Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (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: | \(4.35983195036\) |
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: | \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) |
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 | 373.4 | ||
Root | \(-0.623307 - 1.07960i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.373 |
Dual form | 546.2.k.e.445.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.623307 | − | 1.07960i | 0.278751 | − | 0.482811i | −0.692323 | − | 0.721587i | \(-0.743413\pi\) |
0.971075 | + | 0.238776i | \(0.0767462\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −2.27938 | + | 1.34329i | −0.861524 | + | 0.507717i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.24661 | 0.394214 | ||||||||
\(11\) | −2.49532 | −0.752369 | −0.376184 | − | 0.926545i | \(-0.622764\pi\) | ||||
−0.376184 | + | 0.926545i | \(0.622764\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −0.785103 | + | 3.51904i | −0.217748 | + | 0.976005i | ||||
\(14\) | −2.30301 | − | 1.30235i | −0.615506 | − | 0.348069i | ||||
\(15\) | −0.623307 | + | 1.07960i | −0.160937 | + | 0.278751i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.247662 | + | 0.428963i | −0.0600669 | + | 0.104039i | −0.894495 | − | 0.447078i | \(-0.852465\pi\) |
0.834428 | + | 0.551117i | \(0.185798\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −7.67156 | −1.75998 | −0.879988 | − | 0.474996i | \(-0.842450\pi\) | ||||
−0.879988 | + | 0.474996i | \(0.842450\pi\) | |||||||
\(20\) | 0.623307 | + | 1.07960i | 0.139376 | + | 0.241406i | ||||
\(21\) | 2.27938 | − | 1.34329i | 0.497401 | − | 0.293130i | ||||
\(22\) | −1.24766 | − | 2.16101i | −0.266002 | − | 0.460730i | ||||
\(23\) | −0.224026 | − | 0.388024i | −0.0467127 | − | 0.0809087i | 0.841724 | − | 0.539909i | \(-0.181541\pi\) |
−0.888436 | + | 0.459000i | \(0.848208\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.72298 | + | 2.98428i | 0.344595 | + | 0.596857i | ||||
\(26\) | −3.44013 | + | 1.07960i | −0.674664 | + | 0.211727i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0236360 | − | 2.64565i | −0.00446679 | − | 0.499980i | ||||
\(29\) | −3.71142 | + | 6.42837i | −0.689194 | + | 1.19372i | 0.282905 | + | 0.959148i | \(0.408702\pi\) |
−0.972099 | + | 0.234571i | \(0.924631\pi\) | |||||||
\(30\) | −1.24661 | −0.227599 | ||||||||
\(31\) | −4.06448 | − | 7.03989i | −0.730002 | − | 1.26440i | −0.956882 | − | 0.290478i | \(-0.906186\pi\) |
0.226879 | − | 0.973923i | \(-0.427148\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 2.49532 | 0.434380 | ||||||||
\(34\) | −0.495324 | −0.0849474 | ||||||||
\(35\) | 0.0294650 | + | 3.29810i | 0.00498050 | + | 0.557480i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.37097 | − | 2.37459i | −0.225386 | − | 0.390380i | 0.731049 | − | 0.682325i | \(-0.239031\pi\) |
−0.956435 | + | 0.291945i | \(0.905698\pi\) | |||||||
\(38\) | −3.83578 | − | 6.64376i | −0.622246 | − | 1.07776i | ||||
\(39\) | 0.785103 | − | 3.51904i | 0.125717 | − | 0.563497i | ||||
\(40\) | −0.623307 | + | 1.07960i | −0.0985534 | + | 0.170700i | ||||
\(41\) | −1.87097 | + | 3.24061i | −0.292196 | + | 0.506099i | −0.974329 | − | 0.225130i | \(-0.927719\pi\) |
0.682133 | + | 0.731229i | \(0.261053\pi\) | |||||||
\(42\) | 2.30301 | + | 1.30235i | 0.355363 | + | 0.200958i | ||||
\(43\) | 1.47532 | + | 2.55532i | 0.224983 | + | 0.389683i | 0.956314 | − | 0.292340i | \(-0.0944339\pi\) |
−0.731331 | + | 0.682023i | \(0.761101\pi\) | |||||||
\(44\) | 1.24766 | − | 2.16101i | 0.188092 | − | 0.325785i | ||||
\(45\) | 0.623307 | − | 1.07960i | 0.0929171 | − | 0.160937i | ||||
\(46\) | 0.224026 | − | 0.388024i | 0.0330308 | − | 0.0572111i | ||||
\(47\) | 3.29729 | − | 5.71107i | 0.480959 | − | 0.833046i | −0.518802 | − | 0.854894i | \(-0.673622\pi\) |
0.999761 | + | 0.0218486i | \(0.00695519\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 3.39113 | − | 6.12374i | 0.484447 | − | 0.874820i | ||||
\(50\) | −1.72298 | + | 2.98428i | −0.243666 | + | 0.422042i | ||||
\(51\) | 0.247662 | − | 0.428963i | 0.0346796 | − | 0.0600669i | ||||
\(52\) | −2.65502 | − | 2.43944i | −0.368185 | − | 0.338289i | ||||
\(53\) | 3.86750 | + | 6.69870i | 0.531241 | + | 0.920137i | 0.999335 | + | 0.0364583i | \(0.0116076\pi\) |
−0.468094 | + | 0.883679i | \(0.655059\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −1.55535 | + | 2.69395i | −0.209724 | + | 0.363252i | ||||
\(56\) | 2.27938 | − | 1.34329i | 0.304595 | − | 0.179505i | ||||
\(57\) | 7.67156 | 1.01612 | ||||||||
\(58\) | −7.42285 | −0.974668 | ||||||||
\(59\) | 0.727653 | − | 1.26033i | 0.0947324 | − | 0.164081i | −0.814764 | − | 0.579792i | \(-0.803134\pi\) |
0.909497 | + | 0.415711i | \(0.136467\pi\) | |||||||
\(60\) | −0.623307 | − | 1.07960i | −0.0804686 | − | 0.139376i | ||||
\(61\) | −4.19934 | −0.537671 | −0.268835 | − | 0.963186i | \(-0.586639\pi\) | ||||
−0.268835 | + | 0.963186i | \(0.586639\pi\) | |||||||
\(62\) | 4.06448 | − | 7.03989i | 0.516190 | − | 0.894067i | ||||
\(63\) | −2.27938 | + | 1.34329i | −0.287175 | + | 0.169239i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.30979 | + | 3.04103i | 0.410529 | + | 0.377194i | ||||
\(66\) | 1.24766 | + | 2.16101i | 0.153577 | + | 0.266002i | ||||
\(67\) | 0.0276094 | 0.00337303 | 0.00168652 | − | 0.999999i | \(-0.499463\pi\) | ||||
0.00168652 | + | 0.999999i | \(0.499463\pi\) | |||||||
\(68\) | −0.247662 | − | 0.428963i | −0.0300334 | − | 0.0520194i | ||||
\(69\) | 0.224026 | + | 0.388024i | 0.0269696 | + | 0.0467127i | ||||
\(70\) | −2.84150 | + | 1.67457i | −0.339625 | + | 0.200149i | ||||
\(71\) | 4.68884 | + | 8.12130i | 0.556463 | + | 0.963821i | 0.997788 | + | 0.0664743i | \(0.0211751\pi\) |
−0.441326 | + | 0.897347i | \(0.645492\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −5.07151 | − | 8.78412i | −0.593576 | − | 1.02810i | −0.993746 | − | 0.111663i | \(-0.964382\pi\) |
0.400170 | − | 0.916441i | \(-0.368951\pi\) | |||||||
\(74\) | 1.37097 | − | 2.37459i | 0.159372 | − | 0.276040i | ||||
\(75\) | −1.72298 | − | 2.98428i | −0.198952 | − | 0.344595i | ||||
\(76\) | 3.83578 | − | 6.64376i | 0.439994 | − | 0.762092i | ||||
\(77\) | 5.68779 | − | 3.35195i | 0.648184 | − | 0.381990i | ||||
\(78\) | 3.44013 | − | 1.07960i | 0.389518 | − | 0.122241i | ||||
\(79\) | −4.93545 | + | 8.54845i | −0.555282 | + | 0.961776i | 0.442600 | + | 0.896719i | \(0.354056\pi\) |
−0.997882 | + | 0.0650567i | \(0.979277\pi\) | |||||||
\(80\) | −1.24661 | −0.139376 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.74194 | −0.413228 | ||||||||
\(83\) | 7.42285 | 0.814763 | 0.407382 | − | 0.913258i | \(-0.366442\pi\) | ||||
0.407382 | + | 0.913258i | \(0.366442\pi\) | |||||||
\(84\) | 0.0236360 | + | 2.64565i | 0.00257890 | + | 0.288664i | ||||
\(85\) | 0.308739 | + | 0.534751i | 0.0334874 | + | 0.0580019i | ||||
\(86\) | −1.47532 | + | 2.55532i | −0.159087 | + | 0.275547i | ||||
\(87\) | 3.71142 | − | 6.42837i | 0.397906 | − | 0.689194i | ||||
\(88\) | 2.49532 | 0.266002 | ||||||||
\(89\) | 5.74056 | + | 9.94294i | 0.608498 | + | 1.05395i | 0.991488 | + | 0.130197i | \(0.0415611\pi\) |
−0.382990 | + | 0.923753i | \(0.625106\pi\) | |||||||
\(90\) | 1.24661 | 0.131405 | ||||||||
\(91\) | −2.93755 | − | 9.07584i | −0.307939 | − | 0.951406i | ||||
\(92\) | 0.448052 | 0.0467127 | ||||||||
\(93\) | 4.06448 | + | 7.03989i | 0.421467 | + | 0.730002i | ||||
\(94\) | 6.59458 | 0.680179 | ||||||||
\(95\) | −4.78173 | + | 8.28221i | −0.490596 | + | 0.849736i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −0.509831 | − | 0.883054i | −0.0517655 | − | 0.0896605i | 0.838982 | − | 0.544160i | \(-0.183152\pi\) |
−0.890747 | + | 0.454499i | \(0.849818\pi\) | |||||||
\(98\) | 6.99888 | − | 0.125065i | 0.706994 | − | 0.0126335i | ||||
\(99\) | −2.49532 | −0.250790 | ||||||||
\(100\) | −3.44595 | −0.344595 | ||||||||
\(101\) | 17.9425 | 1.78535 | 0.892675 | − | 0.450701i | \(-0.148826\pi\) | ||||
0.892675 | + | 0.450701i | \(0.148826\pi\) | |||||||
\(102\) | 0.495324 | 0.0490444 | ||||||||
\(103\) | 0.524685 | − | 0.908780i | 0.0516987 | − | 0.0895448i | −0.839018 | − | 0.544104i | \(-0.816870\pi\) |
0.890717 | + | 0.454559i | \(0.150203\pi\) | |||||||
\(104\) | 0.785103 | − | 3.51904i | 0.0769857 | − | 0.345070i | ||||
\(105\) | −0.0294650 | − | 3.29810i | −0.00287549 | − | 0.321861i | ||||
\(106\) | −3.86750 | + | 6.69870i | −0.375644 | + | 0.650635i | ||||
\(107\) | 5.09152 | + | 8.81877i | 0.492216 | + | 0.852543i | 0.999960 | − | 0.00896501i | \(-0.00285369\pi\) |
−0.507744 | + | 0.861508i | \(0.669520\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 9.92285 | + | 17.1869i | 0.950436 | + | 1.64620i | 0.744482 | + | 0.667643i | \(0.232697\pi\) |
0.205955 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(110\) | −3.11070 | −0.296594 | ||||||||
\(111\) | 1.37097 | + | 2.37459i | 0.130127 | + | 0.225386i | ||||
\(112\) | 2.30301 | + | 1.30235i | 0.217614 | + | 0.123061i | ||||
\(113\) | −7.93440 | − | 13.7428i | −0.746406 | − | 1.29281i | −0.949535 | − | 0.313661i | \(-0.898445\pi\) |
0.203129 | − | 0.979152i | \(-0.434889\pi\) | |||||||
\(114\) | 3.83578 | + | 6.64376i | 0.359254 | + | 0.622246i | ||||
\(115\) | −0.558548 | −0.0520848 | ||||||||
\(116\) | −3.71142 | − | 6.42837i | −0.344597 | − | 0.596860i | ||||
\(117\) | −0.785103 | + | 3.51904i | −0.0725828 | + | 0.325335i | ||||
\(118\) | 1.45531 | 0.133972 | ||||||||
\(119\) | −0.0117075 | − | 1.31045i | −0.00107322 | − | 0.120129i | ||||
\(120\) | 0.623307 | − | 1.07960i | 0.0568999 | − | 0.0985534i | ||||
\(121\) | −4.77336 | −0.433942 | ||||||||
\(122\) | −2.09967 | − | 3.63674i | −0.190095 | − | 0.329255i | ||||
\(123\) | 1.87097 | − | 3.24061i | 0.168700 | − | 0.292196i | ||||
\(124\) | 8.12896 | 0.730002 | ||||||||
\(125\) | 10.5288 | 0.941728 | ||||||||
\(126\) | −2.30301 | − | 1.30235i | −0.205169 | − | 0.116023i | ||||
\(127\) | 4.23846 | − | 7.34124i | 0.376103 | − | 0.651429i | −0.614389 | − | 0.789004i | \(-0.710597\pi\) |
0.990491 | + | 0.137574i | \(0.0439306\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.47532 | − | 2.55532i | −0.129894 | − | 0.224983i | ||||
\(130\) | −0.978720 | + | 4.38688i | −0.0858394 | + | 0.384755i | ||||
\(131\) | −8.26678 | + | 14.3185i | −0.722272 | + | 1.25101i | 0.237816 | + | 0.971310i | \(0.423569\pi\) |
−0.960087 | + | 0.279701i | \(0.909765\pi\) | |||||||
\(132\) | −1.24766 | + | 2.16101i | −0.108595 | + | 0.188092i | ||||
\(133\) | 17.4864 | − | 10.3051i | 1.51626 | − | 0.893569i | ||||
\(134\) | 0.0138047 | + | 0.0239105i | 0.00119255 | + | 0.00206555i | ||||
\(135\) | −0.623307 | + | 1.07960i | −0.0536457 | + | 0.0929171i | ||||
\(136\) | 0.247662 | − | 0.428963i | 0.0212368 | − | 0.0367833i | ||||
\(137\) | 0.428418 | − | 0.742042i | 0.0366023 | − | 0.0633970i | −0.847144 | − | 0.531363i | \(-0.821680\pi\) |
0.883746 | + | 0.467966i | \(0.155013\pi\) | |||||||
\(138\) | −0.224026 | + | 0.388024i | −0.0190704 | + | 0.0330308i | ||||
\(139\) | 4.74886 | + | 8.22528i | 0.402793 | + | 0.697659i | 0.994062 | − | 0.108816i | \(-0.0347060\pi\) |
−0.591268 | + | 0.806475i | \(0.701373\pi\) | |||||||
\(140\) | −2.87097 | − | 1.62353i | −0.242641 | − | 0.137213i | ||||
\(141\) | −3.29729 | + | 5.71107i | −0.277682 | + | 0.480959i | ||||
\(142\) | −4.68884 | + | 8.12130i | −0.393478 | + | 0.681525i | ||||
\(143\) | 1.95909 | − | 8.78114i | 0.163827 | − | 0.734315i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 4.62671 | + | 8.01370i | 0.384227 | + | 0.665501i | ||||
\(146\) | 5.07151 | − | 8.78412i | 0.419721 | − | 0.726979i | ||||
\(147\) | −3.39113 | + | 6.12374i | −0.279696 | + | 0.505078i | ||||
\(148\) | 2.74194 | 0.225386 | ||||||||
\(149\) | −4.73744 | −0.388106 | −0.194053 | − | 0.980991i | \(-0.562163\pi\) | ||||
−0.194053 | + | 0.980991i | \(0.562163\pi\) | |||||||
\(150\) | 1.72298 | − | 2.98428i | 0.140681 | − | 0.243666i | ||||
\(151\) | −3.56085 | − | 6.16758i | −0.289778 | − | 0.501911i | 0.683978 | − | 0.729502i | \(-0.260248\pi\) |
−0.973757 | + | 0.227592i | \(0.926915\pi\) | |||||||
\(152\) | 7.67156 | 0.622246 | ||||||||
\(153\) | −0.247662 | + | 0.428963i | −0.0200223 | + | 0.0346796i | ||||
\(154\) | 5.74677 | + | 3.24979i | 0.463088 | + | 0.261876i | ||||
\(155\) | −10.1337 | −0.813956 | ||||||||
\(156\) | 2.65502 | + | 2.43944i | 0.212572 | + | 0.195311i | ||||
\(157\) | −7.52147 | − | 13.0276i | −0.600279 | − | 1.03971i | −0.992779 | − | 0.119961i | \(-0.961723\pi\) |
0.392500 | − | 0.919752i | \(-0.371610\pi\) | |||||||
\(158\) | −9.87090 | −0.785287 | ||||||||
\(159\) | −3.86750 | − | 6.69870i | −0.306712 | − | 0.531241i | ||||
\(160\) | −0.623307 | − | 1.07960i | −0.0492767 | − | 0.0853498i | ||||
\(161\) | 1.03187 | + | 0.583522i | 0.0813228 | + | 0.0459880i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −9.02971 | −0.707261 | −0.353631 | − | 0.935385i | \(-0.615053\pi\) | ||||
−0.353631 | + | 0.935385i | \(0.615053\pi\) | |||||||
\(164\) | −1.87097 | − | 3.24061i | −0.146098 | − | 0.253049i | ||||
\(165\) | 1.55535 | − | 2.69395i | 0.121084 | − | 0.209724i | ||||
\(166\) | 3.71142 | + | 6.42837i | 0.288062 | + | 0.498939i | ||||
\(167\) | 1.42442 | − | 2.46716i | 0.110225 | − | 0.190915i | −0.805636 | − | 0.592411i | \(-0.798176\pi\) |
0.915861 | + | 0.401496i | \(0.131510\pi\) | |||||||
\(168\) | −2.27938 | + | 1.34329i | −0.175858 | + | 0.103637i | ||||
\(169\) | −11.7672 | − | 5.52561i | −0.905171 | − | 0.425047i | ||||
\(170\) | −0.308739 | + | 0.534751i | −0.0236792 | + | 0.0410136i | ||||
\(171\) | −7.67156 | −0.586659 | ||||||||
\(172\) | −2.95063 | −0.224983 | ||||||||
\(173\) | −25.4875 | −1.93778 | −0.968891 | − | 0.247487i | \(-0.920395\pi\) | ||||
−0.968891 | + | 0.247487i | \(0.920395\pi\) | |||||||
\(174\) | 7.42285 | 0.562725 | ||||||||
\(175\) | −7.93608 | − | 4.48785i | −0.599912 | − | 0.339250i | ||||
\(176\) | 1.24766 | + | 2.16101i | 0.0940461 | + | 0.162893i | ||||
\(177\) | −0.727653 | + | 1.26033i | −0.0546938 | + | 0.0947324i | ||||
\(178\) | −5.74056 | + | 9.94294i | −0.430273 | + | 0.745255i | ||||
\(179\) | 18.2006 | 1.36038 | 0.680189 | − | 0.733037i | \(-0.261898\pi\) | ||||
0.680189 | + | 0.733037i | \(0.261898\pi\) | |||||||
\(180\) | 0.623307 | + | 1.07960i | 0.0464585 | + | 0.0804686i | ||||
\(181\) | −13.7305 | −1.02058 | −0.510290 | − | 0.860003i | \(-0.670462\pi\) | ||||
−0.510290 | + | 0.860003i | \(0.670462\pi\) | |||||||
\(182\) | 6.39113 | − | 7.08191i | 0.473742 | − | 0.524946i | ||||
\(183\) | 4.19934 | 0.310424 | ||||||||
\(184\) | 0.224026 | + | 0.388024i | 0.0165154 | + | 0.0286055i | ||||
\(185\) | −3.41814 | −0.251306 | ||||||||
\(186\) | −4.06448 | + | 7.03989i | −0.298022 | + | 0.516190i | ||||
\(187\) | 0.617997 | − | 1.07040i | 0.0451924 | − | 0.0782756i | ||||
\(188\) | 3.29729 | + | 5.71107i | 0.240480 | + | 0.416523i | ||||
\(189\) | 2.27938 | − | 1.34329i | 0.165800 | − | 0.0977101i | ||||
\(190\) | −9.56347 | −0.693807 | ||||||||
\(191\) | 5.28588 | 0.382473 | 0.191236 | − | 0.981544i | \(-0.438750\pi\) | ||||
0.191236 | + | 0.981544i | \(0.438750\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.81197 | 0.346373 | 0.173187 | − | 0.984889i | \(-0.444594\pi\) | ||||
0.173187 | + | 0.984889i | \(0.444594\pi\) | |||||||
\(194\) | 0.509831 | − | 0.883054i | 0.0366038 | − | 0.0633996i | ||||
\(195\) | −3.30979 | − | 3.04103i | −0.237019 | − | 0.217773i | ||||
\(196\) | 3.60775 | + | 5.99868i | 0.257696 | + | 0.428477i | ||||
\(197\) | 11.7743 | − | 20.3937i | 0.838883 | − | 1.45299i | −0.0519458 | − | 0.998650i | \(-0.516542\pi\) |
0.890829 | − | 0.454339i | \(-0.150124\pi\) | |||||||
\(198\) | −1.24766 | − | 2.16101i | −0.0886675 | − | 0.153577i | ||||
\(199\) | −5.63984 | + | 9.76849i | −0.399798 | + | 0.692470i | −0.993701 | − | 0.112067i | \(-0.964253\pi\) |
0.593903 | + | 0.804537i | \(0.297586\pi\) | |||||||
\(200\) | −1.72298 | − | 2.98428i | −0.121833 | − | 0.211021i | ||||
\(201\) | −0.0276094 | −0.00194742 | ||||||||
\(202\) | 8.97127 | + | 15.5387i | 0.631217 | + | 1.09330i | ||||
\(203\) | −0.175447 | − | 19.6382i | −0.0123139 | − | 1.37833i | ||||
\(204\) | 0.247662 | + | 0.428963i | 0.0173398 | + | 0.0300334i | ||||
\(205\) | 2.33237 | + | 4.03979i | 0.162900 | + | 0.282151i | ||||
\(206\) | 1.04937 | 0.0731130 | ||||||||
\(207\) | −0.224026 | − | 0.388024i | −0.0155709 | − | 0.0269696i | ||||
\(208\) | 3.44013 | − | 1.07960i | 0.238530 | − | 0.0748567i | ||||
\(209\) | 19.1430 | 1.32415 | ||||||||
\(210\) | 2.84150 | − | 1.67457i | 0.196082 | − | 0.115556i | ||||
\(211\) | −6.22021 | + | 10.7737i | −0.428217 | + | 0.741693i | −0.996715 | − | 0.0809915i | \(-0.974191\pi\) |
0.568498 | + | 0.822685i | \(0.307525\pi\) | |||||||
\(212\) | −7.73499 | −0.531241 | ||||||||
\(213\) | −4.68884 | − | 8.12130i | −0.321274 | − | 0.556463i | ||||
\(214\) | −5.09152 | + | 8.81877i | −0.348049 | + | 0.602839i | ||||
\(215\) | 3.67830 | 0.250858 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 18.7211 | + | 10.5868i | 1.27087 | + | 0.718678i | ||||
\(218\) | −9.92285 | + | 17.1869i | −0.672060 | + | 1.16404i | ||||
\(219\) | 5.07151 | + | 8.78412i | 0.342701 | + | 0.593576i | ||||
\(220\) | −1.55535 | − | 2.69395i | −0.104862 | − | 0.181626i | ||||
\(221\) | −1.31510 | − | 1.20831i | −0.0884630 | − | 0.0812799i | ||||
\(222\) | −1.37097 | + | 2.37459i | −0.0920134 | + | 0.159372i | ||||
\(223\) | −10.4651 | + | 18.1260i | −0.700793 | + | 1.21381i | 0.267396 | + | 0.963587i | \(0.413837\pi\) |
−0.968188 | + | 0.250222i | \(0.919496\pi\) | |||||||
\(224\) | 0.0236360 | + | 2.64565i | 0.00157925 | + | 0.176770i | ||||
\(225\) | 1.72298 | + | 2.98428i | 0.114865 | + | 0.198952i | ||||
\(226\) | 7.93440 | − | 13.7428i | 0.527789 | − | 0.914157i | ||||
\(227\) | −8.79052 | + | 15.2256i | −0.583447 | + | 1.01056i | 0.411620 | + | 0.911356i | \(0.364963\pi\) |
−0.995067 | + | 0.0992044i | \(0.968370\pi\) | |||||||
\(228\) | −3.83578 | + | 6.64376i | −0.254031 | + | 0.439994i | ||||
\(229\) | 7.24620 | − | 12.5508i | 0.478842 | − | 0.829379i | −0.520863 | − | 0.853640i | \(-0.674390\pi\) |
0.999706 | + | 0.0242609i | \(0.00772324\pi\) | |||||||
\(230\) | −0.279274 | − | 0.483717i | −0.0184148 | − | 0.0318953i | ||||
\(231\) | −5.68779 | + | 3.35195i | −0.374229 | + | 0.220542i | ||||
\(232\) | 3.71142 | − | 6.42837i | 0.243667 | − | 0.422043i | ||||
\(233\) | −7.24897 | + | 12.5556i | −0.474896 | + | 0.822544i | −0.999587 | − | 0.0287492i | \(-0.990848\pi\) |
0.524691 | + | 0.851293i | \(0.324181\pi\) | |||||||
\(234\) | −3.44013 | + | 1.07960i | −0.224888 | + | 0.0705756i | ||||
\(235\) | −4.11045 | − | 7.11950i | −0.268136 | − | 0.464425i | ||||
\(236\) | 0.727653 | + | 1.26033i | 0.0473662 | + | 0.0820407i | ||||
\(237\) | 4.93545 | − | 8.54845i | 0.320592 | − | 0.555282i | ||||
\(238\) | 1.12903 | − | 0.665365i | 0.0731842 | − | 0.0431292i | ||||
\(239\) | 3.15093 | 0.203817 | 0.101908 | − | 0.994794i | \(-0.467505\pi\) | ||||
0.101908 | + | 0.994794i | \(0.467505\pi\) | |||||||
\(240\) | 1.24661 | 0.0804686 | ||||||||
\(241\) | 12.4223 | − | 21.5160i | 0.800189 | − | 1.38597i | −0.119302 | − | 0.992858i | \(-0.538066\pi\) |
0.919491 | − | 0.393111i | \(-0.128601\pi\) | |||||||
\(242\) | −2.38668 | − | 4.13385i | −0.153422 | − | 0.265734i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.09967 | − | 3.63674i | 0.134418 | − | 0.232818i | ||||
\(245\) | −4.49747 | − | 7.47803i | −0.287333 | − | 0.477754i | ||||
\(246\) | 3.74194 | 0.238577 | ||||||||
\(247\) | 6.02296 | − | 26.9965i | 0.383232 | − | 1.71775i | ||||
\(248\) | 4.06448 | + | 7.03989i | 0.258095 | + | 0.447033i | ||||
\(249\) | −7.42285 | −0.470404 | ||||||||
\(250\) | 5.26442 | + | 9.11824i | 0.332951 | + | 0.576688i | ||||
\(251\) | −3.69421 | − | 6.39857i | −0.233177 | − | 0.403874i | 0.725564 | − | 0.688154i | \(-0.241579\pi\) |
−0.958741 | + | 0.284280i | \(0.908245\pi\) | |||||||
\(252\) | −0.0236360 | − | 2.64565i | −0.00148893 | − | 0.166660i | ||||
\(253\) | 0.559018 | + | 0.968247i | 0.0351451 | + | 0.0608732i | ||||
\(254\) | 8.47693 | 0.531890 | ||||||||
\(255\) | −0.308739 | − | 0.534751i | −0.0193340 | − | 0.0334874i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −13.4446 | − | 23.2867i | −0.838650 | − | 1.45258i | −0.891024 | − | 0.453957i | \(-0.850012\pi\) |
0.0523740 | − | 0.998628i | \(-0.483321\pi\) | |||||||
\(258\) | 1.47532 | − | 2.55532i | 0.0918491 | − | 0.159087i | ||||
\(259\) | 6.31472 | + | 3.57097i | 0.392378 | + | 0.221889i | ||||
\(260\) | −4.28851 | + | 1.34584i | −0.265962 | + | 0.0834656i | ||||
\(261\) | −3.71142 | + | 6.42837i | −0.229731 | + | 0.397906i | ||||
\(262\) | −16.5336 | −1.02145 | ||||||||
\(263\) | −2.93123 | −0.180748 | −0.0903738 | − | 0.995908i | \(-0.528806\pi\) | ||||
−0.0903738 | + | 0.995908i | \(0.528806\pi\) | |||||||
\(264\) | −2.49532 | −0.153577 | ||||||||
\(265\) | 9.64254 | 0.592337 | ||||||||
\(266\) | 17.6677 | + | 9.99108i | 1.08328 | + | 0.612592i | ||||
\(267\) | −5.74056 | − | 9.94294i | −0.351317 | − | 0.608498i | ||||
\(268\) | −0.0138047 | + | 0.0239105i | −0.000843258 | + | 0.00146056i | ||||
\(269\) | −1.07222 | + | 1.85713i | −0.0653741 | + | 0.113231i | −0.896860 | − | 0.442315i | \(-0.854157\pi\) |
0.831486 | + | 0.555546i | \(0.187491\pi\) | |||||||
\(270\) | −1.24661 | −0.0758665 | ||||||||
\(271\) | −8.64220 | − | 14.9687i | −0.524976 | − | 0.909285i | −0.999577 | − | 0.0290842i | \(-0.990741\pi\) |
0.474601 | − | 0.880201i | \(-0.342592\pi\) | |||||||
\(272\) | 0.495324 | 0.0300334 | ||||||||
\(273\) | 2.93755 | + | 9.07584i | 0.177788 | + | 0.549295i | ||||
\(274\) | 0.856837 | 0.0517634 | ||||||||
\(275\) | −4.29939 | − | 7.44676i | −0.259263 | − | 0.449056i | ||||
\(276\) | −0.448052 | −0.0269696 | ||||||||
\(277\) | 1.41690 | − | 2.45415i | 0.0851336 | − | 0.147456i | −0.820315 | − | 0.571913i | \(-0.806202\pi\) |
0.905448 | + | 0.424457i | \(0.139535\pi\) | |||||||
\(278\) | −4.74886 | + | 8.22528i | −0.284818 | + | 0.493319i | ||||
\(279\) | −4.06448 | − | 7.03989i | −0.243334 | − | 0.421467i | ||||
\(280\) | −0.0294650 | − | 3.29810i | −0.00176087 | − | 0.197099i | ||||
\(281\) | −28.5254 | −1.70168 | −0.850842 | − | 0.525422i | \(-0.823907\pi\) | ||||
−0.850842 | + | 0.525422i | \(0.823907\pi\) | |||||||
\(282\) | −6.59458 | −0.392702 | ||||||||
\(283\) | −4.59802 | −0.273324 | −0.136662 | − | 0.990618i | \(-0.543637\pi\) | ||||
−0.136662 | + | 0.990618i | \(0.543637\pi\) | |||||||
\(284\) | −9.37767 | −0.556463 | ||||||||
\(285\) | 4.78173 | − | 8.28221i | 0.283245 | − | 0.490596i | ||||
\(286\) | 8.58423 | − | 2.69395i | 0.507596 | − | 0.159297i | ||||
\(287\) | −0.0884446 | − | 9.89984i | −0.00522072 | − | 0.584369i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.37733 | + | 14.5100i | 0.492784 | + | 0.853527i | ||||
\(290\) | −4.62671 | + | 8.01370i | −0.271690 | + | 0.470581i | ||||
\(291\) | 0.509831 | + | 0.883054i | 0.0298868 | + | 0.0517655i | ||||
\(292\) | 10.1430 | 0.593576 | ||||||||
\(293\) | 3.19384 | + | 5.53189i | 0.186586 | + | 0.323177i | 0.944110 | − | 0.329631i | \(-0.106924\pi\) |
−0.757524 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(294\) | −6.99888 | + | 0.125065i | −0.408183 | + | 0.00729395i | ||||
\(295\) | −0.907102 | − | 1.57115i | −0.0528135 | − | 0.0914757i | ||||
\(296\) | 1.37097 | + | 2.37459i | 0.0796859 | + | 0.138020i | ||||
\(297\) | 2.49532 | 0.144793 | ||||||||
\(298\) | −2.36872 | − | 4.10274i | −0.137216 | − | 0.237665i | ||||
\(299\) | 1.54136 | − | 0.483717i | 0.0891389 | − | 0.0279740i | ||||
\(300\) | 3.44595 | 0.198952 | ||||||||
\(301\) | −6.79535 | − | 3.84276i | −0.391677 | − | 0.221493i | ||||
\(302\) | 3.56085 | − | 6.16758i | 0.204904 | − | 0.354904i | ||||
\(303\) | −17.9425 | −1.03077 | ||||||||
\(304\) | 3.83578 | + | 6.64376i | 0.219997 | + | 0.381046i | ||||
\(305\) | −2.61748 | + | 4.53360i | −0.149876 | + | 0.259593i | ||||
\(306\) | −0.495324 | −0.0283158 | ||||||||
\(307\) | −1.39899 | −0.0798446 | −0.0399223 | − | 0.999203i | \(-0.512711\pi\) | ||||
−0.0399223 | + | 0.999203i | \(0.512711\pi\) | |||||||
\(308\) | 0.0589796 | + | 6.60174i | 0.00336067 | + | 0.376169i | ||||
\(309\) | −0.524685 | + | 0.908780i | −0.0298483 | + | 0.0516987i | ||||
\(310\) | −5.06684 | − | 8.77602i | −0.287777 | − | 0.498444i | ||||
\(311\) | −8.55183 | − | 14.8122i | −0.484930 | − | 0.839923i | 0.514920 | − | 0.857238i | \(-0.327822\pi\) |
−0.999850 | + | 0.0173150i | \(0.994488\pi\) | |||||||
\(312\) | −0.785103 | + | 3.51904i | −0.0444477 | + | 0.199226i | ||||
\(313\) | −5.81247 | + | 10.0675i | −0.328540 | + | 0.569048i | −0.982222 | − | 0.187721i | \(-0.939890\pi\) |
0.653682 | + | 0.756769i | \(0.273223\pi\) | |||||||
\(314\) | 7.52147 | − | 13.0276i | 0.424461 | − | 0.735188i | ||||
\(315\) | 0.0294650 | + | 3.29810i | 0.00166017 | + | 0.185827i | ||||
\(316\) | −4.93545 | − | 8.54845i | −0.277641 | − | 0.480888i | ||||
\(317\) | −3.29277 | + | 5.70324i | −0.184940 | + | 0.320326i | −0.943556 | − | 0.331212i | \(-0.892543\pi\) |
0.758616 | + | 0.651538i | \(0.225876\pi\) | |||||||
\(318\) | 3.86750 | − | 6.69870i | 0.216878 | − | 0.375644i | ||||
\(319\) | 9.26121 | − | 16.0409i | 0.518528 | − | 0.898117i | ||||
\(320\) | 0.623307 | − | 1.07960i | 0.0348439 | − | 0.0603514i | ||||
\(321\) | −5.09152 | − | 8.81877i | −0.284181 | − | 0.492216i | ||||
\(322\) | 0.0105902 | + | 1.18539i | 0.000590168 | + | 0.0660590i | ||||
\(323\) | 1.89995 | − | 3.29082i | 0.105716 | − | 0.183106i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −11.8545 | + | 3.72025i | −0.657570 | + | 0.206362i | ||||
\(326\) | −4.51485 | − | 7.81996i | −0.250055 | − | 0.433107i | ||||
\(327\) | −9.92285 | − | 17.1869i | −0.548735 | − | 0.950436i | ||||
\(328\) | 1.87097 | − | 3.24061i | 0.103307 | − | 0.178933i | ||||
\(329\) | 0.155870 | + | 17.4469i | 0.00859338 | + | 0.961880i | ||||
\(330\) | 3.11070 | 0.171239 | ||||||||
\(331\) | −23.2685 | −1.27895 | −0.639477 | − | 0.768810i | \(-0.720849\pi\) | ||||
−0.639477 | + | 0.768810i | \(0.720849\pi\) | |||||||
\(332\) | −3.71142 | + | 6.42837i | −0.203691 | + | 0.352803i | ||||
\(333\) | −1.37097 | − | 2.37459i | −0.0751286 | − | 0.130127i | ||||
\(334\) | 2.84883 | 0.155881 | ||||||||
\(335\) | 0.0172092 | − | 0.0298071i | 0.000940236 | − | 0.00162854i | ||||
\(336\) | −2.30301 | − | 1.30235i | −0.125640 | − | 0.0710492i | ||||
\(337\) | 19.4320 | 1.05853 | 0.529263 | − | 0.848458i | \(-0.322468\pi\) | ||||
0.529263 | + | 0.848458i | \(0.322468\pi\) | |||||||
\(338\) | −1.09829 | − | 12.9535i | −0.0597394 | − | 0.704579i | ||||
\(339\) | 7.93440 | + | 13.7428i | 0.430938 | + | 0.746406i | ||||
\(340\) | −0.617478 | −0.0334874 | ||||||||
\(341\) | 10.1422 | + | 17.5668i | 0.549231 | + | 0.951296i | ||||
\(342\) | −3.83578 | − | 6.64376i | −0.207415 | − | 0.359254i | ||||
\(343\) | 0.496304 | + | 18.5136i | 0.0267979 | + | 0.999641i | ||||
\(344\) | −1.47532 | − | 2.55532i | −0.0795437 | − | 0.137774i | ||||
\(345\) | 0.558548 | 0.0300712 | ||||||||
\(346\) | −12.7438 | − | 22.0729i | −0.685110 | − | 1.18664i | ||||
\(347\) | −14.8354 | + | 25.6956i | −0.796404 | + | 1.37941i | 0.125540 | + | 0.992089i | \(0.459934\pi\) |
−0.921944 | + | 0.387324i | \(0.873400\pi\) | |||||||
\(348\) | 3.71142 | + | 6.42837i | 0.198953 | + | 0.344597i | ||||
\(349\) | −13.3023 | + | 23.0403i | −0.712058 | + | 1.23332i | 0.252025 | + | 0.967721i | \(0.418904\pi\) |
−0.964083 | + | 0.265600i | \(0.914430\pi\) | |||||||
\(350\) | −0.0814487 | − | 9.11678i | −0.00435362 | − | 0.487312i | ||||
\(351\) | 0.785103 | − | 3.51904i | 0.0419057 | − | 0.187832i | ||||
\(352\) | −1.24766 | + | 2.16101i | −0.0665006 | + | 0.115182i | ||||
\(353\) | −13.8188 | −0.735499 | −0.367750 | − | 0.929925i | \(-0.619872\pi\) | ||||
−0.367750 | + | 0.929925i | \(0.619872\pi\) | |||||||
\(354\) | −1.45531 | −0.0773487 | ||||||||
\(355\) | 11.6903 | 0.620458 | ||||||||
\(356\) | −11.4811 | −0.608498 | ||||||||
\(357\) | 0.0117075 | + | 1.31045i | 0.000619627 | + | 0.0693565i | ||||
\(358\) | 9.10030 | + | 15.7622i | 0.480966 | + | 0.833058i | ||||
\(359\) | 1.38095 | − | 2.39188i | 0.0728840 | − | 0.126239i | −0.827280 | − | 0.561790i | \(-0.810113\pi\) |
0.900164 | + | 0.435551i | \(0.143446\pi\) | |||||||
\(360\) | −0.623307 | + | 1.07960i | −0.0328511 | + | 0.0568999i | ||||
\(361\) | 39.8528 | 2.09752 | ||||||||
\(362\) | −6.86524 | − | 11.8910i | −0.360829 | − | 0.624975i | ||||
\(363\) | 4.77336 | 0.250536 | ||||||||
\(364\) | 9.32868 | + | 1.99393i | 0.488956 | + | 0.104510i | ||||
\(365\) | −12.6444 | −0.661840 | ||||||||
\(366\) | 2.09967 | + | 3.63674i | 0.109752 | + | 0.190095i | ||||
\(367\) | −10.9230 | −0.570177 | −0.285089 | − | 0.958501i | \(-0.592023\pi\) | ||||
−0.285089 | + | 0.958501i | \(0.592023\pi\) | |||||||
\(368\) | −0.224026 | + | 0.388024i | −0.0116782 | + | 0.0202272i | ||||
\(369\) | −1.87097 | + | 3.24061i | −0.0973987 | + | 0.168700i | ||||
\(370\) | −1.70907 | − | 2.96019i | −0.0888502 | − | 0.153893i | ||||
\(371\) | −17.8138 | − | 10.0737i | −0.924846 | − | 0.523000i | ||||
\(372\) | −8.12896 | −0.421467 | ||||||||
\(373\) | 19.6861 | 1.01931 | 0.509653 | − | 0.860380i | \(-0.329774\pi\) | ||||
0.509653 | + | 0.860380i | \(0.329774\pi\) | |||||||
\(374\) | 1.23599 | 0.0639117 | ||||||||
\(375\) | −10.5288 | −0.543707 | ||||||||
\(376\) | −3.29729 | + | 5.71107i | −0.170045 | + | 0.294526i | ||||
\(377\) | −19.7078 | − | 18.1076i | −1.01501 | − | 0.932587i | ||||
\(378\) | 2.30301 | + | 1.30235i | 0.118454 | + | 0.0669858i | ||||
\(379\) | −8.31713 | + | 14.4057i | −0.427222 | + | 0.739970i | −0.996625 | − | 0.0820882i | \(-0.973841\pi\) |
0.569403 | + | 0.822059i | \(0.307174\pi\) | |||||||
\(380\) | −4.78173 | − | 8.28221i | −0.245298 | − | 0.424868i | ||||
\(381\) | −4.23846 | + | 7.34124i | −0.217143 | + | 0.376103i | ||||
\(382\) | 2.64294 | + | 4.57771i | 0.135225 | + | 0.234216i | ||||
\(383\) | 36.3667 | 1.85825 | 0.929127 | − | 0.369761i | \(-0.120560\pi\) | ||||
0.929127 | + | 0.369761i | \(0.120560\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −0.0735247 | − | 8.22982i | −0.00374717 | − | 0.419431i | ||||
\(386\) | 2.40599 | + | 4.16729i | 0.122461 | + | 0.212109i | ||||
\(387\) | 1.47532 | + | 2.55532i | 0.0749945 | + | 0.129894i | ||||
\(388\) | 1.01966 | 0.0517655 | ||||||||
\(389\) | 8.89008 | + | 15.3981i | 0.450745 | + | 0.780713i | 0.998432 | − | 0.0559696i | \(-0.0178250\pi\) |
−0.547687 | + | 0.836683i | \(0.684492\pi\) | |||||||
\(390\) | 0.978720 | − | 4.38688i | 0.0495594 | − | 0.222138i | ||||
\(391\) | 0.221931 | 0.0112235 | ||||||||
\(392\) | −3.39113 | + | 6.12374i | −0.171278 | + | 0.309296i | ||||
\(393\) | 8.26678 | − | 14.3185i | 0.417004 | − | 0.722272i | ||||
\(394\) | 23.5486 | 1.18636 | ||||||||
\(395\) | 6.15260 | + | 10.6566i | 0.309571 | + | 0.536192i | ||||
\(396\) | 1.24766 | − | 2.16101i | 0.0626974 | − | 0.108595i | ||||
\(397\) | 8.87904 | 0.445626 | 0.222813 | − | 0.974861i | \(-0.428476\pi\) | ||||
0.222813 | + | 0.974861i | \(0.428476\pi\) | |||||||
\(398\) | −11.2797 | −0.565400 | ||||||||
\(399\) | −17.4864 | + | 10.3051i | −0.875414 | + | 0.515903i | ||||
\(400\) | 1.72298 | − | 2.98428i | 0.0861489 | − | 0.149214i | ||||
\(401\) | 15.0815 | + | 26.1219i | 0.753134 | + | 1.30447i | 0.946297 | + | 0.323300i | \(0.104792\pi\) |
−0.193163 | + | 0.981167i | \(0.561874\pi\) | |||||||
\(402\) | −0.0138047 | − | 0.0239105i | −0.000688517 | − | 0.00119255i | ||||
\(403\) | 27.9647 | − | 8.77602i | 1.39302 | − | 0.437165i | ||||
\(404\) | −8.97127 | + | 15.5387i | −0.446338 | + | 0.773079i | ||||
\(405\) | 0.623307 | − | 1.07960i | 0.0309724 | − | 0.0536457i | ||||
\(406\) | 16.9195 | − | 9.97105i | 0.839700 | − | 0.494855i | ||||
\(407\) | 3.42101 | + | 5.92537i | 0.169573 | + | 0.293709i | ||||
\(408\) | −0.247662 | + | 0.428963i | −0.0122611 | + | 0.0212368i | ||||
\(409\) | −8.38601 | + | 14.5250i | −0.414662 | + | 0.718215i | −0.995393 | − | 0.0958804i | \(-0.969433\pi\) |
0.580731 | + | 0.814095i | \(0.302767\pi\) | |||||||
\(410\) | −2.33237 | + | 4.03979i | −0.115188 | + | 0.199511i | ||||
\(411\) | −0.428418 | + | 0.742042i | −0.0211323 | + | 0.0366023i | ||||
\(412\) | 0.524685 | + | 0.908780i | 0.0258494 | + | 0.0447724i | ||||
\(413\) | 0.0343977 | + | 3.85023i | 0.00169260 | + | 0.189457i | ||||
\(414\) | 0.224026 | − | 0.388024i | 0.0110103 | − | 0.0190704i | ||||
\(415\) | 4.62671 | − | 8.01370i | 0.227116 | − | 0.393377i | ||||
\(416\) | 2.65502 | + | 2.43944i | 0.130173 | + | 0.119603i | ||||
\(417\) | −4.74886 | − | 8.22528i | −0.232553 | − | 0.402793i | ||||
\(418\) | 9.57151 | + | 16.5783i | 0.468158 | + | 0.810873i | ||||
\(419\) | −19.8098 | + | 34.3115i | −0.967770 | + | 1.67623i | −0.265788 | + | 0.964031i | \(0.585632\pi\) |
−0.701982 | + | 0.712195i | \(0.747701\pi\) | |||||||
\(420\) | 2.87097 | + | 1.62353i | 0.140089 | + | 0.0792202i | ||||
\(421\) | −32.2271 | −1.57065 | −0.785326 | − | 0.619083i | \(-0.787505\pi\) | ||||
−0.785326 | + | 0.619083i | \(0.787505\pi\) | |||||||
\(422\) | −12.4404 | −0.605590 | ||||||||
\(423\) | 3.29729 | − | 5.71107i | 0.160320 | − | 0.277682i | ||||
\(424\) | −3.86750 | − | 6.69870i | −0.187822 | − | 0.325318i | ||||
\(425\) | −1.70686 | −0.0827951 | ||||||||
\(426\) | 4.68884 | − | 8.12130i | 0.227175 | − | 0.393478i | ||||
\(427\) | 9.57189 | − | 5.64094i | 0.463216 | − | 0.272984i | ||||
\(428\) | −10.1830 | −0.492216 | ||||||||
\(429\) | −1.95909 | + | 8.78114i | −0.0945856 | + | 0.423957i | ||||
\(430\) | 1.83915 | + | 3.18550i | 0.0886916 | + | 0.153618i | ||||
\(431\) | 11.0013 | 0.529912 | 0.264956 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264956 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 15.9643 | + | 27.6509i | 0.767193 | + | 1.32882i | 0.939079 | + | 0.343701i | \(0.111681\pi\) |
−0.171886 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(434\) | 0.192136 | + | 21.5064i | 0.00922285 | + | 1.03234i | ||||
\(435\) | −4.62671 | − | 8.01370i | −0.221834 | − | 0.384227i | ||||
\(436\) | −19.8457 | −0.950436 | ||||||||
\(437\) | 1.71863 | + | 2.97675i | 0.0822132 | + | 0.142397i | ||||
\(438\) | −5.07151 | + | 8.78412i | −0.242326 | + | 0.419721i | ||||
\(439\) | 0.717628 | + | 1.24297i | 0.0342505 | + | 0.0593236i | 0.882643 | − | 0.470045i | \(-0.155762\pi\) |
−0.848392 | + | 0.529368i | \(0.822429\pi\) | |||||||
\(440\) | 1.55535 | − | 2.69395i | 0.0741485 | − | 0.128429i | ||||
\(441\) | 3.39113 | − | 6.12374i | 0.161482 | − | 0.291607i | ||||
\(442\) | 0.388880 | − | 1.74306i | 0.0184972 | − | 0.0829091i | ||||
\(443\) | 5.72758 | − | 9.92047i | 0.272126 | − | 0.471336i | −0.697280 | − | 0.716799i | \(-0.745607\pi\) |
0.969406 | + | 0.245463i | \(0.0789400\pi\) | |||||||
\(444\) | −2.74194 | −0.130127 | ||||||||
\(445\) | 14.3125 | 0.678479 | ||||||||
\(446\) | −20.9301 | −0.991071 | ||||||||
\(447\) | 4.73744 | 0.224073 | ||||||||
\(448\) | −2.27938 | + | 1.34329i | −0.107691 | + | 0.0634646i | ||||
\(449\) | −17.3713 | − | 30.0880i | −0.819803 | − | 1.41994i | −0.905827 | − | 0.423647i | \(-0.860750\pi\) |
0.0860243 | − | 0.996293i | \(-0.472584\pi\) | |||||||
\(450\) | −1.72298 | + | 2.98428i | −0.0812219 | + | 0.140681i | ||||
\(451\) | 4.66867 | − | 8.08638i | 0.219839 | − | 0.380773i | ||||
\(452\) | 15.8688 | 0.746406 | ||||||||
\(453\) | 3.56085 | + | 6.16758i | 0.167304 | + | 0.289778i | ||||
\(454\) | −17.5810 | −0.825119 | ||||||||
\(455\) | −11.6293 | − | 2.48566i | −0.545188 | − | 0.116529i | ||||
\(456\) | −7.67156 | −0.359254 | ||||||||
\(457\) | −18.4024 | − | 31.8739i | −0.860829 | − | 1.49100i | −0.871130 | − | 0.491053i | \(-0.836612\pi\) |
0.0103007 | − | 0.999947i | \(-0.496721\pi\) | |||||||
\(458\) | 14.4924 | 0.677185 | ||||||||
\(459\) | 0.247662 | − | 0.428963i | 0.0115599 | − | 0.0200223i | ||||
\(460\) | 0.279274 | − | 0.483717i | 0.0130212 | − | 0.0225534i | ||||
\(461\) | −3.99129 | − | 6.91311i | −0.185893 | − | 0.321976i | 0.757984 | − | 0.652273i | \(-0.226184\pi\) |
−0.943877 | + | 0.330297i | \(0.892851\pi\) | |||||||
\(462\) | −5.74677 | − | 3.24979i | −0.267364 | − | 0.151194i | ||||
\(463\) | 26.4799 | 1.23063 | 0.615314 | − | 0.788282i | \(-0.289029\pi\) | ||||
0.615314 | + | 0.788282i | \(0.289029\pi\) | |||||||
\(464\) | 7.42285 | 0.344597 | ||||||||
\(465\) | 10.1337 | 0.469938 | ||||||||
\(466\) | −14.4979 | −0.671604 | ||||||||
\(467\) | −3.12210 | + | 5.40764i | −0.144474 | + | 0.250236i | −0.929176 | − | 0.369636i | \(-0.879482\pi\) |
0.784703 | + | 0.619872i | \(0.212816\pi\) | |||||||
\(468\) | −2.65502 | − | 2.43944i | −0.122728 | − | 0.112763i | ||||
\(469\) | −0.0629324 | + | 0.0370876i | −0.00290595 | + | 0.00171254i | ||||
\(470\) | 4.11045 | − | 7.11950i | 0.189601 | − | 0.328398i | ||||
\(471\) | 7.52147 | + | 13.0276i | 0.346571 | + | 0.600279i | ||||
\(472\) | −0.727653 | + | 1.26033i | −0.0334930 | + | 0.0580115i | ||||
\(473\) | −3.68139 | − | 6.37635i | −0.169270 | − | 0.293185i | ||||
\(474\) | 9.87090 | 0.453385 | ||||||||
\(475\) | −13.2179 | − | 22.8941i | −0.606480 | − | 1.05045i | ||||
\(476\) | 1.14074 | + | 0.645087i | 0.0522857 | + | 0.0295675i | ||||
\(477\) | 3.86750 | + | 6.69870i | 0.177080 | + | 0.306712i | ||||
\(478\) | 1.57547 | + | 2.72879i | 0.0720601 | + | 0.124812i | ||||
\(479\) | 21.5725 | 0.985671 | 0.492836 | − | 0.870122i | \(-0.335960\pi\) | ||||
0.492836 | + | 0.870122i | \(0.335960\pi\) | |||||||
\(480\) | 0.623307 | + | 1.07960i | 0.0284499 | + | 0.0492767i | ||||
\(481\) | 9.43261 | − | 2.96019i | 0.430090 | − | 0.134973i | ||||
\(482\) | 24.8446 | 1.13164 | ||||||||
\(483\) | −1.03187 | − | 0.583522i | −0.0469517 | − | 0.0265512i | ||||
\(484\) | 2.38668 | − | 4.13385i | 0.108485 | − | 0.187902i | ||||
\(485\) | −1.27113 | −0.0577188 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −6.80757 | + | 11.7911i | −0.308481 | + | 0.534304i | −0.978030 | − | 0.208463i | \(-0.933154\pi\) |
0.669550 | + | 0.742767i | \(0.266487\pi\) | |||||||
\(488\) | 4.19934 | 0.190095 | ||||||||
\(489\) | 9.02971 | 0.408337 | ||||||||
\(490\) | 4.22743 | − | 7.63394i | 0.190976 | − | 0.344866i | ||||
\(491\) | 6.14512 | − | 10.6437i | 0.277326 | − | 0.480342i | −0.693394 | − | 0.720559i | \(-0.743885\pi\) |
0.970719 | + | 0.240217i | \(0.0772186\pi\) | |||||||
\(492\) | 1.87097 | + | 3.24061i | 0.0843498 | + | 0.146098i | ||||
\(493\) | −1.83836 | − | 3.18413i | −0.0827955 | − | 0.143406i | ||||
\(494\) | 26.3911 | − | 8.28221i | 1.18739 | − | 0.372634i | ||||
\(495\) | −1.55535 | + | 2.69395i | −0.0699079 | + | 0.121084i | ||||
\(496\) | −4.06448 | + | 7.03989i | −0.182501 | + | 0.316100i | ||||
\(497\) | −21.5969 | − | 12.2130i | −0.968754 | − | 0.547830i | ||||
\(498\) | −3.71142 | − | 6.42837i | −0.166313 | − | 0.288062i | ||||
\(499\) | −7.11789 | + | 12.3285i | −0.318640 | + | 0.551901i | −0.980205 | − | 0.197987i | \(-0.936560\pi\) |
0.661564 | + | 0.749889i | \(0.269893\pi\) | |||||||
\(500\) | −5.26442 | + | 9.11824i | −0.235432 | + | 0.407780i | ||||
\(501\) | −1.42442 | + | 2.46716i | −0.0636382 | + | 0.110225i | ||||
\(502\) | 3.69421 | − | 6.39857i | 0.164881 | − | 0.285582i | ||||
\(503\) | 10.4692 | + | 18.1332i | 0.466798 | + | 0.808518i | 0.999281 | − | 0.0379227i | \(-0.0120741\pi\) |
−0.532482 | + | 0.846441i | \(0.678741\pi\) | |||||||
\(504\) | 2.27938 | − | 1.34329i | 0.101532 | − | 0.0598350i | ||||
\(505\) | 11.1837 | − | 19.3708i | 0.497669 | − | 0.861987i | ||||
\(506\) | −0.559018 | + | 0.968247i | −0.0248514 | + | 0.0430438i | ||||
\(507\) | 11.7672 | + | 5.52561i | 0.522601 | + | 0.245401i | ||||
\(508\) | 4.23846 | + | 7.34124i | 0.188051 | + | 0.325715i | ||||
\(509\) | −6.96485 | − | 12.0635i | −0.308711 | − | 0.534704i | 0.669369 | − | 0.742930i | \(-0.266564\pi\) |
−0.978081 | + | 0.208226i | \(0.933231\pi\) | |||||||
\(510\) | 0.308739 | − | 0.534751i | 0.0136712 | − | 0.0236792i | ||||
\(511\) | 23.3595 | + | 13.2098i | 1.03336 | + | 0.584367i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.67156 | 0.338708 | ||||||||
\(514\) | 13.4446 | − | 23.2867i | 0.593015 | − | 1.02713i | ||||
\(515\) | −0.654079 | − | 1.13290i | −0.0288222 | − | 0.0499214i | ||||
\(516\) | 2.95063 | 0.129894 | ||||||||
\(517\) | −8.22781 | + | 14.2510i | −0.361859 | + | 0.626757i | ||||
\(518\) | 0.0648086 | + | 7.25420i | 0.00284752 | + | 0.318731i | ||||
\(519\) | 25.4875 | 1.11878 | ||||||||
\(520\) | −3.30979 | − | 3.04103i | −0.145144 | − | 0.133358i | ||||
\(521\) | 11.1502 | + | 19.3128i | 0.488501 | + | 0.846109i | 0.999913 | − | 0.0132274i | \(-0.00421053\pi\) |
−0.511412 | + | 0.859336i | \(0.670877\pi\) | |||||||
\(522\) | −7.42285 | −0.324889 | ||||||||
\(523\) | 13.8516 | + | 23.9917i | 0.605689 | + | 1.04908i | 0.991942 | + | 0.126691i | \(0.0404357\pi\) |
−0.386254 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(524\) | −8.26678 | − | 14.3185i | −0.361136 | − | 0.625506i | ||||
\(525\) | 7.93608 | + | 4.48785i | 0.346359 | + | 0.195866i | ||||
\(526\) | −1.46562 | − | 2.53852i | −0.0639040 | − | 0.110685i | ||||
\(527\) | 4.02647 | 0.175396 | ||||||||
\(528\) | −1.24766 | − | 2.16101i | −0.0542975 | − | 0.0940461i | ||||
\(529\) | 11.3996 | − | 19.7447i | 0.495636 | − | 0.858466i | ||||
\(530\) | 4.82127 | + | 8.35069i | 0.209423 | + | 0.362731i | ||||
\(531\) | 0.727653 | − | 1.26033i | 0.0315775 | − | 0.0546938i | ||||
\(532\) | 0.181325 | + | 20.2962i | 0.00786145 | + | 0.879953i | ||||
\(533\) | −9.93493 | − | 9.12822i | −0.430330 | − | 0.395387i | ||||
\(534\) | 5.74056 | − | 9.94294i | 0.248418 | − | 0.430273i | ||||
\(535\) | 12.6943 | 0.548823 | ||||||||
\(536\) | −0.0276094 | −0.00119255 | ||||||||
\(537\) | −18.2006 | −0.785414 | ||||||||
\(538\) | −2.14443 | −0.0924530 | ||||||||
\(539\) | −8.46197 | + | 15.2807i | −0.364483 | + | 0.658187i | ||||
\(540\) | −0.623307 | − | 1.07960i | −0.0268229 | − | 0.0464585i | ||||
\(541\) | 7.32108 | − | 12.6805i | 0.314758 | − | 0.545177i | −0.664628 | − | 0.747174i | \(-0.731410\pi\) |
0.979386 | + | 0.201998i | \(0.0647434\pi\) | |||||||
\(542\) | 8.64220 | − | 14.9687i | 0.371214 | − | 0.642962i | ||||
\(543\) | 13.7305 | 0.589232 | ||||||||
\(544\) | 0.247662 | + | 0.428963i | 0.0106184 | + | 0.0183916i | ||||
\(545\) | 24.7399 | 1.05974 | ||||||||
\(546\) | −6.39113 | + | 7.08191i | −0.273515 | + | 0.303078i | ||||
\(547\) | 21.7401 | 0.929542 | 0.464771 | − | 0.885431i | \(-0.346137\pi\) | ||||
0.464771 | + | 0.885431i | \(0.346137\pi\) | |||||||
\(548\) | 0.428418 | + | 0.742042i | 0.0183011 | + | 0.0316985i | ||||
\(549\) | −4.19934 | −0.179224 | ||||||||
\(550\) | 4.29939 | − | 7.44676i | 0.183326 | − | 0.317531i | ||||
\(551\) | 28.4724 | − | 49.3157i | 1.21297 | − | 2.10092i | ||||
\(552\) | −0.224026 | − | 0.388024i | −0.00953518 | − | 0.0165154i | ||||
\(553\) | −0.233309 | − | 26.1149i | −0.00992131 | − | 1.11052i | ||||
\(554\) | 2.83381 | 0.120397 | ||||||||
\(555\) | 3.41814 | 0.145092 | ||||||||
\(556\) | −9.49773 | −0.402793 | ||||||||
\(557\) | 4.47177 | 0.189475 | 0.0947375 | − | 0.995502i | \(-0.469799\pi\) | ||||
0.0947375 | + | 0.995502i | \(0.469799\pi\) | |||||||
\(558\) | 4.06448 | − | 7.03989i | 0.172063 | − | 0.298022i | ||||
\(559\) | −10.1505 | + | 3.18550i | −0.429322 | + | 0.134732i | ||||
\(560\) | 2.84150 | − | 1.67457i | 0.120075 | − | 0.0707633i | ||||
\(561\) | −0.617997 | + | 1.07040i | −0.0260919 | + | 0.0451924i | ||||
\(562\) | −14.2627 | − | 24.7037i | −0.601636 | − | 1.04206i | ||||
\(563\) | 5.57899 | − | 9.66309i | 0.235126 | − | 0.407251i | −0.724183 | − | 0.689608i | \(-0.757783\pi\) |
0.959309 | + | 0.282357i | \(0.0911163\pi\) | |||||||
\(564\) | −3.29729 | − | 5.71107i | −0.138841 | − | 0.240480i | ||||
\(565\) | −19.7823 | −0.832246 | ||||||||
\(566\) | −2.29901 | − | 3.98201i | −0.0966347 | − | 0.167376i | ||||
\(567\) | −2.27938 | + | 1.34329i | −0.0957249 | + | 0.0564130i | ||||
\(568\) | −4.68884 | − | 8.12130i | −0.196739 | − | 0.340762i | ||||
\(569\) | 18.4409 | + | 31.9406i | 0.773083 | + | 1.33902i | 0.935865 | + | 0.352358i | \(0.114620\pi\) |
−0.162782 | + | 0.986662i | \(0.552047\pi\) | |||||||
\(570\) | 9.56347 | 0.400570 | ||||||||
\(571\) | 0.101526 | + | 0.175849i | 0.00424874 | + | 0.00735904i | 0.868142 | − | 0.496316i | \(-0.165314\pi\) |
−0.863893 | + | 0.503675i | \(0.831981\pi\) | |||||||
\(572\) | 6.62514 | + | 6.08719i | 0.277011 | + | 0.254518i | ||||
\(573\) | −5.28588 | −0.220821 | ||||||||
\(574\) | 8.52929 | − | 5.02652i | 0.356006 | − | 0.209803i | ||||
\(575\) | 0.771984 | − | 1.33711i | 0.0321939 | − | 0.0557615i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.4151 | + | 18.0396i | 0.433588 | + | 0.750997i | 0.997179 | − | 0.0750570i | \(-0.0239139\pi\) |
−0.563591 | + | 0.826054i | \(0.690581\pi\) | |||||||
\(578\) | −8.37733 | + | 14.5100i | −0.348451 | + | 0.603535i | ||||
\(579\) | −4.81197 | −0.199979 | ||||||||
\(580\) | −9.25342 | −0.384227 | ||||||||
\(581\) | −16.9195 | + | 9.97105i | −0.701938 | + | 0.413669i | ||||
\(582\) | −0.509831 | + | 0.883054i | −0.0211332 | + | 0.0366038i | ||||
\(583\) | −9.65066 | − | 16.7154i | −0.399689 | − | 0.692282i | ||||
\(584\) | 5.07151 | + | 8.78412i | 0.209861 | + | 0.363489i | ||||
\(585\) | 3.30979 | + | 3.04103i | 0.136843 | + | 0.125731i | ||||
\(586\) | −3.19384 | + | 5.53189i | −0.131936 | + | 0.228520i | ||||
\(587\) | −8.25511 | + | 14.2983i | −0.340725 | + | 0.590153i | −0.984568 | − | 0.175005i | \(-0.944006\pi\) |
0.643843 | + | 0.765158i | \(0.277339\pi\) | |||||||
\(588\) | −3.60775 | − | 5.99868i | −0.148781 | − | 0.247381i | ||||
\(589\) | 31.1809 | + | 54.0069i | 1.28479 | + | 2.22532i | ||||
\(590\) | 0.907102 | − | 1.57115i | 0.0373448 | − | 0.0646831i | ||||
\(591\) | −11.7743 | + | 20.3937i | −0.484329 | + | 0.838883i | ||||
\(592\) | −1.37097 | + | 2.37459i | −0.0563465 | + | 0.0975950i | ||||
\(593\) | 5.86959 | − | 10.1664i | 0.241035 | − | 0.417485i | −0.719974 | − | 0.694001i | \(-0.755846\pi\) |
0.961009 | + | 0.276515i | \(0.0891797\pi\) | |||||||
\(594\) | 1.24766 | + | 2.16101i | 0.0511922 | + | 0.0886675i | ||||
\(595\) | −1.42206 | − | 0.804174i | −0.0582988 | − | 0.0329679i | ||||
\(596\) | 2.36872 | − | 4.10274i | 0.0970264 | − | 0.168055i | ||||
\(597\) | 5.63984 | − | 9.76849i | 0.230823 | − | 0.399798i | ||||
\(598\) | 1.18959 | + | 1.09299i | 0.0486459 | + | 0.0446959i | ||||
\(599\) | −21.8486 | − | 37.8430i | −0.892711 | − | 1.54622i | −0.836612 | − | 0.547796i | \(-0.815467\pi\) |
−0.0560993 | − | 0.998425i | \(-0.517866\pi\) | |||||||
\(600\) | 1.72298 | + | 2.98428i | 0.0703403 | + | 0.121833i | ||||
\(601\) | 2.84613 | − | 4.92964i | 0.116096 | − | 0.201084i | −0.802121 | − | 0.597161i | \(-0.796295\pi\) |
0.918217 | + | 0.396077i | \(0.129629\pi\) | |||||||
\(602\) | −0.0697412 | − | 7.80632i | −0.00284244 | − | 0.318162i | ||||
\(603\) | 0.0276094 | 0.00112434 | ||||||||
\(604\) | 7.12171 | 0.289778 | ||||||||
\(605\) | −2.97527 | + | 5.15331i | −0.120962 | + | 0.209512i | ||||
\(606\) | −8.97127 | − | 15.5387i | −0.364433 | − | 0.631217i | ||||
\(607\) | −25.0986 | −1.01872 | −0.509360 | − | 0.860553i | \(-0.670118\pi\) | ||||
−0.509360 | + | 0.860553i | \(0.670118\pi\) | |||||||
\(608\) | −3.83578 | + | 6.64376i | −0.155561 | + | 0.269440i | ||||
\(609\) | 0.175447 | + | 19.6382i | 0.00710946 | + | 0.795781i | ||||
\(610\) | −5.23496 | −0.211957 | ||||||||
\(611\) | 17.5088 | + | 16.0871i | 0.708329 | + | 0.650813i | ||||
\(612\) | −0.247662 | − | 0.428963i | −0.0100111 | − | 0.0173398i | ||||
\(613\) | 2.59331 | 0.104743 | 0.0523715 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523715 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(614\) | −0.699495 | − | 1.21156i | −0.0282293 | − | 0.0488947i | ||||
\(615\) | −2.33237 | − | 4.03979i | −0.0940504 | − | 0.162900i | ||||
\(616\) | −5.68779 | + | 3.35195i | −0.229168 | + | 0.135054i | ||||
\(617\) | 8.83438 | + | 15.3016i | 0.355659 | + | 0.616019i | 0.987231 | − | 0.159298i | \(-0.0509231\pi\) |
−0.631572 | + | 0.775318i | \(0.717590\pi\) | |||||||
\(618\) | −1.04937 | −0.0422118 | ||||||||
\(619\) | 20.4642 | + | 35.4450i | 0.822525 | + | 1.42465i | 0.903797 | + | 0.427962i | \(0.140768\pi\) |
−0.0812719 | + | 0.996692i | \(0.525898\pi\) | |||||||
\(620\) | 5.06684 | − | 8.77602i | 0.203489 | − | 0.352453i | ||||
\(621\) | 0.224026 | + | 0.388024i | 0.00898986 | + | 0.0155709i | ||||
\(622\) | 8.55183 | − | 14.8122i | 0.342897 | − | 0.593915i | ||||
\(623\) | −26.4412 | − | 14.9525i | −1.05934 | − | 0.599058i | ||||
\(624\) | −3.44013 | + | 1.07960i | −0.137715 | + | 0.0432185i | ||||
\(625\) | −2.05219 | + | 3.55450i | −0.0820876 | + | 0.142180i | ||||
\(626\) | −11.6249 | −0.464626 | ||||||||
\(627\) | −19.1430 | −0.764499 | ||||||||
\(628\) | 15.0429 | 0.600279 | ||||||||
\(629\) | 1.35815 | 0.0541529 | ||||||||
\(630\) | −2.84150 | + | 1.67457i | −0.113208 | + | 0.0667163i | ||||
\(631\) | 3.58097 | + | 6.20242i | 0.142556 | + | 0.246914i | 0.928459 | − | 0.371436i | \(-0.121135\pi\) |
−0.785902 | + | 0.618351i | \(0.787801\pi\) | |||||||
\(632\) | 4.93545 | − | 8.54845i | 0.196322 | − | 0.340039i | ||||
\(633\) | 6.22021 | − | 10.7737i | 0.247231 | − | 0.428217i | ||||
\(634\) | −6.58554 | −0.261545 | ||||||||
\(635\) | −5.28373 | − | 9.15168i | −0.209678 | − | 0.363173i | ||||
\(636\) | 7.73499 | 0.306712 | ||||||||
\(637\) | 18.8873 | + | 16.7413i | 0.748341 | + | 0.663314i | ||||
\(638\) | 18.5224 | 0.733309 | ||||||||
\(639\) | 4.68884 | + | 8.12130i | 0.185488 | + | 0.321274i | ||||
\(640\) | 1.24661 | 0.0492767 | ||||||||
\(641\) | −1.62960 | + | 2.82254i | −0.0643652 | + | 0.111484i | −0.896412 | − | 0.443221i | \(-0.853836\pi\) |
0.832047 | + | 0.554705i | \(0.187169\pi\) | |||||||
\(642\) | 5.09152 | − | 8.81877i | 0.200946 | − | 0.348049i | ||||
\(643\) | −9.17027 | − | 15.8834i | −0.361640 | − | 0.626379i | 0.626591 | − | 0.779348i | \(-0.284450\pi\) |
−0.988231 | + | 0.152969i | \(0.951116\pi\) | |||||||
\(644\) | −1.02128 | + | 0.601865i | −0.0402441 | + | 0.0237168i | ||||
\(645\) | −3.67830 | −0.144833 | ||||||||
\(646\) | 3.79991 | 0.149505 | ||||||||
\(647\) | 43.8685 | 1.72465 | 0.862325 | − | 0.506355i | \(-0.169008\pi\) | ||||
0.862325 | + | 0.506355i | \(0.169008\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.81573 | + | 3.14494i | −0.0712737 | + | 0.123450i | ||||
\(650\) | −9.14909 | − | 8.40619i | −0.358857 | − | 0.329718i | ||||
\(651\) | −18.7211 | − | 10.5868i | −0.733738 | − | 0.414929i | ||||
\(652\) | 4.51485 | − | 7.81996i | 0.176815 | − | 0.306253i | ||||
\(653\) | −6.64022 | − | 11.5012i | −0.259852 | − | 0.450077i | 0.706350 | − | 0.707863i | \(-0.250340\pi\) |
−0.966202 | + | 0.257786i | \(0.917007\pi\) | |||||||
\(654\) | 9.92285 | − | 17.1869i | 0.388014 | − | 0.672060i | ||||
\(655\) | 10.3055 | + | 17.8496i | 0.402668 | + | 0.697442i | ||||
\(656\) | 3.74194 | 0.146098 | ||||||||
\(657\) | −5.07151 | − | 8.78412i | −0.197859 | − | 0.342701i | ||||
\(658\) | −15.0315 | + | 8.85845i | −0.585991 | + | 0.345338i | ||||
\(659\) | 1.53479 | + | 2.65834i | 0.0597871 | + | 0.103554i | 0.894370 | − | 0.447328i | \(-0.147624\pi\) |
−0.834583 | + | 0.550883i | \(0.814291\pi\) | |||||||
\(660\) | 1.55535 | + | 2.69395i | 0.0605420 | + | 0.104862i | ||||
\(661\) | −29.6068 | −1.15157 | −0.575785 | − | 0.817601i | \(-0.695304\pi\) | ||||
−0.575785 | + | 0.817601i | \(0.695304\pi\) | |||||||
\(662\) | −11.6343 | − | 20.1512i | −0.452179 | − | 0.783197i | ||||
\(663\) | 1.31510 | + | 1.20831i | 0.0510741 | + | 0.0469270i | ||||
\(664\) | −7.42285 | −0.288062 | ||||||||
\(665\) | −0.226043 | − | 25.3015i | −0.00876555 | − | 0.981152i | ||||
\(666\) | 1.37097 | − | 2.37459i | 0.0531240 | − | 0.0920134i | ||||
\(667\) | 3.32582 | 0.128776 | ||||||||
\(668\) | 1.42442 | + | 2.46716i | 0.0551123 | + | 0.0954573i | ||||
\(669\) | 10.4651 | − | 18.1260i | 0.404603 | − | 0.700793i | ||||
\(670\) | 0.0344183 | 0.00132970 | ||||||||
\(671\) | 10.4787 | 0.404526 | ||||||||
\(672\) | −0.0236360 | − | 2.64565i | −0.000911780 | − | 0.102058i | ||||
\(673\) | −4.54511 | + | 7.87235i | −0.175201 | + | 0.303457i | −0.940231 | − | 0.340538i | \(-0.889391\pi\) |
0.765030 | + | 0.643995i | \(0.222724\pi\) | |||||||
\(674\) | 9.71598 | + | 16.8286i | 0.374246 | + | 0.648212i | ||||
\(675\) | −1.72298 | − | 2.98428i | −0.0663174 | − | 0.114865i | ||||
\(676\) | 10.6689 | − | 7.42791i | 0.410344 | − | 0.285689i | ||||
\(677\) | 8.92163 | − | 15.4527i | 0.342886 | − | 0.593896i | −0.642081 | − | 0.766636i | \(-0.721929\pi\) |
0.984967 | + | 0.172741i | \(0.0552622\pi\) | |||||||
\(678\) | −7.93440 | + | 13.7428i | −0.304719 | + | 0.527789i | ||||
\(679\) | 2.34830 | + | 1.32796i | 0.0901194 | + | 0.0509625i | ||||
\(680\) | −0.308739 | − | 0.534751i | −0.0118396 | − | 0.0205068i | ||||
\(681\) | 8.79052 | − | 15.2256i | 0.336853 | − | 0.583447i | ||||
\(682\) | −10.1422 | + | 17.5668i | −0.388365 | + | 0.672668i | ||||
\(683\) | 6.15898 | − | 10.6677i | 0.235667 | − | 0.408187i | −0.723800 | − | 0.690010i | \(-0.757606\pi\) |
0.959466 | + | 0.281824i | \(0.0909393\pi\) | |||||||
\(684\) | 3.83578 | − | 6.64376i | 0.146665 | − | 0.254031i | ||||
\(685\) | −0.534072 | − | 0.925040i | −0.0204058 | − | 0.0353440i | ||||
\(686\) | −15.7851 | + | 9.68662i | −0.602678 | + | 0.369837i | ||||
\(687\) | −7.24620 | + | 12.5508i | −0.276460 | + | 0.478842i | ||||
\(688\) | 1.47532 | − | 2.55532i | 0.0562459 | − | 0.0974207i | ||||
\(689\) | −26.6093 | + | 8.35069i | −1.01374 | + | 0.318136i | ||||
\(690\) | 0.279274 | + | 0.483717i | 0.0106318 | + | 0.0184148i | ||||
\(691\) | 13.5881 | + | 23.5353i | 0.516916 | + | 0.895325i | 0.999807 | + | 0.0196447i | \(0.00625351\pi\) |
−0.482891 | + | 0.875681i | \(0.660413\pi\) | |||||||
\(692\) | 12.7438 | − | 22.0729i | 0.484446 | − | 0.839084i | ||||
\(693\) | 5.68779 | − | 3.35195i | 0.216061 | − | 0.127330i | ||||
\(694\) | −29.6707 | −1.12629 | ||||||||
\(695\) | 11.8400 | 0.449117 | ||||||||
\(696\) | −3.71142 | + | 6.42837i | −0.140681 | + | 0.243667i | ||||
\(697\) | −0.926736 | − | 1.60515i | −0.0351026 | − | 0.0607995i | ||||
\(698\) | −26.6047 | −1.00700 | ||||||||
\(699\) | 7.24897 | − | 12.5556i | 0.274181 | − | 0.474896i | ||||
\(700\) | 7.85464 | − | 4.62892i | 0.296877 | − | 0.174957i | ||||
\(701\) | 38.0704 | 1.43790 | 0.718950 | − | 0.695062i | \(-0.244623\pi\) | ||||
0.718950 | + | 0.695062i | \(0.244623\pi\) | |||||||
\(702\) | 3.44013 | − | 1.07960i | 0.129839 | − | 0.0407468i | ||||
\(703\) | 10.5175 | + | 18.2168i | 0.396674 | + | 0.687059i | ||||
\(704\) | −2.49532 | −0.0940461 | ||||||||
\(705\) | 4.11045 | + | 7.11950i | 0.154808 | + | 0.268136i | ||||
\(706\) | −6.90939 | − | 11.9674i | −0.260038 | − | 0.450400i | ||||
\(707\) | −40.8979 | + | 24.1021i | −1.53812 | + | 0.906452i | ||||
\(708\) | −0.727653 | − | 1.26033i | −0.0273469 | − | 0.0473662i | ||||
\(709\) | −41.5249 | −1.55950 | −0.779750 | − | 0.626091i | \(-0.784654\pi\) | ||||
−0.779750 | + | 0.626091i | \(0.784654\pi\) | |||||||
\(710\) | 5.84517 | + | 10.1241i | 0.219365 | + | 0.379952i | ||||
\(711\) | −4.93545 | + | 8.54845i | −0.185094 | + | 0.320592i | ||||
\(712\) | −5.74056 | − | 9.94294i | −0.215137 | − | 0.372628i | ||||
\(713\) | −1.82110 | + | 3.15424i | −0.0682007 | + | 0.118127i | ||||
\(714\) | −1.12903 | + | 0.665365i | −0.0422529 | + | 0.0249007i | ||||
\(715\) | −8.25899 | − | 7.58837i | −0.308869 | − | 0.283789i | ||||
\(716\) | −9.10030 | + | 15.7622i | −0.340094 | + | 0.589061i | ||||
\(717\) | −3.15093 | −0.117674 | ||||||||
\(718\) | 2.76191 | 0.103074 | ||||||||
\(719\) | 16.6093 | 0.619421 | 0.309710 | − | 0.950831i | \(-0.399768\pi\) | ||||
0.309710 | + | 0.950831i | \(0.399768\pi\) | |||||||
\(720\) | −1.24661 | −0.0464585 | ||||||||
\(721\) | 0.0248029 | + | 2.77626i | 0.000923710 | + | 0.103393i | ||||
\(722\) | 19.9264 | + | 34.5135i | 0.741584 | + | 1.28446i | ||||
\(723\) | −12.4223 | + | 21.5160i | −0.461990 | + | 0.800189i | ||||
\(724\) | 6.86524 | − | 11.8910i | 0.255145 | − | 0.441924i | ||||
\(725\) | −25.5788 | −0.949973 | ||||||||
\(726\) | 2.38668 | + | 4.13385i | 0.0885780 | + | 0.153422i | ||||
\(727\) | −20.2421 | −0.750737 | −0.375368 | − | 0.926876i | \(-0.622484\pi\) | ||||
−0.375368 | + | 0.926876i | \(0.622484\pi\) | |||||||
\(728\) | 2.93755 | + | 9.07584i | 0.108873 | + | 0.336373i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.32222 | − | 10.9504i | −0.233996 | − | 0.405292i | ||||
\(731\) | −1.46152 | −0.0540562 | ||||||||
\(732\) | −2.09967 | + | 3.63674i | −0.0776061 | + | 0.134418i | ||||
\(733\) | −8.42173 | + | 14.5869i | −0.311064 | + | 0.538778i | −0.978593 | − | 0.205805i | \(-0.934019\pi\) |
0.667529 | + | 0.744584i | \(0.267352\pi\) | |||||||
\(734\) | −5.46151 | − | 9.45961i | −0.201588 | − | 0.349161i | ||||
\(735\) | 4.49747 | + | 7.47803i | 0.165892 | + | 0.275831i | ||||
\(736\) | −0.448052 | −0.0165154 | ||||||||
\(737\) | −0.0688945 | −0.00253776 | ||||||||
\(738\) | −3.74194 | −0.137743 | ||||||||
\(739\) | −48.1193 | −1.77010 | −0.885049 | − | 0.465498i | \(-0.845875\pi\) | ||||
−0.885049 | + | 0.465498i | \(0.845875\pi\) | |||||||
\(740\) | 1.70907 | − | 2.96019i | 0.0628266 | − | 0.108819i | ||||
\(741\) | −6.02296 | + | 26.9965i | −0.221259 | + | 0.991741i | ||||
\(742\) | −0.182825 | − | 20.4640i | −0.00671170 | − | 0.751259i | ||||
\(743\) | 2.98460 | − | 5.16948i | 0.109494 | − | 0.189650i | −0.806071 | − | 0.591819i | \(-0.798410\pi\) |
0.915566 | + | 0.402169i | \(0.131744\pi\) | |||||||
\(744\) | −4.06448 | − | 7.03989i | −0.149011 | − | 0.258095i | ||||
\(745\) | −2.95288 | + | 5.11453i | −0.108185 | + | 0.187382i | ||||
\(746\) | 9.84303 | + | 17.0486i | 0.360379 | + | 0.624195i | ||||
\(747\) | 7.42285 | 0.271588 | ||||||||
\(748\) | 0.617997 | + | 1.07040i | 0.0225962 | + | 0.0391378i | ||||
\(749\) | −23.4517 | − | 13.2619i | −0.856906 | − | 0.484580i | ||||
\(750\) | −5.26442 | − | 9.11824i | −0.192229 | − | 0.332951i | ||||
\(751\) | −18.1527 | − | 31.4414i | −0.662401 | − | 1.14731i | −0.979983 | − | 0.199081i | \(-0.936204\pi\) |
0.317582 | − | 0.948231i | \(-0.397129\pi\) | |||||||
\(752\) | −6.59458 | −0.240480 | ||||||||
\(753\) | 3.69421 | + | 6.39857i | 0.134625 | + | 0.233177i | ||||
\(754\) | 5.82770 | − | 26.1213i | 0.212232 | − | 0.951280i | ||||
\(755\) | −8.87802 | −0.323104 | ||||||||
\(756\) | 0.0236360 | + | 2.64565i | 0.000859635 | + | 0.0962212i | ||||
\(757\) | −3.48399 | + | 6.03445i | −0.126628 | + | 0.219326i | −0.922368 | − | 0.386312i | \(-0.873749\pi\) |
0.795740 | + | 0.605638i | \(0.207082\pi\) | |||||||
\(758\) | −16.6343 | −0.604183 | ||||||||
\(759\) | −0.559018 | − | 0.968247i | −0.0202911 | − | 0.0351451i | ||||
\(760\) | 4.78173 | − | 8.28221i | 0.173452 | − | 0.300427i | ||||
\(761\) | −2.95124 | −0.106982 | −0.0534912 | − | 0.998568i | \(-0.517035\pi\) | ||||
−0.0534912 | + | 0.998568i | \(0.517035\pi\) | |||||||
\(762\) | −8.47693 | −0.307087 | ||||||||
\(763\) | −45.7049 | − | 25.8461i | −1.65463 | − | 0.935692i | ||||
\(764\) | −2.64294 | + | 4.57771i | −0.0956182 | + | 0.165616i | ||||
\(765\) | 0.308739 | + | 0.534751i | 0.0111625 | + | 0.0193340i | ||||
\(766\) | 18.1834 | + | 31.4945i | 0.656992 | + | 1.13794i | ||||
\(767\) | 3.86387 | + | 3.55013i | 0.139516 | + | 0.128188i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −21.0168 | + | 36.4022i | −0.757885 | + | 1.31270i | 0.186042 | + | 0.982542i | \(0.440434\pi\) |
−0.943927 | + | 0.330154i | \(0.892899\pi\) | |||||||
\(770\) | 7.09047 | − | 4.17859i | 0.255523 | − | 0.150586i | ||||
\(771\) | 13.4446 | + | 23.2867i | 0.484195 | + | 0.838650i | ||||
\(772\) | −2.40599 | + | 4.16729i | −0.0865933 | + | 0.149984i | ||||
\(773\) | 21.8155 | − | 37.7856i | 0.784650 | − | 1.35905i | −0.144559 | − | 0.989496i | \(-0.546176\pi\) |
0.929208 | − | 0.369557i | \(-0.120490\pi\) | |||||||
\(774\) | −1.47532 | + | 2.55532i | −0.0530291 | + | 0.0918491i | ||||
\(775\) | 14.0060 | − | 24.2591i | 0.503111 | − | 0.871414i | ||||
\(776\) | 0.509831 | + | 0.883054i | 0.0183019 | + | 0.0316998i | ||||
\(777\) | −6.31472 | − | 3.57097i | −0.226539 | − | 0.128108i | ||||
\(778\) | −8.89008 | + | 15.3981i | −0.318725 | + | 0.552048i | ||||
\(779\) | 14.3532 | − | 24.8606i | 0.514258 | − | 0.890722i | ||||
\(780\) | 4.28851 | − | 1.34584i | 0.153553 | − | 0.0481889i | ||||
\(781\) | −11.7002 | − | 20.2653i | −0.418665 | − | 0.725149i | ||||
\(782\) | 0.110966 | + | 0.192198i | 0.00396812 | + | 0.00687298i | ||||
\(783\) | 3.71142 | − | 6.42837i | 0.132635 | − | 0.229731i | ||||
\(784\) | −6.99888 | + | 0.125065i | −0.249960 | + | 0.00446661i | ||||
\(785\) | −18.7527 | −0.669314 | ||||||||
\(786\) | 16.5336 | 0.589732 | ||||||||
\(787\) | −12.1660 | + | 21.0721i | −0.433671 | + | 0.751140i | −0.997186 | − | 0.0749659i | \(-0.976115\pi\) |
0.563515 | + | 0.826106i | \(0.309449\pi\) | |||||||
\(788\) | 11.7743 | + | 20.3937i | 0.419442 | + | 0.726494i | ||||
\(789\) | 2.93123 | 0.104355 | ||||||||
\(790\) | −6.15260 | + | 10.6566i | −0.218900 | + | 0.379145i | ||||
\(791\) | 36.5461 | + | 20.6668i | 1.29943 | + | 0.734826i | ||||
\(792\) | 2.49532 | 0.0886675 | ||||||||
\(793\) | 3.29691 | − | 14.7776i | 0.117077 | − | 0.524769i | ||||
\(794\) | 4.43952 | + | 7.68948i | 0.157553 | + | 0.272889i | ||||
\(795\) | −9.64254 | −0.341986 | ||||||||
\(796\) | −5.63984 | − | 9.76849i | −0.199899 | − | 0.346235i | ||||
\(797\) | −13.8223 | − | 23.9408i | −0.489609 | − | 0.848028i | 0.510319 | − | 0.859985i | \(-0.329527\pi\) |
−0.999929 | + | 0.0119569i | \(0.996194\pi\) | |||||||
\(798\) | −17.6677 | − | 9.99108i | −0.625430 | − | 0.353680i | ||||
\(799\) | 1.63323 | + | 2.82883i | 0.0577794 | + | 0.100077i | ||||
\(800\) | 3.44595 | 0.121833 | ||||||||
\(801\) | 5.74056 | + | 9.94294i | 0.202833 | + | 0.351317i | ||||
\(802\) | −15.0815 | + | 26.1219i | −0.532546 | + | 0.922397i | ||||
\(803\) | 12.6551 | + | 21.9192i | 0.446588 | + | 0.773513i | ||||
\(804\) | 0.0138047 | − | 0.0239105i | 0.000486855 | − | 0.000843258i | ||||
\(805\) | 1.27314 | − | 0.750293i | 0.0448723 | − | 0.0264443i | ||||
\(806\) | 21.5826 | + | 19.8301i | 0.760214 | + | 0.698485i | ||||
\(807\) | 1.07222 | − | 1.85713i | 0.0377438 | − | 0.0653741i | ||||
\(808\) | −17.9425 | −0.631217 | ||||||||
\(809\) | −46.7670 | −1.64424 | −0.822119 | − | 0.569315i | \(-0.807208\pi\) | ||||
−0.822119 | + | 0.569315i | \(0.807208\pi\) | |||||||
\(810\) | 1.24661 | 0.0438015 | ||||||||
\(811\) | −33.4037 | −1.17296 | −0.586481 | − | 0.809963i | \(-0.699487\pi\) | ||||
−0.586481 | + | 0.809963i | \(0.699487\pi\) | |||||||
\(812\) | 17.0949 | + | 9.66717i | 0.599914 | + | 0.339251i | ||||
\(813\) | 8.64220 | + | 14.9687i | 0.303095 | + | 0.524976i | ||||
\(814\) | −3.42101 | + | 5.92537i | −0.119906 | + | 0.207684i | ||||
\(815\) | −5.62828 | + | 9.74846i | −0.197150 | + | 0.341474i | ||||
\(816\) | −0.495324 | −0.0173398 | ||||||||
\(817\) | −11.3180 | − | 19.6033i | −0.395966 | − | 0.685833i | ||||
\(818\) | −16.7720 | −0.586420 | ||||||||
\(819\) | −2.93755 | − | 9.07584i | −0.102646 | − | 0.317135i | ||||
\(820\) | −4.66475 | −0.162900 | ||||||||
\(821\) | −18.7437 | − | 32.4651i | −0.654160 | − | 1.13304i | −0.982104 | − | 0.188342i | \(-0.939689\pi\) |
0.327943 | − | 0.944697i | \(-0.393645\pi\) | |||||||
\(822\) | −0.856837 | −0.0298856 | ||||||||
\(823\) | 24.8772 | − | 43.0886i | 0.867166 | − | 1.50198i | 0.00228512 | − | 0.999997i | \(-0.499273\pi\) |
0.864881 | − | 0.501978i | \(-0.167394\pi\) | |||||||
\(824\) | −0.524685 | + | 0.908780i | −0.0182783 | + | 0.0316589i | ||||
\(825\) | 4.29939 | + | 7.44676i | 0.149685 | + | 0.259263i | ||||
\(826\) | −3.31719 | + | 1.95490i | −0.115420 | + | 0.0680197i | ||||
\(827\) | 3.32250 | 0.115534 | 0.0577672 | − | 0.998330i | \(-0.481602\pi\) | ||||
0.0577672 | + | 0.998330i | \(0.481602\pi\) | |||||||
\(828\) | 0.448052 | 0.0155709 | ||||||||
\(829\) | −16.5097 | −0.573405 | −0.286703 | − | 0.958020i | \(-0.592559\pi\) | ||||
−0.286703 | + | 0.958020i | \(0.592559\pi\) | |||||||
\(830\) | 9.25342 | 0.321191 | ||||||||
\(831\) | −1.41690 | + | 2.45415i | −0.0491519 | + | 0.0851336i | ||||
\(832\) | −0.785103 | + | 3.51904i | −0.0272185 | + | 0.122001i | ||||
\(833\) | 1.78701 | + | 2.97129i | 0.0619161 | + | 0.102949i | ||||
\(834\) | 4.74886 | − | 8.22528i | 0.164440 | − | 0.284818i | ||||
\(835\) | −1.77570 | − | 3.07560i | −0.0614505 | − | 0.106435i | ||||
\(836\) | −9.57151 | + | 16.5783i | −0.331038 | + | 0.573374i | ||||
\(837\) | 4.06448 | + | 7.03989i | 0.140489 | + | 0.243334i | ||||
\(838\) | −39.6195 | −1.36863 | ||||||||
\(839\) | 8.35299 | + | 14.4678i | 0.288377 | + | 0.499484i | 0.973423 | − | 0.229016i | \(-0.0735510\pi\) |
−0.685045 | + | 0.728500i | \(0.740218\pi\) | |||||||
\(840\) | 0.0294650 | + | 3.29810i | 0.00101664 | + | 0.113795i | ||||
\(841\) | −13.0493 | − | 22.6021i | −0.449977 | − | 0.779383i | ||||
\(842\) | −16.1135 | − | 27.9095i | −0.555309 | − | 0.961824i | ||||
\(843\) | 28.5254 | 0.982467 | ||||||||
\(844\) | −6.22021 | − | 10.7737i | −0.214108 | − | 0.370847i | ||||
\(845\) | −13.3000 | + | 9.25974i | −0.457535 | + | 0.318545i | ||||
\(846\) | 6.59458 | 0.226726 | ||||||||
\(847\) | 10.8803 | − | 6.41201i | 0.373851 | − | 0.220319i | ||||
\(848\) | 3.86750 | − | 6.69870i | 0.132810 | − | 0.230034i | ||||
\(849\) | 4.59802 | 0.157804 | ||||||||
\(850\) | −0.853432 | − | 1.47819i | −0.0292725 | − | 0.0507014i | ||||
\(851\) | −0.614265 | + | 1.06394i | −0.0210567 | + | 0.0364714i | ||||
\(852\) | 9.37767 | 0.321274 | ||||||||
\(853\) | 27.5476 | 0.943212 | 0.471606 | − | 0.881809i | \(-0.343674\pi\) | ||||
0.471606 | + | 0.881809i | \(0.343674\pi\) | |||||||
\(854\) | 9.67114 | + | 5.46903i | 0.330940 | + | 0.187146i | ||||
\(855\) | −4.78173 | + | 8.28221i | −0.163532 | + | 0.283245i | ||||
\(856\) | −5.09152 | − | 8.81877i | −0.174025 | − | 0.301419i | ||||
\(857\) | −9.17302 | − | 15.8881i | −0.313344 | − | 0.542729i | 0.665740 | − | 0.746184i | \(-0.268116\pi\) |
−0.979084 | + | 0.203455i | \(0.934783\pi\) | |||||||
\(858\) | −8.58423 | + | 2.69395i | −0.293061 | + | 0.0919699i | ||||
\(859\) | −21.5684 | + | 37.3575i | −0.735903 | + | 1.27462i | 0.218423 | + | 0.975854i | \(0.429909\pi\) |
−0.954326 | + | 0.298767i | \(0.903425\pi\) | |||||||
\(860\) | −1.83915 | + | 3.18550i | −0.0627144 | + | 0.108625i | ||||
\(861\) | 0.0884446 | + | 9.89984i | 0.00301418 | + | 0.337386i | ||||
\(862\) | 5.50063 | + | 9.52738i | 0.187352 | + | 0.324504i | ||||
\(863\) | 22.5095 | − | 38.9876i | 0.766233 | − | 1.32715i | −0.173359 | − | 0.984859i | \(-0.555462\pi\) |
0.939592 | − | 0.342296i | \(-0.111204\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −15.8866 | + | 27.5163i | −0.540159 | + | 0.935583i | ||||
\(866\) | −15.9643 | + | 27.6509i | −0.542488 | + | 0.939616i | ||||
\(867\) | −8.37733 | − | 14.5100i | −0.284509 | − | 0.492784i | ||||
\(868\) | −18.5290 | + | 10.9196i | −0.628915 | + | 0.370634i | ||||
\(869\) | 12.3155 | − | 21.3312i | 0.417776 | − | 0.723610i | ||||
\(870\) | 4.62671 | − | 8.01370i | 0.156860 | − | 0.271690i | ||||
\(871\) | −0.0216763 | + | 0.0971586i | −0.000734472 | + | 0.00329209i | ||||
\(872\) | −9.92285 | − | 17.1869i | −0.336030 | − | 0.582021i | ||||
\(873\) | −0.509831 | − | 0.883054i | −0.0172552 | − | 0.0298868i | ||||
\(874\) | −1.71863 | + | 2.97675i | −0.0581335 | + | 0.100690i | ||||
\(875\) | −23.9992 | + | 14.1433i | −0.811321 | + | 0.478131i | ||||
\(876\) | −10.1430 | −0.342701 | ||||||||
\(877\) | −21.8595 | −0.738142 | −0.369071 | − | 0.929401i | \(-0.620324\pi\) | ||||
−0.369071 | + | 0.929401i | \(0.620324\pi\) | |||||||
\(878\) | −0.717628 | + | 1.24297i | −0.0242188 | + | 0.0419481i | ||||
\(879\) | −3.19384 | − | 5.53189i | −0.107726 | − | 0.186586i | ||||
\(880\) | 3.11070 | 0.104862 | ||||||||
\(881\) | 0.975574 | − | 1.68974i | 0.0328679 | − | 0.0569289i | −0.849124 | − | 0.528194i | \(-0.822869\pi\) |
0.881991 | + | 0.471265i | \(0.156203\pi\) | |||||||
\(882\) | 6.99888 | − | 0.125065i | 0.235665 | − | 0.00421116i | ||||
\(883\) | −20.9397 | −0.704677 | −0.352338 | − | 0.935873i | \(-0.614613\pi\) | ||||
−0.352338 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(884\) | 1.70398 | − | 0.534751i | 0.0573110 | − | 0.0179856i | ||||
\(885\) | 0.907102 | + | 1.57115i | 0.0304919 | + | 0.0528135i | ||||
\(886\) | 11.4552 | 0.384844 | ||||||||
\(887\) | −11.7886 | − | 20.4185i | −0.395823 | − | 0.685586i | 0.597383 | − | 0.801956i | \(-0.296207\pi\) |
−0.993206 | + | 0.116370i | \(0.962874\pi\) | |||||||
\(888\) | −1.37097 | − | 2.37459i | −0.0460067 | − | 0.0796859i | ||||
\(889\) | 0.200361 | + | 22.4270i | 0.00671989 | + | 0.752176i | ||||
\(890\) | 7.15626 | + | 12.3950i | 0.239878 | + | 0.415482i | ||||
\(891\) | −2.49532 | −0.0835965 | ||||||||
\(892\) | −10.4651 | − | 18.1260i | −0.350396 | − | 0.606904i | ||||
\(893\) | −25.2954 | + | 43.8128i | −0.846477 | + | 1.46614i | ||||
\(894\) | 2.36872 | + | 4.10274i | 0.0792218 | + | 0.137216i | ||||
\(895\) | 11.3446 | − | 19.6494i | 0.379207 | − | 0.656806i | ||||
\(896\) | −2.30301 | − | 1.30235i | −0.0769383 | − | 0.0435086i | ||||
\(897\) | −1.54136 | + | 0.483717i | −0.0514644 | + | 0.0161508i | ||||
\(898\) | 17.3713 | − | 30.0880i | 0.579688 | − | 1.00405i | ||||
\(899\) | 60.3401 | 2.01245 | ||||||||
\(900\) | −3.44595 | −0.114865 | ||||||||
\(901\) | −3.83133 | −0.127640 | ||||||||
\(902\) | 9.33735 | 0.310900 | ||||||||
\(903\) | 6.79535 | + | 3.84276i | 0.226135 | + | 0.127879i | ||||
\(904\) | 7.93440 | + | 13.7428i | 0.263894 | + | 0.457078i | ||||
\(905\) | −8.55831 | + | 14.8234i | −0.284488 | + | 0.492747i | ||||
\(906\) | −3.56085 | + | 6.16758i | −0.118301 | + | 0.204904i | ||||
\(907\) | 0.141508 | 0.00469870 | 0.00234935 | − | 0.999997i | \(-0.499252\pi\) | ||||
0.00234935 | + | 0.999997i | \(0.499252\pi\) | |||||||
\(908\) | −8.79052 | − | 15.2256i | −0.291724 | − | 0.505280i | ||||
\(909\) | 17.9425 | 0.595117 | ||||||||
\(910\) | −3.66199 | − | 11.3141i | −0.121394 | − | 0.375057i | ||||
\(911\) | 48.1769 | 1.59617 | 0.798086 | − | 0.602543i | \(-0.205846\pi\) | ||||
0.798086 | + | 0.602543i | \(0.205846\pi\) | |||||||
\(912\) | −3.83578 | − | 6.64376i | −0.127015 | − | 0.219997i | ||||
\(913\) | −18.5224 | −0.613002 | ||||||||
\(914\) | 18.4024 | − | 31.8739i | 0.608698 | − | 1.05430i | ||||
\(915\) | 2.61748 | − | 4.53360i | 0.0865311 | − | 0.149876i | ||||
\(916\) | 7.24620 | + | 12.5508i | 0.239421 | + | 0.414690i | ||||
\(917\) | −0.390788 | − | 43.7419i | −0.0129049 | − | 1.44449i | ||||
\(918\) | 0.495324 | 0.0163481 | ||||||||
\(919\) | 39.6180 | 1.30688 | 0.653439 | − | 0.756980i | \(-0.273326\pi\) | ||||
0.653439 | + | 0.756980i | \(0.273326\pi\) | |||||||
\(920\) | 0.558548 | 0.0184148 | ||||||||
\(921\) | 1.39899 | 0.0460983 | ||||||||
\(922\) | 3.99129 | − | 6.91311i | 0.131446 | − | 0.227671i | ||||
\(923\) | −32.2604 | + | 10.1241i | −1.06186 | + | 0.333240i | ||||
\(924\) | −0.0589796 | − | 6.60174i | −0.00194029 | − | 0.217181i | ||||
\(925\) | 4.72430 | − | 8.18272i | 0.155334 | − | 0.269046i | ||||
\(926\) | 13.2400 | + | 22.9323i | 0.435093 | + | 0.753602i | ||||
\(927\) | 0.524685 | − | 0.908780i | 0.0172329 | − | 0.0298483i | ||||
\(928\) | 3.71142 | + | 6.42837i | 0.121833 | + | 0.211022i | ||||
\(929\) | 36.0334 | 1.18222 | 0.591109 | − | 0.806592i | \(-0.298690\pi\) | ||||
0.591109 | + | 0.806592i | \(0.298690\pi\) | |||||||
\(930\) | 5.06684 | + | 8.77602i | 0.166148 | + | 0.287777i | ||||
\(931\) | −26.0153 | + | 46.9787i | −0.852616 | + | 1.53966i | ||||
\(932\) | −7.24897 | − | 12.5556i | −0.237448 | − | 0.411272i | ||||
\(933\) | 8.55183 | + | 14.8122i | 0.279974 | + | 0.484930i | ||||
\(934\) | −6.24421 | −0.204317 | ||||||||
\(935\) | −0.770404 | − | 1.33438i | −0.0251949 | − | 0.0436388i | ||||
\(936\) | 0.785103 | − | 3.51904i | 0.0256619 | − | 0.115023i | ||||
\(937\) | −2.37671 | −0.0776439 | −0.0388219 | − | 0.999246i | \(-0.512361\pi\) | ||||
−0.0388219 | + | 0.999246i | \(0.512361\pi\) | |||||||
\(938\) | −0.0635849 | − | 0.0359573i | −0.00207612 | − | 0.00117405i | ||||
\(939\) | 5.81247 | − | 10.0675i | 0.189683 | − | 0.328540i | ||||
\(940\) | 8.22089 | 0.268136 | ||||||||
\(941\) | −19.3411 | − | 33.4998i | −0.630503 | − | 1.09206i | −0.987449 | − | 0.157938i | \(-0.949515\pi\) |
0.356946 | − | 0.934125i | \(-0.383818\pi\) | |||||||
\(942\) | −7.52147 | + | 13.0276i | −0.245063 | + | 0.424461i | ||||
\(943\) | 1.67658 | 0.0545971 | ||||||||
\(944\) | −1.45531 | −0.0473662 | ||||||||
\(945\) | −0.0294650 | − | 3.29810i | −0.000958497 | − | 0.107287i | ||||
\(946\) | 3.68139 | − | 6.37635i | 0.119692 | − | 0.207313i | ||||
\(947\) | 7.37320 | + | 12.7708i | 0.239597 | + | 0.414994i | 0.960599 | − | 0.277939i | \(-0.0896514\pi\) |
−0.721002 | + | 0.692933i | \(0.756318\pi\) | |||||||
\(948\) | 4.93545 | + | 8.54845i | 0.160296 | + | 0.277641i | ||||
\(949\) | 34.8933 | − | 10.9504i | 1.13268 | − | 0.355465i | ||||
\(950\) | 13.2179 | − | 22.8941i | 0.428846 | − | 0.742783i | ||||
\(951\) | 3.29277 | − | 5.70324i | 0.106775 | − | 0.184940i | ||||
\(952\) | 0.0117075 | + | 1.31045i | 0.000379442 | + | 0.0424720i | ||||
\(953\) | 8.54843 | + | 14.8063i | 0.276911 | + | 0.479623i | 0.970615 | − | 0.240636i | \(-0.0773561\pi\) |
−0.693705 | + | 0.720259i | \(0.744023\pi\) | |||||||
\(954\) | −3.86750 | + | 6.69870i | −0.125215 | + | 0.216878i | ||||
\(955\) | 3.29473 | − | 5.70663i | 0.106615 | − | 0.184662i | ||||
\(956\) | −1.57547 | + | 2.72879i | −0.0509542 | + | 0.0882553i | ||||
\(957\) | −9.26121 | + | 16.0409i | −0.299372 | + | 0.518528i | ||||
\(958\) | 10.7862 | + | 18.6823i | 0.348487 | + | 0.603598i | ||||
\(959\) | 0.0202522 | + | 2.26689i | 0.000653979 | + | 0.0732016i | ||||
\(960\) | −0.623307 | + | 1.07960i | −0.0201171 | + | 0.0348439i | ||||
\(961\) | −17.5400 | + | 30.3802i | −0.565807 | + | 0.980006i | ||||
\(962\) | 7.27991 | + | 6.68878i | 0.234714 | + | 0.215655i | ||||
\(963\) | 5.09152 | + | 8.81877i | 0.164072 | + | 0.284181i | ||||
\(964\) | 12.4223 | + | 21.5160i | 0.400095 | + | 0.692984i | ||||
\(965\) | 2.99933 | − | 5.19500i | 0.0965520 | − | 0.167233i | ||||
\(966\) | −0.0105902 | − | 1.18539i | −0.000340733 | − | 0.0381392i | ||||
\(967\) | −7.90857 | −0.254323 | −0.127161 | − | 0.991882i | \(-0.540587\pi\) | ||||
−0.127161 | + | 0.991882i | \(0.540587\pi\) | |||||||
\(968\) | 4.77336 | 0.153422 | ||||||||
\(969\) | −1.89995 | + | 3.29082i | −0.0610353 | + | 0.105716i | ||||
\(970\) | −0.635563 | − | 1.10083i | −0.0204067 | − | 0.0353454i | ||||
\(971\) | 3.90099 | 0.125189 | 0.0625944 | − | 0.998039i | \(-0.480063\pi\) | ||||
0.0625944 | + | 0.998039i | \(0.480063\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −21.8734 | − | 12.3694i | −0.701229 | − | 0.396545i | ||||
\(974\) | −13.6151 | −0.436257 | ||||||||
\(975\) | 11.8545 | − | 3.72025i | 0.379648 | − | 0.119143i | ||||
\(976\) | 2.09967 | + | 3.63674i | 0.0672088 | + | 0.116409i | ||||
\(977\) | −51.3897 | −1.64410 | −0.822051 | − | 0.569414i | \(-0.807170\pi\) | ||||
−0.822051 | + | 0.569414i | \(0.807170\pi\) | |||||||
\(978\) | 4.51485 | + | 7.81996i | 0.144369 | + | 0.250055i | ||||
\(979\) | −14.3246 | − | 24.8109i | −0.457815 | − | 0.792959i | ||||
\(980\) | 8.72490 | − | 0.155908i | 0.278707 | − | 0.00498030i | ||||
\(981\) | 9.92285 | + | 17.1869i | 0.316812 | + | 0.548735i | ||||
\(982\) | 12.2902 | 0.392198 | ||||||||
\(983\) | 7.32146 | + | 12.6811i | 0.233518 | + | 0.404465i | 0.958841 | − | 0.283944i | \(-0.0916428\pi\) |
−0.725323 | + | 0.688409i | \(0.758310\pi\) | |||||||
\(984\) | −1.87097 | + | 3.24061i | −0.0596443 | + | 0.103307i | ||||
\(985\) | −14.6780 | − | 25.4230i | −0.467680 | − | 0.810045i | ||||
\(986\) | 1.83836 | − | 3.18413i | 0.0585452 | − | 0.101403i | ||||
\(987\) | −0.155870 | − | 17.4469i | −0.00496139 | − | 0.555342i | ||||
\(988\) | 20.3682 | + | 18.7143i | 0.647998 | + | 0.595381i | ||||
\(989\) | 0.661018 | − | 1.14492i | 0.0210192 | − | 0.0364062i | ||||
\(990\) | −3.11070 | −0.0988647 | ||||||||
\(991\) | −22.5329 | −0.715780 | −0.357890 | − | 0.933764i | \(-0.616504\pi\) | ||||
−0.357890 | + | 0.933764i | \(0.616504\pi\) | |||||||
\(992\) | −8.12896 | −0.258095 | ||||||||
\(993\) | 23.2685 | 0.738405 | ||||||||
\(994\) | −0.221651 | − | 24.8100i | −0.00703035 | − | 0.786925i | ||||
\(995\) | 7.03070 | + | 12.1775i | 0.222888 | + | 0.386054i | ||||
\(996\) | 3.71142 | − | 6.42837i | 0.117601 | − | 0.203691i | ||||
\(997\) | 12.3016 | − | 21.3071i | 0.389597 | − | 0.674801i | −0.602798 | − | 0.797893i | \(-0.705948\pi\) |
0.992395 | + | 0.123092i | \(0.0392810\pi\) | |||||||
\(998\) | −14.2358 | −0.450626 | ||||||||
\(999\) | 1.37097 | + | 2.37459i | 0.0433755 | + | 0.0751286i |
(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 | 546.2.k.e.373.4 | yes | 10 | |
3.2 | odd | 2 | 1638.2.p.j.919.2 | 10 | |||
7.4 | even | 3 | 546.2.j.e.529.4 | yes | 10 | ||
13.3 | even | 3 | 546.2.j.e.289.4 | ✓ | 10 | ||
21.11 | odd | 6 | 1638.2.m.k.1621.2 | 10 | |||
39.29 | odd | 6 | 1638.2.m.k.289.2 | 10 | |||
91.81 | even | 3 | inner | 546.2.k.e.445.4 | yes | 10 | |
273.263 | odd | 6 | 1638.2.p.j.991.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.4 | ✓ | 10 | 13.3 | even | 3 | ||
546.2.j.e.529.4 | yes | 10 | 7.4 | even | 3 | ||
546.2.k.e.373.4 | yes | 10 | 1.1 | even | 1 | trivial | |
546.2.k.e.445.4 | yes | 10 | 91.81 | even | 3 | inner | |
1638.2.m.k.289.2 | 10 | 39.29 | odd | 6 | |||
1638.2.m.k.1621.2 | 10 | 21.11 | odd | 6 | |||
1638.2.p.j.919.2 | 10 | 3.2 | odd | 2 | |||
1638.2.p.j.991.2 | 10 | 273.263 | odd | 6 |