Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(40,363)]
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([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.40");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.g (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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 112.1 | ||
Root | \(-1.43448 + 2.82504i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.112 |
Dual form | 363.3.g.g.94.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.934478 | − | 0.303630i | −0.467239 | − | 0.151815i | 0.0659293 | − | 0.997824i | \(-0.478999\pi\) |
−0.533168 | + | 0.846009i | \(0.678999\pi\) | |||||||
\(3\) | 1.40126 | − | 1.01807i | 0.467086 | − | 0.339358i | ||||
\(4\) | −2.45501 | − | 1.78367i | −0.613752 | − | 0.445917i | ||||
\(5\) | 0.122858 | + | 0.378117i | 0.0245715 | + | 0.0756234i | 0.962590 | − | 0.270961i | \(-0.0873414\pi\) |
−0.938019 | + | 0.346584i | \(0.887341\pi\) | |||||||
\(6\) | −1.61856 | + | 0.525903i | −0.269761 | + | 0.0876506i | ||||
\(7\) | −4.24781 | + | 5.84661i | −0.606830 | + | 0.835230i | −0.996312 | − | 0.0858038i | \(-0.972654\pi\) |
0.389482 | + | 0.921034i | \(0.372654\pi\) | |||||||
\(8\) | 4.06274 | + | 5.59188i | 0.507842 | + | 0.698984i | ||||
\(9\) | 0.927051 | − | 2.85317i | 0.103006 | − | 0.317019i | ||||
\(10\) | − | 0.390645i | − | 0.0390645i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.25601 | −0.438001 | ||||||||
\(13\) | 11.5645 | + | 3.75755i | 0.889581 | + | 0.289042i | 0.717930 | − | 0.696116i | \(-0.245090\pi\) |
0.171651 | + | 0.985158i | \(0.445090\pi\) | |||||||
\(14\) | 5.74470 | − | 4.17377i | 0.410336 | − | 0.298126i | ||||
\(15\) | 0.557106 | + | 0.404761i | 0.0371404 | + | 0.0269841i | ||||
\(16\) | 1.65225 | + | 5.08509i | 0.103265 | + | 0.317818i | ||||
\(17\) | 19.8862 | − | 6.46141i | 1.16977 | − | 0.380083i | 0.341216 | − | 0.939985i | \(-0.389161\pi\) |
0.828559 | + | 0.559902i | \(0.189161\pi\) | |||||||
\(18\) | −1.73262 | + | 2.38474i | −0.0962566 | + | 0.132486i | ||||
\(19\) | 6.53192 | + | 8.99042i | 0.343785 | + | 0.473180i | 0.945542 | − | 0.325499i | \(-0.105532\pi\) |
−0.601757 | + | 0.798679i | \(0.705532\pi\) | |||||||
\(20\) | 0.372819 | − | 1.14742i | 0.0186409 | − | 0.0573709i | ||||
\(21\) | 12.5172i | 0.596057i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.92990 | −0.257822 | −0.128911 | − | 0.991656i | \(-0.541148\pi\) | ||||
−0.128911 | + | 0.991656i | \(0.541148\pi\) | |||||||
\(24\) | 11.3859 | + | 3.69950i | 0.474412 | + | 0.154146i | ||||
\(25\) | 20.0975 | − | 14.6017i | 0.803902 | − | 0.584069i | ||||
\(26\) | −9.66591 | − | 7.02270i | −0.371766 | − | 0.270104i | ||||
\(27\) | −1.60570 | − | 4.94183i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 20.8568 | − | 6.77680i | 0.744887 | − | 0.242029i | ||||
\(29\) | −14.6680 | + | 20.1887i | −0.505791 | + | 0.696162i | −0.983203 | − | 0.182518i | \(-0.941575\pi\) |
0.477411 | + | 0.878680i | \(0.341575\pi\) | |||||||
\(30\) | −0.397706 | − | 0.547395i | −0.0132569 | − | 0.0182465i | ||||
\(31\) | 18.4254 | − | 56.7075i | 0.594368 | − | 1.82928i | 0.0365185 | − | 0.999333i | \(-0.488373\pi\) |
0.557849 | − | 0.829942i | \(-0.311627\pi\) | |||||||
\(32\) | − | 32.9013i | − | 1.02817i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −20.5451 | −0.604267 | ||||||||
\(35\) | −2.73258 | − | 0.887869i | −0.0780737 | − | 0.0253677i | ||||
\(36\) | −7.36503 | + | 5.35101i | −0.204584 | + | 0.148639i | ||||
\(37\) | 4.82743 | + | 3.50733i | 0.130471 | + | 0.0947927i | 0.651107 | − | 0.758986i | \(-0.274305\pi\) |
−0.520636 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(38\) | −3.37417 | − | 10.3846i | −0.0887941 | − | 0.273280i | ||||
\(39\) | 20.0304 | − | 6.50827i | 0.513600 | − | 0.166879i | ||||
\(40\) | −1.61524 | + | 2.22319i | −0.0403811 | + | 0.0555798i | ||||
\(41\) | 30.5881 | + | 42.1009i | 0.746052 | + | 1.02685i | 0.998248 | + | 0.0591757i | \(0.0188472\pi\) |
−0.252196 | + | 0.967676i | \(0.581153\pi\) | |||||||
\(42\) | 3.80060 | − | 11.6971i | 0.0904906 | − | 0.278501i | ||||
\(43\) | − | 17.6439i | − | 0.410323i | −0.978728 | − | 0.205161i | \(-0.934228\pi\) | ||
0.978728 | − | 0.205161i | \(-0.0657719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.19273 | 0.0265050 | ||||||||
\(46\) | 5.54136 | + | 1.80050i | 0.120464 | + | 0.0391412i | ||||
\(47\) | 44.7879 | − | 32.5403i | 0.952934 | − | 0.692347i | 0.00143478 | − | 0.999999i | \(-0.499543\pi\) |
0.951499 | + | 0.307652i | \(0.0995433\pi\) | |||||||
\(48\) | 7.49222 | + | 5.44342i | 0.156088 | + | 0.113405i | ||||
\(49\) | −0.997137 | − | 3.06887i | −0.0203497 | − | 0.0626301i | ||||
\(50\) | −23.2143 | + | 7.54277i | −0.464285 | + | 0.150855i | ||||
\(51\) | 21.2875 | − | 29.2997i | 0.417401 | − | 0.574504i | ||||
\(52\) | −21.6889 | − | 29.8521i | −0.417093 | − | 0.574080i | ||||
\(53\) | −29.2491 | + | 90.0194i | −0.551869 | + | 1.69848i | 0.152202 | + | 0.988349i | \(0.451364\pi\) |
−0.704071 | + | 0.710129i | \(0.748636\pi\) | |||||||
\(54\) | 5.10558i | 0.0945477i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −49.9513 | −0.891987 | ||||||||
\(57\) | 18.3058 | + | 5.94792i | 0.321155 | + | 0.104349i | ||||
\(58\) | 19.8368 | − | 14.4123i | 0.342014 | − | 0.248487i | ||||
\(59\) | 20.3106 | + | 14.7565i | 0.344247 | + | 0.250110i | 0.746452 | − | 0.665440i | \(-0.231756\pi\) |
−0.402205 | + | 0.915550i | \(0.631756\pi\) | |||||||
\(60\) | −0.645741 | − | 1.98739i | −0.0107623 | − | 0.0331231i | ||||
\(61\) | 31.7711 | − | 10.3231i | 0.520838 | − | 0.169231i | −0.0367874 | − | 0.999323i | \(-0.511712\pi\) |
0.557626 | + | 0.830092i | \(0.311712\pi\) | |||||||
\(62\) | −34.4363 | + | 47.3975i | −0.555424 | + | 0.764475i | ||||
\(63\) | 12.7434 | + | 17.5398i | 0.202277 | + | 0.278410i | ||||
\(64\) | −3.38086 | + | 10.4052i | −0.0528260 | + | 0.162582i | ||||
\(65\) | 4.83439i | 0.0743753i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 94.6640 | 1.41290 | 0.706448 | − | 0.707765i | \(-0.250296\pi\) | ||||
0.706448 | + | 0.707765i | \(0.250296\pi\) | |||||||
\(68\) | −60.3457 | − | 19.6075i | −0.887437 | − | 0.288346i | ||||
\(69\) | −8.30932 | + | 6.03707i | −0.120425 | + | 0.0874938i | ||||
\(70\) | 2.28395 | + | 1.65939i | 0.0326279 | + | 0.0237056i | ||||
\(71\) | 25.5632 | + | 78.6753i | 0.360044 | + | 1.10810i | 0.953026 | + | 0.302887i | \(0.0979505\pi\) |
−0.592982 | + | 0.805216i | \(0.702049\pi\) | |||||||
\(72\) | 19.7209 | − | 6.40772i | 0.273902 | − | 0.0889961i | ||||
\(73\) | 27.3783 | − | 37.6830i | 0.375045 | − | 0.516206i | −0.579218 | − | 0.815173i | \(-0.696642\pi\) |
0.954263 | + | 0.298967i | \(0.0966420\pi\) | |||||||
\(74\) | −3.44619 | − | 4.74328i | −0.0465702 | − | 0.0640984i | ||||
\(75\) | 13.2962 | − | 40.9216i | 0.177283 | − | 0.545621i | ||||
\(76\) | − | 33.7223i | − | 0.443715i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −20.6941 | −0.265309 | ||||||||
\(79\) | 57.3669 | + | 18.6396i | 0.726164 | + | 0.235945i | 0.648693 | − | 0.761050i | \(-0.275316\pi\) |
0.0774701 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(80\) | −1.71977 | + | 1.24948i | −0.0214971 | + | 0.0156186i | ||||
\(81\) | −7.28115 | − | 5.29007i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −15.8008 | − | 48.6299i | −0.192693 | − | 0.593047i | ||||
\(83\) | −143.299 | + | 46.5606i | −1.72649 | + | 0.560971i | −0.992935 | − | 0.118659i | \(-0.962140\pi\) |
−0.733555 | + | 0.679630i | \(0.762140\pi\) | |||||||
\(84\) | 22.3265 | − | 30.7299i | 0.265792 | − | 0.365832i | ||||
\(85\) | 4.88633 | + | 6.72546i | 0.0574863 | + | 0.0791231i | ||||
\(86\) | −5.35722 | + | 16.4878i | −0.0622933 | + | 0.191719i | ||||
\(87\) | 43.2227i | 0.496812i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 134.190 | 1.50775 | 0.753874 | − | 0.657019i | \(-0.228183\pi\) | ||||
0.753874 | + | 0.657019i | \(0.228183\pi\) | |||||||
\(90\) | −1.11458 | − | 0.362148i | −0.0123842 | − | 0.00402387i | ||||
\(91\) | −71.0930 | + | 51.6521i | −0.781242 | + | 0.567605i | ||||
\(92\) | 14.5580 | + | 10.5770i | 0.158239 | + | 0.114967i | ||||
\(93\) | −31.9137 | − | 98.2203i | −0.343158 | − | 1.05613i | ||||
\(94\) | −51.7335 | + | 16.8092i | −0.550357 | + | 0.178822i | ||||
\(95\) | −2.59693 | + | 3.57437i | −0.0273361 | + | 0.0376249i | ||||
\(96\) | −33.4960 | − | 46.1033i | −0.348917 | − | 0.480242i | ||||
\(97\) | 11.6211 | − | 35.7659i | 0.119805 | − | 0.368721i | −0.873114 | − | 0.487516i | \(-0.837903\pi\) |
0.992919 | + | 0.118795i | \(0.0379031\pi\) | |||||||
\(98\) | 3.17056i | 0.0323526i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −75.3843 | −0.753843 | ||||||||
\(101\) | −76.8470 | − | 24.9691i | −0.760861 | − | 0.247219i | −0.0972129 | − | 0.995264i | \(-0.530993\pi\) |
−0.663648 | + | 0.748045i | \(0.730993\pi\) | |||||||
\(102\) | −28.7890 | + | 20.9164i | −0.282245 | + | 0.205063i | ||||
\(103\) | −80.6292 | − | 58.5805i | −0.782808 | − | 0.568743i | 0.123013 | − | 0.992405i | \(-0.460744\pi\) |
−0.905820 | + | 0.423662i | \(0.860744\pi\) | |||||||
\(104\) | 25.9719 | + | 79.9334i | 0.249730 | + | 0.768591i | ||||
\(105\) | −4.73297 | + | 1.53783i | −0.0450759 | + | 0.0146460i | ||||
\(106\) | 54.6652 | − | 75.2403i | 0.515710 | − | 0.709814i | ||||
\(107\) | −63.6299 | − | 87.5790i | −0.594672 | − | 0.818495i | 0.400536 | − | 0.916281i | \(-0.368824\pi\) |
−0.995207 | + | 0.0977859i | \(0.968824\pi\) | |||||||
\(108\) | −4.87259 | + | 14.9963i | −0.0451166 | + | 0.138855i | ||||
\(109\) | 175.446i | 1.60960i | 0.593546 | + | 0.804800i | \(0.297727\pi\) | ||||
−0.593546 | + | 0.804800i | \(0.702273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3352 | 0.0931099 | ||||||||
\(112\) | −36.7490 | − | 11.9405i | −0.328116 | − | 0.106611i | ||||
\(113\) | −79.7071 | + | 57.9106i | −0.705373 | + | 0.512483i | −0.881678 | − | 0.471852i | \(-0.843586\pi\) |
0.176305 | + | 0.984336i | \(0.443586\pi\) | |||||||
\(114\) | −15.3004 | − | 11.1164i | −0.134214 | − | 0.0975123i | ||||
\(115\) | −0.728533 | − | 2.24219i | −0.00633507 | − | 0.0194973i | ||||
\(116\) | 72.0199 | − | 23.4007i | 0.620861 | − | 0.201730i | ||||
\(117\) | 21.4419 | − | 29.5122i | 0.183264 | − | 0.252241i | ||||
\(118\) | −14.4993 | − | 19.9565i | −0.122875 | − | 0.169123i | ||||
\(119\) | −46.6954 | + | 143.714i | −0.392398 | + | 1.20768i | ||||
\(120\) | 4.75971i | 0.0396642i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −32.8238 | −0.269048 | ||||||||
\(123\) | 85.7237 | + | 27.8533i | 0.696941 | + | 0.226450i | ||||
\(124\) | −146.382 | + | 106.353i | −1.18050 | + | 0.857683i | ||||
\(125\) | 16.0314 | + | 11.6475i | 0.128251 | + | 0.0931801i | ||||
\(126\) | −6.58284 | − | 20.2599i | −0.0522448 | − | 0.160793i | ||||
\(127\) | −20.7959 | + | 6.75701i | −0.163748 | + | 0.0532048i | −0.389744 | − | 0.920923i | \(-0.627436\pi\) |
0.225996 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(128\) | −71.0370 | + | 97.7740i | −0.554976 | + | 0.763860i | ||||
\(129\) | −17.9628 | − | 24.7236i | −0.139246 | − | 0.191656i | ||||
\(130\) | 1.46787 | − | 4.51764i | 0.0112913 | − | 0.0347511i | ||||
\(131\) | − | 16.3593i | − | 0.124880i | −0.998049 | − | 0.0624402i | \(-0.980112\pi\) | ||
0.998049 | − | 0.0624402i | \(-0.0198883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.3099 | −0.603834 | ||||||||
\(134\) | −88.4615 | − | 28.7429i | −0.660160 | − | 0.214499i | ||||
\(135\) | 1.67132 | − | 1.21428i | 0.0123801 | − | 0.00899470i | ||||
\(136\) | 116.924 | + | 84.9500i | 0.859732 | + | 0.624632i | ||||
\(137\) | 9.45259 | + | 29.0921i | 0.0689970 | + | 0.212351i | 0.979610 | − | 0.200910i | \(-0.0643898\pi\) |
−0.910613 | + | 0.413261i | \(0.864390\pi\) | |||||||
\(138\) | 9.59792 | − | 3.11855i | 0.0695501 | − | 0.0225982i | ||||
\(139\) | 16.3089 | − | 22.4473i | 0.117330 | − | 0.161492i | −0.746312 | − | 0.665596i | \(-0.768177\pi\) |
0.863643 | + | 0.504105i | \(0.168177\pi\) | |||||||
\(140\) | 5.12484 | + | 7.05374i | 0.0366060 | + | 0.0503839i | ||||
\(141\) | 29.6310 | − | 91.1948i | 0.210149 | − | 0.646771i | ||||
\(142\) | − | 81.2821i | − | 0.572409i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 16.0403 | 0.111391 | ||||||||
\(145\) | −9.43576 | − | 3.06586i | −0.0650742 | − | 0.0211439i | ||||
\(146\) | −37.0261 | + | 26.9011i | −0.253604 | + | 0.184254i | ||||
\(147\) | −4.52159 | − | 3.28513i | −0.0307591 | − | 0.0223478i | ||||
\(148\) | −5.59546 | − | 17.2211i | −0.0378072 | − | 0.116359i | ||||
\(149\) | −189.076 | + | 61.4346i | −1.26897 | + | 0.412313i | −0.864682 | − | 0.502320i | \(-0.832480\pi\) |
−0.404286 | + | 0.914633i | \(0.632480\pi\) | |||||||
\(150\) | −24.8501 | + | 34.2032i | −0.165667 | + | 0.228021i | ||||
\(151\) | −76.7103 | − | 105.583i | −0.508015 | − | 0.699223i | 0.475568 | − | 0.879679i | \(-0.342243\pi\) |
−0.983583 | + | 0.180456i | \(0.942243\pi\) | |||||||
\(152\) | −23.7358 | + | 73.0514i | −0.156157 | + | 0.480601i | ||||
\(153\) | − | 62.7286i | − | 0.409991i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.7058 | 0.152940 | ||||||||
\(156\) | −60.7834 | − | 19.7497i | −0.389637 | − | 0.126601i | ||||
\(157\) | 57.1062 | − | 41.4901i | 0.363734 | − | 0.264268i | −0.390874 | − | 0.920444i | \(-0.627827\pi\) |
0.754608 | + | 0.656176i | \(0.227827\pi\) | |||||||
\(158\) | −47.9486 | − | 34.8367i | −0.303472 | − | 0.220485i | ||||
\(159\) | 50.6609 | + | 155.918i | 0.318622 | + | 0.980617i | ||||
\(160\) | 12.4405 | − | 4.04218i | 0.0777534 | − | 0.0252636i | ||||
\(161\) | 25.1891 | − | 34.6698i | 0.156454 | − | 0.215340i | ||||
\(162\) | 5.19785 | + | 7.15423i | 0.0320855 | + | 0.0441619i | ||||
\(163\) | −23.7664 | + | 73.1456i | −0.145806 | + | 0.448746i | −0.997114 | − | 0.0759212i | \(-0.975810\pi\) |
0.851307 | + | 0.524667i | \(0.175810\pi\) | |||||||
\(164\) | − | 157.917i | − | 0.962910i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 148.047 | 0.891848 | ||||||||
\(167\) | −96.7773 | − | 31.4449i | −0.579505 | − | 0.188293i | 0.00457380 | − | 0.999990i | \(-0.498544\pi\) |
−0.584079 | + | 0.811697i | \(0.698544\pi\) | |||||||
\(168\) | −69.9946 | + | 50.8541i | −0.416635 | + | 0.302703i | ||||
\(169\) | −17.1043 | − | 12.4270i | −0.101209 | − | 0.0735324i | ||||
\(170\) | −2.52412 | − | 7.76844i | −0.0148478 | − | 0.0456967i | ||||
\(171\) | 31.7066 | − | 10.3021i | 0.185419 | − | 0.0602462i | ||||
\(172\) | −31.4708 | + | 43.3159i | −0.182970 | + | 0.251837i | ||||
\(173\) | 73.4157 | + | 101.048i | 0.424368 | + | 0.584093i | 0.966649 | − | 0.256104i | \(-0.0824391\pi\) |
−0.542281 | + | 0.840197i | \(0.682439\pi\) | |||||||
\(174\) | 13.1237 | − | 40.3906i | 0.0754236 | − | 0.232130i | ||||
\(175\) | 179.528i | 1.02587i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 43.4836 | 0.245670 | ||||||||
\(178\) | −125.397 | − | 40.7440i | −0.704479 | − | 0.228899i | ||||
\(179\) | 83.5151 | − | 60.6773i | 0.466565 | − | 0.338979i | −0.329536 | − | 0.944143i | \(-0.606892\pi\) |
0.796101 | + | 0.605164i | \(0.206892\pi\) | |||||||
\(180\) | −2.92816 | − | 2.12743i | −0.0162675 | − | 0.0118191i | ||||
\(181\) | −34.7526 | − | 106.957i | −0.192003 | − | 0.590925i | −0.999998 | − | 0.00173608i | \(-0.999447\pi\) |
0.807995 | − | 0.589189i | \(-0.200553\pi\) | |||||||
\(182\) | 82.1180 | − | 26.6818i | 0.451198 | − | 0.146603i | ||||
\(183\) | 34.0099 | − | 46.8107i | 0.185847 | − | 0.255796i | ||||
\(184\) | −24.0916 | − | 33.1592i | −0.130933 | − | 0.180213i | ||||
\(185\) | −0.733095 | + | 2.25623i | −0.00396268 | + | 0.0121959i | ||||
\(186\) | 101.475i | 0.545563i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −167.996 | −0.893595 | ||||||||
\(189\) | 35.7137 | + | 11.6041i | 0.188961 | + | 0.0613973i | ||||
\(190\) | 3.51206 | − | 2.55166i | 0.0184845 | − | 0.0134298i | ||||
\(191\) | −154.580 | − | 112.309i | −0.809321 | − | 0.588006i | 0.104313 | − | 0.994545i | \(-0.466736\pi\) |
−0.913634 | + | 0.406539i | \(0.866736\pi\) | |||||||
\(192\) | 5.85582 | + | 18.0224i | 0.0304991 | + | 0.0938665i | ||||
\(193\) | 51.8875 | − | 16.8593i | 0.268847 | − | 0.0873538i | −0.171491 | − | 0.985186i | \(-0.554858\pi\) |
0.440338 | + | 0.897832i | \(0.354858\pi\) | |||||||
\(194\) | −21.7193 | + | 29.8940i | −0.111955 | + | 0.154093i | ||||
\(195\) | 4.92177 | + | 6.77424i | 0.0252399 | + | 0.0347397i | ||||
\(196\) | −3.02587 | + | 9.31268i | −0.0154381 | + | 0.0475137i | ||||
\(197\) | − | 75.2950i | − | 0.382208i | −0.981570 | − | 0.191104i | \(-0.938793\pi\) | ||
0.981570 | − | 0.191104i | \(-0.0612068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −60.7193 | −0.305122 | −0.152561 | − | 0.988294i | \(-0.548752\pi\) | ||||
−0.152561 | + | 0.988294i | \(0.548752\pi\) | |||||||
\(200\) | 163.302 | + | 53.0600i | 0.816510 | + | 0.265300i | ||||
\(201\) | 132.649 | − | 96.3750i | 0.659944 | − | 0.479478i | ||||
\(202\) | 64.2305 | + | 46.6662i | 0.317973 | + | 0.231021i | ||||
\(203\) | −55.7288 | − | 171.516i | −0.274526 | − | 0.844905i | ||||
\(204\) | −104.522 | + | 33.9612i | −0.512362 | + | 0.166477i | ||||
\(205\) | −12.1611 | + | 16.7383i | −0.0593224 | + | 0.0816503i | ||||
\(206\) | 57.5594 | + | 79.2237i | 0.279415 | + | 0.384581i | ||||
\(207\) | −5.49732 | + | 16.9190i | −0.0265571 | + | 0.0817343i | ||||
\(208\) | 65.0152i | 0.312573i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.88979 | 0.0232847 | ||||||||
\(211\) | 389.165 | + | 126.447i | 1.84438 | + | 0.599276i | 0.997746 | + | 0.0671038i | \(0.0213759\pi\) |
0.846636 | + | 0.532172i | \(0.178624\pi\) | |||||||
\(212\) | 232.371 | − | 168.828i | 1.09609 | − | 0.796357i | ||||
\(213\) | 115.918 | + | 84.2193i | 0.544215 | + | 0.395396i | ||||
\(214\) | 32.8691 | + | 101.161i | 0.153594 | + | 0.472713i | ||||
\(215\) | 6.67145 | − | 2.16769i | 0.0310300 | − | 0.0100823i | ||||
\(216\) | 21.1106 | − | 29.0562i | 0.0977342 | − | 0.134520i | ||||
\(217\) | 253.279 | + | 348.609i | 1.16719 | + | 1.60649i | ||||
\(218\) | 53.2709 | − | 163.951i | 0.244362 | − | 0.752068i | ||||
\(219\) | − | 80.6768i | − | 0.368387i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 254.254 | 1.15047 | ||||||||
\(222\) | −9.65802 | − | 3.13808i | −0.0435046 | − | 0.0141355i | ||||
\(223\) | 119.178 | − | 86.5875i | 0.534428 | − | 0.388285i | −0.287583 | − | 0.957756i | \(-0.592852\pi\) |
0.822012 | + | 0.569471i | \(0.192852\pi\) | |||||||
\(224\) | 192.361 | + | 139.759i | 0.858756 | + | 0.623923i | ||||
\(225\) | −23.0297 | − | 70.8782i | −0.102354 | − | 0.315014i | ||||
\(226\) | 92.0680 | − | 29.9147i | 0.407380 | − | 0.132366i | ||||
\(227\) | 80.5395 | − | 110.853i | 0.354799 | − | 0.488340i | −0.593891 | − | 0.804545i | \(-0.702409\pi\) |
0.948691 | + | 0.316206i | \(0.102409\pi\) | |||||||
\(228\) | −34.3318 | − | 47.2537i | −0.150578 | − | 0.207253i | ||||
\(229\) | 26.4846 | − | 81.5113i | 0.115653 | − | 0.355945i | −0.876429 | − | 0.481531i | \(-0.840081\pi\) |
0.992083 | + | 0.125586i | \(0.0400810\pi\) | |||||||
\(230\) | 2.31649i | 0.0100717i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −172.485 | −0.743469 | ||||||||
\(233\) | 205.838 | + | 66.8808i | 0.883424 | + | 0.287042i | 0.715378 | − | 0.698737i | \(-0.246254\pi\) |
0.168046 | + | 0.985779i | \(0.446254\pi\) | |||||||
\(234\) | −28.9977 | + | 21.0681i | −0.123922 | + | 0.0900346i | ||||
\(235\) | 17.8066 | + | 12.9372i | 0.0757726 | + | 0.0550520i | ||||
\(236\) | −23.5419 | − | 72.4547i | −0.0997540 | − | 0.307011i | ||||
\(237\) | 99.3624 | − | 32.2848i | 0.419251 | − | 0.136223i | ||||
\(238\) | 87.2716 | − | 120.119i | 0.366687 | − | 0.504702i | ||||
\(239\) | −97.1274 | − | 133.684i | −0.406391 | − | 0.559349i | 0.555943 | − | 0.831221i | \(-0.312357\pi\) |
−0.962334 | + | 0.271872i | \(0.912357\pi\) | |||||||
\(240\) | −1.13777 | + | 3.50170i | −0.00474071 | + | 0.0145904i | ||||
\(241\) | − | 233.818i | − | 0.970199i | −0.874459 | − | 0.485100i | \(-0.838783\pi\) | ||
0.874459 | − | 0.485100i | \(-0.161217\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | −96.4114 | − | 31.3260i | −0.395129 | − | 0.128385i | ||||
\(245\) | 1.03789 | − | 0.754069i | 0.00423627 | − | 0.00307783i | ||||
\(246\) | −71.6498 | − | 52.0567i | −0.291260 | − | 0.211612i | ||||
\(247\) | 41.7568 | + | 128.514i | 0.169056 | + | 0.520300i | ||||
\(248\) | 391.959 | − | 127.355i | 1.58048 | − | 0.513529i | ||||
\(249\) | −153.396 | + | 211.132i | −0.616050 | + | 0.847920i | ||||
\(250\) | −11.4445 | − | 15.7520i | −0.0457779 | − | 0.0630079i | ||||
\(251\) | 82.6256 | − | 254.295i | 0.329186 | − | 1.01313i | −0.640330 | − | 0.768100i | \(-0.721202\pi\) |
0.969516 | − | 0.245029i | \(-0.0787976\pi\) | |||||||
\(252\) | − | 65.7905i | − | 0.261074i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.4850 | 0.0845866 | ||||||||
\(255\) | 13.6940 | + | 4.44946i | 0.0537021 | + | 0.0174489i | ||||
\(256\) | 131.475 | − | 95.5218i | 0.513572 | − | 0.373132i | ||||
\(257\) | −40.0571 | − | 29.1032i | −0.155864 | − | 0.113242i | 0.507120 | − | 0.861876i | \(-0.330710\pi\) |
−0.662984 | + | 0.748634i | \(0.730710\pi\) | |||||||
\(258\) | 9.27898 | + | 28.5578i | 0.0359650 | + | 0.110689i | ||||
\(259\) | −41.0120 | + | 13.3256i | −0.158348 | + | 0.0514502i | ||||
\(260\) | 8.62296 | − | 11.8685i | 0.0331652 | − | 0.0456480i | ||||
\(261\) | 44.0039 | + | 60.5661i | 0.168597 | + | 0.232054i | ||||
\(262\) | −4.96719 | + | 15.2875i | −0.0189588 | + | 0.0583490i | ||||
\(263\) | 198.763i | 0.755752i | 0.925856 | + | 0.377876i | \(0.123345\pi\) | ||||
−0.925856 | + | 0.377876i | \(0.876655\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.6313 | −0.142005 | ||||||||
\(266\) | 75.0478 | + | 24.3845i | 0.282135 | + | 0.0916711i | ||||
\(267\) | 188.034 | − | 136.615i | 0.704248 | − | 0.511666i | ||||
\(268\) | −232.401 | − | 168.849i | −0.867168 | − | 0.630035i | ||||
\(269\) | 3.32902 | + | 10.2457i | 0.0123755 | + | 0.0380880i | 0.957054 | − | 0.289911i | \(-0.0936257\pi\) |
−0.944678 | + | 0.327999i | \(0.893626\pi\) | |||||||
\(270\) | −1.93050 | + | 0.627259i | −0.00715002 | + | 0.00232318i | ||||
\(271\) | −171.766 | + | 236.416i | −0.633824 | + | 0.872384i | −0.998267 | − | 0.0588420i | \(-0.981259\pi\) |
0.364444 | + | 0.931225i | \(0.381259\pi\) | |||||||
\(272\) | 65.7137 | + | 90.4471i | 0.241594 | + | 0.332526i | ||||
\(273\) | −47.0340 | + | 144.756i | −0.172286 | + | 0.530241i | ||||
\(274\) | − | 30.0560i | − | 0.109693i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 31.1676 | 0.112926 | ||||||||
\(277\) | −166.782 | − | 54.1909i | −0.602103 | − | 0.195635i | −0.00792475 | − | 0.999969i | \(-0.502523\pi\) |
−0.594178 | + | 0.804334i | \(0.702523\pi\) | |||||||
\(278\) | −22.0560 | + | 16.0246i | −0.0793383 | + | 0.0576426i | ||||
\(279\) | −144.715 | − | 105.142i | −0.518692 | − | 0.376851i | ||||
\(280\) | −6.13689 | − | 18.8874i | −0.0219175 | − | 0.0674551i | ||||
\(281\) | 216.252 | − | 70.2645i | 0.769580 | − | 0.250052i | 0.102195 | − | 0.994764i | \(-0.467414\pi\) |
0.667385 | + | 0.744713i | \(0.267414\pi\) | |||||||
\(282\) | −55.3790 | + | 76.2227i | −0.196379 | + | 0.270293i | ||||
\(283\) | 139.567 | + | 192.098i | 0.493171 | + | 0.678791i | 0.980969 | − | 0.194165i | \(-0.0621997\pi\) |
−0.487798 | + | 0.872957i | \(0.662200\pi\) | |||||||
\(284\) | 77.5729 | − | 238.745i | 0.273144 | − | 0.840651i | ||||
\(285\) | 7.65249i | 0.0268508i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −376.080 | −1.31038 | ||||||||
\(288\) | −93.8731 | − | 30.5012i | −0.325948 | − | 0.105907i | ||||
\(289\) | 119.904 | − | 87.1152i | 0.414892 | − | 0.301437i | ||||
\(290\) | 7.88662 | + | 5.72997i | 0.0271953 | + | 0.0197585i | ||||
\(291\) | −20.1283 | − | 61.9484i | −0.0691693 | − | 0.212881i | ||||
\(292\) | −134.428 | + | 43.6783i | −0.460370 | + | 0.149583i | ||||
\(293\) | −17.2419 | + | 23.7315i | −0.0588462 | + | 0.0809949i | −0.837426 | − | 0.546551i | \(-0.815940\pi\) |
0.778580 | + | 0.627546i | \(0.215940\pi\) | |||||||
\(294\) | 3.22786 | + | 4.44277i | 0.0109791 | + | 0.0151115i | ||||
\(295\) | −3.08437 | + | 9.49272i | −0.0104555 | + | 0.0321787i | ||||
\(296\) | 41.2437i | 0.139337i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 195.341 | 0.655507 | ||||||||
\(299\) | −68.5766 | − | 22.2819i | −0.229353 | − | 0.0745213i | ||||
\(300\) | −105.633 | + | 76.7468i | −0.352110 | + | 0.255823i | ||||
\(301\) | 103.157 | + | 74.9479i | 0.342714 | + | 0.248996i | ||||
\(302\) | 39.6260 | + | 121.956i | 0.131212 | + | 0.403829i | ||||
\(303\) | −133.103 | + | 43.2477i | −0.439283 | + | 0.142732i | ||||
\(304\) | −34.9247 | + | 48.0698i | −0.114884 | + | 0.158124i | ||||
\(305\) | 7.80665 | + | 10.7449i | 0.0255956 | + | 0.0352293i | ||||
\(306\) | −19.0463 | + | 58.6186i | −0.0622429 | + | 0.191564i | ||||
\(307\) | − | 347.331i | − | 1.13137i | −0.824621 | − | 0.565686i | \(-0.808611\pi\) | ||
0.824621 | − | 0.565686i | \(-0.191389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −172.622 | −0.558646 | ||||||||
\(310\) | −22.1525 | − | 7.19780i | −0.0714598 | − | 0.0232187i | ||||
\(311\) | −356.430 | + | 258.961i | −1.14608 | + | 0.832673i | −0.987954 | − | 0.154747i | \(-0.950544\pi\) |
−0.158122 | + | 0.987420i | \(0.550544\pi\) | |||||||
\(312\) | 117.772 | + | 85.5660i | 0.377473 | + | 0.274250i | ||||
\(313\) | −7.86896 | − | 24.2182i | −0.0251405 | − | 0.0773744i | 0.937699 | − | 0.347448i | \(-0.112952\pi\) |
−0.962840 | + | 0.270074i | \(0.912952\pi\) | |||||||
\(314\) | −65.9622 | + | 21.4324i | −0.210071 | + | 0.0682561i | ||||
\(315\) | −5.06648 | + | 6.97341i | −0.0160841 | + | 0.0221378i | ||||
\(316\) | −107.589 | − | 148.084i | −0.340473 | − | 0.468621i | ||||
\(317\) | 28.2391 | − | 86.9111i | 0.0890824 | − | 0.274167i | −0.896584 | − | 0.442874i | \(-0.853959\pi\) |
0.985666 | + | 0.168706i | \(0.0539590\pi\) | |||||||
\(318\) | − | 161.084i | − | 0.506554i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.34975 | −0.0135930 | ||||||||
\(321\) | −178.324 | − | 57.9409i | −0.555526 | − | 0.180501i | ||||
\(322\) | −34.0655 | + | 24.7500i | −0.105793 | + | 0.0768634i | ||||
\(323\) | 187.986 | + | 136.579i | 0.581999 | + | 0.422847i | ||||
\(324\) | 8.43957 | + | 25.9743i | 0.0260481 | + | 0.0801677i | ||||
\(325\) | 287.286 | − | 93.3448i | 0.883956 | − | 0.287215i | ||||
\(326\) | 44.4185 | − | 61.1368i | 0.136253 | − | 0.187536i | ||||
\(327\) | 178.617 | + | 245.846i | 0.546230 | + | 0.751822i | ||||
\(328\) | −111.152 | + | 342.090i | −0.338877 | + | 1.04296i | ||||
\(329\) | 400.083i | 1.21606i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −318.761 | −0.963024 | −0.481512 | − | 0.876439i | \(-0.659912\pi\) | ||||
−0.481512 | + | 0.876439i | \(0.659912\pi\) | |||||||
\(332\) | 434.848 | + | 141.291i | 1.30978 | + | 0.425575i | ||||
\(333\) | 14.4823 | − | 10.5220i | 0.0434903 | − | 0.0315976i | ||||
\(334\) | 80.8887 | + | 58.7691i | 0.242182 | + | 0.175955i | ||||
\(335\) | 11.6302 | + | 35.7941i | 0.0347170 | + | 0.106848i | ||||
\(336\) | −63.6511 | + | 20.6815i | −0.189438 | + | 0.0615521i | ||||
\(337\) | −363.111 | + | 499.779i | −1.07748 | + | 1.48302i | −0.215216 | + | 0.976566i | \(0.569046\pi\) |
−0.862264 | + | 0.506458i | \(0.830954\pi\) | |||||||
\(338\) | 12.2104 | + | 16.8061i | 0.0361253 | + | 0.0497223i | ||||
\(339\) | −52.7330 | + | 162.295i | −0.155555 | + | 0.478748i | ||||
\(340\) | − | 25.2267i | − | 0.0741961i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −32.7572 | −0.0957812 | ||||||||
\(343\) | −314.604 | − | 102.221i | −0.917213 | − | 0.298021i | ||||
\(344\) | 98.6624 | − | 71.6824i | 0.286809 | − | 0.208379i | ||||
\(345\) | −3.30358 | − | 2.40019i | −0.00957560 | − | 0.00695708i | ||||
\(346\) | −37.9242 | − | 116.719i | −0.109607 | − | 0.337337i | ||||
\(347\) | −191.285 | + | 62.1523i | −0.551254 | + | 0.179113i | −0.571382 | − | 0.820684i | \(-0.693593\pi\) |
0.0201283 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(348\) | 77.0949 | − | 106.112i | 0.221537 | − | 0.304920i | ||||
\(349\) | −284.922 | − | 392.161i | −0.816394 | − | 1.12367i | −0.990305 | − | 0.138909i | \(-0.955640\pi\) |
0.173911 | − | 0.984761i | \(-0.444360\pi\) | |||||||
\(350\) | 54.5102 | − | 167.765i | 0.155743 | − | 0.479329i | ||||
\(351\) | − | 63.1836i | − | 0.180010i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 108.957 | 0.308661 | 0.154330 | − | 0.988019i | \(-0.450678\pi\) | ||||
0.154330 | + | 0.988019i | \(0.450678\pi\) | |||||||
\(354\) | −40.6345 | − | 13.2029i | −0.114787 | − | 0.0372964i | ||||
\(355\) | −26.6078 | + | 19.3317i | −0.0749516 | + | 0.0544555i | ||||
\(356\) | −329.437 | − | 239.350i | −0.925384 | − | 0.672330i | ||||
\(357\) | 80.8787 | + | 248.919i | 0.226551 | + | 0.697253i | ||||
\(358\) | −96.4665 | + | 31.3439i | −0.269460 | + | 0.0875527i | ||||
\(359\) | 251.873 | − | 346.674i | 0.701597 | − | 0.965665i | −0.298341 | − | 0.954459i | \(-0.596433\pi\) |
0.999937 | − | 0.0112055i | \(-0.00356689\pi\) | |||||||
\(360\) | 4.84573 | + | 6.66958i | 0.0134604 | + | 0.0185266i | ||||
\(361\) | 73.3935 | − | 225.882i | 0.203306 | − | 0.625712i | ||||
\(362\) | 110.501i | 0.305252i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 266.664 | 0.732594 | ||||||||
\(365\) | 17.6122 | + | 5.72256i | 0.0482526 | + | 0.0156782i | ||||
\(366\) | −45.9947 | + | 33.4171i | −0.125669 | + | 0.0913035i | ||||
\(367\) | −346.207 | − | 251.534i | −0.943344 | − | 0.685379i | 0.00587937 | − | 0.999983i | \(-0.498129\pi\) |
−0.949223 | + | 0.314603i | \(0.898129\pi\) | |||||||
\(368\) | −9.79765 | − | 30.1541i | −0.0266240 | − | 0.0819404i | ||||
\(369\) | 148.478 | − | 48.2434i | 0.402379 | − | 0.130741i | ||||
\(370\) | 1.37012 | − | 1.88581i | 0.00370303 | − | 0.00509679i | ||||
\(371\) | −402.064 | − | 553.393i | −1.08373 | − | 1.49163i | ||||
\(372\) | −96.8441 | + | 298.055i | −0.260333 | + | 0.801224i | ||||
\(373\) | 104.312i | 0.279656i | 0.990176 | + | 0.139828i | \(0.0446549\pi\) | ||||
−0.990176 | + | 0.139828i | \(0.955345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 34.3222 | 0.0915259 | ||||||||
\(376\) | 363.923 | + | 118.246i | 0.967879 | + | 0.314483i | ||||
\(377\) | −245.488 | + | 178.358i | −0.651163 | + | 0.473097i | ||||
\(378\) | −29.8503 | − | 21.6875i | −0.0789691 | − | 0.0573744i | ||||
\(379\) | 69.4233 | + | 213.663i | 0.183175 | + | 0.563755i | 0.999912 | − | 0.0132552i | \(-0.00421938\pi\) |
−0.816737 | + | 0.577010i | \(0.804219\pi\) | |||||||
\(380\) | 12.7510 | − | 4.14305i | 0.0335552 | − | 0.0109028i | ||||
\(381\) | −22.2613 | + | 30.6401i | −0.0584287 | + | 0.0804202i | ||||
\(382\) | 110.351 | + | 151.886i | 0.288878 | + | 0.397607i | ||||
\(383\) | 18.3147 | − | 56.3668i | 0.0478190 | − | 0.147172i | −0.924296 | − | 0.381676i | \(-0.875347\pi\) |
0.972115 | + | 0.234505i | \(0.0753468\pi\) | |||||||
\(384\) | 209.328i | 0.545124i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −53.6068 | −0.138878 | ||||||||
\(387\) | −50.3410 | − | 16.3568i | −0.130080 | − | 0.0422656i | ||||
\(388\) | −92.3244 | + | 67.0776i | −0.237950 | + | 0.172880i | ||||
\(389\) | 333.456 | + | 242.270i | 0.857212 | + | 0.622801i | 0.927125 | − | 0.374752i | \(-0.122272\pi\) |
−0.0699129 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(390\) | −2.54242 | − | 7.82478i | −0.00651904 | − | 0.0200635i | ||||
\(391\) | −117.923 | + | 38.3155i | −0.301593 | + | 0.0979935i | ||||
\(392\) | 13.1097 | − | 18.0439i | 0.0334430 | − | 0.0460303i | ||||
\(393\) | −16.6550 | − | 22.9237i | −0.0423792 | − | 0.0583299i | ||||
\(394\) | −22.8618 | + | 70.3615i | −0.0580250 | + | 0.178583i | ||||
\(395\) | 23.9814i | 0.0607125i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 619.925 | 1.56152 | 0.780762 | − | 0.624829i | \(-0.214831\pi\) | ||||
0.780762 | + | 0.624829i | \(0.214831\pi\) | |||||||
\(398\) | 56.7408 | + | 18.4362i | 0.142565 | + | 0.0463222i | ||||
\(399\) | −112.535 | + | 81.7614i | −0.282042 | + | 0.204916i | ||||
\(400\) | 107.457 | + | 78.0722i | 0.268643 | + | 0.195180i | ||||
\(401\) | −207.684 | − | 639.187i | −0.517916 | − | 1.59398i | −0.777913 | − | 0.628373i | \(-0.783721\pi\) |
0.259996 | − | 0.965610i | \(-0.416279\pi\) | |||||||
\(402\) | −153.220 | + | 49.7841i | −0.381144 | + | 0.123841i | ||||
\(403\) | 426.163 | − | 586.563i | 1.05748 | − | 1.45549i | ||||
\(404\) | 144.123 | + | 198.369i | 0.356741 | + | 0.491012i | ||||
\(405\) | 1.10572 | − | 3.40305i | 0.00273017 | − | 0.00840260i | ||||
\(406\) | 177.199i | 0.436450i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 250.326 | 0.613543 | ||||||||
\(409\) | −584.277 | − | 189.843i | −1.42855 | − | 0.464164i | −0.510243 | − | 0.860031i | \(-0.670444\pi\) |
−0.918308 | + | 0.395866i | \(0.870444\pi\) | |||||||
\(410\) | 16.4465 | − | 11.9491i | 0.0401135 | − | 0.0291442i | ||||
\(411\) | 42.8634 | + | 31.1421i | 0.104291 | + | 0.0757715i | ||||
\(412\) | 93.4571 | + | 287.632i | 0.226838 | + | 0.698135i | ||||
\(413\) | −172.551 | + | 56.0652i | −0.417799 | + | 0.135751i | ||||
\(414\) | 10.2742 | − | 14.1413i | 0.0248170 | − | 0.0341577i | ||||
\(415\) | −35.2107 | − | 48.4633i | −0.0848450 | − | 0.116779i | ||||
\(416\) | 123.628 | − | 380.489i | 0.297184 | − | 0.914637i | ||||
\(417\) | − | 48.0582i | − | 0.115247i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −60.9488 | −0.145462 | −0.0727312 | − | 0.997352i | \(-0.523172\pi\) | ||||
−0.0727312 | + | 0.997352i | \(0.523172\pi\) | |||||||
\(420\) | 14.3625 | + | 4.66665i | 0.0341963 | + | 0.0111111i | ||||
\(421\) | −168.768 | + | 122.617i | −0.400873 | + | 0.291251i | −0.769897 | − | 0.638169i | \(-0.779692\pi\) |
0.369023 | + | 0.929420i | \(0.379692\pi\) | |||||||
\(422\) | −325.273 | − | 236.324i | −0.770788 | − | 0.560011i | ||||
\(423\) | −51.3223 | − | 157.954i | −0.121329 | − | 0.373414i | ||||
\(424\) | −622.208 | + | 202.168i | −1.46747 | + | 0.476811i | ||||
\(425\) | 305.315 | − | 420.231i | 0.718389 | − | 0.988778i | ||||
\(426\) | −82.7512 | − | 113.897i | −0.194252 | − | 0.267364i | ||||
\(427\) | −74.6029 | + | 229.604i | −0.174714 | + | 0.537714i | ||||
\(428\) | 328.502i | 0.767528i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.89250 | −0.0160291 | ||||||||
\(431\) | 257.472 | + | 83.6576i | 0.597382 | + | 0.194101i | 0.592072 | − | 0.805885i | \(-0.298310\pi\) |
0.00530937 | + | 0.999986i | \(0.498310\pi\) | |||||||
\(432\) | 22.4767 | − | 16.3303i | 0.0520293 | − | 0.0378015i | ||||
\(433\) | 507.498 | + | 368.719i | 1.17205 | + | 0.851545i | 0.991253 | − | 0.131976i | \(-0.0421321\pi\) |
0.180798 | + | 0.983520i | \(0.442132\pi\) | |||||||
\(434\) | −130.836 | − | 402.671i | −0.301465 | − | 0.927814i | ||||
\(435\) | −16.3432 | + | 5.31023i | −0.0375706 | + | 0.0122074i | ||||
\(436\) | 312.938 | − | 430.722i | 0.717748 | − | 0.987896i | ||||
\(437\) | −38.7336 | − | 53.3122i | −0.0886353 | − | 0.121996i | ||||
\(438\) | −24.4959 | + | 75.3907i | −0.0559268 | + | 0.172125i | ||||
\(439\) | − | 495.244i | − | 1.12812i | −0.825734 | − | 0.564060i | \(-0.809239\pi\) | ||
0.825734 | − | 0.564060i | \(-0.190761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.68041 | −0.0219510 | ||||||||
\(442\) | −237.594 | − | 77.1991i | −0.537544 | − | 0.174659i | ||||
\(443\) | −600.294 | + | 436.139i | −1.35507 | + | 0.984513i | −0.356324 | + | 0.934363i | \(0.615970\pi\) |
−0.998742 | + | 0.0501502i | \(0.984030\pi\) | |||||||
\(444\) | −25.3730 | − | 18.4346i | −0.0571464 | − | 0.0415193i | ||||
\(445\) | 16.4862 | + | 50.7393i | 0.0370477 | + | 0.114021i | ||||
\(446\) | −137.659 | + | 44.7283i | −0.308653 | + | 0.100288i | ||||
\(447\) | −202.400 | + | 278.579i | −0.452796 | + | 0.623220i | ||||
\(448\) | −46.4740 | − | 63.9660i | −0.103737 | − | 0.142781i | ||||
\(449\) | −220.504 | + | 678.641i | −0.491100 | + | 1.51145i | 0.331847 | + | 0.943333i | \(0.392328\pi\) |
−0.822947 | + | 0.568118i | \(0.807672\pi\) | |||||||
\(450\) | 73.2267i | 0.162726i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 298.975 | 0.661449 | ||||||||
\(453\) | −214.982 | − | 69.8519i | −0.474574 | − | 0.154198i | ||||
\(454\) | −108.921 | + | 79.1356i | −0.239914 | + | 0.174307i | ||||
\(455\) | −28.2648 | − | 20.5356i | −0.0621205 | − | 0.0451332i | ||||
\(456\) | 41.1117 | + | 126.529i | 0.0901571 | + | 0.277475i | ||||
\(457\) | −268.687 | + | 87.3016i | −0.587936 | + | 0.191032i | −0.587853 | − | 0.808968i | \(-0.700027\pi\) |
−8.33060e−5 | 1.00000i | \(0.500027\pi\) | ||||||||
\(458\) | −49.4986 | + | 68.1290i | −0.108076 | + | 0.148753i | ||||
\(459\) | −63.8624 | − | 87.8991i | −0.139134 | − | 0.191501i | ||||
\(460\) | −2.21078 | + | 6.80407i | −0.00480604 | + | 0.0147915i | ||||
\(461\) | 198.186i | 0.429905i | 0.976624 | + | 0.214953i | \(0.0689597\pi\) | ||||
−0.976624 | + | 0.214953i | \(0.931040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −226.915 | −0.490097 | −0.245049 | − | 0.969511i | \(-0.578804\pi\) | ||||
−0.245049 | + | 0.969511i | \(0.578804\pi\) | |||||||
\(464\) | −126.896 | − | 41.2312i | −0.273484 | − | 0.0888602i | ||||
\(465\) | 33.2179 | − | 24.1342i | 0.0714364 | − | 0.0519016i | ||||
\(466\) | −172.044 | − | 124.997i | −0.369193 | − | 0.268235i | ||||
\(467\) | 46.2471 | + | 142.334i | 0.0990302 | + | 0.304784i | 0.988283 | − | 0.152632i | \(-0.0487750\pi\) |
−0.889253 | + | 0.457416i | \(0.848775\pi\) | |||||||
\(468\) | −105.280 | + | 34.2075i | −0.224957 | + | 0.0730930i | ||||
\(469\) | −402.115 | + | 553.464i | −0.857388 | + | 1.18009i | ||||
\(470\) | −12.7117 | − | 17.4962i | −0.0270462 | − | 0.0372259i | ||||
\(471\) | 37.7806 | − | 116.277i | 0.0802136 | − | 0.246872i | ||||
\(472\) | 173.526i | 0.367640i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −102.655 | −0.216571 | ||||||||
\(475\) | 262.551 | + | 85.3080i | 0.552739 | + | 0.179596i | ||||
\(476\) | 370.975 | − | 269.529i | 0.779359 | − | 0.566238i | ||||
\(477\) | 229.725 | + | 166.905i | 0.481604 | + | 0.349906i | ||||
\(478\) | 50.1728 | + | 154.416i | 0.104964 | + | 0.323046i | ||||
\(479\) | 309.826 | − | 100.668i | 0.646818 | − | 0.210164i | 0.0328073 | − | 0.999462i | \(-0.489555\pi\) |
0.614011 | + | 0.789298i | \(0.289555\pi\) | |||||||
\(480\) | 13.3172 | − | 18.3295i | 0.0277441 | − | 0.0381865i | ||||
\(481\) | 42.6480 | + | 58.7000i | 0.0886654 | + | 0.122037i | ||||
\(482\) | −70.9943 | + | 218.498i | −0.147291 | + | 0.453315i | ||||
\(483\) | − | 74.2257i | − | 0.153676i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.9514 | 0.0308277 | ||||||||
\(486\) | 14.5671 | + | 4.73313i | 0.0299734 | + | 0.00973895i | ||||
\(487\) | 248.307 | − | 180.405i | 0.509870 | − | 0.370442i | −0.302904 | − | 0.953021i | \(-0.597956\pi\) |
0.812774 | + | 0.582579i | \(0.197956\pi\) | |||||||
\(488\) | 186.803 | + | 135.720i | 0.382793 | + | 0.278115i | ||||
\(489\) | 41.1647 | + | 126.692i | 0.0841814 | + | 0.259084i | ||||
\(490\) | −1.19884 | + | 0.389527i | −0.00244661 | + | 0.000794953i | ||||
\(491\) | 360.826 | − | 496.635i | 0.734880 | − | 1.01148i | −0.264017 | − | 0.964518i | \(-0.585047\pi\) |
0.998897 | − | 0.0469576i | \(-0.0149526\pi\) | |||||||
\(492\) | −160.771 | − | 221.283i | −0.326771 | − | 0.449762i | ||||
\(493\) | −161.242 | + | 496.251i | −0.327063 | + | 1.00660i | ||||
\(494\) | − | 132.772i | − | 0.268770i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 318.806 | 0.642754 | ||||||||
\(497\) | −568.572 | − | 184.740i | −1.14401 | − | 0.371710i | ||||
\(498\) | 207.452 | − | 150.723i | 0.416570 | − | 0.302656i | ||||
\(499\) | −331.265 | − | 240.678i | −0.663858 | − | 0.482321i | 0.204106 | − | 0.978949i | \(-0.434571\pi\) |
−0.867964 | + | 0.496628i | \(0.834571\pi\) | |||||||
\(500\) | −18.5820 | − | 57.1895i | −0.0371640 | − | 0.114379i | ||||
\(501\) | −167.623 | + | 54.4641i | −0.334577 | + | 0.108711i | ||||
\(502\) | −154.424 | + | 212.546i | −0.307617 | + | 0.423398i | ||||
\(503\) | −416.031 | − | 572.618i | −0.827100 | − | 1.13841i | −0.988456 | − | 0.151509i | \(-0.951587\pi\) |
0.161356 | − | 0.986896i | \(-0.448413\pi\) | |||||||
\(504\) | −46.3074 | + | 142.519i | −0.0918797 | + | 0.282777i | ||||
\(505\) | − | 32.1248i | − | 0.0636134i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.6191 | −0.0722270 | ||||||||
\(508\) | 63.1065 | + | 20.5045i | 0.124225 | + | 0.0403633i | ||||
\(509\) | −166.615 | + | 121.053i | −0.327339 | + | 0.237826i | −0.739301 | − | 0.673376i | \(-0.764844\pi\) |
0.411962 | + | 0.911201i | \(0.364844\pi\) | |||||||
\(510\) | −11.4458 | − | 8.31585i | −0.0224427 | − | 0.0163056i | ||||
\(511\) | 104.020 | + | 320.141i | 0.203562 | + | 0.626499i | ||||
\(512\) | 307.898 | − | 100.042i | 0.601362 | − | 0.195394i | ||||
\(513\) | 33.9408 | − | 46.7156i | 0.0661615 | − | 0.0910635i | ||||
\(514\) | 28.5959 | + | 39.3588i | 0.0556340 | + | 0.0765736i | ||||
\(515\) | 12.2444 | − | 37.6843i | 0.0237755 | − | 0.0731734i | ||||
\(516\) | 92.7364i | 0.179722i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 42.3709 | 0.0817971 | ||||||||
\(519\) | 205.749 | + | 66.8519i | 0.396433 | + | 0.128809i | ||||
\(520\) | −27.0333 | + | 19.6409i | −0.0519872 | + | 0.0377709i | ||||
\(521\) | 268.961 | + | 195.412i | 0.516240 | + | 0.375070i | 0.815186 | − | 0.579200i | \(-0.196635\pi\) |
−0.298946 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(522\) | −22.7309 | − | 69.9586i | −0.0435459 | − | 0.134020i | ||||
\(523\) | 297.488 | − | 96.6596i | 0.568810 | − | 0.184818i | −0.0104714 | − | 0.999945i | \(-0.503333\pi\) |
0.579281 | + | 0.815128i | \(0.303333\pi\) | |||||||
\(524\) | −29.1796 | + | 40.1623i | −0.0556863 | + | 0.0766457i | ||||
\(525\) | 182.773 | + | 251.565i | 0.348139 | + | 0.479172i | ||||
\(526\) | 60.3504 | − | 185.740i | 0.114735 | − | 0.353117i | ||||
\(527\) | − | 1246.75i | − | 2.36575i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −493.836 | −0.933528 | ||||||||
\(530\) | 35.1657 | + | 11.4260i | 0.0663503 | + | 0.0215585i | ||||
\(531\) | 60.9317 | − | 44.2695i | 0.114749 | − | 0.0833700i | ||||
\(532\) | 197.161 | + | 143.246i | 0.370604 | + | 0.269260i | ||||
\(533\) | 195.541 | + | 601.815i | 0.366869 | + | 1.12911i | ||||
\(534\) | −217.194 | + | 70.5707i | −0.406731 | + | 0.132155i | ||||
\(535\) | 25.2977 | − | 34.8193i | 0.0472854 | − | 0.0650827i | ||||
\(536\) | 384.595 | + | 529.349i | 0.717528 | + | 0.987592i | ||||
\(537\) | 55.2523 | − | 170.049i | 0.102891 | − | 0.316665i | ||||
\(538\) | − | 10.5851i | − | 0.0196750i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.26898 | −0.0116092 | ||||||||
\(541\) | 58.0809 | + | 18.8716i | 0.107358 | + | 0.0348828i | 0.362204 | − | 0.932099i | \(-0.382025\pi\) |
−0.254845 | + | 0.966982i | \(0.582025\pi\) | |||||||
\(542\) | 232.295 | − | 168.772i | 0.428588 | − | 0.311388i | ||||
\(543\) | −157.588 | − | 114.494i | −0.290217 | − | 0.210855i | ||||
\(544\) | −212.589 | − | 654.281i | −0.390788 | − | 1.20272i | ||||
\(545\) | −66.3392 | + | 21.5549i | −0.121723 | + | 0.0395503i | ||||
\(546\) | 87.9045 | − | 120.990i | 0.160997 | − | 0.221594i | ||||
\(547\) | −335.676 | − | 462.018i | −0.613667 | − | 0.844640i | 0.383206 | − | 0.923663i | \(-0.374820\pi\) |
−0.996873 | + | 0.0790232i | \(0.974820\pi\) | |||||||
\(548\) | 28.6844 | − | 88.2816i | 0.0523439 | − | 0.161098i | ||||
\(549\) | − | 100.218i | − | 0.182547i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −277.315 | −0.503294 | ||||||||
\(552\) | −67.5171 | − | 21.9376i | −0.122314 | − | 0.0397421i | ||||
\(553\) | −352.663 | + | 256.224i | −0.637726 | + | 0.463335i | ||||
\(554\) | 139.401 | + | 101.280i | 0.251626 | + | 0.182817i | ||||
\(555\) | 1.26976 | + | 3.90791i | 0.00228785 | + | 0.00704128i | ||||
\(556\) | −80.0772 | + | 26.0186i | −0.144024 | + | 0.0467961i | ||||
\(557\) | −413.872 | + | 569.646i | −0.743038 | + | 1.02270i | 0.255400 | + | 0.966836i | \(0.417793\pi\) |
−0.998438 | + | 0.0558690i | \(0.982207\pi\) | |||||||
\(558\) | 103.309 | + | 142.192i | 0.185141 | + | 0.254825i | ||||
\(559\) | 66.2978 | − | 204.044i | 0.118601 | − | 0.365015i | ||||
\(560\) | − | 15.3624i | − | 0.0274328i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −223.417 | −0.397539 | ||||||||
\(563\) | −480.301 | − | 156.059i | −0.853110 | − | 0.277192i | −0.150362 | − | 0.988631i | \(-0.548044\pi\) |
−0.702748 | + | 0.711439i | \(0.748044\pi\) | |||||||
\(564\) | −235.406 | + | 171.032i | −0.417386 | + | 0.303248i | ||||
\(565\) | −31.6896 | − | 23.0238i | −0.0560878 | − | 0.0407502i | ||||
\(566\) | −72.0959 | − | 221.888i | −0.127378 | − | 0.392029i | ||||
\(567\) | 61.8580 | − | 20.0989i | 0.109097 | − | 0.0354477i | ||||
\(568\) | −336.086 | + | 462.583i | −0.591701 | + | 0.814406i | ||||
\(569\) | 395.867 | + | 544.864i | 0.695724 | + | 0.957582i | 0.999988 | + | 0.00499388i | \(0.00158961\pi\) |
−0.304264 | + | 0.952588i | \(0.598410\pi\) | |||||||
\(570\) | 2.32353 | − | 7.15108i | 0.00407636 | − | 0.0125458i | ||||
\(571\) | 446.598i | 0.782134i | 0.920362 | + | 0.391067i | \(0.127894\pi\) | ||||
−0.920362 | + | 0.391067i | \(0.872106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −330.946 | −0.577567 | ||||||||
\(574\) | 351.439 | + | 114.189i | 0.612263 | + | 0.198936i | ||||
\(575\) | −119.176 | + | 86.5867i | −0.207263 | + | 0.150586i | ||||
\(576\) | 26.5536 | + | 19.2923i | 0.0461001 | + | 0.0334937i | ||||
\(577\) | −178.207 | − | 548.465i | −0.308851 | − | 0.950546i | −0.978212 | − | 0.207609i | \(-0.933432\pi\) |
0.669361 | − | 0.742937i | \(-0.266568\pi\) | |||||||
\(578\) | −138.498 | + | 45.0008i | −0.239616 | + | 0.0778561i | ||||
\(579\) | 55.5439 | − | 76.4496i | 0.0959307 | − | 0.132037i | ||||
\(580\) | 17.6964 | + | 24.3570i | 0.0305110 | + | 0.0419948i | ||||
\(581\) | 336.484 | − | 1035.59i | 0.579147 | − | 1.78243i | ||||
\(582\) | 64.0010i | 0.109967i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 321.949 | 0.551283 | ||||||||
\(585\) | 13.7933 | + | 4.48173i | 0.0235784 | + | 0.00766108i | ||||
\(586\) | 23.3178 | − | 16.9414i | 0.0397915 | − | 0.0289102i | ||||
\(587\) | −733.234 | − | 532.726i | −1.24912 | − | 0.907539i | −0.250950 | − | 0.968000i | \(-0.580743\pi\) |
−0.998171 | + | 0.0604605i | \(0.980743\pi\) | |||||||
\(588\) | 5.24096 | + | 16.1300i | 0.00891320 | + | 0.0274320i | ||||
\(589\) | 630.178 | − | 204.757i | 1.06991 | − | 0.347635i | ||||
\(590\) | 5.76456 | − | 7.93423i | 0.00977044 | − | 0.0134479i | ||||
\(591\) | −76.6558 | − | 105.508i | −0.129705 | − | 0.178524i | ||||
\(592\) | −9.85900 | + | 30.3429i | −0.0166537 | + | 0.0512549i | ||||
\(593\) | 724.877i | 1.22239i | 0.791480 | + | 0.611195i | \(0.209311\pi\) | ||||
−0.791480 | + | 0.611195i | \(0.790689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −60.0774 | −0.100970 | ||||||||
\(596\) | 573.763 | + | 186.427i | 0.962689 | + | 0.312797i | ||||
\(597\) | −85.0834 | + | 61.8167i | −0.142518 | + | 0.103546i | ||||
\(598\) | 57.3179 | + | 41.6439i | 0.0958493 | + | 0.0696386i | ||||
\(599\) | 123.082 | + | 378.807i | 0.205479 | + | 0.632399i | 0.999693 | + | 0.0247616i | \(0.00788267\pi\) |
−0.794214 | + | 0.607638i | \(0.792117\pi\) | |||||||
\(600\) | 282.847 | − | 91.9027i | 0.471412 | − | 0.153171i | ||||
\(601\) | 579.244 | − | 797.261i | 0.963800 | − | 1.32656i | 0.0186828 | − | 0.999825i | \(-0.494053\pi\) |
0.945117 | − | 0.326731i | \(-0.105947\pi\) | |||||||
\(602\) | −73.6415 | − | 101.359i | −0.122328 | − | 0.168370i | ||||
\(603\) | 87.7584 | − | 270.093i | 0.145536 | − | 0.447915i | ||||
\(604\) | 396.032i | 0.655682i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 137.513 | 0.226919 | ||||||||
\(607\) | −170.210 | − | 55.3045i | −0.280411 | − | 0.0911112i | 0.165435 | − | 0.986221i | \(-0.447097\pi\) |
−0.445846 | + | 0.895110i | \(0.647097\pi\) | |||||||
\(608\) | 295.797 | − | 214.909i | 0.486508 | − | 0.353468i | ||||
\(609\) | −252.706 | − | 183.602i | −0.414953 | − | 0.301481i | ||||
\(610\) | −4.03266 | − | 12.4112i | −0.00661092 | − | 0.0203463i | ||||
\(611\) | 640.223 | − | 208.021i | 1.04783 | − | 0.340460i | ||||
\(612\) | −111.887 | + | 153.999i | −0.182822 | + | 0.251633i | ||||
\(613\) | 623.575 | + | 858.277i | 1.01725 | + | 1.40013i | 0.914114 | + | 0.405458i | \(0.132888\pi\) |
0.103137 | + | 0.994667i | \(0.467112\pi\) | |||||||
\(614\) | −105.460 | + | 324.573i | −0.171759 | + | 0.528621i | ||||
\(615\) | 35.8356i | 0.0582692i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 55.3570 | 0.0897196 | 0.0448598 | − | 0.998993i | \(-0.485716\pi\) | ||||
0.0448598 | + | 0.998993i | \(0.485716\pi\) | |||||||
\(618\) | 161.311 | + | 52.4132i | 0.261021 | + | 0.0848110i | ||||
\(619\) | 608.814 | − | 442.329i | 0.983544 | − | 0.714587i | 0.0250465 | − | 0.999686i | \(-0.492027\pi\) |
0.958498 | + | 0.285099i | \(0.0920266\pi\) | |||||||
\(620\) | −58.1979 | − | 42.2833i | −0.0938676 | − | 0.0681988i | ||||
\(621\) | 9.52163 | + | 29.3046i | 0.0153327 | + | 0.0471893i | ||||
\(622\) | 411.704 | − | 133.771i | 0.661904 | − | 0.215066i | ||||
\(623\) | −570.012 | + | 784.554i | −0.914947 | + | 1.25932i | ||||
\(624\) | 66.1902 | + | 91.1031i | 0.106074 | + | 0.145998i | ||||
\(625\) | 189.480 | − | 583.159i | 0.303168 | − | 0.933055i | ||||
\(626\) | 25.0206i | 0.0399690i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −214.201 | −0.341084 | ||||||||
\(629\) | 118.661 | + | 38.5554i | 0.188651 | + | 0.0612963i | ||||
\(630\) | 6.85186 | − | 4.97817i | 0.0108760 | − | 0.00790185i | ||||
\(631\) | 271.603 | + | 197.331i | 0.430433 | + | 0.312728i | 0.781822 | − | 0.623502i | \(-0.214291\pi\) |
−0.351389 | + | 0.936230i | \(0.614291\pi\) | |||||||
\(632\) | 128.836 | + | 396.517i | 0.203854 | + | 0.627400i | ||||
\(633\) | 674.053 | − | 219.013i | 1.06485 | − | 0.345992i | ||||
\(634\) | −52.7777 | + | 72.6423i | −0.0832456 | + | 0.114578i | ||||
\(635\) | −5.10988 | − | 7.03314i | −0.00804705 | − | 0.0110758i | ||||
\(636\) | 153.733 | − | 473.143i | 0.241719 | − | 0.743935i | ||||
\(637\) | − | 39.2369i | − | 0.0615964i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 248.172 | 0.388376 | ||||||||
\(640\) | −45.6974 | − | 14.8480i | −0.0714022 | − | 0.0232000i | ||||
\(641\) | 446.652 | − | 324.512i | 0.696805 | − | 0.506259i | −0.182085 | − | 0.983283i | \(-0.558285\pi\) |
0.878890 | + | 0.477024i | \(0.158285\pi\) | |||||||
\(642\) | 149.047 | + | 108.289i | 0.232161 | + | 0.168675i | ||||
\(643\) | −42.7550 | − | 131.586i | −0.0664930 | − | 0.204644i | 0.912290 | − | 0.409546i | \(-0.134313\pi\) |
−0.978783 | + | 0.204901i | \(0.934313\pi\) | |||||||
\(644\) | −123.679 | + | 40.1857i | −0.192048 | + | 0.0624002i | ||||
\(645\) | 7.14156 | − | 9.82952i | 0.0110722 | − | 0.0152396i | ||||
\(646\) | −134.199 | − | 184.709i | −0.207738 | − | 0.285927i | ||||
\(647\) | −312.989 | + | 963.280i | −0.483754 | + | 1.48884i | 0.350024 | + | 0.936741i | \(0.386173\pi\) |
−0.833778 | + | 0.552100i | \(0.813827\pi\) | |||||||
\(648\) | − | 62.2074i | − | 0.0959991i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −296.805 | −0.456623 | ||||||||
\(651\) | 709.820 | + | 230.634i | 1.09035 | + | 0.354277i | ||||
\(652\) | 188.814 | − | 137.182i | 0.289593 | − | 0.210401i | ||||
\(653\) | 6.23536 | + | 4.53025i | 0.00954878 | + | 0.00693760i | 0.592549 | − | 0.805534i | \(-0.298121\pi\) |
−0.583001 | + | 0.812472i | \(0.698121\pi\) | |||||||
\(654\) | −92.2678 | − | 283.971i | −0.141082 | − | 0.434207i | ||||
\(655\) | 6.18574 | − | 2.00987i | 0.00944388 | − | 0.00306850i | ||||
\(656\) | −163.548 | + | 225.104i | −0.249311 | + | 0.343147i | ||||
\(657\) | −82.1349 | − | 113.049i | −0.125015 | − | 0.172069i | ||||
\(658\) | 121.477 | − | 373.869i | 0.184616 | − | 0.568189i | ||||
\(659\) | − | 736.073i | − | 1.11695i | −0.829520 | − | 0.558477i | \(-0.811386\pi\) | ||
0.829520 | − | 0.558477i | \(-0.188614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −471.170 | −0.712813 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(662\) | 297.875 | + | 96.7855i | 0.449963 | + | 0.146202i | ||||
\(663\) | 356.275 | − | 258.849i | 0.537368 | − | 0.390421i | ||||
\(664\) | −842.545 | − | 612.145i | −1.26889 | − | 0.921905i | ||||
\(665\) | −9.86668 | − | 30.3665i | −0.0148371 | − | 0.0456639i | ||||
\(666\) | −16.7282 | + | 5.43531i | −0.0251174 | + | 0.00816113i | ||||
\(667\) | 86.9794 | − | 119.717i | 0.130404 | − | 0.179486i | ||||
\(668\) | 181.502 | + | 249.816i | 0.271710 | + | 0.373976i | ||||
\(669\) | 78.8460 | − | 242.663i | 0.117857 | − | 0.362725i | ||||
\(670\) | − | 36.9801i | − | 0.0551941i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 411.833 | 0.612846 | ||||||||
\(673\) | 1094.16 | + | 355.513i | 1.62579 | + | 0.528251i | 0.973298 | − | 0.229546i | \(-0.0737241\pi\) |
0.652491 | + | 0.757797i | \(0.273724\pi\) | |||||||
\(674\) | 491.068 | − | 356.781i | 0.728587 | − | 0.529349i | ||||
\(675\) | −104.430 | − | 75.8728i | −0.154711 | − | 0.112404i | ||||
\(676\) | 19.8255 | + | 61.0167i | 0.0293277 | + | 0.0902614i | ||||
\(677\) | −1115.02 | + | 362.292i | −1.64700 | + | 0.535143i | −0.978087 | − | 0.208196i | \(-0.933241\pi\) |
−0.668914 | + | 0.743339i | \(0.733241\pi\) | |||||||
\(678\) | 98.5557 | − | 135.650i | 0.145362 | − | 0.200074i | ||||
\(679\) | 159.746 | + | 219.871i | 0.235266 | + | 0.323816i | ||||
\(680\) | −17.7561 | + | 54.6475i | −0.0261119 | + | 0.0803640i | ||||
\(681\) | − | 237.329i | − | 0.348501i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −329.083 | −0.481820 | −0.240910 | − | 0.970547i | \(-0.577446\pi\) | ||||
−0.240910 | + | 0.970547i | \(0.577446\pi\) | |||||||
\(684\) | −96.2155 | − | 31.2623i | −0.140666 | − | 0.0457052i | ||||
\(685\) | −9.83888 | + | 7.14837i | −0.0143633 | + | 0.0104356i | ||||
\(686\) | 262.953 | + | 191.047i | 0.383314 | + | 0.278494i | ||||
\(687\) | −45.8727 | − | 141.182i | −0.0667726 | − | 0.205505i | ||||
\(688\) | 89.7207 | − | 29.1520i | 0.130408 | − | 0.0423721i | ||||
\(689\) | −676.505 | + | 931.129i | −0.981864 | + | 1.35142i | ||||
\(690\) | 2.35835 | + | 3.24600i | 0.00341791 | + | 0.00470434i | ||||
\(691\) | 222.209 | − | 683.889i | 0.321576 | − | 0.989709i | −0.651387 | − | 0.758746i | \(-0.725812\pi\) |
0.972963 | − | 0.230963i | \(-0.0741875\pi\) | |||||||
\(692\) | − | 379.023i | − | 0.547722i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 197.623 | 0.284760 | ||||||||
\(695\) | 10.4914 | + | 3.40886i | 0.0150955 | + | 0.00490483i | ||||
\(696\) | −241.696 | + | 175.602i | −0.347264 | + | 0.252302i | ||||
\(697\) | 880.311 | + | 639.584i | 1.26300 | + | 0.917624i | ||||
\(698\) | 147.181 | + | 452.977i | 0.210861 | + | 0.648964i | ||||
\(699\) | 356.522 | − | 115.841i | 0.510045 | − | 0.165724i | ||||
\(700\) | 320.218 | − | 440.743i | 0.457455 | − | 0.629633i | ||||
\(701\) | −59.1830 | − | 81.4584i | −0.0844266 | − | 0.116203i | 0.764715 | − | 0.644369i | \(-0.222880\pi\) |
−0.849141 | + | 0.528166i | \(0.822880\pi\) | |||||||
\(702\) | −19.1845 | + | 59.0437i | −0.0273283 | + | 0.0841078i | ||||
\(703\) | 66.3102i | 0.0943246i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38.1227 | 0.0540747 | ||||||||
\(706\) | −101.818 | − | 33.0827i | −0.144218 | − | 0.0468594i | ||||
\(707\) | 472.416 | − | 343.230i | 0.668198 | − | 0.485474i | ||||
\(708\) | −106.753 | − | 77.5603i | −0.150780 | − | 0.109548i | ||||
\(709\) | 85.1586 | + | 262.091i | 0.120111 | + | 0.369663i | 0.992979 | − | 0.118293i | \(-0.0377424\pi\) |
−0.872868 | + | 0.487957i | \(0.837742\pi\) | |||||||
\(710\) | 30.7341 | − | 9.98613i | 0.0432875 | − | 0.0140650i | ||||
\(711\) | 106.364 | − | 146.398i | 0.149598 | − | 0.205904i | ||||
\(712\) | 545.176 | + | 750.371i | 0.765697 | + | 1.05389i | ||||
\(713\) | −109.261 | + | 336.270i | −0.153241 | + | 0.471627i | ||||
\(714\) | − | 257.167i | − | 0.360178i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −313.258 | −0.437512 | ||||||||
\(717\) | −272.201 | − | 88.4435i | −0.379639 | − | 0.123352i | ||||
\(718\) | −340.631 | + | 247.483i | −0.474416 | + | 0.344683i | ||||
\(719\) | −75.0029 | − | 54.4928i | −0.104316 | − | 0.0757897i | 0.534405 | − | 0.845229i | \(-0.320536\pi\) |
−0.638720 | + | 0.769439i | \(0.720536\pi\) | |||||||
\(720\) | 1.97068 | + | 6.06512i | 0.00273705 | + | 0.00842378i | ||||
\(721\) | 684.995 | − | 222.569i | 0.950063 | − | 0.308694i | ||||
\(722\) | −137.169 | + | 188.797i | −0.189985 | + | 0.261492i | ||||
\(723\) | −238.044 | − | 327.640i | −0.329245 | − | 0.453167i | ||||
\(724\) | −105.459 | + | 324.569i | −0.145661 | + | 0.448299i | ||||
\(725\) | 619.921i | 0.855063i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.4150 | 0.0555915 | 0.0277958 | − | 0.999614i | \(-0.491151\pi\) | ||||
0.0277958 | + | 0.999614i | \(0.491151\pi\) | |||||||
\(728\) | −577.664 | − | 187.694i | −0.793494 | − | 0.257822i | ||||
\(729\) | −21.8435 | + | 15.8702i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −14.7207 | − | 10.6952i | −0.0201653 | − | 0.0146510i | ||||
\(731\) | −114.004 | − | 350.869i | −0.155957 | − | 0.479985i | ||||
\(732\) | −166.989 | + | 54.2582i | −0.228128 | + | 0.0741232i | ||||
\(733\) | −419.892 | + | 577.932i | −0.572841 | + | 0.788448i | −0.992888 | − | 0.119054i | \(-0.962014\pi\) |
0.420047 | + | 0.907502i | \(0.362014\pi\) | |||||||
\(734\) | 247.150 | + | 340.172i | 0.336716 | + | 0.463450i | ||||
\(735\) | 0.686650 | − | 2.11329i | 0.000934218 | − | 0.00287523i | ||||
\(736\) | 195.102i | 0.265084i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −153.397 | −0.207856 | ||||||||
\(739\) | −49.0539 | − | 15.9386i | −0.0663787 | − | 0.0215678i | 0.275639 | − | 0.961261i | \(-0.411110\pi\) |
−0.342018 | + | 0.939693i | \(0.611110\pi\) | |||||||
\(740\) | 5.82413 | − | 4.23148i | 0.00787045 | − | 0.00571821i | ||||
\(741\) | 189.349 | + | 137.570i | 0.255532 | + | 0.185655i | ||||
\(742\) | 207.693 | + | 639.213i | 0.279910 | + | 0.861473i | ||||
\(743\) | −854.598 | + | 277.676i | −1.15020 | + | 0.373722i | −0.821218 | − | 0.570614i | \(-0.806705\pi\) |
−0.328981 | + | 0.944337i | \(0.606705\pi\) | |||||||
\(744\) | 419.579 | − | 577.501i | 0.563950 | − | 0.776211i | ||||
\(745\) | −46.4589 | − | 63.9452i | −0.0623609 | − | 0.0858325i | ||||
\(746\) | 31.6722 | − | 97.4770i | 0.0424560 | − | 0.130666i | ||||
\(747\) | 452.019i | 0.605113i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 782.328 | 1.04450 | ||||||||
\(750\) | −32.0734 | − | 10.4213i | −0.0427645 | − | 0.0138950i | ||||
\(751\) | −276.730 | + | 201.056i | −0.368482 | + | 0.267718i | −0.756581 | − | 0.653900i | \(-0.773132\pi\) |
0.388099 | + | 0.921618i | \(0.373132\pi\) | |||||||
\(752\) | 239.471 | + | 173.986i | 0.318445 | + | 0.231364i | ||||
\(753\) | −143.112 | − | 440.453i | −0.190055 | − | 0.584930i | ||||
\(754\) | 283.558 | − | 92.1337i | 0.376072 | − | 0.122193i | ||||
\(755\) | 30.4981 | − | 41.9771i | 0.0403949 | − | 0.0555988i | ||||
\(756\) | −66.9796 | − | 92.1896i | −0.0885974 | − | 0.121944i | ||||
\(757\) | −249.673 | + | 768.416i | −0.329820 | + | 1.01508i | 0.639398 | + | 0.768876i | \(0.279184\pi\) |
−0.969218 | + | 0.246205i | \(0.920816\pi\) | |||||||
\(758\) | − | 220.743i | − | 0.291217i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.5381 | −0.0401817 | ||||||||
\(761\) | −744.066 | − | 241.762i | −0.977748 | − | 0.317690i | −0.223808 | − | 0.974633i | \(-0.571849\pi\) |
−0.753940 | + | 0.656944i | \(0.771849\pi\) | |||||||
\(762\) | 30.1060 | − | 21.8733i | 0.0395092 | − | 0.0287051i | ||||
\(763\) | −1025.77 | − | 745.263i | −1.34439 | − | 0.976754i | ||||
\(764\) | 179.174 | + | 551.440i | 0.234521 | + | 0.721780i | ||||
\(765\) | 23.7188 | − | 7.70669i | 0.0310049 | − | 0.0100741i | ||||
\(766\) | −34.2293 | + | 47.1126i | −0.0446858 | + | 0.0615047i | ||||
\(767\) | 179.434 | + | 246.970i | 0.233943 | + | 0.321995i | ||||
\(768\) | 86.9815 | − | 267.702i | 0.113257 | − | 0.348570i | ||||
\(769\) | − | 652.678i | − | 0.848736i | −0.905490 | − | 0.424368i | \(-0.860496\pi\) | ||
0.905490 | − | 0.424368i | \(-0.139504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −85.7595 | −0.111232 | ||||||||
\(772\) | −157.456 | − | 51.1605i | −0.203958 | − | 0.0662700i | ||||
\(773\) | 699.578 | − | 508.273i | 0.905016 | − | 0.657533i | −0.0347331 | − | 0.999397i | \(-0.511058\pi\) |
0.939750 | + | 0.341864i | \(0.111058\pi\) | |||||||
\(774\) | 42.0762 | + | 30.5701i | 0.0543620 | + | 0.0394963i | ||||
\(775\) | −457.722 | − | 1408.72i | −0.590610 | − | 1.81771i | ||||
\(776\) | 247.212 | − | 80.3241i | 0.318572 | − | 0.103510i | ||||
\(777\) | −43.9020 | + | 60.4259i | −0.0565019 | + | 0.0777682i | ||||
\(778\) | −238.047 | − | 327.643i | −0.305972 | − | 0.421135i | ||||
\(779\) | −178.706 | + | 550.000i | −0.229404 | + | 0.706033i | ||||
\(780\) | − | 25.4096i | − | 0.0325764i | ||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 121.830 | 0.155793 | ||||||||
\(783\) | 123.322 | + | 40.0696i | 0.157499 | + | 0.0511745i | ||||
\(784\) | 13.9580 | − | 10.1411i | 0.0178035 | − | 0.0129350i | ||||
\(785\) | 22.7041 | + | 16.4955i | 0.0289224 | + | 0.0210133i | ||||
\(786\) | 8.60343 | + | 26.4786i | 0.0109458 | + | 0.0336878i | ||||
\(787\) | −415.256 | + | 134.925i | −0.527644 | + | 0.171442i | −0.560712 | − | 0.828011i | \(-0.689472\pi\) |
0.0330674 | + | 0.999453i | \(0.489472\pi\) | |||||||
\(788\) | −134.301 | + | 184.850i | −0.170433 | + | 0.234581i | ||||
\(789\) | 202.355 | + | 278.518i | 0.256470 | + | 0.353001i | ||||
\(790\) | 7.28149 | − | 22.4101i | 0.00921708 | − | 0.0283672i | ||||
\(791\) | − | 712.010i | − | 0.900139i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 406.208 | 0.512243 | ||||||||
\(794\) | −579.306 | − | 188.228i | −0.729605 | − | 0.237063i | ||||
\(795\) | −52.7312 | + | 38.3115i | −0.0663286 | + | 0.0481905i | ||||
\(796\) | 149.066 | + | 108.303i | 0.187269 | + | 0.136059i | ||||
\(797\) | 140.019 | + | 430.933i | 0.175682 | + | 0.540693i | 0.999664 | − | 0.0259226i | \(-0.00825233\pi\) |
−0.823982 | + | 0.566616i | \(0.808252\pi\) | |||||||
\(798\) | 129.987 | − | 42.2352i | 0.162891 | − | 0.0529263i | ||||
\(799\) | 680.403 | − | 936.494i | 0.851568 | − | 1.17208i | ||||
\(800\) | −480.416 | − | 661.236i | −0.600520 | − | 0.826545i | ||||
\(801\) | 124.401 | − | 382.865i | 0.155307 | − | 0.477984i | ||||
\(802\) | 660.366i | 0.823399i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −497.555 | −0.618850 | ||||||||
\(805\) | 16.2039 | + | 5.26497i | 0.0201291 | + | 0.00654034i | ||||
\(806\) | −576.338 | + | 418.734i | −0.715060 | + | 0.519521i | ||||
\(807\) | 15.0957 | + | 10.9676i | 0.0187059 | + | 0.0135906i | ||||
\(808\) | −172.585 | − | 531.161i | −0.213595 | − | 0.657378i | ||||
\(809\) | 109.603 | − | 35.6121i | 0.135479 | − | 0.0440199i | −0.240493 | − | 0.970651i | \(-0.577309\pi\) |
0.375972 | + | 0.926631i | \(0.377309\pi\) | |||||||
\(810\) | −2.06654 | + | 2.84435i | −0.00255128 | + | 0.00351154i | ||||
\(811\) | −19.5545 | − | 26.9145i | −0.0241116 | − | 0.0331868i | 0.796791 | − | 0.604255i | \(-0.206529\pi\) |
−0.820903 | + | 0.571068i | \(0.806529\pi\) | |||||||
\(812\) | −169.112 | + | 520.474i | −0.208266 | + | 0.640978i | ||||
\(813\) | 506.151i | 0.622571i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.5775 | −0.0375184 | ||||||||
\(816\) | 184.164 | + | 59.8384i | 0.225691 | + | 0.0733314i | ||||
\(817\) | 158.626 | − | 115.248i | 0.194156 | − | 0.141063i | ||||
\(818\) | 488.352 | + | 354.809i | 0.597008 | + | 0.433751i | ||||
\(819\) | 81.4653 | + | 250.724i | 0.0994692 | + | 0.306135i | ||||
\(820\) | 59.7112 | − | 19.4013i | 0.0728185 | − | 0.0236602i | ||||
\(821\) | 420.301 | − | 578.494i | 0.511937 | − | 0.704621i | −0.472307 | − | 0.881434i | \(-0.656579\pi\) |
0.984245 | + | 0.176813i | \(0.0565787\pi\) | |||||||
\(822\) | −30.5992 | − | 42.1162i | −0.0372254 | − | 0.0512363i | ||||
\(823\) | −48.5278 | + | 149.353i | −0.0589645 | + | 0.181474i | −0.976200 | − | 0.216870i | \(-0.930415\pi\) |
0.917236 | + | 0.398344i | \(0.130415\pi\) | |||||||
\(824\) | − | 688.866i | − | 0.836002i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 178.268 | 0.215821 | ||||||||
\(827\) | −812.497 | − | 263.996i | −0.982463 | − | 0.319222i | −0.226626 | − | 0.973982i | \(-0.572770\pi\) |
−0.755837 | + | 0.654760i | \(0.772770\pi\) | |||||||
\(828\) | 43.6739 | − | 31.7309i | 0.0527462 | − | 0.0383224i | ||||
\(829\) | 1111.73 | + | 807.718i | 1.34105 | + | 0.974328i | 0.999405 | + | 0.0344983i | \(0.0109833\pi\) |
0.341643 | + | 0.939830i | \(0.389017\pi\) | |||||||
\(830\) | 18.1887 | + | 55.9790i | 0.0219141 | + | 0.0674445i | ||||
\(831\) | −288.876 | + | 93.8614i | −0.347624 | + | 0.112950i | ||||
\(832\) | −78.1963 | + | 107.628i | −0.0939859 | + | 0.129361i | ||||
\(833\) | −39.6585 | − | 54.5852i | −0.0476092 | − | 0.0655285i | ||||
\(834\) | −14.5919 | + | 44.9093i | −0.0174963 | + | 0.0538481i | ||||
\(835\) | − | 40.4564i | − | 0.0484508i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −309.825 | −0.370161 | ||||||||
\(838\) | 56.9553 | + | 18.5059i | 0.0679658 | + | 0.0220834i | ||||
\(839\) | −527.913 | + | 383.551i | −0.629217 | + | 0.457153i | −0.856129 | − | 0.516762i | \(-0.827137\pi\) |
0.226912 | + | 0.973915i | \(0.427137\pi\) | |||||||
\(840\) | −27.8282 | − | 20.2183i | −0.0331288 | − | 0.0240695i | ||||
\(841\) | 67.4483 | + | 207.585i | 0.0802002 | + | 0.246831i | ||||
\(842\) | 194.940 | − | 63.3398i | 0.231520 | − | 0.0752254i | ||||
\(843\) | 231.490 | − | 318.619i | 0.274603 | − | 0.377959i | ||||
\(844\) | −729.863 | − | 1004.57i | −0.864766 | − | 1.19025i | ||||
\(845\) | 2.59746 | − | 7.99416i | 0.00307392 | − | 0.00946055i | ||||
\(846\) | 163.188i | 0.192893i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −506.083 | −0.596796 | ||||||||
\(849\) | 391.140 | + | 127.089i | 0.460707 | + | 0.149693i | ||||
\(850\) | −412.905 | + | 299.993i | −0.485771 | + | 0.352933i | ||||
\(851\) | −28.6261 | − | 20.7981i | −0.0336382 | − | 0.0244396i | ||||
\(852\) | −134.360 | − | 413.518i | −0.157700 | − | 0.485350i | ||||
\(853\) | −1258.93 | + | 409.050i | −1.47588 | + | 0.479543i | −0.932880 | − | 0.360188i | \(-0.882712\pi\) |
−0.543002 | + | 0.839731i | \(0.682712\pi\) | |||||||
\(854\) | 139.430 | − | 191.908i | 0.163266 | − | 0.224717i | ||||
\(855\) | 7.79080 | + | 10.7231i | 0.00911204 | + | 0.0125416i | ||||
\(856\) | 231.219 | − | 711.620i | 0.270116 | − | 0.831332i | ||||
\(857\) | − | 38.8452i | − | 0.0453269i | −0.999743 | − | 0.0226634i | \(-0.992785\pi\) | ||
0.999743 | − | 0.0226634i | \(-0.00721462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 227.261 | 0.264564 | 0.132282 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(860\) | −20.2449 | − | 6.57797i | −0.0235406 | − | 0.00764880i | ||||
\(861\) | −526.986 | + | 382.878i | −0.612063 | + | 0.444690i | ||||
\(862\) | −215.201 | − | 156.352i | −0.249653 | − | 0.181383i | ||||
\(863\) | 295.799 | + | 910.375i | 0.342757 | + | 1.05490i | 0.962774 | + | 0.270308i | \(0.0871256\pi\) |
−0.620017 | + | 0.784588i | \(0.712874\pi\) | |||||||
\(864\) | −162.593 | + | 52.8296i | −0.188186 | + | 0.0611454i | ||||
\(865\) | −29.1883 | + | 40.1743i | −0.0337437 | + | 0.0464442i | ||||
\(866\) | −362.292 | − | 498.652i | −0.418351 | − | 0.575810i | ||||
\(867\) | 79.3265 | − | 244.142i | 0.0914954 | − | 0.281594i | ||||
\(868\) | − | 1307.61i | − | 1.50646i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 16.8847 | 0.0194077 | ||||||||
\(871\) | 1094.75 | + | 355.705i | 1.25689 | + | 0.408387i | ||||
\(872\) | −981.074 | + | 712.792i | −1.12508 | + | 0.817422i | ||||
\(873\) | −91.2730 | − | 66.3137i | −0.104551 | − | 0.0759607i | ||||
\(874\) | 20.0085 | + | 61.5798i | 0.0228930 | + | 0.0704575i | ||||
\(875\) | −136.197 | + | 44.2531i | −0.155654 | + | 0.0505750i | ||||
\(876\) | −143.901 | + | 198.062i | −0.164270 | + | 0.226098i | ||||
\(877\) | −707.661 | − | 974.011i | −0.806911 | − | 1.11062i | −0.991793 | − | 0.127856i | \(-0.959190\pi\) |
0.184882 | − | 0.982761i | \(-0.440810\pi\) | |||||||
\(878\) | −150.371 | + | 462.795i | −0.171266 | + | 0.527102i | ||||
\(879\) | 50.8075i | 0.0578015i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1170.77 | 1.32892 | 0.664458 | − | 0.747326i | \(-0.268663\pi\) | ||||
0.664458 | + | 0.747326i | \(0.268663\pi\) | |||||||
\(882\) | 9.04614 | + | 2.93927i | 0.0102564 | + | 0.00333250i | ||||
\(883\) | −294.659 | + | 214.082i | −0.333702 | + | 0.242449i | −0.742000 | − | 0.670400i | \(-0.766122\pi\) |
0.408298 | + | 0.912849i | \(0.366122\pi\) | |||||||
\(884\) | −624.195 | − | 453.504i | −0.706103 | − | 0.513014i | ||||
\(885\) | 5.34229 | + | 16.4419i | 0.00603648 | + | 0.0185784i | ||||
\(886\) | 693.387 | − | 225.295i | 0.782604 | − | 0.254283i | ||||
\(887\) | 167.359 | − | 230.350i | 0.188680 | − | 0.259695i | −0.704189 | − | 0.710013i | \(-0.748689\pi\) |
0.892869 | + | 0.450317i | \(0.148689\pi\) | |||||||
\(888\) | 41.9892 | + | 57.7931i | 0.0472851 | + | 0.0650824i | ||||
\(889\) | 48.8316 | − | 150.288i | 0.0549287 | − | 0.169053i | ||||
\(890\) | − | 52.4205i | − | 0.0588995i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −447.025 | −0.501150 | ||||||||
\(893\) | 585.102 | + | 190.111i | 0.655209 | + | 0.212890i | ||||
\(894\) | 273.723 | − | 198.872i | 0.306178 | − | 0.222451i | ||||
\(895\) | 33.2036 | + | 24.1238i | 0.0370990 | + | 0.0269540i | ||||
\(896\) | −269.895 | − | 830.652i | −0.301222 | − | 0.927066i | ||||
\(897\) | −118.778 | + | 38.5934i | −0.132417 | + | 0.0430249i | ||||
\(898\) | 412.112 | − | 567.224i | 0.458922 | − | 0.631653i | ||||
\(899\) | 874.589 | + | 1203.77i | 0.972846 | + | 1.33901i | ||||
\(900\) | −69.8851 | + | 215.084i | −0.0776501 | + | 0.238982i | ||||
\(901\) | 1979.13i | 2.19659i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 220.852 | 0.244576 | ||||||||
\(904\) | −647.658 | − | 210.437i | −0.716435 | − | 0.232784i | ||||
\(905\) | 36.1728 | − | 26.2811i | 0.0399699 | − | 0.0290399i | ||||
\(906\) | 179.687 | + | 130.550i | 0.198330 | + | 0.144095i | ||||
\(907\) | 233.842 | + | 719.693i | 0.257820 | + | 0.793487i | 0.993261 | + | 0.115899i | \(0.0369749\pi\) |
−0.735441 | + | 0.677588i | \(0.763025\pi\) | |||||||
\(908\) | −395.450 | + | 128.490i | −0.435518 | + | 0.141508i | ||||
\(909\) | −142.482 | + | 196.110i | −0.156746 | + | 0.215742i | ||||
\(910\) | 20.1776 | + | 27.7721i | 0.0221732 | + | 0.0305188i | ||||
\(911\) | −203.748 | + | 627.072i | −0.223653 | + | 0.688334i | 0.774772 | + | 0.632240i | \(0.217865\pi\) |
−0.998426 | + | 0.0560936i | \(0.982135\pi\) | |||||||
\(912\) | 102.914i | 0.112844i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 277.589 | 0.303708 | ||||||||
\(915\) | 21.8783 | + | 7.10868i | 0.0239107 | + | 0.00776905i | ||||
\(916\) | −210.409 | + | 152.871i | −0.229704 | + | 0.166890i | ||||
\(917\) | 95.6467 | + | 69.4914i | 0.104304 | + | 0.0757813i | ||||
\(918\) | 32.9892 | + | 101.530i | 0.0359360 | + | 0.110599i | ||||
\(919\) | −710.379 | + | 230.816i | −0.772991 | + | 0.251160i | −0.668845 | − | 0.743402i | \(-0.733211\pi\) |
−0.104146 | + | 0.994562i | \(0.533211\pi\) | |||||||
\(920\) | 9.57823 | − | 13.1833i | 0.0104111 | − | 0.0143297i | ||||
\(921\) | −353.609 | − | 486.701i | −0.383940 | − | 0.528448i | ||||
\(922\) | 60.1754 | − | 185.201i | 0.0652661 | − | 0.200869i | ||||
\(923\) | 1005.90i | 1.08981i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 148.233 | 0.160251 | ||||||||
\(926\) | 212.047 | + | 68.8983i | 0.228993 | + | 0.0744042i | ||||
\(927\) | −241.888 | + | 175.742i | −0.260936 | + | 0.189581i | ||||
\(928\) | 664.235 | + | 482.595i | 0.715771 | + | 0.520038i | ||||
\(929\) | −374.720 | − | 1153.27i | −0.403358 | − | 1.24141i | −0.922258 | − | 0.386574i | \(-0.873658\pi\) |
0.518900 | − | 0.854835i | \(-0.326342\pi\) | |||||||
\(930\) | −38.3693 | + | 12.4669i | −0.0412573 | + | 0.0134053i | ||||
\(931\) | 21.0772 | − | 29.0103i | 0.0226393 | − | 0.0311604i | ||||
\(932\) | −386.041 | − | 531.340i | −0.414207 | − | 0.570107i | ||||
\(933\) | −235.808 | + | 725.743i | −0.252742 | + | 0.777860i | ||||
\(934\) | − | 147.050i | − | 0.157441i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 252.141 | 0.269381 | ||||||||
\(937\) | −1513.93 | − | 491.905i | −1.61572 | − | 0.524978i | −0.644791 | − | 0.764359i | \(-0.723056\pi\) |
−0.970926 | + | 0.239380i | \(0.923056\pi\) | |||||||
\(938\) | 543.816 | − | 395.106i | 0.579762 | − | 0.421222i | ||||
\(939\) | −35.6824 | − | 25.9247i | −0.0380004 | − | 0.0276089i | ||||
\(940\) | −20.6396 | − | 63.5220i | −0.0219570 | − | 0.0675766i | ||||
\(941\) | 567.597 | − | 184.423i | 0.603185 | − | 0.195987i | 0.00852449 | − | 0.999964i | \(-0.497287\pi\) |
0.594660 | + | 0.803977i | \(0.297287\pi\) | |||||||
\(942\) | −70.6103 | + | 97.1868i | −0.0749579 | + | 0.103171i | ||||
\(943\) | −181.384 | − | 249.654i | −0.192348 | − | 0.264745i | ||||
\(944\) | −41.4800 | + | 127.662i | −0.0439407 | + | 0.135236i | ||||
\(945\) | 14.9296i | 0.0157985i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −883.411 | −0.932852 | −0.466426 | − | 0.884560i | \(-0.654459\pi\) | ||||
−0.466426 | + | 0.884560i | \(0.654459\pi\) | |||||||
\(948\) | −301.521 | − | 97.9701i | −0.318060 | − | 0.103344i | ||||
\(949\) | 458.214 | − | 332.912i | 0.482838 | − | 0.350803i | ||||
\(950\) | −219.446 | − | 159.437i | −0.230996 | − | 0.167828i | ||||
\(951\) | −48.9116 | − | 150.534i | −0.0514318 | − | 0.158291i | ||||
\(952\) | −993.339 | + | 322.755i | −1.04342 | + | 0.339029i | ||||
\(953\) | 166.265 | − | 228.844i | 0.174465 | − | 0.240130i | −0.712826 | − | 0.701341i | \(-0.752585\pi\) |
0.887290 | + | 0.461211i | \(0.152585\pi\) | |||||||
\(954\) | −163.996 | − | 225.721i | −0.171903 | − | 0.236605i | ||||
\(955\) | 23.4746 | − | 72.2474i | 0.0245808 | − | 0.0756518i | ||||
\(956\) | 501.440i | 0.524518i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −320.091 | −0.334125 | ||||||||
\(959\) | −210.243 | − | 68.3121i | −0.219231 | − | 0.0712326i | ||||
\(960\) | −6.09513 | + | 4.42837i | −0.00634910 | + | 0.00461289i | ||||
\(961\) | −2098.78 | − | 1524.86i | −2.18396 | − | 1.58674i | ||||
\(962\) | −22.0306 | − | 67.8031i | −0.0229008 | − | 0.0704814i | ||||
\(963\) | −308.866 | + | 100.357i | −0.320733 | + | 0.104212i | ||||
\(964\) | −417.054 | + | 574.026i | −0.432629 | + | 0.595462i | ||||
\(965\) | 12.7496 | + | 17.5483i | 0.0132120 | + | 0.0181847i | ||||
\(966\) | −22.5372 | + | 69.3624i | −0.0233304 | + | 0.0718037i | ||||
\(967\) | 335.731i | 0.347188i | 0.984817 | + | 0.173594i | \(0.0555381\pi\) | ||||
−0.984817 | + | 0.173594i | \(0.944462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 402.464 | 0.415340 | ||||||||
\(970\) | −13.9718 | − | 4.53971i | −0.0144039 | − | 0.00468012i | ||||
\(971\) | −1128.85 | + | 820.158i | −1.16257 | + | 0.844653i | −0.990100 | − | 0.140362i | \(-0.955173\pi\) |
−0.172465 | + | 0.985016i | \(0.555173\pi\) | |||||||
\(972\) | 38.2698 | + | 27.8046i | 0.0393722 | + | 0.0286056i | ||||
\(973\) | 61.9635 | + | 190.704i | 0.0636829 | + | 0.195996i | ||||
\(974\) | −286.814 | + | 93.1914i | −0.294470 | + | 0.0956791i | ||||
\(975\) | 307.530 | − | 423.278i | 0.315415 | − | 0.434132i | ||||
\(976\) | 104.987 | + | 144.503i | 0.107569 | + | 0.148056i | ||||
\(977\) | −359.643 | + | 1106.87i | −0.368110 | + | 1.13293i | 0.579901 | + | 0.814687i | \(0.303091\pi\) |
−0.948011 | + | 0.318239i | \(0.896909\pi\) | |||||||
\(978\) | − | 130.890i | − | 0.133834i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.89303 | −0.00397248 | ||||||||
\(981\) | 500.578 | + | 162.648i | 0.510273 | + | 0.165798i | ||||
\(982\) | −487.978 | + | 354.536i | −0.496922 | + | 0.361035i | ||||
\(983\) | 331.526 | + | 240.867i | 0.337259 | + | 0.245033i | 0.743504 | − | 0.668731i | \(-0.233162\pi\) |
−0.406245 | + | 0.913764i | \(0.633162\pi\) | |||||||
\(984\) | 192.520 | + | 592.517i | 0.195651 | + | 0.602151i | ||||
\(985\) | 28.4703 | − | 9.25056i | 0.0289038 | − | 0.00939143i | ||||
\(986\) | 301.354 | − | 414.778i | 0.305633 | − | 0.420668i | ||||
\(987\) | 407.314 | + | 560.619i | 0.412678 | + | 0.568003i | ||||
\(988\) | 126.713 | − | 389.984i | 0.128252 | − | 0.394720i | ||||
\(989\) | 104.626i | 0.105790i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1604.17 | 1.61874 | 0.809372 | − | 0.587297i | \(-0.199808\pi\) | ||||
0.809372 | + | 0.587297i | \(0.199808\pi\) | |||||||
\(992\) | −1865.75 | − | 606.220i | −1.88080 | − | 0.611109i | ||||
\(993\) | −446.667 | + | 324.522i | −0.449815 | + | 0.326810i | ||||
\(994\) | 475.225 | + | 345.271i | 0.478094 | + | 0.347355i | ||||
\(995\) | −7.45982 | − | 22.9590i | −0.00749731 | − | 0.0230744i | ||||
\(996\) | 753.179 | − | 244.723i | 0.756204 | − | 0.245706i | ||||
\(997\) | −42.5464 | + | 58.5601i | −0.0426744 | + | 0.0587363i | −0.829821 | − | 0.558030i | \(-0.811558\pi\) |
0.787147 | + | 0.616766i | \(0.211558\pi\) | |||||||
\(998\) | 236.483 | + | 325.491i | 0.236957 | + | 0.326143i | ||||
\(999\) | 9.58125 | − | 29.4881i | 0.00959085 | − | 0.0295176i |
(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 | 363.3.g.g.112.1 | 16 | ||
11.2 | odd | 10 | 33.3.g.a.19.1 | yes | 16 | ||
11.3 | even | 5 | 33.3.g.a.7.1 | ✓ | 16 | ||
11.4 | even | 5 | 363.3.c.e.241.7 | 16 | |||
11.5 | even | 5 | 363.3.g.a.94.4 | 16 | |||
11.6 | odd | 10 | inner | 363.3.g.g.94.1 | 16 | ||
11.7 | odd | 10 | 363.3.c.e.241.10 | 16 | |||
11.8 | odd | 10 | 363.3.g.f.40.4 | 16 | |||
11.9 | even | 5 | 363.3.g.f.118.4 | 16 | |||
11.10 | odd | 2 | 363.3.g.a.112.4 | 16 | |||
33.2 | even | 10 | 99.3.k.c.19.4 | 16 | |||
33.14 | odd | 10 | 99.3.k.c.73.4 | 16 | |||
33.26 | odd | 10 | 1089.3.c.m.604.10 | 16 | |||
33.29 | even | 10 | 1089.3.c.m.604.7 | 16 | |||
44.3 | odd | 10 | 528.3.bf.b.337.3 | 16 | |||
44.35 | even | 10 | 528.3.bf.b.481.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.7.1 | ✓ | 16 | 11.3 | even | 5 | ||
33.3.g.a.19.1 | yes | 16 | 11.2 | odd | 10 | ||
99.3.k.c.19.4 | 16 | 33.2 | even | 10 | |||
99.3.k.c.73.4 | 16 | 33.14 | odd | 10 | |||
363.3.c.e.241.7 | 16 | 11.4 | even | 5 | |||
363.3.c.e.241.10 | 16 | 11.7 | odd | 10 | |||
363.3.g.a.94.4 | 16 | 11.5 | even | 5 | |||
363.3.g.a.112.4 | 16 | 11.10 | odd | 2 | |||
363.3.g.f.40.4 | 16 | 11.8 | odd | 10 | |||
363.3.g.f.118.4 | 16 | 11.9 | even | 5 | |||
363.3.g.g.94.1 | 16 | 11.6 | odd | 10 | inner | ||
363.3.g.g.112.1 | 16 | 1.1 | even | 1 | trivial | ||
528.3.bf.b.337.3 | 16 | 44.3 | odd | 10 | |||
528.3.bf.b.481.3 | 16 | 44.35 | even | 10 | |||
1089.3.c.m.604.7 | 16 | 33.29 | even | 10 | |||
1089.3.c.m.604.10 | 16 | 33.26 | odd | 10 |