Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} - 12852 x + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(-1.33997 + 2.32090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.16 |
Dual form | 105.4.i.d.46.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83997 | + | 3.18692i | −0.650528 | + | 1.12675i | 0.332467 | + | 0.943115i | \(0.392119\pi\) |
−0.982995 | + | 0.183633i | \(0.941214\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.77099 | − | 4.79950i | −0.346374 | − | 0.599938i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 11.0398 | 0.751165 | ||||||||
\(7\) | 5.08172 | + | 17.8094i | 0.274387 | + | 0.961619i | ||||
\(8\) | −9.04535 | −0.399752 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −9.19986 | − | 15.9346i | −0.290925 | − | 0.503897i | ||||
\(11\) | −32.5290 | − | 56.3418i | −0.891622 | − | 1.54434i | −0.837930 | − | 0.545778i | \(-0.816234\pi\) |
−0.0536927 | − | 0.998558i | \(-0.517099\pi\) | |||||||
\(12\) | −8.31298 | + | 14.3985i | −0.199979 | + | 0.346374i | ||||
\(13\) | −6.87328 | −0.146639 | −0.0733195 | − | 0.997309i | \(-0.523359\pi\) | ||||
−0.0733195 | + | 0.997309i | \(0.523359\pi\) | |||||||
\(14\) | −66.1076 | − | 16.5738i | −1.26200 | − | 0.316395i | ||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 38.8111 | − | 67.2229i | 0.606424 | − | 1.05036i | ||||
\(17\) | −34.0063 | − | 58.9006i | −0.485161 | − | 0.840323i | 0.514694 | − | 0.857374i | \(-0.327906\pi\) |
−0.999855 | + | 0.0170509i | \(0.994572\pi\) | |||||||
\(18\) | −16.5597 | − | 28.6823i | −0.216843 | − | 0.375583i | ||||
\(19\) | −11.7761 | + | 20.3968i | −0.142191 | + | 0.246282i | −0.928321 | − | 0.371779i | \(-0.878748\pi\) |
0.786131 | + | 0.618060i | \(0.212081\pi\) | |||||||
\(20\) | 27.7099 | 0.309806 | ||||||||
\(21\) | 38.6477 | − | 39.9169i | 0.401601 | − | 0.414789i | ||||
\(22\) | 239.409 | 2.32010 | ||||||||
\(23\) | 2.74967 | − | 4.76257i | 0.0249281 | − | 0.0431767i | −0.853292 | − | 0.521433i | \(-0.825398\pi\) |
0.878220 | + | 0.478256i | \(0.158731\pi\) | |||||||
\(24\) | 13.5680 | + | 23.5005i | 0.115398 | + | 0.199876i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 12.6467 | − | 21.9046i | 0.0953928 | − | 0.165225i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 71.3950 | − | 73.7396i | 0.481871 | − | 0.497695i | ||||
\(29\) | −138.643 | −0.887770 | −0.443885 | − | 0.896084i | \(-0.646400\pi\) | ||||
−0.443885 | + | 0.896084i | \(0.646400\pi\) | |||||||
\(30\) | −27.5996 | + | 47.8039i | −0.167966 | + | 0.290925i | ||||
\(31\) | −125.954 | − | 218.158i | −0.729741 | − | 1.26395i | −0.956992 | − | 0.290113i | \(-0.906307\pi\) |
0.227251 | − | 0.973836i | \(-0.427026\pi\) | |||||||
\(32\) | 106.641 | + | 184.708i | 0.589116 | + | 1.02038i | ||||
\(33\) | −97.5869 | + | 169.025i | −0.514778 | + | 0.891622i | ||||
\(34\) | 250.282 | 1.26244 | ||||||||
\(35\) | −89.8214 | − | 22.5191i | −0.433788 | − | 0.108755i | ||||
\(36\) | 49.8779 | 0.230916 | ||||||||
\(37\) | −63.7644 | + | 110.443i | −0.283319 | + | 0.490723i | −0.972200 | − | 0.234152i | \(-0.924769\pi\) |
0.688881 | + | 0.724874i | \(0.258102\pi\) | |||||||
\(38\) | −43.3354 | − | 75.0591i | −0.184998 | − | 0.320426i | ||||
\(39\) | 10.3099 | + | 17.8573i | 0.0423310 | + | 0.0733195i | ||||
\(40\) | 22.6134 | − | 39.1675i | 0.0893872 | − | 0.154823i | ||||
\(41\) | −126.581 | −0.482163 | −0.241082 | − | 0.970505i | \(-0.577502\pi\) | ||||
−0.241082 | + | 0.970505i | \(0.577502\pi\) | |||||||
\(42\) | 56.1014 | + | 196.613i | 0.206110 | + | 0.722335i | ||||
\(43\) | 91.5924 | 0.324830 | 0.162415 | − | 0.986723i | \(-0.448072\pi\) | ||||
0.162415 | + | 0.986723i | \(0.448072\pi\) | |||||||
\(44\) | −180.275 | + | 312.245i | −0.617670 | + | 1.06984i | ||||
\(45\) | −22.5000 | − | 38.9711i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 10.1186 | + | 17.5260i | 0.0324328 | + | 0.0561753i | ||||
\(47\) | −284.233 | + | 492.306i | −0.882119 | + | 1.52788i | −0.0331392 | + | 0.999451i | \(0.510550\pi\) |
−0.848980 | + | 0.528425i | \(0.822783\pi\) | |||||||
\(48\) | −232.867 | −0.700238 | ||||||||
\(49\) | −291.352 | + | 181.005i | −0.849423 | + | 0.527712i | ||||
\(50\) | 91.9986 | 0.260211 | ||||||||
\(51\) | −102.019 | + | 176.702i | −0.280108 | + | 0.485161i | ||||
\(52\) | 19.0458 | + | 32.9883i | 0.0507919 | + | 0.0879742i | ||||
\(53\) | 295.199 | + | 511.300i | 0.765071 | + | 1.32514i | 0.940209 | + | 0.340598i | \(0.110629\pi\) |
−0.175138 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(54\) | −49.6792 | + | 86.0470i | −0.125194 | + | 0.216843i | ||||
\(55\) | 325.290 | 0.797491 | ||||||||
\(56\) | −45.9660 | − | 161.093i | −0.109687 | − | 0.384409i | ||||
\(57\) | 70.6566 | 0.164188 | ||||||||
\(58\) | 255.099 | − | 441.844i | 0.577520 | − | 1.00029i | ||||
\(59\) | −254.890 | − | 441.483i | −0.562438 | − | 0.974172i | −0.997283 | − | 0.0736665i | \(-0.976530\pi\) |
0.434844 | − | 0.900506i | \(-0.356803\pi\) | |||||||
\(60\) | −41.5649 | − | 71.9925i | −0.0894334 | − | 0.154903i | ||||
\(61\) | −130.771 | + | 226.502i | −0.274483 | + | 0.475419i | −0.970005 | − | 0.243086i | \(-0.921840\pi\) |
0.695521 | + | 0.718506i | \(0.255174\pi\) | |||||||
\(62\) | 927.006 | 1.89887 | ||||||||
\(63\) | −161.679 | − | 40.5344i | −0.323327 | − | 0.0810611i | ||||
\(64\) | −163.890 | −0.320099 | ||||||||
\(65\) | 17.1832 | − | 29.7622i | 0.0327895 | − | 0.0567930i | ||||
\(66\) | −359.114 | − | 622.004i | −0.669756 | − | 1.16005i | ||||
\(67\) | 461.391 | + | 799.152i | 0.841311 | + | 1.45719i | 0.888787 | + | 0.458321i | \(0.151549\pi\) |
−0.0474760 | + | 0.998872i | \(0.515118\pi\) | |||||||
\(68\) | −188.462 | + | 326.426i | −0.336094 | + | 0.582132i | ||||
\(69\) | −16.4980 | −0.0287845 | ||||||||
\(70\) | 237.036 | − | 244.820i | 0.404731 | − | 0.418022i | ||||
\(71\) | 519.662 | 0.868627 | 0.434314 | − | 0.900762i | \(-0.356991\pi\) | ||||
0.434314 | + | 0.900762i | \(0.356991\pi\) | |||||||
\(72\) | 40.7041 | − | 70.5015i | 0.0666253 | − | 0.115398i | ||||
\(73\) | −533.244 | − | 923.606i | −0.854952 | − | 1.48082i | −0.876689 | − | 0.481057i | \(-0.840253\pi\) |
0.0217370 | − | 0.999764i | \(-0.493080\pi\) | |||||||
\(74\) | −234.649 | − | 406.424i | −0.368614 | − | 0.638458i | ||||
\(75\) | −37.5000 | + | 64.9519i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 130.526 | 0.197005 | ||||||||
\(77\) | 838.113 | − | 865.636i | 1.24041 | − | 1.28115i | ||||
\(78\) | −75.8799 | −0.110150 | ||||||||
\(79\) | 56.4067 | − | 97.6992i | 0.0803322 | − | 0.139139i | −0.823060 | − | 0.567954i | \(-0.807735\pi\) |
0.903393 | + | 0.428814i | \(0.141069\pi\) | |||||||
\(80\) | 194.056 | + | 336.114i | 0.271201 | + | 0.469734i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 232.906 | − | 403.405i | 0.313661 | − | 0.543277i | ||||
\(83\) | −593.552 | −0.784949 | −0.392474 | − | 0.919763i | \(-0.628381\pi\) | ||||
−0.392474 | + | 0.919763i | \(0.628381\pi\) | |||||||
\(84\) | −298.674 | − | 74.8803i | −0.387952 | − | 0.0972632i | ||||
\(85\) | 340.063 | 0.433941 | ||||||||
\(86\) | −168.527 | + | 291.898i | −0.211311 | + | 0.366002i | ||||
\(87\) | 207.964 | + | 360.205i | 0.256277 | + | 0.443885i | ||||
\(88\) | 294.236 | + | 509.631i | 0.356428 | + | 0.617351i | ||||
\(89\) | 121.163 | − | 209.860i | 0.144306 | − | 0.249945i | −0.784808 | − | 0.619739i | \(-0.787238\pi\) |
0.929114 | + | 0.369794i | \(0.120572\pi\) | |||||||
\(90\) | 165.597 | 0.193950 | ||||||||
\(91\) | −34.9281 | − | 122.409i | −0.0402359 | − | 0.141011i | ||||
\(92\) | −30.4773 | −0.0345378 | ||||||||
\(93\) | −377.862 | + | 654.475i | −0.421316 | + | 0.729741i | ||||
\(94\) | −1045.96 | − | 1811.66i | −1.14769 | − | 1.98785i | ||||
\(95\) | −58.8805 | − | 101.984i | −0.0635896 | − | 0.110140i | ||||
\(96\) | 319.924 | − | 554.125i | 0.340126 | − | 0.589116i | ||||
\(97\) | −1536.88 | −1.60873 | −0.804366 | − | 0.594134i | \(-0.797495\pi\) | ||||
−0.804366 | + | 0.594134i | \(0.797495\pi\) | |||||||
\(98\) | −40.7705 | − | 1261.56i | −0.0420249 | − | 1.30038i | ||||
\(99\) | 585.521 | 0.594415 | ||||||||
\(100\) | −69.2748 | + | 119.988i | −0.0692748 | + | 0.119988i | ||||
\(101\) | 857.920 | + | 1485.96i | 0.845210 | + | 1.46395i | 0.885439 | + | 0.464756i | \(0.153858\pi\) |
−0.0402290 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(102\) | −375.424 | − | 650.253i | −0.364436 | − | 0.631222i | ||||
\(103\) | 143.826 | − | 249.114i | 0.137588 | − | 0.238310i | −0.788995 | − | 0.614400i | \(-0.789398\pi\) |
0.926583 | + | 0.376090i | \(0.122732\pi\) | |||||||
\(104\) | 62.1713 | 0.0586192 | ||||||||
\(105\) | 76.2259 | + | 267.142i | 0.0708465 | + | 0.248289i | ||||
\(106\) | −2172.63 | −1.99080 | ||||||||
\(107\) | 525.298 | − | 909.842i | 0.474602 | − | 0.822035i | −0.524975 | − | 0.851118i | \(-0.675925\pi\) |
0.999577 | + | 0.0290827i | \(0.00925862\pi\) | |||||||
\(108\) | −74.8168 | − | 129.587i | −0.0666597 | − | 0.115458i | ||||
\(109\) | 92.4004 | + | 160.042i | 0.0811959 | + | 0.140635i | 0.903764 | − | 0.428031i | \(-0.140793\pi\) |
−0.822568 | + | 0.568667i | \(0.807459\pi\) | |||||||
\(110\) | −598.524 | + | 1036.67i | −0.518791 | + | 0.898572i | ||||
\(111\) | 382.586 | 0.327148 | ||||||||
\(112\) | 1394.43 | + | 349.597i | 1.17644 | + | 0.294944i | ||||
\(113\) | −2100.22 | −1.74842 | −0.874212 | − | 0.485545i | \(-0.838621\pi\) | ||||
−0.874212 | + | 0.485545i | \(0.838621\pi\) | |||||||
\(114\) | −130.006 | + | 225.177i | −0.106809 | + | 0.184998i | ||||
\(115\) | 13.7483 | + | 23.8128i | 0.0111482 | + | 0.0193092i | ||||
\(116\) | 384.178 | + | 665.417i | 0.307501 | + | 0.532607i | ||||
\(117\) | 30.9298 | − | 53.5720i | 0.0244398 | − | 0.0423310i | ||||
\(118\) | 1875.96 | 1.46353 | ||||||||
\(119\) | 876.176 | − | 904.949i | 0.674949 | − | 0.697114i | ||||
\(120\) | −135.680 | −0.103215 | ||||||||
\(121\) | −1450.77 | + | 2512.80i | −1.08998 | + | 1.88790i | ||||
\(122\) | −481.229 | − | 833.514i | −0.357118 | − | 0.618547i | ||||
\(123\) | 189.872 | + | 328.868i | 0.139189 | + | 0.241082i | ||||
\(124\) | −698.035 | + | 1209.03i | −0.505527 | + | 0.875599i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 426.664 | − | 440.675i | 0.301669 | − | 0.311575i | ||||
\(127\) | 760.110 | 0.531094 | 0.265547 | − | 0.964098i | \(-0.414448\pi\) | ||||
0.265547 | + | 0.964098i | \(0.414448\pi\) | |||||||
\(128\) | −551.577 | + | 955.360i | −0.380883 | + | 0.659708i | ||||
\(129\) | −137.389 | − | 237.964i | −0.0937704 | − | 0.162415i | ||||
\(130\) | 63.2333 | + | 109.523i | 0.0426609 | + | 0.0738909i | ||||
\(131\) | 5.05499 | − | 8.75549i | 0.00337142 | − | 0.00583947i | −0.864335 | − | 0.502917i | \(-0.832260\pi\) |
0.867706 | + | 0.497077i | \(0.165594\pi\) | |||||||
\(132\) | 1081.65 | 0.713224 | ||||||||
\(133\) | −423.099 | − | 106.075i | −0.275844 | − | 0.0691568i | ||||
\(134\) | −3395.78 | −2.18919 | ||||||||
\(135\) | −67.5000 | + | 116.913i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 307.599 | + | 532.777i | 0.193944 | + | 0.335921i | ||||
\(137\) | −1395.86 | − | 2417.70i | −0.870485 | − | 1.50772i | −0.861496 | − | 0.507764i | \(-0.830472\pi\) |
−0.00898882 | − | 0.999960i | \(-0.502861\pi\) | |||||||
\(138\) | 30.3559 | − | 52.5779i | 0.0187251 | − | 0.0324328i | ||||
\(139\) | 517.250 | 0.315630 | 0.157815 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157815 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(140\) | 140.814 | + | 493.498i | 0.0850070 | + | 0.297916i | ||||
\(141\) | 1705.40 | 1.01858 | ||||||||
\(142\) | −956.163 | + | 1656.12i | −0.565067 | + | 0.978724i | ||||
\(143\) | 223.581 | + | 387.253i | 0.130747 | + | 0.226460i | ||||
\(144\) | 349.300 | + | 605.006i | 0.202141 | + | 0.350119i | ||||
\(145\) | 346.607 | − | 600.341i | 0.198511 | − | 0.343832i | ||||
\(146\) | 3924.62 | 2.22468 | ||||||||
\(147\) | 907.294 | + | 485.447i | 0.509063 | + | 0.272374i | ||||
\(148\) | 706.762 | 0.392537 | ||||||||
\(149\) | 985.657 | − | 1707.21i | 0.541934 | − | 0.938658i | −0.456859 | − | 0.889539i | \(-0.651025\pi\) |
0.998793 | − | 0.0491184i | \(-0.0156412\pi\) | |||||||
\(150\) | −137.998 | − | 239.019i | −0.0751165 | − | 0.130106i | ||||
\(151\) | 80.8806 | + | 140.089i | 0.0435892 | + | 0.0754987i | 0.886997 | − | 0.461775i | \(-0.152787\pi\) |
−0.843408 | + | 0.537274i | \(0.819454\pi\) | |||||||
\(152\) | 106.519 | − | 184.496i | 0.0568410 | − | 0.0984515i | ||||
\(153\) | 612.113 | 0.323441 | ||||||||
\(154\) | 1216.61 | + | 4263.75i | 0.636607 | + | 2.23106i | ||||
\(155\) | 1259.54 | 0.652700 | ||||||||
\(156\) | 57.1375 | − | 98.9650i | 0.0293247 | − | 0.0507919i | ||||
\(157\) | 53.7440 | + | 93.0873i | 0.0273200 | + | 0.0473196i | 0.879362 | − | 0.476154i | \(-0.157969\pi\) |
−0.852042 | + | 0.523473i | \(0.824636\pi\) | |||||||
\(158\) | 207.573 | + | 359.528i | 0.104517 | + | 0.181028i | ||||
\(159\) | 885.598 | − | 1533.90i | 0.441714 | − | 0.765071i | ||||
\(160\) | −1066.41 | −0.526921 | ||||||||
\(161\) | 98.7917 | + | 24.7680i | 0.0483595 | + | 0.0121242i | ||||
\(162\) | 298.075 | 0.144562 | ||||||||
\(163\) | 1004.14 | − | 1739.21i | 0.482515 | − | 0.835741i | −0.517283 | − | 0.855814i | \(-0.673057\pi\) |
0.999799 | + | 0.0200735i | \(0.00639003\pi\) | |||||||
\(164\) | 350.756 | + | 607.528i | 0.167009 | + | 0.289268i | ||||
\(165\) | −487.934 | − | 845.127i | −0.230216 | − | 0.398746i | ||||
\(166\) | 1092.12 | − | 1891.60i | 0.510632 | − | 0.884440i | ||||
\(167\) | −566.505 | −0.262500 | −0.131250 | − | 0.991349i | \(-0.541899\pi\) | ||||
−0.131250 | + | 0.991349i | \(0.541899\pi\) | |||||||
\(168\) | −349.582 | + | 361.062i | −0.160541 | + | 0.165813i | ||||
\(169\) | −2149.76 | −0.978497 | ||||||||
\(170\) | −625.706 | + | 1083.75i | −0.282291 | + | 0.488942i | ||||
\(171\) | −105.985 | − | 183.571i | −0.0473969 | − | 0.0820938i | ||||
\(172\) | −253.802 | − | 439.598i | −0.112513 | − | 0.194878i | ||||
\(173\) | 373.967 | − | 647.729i | 0.164348 | − | 0.284659i | −0.772076 | − | 0.635531i | \(-0.780781\pi\) |
0.936423 | + | 0.350872i | \(0.114115\pi\) | |||||||
\(174\) | −1530.59 | −0.666862 | ||||||||
\(175\) | 322.064 | − | 332.641i | 0.139119 | − | 0.143687i | ||||
\(176\) | −5049.94 | −2.16281 | ||||||||
\(177\) | −764.670 | + | 1324.45i | −0.324724 | + | 0.562438i | ||||
\(178\) | 445.872 | + | 772.272i | 0.187750 | + | 0.325192i | ||||
\(179\) | 2023.57 | + | 3504.93i | 0.844965 | + | 1.46352i | 0.885651 | + | 0.464351i | \(0.153712\pi\) |
−0.0406860 | + | 0.999172i | \(0.512954\pi\) | |||||||
\(180\) | −124.695 | + | 215.978i | −0.0516344 | + | 0.0894334i | ||||
\(181\) | −2930.28 | −1.20335 | −0.601673 | − | 0.798742i | \(-0.705499\pi\) | ||||
−0.601673 | + | 0.798742i | \(0.705499\pi\) | |||||||
\(182\) | 454.376 | + | 113.916i | 0.185058 | + | 0.0463959i | ||||
\(183\) | 784.625 | 0.316946 | ||||||||
\(184\) | −24.8717 | + | 43.0791i | −0.00996504 | + | 0.0172600i | ||||
\(185\) | −318.822 | − | 552.216i | −0.126704 | − | 0.219458i | ||||
\(186\) | −1390.51 | − | 2408.43i | −0.548156 | − | 0.949435i | ||||
\(187\) | −2212.38 | + | 3831.95i | −0.865160 | + | 1.49850i | ||||
\(188\) | 3150.43 | 1.22217 | ||||||||
\(189\) | 137.207 | + | 480.855i | 0.0528059 | + | 0.185064i | ||||
\(190\) | 433.354 | 0.165467 | ||||||||
\(191\) | −1508.61 | + | 2613.00i | −0.571516 | + | 0.989894i | 0.424895 | + | 0.905243i | \(0.360311\pi\) |
−0.996411 | + | 0.0846516i | \(0.973022\pi\) | |||||||
\(192\) | 245.836 | + | 425.800i | 0.0924045 | + | 0.160049i | ||||
\(193\) | −393.459 | − | 681.491i | −0.146745 | − | 0.254170i | 0.783278 | − | 0.621672i | \(-0.213546\pi\) |
−0.930023 | + | 0.367502i | \(0.880213\pi\) | |||||||
\(194\) | 2827.82 | − | 4897.94i | 1.04653 | − | 1.81264i | ||||
\(195\) | −103.099 | −0.0378620 | ||||||||
\(196\) | 1676.07 | + | 896.781i | 0.610813 | + | 0.326815i | ||||
\(197\) | −2009.92 | −0.726910 | −0.363455 | − | 0.931612i | \(-0.618403\pi\) | ||||
−0.363455 | + | 0.931612i | \(0.618403\pi\) | |||||||
\(198\) | −1077.34 | + | 1866.01i | −0.386684 | + | 0.669756i | ||||
\(199\) | −1360.62 | − | 2356.66i | −0.484681 | − | 0.839492i | 0.515164 | − | 0.857091i | \(-0.327731\pi\) |
−0.999845 | + | 0.0175996i | \(0.994398\pi\) | |||||||
\(200\) | 113.067 | + | 195.838i | 0.0399752 | + | 0.0692391i | ||||
\(201\) | 1384.17 | − | 2397.46i | 0.485731 | − | 0.841311i | ||||
\(202\) | −6314.19 | −2.19933 | ||||||||
\(203\) | −704.545 | − | 2469.15i | −0.243593 | − | 0.853697i | ||||
\(204\) | 1130.77 | 0.388088 | ||||||||
\(205\) | 316.454 | − | 548.114i | 0.107815 | − | 0.186741i | ||||
\(206\) | 529.271 | + | 916.725i | 0.179010 | + | 0.310055i | ||||
\(207\) | 24.7470 | + | 42.8631i | 0.00830936 | + | 0.0143922i | ||||
\(208\) | −266.760 | + | 462.042i | −0.0889254 | + | 0.154023i | ||||
\(209\) | 1532.26 | 0.507122 | ||||||||
\(210\) | −991.614 | − | 248.607i | −0.325847 | − | 0.0816929i | ||||
\(211\) | 640.229 | 0.208887 | 0.104444 | − | 0.994531i | \(-0.466694\pi\) | ||||
0.104444 | + | 0.994531i | \(0.466694\pi\) | |||||||
\(212\) | 1635.99 | − | 2833.62i | 0.530002 | − | 0.917990i | ||||
\(213\) | −779.493 | − | 1350.12i | −0.250751 | − | 0.434314i | ||||
\(214\) | 1933.07 | + | 3348.17i | 0.617484 | + | 1.06951i | ||||
\(215\) | −228.981 | + | 396.607i | −0.0726343 | + | 0.125806i | ||||
\(216\) | −244.225 | −0.0769323 | ||||||||
\(217\) | 3245.22 | − | 3351.79i | 1.01521 | − | 1.04854i | ||||
\(218\) | −680.057 | −0.211281 | ||||||||
\(219\) | −1599.73 | + | 2770.82i | −0.493607 | + | 0.854952i | ||||
\(220\) | −901.375 | − | 1561.23i | −0.276230 | − | 0.478445i | ||||
\(221\) | 233.735 | + | 404.841i | 0.0711435 | + | 0.123224i | ||||
\(222\) | −703.948 | + | 1219.27i | −0.212819 | + | 0.368614i | ||||
\(223\) | −1970.27 | −0.591655 | −0.295828 | − | 0.955241i | \(-0.595595\pi\) | ||||
−0.295828 | + | 0.955241i | \(0.595595\pi\) | |||||||
\(224\) | −2747.63 | + | 2837.86i | −0.819570 | + | 0.846484i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 3864.34 | − | 6693.24i | 1.13740 | − | 1.97003i | ||||
\(227\) | 2298.03 | + | 3980.31i | 0.671920 | + | 1.16380i | 0.977359 | + | 0.211588i | \(0.0678636\pi\) |
−0.305439 | + | 0.952212i | \(0.598803\pi\) | |||||||
\(228\) | −195.789 | − | 339.116i | −0.0568704 | − | 0.0985024i | ||||
\(229\) | 2312.71 | − | 4005.73i | 0.667371 | − | 1.15592i | −0.311266 | − | 0.950323i | \(-0.600753\pi\) |
0.978637 | − | 0.205598i | \(-0.0659138\pi\) | |||||||
\(230\) | −101.186 | −0.0290088 | ||||||||
\(231\) | −3506.16 | − | 879.027i | −0.998650 | − | 0.250371i | ||||
\(232\) | 1254.07 | 0.354888 | ||||||||
\(233\) | 948.296 | − | 1642.50i | 0.266631 | − | 0.461818i | −0.701359 | − | 0.712808i | \(-0.747423\pi\) |
0.967990 | + | 0.250990i | \(0.0807563\pi\) | |||||||
\(234\) | 113.820 | + | 197.142i | 0.0317976 | + | 0.0550750i | ||||
\(235\) | −1421.16 | − | 2461.53i | −0.394496 | − | 0.683287i | ||||
\(236\) | −1412.60 | + | 2446.69i | −0.389628 | + | 0.674856i | ||||
\(237\) | −338.440 | −0.0927596 | ||||||||
\(238\) | 1271.87 | + | 4457.39i | 0.346398 | + | 1.21399i | ||||
\(239\) | 7217.92 | 1.95351 | 0.976754 | − | 0.214362i | \(-0.0687673\pi\) | ||||
0.976754 | + | 0.214362i | \(0.0687673\pi\) | |||||||
\(240\) | 582.167 | − | 1008.34i | 0.156578 | − | 0.271201i | ||||
\(241\) | −480.020 | − | 831.419i | −0.128302 | − | 0.222226i | 0.794717 | − | 0.606980i | \(-0.207619\pi\) |
−0.923019 | + | 0.384755i | \(0.874286\pi\) | |||||||
\(242\) | −5338.73 | − | 9246.96i | −1.41813 | − | 2.45627i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 1449.46 | 0.380296 | ||||||||
\(245\) | −55.3955 | − | 1714.11i | −0.0144453 | − | 0.446980i | ||||
\(246\) | −1397.44 | −0.362184 | ||||||||
\(247\) | 80.9405 | − | 140.193i | 0.0208507 | − | 0.0361145i | ||||
\(248\) | 1139.30 | + | 1973.32i | 0.291715 | + | 0.505266i | ||||
\(249\) | 890.328 | + | 1542.09i | 0.226595 | + | 0.392474i | ||||
\(250\) | −229.996 | + | 398.366i | −0.0581850 | + | 0.100779i | ||||
\(251\) | 2907.61 | 0.731183 | 0.365592 | − | 0.930775i | \(-0.380867\pi\) | ||||
0.365592 | + | 0.930775i | \(0.380867\pi\) | |||||||
\(252\) | 253.466 | + | 888.297i | 0.0633604 | + | 0.222053i | ||||
\(253\) | −357.775 | −0.0889057 | ||||||||
\(254\) | −1398.58 | + | 2422.41i | −0.345491 | + | 0.598409i | ||||
\(255\) | −510.094 | − | 883.509i | −0.125268 | − | 0.216970i | ||||
\(256\) | −2685.34 | − | 4651.14i | −0.655599 | − | 1.13553i | ||||
\(257\) | −1839.05 | + | 3185.32i | −0.446368 | + | 0.773132i | −0.998146 | − | 0.0608588i | \(-0.980616\pi\) |
0.551778 | + | 0.833991i | \(0.313949\pi\) | |||||||
\(258\) | 1011.16 | 0.244001 | ||||||||
\(259\) | −2290.96 | − | 574.366i | −0.549627 | − | 0.137797i | ||||
\(260\) | −190.458 | −0.0454297 | ||||||||
\(261\) | 623.893 | − | 1080.61i | 0.147962 | − | 0.256277i | ||||
\(262\) | 18.6021 | + | 32.2197i | 0.00438641 | + | 0.00759749i | ||||
\(263\) | 2934.87 | + | 5083.35i | 0.688107 | + | 1.19184i | 0.972450 | + | 0.233113i | \(0.0748913\pi\) |
−0.284343 | + | 0.958723i | \(0.591775\pi\) | |||||||
\(264\) | 882.707 | − | 1528.89i | 0.205784 | − | 0.356428i | ||||
\(265\) | −2951.99 | −0.684300 | ||||||||
\(266\) | 1116.54 | − | 1153.21i | 0.257367 | − | 0.265819i | ||||
\(267\) | −726.976 | −0.166630 | ||||||||
\(268\) | 2557.02 | − | 4428.89i | 0.582817 | − | 1.00947i | ||||
\(269\) | −230.381 | − | 399.031i | −0.0522177 | − | 0.0904438i | 0.838735 | − | 0.544540i | \(-0.183296\pi\) |
−0.890953 | + | 0.454096i | \(0.849962\pi\) | |||||||
\(270\) | −248.396 | − | 430.235i | −0.0559886 | − | 0.0969750i | ||||
\(271\) | 2657.50 | − | 4602.93i | 0.595689 | − | 1.03176i | −0.397760 | − | 0.917490i | \(-0.630212\pi\) |
0.993449 | − | 0.114275i | \(-0.0364544\pi\) | |||||||
\(272\) | −5279.29 | −1.17685 | ||||||||
\(273\) | −265.637 | + | 274.360i | −0.0588903 | + | 0.0608243i | ||||
\(274\) | 10273.4 | 2.26510 | ||||||||
\(275\) | −813.224 | + | 1408.54i | −0.178324 | + | 0.308867i | ||||
\(276\) | 45.7159 | + | 79.1822i | 0.00997019 | + | 0.0172689i | ||||
\(277\) | 1190.29 | + | 2061.65i | 0.258187 | + | 0.447193i | 0.965756 | − | 0.259451i | \(-0.0835415\pi\) |
−0.707569 | + | 0.706644i | \(0.750208\pi\) | |||||||
\(278\) | −951.725 | + | 1648.44i | −0.205326 | + | 0.355635i | ||||
\(279\) | 2267.17 | 0.486494 | ||||||||
\(280\) | 812.467 | + | 203.693i | 0.173408 | + | 0.0434750i | ||||
\(281\) | 1769.23 | 0.375599 | 0.187800 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187800 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(282\) | −3137.88 | + | 5434.97i | −0.662618 | + | 1.14769i | ||||
\(283\) | −728.463 | − | 1261.74i | −0.153013 | − | 0.265026i | 0.779321 | − | 0.626625i | \(-0.215564\pi\) |
−0.932334 | + | 0.361599i | \(0.882231\pi\) | |||||||
\(284\) | −1439.98 | − | 2494.12i | −0.300870 | − | 0.521122i | ||||
\(285\) | −176.642 | + | 305.952i | −0.0367135 | + | 0.0635896i | ||||
\(286\) | −1645.53 | −0.340217 | ||||||||
\(287\) | −643.252 | − | 2254.34i | −0.132299 | − | 0.463658i | ||||
\(288\) | −1919.55 | −0.392744 | ||||||||
\(289\) | 143.647 | − | 248.803i | 0.0292381 | − | 0.0506418i | ||||
\(290\) | 1275.49 | + | 2209.22i | 0.258275 | + | 0.447345i | ||||
\(291\) | 2305.33 | + | 3992.94i | 0.464401 | + | 0.804366i | ||||
\(292\) | −2955.23 | + | 5118.61i | −0.592267 | + | 1.02584i | ||||
\(293\) | −2743.56 | −0.547032 | −0.273516 | − | 0.961868i | \(-0.588187\pi\) | ||||
−0.273516 | + | 0.961868i | \(0.588187\pi\) | |||||||
\(294\) | −3216.48 | + | 1998.27i | −0.638057 | + | 0.396399i | ||||
\(295\) | 2548.90 | 0.503060 | ||||||||
\(296\) | 576.771 | − | 998.997i | 0.113257 | − | 0.196167i | ||||
\(297\) | −878.282 | − | 1521.23i | −0.171593 | − | 0.297207i | ||||
\(298\) | 3627.16 | + | 6282.43i | 0.705087 | + | 1.22125i | ||||
\(299\) | −18.8993 | + | 32.7345i | −0.00365543 | + | 0.00633138i | ||||
\(300\) | 415.649 | 0.0799917 | ||||||||
\(301\) | 465.447 | + | 1631.21i | 0.0891293 | + | 0.312363i | ||||
\(302\) | −595.272 | −0.113424 | ||||||||
\(303\) | 2573.76 | − | 4457.88i | 0.487982 | − | 0.845210i | ||||
\(304\) | 914.088 | + | 1583.25i | 0.172456 | + | 0.298702i | ||||
\(305\) | −653.854 | − | 1132.51i | −0.122753 | − | 0.212614i | ||||
\(306\) | −1126.27 | + | 1950.76i | −0.210407 | + | 0.364436i | ||||
\(307\) | 3367.27 | 0.625995 | 0.312997 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312997 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(308\) | −6477.02 | − | 1623.85i | −1.19826 | − | 0.300414i | ||||
\(309\) | −862.955 | −0.158873 | ||||||||
\(310\) | −2317.52 | + | 4014.05i | −0.424600 | + | 0.735429i | ||||
\(311\) | 3100.15 | + | 5369.61i | 0.565251 | + | 0.979044i | 0.997026 | + | 0.0770626i | \(0.0245541\pi\) |
−0.431775 | + | 0.901981i | \(0.642113\pi\) | |||||||
\(312\) | −93.2569 | − | 161.526i | −0.0169219 | − | 0.0293096i | ||||
\(313\) | −5169.97 | + | 8954.65i | −0.933622 | + | 1.61708i | −0.156550 | + | 0.987670i | \(0.550037\pi\) |
−0.777072 | + | 0.629412i | \(0.783296\pi\) | |||||||
\(314\) | −395.550 | −0.0710897 | ||||||||
\(315\) | 579.715 | − | 598.753i | 0.103693 | − | 0.107098i | ||||
\(316\) | −625.210 | −0.111300 | ||||||||
\(317\) | −1488.66 | + | 2578.43i | −0.263758 | + | 0.456842i | −0.967237 | − | 0.253873i | \(-0.918295\pi\) |
0.703480 | + | 0.710715i | \(0.251629\pi\) | |||||||
\(318\) | 3258.95 | + | 5644.67i | 0.574695 | + | 0.995401i | ||||
\(319\) | 4509.91 | + | 7811.39i | 0.791556 | + | 1.37102i | ||||
\(320\) | 409.726 | − | 709.667i | 0.0715762 | − | 0.123974i | ||||
\(321\) | −3151.79 | −0.548023 | ||||||||
\(322\) | −260.708 | + | 269.269i | −0.0451201 | + | 0.0466018i | ||||
\(323\) | 1601.85 | 0.275941 | ||||||||
\(324\) | −224.450 | + | 388.760i | −0.0384860 | + | 0.0666597i | ||||
\(325\) | 85.9161 | + | 148.811i | 0.0146639 | + | 0.0253986i | ||||
\(326\) | 3695.16 | + | 6400.21i | 0.627779 | + | 1.08735i | ||||
\(327\) | 277.201 | − | 480.127i | 0.0468785 | − | 0.0811959i | ||||
\(328\) | 1144.97 | 0.192746 | ||||||||
\(329\) | −10212.1 | − | 2560.26i | −1.71128 | − | 0.429033i | ||||
\(330\) | 3591.14 | 0.599048 | ||||||||
\(331\) | 3378.51 | − | 5851.75i | 0.561027 | − | 0.971727i | −0.436381 | − | 0.899762i | \(-0.643740\pi\) |
0.997407 | − | 0.0719644i | \(-0.0229268\pi\) | |||||||
\(332\) | 1644.73 | + | 2848.75i | 0.271886 | + | 0.470920i | ||||
\(333\) | −573.879 | − | 993.988i | −0.0944396 | − | 0.163574i | ||||
\(334\) | 1042.35 | − | 1805.41i | 0.170764 | − | 0.295771i | ||||
\(335\) | −4613.91 | −0.752491 | ||||||||
\(336\) | −1183.36 | − | 4147.23i | −0.192136 | − | 0.673363i | ||||
\(337\) | 10292.1 | 1.66364 | 0.831818 | − | 0.555048i | \(-0.187300\pi\) | ||||
0.831818 | + | 0.555048i | \(0.187300\pi\) | |||||||
\(338\) | 3955.49 | − | 6851.12i | 0.636540 | − | 1.10252i | ||||
\(339\) | 3150.33 | + | 5456.53i | 0.504726 | + | 0.874212i | ||||
\(340\) | −942.312 | − | 1632.13i | −0.150306 | − | 0.260338i | ||||
\(341\) | −8194.29 | + | 14192.9i | −1.30131 | + | 2.25393i | ||||
\(342\) | 780.037 | 0.123332 | ||||||||
\(343\) | −4704.17 | − | 4269.00i | −0.740529 | − | 0.672024i | ||||
\(344\) | −828.485 | −0.129852 | ||||||||
\(345\) | 41.2450 | − | 71.4385i | 0.00643640 | − | 0.0111482i | ||||
\(346\) | 1376.18 | + | 2383.61i | 0.213826 | + | 0.370357i | ||||
\(347\) | −4520.22 | − | 7829.25i | −0.699303 | − | 1.21123i | −0.968708 | − | 0.248201i | \(-0.920161\pi\) |
0.269406 | − | 0.963027i | \(-0.413173\pi\) | |||||||
\(348\) | 1152.54 | − | 1996.25i | 0.177536 | − | 0.307501i | ||||
\(349\) | −7449.27 | −1.14255 | −0.571275 | − | 0.820759i | \(-0.693551\pi\) | ||||
−0.571275 | + | 0.820759i | \(0.693551\pi\) | |||||||
\(350\) | 467.511 | + | 1638.44i | 0.0713987 | + | 0.250224i | ||||
\(351\) | −185.579 | −0.0282207 | ||||||||
\(352\) | 6937.87 | − | 12016.7i | 1.05054 | − | 1.81959i | ||||
\(353\) | −848.018 | − | 1468.81i | −0.127862 | − | 0.221464i | 0.794986 | − | 0.606628i | \(-0.207478\pi\) |
−0.922848 | + | 0.385164i | \(0.874145\pi\) | |||||||
\(354\) | −2813.94 | − | 4873.89i | −0.422484 | − | 0.731764i | ||||
\(355\) | −1299.16 | + | 2250.20i | −0.194231 | + | 0.336418i | ||||
\(356\) | −1342.96 | −0.199935 | ||||||||
\(357\) | −3665.39 | − | 918.948i | −0.543398 | − | 0.136235i | ||||
\(358\) | −14893.3 | −2.19870 | ||||||||
\(359\) | −2393.00 | + | 4144.81i | −0.351805 | + | 0.609344i | −0.986566 | − | 0.163365i | \(-0.947765\pi\) |
0.634761 | + | 0.772709i | \(0.281099\pi\) | |||||||
\(360\) | 203.520 | + | 352.508i | 0.0297957 | + | 0.0516077i | ||||
\(361\) | 3152.15 | + | 5459.68i | 0.459564 | + | 0.795988i | ||||
\(362\) | 5391.63 | − | 9338.57i | 0.782811 | − | 1.35587i | ||||
\(363\) | 8704.59 | 1.25860 | ||||||||
\(364\) | −490.718 | + | 506.833i | −0.0706610 | + | 0.0729815i | ||||
\(365\) | 5332.44 | 0.764693 | ||||||||
\(366\) | −1443.69 | + | 2500.54i | −0.206182 | + | 0.357118i | ||||
\(367\) | −956.276 | − | 1656.32i | −0.136014 | − | 0.235583i | 0.789970 | − | 0.613145i | \(-0.210096\pi\) |
−0.925984 | + | 0.377562i | \(0.876763\pi\) | |||||||
\(368\) | −213.436 | − | 369.681i | −0.0302340 | − | 0.0523668i | ||||
\(369\) | 569.616 | − | 986.605i | 0.0803606 | − | 0.139189i | ||||
\(370\) | 2346.49 | 0.329698 | ||||||||
\(371\) | −7605.85 | + | 7855.62i | −1.06436 | + | 1.09931i | ||||
\(372\) | 4188.21 | 0.583732 | ||||||||
\(373\) | 6402.04 | − | 11088.7i | 0.888700 | − | 1.53927i | 0.0472865 | − | 0.998881i | \(-0.484943\pi\) |
0.841413 | − | 0.540392i | \(-0.181724\pi\) | |||||||
\(374\) | −8141.42 | − | 14101.4i | −1.12562 | − | 1.94964i | ||||
\(375\) | −187.500 | − | 324.760i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 2570.99 | − | 4453.08i | 0.352629 | − | 0.610771i | ||||
\(377\) | 952.932 | 0.130182 | ||||||||
\(378\) | −1784.90 | − | 447.492i | −0.242872 | − | 0.0608903i | ||||
\(379\) | −5817.74 | −0.788489 | −0.394244 | − | 0.919006i | \(-0.628994\pi\) | ||||
−0.394244 | + | 0.919006i | \(0.628994\pi\) | |||||||
\(380\) | −326.315 | + | 565.194i | −0.0440516 | + | 0.0762996i | ||||
\(381\) | −1140.17 | − | 1974.82i | −0.153314 | − | 0.265547i | ||||
\(382\) | −5551.62 | − | 9615.68i | −0.743574 | − | 1.28791i | ||||
\(383\) | 5650.48 | − | 9786.92i | 0.753854 | − | 1.30571i | −0.192088 | − | 0.981378i | \(-0.561526\pi\) |
0.945942 | − | 0.324335i | \(-0.105141\pi\) | |||||||
\(384\) | 3309.46 | 0.439806 | ||||||||
\(385\) | 1653.03 | + | 5793.22i | 0.218822 | + | 0.766883i | ||||
\(386\) | 2895.81 | 0.381847 | ||||||||
\(387\) | −412.166 | + | 713.892i | −0.0541384 | + | 0.0937704i | ||||
\(388\) | 4258.70 | + | 7376.28i | 0.557223 | + | 0.965139i | ||||
\(389\) | −635.322 | − | 1100.41i | −0.0828075 | − | 0.143427i | 0.821647 | − | 0.569996i | \(-0.193055\pi\) |
−0.904455 | + | 0.426569i | \(0.859722\pi\) | |||||||
\(390\) | 189.700 | − | 328.570i | 0.0246303 | − | 0.0426609i | ||||
\(391\) | −374.024 | −0.0483765 | ||||||||
\(392\) | 2635.38 | − | 1637.26i | 0.339559 | − | 0.210954i | ||||
\(393\) | −30.3299 | −0.00389298 | ||||||||
\(394\) | 3698.21 | − | 6405.48i | 0.472875 | − | 0.819044i | ||||
\(395\) | 282.033 | + | 488.496i | 0.0359257 | + | 0.0622251i | ||||
\(396\) | −1622.47 | − | 2810.21i | −0.205890 | − | 0.356612i | ||||
\(397\) | −5657.04 | + | 9798.28i | −0.715161 | + | 1.23869i | 0.247737 | + | 0.968827i | \(0.420313\pi\) |
−0.962898 | + | 0.269867i | \(0.913020\pi\) | |||||||
\(398\) | 10014.0 | 1.26119 | ||||||||
\(399\) | 359.057 | + | 1258.35i | 0.0450510 | + | 0.157886i | ||||
\(400\) | −1940.56 | −0.242570 | ||||||||
\(401\) | 3398.03 | − | 5885.57i | 0.423166 | − | 0.732945i | −0.573081 | − | 0.819499i | \(-0.694252\pi\) |
0.996247 | + | 0.0865533i | \(0.0275853\pi\) | |||||||
\(402\) | 5093.67 | + | 8822.50i | 0.631964 | + | 1.09459i | ||||
\(403\) | 865.717 | + | 1499.47i | 0.107008 | + | 0.185344i | ||||
\(404\) | 4754.58 | − | 8235.17i | 0.585518 | − | 1.01415i | ||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 9165.34 | + | 2297.84i | 1.12037 | + | 0.280886i | ||||
\(407\) | 8296.75 | 1.01045 | ||||||||
\(408\) | 922.796 | − | 1598.33i | 0.111974 | − | 0.193944i | ||||
\(409\) | −4012.23 | − | 6949.39i | −0.485067 | − | 0.840160i | 0.514786 | − | 0.857319i | \(-0.327871\pi\) |
−0.999853 | + | 0.0171587i | \(0.994538\pi\) | |||||||
\(410\) | 1164.53 | + | 2017.03i | 0.140273 | + | 0.242961i | ||||
\(411\) | −4187.58 | + | 7253.10i | −0.502575 | + | 0.870485i | ||||
\(412\) | −1594.16 | −0.190628 | ||||||||
\(413\) | 6567.28 | − | 6782.94i | 0.782457 | − | 0.808152i | ||||
\(414\) | −182.135 | −0.0216219 | ||||||||
\(415\) | 1483.88 | − | 2570.15i | 0.175520 | − | 0.304009i | ||||
\(416\) | −732.977 | − | 1269.55i | −0.0863874 | − | 0.149627i | ||||
\(417\) | −775.874 | − | 1343.85i | −0.0911145 | − | 0.157815i | ||||
\(418\) | −2819.31 | + | 4883.19i | −0.329897 | + | 0.571398i | ||||
\(419\) | 2524.40 | 0.294332 | 0.147166 | − | 0.989112i | \(-0.452985\pi\) | ||||
0.147166 | + | 0.989112i | \(0.452985\pi\) | |||||||
\(420\) | 1070.92 | − | 1106.09i | 0.124419 | − | 0.128504i | ||||
\(421\) | −7844.12 | −0.908074 | −0.454037 | − | 0.890983i | \(-0.650017\pi\) | ||||
−0.454037 | + | 0.890983i | \(0.650017\pi\) | |||||||
\(422\) | −1178.00 | + | 2040.36i | −0.135887 | + | 0.235363i | ||||
\(423\) | −2558.09 | − | 4430.75i | −0.294040 | − | 0.509292i | ||||
\(424\) | −2670.18 | − | 4624.89i | −0.305839 | − | 0.529728i | ||||
\(425\) | −850.157 | + | 1472.51i | −0.0970322 | + | 0.168065i | ||||
\(426\) | 5736.98 | 0.652483 | ||||||||
\(427\) | −4698.41 | − | 1177.94i | −0.532487 | − | 0.133500i | ||||
\(428\) | −5822.38 | −0.657560 | ||||||||
\(429\) | 670.742 | − | 1161.76i | 0.0754866 | − | 0.130747i | ||||
\(430\) | −842.637 | − | 1459.49i | −0.0945013 | − | 0.163681i | ||||
\(431\) | −3411.88 | − | 5909.55i | −0.381310 | − | 0.660448i | 0.609940 | − | 0.792448i | \(-0.291193\pi\) |
−0.991250 | + | 0.132000i | \(0.957860\pi\) | |||||||
\(432\) | 1047.90 | − | 1815.02i | 0.116706 | − | 0.202141i | ||||
\(433\) | −9283.82 | −1.03037 | −0.515187 | − | 0.857078i | \(-0.672277\pi\) | ||||
−0.515187 | + | 0.857078i | \(0.672277\pi\) | |||||||
\(434\) | 4710.79 | + | 16509.5i | 0.521026 | + | 1.82599i | ||||
\(435\) | −2079.64 | −0.229221 | ||||||||
\(436\) | 512.082 | − | 886.952i | 0.0562483 | − | 0.0974250i | ||||
\(437\) | 64.7608 | + | 112.169i | 0.00708908 | + | 0.0122786i | ||||
\(438\) | −5886.93 | − | 10196.5i | −0.642211 | − | 1.11234i | ||||
\(439\) | −334.674 | + | 579.672i | −0.0363852 | + | 0.0630210i | −0.883645 | − | 0.468158i | \(-0.844918\pi\) |
0.847259 | + | 0.531179i | \(0.178251\pi\) | |||||||
\(440\) | −2942.36 | −0.318799 | ||||||||
\(441\) | −99.7119 | − | 3085.39i | −0.0107669 | − | 0.333159i | ||||
\(442\) | −1720.26 | −0.185123 | ||||||||
\(443\) | −4874.38 | + | 8442.68i | −0.522774 | + | 0.905472i | 0.476875 | + | 0.878971i | \(0.341770\pi\) |
−0.999649 | + | 0.0265002i | \(0.991564\pi\) | |||||||
\(444\) | −1060.14 | − | 1836.22i | −0.113316 | − | 0.196269i | ||||
\(445\) | 605.813 | + | 1049.30i | 0.0645355 | + | 0.111779i | ||||
\(446\) | 3625.24 | − | 6279.11i | 0.384888 | − | 0.666646i | ||||
\(447\) | −5913.94 | −0.625772 | ||||||||
\(448\) | −832.846 | − | 2918.80i | −0.0878310 | − | 0.307813i | ||||
\(449\) | 5113.54 | 0.537467 | 0.268734 | − | 0.963215i | \(-0.413395\pi\) | ||||
0.268734 | + | 0.963215i | \(0.413395\pi\) | |||||||
\(450\) | −413.994 | + | 717.058i | −0.0433686 | + | 0.0751165i | ||||
\(451\) | 4117.56 | + | 7131.82i | 0.429908 | + | 0.744622i | ||||
\(452\) | 5819.69 | + | 10080.0i | 0.605609 | + | 1.04895i | ||||
\(453\) | 242.642 | − | 420.268i | 0.0251662 | − | 0.0435892i | ||||
\(454\) | −16913.3 | −1.74841 | ||||||||
\(455\) | 617.368 | + | 154.780i | 0.0636103 | + | 0.0159477i | ||||
\(456\) | −639.114 | −0.0656343 | ||||||||
\(457\) | 1739.10 | − | 3012.20i | 0.178012 | − | 0.308326i | −0.763187 | − | 0.646177i | \(-0.776367\pi\) |
0.941200 | + | 0.337851i | \(0.109700\pi\) | |||||||
\(458\) | 8510.63 | + | 14740.8i | 0.868287 | + | 1.50392i | ||||
\(459\) | −918.169 | − | 1590.32i | −0.0933692 | − | 0.161720i | ||||
\(460\) | 76.1931 | − | 131.970i | 0.00772288 | − | 0.0133764i | ||||
\(461\) | −996.935 | −0.100720 | −0.0503600 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503600 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(462\) | 9252.62 | − | 9556.47i | 0.931755 | − | 0.962354i | ||||
\(463\) | −12681.1 | −1.27287 | −0.636436 | − | 0.771330i | \(-0.719592\pi\) | ||||
−0.636436 | + | 0.771330i | \(0.719592\pi\) | |||||||
\(464\) | −5380.89 | + | 9319.97i | −0.538365 | + | 0.932476i | ||||
\(465\) | −1889.31 | − | 3272.38i | −0.188418 | − | 0.326350i | ||||
\(466\) | 3489.68 | + | 6044.30i | 0.346902 | + | 0.600851i | ||||
\(467\) | 33.5108 | − | 58.0425i | 0.00332055 | − | 0.00575136i | −0.864360 | − | 0.502873i | \(-0.832276\pi\) |
0.867681 | + | 0.497122i | \(0.165610\pi\) | |||||||
\(468\) | −342.825 | −0.0338613 | ||||||||
\(469\) | −11887.8 | + | 12278.2i | −1.17042 | + | 1.20886i | ||||
\(470\) | 10459.6 | 1.02652 | ||||||||
\(471\) | 161.232 | − | 279.262i | 0.0157732 | − | 0.0273200i | ||||
\(472\) | 2305.57 | + | 3993.37i | 0.224836 | + | 0.389427i | ||||
\(473\) | −2979.40 | − | 5160.48i | −0.289626 | − | 0.501647i | ||||
\(474\) | 622.720 | − | 1078.58i | 0.0603428 | − | 0.104517i | ||||
\(475\) | 588.805 | 0.0568763 | ||||||||
\(476\) | −6771.18 | − | 1697.60i | −0.652010 | − | 0.163465i | ||||
\(477\) | −5313.59 | −0.510047 | ||||||||
\(478\) | −13280.8 | + | 23003.0i | −1.27081 | + | 2.20111i | ||||
\(479\) | −7832.74 | − | 13566.7i | −0.747155 | − | 1.29411i | −0.949181 | − | 0.314730i | \(-0.898086\pi\) |
0.202027 | − | 0.979380i | \(-0.435247\pi\) | |||||||
\(480\) | 1599.62 | + | 2770.62i | 0.152109 | + | 0.263461i | ||||
\(481\) | 438.271 | − | 759.107i | 0.0415456 | − | 0.0719590i | ||||
\(482\) | 3532.89 | 0.333857 | ||||||||
\(483\) | −83.8384 | − | 293.820i | −0.00789809 | − | 0.0276797i | ||||
\(484\) | 16080.2 | 1.51017 | ||||||||
\(485\) | 3842.21 | − | 6654.91i | 0.359723 | − | 0.623059i | ||||
\(486\) | −447.113 | − | 774.423i | −0.0417314 | − | 0.0722809i | ||||
\(487\) | 5862.43 | + | 10154.0i | 0.545486 | + | 0.944810i | 0.998576 | + | 0.0533453i | \(0.0169884\pi\) |
−0.453090 | + | 0.891465i | \(0.649678\pi\) | |||||||
\(488\) | 1182.87 | − | 2048.79i | 0.109725 | − | 0.190050i | ||||
\(489\) | −6024.81 | −0.557160 | ||||||||
\(490\) | 5564.65 | + | 2977.36i | 0.513031 | + | 0.274497i | ||||
\(491\) | 10584.2 | 0.972823 | 0.486412 | − | 0.873730i | \(-0.338306\pi\) | ||||
0.486412 | + | 0.873730i | \(0.338306\pi\) | |||||||
\(492\) | 1052.27 | − | 1822.58i | 0.0964226 | − | 0.167009i | ||||
\(493\) | 4714.73 | + | 8166.15i | 0.430711 | + | 0.746014i | ||||
\(494\) | 297.857 | + | 515.903i | 0.0271279 | + | 0.0469870i | ||||
\(495\) | −1463.80 | + | 2535.38i | −0.132915 | + | 0.230216i | ||||
\(496\) | −19553.7 | −1.77013 | ||||||||
\(497\) | 2640.78 | + | 9254.89i | 0.238340 | + | 0.835289i | ||||
\(498\) | −6552.71 | −0.589626 | ||||||||
\(499\) | −5221.55 | + | 9044.00i | −0.468435 | + | 0.811352i | −0.999349 | − | 0.0360729i | \(-0.988515\pi\) |
0.530915 | + | 0.847425i | \(0.321848\pi\) | |||||||
\(500\) | −346.374 | − | 599.938i | −0.0309806 | − | 0.0536601i | ||||
\(501\) | 849.758 | + | 1471.82i | 0.0757772 | + | 0.131250i | ||||
\(502\) | −5349.93 | + | 9266.35i | −0.475655 | + | 0.823859i | ||||
\(503\) | −13824.2 | −1.22543 | −0.612713 | − | 0.790305i | \(-0.709922\pi\) | ||||
−0.612713 | + | 0.790305i | \(0.709922\pi\) | |||||||
\(504\) | 1462.44 | + | 366.647i | 0.129250 | + | 0.0324043i | ||||
\(505\) | −8579.20 | −0.755979 | ||||||||
\(506\) | 658.297 | − | 1140.20i | 0.0578357 | − | 0.100174i | ||||
\(507\) | 3224.64 | + | 5585.24i | 0.282468 | + | 0.489249i | ||||
\(508\) | −2106.26 | − | 3648.15i | −0.183957 | − | 0.318623i | ||||
\(509\) | 2750.71 | − | 4764.38i | 0.239535 | − | 0.414887i | −0.721046 | − | 0.692887i | \(-0.756338\pi\) |
0.960581 | + | 0.278001i | \(0.0896717\pi\) | |||||||
\(510\) | 3754.24 | 0.325961 | ||||||||
\(511\) | 13739.1 | − | 14190.3i | 1.18940 | − | 1.22846i | ||||
\(512\) | 10938.5 | 0.944178 | ||||||||
\(513\) | −317.955 | + | 550.714i | −0.0273646 | + | 0.0473969i | ||||
\(514\) | −6767.59 | − | 11721.8i | −0.580750 | − | 1.00589i | ||||
\(515\) | 719.130 | + | 1245.57i | 0.0615313 | + | 0.106575i | ||||
\(516\) | −761.405 | + | 1318.79i | −0.0649593 | + | 0.112513i | ||||
\(517\) | 36983.2 | 3.14607 | ||||||||
\(518\) | 6045.77 | − | 6244.31i | 0.512810 | − | 0.529651i | ||||
\(519\) | −2243.80 | −0.189772 | ||||||||
\(520\) | −155.428 | + | 269.210i | −0.0131076 | + | 0.0227031i | ||||
\(521\) | −4102.73 | − | 7106.13i | −0.344998 | − | 0.597553i | 0.640356 | − | 0.768079i | \(-0.278787\pi\) |
−0.985353 | + | 0.170525i | \(0.945454\pi\) | |||||||
\(522\) | 2295.89 | + | 3976.60i | 0.192507 | + | 0.333431i | ||||
\(523\) | 9320.29 | − | 16143.2i | 0.779250 | − | 1.34970i | −0.153125 | − | 0.988207i | \(-0.548934\pi\) |
0.932375 | − | 0.361494i | \(-0.117733\pi\) | |||||||
\(524\) | −56.0293 | −0.00467109 | ||||||||
\(525\) | −1347.32 | − | 337.786i | −0.112004 | − | 0.0280804i | ||||
\(526\) | −21600.3 | −1.79053 | ||||||||
\(527\) | −8566.44 | + | 14837.5i | −0.708084 | + | 1.22644i | ||||
\(528\) | 7574.91 | + | 13120.1i | 0.624348 | + | 1.08140i | ||||
\(529\) | 6068.38 | + | 10510.7i | 0.498757 | + | 0.863873i | ||||
\(530\) | 5431.59 | − | 9407.78i | 0.445157 | − | 0.771034i | ||||
\(531\) | 4588.02 | 0.374959 | ||||||||
\(532\) | 663.297 | + | 2324.59i | 0.0540556 | + | 0.189444i | ||||
\(533\) | 870.030 | 0.0707039 | ||||||||
\(534\) | 1337.61 | − | 2316.82i | 0.108397 | − | 0.187750i | ||||
\(535\) | 2626.49 | + | 4549.21i | 0.212249 | + | 0.367625i | ||||
\(536\) | −4173.44 | − | 7228.61i | −0.336316 | − | 0.582516i | ||||
\(537\) | 6070.71 | − | 10514.8i | 0.487841 | − | 0.844965i | ||||
\(538\) | 1695.58 | 0.135876 | ||||||||
\(539\) | 19675.5 | + | 10527.4i | 1.57233 | + | 0.841274i | ||||
\(540\) | 748.168 | 0.0596223 | ||||||||
\(541\) | −2401.26 | + | 4159.10i | −0.190829 | + | 0.330525i | −0.945525 | − | 0.325549i | \(-0.894451\pi\) |
0.754697 | + | 0.656074i | \(0.227784\pi\) | |||||||
\(542\) | 9779.46 | + | 16938.5i | 0.775025 | + | 1.34238i | ||||
\(543\) | 4395.42 | + | 7613.08i | 0.347376 | + | 0.601673i | ||||
\(544\) | 7252.95 | − | 12562.5i | 0.571632 | − | 0.990096i | ||||
\(545\) | −924.004 | −0.0726238 | ||||||||
\(546\) | −385.601 | − | 1351.38i | −0.0302238 | − | 0.105922i | ||||
\(547\) | 1125.69 | 0.0879913 | 0.0439956 | − | 0.999032i | \(-0.485991\pi\) | ||||
0.0439956 | + | 0.999032i | \(0.485991\pi\) | |||||||
\(548\) | −7735.84 | + | 13398.9i | −0.603027 | + | 1.04447i | ||||
\(549\) | −1176.94 | − | 2038.52i | −0.0914945 | − | 0.158473i | ||||
\(550\) | −2992.62 | − | 5183.37i | −0.232010 | − | 0.401854i | ||||
\(551\) | 1632.67 | − | 2827.87i | 0.126233 | − | 0.218641i | ||||
\(552\) | 149.230 | 0.0115066 | ||||||||
\(553\) | 2026.61 | + | 508.090i | 0.155841 | + | 0.0390709i | ||||
\(554\) | −8760.43 | −0.671832 | ||||||||
\(555\) | −956.465 | + | 1656.65i | −0.0731526 | + | 0.126704i | ||||
\(556\) | −1433.30 | − | 2482.54i | −0.109326 | − | 0.189358i | ||||
\(557\) | −4482.81 | − | 7764.45i | −0.341010 | − | 0.590647i | 0.643611 | − | 0.765353i | \(-0.277436\pi\) |
−0.984621 | + | 0.174707i | \(0.944102\pi\) | |||||||
\(558\) | −4171.53 | + | 7225.30i | −0.316478 | + | 0.548156i | ||||
\(559\) | −629.540 | −0.0476328 | ||||||||
\(560\) | −4999.87 | + | 5164.06i | −0.377291 | + | 0.389681i | ||||
\(561\) | 13274.3 | 0.999001 | ||||||||
\(562\) | −3255.33 | + | 5638.40i | −0.244338 | + | 0.423206i | ||||
\(563\) | −6032.82 | − | 10449.2i | −0.451604 | − | 0.782201i | 0.546882 | − | 0.837210i | \(-0.315815\pi\) |
−0.998486 | + | 0.0550087i | \(0.982481\pi\) | |||||||
\(564\) | −4725.64 | − | 8185.05i | −0.352811 | − | 0.611087i | ||||
\(565\) | 5250.55 | − | 9094.21i | 0.390959 | − | 0.677162i | ||||
\(566\) | 5361.41 | 0.398157 | ||||||||
\(567\) | 1043.49 | − | 1077.76i | 0.0772881 | − | 0.0798262i | ||||
\(568\) | −4700.53 | −0.347235 | ||||||||
\(569\) | −5902.60 | + | 10223.6i | −0.434886 | + | 0.753244i | −0.997286 | − | 0.0736208i | \(-0.976545\pi\) |
0.562401 | + | 0.826865i | \(0.309878\pi\) | |||||||
\(570\) | −650.031 | − | 1125.89i | −0.0477663 | − | 0.0827337i | ||||
\(571\) | −514.397 | − | 890.962i | −0.0377003 | − | 0.0652988i | 0.846560 | − | 0.532294i | \(-0.178670\pi\) |
−0.884260 | + | 0.466995i | \(0.845337\pi\) | |||||||
\(572\) | 1239.08 | − | 2146.15i | 0.0905745 | − | 0.156880i | ||||
\(573\) | 9051.69 | 0.659930 | ||||||||
\(574\) | 8367.99 | + | 2097.93i | 0.608490 | + | 0.152554i | ||||
\(575\) | −137.483 | −0.00997123 | ||||||||
\(576\) | 737.507 | − | 1277.40i | 0.0533498 | − | 0.0924045i | ||||
\(577\) | −5312.66 | − | 9201.79i | −0.383308 | − | 0.663909i | 0.608225 | − | 0.793765i | \(-0.291882\pi\) |
−0.991533 | + | 0.129856i | \(0.958549\pi\) | |||||||
\(578\) | 528.612 | + | 915.582i | 0.0380404 | + | 0.0658879i | ||||
\(579\) | −1180.38 | + | 2044.47i | −0.0847233 | + | 0.146745i | ||||
\(580\) | −3841.78 | −0.275037 | ||||||||
\(581\) | −3016.27 | − | 10570.8i | −0.215380 | − | 0.754822i | ||||
\(582\) | −16966.9 | −1.20842 | ||||||||
\(583\) | 19205.1 | − | 33264.1i | 1.36431 | − | 2.36305i | ||||
\(584\) | 4823.38 | + | 8354.34i | 0.341769 | + | 0.591961i | ||||
\(585\) | 154.649 | + | 267.860i | 0.0109298 | + | 0.0189310i | ||||
\(586\) | 5048.07 | − | 8743.51i | 0.355860 | − | 0.616367i | ||||
\(587\) | −4881.61 | −0.343246 | −0.171623 | − | 0.985163i | \(-0.554901\pi\) | ||||
−0.171623 | + | 0.985163i | \(0.554901\pi\) | |||||||
\(588\) | −184.201 | − | 5699.73i | −0.0129189 | − | 0.399750i | ||||
\(589\) | 5932.98 | 0.415050 | ||||||||
\(590\) | −4689.91 | + | 8123.16i | −0.327255 | + | 0.566822i | ||||
\(591\) | 3014.89 | + | 5221.94i | 0.209841 | + | 0.363455i | ||||
\(592\) | 4949.54 | + | 8572.85i | 0.343623 | + | 0.595172i | ||||
\(593\) | −6931.35 | + | 12005.4i | −0.479994 | + | 0.831373i | −0.999737 | − | 0.0229493i | \(-0.992694\pi\) |
0.519743 | + | 0.854323i | \(0.326028\pi\) | |||||||
\(594\) | 6464.05 | 0.446504 | ||||||||
\(595\) | 1728.10 | + | 6056.33i | 0.119068 | + | 0.417286i | ||||
\(596\) | −10925.0 | −0.750848 | ||||||||
\(597\) | −4081.85 | + | 7069.97i | −0.279831 | + | 0.484681i | ||||
\(598\) | −69.5482 | − | 120.461i | −0.00475592 | − | 0.00823749i | ||||
\(599\) | −12524.5 | − | 21693.1i | −0.854320 | − | 1.47973i | −0.877274 | − | 0.479989i | \(-0.840641\pi\) |
0.0229544 | − | 0.999737i | \(-0.492693\pi\) | |||||||
\(600\) | 339.201 | − | 587.513i | 0.0230797 | − | 0.0399752i | ||||
\(601\) | 20281.5 | 1.37654 | 0.688268 | − | 0.725457i | \(-0.258371\pi\) | ||||
0.688268 | + | 0.725457i | \(0.258371\pi\) | |||||||
\(602\) | −6054.95 | − | 1518.03i | −0.409936 | − | 0.102775i | ||||
\(603\) | −8305.03 | −0.560874 | ||||||||
\(604\) | 448.239 | − | 776.373i | 0.0301963 | − | 0.0523016i | ||||
\(605\) | −7253.83 | − | 12564.0i | −0.487454 | − | 0.844296i | ||||
\(606\) | 9471.29 | + | 16404.8i | 0.634892 | + | 1.09967i | ||||
\(607\) | 681.260 | − | 1179.98i | 0.0455544 | − | 0.0789025i | −0.842349 | − | 0.538932i | \(-0.818828\pi\) |
0.887904 | + | 0.460030i | \(0.152161\pi\) | |||||||
\(608\) | −5023.28 | −0.335067 | ||||||||
\(609\) | −5358.23 | + | 5534.19i | −0.356529 | + | 0.368238i | ||||
\(610\) | 4812.29 | 0.319416 | ||||||||
\(611\) | 1953.61 | − | 3383.76i | 0.129353 | − | 0.224046i | ||||
\(612\) | −1696.16 | − | 2937.84i | −0.112031 | − | 0.194044i | ||||
\(613\) | 6988.02 | + | 12103.6i | 0.460430 | + | 0.797488i | 0.998982 | − | 0.0451040i | \(-0.0143619\pi\) |
−0.538552 | + | 0.842592i | \(0.681029\pi\) | |||||||
\(614\) | −6195.68 | + | 10731.2i | −0.407227 | + | 0.705338i | ||||
\(615\) | −1898.72 | −0.124494 | ||||||||
\(616\) | −7581.02 | + | 7829.98i | −0.495857 | + | 0.512141i | ||||
\(617\) | −3529.04 | −0.230265 | −0.115133 | − | 0.993350i | \(-0.536729\pi\) | ||||
−0.115133 | + | 0.993350i | \(0.536729\pi\) | |||||||
\(618\) | 1587.81 | − | 2750.17i | 0.103352 | − | 0.179010i | ||||
\(619\) | −4348.23 | − | 7531.36i | −0.282343 | − | 0.489032i | 0.689618 | − | 0.724173i | \(-0.257778\pi\) |
−0.971961 | + | 0.235141i | \(0.924445\pi\) | |||||||
\(620\) | −3490.17 | − | 6045.16i | −0.226079 | − | 0.391580i | ||||
\(621\) | 74.2411 | − | 128.589i | 0.00479741 | − | 0.00830936i | ||||
\(622\) | −22816.7 | −1.47085 | ||||||||
\(623\) | 4353.20 | + | 1091.39i | 0.279948 | + | 0.0701855i | ||||
\(624\) | 1600.56 | 0.102682 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −19025.2 | − | 32952.6i | −1.21470 | − | 2.10391i | ||||
\(627\) | −2298.39 | − | 3980.92i | −0.146393 | − | 0.253561i | ||||
\(628\) | 297.848 | − | 515.889i | 0.0189259 | − | 0.0327806i | ||||
\(629\) | 8673.55 | 0.549821 | ||||||||
\(630\) | 841.521 | + | 2949.20i | 0.0532174 | + | 0.186506i | ||||
\(631\) | −24940.4 | −1.57347 | −0.786737 | − | 0.617289i | \(-0.788231\pi\) | ||||
−0.786737 | + | 0.617289i | \(0.788231\pi\) | |||||||
\(632\) | −510.218 | + | 883.724i | −0.0321129 | + | 0.0556213i | ||||
\(633\) | −960.344 | − | 1663.36i | −0.0603006 | − | 0.104444i | ||||
\(634\) | −5478.17 | − | 9488.47i | −0.343164 | − | 0.594377i | ||||
\(635\) | −1900.28 | + | 3291.37i | −0.118756 | + | 0.205692i | ||||
\(636\) | −9815.95 | −0.611993 | ||||||||
\(637\) | 2002.55 | − | 1244.10i | 0.124559 | − | 0.0773832i | ||||
\(638\) | −33192.4 | −2.05972 | ||||||||
\(639\) | −2338.48 | + | 4050.36i | −0.144771 | + | 0.250751i | ||||
\(640\) | −2757.89 | − | 4776.80i | −0.170336 | − | 0.295031i | ||||
\(641\) | −10589.4 | − | 18341.3i | −0.652503 | − | 1.13017i | −0.982514 | − | 0.186191i | \(-0.940386\pi\) |
0.330011 | − | 0.943977i | \(-0.392948\pi\) | |||||||
\(642\) | 5799.20 | − | 10044.5i | 0.356505 | − | 0.617484i | ||||
\(643\) | 27000.8 | 1.65600 | 0.828001 | − | 0.560727i | \(-0.189478\pi\) | ||||
0.828001 | + | 0.560727i | \(0.189478\pi\) | |||||||
\(644\) | −154.877 | − | 542.783i | −0.00947672 | − | 0.0332122i | ||||
\(645\) | 1373.89 | 0.0838708 | ||||||||
\(646\) | −2947.35 | + | 5104.96i | −0.179508 | + | 0.310916i | ||||
\(647\) | −7642.44 | − | 13237.1i | −0.464382 | − | 0.804334i | 0.534791 | − | 0.844984i | \(-0.320390\pi\) |
−0.999173 | + | 0.0406506i | \(0.987057\pi\) | |||||||
\(648\) | 366.337 | + | 634.514i | 0.0222084 | + | 0.0384661i | ||||
\(649\) | −16582.6 | + | 28721.9i | −1.00297 | + | 1.73719i | ||||
\(650\) | −632.333 | −0.0381571 | ||||||||
\(651\) | −13576.0 | − | 3403.64i | −0.817337 | − | 0.204914i | ||||
\(652\) | −11129.8 | −0.668523 | ||||||||
\(653\) | −138.967 | + | 240.698i | −0.00832802 | + | 0.0144246i | −0.870159 | − | 0.492770i | \(-0.835984\pi\) |
0.861831 | + | 0.507195i | \(0.169318\pi\) | |||||||
\(654\) | 1020.09 | + | 1766.84i | 0.0609916 | + | 0.105640i | ||||
\(655\) | 25.2749 | + | 43.7775i | 0.00150775 | + | 0.00261149i | ||||
\(656\) | −4912.77 | + | 8509.17i | −0.292395 | + | 0.506444i | ||||
\(657\) | 9598.40 | 0.569968 | ||||||||
\(658\) | 26949.3 | − | 27834.3i | 1.59665 | − | 1.64908i | ||||
\(659\) | 31344.1 | 1.85280 | 0.926398 | − | 0.376545i | \(-0.122888\pi\) | ||||
0.926398 | + | 0.376545i | \(0.122888\pi\) | |||||||
\(660\) | −2704.12 | + | 4683.68i | −0.159482 | + | 0.276230i | ||||
\(661\) | 16157.6 | + | 27985.8i | 0.950768 | + | 1.64678i | 0.743768 | + | 0.668438i | \(0.233037\pi\) |
0.207000 | + | 0.978341i | \(0.433630\pi\) | |||||||
\(662\) | 12432.7 | + | 21534.1i | 0.729927 | + | 1.26427i | ||||
\(663\) | 701.204 | − | 1214.52i | 0.0410747 | − | 0.0711435i | ||||
\(664\) | 5368.88 | 0.313785 | ||||||||
\(665\) | 1517.06 | − | 1566.88i | 0.0884650 | − | 0.0913701i | ||||
\(666\) | 4223.69 | 0.245743 | ||||||||
\(667\) | −381.222 | + | 660.296i | −0.0221304 | + | 0.0383310i | ||||
\(668\) | 1569.78 | + | 2718.94i | 0.0909232 | + | 0.157484i | ||||
\(669\) | 2955.41 | + | 5118.91i | 0.170796 | + | 0.295828i | ||||
\(670\) | 8489.46 | − | 14704.2i | 0.489517 | − | 0.847868i | ||||
\(671\) | 17015.4 | 0.978942 | ||||||||
\(672\) | 11494.4 | + | 2881.76i | 0.659832 | + | 0.165426i | ||||
\(673\) | 19454.9 | 1.11431 | 0.557156 | − | 0.830408i | \(-0.311892\pi\) | ||||
0.557156 | + | 0.830408i | \(0.311892\pi\) | |||||||
\(674\) | −18937.1 | + | 32800.1i | −1.08224 | + | 1.87450i | ||||
\(675\) | −337.500 | − | 584.567i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 5956.96 | + | 10317.8i | 0.338926 | + | 0.587037i | ||||
\(677\) | −2611.65 | + | 4523.51i | −0.148263 | + | 0.256799i | −0.930585 | − | 0.366075i | \(-0.880701\pi\) |
0.782323 | + | 0.622873i | \(0.214035\pi\) | |||||||
\(678\) | −23186.1 | −1.31336 | ||||||||
\(679\) | −7810.02 | − | 27371.1i | −0.441416 | − | 1.54699i | ||||
\(680\) | −3075.99 | −0.173469 | ||||||||
\(681\) | 6894.10 | − | 11940.9i | 0.387933 | − | 0.671920i | ||||
\(682\) | −30154.5 | − | 52229.2i | −1.69307 | − | 2.93249i | ||||
\(683\) | 9508.03 | + | 16468.4i | 0.532672 | + | 0.922614i | 0.999272 | + | 0.0381462i | \(0.0121452\pi\) |
−0.466601 | + | 0.884468i | \(0.654521\pi\) | |||||||
\(684\) | −587.367 | + | 1017.35i | −0.0328341 | + | 0.0568704i | ||||
\(685\) | 13958.6 | 0.778585 | ||||||||
\(686\) | 22260.5 | − | 7137.01i | 1.23894 | − | 0.397219i | ||||
\(687\) | −13876.2 | −0.770614 | ||||||||
\(688\) | 3554.80 | − | 6157.10i | 0.196985 | − | 0.341188i | ||||
\(689\) | −2028.99 | − | 3514.31i | −0.112189 | − | 0.194317i | ||||
\(690\) | 151.779 | + | 262.890i | 0.00837412 | + | 0.0145044i | ||||
\(691\) | −2024.13 | + | 3505.90i | −0.111435 | + | 0.193011i | −0.916349 | − | 0.400380i | \(-0.868878\pi\) |
0.804914 | + | 0.593391i | \(0.202211\pi\) | |||||||
\(692\) | −4145.04 | −0.227703 | ||||||||
\(693\) | 2975.46 | + | 10427.8i | 0.163100 | + | 0.571601i | ||||
\(694\) | 33268.3 | 1.81967 | ||||||||
\(695\) | −1293.12 | + | 2239.76i | −0.0705770 | + | 0.122243i | ||||
\(696\) | −1881.11 | − | 3258.18i | −0.102447 | − | 0.177444i | ||||
\(697\) | 4304.56 | + | 7455.72i | 0.233927 | + | 0.405173i | ||||
\(698\) | 13706.4 | − | 23740.3i | 0.743261 | − | 1.28737i | ||||
\(699\) | −5689.78 | −0.307879 | ||||||||
\(700\) | −2488.95 | − | 624.002i | −0.134390 | − | 0.0336930i | ||||
\(701\) | 12385.2 | 0.667306 | 0.333653 | − | 0.942696i | \(-0.391719\pi\) | ||||
0.333653 | + | 0.942696i | \(0.391719\pi\) | |||||||
\(702\) | 341.460 | − | 591.425i | 0.0183583 | − | 0.0317976i | ||||
\(703\) | −1501.79 | − | 2601.18i | −0.0805706 | − | 0.139552i | ||||
\(704\) | 5331.19 | + | 9233.88i | 0.285407 | + | 0.494340i | ||||
\(705\) | −4263.49 | + | 7384.58i | −0.227762 | + | 0.394496i | ||||
\(706\) | 6241.32 | 0.332713 | ||||||||
\(707\) | −22104.4 | + | 22830.3i | −1.17584 | + | 1.21446i | ||||
\(708\) | 8475.59 | 0.449904 | ||||||||
\(709\) | 2630.05 | − | 4555.37i | 0.139314 | − | 0.241298i | −0.787923 | − | 0.615773i | \(-0.788844\pi\) |
0.927237 | + | 0.374475i | \(0.122177\pi\) | |||||||
\(710\) | −4780.82 | − | 8280.62i | −0.252705 | − | 0.437699i | ||||
\(711\) | 507.660 | + | 879.293i | 0.0267774 | + | 0.0463798i | ||||
\(712\) | −1095.96 | + | 1898.26i | −0.0576865 | + | 0.0999159i | ||||
\(713\) | −1385.33 | −0.0727642 | ||||||||
\(714\) | 9672.84 | − | 9990.49i | 0.506998 | − | 0.523648i | ||||
\(715\) | −2235.81 | −0.116943 | ||||||||
\(716\) | 11214.6 | − | 19424.3i | 0.585348 | − | 1.01385i | ||||
\(717\) | −10826.9 | − | 18752.7i | −0.563929 | − | 0.976754i | ||||
\(718\) | −8806.12 | − | 15252.7i | −0.457718 | − | 0.792791i | ||||
\(719\) | −676.337 | + | 1171.45i | −0.0350808 | + | 0.0607618i | −0.883033 | − | 0.469311i | \(-0.844502\pi\) |
0.847952 | + | 0.530073i | \(0.177836\pi\) | |||||||
\(720\) | −3493.00 | −0.180801 | ||||||||
\(721\) | 5167.46 | + | 1295.53i | 0.266916 | + | 0.0669183i | ||||
\(722\) | −23199.4 | −1.19584 | ||||||||
\(723\) | −1440.06 | + | 2494.26i | −0.0740753 | + | 0.128302i | ||||
\(724\) | 8119.78 | + | 14063.9i | 0.416808 | + | 0.721933i | ||||
\(725\) | 1733.04 | + | 3001.71i | 0.0887770 | + | 0.153766i | ||||
\(726\) | −16016.2 | + | 27740.9i | −0.818756 | + | 1.41813i | ||||
\(727\) | −2491.53 | −0.127106 | −0.0635528 | − | 0.997978i | \(-0.520243\pi\) | ||||
−0.0635528 | + | 0.997978i | \(0.520243\pi\) | |||||||
\(728\) | 315.937 | + | 1107.24i | 0.0160844 | + | 0.0563693i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −9811.54 | + | 16994.1i | −0.497454 | + | 0.861616i | ||||
\(731\) | −3114.71 | − | 5394.84i | −0.157595 | − | 0.272962i | ||||
\(732\) | −2174.19 | − | 3765.81i | −0.109782 | − | 0.190148i | ||||
\(733\) | −13868.1 | + | 24020.2i | −0.698811 | + | 1.21038i | 0.270068 | + | 0.962841i | \(0.412954\pi\) |
−0.968879 | + | 0.247535i | \(0.920380\pi\) | |||||||
\(734\) | 7038.08 | 0.353924 | ||||||||
\(735\) | −4370.28 | + | 2715.08i | −0.219320 | + | 0.136255i | ||||
\(736\) | 1172.91 | 0.0587421 | ||||||||
\(737\) | 30017.1 | − | 51991.1i | 1.50026 | − | 2.59853i | ||||
\(738\) | 2096.16 | + | 3630.65i | 0.104554 | + | 0.181092i | ||||
\(739\) | −19681.8 | − | 34089.9i | −0.979713 | − | 1.69691i | −0.663414 | − | 0.748253i | \(-0.730893\pi\) |
−0.316299 | − | 0.948659i | \(-0.602440\pi\) | |||||||
\(740\) | −1766.91 | + | 3060.37i | −0.0877740 | + | 0.152029i | ||||
\(741\) | −485.643 | −0.0240763 | ||||||||
\(742\) | −11040.7 | − | 38693.4i | −0.546251 | − | 1.91439i | ||||
\(743\) | −14854.4 | −0.733451 | −0.366725 | − | 0.930329i | \(-0.619521\pi\) | ||||
−0.366725 | + | 0.930329i | \(0.619521\pi\) | |||||||
\(744\) | 3417.89 | − | 5919.96i | 0.168422 | − | 0.291715i | ||||
\(745\) | 4928.29 | + | 8536.04i | 0.242360 | + | 0.419780i | ||||
\(746\) | 23559.1 | + | 40805.6i | 1.15625 | + | 2.00268i | ||||
\(747\) | 2670.98 | − | 4626.28i | 0.130825 | − | 0.226595i | ||||
\(748\) | 24521.9 | 1.19868 | ||||||||
\(749\) | 18873.2 | + | 4731.69i | 0.920710 | + | 0.230831i | ||||
\(750\) | 1379.98 | 0.0671863 | ||||||||
\(751\) | −19784.3 | + | 34267.4i | −0.961302 | + | 1.66502i | −0.242065 | + | 0.970260i | \(0.577825\pi\) |
−0.719237 | + | 0.694765i | \(0.755508\pi\) | |||||||
\(752\) | 22062.8 | + | 38213.9i | 1.06988 | + | 1.85308i | ||||
\(753\) | −4361.42 | − | 7554.20i | −0.211074 | − | 0.365592i | ||||
\(754\) | −1753.37 | + | 3036.92i | −0.0846869 | + | 0.146682i | ||||
\(755\) | −808.806 | −0.0389874 | ||||||||
\(756\) | 1927.66 | − | 1990.97i | 0.0927361 | − | 0.0957815i | ||||
\(757\) | −8043.85 | −0.386207 | −0.193103 | − | 0.981178i | \(-0.561855\pi\) | ||||
−0.193103 | + | 0.981178i | \(0.561855\pi\) | |||||||
\(758\) | 10704.5 | − | 18540.7i | 0.512934 | − | 0.888428i | ||||
\(759\) | 536.663 | + | 929.528i | 0.0256649 | + | 0.0444529i | ||||
\(760\) | 532.595 | + | 922.482i | 0.0254201 | + | 0.0440288i | ||||
\(761\) | −16112.9 | + | 27908.4i | −0.767532 | + | 1.32940i | 0.171365 | + | 0.985208i | \(0.445182\pi\) |
−0.938897 | + | 0.344197i | \(0.888151\pi\) | |||||||
\(762\) | 8391.49 | 0.398939 | ||||||||
\(763\) | −2380.71 | + | 2458.89i | −0.112959 | + | 0.116668i | ||||
\(764\) | 16721.4 | 0.791833 | ||||||||
\(765\) | −1530.28 | + | 2650.53i | −0.0723235 | + | 0.125268i | ||||
\(766\) | 20793.4 | + | 36015.3i | 0.980806 | + | 1.69881i | ||||
\(767\) | 1751.93 | + | 3034.44i | 0.0824754 | + | 0.142852i | ||||
\(768\) | −8056.01 | + | 13953.4i | −0.378511 | + | 0.655599i | ||||
\(769\) | 11196.5 | 0.525041 | 0.262521 | − | 0.964926i | \(-0.415446\pi\) | ||||
0.262521 | + | 0.964926i | \(0.415446\pi\) | |||||||
\(770\) | −21504.1 | − | 5391.28i | −1.00643 | − | 0.252322i | ||||
\(771\) | 11034.3 | 0.515421 | ||||||||
\(772\) | −2180.54 | + | 3776.81i | −0.101657 | + | 0.176076i | ||||
\(773\) | 10198.4 | + | 17664.1i | 0.474528 | + | 0.821907i | 0.999575 | − | 0.0291664i | \(-0.00928527\pi\) |
−0.525046 | + | 0.851074i | \(0.675952\pi\) | |||||||
\(774\) | −1516.75 | − | 2627.08i | −0.0704371 | − | 0.122001i | ||||
\(775\) | −3148.85 | + | 5453.96i | −0.145948 | + | 0.252790i | ||||
\(776\) | 13901.7 | 0.643094 | ||||||||
\(777\) | 1944.20 | + | 6813.64i | 0.0897654 | + | 0.314592i | ||||
\(778\) | 4675.90 | 0.215474 | ||||||||
\(779\) | 1490.64 | − | 2581.86i | 0.0685591 | − | 0.118748i | ||||
\(780\) | 285.687 | + | 494.825i | 0.0131144 | + | 0.0227148i | ||||
\(781\) | −16904.1 | − | 29278.7i | −0.774488 | − | 1.34145i | ||||
\(782\) | 688.194 | − | 1191.99i | 0.0314703 | − | 0.0545081i | ||||
\(783\) | −3743.36 | −0.170851 | ||||||||
\(784\) | 859.985 | + | 26610.5i | 0.0391757 | + | 1.21222i | ||||
\(785\) | −537.440 | −0.0244357 | ||||||||
\(786\) | 55.8062 | − | 96.6592i | 0.00253250 | − | 0.00438641i | ||||
\(787\) | −11037.5 | − | 19117.5i | −0.499928 | − | 0.865901i | 0.500072 | − | 0.865984i | \(-0.333307\pi\) |
−1.00000 | 8.30685e-5i | \(0.999974\pi\) | ||||||||
\(788\) | 5569.49 | + | 9646.64i | 0.251783 | + | 0.436100i | ||||
\(789\) | 8804.62 | − | 15250.1i | 0.397279 | − | 0.688107i | ||||
\(790\) | −2075.73 | −0.0934826 | ||||||||
\(791\) | −10672.7 | − | 37403.7i | −0.479745 | − | 1.68132i | ||||
\(792\) | −5296.24 | −0.237619 | ||||||||
\(793\) | 898.825 | − | 1556.81i | 0.0402500 | − | 0.0697150i | ||||
\(794\) | −20817.6 | − | 36057.1i | −0.930465 | − | 1.61161i | ||||
\(795\) | 4427.99 | + | 7669.51i | 0.197540 | + | 0.342150i | ||||
\(796\) | −7540.51 | + | 13060.6i | −0.335762 | + | 0.581557i | ||||
\(797\) | 9131.50 | 0.405840 | 0.202920 | − | 0.979195i | \(-0.434957\pi\) | ||||
0.202920 | + | 0.979195i | \(0.434957\pi\) | |||||||
\(798\) | −4670.94 | − | 1171.05i | −0.207205 | − | 0.0519482i | ||||
\(799\) | 38662.8 | 1.71188 | ||||||||
\(800\) | 2666.04 | − | 4617.71i | 0.117823 | − | 0.204076i | ||||
\(801\) | 1090.46 | + | 1888.74i | 0.0481019 | + | 0.0833150i | ||||
\(802\) | 12504.6 | + | 21658.6i | 0.550563 | + | 0.953604i | ||||
\(803\) | −34691.8 | + | 60087.9i | −1.52459 | + | 2.64067i | ||||
\(804\) | −15342.1 | −0.672979 | ||||||||
\(805\) | −354.228 | + | 365.861i | −0.0155092 | + | 0.0160185i | ||||
\(806\) | −6371.58 | −0.278448 | ||||||||
\(807\) | −691.143 | + | 1197.09i | −0.0301479 | + | 0.0522177i | ||||
\(808\) | −7760.19 | − | 13441.0i | −0.337874 | − | 0.585215i | ||||
\(809\) | 9548.26 | + | 16538.1i | 0.414956 | + | 0.718724i | 0.995424 | − | 0.0955587i | \(-0.0304638\pi\) |
−0.580468 | + | 0.814283i | \(0.697130\pi\) | |||||||
\(810\) | −745.189 | + | 1290.70i | −0.0323250 | + | 0.0559886i | ||||
\(811\) | −9090.20 | −0.393588 | −0.196794 | − | 0.980445i | \(-0.563053\pi\) | ||||
−0.196794 | + | 0.980445i | \(0.563053\pi\) | |||||||
\(812\) | −9898.41 | + | 10223.5i | −0.427791 | + | 0.441839i | ||||
\(813\) | −15945.0 | −0.687843 | ||||||||
\(814\) | −15265.8 | + | 26441.1i | −0.657329 | + | 1.13853i | ||||
\(815\) | 5020.68 | + | 8696.07i | 0.215787 | + | 0.373755i | ||||
\(816\) | 7918.93 | + | 13716.0i | 0.339728 | + | 0.588426i | ||||
\(817\) | −1078.60 | + | 1868.19i | −0.0461878 | + | 0.0799997i | ||||
\(818\) | 29529.6 | 1.26220 | ||||||||
\(819\) | 1111.26 | + | 278.604i | 0.0474123 | + | 0.0118867i | ||||
\(820\) | −3507.56 | −0.149377 | ||||||||
\(821\) | −10587.9 | + | 18338.8i | −0.450085 | + | 0.779571i | −0.998391 | − | 0.0567074i | \(-0.981940\pi\) |
0.548305 | + | 0.836278i | \(0.315273\pi\) | |||||||
\(822\) | −15410.1 | − | 26691.0i | −0.653878 | − | 1.13255i | ||||
\(823\) | −7456.89 | − | 12915.7i | −0.315833 | − | 0.547040i | 0.663781 | − | 0.747927i | \(-0.268951\pi\) |
−0.979614 | + | 0.200888i | \(0.935617\pi\) | |||||||
\(824\) | −1300.96 | + | 2253.32i | −0.0550012 | + | 0.0952648i | ||||
\(825\) | 4879.34 | 0.205911 | ||||||||
\(826\) | 9533.13 | + | 33409.8i | 0.401574 | + | 1.40736i | ||||
\(827\) | −36795.0 | −1.54714 | −0.773571 | − | 0.633710i | \(-0.781531\pi\) | ||||
−0.773571 | + | 0.633710i | \(0.781531\pi\) | |||||||
\(828\) | 137.148 | − | 237.547i | 0.00575629 | − | 0.00997019i | ||||
\(829\) | −6029.62 | − | 10443.6i | −0.252614 | − | 0.437541i | 0.711631 | − | 0.702554i | \(-0.247957\pi\) |
−0.964245 | + | 0.265013i | \(0.914624\pi\) | |||||||
\(830\) | 5460.59 | + | 9458.02i | 0.228361 | + | 0.395533i | ||||
\(831\) | 3570.88 | − | 6184.95i | 0.149064 | − | 0.258187i | ||||
\(832\) | 1126.47 | 0.0469389 | ||||||||
\(833\) | 20569.1 | + | 11005.5i | 0.855556 | + | 0.457765i | ||||
\(834\) | 5710.35 | 0.237090 | ||||||||
\(835\) | 1416.26 | − | 2453.04i | 0.0586968 | − | 0.101666i | ||||
\(836\) | −4245.87 | − | 7354.07i | −0.175654 | − | 0.304241i | ||||
\(837\) | −3400.75 | − | 5890.28i | −0.140439 | − | 0.243247i | ||||
\(838\) | −4644.82 | + | 8045.07i | −0.191471 | + | 0.331638i | ||||
\(839\) | −30556.5 | −1.25736 | −0.628681 | − | 0.777663i | \(-0.716405\pi\) | ||||
−0.628681 | + | 0.777663i | \(0.716405\pi\) | |||||||
\(840\) | −689.490 | − | 2416.39i | −0.0283210 | − | 0.0992540i | ||||
\(841\) | −5167.15 | −0.211864 | ||||||||
\(842\) | 14433.0 | − | 24998.6i | 0.590728 | − | 1.02317i | ||||
\(843\) | −2653.84 | − | 4596.59i | −0.108426 | − | 0.187800i | ||||
\(844\) | −1774.07 | − | 3072.78i | −0.0723531 | − | 0.125319i | ||||
\(845\) | 5374.39 | − | 9308.73i | 0.218799 | − | 0.378970i | ||||
\(846\) | 18827.3 | 0.765125 | ||||||||
\(847\) | −52123.9 | − | 13068.0i | −2.11452 | − | 0.530130i | ||||
\(848\) | 45828.1 | 1.85583 | ||||||||
\(849\) | −2185.39 | + | 3785.21i | −0.0883420 | + | 0.153013i | ||||
\(850\) | −3128.53 | − | 5418.77i | −0.126244 | − | 0.218662i | ||||
\(851\) | 350.662 | + | 607.364i | 0.0141252 | + | 0.0244655i | ||||
\(852\) | −4319.94 | + | 7482.35i | −0.173707 | + | 0.300870i | ||||
\(853\) | −42918.6 | −1.72275 | −0.861375 | − | 0.507969i | \(-0.830396\pi\) | ||||
−0.861375 | + | 0.507969i | \(0.830396\pi\) | |||||||
\(854\) | 12398.9 | − | 12806.1i | 0.496818 | − | 0.513134i | ||||
\(855\) | 1059.85 | 0.0423931 | ||||||||
\(856\) | −4751.50 | + | 8229.84i | −0.189723 | + | 0.328610i | ||||
\(857\) | 3089.36 | + | 5350.92i | 0.123139 | + | 0.213284i | 0.921004 | − | 0.389553i | \(-0.127370\pi\) |
−0.797865 | + | 0.602837i | \(0.794037\pi\) | |||||||
\(858\) | 2468.29 | + | 4275.21i | 0.0982123 | + | 0.170109i | ||||
\(859\) | −2545.27 | + | 4408.53i | −0.101098 | + | 0.175107i | −0.912137 | − | 0.409885i | \(-0.865569\pi\) |
0.811039 | + | 0.584992i | \(0.198902\pi\) | |||||||
\(860\) | 2538.02 | 0.100635 | ||||||||
\(861\) | −4892.08 | + | 5052.73i | −0.193637 | + | 0.199996i | ||||
\(862\) | 25111.0 | 0.992211 | ||||||||
\(863\) | −5734.20 | + | 9931.92i | −0.226181 | + | 0.391757i | −0.956673 | − | 0.291164i | \(-0.905957\pi\) |
0.730492 | + | 0.682921i | \(0.239291\pi\) | |||||||
\(864\) | 2879.32 | + | 4987.12i | 0.113375 | + | 0.196372i | ||||
\(865\) | 1869.83 | + | 3238.65i | 0.0734985 | + | 0.127303i | ||||
\(866\) | 17082.0 | − | 29586.8i | 0.670287 | − | 1.16097i | ||||
\(867\) | −861.880 | −0.0337612 | ||||||||
\(868\) | −25079.4 | − | 6287.64i | −0.980703 | − | 0.245871i | ||||
\(869\) | −7339.40 | −0.286504 | ||||||||
\(870\) | 3826.48 | − | 6627.67i | 0.149115 | − | 0.258275i | ||||
\(871\) | −3171.27 | − | 5492.80i | −0.123369 | − | 0.213681i | ||||
\(872\) | −835.794 | − | 1447.64i | −0.0324582 | − | 0.0562193i | ||||
\(873\) | 6915.98 | − | 11978.8i | 0.268122 | − | 0.464401i | ||||
\(874\) | −476.632 | −0.0184466 | ||||||||
\(875\) | 635.215 | + | 2226.18i | 0.0245419 | + | 0.0860098i | ||||
\(876\) | 17731.4 | 0.683891 | ||||||||
\(877\) | 2773.13 | − | 4803.21i | 0.106775 | − | 0.184940i | −0.807687 | − | 0.589612i | \(-0.799281\pi\) |
0.914462 | + | 0.404671i | \(0.132614\pi\) | |||||||
\(878\) | −1231.58 | − | 2133.16i | −0.0473392 | − | 0.0819939i | ||||
\(879\) | 4115.33 | + | 7127.97i | 0.157914 | + | 0.273516i | ||||
\(880\) | 12624.9 | − | 21866.9i | 0.483618 | − | 0.837651i | ||||
\(881\) | 1259.32 | 0.0481586 | 0.0240793 | − | 0.999710i | \(-0.492335\pi\) | ||||
0.0240793 | + | 0.999710i | \(0.492335\pi\) | |||||||
\(882\) | 10016.4 | + | 5359.26i | 0.382391 | + | 0.204598i | ||||
\(883\) | −155.096 | −0.00591100 | −0.00295550 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295550 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(884\) | 1295.36 | − | 2243.62i | 0.0492845 | − | 0.0853633i | ||||
\(885\) | −3823.35 | − | 6622.24i | −0.145221 | − | 0.251530i | ||||
\(886\) | −17937.5 | − | 31068.6i | −0.680159 | − | 1.17807i | ||||
\(887\) | 10447.4 | − | 18095.5i | 0.395479 | − | 0.684990i | −0.597683 | − | 0.801733i | \(-0.703912\pi\) |
0.993162 | + | 0.116742i | \(0.0372451\pi\) | |||||||
\(888\) | −3460.63 | −0.130778 | ||||||||
\(889\) | 3862.67 | + | 13537.1i | 0.145725 | + | 0.510710i | ||||
\(890\) | −4458.72 | −0.167929 | ||||||||
\(891\) | −2634.84 | + | 4563.69i | −0.0990692 | + | 0.171593i | ||||
\(892\) | 5459.61 | + | 9456.32i | 0.204934 | + | 0.354956i | ||||
\(893\) | −6694.31 | − | 11594.9i | −0.250858 | − | 0.434499i | ||||
\(894\) | 10881.5 | − | 18847.3i | 0.407082 | − | 0.705087i | ||||
\(895\) | −20235.7 | −0.755760 | ||||||||
\(896\) | −19817.4 | − | 4968.41i | −0.738898 | − | 0.185249i | ||||
\(897\) | 113.396 | 0.00422092 | ||||||||
\(898\) | −9408.77 | + | 16296.5i | −0.349638 | + | 0.605590i | ||||
\(899\) | 17462.6 | + | 30246.1i | 0.647843 | + | 1.12210i | ||||
\(900\) | −623.473 | − | 1079.89i | −0.0230916 | − | 0.0399958i | ||||
\(901\) | 20077.3 | − | 34774.8i | 0.742365 | − | 1.28581i | ||||
\(902\) | −30304.8 | −1.11867 | ||||||||
\(903\) | 3539.83 | − | 3656.08i | 0.130452 | − | 0.134736i | ||||
\(904\) | 18997.2 | 0.698936 | ||||||||
\(905\) | 7325.69 | − | 12688.5i | 0.269077 | − | 0.466054i | ||||
\(906\) | 892.908 | + | 1546.56i | 0.0327427 | + | 0.0567120i | ||||
\(907\) | 19876.3 | + | 34426.7i | 0.727653 | + | 1.26033i | 0.957873 | + | 0.287193i | \(0.0927220\pi\) |
−0.230220 | + | 0.973139i | \(0.573945\pi\) | |||||||
\(908\) | 12735.7 | − | 22058.8i | 0.465472 | − | 0.806221i | ||||
\(909\) | −15442.6 | −0.563473 | ||||||||
\(910\) | −1629.21 | + | 1682.72i | −0.0593493 | + | 0.0612983i | ||||
\(911\) | 494.980 | 0.0180015 | 0.00900077 | − | 0.999959i | \(-0.497135\pi\) | ||||
0.00900077 | + | 0.999959i | \(0.497135\pi\) | |||||||
\(912\) | 2742.26 | − | 4749.74i | 0.0995674 | − | 0.172456i | ||||
\(913\) | 19307.6 | + | 33441.8i | 0.699878 | + | 1.21222i | ||||
\(914\) | 6399.78 | + | 11084.7i | 0.231604 | + | 0.401149i | ||||
\(915\) | −1961.56 | + | 3397.53i | −0.0708713 | + | 0.122753i | ||||
\(916\) | −25634.0 | −0.924640 | ||||||||
\(917\) | 181.618 | + | 45.5335i | 0.00654043 | + | 0.00163975i | ||||
\(918\) | 6757.62 | 0.242957 | ||||||||
\(919\) | 16893.8 | − | 29260.9i | 0.606393 | − | 1.05030i | −0.385437 | − | 0.922734i | \(-0.625949\pi\) |
0.991830 | − | 0.127569i | \(-0.0407173\pi\) | |||||||
\(920\) | −124.359 | − | 215.395i | −0.00445650 | − | 0.00771889i | ||||
\(921\) | −5050.91 | − | 8748.43i | −0.180709 | − | 0.312997i | ||||
\(922\) | 1834.33 | − | 3177.16i | 0.0655212 | − | 0.113486i | ||||
\(923\) | −3571.78 | −0.127375 | ||||||||
\(924\) | 5496.65 | + | 19263.6i | 0.195700 | + | 0.685850i | ||||
\(925\) | 3188.22 | 0.113328 | ||||||||
\(926\) | 23332.8 | − | 40413.6i | 0.828039 | − | 1.43421i | ||||
\(927\) | 1294.43 | + | 2242.02i | 0.0458627 | + | 0.0794366i | ||||
\(928\) | −14785.1 | − | 25608.5i | −0.523000 | − | 0.905862i | ||||
\(929\) | 19884.7 | − | 34441.3i | 0.702256 | − | 1.21634i | −0.265416 | − | 0.964134i | \(-0.585509\pi\) |
0.967673 | − | 0.252210i | \(-0.0811573\pi\) | |||||||
\(930\) | 13905.1 | 0.490286 | ||||||||
\(931\) | −260.937 | − | 8074.19i | −0.00918569 | − | 0.284233i | ||||
\(932\) | −10510.9 | −0.369416 | ||||||||
\(933\) | 9300.44 | − | 16108.8i | 0.326348 | − | 0.565251i | ||||
\(934\) | 123.318 | + | 213.593i | 0.00432022 | + | 0.00748284i | ||||
\(935\) | −11061.9 | − | 19159.7i | −0.386912 | − | 0.670150i | ||||
\(936\) | −279.771 | + | 484.577i | −0.00976987 | + | 0.0169219i | ||||
\(937\) | 16823.9 | 0.586568 | 0.293284 | − | 0.956025i | \(-0.405252\pi\) | ||||
0.293284 | + | 0.956025i | \(0.405252\pi\) | |||||||
\(938\) | −17256.4 | − | 60477.0i | −0.600685 | − | 2.10516i | ||||
\(939\) | 31019.8 | 1.07805 | ||||||||
\(940\) | −7876.07 | + | 13641.8i | −0.273286 | + | 0.473346i | ||||
\(941\) | 307.746 | + | 533.031i | 0.0106612 | + | 0.0184658i | 0.871307 | − | 0.490739i | \(-0.163273\pi\) |
−0.860646 | + | 0.509204i | \(0.829940\pi\) | |||||||
\(942\) | 593.324 | + | 1027.67i | 0.0205218 | + | 0.0355448i | ||||
\(943\) | −348.057 | + | 602.852i | −0.0120194 | + | 0.0208182i | ||||
\(944\) | −39570.3 | −1.36430 | ||||||||
\(945\) | −2425.18 | − | 608.015i | −0.0834826 | − | 0.0209299i | ||||
\(946\) | 21928.1 | 0.753640 | ||||||||
\(947\) | −21017.8 | + | 36403.9i | −0.721211 | + | 1.24917i | 0.239303 | + | 0.970945i | \(0.423081\pi\) |
−0.960515 | + | 0.278230i | \(0.910252\pi\) | |||||||
\(948\) | 937.815 | + | 1624.34i | 0.0321295 | + | 0.0556500i | ||||
\(949\) | 3665.14 | + | 6348.21i | 0.125369 | + | 0.217146i | ||||
\(950\) | −1083.38 | + | 1876.48i | −0.0369996 | + | 0.0640852i | ||||
\(951\) | 8931.93 | 0.304561 | ||||||||
\(952\) | −7925.32 | + | 8185.58i | −0.269812 | + | 0.278673i | ||||
\(953\) | −16830.2 | −0.572070 | −0.286035 | − | 0.958219i | \(-0.592337\pi\) | ||||
−0.286035 | + | 0.958219i | \(0.592337\pi\) | |||||||
\(954\) | 9776.86 | − | 16934.0i | 0.331800 | − | 0.574695i | ||||
\(955\) | −7543.07 | − | 13065.0i | −0.255590 | − | 0.442694i | ||||
\(956\) | −20000.8 | − | 34642.4i | −0.676645 | − | 1.17198i | ||||
\(957\) | 13529.7 | − | 23434.2i | 0.457005 | − | 0.791556i | ||||
\(958\) | 57648.1 | 1.94418 | ||||||||
\(959\) | 35964.5 | − | 37145.6i | 1.21101 | − | 1.25078i | ||||
\(960\) | −2458.36 | −0.0826491 | ||||||||
\(961\) | −16833.3 | + | 29156.0i | −0.565045 | + | 0.978686i | ||||
\(962\) | 1612.81 | + | 2793.47i | 0.0540531 | + | 0.0936228i | ||||
\(963\) | 4727.68 | + | 8188.58i | 0.158201 | + | 0.274012i | ||||
\(964\) | −2660.27 | + | 4607.71i | −0.0888811 | + | 0.153947i | ||||
\(965\) | 3934.59 | 0.131253 | ||||||||
\(966\) | 1090.64 | + | 273.435i | 0.0363260 | + | 0.00910726i | ||||
\(967\) | −3695.45 | −0.122893 | −0.0614466 | − | 0.998110i | \(-0.519571\pi\) | ||||
−0.0614466 | + | 0.998110i | \(0.519571\pi\) | |||||||
\(968\) | 13122.7 | − | 22729.2i | 0.435722 | − | 0.754693i | ||||
\(969\) | −2402.77 | − | 4161.72i | −0.0796574 | − | 0.137971i | ||||
\(970\) | 14139.1 | + | 24489.7i | 0.468020 | + | 0.810635i | ||||
\(971\) | −11182.2 | + | 19368.1i | −0.369571 | + | 0.640115i | −0.989498 | − | 0.144544i | \(-0.953829\pi\) |
0.619928 | + | 0.784659i | \(0.287162\pi\) | |||||||
\(972\) | 1346.70 | 0.0444398 | ||||||||
\(973\) | 2628.52 | + | 9211.93i | 0.0866048 | + | 0.303516i | ||||
\(974\) | −43146.8 | −1.41942 | ||||||||
\(975\) | 257.748 | − | 446.433i | 0.00846620 | − | 0.0146639i | ||||
\(976\) | 10150.7 | + | 17581.6i | 0.332907 | + | 0.576611i | ||||
\(977\) | 17216.9 | + | 29820.6i | 0.563786 | + | 0.976505i | 0.997162 | + | 0.0752921i | \(0.0239889\pi\) |
−0.433376 | + | 0.901213i | \(0.642678\pi\) | |||||||
\(978\) | 11085.5 | − | 19200.6i | 0.362449 | − | 0.627779i | ||||
\(979\) | −15765.2 | −0.514665 | ||||||||
\(980\) | −8073.35 | + | 5015.64i | −0.263157 | + | 0.163489i | ||||
\(981\) | −1663.21 | −0.0541306 | ||||||||
\(982\) | −19474.6 | + | 33730.9i | −0.632849 | + | 1.09613i | ||||
\(983\) | −3696.27 | − | 6402.13i | −0.119932 | − | 0.207728i | 0.799809 | − | 0.600255i | \(-0.204934\pi\) |
−0.919740 | + | 0.392527i | \(0.871601\pi\) | |||||||
\(984\) | −1717.46 | − | 2974.73i | −0.0556409 | − | 0.0963729i | ||||
\(985\) | 5024.81 | − | 8703.23i | 0.162542 | − | 0.281531i | ||||
\(986\) | −34699.9 | −1.12076 | ||||||||
\(987\) | 8666.35 | + | 30372.2i | 0.279486 | + | 0.979490i | ||||
\(988\) | −897.142 | −0.0288886 | ||||||||
\(989\) | 251.849 | − | 436.215i | 0.00809739 | − | 0.0140251i | ||||
\(990\) | −5386.71 | − | 9330.06i | −0.172930 | − | 0.299524i | ||||
\(991\) | −20793.5 | − | 36015.4i | −0.666526 | − | 1.15446i | −0.978869 | − | 0.204487i | \(-0.934447\pi\) |
0.312344 | − | 0.949969i | \(-0.398886\pi\) | |||||||
\(992\) | 26863.8 | − | 46529.5i | 0.859805 | − | 1.48923i | ||||
\(993\) | −20271.1 | −0.647818 | ||||||||
\(994\) | −34353.6 | − | 8612.77i | −1.09621 | − | 0.274829i | ||||
\(995\) | 13606.2 | 0.433512 | ||||||||
\(996\) | 4934.18 | − | 8546.26i | 0.156973 | − | 0.271886i | ||||
\(997\) | 5336.16 | + | 9242.51i | 0.169507 | + | 0.293594i | 0.938246 | − | 0.345968i | \(-0.112449\pi\) |
−0.768740 | + | 0.639561i | \(0.779116\pi\) | |||||||
\(998\) | −19215.0 | − | 33281.4i | −0.609460 | − | 1.05562i | ||||
\(999\) | −1721.64 | + | 2981.96i | −0.0545247 | + | 0.0944396i |
(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 | 105.4.i.d.16.2 | ✓ | 10 | |
3.2 | odd | 2 | 315.4.j.h.226.4 | 10 | |||
7.2 | even | 3 | 735.4.a.ba.1.4 | 5 | |||
7.4 | even | 3 | inner | 105.4.i.d.46.2 | yes | 10 | |
7.5 | odd | 6 | 735.4.a.z.1.4 | 5 | |||
21.2 | odd | 6 | 2205.4.a.br.1.2 | 5 | |||
21.5 | even | 6 | 2205.4.a.bs.1.2 | 5 | |||
21.11 | odd | 6 | 315.4.j.h.46.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.i.d.16.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
105.4.i.d.46.2 | yes | 10 | 7.4 | even | 3 | inner | |
315.4.j.h.46.4 | 10 | 21.11 | odd | 6 | |||
315.4.j.h.226.4 | 10 | 3.2 | odd | 2 | |||
735.4.a.z.1.4 | 5 | 7.5 | odd | 6 | |||
735.4.a.ba.1.4 | 5 | 7.2 | even | 3 | |||
2205.4.a.br.1.2 | 5 | 21.2 | odd | 6 | |||
2205.4.a.bs.1.2 | 5 | 21.5 | even | 6 |