Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), not 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.26873856000000000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 233.4 | ||
Root | \(-0.575212 + 1.29195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.233 |
Dual form | 363.2.f.h.215.4 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.756934 | − | 2.32960i | 0.535233 | − | 1.64728i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.743145 | − | 0.669131i | \(-0.233333\pi\) | |||||||
\(3\) | 1.72256 | − | 0.181049i | 0.994522 | − | 0.104528i | ||||
\(4\) | −3.23607 | − | 2.35114i | −1.61803 | − | 1.17557i | ||||
\(5\) | 1.64728 | − | 0.535233i | 0.736685 | − | 0.239364i | 0.0834430 | − | 0.996513i | \(-0.473408\pi\) |
0.653242 | + | 0.757149i | \(0.273408\pi\) | |||||||
\(6\) | 0.882095 | − | 4.14993i | 0.360114 | − | 1.69420i | ||||
\(7\) | −0.831254 | + | 1.14412i | −0.314184 | + | 0.432438i | −0.936680 | − | 0.350185i | \(-0.886119\pi\) |
0.622496 | + | 0.782623i | \(0.286119\pi\) | |||||||
\(8\) | −3.96336 | + | 2.87955i | −1.40126 | + | 1.01807i | ||||
\(9\) | 2.93444 | − | 0.623735i | 0.978148 | − | 0.207912i | ||||
\(10\) | − | 4.24264i | − | 1.34164i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −6.00000 | − | 3.46410i | −1.73205 | − | 1.00000i | ||||
\(13\) | −2.68999 | − | 0.874032i | −0.746070 | − | 0.242413i | −0.0887808 | − | 0.996051i | \(-0.528297\pi\) |
−0.657289 | + | 0.753638i | \(0.728297\pi\) | |||||||
\(14\) | 2.03615 | + | 2.80252i | 0.544183 | + | 0.749004i | ||||
\(15\) | 2.74064 | − | 1.22021i | 0.707629 | − | 0.315057i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.309017 | + | 0.951057i | ||||
\(17\) | 0.756934 | + | 2.32960i | 0.183583 | + | 0.565012i | 0.999921 | − | 0.0125632i | \(-0.00399911\pi\) |
−0.816338 | + | 0.577575i | \(0.803999\pi\) | |||||||
\(18\) | 0.768124 | − | 7.30821i | 0.181049 | − | 1.72256i | ||||
\(19\) | −1.66251 | − | 2.28825i | −0.381405 | − | 0.524960i | 0.574551 | − | 0.818469i | \(-0.305177\pi\) |
−0.955956 | + | 0.293509i | \(0.905177\pi\) | |||||||
\(20\) | −6.58911 | − | 2.14093i | −1.47337 | − | 0.478727i | ||||
\(21\) | −1.22474 | + | 2.12132i | −0.267261 | + | 0.462910i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.66025i | 1.80579i | 0.429863 | + | 0.902894i | \(0.358562\pi\) | ||||
−0.429863 | + | 0.902894i | \(0.641438\pi\) | |||||||
\(24\) | −6.30579 | + | 5.67776i | −1.28716 | + | 1.15897i | ||||
\(25\) | −1.61803 | + | 1.17557i | −0.323607 | + | 0.235114i | ||||
\(26\) | −4.07230 | + | 5.60503i | −0.798643 | + | 1.09924i | ||||
\(27\) | 4.94183 | − | 1.60570i | 0.951057 | − | 0.309017i | ||||
\(28\) | 5.37999 | − | 1.74806i | 1.01672 | − | 0.330353i | ||||
\(29\) | 3.96336 | + | 2.87955i | 0.735977 | + | 0.534719i | 0.891449 | − | 0.453122i | \(-0.149690\pi\) |
−0.155472 | + | 0.987840i | \(0.549690\pi\) | |||||||
\(30\) | −0.768124 | − | 7.30821i | −0.140240 | − | 1.33429i | ||||
\(31\) | 0.927051 | − | 2.85317i | 0.166503 | − | 0.512444i | −0.832641 | − | 0.553814i | \(-0.813172\pi\) |
0.999144 | + | 0.0413693i | \(0.0131720\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −0.756934 | + | 2.32960i | −0.127945 | + | 0.393775i | ||||
\(36\) | −10.9625 | − | 4.88084i | −1.82709 | − | 0.813473i | ||||
\(37\) | −2.42705 | − | 1.76336i | −0.399005 | − | 0.289894i | 0.370131 | − | 0.928980i | \(-0.379313\pi\) |
−0.769135 | + | 0.639086i | \(0.779313\pi\) | |||||||
\(38\) | −6.58911 | + | 2.14093i | −1.06890 | + | 0.347305i | ||||
\(39\) | −4.79193 | − | 1.01856i | −0.767322 | − | 0.163099i | ||||
\(40\) | −4.98752 | + | 6.86474i | −0.788597 | + | 1.08541i | ||||
\(41\) | 7.92672 | − | 5.75910i | 1.23794 | − | 0.899420i | 0.240485 | − | 0.970653i | \(-0.422693\pi\) |
0.997460 | + | 0.0712331i | \(0.0226934\pi\) | |||||||
\(42\) | 4.01478 | + | 4.45887i | 0.619495 | + | 0.688018i | ||||
\(43\) | 9.89949i | 1.50966i | 0.655921 | + | 0.754829i | \(0.272280\pi\) | ||||
−0.655921 | + | 0.754829i | \(0.727720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.50000 | − | 2.59808i | 0.670820 | − | 0.387298i | ||||
\(46\) | 20.1750 | + | 6.55524i | 2.97463 | + | 0.966517i | ||||
\(47\) | −4.07230 | − | 5.60503i | −0.594005 | − | 0.817578i | 0.401138 | − | 0.916018i | \(-0.368615\pi\) |
−0.995143 | + | 0.0984395i | \(0.968615\pi\) | |||||||
\(48\) | 2.81795 | + | 6.32923i | 0.406737 | + | 0.913545i | ||||
\(49\) | 1.54508 | + | 4.75528i | 0.220726 | + | 0.679326i | ||||
\(50\) | 1.51387 | + | 4.65921i | 0.214093 | + | 0.658911i | ||||
\(51\) | 1.72564 | + | 3.87585i | 0.241638 | + | 0.542727i | ||||
\(52\) | 6.65003 | + | 9.15298i | 0.922193 | + | 1.26929i | ||||
\(53\) | −3.29456 | − | 1.07047i | −0.452542 | − | 0.147040i | 0.0738728 | − | 0.997268i | \(-0.476464\pi\) |
−0.526415 | + | 0.850228i | \(0.676464\pi\) | |||||||
\(54\) | − | 12.7279i | − | 1.73205i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 6.92820i | − | 0.925820i | ||||||
\(57\) | −3.27806 | − | 3.64065i | −0.434189 | − | 0.482216i | ||||
\(58\) | 9.70820 | − | 7.05342i | 1.27475 | − | 0.926160i | ||||
\(59\) | −1.01807 | + | 1.40126i | −0.132542 | + | 0.182428i | −0.870129 | − | 0.492823i | \(-0.835965\pi\) |
0.737588 | + | 0.675252i | \(0.235965\pi\) | |||||||
\(60\) | −11.7378 | − | 2.49494i | −1.51534 | − | 0.322095i | ||||
\(61\) | 2.68999 | − | 0.874032i | 0.344418 | − | 0.111908i | −0.131700 | − | 0.991290i | \(-0.542043\pi\) |
0.476118 | + | 0.879381i | \(0.342043\pi\) | |||||||
\(62\) | −5.94504 | − | 4.31932i | −0.755020 | − | 0.548554i | ||||
\(63\) | −1.72564 | + | 3.87585i | −0.217410 | + | 0.488311i | ||||
\(64\) | −2.47214 | + | 7.60845i | −0.309017 | + | 0.951057i | ||||
\(65\) | −4.89898 | −0.607644 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | −0.366508 | −0.183254 | − | 0.983066i | \(-0.558663\pi\) | ||||
−0.183254 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(68\) | 3.02774 | − | 9.31841i | 0.367167 | − | 1.13002i | ||||
\(69\) | 1.56793 | + | 14.9178i | 0.188756 | + | 1.79590i | ||||
\(70\) | 4.85410 | + | 3.52671i | 0.580176 | + | 0.421523i | ||||
\(71\) | 1.64728 | − | 0.535233i | 0.195496 | − | 0.0635205i | −0.209633 | − | 0.977780i | \(-0.567227\pi\) |
0.405129 | + | 0.914260i | \(0.367227\pi\) | |||||||
\(72\) | −9.83417 | + | 10.9220i | −1.15897 | + | 1.28716i | ||||
\(73\) | 3.32502 | − | 4.57649i | 0.389164 | − | 0.535638i | −0.568819 | − | 0.822462i | \(-0.692600\pi\) |
0.957983 | + | 0.286825i | \(0.0925997\pi\) | |||||||
\(74\) | −5.94504 | + | 4.31932i | −0.691096 | + | 0.502111i | ||||
\(75\) | −2.57433 | + | 2.31794i | −0.297258 | + | 0.267652i | ||||
\(76\) | 11.3137i | 1.29777i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | + | 10.3923i | −0.679366 | + | 1.17670i | ||||
\(79\) | −9.41498 | − | 3.05911i | −1.05927 | − | 0.344177i | −0.272969 | − | 0.962023i | \(-0.588006\pi\) |
−0.786299 | + | 0.617846i | \(0.788006\pi\) | |||||||
\(80\) | 4.07230 | + | 5.60503i | 0.455296 | + | 0.626662i | ||||
\(81\) | 8.22191 | − | 3.66063i | 0.913545 | − | 0.406737i | ||||
\(82\) | −7.41641 | − | 22.8254i | −0.819005 | − | 2.52064i | ||||
\(83\) | −0.756934 | − | 2.32960i | −0.0830843 | − | 0.255707i | 0.900881 | − | 0.434066i | \(-0.142921\pi\) |
−0.983966 | + | 0.178358i | \(0.942921\pi\) | |||||||
\(84\) | 8.95088 | − | 3.98519i | 0.976621 | − | 0.434820i | ||||
\(85\) | 2.49376 | + | 3.43237i | 0.270486 | + | 0.372293i | ||||
\(86\) | 23.0619 | + | 7.49326i | 2.48683 | + | 0.808019i | ||||
\(87\) | 7.34847 | + | 4.24264i | 0.787839 | + | 0.454859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.66025i | − | 0.917985i | −0.888440 | − | 0.458993i | \(-0.848210\pi\) | ||
0.888440 | − | 0.458993i | \(-0.151790\pi\) | |||||||
\(90\) | −2.64628 | − | 12.4498i | −0.278943 | − | 1.31232i | ||||
\(91\) | 3.23607 | − | 2.35114i | 0.339232 | − | 0.246467i | ||||
\(92\) | 20.3615 | − | 28.0252i | 2.12283 | − | 2.92183i | ||||
\(93\) | 1.08034 | − | 5.08260i | 0.112026 | − | 0.527041i | ||||
\(94\) | −16.1400 | + | 5.24419i | −1.66471 | + | 0.540897i | ||||
\(95\) | −3.96336 | − | 2.87955i | −0.406632 | − | 0.295435i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.01722 | − | 12.3637i | 0.407887 | − | 1.25535i | −0.510573 | − | 0.859834i | \(-0.670567\pi\) |
0.918460 | − | 0.395513i | \(-0.129433\pi\) | |||||||
\(98\) | 12.2474 | 1.23718 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000 | 0.800000 | ||||||||
\(101\) | −3.78467 | + | 11.6480i | −0.376589 | + | 1.15902i | 0.565812 | + | 0.824534i | \(0.308563\pi\) |
−0.942401 | + | 0.334486i | \(0.891437\pi\) | |||||||
\(102\) | 10.3354 | − | 1.08629i | 1.02335 | − | 0.107559i | ||||
\(103\) | 1.61803 | + | 1.17557i | 0.159430 | + | 0.115832i | 0.664640 | − | 0.747164i | \(-0.268585\pi\) |
−0.505210 | + | 0.862996i | \(0.668585\pi\) | |||||||
\(104\) | 13.1782 | − | 4.28187i | 1.29223 | − | 0.419871i | ||||
\(105\) | −0.882095 | + | 4.14993i | −0.0860836 | + | 0.404992i | ||||
\(106\) | −4.98752 | + | 6.86474i | −0.484431 | + | 0.666762i | ||||
\(107\) | 1.98168 | − | 1.43977i | 0.191576 | − | 0.139188i | −0.487863 | − | 0.872920i | \(-0.662223\pi\) |
0.679439 | + | 0.733732i | \(0.262223\pi\) | |||||||
\(108\) | −19.7673 | − | 6.42280i | −1.90211 | − | 0.618034i | ||||
\(109\) | − | 18.3848i | − | 1.76094i | −0.474100 | − | 0.880471i | \(-0.657226\pi\) | ||
0.474100 | − | 0.880471i | \(-0.342774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | − | 2.59808i | −0.427121 | − | 0.246598i | ||||
\(112\) | −5.37999 | − | 1.74806i | −0.508361 | − | 0.165177i | ||||
\(113\) | 1.01807 | + | 1.40126i | 0.0957723 | + | 0.131819i | 0.854214 | − | 0.519922i | \(-0.174039\pi\) |
−0.758442 | + | 0.651741i | \(0.774039\pi\) | |||||||
\(114\) | −10.9625 | + | 4.88084i | −1.02674 | + | 0.457133i | ||||
\(115\) | 4.63525 | + | 14.2658i | 0.432240 | + | 1.33030i | ||||
\(116\) | −6.05547 | − | 18.6368i | −0.562236 | − | 1.73039i | ||||
\(117\) | −8.43880 | − | 0.886953i | −0.780167 | − | 0.0819989i | ||||
\(118\) | 2.49376 | + | 3.43237i | 0.229569 | + | 0.315975i | ||||
\(119\) | −3.29456 | − | 1.07047i | −0.302011 | − | 0.0981295i | ||||
\(120\) | −7.34847 | + | 12.7279i | −0.670820 | + | 1.16190i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 6.92820i | − | 0.627250i | ||||||
\(123\) | 12.6116 | − | 11.3555i | 1.13715 | − | 1.02389i | ||||
\(124\) | −9.70820 | + | 7.05342i | −0.871822 | + | 0.633416i | ||||
\(125\) | −7.12652 | + | 9.80881i | −0.637415 | + | 0.877327i | ||||
\(126\) | 7.72299 | + | 6.95381i | 0.688018 | + | 0.619495i | ||||
\(127\) | 2.68999 | − | 0.874032i | 0.238698 | − | 0.0775578i | −0.187225 | − | 0.982317i | \(-0.559949\pi\) |
0.425923 | + | 0.904759i | \(0.359949\pi\) | |||||||
\(128\) | 15.8534 | + | 11.5182i | 1.40126 | + | 1.01807i | ||||
\(129\) | 1.79229 | + | 17.0525i | 0.157802 | + | 1.50139i | ||||
\(130\) | −3.70820 | + | 11.4127i | −0.325231 | + | 1.00096i | ||||
\(131\) | 12.2474 | 1.07006 | 0.535032 | − | 0.844832i | \(-0.320299\pi\) | ||||
0.535032 | + | 0.844832i | \(0.320299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | −2.27080 | + | 6.98881i | −0.196167 | + | 0.603741i | ||||
\(135\) | 7.28115 | − | 5.29007i | 0.626662 | − | 0.455296i | ||||
\(136\) | −9.70820 | − | 7.05342i | −0.832472 | − | 0.604826i | ||||
\(137\) | −14.8255 | + | 4.81710i | −1.26663 | + | 0.411552i | −0.863852 | − | 0.503746i | \(-0.831955\pi\) |
−0.402776 | + | 0.915298i | \(0.631955\pi\) | |||||||
\(138\) | 35.9394 | + | 7.63916i | 3.05937 | + | 0.650289i | ||||
\(139\) | −9.14379 | + | 12.5854i | −0.775566 | + | 1.06748i | 0.220191 | + | 0.975457i | \(0.429332\pi\) |
−0.995757 | + | 0.0920187i | \(0.970668\pi\) | |||||||
\(140\) | 7.92672 | − | 5.75910i | 0.669930 | − | 0.486732i | ||||
\(141\) | −8.02957 | − | 8.91774i | −0.676212 | − | 0.751009i | ||||
\(142\) | − | 4.24264i | − | 0.356034i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(145\) | 8.06998 | + | 2.62210i | 0.670176 | + | 0.217753i | ||||
\(146\) | −8.14459 | − | 11.2101i | −0.674051 | − | 0.927752i | ||||
\(147\) | 3.52244 | + | 7.91154i | 0.290526 | + | 0.652532i | ||||
\(148\) | 3.70820 | + | 11.4127i | 0.304812 | + | 0.938116i | ||||
\(149\) | 0.756934 | + | 2.32960i | 0.0620104 | + | 0.190849i | 0.977262 | − | 0.212033i | \(-0.0680085\pi\) |
−0.915252 | + | 0.402882i | \(0.868009\pi\) | |||||||
\(150\) | 3.45127 | + | 7.75169i | 0.281795 | + | 0.632923i | ||||
\(151\) | −5.81878 | − | 8.00886i | −0.473525 | − | 0.651752i | 0.503719 | − | 0.863867i | \(-0.331965\pi\) |
−0.977245 | + | 0.212116i | \(0.931965\pi\) | |||||||
\(152\) | 13.1782 | + | 4.28187i | 1.06890 | + | 0.347305i | ||||
\(153\) | 3.67423 | + | 6.36396i | 0.297044 | + | 0.514496i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.19615i | − | 0.417365i | ||||||
\(156\) | 13.1122 | + | 14.5626i | 1.04982 | + | 1.16594i | ||||
\(157\) | −12.1353 | + | 8.81678i | −0.968499 | + | 0.703656i | −0.955109 | − | 0.296255i | \(-0.904262\pi\) |
−0.0133898 | + | 0.999910i | \(0.504262\pi\) | |||||||
\(158\) | −14.2530 | + | 19.6176i | −1.13391 | + | 1.56069i | ||||
\(159\) | −5.86889 | − | 1.24747i | −0.465433 | − | 0.0989308i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.90839 | − | 7.19887i | −0.780891 | − | 0.567350i | ||||
\(162\) | −2.30437 | − | 21.9246i | −0.181049 | − | 1.72256i | ||||
\(163\) | −3.09017 | + | 9.51057i | −0.242041 | + | 0.744925i | 0.754068 | + | 0.656796i | \(0.228089\pi\) |
−0.996109 | + | 0.0881289i | \(0.971911\pi\) | |||||||
\(164\) | −39.1918 | −3.06037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −6.05547 | + | 18.6368i | −0.468586 | + | 1.44216i | 0.385829 | + | 0.922570i | \(0.373915\pi\) |
−0.854415 | + | 0.519591i | \(0.826085\pi\) | |||||||
\(168\) | −1.25434 | − | 11.9343i | −0.0967746 | − | 0.920748i | ||||
\(169\) | −4.04508 | − | 2.93893i | −0.311160 | − | 0.226071i | ||||
\(170\) | 9.88367 | − | 3.21140i | 0.758043 | − | 0.246303i | ||||
\(171\) | −6.30579 | − | 5.67776i | −0.482216 | − | 0.434189i | ||||
\(172\) | 23.2751 | − | 32.0354i | 1.77471 | − | 2.44268i | ||||
\(173\) | −1.98168 | + | 1.43977i | −0.150664 | + | 0.109464i | −0.660564 | − | 0.750770i | \(-0.729683\pi\) |
0.509899 | + | 0.860234i | \(0.329683\pi\) | |||||||
\(174\) | 15.4460 | − | 13.9076i | 1.17096 | − | 1.05433i | ||||
\(175\) | − | 2.82843i | − | 0.213809i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | −20.1750 | − | 6.55524i | −1.51218 | − | 0.491336i | ||||
\(179\) | −9.16267 | − | 12.6113i | −0.684850 | − | 0.942615i | 0.315130 | − | 0.949049i | \(-0.397952\pi\) |
−0.999979 | + | 0.00643384i | \(0.997952\pi\) | |||||||
\(180\) | −20.6707 | − | 2.17258i | −1.54071 | − | 0.161935i | ||||
\(181\) | −1.54508 | − | 4.75528i | −0.114845 | − | 0.353457i | 0.877069 | − | 0.480364i | \(-0.159495\pi\) |
−0.991915 | + | 0.126906i | \(0.959495\pi\) | |||||||
\(182\) | −3.02774 | − | 9.31841i | −0.224431 | − | 0.690727i | ||||
\(183\) | 4.47544 | − | 1.99259i | 0.330834 | − | 0.147297i | ||||
\(184\) | −24.9376 | − | 34.3237i | −1.83843 | − | 2.53038i | ||||
\(185\) | −4.94183 | − | 1.60570i | −0.363331 | − | 0.118053i | ||||
\(186\) | −11.0227 | − | 6.36396i | −0.808224 | − | 0.466628i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 27.7128i | 2.02116i | ||||||||
\(189\) | −2.27080 | + | 6.98881i | −0.165177 | + | 0.508361i | ||||
\(190\) | −9.70820 | + | 7.05342i | −0.704307 | + | 0.511709i | ||||
\(191\) | 3.05422 | − | 4.20378i | 0.220996 | − | 0.304175i | −0.684095 | − | 0.729393i | \(-0.739803\pi\) |
0.905091 | + | 0.425218i | \(0.139803\pi\) | |||||||
\(192\) | −2.88091 | + | 13.5536i | −0.207912 | + | 0.978148i | ||||
\(193\) | 13.4500 | − | 4.37016i | 0.968150 | − | 0.314571i | 0.218081 | − | 0.975931i | \(-0.430020\pi\) |
0.750069 | + | 0.661360i | \(0.230020\pi\) | |||||||
\(194\) | −25.7618 | − | 18.7171i | −1.84959 | − | 1.34381i | ||||
\(195\) | −8.43880 | + | 0.886953i | −0.604315 | + | 0.0635161i | ||||
\(196\) | 6.18034 | − | 19.0211i | 0.441453 | − | 1.35865i | ||||
\(197\) | −7.34847 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 3.02774 | − | 9.31841i | 0.214093 | − | 0.658911i | ||||
\(201\) | −5.16769 | + | 0.543146i | −0.364501 | + | 0.0383106i | ||||
\(202\) | 24.2705 | + | 17.6336i | 1.70767 | + | 1.24069i | ||||
\(203\) | −6.58911 | + | 2.14093i | −0.462465 | + | 0.150264i | ||||
\(204\) | 3.52838 | − | 16.5997i | 0.247036 | − | 1.16221i | ||||
\(205\) | 9.97505 | − | 13.7295i | 0.696687 | − | 0.958908i | ||||
\(206\) | 3.96336 | − | 2.87955i | 0.276140 | − | 0.200628i | ||||
\(207\) | 5.40170 | + | 25.4130i | 0.375444 | + | 1.76633i | ||||
\(208\) | − | 11.3137i | − | 0.784465i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.00000 | + | 5.19615i | 0.621059 | + | 0.358569i | ||||
\(211\) | −5.37999 | − | 1.74806i | −0.370374 | − | 0.120342i | 0.117915 | − | 0.993024i | \(-0.462379\pi\) |
−0.488289 | + | 0.872682i | \(0.662379\pi\) | |||||||
\(212\) | 8.14459 | + | 11.2101i | 0.559373 | + | 0.769911i | ||||
\(213\) | 2.74064 | − | 1.22021i | 0.187785 | − | 0.0836074i | ||||
\(214\) | −1.85410 | − | 5.70634i | −0.126744 | − | 0.390077i | ||||
\(215\) | 5.29854 | + | 16.3072i | 0.361357 | + | 1.11214i | ||||
\(216\) | −14.9626 | + | 20.5942i | −1.01807 | + | 1.40126i | ||||
\(217\) | 2.49376 | + | 3.43237i | 0.169288 | + | 0.233004i | ||||
\(218\) | −42.8292 | − | 13.9161i | −2.90076 | − | 0.942515i | ||||
\(219\) | 4.89898 | − | 8.48528i | 0.331042 | − | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.92820i | − | 0.466041i | ||||||
\(222\) | −9.45869 | + | 8.51664i | −0.634826 | + | 0.571600i | ||||
\(223\) | 8.89919 | − | 6.46564i | 0.595934 | − | 0.432971i | −0.248500 | − | 0.968632i | \(-0.579937\pi\) |
0.844433 | + | 0.535661i | \(0.179937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.01478 | + | 4.45887i | −0.267652 | + | 0.297258i | ||||
\(226\) | 4.03499 | − | 1.31105i | 0.268404 | − | 0.0872096i | ||||
\(227\) | 17.8351 | + | 12.9580i | 1.18376 | + | 0.860050i | 0.992591 | − | 0.121507i | \(-0.0387727\pi\) |
0.191167 | + | 0.981557i | \(0.438773\pi\) | |||||||
\(228\) | 2.04833 | + | 19.4886i | 0.135654 | + | 1.29066i | ||||
\(229\) | −2.78115 | + | 8.55951i | −0.183784 | + | 0.565628i | −0.999925 | − | 0.0122238i | \(-0.996109\pi\) |
0.816142 | + | 0.577852i | \(0.196109\pi\) | |||||||
\(230\) | 36.7423 | 2.42272 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.0000 | −1.57568 | ||||||||
\(233\) | 7.56934 | − | 23.2960i | 0.495884 | − | 1.52617i | −0.319691 | − | 0.947522i | \(-0.603579\pi\) |
0.815575 | − | 0.578652i | \(-0.196421\pi\) | |||||||
\(234\) | −8.45386 | + | 18.9877i | −0.552646 | + | 1.24126i | ||||
\(235\) | −9.70820 | − | 7.05342i | −0.633293 | − | 0.460115i | ||||
\(236\) | 6.58911 | − | 2.14093i | 0.428915 | − | 0.139363i | ||||
\(237\) | −16.7717 | − | 3.56494i | −1.08944 | − | 0.231568i | ||||
\(238\) | −4.98752 | + | 6.86474i | −0.323293 | + | 0.444975i | ||||
\(239\) | −17.8351 | + | 12.9580i | −1.15366 | + | 0.838181i | −0.988963 | − | 0.148164i | \(-0.952664\pi\) |
−0.164694 | + | 0.986345i | \(0.552664\pi\) | |||||||
\(240\) | 8.02957 | + | 8.91774i | 0.518306 | + | 0.575638i | ||||
\(241\) | 2.82843i | 0.182195i | 0.995842 | + | 0.0910975i | \(0.0290375\pi\) | ||||
−0.995842 | + | 0.0910975i | \(0.970963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | −10.7600 | − | 3.49613i | −0.688837 | − | 0.223817i | ||||
\(245\) | 5.09037 | + | 7.00629i | 0.325212 | + | 0.447616i | ||||
\(246\) | −16.9077 | − | 37.9754i | −1.07800 | − | 2.42122i | ||||
\(247\) | 2.47214 | + | 7.60845i | 0.157298 | + | 0.484114i | ||||
\(248\) | 4.54160 | + | 13.9776i | 0.288392 | + | 0.887580i | ||||
\(249\) | −1.72564 | − | 3.87585i | −0.109358 | − | 0.245622i | ||||
\(250\) | 17.4563 | + | 24.0266i | 1.10404 | + | 1.51957i | ||||
\(251\) | 14.8255 | + | 4.81710i | 0.935778 | + | 0.304053i | 0.736923 | − | 0.675977i | \(-0.236278\pi\) |
0.198854 | + | 0.980029i | \(0.436278\pi\) | |||||||
\(252\) | 14.6969 | − | 8.48528i | 0.925820 | − | 0.534522i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 6.92820i | − | 0.434714i | ||||||
\(255\) | 4.91709 | + | 5.46098i | 0.307920 | + | 0.341980i | ||||
\(256\) | 25.8885 | − | 18.8091i | 1.61803 | − | 1.17557i | ||||
\(257\) | −6.10844 | + | 8.40755i | −0.381034 | + | 0.524449i | −0.955858 | − | 0.293828i | \(-0.905071\pi\) |
0.574824 | + | 0.818277i | \(0.305071\pi\) | |||||||
\(258\) | 41.0822 | + | 8.73229i | 2.55767 | + | 0.543649i | ||||
\(259\) | 4.03499 | − | 1.31105i | 0.250722 | − | 0.0814646i | ||||
\(260\) | 15.8534 | + | 11.5182i | 0.983188 | + | 0.714328i | ||||
\(261\) | 13.4263 | + | 5.97778i | 0.831068 | + | 0.370016i | ||||
\(262\) | 9.27051 | − | 28.5317i | 0.572734 | − | 1.76269i | ||||
\(263\) | −12.2474 | −0.755210 | −0.377605 | − | 0.925967i | \(-0.623252\pi\) | ||||
−0.377605 | + | 0.925967i | \(0.623252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 3.02774 | − | 9.31841i | 0.185642 | − | 0.571349i | ||||
\(267\) | −1.56793 | − | 14.9178i | −0.0959556 | − | 0.912956i | ||||
\(268\) | 9.70820 | + | 7.05342i | 0.593023 | + | 0.430856i | ||||
\(269\) | 16.4728 | − | 5.35233i | 1.00436 | − | 0.326337i | 0.239755 | − | 0.970833i | \(-0.422933\pi\) |
0.764608 | + | 0.644496i | \(0.222933\pi\) | |||||||
\(270\) | −6.81241 | − | 20.9664i | −0.414590 | − | 1.27598i | ||||
\(271\) | −3.32502 | + | 4.57649i | −0.201980 | + | 0.278002i | −0.897976 | − | 0.440043i | \(-0.854963\pi\) |
0.695996 | + | 0.718045i | \(0.254963\pi\) | |||||||
\(272\) | −7.92672 | + | 5.75910i | −0.480628 | + | 0.349196i | ||||
\(273\) | 5.14866 | − | 4.63587i | 0.311611 | − | 0.280576i | ||||
\(274\) | 38.1838i | 2.30677i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 30.0000 | − | 51.9615i | 1.80579 | − | 3.12772i | ||||
\(277\) | 17.4850 | + | 5.68121i | 1.05057 | + | 0.341351i | 0.782892 | − | 0.622158i | \(-0.213744\pi\) |
0.267678 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(278\) | 22.3976 | + | 30.8277i | 1.34332 | + | 1.84892i | ||||
\(279\) | 0.940756 | − | 8.95070i | 0.0563216 | − | 0.535864i | ||||
\(280\) | −3.70820 | − | 11.4127i | −0.221608 | − | 0.682038i | ||||
\(281\) | −6.81241 | − | 20.9664i | −0.406394 | − | 1.25075i | −0.919726 | − | 0.392562i | \(-0.871589\pi\) |
0.513332 | − | 0.858190i | \(-0.328411\pi\) | |||||||
\(282\) | −26.8526 | + | 11.9556i | −1.59905 | + | 0.711944i | ||||
\(283\) | −11.6376 | − | 16.0177i | −0.691781 | − | 0.952155i | −1.00000 | 0.000839101i | \(-0.999733\pi\) | |
0.308219 | − | 0.951315i | \(-0.400267\pi\) | |||||||
\(284\) | −6.58911 | − | 2.14093i | −0.390992 | − | 0.127041i | ||||
\(285\) | −7.34847 | − | 4.24264i | −0.435286 | − | 0.251312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.8564i | 0.817918i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.89919 | − | 6.46564i | 0.523482 | − | 0.380332i | ||||
\(290\) | 12.2169 | − | 16.8151i | 0.717400 | − | 0.987417i | ||||
\(291\) | 4.68148 | − | 22.0246i | 0.274433 | − | 1.29111i | ||||
\(292\) | −21.5200 | + | 6.99226i | −1.25936 | + | 0.409191i | ||||
\(293\) | 3.96336 | + | 2.87955i | 0.231542 | + | 0.168225i | 0.697507 | − | 0.716578i | \(-0.254293\pi\) |
−0.465965 | + | 0.884803i | \(0.654293\pi\) | |||||||
\(294\) | 21.0970 | − | 2.21738i | 1.23040 | − | 0.129320i | ||||
\(295\) | −0.927051 | + | 2.85317i | −0.0539750 | + | 0.166118i | ||||
\(296\) | 14.6969 | 0.854242 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 7.56934 | − | 23.2960i | 0.437746 | − | 1.34724i | ||||
\(300\) | 13.7805 | − | 1.44839i | 0.795618 | − | 0.0836228i | ||||
\(301\) | −11.3262 | − | 8.22899i | −0.652834 | − | 0.474311i | ||||
\(302\) | −23.0619 | + | 7.49326i | −1.32706 | + | 0.431189i | ||||
\(303\) | −4.41047 | + | 20.7496i | −0.253375 | + | 1.19204i | ||||
\(304\) | 6.65003 | − | 9.15298i | 0.381405 | − | 0.524960i | ||||
\(305\) | 3.96336 | − | 2.87955i | 0.226941 | − | 0.164882i | ||||
\(306\) | 17.6067 | − | 3.74241i | 1.00651 | − | 0.213939i | ||||
\(307\) | 2.82843i | 0.161427i | 0.996737 | + | 0.0807134i | \(0.0257199\pi\) | ||||
−0.996737 | + | 0.0807134i | \(0.974280\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.00000 | + | 1.73205i | 0.170664 | + | 0.0985329i | ||||
\(310\) | −12.1050 | − | 3.93314i | −0.687516 | − | 0.223388i | ||||
\(311\) | 10.1807 | + | 14.0126i | 0.577297 | + | 0.794581i | 0.993396 | − | 0.114739i | \(-0.0366030\pi\) |
−0.416099 | + | 0.909319i | \(0.636603\pi\) | |||||||
\(312\) | 21.9251 | − | 9.76168i | 1.24126 | − | 0.552646i | ||||
\(313\) | −10.1976 | − | 31.3849i | −0.576400 | − | 1.77398i | −0.631361 | − | 0.775489i | \(-0.717503\pi\) |
0.0549609 | − | 0.998489i | \(-0.482497\pi\) | |||||||
\(314\) | 11.3540 | + | 34.9440i | 0.640744 | + | 1.97201i | ||||
\(315\) | −0.768124 | + | 7.30821i | −0.0432789 | + | 0.411771i | ||||
\(316\) | 23.2751 | + | 32.0354i | 1.30933 | + | 1.80213i | ||||
\(317\) | −1.64728 | − | 0.535233i | −0.0925204 | − | 0.0300617i | 0.262391 | − | 0.964962i | \(-0.415489\pi\) |
−0.354911 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(318\) | −7.34847 | + | 12.7279i | −0.412082 | + | 0.713746i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.8564i | 0.774597i | ||||||||
\(321\) | 3.15290 | − | 2.83888i | 0.175978 | − | 0.158451i | ||||
\(322\) | −24.2705 | + | 17.6336i | −1.35254 | + | 0.982680i | ||||
\(323\) | 4.07230 | − | 5.60503i | 0.226589 | − | 0.311872i | ||||
\(324\) | −35.2133 | − | 7.48482i | −1.95630 | − | 0.415823i | ||||
\(325\) | 5.37999 | − | 1.74806i | 0.298428 | − | 0.0969651i | ||||
\(326\) | 19.8168 | + | 14.3977i | 1.09755 | + | 0.797417i | ||||
\(327\) | −3.32854 | − | 31.6689i | −0.184069 | − | 1.75130i | ||||
\(328\) | −14.8328 | + | 45.6507i | −0.819005 | + | 2.52064i | ||||
\(329\) | 9.79796 | 0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | −3.02774 | + | 9.31841i | −0.166169 | + | 0.511414i | ||||
\(333\) | −8.22191 | − | 3.66063i | −0.450558 | − | 0.200601i | ||||
\(334\) | 38.8328 | + | 28.2137i | 2.12484 | + | 1.54378i | ||||
\(335\) | −4.94183 | + | 1.60570i | −0.270001 | + | 0.0877287i | ||||
\(336\) | −9.58385 | − | 2.03711i | −0.522842 | − | 0.111133i | ||||
\(337\) | 14.1313 | − | 19.4501i | 0.769782 | − | 1.05951i | −0.226555 | − | 0.973998i | \(-0.572746\pi\) |
0.996337 | − | 0.0855154i | \(-0.0272537\pi\) | |||||||
\(338\) | −9.90839 | + | 7.19887i | −0.538946 | + | 0.391567i | ||||
\(339\) | 2.00739 | + | 2.22943i | 0.109027 | + | 0.121086i | ||||
\(340\) | − | 16.9706i | − | 0.920358i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −18.0000 | + | 10.3923i | −0.973329 | + | 0.561951i | ||||
\(343\) | −16.1400 | − | 5.24419i | −0.871476 | − | 0.283160i | ||||
\(344\) | −28.5061 | − | 39.2352i | −1.53694 | − | 2.11542i | ||||
\(345\) | 10.5673 | + | 23.7346i | 0.568926 | + | 1.27783i | ||||
\(346\) | 1.85410 | + | 5.70634i | 0.0996771 | + | 0.306775i | ||||
\(347\) | 3.02774 | + | 9.31841i | 0.162537 | + | 0.500239i | 0.998846 | − | 0.0480198i | \(-0.0152910\pi\) |
−0.836309 | + | 0.548258i | \(0.815291\pi\) | |||||||
\(348\) | −13.8051 | − | 31.0068i | −0.740031 | − | 1.66214i | ||||
\(349\) | −5.81878 | − | 8.00886i | −0.311472 | − | 0.428704i | 0.624368 | − | 0.781131i | \(-0.285357\pi\) |
−0.935840 | + | 0.352426i | \(0.885357\pi\) | |||||||
\(350\) | −6.58911 | − | 2.14093i | −0.352203 | − | 0.114438i | ||||
\(351\) | −14.6969 | −0.784465 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9808i | 1.38282i | 0.722464 | + | 0.691408i | \(0.243009\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(354\) | 4.91709 | + | 5.46098i | 0.261340 | + | 0.290248i | ||||
\(355\) | 2.42705 | − | 1.76336i | 0.128814 | − | 0.0935892i | ||||
\(356\) | −20.3615 | + | 28.0252i | −1.07916 | + | 1.48533i | ||||
\(357\) | −5.86889 | − | 1.24747i | −0.310614 | − | 0.0660231i | ||||
\(358\) | −36.3149 | + | 11.7994i | −1.91930 | + | 0.623619i | ||||
\(359\) | −19.8168 | − | 14.3977i | −1.04589 | − | 0.759884i | −0.0744635 | − | 0.997224i | \(-0.523724\pi\) |
−0.971427 | + | 0.237340i | \(0.923724\pi\) | |||||||
\(360\) | −10.3538 | + | 23.2551i | −0.545694 | + | 1.22565i | ||||
\(361\) | 3.39919 | − | 10.4616i | 0.178905 | − | 0.550612i | ||||
\(362\) | −12.2474 | −0.643712 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.0000 | −0.838628 | ||||||||
\(365\) | 3.02774 | − | 9.31841i | 0.158479 | − | 0.487748i | ||||
\(366\) | −1.25434 | − | 11.9343i | −0.0655655 | − | 0.623814i | ||||
\(367\) | 5.66312 | + | 4.11450i | 0.295612 | + | 0.214775i | 0.725698 | − | 0.688013i | \(-0.241517\pi\) |
−0.430086 | + | 0.902788i | \(0.641517\pi\) | |||||||
\(368\) | −32.9456 | + | 10.7047i | −1.71741 | + | 0.558019i | ||||
\(369\) | 19.6683 | − | 21.8439i | 1.02389 | − | 1.13715i | ||||
\(370\) | −7.48128 | + | 10.2971i | −0.388933 | + | 0.535321i | ||||
\(371\) | 3.96336 | − | 2.87955i | 0.205767 | − | 0.149499i | ||||
\(372\) | −15.4460 | + | 13.9076i | −0.800837 | + | 0.721076i | ||||
\(373\) | − | 32.5269i | − | 1.68418i | −0.539337 | − | 0.842090i | \(-0.681325\pi\) | ||
0.539337 | − | 0.842090i | \(-0.318675\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5000 | + | 18.1865i | −0.542218 | + | 0.939149i | ||||
\(376\) | 32.2799 | + | 10.4884i | 1.66471 | + | 0.540897i | ||||
\(377\) | −8.14459 | − | 11.2101i | −0.419468 | − | 0.577348i | ||||
\(378\) | 14.5623 | + | 10.5801i | 0.749004 | + | 0.544183i | ||||
\(379\) | 5.25329 | + | 16.1680i | 0.269843 | + | 0.830492i | 0.990538 | + | 0.137240i | \(0.0438230\pi\) |
−0.720695 | + | 0.693253i | \(0.756177\pi\) | |||||||
\(380\) | 6.05547 | + | 18.6368i | 0.310639 | + | 0.956049i | ||||
\(381\) | 4.47544 | − | 1.99259i | 0.229284 | − | 0.102084i | ||||
\(382\) | −7.48128 | − | 10.2971i | −0.382776 | − | 0.526846i | ||||
\(383\) | 21.4146 | + | 6.95803i | 1.09424 | + | 0.355539i | 0.799882 | − | 0.600158i | \(-0.204896\pi\) |
0.294354 | + | 0.955696i | \(0.404896\pi\) | |||||||
\(384\) | 29.3939 | + | 16.9706i | 1.50000 | + | 0.866025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 34.6410i | − | 1.76318i | ||||||
\(387\) | 6.17466 | + | 29.0495i | 0.313876 | + | 1.47667i | ||||
\(388\) | −42.0689 | + | 30.5648i | −2.13572 | + | 1.55169i | ||||
\(389\) | 13.2350 | − | 18.2164i | 0.671039 | − | 0.923606i | −0.328744 | − | 0.944419i | \(-0.606625\pi\) |
0.999783 | + | 0.0208128i | \(0.00662541\pi\) | |||||||
\(390\) | −4.32136 | + | 20.3304i | −0.218821 | + | 1.02947i | ||||
\(391\) | −20.1750 | + | 6.55524i | −1.02029 | + | 0.331513i | ||||
\(392\) | −19.8168 | − | 14.3977i | −1.00090 | − | 0.727196i | ||||
\(393\) | 21.0970 | − | 2.21738i | 1.06420 | − | 0.111852i | ||||
\(394\) | −5.56231 | + | 17.1190i | −0.280225 | + | 0.862444i | ||||
\(395\) | −17.1464 | −0.862730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0000 | 1.60603 | 0.803017 | − | 0.595956i | \(-0.203227\pi\) | ||||
0.803017 | + | 0.595956i | \(0.203227\pi\) | |||||||
\(398\) | −13.6248 | + | 41.9329i | −0.682950 | + | 2.10190i | ||||
\(399\) | 6.89025 | − | 0.724194i | 0.344944 | − | 0.0362551i | ||||
\(400\) | −6.47214 | − | 4.70228i | −0.323607 | − | 0.235114i | ||||
\(401\) | 9.88367 | − | 3.21140i | 0.493567 | − | 0.160370i | −0.0516490 | − | 0.998665i | \(-0.516448\pi\) |
0.545216 | + | 0.838296i | \(0.316448\pi\) | |||||||
\(402\) | −2.64628 | + | 12.4498i | −0.131985 | + | 0.620939i | ||||
\(403\) | −4.98752 | + | 6.86474i | −0.248446 | + | 0.341957i | ||||
\(404\) | 39.6336 | − | 28.7955i | 1.97184 | − | 1.43263i | ||||
\(405\) | 11.5845 | − | 10.4307i | 0.575638 | − | 0.518306i | ||||
\(406\) | 16.9706i | 0.842235i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.0000 | − | 10.3923i | −0.891133 | − | 0.514496i | ||||
\(409\) | 17.4850 | + | 5.68121i | 0.864576 | + | 0.280918i | 0.707538 | − | 0.706675i | \(-0.249806\pi\) |
0.157037 | + | 0.987593i | \(0.449806\pi\) | |||||||
\(410\) | −24.4338 | − | 33.6302i | −1.20670 | − | 1.66088i | ||||
\(411\) | −24.6657 | + | 10.9819i | −1.21667 | + | 0.541697i | ||||
\(412\) | −2.47214 | − | 7.60845i | −0.121793 | − | 0.374842i | ||||
\(413\) | −0.756934 | − | 2.32960i | −0.0372463 | − | 0.114632i | ||||
\(414\) | 63.2910 | + | 6.65215i | 3.11058 | + | 0.326935i | ||||
\(415\) | −2.49376 | − | 3.43237i | −0.122414 | − | 0.168488i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.4722 | + | 23.3345i | −0.659736 | + | 1.14270i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.92820i | − | 0.338465i | −0.985576 | − | 0.169232i | \(-0.945871\pi\) | ||
0.985576 | − | 0.169232i | \(-0.0541289\pi\) | |||||||
\(420\) | 12.6116 | − | 11.3555i | 0.615382 | − | 0.554093i | ||||
\(421\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(422\) | −8.14459 | + | 11.2101i | −0.396473 | + | 0.545698i | ||||
\(423\) | −15.4460 | − | 13.9076i | −0.751009 | − | 0.676212i | ||||
\(424\) | 16.1400 | − | 5.24419i | 0.783826 | − | 0.254680i | ||||
\(425\) | −3.96336 | − | 2.87955i | −0.192251 | − | 0.139679i | ||||
\(426\) | −0.768124 | − | 7.30821i | −0.0372157 | − | 0.354084i | ||||
\(427\) | −1.23607 | + | 3.80423i | −0.0598175 | + | 0.184099i | ||||
\(428\) | −9.79796 | −0.473602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 42.0000 | 2.02542 | ||||||||
\(431\) | 2.27080 | − | 6.98881i | 0.109381 | − | 0.336639i | −0.881353 | − | 0.472458i | \(-0.843367\pi\) |
0.990734 | + | 0.135819i | \(0.0433667\pi\) | |||||||
\(432\) | 12.2169 | + | 16.8151i | 0.587785 | + | 0.809017i | ||||
\(433\) | −4.04508 | − | 2.93893i | −0.194394 | − | 0.141236i | 0.486331 | − | 0.873775i | \(-0.338335\pi\) |
−0.680725 | + | 0.732539i | \(0.738335\pi\) | |||||||
\(434\) | 9.88367 | − | 3.21140i | 0.474431 | − | 0.154152i | ||||
\(435\) | 14.3758 | + | 3.05567i | 0.689266 | + | 0.146508i | ||||
\(436\) | −43.2252 | + | 59.4944i | −2.07011 | + | 2.84926i | ||||
\(437\) | 19.8168 | − | 14.3977i | 0.947966 | − | 0.688737i | ||||
\(438\) | −16.0591 | − | 17.8355i | −0.767335 | − | 0.852212i | ||||
\(439\) | 5.65685i | 0.269987i | 0.990846 | + | 0.134993i | \(0.0431013\pi\) | ||||
−0.990846 | + | 0.134993i | \(0.956899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.50000 | + | 12.9904i | 0.357143 | + | 0.618590i | ||||
\(442\) | −16.1400 | − | 5.24419i | −0.767700 | − | 0.249441i | ||||
\(443\) | 15.2711 | + | 21.0189i | 0.725552 | + | 0.998637i | 0.999321 | + | 0.0368415i | \(0.0117297\pi\) |
−0.273769 | + | 0.961796i | \(0.588270\pi\) | |||||||
\(444\) | 8.45386 | + | 18.9877i | 0.401203 | + | 0.901116i | ||||
\(445\) | −4.63525 | − | 14.2658i | −0.219732 | − | 0.676266i | ||||
\(446\) | −8.32627 | − | 25.6256i | −0.394260 | − | 1.21341i | ||||
\(447\) | 1.72564 | + | 3.87585i | 0.0816198 | + | 0.183321i | ||||
\(448\) | −6.65003 | − | 9.15298i | −0.314184 | − | 0.432438i | ||||
\(449\) | −11.5309 | − | 3.74663i | −0.544179 | − | 0.176814i | 0.0240112 | − | 0.999712i | \(-0.492356\pi\) |
−0.568190 | + | 0.822897i | \(0.692356\pi\) | |||||||
\(450\) | 7.34847 | + | 12.7279i | 0.346410 | + | 0.600000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.92820i | − | 0.325875i | ||||||
\(453\) | −11.4732 | − | 12.7423i | −0.539058 | − | 0.598685i | ||||
\(454\) | 43.6869 | − | 31.7404i | 2.05033 | − | 1.48965i | ||||
\(455\) | 4.07230 | − | 5.60503i | 0.190912 | − | 0.262768i | ||||
\(456\) | 23.4755 | + | 4.98988i | 1.09934 | + | 0.233673i | ||||
\(457\) | 29.5899 | − | 9.61435i | 1.38416 | − | 0.449740i | 0.480124 | − | 0.877200i | \(-0.340591\pi\) |
0.904034 | + | 0.427460i | \(0.140591\pi\) | |||||||
\(458\) | 17.8351 | + | 12.9580i | 0.833380 | + | 0.605486i | ||||
\(459\) | 7.48128 | + | 10.2971i | 0.349196 | + | 0.480628i | ||||
\(460\) | 18.5410 | − | 57.0634i | 0.864479 | − | 2.66059i | ||||
\(461\) | 4.89898 | 0.228168 | 0.114084 | − | 0.993471i | \(-0.463607\pi\) | ||||
0.114084 | + | 0.993471i | \(0.463607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0000 | 0.883005 | 0.441502 | − | 0.897260i | \(-0.354446\pi\) | ||||
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(464\) | −6.05547 | + | 18.6368i | −0.281118 | + | 0.865193i | ||||
\(465\) | −0.940756 | − | 8.95070i | −0.0436265 | − | 0.415079i | ||||
\(466\) | −48.5410 | − | 35.2671i | −2.24862 | − | 1.63372i | ||||
\(467\) | 24.7092 | − | 8.02850i | 1.14340 | − | 0.371515i | 0.324749 | − | 0.945800i | \(-0.394720\pi\) |
0.818655 | + | 0.574286i | \(0.194720\pi\) | |||||||
\(468\) | 25.2232 | + | 22.7110i | 1.16594 | + | 1.04982i | ||||
\(469\) | 2.49376 | − | 3.43237i | 0.115151 | − | 0.158492i | ||||
\(470\) | −23.7801 | + | 17.2773i | −1.09690 | + | 0.796942i | ||||
\(471\) | −19.3075 | + | 17.3845i | −0.889641 | + | 0.801037i | ||||
\(472\) | − | 8.48528i | − | 0.390567i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −21.0000 | + | 36.3731i | −0.964562 | + | 1.67067i | ||||
\(475\) | 5.37999 | + | 1.74806i | 0.246851 | + | 0.0802067i | ||||
\(476\) | 8.14459 | + | 11.2101i | 0.373307 | + | 0.513813i | ||||
\(477\) | −10.3354 | − | 1.08629i | −0.473224 | − | 0.0497379i | ||||
\(478\) | 16.6869 | + | 51.3571i | 0.763242 | + | 2.34902i | ||||
\(479\) | −9.08321 | − | 27.9552i | −0.415022 | − | 1.27731i | −0.912231 | − | 0.409676i | \(-0.865642\pi\) |
0.497209 | − | 0.867631i | \(-0.334358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.98752 | + | 6.86474i | 0.227411 | + | 0.313005i | ||||
\(482\) | 6.58911 | + | 2.14093i | 0.300126 | + | 0.0975168i | ||||
\(483\) | −18.3712 | − | 10.6066i | −0.835917 | − | 0.482617i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 22.5167i | − | 1.02243i | ||||||
\(486\) | −7.93885 | − | 37.3494i | −0.360114 | − | 1.69420i | ||||
\(487\) | −21.8435 | + | 15.8702i | −0.989822 | + | 0.719147i | −0.959882 | − | 0.280404i | \(-0.909531\pi\) |
−0.0299396 | + | 0.999552i | \(0.509531\pi\) | |||||||
\(488\) | −8.14459 | + | 11.2101i | −0.368688 | + | 0.507456i | ||||
\(489\) | −3.60114 | + | 16.9420i | −0.162849 | + | 0.766144i | ||||
\(490\) | 20.1750 | − | 6.55524i | 0.911412 | − | 0.296136i | ||||
\(491\) | 19.8168 | + | 14.3977i | 0.894319 | + | 0.649761i | 0.937001 | − | 0.349328i | \(-0.113590\pi\) |
−0.0426814 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(492\) | −67.5104 | + | 7.09563i | −3.04360 | + | 0.319896i | ||||
\(493\) | −3.70820 | + | 11.4127i | −0.167009 | + | 0.514001i | ||||
\(494\) | 19.5959 | 0.881662 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | −0.756934 | + | 2.32960i | −0.0339531 | + | 0.104497i | ||||
\(498\) | −10.3354 | + | 1.08629i | −0.463139 | + | 0.0486779i | ||||
\(499\) | −4.85410 | − | 3.52671i | −0.217299 | − | 0.157877i | 0.473811 | − | 0.880627i | \(-0.342878\pi\) |
−0.691110 | + | 0.722749i | \(0.742878\pi\) | |||||||
\(500\) | 46.1238 | − | 14.9865i | 2.06272 | − | 0.670218i | ||||
\(501\) | −7.05676 | + | 33.1994i | −0.315273 | + | 1.48324i | ||||
\(502\) | 22.4439 | − | 30.8913i | 1.00172 | − | 1.37875i | ||||
\(503\) | −17.8351 | + | 12.9580i | −0.795228 | + | 0.577767i | −0.909510 | − | 0.415681i | \(-0.863543\pi\) |
0.114282 | + | 0.993448i | \(0.463543\pi\) | |||||||
\(504\) | −4.32136 | − | 20.3304i | −0.192489 | − | 0.905589i | ||||
\(505\) | 21.2132i | 0.943975i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.50000 | − | 4.33013i | −0.333087 | − | 0.192308i | ||||
\(508\) | −10.7600 | − | 3.49613i | −0.477397 | − | 0.155116i | ||||
\(509\) | 17.3073 | + | 23.8214i | 0.767131 | + | 1.05586i | 0.996587 | + | 0.0825459i | \(0.0263051\pi\) |
−0.229457 | + | 0.973319i | \(0.573695\pi\) | |||||||
\(510\) | 16.4438 | − | 7.32126i | 0.728145 | − | 0.324191i | ||||
\(511\) | 2.47214 | + | 7.60845i | 0.109361 | + | 0.336578i | ||||
\(512\) | −12.1109 | − | 37.2737i | −0.535233 | − | 1.64728i | ||||
\(513\) | −11.8901 | − | 8.63864i | −0.524960 | − | 0.381405i | ||||
\(514\) | 14.9626 | + | 20.5942i | 0.659971 | + | 0.908372i | ||||
\(515\) | 3.29456 | + | 1.07047i | 0.145176 | + | 0.0471704i | ||||
\(516\) | 34.2929 | − | 59.3970i | 1.50966 | − | 2.61481i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 10.3923i | − | 0.456612i | ||||||
\(519\) | −3.15290 | + | 2.83888i | −0.138397 | + | 0.124613i | ||||
\(520\) | 19.4164 | − | 14.1068i | 0.851466 | − | 0.618626i | ||||
\(521\) | 23.4157 | − | 32.2289i | 1.02586 | − | 1.41198i | 0.117848 | − | 0.993032i | \(-0.462400\pi\) |
0.908012 | − | 0.418944i | \(-0.137600\pi\) | |||||||
\(522\) | 24.0887 | − | 26.7532i | 1.05433 | − | 1.17096i | ||||
\(523\) | −26.8999 | + | 8.74032i | −1.17625 | + | 0.382188i | −0.830973 | − | 0.556313i | \(-0.812216\pi\) |
−0.345279 | + | 0.938500i | \(0.612216\pi\) | |||||||
\(524\) | −39.6336 | − | 28.7955i | −1.73140 | − | 1.25794i | ||||
\(525\) | −0.512083 | − | 4.87214i | −0.0223491 | − | 0.212638i | ||||
\(526\) | −9.27051 | + | 28.5317i | −0.404213 | + | 1.24404i | ||||
\(527\) | 7.34847 | 0.320104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.0000 | −2.26087 | ||||||||
\(530\) | −4.54160 | + | 13.9776i | −0.197275 | + | 0.607149i | ||||
\(531\) | −2.11347 | + | 4.74692i | −0.0917166 | + | 0.205999i | ||||
\(532\) | −12.9443 | − | 9.40456i | −0.561205 | − | 0.407740i | ||||
\(533\) | −26.3565 | + | 8.56373i | −1.14162 | + | 0.370936i | ||||
\(534\) | −35.9394 | − | 7.63916i | −1.55525 | − | 0.330579i | ||||
\(535\) | 2.49376 | − | 3.43237i | 0.107815 | − | 0.148394i | ||||
\(536\) | 11.8901 | − | 8.63864i | 0.513573 | − | 0.373133i | ||||
\(537\) | −18.0665 | − | 20.0649i | −0.779628 | − | 0.865865i | ||||
\(538\) | − | 42.4264i | − | 1.82913i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −36.0000 | −1.54919 | ||||||||
\(541\) | −13.4500 | − | 4.37016i | −0.578259 | − | 0.187888i | 0.00526127 | − | 0.999986i | \(-0.498325\pi\) |
−0.583521 | + | 0.812098i | \(0.698325\pi\) | |||||||
\(542\) | 8.14459 | + | 11.2101i | 0.349840 | + | 0.481514i | ||||
\(543\) | −3.52244 | − | 7.91154i | −0.151162 | − | 0.339516i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.84014 | − | 30.2848i | −0.421505 | − | 1.29726i | ||||
\(546\) | −6.90255 | − | 15.5034i | −0.295402 | − | 0.663483i | ||||
\(547\) | 8.31254 | + | 11.4412i | 0.355418 | + | 0.489192i | 0.948865 | − | 0.315682i | \(-0.102233\pi\) |
−0.593447 | + | 0.804873i | \(0.702233\pi\) | |||||||
\(548\) | 59.3020 | + | 19.2684i | 2.53326 | + | 0.823105i | ||||
\(549\) | 7.34847 | − | 4.24264i | 0.313625 | − | 0.181071i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8564i | − | 0.590303i | ||||||
\(552\) | −49.1709 | − | 54.6098i | −2.09285 | − | 2.32435i | ||||
\(553\) | 11.3262 | − | 8.22899i | 0.481641 | − | 0.349932i | ||||
\(554\) | 26.4699 | − | 36.4327i | 1.12460 | − | 1.54788i | ||||
\(555\) | −8.80333 | − | 1.87121i | −0.373680 | − | 0.0794282i | ||||
\(556\) | 59.1799 | − | 19.2287i | 2.50979 | − | 0.815479i | ||||
\(557\) | −25.7618 | − | 18.7171i | −1.09156 | − | 0.793067i | −0.111901 | − | 0.993719i | \(-0.535694\pi\) |
−0.979663 | + | 0.200652i | \(0.935694\pi\) | |||||||
\(558\) | −20.1395 | − | 8.96668i | −0.852572 | − | 0.379590i | ||||
\(559\) | 8.65248 | − | 26.6296i | 0.365961 | − | 1.12631i | ||||
\(560\) | −9.79796 | −0.414039 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.0000 | −2.27785 | ||||||||
\(563\) | 1.51387 | − | 4.65921i | 0.0638019 | − | 0.196362i | −0.914074 | − | 0.405547i | \(-0.867081\pi\) |
0.977876 | + | 0.209185i | \(0.0670810\pi\) | |||||||
\(564\) | 5.01737 | + | 47.7371i | 0.211269 | + | 2.01009i | ||||
\(565\) | 2.42705 | + | 1.76336i | 0.102107 | + | 0.0741849i | ||||
\(566\) | −46.1238 | + | 14.9865i | −1.93873 | + | 0.629931i | ||||
\(567\) | −2.64628 | + | 12.4498i | −0.111133 | + | 0.522842i | ||||
\(568\) | −4.98752 | + | 6.86474i | −0.209272 | + | 0.288038i | ||||
\(569\) | −23.7801 | + | 17.2773i | −0.996916 | + | 0.724302i | −0.961425 | − | 0.275068i | \(-0.911299\pi\) |
−0.0354909 | + | 0.999370i | \(0.511299\pi\) | |||||||
\(570\) | −15.4460 | + | 13.9076i | −0.646961 | + | 0.582526i | ||||
\(571\) | 19.7990i | 0.828562i | 0.910149 | + | 0.414281i | \(0.135967\pi\) | ||||
−0.910149 | + | 0.414281i | \(0.864033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.50000 | − | 7.79423i | 0.187990 | − | 0.325609i | ||||
\(574\) | 32.2799 | + | 10.4884i | 1.34734 | + | 0.437777i | ||||
\(575\) | −10.1807 | − | 14.0126i | −0.424566 | − | 0.584365i | ||||
\(576\) | −2.50868 | + | 23.8685i | −0.104528 | + | 0.994522i | ||||
\(577\) | 0.927051 | + | 2.85317i | 0.0385936 | + | 0.118779i | 0.968497 | − | 0.249024i | \(-0.0801099\pi\) |
−0.929904 | + | 0.367803i | \(0.880110\pi\) | |||||||
\(578\) | −8.32627 | − | 25.6256i | −0.346327 | − | 1.06589i | ||||
\(579\) | 22.3772 | − | 9.96297i | 0.929965 | − | 0.414047i | ||||
\(580\) | −19.9501 | − | 27.4589i | −0.828383 | − | 1.14017i | ||||
\(581\) | 3.29456 | + | 1.07047i | 0.136681 | + | 0.0444104i | ||||
\(582\) | −47.7650 | − | 27.5772i | −1.97993 | − | 1.14311i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 27.7128i | 1.14676i | ||||||||
\(585\) | −14.3758 | + | 3.05567i | −0.594365 | + | 0.126336i | ||||
\(586\) | 9.70820 | − | 7.05342i | 0.401042 | − | 0.291374i | ||||
\(587\) | −16.2892 | + | 22.4201i | −0.672327 | + | 0.925378i | −0.999810 | − | 0.0194787i | \(-0.993799\pi\) |
0.327484 | + | 0.944857i | \(0.393799\pi\) | |||||||
\(588\) | 7.20227 | − | 33.8840i | 0.297017 | − | 1.39735i | ||||
\(589\) | −8.06998 | + | 2.62210i | −0.332518 | + | 0.108042i | ||||
\(590\) | 5.94504 | + | 4.31932i | 0.244753 | + | 0.177824i | ||||
\(591\) | −12.6582 | + | 1.33043i | −0.520689 | + | 0.0547266i | ||||
\(592\) | 3.70820 | − | 11.4127i | 0.152406 | − | 0.469058i | ||||
\(593\) | 19.5959 | 0.804708 | 0.402354 | − | 0.915484i | \(-0.368192\pi\) | ||||
0.402354 | + | 0.915484i | \(0.368192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 3.02774 | − | 9.31841i | 0.124021 | − | 0.381697i | ||||
\(597\) | −31.0061 | + | 3.25887i | −1.26900 | + | 0.133377i | ||||
\(598\) | −48.5410 | − | 35.2671i | −1.98499 | − | 1.44218i | ||||
\(599\) | 19.7673 | − | 6.42280i | 0.807672 | − | 0.262428i | 0.124060 | − | 0.992275i | \(-0.460408\pi\) |
0.683611 | + | 0.729846i | \(0.260408\pi\) | |||||||
\(600\) | 3.52838 | − | 16.5997i | 0.144045 | − | 0.677681i | ||||
\(601\) | 0.831254 | − | 1.14412i | 0.0339076 | − | 0.0466697i | −0.791727 | − | 0.610876i | \(-0.790818\pi\) |
0.825634 | + | 0.564206i | \(0.190818\pi\) | |||||||
\(602\) | −27.7435 | + | 20.1568i | −1.13074 | + | 0.821531i | ||||
\(603\) | −8.80333 | + | 1.87121i | −0.358499 | + | 0.0762014i | ||||
\(604\) | 39.5980i | 1.61122i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 45.0000 | + | 25.9808i | 1.82800 | + | 1.05540i | ||||
\(607\) | −9.41498 | − | 3.05911i | −0.382142 | − | 0.124166i | 0.111645 | − | 0.993748i | \(-0.464388\pi\) |
−0.493788 | + | 0.869583i | \(0.664388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.9625 | + | 4.88084i | −0.444225 | + | 0.197782i | ||||
\(610\) | −3.70820 | − | 11.4127i | −0.150141 | − | 0.462086i | ||||
\(611\) | 6.05547 | + | 18.6368i | 0.244978 | + | 0.753965i | ||||
\(612\) | 3.07250 | − | 29.2329i | 0.124198 | − | 1.18167i | ||||
\(613\) | 6.65003 | + | 9.15298i | 0.268592 | + | 0.369685i | 0.921914 | − | 0.387395i | \(-0.126625\pi\) |
−0.653322 | + | 0.757081i | \(0.726625\pi\) | |||||||
\(614\) | 6.58911 | + | 2.14093i | 0.265915 | + | 0.0864010i | ||||
\(615\) | 14.6969 | − | 25.4558i | 0.592638 | − | 1.02648i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3923i | 0.418378i | 0.977875 | + | 0.209189i | \(0.0670825\pi\) | ||||
−0.977875 | + | 0.209189i | \(0.932918\pi\) | |||||||
\(618\) | 6.30579 | − | 5.67776i | 0.253656 | − | 0.228393i | ||||
\(619\) | 20.2254 | − | 14.6946i | 0.812928 | − | 0.590627i | −0.101750 | − | 0.994810i | \(-0.532444\pi\) |
0.914678 | + | 0.404183i | \(0.132444\pi\) | |||||||
\(620\) | −12.2169 | + | 16.8151i | −0.490642 | + | 0.675311i | ||||
\(621\) | 13.9058 | + | 42.7975i | 0.558019 | + | 1.71741i | ||||
\(622\) | 40.3499 | − | 13.1105i | 1.61788 | − | 0.525682i | ||||
\(623\) | 9.90839 | + | 7.19887i | 0.396971 | + | 0.288417i | ||||
\(624\) | −2.04833 | − | 19.4886i | −0.0819989 | − | 0.780167i | ||||
\(625\) | −3.39919 | + | 10.4616i | −0.135967 | + | 0.418465i | ||||
\(626\) | −80.8332 | −3.23074 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 60.0000 | 2.39426 | ||||||||
\(629\) | 2.27080 | − | 6.98881i | 0.0905428 | − | 0.278662i | ||||
\(630\) | 16.4438 | + | 7.32126i | 0.655137 | + | 0.291686i | ||||
\(631\) | 31.5517 | + | 22.9236i | 1.25605 | + | 0.912575i | 0.998557 | − | 0.0537045i | \(-0.0171029\pi\) |
0.257495 | + | 0.966280i | \(0.417103\pi\) | |||||||
\(632\) | 46.1238 | − | 14.9865i | 1.83471 | − | 0.596132i | ||||
\(633\) | −9.58385 | − | 2.03711i | −0.380924 | − | 0.0809679i | ||||
\(634\) | −2.49376 | + | 3.43237i | −0.0990399 | + | 0.136317i | ||||
\(635\) | 3.96336 | − | 2.87955i | 0.157281 | − | 0.114271i | ||||
\(636\) | 16.0591 | + | 17.8355i | 0.636786 | + | 0.707223i | ||||
\(637\) | − | 14.1421i | − | 0.560332i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.50000 | − | 2.59808i | 0.178017 | − | 0.102778i | ||||
\(640\) | 32.2799 | + | 10.4884i | 1.27598 | + | 0.414590i | ||||
\(641\) | −5.09037 | − | 7.00629i | −0.201058 | − | 0.276732i | 0.696568 | − | 0.717491i | \(-0.254709\pi\) |
−0.897626 | + | 0.440759i | \(0.854709\pi\) | |||||||
\(642\) | −4.22693 | − | 9.49384i | −0.166824 | − | 0.374692i | ||||
\(643\) | 2.16312 | + | 6.65740i | 0.0853051 | + | 0.262542i | 0.984606 | − | 0.174788i | \(-0.0559241\pi\) |
−0.899301 | + | 0.437330i | \(0.855924\pi\) | |||||||
\(644\) | 15.1387 | + | 46.5921i | 0.596548 | + | 1.83598i | ||||
\(645\) | 12.0795 | + | 27.1309i | 0.475628 | + | 1.06828i | ||||
\(646\) | −9.97505 | − | 13.7295i | −0.392463 | − | 0.540179i | ||||
\(647\) | −28.0037 | − | 9.09896i | −1.10094 | − | 0.357717i | −0.298476 | − | 0.954417i | \(-0.596478\pi\) |
−0.802464 | + | 0.596700i | \(0.796478\pi\) | |||||||
\(648\) | −22.0454 | + | 38.1838i | −0.866025 | + | 1.50000i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 13.8564i | − | 0.543493i | ||||||
\(651\) | 4.91709 | + | 5.46098i | 0.192716 | + | 0.214033i | ||||
\(652\) | 32.3607 | − | 23.5114i | 1.26734 | − | 0.920778i | ||||
\(653\) | −1.01807 | + | 1.40126i | −0.0398403 | + | 0.0548355i | −0.828472 | − | 0.560030i | \(-0.810790\pi\) |
0.788632 | + | 0.614865i | \(0.210790\pi\) | |||||||
\(654\) | −76.2955 | − | 16.2171i | −2.98339 | − | 0.634139i | ||||
\(655\) | 20.1750 | − | 6.55524i | 0.788301 | − | 0.256134i | ||||
\(656\) | 31.7069 | + | 23.0364i | 1.23794 | + | 0.899420i | ||||
\(657\) | 6.90255 | − | 15.5034i | 0.269294 | − | 0.604844i | ||||
\(658\) | 7.41641 | − | 22.8254i | 0.289122 | − | 0.889825i | ||||
\(659\) | 36.7423 | 1.43128 | 0.715639 | − | 0.698470i | \(-0.246135\pi\) | ||||
0.715639 | + | 0.698470i | \(0.246135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0000 | 0.583432 | 0.291716 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291716 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(662\) | 3.78467 | − | 11.6480i | 0.147095 | − | 0.452713i | ||||
\(663\) | −1.25434 | − | 11.9343i | −0.0487146 | − | 0.463488i | ||||
\(664\) | 9.70820 | + | 7.05342i | 0.376751 | + | 0.273726i | ||||
\(665\) | 6.58911 | − | 2.14093i | 0.255515 | − | 0.0830218i | ||||
\(666\) | −14.7513 | + | 16.3829i | −0.571600 | + | 0.634826i | ||||
\(667\) | −24.9376 | + | 34.3237i | −0.965588 | + | 1.32902i | ||||
\(668\) | 63.4137 | − | 46.0728i | 2.45355 | − | 1.78261i | ||||
\(669\) | 14.1588 | − | 12.7487i | 0.547411 | − | 0.492891i | ||||
\(670\) | 12.7279i | 0.491723i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.9349 | + | 10.0514i | 1.19245 | + | 0.387452i | 0.836980 | − | 0.547234i | \(-0.184319\pi\) |
0.355474 | + | 0.934686i | \(0.384319\pi\) | |||||||
\(674\) | −34.6145 | − | 47.6428i | −1.33330 | − | 1.83513i | ||||
\(675\) | −6.10844 | + | 8.40755i | −0.235114 | + | 0.323607i | ||||
\(676\) | 6.18034 | + | 19.0211i | 0.237705 | + | 0.731582i | ||||
\(677\) | 12.8679 | + | 39.6033i | 0.494553 | + | 1.52208i | 0.817653 | + | 0.575712i | \(0.195275\pi\) |
−0.323100 | + | 0.946365i | \(0.604725\pi\) | |||||||
\(678\) | 6.71316 | − | 2.98889i | 0.257817 | − | 0.114788i | ||||
\(679\) | 10.8063 | + | 14.8736i | 0.414708 | + | 0.570796i | ||||
\(680\) | −19.7673 | − | 6.42280i | −0.758043 | − | 0.246303i | ||||
\(681\) | 33.0681 | + | 19.0919i | 1.26717 | + | 0.731603i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 45.0333i | − | 1.72315i | −0.507628 | − | 0.861576i | \(-0.669478\pi\) | ||
0.507628 | − | 0.861576i | \(-0.330522\pi\) | |||||||
\(684\) | 7.05676 | + | 33.1994i | 0.269822 | + | 1.26941i | ||||
\(685\) | −21.8435 | + | 15.8702i | −0.834596 | + | 0.606369i | ||||
\(686\) | −24.4338 | + | 33.6302i | −0.932886 | + | 1.28401i | ||||
\(687\) | −3.24102 | + | 15.2478i | −0.123653 | + | 0.581740i | ||||
\(688\) | −37.6599 | + | 12.2364i | −1.43577 | + | 0.466510i | ||||
\(689\) | 7.92672 | + | 5.75910i | 0.301984 | + | 0.219404i | ||||
\(690\) | 63.2910 | − | 6.65215i | 2.40945 | − | 0.253243i | ||||
\(691\) | 1.54508 | − | 4.75528i | 0.0587778 | − | 0.180899i | −0.917357 | − | 0.398066i | \(-0.869681\pi\) |
0.976135 | + | 0.217167i | \(0.0696815\pi\) | |||||||
\(692\) | 9.79796 | 0.372463 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −8.32627 | + | 25.6256i | −0.315834 | + | 0.972036i | ||||
\(696\) | −41.3415 | + | 4.34517i | −1.56705 | + | 0.164703i | ||||
\(697\) | 19.4164 | + | 14.1068i | 0.735449 | + | 0.534335i | ||||
\(698\) | −23.0619 | + | 7.49326i | −0.872906 | + | 0.283624i | ||||
\(699\) | 8.82095 | − | 41.4993i | 0.333639 | − | 1.56965i | ||||
\(700\) | −6.65003 | + | 9.15298i | −0.251348 | + | 0.345950i | ||||
\(701\) | −21.7985 | + | 15.8375i | −0.823317 | + | 0.598175i | −0.917661 | − | 0.397365i | \(-0.869925\pi\) |
0.0943439 | + | 0.995540i | \(0.469925\pi\) | |||||||
\(702\) | −11.1246 | + | 34.2380i | −0.419871 | + | 1.29223i | ||||
\(703\) | 8.48528i | 0.320028i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.0000 | − | 10.3923i | −0.677919 | − | 0.391397i | ||||
\(706\) | 60.5249 | + | 19.6657i | 2.27788 | + | 0.740129i | ||||
\(707\) | −10.1807 | − | 14.0126i | −0.382886 | − | 0.526998i | ||||
\(708\) | 10.9625 | − | 4.88084i | 0.411998 | − | 0.183433i | ||||
\(709\) | 0.927051 | + | 2.85317i | 0.0348161 | + | 0.107153i | 0.966954 | − | 0.254950i | \(-0.0820589\pi\) |
−0.932138 | + | 0.362103i | \(0.882059\pi\) | |||||||
\(710\) | −2.27080 | − | 6.98881i | −0.0852217 | − | 0.262285i | ||||
\(711\) | −29.5358 | − | 3.10434i | −1.10768 | − | 0.116422i | ||||
\(712\) | 24.9376 | + | 34.3237i | 0.934577 | + | 1.28633i | ||||
\(713\) | 24.7092 | + | 8.02850i | 0.925366 | + | 0.300670i | ||||
\(714\) | −7.34847 | + | 12.7279i | −0.275010 | + | 0.476331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 62.3538i | 2.33027i | ||||||||
\(717\) | −28.3761 | + | 25.5499i | −1.05972 | + | 0.954179i | ||||
\(718\) | −48.5410 | + | 35.2671i | −1.81153 | + | 1.31616i | ||||
\(719\) | −7.12652 | + | 9.80881i | −0.265774 | + | 0.365807i | −0.920957 | − | 0.389663i | \(-0.872591\pi\) |
0.655183 | + | 0.755470i | \(0.272591\pi\) | |||||||
\(720\) | 15.4460 | + | 13.9076i | 0.575638 | + | 0.518306i | ||||
\(721\) | −2.68999 | + | 0.874032i | −0.100181 | + | 0.0325507i | ||||
\(722\) | −21.7985 | − | 15.8375i | −0.811255 | − | 0.589411i | ||||
\(723\) | 0.512083 | + | 4.87214i | 0.0190446 | + | 0.181197i | ||||
\(724\) | −6.18034 | + | 19.0211i | −0.229691 | + | 0.706915i | ||||
\(725\) | −9.79796 | −0.363887 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.00000 | −0.111264 | −0.0556319 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556319 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(728\) | −6.05547 | + | 18.6368i | −0.224431 | + | 0.690727i | ||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | −19.4164 | − | 14.1068i | −0.718633 | − | 0.522118i | ||||
\(731\) | −23.0619 | + | 7.49326i | −0.852975 | + | 0.277148i | ||||
\(732\) | −19.1677 | − | 4.07422i | −0.708459 | − | 0.150588i | ||||
\(733\) | −21.6126 | + | 29.7472i | −0.798280 | + | 1.09874i | 0.194748 | + | 0.980853i | \(0.437611\pi\) |
−0.993027 | + | 0.117884i | \(0.962389\pi\) | |||||||
\(734\) | 13.8718 | − | 10.0784i | 0.512016 | − | 0.372001i | ||||
\(735\) | 10.0370 | + | 11.1472i | 0.370219 | + | 0.411170i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −36.0000 | − | 62.3538i | −1.32518 | − | 2.29528i | ||||
\(739\) | −49.7649 | − | 16.1696i | −1.83063 | − | 0.594808i | −0.999234 | − | 0.0391291i | \(-0.987542\pi\) |
−0.831397 | − | 0.555679i | \(-0.812458\pi\) | |||||||
\(740\) | 12.2169 | + | 16.8151i | 0.449102 | + | 0.618135i | ||||
\(741\) | 5.63591 | + | 12.6585i | 0.207040 | + | 0.465020i | ||||
\(742\) | −3.70820 | − | 11.4127i | −0.136132 | − | 0.418973i | ||||
\(743\) | −4.54160 | − | 13.9776i | −0.166615 | − | 0.512789i | 0.832536 | − | 0.553970i | \(-0.186888\pi\) |
−0.999152 | + | 0.0411812i | \(0.986888\pi\) | |||||||
\(744\) | 10.3538 | + | 23.2551i | 0.379590 | + | 0.852572i | ||||
\(745\) | 2.49376 | + | 3.43237i | 0.0913644 | + | 0.125752i | ||||
\(746\) | −75.7748 | − | 24.6207i | −2.77431 | − | 0.901429i | ||||
\(747\) | −3.67423 | − | 6.36396i | −0.134433 | − | 0.232845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.46410i | 0.126576i | ||||||||
\(750\) | 34.4196 | + | 38.2268i | 1.25683 | + | 1.39585i | ||||
\(751\) | −21.8435 | + | 15.8702i | −0.797079 | + | 0.579112i | −0.910056 | − | 0.414486i | \(-0.863961\pi\) |
0.112977 | + | 0.993598i | \(0.463961\pi\) | |||||||
\(752\) | 16.2892 | − | 22.4201i | 0.594005 | − | 0.817578i | ||||
\(753\) | 26.4100 | + | 5.61362i | 0.962433 | + | 0.204572i | ||||
\(754\) | −32.2799 | + | 10.4884i | −1.17557 | + | 0.381964i | ||||
\(755\) | −13.8718 | − | 10.0784i | −0.504845 | − | 0.366791i | ||||
\(756\) | 23.7801 | − | 17.2773i | 0.864876 | − | 0.628369i | ||||
\(757\) | −9.27051 | + | 28.5317i | −0.336942 | + | 1.03700i | 0.628815 | + | 0.777555i | \(0.283540\pi\) |
−0.965757 | + | 0.259447i | \(0.916460\pi\) | |||||||
\(758\) | 41.6413 | 1.51248 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.0000 | 0.870572 | ||||||||
\(761\) | −7.56934 | + | 23.2960i | −0.274388 | + | 0.844480i | 0.714992 | + | 0.699132i | \(0.246430\pi\) |
−0.989381 | + | 0.145348i | \(0.953570\pi\) | |||||||
\(762\) | −1.25434 | − | 11.9343i | −0.0454400 | − | 0.432333i | ||||
\(763\) | 21.0344 | + | 15.2824i | 0.761498 | + | 0.553261i | ||||
\(764\) | −19.7673 | + | 6.42280i | −0.715157 | + | 0.232369i | ||||
\(765\) | 9.45869 | + | 8.51664i | 0.341980 | + | 0.307920i | ||||
\(766\) | 32.4189 | − | 44.6208i | 1.17134 | − | 1.61221i | ||||
\(767\) | 3.96336 | − | 2.87955i | 0.143109 | − | 0.103974i | ||||
\(768\) | 41.1893 | − | 37.0870i | 1.48629 | − | 1.33826i | ||||
\(769\) | − | 14.1421i | − | 0.509978i | −0.966944 | − | 0.254989i | \(-0.917928\pi\) | ||
0.966944 | − | 0.254989i | \(-0.0820719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | + | 15.5885i | −0.324127 | + | 0.561405i | ||||
\(772\) | −53.7999 | − | 17.4806i | −1.93630 | − | 0.629142i | ||||
\(773\) | 2.03615 | + | 2.80252i | 0.0732351 | + | 0.100800i | 0.844063 | − | 0.536244i | \(-0.180157\pi\) |
−0.770828 | + | 0.637043i | \(0.780157\pi\) | |||||||
\(774\) | 72.3476 | + | 7.60404i | 2.60048 | + | 0.273322i | ||||
\(775\) | 1.85410 | + | 5.70634i | 0.0666013 | + | 0.204978i | ||||
\(776\) | 19.6803 | + | 60.5697i | 0.706481 | + | 2.17432i | ||||
\(777\) | 6.71316 | − | 2.98889i | 0.240833 | − | 0.107226i | ||||
\(778\) | −32.4189 | − | 44.6208i | −1.16227 | − | 1.59973i | ||||
\(779\) | −26.3565 | − | 8.56373i | −0.944318 | − | 0.306827i | ||||
\(780\) | 29.3939 | + | 16.9706i | 1.05247 | + | 0.607644i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 51.9615i | 1.85814i | ||||||||
\(783\) | 24.2099 | + | 7.86629i | 0.865193 | + | 0.281118i | ||||
\(784\) | −16.1803 | + | 11.7557i | −0.577869 | + | 0.419847i | ||||
\(785\) | −15.2711 | + | 21.0189i | −0.545049 | + | 0.750196i | ||||
\(786\) | 10.8034 | − | 50.8260i | 0.385345 | − | 1.81290i | ||||
\(787\) | −26.8999 | + | 8.74032i | −0.958879 | + | 0.311559i | −0.746318 | − | 0.665589i | \(-0.768180\pi\) |
−0.212561 | + | 0.977148i | \(0.568180\pi\) | |||||||
\(788\) | 23.7801 | + | 17.2773i | 0.847133 | + | 0.615478i | ||||
\(789\) | −21.0970 | + | 2.21738i | −0.751073 | + | 0.0789409i | ||||
\(790\) | −12.9787 | + | 39.9444i | −0.461762 | + | 1.42116i | ||||
\(791\) | −2.44949 | −0.0870938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | 24.2219 | − | 74.5473i | 0.859603 | − | 2.64558i | ||||
\(795\) | −10.3354 | + | 1.08629i | −0.366558 | + | 0.0385268i | ||||
\(796\) | 58.2492 | + | 42.3205i | 2.06459 | + | 1.50001i | ||||
\(797\) | −31.2983 | + | 10.1694i | −1.10864 | + | 0.360220i | −0.805423 | − | 0.592701i | \(-0.798062\pi\) |
−0.303220 | + | 0.952921i | \(0.598062\pi\) | |||||||
\(798\) | 3.52838 | − | 16.5997i | 0.124903 | − | 0.587624i | ||||
\(799\) | 9.97505 | − | 13.7295i | 0.352892 | − | 0.485714i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.40170 | − | 25.4130i | −0.190860 | − | 0.897925i | ||||
\(802\) | − | 25.4558i | − | 0.898877i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 18.0000 | + | 10.3923i | 0.634811 | + | 0.366508i | ||||
\(805\) | −20.1750 | − | 6.55524i | −0.711074 | − | 0.231042i | ||||
\(806\) | 12.2169 | + | 16.8151i | 0.430321 | + | 0.592287i | ||||
\(807\) | 27.4064 | − | 12.2021i | 0.964750 | − | 0.429534i | ||||
\(808\) | −18.5410 | − | 57.0634i | −0.652271 | − | 2.00748i | ||||
\(809\) | 15.1387 | + | 46.5921i | 0.532248 | + | 1.63809i | 0.749522 | + | 0.661979i | \(0.230283\pi\) |
−0.217275 | + | 0.976111i | \(0.569717\pi\) | |||||||
\(810\) | −15.5307 | − | 34.8826i | −0.545694 | − | 1.22565i | ||||
\(811\) | 9.14379 | + | 12.5854i | 0.321082 | + | 0.441931i | 0.938797 | − | 0.344470i | \(-0.111942\pi\) |
−0.617715 | + | 0.786402i | \(0.711942\pi\) | |||||||
\(812\) | 26.3565 | + | 8.56373i | 0.924930 | + | 0.300528i | ||||
\(813\) | −4.89898 | + | 8.48528i | −0.171815 | + | 0.297592i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.3205i | 0.606711i | ||||||||
\(816\) | −12.6116 | + | 11.3555i | −0.441494 | + | 0.397523i | ||||
\(817\) | 22.6525 | − | 16.4580i | 0.792510 | − | 0.575792i | ||||
\(818\) | 26.4699 | − | 36.4327i | 0.925499 | − | 1.27384i | ||||
\(819\) | 8.02957 | − | 8.91774i | 0.280576 | − | 0.311611i | ||||
\(820\) | −64.5599 | + | 20.9768i | −2.25453 | + | 0.732541i | ||||
\(821\) | 25.7618 | + | 18.7171i | 0.899094 | + | 0.653230i | 0.938233 | − | 0.346004i | \(-0.112462\pi\) |
−0.0391392 | + | 0.999234i | \(0.512462\pi\) | |||||||
\(822\) | 6.91312 | + | 65.7739i | 0.241123 | + | 2.29413i | ||||
\(823\) | 9.57953 | − | 29.4828i | 0.333921 | − | 1.02770i | −0.633330 | − | 0.773882i | \(-0.718312\pi\) |
0.967251 | − | 0.253822i | \(-0.0816877\pi\) | |||||||
\(824\) | −9.79796 | −0.341328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 1.51387 | − | 4.65921i | 0.0526423 | − | 0.162016i | −0.921279 | − | 0.388902i | \(-0.872854\pi\) |
0.973921 | + | 0.226886i | \(0.0728544\pi\) | |||||||
\(828\) | 42.2693 | − | 94.9384i | 1.46896 | − | 3.29934i | ||||
\(829\) | −25.0795 | − | 18.2213i | −0.871048 | − | 0.632853i | 0.0598200 | − | 0.998209i | \(-0.480947\pi\) |
−0.930868 | + | 0.365356i | \(0.880947\pi\) | |||||||
\(830\) | −9.88367 | + | 3.21140i | −0.343067 | + | 0.111469i | ||||
\(831\) | 31.1475 | + | 6.62061i | 1.08050 | + | 0.229666i | ||||
\(832\) | 13.3001 | − | 18.3060i | 0.461097 | − | 0.634645i | ||||
\(833\) | −9.90839 | + | 7.19887i | −0.343306 | + | 0.249426i | ||||
\(834\) | 44.1626 | + | 49.0476i | 1.52923 | + | 1.69838i | ||||
\(835\) | 33.9411i | 1.17458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 15.5885i | − | 0.538816i | ||||||
\(838\) | −16.1400 | − | 5.24419i | −0.557546 | − | 0.181158i | ||||
\(839\) | 27.4880 | + | 37.8340i | 0.948991 | + | 1.30617i | 0.951974 | + | 0.306179i | \(0.0990504\pi\) |
−0.00298311 | + | 0.999996i | \(0.500950\pi\) | |||||||
\(840\) | −8.45386 | − | 18.9877i | −0.291686 | − | 0.655137i | ||||
\(841\) | −1.54508 | − | 4.75528i | −0.0532788 | − | 0.163975i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.5307 | − | 34.8826i | −0.534907 | − | 1.20142i | ||||
\(844\) | 13.3001 | + | 18.3060i | 0.457807 | + | 0.630117i | ||||
\(845\) | −8.23639 | − | 2.67617i | −0.283340 | − | 0.0920629i | ||||
\(846\) | −44.0908 | + | 25.4558i | −1.51587 | + | 0.875190i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 13.8564i | − | 0.475831i | ||||||
\(849\) | −22.9464 | − | 25.4846i | −0.787518 | − | 0.874628i | ||||
\(850\) | −9.70820 | + | 7.05342i | −0.332989 | + | 0.241930i | ||||
\(851\) | 15.2711 | − | 21.0189i | 0.523487 | − | 0.720518i | ||||
\(852\) | −11.7378 | − | 2.49494i | −0.402129 | − | 0.0854752i | ||||
\(853\) | −55.1449 | + | 17.9177i | −1.88812 | + | 0.613489i | −0.906654 | + | 0.421874i | \(0.861372\pi\) |
−0.981470 | + | 0.191615i | \(0.938628\pi\) | |||||||
\(854\) | 7.92672 | + | 5.75910i | 0.271247 | + | 0.197072i | ||||
\(855\) | −13.4263 | − | 5.97778i | −0.459171 | − | 0.204436i | ||||
\(856\) | −3.70820 | + | 11.4127i | −0.126744 | + | 0.390077i | ||||
\(857\) | 19.5959 | 0.669384 | 0.334692 | − | 0.942328i | \(-0.391368\pi\) | ||||
0.334692 | + | 0.942328i | \(0.391368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0000 | 0.852989 | 0.426494 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426494 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(860\) | 21.1942 | − | 65.2289i | 0.722715 | − | 2.22429i | ||||
\(861\) | 2.50868 | + | 23.8685i | 0.0854957 | + | 0.813437i | ||||
\(862\) | −14.5623 | − | 10.5801i | −0.495994 | − | 0.360361i | ||||
\(863\) | 19.7673 | − | 6.42280i | 0.672888 | − | 0.218635i | 0.0474090 | − | 0.998876i | \(-0.484904\pi\) |
0.625479 | + | 0.780241i | \(0.284904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.49376 | + | 3.43237i | −0.0847904 | + | 0.116704i | ||||
\(866\) | −9.90839 | + | 7.19887i | −0.336701 | + | 0.244628i | ||||
\(867\) | 14.1588 | − | 12.7487i | 0.480858 | − | 0.432967i | ||||
\(868\) | − | 16.9706i | − | 0.576018i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | − | 31.1769i | 0.610257 | − | 1.05700i | ||||
\(871\) | 8.06998 | + | 2.62210i | 0.273441 | + | 0.0888463i | ||||
\(872\) | 52.9398 | + | 72.8654i | 1.79277 | + | 2.46754i | ||||
\(873\) | 4.07661 | − | 38.7864i | 0.137972 | − | 1.31272i | ||||
\(874\) | −18.5410 | − | 57.0634i | −0.627159 | − | 1.93020i | ||||
\(875\) | −5.29854 | − | 16.3072i | −0.179123 | − | 0.551285i | ||||
\(876\) | −35.8035 | + | 15.9408i | −1.20969 | + | 0.538588i | ||||
\(877\) | −16.6251 | − | 22.8825i | −0.561389 | − | 0.772686i | 0.430113 | − | 0.902775i | \(-0.358474\pi\) |
−0.991502 | + | 0.130089i | \(0.958474\pi\) | |||||||
\(878\) | 13.1782 | + | 4.28187i | 0.444744 | + | 0.144506i | ||||
\(879\) | 7.34847 | + | 4.24264i | 0.247858 | + | 0.143101i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.73205i | 0.0583543i | 0.999574 | + | 0.0291771i | \(0.00928869\pi\) | ||||
−0.999574 | + | 0.0291771i | \(0.990711\pi\) | |||||||
\(882\) | 35.9394 | − | 7.63916i | 1.21014 | − | 0.257224i | ||||
\(883\) | −4.85410 | + | 3.52671i | −0.163354 | + | 0.118683i | −0.666459 | − | 0.745542i | \(-0.732191\pi\) |
0.503105 | + | 0.864225i | \(0.332191\pi\) | |||||||
\(884\) | −16.2892 | + | 22.4201i | −0.547865 | + | 0.754071i | ||||
\(885\) | −1.08034 | + | 5.08260i | −0.0363153 | + | 0.170850i | ||||
\(886\) | 60.5249 | − | 19.6657i | 2.03337 | − | 0.660683i | ||||
\(887\) | 17.8351 | + | 12.9580i | 0.598844 | + | 0.435086i | 0.845468 | − | 0.534025i | \(-0.179321\pi\) |
−0.246624 | + | 0.969111i | \(0.579321\pi\) | |||||||
\(888\) | 25.3164 | − | 2.66086i | 0.849563 | − | 0.0892926i | ||||
\(889\) | −1.23607 | + | 3.80423i | −0.0414564 | + | 0.127590i | ||||
\(890\) | −36.7423 | −1.23161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −44.0000 | −1.47323 | ||||||||
\(893\) | −6.05547 | + | 18.6368i | −0.202639 | + | 0.623658i | ||||
\(894\) | 10.3354 | − | 1.08629i | 0.345667 | − | 0.0363310i | ||||
\(895\) | −21.8435 | − | 15.8702i | −0.730146 | − | 0.530482i | ||||
\(896\) | −26.3565 | + | 8.56373i | −0.880507 | + | 0.286094i | ||||
\(897\) | 8.82095 | − | 41.4993i | 0.294523 | − | 1.38562i | ||||
\(898\) | −17.4563 | + | 24.0266i | −0.582525 | + | 0.801777i | ||||
\(899\) | 11.8901 | − | 8.63864i | 0.396556 | − | 0.288115i | ||||
\(900\) | 23.4755 | − | 4.98988i | 0.782518 | − | 0.166329i | ||||
\(901\) | − | 8.48528i | − | 0.282686i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.0000 | − | 12.1244i | −0.698836 | − | 0.403473i | ||||
\(904\) | −8.06998 | − | 2.62210i | −0.268404 | − | 0.0872096i | ||||
\(905\) | −5.09037 | − | 7.00629i | −0.169210 | − | 0.232897i | ||||
\(906\) | −38.3689 | + | 17.0829i | −1.27472 | + | 0.567543i | ||||
\(907\) | 6.79837 | + | 20.9232i | 0.225736 | + | 0.694745i | 0.998216 | + | 0.0597055i | \(0.0190162\pi\) |
−0.772480 | + | 0.635039i | \(0.780984\pi\) | |||||||
\(908\) | −27.2496 | − | 83.8657i | −0.904310 | − | 2.78318i | ||||
\(909\) | −3.84062 | + | 36.5411i | −0.127385 | + | 1.21199i | ||||
\(910\) | −9.97505 | − | 13.7295i | −0.330670 | − | 0.455128i | ||||
\(911\) | 3.29456 | + | 1.07047i | 0.109154 | + | 0.0354661i | 0.363085 | − | 0.931756i | \(-0.381724\pi\) |
−0.253931 | + | 0.967222i | \(0.581724\pi\) | |||||||
\(912\) | 9.79796 | − | 16.9706i | 0.324443 | − | 0.561951i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 76.2102i | − | 2.52081i | ||||||
\(915\) | 6.30579 | − | 5.67776i | 0.208463 | − | 0.187701i | ||||
\(916\) | 29.1246 | − | 21.1603i | 0.962304 | − | 0.699155i | ||||
\(917\) | −10.1807 | + | 14.0126i | −0.336198 | + | 0.462736i | ||||
\(918\) | 29.6510 | − | 9.63420i | 0.978629 | − | 0.317976i | ||||
\(919\) | 6.72499 | − | 2.18508i | 0.221837 | − | 0.0720791i | −0.195990 | − | 0.980606i | \(-0.562792\pi\) |
0.417827 | + | 0.908527i | \(0.362792\pi\) | |||||||
\(920\) | −59.4504 | − | 43.1932i | −1.96002 | − | 1.42404i | ||||
\(921\) | 0.512083 | + | 4.87214i | 0.0168737 | + | 0.160543i | ||||
\(922\) | 3.70820 | − | 11.4127i | 0.122123 | − | 0.375857i | ||||
\(923\) | −4.89898 | −0.161252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 14.3817 | − | 44.2625i | 0.472613 | − | 1.45455i | ||||
\(927\) | 5.48127 | + | 2.44042i | 0.180029 | + | 0.0801539i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.8292 | − | 13.9161i | 1.40518 | − | 0.456571i | 0.494319 | − | 0.869281i | \(-0.335418\pi\) |
0.910863 | + | 0.412709i | \(0.135418\pi\) | |||||||
\(930\) | −21.5637 | − | 4.58350i | −0.707100 | − | 0.150299i | ||||
\(931\) | 8.31254 | − | 11.4412i | 0.272432 | − | 0.374971i | ||||
\(932\) | −79.2672 | + | 57.5910i | −2.59648 | + | 1.88645i | ||||
\(933\) | 20.0739 | + | 22.2943i | 0.657191 | + | 0.729884i | ||||
\(934\) | − | 63.6396i | − | 2.08235i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 36.0000 | − | 20.7846i | 1.17670 | − | 0.679366i | ||||
\(937\) | 53.7999 | + | 17.4806i | 1.75757 | + | 0.571068i | 0.996943 | − | 0.0781272i | \(-0.0248940\pi\) |
0.760622 | + | 0.649195i | \(0.224894\pi\) | |||||||
\(938\) | −6.10844 | − | 8.40755i | −0.199448 | − | 0.274516i | ||||
\(939\) | −23.2481 | − | 52.2161i | −0.758674 | − | 1.70401i | ||||
\(940\) | 14.8328 | + | 45.6507i | 0.483793 | + | 1.48896i | ||||
\(941\) | −2.27080 | − | 6.98881i | −0.0740260 | − | 0.227829i | 0.907197 | − | 0.420707i | \(-0.138218\pi\) |
−0.981223 | + | 0.192878i | \(0.938218\pi\) | |||||||
\(942\) | 25.8846 | + | 58.1377i | 0.843365 | + | 1.89423i | ||||
\(943\) | 49.8752 | + | 68.6474i | 1.62416 | + | 2.23547i | ||||
\(944\) | −6.58911 | − | 2.14093i | −0.214457 | − | 0.0696814i | ||||
\(945\) | 12.7279i | 0.414039i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.2295i | 1.63224i | 0.577883 | + | 0.816119i | \(0.303879\pi\) | ||||
−0.577883 | + | 0.816119i | \(0.696121\pi\) | |||||||
\(948\) | 45.8928 | + | 50.9691i | 1.49053 | + | 1.65540i | ||||
\(949\) | −12.9443 | + | 9.40456i | −0.420189 | + | 0.305285i | ||||
\(950\) | 8.14459 | − | 11.2101i | 0.264245 | − | 0.363703i | ||||
\(951\) | −2.93444 | − | 0.623735i | −0.0951558 | − | 0.0202260i | ||||
\(952\) | 16.1400 | − | 5.24419i | 0.523099 | − | 0.169965i | ||||
\(953\) | −5.94504 | − | 4.31932i | −0.192579 | − | 0.139917i | 0.487318 | − | 0.873225i | \(-0.337975\pi\) |
−0.679896 | + | 0.733308i | \(0.737975\pi\) | |||||||
\(954\) | −10.3538 | + | 23.2551i | −0.335217 | + | 0.752911i | ||||
\(955\) | 2.78115 | − | 8.55951i | 0.0899960 | − | 0.276979i | ||||
\(956\) | 88.1816 | 2.85200 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −72.0000 | −2.32621 | ||||||||
\(959\) | 6.81241 | − | 20.9664i | 0.219984 | − | 0.677041i | ||||
\(960\) | 2.50868 | + | 23.8685i | 0.0809674 | + | 0.770353i | ||||
\(961\) | 17.7984 | + | 12.9313i | 0.574141 | + | 0.417138i | ||||
\(962\) | 19.7673 | − | 6.42280i | 0.637325 | − | 0.207079i | ||||
\(963\) | 4.91709 | − | 5.46098i | 0.158451 | − | 0.175978i | ||||
\(964\) | 6.65003 | − | 9.15298i | 0.214183 | − | 0.294798i | ||||
\(965\) | 19.8168 | − | 14.3977i | 0.637925 | − | 0.463480i | ||||
\(966\) | −38.6149 | + | 34.7690i | −1.24242 | + | 1.11868i | ||||
\(967\) | 31.1127i | 1.00052i | 0.865876 | + | 0.500258i | \(0.166762\pi\) | ||||
−0.865876 | + | 0.500258i | \(0.833238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | −52.4549 | − | 17.0436i | −1.68422 | − | 0.547238i | ||||
\(971\) | −23.4157 | − | 32.2289i | −0.751446 | − | 1.03428i | −0.997878 | − | 0.0651161i | \(-0.979258\pi\) |
0.246432 | − | 0.969160i | \(-0.420742\pi\) | |||||||
\(972\) | −62.0122 | − | 6.51775i | −1.98904 | − | 0.209057i | ||||
\(973\) | −6.79837 | − | 20.9232i | −0.217946 | − | 0.670768i | ||||
\(974\) | 20.4372 | + | 62.8993i | 0.654851 | + | 2.01542i | ||||
\(975\) | 8.95088 | − | 3.98519i | 0.286658 | − | 0.127628i | ||||
\(976\) | 6.65003 | + | 9.15298i | 0.212862 | + | 0.292980i | ||||
\(977\) | −34.5928 | − | 11.2399i | −1.10672 | − | 0.359596i | −0.302037 | − | 0.953296i | \(-0.597667\pi\) |
−0.804686 | + | 0.593700i | \(0.797667\pi\) | |||||||
\(978\) | 36.7423 | + | 21.2132i | 1.17489 | + | 0.678323i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 34.6410i | − | 1.10657i | ||||||
\(981\) | −11.4672 | − | 53.9491i | −0.366120 | − | 1.72246i | ||||
\(982\) | 48.5410 | − | 35.2671i | 1.54901 | − | 1.12542i | ||||
\(983\) | −1.01807 | + | 1.40126i | −0.0324715 | + | 0.0446932i | −0.824944 | − | 0.565214i | \(-0.808793\pi\) |
0.792473 | + | 0.609908i | \(0.208793\pi\) | |||||||
\(984\) | −17.2855 | + | 81.3217i | −0.551040 | + | 2.59244i | ||||
\(985\) | −12.1050 | + | 3.93314i | −0.385697 | + | 0.125320i | ||||
\(986\) | 23.7801 | + | 17.2773i | 0.757314 | + | 0.550221i | ||||
\(987\) | 16.8776 | − | 1.77391i | 0.537220 | − | 0.0564641i | ||||
\(988\) | 9.88854 | − | 30.4338i | 0.314596 | − | 0.968228i | ||||
\(989\) | −85.7321 | −2.72612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000 | 0.571789 | 0.285894 | − | 0.958261i | \(-0.407709\pi\) | ||||
0.285894 | + | 0.958261i | \(0.407709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.61281 | − | 0.905243i | 0.273319 | − | 0.0287270i | ||||
\(994\) | 4.85410 | + | 3.52671i | 0.153963 | + | 0.111860i | ||||
\(995\) | −29.6510 | + | 9.63420i | −0.940000 | + | 0.305425i | ||||
\(996\) | −3.52838 | + | 16.5997i | −0.111801 | + | 0.525982i | ||||
\(997\) | 0.831254 | − | 1.14412i | 0.0263261 | − | 0.0362347i | −0.795651 | − | 0.605755i | \(-0.792871\pi\) |
0.821977 | + | 0.569520i | \(0.192871\pi\) | |||||||
\(998\) | −11.8901 | + | 8.63864i | −0.376374 | + | 0.273451i | ||||
\(999\) | −14.8255 | − | 4.81710i | −0.469058 | − | 0.152406i |
(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 | 363.2.f.h.233.4 | 16 | ||
3.2 | odd | 2 | inner | 363.2.f.h.233.1 | 16 | ||
11.2 | odd | 10 | inner | 363.2.f.h.239.4 | 16 | ||
11.3 | even | 5 | inner | 363.2.f.h.161.1 | 16 | ||
11.4 | even | 5 | 363.2.d.c.362.3 | yes | 4 | ||
11.5 | even | 5 | inner | 363.2.f.h.215.3 | 16 | ||
11.6 | odd | 10 | inner | 363.2.f.h.215.1 | 16 | ||
11.7 | odd | 10 | 363.2.d.c.362.1 | ✓ | 4 | ||
11.8 | odd | 10 | inner | 363.2.f.h.161.3 | 16 | ||
11.9 | even | 5 | inner | 363.2.f.h.239.2 | 16 | ||
11.10 | odd | 2 | inner | 363.2.f.h.233.2 | 16 | ||
33.2 | even | 10 | inner | 363.2.f.h.239.1 | 16 | ||
33.5 | odd | 10 | inner | 363.2.f.h.215.2 | 16 | ||
33.8 | even | 10 | inner | 363.2.f.h.161.2 | 16 | ||
33.14 | odd | 10 | inner | 363.2.f.h.161.4 | 16 | ||
33.17 | even | 10 | inner | 363.2.f.h.215.4 | 16 | ||
33.20 | odd | 10 | inner | 363.2.f.h.239.3 | 16 | ||
33.26 | odd | 10 | 363.2.d.c.362.2 | yes | 4 | ||
33.29 | even | 10 | 363.2.d.c.362.4 | yes | 4 | ||
33.32 | even | 2 | inner | 363.2.f.h.233.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.c.362.1 | ✓ | 4 | 11.7 | odd | 10 | ||
363.2.d.c.362.2 | yes | 4 | 33.26 | odd | 10 | ||
363.2.d.c.362.3 | yes | 4 | 11.4 | even | 5 | ||
363.2.d.c.362.4 | yes | 4 | 33.29 | even | 10 | ||
363.2.f.h.161.1 | 16 | 11.3 | even | 5 | inner | ||
363.2.f.h.161.2 | 16 | 33.8 | even | 10 | inner | ||
363.2.f.h.161.3 | 16 | 11.8 | odd | 10 | inner | ||
363.2.f.h.161.4 | 16 | 33.14 | odd | 10 | inner | ||
363.2.f.h.215.1 | 16 | 11.6 | odd | 10 | inner | ||
363.2.f.h.215.2 | 16 | 33.5 | odd | 10 | inner | ||
363.2.f.h.215.3 | 16 | 11.5 | even | 5 | inner | ||
363.2.f.h.215.4 | 16 | 33.17 | even | 10 | inner | ||
363.2.f.h.233.1 | 16 | 3.2 | odd | 2 | inner | ||
363.2.f.h.233.2 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.h.233.3 | 16 | 33.32 | even | 2 | inner | ||
363.2.f.h.233.4 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.h.239.1 | 16 | 33.2 | even | 10 | inner | ||
363.2.f.h.239.2 | 16 | 11.9 | even | 5 | inner | ||
363.2.f.h.239.3 | 16 | 33.20 | odd | 10 | inner | ||
363.2.f.h.239.4 | 16 | 11.2 | odd | 10 | inner |