590 | + | 0.468597i | −0.954401 | − | 0.298529i | \(-0.903504\pi\) |
−0.641496 | + | 0.767127i | \(0.721686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.89720 | − | 0.105505i | 0.316904 | − | 0.00423376i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.18619 | + | 17.9253i | 0.327973 | + | 0.718160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.49457 | − | 9.84173i | 0.179783 | − | 0.393669i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.77527 | − | 25.3842i | 0.190706 | − | 1.01375i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.23961 | − | 0.178229i | −0.0494266 | − | 0.00710647i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.6056 | − | 33.6190i | 0.860105 | − | 1.33835i | −0.0797638 | − | 0.996814i | \(-0.525417\pi\) |
0.939869 | − | 0.341536i | \(-0.110947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.6266 | + | 1.02005i | 0.939073 | + | 0.0405432i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.892132 | − | 1.95350i | 0.0354032 | − | 0.0775222i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.18548 | − | 1.02722i | 0.0469705 | − | 0.0407001i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.52564 | − | 7.15669i | 0.218591 | − | 0.283114i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.3864 | 0.844712 | 0.422356 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422356 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.2695 | + | 4.77715i | 0.641606 | + | 0.188393i | 0.586322 | − | 0.810078i | \(-0.300575\pi\) |
0.0552841 | + | 0.998471i | \(0.482394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.766402 | − | 1.31390i | −0.0301770 | − | 0.0517348i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.74123 | + | 10.3819i | 0.186397 | + | 0.408153i | 0.979643 | − | 0.200749i | \(-0.0643376\pi\) |
−0.793246 | + | 0.608902i | \(0.791610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.55413 | − | 8.69858i | 0.100259 | − | 0.341449i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.23544 | + | 9.11676i | 0.283579 | + | 0.357314i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.71761 | − | 46.7220i | 0.262880 | − | 1.82837i | −0.248045 | − | 0.968749i | \(-0.579788\pi\) |
0.510925 | − | 0.859625i | \(-0.329303\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.11229 | + | 5.29633i | −0.238827 | + | 0.206945i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.46827 | − | 4.46160i | 0.330379 | − | 0.174064i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1587 | − | 38.0030i | −0.434681 | − | 1.48039i | −0.827865 | − | 0.560927i | \(-0.810445\pi\) |
0.393185 | − | 0.919459i | \(-0.371373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.78336 | + | 1.54529i | 0.0693648 | + | 0.0601049i | 0.688853 | − | 0.724901i | \(-0.258114\pi\) |
−0.619488 | + | 0.785006i | \(0.712660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.01720 | − | 2.13453i | 0.0783415 | − | 0.0828982i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.09691 | − | 10.5471i | −0.120093 | − | 0.409000i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.642015 | − | 1.40582i | −0.0248589 | − | 0.0544335i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.9417 | + | 0.515567i | 0.461692 | + | 0.0199330i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.29149i | − | 0.0884622i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.5482 | + | 16.6910i | −1.40883 | + | 0.643391i | −0.967249 | − | 0.253830i | \(-0.918309\pi\) |
−0.441581 | + | 0.897221i | \(0.645582\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.4603 | − | 3.22129i | 0.787519 | − | 0.123987i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.77120 | − | 11.2766i | 0.375538 | − | 0.433393i | −0.536248 | − | 0.844061i | \(-0.680159\pi\) |
0.911785 | + | 0.410667i | \(0.134704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.66039 | + | 5.37838i | −0.178849 | + | 0.206403i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.03392 | + | 36.5276i | 0.346180 | + | 1.39974i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6644 | − | 19.0642i | 1.13508 | − | 0.729471i | 0.168465 | − | 0.985708i | \(-0.446119\pi\) |
0.966614 | + | 0.256237i | \(0.0824828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0660 | − | 12.7708i | −0.422810 | − | 0.487949i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.4166 | + | 5.53385i | 1.12232 | + | 0.211130i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.62411 | + | 3.14031i | −0.138068 | + | 0.119636i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.16029 | − | 0.340691i | −0.0441395 | − | 0.0129605i | 0.259588 | − | 0.965719i | \(-0.416413\pi\) |
−0.303728 | + | 0.952759i | \(0.598231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.2244 | − | 5.77764i | 0.616315 | − | 0.219474i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.41413 | + | 6.86852i | 0.167438 | + | 0.260538i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.89020 | − | 13.2488i | 0.147352 | − | 0.501834i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0505 | + | 1.03835i | 0.909675 | + | 0.0392740i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.7655 | − | 14.6305i | −0.859840 | − | 0.552585i | 0.0347895 | − | 0.999395i | \(-0.488924\pi\) |
−0.894629 | + | 0.446809i | \(0.852560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.44425 | + | 1.66676i | 0.0544711 | + | 0.0628630i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.86529 | + | 1.46105i | 0.107913 | + | 0.0550262i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.93114i | 0.260672i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.0873 | − | 13.5520i | −0.791950 | − | 0.508956i | 0.0810296 | − | 0.996712i | \(-0.474179\pi\) |
−0.872980 | + | 0.487756i | \(0.837816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.249401 | − | 0.0581570i | −0.00935325 | − | 0.00218106i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.709055 | + | 4.93159i | −0.0265543 | + | 0.184689i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.43826 | + | 0.656829i | 0.0537877 | + | 0.0245640i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.13943 | + | 5.27582i | 0.0798984 | + | 0.197029i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.2245 | − | 5.20830i | 1.35095 | − | 0.194237i | 0.571447 | − | 0.820639i | \(-0.306382\pi\) |
0.779500 | + | 0.626402i | \(0.215473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.63928 | + | 19.2056i | 0.210018 | + | 0.715255i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.33376 | − | 43.3446i | −0.161174 | − | 1.61200i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.19124 | − | 3.40963i | −0.0813805 | − | 0.126631i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.87291 | + | 1.31201i | 0.106550 | + | 0.0486599i | 0.467977 | − | 0.883741i | \(-0.344983\pi\) |
−0.361427 | + | 0.932401i | \(0.617710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.2201 | + | 19.9256i | 0.674817 | + | 0.737985i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.53051 | − | 0.743026i | −0.0935945 | − | 0.0274818i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.93442 | − | 0.278128i | 0.0714494 | − | 0.0102729i | −0.106497 | − | 0.994313i | \(-0.533964\pi\) |
0.177947 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.35106 | + | 3.54597i | −0.123606 | + | 0.130795i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.4883 | + | 7.97975i | −0.791532 | + | 0.293938i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9300 | − | 13.8034i | −0.585995 | − | 0.507768i | 0.310646 | − | 0.950526i | \(-0.399455\pi\) |
−0.896641 | + | 0.442758i | \(0.854000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.14627 | + | 0.514545i | −0.189053 | + | 0.0189023i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.85255 | − | 23.3376i | 0.251396 | − | 0.856175i | −0.733003 | − | 0.680225i | \(-0.761882\pi\) |
0.984399 | − | 0.175950i | \(-0.0562998\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6328 | + | 18.1010i | −0.426194 | + | 0.663171i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.9270 | + | 15.7938i | 1.02180 | + | 0.577863i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6636 | − | 7.49574i | 0.426178 | − | 0.273888i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.12290 | + | 14.7651i | 0.0774656 | + | 0.538785i | 0.991190 | + | 0.132450i | \(0.0422844\pi\) |
−0.913724 | + | 0.406335i | \(0.866807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.0257 | − | 4.21076i | 0.620452 | − | 0.153449i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.191306 | + | 1.33056i | 0.00696233 | + | 0.0484241i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.05419 | − | 0.481431i | 0.0383150 | − | 0.0174979i | −0.396165 | − | 0.918179i | \(-0.629659\pi\) |
0.434480 | + | 0.900681i | \(0.356932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.56782 | + | 3.34901i | 0.238397 | + | 0.121561i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.9508 | + | 3.44360i | 0.868215 | + | 0.124830i | 0.562005 | − | 0.827134i | \(-0.310030\pi\) |
0.306209 | + | 0.951964i | \(0.400939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.27780 | + | 29.7527i | −0.154867 | + | 1.07712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.58248 | + | 7.23031i | −0.201835 | + | 0.261412i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.81528 | −0.0655460 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4927 | + | 7.07527i | 0.558680 | + | 0.255141i | 0.674682 | − | 0.738108i | \(-0.264281\pi\) |
−0.116002 | + | 0.993249i | \(0.537008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4602 | − | 11.4762i | 0.520772 | − | 0.413306i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.4824 | − | 22.5351i | 0.520897 | − | 0.810531i | −0.476754 | − | 0.879037i | \(-0.658187\pi\) |
0.997651 | + | 0.0685055i | \(0.0218231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.0661i | 0.469350i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.474771 | + | 1.39178i | −0.0170323 | + | 0.0499299i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.4563 | + | 13.1465i | −0.732923 | + | 0.471021i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.67729 | − | 3.50610i | 0.274715 | − | 0.125458i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.13041 | − | 4.83485i | 0.0761348 | − | 0.172784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0664 | − | 16.2335i | −0.502052 | − | 0.579399i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.61100 | − | 0.375406i | −0.0930723 | − | 0.0133818i | 0.0956213 | − | 0.995418i | \(-0.469516\pi\) |
−0.188694 | + | 0.982036i | \(0.560425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.6708 | − | 21.9607i | 0.985107 | − | 0.781822i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.3991 | + | 22.4054i | 0.511973 | + | 0.796646i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.440249 | + | 0.129269i | −0.0156337 | + | 0.00459046i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2445 | − | 10.8403i | 0.363334 | − | 0.384467i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.9982 | − | 24.2605i | −0.991746 | − | 0.859352i | −0.00168569 | − | 0.999999i | \(-0.500537\pi\) |
−0.990060 | + | 0.140646i | \(0.955082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.35070 | − | 1.57111i | 0.189294 | − | 0.0555818i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.1668 | + | 9.67429i | −0.959891 | + | 0.341824i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.93481 | 0.315303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.13751 | 0.110583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.1371 | + | 12.2210i | −1.06087 | + | 0.430201i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0045 | − | 4.69934i | 0.562688 | − | 0.165220i | 0.0119949 | − | 0.999928i | \(-0.496182\pi\) |
0.550693 | + | 0.834708i | \(0.314364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7879 | + | 18.0128i | 0.729963 | + | 0.632517i | 0.938413 | − | 0.345516i | \(-0.112296\pi\) |
−0.208450 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.3179 | − | 13.5309i | −0.502150 | − | 0.474548i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.42741 | − | 0.419125i | 0.0499999 | − | 0.0146813i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.51097 | + | 3.90715i | 0.0878477 | + | 0.136694i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.02527 | − | 2.79115i | −0.0707688 | − | 0.0975308i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.8405 | + | 2.13374i | 0.517936 | + | 0.0744679i | 0.396326 | − | 0.918110i | \(-0.370285\pi\) |
0.121610 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.65464 | − | 9.98799i | −0.301682 | − | 0.348159i | 0.584587 | − | 0.811331i | \(-0.301257\pi\) |
−0.886268 | + | 0.463172i | \(0.846711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.2988 | + | 6.24217i | 0.637083 | + | 0.217325i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8256 | − | 8.14067i | 0.619856 | − | 0.283079i | −0.0806307 | − | 0.996744i | \(-0.525693\pi\) |
0.700487 | + | 0.713665i | \(0.252966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.02006 | + | 3.86886i | −0.209085 | + | 0.134371i | −0.640993 | − | 0.767547i | \(-0.721477\pi\) |
0.431907 | + | 0.901918i | \(0.357841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.6156 | − | 6.69135i | −0.680457 | − | 0.232121i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.45928i | 0.293097i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.36637 | − | 2.12612i | 0.0472853 | − | 0.0735774i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.2045 | + | 9.39912i | −0.490978 | + | 0.324881i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.63535 | + | 3.48695i | 0.263601 | + | 0.120383i | 0.542832 | − | 0.839841i | \(-0.317352\pi\) |
−0.279230 | + | 0.960224i | \(0.590079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9661 | 0.964349 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.07791 | − | 3.58199i | −0.174893 | − | 0.123370i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.81785 | + | 12.6434i | −0.0625360 | + | 0.434948i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.40775 | − | 0.921296i | −0.220173 | − | 0.0316561i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.96902 | − | 17.5893i | 0.307816 | − | 0.603664i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.572603 | + | 0.261499i | −0.0196286 | + | 0.00896406i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.63189 | + | 11.3501i | 0.0558749 | + | 0.388619i | 0.998499 | + | 0.0547635i | \(0.0174405\pi\) |
−0.942624 | + | 0.333855i | \(0.891650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.7679 | − | 3.18491i | 0.539250 | − | 0.108922i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.83260 | + | 12.7460i | 0.0626003 | + | 0.435395i | 0.996885 | + | 0.0788672i | \(0.0251303\pi\) |
−0.934285 | + | 0.356527i | \(0.883961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8921 | + | 7.64260i | −0.405754 | + | 0.260762i | −0.727561 | − | 0.686043i | \(-0.759346\pi\) |
0.321807 | + | 0.946805i | \(0.395710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.4442 | − | 7.36526i | −0.492256 | − | 0.251008i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.0327 | − | 17.1672i | 0.375557 | − | 0.584378i | −0.601102 | − | 0.799172i | \(-0.705272\pi\) |
0.976659 | + | 0.214794i | \(0.0689079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.54504 | + | 12.0733i | −0.120535 | + | 0.410504i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.35370 | − | 13.5392i | −0.0459742 | − | 0.459816i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.180663 | − | 0.156545i | −0.00612857 | − | 0.00531044i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.74530 | + | 3.67824i | 0.0930209 | + | 0.124632i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.25366 | − | 7.47302i | −0.245499 | − | 0.252923i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.3604 | − | 2.63983i | 0.620696 | − | 0.0892426i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6670 | + | 3.13210i | 0.360197 | + | 0.105763i | 0.456824 | − | 0.889557i | \(-0.348987\pi\) |
−0.0966264 | + | 0.995321i | \(0.530805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.88187 | + | 14.0088i | −0.333307 | + | 0.472504i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.6371 | + | 6.68455i | 0.493137 | + | 0.225208i | 0.646431 | − | 0.762973i | \(-0.276261\pi\) |
−0.153294 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8188 | + | 19.9464i | 0.431385 | + | 0.671249i | 0.987096 | − | 0.160127i | \(-0.0511903\pi\) |
−0.555711 | + | 0.831375i | \(0.687554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.61808 | − | 0.561718i | 0.188850 | − | 0.0188819i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8144 | + | 40.2361i | 0.396688 | + | 1.35100i | 0.879761 | + | 0.475416i | \(0.157703\pi\) |
−0.483073 | + | 0.875580i | \(0.660479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.32775 | + | 0.622237i | −0.145148 | + | 0.0208691i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.37724 | + | 24.3833i | 0.213646 | + | 0.816871i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.93306 | − | 4.07959i | −0.298933 | − | 0.136518i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.58333 | + | 11.0123i | −0.0529249 | + | 0.368101i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.272915 | − | 1.45075i | 0.00911238 | − | 0.0484393i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.80388 | + | 1.80194i | 0.0935146 | + | 0.0600982i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.8607i | − | 0.861546i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.40676 | + | 2.75883i | −0.0468141 | + | 0.0918082i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.614810 | − | 0.709529i | −0.0204370 | − | 0.0235855i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.9158 | − | 21.1537i | −1.09295 | − | 0.702396i | −0.135437 | − | 0.990786i | \(-0.543244\pi\) |
−0.957513 | + | 0.288390i | \(0.906880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.1053 | − | 0.874197i | −0.335172 | − | 0.0289953i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.40813 | + | 32.0411i | −0.311705 | + | 1.06157i | 0.643456 | + | 0.765483i | \(0.277500\pi\) |
−0.955161 | + | 0.296087i | \(0.904318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.1916 | + | 25.1946i | 0.535863 | + | 0.833819i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.32252 | − | 0.536301i | 0.0437210 | − | 0.0177296i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.7989 | + | 4.63897i | 0.521725 | + | 0.153192i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5490 | − | 11.7403i | 0.446940 | − | 0.387276i | −0.402107 | − | 0.915593i | \(-0.631722\pi\) |
0.849047 | + | 0.528317i | \(0.177177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.97196 | + | 10.4825i | −0.0649783 | + | 0.345409i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.10670 | − | 1.27720i | −0.0364274 | − | 0.0420394i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.38878 | + | 0.892512i | −0.0456627 | + | 0.0293456i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.7123 | + | 5.79951i | −0.943036 | + | 0.190481i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.2500 | − | 30.2941i | 0.861235 | − | 0.993918i | −0.138759 | − | 0.990326i | \(-0.544311\pi\) |
0.999994 | − | 0.00359196i | \(-0.00114336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.75547 | − | 11.2584i | 0.319723 | − | 0.368980i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −56.9278 | + | 14.0793i | −1.86373 | + | 0.460934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.75627 | + | 3.54217i | −0.253657 | + | 0.115841i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.6410i | − | 0.543638i | −0.962348 | − | 0.271819i | \(-0.912375\pi\) | ||
0.962348 | − | 0.271819i | \(-0.0876253\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.79273 | − | 41.5236i | 0.0585035 | − | 1.35507i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.6549 | + | 23.3310i | 0.347340 | + | 0.760568i | 0.999996 | + | 0.00291342i | \(0.000927371\pi\) |
−0.652656 | + | 0.757654i | \(0.726345\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.95537 | − | 6.65940i | −0.0636758 | − | 0.216860i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.13168 | + | 8.01159i | 0.231993 | + | 0.260617i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.8510 | − | 22.4001i | −0.840046 | − | 0.727904i | 0.124386 | − | 0.992234i | \(-0.460304\pi\) |
−0.964432 | + | 0.264330i | \(0.914849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.504034 | − | 1.71658i | −0.0163616 | − | 0.0557226i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.2162 | − | 29.5150i | −0.558274 | − | 0.957091i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3020 | − | 27.9898i | 1.04636 | − | 0.906680i | 0.0506091 | − | 0.998719i | \(-0.483884\pi\) |
0.995755 | + | 0.0920385i | \(0.0293383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.37032 | − | 9.53079i | 0.0443425 | − | 0.308409i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.86309 | − | 3.06591i | 0.124876 | − | 0.0991067i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.69253 | + | 33.0097i | −0.312988 | + | 1.06594i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.41431 | + | 18.4248i | 0.271429 | + | 0.594347i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.45740 | + | 17.9505i | 0.304760 | + | 0.578445i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.1378 | − | 6.79388i | −0.744833 | − | 0.218703i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.9422 | 0.834244 | 0.417122 | − | 0.908850i | \(-0.363039\pi\) | ||||
0.417122 | + | 0.908850i | \(0.363039\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0772 | − | 22.7915i | 0.516476 | − | 0.732167i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.7269 | + | 26.6250i | −0.986072 | + | 0.854436i | −0.989350 | − | 0.145558i | \(-0.953502\pi\) |
0.00327763 | + | 0.999995i | \(0.498957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.90521 | − | 15.1203i | 0.221371 | − | 0.484735i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.166985 | − | 3.86775i | 0.00534781 | − | 0.123867i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.2919 | + | 17.5706i | −0.361261 | + | 0.562133i | −0.973542 | − | 0.228507i | \(-0.926616\pi\) |
0.612281 | + | 0.790640i | \(0.290252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.6451 | − | 3.83099i | −0.851581 | − | 0.122439i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.8388 | − | 9.98945i | −1.36774 | − | 0.318939i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.2208 | − | 42.0876i | 0.613047 | − | 1.34239i | −0.307423 | − | 0.951573i | \(-0.599467\pi\) |
0.920470 | − | 0.390813i | \(-0.127806\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.40441 | − | 9.64431i | −0.140336 | − | 0.307293i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.651455 | − | 6.51560i | −0.0207361 | − | 0.207394i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.27194 | + | 0.373476i | −0.0404454 | + | 0.0118758i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.8046 | − | 5.00415i | 1.10560 | − | 0.158962i | 0.434750 | − | 0.900551i | \(-0.356837\pi\) |
0.670854 | + | 0.741589i | \(0.265928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.37862 | − | 12.6497i | −0.234153 | − | 0.401427i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.65934 | − | 10.2025i | 0.147711 | − | 0.323442i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6314 | + | 24.8269i | 1.22347 | + | 0.786275i | 0.982861 | − | 0.184348i | \(-0.0590173\pi\) |
0.240606 | + | 0.970623i | \(0.422654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.96928 | − | 0.867737i | −0.0623053 | − | 0.0274540i |
(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 | 804.2.s.b.5.15 | yes | 200 | |
3.2 | odd | 2 | inner | 804.2.s.b.5.8 | ✓ | 200 | |
67.27 | odd | 22 | inner | 804.2.s.b.161.8 | yes | 200 | |
201.161 | even | 22 | inner | 804.2.s.b.161.15 | yes | 200 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.b.5.8 | ✓ | 200 | 3.2 | odd | 2 | inner | |
804.2.s.b.5.15 | yes | 200 | 1.1 | even | 1 | trivial | |
804.2.s.b.161.8 | yes | 200 | 67.27 | odd | 22 | inner | |
804.2.s.b.161.15 | yes | 200 | 201.161 | even | 22 | inner |