Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,3,Mod(7,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.l (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.12534606201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.67 |
Dual form | 78.3.l.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.683013 | − | 0.183013i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.73205 | + | 1.00000i | 0.433013 | + | 0.250000i | ||||
\(5\) | −4.73205 | + | 4.73205i | −0.946410 | + | 0.946410i | −0.998635 | − | 0.0522252i | \(-0.983369\pi\) |
0.0522252 | + | 0.998635i | \(0.483369\pi\) | |||||||
\(6\) | −0.633975 | − | 2.36603i | −0.105662 | − | 0.394338i | ||||
\(7\) | −2.50000 | + | 0.669873i | −0.357143 | + | 0.0956961i | −0.432929 | − | 0.901428i | \(-0.642520\pi\) |
0.0757863 | + | 0.997124i | \(0.475853\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 8.19615 | − | 4.73205i | 0.819615 | − | 0.473205i | ||||
\(11\) | −3.92820 | + | 14.6603i | −0.357109 | + | 1.33275i | 0.520700 | + | 0.853740i | \(0.325671\pi\) |
−0.877809 | + | 0.479011i | \(0.840996\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 11.2583 | + | 6.50000i | 0.866025 | + | 0.500000i | ||||
\(14\) | 3.66025 | 0.261447 | ||||||||
\(15\) | −11.1962 | − | 3.00000i | −0.746410 | − | 0.200000i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −4.39230 | − | 2.53590i | −0.258371 | − | 0.149170i | 0.365220 | − | 0.930921i | \(-0.380994\pi\) |
−0.623591 | + | 0.781751i | \(0.714327\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | −0.954483 | − | 3.56218i | −0.0502359 | − | 0.187483i | 0.936248 | − | 0.351339i | \(-0.114273\pi\) |
−0.986484 | + | 0.163856i | \(0.947607\pi\) | |||||||
\(20\) | −12.9282 | + | 3.46410i | −0.646410 | + | 0.173205i | ||||
\(21\) | −3.16987 | − | 3.16987i | −0.150946 | − | 0.150946i | ||||
\(22\) | 10.7321 | − | 18.5885i | 0.487820 | − | 0.844930i | ||||
\(23\) | 27.5885 | − | 15.9282i | 1.19950 | − | 0.692531i | 0.239055 | − | 0.971006i | \(-0.423162\pi\) |
0.960443 | + | 0.278476i | \(0.0898291\pi\) | |||||||
\(24\) | 1.26795 | − | 4.73205i | 0.0528312 | − | 0.197169i | ||||
\(25\) | − | 19.7846i | − | 0.791384i | ||||||
\(26\) | −13.0000 | − | 13.0000i | −0.500000 | − | 0.500000i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −5.00000 | − | 1.33975i | −0.178571 | − | 0.0478481i | ||||
\(29\) | −8.66025 | − | 15.0000i | −0.298629 | − | 0.517241i | 0.677193 | − | 0.735805i | \(-0.263196\pi\) |
−0.975823 | + | 0.218564i | \(0.929863\pi\) | |||||||
\(30\) | 14.1962 | + | 8.19615i | 0.473205 | + | 0.273205i | ||||
\(31\) | 30.8301 | − | 30.8301i | 0.994520 | − | 0.994520i | −0.00546484 | − | 0.999985i | \(-0.501740\pi\) |
0.999985 | + | 0.00546484i | \(0.00173952\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.0457532 | − | 0.170753i | ||||
\(33\) | −25.3923 | + | 6.80385i | −0.769464 | + | 0.206177i | ||||
\(34\) | 5.07180 | + | 5.07180i | 0.149170 | + | 0.149170i | ||||
\(35\) | 8.66025 | − | 15.0000i | 0.247436 | − | 0.428571i | ||||
\(36\) | −5.19615 | + | 3.00000i | −0.144338 | + | 0.0833333i | ||||
\(37\) | −13.2417 | + | 49.4186i | −0.357883 | + | 1.33564i | 0.518934 | + | 0.854814i | \(0.326329\pi\) |
−0.876817 | + | 0.480823i | \(0.840338\pi\) | |||||||
\(38\) | 5.21539i | 0.137247i | ||||||||
\(39\) | 22.5167i | 0.577350i | ||||||||
\(40\) | 18.9282 | 0.473205 | ||||||||
\(41\) | −41.3205 | − | 11.0718i | −1.00782 | − | 0.270044i | −0.283100 | − | 0.959090i | \(-0.591363\pi\) |
−0.724717 | + | 0.689047i | \(0.758030\pi\) | |||||||
\(42\) | 3.16987 | + | 5.49038i | 0.0754732 | + | 0.130723i | ||||
\(43\) | 28.2846 | + | 16.3301i | 0.657782 | + | 0.379770i | 0.791431 | − | 0.611258i | \(-0.209336\pi\) |
−0.133650 | + | 0.991029i | \(0.542670\pi\) | |||||||
\(44\) | −21.4641 | + | 21.4641i | −0.487820 | + | 0.487820i | ||||
\(45\) | −5.19615 | − | 19.3923i | −0.115470 | − | 0.430940i | ||||
\(46\) | −43.5167 | + | 11.6603i | −0.946014 | + | 0.253484i | ||||
\(47\) | 58.9808 | + | 58.9808i | 1.25491 | + | 1.25491i | 0.953492 | + | 0.301418i | \(0.0974598\pi\) |
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(48\) | −3.46410 | + | 6.00000i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −36.6340 | + | 21.1506i | −0.747632 | + | 0.431646i | ||||
\(50\) | −7.24167 | + | 27.0263i | −0.144833 | + | 0.540526i | ||||
\(51\) | − | 8.78461i | − | 0.172247i | ||||||
\(52\) | 13.0000 | + | 22.5167i | 0.250000 | + | 0.433013i | ||||
\(53\) | 97.6743 | 1.84291 | 0.921456 | − | 0.388483i | \(-0.127001\pi\) | ||||
0.921456 | + | 0.388483i | \(0.127001\pi\) | |||||||
\(54\) | 7.09808 | + | 1.90192i | 0.131446 | + | 0.0352208i | ||||
\(55\) | −50.7846 | − | 87.9615i | −0.923357 | − | 1.59930i | ||||
\(56\) | 6.33975 | + | 3.66025i | 0.113210 | + | 0.0653617i | ||||
\(57\) | 4.51666 | − | 4.51666i | 0.0792397 | − | 0.0792397i | ||||
\(58\) | 6.33975 | + | 23.6603i | 0.109306 | + | 0.407935i | ||||
\(59\) | 59.1051 | − | 15.8372i | 1.00178 | − | 0.268427i | 0.279590 | − | 0.960120i | \(-0.409801\pi\) |
0.722192 | + | 0.691693i | \(0.243135\pi\) | |||||||
\(60\) | −16.3923 | − | 16.3923i | −0.273205 | − | 0.273205i | ||||
\(61\) | −39.6506 | + | 68.6769i | −0.650010 | + | 1.12585i | 0.333109 | + | 0.942888i | \(0.391902\pi\) |
−0.983120 | + | 0.182963i | \(0.941431\pi\) | |||||||
\(62\) | −53.3993 | + | 30.8301i | −0.861280 | + | 0.497260i | ||||
\(63\) | 2.00962 | − | 7.50000i | 0.0318987 | − | 0.119048i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −84.0333 | + | 22.5167i | −1.29282 | + | 0.346410i | ||||
\(66\) | 37.1769 | 0.563287 | ||||||||
\(67\) | −63.8468 | − | 17.1077i | −0.952937 | − | 0.255339i | −0.251329 | − | 0.967902i | \(-0.580868\pi\) |
−0.701608 | + | 0.712563i | \(0.747534\pi\) | |||||||
\(68\) | −5.07180 | − | 8.78461i | −0.0745852 | − | 0.129185i | ||||
\(69\) | 47.7846 | + | 27.5885i | 0.692531 | + | 0.399833i | ||||
\(70\) | −17.3205 | + | 17.3205i | −0.247436 | + | 0.247436i | ||||
\(71\) | −13.8897 | − | 51.8372i | −0.195630 | − | 0.730101i | −0.992103 | − | 0.125427i | \(-0.959970\pi\) |
0.796473 | − | 0.604674i | \(-0.206697\pi\) | |||||||
\(72\) | 8.19615 | − | 2.19615i | 0.113835 | − | 0.0305021i | ||||
\(73\) | −27.5814 | − | 27.5814i | −0.377828 | − | 0.377828i | 0.492490 | − | 0.870318i | \(-0.336087\pi\) |
−0.870318 | + | 0.492490i | \(0.836087\pi\) | |||||||
\(74\) | 36.1769 | − | 62.6603i | 0.488877 | − | 0.846760i | ||||
\(75\) | 29.6769 | − | 17.1340i | 0.395692 | − | 0.228453i | ||||
\(76\) | 1.90897 | − | 7.12436i | 0.0251180 | − | 0.0937415i | ||||
\(77\) | − | 39.2820i | − | 0.510156i | ||||||
\(78\) | 8.24167 | − | 30.7583i | 0.105662 | − | 0.394338i | ||||
\(79\) | 36.1244 | 0.457270 | 0.228635 | − | 0.973512i | \(-0.426574\pi\) | ||||
0.228635 | + | 0.973512i | \(0.426574\pi\) | |||||||
\(80\) | −25.8564 | − | 6.92820i | −0.323205 | − | 0.0866025i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 52.3923 | + | 30.2487i | 0.638931 | + | 0.368887i | ||||
\(83\) | 20.9667 | − | 20.9667i | 0.252611 | − | 0.252611i | −0.569430 | − | 0.822040i | \(-0.692836\pi\) |
0.822040 | + | 0.569430i | \(0.192836\pi\) | |||||||
\(84\) | −2.32051 | − | 8.66025i | −0.0276251 | − | 0.103098i | ||||
\(85\) | 32.7846 | − | 8.78461i | 0.385701 | − | 0.103348i | ||||
\(86\) | −32.6603 | − | 32.6603i | −0.379770 | − | 0.379770i | ||||
\(87\) | 15.0000 | − | 25.9808i | 0.172414 | − | 0.298629i | ||||
\(88\) | 37.1769 | − | 21.4641i | 0.422465 | − | 0.243910i | ||||
\(89\) | −18.0666 | + | 67.4256i | −0.202996 | + | 0.757591i | 0.787055 | + | 0.616883i | \(0.211605\pi\) |
−0.990051 | + | 0.140709i | \(0.955062\pi\) | |||||||
\(90\) | 28.3923i | 0.315470i | ||||||||
\(91\) | −32.5000 | − | 8.70835i | −0.357143 | − | 0.0956961i | ||||
\(92\) | 63.7128 | 0.692531 | ||||||||
\(93\) | 72.9449 | + | 19.5455i | 0.784353 | + | 0.210167i | ||||
\(94\) | −58.9808 | − | 102.158i | −0.627455 | − | 1.08678i | ||||
\(95\) | 21.3731 | + | 12.3397i | 0.224980 | + | 0.129892i | ||||
\(96\) | 6.92820 | − | 6.92820i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 4.75387 | + | 17.7417i | 0.0490089 | + | 0.182904i | 0.986091 | − | 0.166205i | \(-0.0531512\pi\) |
−0.937082 | + | 0.349108i | \(0.886485\pi\) | |||||||
\(98\) | 57.7846 | − | 15.4833i | 0.589639 | − | 0.157993i | ||||
\(99\) | −32.1962 | − | 32.1962i | −0.325214 | − | 0.325214i | ||||
\(100\) | 19.7846 | − | 34.2679i | 0.197846 | − | 0.342679i | ||||
\(101\) | −120.215 | + | 69.4064i | −1.19025 | + | 0.687192i | −0.958364 | − | 0.285551i | \(-0.907824\pi\) |
−0.231888 | + | 0.972743i | \(0.574490\pi\) | |||||||
\(102\) | −3.21539 | + | 12.0000i | −0.0315234 | + | 0.117647i | ||||
\(103\) | 107.263i | 1.04139i | 0.853744 | + | 0.520693i | \(0.174326\pi\) | ||||
−0.853744 | + | 0.520693i | \(0.825674\pi\) | |||||||
\(104\) | −9.51666 | − | 35.5167i | −0.0915064 | − | 0.341506i | ||||
\(105\) | 30.0000 | 0.285714 | ||||||||
\(106\) | −133.426 | − | 35.7513i | −1.25873 | − | 0.337276i | ||||
\(107\) | −2.75129 | − | 4.76537i | −0.0257130 | − | 0.0445362i | 0.852883 | − | 0.522103i | \(-0.174852\pi\) |
−0.878596 | + | 0.477567i | \(0.841519\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 108.811 | − | 108.811i | 0.998265 | − | 0.998265i | −0.00173346 | − | 0.999998i | \(-0.500552\pi\) |
0.999998 | + | 0.00173346i | \(0.000551778\pi\) | |||||||
\(110\) | 37.1769 | + | 138.746i | 0.337972 | + | 1.26133i | ||||
\(111\) | −85.5955 | + | 22.9352i | −0.771131 | + | 0.206624i | ||||
\(112\) | −7.32051 | − | 7.32051i | −0.0653617 | − | 0.0653617i | ||||
\(113\) | 43.3923 | − | 75.1577i | 0.384003 | − | 0.665112i | −0.607628 | − | 0.794222i | \(-0.707879\pi\) |
0.991630 | + | 0.129110i | \(0.0412120\pi\) | |||||||
\(114\) | −7.82309 | + | 4.51666i | −0.0686236 | + | 0.0396198i | ||||
\(115\) | −55.1769 | + | 205.923i | −0.479799 | + | 1.79064i | ||||
\(116\) | − | 34.6410i | − | 0.298629i | ||||||
\(117\) | −33.7750 | + | 19.5000i | −0.288675 | + | 0.166667i | ||||
\(118\) | −86.5359 | −0.733355 | ||||||||
\(119\) | 12.6795 | + | 3.39746i | 0.106550 | + | 0.0285501i | ||||
\(120\) | 16.3923 | + | 28.3923i | 0.136603 | + | 0.236603i | ||||
\(121\) | −94.7032 | − | 54.6769i | −0.782671 | − | 0.451875i | ||||
\(122\) | 79.3013 | − | 79.3013i | 0.650010 | − | 0.650010i | ||||
\(123\) | −19.1769 | − | 71.5692i | −0.155910 | − | 0.581864i | ||||
\(124\) | 84.2295 | − | 22.5692i | 0.679270 | − | 0.182010i | ||||
\(125\) | −24.6795 | − | 24.6795i | −0.197436 | − | 0.197436i | ||||
\(126\) | −5.49038 | + | 9.50962i | −0.0435745 | + | 0.0754732i | ||||
\(127\) | 154.885 | − | 89.4230i | 1.21957 | − | 0.704118i | 0.254743 | − | 0.967009i | \(-0.418009\pi\) |
0.964826 | + | 0.262890i | \(0.0846757\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | 56.5692i | 0.438521i | ||||||||
\(130\) | 123.033 | 0.946410 | ||||||||
\(131\) | 53.6359 | 0.409434 | 0.204717 | − | 0.978821i | \(-0.434373\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434373\pi\) | |||||||
\(132\) | −50.7846 | − | 13.6077i | −0.384732 | − | 0.103089i | ||||
\(133\) | 4.77241 | + | 8.26606i | 0.0358828 | + | 0.0621508i | ||||
\(134\) | 80.9545 | + | 46.7391i | 0.604138 | + | 0.348799i | ||||
\(135\) | 24.5885 | − | 24.5885i | 0.182137 | − | 0.182137i | ||||
\(136\) | 3.71281 | + | 13.8564i | 0.0273001 | + | 0.101885i | ||||
\(137\) | −119.478 | + | 32.0141i | −0.872104 | + | 0.233679i | −0.666997 | − | 0.745060i | \(-0.732421\pi\) |
−0.205106 | + | 0.978740i | \(0.565754\pi\) | |||||||
\(138\) | −55.1769 | − | 55.1769i | −0.399833 | − | 0.399833i | ||||
\(139\) | −76.8538 | + | 133.115i | −0.552905 | + | 0.957660i | 0.445158 | + | 0.895452i | \(0.353148\pi\) |
−0.998063 | + | 0.0622079i | \(0.980186\pi\) | |||||||
\(140\) | 30.0000 | − | 17.3205i | 0.214286 | − | 0.123718i | ||||
\(141\) | −37.3923 | + | 139.550i | −0.265194 | + | 0.989716i | ||||
\(142\) | 75.8949i | 0.534471i | ||||||||
\(143\) | −139.517 | + | 139.517i | −0.975641 | + | 0.975641i | ||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 111.962 | + | 30.0000i | 0.772148 | + | 0.206897i | ||||
\(146\) | 27.5814 | + | 47.7724i | 0.188914 | + | 0.327208i | ||||
\(147\) | −63.4519 | − | 36.6340i | −0.431646 | − | 0.249211i | ||||
\(148\) | −72.3538 | + | 72.3538i | −0.488877 | + | 0.488877i | ||||
\(149\) | −41.0718 | − | 153.282i | −0.275650 | − | 1.02874i | −0.955405 | − | 0.295299i | \(-0.904581\pi\) |
0.679755 | − | 0.733439i | \(-0.262086\pi\) | |||||||
\(150\) | −46.8109 | + | 12.5429i | −0.312073 | + | 0.0836196i | ||||
\(151\) | −158.962 | − | 158.962i | −1.05273 | − | 1.05273i | −0.998530 | − | 0.0541950i | \(-0.982741\pi\) |
−0.0541950 | − | 0.998530i | \(-0.517259\pi\) | |||||||
\(152\) | −5.21539 | + | 9.03332i | −0.0343118 | + | 0.0594297i | ||||
\(153\) | 13.1769 | − | 7.60770i | 0.0861236 | − | 0.0497235i | ||||
\(154\) | −14.3782 | + | 53.6603i | −0.0933651 | + | 0.348443i | ||||
\(155\) | 291.779i | 1.88245i | ||||||||
\(156\) | −22.5167 | + | 39.0000i | −0.144338 | + | 0.250000i | ||||
\(157\) | 138.569 | 0.882606 | 0.441303 | − | 0.897358i | \(-0.354516\pi\) | ||||
0.441303 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(158\) | −49.3468 | − | 13.2224i | −0.312321 | − | 0.0836863i | ||||
\(159\) | 84.5885 | + | 146.512i | 0.532003 | + | 0.921456i | ||||
\(160\) | 32.7846 | + | 18.9282i | 0.204904 | + | 0.118301i | ||||
\(161\) | −58.3013 | + | 58.3013i | −0.362120 | + | 0.362120i | ||||
\(162\) | 3.29423 | + | 12.2942i | 0.0203347 | + | 0.0758903i | ||||
\(163\) | 270.947 | − | 72.6000i | 1.66225 | − | 0.445399i | 0.699245 | − | 0.714882i | \(-0.253520\pi\) |
0.963005 | + | 0.269484i | \(0.0868530\pi\) | |||||||
\(164\) | −60.4974 | − | 60.4974i | −0.368887 | − | 0.368887i | ||||
\(165\) | 87.9615 | − | 152.354i | 0.533100 | − | 0.923357i | ||||
\(166\) | −36.3154 | + | 20.9667i | −0.218767 | + | 0.126305i | ||||
\(167\) | 72.3154 | − | 269.885i | 0.433026 | − | 1.61608i | −0.312720 | − | 0.949845i | \(-0.601240\pi\) |
0.745746 | − | 0.666230i | \(-0.232093\pi\) | |||||||
\(168\) | 12.6795i | 0.0754732i | ||||||||
\(169\) | 84.5000 | + | 146.358i | 0.500000 | + | 0.866025i | ||||
\(170\) | −48.0000 | −0.282353 | ||||||||
\(171\) | 10.6865 | + | 2.86345i | 0.0624943 | + | 0.0167453i | ||||
\(172\) | 32.6603 | + | 56.5692i | 0.189885 | + | 0.328891i | ||||
\(173\) | −58.4923 | − | 33.7705i | −0.338106 | − | 0.195205i | 0.321328 | − | 0.946968i | \(-0.395871\pi\) |
−0.659434 | + | 0.751762i | \(0.729204\pi\) | |||||||
\(174\) | −30.0000 | + | 30.0000i | −0.172414 | + | 0.172414i | ||||
\(175\) | 13.2532 | + | 49.4615i | 0.0757324 | + | 0.282637i | ||||
\(176\) | −58.6410 | + | 15.7128i | −0.333188 | + | 0.0892773i | ||||
\(177\) | 74.9423 | + | 74.9423i | 0.423403 | + | 0.423403i | ||||
\(178\) | 49.3590 | − | 85.4923i | 0.277298 | − | 0.480294i | ||||
\(179\) | 43.4923 | − | 25.1103i | 0.242974 | − | 0.140281i | −0.373569 | − | 0.927602i | \(-0.621866\pi\) |
0.616543 | + | 0.787322i | \(0.288533\pi\) | |||||||
\(180\) | 10.3923 | − | 38.7846i | 0.0577350 | − | 0.215470i | ||||
\(181\) | − | 302.354i | − | 1.67046i | −0.549898 | − | 0.835232i | \(-0.685334\pi\) | ||
0.549898 | − | 0.835232i | \(-0.314666\pi\) | |||||||
\(182\) | 41.2083 | + | 23.7917i | 0.226419 | + | 0.130723i | ||||
\(183\) | −137.354 | −0.750567 | ||||||||
\(184\) | −87.0333 | − | 23.3205i | −0.473007 | − | 0.126742i | ||||
\(185\) | −171.191 | − | 296.512i | −0.925357 | − | 1.60276i | ||||
\(186\) | −92.4904 | − | 53.3993i | −0.497260 | − | 0.287093i | ||||
\(187\) | 54.4308 | − | 54.4308i | 0.291074 | − | 0.291074i | ||||
\(188\) | 43.1769 | + | 161.138i | 0.229664 | + | 0.857119i | ||||
\(189\) | 12.9904 | − | 3.48076i | 0.0687322 | − | 0.0184167i | ||||
\(190\) | −24.6795 | − | 24.6795i | −0.129892 | − | 0.129892i | ||||
\(191\) | −81.3397 | + | 140.885i | −0.425863 | + | 0.737616i | −0.996501 | − | 0.0835862i | \(-0.973363\pi\) |
0.570638 | + | 0.821202i | \(0.306696\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 21.2846 | − | 79.4352i | 0.110283 | − | 0.411582i | −0.888608 | − | 0.458668i | \(-0.848327\pi\) |
0.998891 | + | 0.0470861i | \(0.0149935\pi\) | |||||||
\(194\) | − | 25.9756i | − | 0.133895i | ||||||
\(195\) | −106.550 | − | 106.550i | −0.546410 | − | 0.546410i | ||||
\(196\) | −84.6025 | −0.431646 | ||||||||
\(197\) | 260.851 | + | 69.8949i | 1.32412 | + | 0.354796i | 0.850519 | − | 0.525944i | \(-0.176288\pi\) |
0.473599 | + | 0.880741i | \(0.342955\pi\) | |||||||
\(198\) | 32.1962 | + | 55.7654i | 0.162607 | + | 0.281643i | ||||
\(199\) | −55.2391 | − | 31.8923i | −0.277583 | − | 0.160263i | 0.354745 | − | 0.934963i | \(-0.384568\pi\) |
−0.632329 | + | 0.774700i | \(0.717901\pi\) | |||||||
\(200\) | −39.5692 | + | 39.5692i | −0.197846 | + | 0.197846i | ||||
\(201\) | −29.6314 | − | 110.586i | −0.147420 | − | 0.550179i | ||||
\(202\) | 189.622 | − | 50.8090i | 0.938722 | − | 0.251530i | ||||
\(203\) | 31.6987 | + | 31.6987i | 0.156151 | + | 0.156151i | ||||
\(204\) | 8.78461 | − | 15.2154i | 0.0430618 | − | 0.0745852i | ||||
\(205\) | 247.923 | − | 143.138i | 1.20938 | − | 0.698236i | ||||
\(206\) | 39.2609 | − | 146.524i | 0.190587 | − | 0.711280i | ||||
\(207\) | 95.5692i | 0.461687i | ||||||||
\(208\) | 52.0000i | 0.250000i | ||||||||
\(209\) | 55.9718 | 0.267808 | ||||||||
\(210\) | −40.9808 | − | 10.9808i | −0.195146 | − | 0.0522893i | ||||
\(211\) | −123.899 | − | 214.600i | −0.587201 | − | 1.01706i | −0.994597 | − | 0.103810i | \(-0.966897\pi\) |
0.407396 | − | 0.913251i | \(-0.366437\pi\) | |||||||
\(212\) | 169.177 | + | 97.6743i | 0.798004 | + | 0.460728i | ||||
\(213\) | 65.7269 | − | 65.7269i | 0.308577 | − | 0.308577i | ||||
\(214\) | 2.01408 | + | 7.51666i | 0.00941160 | + | 0.0351246i | ||||
\(215\) | −211.119 | + | 56.5692i | −0.981950 | + | 0.263113i | ||||
\(216\) | 10.3923 | + | 10.3923i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −56.4230 | + | 97.7276i | −0.260014 | + | 0.450358i | ||||
\(218\) | −188.466 | + | 108.811i | −0.864523 | + | 0.499133i | ||||
\(219\) | 17.4859 | − | 65.2583i | 0.0798444 | − | 0.297983i | ||||
\(220\) | − | 203.138i | − | 0.923357i | ||||||
\(221\) | −32.9667 | − | 57.1000i | −0.149170 | − | 0.258371i | ||||
\(222\) | 125.321 | 0.564507 | ||||||||
\(223\) | −44.4378 | − | 11.9071i | −0.199273 | − | 0.0533950i | 0.157802 | − | 0.987471i | \(-0.449559\pi\) |
−0.357075 | + | 0.934076i | \(0.616226\pi\) | |||||||
\(224\) | 7.32051 | + | 12.6795i | 0.0326808 | + | 0.0566049i | ||||
\(225\) | 51.4019 | + | 29.6769i | 0.228453 | + | 0.131897i | ||||
\(226\) | −86.7846 | + | 86.7846i | −0.384003 | + | 0.384003i | ||||
\(227\) | 3.55514 | + | 13.2679i | 0.0156614 | + | 0.0584491i | 0.973314 | − | 0.229476i | \(-0.0737012\pi\) |
−0.957653 | + | 0.287925i | \(0.907035\pi\) | |||||||
\(228\) | 12.3397 | − | 3.30642i | 0.0541217 | − | 0.0145019i | ||||
\(229\) | 287.315 | + | 287.315i | 1.25465 | + | 1.25465i | 0.953611 | + | 0.301041i | \(0.0973341\pi\) |
0.301041 | + | 0.953611i | \(0.402666\pi\) | |||||||
\(230\) | 150.746 | − | 261.100i | 0.655418 | − | 1.13522i | ||||
\(231\) | 58.9230 | − | 34.0192i | 0.255078 | − | 0.147269i | ||||
\(232\) | −12.6795 | + | 47.3205i | −0.0546530 | + | 0.203968i | ||||
\(233\) | − | 27.3308i | − | 0.117300i | −0.998279 | − | 0.0586498i | \(-0.981320\pi\) | ||
0.998279 | − | 0.0586498i | \(-0.0186795\pi\) | |||||||
\(234\) | 53.2750 | − | 14.2750i | 0.227671 | − | 0.0610042i | ||||
\(235\) | −558.200 | −2.37532 | ||||||||
\(236\) | 118.210 | + | 31.6743i | 0.500891 | + | 0.134213i | ||||
\(237\) | 31.2846 | + | 54.1865i | 0.132003 | + | 0.228635i | ||||
\(238\) | −16.0770 | − | 9.28203i | −0.0675502 | − | 0.0390001i | ||||
\(239\) | −0.861561 | + | 0.861561i | −0.00360486 | + | 0.00360486i | −0.708907 | − | 0.705302i | \(-0.750811\pi\) |
0.705302 | + | 0.708907i | \(0.250811\pi\) | |||||||
\(240\) | −12.0000 | − | 44.7846i | −0.0500000 | − | 0.186603i | ||||
\(241\) | 82.2032 | − | 22.0263i | 0.341092 | − | 0.0913954i | −0.0842068 | − | 0.996448i | \(-0.526836\pi\) |
0.425299 | + | 0.905053i | \(0.360169\pi\) | |||||||
\(242\) | 109.354 | + | 109.354i | 0.451875 | + | 0.451875i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −137.354 | + | 79.3013i | −0.562926 | + | 0.325005i | ||||
\(245\) | 73.2679 | − | 273.440i | 0.299053 | − | 1.11608i | ||||
\(246\) | 104.785i | 0.425954i | ||||||||
\(247\) | 12.4083 | − | 46.3083i | 0.0502359 | − | 0.187483i | ||||
\(248\) | −123.321 | −0.497260 | ||||||||
\(249\) | 49.6077 | + | 13.2923i | 0.199228 | + | 0.0533829i | ||||
\(250\) | 24.6795 | + | 42.7461i | 0.0987180 | + | 0.170985i | ||||
\(251\) | −35.2539 | − | 20.3538i | −0.140454 | − | 0.0810910i | 0.428127 | − | 0.903719i | \(-0.359174\pi\) |
−0.568580 | + | 0.822628i | \(0.692507\pi\) | |||||||
\(252\) | 10.9808 | − | 10.9808i | 0.0435745 | − | 0.0435745i | ||||
\(253\) | 125.138 | + | 467.023i | 0.494618 | + | 1.84594i | ||||
\(254\) | −244.308 | + | 65.4622i | −0.961844 | + | 0.257725i | ||||
\(255\) | 41.5692 | + | 41.5692i | 0.163017 | + | 0.163017i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −268.277 | + | 154.890i | −1.04388 | + | 0.602684i | −0.920930 | − | 0.389729i | \(-0.872569\pi\) |
−0.122949 | + | 0.992413i | \(0.539235\pi\) | |||||||
\(258\) | 20.7058 | − | 77.2750i | 0.0802549 | − | 0.299515i | ||||
\(259\) | − | 132.417i | − | 0.511261i | ||||||
\(260\) | −168.067 | − | 45.0333i | −0.646410 | − | 0.173205i | ||||
\(261\) | 51.9615 | 0.199086 | ||||||||
\(262\) | −73.2679 | − | 19.6321i | −0.279649 | − | 0.0749316i | ||||
\(263\) | 143.818 | + | 249.100i | 0.546836 | + | 0.947148i | 0.998489 | + | 0.0549543i | \(0.0175013\pi\) |
−0.451653 | + | 0.892194i | \(0.649165\pi\) | |||||||
\(264\) | 64.3923 | + | 37.1769i | 0.243910 | + | 0.140822i | ||||
\(265\) | −462.200 | + | 462.200i | −1.74415 | + | 1.74415i | ||||
\(266\) | −3.49365 | − | 13.0385i | −0.0131340 | − | 0.0490168i | ||||
\(267\) | −116.785 | + | 31.2923i | −0.437396 | + | 0.117200i | ||||
\(268\) | −93.4782 | − | 93.4782i | −0.348799 | − | 0.348799i | ||||
\(269\) | −81.8705 | + | 141.804i | −0.304351 | + | 0.527152i | −0.977117 | − | 0.212704i | \(-0.931773\pi\) |
0.672765 | + | 0.739856i | \(0.265106\pi\) | |||||||
\(270\) | −42.5885 | + | 24.5885i | −0.157735 | + | 0.0910684i | ||||
\(271\) | −84.1692 | + | 314.124i | −0.310587 | + | 1.15913i | 0.617441 | + | 0.786617i | \(0.288170\pi\) |
−0.928028 | + | 0.372510i | \(0.878497\pi\) | |||||||
\(272\) | − | 20.2872i | − | 0.0745852i | ||||||
\(273\) | −15.0833 | − | 56.2917i | −0.0552502 | − | 0.206197i | ||||
\(274\) | 174.928 | 0.638424 | ||||||||
\(275\) | 290.047 | + | 77.7180i | 1.05472 | + | 0.282611i | ||||
\(276\) | 55.1769 | + | 95.5692i | 0.199916 | + | 0.346265i | ||||
\(277\) | −116.900 | − | 67.4923i | −0.422022 | − | 0.243654i | 0.273920 | − | 0.961752i | \(-0.411680\pi\) |
−0.695942 | + | 0.718098i | \(0.745013\pi\) | |||||||
\(278\) | 153.708 | − | 153.708i | 0.552905 | − | 0.552905i | ||||
\(279\) | 33.8538 | + | 126.344i | 0.121340 | + | 0.452847i | ||||
\(280\) | −47.3205 | + | 12.6795i | −0.169002 | + | 0.0452839i | ||||
\(281\) | 323.545 | + | 323.545i | 1.15141 | + | 1.15141i | 0.986271 | + | 0.165134i | \(0.0528056\pi\) |
0.165134 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(282\) | 102.158 | − | 176.942i | 0.362261 | − | 0.627455i | ||||
\(283\) | −122.416 | + | 70.6769i | −0.432565 | + | 0.249742i | −0.700439 | − | 0.713712i | \(-0.747012\pi\) |
0.267874 | + | 0.963454i | \(0.413679\pi\) | |||||||
\(284\) | 27.7795 | − | 103.674i | 0.0978150 | − | 0.365050i | ||||
\(285\) | 42.7461i | 0.149986i | ||||||||
\(286\) | 241.650 | − | 139.517i | 0.844930 | − | 0.487820i | ||||
\(287\) | 110.718 | 0.385777 | ||||||||
\(288\) | 16.3923 | + | 4.39230i | 0.0569177 | + | 0.0152511i | ||||
\(289\) | −131.638 | − | 228.004i | −0.455496 | − | 0.788943i | ||||
\(290\) | −141.962 | − | 81.9615i | −0.489522 | − | 0.282626i | ||||
\(291\) | −22.4955 | + | 22.4955i | −0.0773042 | + | 0.0773042i | ||||
\(292\) | −20.1910 | − | 75.3538i | −0.0691473 | − | 0.258061i | ||||
\(293\) | 287.512 | − | 77.0385i | 0.981268 | − | 0.262930i | 0.267689 | − | 0.963505i | \(-0.413740\pi\) |
0.713578 | + | 0.700575i | \(0.247073\pi\) | |||||||
\(294\) | 73.2679 | + | 73.2679i | 0.249211 | + | 0.249211i | ||||
\(295\) | −204.746 | + | 354.631i | −0.694055 | + | 1.20214i | ||||
\(296\) | 125.321 | − | 72.3538i | 0.423380 | − | 0.244439i | ||||
\(297\) | 20.4115 | − | 76.1769i | 0.0687257 | − | 0.256488i | ||||
\(298\) | 224.420i | 0.753089i | ||||||||
\(299\) | 414.133 | 1.38506 | ||||||||
\(300\) | 68.5359 | 0.228453 | ||||||||
\(301\) | −81.6506 | − | 21.8782i | −0.271265 | − | 0.0726851i | ||||
\(302\) | 158.962 | + | 275.329i | 0.526363 | + | 0.911687i | ||||
\(303\) | −208.219 | − | 120.215i | −0.687192 | − | 0.396750i | ||||
\(304\) | 10.4308 | − | 10.4308i | 0.0343118 | − | 0.0343118i | ||||
\(305\) | −137.354 | − | 512.611i | −0.450340 | − | 1.68069i | ||||
\(306\) | −20.7846 | + | 5.56922i | −0.0679236 | + | 0.0182001i | ||||
\(307\) | −70.0685 | − | 70.0685i | −0.228236 | − | 0.228236i | 0.583719 | − | 0.811956i | \(-0.301597\pi\) |
−0.811956 | + | 0.583719i | \(0.801597\pi\) | |||||||
\(308\) | 39.2820 | − | 68.0385i | 0.127539 | − | 0.220904i | ||||
\(309\) | −160.894 | + | 92.8923i | −0.520693 | + | 0.300622i | ||||
\(310\) | 106.799 | − | 398.578i | 0.344512 | − | 1.28574i | ||||
\(311\) | − | 140.238i | − | 0.450927i | −0.974252 | − | 0.225464i | \(-0.927610\pi\) | ||
0.974252 | − | 0.225464i | \(-0.0723897\pi\) | |||||||
\(312\) | 45.0333 | − | 45.0333i | 0.144338 | − | 0.144338i | ||||
\(313\) | −550.286 | −1.75810 | −0.879051 | − | 0.476728i | \(-0.841823\pi\) | ||||
−0.879051 | + | 0.476728i | \(0.841823\pi\) | |||||||
\(314\) | −189.289 | − | 50.7199i | −0.602831 | − | 0.161528i | ||||
\(315\) | 25.9808 | + | 45.0000i | 0.0824786 | + | 0.142857i | ||||
\(316\) | 62.5692 | + | 36.1244i | 0.198004 | + | 0.114318i | ||||
\(317\) | −31.2923 | + | 31.2923i | −0.0987140 | + | 0.0987140i | −0.754739 | − | 0.656025i | \(-0.772237\pi\) |
0.656025 | + | 0.754739i | \(0.272237\pi\) | |||||||
\(318\) | −61.9230 | − | 231.100i | −0.194727 | − | 0.726729i | ||||
\(319\) | 253.923 | − | 68.0385i | 0.795997 | − | 0.213287i | ||||
\(320\) | −37.8564 | − | 37.8564i | −0.118301 | − | 0.118301i | ||||
\(321\) | 4.76537 | − | 8.25387i | 0.0148454 | − | 0.0257130i | ||||
\(322\) | 100.981 | − | 58.3013i | 0.313605 | − | 0.181060i | ||||
\(323\) | −4.84094 | + | 18.0666i | −0.0149874 | + | 0.0559339i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 128.600 | − | 222.742i | 0.395692 | − | 0.685359i | ||||
\(326\) | −396.694 | −1.21685 | ||||||||
\(327\) | 257.449 | + | 68.9833i | 0.787307 | + | 0.210958i | ||||
\(328\) | 60.4974 | + | 104.785i | 0.184443 | + | 0.319465i | ||||
\(329\) | −186.962 | − | 107.942i | −0.568272 | − | 0.328092i | ||||
\(330\) | −175.923 | + | 175.923i | −0.533100 | + | 0.533100i | ||||
\(331\) | −104.546 | − | 390.169i | −0.315847 | − | 1.17876i | −0.923198 | − | 0.384325i | \(-0.874434\pi\) |
0.607350 | − | 0.794434i | \(-0.292232\pi\) | |||||||
\(332\) | 57.2820 | − | 15.3487i | 0.172536 | − | 0.0462309i | ||||
\(333\) | −108.531 | − | 108.531i | −0.325918 | − | 0.325918i | ||||
\(334\) | −197.569 | + | 342.200i | −0.591525 | + | 1.02455i | ||||
\(335\) | 383.081 | − | 221.172i | 1.14352 | − | 0.660214i | ||||
\(336\) | 4.64102 | − | 17.3205i | 0.0138125 | − | 0.0515491i | ||||
\(337\) | − | 638.492i | − | 1.89464i | −0.320295 | − | 0.947318i | \(-0.603782\pi\) | ||
0.320295 | − | 0.947318i | \(-0.396218\pi\) | |||||||
\(338\) | −61.8583 | − | 230.858i | −0.183013 | − | 0.683013i | ||||
\(339\) | 150.315 | 0.443408 | ||||||||
\(340\) | 65.5692 | + | 17.5692i | 0.192851 | + | 0.0516742i | ||||
\(341\) | 330.870 | + | 573.084i | 0.970295 | + | 1.68060i | ||||
\(342\) | −13.5500 | − | 7.82309i | −0.0396198 | − | 0.0228745i | ||||
\(343\) | 167.093 | − | 167.093i | 0.487151 | − | 0.487151i | ||||
\(344\) | −23.9090 | − | 89.2295i | −0.0695028 | − | 0.259388i | ||||
\(345\) | −356.669 | + | 95.5692i | −1.03382 | + | 0.277012i | ||||
\(346\) | 67.5411 | + | 67.5411i | 0.195205 | + | 0.195205i | ||||
\(347\) | 2.85125 | − | 4.93851i | 0.00821686 | − | 0.0142320i | −0.861888 | − | 0.507099i | \(-0.830718\pi\) |
0.870105 | + | 0.492867i | \(0.164051\pi\) | |||||||
\(348\) | 51.9615 | − | 30.0000i | 0.149315 | − | 0.0862069i | ||||
\(349\) | 46.8890 | − | 174.992i | 0.134353 | − | 0.501411i | −0.865647 | − | 0.500655i | \(-0.833093\pi\) |
1.00000 | 0.000755966i | \(-0.000240632\pi\) | ||||||||
\(350\) | − | 72.4167i | − | 0.206905i | ||||||
\(351\) | −58.5000 | − | 33.7750i | −0.166667 | − | 0.0962250i | ||||
\(352\) | 85.8564 | 0.243910 | ||||||||
\(353\) | −280.086 | − | 75.0488i | −0.793444 | − | 0.212603i | −0.160741 | − | 0.986997i | \(-0.551388\pi\) |
−0.632704 | + | 0.774394i | \(0.718055\pi\) | |||||||
\(354\) | −74.9423 | − | 129.804i | −0.211701 | − | 0.366678i | ||||
\(355\) | 311.023 | + | 179.569i | 0.876121 | + | 0.505829i | ||||
\(356\) | −98.7180 | + | 98.7180i | −0.277298 | + | 0.277298i | ||||
\(357\) | 5.88457 | + | 21.9615i | 0.0164834 | + | 0.0615169i | ||||
\(358\) | −68.6025 | + | 18.3820i | −0.191627 | + | 0.0513464i | ||||
\(359\) | −268.277 | − | 268.277i | −0.747289 | − | 0.747289i | 0.226680 | − | 0.973969i | \(-0.427213\pi\) |
−0.973969 | + | 0.226680i | \(0.927213\pi\) | |||||||
\(360\) | −28.3923 | + | 49.1769i | −0.0788675 | + | 0.136603i | ||||
\(361\) | 300.857 | − | 173.700i | 0.833399 | − | 0.481163i | ||||
\(362\) | −110.669 | + | 413.023i | −0.305716 | + | 1.14095i | ||||
\(363\) | − | 189.406i | − | 0.521781i | ||||||
\(364\) | −47.5833 | − | 47.5833i | −0.130723 | − | 0.130723i | ||||
\(365\) | 261.033 | 0.715160 | ||||||||
\(366\) | 187.629 | + | 50.2750i | 0.512647 | + | 0.137363i | ||||
\(367\) | 88.1077 | + | 152.607i | 0.240075 | + | 0.415823i | 0.960736 | − | 0.277466i | \(-0.0894945\pi\) |
−0.720660 | + | 0.693289i | \(0.756161\pi\) | |||||||
\(368\) | 110.354 | + | 63.7128i | 0.299875 | + | 0.173133i | ||||
\(369\) | 90.7461 | − | 90.7461i | 0.245924 | − | 0.245924i | ||||
\(370\) | 125.321 | + | 467.703i | 0.338704 | + | 1.26406i | ||||
\(371\) | −244.186 | + | 65.4294i | −0.658183 | + | 0.176360i | ||||
\(372\) | 106.799 | + | 106.799i | 0.287093 | + | 0.287093i | ||||
\(373\) | −241.803 | + | 418.815i | −0.648266 | + | 1.12283i | 0.335271 | + | 0.942122i | \(0.391172\pi\) |
−0.983537 | + | 0.180708i | \(0.942161\pi\) | |||||||
\(374\) | −94.2769 | + | 54.4308i | −0.252077 | + | 0.145537i | ||||
\(375\) | 15.6462 | − | 58.3923i | 0.0417231 | − | 0.155713i | ||||
\(376\) | − | 235.923i | − | 0.627455i | ||||||
\(377\) | − | 225.167i | − | 0.597259i | ||||||
\(378\) | −19.0192 | −0.0503154 | ||||||||
\(379\) | 278.815 | + | 74.7083i | 0.735661 | + | 0.197120i | 0.607149 | − | 0.794588i | \(-0.292313\pi\) |
0.128512 | + | 0.991708i | \(0.458980\pi\) | |||||||
\(380\) | 24.6795 | + | 42.7461i | 0.0649460 | + | 0.112490i | ||||
\(381\) | 268.269 | + | 154.885i | 0.704118 | + | 0.406523i | ||||
\(382\) | 162.679 | − | 162.679i | 0.425863 | − | 0.425863i | ||||
\(383\) | −68.1718 | − | 254.420i | −0.177994 | − | 0.664283i | −0.996022 | − | 0.0891049i | \(-0.971599\pi\) |
0.818028 | − | 0.575178i | \(-0.195067\pi\) | |||||||
\(384\) | 18.9282 | − | 5.07180i | 0.0492922 | − | 0.0132078i | ||||
\(385\) | 185.885 | + | 185.885i | 0.482817 | + | 0.482817i | ||||
\(386\) | −58.1506 | + | 100.720i | −0.150649 | + | 0.260932i | ||||
\(387\) | −84.8538 | + | 48.9904i | −0.219261 | + | 0.126590i | ||||
\(388\) | −9.50773 | + | 35.4833i | −0.0245045 | + | 0.0914519i | ||||
\(389\) | 66.2487i | 0.170305i | 0.996368 | + | 0.0851526i | \(0.0271378\pi\) | ||||
−0.996368 | + | 0.0851526i | \(0.972862\pi\) | |||||||
\(390\) | 106.550 | + | 184.550i | 0.273205 | + | 0.473205i | ||||
\(391\) | −161.569 | −0.413221 | ||||||||
\(392\) | 115.569 | + | 30.9667i | 0.294819 | + | 0.0789966i | ||||
\(393\) | 46.4500 | + | 80.4538i | 0.118193 | + | 0.204717i | ||||
\(394\) | −330.746 | − | 190.956i | −0.839457 | − | 0.484661i | ||||
\(395\) | −170.942 | + | 170.942i | −0.432765 | + | 0.432765i | ||||
\(396\) | −23.5692 | − | 87.9615i | −0.0595182 | − | 0.222125i | ||||
\(397\) | −130.651 | + | 35.0077i | −0.329095 | + | 0.0881807i | −0.419583 | − | 0.907717i | \(-0.637824\pi\) |
0.0904886 | + | 0.995897i | \(0.471157\pi\) | |||||||
\(398\) | 63.7846 | + | 63.7846i | 0.160263 | + | 0.160263i | ||||
\(399\) | −8.26606 | + | 14.3172i | −0.0207169 | + | 0.0358828i | ||||
\(400\) | 68.5359 | − | 39.5692i | 0.171340 | − | 0.0989230i | ||||
\(401\) | −49.5654 | + | 184.981i | −0.123605 | + | 0.461299i | −0.999786 | − | 0.0206827i | \(-0.993416\pi\) |
0.876181 | + | 0.481981i | \(0.160083\pi\) | |||||||
\(402\) | 161.909i | 0.402759i | ||||||||
\(403\) | 547.492 | − | 146.700i | 1.35854 | − | 0.364020i | ||||
\(404\) | −277.626 | −0.687192 | ||||||||
\(405\) | 58.1769 | + | 15.5885i | 0.143647 | + | 0.0384900i | ||||
\(406\) | −31.6987 | − | 54.9038i | −0.0780757 | − | 0.135231i | ||||
\(407\) | −672.473 | − | 388.252i | −1.65227 | − | 0.953937i | ||||
\(408\) | −17.5692 | + | 17.5692i | −0.0430618 | + | 0.0430618i | ||||
\(409\) | 143.838 | + | 536.812i | 0.351683 | + | 1.31250i | 0.884608 | + | 0.466336i | \(0.154426\pi\) |
−0.532925 | + | 0.846163i | \(0.678907\pi\) | |||||||
\(410\) | −391.061 | + | 104.785i | −0.953809 | + | 0.255572i | ||||
\(411\) | −151.492 | − | 151.492i | −0.368594 | − | 0.368594i | ||||
\(412\) | −107.263 | + | 185.785i | −0.260347 | + | 0.450934i | ||||
\(413\) | −137.154 | + | 79.1858i | −0.332092 | + | 0.191733i | ||||
\(414\) | 34.9808 | − | 130.550i | 0.0844946 | − | 0.315338i | ||||
\(415\) | 198.431i | 0.478146i | ||||||||
\(416\) | 19.0333 | − | 71.0333i | 0.0457532 | − | 0.170753i | ||||
\(417\) | −266.229 | −0.638440 | ||||||||
\(418\) | −76.4589 | − | 20.4871i | −0.182916 | − | 0.0490122i | ||||
\(419\) | 328.823 | + | 569.538i | 0.784781 | + | 1.35928i | 0.929130 | + | 0.369753i | \(0.120558\pi\) |
−0.144349 | + | 0.989527i | \(0.546109\pi\) | |||||||
\(420\) | 51.9615 | + | 30.0000i | 0.123718 | + | 0.0714286i | ||||
\(421\) | 328.035 | − | 328.035i | 0.779181 | − | 0.779181i | −0.200511 | − | 0.979692i | \(-0.564260\pi\) |
0.979692 | + | 0.200511i | \(0.0642601\pi\) | |||||||
\(422\) | 90.7006 | + | 338.499i | 0.214930 | + | 0.802131i | ||||
\(423\) | −241.708 | + | 64.7654i | −0.571413 | + | 0.153110i | ||||
\(424\) | −195.349 | − | 195.349i | −0.460728 | − | 0.460728i | ||||
\(425\) | −50.1718 | + | 86.9000i | −0.118051 | + | 0.204471i | ||||
\(426\) | −113.842 | + | 65.7269i | −0.267236 | + | 0.154288i | ||||
\(427\) | 53.1218 | − | 198.253i | 0.124407 | − | 0.464293i | ||||
\(428\) | − | 11.0052i | − | 0.0257130i | ||||||
\(429\) | −330.100 | − | 88.4500i | −0.769464 | − | 0.206177i | ||||
\(430\) | 309.100 | 0.718837 | ||||||||
\(431\) | −30.9948 | − | 8.30504i | −0.0719138 | − | 0.0192692i | 0.222683 | − | 0.974891i | \(-0.428519\pi\) |
−0.294597 | + | 0.955622i | \(0.595185\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 169.928 | + | 98.1077i | 0.392442 | + | 0.226577i | 0.683218 | − | 0.730215i | \(-0.260580\pi\) |
−0.290776 | + | 0.956791i | \(0.593913\pi\) | |||||||
\(434\) | 112.846 | − | 112.846i | 0.260014 | − | 0.260014i | ||||
\(435\) | 51.9615 | + | 193.923i | 0.119452 | + | 0.445800i | ||||
\(436\) | 297.277 | − | 79.6551i | 0.681828 | − | 0.182695i | ||||
\(437\) | −83.0718 | − | 83.0718i | −0.190096 | − | 0.190096i | ||||
\(438\) | −47.7724 | + | 82.7442i | −0.109069 | + | 0.188914i | ||||
\(439\) | 35.9078 | − | 20.7314i | 0.0817945 | − | 0.0472241i | −0.458545 | − | 0.888671i | \(-0.651629\pi\) |
0.540339 | + | 0.841447i | \(0.318296\pi\) | |||||||
\(440\) | −74.3538 | + | 277.492i | −0.168986 | + | 0.630664i | ||||
\(441\) | − | 126.904i | − | 0.287764i | ||||||
\(442\) | 24.1333 | + | 90.0666i | 0.0546002 | + | 0.203771i | ||||
\(443\) | −19.9718 | −0.0450831 | −0.0225416 | − | 0.999746i | \(-0.507176\pi\) | ||||
−0.0225416 | + | 0.999746i | \(0.507176\pi\) | |||||||
\(444\) | −171.191 | − | 45.8705i | −0.385565 | − | 0.103312i | ||||
\(445\) | −233.569 | − | 404.554i | −0.524875 | − | 0.909110i | ||||
\(446\) | 56.3449 | + | 32.5307i | 0.126334 | + | 0.0729389i | ||||
\(447\) | 194.354 | − | 194.354i | 0.434796 | − | 0.434796i | ||||
\(448\) | −5.35898 | − | 20.0000i | −0.0119620 | − | 0.0446429i | ||||
\(449\) | 127.459 | − | 34.1525i | 0.283873 | − | 0.0760635i | −0.114073 | − | 0.993472i | \(-0.536390\pi\) |
0.397946 | + | 0.917409i | \(0.369723\pi\) | |||||||
\(450\) | −59.3538 | − | 59.3538i | −0.131897 | − | 0.131897i | ||||
\(451\) | 324.631 | − | 562.277i | 0.719802 | − | 1.24673i | ||||
\(452\) | 150.315 | − | 86.7846i | 0.332556 | − | 0.192001i | ||||
\(453\) | 100.778 | − | 376.107i | 0.222467 | − | 0.830258i | ||||
\(454\) | − | 19.4256i | − | 0.0427877i | ||||||
\(455\) | 195.000 | − | 112.583i | 0.428571 | − | 0.247436i | ||||
\(456\) | −18.0666 | −0.0396198 | ||||||||
\(457\) | −284.842 | − | 76.3231i | −0.623286 | − | 0.167009i | −0.0666648 | − | 0.997775i | \(-0.521236\pi\) |
−0.556621 | + | 0.830766i | \(0.687902\pi\) | |||||||
\(458\) | −287.315 | − | 497.645i | −0.627326 | − | 1.08656i | ||||
\(459\) | 22.8231 | + | 13.1769i | 0.0497235 | + | 0.0287079i | ||||
\(460\) | −301.492 | + | 301.492i | −0.655418 | + | 0.655418i | ||||
\(461\) | 121.565 | + | 453.688i | 0.263699 | + | 0.984140i | 0.963042 | + | 0.269353i | \(0.0868097\pi\) |
−0.699342 | + | 0.714787i | \(0.746524\pi\) | |||||||
\(462\) | −92.9423 | + | 24.9038i | −0.201174 | + | 0.0539044i | ||||
\(463\) | 462.599 | + | 462.599i | 0.999134 | + | 0.999134i | 1.00000 | 0.000865128i | \(-0.000275379\pi\) | |
−0.000865128 | 1.00000i | \(0.500275\pi\) | ||||||||
\(464\) | 34.6410 | − | 60.0000i | 0.0746574 | − | 0.129310i | ||||
\(465\) | −437.669 | + | 252.688i | −0.941224 | + | 0.543416i | ||||
\(466\) | −10.0038 | + | 37.3346i | −0.0214673 | + | 0.0801171i | ||||
\(467\) | 396.649i | 0.849355i | 0.905345 | + | 0.424677i | \(0.139612\pi\) | ||||
−0.905345 | + | 0.424677i | \(0.860388\pi\) | |||||||
\(468\) | −78.0000 | −0.166667 | ||||||||
\(469\) | 171.077 | 0.364770 | ||||||||
\(470\) | 762.515 | + | 204.315i | 1.62237 | + | 0.434714i | ||||
\(471\) | 120.004 | + | 207.854i | 0.254787 | + | 0.441303i | ||||
\(472\) | −149.885 | − | 86.5359i | −0.317552 | − | 0.183339i | ||||
\(473\) | −350.512 | + | 350.512i | −0.741039 | + | 0.741039i | ||||
\(474\) | −22.9019 | − | 85.4711i | −0.0483163 | − | 0.180319i | ||||
\(475\) | −70.4763 | + | 18.8841i | −0.148371 | + | 0.0397559i | ||||
\(476\) | 18.5641 | + | 18.5641i | 0.0390001 | + | 0.0390001i | ||||
\(477\) | −146.512 | + | 253.765i | −0.307152 | + | 0.532003i | ||||
\(478\) | 1.49227 | − | 0.861561i | 0.00312190 | − | 0.00180243i | ||||
\(479\) | 93.1666 | − | 347.703i | 0.194502 | − | 0.725892i | −0.797893 | − | 0.602799i | \(-0.794052\pi\) |
0.992395 | − | 0.123093i | \(-0.0392814\pi\) | |||||||
\(480\) | 65.5692i | 0.136603i | ||||||||
\(481\) | −470.300 | + | 470.300i | −0.977754 | + | 0.977754i | ||||
\(482\) | −120.354 | −0.249697 | ||||||||
\(483\) | −137.942 | − | 36.9615i | −0.285595 | − | 0.0765249i | ||||
\(484\) | −109.354 | − | 189.406i | −0.225938 | − | 0.391336i | ||||
\(485\) | −106.450 | − | 61.4589i | −0.219485 | − | 0.126719i | ||||
\(486\) | −15.5885 | + | 15.5885i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | −50.1455 | − | 187.145i | −0.102968 | − | 0.384282i | 0.895139 | − | 0.445788i | \(-0.147076\pi\) |
−0.998107 | + | 0.0615056i | \(0.980410\pi\) | |||||||
\(488\) | 216.655 | − | 58.0526i | 0.443965 | − | 0.118960i | ||||
\(489\) | 343.547 | + | 343.547i | 0.702550 | + | 0.702550i | ||||
\(490\) | −200.172 | + | 346.708i | −0.408514 | + | 0.707567i | ||||
\(491\) | 19.9808 | − | 11.5359i | 0.0406940 | − | 0.0234947i | −0.479515 | − | 0.877534i | \(-0.659187\pi\) |
0.520209 | + | 0.854039i | \(0.325854\pi\) | |||||||
\(492\) | 38.3538 | − | 143.138i | 0.0779549 | − | 0.290932i | ||||
\(493\) | 87.8461i | 0.178187i | ||||||||
\(494\) | −33.9000 | + | 58.7166i | −0.0686236 | + | 0.118859i | ||||
\(495\) | 304.708 | 0.615571 | ||||||||
\(496\) | 168.459 | + | 45.1384i | 0.339635 | + | 0.0910049i | ||||
\(497\) | 69.4486 | + | 120.289i | 0.139736 | + | 0.242029i | ||||
\(498\) | −62.9000 | − | 36.3154i | −0.126305 | − | 0.0729224i | ||||
\(499\) | −160.769 | + | 160.769i | −0.322183 | + | 0.322183i | −0.849604 | − | 0.527421i | \(-0.823159\pi\) |
0.527421 | + | 0.849604i | \(0.323159\pi\) | |||||||
\(500\) | −18.0666 | − | 67.4256i | −0.0361333 | − | 0.134851i | ||||
\(501\) | 467.454 | − | 125.254i | 0.933042 | − | 0.250008i | ||||
\(502\) | 40.7077 | + | 40.7077i | 0.0810910 | + | 0.0810910i | ||||
\(503\) | 300.622 | − | 520.692i | 0.597658 | − | 1.03517i | −0.395508 | − | 0.918462i | \(-0.629432\pi\) |
0.993166 | − | 0.116711i | \(-0.0372351\pi\) | |||||||
\(504\) | −19.0192 | + | 10.9808i | −0.0377366 | + | 0.0217872i | ||||
\(505\) | 240.431 | − | 897.300i | 0.476101 | − | 1.77683i | ||||
\(506\) | − | 683.769i | − | 1.35132i | ||||||
\(507\) | −146.358 | + | 253.500i | −0.288675 | + | 0.500000i | ||||
\(508\) | 357.692 | 0.704118 | ||||||||
\(509\) | −475.028 | − | 127.283i | −0.933258 | − | 0.250066i | −0.240014 | − | 0.970769i | \(-0.577152\pi\) |
−0.693243 | + | 0.720704i | \(0.743819\pi\) | |||||||
\(510\) | −41.5692 | − | 72.0000i | −0.0815083 | − | 0.141176i | ||||
\(511\) | 87.4296 | + | 50.4775i | 0.171095 | + | 0.0987818i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 4.95964 | + | 18.5096i | 0.00966791 | + | 0.0360811i | ||||
\(514\) | 423.167 | − | 113.387i | 0.823281 | − | 0.220598i | ||||
\(515\) | −507.573 | − | 507.573i | −0.985579 | − | 0.985579i | ||||
\(516\) | −56.5692 | + | 97.9808i | −0.109630 | + | 0.189885i | ||||
\(517\) | −1096.36 | + | 632.985i | −2.12062 | + | 1.22434i | ||||
\(518\) | −48.4679 | + | 180.885i | −0.0935673 | + | 0.349198i | ||||
\(519\) | − | 116.985i | − | 0.225404i | ||||||
\(520\) | 213.100 | + | 123.033i | 0.409808 | + | 0.236603i | ||||
\(521\) | 647.951 | 1.24367 | 0.621834 | − | 0.783149i | \(-0.286388\pi\) | ||||
0.621834 | + | 0.783149i | \(0.286388\pi\) | |||||||
\(522\) | −70.9808 | − | 19.0192i | −0.135978 | − | 0.0364353i | ||||
\(523\) | 82.9615 | + | 143.694i | 0.158626 | + | 0.274749i | 0.934374 | − | 0.356295i | \(-0.115960\pi\) |
−0.775747 | + | 0.631044i | \(0.782627\pi\) | |||||||
\(524\) | 92.9000 | + | 53.6359i | 0.177290 | + | 0.102359i | ||||
\(525\) | −62.7147 | + | 62.7147i | −0.119457 | + | 0.119457i | ||||
\(526\) | −105.282 | − | 392.918i | −0.200156 | − | 0.746992i | ||||
\(527\) | −213.597 | + | 57.2332i | −0.405308 | + | 0.108602i | ||||
\(528\) | −74.3538 | − | 74.3538i | −0.140822 | − | 0.140822i | ||||
\(529\) | 242.915 | − | 420.742i | 0.459197 | − | 0.795353i | ||||
\(530\) | 800.554 | − | 462.200i | 1.51048 | − | 0.872075i | ||||
\(531\) | −47.5115 | + | 177.315i | −0.0894755 | + | 0.333927i | ||||
\(532\) | 19.0897i | 0.0358828i | ||||||||
\(533\) | −393.233 | − | 393.233i | −0.737773 | − | 0.737773i | ||||
\(534\) | 170.985 | 0.320196 | ||||||||
\(535\) | 35.5692 | + | 9.53074i | 0.0664845 | + | 0.0178145i | ||||
\(536\) | 93.4782 | + | 161.909i | 0.174400 | + | 0.302069i | ||||
\(537\) | 75.3308 | + | 43.4923i | 0.140281 | + | 0.0809912i | ||||
\(538\) | 163.741 | − | 163.741i | 0.304351 | − | 0.304351i | ||||
\(539\) | −166.168 | − | 620.147i | −0.308289 | − | 1.15055i | ||||
\(540\) | 67.1769 | − | 18.0000i | 0.124402 | − | 0.0333333i | ||||
\(541\) | −210.557 | − | 210.557i | −0.389200 | − | 0.389200i | 0.485202 | − | 0.874402i | \(-0.338746\pi\) |
−0.874402 | + | 0.485202i | \(0.838746\pi\) | |||||||
\(542\) | 229.954 | − | 398.293i | 0.424270 | − | 0.734858i | ||||
\(543\) | 453.531 | − | 261.846i | 0.835232 | − | 0.482221i | ||||
\(544\) | −7.42563 | + | 27.7128i | −0.0136500 | + | 0.0509427i | ||||
\(545\) | 1029.80i | 1.88954i | ||||||||
\(546\) | 82.4167i | 0.150946i | ||||||||
\(547\) | −392.492 | −0.717536 | −0.358768 | − | 0.933427i | \(-0.616803\pi\) | ||||
−0.358768 | + | 0.933427i | \(0.616803\pi\) | |||||||
\(548\) | −238.956 | − | 64.0282i | −0.436052 | − | 0.116840i | ||||
\(549\) | −118.952 | − | 206.031i | −0.216670 | − | 0.375284i | ||||
\(550\) | −367.765 | − | 212.329i | −0.668664 | − | 0.386054i | ||||
\(551\) | −45.1666 | + | 45.1666i | −0.0819721 | + | 0.0819721i | ||||
\(552\) | −40.3923 | − | 150.746i | −0.0731745 | − | 0.273091i | ||||
\(553\) | −90.3109 | + | 24.1987i | −0.163311 | + | 0.0437590i | ||||
\(554\) | 134.985 | + | 134.985i | 0.243654 | + | 0.243654i | ||||
\(555\) | 296.512 | − | 513.573i | 0.534255 | − | 0.925357i | ||||
\(556\) | −266.229 | + | 153.708i | −0.478830 | + | 0.276453i | ||||
\(557\) | 18.3576 | − | 68.5115i | 0.0329580 | − | 0.123001i | −0.947487 | − | 0.319794i | \(-0.896386\pi\) |
0.980445 | + | 0.196793i | \(0.0630528\pi\) | |||||||
\(558\) | − | 184.981i | − | 0.331507i | ||||||
\(559\) | 212.292 | + | 367.700i | 0.379770 | + | 0.657782i | ||||
\(560\) | 69.2820 | 0.123718 | ||||||||
\(561\) | 128.785 | + | 34.5077i | 0.229563 | + | 0.0615111i | ||||
\(562\) | −323.545 | − | 560.396i | −0.575703 | − | 0.997146i | ||||
\(563\) | 721.161 | + | 416.363i | 1.28093 | + | 0.739543i | 0.977018 | − | 0.213158i | \(-0.0683750\pi\) |
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(564\) | −204.315 | + | 204.315i | −0.362261 | + | 0.362261i | ||||
\(565\) | 150.315 | + | 560.985i | 0.266045 | + | 0.992893i | ||||
\(566\) | 193.093 | − | 51.7391i | 0.341154 | − | 0.0914118i | ||||
\(567\) | 16.4711 | + | 16.4711i | 0.0290496 | + | 0.0290496i | ||||
\(568\) | −75.8949 | + | 131.454i | −0.133618 | + | 0.231433i | ||||
\(569\) | 301.750 | − | 174.215i | 0.530316 | − | 0.306178i | −0.210829 | − | 0.977523i | \(-0.567616\pi\) |
0.741145 | + | 0.671345i | \(0.234283\pi\) | |||||||
\(570\) | 15.6462 | − | 58.3923i | 0.0274494 | − | 0.102443i | ||||
\(571\) | − | 411.892i | − | 0.721352i | −0.932691 | − | 0.360676i | \(-0.882546\pi\) | ||
0.932691 | − | 0.360676i | \(-0.117454\pi\) | |||||||
\(572\) | −381.167 | + | 102.133i | −0.666375 | + | 0.178555i | ||||
\(573\) | −281.769 | −0.491744 | ||||||||
\(574\) | −151.244 | − | 40.5256i | −0.263491 | − | 0.0706021i | ||||
\(575\) | −315.133 | − | 545.827i | −0.548058 | − | 0.949264i | ||||
\(576\) | −20.7846 | − | 12.0000i | −0.0360844 | − | 0.0208333i | ||||
\(577\) | 39.6692 | − | 39.6692i | 0.0687507 | − | 0.0687507i | −0.671895 | − | 0.740646i | \(-0.734520\pi\) |
0.740646 | + | 0.671895i | \(0.234520\pi\) | |||||||
\(578\) | 96.3660 | + | 359.643i | 0.166723 | + | 0.622220i | ||||
\(579\) | 137.586 | − | 36.8660i | 0.237627 | − | 0.0636719i | ||||
\(580\) | 163.923 | + | 163.923i | 0.282626 | + | 0.282626i | ||||
\(581\) | −38.3717 | + | 66.4617i | −0.0660442 | + | 0.114392i | ||||
\(582\) | 38.9634 | − | 22.4955i | 0.0669474 | − | 0.0386521i | ||||
\(583\) | −383.685 | + | 1431.93i | −0.658121 | + | 2.45614i | ||||
\(584\) | 110.326i | 0.188914i | ||||||||
\(585\) | 67.5500 | − | 252.100i | 0.115470 | − | 0.430940i | ||||
\(586\) | −420.946 | −0.718338 | ||||||||
\(587\) | −505.435 | − | 135.431i | −0.861047 | − | 0.230717i | −0.198835 | − | 0.980033i | \(-0.563716\pi\) |
−0.662212 | + | 0.749316i | \(0.730382\pi\) | |||||||
\(588\) | −73.2679 | − | 126.904i | −0.124605 | − | 0.215823i | ||||
\(589\) | −139.249 | − | 80.3956i | −0.236416 | − | 0.136495i | ||||
\(590\) | 409.492 | − | 409.492i | 0.694055 | − | 0.694055i | ||||
\(591\) | 121.061 | + | 451.808i | 0.204842 | + | 0.764480i | ||||
\(592\) | −197.674 | + | 52.9667i | −0.333909 | + | 0.0894707i | ||||
\(593\) | 234.771 | + | 234.771i | 0.395903 | + | 0.395903i | 0.876785 | − | 0.480882i | \(-0.159684\pi\) |
−0.480882 | + | 0.876785i | \(0.659684\pi\) | |||||||
\(594\) | −55.7654 | + | 96.5885i | −0.0938811 | + | 0.162607i | ||||
\(595\) | −76.0770 | + | 43.9230i | −0.127860 | + | 0.0738202i | ||||
\(596\) | 82.1436 | − | 306.564i | 0.137825 | − | 0.514369i | ||||
\(597\) | − | 110.478i | − | 0.185056i | ||||||
\(598\) | −565.717 | − | 151.583i | −0.946014 | − | 0.253484i | ||||
\(599\) | −652.908 | −1.09000 | −0.544998 | − | 0.838437i | \(-0.683470\pi\) | ||||
−0.544998 | + | 0.838437i | \(0.683470\pi\) | |||||||
\(600\) | −93.6218 | − | 25.0859i | −0.156036 | − | 0.0418098i | ||||
\(601\) | −32.7846 | − | 56.7846i | −0.0545501 | − | 0.0944835i | 0.837461 | − | 0.546497i | \(-0.184039\pi\) |
−0.892011 | + | 0.452014i | \(0.850706\pi\) | |||||||
\(602\) | 103.529 | + | 59.7724i | 0.171975 | + | 0.0992897i | ||||
\(603\) | 140.217 | − | 140.217i | 0.232533 | − | 0.232533i | ||||
\(604\) | −116.368 | − | 434.291i | −0.192662 | − | 0.719025i | ||||
\(605\) | 706.874 | − | 189.406i | 1.16839 | − | 0.313068i | ||||
\(606\) | 240.431 | + | 240.431i | 0.396750 | + | 0.396750i | ||||
\(607\) | 388.300 | − | 672.555i | 0.639703 | − | 1.10800i | −0.345795 | − | 0.938310i | \(-0.612391\pi\) |
0.985498 | − | 0.169688i | \(-0.0542761\pi\) | |||||||
\(608\) | −18.0666 | + | 10.4308i | −0.0297149 | + | 0.0171559i | ||||
\(609\) | −20.0962 | + | 75.0000i | −0.0329987 | + | 0.123153i | ||||
\(610\) | 750.515i | 1.23035i | ||||||||
\(611\) | 280.650 | + | 1047.40i | 0.459329 | + | 1.71424i | ||||
\(612\) | 30.4308 | 0.0497235 | ||||||||
\(613\) | −410.842 | − | 110.085i | −0.670215 | − | 0.179583i | −0.0923632 | − | 0.995725i | \(-0.529442\pi\) |
−0.577852 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(614\) | 70.0685 | + | 121.362i | 0.114118 | + | 0.197658i | ||||
\(615\) | 429.415 | + | 247.923i | 0.698236 | + | 0.403127i | ||||
\(616\) | −78.5641 | + | 78.5641i | −0.127539 | + | 0.127539i | ||||
\(617\) | −35.0141 | − | 130.674i | −0.0567489 | − | 0.211790i | 0.931729 | − | 0.363154i | \(-0.118300\pi\) |
−0.988478 | + | 0.151364i | \(0.951633\pi\) | |||||||
\(618\) | 253.786 | − | 68.0019i | 0.410658 | − | 0.110035i | ||||
\(619\) | −661.030 | − | 661.030i | −1.06790 | − | 1.06790i | −0.997520 | − | 0.0703796i | \(-0.977579\pi\) |
−0.0703796 | − | 0.997520i | \(-0.522421\pi\) | |||||||
\(620\) | −291.779 | + | 505.377i | −0.470612 | + | 0.815124i | ||||
\(621\) | −143.354 | + | 82.7654i | −0.230844 | + | 0.133278i | ||||
\(622\) | −51.3308 | + | 191.569i | −0.0825254 | + | 0.307989i | ||||
\(623\) | − | 180.666i | − | 0.289994i | ||||||
\(624\) | −78.0000 | + | 45.0333i | −0.125000 | + | 0.0721688i | ||||
\(625\) | 728.184 | 1.16510 | ||||||||
\(626\) | 751.704 | + | 201.419i | 1.20081 | + | 0.321755i | ||||
\(627\) | 48.4730 | + | 83.9578i | 0.0773095 | + | 0.133904i | ||||
\(628\) | 240.009 | + | 138.569i | 0.382180 | + | 0.220652i | ||||
\(629\) | 183.482 | − | 183.482i | 0.291704 | − | 0.291704i | ||||
\(630\) | −19.0192 | − | 70.9808i | −0.0301893 | − | 0.112668i | ||||
\(631\) | 374.899 | − | 100.454i | 0.594135 | − | 0.159198i | 0.0507928 | − | 0.998709i | \(-0.483825\pi\) |
0.543342 | + | 0.839511i | \(0.317159\pi\) | |||||||
\(632\) | −72.2487 | − | 72.2487i | −0.114318 | − | 0.114318i | ||||
\(633\) | 214.600 | − | 371.698i | 0.339020 | − | 0.587201i | ||||
\(634\) | 54.1999 | − | 31.2923i | 0.0854888 | − | 0.0493570i | ||||
\(635\) | −309.771 | + | 1156.08i | −0.487828 | + | 1.82060i | ||||
\(636\) | 338.354i | 0.532003i | ||||||||
\(637\) | −549.917 | −0.863291 | ||||||||
\(638\) | −371.769 | −0.582710 | ||||||||
\(639\) | 155.512 | + | 41.6692i | 0.243367 | + | 0.0652100i | ||||
\(640\) | 37.8564 | + | 65.5692i | 0.0591506 | + | 0.102452i | ||||
\(641\) | 539.869 | + | 311.694i | 0.842229 | + | 0.486261i | 0.858021 | − | 0.513614i | \(-0.171694\pi\) |
−0.0157919 | + | 0.999875i | \(0.505027\pi\) | |||||||
\(642\) | −9.53074 | + | 9.53074i | −0.0148454 | + | 0.0148454i | ||||
\(643\) | 211.661 | + | 789.931i | 0.329178 | + | 1.22851i | 0.910045 | + | 0.414510i | \(0.136047\pi\) |
−0.580867 | + | 0.813999i | \(0.697286\pi\) | |||||||
\(644\) | −159.282 | + | 42.6795i | −0.247332 | + | 0.0662725i | ||||
\(645\) | −267.688 | − | 267.688i | −0.415021 | − | 0.415021i | ||||
\(646\) | 13.2257 | − | 22.9076i | 0.0204732 | − | 0.0354607i | ||||
\(647\) | −248.412 | + | 143.420i | −0.383944 | + | 0.221670i | −0.679533 | − | 0.733645i | \(-0.737817\pi\) |
0.295589 | + | 0.955315i | \(0.404484\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.0101674 | + | 0.0379452i | ||||
\(649\) | 928.708i | 1.43098i | ||||||||
\(650\) | −257.200 | + | 257.200i | −0.395692 | + | 0.395692i | ||||
\(651\) | −195.455 | −0.300238 | ||||||||
\(652\) | 541.894 | + | 145.200i | 0.831125 | + | 0.222699i | ||||
\(653\) | −324.424 | − | 561.919i | −0.496821 | − | 0.860520i | 0.503172 | − | 0.864186i | \(-0.332166\pi\) |
−0.999993 | + | 0.00366668i | \(0.998833\pi\) | |||||||
\(654\) | −326.433 | − | 188.466i | −0.499133 | − | 0.288174i | ||||
\(655\) | −253.808 | + | 253.808i | −0.387493 | + | 0.387493i | ||||
\(656\) | −44.2872 | − | 165.282i | −0.0675110 | − | 0.251954i | ||||
\(657\) | 113.031 | − | 30.2865i | 0.172041 | − | 0.0460982i | ||||
\(658\) | 215.885 | + | 215.885i | 0.328092 | + | 0.328092i | ||||
\(659\) | −228.158 | + | 395.181i | −0.346218 | + | 0.599667i | −0.985574 | − | 0.169243i | \(-0.945868\pi\) |
0.639356 | + | 0.768911i | \(0.279201\pi\) | |||||||
\(660\) | 304.708 | − | 175.923i | 0.461678 | − | 0.266550i | ||||
\(661\) | −84.1814 | + | 314.169i | −0.127355 | + | 0.475294i | −0.999913 | − | 0.0132166i | \(-0.995793\pi\) |
0.872558 | + | 0.488510i | \(0.162460\pi\) | |||||||
\(662\) | 571.247i | 0.862911i | ||||||||
\(663\) | 57.1000 | − | 98.9000i | 0.0861236 | − | 0.149170i | ||||
\(664\) | −83.8667 | −0.126305 | ||||||||
\(665\) | −61.6987 | − | 16.5321i | −0.0927800 | − | 0.0248603i | ||||
\(666\) | 108.531 | + | 187.981i | 0.162959 | + | 0.282253i | ||||
\(667\) | −477.846 | − | 275.885i | −0.716411 | − | 0.413620i | ||||
\(668\) | 395.138 | − | 395.138i | 0.591525 | − | 0.591525i | ||||
\(669\) | −20.6237 | − | 76.9686i | −0.0308276 | − | 0.115050i | ||||
\(670\) | −604.252 | + | 161.909i | −0.901869 | + | 0.241655i | ||||
\(671\) | −851.065 | − | 851.065i | −1.26835 | − | 1.26835i | ||||
\(672\) | −12.6795 | + | 21.9615i | −0.0188683 | + | 0.0326808i | ||||
\(673\) | 904.138 | − | 522.004i | 1.34344 | − | 0.775638i | 0.356133 | − | 0.934435i | \(-0.384095\pi\) |
0.987311 | + | 0.158797i | \(0.0507615\pi\) | |||||||
\(674\) | −233.704 | + | 872.197i | −0.346742 | + | 1.29406i | ||||
\(675\) | 102.804i | 0.152302i | ||||||||
\(676\) | 338.000i | 0.500000i | ||||||||
\(677\) | −193.408 | −0.285684 | −0.142842 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142842 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(678\) | −205.335 | − | 55.0192i | −0.302853 | − | 0.0811493i | ||||
\(679\) | −23.7693 | − | 41.1697i | −0.0350064 | − | 0.0606328i | ||||
\(680\) | −83.1384 | − | 48.0000i | −0.122262 | − | 0.0705882i | ||||
\(681\) | −16.8231 | + | 16.8231i | −0.0247035 | + | 0.0247035i | ||||
\(682\) | −242.214 | − | 903.955i | −0.355153 | − | 1.32545i | ||||
\(683\) | −802.783 | + | 215.105i | −1.17538 | + | 0.314942i | −0.793092 | − | 0.609102i | \(-0.791530\pi\) |
−0.382286 | + | 0.924044i | \(0.624863\pi\) | |||||||
\(684\) | 15.6462 | + | 15.6462i | 0.0228745 | + | 0.0228745i | ||||
\(685\) | 413.885 | − | 716.869i | 0.604211 | − | 1.04652i | ||||
\(686\) | −289.413 | + | 167.093i | −0.421885 | + | 0.243576i | ||||
\(687\) | −182.151 | + | 679.795i | −0.265139 | + | 0.989513i | ||||
\(688\) | 130.641i | 0.189885i | ||||||||
\(689\) | 1099.65 | + | 634.883i | 1.59601 | + | 0.921456i | ||||
\(690\) | 522.200 | 0.756811 | ||||||||
\(691\) | 224.069 | + | 60.0392i | 0.324268 | + | 0.0868874i | 0.417281 | − | 0.908778i | \(-0.362983\pi\) |
−0.0930129 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(692\) | −67.5411 | − | 116.985i | −0.0976027 | − | 0.169053i | ||||
\(693\) | 102.058 | + | 58.9230i | 0.147269 | + | 0.0850260i | ||||
\(694\) | −5.70250 | + | 5.70250i | −0.00821686 | + | 0.00821686i | ||||
\(695\) | −266.229 | − | 993.582i | −0.383064 | − | 1.42961i | ||||
\(696\) | −81.9615 | + | 21.9615i | −0.117761 | + | 0.0315539i | ||||
\(697\) | 153.415 | + | 153.415i | 0.220108 | + | 0.220108i | ||||
\(698\) | −128.103 | + | 221.881i | −0.183529 | + | 0.317882i | ||||
\(699\) | 40.9962 | − | 23.6692i | 0.0586498 | − | 0.0338615i | ||||
\(700\) | −26.5064 | + | 98.9230i | −0.0378662 | + | 0.141319i | ||||
\(701\) | 55.6565i | 0.0793958i | 0.999212 | + | 0.0396979i | \(0.0126396\pi\) | ||||
−0.999212 | + | 0.0396979i | \(0.987360\pi\) | |||||||
\(702\) | 67.5500 | + | 67.5500i | 0.0962250 | + | 0.0962250i | ||||
\(703\) | 188.677 | 0.268388 | ||||||||
\(704\) | −117.282 | − | 31.4256i | −0.166594 | − | 0.0446387i | ||||
\(705\) | −483.415 | − | 837.300i | −0.685695 | − | 1.18766i | ||||
\(706\) | 355.135 | + | 205.037i | 0.503024 | + | 0.290421i | ||||
\(707\) | 254.045 | − | 254.045i | 0.359328 | − | 0.359328i | ||||
\(708\) | 54.8616 | + | 204.746i | 0.0774881 | + | 0.289189i | ||||
\(709\) | −299.954 | + | 80.3724i | −0.423066 | + | 0.113360i | −0.464069 | − | 0.885799i | \(-0.653611\pi\) |
0.0410035 | + | 0.999159i | \(0.486945\pi\) | |||||||
\(710\) | −359.138 | − | 359.138i | −0.505829 | − | 0.505829i | ||||
\(711\) | −54.1865 | + | 93.8538i | −0.0762117 | + | 0.132003i | ||||
\(712\) | 170.985 | − | 98.7180i | 0.240147 | − | 0.138649i | ||||
\(713\) | 359.487 | − | 1341.62i | 0.504189 | − | 1.88166i | ||||
\(714\) | − | 32.1539i | − | 0.0450335i | ||||||
\(715\) | − | 1320.40i | − | 1.84671i | ||||||
\(716\) | 100.441 | 0.140281 | ||||||||
\(717\) | −2.03848 | − | 0.546208i | −0.00284306 | − | 0.000761796i | ||||
\(718\) | 268.277 | + | 464.669i | 0.373645 | + | 0.647172i | ||||
\(719\) | 269.785 | + | 155.760i | 0.375222 | + | 0.216635i | 0.675737 | − | 0.737142i | \(-0.263825\pi\) |
−0.300515 | + | 0.953777i | \(0.597159\pi\) | |||||||
\(720\) | 56.7846 | − | 56.7846i | 0.0788675 | − | 0.0788675i | ||||
\(721\) | −71.8524 | − | 268.157i | −0.0996567 | − | 0.371924i | ||||
\(722\) | −474.557 | + | 127.157i | −0.657281 | + | 0.176118i | ||||
\(723\) | 104.229 | + | 104.229i | 0.144162 | + | 0.144162i | ||||
\(724\) | 302.354 | − | 523.692i | 0.417616 | − | 0.723332i | ||||
\(725\) | −296.769 | + | 171.340i | −0.409337 | + | 0.236331i | ||||
\(726\) | −69.3275 | + | 258.734i | −0.0954925 | + | 0.356383i | ||||
\(727\) | 379.585i | 0.522125i | 0.965322 | + | 0.261062i | \(0.0840728\pi\) | ||||
−0.965322 | + | 0.261062i | \(0.915927\pi\) | |||||||
\(728\) | 47.5833 | + | 82.4167i | 0.0653617 | + | 0.113210i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −356.578 | − | 95.5448i | −0.488463 | − | 0.130883i | ||||
\(731\) | −82.8231 | − | 143.454i | −0.113301 | − | 0.196243i | ||||
\(732\) | −237.904 | − | 137.354i | −0.325005 | − | 0.187642i | ||||
\(733\) | 769.627 | − | 769.627i | 1.04997 | − | 1.04997i | 0.0512852 | − | 0.998684i | \(-0.483668\pi\) |
0.998684 | − | 0.0512852i | \(-0.0163317\pi\) | |||||||
\(734\) | −64.4993 | − | 240.715i | −0.0878737 | − | 0.327949i | ||||
\(735\) | 473.611 | − | 126.904i | 0.644369 | − | 0.172658i | ||||
\(736\) | −127.426 | − | 127.426i | −0.173133 | − | 0.173133i | ||||
\(737\) | 501.606 | − | 868.808i | 0.680606 | − | 1.17884i | ||||
\(738\) | −157.177 | + | 90.7461i | −0.212977 | + | 0.122962i | ||||
\(739\) | 69.2379 | − | 258.399i | 0.0936913 | − | 0.349661i | −0.903126 | − | 0.429375i | \(-0.858734\pi\) |
0.996818 | + | 0.0797139i | \(0.0254007\pi\) | |||||||
\(740\) | − | 684.764i | − | 0.925357i | ||||||
\(741\) | 80.2083 | − | 21.4918i | 0.108243 | − | 0.0290037i | ||||
\(742\) | 357.513 | 0.481823 | ||||||||
\(743\) | −1070.47 | − | 286.832i | −1.44074 | − | 0.386046i | −0.547949 | − | 0.836512i | \(-0.684591\pi\) |
−0.892794 | + | 0.450466i | \(0.851258\pi\) | |||||||
\(744\) | −106.799 | − | 184.981i | −0.143547 | − | 0.248630i | ||||
\(745\) | 919.692 | + | 530.985i | 1.23449 | + | 0.712731i | ||||
\(746\) | 483.606 | − | 483.606i | 0.648266 | − | 0.648266i | ||||
\(747\) | 23.0230 | + | 85.9230i | 0.0308206 | + | 0.115024i | ||||
\(748\) | 148.708 | − | 39.8461i | 0.198807 | − | 0.0532702i | ||||
\(749\) | 10.0704 | + | 10.0704i | 0.0134451 | + | 0.0134451i | ||||
\(750\) | −42.7461 | + | 74.0385i | −0.0569948 | + | 0.0987180i | ||||
\(751\) | 318.631 | − | 183.962i | 0.424275 | − | 0.244955i | −0.272630 | − | 0.962119i | \(-0.587893\pi\) |
0.696905 | + | 0.717164i | \(0.254560\pi\) | |||||||
\(752\) | −86.3538 | + | 322.277i | −0.114832 | + | 0.428560i | ||||
\(753\) | − | 70.5077i | − | 0.0936358i | ||||||
\(754\) | −82.4167 | + | 307.583i | −0.109306 | + | 0.407935i | ||||
\(755\) | 1504.43 | 1.99262 | ||||||||
\(756\) | 25.9808 | + | 6.96152i | 0.0343661 | + | 0.00920837i | ||||
\(757\) | −97.6922 | − | 169.208i | −0.129052 | − | 0.223524i | 0.794258 | − | 0.607581i | \(-0.207860\pi\) |
−0.923309 | + | 0.384057i | \(0.874527\pi\) | |||||||
\(758\) | −353.524 | − | 204.107i | −0.466390 | − | 0.269270i | ||||
\(759\) | −592.161 | + | 592.161i | −0.780186 | + | 0.780186i | ||||
\(760\) | −18.0666 | − | 67.4256i | −0.0237719 | − | 0.0887179i | ||||
\(761\) | 1176.65 | − | 315.282i | 1.54619 | − | 0.414300i | 0.617928 | − | 0.786234i | \(-0.287972\pi\) |
0.928259 | + | 0.371935i | \(0.121305\pi\) | |||||||
\(762\) | −309.771 | − | 309.771i | −0.406523 | − | 0.406523i | ||||
\(763\) | −199.138 | + | 344.917i | −0.260993 | + | 0.452053i | ||||
\(764\) | −281.769 | + | 162.679i | −0.368808 | + | 0.212931i | ||||
\(765\) | −26.3538 | + | 98.3538i | −0.0344494 | + | 0.128567i | ||||
\(766\) | 372.497i | 0.486289i | ||||||||
\(767\) | 768.367 | + | 205.883i | 1.00178 | + | 0.268427i | ||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | −1000.87 | − | 268.181i | −1.30152 | − | 0.348740i | −0.459493 | − | 0.888181i | \(-0.651969\pi\) |
−0.842023 | + | 0.539441i | \(0.818635\pi\) | |||||||
\(770\) | −185.885 | − | 321.962i | −0.241409 | − | 0.418132i | ||||
\(771\) | −464.669 | − | 268.277i | −0.602684 | − | 0.347960i | ||||
\(772\) | 116.301 | − | 116.301i | 0.150649 | − | 0.150649i | ||||
\(773\) | 242.394 | + | 904.626i | 0.313575 | + | 1.17028i | 0.925309 | + | 0.379215i | \(0.123806\pi\) |
−0.611733 | + | 0.791064i | \(0.709527\pi\) | |||||||
\(774\) | 133.844 | − | 35.8634i | 0.172925 | − | 0.0463352i | ||||
\(775\) | −609.962 | − | 609.962i | −0.787048 | − | 0.787048i | ||||
\(776\) | 25.9756 | − | 44.9911i | 0.0334737 | − | 0.0579782i | ||||
\(777\) | 198.625 | − | 114.676i | 0.255631 | − | 0.147588i | ||||
\(778\) | 24.2487 | − | 90.4974i | 0.0311680 | − | 0.116321i | ||||
\(779\) | 157.759i | 0.202515i | ||||||||
\(780\) | −78.0000 | − | 291.100i | −0.100000 | − | 0.373205i | ||||
\(781\) | 814.508 | 1.04290 | ||||||||
\(782\) | 220.708 | + | 59.1384i | 0.282235 | + | 0.0756246i | ||||
\(783\) | 45.0000 | + | 77.9423i | 0.0574713 | + | 0.0995431i | ||||
\(784\) | −146.536 | − | 84.6025i | −0.186908 | − | 0.107911i | ||||
\(785\) | −655.717 | + | 655.717i | −0.835308 | + | 0.835308i | ||||
\(786\) | −34.0038 | − | 126.904i | −0.0432618 | − | 0.161455i | ||||
\(787\) | −925.546 | + | 247.999i | −1.17604 | + | 0.315120i | −0.793356 | − | 0.608758i | \(-0.791668\pi\) |
−0.382687 | + | 0.923878i | \(0.625001\pi\) | |||||||
\(788\) | 381.913 | + | 381.913i | 0.484661 | + | 0.484661i | ||||
\(789\) | −249.100 | + | 431.454i | −0.315716 | + | 0.546836i | ||||
\(790\) | 296.081 | − | 170.942i | 0.374786 | − | 0.216383i | ||||
\(791\) | −58.1347 | + | 216.962i | −0.0734952 | + | 0.274288i | ||||
\(792\) | 128.785i | 0.162607i | ||||||||
\(793\) | −892.800 | + | 515.458i | −1.12585 | + | 0.650010i | ||||
\(794\) | 191.286 | 0.240914 | ||||||||
\(795\) | −1093.58 | − | 293.023i | −1.37557 | − | 0.368582i | ||||
\(796\) | −63.7846 | − | 110.478i | −0.0801314 | − | 0.138792i | ||||
\(797\) | 324.862 | + | 187.559i | 0.407605 | + | 0.235331i | 0.689760 | − | 0.724038i | \(-0.257716\pi\) |
−0.282155 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(798\) | 16.5321 | − | 16.5321i | 0.0207169 | − | 0.0207169i | ||||
\(799\) | −109.492 | − | 408.631i | −0.137037 | − | 0.511428i | ||||
\(800\) | −108.105 | + | 28.9667i | −0.135131 | + | 0.0362083i | ||||
\(801\) | −148.077 | − | 148.077i | −0.184865 | − | 0.184865i | ||||
\(802\) | 135.415 | − | 234.546i | 0.168847 | − | 0.292452i | ||||
\(803\) | 512.696 | − | 296.005i | 0.638476 | − | 0.368624i | ||||
\(804\) | 59.2628 | − | 221.172i | 0.0737099 | − | 0.275089i | ||||
\(805\) | − | 551.769i | − | 0.685428i | ||||||
\(806\) | −801.583 | −0.994520 | ||||||||
\(807\) | −283.608 | −0.351435 | ||||||||
\(808\) | 379.244 | + | 101.618i | 0.469361 | + | 0.125765i | ||||
\(809\) | −376.277 | − | 651.731i | −0.465114 | − | 0.805600i | 0.534093 | − | 0.845426i | \(-0.320653\pi\) |
−0.999207 | + | 0.0398253i | \(0.987320\pi\) | |||||||
\(810\) | −73.7654 | − | 42.5885i | −0.0910684 | − | 0.0525783i | ||||
\(811\) | −49.8071 | + | 49.8071i | −0.0614144 | + | 0.0614144i | −0.737147 | − | 0.675732i | \(-0.763827\pi\) |
0.675732 | + | 0.737147i | \(0.263827\pi\) | |||||||
\(812\) | 23.2051 | + | 86.6025i | 0.0285777 | + | 0.106653i | ||||
\(813\) | −544.078 | + | 145.785i | −0.669223 | + | 0.179318i | ||||
\(814\) | 776.505 | + | 776.505i | 0.953937 | + | 0.953937i | ||||
\(815\) | −938.587 | + | 1625.68i | −1.15164 | + | 1.99470i | ||||
\(816\) | 30.4308 | − | 17.5692i | 0.0372926 | − | 0.0215309i | ||||
\(817\) | 31.1736 | − | 116.342i | 0.0381562 | − | 0.142401i | ||||
\(818\) | − | 785.947i | − | 0.960816i | ||||||
\(819\) | 71.3750 | − | 71.3750i | 0.0871489 | − | 0.0871489i | ||||
\(820\) | 572.554 | 0.698236 | ||||||||
\(821\) | 367.119 | + | 98.3693i | 0.447161 | + | 0.119816i | 0.475371 | − | 0.879786i | \(-0.342314\pi\) |
−0.0282097 | + | 0.999602i | \(0.508981\pi\) | |||||||
\(822\) | 151.492 | + | 262.392i | 0.184297 | + | 0.319212i | ||||
\(823\) | 1149.07 | + | 663.415i | 1.39620 | + | 0.806094i | 0.993992 | − | 0.109456i | \(-0.0349109\pi\) |
0.402204 | + | 0.915550i | \(0.368244\pi\) | |||||||
\(824\) | 214.526 | − | 214.526i | 0.260347 | − | 0.260347i | ||||
\(825\) | 134.611 | + | 502.377i | 0.163165 | + | 0.608942i | ||||
\(826\) | 216.340 | − | 57.9681i | 0.261913 | − | 0.0701792i | ||||
\(827\) | −178.410 | − | 178.410i | −0.215732 | − | 0.215732i | 0.590965 | − | 0.806697i | \(-0.298747\pi\) |
−0.806697 | + | 0.590965i | \(0.798747\pi\) | |||||||
\(828\) | −95.5692 | + | 165.531i | −0.115422 | + | 0.199916i | ||||
\(829\) | −839.258 | + | 484.546i | −1.01237 | + | 0.584495i | −0.911886 | − | 0.410444i | \(-0.865374\pi\) |
−0.100488 | + | 0.994938i | \(0.532041\pi\) | |||||||
\(830\) | 72.6307 | − | 271.061i | 0.0875069 | − | 0.326580i | ||||
\(831\) | − | 233.800i | − | 0.281348i | ||||||
\(832\) | −52.0000 | + | 90.0666i | −0.0625000 | + | 0.108253i | ||||
\(833\) | 214.543 | 0.257555 | ||||||||
\(834\) | 363.676 | + | 97.4468i | 0.436063 | + | 0.116843i | ||||
\(835\) | 934.908 | + | 1619.31i | 1.11965 | + | 1.93929i | ||||
\(836\) | 96.9461 | + | 55.9718i | 0.115964 | + | 0.0669520i | ||||
\(837\) | −160.198 | + | 160.198i | −0.191396 | + | 0.191396i | ||||
\(838\) | −240.715 | − | 898.361i | −0.287250 | − | 1.07203i | ||||
\(839\) | −210.464 | + | 56.3937i | −0.250851 | + | 0.0672154i | −0.382053 | − | 0.924140i | \(-0.624783\pi\) |
0.131202 | + | 0.991356i | \(0.458116\pi\) | |||||||
\(840\) | −60.0000 | − | 60.0000i | −0.0714286 | − | 0.0714286i | ||||
\(841\) | 270.500 | − | 468.520i | 0.321641 | − | 0.557098i | ||||
\(842\) | −568.174 | + | 328.035i | −0.674791 | + | 0.389591i | ||||
\(843\) | −205.119 | + | 765.515i | −0.243321 | + | 0.908085i | ||||
\(844\) | − | 495.597i | − | 0.587201i | ||||||
\(845\) | −1092.43 | − | 292.717i | −1.29282 | − | 0.346410i | ||||
\(846\) | 353.885 | 0.418303 | ||||||||
\(847\) | 273.385 | + | 73.2532i | 0.322768 | + | 0.0864854i | ||||
\(848\) | 195.349 | + | 338.354i | 0.230364 | + | 0.399002i | ||||
\(849\) | −212.031 | − | 122.416i | −0.249742 | − | 0.144188i | ||||
\(850\) | 100.344 | − | 100.344i | 0.118051 | − | 0.118051i | ||||
\(851\) | 421.832 | + | 1574.30i | 0.495690 | + | 1.84994i | ||||
\(852\) | 179.569 | − | 48.1154i | 0.210762 | − | 0.0564735i | ||||
\(853\) | −173.527 | − | 173.527i | −0.203432 | − | 0.203432i | 0.598037 | − | 0.801469i | \(-0.295948\pi\) |
−0.801469 | + | 0.598037i | \(0.795948\pi\) | |||||||
\(854\) | −145.131 | + | 251.375i | −0.169943 | + | 0.294350i | ||||
\(855\) | −64.1192 | + | 37.0192i | −0.0749932 | + | 0.0432974i | ||||
\(856\) | −4.02817 | + | 15.0333i | −0.00470580 | + | 0.0175623i | ||||
\(857\) | − | 616.543i | − | 0.719421i | −0.933064 | − | 0.359710i | \(-0.882876\pi\) | ||
0.933064 | − | 0.359710i | \(-0.117124\pi\) | |||||||
\(858\) | 418.550 | + | 241.650i | 0.487820 | + | 0.281643i | ||||
\(859\) | 566.398 | 0.659370 | 0.329685 | − | 0.944091i | \(-0.393058\pi\) | ||||
0.329685 | + | 0.944091i | \(0.393058\pi\) | |||||||
\(860\) | −422.238 | − | 113.138i | −0.490975 | − | 0.131556i | ||||
\(861\) | 95.8846 | + | 166.077i | 0.111364 | + | 0.192888i | ||||
\(862\) | 39.2999 | + | 22.6898i | 0.0455915 | + | 0.0263223i | ||||
\(863\) | 656.627 | − | 656.627i | 0.760866 | − | 0.760866i | −0.215613 | − | 0.976479i | \(-0.569175\pi\) |
0.976479 | + | 0.215613i | \(0.0691751\pi\) | |||||||
\(864\) | 7.60770 | + | 28.3923i | 0.00880520 | + | 0.0328615i | ||||
\(865\) | 436.592 | − | 116.985i | 0.504731 | − | 0.135242i | ||||
\(866\) | −196.215 | − | 196.215i | −0.226577 | − | 0.226577i | ||||
\(867\) | 228.004 | − | 394.915i | 0.262981 | − | 0.455496i | ||||
\(868\) | −195.455 | + | 112.846i | −0.225179 | + | 0.130007i | ||||
\(869\) | −141.904 | + | 529.592i | −0.163296 | + | 0.609427i | ||||
\(870\) | − | 283.923i | − | 0.326348i | ||||||
\(871\) | −607.608 | − | 607.608i | −0.697598 | − | 0.697598i | ||||
\(872\) | −435.244 | −0.499133 | ||||||||
\(873\) | −53.2250 | − | 14.2616i | −0.0609679 | − | 0.0163363i | ||||
\(874\) | 83.0718 | + | 143.885i | 0.0950478 | + | 0.164628i | ||||
\(875\) | 78.2309 | + | 45.1666i | 0.0894067 | + | 0.0516190i | ||||
\(876\) | 95.5448 | − | 95.5448i | 0.109069 | − | 0.109069i | ||||
\(877\) | 172.789 | + | 644.858i | 0.197023 | + | 0.735300i | 0.991734 | + | 0.128312i | \(0.0409559\pi\) |
−0.794711 | + | 0.606988i | \(0.792377\pi\) | |||||||
\(878\) | −56.6391 | + | 15.1764i | −0.0645093 | + | 0.0172852i | ||||
\(879\) | 364.550 | + | 364.550i | 0.414733 | + | 0.414733i | ||||
\(880\) | 203.138 | − | 351.846i | 0.230839 | − | 0.399825i | ||||
\(881\) | −880.173 | + | 508.168i | −0.999061 | + | 0.576808i | −0.907970 | − | 0.419034i | \(-0.862369\pi\) |
−0.0910907 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(882\) | −46.4500 | + | 173.354i | −0.0526644 | + | 0.196546i | ||||
\(883\) | 785.277i | 0.889328i | 0.895697 | + | 0.444664i | \(0.146677\pi\) | ||||
−0.895697 | + | 0.444664i | \(0.853323\pi\) | |||||||
\(884\) | − | 131.867i | − | 0.149170i | ||||||
\(885\) | −709.261 | −0.801425 | ||||||||
\(886\) | 27.2820 | + | 7.31020i | 0.0307924 | + | 0.00825079i | ||||
\(887\) | −642.531 | − | 1112.90i | −0.724386 | − | 1.25467i | −0.959226 | − | 0.282640i | \(-0.908790\pi\) |
0.234840 | − | 0.972034i | \(-0.424543\pi\) | |||||||
\(888\) | 217.061 | + | 125.321i | 0.244439 | + | 0.141127i | ||||
\(889\) | −327.311 | + | 327.311i | −0.368179 | + | 0.368179i | ||||
\(890\) | 170.985 | + | 638.123i | 0.192117 | + | 0.716992i | ||||
\(891\) | 131.942 | − | 35.3538i | 0.148083 | − | 0.0396788i | ||||
\(892\) | −65.0615 | − | 65.0615i | −0.0729389 | − | 0.0729389i | ||||
\(893\) | 153.804 | − | 266.396i | 0.172233 | − | 0.298316i | ||||
\(894\) | −336.631 | + | 194.354i | −0.376544 | + | 0.217398i | ||||
\(895\) | −86.9845 | + | 324.631i | −0.0971894 | + | 0.362716i | ||||
\(896\) | 29.2820i | 0.0326808i | ||||||||
\(897\) | 358.650 | + | 621.200i | 0.399833 | + | 0.692531i | ||||
\(898\) | −186.613 | −0.207809 | ||||||||
\(899\) | −729.449 | − | 195.455i | −0.811400 | − | 0.217414i | ||||
\(900\) | 59.3538 | + | 102.804i | 0.0659487 | + | 0.114226i | ||||
\(901\) | −429.015 | − | 247.692i | −0.476155 | − | 0.274908i | ||||
\(902\) | −649.261 | + | 649.261i | −0.719802 | + | 0.719802i | ||||
\(903\) | −37.8942 | − | 141.423i | −0.0419648 | − | 0.156615i | ||||
\(904\) | −237.100 | + | 63.5307i | −0.262279 | + | 0.0702774i | ||||
\(905\) | 1430.75 | + | 1430.75i | 1.58094 | + | 1.58094i | ||||
\(906\) | −275.329 | + | 476.885i | −0.303896 | + | 0.526363i | ||||
\(907\) | −241.501 | + | 139.431i | −0.266264 | + | 0.153727i | −0.627189 | − | 0.778867i | \(-0.715794\pi\) |
0.360925 | + | 0.932595i | \(0.382461\pi\) | |||||||
\(908\) | −7.11027 | + | 26.5359i | −0.00783070 | + | 0.0292246i | ||||
\(909\) | − | 416.438i | − | 0.458128i | ||||||
\(910\) | −307.583 | + | 82.4167i | −0.338004 | + | 0.0905678i | ||||
\(911\) | 86.7668 | 0.0952434 | 0.0476217 | − | 0.998865i | \(-0.484836\pi\) | ||||
0.0476217 | + | 0.998865i | \(0.484836\pi\) | |||||||
\(912\) | 24.6795 | + | 6.61285i | 0.0270608 | + | 0.00725093i | ||||
\(913\) | 225.015 | + | 389.738i | 0.246457 | + | 0.426876i | ||||
\(914\) | 361.165 | + | 208.519i | 0.395147 | + | 0.228138i | ||||
\(915\) | 649.965 | − | 649.965i | 0.710345 | − | 0.710345i | ||||
\(916\) | 210.329 | + | 784.960i | 0.229617 | + | 0.856943i | ||||
\(917\) | −134.090 | + | 35.9292i | −0.146226 | + | 0.0391813i | ||||
\(918\) | −26.3538 | − | 26.3538i | −0.0287079 | − | 0.0287079i | ||||
\(919\) | −288.431 | + | 499.577i | −0.313853 | + | 0.543609i | −0.979193 | − | 0.202931i | \(-0.934953\pi\) |
0.665340 | + | 0.746540i | \(0.268287\pi\) | |||||||
\(920\) | 522.200 | − | 301.492i | 0.567609 | − | 0.327709i | ||||
\(921\) | 44.4217 | − | 165.784i | 0.0482320 | − | 0.180004i | ||||
\(922\) | − | 664.246i | − | 0.720440i | ||||||
\(923\) | 180.566 | − | 673.883i | 0.195630 | − | 0.730101i | ||||
\(924\) | 136.077 | 0.147269 | ||||||||
\(925\) | 977.727 | + | 261.981i | 1.05700 | + | 0.283223i | ||||
\(926\) | −462.599 | − | 801.245i | −0.499567 | − | 0.865276i | ||||
\(927\) | −278.677 | − | 160.894i | −0.300622 | − | 0.173564i | ||||
\(928\) | −69.2820 | + | 69.2820i | −0.0746574 | + | 0.0746574i | ||||
\(929\) | 3.85917 | + | 14.4026i | 0.00415411 | + | 0.0155034i | 0.967972 | − | 0.251059i | \(-0.0807788\pi\) |
−0.963818 | + | 0.266562i | \(0.914112\pi\) | |||||||
\(930\) | 690.358 | − | 184.981i | 0.742320 | − | 0.198904i | ||||
\(931\) | 110.309 | + | 110.309i | 0.118484 | + | 0.118484i | ||||
\(932\) | 27.3308 | − | 47.3384i | 0.0293249 | − | 0.0507922i | ||||
\(933\) | 210.358 | − | 121.450i | 0.225464 | − | 0.130172i | ||||
\(934\) | 145.183 | − | 541.832i | 0.155443 | − | 0.580120i | ||||
\(935\) | 515.138i | 0.550950i | ||||||||
\(936\) | 106.550 | + | 28.5500i | 0.113835 | + | 0.0305021i | ||||
\(937\) | 700.477 | 0.747574 | 0.373787 | − | 0.927515i | \(-0.378059\pi\) | ||||
0.373787 | + | 0.927515i | \(0.378059\pi\) | |||||||
\(938\) | −233.695 | − | 62.6185i | −0.249142 | − | 0.0667575i | ||||
\(939\) | −476.561 | − | 825.429i | −0.507520 | − | 0.879051i | ||||
\(940\) | −966.831 | − | 558.200i | −1.02854 | − | 0.593830i | ||||
\(941\) | −1147.05 | + | 1147.05i | −1.21897 | + | 1.21897i | −0.250983 | + | 0.967992i | \(0.580754\pi\) |
−0.967992 | + | 0.250983i | \(0.919246\pi\) | |||||||
\(942\) | −87.8494 | − | 327.858i | −0.0932583 | − | 0.348045i | ||||
\(943\) | −1316.32 | + | 352.708i | −1.39589 | + | 0.374027i | ||||
\(944\) | 173.072 | + | 173.072i | 0.183339 | + | 0.183339i | ||||
\(945\) | −45.0000 | + | 77.9423i | −0.0476190 | + | 0.0824786i | ||||
\(946\) | 607.104 | − | 350.512i | 0.641759 | − | 0.370520i | ||||
\(947\) | 317.902 | − | 1186.43i | 0.335694 | − | 1.25283i | −0.567420 | − | 0.823428i | \(-0.692059\pi\) |
0.903115 | − | 0.429400i | \(-0.141275\pi\) | |||||||
\(948\) | 125.138i | 0.132003i | ||||||||
\(949\) | −131.241 | − | 489.800i | −0.138295 | − | 0.516122i | ||||
\(950\) | 103.184 | 0.108615 | ||||||||
\(951\) | −74.0385 | − | 19.8385i | −0.0778533 | − | 0.0208607i | ||||
\(952\) | −18.5641 | − | 32.1539i | −0.0195001 | − | 0.0337751i | ||||
\(953\) | −941.038 | − | 543.309i | −0.987449 | − | 0.570104i | −0.0829379 | − | 0.996555i | \(-0.526430\pi\) |
−0.904511 | + | 0.426451i | \(0.859764\pi\) | |||||||
\(954\) | 293.023 | − | 293.023i | 0.307152 | − | 0.307152i | ||||
\(955\) | −281.769 | − | 1051.58i | −0.295046 | − | 1.10113i | ||||
\(956\) | −2.35383 | + | 0.630707i | −0.00246216 | + | 0.000659735i | ||||
\(957\) | 321.962 | + | 321.962i | 0.336428 | + | 0.336428i | ||||
\(958\) | −254.536 | + | 440.869i | −0.265695 | + | 0.460197i | ||||
\(959\) | 277.250 | − | 160.070i | 0.289103 | − | 0.166914i | ||||
\(960\) | 24.0000 | − | 89.5692i | 0.0250000 | − | 0.0933013i | ||||
\(961\) | − | 939.993i | − | 0.978141i | ||||||
\(962\) | 814.583 | − | 470.300i | 0.846760 | − | 0.488877i | ||||
\(963\) | 16.5077 | 0.0171420 | ||||||||
\(964\) | 164.406 | + | 44.0526i | 0.170546 | + | 0.0456977i | ||||
\(965\) | 275.172 | + | 476.611i | 0.285152 | + | 0.493898i | ||||
\(966\) | 174.904 | + | 100.981i | 0.181060 | + | 0.104535i | ||||
\(967\) | 827.831 | − | 827.831i | 0.856081 | − | 0.856081i | −0.134793 | − | 0.990874i | \(-0.543037\pi\) |
0.990874 | + | 0.134793i | \(0.0430368\pi\) | |||||||
\(968\) | 80.0526 | + | 298.760i | 0.0826989 | + | 0.308637i | ||||
\(969\) | −31.2923 | + | 8.38476i | −0.0322934 | + | 0.00865300i | ||||
\(970\) | 122.918 | + | 122.918i | 0.126719 | + | 0.126719i | ||||
\(971\) | 571.850 | − | 990.473i | 0.588929 | − | 1.02005i | −0.405444 | − | 0.914120i | \(-0.632883\pi\) |
0.994373 | − | 0.105935i | \(-0.0337835\pi\) | |||||||
\(972\) | 27.0000 | − | 15.5885i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | 102.965 | − | 384.269i | 0.105822 | − | 0.394932i | ||||
\(974\) | 274.000i | 0.281314i | ||||||||
\(975\) | 445.483 | 0.456906 | ||||||||
\(976\) | −317.205 | −0.325005 | ||||||||
\(977\) | 331.990 | + | 88.9564i | 0.339805 | + | 0.0910505i | 0.424686 | − | 0.905341i | \(-0.360384\pi\) |
−0.0848811 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(978\) | −343.547 | − | 595.040i | −0.351275 | − | 0.608426i | ||||
\(979\) | −917.507 | − | 529.723i | −0.937188 | − | 0.541086i | ||||
\(980\) | 400.344 | − | 400.344i | 0.408514 | − | 0.408514i | ||||
\(981\) | 119.483 | + | 445.915i | 0.121797 | + | 0.454552i | ||||
\(982\) | −31.5167 | + | 8.44486i | −0.0320944 | + | 0.00859966i | ||||
\(983\) | 630.073 | + | 630.073i | 0.640970 | + | 0.640970i | 0.950794 | − | 0.309824i | \(-0.100270\pi\) |
−0.309824 | + | 0.950794i | \(0.600270\pi\) | |||||||
\(984\) | −104.785 | + | 181.492i | −0.106488 | + | 0.184443i | ||||
\(985\) | −1565.11 | + | 903.615i | −1.58894 | + | 0.917376i | ||||
\(986\) | 32.1539 | − | 120.000i | 0.0326104 | − | 0.121704i | ||||
\(987\) | − | 373.923i | − | 0.378848i | ||||||
\(988\) | 67.8001 | − | 67.8001i | 0.0686236 | − | 0.0686236i | ||||
\(989\) | 1040.44 | 1.05201 | ||||||||
\(990\) | −416.238 | − | 111.531i | −0.420443 | − | 0.112657i | ||||
\(991\) | 478.369 | + | 828.560i | 0.482714 | + | 0.836085i | 0.999803 | − | 0.0198468i | \(-0.00631784\pi\) |
−0.517089 | + | 0.855931i | \(0.672985\pi\) | |||||||
\(992\) | −213.597 | − | 123.321i | −0.215320 | − | 0.124315i | ||||
\(993\) | 494.715 | − | 494.715i | 0.498202 | − | 0.498202i | ||||
\(994\) | −50.8399 | − | 189.737i | −0.0511468 | − | 0.190883i | ||||
\(995\) | 412.310 | − | 110.478i | 0.414382 | − | 0.111033i | ||||
\(996\) | 72.6307 | + | 72.6307i | 0.0729224 | + | 0.0729224i | ||||
\(997\) | 83.5845 | − | 144.773i | 0.0838360 | − | 0.145208i | −0.821059 | − | 0.570844i | \(-0.806616\pi\) |
0.904895 | + | 0.425636i | \(0.139949\pi\) | |||||||
\(998\) | 278.460 | − | 160.769i | 0.279018 | − | 0.161091i | ||||
\(999\) | 68.8057 | − | 256.786i | 0.0688746 | − | 0.257044i |
(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 | 78.3.l.a.67.1 | yes | 4 | |
3.2 | odd | 2 | 234.3.bb.c.145.1 | 4 | |||
13.2 | odd | 12 | 1014.3.f.d.775.1 | 4 | |||
13.3 | even | 3 | 1014.3.f.e.577.1 | 4 | |||
13.7 | odd | 12 | inner | 78.3.l.a.7.1 | ✓ | 4 | |
13.10 | even | 6 | 1014.3.f.d.577.1 | 4 | |||
13.11 | odd | 12 | 1014.3.f.e.775.1 | 4 | |||
39.20 | even | 12 | 234.3.bb.c.163.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.a.7.1 | ✓ | 4 | 13.7 | odd | 12 | inner | |
78.3.l.a.67.1 | yes | 4 | 1.1 | even | 1 | trivial | |
234.3.bb.c.145.1 | 4 | 3.2 | odd | 2 | |||
234.3.bb.c.163.1 | 4 | 39.20 | even | 12 | |||
1014.3.f.d.577.1 | 4 | 13.10 | even | 6 | |||
1014.3.f.d.775.1 | 4 | 13.2 | odd | 12 | |||
1014.3.f.e.577.1 | 4 | 13.3 | even | 3 | |||
1014.3.f.e.775.1 | 4 | 13.11 | odd | 12 |