Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(37,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(0.947050 - 1.64034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.163 |
Dual form | 201.2.e.b.37.2 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.947050 | + | 1.64034i | −0.669666 | + | 1.15989i | 0.308332 | + | 0.951279i | \(0.400229\pi\) |
−0.977998 | + | 0.208616i | \(0.933104\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.793808 | − | 1.37492i | −0.396904 | − | 0.687458i | ||||
\(5\) | 1.30648 | 0.584277 | 0.292139 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292139 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(6\) | 0.947050 | − | 1.64034i | 0.386632 | − | 0.669666i | ||||
\(7\) | 2.53710 | + | 4.39438i | 0.958933 | + | 1.66092i | 0.725100 | + | 0.688643i | \(0.241793\pi\) |
0.233833 | + | 0.972277i | \(0.424873\pi\) | |||||||
\(8\) | −0.781096 | −0.276159 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.23731 | + | 2.14308i | −0.391271 | + | 0.677700i | ||||
\(11\) | −1.88386 | − | 3.26293i | −0.568004 | − | 0.983812i | −0.996763 | − | 0.0803928i | \(-0.974383\pi\) |
0.428759 | − | 0.903419i | \(-0.358951\pi\) | |||||||
\(12\) | 0.793808 | + | 1.37492i | 0.229153 | + | 0.396904i | ||||
\(13\) | −2.77440 | + | 4.80541i | −0.769481 | + | 1.33278i | 0.168363 | + | 0.985725i | \(0.446152\pi\) |
−0.937845 | + | 0.347055i | \(0.887182\pi\) | |||||||
\(14\) | −9.61104 | −2.56866 | ||||||||
\(15\) | −1.30648 | −0.337333 | ||||||||
\(16\) | 2.32735 | − | 4.03109i | 0.581838 | − | 1.00777i | ||||
\(17\) | −2.28465 | + | 3.95713i | −0.554109 | + | 0.959744i | 0.443864 | + | 0.896094i | \(0.353607\pi\) |
−0.997972 | + | 0.0636500i | \(0.979726\pi\) | |||||||
\(18\) | −0.947050 | + | 1.64034i | −0.223222 | + | 0.386632i | ||||
\(19\) | 0.737306 | − | 1.27705i | 0.169150 | − | 0.292976i | −0.768972 | − | 0.639283i | \(-0.779231\pi\) |
0.938121 | + | 0.346307i | \(0.112565\pi\) | |||||||
\(20\) | −1.03710 | − | 1.79631i | −0.231902 | − | 0.401666i | ||||
\(21\) | −2.53710 | − | 4.39438i | −0.553640 | − | 0.958933i | ||||
\(22\) | 7.13642 | 1.52149 | ||||||||
\(23\) | 1.39410 | − | 2.41465i | 0.290690 | − | 0.503490i | −0.683283 | − | 0.730154i | \(-0.739448\pi\) |
0.973973 | + | 0.226664i | \(0.0727818\pi\) | |||||||
\(24\) | 0.781096 | 0.159441 | ||||||||
\(25\) | −3.29310 | −0.658620 | ||||||||
\(26\) | −5.25500 | − | 9.10193i | −1.03059 | − | 1.78503i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.02794 | − | 6.97659i | 0.761209 | − | 1.31845i | ||||
\(29\) | 2.62785 | + | 4.55158i | 0.487980 | + | 0.845207i | 0.999904 | − | 0.0138241i | \(-0.00440048\pi\) |
−0.511924 | + | 0.859031i | \(0.671067\pi\) | |||||||
\(30\) | 1.23731 | − | 2.14308i | 0.225900 | − | 0.391271i | ||||
\(31\) | 0.883856 | + | 1.53088i | 0.158745 | + | 0.274955i | 0.934416 | − | 0.356182i | \(-0.115922\pi\) |
−0.775671 | + | 0.631137i | \(0.782589\pi\) | |||||||
\(32\) | 3.62715 | + | 6.28240i | 0.641195 | + | 1.11058i | ||||
\(33\) | 1.88386 | + | 3.26293i | 0.327937 | + | 0.568004i | ||||
\(34\) | −4.32735 | − | 7.49520i | −0.742135 | − | 1.28542i | ||||
\(35\) | 3.31468 | + | 5.74119i | 0.560283 | + | 0.970438i | ||||
\(36\) | −0.793808 | − | 1.37492i | −0.132301 | − | 0.229153i | ||||
\(37\) | 3.48841 | − | 6.04210i | 0.573491 | − | 0.993315i | −0.422713 | − | 0.906264i | \(-0.638922\pi\) |
0.996204 | − | 0.0870517i | \(-0.0277445\pi\) | |||||||
\(38\) | 1.39653 | + | 2.41886i | 0.226547 | + | 0.392391i | ||||
\(39\) | 2.77440 | − | 4.80541i | 0.444260 | − | 0.769481i | ||||
\(40\) | −1.02049 | −0.161354 | ||||||||
\(41\) | 4.25612 | + | 7.37182i | 0.664694 | + | 1.15128i | 0.979368 | + | 0.202084i | \(0.0647716\pi\) |
−0.314674 | + | 0.949200i | \(0.601895\pi\) | |||||||
\(42\) | 9.61104 | 1.48302 | ||||||||
\(43\) | 8.89927 | 1.35713 | 0.678563 | − | 0.734542i | \(-0.262603\pi\) | ||||
0.678563 | + | 0.734542i | \(0.262603\pi\) | |||||||
\(44\) | −2.99084 | + | 5.18029i | −0.450886 | + | 0.780958i | ||||
\(45\) | 1.30648 | 0.194759 | ||||||||
\(46\) | 2.64057 | + | 4.57359i | 0.389330 | + | 0.674340i | ||||
\(47\) | −2.59431 | − | 4.49347i | −0.378419 | − | 0.655441i | 0.612414 | − | 0.790538i | \(-0.290199\pi\) |
−0.990832 | + | 0.135097i | \(0.956865\pi\) | |||||||
\(48\) | −2.32735 | + | 4.03109i | −0.335925 | + | 0.581838i | ||||
\(49\) | −9.37373 | + | 16.2358i | −1.33910 | + | 2.31940i | ||||
\(50\) | 3.11873 | − | 5.40180i | 0.441055 | − | 0.763930i | ||||
\(51\) | 2.28465 | − | 3.95713i | 0.319915 | − | 0.554109i | ||||
\(52\) | 8.80938 | 1.22164 | ||||||||
\(53\) | −2.37365 | −0.326046 | −0.163023 | − | 0.986622i | \(-0.552124\pi\) | ||||
−0.163023 | + | 0.986622i | \(0.552124\pi\) | |||||||
\(54\) | 0.947050 | − | 1.64034i | 0.128877 | − | 0.223222i | ||||
\(55\) | −2.46123 | − | 4.26297i | −0.331872 | − | 0.574819i | ||||
\(56\) | −1.98172 | − | 3.43243i | −0.264818 | − | 0.458678i | ||||
\(57\) | −0.737306 | + | 1.27705i | −0.0976586 | + | 0.169150i | ||||
\(58\) | −9.95484 | −1.30713 | ||||||||
\(59\) | 10.8348 | 1.41057 | 0.705286 | − | 0.708923i | \(-0.250819\pi\) | ||||
0.705286 | + | 0.708923i | \(0.250819\pi\) | |||||||
\(60\) | 1.03710 | + | 1.79631i | 0.133889 | + | 0.231902i | ||||
\(61\) | 6.21229 | − | 10.7600i | 0.795403 | − | 1.37768i | −0.127180 | − | 0.991880i | \(-0.540593\pi\) |
0.922583 | − | 0.385798i | \(-0.126074\pi\) | |||||||
\(62\) | −3.34822 | −0.425225 | ||||||||
\(63\) | 2.53710 | + | 4.39438i | 0.319644 | + | 0.553640i | ||||
\(64\) | −4.43094 | −0.553868 | ||||||||
\(65\) | −3.62471 | + | 6.27819i | −0.449590 | + | 0.778714i | ||||
\(66\) | −7.13642 | −0.878433 | ||||||||
\(67\) | 8.01183 | − | 1.67649i | 0.978801 | − | 0.204815i | ||||
\(68\) | 7.25429 | 0.879712 | ||||||||
\(69\) | −1.39410 | + | 2.41465i | −0.167830 | + | 0.290690i | ||||
\(70\) | −12.5567 | −1.50081 | ||||||||
\(71\) | −4.98658 | − | 8.63701i | −0.591798 | − | 1.02502i | −0.993990 | − | 0.109469i | \(-0.965085\pi\) |
0.402192 | − | 0.915555i | \(-0.368248\pi\) | |||||||
\(72\) | −0.781096 | −0.0920530 | ||||||||
\(73\) | 2.00845 | − | 3.47874i | 0.235071 | − | 0.407156i | −0.724222 | − | 0.689567i | \(-0.757801\pi\) |
0.959293 | + | 0.282411i | \(0.0911343\pi\) | |||||||
\(74\) | 6.60740 | + | 11.4443i | 0.768094 | + | 1.33038i | ||||
\(75\) | 3.29310 | 0.380254 | ||||||||
\(76\) | −2.34112 | −0.268545 | ||||||||
\(77\) | 9.55905 | − | 16.5568i | 1.08936 | − | 1.88682i | ||||
\(78\) | 5.25500 | + | 9.10193i | 0.595011 | + | 1.03059i | ||||
\(79\) | −0.880303 | − | 1.52473i | −0.0990419 | − | 0.171546i | 0.812246 | − | 0.583314i | \(-0.198244\pi\) |
−0.911288 | + | 0.411769i | \(0.864911\pi\) | |||||||
\(80\) | 3.04065 | − | 5.26656i | 0.339955 | − | 0.588819i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.1230 | −1.78049 | ||||||||
\(83\) | 1.08406 | − | 1.87765i | 0.118991 | − | 0.206099i | −0.800377 | − | 0.599497i | \(-0.795367\pi\) |
0.919368 | + | 0.393398i | \(0.128701\pi\) | |||||||
\(84\) | −4.02794 | + | 6.97659i | −0.439484 | + | 0.761209i | ||||
\(85\) | −2.98486 | + | 5.16992i | −0.323753 | + | 0.560757i | ||||
\(86\) | −8.42806 | + | 14.5978i | −0.908821 | + | 1.57412i | ||||
\(87\) | −2.62785 | − | 4.55158i | −0.281736 | − | 0.487980i | ||||
\(88\) | 1.47147 | + | 2.54866i | 0.156859 | + | 0.271689i | ||||
\(89\) | 7.24943 | 0.768438 | 0.384219 | − | 0.923242i | \(-0.374471\pi\) | ||||
0.384219 | + | 0.923242i | \(0.374471\pi\) | |||||||
\(90\) | −1.23731 | + | 2.14308i | −0.130424 | + | 0.225900i | ||||
\(91\) | −28.1557 | −2.95152 | ||||||||
\(92\) | −4.42659 | −0.461504 | ||||||||
\(93\) | −0.883856 | − | 1.53088i | −0.0916516 | − | 0.158745i | ||||
\(94\) | 9.82776 | 1.01366 | ||||||||
\(95\) | 0.963278 | − | 1.66845i | 0.0988303 | − | 0.171179i | ||||
\(96\) | −3.62715 | − | 6.28240i | −0.370194 | − | 0.641195i | ||||
\(97\) | −2.81823 | + | 4.88132i | −0.286148 | + | 0.495623i | −0.972887 | − | 0.231281i | \(-0.925708\pi\) |
0.686739 | + | 0.726904i | \(0.259042\pi\) | |||||||
\(98\) | −17.7548 | − | 30.7522i | −1.79350 | − | 3.10644i | ||||
\(99\) | −1.88386 | − | 3.26293i | −0.189335 | − | 0.327937i | ||||
\(100\) | 2.61409 | + | 4.52774i | 0.261409 | + | 0.452774i | ||||
\(101\) | 2.45278 | + | 4.24833i | 0.244060 | + | 0.422725i | 0.961867 | − | 0.273518i | \(-0.0881872\pi\) |
−0.717807 | + | 0.696242i | \(0.754854\pi\) | |||||||
\(102\) | 4.32735 | + | 7.49520i | 0.428472 | + | 0.742135i | ||||
\(103\) | −1.83199 | − | 3.17310i | −0.180511 | − | 0.312655i | 0.761543 | − | 0.648114i | \(-0.224442\pi\) |
−0.942055 | + | 0.335459i | \(0.891109\pi\) | |||||||
\(104\) | 2.16708 | − | 3.75348i | 0.212499 | − | 0.368059i | ||||
\(105\) | −3.31468 | − | 5.74119i | −0.323479 | − | 0.560283i | ||||
\(106\) | 2.24796 | − | 3.89359i | 0.218341 | − | 0.378179i | ||||
\(107\) | −11.8927 | −1.14971 | −0.574855 | − | 0.818256i | \(-0.694941\pi\) | ||||
−0.574855 | + | 0.818256i | \(0.694941\pi\) | |||||||
\(108\) | 0.793808 | + | 1.37492i | 0.0763842 | + | 0.132301i | ||||
\(109\) | −2.84549 | −0.272549 | −0.136274 | − | 0.990671i | \(-0.543513\pi\) | ||||
−0.136274 | + | 0.990671i | \(0.543513\pi\) | |||||||
\(110\) | 9.32362 | 0.888973 | ||||||||
\(111\) | −3.48841 | + | 6.04210i | −0.331105 | + | 0.573491i | ||||
\(112\) | 23.6189 | 2.23178 | ||||||||
\(113\) | 7.73768 | + | 13.4021i | 0.727900 | + | 1.26076i | 0.957769 | + | 0.287538i | \(0.0928368\pi\) |
−0.229869 | + | 0.973222i | \(0.573830\pi\) | |||||||
\(114\) | −1.39653 | − | 2.41886i | −0.130797 | − | 0.226547i | ||||
\(115\) | 1.82137 | − | 3.15471i | 0.169844 | − | 0.294178i | ||||
\(116\) | 4.17202 | − | 7.22616i | 0.387363 | − | 0.670932i | ||||
\(117\) | −2.77440 | + | 4.80541i | −0.256494 | + | 0.444260i | ||||
\(118\) | −10.2611 | + | 17.7727i | −0.944611 | + | 1.63611i | ||||
\(119\) | −23.1855 | −2.12541 | ||||||||
\(120\) | 1.02049 | 0.0931575 | ||||||||
\(121\) | −1.59782 | + | 2.76751i | −0.145257 | + | 0.251592i | ||||
\(122\) | 11.7667 | + | 20.3805i | 1.06531 | + | 1.84517i | ||||
\(123\) | −4.25612 | − | 7.37182i | −0.383761 | − | 0.664694i | ||||
\(124\) | 1.40322 | − | 2.43045i | 0.126013 | − | 0.218261i | ||||
\(125\) | −10.8348 | −0.969094 | ||||||||
\(126\) | −9.61104 | −0.856219 | ||||||||
\(127\) | −0.232407 | − | 0.402541i | −0.0206228 | − | 0.0357198i | 0.855530 | − | 0.517754i | \(-0.173232\pi\) |
−0.876153 | + | 0.482034i | \(0.839898\pi\) | |||||||
\(128\) | −3.05797 | + | 5.29655i | −0.270289 | + | 0.468154i | ||||
\(129\) | −8.89927 | −0.783537 | ||||||||
\(130\) | −6.86557 | − | 11.8915i | −0.602151 | − | 1.04296i | ||||
\(131\) | 5.79113 | 0.505973 | 0.252987 | − | 0.967470i | \(-0.418587\pi\) | ||||
0.252987 | + | 0.967470i | \(0.418587\pi\) | |||||||
\(132\) | 2.99084 | − | 5.18029i | 0.260319 | − | 0.450886i | ||||
\(133\) | 7.48247 | 0.648812 | ||||||||
\(134\) | −4.83760 | + | 14.7298i | −0.417905 | + | 1.27246i | ||||
\(135\) | −1.30648 | −0.112444 | ||||||||
\(136\) | 1.78453 | − | 3.09090i | 0.153022 | − | 0.265042i | ||||
\(137\) | 10.9296 | 0.933775 | 0.466888 | − | 0.884317i | \(-0.345375\pi\) | ||||
0.466888 | + | 0.884317i | \(0.345375\pi\) | |||||||
\(138\) | −2.64057 | − | 4.57359i | −0.224780 | − | 0.389330i | ||||
\(139\) | −1.23335 | −0.104611 | −0.0523057 | − | 0.998631i | \(-0.516657\pi\) | ||||
−0.0523057 | + | 0.998631i | \(0.516657\pi\) | |||||||
\(140\) | 5.26244 | − | 9.11481i | 0.444757 | − | 0.770342i | ||||
\(141\) | 2.59431 | + | 4.49347i | 0.218480 | + | 0.378419i | ||||
\(142\) | 18.8902 | 1.58523 | ||||||||
\(143\) | 20.9063 | 1.74827 | ||||||||
\(144\) | 2.32735 | − | 4.03109i | 0.193946 | − | 0.335925i | ||||
\(145\) | 3.43325 | + | 5.94656i | 0.285116 | + | 0.493835i | ||||
\(146\) | 3.80421 | + | 6.58908i | 0.314838 | + | 0.545316i | ||||
\(147\) | 9.37373 | − | 16.2358i | 0.773132 | − | 1.33910i | ||||
\(148\) | −11.0765 | −0.910484 | ||||||||
\(149\) | −9.27620 | −0.759936 | −0.379968 | − | 0.925000i | \(-0.624065\pi\) | ||||
−0.379968 | + | 0.925000i | \(0.624065\pi\) | |||||||
\(150\) | −3.11873 | + | 5.40180i | −0.254643 | + | 0.441055i | ||||
\(151\) | −1.05893 | + | 1.83413i | −0.0861748 | + | 0.149259i | −0.905891 | − | 0.423510i | \(-0.860798\pi\) |
0.819716 | + | 0.572770i | \(0.194131\pi\) | |||||||
\(152\) | −0.575907 | + | 0.997500i | −0.0467122 | + | 0.0809079i | ||||
\(153\) | −2.28465 | + | 3.95713i | −0.184703 | + | 0.319915i | ||||
\(154\) | 18.1058 | + | 31.3602i | 1.45901 | + | 2.52707i | ||||
\(155\) | 1.15474 | + | 2.00007i | 0.0927512 | + | 0.160650i | ||||
\(156\) | −8.80938 | −0.705315 | ||||||||
\(157\) | 3.57954 | − | 6.19995i | 0.285679 | − | 0.494810i | −0.687095 | − | 0.726568i | \(-0.741114\pi\) |
0.972773 | + | 0.231758i | \(0.0744477\pi\) | |||||||
\(158\) | 3.33477 | 0.265300 | ||||||||
\(159\) | 2.37365 | 0.188242 | ||||||||
\(160\) | 4.73881 | + | 8.20786i | 0.374636 | + | 0.648888i | ||||
\(161\) | 14.1479 | 1.11501 | ||||||||
\(162\) | −0.947050 | + | 1.64034i | −0.0744073 | + | 0.128877i | ||||
\(163\) | −4.15131 | − | 7.19028i | −0.325156 | − | 0.563186i | 0.656388 | − | 0.754423i | \(-0.272083\pi\) |
−0.981544 | + | 0.191237i | \(0.938750\pi\) | |||||||
\(164\) | 6.75709 | − | 11.7036i | 0.527640 | − | 0.913899i | ||||
\(165\) | 2.46123 | + | 4.26297i | 0.191606 | + | 0.331872i | ||||
\(166\) | 2.05333 | + | 3.55646i | 0.159369 | + | 0.276035i | ||||
\(167\) | 3.39055 | + | 5.87260i | 0.262368 | + | 0.454436i | 0.966871 | − | 0.255266i | \(-0.0821631\pi\) |
−0.704502 | + | 0.709702i | \(0.748830\pi\) | |||||||
\(168\) | 1.98172 | + | 3.43243i | 0.152893 | + | 0.264818i | ||||
\(169\) | −8.89463 | − | 15.4060i | −0.684202 | − | 1.18507i | ||||
\(170\) | −5.65362 | − | 9.79235i | −0.433613 | − | 0.751039i | ||||
\(171\) | 0.737306 | − | 1.27705i | 0.0563832 | − | 0.0976586i | ||||
\(172\) | −7.06432 | − | 12.2358i | −0.538649 | − | 0.932967i | ||||
\(173\) | 6.56276 | − | 11.3670i | 0.498957 | − | 0.864220i | −0.501042 | − | 0.865423i | \(-0.667050\pi\) |
0.999999 | + | 0.00120350i | \(0.000383085\pi\) | |||||||
\(174\) | 9.95484 | 0.754674 | ||||||||
\(175\) | −8.35492 | − | 14.4711i | −0.631572 | − | 1.09392i | ||||
\(176\) | −17.5376 | −1.32195 | ||||||||
\(177\) | −10.8348 | −0.814394 | ||||||||
\(178\) | −6.86557 | + | 11.8915i | −0.514596 | + | 0.891307i | ||||
\(179\) | −7.19424 | −0.537723 | −0.268861 | − | 0.963179i | \(-0.586647\pi\) | ||||
−0.268861 | + | 0.963179i | \(0.586647\pi\) | |||||||
\(180\) | −1.03710 | − | 1.79631i | −0.0773007 | − | 0.133889i | ||||
\(181\) | 12.8219 | + | 22.2081i | 0.953042 | + | 1.65072i | 0.738787 | + | 0.673939i | \(0.235399\pi\) |
0.214255 | + | 0.976778i | \(0.431268\pi\) | |||||||
\(182\) | 26.6649 | − | 46.1849i | 1.97653 | − | 3.42346i | ||||
\(183\) | −6.21229 | + | 10.7600i | −0.459226 | + | 0.795403i | ||||
\(184\) | −1.08893 | + | 1.88608i | −0.0802767 | + | 0.139043i | ||||
\(185\) | 4.55755 | − | 7.89391i | 0.335078 | − | 0.580372i | ||||
\(186\) | 3.34822 | 0.245504 | ||||||||
\(187\) | 17.2158 | 1.25894 | ||||||||
\(188\) | −4.11877 | + | 7.13391i | −0.300392 | + | 0.520294i | ||||
\(189\) | −2.53710 | − | 4.39438i | −0.184547 | − | 0.319644i | ||||
\(190\) | 1.82455 | + | 3.16021i | 0.132366 | + | 0.229265i | ||||
\(191\) | 1.62654 | − | 2.81726i | 0.117693 | − | 0.203850i | −0.801160 | − | 0.598450i | \(-0.795784\pi\) |
0.918853 | + | 0.394600i | \(0.129117\pi\) | |||||||
\(192\) | 4.43094 | 0.319776 | ||||||||
\(193\) | −21.0010 | −1.51168 | −0.755842 | − | 0.654754i | \(-0.772772\pi\) | ||||
−0.755842 | + | 0.654754i | \(0.772772\pi\) | |||||||
\(194\) | −5.33801 | − | 9.24571i | −0.383247 | − | 0.663803i | ||||
\(195\) | 3.62471 | − | 6.27819i | 0.259571 | − | 0.449590i | ||||
\(196\) | 29.7638 | 2.12598 | ||||||||
\(197\) | 0.543826 | + | 0.941935i | 0.0387460 | + | 0.0671101i | 0.884748 | − | 0.466070i | \(-0.154330\pi\) |
−0.846002 | + | 0.533180i | \(0.820997\pi\) | |||||||
\(198\) | 7.13642 | 0.507164 | ||||||||
\(199\) | 3.69988 | − | 6.40838i | 0.262278 | − | 0.454278i | −0.704569 | − | 0.709635i | \(-0.748860\pi\) |
0.966847 | + | 0.255357i | \(0.0821931\pi\) | |||||||
\(200\) | 2.57223 | 0.181884 | ||||||||
\(201\) | −8.01183 | + | 1.67649i | −0.565111 | + | 0.118250i | ||||
\(202\) | −9.29161 | −0.653755 | ||||||||
\(203\) | −13.3342 | + | 23.0956i | −0.935880 | + | 1.62099i | ||||
\(204\) | −7.25429 | −0.507902 | ||||||||
\(205\) | 5.56055 | + | 9.63116i | 0.388366 | + | 0.672669i | ||||
\(206\) | 6.93995 | 0.483529 | ||||||||
\(207\) | 1.39410 | − | 2.41465i | 0.0968967 | − | 0.167830i | ||||
\(208\) | 12.9140 | + | 22.3678i | 0.895427 | + | 1.55093i | ||||
\(209\) | −5.55591 | −0.384310 | ||||||||
\(210\) | 12.5567 | 0.866492 | ||||||||
\(211\) | 3.51731 | − | 6.09217i | 0.242142 | − | 0.419402i | −0.719182 | − | 0.694821i | \(-0.755483\pi\) |
0.961324 | + | 0.275419i | \(0.0888167\pi\) | |||||||
\(212\) | 1.88422 | + | 3.26357i | 0.129409 | + | 0.224143i | ||||
\(213\) | 4.98658 | + | 8.63701i | 0.341675 | + | 0.591798i | ||||
\(214\) | 11.2630 | − | 19.5080i | 0.769921 | − | 1.33354i | ||||
\(215\) | 11.6268 | 0.792938 | ||||||||
\(216\) | 0.781096 | 0.0531468 | ||||||||
\(217\) | −4.48486 | + | 7.76800i | −0.304452 | + | 0.527326i | ||||
\(218\) | 2.69483 | − | 4.66758i | 0.182517 | − | 0.316128i | ||||
\(219\) | −2.00845 | + | 3.47874i | −0.135719 | + | 0.235071i | ||||
\(220\) | −3.90748 | + | 6.76796i | −0.263443 | + | 0.456296i | ||||
\(221\) | −12.6771 | − | 21.9573i | −0.852752 | − | 1.47701i | ||||
\(222\) | −6.60740 | − | 11.4443i | −0.443459 | − | 0.768094i | ||||
\(223\) | −14.3934 | −0.963854 | −0.481927 | − | 0.876211i | \(-0.660063\pi\) | ||||
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(224\) | −18.4048 | + | 31.8781i | −1.22973 | + | 2.12995i | ||||
\(225\) | −3.29310 | −0.219540 | ||||||||
\(226\) | −29.3119 | −1.94980 | ||||||||
\(227\) | 12.5810 | + | 21.7909i | 0.835031 | + | 1.44632i | 0.894005 | + | 0.448056i | \(0.147884\pi\) |
−0.0589747 | + | 0.998259i | \(0.518783\pi\) | |||||||
\(228\) | 2.34112 | 0.155044 | ||||||||
\(229\) | 8.38027 | − | 14.5150i | 0.553784 | − | 0.959181i | −0.444213 | − | 0.895921i | \(-0.646517\pi\) |
0.997997 | − | 0.0632604i | \(-0.0201499\pi\) | |||||||
\(230\) | 3.44986 | + | 5.97533i | 0.227477 | + | 0.394001i | ||||
\(231\) | −9.55905 | + | 16.5568i | −0.628939 | + | 1.08936i | ||||
\(232\) | −2.05261 | − | 3.55522i | −0.134760 | − | 0.233412i | ||||
\(233\) | −13.2071 | − | 22.8754i | −0.865226 | − | 1.49862i | −0.866823 | − | 0.498617i | \(-0.833841\pi\) |
0.00159640 | − | 0.999999i | \(-0.499492\pi\) | |||||||
\(234\) | −5.25500 | − | 9.10193i | −0.343530 | − | 0.595011i | ||||
\(235\) | −3.38942 | − | 5.87065i | −0.221102 | − | 0.382959i | ||||
\(236\) | −8.60075 | − | 14.8969i | −0.559861 | − | 0.969708i | ||||
\(237\) | 0.880303 | + | 1.52473i | 0.0571818 | + | 0.0990419i | ||||
\(238\) | 21.9578 | − | 38.0321i | 1.42332 | − | 2.46525i | ||||
\(239\) | −0.221715 | − | 0.384022i | −0.0143416 | − | 0.0248403i | 0.858766 | − | 0.512369i | \(-0.171232\pi\) |
−0.873107 | + | 0.487528i | \(0.837899\pi\) | |||||||
\(240\) | −3.04065 | + | 5.26656i | −0.196273 | + | 0.339955i | ||||
\(241\) | −21.3462 | −1.37503 | −0.687515 | − | 0.726170i | \(-0.741299\pi\) | ||||
−0.687515 | + | 0.726170i | \(0.741299\pi\) | |||||||
\(242\) | −3.02644 | − | 5.24195i | −0.194547 | − | 0.336965i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.7255 | −1.26279 | ||||||||
\(245\) | −12.2466 | + | 21.2118i | −0.782408 | + | 1.35517i | ||||
\(246\) | 16.1230 | 1.02797 | ||||||||
\(247\) | 4.09117 | + | 7.08611i | 0.260315 | + | 0.450879i | ||||
\(248\) | −0.690376 | − | 1.19577i | −0.0438389 | − | 0.0759313i | ||||
\(249\) | −1.08406 | + | 1.87765i | −0.0686998 | + | 0.118991i | ||||
\(250\) | 10.2611 | − | 17.7727i | 0.648969 | − | 1.12405i | ||||
\(251\) | 9.72392 | − | 16.8423i | 0.613768 | − | 1.06308i | −0.376831 | − | 0.926282i | \(-0.622986\pi\) |
0.990599 | − | 0.136796i | \(-0.0436805\pi\) | |||||||
\(252\) | 4.02794 | − | 6.97659i | 0.253736 | − | 0.439484i | ||||
\(253\) | −10.5051 | −0.660452 | ||||||||
\(254\) | 0.880406 | 0.0552416 | ||||||||
\(255\) | 2.98486 | − | 5.16992i | 0.186919 | − | 0.323753i | ||||
\(256\) | −10.2230 | − | 17.7068i | −0.638940 | − | 1.10668i | ||||
\(257\) | −2.60822 | − | 4.51758i | −0.162697 | − | 0.281799i | 0.773138 | − | 0.634237i | \(-0.218686\pi\) |
−0.935835 | + | 0.352439i | \(0.885352\pi\) | |||||||
\(258\) | 8.42806 | − | 14.5978i | 0.524708 | − | 0.908821i | ||||
\(259\) | 35.4017 | 2.19976 | ||||||||
\(260\) | 11.5093 | 0.713777 | ||||||||
\(261\) | 2.62785 | + | 4.55158i | 0.162660 | + | 0.281736i | ||||
\(262\) | −5.48449 | + | 9.49942i | −0.338833 | + | 0.586876i | ||||
\(263\) | 13.6157 | 0.839578 | 0.419789 | − | 0.907622i | \(-0.362104\pi\) | ||||
0.419789 | + | 0.907622i | \(0.362104\pi\) | |||||||
\(264\) | −1.47147 | − | 2.54866i | −0.0905628 | − | 0.156859i | ||||
\(265\) | −3.10113 | −0.190501 | ||||||||
\(266\) | −7.08627 | + | 12.2738i | −0.434487 | + | 0.752554i | ||||
\(267\) | −7.24943 | −0.443658 | ||||||||
\(268\) | −8.66488 | − | 9.68478i | −0.529292 | − | 0.591592i | ||||
\(269\) | −19.0352 | −1.16060 | −0.580298 | − | 0.814405i | \(-0.697064\pi\) | ||||
−0.580298 | + | 0.814405i | \(0.697064\pi\) | |||||||
\(270\) | 1.23731 | − | 2.14308i | 0.0753000 | − | 0.130424i | ||||
\(271\) | 10.4679 | 0.635883 | 0.317941 | − | 0.948110i | \(-0.397009\pi\) | ||||
0.317941 | + | 0.948110i | \(0.397009\pi\) | |||||||
\(272\) | 10.6344 | + | 18.4193i | 0.644803 | + | 1.11683i | ||||
\(273\) | 28.1557 | 1.70406 | ||||||||
\(274\) | −10.3508 | + | 17.9282i | −0.625317 | + | 1.08308i | ||||
\(275\) | 6.20372 | + | 10.7452i | 0.374099 | + | 0.647958i | ||||
\(276\) | 4.42659 | 0.266450 | ||||||||
\(277\) | 7.44098 | 0.447085 | 0.223542 | − | 0.974694i | \(-0.428238\pi\) | ||||
0.223542 | + | 0.974694i | \(0.428238\pi\) | |||||||
\(278\) | 1.16805 | − | 2.02311i | 0.0700547 | − | 0.121338i | ||||
\(279\) | 0.883856 | + | 1.53088i | 0.0529151 | + | 0.0916516i | ||||
\(280\) | −2.58908 | − | 4.48442i | −0.154727 | − | 0.267995i | ||||
\(281\) | −9.72183 | + | 16.8387i | −0.579956 | + | 1.00451i | 0.415528 | + | 0.909581i | \(0.363597\pi\) |
−0.995484 | + | 0.0949327i | \(0.969736\pi\) | |||||||
\(282\) | −9.82776 | −0.585235 | ||||||||
\(283\) | −28.0749 | −1.66888 | −0.834441 | − | 0.551097i | \(-0.814209\pi\) | ||||
−0.834441 | + | 0.551097i | \(0.814209\pi\) | |||||||
\(284\) | −7.91677 | + | 13.7123i | −0.469774 | + | 0.813673i | ||||
\(285\) | −0.963278 | + | 1.66845i | −0.0570597 | + | 0.0988303i | ||||
\(286\) | −19.7993 | + | 34.2934i | −1.17076 | + | 2.02781i | ||||
\(287\) | −21.5964 | + | 37.4060i | −1.27479 | + | 2.20801i | ||||
\(288\) | 3.62715 | + | 6.28240i | 0.213732 | + | 0.370194i | ||||
\(289\) | −1.93924 | − | 3.35886i | −0.114073 | − | 0.197580i | ||||
\(290\) | −13.0058 | −0.763729 | ||||||||
\(291\) | 2.81823 | − | 4.88132i | 0.165208 | − | 0.286148i | ||||
\(292\) | −6.37730 | −0.373203 | ||||||||
\(293\) | −15.9270 | −0.930467 | −0.465234 | − | 0.885188i | \(-0.654030\pi\) | ||||
−0.465234 | + | 0.885188i | \(0.654030\pi\) | |||||||
\(294\) | 17.7548 | + | 30.7522i | 1.03548 | + | 1.79350i | ||||
\(295\) | 14.1555 | 0.824165 | ||||||||
\(296\) | −2.72478 | + | 4.71946i | −0.158375 | + | 0.274313i | ||||
\(297\) | 1.88386 | + | 3.26293i | 0.109312 | + | 0.189335i | ||||
\(298\) | 8.78502 | − | 15.2161i | 0.508903 | − | 0.881446i | ||||
\(299\) | 7.73559 | + | 13.3984i | 0.447361 | + | 0.774852i | ||||
\(300\) | −2.61409 | − | 4.52774i | −0.150925 | − | 0.261409i | ||||
\(301\) | 22.5783 | + | 39.1068i | 1.30139 | + | 2.25408i | ||||
\(302\) | −2.00573 | − | 3.47402i | −0.115417 | − | 0.199907i | ||||
\(303\) | −2.45278 | − | 4.24833i | −0.140908 | − | 0.244060i | ||||
\(304\) | −3.43194 | − | 5.94430i | −0.196835 | − | 0.340929i | ||||
\(305\) | 8.11626 | − | 14.0578i | 0.464736 | − | 0.804946i | ||||
\(306\) | −4.32735 | − | 7.49520i | −0.247378 | − | 0.428472i | ||||
\(307\) | 6.60681 | − | 11.4433i | 0.377070 | − | 0.653105i | −0.613564 | − | 0.789645i | \(-0.710265\pi\) |
0.990635 | + | 0.136540i | \(0.0435981\pi\) | |||||||
\(308\) | −30.3522 | −1.72948 | ||||||||
\(309\) | 1.83199 | + | 3.17310i | 0.104218 | + | 0.180511i | ||||
\(310\) | −4.37440 | −0.248449 | ||||||||
\(311\) | 7.96043 | 0.451395 | 0.225697 | − | 0.974197i | \(-0.427534\pi\) | ||||
0.225697 | + | 0.974197i | \(0.427534\pi\) | |||||||
\(312\) | −2.16708 | + | 3.75348i | −0.122686 | + | 0.212499i | ||||
\(313\) | 15.3567 | 0.868015 | 0.434007 | − | 0.900909i | \(-0.357099\pi\) | ||||
0.434007 | + | 0.900909i | \(0.357099\pi\) | |||||||
\(314\) | 6.78001 | + | 11.7433i | 0.382618 | + | 0.662714i | ||||
\(315\) | 3.31468 | + | 5.74119i | 0.186761 | + | 0.323479i | ||||
\(316\) | −1.39758 | + | 2.42069i | −0.0786202 | + | 0.136174i | ||||
\(317\) | −6.42765 | + | 11.1330i | −0.361013 | + | 0.625292i | −0.988128 | − | 0.153634i | \(-0.950902\pi\) |
0.627115 | + | 0.778927i | \(0.284236\pi\) | |||||||
\(318\) | −2.24796 | + | 3.89359i | −0.126060 | + | 0.218341i | ||||
\(319\) | 9.90100 | − | 17.1490i | 0.554349 | − | 0.960161i | ||||
\(320\) | −5.78895 | −0.323612 | ||||||||
\(321\) | 11.8927 | 0.663785 | ||||||||
\(322\) | −13.3987 | + | 23.2073i | −0.746683 | + | 1.29329i | ||||
\(323\) | 3.36897 | + | 5.83523i | 0.187454 | + | 0.324681i | ||||
\(324\) | −0.793808 | − | 1.37492i | −0.0441005 | − | 0.0763842i | ||||
\(325\) | 9.13639 | − | 15.8247i | 0.506796 | − | 0.877796i | ||||
\(326\) | 15.7260 | 0.870982 | ||||||||
\(327\) | 2.84549 | 0.157356 | ||||||||
\(328\) | −3.32444 | − | 5.75810i | −0.183561 | − | 0.317938i | ||||
\(329\) | 13.1640 | − | 22.8008i | 0.725756 | − | 1.25705i | ||||
\(330\) | −9.32362 | −0.513249 | ||||||||
\(331\) | −8.64872 | − | 14.9800i | −0.475377 | − | 0.823376i | 0.524226 | − | 0.851579i | \(-0.324355\pi\) |
−0.999602 | + | 0.0282030i | \(0.991022\pi\) | |||||||
\(332\) | −3.44216 | −0.188913 | ||||||||
\(333\) | 3.48841 | − | 6.04210i | 0.191164 | − | 0.331105i | ||||
\(334\) | −12.8441 | −0.702797 | ||||||||
\(335\) | 10.4673 | − | 2.19030i | 0.571891 | − | 0.119669i | ||||
\(336\) | −23.6189 | −1.28852 | ||||||||
\(337\) | 10.5384 | − | 18.2531i | 0.574064 | − | 0.994307i | −0.422079 | − | 0.906559i | \(-0.638700\pi\) |
0.996143 | − | 0.0877484i | \(-0.0279671\pi\) | |||||||
\(338\) | 33.6947 | 1.83275 | ||||||||
\(339\) | −7.73768 | − | 13.4021i | −0.420253 | − | 0.727900i | ||||
\(340\) | 9.47761 | 0.513996 | ||||||||
\(341\) | 3.33011 | − | 5.76793i | 0.180336 | − | 0.312351i | ||||
\(342\) | 1.39653 | + | 2.41886i | 0.0755158 | + | 0.130797i | ||||
\(343\) | −59.6089 | −3.21858 | ||||||||
\(344\) | −6.95119 | −0.374783 | ||||||||
\(345\) | −1.82137 | + | 3.15471i | −0.0980593 | + | 0.169844i | ||||
\(346\) | 12.4305 | + | 21.5303i | 0.668269 | + | 1.15748i | ||||
\(347\) | −4.91238 | − | 8.50850i | −0.263711 | − | 0.456760i | 0.703514 | − | 0.710681i | \(-0.251613\pi\) |
−0.967225 | + | 0.253921i | \(0.918280\pi\) | |||||||
\(348\) | −4.17202 | + | 7.22616i | −0.223644 | + | 0.387363i | ||||
\(349\) | −21.7712 | −1.16538 | −0.582692 | − | 0.812693i | \(-0.698000\pi\) | ||||
−0.582692 | + | 0.812693i | \(0.698000\pi\) | |||||||
\(350\) | 31.6501 | 1.69177 | ||||||||
\(351\) | 2.77440 | − | 4.80541i | 0.148087 | − | 0.256494i | ||||
\(352\) | 13.6660 | − | 23.6703i | 0.728402 | − | 1.26163i | ||||
\(353\) | 2.19536 | − | 3.80247i | 0.116847 | − | 0.202385i | −0.801670 | − | 0.597767i | \(-0.796055\pi\) |
0.918517 | + | 0.395382i | \(0.129388\pi\) | |||||||
\(354\) | 10.2611 | − | 17.7727i | 0.545371 | − | 0.944611i | ||||
\(355\) | −6.51489 | − | 11.2841i | −0.345774 | − | 0.598899i | ||||
\(356\) | −5.75466 | − | 9.96736i | −0.304996 | − | 0.528269i | ||||
\(357\) | 23.1855 | 1.22711 | ||||||||
\(358\) | 6.81331 | − | 11.8010i | 0.360094 | − | 0.623702i | ||||
\(359\) | −26.4848 | −1.39781 | −0.698907 | − | 0.715212i | \(-0.746330\pi\) | ||||
−0.698907 | + | 0.715212i | \(0.746330\pi\) | |||||||
\(360\) | −1.02049 | −0.0537845 | ||||||||
\(361\) | 8.41276 | + | 14.5713i | 0.442777 | + | 0.766912i | ||||
\(362\) | −48.5718 | −2.55288 | ||||||||
\(363\) | 1.59782 | − | 2.76751i | 0.0838640 | − | 0.145257i | ||||
\(364\) | 22.3503 | + | 38.7118i | 1.17147 | + | 2.02905i | ||||
\(365\) | 2.62401 | − | 4.54492i | 0.137347 | − | 0.237892i | ||||
\(366\) | −11.7667 | − | 20.3805i | −0.615056 | − | 1.06531i | ||||
\(367\) | 1.03235 | + | 1.78809i | 0.0538885 | + | 0.0933375i | 0.891711 | − | 0.452605i | \(-0.149505\pi\) |
−0.837823 | + | 0.545942i | \(0.816172\pi\) | |||||||
\(368\) | −6.48913 | − | 11.2395i | −0.338269 | − | 0.585899i | ||||
\(369\) | 4.25612 | + | 7.37182i | 0.221565 | + | 0.383761i | ||||
\(370\) | 8.63246 | + | 14.9519i | 0.448780 | + | 0.777310i | ||||
\(371\) | −6.02218 | − | 10.4307i | −0.312656 | − | 0.541536i | ||||
\(372\) | −1.40322 | + | 2.43045i | −0.0727538 | + | 0.126013i | ||||
\(373\) | −0.0539160 | − | 0.0933852i | −0.00279166 | − | 0.00483530i | 0.864626 | − | 0.502416i | \(-0.167555\pi\) |
−0.867418 | + | 0.497580i | \(0.834222\pi\) | |||||||
\(374\) | −16.3042 | + | 28.2397i | −0.843071 | + | 1.46024i | ||||
\(375\) | 10.8348 | 0.559507 | ||||||||
\(376\) | 2.02640 | + | 3.50983i | 0.104504 | + | 0.181006i | ||||
\(377\) | −29.1629 | −1.50197 | ||||||||
\(378\) | 9.61104 | 0.494338 | ||||||||
\(379\) | 1.97499 | − | 3.42078i | 0.101448 | − | 0.175714i | −0.810833 | − | 0.585277i | \(-0.800986\pi\) |
0.912282 | + | 0.409564i | \(0.134319\pi\) | |||||||
\(380\) | −3.05863 | −0.156905 | ||||||||
\(381\) | 0.232407 | + | 0.402541i | 0.0119066 | + | 0.0206228i | ||||
\(382\) | 3.08084 | + | 5.33617i | 0.157629 | + | 0.273022i | ||||
\(383\) | 2.53694 | − | 4.39411i | 0.129632 | − | 0.224529i | −0.793902 | − | 0.608045i | \(-0.791954\pi\) |
0.923534 | + | 0.383517i | \(0.125287\pi\) | |||||||
\(384\) | 3.05797 | − | 5.29655i | 0.156051 | − | 0.270289i | ||||
\(385\) | 12.4887 | − | 21.6311i | 0.636486 | − | 1.10243i | ||||
\(386\) | 19.8890 | − | 34.4487i | 1.01232 | − | 1.75339i | ||||
\(387\) | 8.89927 | 0.452375 | ||||||||
\(388\) | 8.94854 | 0.454293 | ||||||||
\(389\) | 3.47440 | − | 6.01784i | 0.176159 | − | 0.305117i | −0.764403 | − | 0.644739i | \(-0.776966\pi\) |
0.940562 | + | 0.339623i | \(0.110299\pi\) | |||||||
\(390\) | 6.86557 | + | 11.8915i | 0.347652 | + | 0.602151i | ||||
\(391\) | 6.37006 | + | 11.0333i | 0.322148 | + | 0.557976i | ||||
\(392\) | 7.32178 | − | 12.6817i | 0.369806 | − | 0.640523i | ||||
\(393\) | −5.79113 | −0.292124 | ||||||||
\(394\) | −2.06012 | −0.103788 | ||||||||
\(395\) | −1.15010 | − | 1.99204i | −0.0578679 | − | 0.100230i | ||||
\(396\) | −2.99084 | + | 5.18029i | −0.150295 | + | 0.260319i | ||||
\(397\) | −22.0237 | −1.10534 | −0.552668 | − | 0.833402i | \(-0.686390\pi\) | ||||
−0.552668 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(398\) | 7.00794 | + | 12.1381i | 0.351276 | + | 0.608429i | ||||
\(399\) | −7.48247 | −0.374592 | ||||||||
\(400\) | −7.66421 | + | 13.2748i | −0.383210 | + | 0.663740i | ||||
\(401\) | 4.46178 | 0.222810 | 0.111405 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111405 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(402\) | 4.83760 | − | 14.7298i | 0.241277 | − | 0.734657i | ||||
\(403\) | −9.80869 | −0.488606 | ||||||||
\(404\) | 3.89407 | − | 6.74472i | 0.193737 | − | 0.335563i | ||||
\(405\) | 1.30648 | 0.0649197 | ||||||||
\(406\) | −25.2564 | − | 43.7454i | −1.25345 | − | 2.17105i | ||||
\(407\) | −26.2866 | −1.30298 | ||||||||
\(408\) | −1.78453 | + | 3.09090i | −0.0883474 | + | 0.153022i | ||||
\(409\) | 0.523372 | + | 0.906507i | 0.0258791 | + | 0.0448239i | 0.878675 | − | 0.477421i | \(-0.158428\pi\) |
−0.852796 | + | 0.522244i | \(0.825095\pi\) | |||||||
\(410\) | −21.0645 | −1.04030 | ||||||||
\(411\) | −10.9296 | −0.539115 | ||||||||
\(412\) | −2.90850 | + | 5.03767i | −0.143291 | + | 0.248188i | ||||
\(413\) | 27.4890 | + | 47.6123i | 1.35264 | + | 2.34285i | ||||
\(414\) | 2.64057 | + | 4.57359i | 0.129777 | + | 0.224780i | ||||
\(415\) | 1.41631 | − | 2.45312i | 0.0695240 | − | 0.120419i | ||||
\(416\) | −40.2527 | −1.97355 | ||||||||
\(417\) | 1.23335 | 0.0603975 | ||||||||
\(418\) | 5.26173 | − | 9.11358i | 0.257360 | − | 0.445760i | ||||
\(419\) | 7.75058 | − | 13.4244i | 0.378641 | − | 0.655825i | −0.612224 | − | 0.790684i | \(-0.709725\pi\) |
0.990865 | + | 0.134859i | \(0.0430583\pi\) | |||||||
\(420\) | −5.26244 | + | 9.11481i | −0.256781 | + | 0.444757i | ||||
\(421\) | 9.60643 | − | 16.6388i | 0.468189 | − | 0.810927i | −0.531150 | − | 0.847278i | \(-0.678240\pi\) |
0.999339 | + | 0.0363508i | \(0.0115734\pi\) | |||||||
\(422\) | 6.66214 | + | 11.5392i | 0.324308 | + | 0.561718i | ||||
\(423\) | −2.59431 | − | 4.49347i | −0.126140 | − | 0.218480i | ||||
\(424\) | 1.85405 | 0.0900405 | ||||||||
\(425\) | 7.52357 | − | 13.0312i | 0.364947 | − | 0.632107i | ||||
\(426\) | −18.8902 | −0.915231 | ||||||||
\(427\) | 63.0448 | 3.05095 | ||||||||
\(428\) | 9.44051 | + | 16.3514i | 0.456324 | + | 0.790377i | ||||
\(429\) | −20.9063 | −1.00937 | ||||||||
\(430\) | −11.0111 | + | 19.0718i | −0.531004 | + | 0.919725i | ||||
\(431\) | 17.0369 | + | 29.5088i | 0.820638 | + | 1.42139i | 0.905208 | + | 0.424969i | \(0.139715\pi\) |
−0.0845698 | + | 0.996418i | \(0.526952\pi\) | |||||||
\(432\) | −2.32735 | + | 4.03109i | −0.111975 | + | 0.193946i | ||||
\(433\) | 5.43994 | + | 9.42226i | 0.261427 | + | 0.452805i | 0.966621 | − | 0.256209i | \(-0.0824736\pi\) |
−0.705194 | + | 0.709014i | \(0.749140\pi\) | |||||||
\(434\) | −8.49477 | − | 14.7134i | −0.407762 | − | 0.706264i | ||||
\(435\) | −3.43325 | − | 5.94656i | −0.164612 | − | 0.285116i | ||||
\(436\) | 2.25878 | + | 3.91232i | 0.108176 | + | 0.187366i | ||||
\(437\) | −2.05576 | − | 3.56068i | −0.0983402 | − | 0.170330i | ||||
\(438\) | −3.80421 | − | 6.58908i | −0.181772 | − | 0.314838i | ||||
\(439\) | −2.66780 | + | 4.62076i | −0.127327 | + | 0.220537i | −0.922640 | − | 0.385662i | \(-0.873973\pi\) |
0.795313 | + | 0.606199i | \(0.207306\pi\) | |||||||
\(440\) | 1.92245 | + | 3.32979i | 0.0916494 | + | 0.158741i | ||||
\(441\) | −9.37373 | + | 16.2358i | −0.446368 | + | 0.773132i | ||||
\(442\) | 48.0233 | 2.28424 | ||||||||
\(443\) | 14.4937 | + | 25.1038i | 0.688615 | + | 1.19272i | 0.972286 | + | 0.233794i | \(0.0751142\pi\) |
−0.283671 | + | 0.958922i | \(0.591552\pi\) | |||||||
\(444\) | 11.0765 | 0.525668 | ||||||||
\(445\) | 9.47126 | 0.448981 | ||||||||
\(446\) | 13.6313 | − | 23.6101i | 0.645460 | − | 1.11797i | ||||
\(447\) | 9.27620 | 0.438749 | ||||||||
\(448\) | −11.2417 | − | 19.4712i | −0.531122 | − | 0.919930i | ||||
\(449\) | −18.5754 | − | 32.1735i | −0.876626 | − | 1.51836i | −0.855021 | − | 0.518594i | \(-0.826456\pi\) |
−0.0216050 | − | 0.999767i | \(-0.506878\pi\) | |||||||
\(450\) | 3.11873 | − | 5.40180i | 0.147018 | − | 0.254643i | ||||
\(451\) | 16.0358 | − | 27.7749i | 0.755098 | − | 1.30787i | ||||
\(452\) | 12.2845 | − | 21.2773i | 0.577813 | − | 1.00080i | ||||
\(453\) | 1.05893 | − | 1.83413i | 0.0497530 | − | 0.0861748i | ||||
\(454\) | −47.6594 | −2.23677 | ||||||||
\(455\) | −36.7850 | −1.72451 | ||||||||
\(456\) | 0.575907 | − | 0.997500i | 0.0269693 | − | 0.0467122i | ||||
\(457\) | 11.0230 | + | 19.0923i | 0.515633 | + | 0.893102i | 0.999835 | + | 0.0181464i | \(0.00577648\pi\) |
−0.484202 | + | 0.874956i | \(0.660890\pi\) | |||||||
\(458\) | 15.8731 | + | 27.4930i | 0.741700 | + | 1.28466i | ||||
\(459\) | 2.28465 | − | 3.95713i | 0.106638 | − | 0.184703i | ||||
\(460\) | −5.78327 | −0.269647 | ||||||||
\(461\) | 34.2504 | 1.59520 | 0.797601 | − | 0.603186i | \(-0.206102\pi\) | ||||
0.797601 | + | 0.603186i | \(0.206102\pi\) | |||||||
\(462\) | −18.1058 | − | 31.3602i | −0.842358 | − | 1.45901i | ||||
\(463\) | −6.00012 | + | 10.3925i | −0.278849 | + | 0.482981i | −0.971099 | − | 0.238677i | \(-0.923286\pi\) |
0.692250 | + | 0.721658i | \(0.256620\pi\) | |||||||
\(464\) | 24.4638 | 1.13570 | ||||||||
\(465\) | −1.15474 | − | 2.00007i | −0.0535499 | − | 0.0927512i | ||||
\(466\) | 50.0312 | 2.31765 | ||||||||
\(467\) | 4.53905 | − | 7.86186i | 0.210042 | − | 0.363803i | −0.741685 | − | 0.670748i | \(-0.765973\pi\) |
0.951727 | + | 0.306944i | \(0.0993066\pi\) | |||||||
\(468\) | 8.80938 | 0.407214 | ||||||||
\(469\) | 27.6939 | + | 30.9536i | 1.27879 | + | 1.42931i | ||||
\(470\) | 12.8398 | 0.592256 | ||||||||
\(471\) | −3.57954 | + | 6.19995i | −0.164937 | + | 0.285679i | ||||
\(472\) | −8.46302 | −0.389542 | ||||||||
\(473\) | −16.7649 | − | 29.0377i | −0.770853 | − | 1.33516i | ||||
\(474\) | −3.33477 | −0.153171 | ||||||||
\(475\) | −2.42802 | + | 4.20546i | −0.111405 | + | 0.192960i | ||||
\(476\) | 18.4048 | + | 31.8781i | 0.843585 | + | 1.46113i | ||||
\(477\) | −2.37365 | −0.108682 | ||||||||
\(478\) | 0.839902 | 0.0384162 | ||||||||
\(479\) | 5.28318 | − | 9.15074i | 0.241395 | − | 0.418108i | −0.719717 | − | 0.694268i | \(-0.755728\pi\) |
0.961112 | + | 0.276159i | \(0.0890618\pi\) | |||||||
\(480\) | −4.73881 | − | 8.20786i | −0.216296 | − | 0.374636i | ||||
\(481\) | 19.3565 | + | 33.5265i | 0.882581 | + | 1.52867i | ||||
\(482\) | 20.2159 | − | 35.0150i | 0.920811 | − | 1.59489i | ||||
\(483\) | −14.1479 | −0.643751 | ||||||||
\(484\) | 5.07347 | 0.230612 | ||||||||
\(485\) | −3.68197 | + | 6.37736i | −0.167190 | + | 0.289581i | ||||
\(486\) | 0.947050 | − | 1.64034i | 0.0429591 | − | 0.0744073i | ||||
\(487\) | −10.8033 | + | 18.7119i | −0.489545 | + | 0.847916i | −0.999928 | − | 0.0120311i | \(-0.996170\pi\) |
0.510383 | + | 0.859947i | \(0.329504\pi\) | |||||||
\(488\) | −4.85240 | + | 8.40460i | −0.219658 | + | 0.380458i | ||||
\(489\) | 4.15131 | + | 7.19028i | 0.187729 | + | 0.325156i | ||||
\(490\) | −23.1963 | − | 40.1772i | −1.04790 | − | 1.81502i | ||||
\(491\) | −16.9759 | −0.766113 | −0.383056 | − | 0.923725i | \(-0.625128\pi\) | ||||
−0.383056 | + | 0.923725i | \(0.625128\pi\) | |||||||
\(492\) | −6.75709 | + | 11.7036i | −0.304633 | + | 0.527640i | ||||
\(493\) | −24.0149 | −1.08158 | ||||||||
\(494\) | −15.4982 | −0.697296 | ||||||||
\(495\) | −2.46123 | − | 4.26297i | −0.110624 | − | 0.191606i | ||||
\(496\) | 8.22818 | 0.369456 | ||||||||
\(497\) | 25.3029 | − | 43.8259i | 1.13499 | − | 1.96586i | ||||
\(498\) | −2.05333 | − | 3.55646i | −0.0920117 | − | 0.159369i | ||||
\(499\) | −0.759399 | + | 1.31532i | −0.0339954 | + | 0.0588817i | −0.882523 | − | 0.470270i | \(-0.844156\pi\) |
0.848527 | + | 0.529152i | \(0.177490\pi\) | |||||||
\(500\) | 8.60075 | + | 14.8969i | 0.384637 | + | 0.666212i | ||||
\(501\) | −3.39055 | − | 5.87260i | −0.151479 | − | 0.262368i | ||||
\(502\) | 18.4181 | + | 31.9011i | 0.822039 | + | 1.42381i | ||||
\(503\) | −12.9835 | − | 22.4881i | −0.578905 | − | 1.00269i | −0.995605 | − | 0.0936493i | \(-0.970147\pi\) |
0.416700 | − | 0.909044i | \(-0.363187\pi\) | |||||||
\(504\) | −1.98172 | − | 3.43243i | −0.0882727 | − | 0.152893i | ||||
\(505\) | 3.20451 | + | 5.55038i | 0.142599 | + | 0.246989i | ||||
\(506\) | 9.94889 | − | 17.2320i | 0.442282 | − | 0.766055i | ||||
\(507\) | 8.89463 | + | 15.4060i | 0.395024 | + | 0.684202i | ||||
\(508\) | −0.368974 | + | 0.639081i | −0.0163706 | + | 0.0283546i | ||||
\(509\) | 14.0774 | 0.623971 | 0.311986 | − | 0.950087i | \(-0.399006\pi\) | ||||
0.311986 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(510\) | 5.65362 | + | 9.79235i | 0.250346 | + | 0.433613i | ||||
\(511\) | 20.3825 | 0.901671 | ||||||||
\(512\) | 26.4951 | 1.17093 | ||||||||
\(513\) | −0.737306 | + | 1.27705i | −0.0325529 | + | 0.0563832i | ||||
\(514\) | 9.88048 | 0.435809 | ||||||||
\(515\) | −2.39347 | − | 4.14561i | −0.105469 | − | 0.182677i | ||||
\(516\) | 7.06432 | + | 12.2358i | 0.310989 | + | 0.538649i | ||||
\(517\) | −9.77461 | + | 16.9301i | −0.429887 | + | 0.744586i | ||||
\(518\) | −33.5272 | + | 58.0709i | −1.47310 | + | 2.55149i | ||||
\(519\) | −6.56276 | + | 11.3670i | −0.288073 | + | 0.498957i | ||||
\(520\) | 2.83125 | − | 4.90387i | 0.124159 | − | 0.215049i | ||||
\(521\) | 41.5898 | 1.82208 | 0.911042 | − | 0.412314i | \(-0.135279\pi\) | ||||
0.911042 | + | 0.412314i | \(0.135279\pi\) | |||||||
\(522\) | −9.95484 | −0.435711 | ||||||||
\(523\) | 2.16181 | − | 3.74437i | 0.0945294 | − | 0.163730i | −0.814883 | − | 0.579626i | \(-0.803199\pi\) |
0.909412 | + | 0.415896i | \(0.136532\pi\) | |||||||
\(524\) | −4.59705 | − | 7.96232i | −0.200823 | − | 0.347836i | ||||
\(525\) | 8.35492 | + | 14.4711i | 0.364638 | + | 0.631572i | ||||
\(526\) | −12.8947 | + | 22.3343i | −0.562236 | + | 0.973822i | ||||
\(527\) | −8.07720 | −0.351848 | ||||||||
\(528\) | 17.5376 | 0.763226 | ||||||||
\(529\) | 7.61297 | + | 13.1860i | 0.330999 | + | 0.573306i | ||||
\(530\) | 2.93693 | − | 5.08691i | 0.127572 | − | 0.220961i | ||||
\(531\) | 10.8348 | 0.470190 | ||||||||
\(532\) | −5.93965 | − | 10.2878i | −0.257516 | − | 0.446031i | ||||
\(533\) | −47.2328 | −2.04588 | ||||||||
\(534\) | 6.86557 | − | 11.8915i | 0.297102 | − | 0.514596i | ||||
\(535\) | −15.5376 | −0.671749 | ||||||||
\(536\) | −6.25801 | + | 1.30950i | −0.270305 | + | 0.0565616i | ||||
\(537\) | 7.19424 | 0.310454 | ||||||||
\(538\) | 18.0273 | − | 31.2241i | 0.777211 | − | 1.34617i | ||||
\(539\) | 70.6350 | 3.04247 | ||||||||
\(540\) | 1.03710 | + | 1.79631i | 0.0446296 | + | 0.0773007i | ||||
\(541\) | −31.6753 | −1.36183 | −0.680914 | − | 0.732363i | \(-0.738417\pi\) | ||||
−0.680914 | + | 0.732363i | \(0.738417\pi\) | |||||||
\(542\) | −9.91367 | + | 17.1710i | −0.425829 | + | 0.737557i | ||||
\(543\) | −12.8219 | − | 22.2081i | −0.550239 | − | 0.953042i | ||||
\(544\) | −33.1470 | −1.42117 | ||||||||
\(545\) | −3.71759 | −0.159244 | ||||||||
\(546\) | −26.6649 | + | 46.1849i | −1.14115 | + | 1.97653i | ||||
\(547\) | 21.0146 | + | 36.3983i | 0.898518 | + | 1.55628i | 0.829389 | + | 0.558671i | \(0.188689\pi\) |
0.0691286 | + | 0.997608i | \(0.477978\pi\) | |||||||
\(548\) | −8.67597 | − | 15.0272i | −0.370619 | − | 0.641931i | ||||
\(549\) | 6.21229 | − | 10.7600i | 0.265134 | − | 0.459226i | ||||
\(550\) | −23.5010 | −1.00208 | ||||||||
\(551\) | 7.75013 | 0.330167 | ||||||||
\(552\) | 1.08893 | − | 1.88608i | 0.0463478 | − | 0.0802767i | ||||
\(553\) | 4.46683 | − | 7.73678i | 0.189949 | − | 0.329001i | ||||
\(554\) | −7.04698 | + | 12.2057i | −0.299397 | + | 0.518571i | ||||
\(555\) | −4.55755 | + | 7.89391i | −0.193457 | + | 0.335078i | ||||
\(556\) | 0.979044 | + | 1.69575i | 0.0415207 | + | 0.0719160i | ||||
\(557\) | −13.9900 | − | 24.2315i | −0.592777 | − | 1.02672i | −0.993856 | − | 0.110677i | \(-0.964698\pi\) |
0.401079 | − | 0.916043i | \(-0.368635\pi\) | |||||||
\(558\) | −3.34822 | −0.141742 | ||||||||
\(559\) | −24.6902 | + | 42.7646i | −1.04428 | + | 1.80875i | ||||
\(560\) | 30.8577 | 1.30398 | ||||||||
\(561\) | −17.2158 | −0.726851 | ||||||||
\(562\) | −18.4141 | − | 31.8942i | −0.776753 | − | 1.34538i | ||||
\(563\) | −10.1948 | −0.429661 | −0.214830 | − | 0.976651i | \(-0.568920\pi\) | ||||
−0.214830 | + | 0.976651i | \(0.568920\pi\) | |||||||
\(564\) | 4.11877 | − | 7.13391i | 0.173431 | − | 0.300392i | ||||
\(565\) | 10.1092 | + | 17.5096i | 0.425295 | + | 0.736633i | ||||
\(566\) | 26.5884 | − | 46.0524i | 1.11759 | − | 1.93573i | ||||
\(567\) | 2.53710 | + | 4.39438i | 0.106548 | + | 0.184547i | ||||
\(568\) | 3.89500 | + | 6.74633i | 0.163430 | + | 0.283070i | ||||
\(569\) | −6.73089 | − | 11.6582i | −0.282173 | − | 0.488739i | 0.689746 | − | 0.724051i | \(-0.257722\pi\) |
−0.971920 | + | 0.235312i | \(0.924389\pi\) | |||||||
\(570\) | −1.82455 | − | 3.16021i | −0.0764218 | − | 0.132366i | ||||
\(571\) | −0.0508949 | − | 0.0881525i | −0.00212988 | − | 0.00368907i | 0.864958 | − | 0.501843i | \(-0.167345\pi\) |
−0.867088 | + | 0.498154i | \(0.834011\pi\) | |||||||
\(572\) | −16.5956 | − | 28.7444i | −0.693897 | − | 1.20186i | ||||
\(573\) | −1.62654 | + | 2.81726i | −0.0679499 | + | 0.117693i | ||||
\(574\) | −40.9057 | − | 70.8508i | −1.70737 | − | 2.95726i | ||||
\(575\) | −4.59091 | + | 7.95169i | −0.191454 | + | 0.331608i | ||||
\(576\) | −4.43094 | −0.184623 | ||||||||
\(577\) | −11.6556 | − | 20.1881i | −0.485228 | − | 0.840440i | 0.514628 | − | 0.857414i | \(-0.327930\pi\) |
−0.999856 | + | 0.0169740i | \(0.994597\pi\) | |||||||
\(578\) | 7.34622 | 0.305562 | ||||||||
\(579\) | 21.0010 | 0.872771 | ||||||||
\(580\) | 5.45068 | − | 9.44086i | 0.226327 | − | 0.392010i | ||||
\(581\) | 11.0015 | 0.456419 | ||||||||
\(582\) | 5.33801 | + | 9.24571i | 0.221268 | + | 0.383247i | ||||
\(583\) | 4.47161 | + | 7.74505i | 0.185195 | + | 0.320767i | ||||
\(584\) | −1.56879 | + | 2.71723i | −0.0649171 | + | 0.112440i | ||||
\(585\) | −3.62471 | + | 6.27819i | −0.149863 | + | 0.259571i | ||||
\(586\) | 15.0837 | − | 26.1257i | 0.623102 | − | 1.07924i | ||||
\(587\) | −20.8906 | + | 36.1835i | −0.862246 | + | 1.49345i | 0.00750931 | + | 0.999972i | \(0.497610\pi\) |
−0.869756 | + | 0.493483i | \(0.835724\pi\) | |||||||
\(588\) | −29.7638 | −1.22744 | ||||||||
\(589\) | 2.60669 | 0.107407 | ||||||||
\(590\) | −13.4060 | + | 23.2198i | −0.551915 | + | 0.955945i | ||||
\(591\) | −0.543826 | − | 0.941935i | −0.0223700 | − | 0.0387460i | ||||
\(592\) | −16.2375 | − | 28.1242i | −0.667358 | − | 1.15590i | ||||
\(593\) | −21.8783 | + | 37.8943i | −0.898433 | + | 1.55613i | −0.0689346 | + | 0.997621i | \(0.521960\pi\) |
−0.829498 | + | 0.558510i | \(0.811373\pi\) | |||||||
\(594\) | −7.13642 | −0.292811 | ||||||||
\(595\) | −30.2915 | −1.24183 | ||||||||
\(596\) | 7.36352 | + | 12.7540i | 0.301622 | + | 0.522424i | ||||
\(597\) | −3.69988 | + | 6.40838i | −0.151426 | + | 0.262278i | ||||
\(598\) | −29.3040 | −1.19833 | ||||||||
\(599\) | −18.0305 | − | 31.2298i | −0.736708 | − | 1.27602i | −0.953970 | − | 0.299902i | \(-0.903046\pi\) |
0.217262 | − | 0.976113i | \(-0.430287\pi\) | |||||||
\(600\) | −2.57223 | −0.105011 | ||||||||
\(601\) | −20.2419 | + | 35.0600i | −0.825684 | + | 1.43013i | 0.0757120 | + | 0.997130i | \(0.475877\pi\) |
−0.901396 | + | 0.432996i | \(0.857456\pi\) | |||||||
\(602\) | −85.5312 | −3.48599 | ||||||||
\(603\) | 8.01183 | − | 1.67649i | 0.326267 | − | 0.0682718i | ||||
\(604\) | 3.36236 | 0.136812 | ||||||||
\(605\) | −2.08753 | + | 3.61571i | −0.0848703 | + | 0.147000i | ||||
\(606\) | 9.29161 | 0.377446 | ||||||||
\(607\) | −7.43613 | − | 12.8798i | −0.301823 | − | 0.522773i | 0.674726 | − | 0.738069i | \(-0.264262\pi\) |
−0.976549 | + | 0.215295i | \(0.930929\pi\) | |||||||
\(608\) | 10.6973 | 0.433831 | ||||||||
\(609\) | 13.3342 | − | 23.0956i | 0.540331 | − | 0.935880i | ||||
\(610\) | 15.3730 | + | 26.6268i | 0.622435 | + | 1.07809i | ||||
\(611\) | 28.7906 | 1.16474 | ||||||||
\(612\) | 7.25429 | 0.293237 | ||||||||
\(613\) | 16.4986 | − | 28.5764i | 0.666372 | − | 1.15419i | −0.312539 | − | 0.949905i | \(-0.601180\pi\) |
0.978911 | − | 0.204286i | \(-0.0654871\pi\) | |||||||
\(614\) | 12.5140 | + | 21.6748i | 0.505022 | + | 0.874724i | ||||
\(615\) | −5.56055 | − | 9.63116i | −0.224223 | − | 0.388366i | ||||
\(616\) | −7.46654 | + | 12.9324i | −0.300835 | + | 0.521062i | ||||
\(617\) | −3.38641 | −0.136332 | −0.0681659 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681659 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(618\) | −6.93995 | −0.279166 | ||||||||
\(619\) | −7.66331 | + | 13.2732i | −0.308015 | + | 0.533497i | −0.977928 | − | 0.208942i | \(-0.932998\pi\) |
0.669913 | + | 0.742439i | \(0.266331\pi\) | |||||||
\(620\) | 1.83329 | − | 3.17535i | 0.0736267 | − | 0.127525i | ||||
\(621\) | −1.39410 | + | 2.41465i | −0.0559433 | + | 0.0968967i | ||||
\(622\) | −7.53893 | + | 13.0578i | −0.302283 | + | 0.523570i | ||||
\(623\) | 18.3925 | + | 31.8568i | 0.736880 | + | 1.27631i | ||||
\(624\) | −12.9140 | − | 22.3678i | −0.516975 | − | 0.895427i | ||||
\(625\) | 2.31000 | 0.0924001 | ||||||||
\(626\) | −14.5436 | + | 25.1903i | −0.581280 | + | 1.00681i | ||||
\(627\) | 5.55591 | 0.221882 | ||||||||
\(628\) | −11.3659 | −0.453548 | ||||||||
\(629\) | 15.9396 | + | 27.6082i | 0.635553 | + | 1.10081i | ||||
\(630\) | −12.5567 | −0.500269 | ||||||||
\(631\) | −10.6274 | + | 18.4072i | −0.423069 | + | 0.732777i | −0.996238 | − | 0.0866599i | \(-0.972381\pi\) |
0.573169 | + | 0.819437i | \(0.305714\pi\) | |||||||
\(632\) | 0.687601 | + | 1.19096i | 0.0273513 | + | 0.0473739i | ||||
\(633\) | −3.51731 | + | 6.09217i | −0.139801 | + | 0.242142i | ||||
\(634\) | −12.1746 | − | 21.0870i | −0.483515 | − | 0.837473i | ||||
\(635\) | −0.303636 | − | 0.525914i | −0.0120494 | − | 0.0208703i | ||||
\(636\) | −1.88422 | − | 3.26357i | −0.0747142 | − | 0.129409i | ||||
\(637\) | −52.0130 | − | 90.0892i | −2.06083 | − | 3.56946i | ||||
\(638\) | 18.7535 | + | 32.4820i | 0.742457 | + | 1.28597i | ||||
\(639\) | −4.98658 | − | 8.63701i | −0.197266 | − | 0.341675i | ||||
\(640\) | −3.99519 | + | 6.91986i | −0.157924 | + | 0.273532i | ||||
\(641\) | 15.3831 | + | 26.6443i | 0.607595 | + | 1.05239i | 0.991636 | + | 0.129070i | \(0.0411991\pi\) |
−0.384040 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(642\) | −11.2630 | + | 19.5080i | −0.444514 | + | 0.769921i | ||||
\(643\) | 26.8566 | 1.05912 | 0.529560 | − | 0.848272i | \(-0.322357\pi\) | ||||
0.529560 | + | 0.848272i | \(0.322357\pi\) | |||||||
\(644\) | −11.2307 | − | 19.4521i | −0.442552 | − | 0.766522i | ||||
\(645\) | −11.6268 | −0.457803 | ||||||||
\(646\) | −12.7623 | −0.502127 | ||||||||
\(647\) | 1.93564 | − | 3.35262i | 0.0760978 | − | 0.131805i | −0.825465 | − | 0.564453i | \(-0.809087\pi\) |
0.901563 | + | 0.432648i | \(0.142421\pi\) | |||||||
\(648\) | −0.781096 | −0.0306843 | ||||||||
\(649\) | −20.4112 | − | 35.3532i | −0.801210 | − | 1.38774i | ||||
\(650\) | 17.3052 | + | 29.9735i | 0.678767 | + | 1.17566i | ||||
\(651\) | 4.48486 | − | 7.76800i | 0.175775 | − | 0.304452i | ||||
\(652\) | −6.59069 | + | 11.4154i | −0.258111 | + | 0.447062i | ||||
\(653\) | 12.6197 | − | 21.8580i | 0.493847 | − | 0.855369i | −0.506128 | − | 0.862459i | \(-0.668923\pi\) |
0.999975 | + | 0.00708998i | \(0.00225683\pi\) | |||||||
\(654\) | −2.69483 | + | 4.66758i | −0.105376 | + | 0.182517i | ||||
\(655\) | 7.56602 | 0.295629 | ||||||||
\(656\) | 39.6220 | 1.54698 | ||||||||
\(657\) | 2.00845 | − | 3.47874i | 0.0783571 | − | 0.135719i | ||||
\(658\) | 24.9340 | + | 43.1869i | 0.972028 | + | 1.68360i | ||||
\(659\) | −16.5882 | − | 28.7317i | −0.646186 | − | 1.11923i | −0.984026 | − | 0.178024i | \(-0.943030\pi\) |
0.337840 | − | 0.941204i | \(-0.390304\pi\) | |||||||
\(660\) | 3.90748 | − | 6.76796i | 0.152099 | − | 0.263443i | ||||
\(661\) | 11.6142 | 0.451739 | 0.225869 | − | 0.974158i | \(-0.427478\pi\) | ||||
0.225869 | + | 0.974158i | \(0.427478\pi\) | |||||||
\(662\) | 32.7631 | 1.27337 | ||||||||
\(663\) | 12.6771 | + | 21.9573i | 0.492337 | + | 0.852752i | ||||
\(664\) | −0.846758 | + | 1.46663i | −0.0328606 | + | 0.0569162i | ||||
\(665\) | 9.77573 | 0.379086 | ||||||||
\(666\) | 6.60740 | + | 11.4443i | 0.256031 | + | 0.443459i | ||||
\(667\) | 14.6540 | 0.567404 | ||||||||
\(668\) | 5.38289 | − | 9.32344i | 0.208270 | − | 0.360735i | ||||
\(669\) | 14.3934 | 0.556481 | ||||||||
\(670\) | −6.32024 | + | 19.2443i | −0.244172 | + | 0.743472i | ||||
\(671\) | −46.8123 | −1.80717 | ||||||||
\(672\) | 18.4048 | − | 31.8781i | 0.709982 | − | 1.22973i | ||||
\(673\) | −47.1987 | −1.81938 | −0.909688 | − | 0.415292i | \(-0.863679\pi\) | ||||
−0.909688 | + | 0.415292i | \(0.863679\pi\) | |||||||
\(674\) | 19.9608 | + | 34.5731i | 0.768861 | + | 1.33171i | ||||
\(675\) | 3.29310 | 0.126751 | ||||||||
\(676\) | −14.1213 | + | 24.4587i | −0.543126 | + | 0.940721i | ||||
\(677\) | −9.48232 | − | 16.4239i | −0.364435 | − | 0.631220i | 0.624250 | − | 0.781224i | \(-0.285405\pi\) |
−0.988685 | + | 0.150004i | \(0.952071\pi\) | |||||||
\(678\) | 29.3119 | 1.12572 | ||||||||
\(679\) | −28.6005 | −1.09759 | ||||||||
\(680\) | 2.33146 | − | 4.03821i | 0.0894074 | − | 0.154858i | ||||
\(681\) | −12.5810 | − | 21.7909i | −0.482105 | − | 0.835031i | ||||
\(682\) | 6.30757 | + | 10.9250i | 0.241529 | + | 0.418341i | ||||
\(683\) | −8.95805 | + | 15.5158i | −0.342770 | + | 0.593696i | −0.984946 | − | 0.172862i | \(-0.944699\pi\) |
0.642176 | + | 0.766557i | \(0.278032\pi\) | |||||||
\(684\) | −2.34112 | −0.0895149 | ||||||||
\(685\) | 14.2793 | 0.545584 | ||||||||
\(686\) | 56.4526 | − | 97.7788i | 2.15537 | − | 3.73321i | ||||
\(687\) | −8.38027 | + | 14.5150i | −0.319727 | + | 0.553784i | ||||
\(688\) | 20.7118 | − | 35.8738i | 0.789628 | − | 1.36768i | ||||
\(689\) | 6.58546 | − | 11.4063i | 0.250886 | − | 0.434547i | ||||
\(690\) | −3.44986 | − | 5.97533i | −0.131334 | − | 0.227477i | ||||
\(691\) | 16.9922 | + | 29.4314i | 0.646414 | + | 1.11962i | 0.983973 | + | 0.178318i | \(0.0570655\pi\) |
−0.337559 | + | 0.941304i | \(0.609601\pi\) | |||||||
\(692\) | −20.8383 | −0.792153 | ||||||||
\(693\) | 9.55905 | − | 16.5568i | 0.363118 | − | 0.628939i | ||||
\(694\) | 18.6091 | 0.706392 | ||||||||
\(695\) | −1.61135 | −0.0611221 | ||||||||
\(696\) | 2.05261 | + | 3.55522i | 0.0778038 | + | 0.134760i | ||||
\(697\) | −38.8950 | −1.47325 | ||||||||
\(698\) | 20.6184 | − | 35.7121i | 0.780417 | − | 1.35172i | ||||
\(699\) | 13.2071 | + | 22.8754i | 0.499539 | + | 0.865226i | ||||
\(700\) | −13.2644 | + | 22.9746i | −0.501347 | + | 0.868359i | ||||
\(701\) | −18.2611 | − | 31.6291i | −0.689712 | − | 1.19462i | −0.971931 | − | 0.235266i | \(-0.924404\pi\) |
0.282220 | − | 0.959350i | \(-0.408929\pi\) | |||||||
\(702\) | 5.25500 | + | 9.10193i | 0.198337 | + | 0.343530i | ||||
\(703\) | −5.14405 | − | 8.90976i | −0.194012 | − | 0.336038i | ||||
\(704\) | 8.34725 | + | 14.4579i | 0.314599 | + | 0.544901i | ||||
\(705\) | 3.38942 | + | 5.87065i | 0.127653 | + | 0.221102i | ||||
\(706\) | 4.15823 | + | 7.20226i | 0.156497 | + | 0.271061i | ||||
\(707\) | −12.4459 | + | 21.5569i | −0.468075 | + | 0.810730i | ||||
\(708\) | 8.60075 | + | 14.8969i | 0.323236 | + | 0.559861i | ||||
\(709\) | 2.58582 | − | 4.47877i | 0.0971126 | − | 0.168204i | −0.813376 | − | 0.581739i | \(-0.802373\pi\) |
0.910488 | + | 0.413535i | \(0.135706\pi\) | |||||||
\(710\) | 24.6797 | 0.926212 | ||||||||
\(711\) | −0.880303 | − | 1.52473i | −0.0330140 | − | 0.0571818i | ||||
\(712\) | −5.66250 | −0.212211 | ||||||||
\(713\) | 4.92873 | 0.184583 | ||||||||
\(714\) | −21.9578 | + | 38.0321i | −0.821751 | + | 1.42332i | ||||
\(715\) | 27.3138 | 1.02148 | ||||||||
\(716\) | 5.71085 | + | 9.89148i | 0.213424 | + | 0.369662i | ||||
\(717\) | 0.221715 | + | 0.384022i | 0.00828011 | + | 0.0143416i | ||||
\(718\) | 25.0824 | − | 43.4441i | 0.936069 | − | 1.62132i | ||||
\(719\) | 1.11728 | − | 1.93519i | 0.0416675 | − | 0.0721703i | −0.844440 | − | 0.535651i | \(-0.820066\pi\) |
0.886107 | + | 0.463481i | \(0.153400\pi\) | |||||||
\(720\) | 3.04065 | − | 5.26656i | 0.113318 | − | 0.196273i | ||||
\(721\) | 9.29588 | − | 16.1009i | 0.346197 | − | 0.599630i | ||||
\(722\) | −31.8692 | −1.18605 | ||||||||
\(723\) | 21.3462 | 0.793874 | ||||||||
\(724\) | 20.3562 | − | 35.2580i | 0.756532 | − | 1.31035i | ||||
\(725\) | −8.65378 | − | 14.9888i | −0.321393 | − | 0.556670i | ||||
\(726\) | 3.02644 | + | 5.24195i | 0.112322 | + | 0.194547i | ||||
\(727\) | −1.05448 | + | 1.82642i | −0.0391086 | + | 0.0677380i | −0.884917 | − | 0.465748i | \(-0.845785\pi\) |
0.845809 | + | 0.533487i | \(0.179118\pi\) | |||||||
\(728\) | 21.9923 | 0.815090 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.97014 | + | 8.60853i | 0.183953 | + | 0.318616i | ||||
\(731\) | −20.3317 | + | 35.2156i | −0.751995 | + | 1.30249i | ||||
\(732\) | 19.7255 | 0.729075 | ||||||||
\(733\) | 8.03807 | + | 13.9223i | 0.296893 | + | 0.514233i | 0.975423 | − | 0.220339i | \(-0.0707163\pi\) |
−0.678531 | + | 0.734572i | \(0.737383\pi\) | |||||||
\(734\) | −3.91077 | −0.144349 | ||||||||
\(735\) | 12.2466 | − | 21.2118i | 0.451724 | − | 0.782408i | ||||
\(736\) | 20.2264 | 0.745556 | ||||||||
\(737\) | −20.5634 | − | 22.9838i | −0.757462 | − | 0.846619i | ||||
\(738\) | −16.1230 | −0.593497 | ||||||||
\(739\) | −5.54518 | + | 9.60454i | −0.203983 | + | 0.353309i | −0.949808 | − | 0.312833i | \(-0.898722\pi\) |
0.745825 | + | 0.666142i | \(0.232055\pi\) | |||||||
\(740\) | −14.4713 | −0.531975 | ||||||||
\(741\) | −4.09117 | − | 7.08611i | −0.150293 | − | 0.260315i | ||||
\(742\) | 22.8132 | 0.837499 | ||||||||
\(743\) | 20.1297 | − | 34.8657i | 0.738488 | − | 1.27910i | −0.214688 | − | 0.976683i | \(-0.568873\pi\) |
0.953176 | − | 0.302416i | \(-0.0977933\pi\) | |||||||
\(744\) | 0.690376 | + | 1.19577i | 0.0253104 | + | 0.0438389i | ||||
\(745\) | −12.1192 | −0.444013 | ||||||||
\(746\) | 0.204244 | 0.00747792 | ||||||||
\(747\) | 1.08406 | − | 1.87765i | 0.0396638 | − | 0.0686998i | ||||
\(748\) | −13.6660 | − | 23.6703i | −0.499680 | − | 0.865471i | ||||
\(749\) | −30.1729 | − | 52.2610i | −1.10249 | − | 1.90958i | ||||
\(750\) | −10.2611 | + | 17.7727i | −0.374682 | + | 0.648969i | ||||
\(751\) | 45.1172 | 1.64635 | 0.823174 | − | 0.567789i | \(-0.192201\pi\) | ||||
0.823174 | + | 0.567789i | \(0.192201\pi\) | |||||||
\(752\) | −24.1515 | −0.880714 | ||||||||
\(753\) | −9.72392 | + | 16.8423i | −0.354359 | + | 0.613768i | ||||
\(754\) | 27.6187 | − | 47.8371i | 1.00582 | − | 1.74212i | ||||
\(755\) | −1.38348 | + | 2.39626i | −0.0503500 | + | 0.0872087i | ||||
\(756\) | −4.02794 | + | 6.97659i | −0.146495 | + | 0.253736i | ||||
\(757\) | −10.0985 | − | 17.4911i | −0.367036 | − | 0.635725i | 0.622065 | − | 0.782966i | \(-0.286294\pi\) |
−0.989101 | + | 0.147241i | \(0.952961\pi\) | |||||||
\(758\) | 3.74083 | + | 6.47930i | 0.135873 | + | 0.235339i | ||||
\(759\) | 10.5051 | 0.381312 | ||||||||
\(760\) | −0.752413 | + | 1.30322i | −0.0272929 | + | 0.0472727i | ||||
\(761\) | 53.1019 | 1.92494 | 0.962471 | − | 0.271386i | \(-0.0874820\pi\) | ||||
0.962471 | + | 0.271386i | \(0.0874820\pi\) | |||||||
\(762\) | −0.880406 | −0.0318937 | ||||||||
\(763\) | −7.21930 | − | 12.5042i | −0.261356 | − | 0.452682i | ||||
\(764\) | −5.16466 | −0.186851 | ||||||||
\(765\) | −2.98486 | + | 5.16992i | −0.107918 | + | 0.186919i | ||||
\(766\) | 4.80522 | + | 8.32289i | 0.173620 | + | 0.300718i | ||||
\(767\) | −30.0601 | + | 52.0656i | −1.08541 | + | 1.87998i | ||||
\(768\) | 10.2230 | + | 17.7068i | 0.368892 | + | 0.638940i | ||||
\(769\) | 20.8702 | + | 36.1483i | 0.752600 | + | 1.30354i | 0.946559 | + | 0.322531i | \(0.104534\pi\) |
−0.193959 | + | 0.981010i | \(0.562133\pi\) | |||||||
\(770\) | 23.6549 | + | 40.9716i | 0.852465 | + | 1.47651i | ||||
\(771\) | 2.60822 | + | 4.51758i | 0.0939329 | + | 0.162697i | ||||
\(772\) | 16.6708 | + | 28.8746i | 0.599994 | + | 1.03922i | ||||
\(773\) | 23.8426 | + | 41.2965i | 0.857557 | + | 1.48533i | 0.874252 | + | 0.485472i | \(0.161352\pi\) |
−0.0166951 | + | 0.999861i | \(0.505314\pi\) | |||||||
\(774\) | −8.42806 | + | 14.5978i | −0.302940 | + | 0.524708i | ||||
\(775\) | −2.91062 | − | 5.04135i | −0.104553 | − | 0.181091i | ||||
\(776\) | 2.20131 | − | 3.81278i | 0.0790224 | − | 0.136871i | ||||
\(777\) | −35.4017 | −1.27003 | ||||||||
\(778\) | 6.58087 | + | 11.3984i | 0.235935 | + | 0.408652i | ||||
\(779\) | 12.5523 | 0.449731 | ||||||||
\(780\) | −11.5093 | −0.412099 | ||||||||
\(781\) | −18.7880 | + | 32.5418i | −0.672287 | + | 1.16444i | ||||
\(782\) | −24.1311 | −0.862925 | ||||||||
\(783\) | −2.62785 | − | 4.55158i | −0.0939118 | − | 0.162660i | ||||
\(784\) | 43.6320 | + | 75.5728i | 1.55828 | + | 2.69903i | ||||
\(785\) | 4.67661 | − | 8.10013i | 0.166916 | − | 0.289106i | ||||
\(786\) | 5.48449 | − | 9.49942i | 0.195625 | − | 0.338833i | ||||
\(787\) | 17.8793 | − | 30.9679i | 0.637328 | − | 1.10388i | −0.348689 | − | 0.937239i | \(-0.613373\pi\) |
0.986017 | − | 0.166646i | \(-0.0532937\pi\) | |||||||
\(788\) | 0.863388 | − | 1.49543i | 0.0307569 | − | 0.0532725i | ||||
\(789\) | −13.6157 | −0.484730 | ||||||||
\(790\) | 4.35682 | 0.155009 | ||||||||
\(791\) | −39.2625 | + | 68.0047i | −1.39601 | + | 2.41797i | ||||
\(792\) | 1.47147 | + | 2.54866i | 0.0522865 | + | 0.0905628i | ||||
\(793\) | 34.4708 | + | 59.7052i | 1.22409 | + | 2.12019i | ||||
\(794\) | 20.8575 | − | 36.1263i | 0.740205 | − | 1.28207i | ||||
\(795\) | 3.10113 | 0.109986 | ||||||||
\(796\) | −11.7480 | −0.416396 | ||||||||
\(797\) | −1.46925 | − | 2.54481i | −0.0520434 | − | 0.0901417i | 0.838830 | − | 0.544393i | \(-0.183240\pi\) |
−0.890873 | + | 0.454252i | \(0.849907\pi\) | |||||||
\(798\) | 7.08627 | − | 12.2738i | 0.250851 | − | 0.434487i | ||||
\(799\) | 23.7083 | 0.838741 | ||||||||
\(800\) | −11.9446 | − | 20.6886i | −0.422304 | − | 0.731451i | ||||
\(801\) | 7.24943 | 0.256146 | ||||||||
\(802\) | −4.22553 | + | 7.31882i | −0.149208 | + | 0.258437i | ||||
\(803\) | −15.1345 | −0.534086 | ||||||||
\(804\) | 8.66488 | + | 9.68478i | 0.305587 | + | 0.341556i | ||||
\(805\) | 18.4840 | 0.651474 | ||||||||
\(806\) | 9.28932 | − | 16.0896i | 0.327202 | − | 0.566731i | ||||
\(807\) | 19.0352 | 0.670070 | ||||||||
\(808\) | −1.91585 | − | 3.31836i | −0.0673995 | − | 0.116739i | ||||
\(809\) | 47.7915 | 1.68026 | 0.840130 | − | 0.542384i | \(-0.182478\pi\) | ||||
0.840130 | + | 0.542384i | \(0.182478\pi\) | |||||||
\(810\) | −1.23731 | + | 2.14308i | −0.0434745 | + | 0.0753000i | ||||
\(811\) | −16.1468 | − | 27.9670i | −0.566989 | − | 0.982054i | −0.996862 | − | 0.0791643i | \(-0.974775\pi\) |
0.429872 | − | 0.902890i | \(-0.358559\pi\) | |||||||
\(812\) | 42.3393 | 1.48582 | ||||||||
\(813\) | −10.4679 | −0.367127 | ||||||||
\(814\) | 24.8948 | − | 43.1190i | 0.872561 | − | 1.51132i | ||||
\(815\) | −5.42362 | − | 9.39399i | −0.189981 | − | 0.329057i | ||||
\(816\) | −10.6344 | − | 18.4193i | −0.372277 | − | 0.644803i | ||||
\(817\) | 6.56149 | − | 11.3648i | 0.229557 | − | 0.397605i | ||||
\(818\) | −1.98264 | −0.0693213 | ||||||||
\(819\) | −28.1557 | −0.983841 | ||||||||
\(820\) | 8.82803 | − | 15.2906i | 0.308288 | − | 0.533971i | ||||
\(821\) | −2.73257 | + | 4.73296i | −0.0953675 | + | 0.165181i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) |
0.814394 | + | 0.580312i | \(0.197069\pi\) | |||||||
\(822\) | 10.3508 | − | 17.9282i | 0.361027 | − | 0.625317i | ||||
\(823\) | −11.0975 | + | 19.2214i | −0.386833 | + | 0.670015i | −0.992022 | − | 0.126067i | \(-0.959764\pi\) |
0.605188 | + | 0.796082i | \(0.293098\pi\) | |||||||
\(824\) | 1.43096 | + | 2.47850i | 0.0498499 | + | 0.0863425i | ||||
\(825\) | −6.20372 | − | 10.7452i | −0.215986 | − | 0.374099i | ||||
\(826\) | −104.134 | −3.62327 | ||||||||
\(827\) | 14.5565 | − | 25.2127i | 0.506181 | − | 0.876731i | −0.493794 | − | 0.869579i | \(-0.664390\pi\) |
0.999974 | − | 0.00715162i | \(-0.00227645\pi\) | |||||||
\(828\) | −4.42659 | −0.153835 | ||||||||
\(829\) | 28.8657 | 1.00255 | 0.501274 | − | 0.865289i | \(-0.332865\pi\) | ||||
0.501274 | + | 0.865289i | \(0.332865\pi\) | |||||||
\(830\) | 2.68264 | + | 4.64646i | 0.0931157 | + | 0.161281i | ||||
\(831\) | −7.44098 | −0.258125 | ||||||||
\(832\) | 12.2932 | − | 21.2925i | 0.426191 | − | 0.738184i | ||||
\(833\) | −42.8314 | − | 74.1861i | −1.48402 | − | 2.57040i | ||||
\(834\) | −1.16805 | + | 2.02311i | −0.0404461 | + | 0.0700547i | ||||
\(835\) | 4.42970 | + | 7.67246i | 0.153296 | + | 0.265516i | ||||
\(836\) | 4.41033 | + | 7.63891i | 0.152534 | + | 0.264197i | ||||
\(837\) | −0.883856 | − | 1.53088i | −0.0305505 | − | 0.0529151i | ||||
\(838\) | 14.6804 | + | 25.4272i | 0.507125 | + | 0.878367i | ||||
\(839\) | −17.3078 | − | 29.9780i | −0.597532 | − | 1.03496i | −0.993184 | − | 0.116555i | \(-0.962815\pi\) |
0.395652 | − | 0.918400i | \(-0.370519\pi\) | |||||||
\(840\) | 2.58908 | + | 4.48442i | 0.0893318 | + | 0.154727i | ||||
\(841\) | 0.688767 | − | 1.19298i | 0.0237506 | − | 0.0411372i | ||||
\(842\) | 18.1955 | + | 31.5156i | 0.627060 | + | 1.08610i | ||||
\(843\) | 9.72183 | − | 16.8387i | 0.334838 | − | 0.579956i | ||||
\(844\) | −11.1683 | −0.384428 | ||||||||
\(845\) | −11.6207 | − | 20.1276i | −0.399764 | − | 0.692412i | ||||
\(846\) | 9.82776 | 0.337885 | ||||||||
\(847\) | −16.2153 | −0.557166 | ||||||||
\(848\) | −5.52432 | + | 9.56840i | −0.189706 | + | 0.328580i | ||||
\(849\) | 28.0749 | 0.963530 | ||||||||
\(850\) | 14.2504 | + | 24.6824i | 0.488785 | + | 0.846600i | ||||
\(851\) | −9.72639 | − | 16.8466i | −0.333416 | − | 0.577494i | ||||
\(852\) | 7.91677 | − | 13.7123i | 0.271224 | − | 0.469774i | ||||
\(853\) | 21.8097 | − | 37.7756i | 0.746751 | − | 1.29341i | −0.202622 | − | 0.979257i | \(-0.564946\pi\) |
0.949372 | − | 0.314153i | \(-0.101721\pi\) | |||||||
\(854\) | −59.7066 | + | 103.415i | −2.04312 | + | 3.53878i | ||||
\(855\) | 0.963278 | − | 1.66845i | 0.0329434 | − | 0.0570597i | ||||
\(856\) | 9.28933 | 0.317503 | ||||||||
\(857\) | 14.3293 | 0.489480 | 0.244740 | − | 0.969589i | \(-0.421297\pi\) | ||||
0.244740 | + | 0.969589i | \(0.421297\pi\) | |||||||
\(858\) | 19.7993 | − | 34.2934i | 0.675938 | − | 1.17076i | ||||
\(859\) | −1.29747 | − | 2.24728i | −0.0442690 | − | 0.0766762i | 0.843042 | − | 0.537848i | \(-0.180763\pi\) |
−0.887311 | + | 0.461172i | \(0.847429\pi\) | |||||||
\(860\) | −9.22942 | − | 15.9858i | −0.314720 | − | 0.545112i | ||||
\(861\) | 21.5964 | − | 37.4060i | 0.736003 | − | 1.27479i | ||||
\(862\) | −64.5392 | −2.19821 | ||||||||
\(863\) | −8.33860 | −0.283849 | −0.141925 | − | 0.989877i | \(-0.545329\pi\) | ||||
−0.141925 | + | 0.989877i | \(0.545329\pi\) | |||||||
\(864\) | −3.62715 | − | 6.28240i | −0.123398 | − | 0.213732i | ||||
\(865\) | 8.57414 | − | 14.8508i | 0.291530 | − | 0.504944i | ||||
\(866\) | −20.6076 | −0.700274 | ||||||||
\(867\) | 1.93924 | + | 3.35886i | 0.0658599 | + | 0.114073i | ||||
\(868\) | 14.2405 | 0.483353 | ||||||||
\(869\) | −3.31673 | + | 5.74474i | −0.112512 | + | 0.194877i | ||||
\(870\) | 13.0058 | 0.440939 | ||||||||
\(871\) | −14.1718 | + | 43.1514i | −0.480195 | + | 1.46213i | ||||
\(872\) | 2.22260 | 0.0752669 | ||||||||
\(873\) | −2.81823 | + | 4.88132i | −0.0953826 | + | 0.165208i | ||||
\(874\) | 7.78762 | 0.263420 | ||||||||
\(875\) | −27.4890 | − | 47.6123i | −0.929296 | − | 1.60959i | ||||
\(876\) | 6.37730 | 0.215469 | ||||||||
\(877\) | 18.2965 | − | 31.6905i | 0.617830 | − | 1.07011i | −0.372051 | − | 0.928212i | \(-0.621345\pi\) |
0.989881 | − | 0.141900i | \(-0.0453212\pi\) | |||||||
\(878\) | −5.05308 | − | 8.75219i | −0.170533 | − | 0.295372i | ||||
\(879\) | 15.9270 | 0.537205 | ||||||||
\(880\) | −22.9126 | −0.772383 | ||||||||
\(881\) | 2.96911 | − | 5.14265i | 0.100032 | − | 0.173260i | −0.811666 | − | 0.584122i | \(-0.801439\pi\) |
0.911698 | + | 0.410862i | \(0.134772\pi\) | |||||||
\(882\) | −17.7548 | − | 30.7522i | −0.597835 | − | 1.03548i | ||||
\(883\) | −18.1563 | − | 31.4477i | −0.611009 | − | 1.05830i | −0.991071 | − | 0.133337i | \(-0.957431\pi\) |
0.380062 | − | 0.924961i | \(-0.375903\pi\) | |||||||
\(884\) | −20.1263 | + | 34.8598i | −0.676922 | + | 1.17246i | ||||
\(885\) | −14.1555 | −0.475832 | ||||||||
\(886\) | −54.9049 | −1.84457 | ||||||||
\(887\) | −2.14151 | + | 3.70921i | −0.0719049 | + | 0.124543i | −0.899736 | − | 0.436434i | \(-0.856241\pi\) |
0.827831 | + | 0.560977i | \(0.189574\pi\) | |||||||
\(888\) | 2.72478 | − | 4.71946i | 0.0914377 | − | 0.158375i | ||||
\(889\) | 1.17928 | − | 2.04257i | 0.0395518 | − | 0.0685057i | ||||
\(890\) | −8.96976 | + | 15.5361i | −0.300667 | + | 0.520771i | ||||
\(891\) | −1.88386 | − | 3.26293i | −0.0631115 | − | 0.109312i | ||||
\(892\) | 11.4256 | + | 19.7897i | 0.382558 | + | 0.662609i | ||||
\(893\) | −7.65120 | −0.256038 | ||||||||
\(894\) | −8.78502 | + | 15.2161i | −0.293815 | + | 0.508903i | ||||
\(895\) | −9.39916 | −0.314179 | ||||||||
\(896\) | −31.0334 | −1.03675 | ||||||||
\(897\) | −7.73559 | − | 13.3984i | −0.258284 | − | 0.447361i | ||||
\(898\) | 70.3672 | 2.34818 | ||||||||
\(899\) | −4.64529 | + | 8.04587i | −0.154929 | + | 0.268345i | ||||
\(900\) | 2.61409 | + | 4.52774i | 0.0871363 | + | 0.150925i | ||||
\(901\) | 5.42295 | − | 9.39282i | 0.180665 | − | 0.312920i | ||||
\(902\) | 30.3735 | + | 52.6084i | 1.01133 | + | 1.75167i | ||||
\(903\) | −22.5783 | − | 39.1068i | −0.751360 | − | 1.30139i | ||||
\(904\) | −6.04387 | − | 10.4683i | −0.201016 | − | 0.348170i | ||||
\(905\) | 16.7516 | + | 29.0146i | 0.556841 | + | 0.964476i | ||||
\(906\) | 2.00573 | + | 3.47402i | 0.0666358 | + | 0.115417i | ||||
\(907\) | −21.1344 | − | 36.6059i | −0.701757 | − | 1.21548i | −0.967849 | − | 0.251531i | \(-0.919066\pi\) |
0.266092 | − | 0.963948i | \(-0.414267\pi\) | |||||||
\(908\) | 19.9738 | − | 34.5957i | 0.662854 | − | 1.14810i | ||||
\(909\) | 2.45278 | + | 4.24833i | 0.0813535 | + | 0.140908i | ||||
\(910\) | 34.8373 | − | 60.3399i | 1.15484 | − | 2.00025i | ||||
\(911\) | −22.1085 | −0.732488 | −0.366244 | − | 0.930519i | \(-0.619356\pi\) | ||||
−0.366244 | + | 0.930519i | \(0.619356\pi\) | |||||||
\(912\) | 3.43194 | + | 5.94430i | 0.113643 | + | 0.196835i | ||||
\(913\) | −8.16888 | −0.270350 | ||||||||
\(914\) | −41.7572 | −1.38121 | ||||||||
\(915\) | −8.11626 | + | 14.0578i | −0.268315 | + | 0.464736i | ||||
\(916\) | −26.6093 | −0.879196 | ||||||||
\(917\) | 14.6927 | + | 25.4484i | 0.485195 | + | 0.840382i | ||||
\(918\) | 4.32735 | + | 7.49520i | 0.142824 | + | 0.247378i | ||||
\(919\) | 12.7249 | − | 22.0402i | 0.419756 | − | 0.727038i | −0.576159 | − | 0.817338i | \(-0.695449\pi\) |
0.995915 | + | 0.0902993i | \(0.0287824\pi\) | |||||||
\(920\) | −1.42266 | + | 2.46413i | −0.0469039 | + | 0.0812399i | ||||
\(921\) | −6.60681 | + | 11.4433i | −0.217702 | + | 0.377070i | ||||
\(922\) | −32.4369 | + | 56.1823i | −1.06825 | + | 1.85027i | ||||
\(923\) | 55.3391 | 1.82151 | ||||||||
\(924\) | 30.3522 | 0.998515 | ||||||||
\(925\) | −11.4877 | + | 19.8972i | −0.377713 | + | 0.654217i | ||||
\(926\) | −11.3648 | − | 19.6845i | −0.373471 | − | 0.646871i | ||||
\(927\) | −1.83199 | − | 3.17310i | −0.0601705 | − | 0.104218i | ||||
\(928\) | −19.0632 | + | 33.0185i | −0.625781 | + | 1.08388i | ||||
\(929\) | −46.8292 | −1.53642 | −0.768208 | − | 0.640200i | \(-0.778851\pi\) | ||||
−0.768208 | + | 0.640200i | \(0.778851\pi\) | |||||||
\(930\) | 4.37440 | 0.143442 | ||||||||
\(931\) | 13.8226 | + | 23.9415i | 0.453018 | + | 0.784650i | ||||
\(932\) | −20.9678 | + | 36.3173i | −0.686824 | + | 1.18961i | ||||
\(933\) | −7.96043 | −0.260613 | ||||||||
\(934\) | 8.59741 | + | 14.8912i | 0.281316 | + | 0.487253i | ||||
\(935\) | 22.4922 | 0.735572 | ||||||||
\(936\) | 2.16708 | − | 3.75348i | 0.0708331 | − | 0.122686i | ||||
\(937\) | 23.0724 | 0.753743 | 0.376872 | − | 0.926266i | \(-0.377000\pi\) | ||||
0.376872 | + | 0.926266i | \(0.377000\pi\) | |||||||
\(938\) | −77.0020 | + | 16.1128i | −2.51420 | + | 0.526101i | ||||
\(939\) | −15.3567 | −0.501148 | ||||||||
\(940\) | −5.38110 | + | 9.32034i | −0.175512 | + | 0.303996i | ||||
\(941\) | −40.1417 | −1.30858 | −0.654291 | − | 0.756243i | \(-0.727033\pi\) | ||||
−0.654291 | + | 0.756243i | \(0.727033\pi\) | |||||||
\(942\) | −6.78001 | − | 11.7433i | −0.220905 | − | 0.382618i | ||||
\(943\) | 23.7338 | 0.772880 | ||||||||
\(944\) | 25.2164 | − | 43.6761i | 0.820724 | − | 1.42154i | ||||
\(945\) | −3.31468 | − | 5.74119i | −0.107826 | − | 0.186761i | ||||
\(946\) | 63.5090 | 2.06486 | ||||||||
\(947\) | −2.23315 | −0.0725675 | −0.0362838 | − | 0.999342i | \(-0.511552\pi\) | ||||
−0.0362838 | + | 0.999342i | \(0.511552\pi\) | |||||||
\(948\) | 1.39758 | − | 2.42069i | 0.0453914 | − | 0.0786202i | ||||
\(949\) | 11.1445 | + | 19.3029i | 0.361766 | + | 0.626597i | ||||
\(950\) | −4.59892 | − | 7.96556i | −0.149209 | − | 0.258437i | ||||
\(951\) | 6.42765 | − | 11.1330i | 0.208431 | − | 0.361013i | ||||
\(952\) | 18.1101 | 0.586952 | ||||||||
\(953\) | −9.44942 | −0.306097 | −0.153048 | − | 0.988219i | \(-0.548909\pi\) | ||||
−0.153048 | + | 0.988219i | \(0.548909\pi\) | |||||||
\(954\) | 2.24796 | − | 3.89359i | 0.0727805 | − | 0.126060i | ||||
\(955\) | 2.12505 | − | 3.68070i | 0.0687651 | − | 0.119105i | ||||
\(956\) | −0.351999 | + | 0.609680i | −0.0113845 | + | 0.0197184i | ||||
\(957\) | −9.90100 | + | 17.1490i | −0.320054 | + | 0.554349i | ||||
\(958\) | 10.0069 | + | 17.3324i | 0.323308 | + | 0.559985i | ||||
\(959\) | 27.7294 | + | 48.0287i | 0.895428 | + | 1.55093i | ||||
\(960\) | 5.78895 | 0.186838 | ||||||||
\(961\) | 13.9376 | − | 24.1406i | 0.449600 | − | 0.778730i | ||||
\(962\) | −73.3263 | −2.36414 | ||||||||
\(963\) | −11.8927 | −0.383236 | ||||||||
\(964\) | 16.9448 | + | 29.3493i | 0.545755 | + | 0.945276i | ||||
\(965\) | −27.4375 | −0.883243 | ||||||||
\(966\) | 13.3987 | − | 23.2073i | 0.431098 | − | 0.746683i | ||||
\(967\) | −4.79203 | − | 8.30003i | −0.154101 | − | 0.266911i | 0.778630 | − | 0.627483i | \(-0.215915\pi\) |
−0.932731 | + | 0.360572i | \(0.882582\pi\) | |||||||
\(968\) | 1.24805 | − | 2.16169i | 0.0401140 | − | 0.0694795i | ||||
\(969\) | −3.36897 | − | 5.83523i | −0.108227 | − | 0.187454i | ||||
\(970\) | −6.97403 | − | 12.0794i | −0.223922 | − | 0.387845i | ||||
\(971\) | −21.2948 | − | 36.8837i | −0.683384 | − | 1.18366i | −0.973942 | − | 0.226798i | \(-0.927174\pi\) |
0.290558 | − | 0.956857i | \(-0.406159\pi\) | |||||||
\(972\) | 0.793808 | + | 1.37492i | 0.0254614 | + | 0.0441005i | ||||
\(973\) | −3.12913 | − | 5.41982i | −0.100315 | − | 0.173751i | ||||
\(974\) | −20.4625 | − | 35.4422i | −0.655662 | − | 1.13564i | ||||
\(975\) | −9.13639 | + | 15.8247i | −0.292599 | + | 0.506796i | ||||
\(976\) | −28.9164 | − | 50.0847i | −0.925592 | − | 1.60317i | ||||
\(977\) | −19.6324 | + | 34.0043i | −0.628096 | + | 1.08789i | 0.359837 | + | 0.933015i | \(0.382832\pi\) |
−0.987933 | + | 0.154879i | \(0.950501\pi\) | |||||||
\(978\) | −15.7260 | −0.502862 | ||||||||
\(979\) | −13.6569 | − | 23.6544i | −0.436476 | − | 0.755998i | ||||
\(980\) | 38.8859 | 1.24216 | ||||||||
\(981\) | −2.84549 | −0.0908496 | ||||||||
\(982\) | 16.0771 | − | 27.8463i | 0.513039 | − | 0.888610i | ||||
\(983\) | 31.2624 | 0.997115 | 0.498558 | − | 0.866856i | \(-0.333863\pi\) | ||||
0.498558 | + | 0.866856i | \(0.333863\pi\) | |||||||
\(984\) | 3.32444 | + | 5.75810i | 0.105979 | + | 0.183561i | ||||
\(985\) | 0.710500 | + | 1.23062i | 0.0226384 | + | 0.0392109i | ||||
\(986\) | 22.7433 | − | 39.3926i | 0.724294 | − | 1.25451i | ||||
\(987\) | −13.1640 | + | 22.8008i | −0.419016 | + | 0.725756i | ||||
\(988\) | 6.49521 | − | 11.2500i | 0.206640 | − | 0.357911i | ||||
\(989\) | 12.4065 | − | 21.4887i | 0.394503 | − | 0.683299i | ||||
\(990\) | 9.32362 | 0.296324 | ||||||||
\(991\) | −25.9571 | −0.824555 | −0.412277 | − | 0.911058i | \(-0.635267\pi\) | ||||
−0.412277 | + | 0.911058i | \(0.635267\pi\) | |||||||
\(992\) | −6.41175 | + | 11.1055i | −0.203573 | + | 0.352599i | ||||
\(993\) | 8.64872 | + | 14.9800i | 0.274459 | + | 0.475377i | ||||
\(994\) | 47.9262 | + | 83.0106i | 1.52013 | + | 2.63294i | ||||
\(995\) | 4.83383 | − | 8.37245i | 0.153243 | − | 0.265424i | ||||
\(996\) | 3.44216 | 0.109069 | ||||||||
\(997\) | −2.89021 | −0.0915337 | −0.0457669 | − | 0.998952i | \(-0.514573\pi\) | ||||
−0.0457669 | + | 0.998952i | \(0.514573\pi\) | |||||||
\(998\) | −1.43838 | − | 2.49134i | −0.0455311 | − | 0.0788621i | ||||
\(999\) | −3.48841 | + | 6.04210i | −0.110368 | + | 0.191164i |
(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 | 201.2.e.b.163.2 | yes | 10 | |
3.2 | odd | 2 | 603.2.g.g.163.4 | 10 | |||
67.37 | even | 3 | inner | 201.2.e.b.37.2 | ✓ | 10 | |
201.104 | odd | 6 | 603.2.g.g.37.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.e.b.37.2 | ✓ | 10 | 67.37 | even | 3 | inner | |
201.2.e.b.163.2 | yes | 10 | 1.1 | even | 1 | trivial | |
603.2.g.g.37.4 | 10 | 201.104 | odd | 6 | |||
603.2.g.g.163.4 | 10 | 3.2 | odd | 2 |