Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (of order \(4\), 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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 93.3 | ||
Root | \(-2.41818 - 2.41818i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.93 |
Dual form | 230.3.f.a.47.3 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | −2.41818 | − | 2.41818i | −0.806061 | − | 0.806061i | 0.177974 | − | 0.984035i | \(-0.443046\pi\) |
−0.984035 | + | 0.177974i | \(0.943046\pi\) | |||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −4.87518 | − | 1.11024i | −0.975036 | − | 0.222047i | ||||
\(6\) | 4.83636 | 0.806061 | ||||||||
\(7\) | 3.71756 | − | 3.71756i | 0.531079 | − | 0.531079i | −0.389814 | − | 0.920894i | \(-0.627461\pi\) |
0.920894 | + | 0.389814i | \(0.127461\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.69521i | 0.299468i | ||||||||
\(10\) | 5.98542 | − | 3.76494i | 0.598542 | − | 0.376494i | ||||
\(11\) | 5.66411 | 0.514919 | 0.257459 | − | 0.966289i | \(-0.417115\pi\) | ||||
0.257459 | + | 0.966289i | \(0.417115\pi\) | |||||||
\(12\) | −4.83636 | + | 4.83636i | −0.403030 | + | 0.403030i | ||||
\(13\) | −11.2692 | − | 11.2692i | −0.866863 | − | 0.866863i | 0.125261 | − | 0.992124i | \(-0.460023\pi\) |
−0.992124 | + | 0.125261i | \(0.960023\pi\) | |||||||
\(14\) | 7.43511i | 0.531079i | ||||||||
\(15\) | 9.10432 | + | 14.4738i | 0.606955 | + | 0.964922i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −19.5050 | + | 19.5050i | −1.14735 | + | 1.14735i | −0.160278 | + | 0.987072i | \(0.551239\pi\) |
−0.987072 | + | 0.160278i | \(0.948761\pi\) | |||||||
\(18\) | −2.69521 | − | 2.69521i | −0.149734 | − | 0.149734i | ||||
\(19\) | 21.5835i | 1.13597i | 0.823038 | + | 0.567986i | \(0.192277\pi\) | ||||
−0.823038 | + | 0.567986i | \(0.807723\pi\) | |||||||
\(20\) | −2.22047 | + | 9.75036i | −0.111024 | + | 0.487518i | ||||
\(21\) | −17.9795 | −0.856164 | ||||||||
\(22\) | −5.66411 | + | 5.66411i | −0.257459 | + | 0.257459i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | − | 9.67273i | − | 0.403030i | ||||||
\(25\) | 22.5348 | + | 10.8252i | 0.901390 | + | 0.433008i | ||||
\(26\) | 22.5384 | 0.866863 | ||||||||
\(27\) | −15.2461 | + | 15.2461i | −0.564671 | + | 0.564671i | ||||
\(28\) | −7.43511 | − | 7.43511i | −0.265540 | − | 0.265540i | ||||
\(29\) | 38.9519i | 1.34317i | 0.740928 | + | 0.671585i | \(0.234386\pi\) | ||||
−0.740928 | + | 0.671585i | \(0.765614\pi\) | |||||||
\(30\) | −23.5781 | − | 5.36951i | −0.785938 | − | 0.178984i | ||||
\(31\) | −39.9726 | −1.28944 | −0.644720 | − | 0.764419i | \(-0.723026\pi\) | ||||
−0.644720 | + | 0.764419i | \(0.723026\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −13.6968 | − | 13.6968i | −0.415056 | − | 0.415056i | ||||
\(34\) | − | 39.0099i | − | 1.14735i | ||||||
\(35\) | −22.2511 | + | 13.9964i | −0.635746 | + | 0.399897i | ||||
\(36\) | 5.39042 | 0.149734 | ||||||||
\(37\) | 34.6377 | − | 34.6377i | 0.936154 | − | 0.936154i | −0.0619270 | − | 0.998081i | \(-0.519725\pi\) |
0.998081 | + | 0.0619270i | \(0.0197246\pi\) | |||||||
\(38\) | −21.5835 | − | 21.5835i | −0.567986 | − | 0.567986i | ||||
\(39\) | 54.5020i | 1.39749i | ||||||||
\(40\) | −7.52989 | − | 11.9708i | −0.188247 | − | 0.299271i | ||||
\(41\) | 65.8264 | 1.60552 | 0.802761 | − | 0.596301i | \(-0.203363\pi\) | ||||
0.802761 | + | 0.596301i | \(0.203363\pi\) | |||||||
\(42\) | 17.9795 | − | 17.9795i | 0.428082 | − | 0.428082i | ||||
\(43\) | −35.5529 | − | 35.5529i | −0.826812 | − | 0.826812i | 0.160263 | − | 0.987074i | \(-0.448766\pi\) |
−0.987074 | + | 0.160263i | \(0.948766\pi\) | |||||||
\(44\) | − | 11.3282i | − | 0.257459i | ||||||
\(45\) | 2.99232 | − | 13.1396i | 0.0664960 | − | 0.291992i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −45.5584 | + | 45.5584i | −0.969327 | + | 0.969327i | −0.999543 | − | 0.0302163i | \(-0.990380\pi\) |
0.0302163 | + | 0.999543i | \(0.490380\pi\) | |||||||
\(48\) | 9.67273 | + | 9.67273i | 0.201515 | + | 0.201515i | ||||
\(49\) | 21.3596i | 0.435910i | ||||||||
\(50\) | −33.3600 | + | 11.7095i | −0.667199 | + | 0.234191i | ||||
\(51\) | 94.3331 | 1.84967 | ||||||||
\(52\) | −22.5384 | + | 22.5384i | −0.433431 | + | 0.433431i | ||||
\(53\) | −33.1565 | − | 33.1565i | −0.625595 | − | 0.625595i | 0.321361 | − | 0.946957i | \(-0.395860\pi\) |
−0.946957 | + | 0.321361i | \(0.895860\pi\) | |||||||
\(54\) | − | 30.4923i | − | 0.564671i | ||||||
\(55\) | −27.6135 | − | 6.28850i | −0.502064 | − | 0.114336i | ||||
\(56\) | 14.8702 | 0.265540 | ||||||||
\(57\) | 52.1928 | − | 52.1928i | 0.915662 | − | 0.915662i | ||||
\(58\) | −38.9519 | − | 38.9519i | −0.671585 | − | 0.671585i | ||||
\(59\) | − | 32.5546i | − | 0.551773i | −0.961190 | − | 0.275886i | \(-0.911029\pi\) | ||
0.961190 | − | 0.275886i | \(-0.0889714\pi\) | |||||||
\(60\) | 28.9477 | − | 18.2086i | 0.482461 | − | 0.303477i | ||||
\(61\) | −17.0786 | −0.279978 | −0.139989 | − | 0.990153i | \(-0.544707\pi\) | ||||
−0.139989 | + | 0.990153i | \(0.544707\pi\) | |||||||
\(62\) | 39.9726 | − | 39.9726i | 0.644720 | − | 0.644720i | ||||
\(63\) | 10.0196 | + | 10.0196i | 0.159041 | + | 0.159041i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 42.4280 | + | 67.4510i | 0.652738 | + | 1.03771i | ||||
\(66\) | 27.3937 | 0.415056 | ||||||||
\(67\) | −15.3270 | + | 15.3270i | −0.228761 | + | 0.228761i | −0.812175 | − | 0.583414i | \(-0.801717\pi\) |
0.583414 | + | 0.812175i | \(0.301717\pi\) | |||||||
\(68\) | 39.0099 | + | 39.0099i | 0.573675 | + | 0.573675i | ||||
\(69\) | − | 16.4009i | − | 0.237694i | ||||||
\(70\) | 8.25473 | − | 36.2475i | 0.117925 | − | 0.517821i | ||||
\(71\) | 38.4278 | 0.541237 | 0.270619 | − | 0.962687i | \(-0.412772\pi\) | ||||
0.270619 | + | 0.962687i | \(0.412772\pi\) | |||||||
\(72\) | −5.39042 | + | 5.39042i | −0.0748670 | + | 0.0748670i | ||||
\(73\) | −14.7326 | − | 14.7326i | −0.201817 | − | 0.201817i | 0.598961 | − | 0.800778i | \(-0.295580\pi\) |
−0.800778 | + | 0.598961i | \(0.795580\pi\) | |||||||
\(74\) | 69.2754i | 0.936154i | ||||||||
\(75\) | −28.3158 | − | 80.6704i | −0.377544 | − | 1.07561i | ||||
\(76\) | 43.1669 | 0.567986 | ||||||||
\(77\) | 21.0566 | − | 21.0566i | 0.273463 | − | 0.273463i | ||||
\(78\) | −54.5020 | − | 54.5020i | −0.698744 | − | 0.698744i | ||||
\(79\) | 32.7703i | 0.414814i | 0.978255 | + | 0.207407i | \(0.0665024\pi\) | ||||
−0.978255 | + | 0.207407i | \(0.933498\pi\) | |||||||
\(80\) | 19.5007 | + | 4.44094i | 0.243759 | + | 0.0555118i | ||||
\(81\) | 97.9927 | 1.20979 | ||||||||
\(82\) | −65.8264 | + | 65.8264i | −0.802761 | + | 0.802761i | ||||
\(83\) | −1.79999 | − | 1.79999i | −0.0216867 | − | 0.0216867i | 0.696180 | − | 0.717867i | \(-0.254881\pi\) |
−0.717867 | + | 0.696180i | \(0.754881\pi\) | |||||||
\(84\) | 35.9589i | 0.428082i | ||||||||
\(85\) | 116.745 | − | 73.4350i | 1.37347 | − | 0.863942i | ||||
\(86\) | 71.1058 | 0.826812 | ||||||||
\(87\) | 94.1928 | − | 94.1928i | 1.08268 | − | 1.08268i | ||||
\(88\) | 11.3282 | + | 11.3282i | 0.128730 | + | 0.128730i | ||||
\(89\) | 130.635i | 1.46781i | 0.679253 | + | 0.733904i | \(0.262304\pi\) | ||||
−0.679253 | + | 0.733904i | \(0.737696\pi\) | |||||||
\(90\) | 10.1473 | + | 16.1320i | 0.112748 | + | 0.179244i | ||||
\(91\) | −83.7879 | −0.920746 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 96.6611 | + | 96.6611i | 1.03937 | + | 1.03937i | ||||
\(94\) | − | 91.1167i | − | 0.969327i | ||||||
\(95\) | 23.9627 | − | 105.223i | 0.252239 | − | 1.10761i | ||||
\(96\) | −19.3455 | −0.201515 | ||||||||
\(97\) | 46.8143 | − | 46.8143i | 0.482622 | − | 0.482622i | −0.423346 | − | 0.905968i | \(-0.639145\pi\) |
0.905968 | + | 0.423346i | \(0.139145\pi\) | |||||||
\(98\) | −21.3596 | − | 21.3596i | −0.217955 | − | 0.217955i | ||||
\(99\) | 15.2660i | 0.154202i | ||||||||
\(100\) | 21.6504 | − | 45.0695i | 0.216504 | − | 0.450695i | ||||
\(101\) | −153.927 | −1.52403 | −0.762016 | − | 0.647558i | \(-0.775790\pi\) | ||||
−0.762016 | + | 0.647558i | \(0.775790\pi\) | |||||||
\(102\) | −94.3331 | + | 94.3331i | −0.924834 | + | 0.924834i | ||||
\(103\) | 12.7878 | + | 12.7878i | 0.124153 | + | 0.124153i | 0.766453 | − | 0.642300i | \(-0.222020\pi\) |
−0.642300 | + | 0.766453i | \(0.722020\pi\) | |||||||
\(104\) | − | 45.0769i | − | 0.433431i | ||||||
\(105\) | 87.6531 | + | 19.9614i | 0.834791 | + | 0.190109i | ||||
\(106\) | 66.3131 | 0.625595 | ||||||||
\(107\) | −126.065 | + | 126.065i | −1.17817 | + | 1.17817i | −0.197965 | + | 0.980209i | \(0.563433\pi\) |
−0.980209 | + | 0.197965i | \(0.936567\pi\) | |||||||
\(108\) | 30.4923 | + | 30.4923i | 0.282336 | + | 0.282336i | ||||
\(109\) | − | 169.079i | − | 1.55119i | −0.631234 | − | 0.775593i | \(-0.717451\pi\) | ||
0.631234 | − | 0.775593i | \(-0.282549\pi\) | |||||||
\(110\) | 33.9020 | − | 21.3250i | 0.308200 | − | 0.193864i | ||||
\(111\) | −167.520 | −1.50919 | ||||||||
\(112\) | −14.8702 | + | 14.8702i | −0.132770 | + | 0.132770i | ||||
\(113\) | −44.1668 | − | 44.1668i | −0.390857 | − | 0.390857i | 0.484136 | − | 0.874993i | \(-0.339134\pi\) |
−0.874993 | + | 0.484136i | \(0.839134\pi\) | |||||||
\(114\) | 104.386i | 0.915662i | ||||||||
\(115\) | −12.7675 | − | 20.2975i | −0.111022 | − | 0.176500i | ||||
\(116\) | 77.9038 | 0.671585 | ||||||||
\(117\) | 30.3729 | − | 30.3729i | 0.259598 | − | 0.259598i | ||||
\(118\) | 32.5546 | + | 32.5546i | 0.275886 | + | 0.275886i | ||||
\(119\) | 145.021i | 1.21867i | ||||||||
\(120\) | −10.7390 | + | 47.1563i | −0.0894918 | + | 0.392969i | ||||
\(121\) | −88.9179 | −0.734858 | ||||||||
\(122\) | 17.0786 | − | 17.0786i | 0.139989 | − | 0.139989i | ||||
\(123\) | −159.180 | − | 159.180i | −1.29415 | − | 1.29415i | ||||
\(124\) | 79.9452i | 0.644720i | ||||||||
\(125\) | −97.8424 | − | 77.7937i | −0.782739 | − | 0.622350i | ||||
\(126\) | −20.0392 | −0.159041 | ||||||||
\(127\) | −85.3322 | + | 85.3322i | −0.671907 | + | 0.671907i | −0.958155 | − | 0.286248i | \(-0.907592\pi\) |
0.286248 | + | 0.958155i | \(0.407592\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 171.947i | 1.33292i | ||||||||
\(130\) | −109.879 | − | 25.0230i | −0.845222 | − | 0.192485i | ||||
\(131\) | −134.789 | −1.02892 | −0.514460 | − | 0.857514i | \(-0.672008\pi\) | ||||
−0.514460 | + | 0.857514i | \(0.672008\pi\) | |||||||
\(132\) | −27.3937 | + | 27.3937i | −0.207528 | + | 0.207528i | ||||
\(133\) | 80.2377 | + | 80.2377i | 0.603291 | + | 0.603291i | ||||
\(134\) | − | 30.6540i | − | 0.228761i | ||||||
\(135\) | 91.2544 | − | 57.4008i | 0.675959 | − | 0.425191i | ||||
\(136\) | −78.0198 | −0.573675 | ||||||||
\(137\) | −31.3211 | + | 31.3211i | −0.228621 | + | 0.228621i | −0.812116 | − | 0.583495i | \(-0.801685\pi\) |
0.583495 | + | 0.812116i | \(0.301685\pi\) | |||||||
\(138\) | 16.4009 | + | 16.4009i | 0.118847 | + | 0.118847i | ||||
\(139\) | − | 47.8983i | − | 0.344592i | −0.985045 | − | 0.172296i | \(-0.944881\pi\) | ||
0.985045 | − | 0.172296i | \(-0.0551186\pi\) | |||||||
\(140\) | 27.9928 | + | 44.5022i | 0.199948 | + | 0.317873i | ||||
\(141\) | 220.337 | 1.56267 | ||||||||
\(142\) | −38.4278 | + | 38.4278i | −0.270619 | + | 0.270619i | ||||
\(143\) | −63.8301 | − | 63.8301i | −0.446364 | − | 0.446364i | ||||
\(144\) | − | 10.7808i | − | 0.0748670i | ||||||
\(145\) | 43.2458 | − | 189.898i | 0.298247 | − | 1.30964i | ||||
\(146\) | 29.4653 | 0.201817 | ||||||||
\(147\) | 51.6513 | − | 51.6513i | 0.351370 | − | 0.351370i | ||||
\(148\) | −69.2754 | − | 69.2754i | −0.468077 | − | 0.468077i | ||||
\(149\) | − | 145.445i | − | 0.976144i | −0.872803 | − | 0.488072i | \(-0.837700\pi\) | ||
0.872803 | − | 0.488072i | \(-0.162300\pi\) | |||||||
\(150\) | 108.986 | + | 52.3546i | 0.726575 | + | 0.349031i | ||||
\(151\) | −146.442 | −0.969812 | −0.484906 | − | 0.874566i | \(-0.661146\pi\) | ||||
−0.484906 | + | 0.874566i | \(0.661146\pi\) | |||||||
\(152\) | −43.1669 | + | 43.1669i | −0.283993 | + | 0.283993i | ||||
\(153\) | −52.5700 | − | 52.5700i | −0.343595 | − | 0.343595i | ||||
\(154\) | 42.1133i | 0.273463i | ||||||||
\(155\) | 194.874 | + | 44.3790i | 1.25725 | + | 0.286316i | ||||
\(156\) | 109.004 | 0.698744 | ||||||||
\(157\) | 57.8019 | − | 57.8019i | 0.368165 | − | 0.368165i | −0.498643 | − | 0.866808i | \(-0.666168\pi\) |
0.866808 | + | 0.498643i | \(0.166168\pi\) | |||||||
\(158\) | −32.7703 | − | 32.7703i | −0.207407 | − | 0.207407i | ||||
\(159\) | 160.357i | 1.00854i | ||||||||
\(160\) | −23.9417 | + | 15.0598i | −0.149635 | + | 0.0941236i | ||||
\(161\) | 25.2137 | 0.156607 | ||||||||
\(162\) | −97.9927 | + | 97.9927i | −0.604893 | + | 0.604893i | ||||
\(163\) | −93.7188 | − | 93.7188i | −0.574962 | − | 0.574962i | 0.358549 | − | 0.933511i | \(-0.383272\pi\) |
−0.933511 | + | 0.358549i | \(0.883272\pi\) | |||||||
\(164\) | − | 131.653i | − | 0.802761i | ||||||
\(165\) | 51.5679 | + | 81.9813i | 0.312532 | + | 0.496857i | ||||
\(166\) | 3.59999 | 0.0216867 | ||||||||
\(167\) | −78.7266 | + | 78.7266i | −0.471417 | + | 0.471417i | −0.902373 | − | 0.430956i | \(-0.858176\pi\) |
0.430956 | + | 0.902373i | \(0.358176\pi\) | |||||||
\(168\) | −35.9589 | − | 35.9589i | −0.214041 | − | 0.214041i | ||||
\(169\) | 84.9906i | 0.502903i | ||||||||
\(170\) | −43.3102 | + | 190.180i | −0.254766 | + | 1.11871i | ||||
\(171\) | −58.1720 | −0.340187 | ||||||||
\(172\) | −71.1058 | + | 71.1058i | −0.413406 | + | 0.413406i | ||||
\(173\) | 155.096 | + | 155.096i | 0.896511 | + | 0.896511i | 0.995126 | − | 0.0986144i | \(-0.0314410\pi\) |
−0.0986144 | + | 0.995126i | \(0.531441\pi\) | |||||||
\(174\) | 188.386i | 1.08268i | ||||||||
\(175\) | 124.017 | − | 43.5309i | 0.708671 | − | 0.248748i | ||||
\(176\) | −22.6564 | −0.128730 | ||||||||
\(177\) | −78.7229 | + | 78.7229i | −0.444762 | + | 0.444762i | ||||
\(178\) | −130.635 | − | 130.635i | −0.733904 | − | 0.733904i | ||||
\(179\) | − | 168.381i | − | 0.940677i | −0.882486 | − | 0.470338i | \(-0.844132\pi\) | ||
0.882486 | − | 0.470338i | \(-0.155868\pi\) | |||||||
\(180\) | −26.2793 | − | 5.98464i | −0.145996 | − | 0.0332480i | ||||
\(181\) | −243.240 | −1.34387 | −0.671933 | − | 0.740612i | \(-0.734536\pi\) | ||||
−0.671933 | + | 0.740612i | \(0.734536\pi\) | |||||||
\(182\) | 83.7879 | − | 83.7879i | 0.460373 | − | 0.460373i | ||||
\(183\) | 41.2993 | + | 41.2993i | 0.225679 | + | 0.225679i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −207.321 | + | 130.409i | −1.12065 | + | 0.704913i | ||||
\(186\) | −193.322 | −1.03937 | ||||||||
\(187\) | −110.478 | + | 110.478i | −0.590792 | + | 0.590792i | ||||
\(188\) | 91.1167 | + | 91.1167i | 0.484664 | + | 0.484664i | ||||
\(189\) | 113.357i | 0.599771i | ||||||||
\(190\) | 81.2605 | + | 129.186i | 0.427687 | + | 0.679926i | ||||
\(191\) | 40.3889 | 0.211460 | 0.105730 | − | 0.994395i | \(-0.466282\pi\) | ||||
0.105730 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(192\) | 19.3455 | − | 19.3455i | 0.100758 | − | 0.100758i | ||||
\(193\) | 10.5251 | + | 10.5251i | 0.0545339 | + | 0.0545339i | 0.733848 | − | 0.679314i | \(-0.237723\pi\) |
−0.679314 | + | 0.733848i | \(0.737723\pi\) | |||||||
\(194\) | 93.6287i | 0.482622i | ||||||||
\(195\) | 60.5101 | − | 265.707i | 0.310308 | − | 1.36260i | ||||
\(196\) | 42.7191 | 0.217955 | ||||||||
\(197\) | 206.579 | − | 206.579i | 1.04863 | − | 1.04863i | 0.0498700 | − | 0.998756i | \(-0.484119\pi\) |
0.998756 | − | 0.0498700i | \(-0.0158807\pi\) | |||||||
\(198\) | −15.2660 | − | 15.2660i | −0.0771009 | − | 0.0771009i | ||||
\(199\) | 53.8703i | 0.270705i | 0.990798 | + | 0.135353i | \(0.0432167\pi\) | ||||
−0.990798 | + | 0.135353i | \(0.956783\pi\) | |||||||
\(200\) | 23.4191 | + | 66.7199i | 0.117095 | + | 0.333600i | ||||
\(201\) | 74.1269 | 0.368791 | ||||||||
\(202\) | 153.927 | − | 153.927i | 0.762016 | − | 0.762016i | ||||
\(203\) | 144.806 | + | 144.806i | 0.713330 | + | 0.713330i | ||||
\(204\) | − | 188.666i | − | 0.924834i | ||||||
\(205\) | −320.916 | − | 73.0829i | −1.56544 | − | 0.356502i | ||||
\(206\) | −25.5756 | −0.124153 | ||||||||
\(207\) | −9.13991 | + | 9.13991i | −0.0441541 | + | 0.0441541i | ||||
\(208\) | 45.0769 | + | 45.0769i | 0.216716 | + | 0.216716i | ||||
\(209\) | 122.251i | 0.584933i | ||||||||
\(210\) | −107.614 | + | 67.6916i | −0.512450 | + | 0.322341i | ||||
\(211\) | 141.933 | 0.672670 | 0.336335 | − | 0.941742i | \(-0.390813\pi\) | ||||
0.336335 | + | 0.941742i | \(0.390813\pi\) | |||||||
\(212\) | −66.3131 | + | 66.3131i | −0.312798 | + | 0.312798i | ||||
\(213\) | −92.9255 | − | 92.9255i | −0.436270 | − | 0.436270i | ||||
\(214\) | − | 252.129i | − | 1.17817i | ||||||
\(215\) | 133.855 | + | 212.799i | 0.622580 | + | 0.989762i | ||||
\(216\) | −60.9845 | −0.282336 | ||||||||
\(217\) | −148.600 | + | 148.600i | −0.684794 | + | 0.684794i | ||||
\(218\) | 169.079 | + | 169.079i | 0.775593 | + | 0.775593i | ||||
\(219\) | 71.2524i | 0.325353i | ||||||||
\(220\) | −12.5770 | + | 55.2271i | −0.0571682 | + | 0.251032i | ||||
\(221\) | 439.611 | 1.98919 | ||||||||
\(222\) | 167.520 | − | 167.520i | 0.754597 | − | 0.754597i | ||||
\(223\) | 97.6474 | + | 97.6474i | 0.437881 | + | 0.437881i | 0.891298 | − | 0.453418i | \(-0.149795\pi\) |
−0.453418 | + | 0.891298i | \(0.649795\pi\) | |||||||
\(224\) | − | 29.7404i | − | 0.132770i | ||||||
\(225\) | −29.1762 | + | 60.7359i | −0.129672 | + | 0.269937i | ||||
\(226\) | 88.3336 | 0.390857 | ||||||||
\(227\) | −257.473 | + | 257.473i | −1.13424 | + | 1.13424i | −0.144781 | + | 0.989464i | \(0.546248\pi\) |
−0.989464 | + | 0.144781i | \(0.953752\pi\) | |||||||
\(228\) | −104.386 | − | 104.386i | −0.457831 | − | 0.457831i | ||||
\(229\) | − | 83.2942i | − | 0.363730i | −0.983323 | − | 0.181865i | \(-0.941787\pi\) | ||
0.983323 | − | 0.181865i | \(-0.0582134\pi\) | |||||||
\(230\) | 33.0651 | + | 7.52999i | 0.143761 | + | 0.0327391i | ||||
\(231\) | −101.838 | −0.440855 | ||||||||
\(232\) | −77.9038 | + | 77.9038i | −0.335792 | + | 0.335792i | ||||
\(233\) | 240.294 | + | 240.294i | 1.03130 | + | 1.03130i | 0.999494 | + | 0.0318109i | \(0.0101274\pi\) |
0.0318109 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(234\) | 60.7459i | 0.259598i | ||||||||
\(235\) | 272.686 | − | 171.525i | 1.16037 | − | 0.729892i | ||||
\(236\) | −65.1092 | −0.275886 | ||||||||
\(237\) | 79.2445 | − | 79.2445i | 0.334365 | − | 0.334365i | ||||
\(238\) | −145.021 | − | 145.021i | −0.609334 | − | 0.609334i | ||||
\(239\) | − | 317.238i | − | 1.32736i | −0.748018 | − | 0.663678i | \(-0.768994\pi\) | ||
0.748018 | − | 0.663678i | \(-0.231006\pi\) | |||||||
\(240\) | −36.4173 | − | 57.8953i | −0.151739 | − | 0.241230i | ||||
\(241\) | −30.4932 | −0.126528 | −0.0632640 | − | 0.997997i | \(-0.520151\pi\) | ||||
−0.0632640 | + | 0.997997i | \(0.520151\pi\) | |||||||
\(242\) | 88.9179 | − | 88.9179i | 0.367429 | − | 0.367429i | ||||
\(243\) | −99.7492 | − | 99.7492i | −0.410490 | − | 0.410490i | ||||
\(244\) | 34.1573i | 0.139989i | ||||||||
\(245\) | 23.7142 | − | 104.132i | 0.0967925 | − | 0.425027i | ||||
\(246\) | 318.360 | 1.29415 | ||||||||
\(247\) | 243.229 | − | 243.229i | 0.984732 | − | 0.984732i | ||||
\(248\) | −79.9452 | − | 79.9452i | −0.322360 | − | 0.322360i | ||||
\(249\) | 8.70543i | 0.0349616i | ||||||||
\(250\) | 175.636 | − | 20.0487i | 0.702545 | − | 0.0801949i | ||||
\(251\) | −117.061 | −0.466377 | −0.233188 | − | 0.972432i | \(-0.574916\pi\) | ||||
−0.233188 | + | 0.972432i | \(0.574916\pi\) | |||||||
\(252\) | 20.0392 | − | 20.0392i | 0.0795206 | − | 0.0795206i | ||||
\(253\) | 19.2079 | + | 19.2079i | 0.0759207 | + | 0.0759207i | ||||
\(254\) | − | 170.664i | − | 0.671907i | ||||||
\(255\) | −459.891 | − | 104.732i | −1.80349 | − | 0.410714i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 147.733 | − | 147.733i | 0.574837 | − | 0.574837i | −0.358639 | − | 0.933476i | \(-0.616759\pi\) |
0.933476 | + | 0.358639i | \(0.116759\pi\) | |||||||
\(258\) | −171.947 | − | 171.947i | −0.666460 | − | 0.666460i | ||||
\(259\) | − | 257.535i | − | 0.994344i | ||||||
\(260\) | 134.902 | − | 84.8559i | 0.518854 | − | 0.326369i | ||||
\(261\) | −104.984 | −0.402236 | ||||||||
\(262\) | 134.789 | − | 134.789i | 0.514460 | − | 0.514460i | ||||
\(263\) | −118.051 | − | 118.051i | −0.448863 | − | 0.448863i | 0.446113 | − | 0.894977i | \(-0.352808\pi\) |
−0.894977 | + | 0.446113i | \(0.852808\pi\) | |||||||
\(264\) | − | 54.7874i | − | 0.207528i | ||||||
\(265\) | 124.833 | + | 198.456i | 0.471066 | + | 0.748890i | ||||
\(266\) | −160.475 | −0.603291 | ||||||||
\(267\) | 315.899 | − | 315.899i | 1.18314 | − | 1.18314i | ||||
\(268\) | 30.6540 | + | 30.6540i | 0.114381 | + | 0.114381i | ||||
\(269\) | − | 359.618i | − | 1.33687i | −0.743771 | − | 0.668435i | \(-0.766965\pi\) | ||
0.743771 | − | 0.668435i | \(-0.233035\pi\) | |||||||
\(270\) | −33.8536 | + | 148.655i | −0.125384 | + | 0.550575i | ||||
\(271\) | 355.547 | 1.31198 | 0.655992 | − | 0.754768i | \(-0.272251\pi\) | ||||
0.655992 | + | 0.754768i | \(0.272251\pi\) | |||||||
\(272\) | 78.0198 | − | 78.0198i | 0.286838 | − | 0.286838i | ||||
\(273\) | 202.614 | + | 202.614i | 0.742177 | + | 0.742177i | ||||
\(274\) | − | 62.6422i | − | 0.228621i | ||||||
\(275\) | 127.639 | + | 61.3151i | 0.464143 | + | 0.222964i | ||||
\(276\) | −32.8018 | −0.118847 | ||||||||
\(277\) | −182.970 | + | 182.970i | −0.660543 | + | 0.660543i | −0.955508 | − | 0.294965i | \(-0.904692\pi\) |
0.294965 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(278\) | 47.8983 | + | 47.8983i | 0.172296 | + | 0.172296i | ||||
\(279\) | − | 107.735i | − | 0.386146i | ||||||
\(280\) | −72.4950 | − | 16.5095i | −0.258911 | − | 0.0589623i | ||||
\(281\) | −430.771 | −1.53299 | −0.766497 | − | 0.642248i | \(-0.778002\pi\) | ||||
−0.766497 | + | 0.642248i | \(0.778002\pi\) | |||||||
\(282\) | −220.337 | + | 220.337i | −0.781337 | + | 0.781337i | ||||
\(283\) | −175.608 | − | 175.608i | −0.620523 | − | 0.620523i | 0.325142 | − | 0.945665i | \(-0.394588\pi\) |
−0.945665 | + | 0.325142i | \(0.894588\pi\) | |||||||
\(284\) | − | 76.8557i | − | 0.270619i | ||||||
\(285\) | −312.395 | + | 196.503i | −1.09612 | + | 0.689483i | ||||
\(286\) | 127.660 | 0.446364 | ||||||||
\(287\) | 244.713 | − | 244.713i | 0.852659 | − | 0.852659i | ||||
\(288\) | 10.7808 | + | 10.7808i | 0.0374335 | + | 0.0374335i | ||||
\(289\) | − | 471.886i | − | 1.63282i | ||||||
\(290\) | 146.652 | + | 233.143i | 0.505696 | + | 0.803943i | ||||
\(291\) | −226.411 | −0.778045 | ||||||||
\(292\) | −29.4653 | + | 29.4653i | −0.100908 | + | 0.100908i | ||||
\(293\) | 206.915 | + | 206.915i | 0.706194 | + | 0.706194i | 0.965733 | − | 0.259539i | \(-0.0835705\pi\) |
−0.259539 | + | 0.965733i | \(0.583570\pi\) | |||||||
\(294\) | 103.303i | 0.351370i | ||||||||
\(295\) | −36.1433 | + | 158.709i | −0.122520 | + | 0.537998i | ||||
\(296\) | 138.551 | 0.468077 | ||||||||
\(297\) | −86.3557 | + | 86.3557i | −0.290760 | + | 0.290760i | ||||
\(298\) | 145.445 | + | 145.445i | 0.488072 | + | 0.488072i | ||||
\(299\) | − | 76.4316i | − | 0.255624i | ||||||
\(300\) | −161.341 | + | 56.6317i | −0.537803 | + | 0.188772i | ||||
\(301\) | −264.340 | −0.878205 | ||||||||
\(302\) | 146.442 | − | 146.442i | 0.484906 | − | 0.484906i | ||||
\(303\) | 372.224 | + | 372.224i | 1.22846 | + | 1.22846i | ||||
\(304\) | − | 86.3339i | − | 0.283993i | ||||||
\(305\) | 83.2615 | + | 18.9613i | 0.272988 | + | 0.0621683i | ||||
\(306\) | 105.140 | 0.343595 | ||||||||
\(307\) | −391.647 | + | 391.647i | −1.27572 | + | 1.27572i | −0.332684 | + | 0.943038i | \(0.607954\pi\) |
−0.943038 | + | 0.332684i | \(0.892046\pi\) | |||||||
\(308\) | −42.1133 | − | 42.1133i | −0.136731 | − | 0.136731i | ||||
\(309\) | − | 61.8464i | − | 0.200150i | ||||||
\(310\) | −239.253 | + | 150.495i | −0.771783 | + | 0.485467i | ||||
\(311\) | 214.460 | 0.689581 | 0.344791 | − | 0.938680i | \(-0.387950\pi\) | ||||
0.344791 | + | 0.938680i | \(0.387950\pi\) | |||||||
\(312\) | −109.004 | + | 109.004i | −0.349372 | + | 0.349372i | ||||
\(313\) | −37.5054 | − | 37.5054i | −0.119826 | − | 0.119826i | 0.644651 | − | 0.764477i | \(-0.277003\pi\) |
−0.764477 | + | 0.644651i | \(0.777003\pi\) | |||||||
\(314\) | 115.604i | 0.368165i | ||||||||
\(315\) | −37.7232 | − | 59.9715i | −0.119756 | − | 0.190386i | ||||
\(316\) | 65.5406 | 0.207407 | ||||||||
\(317\) | −140.447 | + | 140.447i | −0.443052 | + | 0.443052i | −0.893036 | − | 0.449984i | \(-0.851430\pi\) |
0.449984 | + | 0.893036i | \(0.351430\pi\) | |||||||
\(318\) | −160.357 | − | 160.357i | −0.504268 | − | 0.504268i | ||||
\(319\) | 220.628i | 0.691624i | ||||||||
\(320\) | 8.88189 | − | 39.0014i | 0.0277559 | − | 0.121879i | ||||
\(321\) | 609.695 | 1.89936 | ||||||||
\(322\) | −25.2137 | + | 25.2137i | −0.0783034 | + | 0.0783034i | ||||
\(323\) | −420.984 | − | 420.984i | −1.30336 | − | 1.30336i | ||||
\(324\) | − | 195.985i | − | 0.604893i | ||||||
\(325\) | −131.957 | − | 375.941i | −0.406023 | − | 1.15674i | ||||
\(326\) | 187.438 | 0.574962 | ||||||||
\(327\) | −408.864 | + | 408.864i | −1.25035 | + | 1.25035i | ||||
\(328\) | 131.653 | + | 131.653i | 0.401380 | + | 0.401380i | ||||
\(329\) | 338.732i | 1.02958i | ||||||||
\(330\) | −133.549 | − | 30.4135i | −0.404694 | − | 0.0921620i | ||||
\(331\) | −89.9646 | −0.271796 | −0.135898 | − | 0.990723i | \(-0.543392\pi\) | ||||
−0.135898 | + | 0.990723i | \(0.543392\pi\) | |||||||
\(332\) | −3.59999 | + | 3.59999i | −0.0108433 | + | 0.0108433i | ||||
\(333\) | 93.3559 | + | 93.3559i | 0.280348 | + | 0.280348i | ||||
\(334\) | − | 157.453i | − | 0.471417i | ||||||
\(335\) | 91.7384 | − | 57.7053i | 0.273846 | − | 0.172255i | ||||
\(336\) | 71.9178 | 0.214041 | ||||||||
\(337\) | 285.730 | − | 285.730i | 0.847862 | − | 0.847862i | −0.142004 | − | 0.989866i | \(-0.545355\pi\) |
0.989866 | + | 0.142004i | \(0.0453546\pi\) | |||||||
\(338\) | −84.9906 | − | 84.9906i | −0.251451 | − | 0.251451i | ||||
\(339\) | 213.607i | 0.630108i | ||||||||
\(340\) | −146.870 | − | 233.490i | −0.431971 | − | 0.686737i | ||||
\(341\) | −226.409 | −0.663957 | ||||||||
\(342\) | 58.1720 | − | 58.1720i | 0.170094 | − | 0.170094i | ||||
\(343\) | 261.566 | + | 261.566i | 0.762582 | + | 0.762582i | ||||
\(344\) | − | 142.212i | − | 0.413406i | ||||||
\(345\) | −18.2089 | + | 79.9574i | −0.0527794 | + | 0.231761i | ||||
\(346\) | −310.193 | −0.896511 | ||||||||
\(347\) | −389.916 | + | 389.916i | −1.12368 | + | 1.12368i | −0.132493 | + | 0.991184i | \(0.542298\pi\) |
−0.991184 | + | 0.132493i | \(0.957702\pi\) | |||||||
\(348\) | −188.386 | − | 188.386i | −0.541338 | − | 0.541338i | ||||
\(349\) | 459.513i | 1.31666i | 0.752731 | + | 0.658329i | \(0.228736\pi\) | ||||
−0.752731 | + | 0.658329i | \(0.771264\pi\) | |||||||
\(350\) | −80.4866 | + | 167.548i | −0.229962 | + | 0.478710i | ||||
\(351\) | 343.624 | 0.978985 | ||||||||
\(352\) | 22.6564 | − | 22.6564i | 0.0643649 | − | 0.0643649i | ||||
\(353\) | −40.4868 | − | 40.4868i | −0.114694 | − | 0.114694i | 0.647431 | − | 0.762124i | \(-0.275844\pi\) |
−0.762124 | + | 0.647431i | \(0.775844\pi\) | |||||||
\(354\) | − | 157.446i | − | 0.444762i | ||||||
\(355\) | −187.343 | − | 42.6640i | −0.527726 | − | 0.120180i | ||||
\(356\) | 261.270 | 0.733904 | ||||||||
\(357\) | 350.688 | − | 350.688i | 0.982320 | − | 0.982320i | ||||
\(358\) | 168.381 | + | 168.381i | 0.470338 | + | 0.470338i | ||||
\(359\) | 433.495i | 1.20751i | 0.797171 | + | 0.603753i | \(0.206329\pi\) | ||||
−0.797171 | + | 0.603753i | \(0.793671\pi\) | |||||||
\(360\) | 32.2639 | − | 20.2946i | 0.0896220 | − | 0.0563740i | ||||
\(361\) | −104.846 | −0.290432 | ||||||||
\(362\) | 243.240 | − | 243.240i | 0.671933 | − | 0.671933i | ||||
\(363\) | 215.020 | + | 215.020i | 0.592341 | + | 0.592341i | ||||
\(364\) | 167.576i | 0.460373i | ||||||||
\(365\) | 55.4675 | + | 88.1809i | 0.151966 | + | 0.241592i | ||||
\(366\) | −82.5986 | −0.225679 | ||||||||
\(367\) | −23.7488 | + | 23.7488i | −0.0647106 | + | 0.0647106i | −0.738721 | − | 0.674011i | \(-0.764570\pi\) |
0.674011 | + | 0.738721i | \(0.264570\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 177.416i | 0.480802i | ||||||||
\(370\) | 76.9120 | − | 337.730i | 0.207870 | − | 0.912783i | ||||
\(371\) | −246.523 | −0.664481 | ||||||||
\(372\) | 193.322 | − | 193.322i | 0.519683 | − | 0.519683i | ||||
\(373\) | 66.5228 | + | 66.5228i | 0.178345 | + | 0.178345i | 0.790634 | − | 0.612289i | \(-0.209751\pi\) |
−0.612289 | + | 0.790634i | \(0.709751\pi\) | |||||||
\(374\) | − | 220.956i | − | 0.590792i | ||||||
\(375\) | 48.4815 | + | 424.720i | 0.129284 | + | 1.13259i | ||||
\(376\) | −182.233 | −0.484664 | ||||||||
\(377\) | 438.958 | − | 438.958i | 1.16434 | − | 1.16434i | ||||
\(378\) | −113.357 | − | 113.357i | −0.299885 | − | 0.299885i | ||||
\(379\) | 323.563i | 0.853728i | 0.904316 | + | 0.426864i | \(0.140382\pi\) | ||||
−0.904316 | + | 0.426864i | \(0.859618\pi\) | |||||||
\(380\) | −210.447 | − | 47.9255i | −0.553807 | − | 0.126120i | ||||
\(381\) | 412.698 | 1.08320 | ||||||||
\(382\) | −40.3889 | + | 40.3889i | −0.105730 | + | 0.105730i | ||||
\(383\) | −299.857 | − | 299.857i | −0.782917 | − | 0.782917i | 0.197405 | − | 0.980322i | \(-0.436749\pi\) |
−0.980322 | + | 0.197405i | \(0.936749\pi\) | |||||||
\(384\) | 38.6909i | 0.100758i | ||||||||
\(385\) | −126.033 | + | 79.2770i | −0.327358 | + | 0.205914i | ||||
\(386\) | −21.0501 | −0.0545339 | ||||||||
\(387\) | 95.8226 | − | 95.8226i | 0.247604 | − | 0.247604i | ||||
\(388\) | −93.6287 | − | 93.6287i | −0.241311 | − | 0.241311i | ||||
\(389\) | 64.2288i | 0.165113i | 0.996586 | + | 0.0825563i | \(0.0263084\pi\) | ||||
−0.996586 | + | 0.0825563i | \(0.973692\pi\) | |||||||
\(390\) | 205.197 | + | 326.217i | 0.526146 | + | 0.836455i | ||||
\(391\) | −132.289 | −0.338335 | ||||||||
\(392\) | −42.7191 | + | 42.7191i | −0.108977 | + | 0.108977i | ||||
\(393\) | 325.943 | + | 325.943i | 0.829372 | + | 0.829372i | ||||
\(394\) | 413.159i | 1.04863i | ||||||||
\(395\) | 36.3827 | − | 159.761i | 0.0921082 | − | 0.404458i | ||||
\(396\) | 30.5319 | 0.0771009 | ||||||||
\(397\) | 489.291 | − | 489.291i | 1.23247 | − | 1.23247i | 0.269460 | − | 0.963012i | \(-0.413155\pi\) |
0.963012 | − | 0.269460i | \(-0.0868450\pi\) | |||||||
\(398\) | −53.8703 | − | 53.8703i | −0.135353 | − | 0.135353i | ||||
\(399\) | − | 388.059i | − | 0.972579i | ||||||
\(400\) | −90.1390 | − | 43.3008i | −0.225348 | − | 0.108252i | ||||
\(401\) | −615.748 | −1.53553 | −0.767765 | − | 0.640731i | \(-0.778631\pi\) | ||||
−0.767765 | + | 0.640731i | \(0.778631\pi\) | |||||||
\(402\) | −74.1269 | + | 74.1269i | −0.184395 | + | 0.184395i | ||||
\(403\) | 450.460 | + | 450.460i | 1.11777 | + | 1.11777i | ||||
\(404\) | 307.855i | 0.762016i | ||||||||
\(405\) | −477.732 | − | 108.795i | −1.17959 | − | 0.268630i | ||||
\(406\) | −289.612 | −0.713330 | ||||||||
\(407\) | 196.192 | − | 196.192i | 0.482043 | − | 0.482043i | ||||
\(408\) | 188.666 | + | 188.666i | 0.462417 | + | 0.462417i | ||||
\(409\) | − | 43.1536i | − | 0.105510i | −0.998607 | − | 0.0527551i | \(-0.983200\pi\) | ||
0.998607 | − | 0.0527551i | \(-0.0168003\pi\) | |||||||
\(410\) | 393.998 | − | 247.833i | 0.960972 | − | 0.604470i | ||||
\(411\) | 151.480 | 0.368565 | ||||||||
\(412\) | 25.5756 | − | 25.5756i | 0.0620767 | − | 0.0620767i | ||||
\(413\) | −121.023 | − | 121.023i | −0.293035 | − | 0.293035i | ||||
\(414\) | − | 18.2798i | − | 0.0441541i | ||||||
\(415\) | 6.77688 | + | 10.7737i | 0.0163298 | + | 0.0259608i | ||||
\(416\) | −90.1537 | −0.216716 | ||||||||
\(417\) | −115.827 | + | 115.827i | −0.277762 | + | 0.277762i | ||||
\(418\) | −122.251 | − | 122.251i | −0.292467 | − | 0.292467i | ||||
\(419\) | − | 49.6628i | − | 0.118527i | −0.998242 | − | 0.0592635i | \(-0.981125\pi\) | ||
0.998242 | − | 0.0592635i | \(-0.0188752\pi\) | |||||||
\(420\) | 39.9229 | − | 175.306i | 0.0950545 | − | 0.417396i | ||||
\(421\) | −95.0400 | −0.225748 | −0.112874 | − | 0.993609i | \(-0.536006\pi\) | ||||
−0.112874 | + | 0.993609i | \(0.536006\pi\) | |||||||
\(422\) | −141.933 | + | 141.933i | −0.336335 | + | 0.336335i | ||||
\(423\) | −122.789 | − | 122.789i | −0.290282 | − | 0.290282i | ||||
\(424\) | − | 132.626i | − | 0.312798i | ||||||
\(425\) | −650.684 | + | 228.394i | −1.53102 | + | 0.537398i | ||||
\(426\) | 185.851 | 0.436270 | ||||||||
\(427\) | −63.4908 | + | 63.4908i | −0.148690 | + | 0.148690i | ||||
\(428\) | 252.129 | + | 252.129i | 0.589087 | + | 0.589087i | ||||
\(429\) | 308.706i | 0.719593i | ||||||||
\(430\) | −346.654 | − | 78.9442i | −0.806171 | − | 0.183591i | ||||
\(431\) | −697.801 | −1.61903 | −0.809514 | − | 0.587100i | \(-0.800270\pi\) | ||||
−0.809514 | + | 0.587100i | \(0.800270\pi\) | |||||||
\(432\) | 60.9845 | − | 60.9845i | 0.141168 | − | 0.141168i | ||||
\(433\) | 387.368 | + | 387.368i | 0.894614 | + | 0.894614i | 0.994953 | − | 0.100340i | \(-0.0319930\pi\) |
−0.100340 | + | 0.994953i | \(0.531993\pi\) | |||||||
\(434\) | − | 297.201i | − | 0.684794i | ||||||
\(435\) | −563.783 | + | 354.631i | −1.29605 | + | 0.815243i | ||||
\(436\) | −338.158 | −0.775593 | ||||||||
\(437\) | −73.1931 | + | 73.1931i | −0.167490 | + | 0.167490i | ||||
\(438\) | −71.2524 | − | 71.2524i | −0.162677 | − | 0.162677i | ||||
\(439\) | − | 186.351i | − | 0.424490i | −0.977216 | − | 0.212245i | \(-0.931923\pi\) | ||
0.977216 | − | 0.212245i | \(-0.0680775\pi\) | |||||||
\(440\) | −42.6501 | − | 67.8041i | −0.0969320 | − | 0.154100i | ||||
\(441\) | −57.5686 | −0.130541 | ||||||||
\(442\) | −439.611 | + | 439.611i | −0.994595 | + | 0.994595i | ||||
\(443\) | 344.391 | + | 344.391i | 0.777407 | + | 0.777407i | 0.979389 | − | 0.201982i | \(-0.0647383\pi\) |
−0.201982 | + | 0.979389i | \(0.564738\pi\) | |||||||
\(444\) | 335.041i | 0.754597i | ||||||||
\(445\) | 145.036 | − | 636.869i | 0.325923 | − | 1.43117i | ||||
\(446\) | −195.295 | −0.437881 | ||||||||
\(447\) | −351.714 | + | 351.714i | −0.786831 | + | 0.786831i | ||||
\(448\) | 29.7404 | + | 29.7404i | 0.0663849 | + | 0.0663849i | ||||
\(449\) | 85.4403i | 0.190290i | 0.995463 | + | 0.0951451i | \(0.0303315\pi\) | ||||
−0.995463 | + | 0.0951451i | \(0.969668\pi\) | |||||||
\(450\) | −31.5597 | − | 89.9121i | −0.0701327 | − | 0.199805i | ||||
\(451\) | 372.848 | 0.826714 | ||||||||
\(452\) | −88.3336 | + | 88.3336i | −0.195428 | + | 0.195428i | ||||
\(453\) | 354.123 | + | 354.123i | 0.781728 | + | 0.781728i | ||||
\(454\) | − | 514.947i | − | 1.13424i | ||||||
\(455\) | 408.481 | + | 93.0243i | 0.897760 | + | 0.204449i | ||||
\(456\) | 208.771 | 0.457831 | ||||||||
\(457\) | 238.455 | − | 238.455i | 0.521784 | − | 0.521784i | −0.396326 | − | 0.918110i | \(-0.629715\pi\) |
0.918110 | + | 0.396326i | \(0.129715\pi\) | |||||||
\(458\) | 83.2942 | + | 83.2942i | 0.181865 | + | 0.181865i | ||||
\(459\) | − | 594.750i | − | 1.29575i | ||||||
\(460\) | −40.5951 | + | 25.5351i | −0.0882501 | + | 0.0555111i | ||||
\(461\) | 278.593 | 0.604323 | 0.302161 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302161 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(462\) | 101.838 | − | 101.838i | 0.220428 | − | 0.220428i | ||||
\(463\) | 317.977 | + | 317.977i | 0.686775 | + | 0.686775i | 0.961518 | − | 0.274743i | \(-0.0885927\pi\) |
−0.274743 | + | 0.961518i | \(0.588593\pi\) | |||||||
\(464\) | − | 155.808i | − | 0.335792i | ||||||
\(465\) | −363.923 | − | 578.557i | −0.782631 | − | 1.24421i | ||||
\(466\) | −480.588 | −1.03130 | ||||||||
\(467\) | 164.319 | − | 164.319i | 0.351861 | − | 0.351861i | −0.508940 | − | 0.860802i | \(-0.669963\pi\) |
0.860802 | + | 0.508940i | \(0.169963\pi\) | |||||||
\(468\) | −60.7459 | − | 60.7459i | −0.129799 | − | 0.129799i | ||||
\(469\) | 113.958i | 0.242981i | ||||||||
\(470\) | −101.161 | + | 444.210i | −0.215236 | + | 0.945129i | ||||
\(471\) | −279.551 | −0.593527 | ||||||||
\(472\) | 65.1092 | − | 65.1092i | 0.137943 | − | 0.137943i | ||||
\(473\) | −201.375 | − | 201.375i | −0.425741 | − | 0.425741i | ||||
\(474\) | 158.489i | 0.334365i | ||||||||
\(475\) | −233.645 | + | 486.378i | −0.491885 | + | 1.02395i | ||||
\(476\) | 290.043 | 0.609334 | ||||||||
\(477\) | 89.3639 | − | 89.3639i | 0.187346 | − | 0.187346i | ||||
\(478\) | 317.238 | + | 317.238i | 0.663678 | + | 0.663678i | ||||
\(479\) | − | 55.2512i | − | 0.115347i | −0.998335 | − | 0.0576735i | \(-0.981632\pi\) | ||
0.998335 | − | 0.0576735i | \(-0.0183682\pi\) | |||||||
\(480\) | 94.3126 | + | 21.4780i | 0.196485 | + | 0.0447459i | ||||
\(481\) | −780.679 | −1.62303 | ||||||||
\(482\) | 30.4932 | − | 30.4932i | 0.0632640 | − | 0.0632640i | ||||
\(483\) | −60.9713 | − | 60.9713i | −0.126235 | − | 0.126235i | ||||
\(484\) | 177.836i | 0.367429i | ||||||||
\(485\) | −280.203 | + | 176.253i | −0.577739 | + | 0.363409i | ||||
\(486\) | 199.498 | 0.410490 | ||||||||
\(487\) | 353.979 | − | 353.979i | 0.726857 | − | 0.726857i | −0.243136 | − | 0.969992i | \(-0.578176\pi\) |
0.969992 | + | 0.243136i | \(0.0781760\pi\) | |||||||
\(488\) | −34.1573 | − | 34.1573i | −0.0699945 | − | 0.0699945i | ||||
\(489\) | 453.258i | 0.926908i | ||||||||
\(490\) | 80.4176 | + | 127.846i | 0.164117 | + | 0.260910i | ||||
\(491\) | −698.356 | −1.42231 | −0.711157 | − | 0.703034i | \(-0.751828\pi\) | ||||
−0.711157 | + | 0.703034i | \(0.751828\pi\) | |||||||
\(492\) | −318.360 | + | 318.360i | −0.647074 | + | 0.647074i | ||||
\(493\) | −759.755 | − | 759.755i | −1.54109 | − | 1.54109i | ||||
\(494\) | 486.458i | 0.984732i | ||||||||
\(495\) | 16.9488 | − | 74.4244i | 0.0342401 | − | 0.150352i | ||||
\(496\) | 159.890 | 0.322360 | ||||||||
\(497\) | 142.858 | − | 142.858i | 0.287440 | − | 0.287440i | ||||
\(498\) | −8.70543 | − | 8.70543i | −0.0174808 | − | 0.0174808i | ||||
\(499\) | − | 27.0217i | − | 0.0541518i | −0.999633 | − | 0.0270759i | \(-0.991380\pi\) | ||
0.999633 | − | 0.0270759i | \(-0.00861958\pi\) | |||||||
\(500\) | −155.587 | + | 195.685i | −0.311175 | + | 0.391370i | ||||
\(501\) | 380.751 | 0.759981 | ||||||||
\(502\) | 117.061 | − | 117.061i | 0.233188 | − | 0.233188i | ||||
\(503\) | −673.941 | − | 673.941i | −1.33984 | − | 1.33984i | −0.896208 | − | 0.443634i | \(-0.853689\pi\) |
−0.443634 | − | 0.896208i | \(-0.646311\pi\) | |||||||
\(504\) | 40.0784i | 0.0795206i | ||||||||
\(505\) | 750.423 | + | 170.896i | 1.48599 | + | 0.338407i | ||||
\(506\) | −38.4159 | −0.0759207 | ||||||||
\(507\) | 205.523 | − | 205.523i | 0.405370 | − | 0.405370i | ||||
\(508\) | 170.664 | + | 170.664i | 0.335954 | + | 0.335954i | ||||
\(509\) | − | 809.386i | − | 1.59015i | −0.606512 | − | 0.795074i | \(-0.707432\pi\) | ||
0.606512 | − | 0.795074i | \(-0.292568\pi\) | |||||||
\(510\) | 564.623 | − | 355.159i | 1.10710 | − | 0.696389i | ||||
\(511\) | −109.539 | −0.214361 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −329.064 | − | 329.064i | −0.641451 | − | 0.641451i | ||||
\(514\) | 295.466i | 0.574837i | ||||||||
\(515\) | −48.1453 | − | 76.5403i | −0.0934861 | − | 0.148622i | ||||
\(516\) | 343.894 | 0.666460 | ||||||||
\(517\) | −258.048 | + | 258.048i | −0.499125 | + | 0.499125i | ||||
\(518\) | 257.535 | + | 257.535i | 0.497172 | + | 0.497172i | ||||
\(519\) | − | 750.103i | − | 1.44529i | ||||||
\(520\) | −50.0460 | + | 219.758i | −0.0962423 | + | 0.422611i | ||||
\(521\) | −310.331 | −0.595645 | −0.297822 | − | 0.954621i | \(-0.596260\pi\) | ||||
−0.297822 | + | 0.954621i | \(0.596260\pi\) | |||||||
\(522\) | 104.984 | − | 104.984i | 0.201118 | − | 0.201118i | ||||
\(523\) | 464.606 | + | 464.606i | 0.888347 | + | 0.888347i | 0.994364 | − | 0.106017i | \(-0.0338098\pi\) |
−0.106017 | + | 0.994364i | \(0.533810\pi\) | |||||||
\(524\) | 269.577i | 0.514460i | ||||||||
\(525\) | −405.162 | − | 194.631i | −0.771738 | − | 0.370726i | ||||
\(526\) | 236.102 | 0.448863 | ||||||||
\(527\) | 779.664 | − | 779.664i | 1.47944 | − | 1.47944i | ||||
\(528\) | 54.7874 | + | 54.7874i | 0.103764 | + | 0.103764i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −323.288 | − | 73.6232i | −0.609978 | − | 0.138912i | ||||
\(531\) | 87.7415 | 0.165238 | ||||||||
\(532\) | 160.475 | − | 160.475i | 0.301646 | − | 0.301646i | ||||
\(533\) | −741.812 | − | 741.812i | −1.39177 | − | 1.39177i | ||||
\(534\) | 631.798i | 1.18314i | ||||||||
\(535\) | 754.549 | − | 474.626i | 1.41037 | − | 0.887152i | ||||
\(536\) | −61.3080 | −0.114381 | ||||||||
\(537\) | −407.176 | + | 407.176i | −0.758243 | + | 0.758243i | ||||
\(538\) | 359.618 | + | 359.618i | 0.668435 | + | 0.668435i | ||||
\(539\) | 120.983i | 0.224458i | ||||||||
\(540\) | −114.802 | − | 182.509i | −0.212596 | − | 0.337979i | ||||
\(541\) | 807.280 | 1.49220 | 0.746100 | − | 0.665834i | \(-0.231924\pi\) | ||||
0.746100 | + | 0.665834i | \(0.231924\pi\) | |||||||
\(542\) | −355.547 | + | 355.547i | −0.655992 | + | 0.655992i | ||||
\(543\) | 588.198 | + | 588.198i | 1.08324 | + | 1.08324i | ||||
\(544\) | 156.040i | 0.286838i | ||||||||
\(545\) | −187.718 | + | 824.291i | −0.344436 | + | 1.51246i | ||||
\(546\) | −405.229 | −0.742177 | ||||||||
\(547\) | −419.482 | + | 419.482i | −0.766877 | + | 0.766877i | −0.977555 | − | 0.210678i | \(-0.932433\pi\) |
0.210678 | + | 0.977555i | \(0.432433\pi\) | |||||||
\(548\) | 62.6422 | + | 62.6422i | 0.114311 | + | 0.114311i | ||||
\(549\) | − | 46.0306i | − | 0.0838444i | ||||||
\(550\) | −188.954 | + | 66.3242i | −0.343553 | + | 0.120589i | ||||
\(551\) | −840.717 | −1.52580 | ||||||||
\(552\) | 32.8018 | − | 32.8018i | 0.0594236 | − | 0.0594236i | ||||
\(553\) | 121.825 | + | 121.825i | 0.220299 | + | 0.220299i | ||||
\(554\) | − | 365.941i | − | 0.660543i | ||||||
\(555\) | 816.692 | + | 185.987i | 1.47152 | + | 0.335112i | ||||
\(556\) | −95.7966 | −0.172296 | ||||||||
\(557\) | 193.565 | − | 193.565i | 0.347514 | − | 0.347514i | −0.511669 | − | 0.859183i | \(-0.670973\pi\) |
0.859183 | + | 0.511669i | \(0.170973\pi\) | |||||||
\(558\) | 107.735 | + | 107.735i | 0.193073 | + | 0.193073i | ||||
\(559\) | 801.307i | 1.43346i | ||||||||
\(560\) | 89.0045 | − | 55.9855i | 0.158937 | − | 0.0999742i | ||||
\(561\) | 534.313 | 0.952429 | ||||||||
\(562\) | 430.771 | − | 430.771i | 0.766497 | − | 0.766497i | ||||
\(563\) | −180.193 | − | 180.193i | −0.320058 | − | 0.320058i | 0.528731 | − | 0.848789i | \(-0.322668\pi\) |
−0.848789 | + | 0.528731i | \(0.822668\pi\) | |||||||
\(564\) | − | 440.674i | − | 0.781337i | ||||||
\(565\) | 166.286 | + | 264.357i | 0.294311 | + | 0.467888i | ||||
\(566\) | 351.216 | 0.620523 | ||||||||
\(567\) | 364.293 | − | 364.293i | 0.642493 | − | 0.642493i | ||||
\(568\) | 76.8557 | + | 76.8557i | 0.135309 | + | 0.135309i | ||||
\(569\) | − | 26.7672i | − | 0.0470425i | −0.999723 | − | 0.0235213i | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235213i | \(-0.00748774\pi\) | |||||||
\(570\) | 115.893 | − | 508.898i | 0.203320 | − | 0.892804i | ||||
\(571\) | 687.381 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(572\) | −127.660 | + | 127.660i | −0.223182 | + | 0.223182i | ||||
\(573\) | −97.6678 | − | 97.6678i | −0.170450 | − | 0.170450i | ||||
\(574\) | 489.427i | 0.852659i | ||||||||
\(575\) | 39.7090 | + | 113.129i | 0.0690592 | + | 0.196746i | ||||
\(576\) | −21.5617 | −0.0374335 | ||||||||
\(577\) | −153.323 | + | 153.323i | −0.265725 | + | 0.265725i | −0.827375 | − | 0.561650i | \(-0.810167\pi\) |
0.561650 | + | 0.827375i | \(0.310167\pi\) | |||||||
\(578\) | 471.886 | + | 471.886i | 0.816412 | + | 0.816412i | ||||
\(579\) | − | 50.9030i | − | 0.0879153i | ||||||
\(580\) | −379.795 | − | 86.4917i | −0.654819 | − | 0.149124i | ||||
\(581\) | −13.3832 | −0.0230347 | ||||||||
\(582\) | 226.411 | − | 226.411i | 0.389023 | − | 0.389023i | ||||
\(583\) | −187.802 | − | 187.802i | −0.322131 | − | 0.322131i | ||||
\(584\) | − | 58.9305i | − | 0.100908i | ||||||
\(585\) | −181.795 | + | 114.352i | −0.310760 | + | 0.195474i | ||||
\(586\) | −413.830 | −0.706194 | ||||||||
\(587\) | 588.851 | − | 588.851i | 1.00315 | − | 1.00315i | 0.00315852 | − | 0.999995i | \(-0.498995\pi\) |
0.999995 | − | 0.00315852i | \(-0.00100539\pi\) | |||||||
\(588\) | −103.303 | − | 103.303i | −0.175685 | − | 0.175685i | ||||
\(589\) | − | 862.748i | − | 1.46477i | ||||||
\(590\) | −122.566 | − | 194.853i | −0.207739 | − | 0.330259i | ||||
\(591\) | −999.093 | −1.69051 | ||||||||
\(592\) | −138.551 | + | 138.551i | −0.234038 | + | 0.234038i | ||||
\(593\) | −465.426 | − | 465.426i | −0.784866 | − | 0.784866i | 0.195781 | − | 0.980648i | \(-0.437276\pi\) |
−0.980648 | + | 0.195781i | \(0.937276\pi\) | |||||||
\(594\) | − | 172.711i | − | 0.290760i | ||||||
\(595\) | 161.008 | − | 707.006i | 0.270602 | − | 1.18824i | ||||
\(596\) | −290.891 | −0.488072 | ||||||||
\(597\) | 130.268 | − | 130.268i | 0.218205 | − | 0.218205i | ||||
\(598\) | 76.4316 | + | 76.4316i | 0.127812 | + | 0.127812i | ||||
\(599\) | − | 552.633i | − | 0.922592i | −0.887246 | − | 0.461296i | \(-0.847385\pi\) | ||
0.887246 | − | 0.461296i | \(-0.152615\pi\) | |||||||
\(600\) | 104.709 | − | 217.973i | 0.174515 | − | 0.363288i | ||||
\(601\) | 597.140 | 0.993577 | 0.496788 | − | 0.867872i | \(-0.334512\pi\) | ||||
0.496788 | + | 0.867872i | \(0.334512\pi\) | |||||||
\(602\) | 264.340 | − | 264.340i | 0.439102 | − | 0.439102i | ||||
\(603\) | −41.3095 | − | 41.3095i | −0.0685066 | − | 0.0685066i | ||||
\(604\) | 292.883i | 0.484906i | ||||||||
\(605\) | 433.491 | + | 98.7198i | 0.716513 | + | 0.163173i | ||||
\(606\) | −744.448 | −1.22846 | ||||||||
\(607\) | −535.238 | + | 535.238i | −0.881776 | + | 0.881776i | −0.993715 | − | 0.111939i | \(-0.964294\pi\) |
0.111939 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(608\) | 86.3339 | + | 86.3339i | 0.141996 | + | 0.141996i | ||||
\(609\) | − | 700.334i | − | 1.14997i | ||||||
\(610\) | −102.223 | + | 64.3001i | −0.167578 | + | 0.105410i | ||||
\(611\) | 1026.81 | 1.68055 | ||||||||
\(612\) | −105.140 | + | 105.140i | −0.171797 | + | 0.171797i | ||||
\(613\) | −697.916 | − | 697.916i | −1.13853 | − | 1.13853i | −0.988715 | − | 0.149811i | \(-0.952134\pi\) |
−0.149811 | − | 0.988715i | \(-0.547866\pi\) | |||||||
\(614\) | − | 783.293i | − | 1.27572i | ||||||
\(615\) | 599.305 | + | 952.760i | 0.974479 | + | 1.54920i | ||||
\(616\) | 84.2265 | 0.136731 | ||||||||
\(617\) | −758.632 | + | 758.632i | −1.22955 | + | 1.22955i | −0.265416 | + | 0.964134i | \(0.585509\pi\) |
−0.964134 | + | 0.265416i | \(0.914491\pi\) | |||||||
\(618\) | 61.8464 | + | 61.8464i | 0.100075 | + | 0.100075i | ||||
\(619\) | − | 550.862i | − | 0.889923i | −0.895550 | − | 0.444961i | \(-0.853217\pi\) | ||
0.895550 | − | 0.444961i | \(-0.146783\pi\) | |||||||
\(620\) | 88.7581 | − | 389.747i | 0.143158 | − | 0.628625i | ||||
\(621\) | −103.404 | −0.166513 | ||||||||
\(622\) | −214.460 | + | 214.460i | −0.344791 | + | 0.344791i | ||||
\(623\) | 485.643 | + | 485.643i | 0.779523 | + | 0.779523i | ||||
\(624\) | − | 218.008i | − | 0.349372i | ||||||
\(625\) | 390.630 | + | 487.886i | 0.625008 | + | 0.780618i | ||||
\(626\) | 75.0109 | 0.119826 | ||||||||
\(627\) | 295.625 | − | 295.625i | 0.471492 | − | 0.471492i | ||||
\(628\) | −115.604 | − | 115.604i | −0.184083 | − | 0.184083i | ||||
\(629\) | 1351.21i | 2.14819i | ||||||||
\(630\) | 97.6947 | + | 22.2482i | 0.155071 | + | 0.0353147i | ||||
\(631\) | 676.596 | 1.07226 | 0.536130 | − | 0.844136i | \(-0.319886\pi\) | ||||
0.536130 | + | 0.844136i | \(0.319886\pi\) | |||||||
\(632\) | −65.5406 | + | 65.5406i | −0.103703 | + | 0.103703i | ||||
\(633\) | −343.221 | − | 343.221i | −0.542213 | − | 0.542213i | ||||
\(634\) | − | 280.895i | − | 0.443052i | ||||||
\(635\) | 510.749 | − | 321.271i | 0.804329 | − | 0.505938i | ||||
\(636\) | 320.714 | 0.504268 | ||||||||
\(637\) | 240.706 | − | 240.706i | 0.377874 | − | 0.377874i | ||||
\(638\) | −220.628 | − | 220.628i | −0.345812 | − | 0.345812i | ||||
\(639\) | 103.571i | 0.162083i | ||||||||
\(640\) | 30.1195 | + | 47.8833i | 0.0470618 | + | 0.0748177i | ||||
\(641\) | 786.673 | 1.22726 | 0.613630 | − | 0.789594i | \(-0.289709\pi\) | ||||
0.613630 | + | 0.789594i | \(0.289709\pi\) | |||||||
\(642\) | −609.695 | + | 609.695i | −0.949680 | + | 0.949680i | ||||
\(643\) | −632.234 | − | 632.234i | −0.983256 | − | 0.983256i | 0.0166059 | − | 0.999862i | \(-0.494714\pi\) |
−0.999862 | + | 0.0166059i | \(0.994714\pi\) | |||||||
\(644\) | − | 50.4274i | − | 0.0783034i | ||||||
\(645\) | 190.902 | − | 838.271i | 0.295971 | − | 1.29965i | ||||
\(646\) | 841.969 | 1.30336 | ||||||||
\(647\) | 387.458 | − | 387.458i | 0.598853 | − | 0.598853i | −0.341154 | − | 0.940007i | \(-0.610818\pi\) |
0.940007 | + | 0.341154i | \(0.110818\pi\) | |||||||
\(648\) | 195.985 | + | 195.985i | 0.302447 | + | 0.302447i | ||||
\(649\) | − | 184.393i | − | 0.284118i | ||||||
\(650\) | 507.898 | + | 243.983i | 0.781382 | + | 0.375359i | ||||
\(651\) | 718.686 | 1.10397 | ||||||||
\(652\) | −187.438 | + | 187.438i | −0.287481 | + | 0.287481i | ||||
\(653\) | 15.7216 | + | 15.7216i | 0.0240760 | + | 0.0240760i | 0.719042 | − | 0.694966i | \(-0.244581\pi\) |
−0.694966 | + | 0.719042i | \(0.744581\pi\) | |||||||
\(654\) | − | 817.729i | − | 1.25035i | ||||||
\(655\) | 657.119 | + | 149.647i | 1.00323 | + | 0.228469i | ||||
\(656\) | −263.306 | −0.401380 | ||||||||
\(657\) | 39.7076 | − | 39.7076i | 0.0604377 | − | 0.0604377i | ||||
\(658\) | −338.732 | − | 338.732i | −0.514790 | − | 0.514790i | ||||
\(659\) | 387.603i | 0.588169i | 0.955779 | + | 0.294084i | \(0.0950147\pi\) | ||||
−0.955779 | + | 0.294084i | \(0.904985\pi\) | |||||||
\(660\) | 163.963 | − | 103.136i | 0.248428 | − | 0.156266i | ||||
\(661\) | −1281.37 | −1.93853 | −0.969266 | − | 0.246017i | \(-0.920878\pi\) | ||||
−0.969266 | + | 0.246017i | \(0.920878\pi\) | |||||||
\(662\) | 89.9646 | − | 89.9646i | 0.135898 | − | 0.135898i | ||||
\(663\) | −1063.06 | − | 1063.06i | −1.60341 | − | 1.60341i | ||||
\(664\) | − | 7.19998i | − | 0.0108433i | ||||||
\(665\) | −302.090 | − | 480.256i | −0.454271 | − | 0.722190i | ||||
\(666\) | −186.712 | −0.280348 | ||||||||
\(667\) | −132.092 | + | 132.092i | −0.198040 | + | 0.198040i | ||||
\(668\) | 157.453 | + | 157.453i | 0.235708 | + | 0.235708i | ||||
\(669\) | − | 472.258i | − | 0.705917i | ||||||
\(670\) | −34.0332 | + | 149.444i | −0.0507958 | + | 0.223050i | ||||
\(671\) | −96.7353 | −0.144166 | ||||||||
\(672\) | −71.9178 | + | 71.9178i | −0.107021 | + | 0.107021i | ||||
\(673\) | −44.9321 | − | 44.9321i | −0.0667639 | − | 0.0667639i | 0.672936 | − | 0.739700i | \(-0.265033\pi\) |
−0.739700 | + | 0.672936i | \(0.765033\pi\) | |||||||
\(674\) | 571.459i | 0.847862i | ||||||||
\(675\) | −508.610 | + | 178.525i | −0.753496 | + | 0.264482i | ||||
\(676\) | 169.981 | 0.251451 | ||||||||
\(677\) | −480.166 | + | 480.166i | −0.709255 | + | 0.709255i | −0.966379 | − | 0.257124i | \(-0.917225\pi\) |
0.257124 | + | 0.966379i | \(0.417225\pi\) | |||||||
\(678\) | −213.607 | − | 213.607i | −0.315054 | − | 0.315054i | ||||
\(679\) | − | 348.070i | − | 0.512621i | ||||||
\(680\) | 380.361 | + | 86.6204i | 0.559354 | + | 0.127383i | ||||
\(681\) | 1245.24 | 1.82854 | ||||||||
\(682\) | 226.409 | − | 226.409i | 0.331978 | − | 0.331978i | ||||
\(683\) | 895.860 | + | 895.860i | 1.31165 | + | 1.31165i | 0.920196 | + | 0.391459i | \(0.128029\pi\) |
0.391459 | + | 0.920196i | \(0.371971\pi\) | |||||||
\(684\) | 116.344i | 0.170094i | ||||||||
\(685\) | 187.470 | − | 117.922i | 0.273678 | − | 0.172149i | ||||
\(686\) | −523.131 | −0.762582 | ||||||||
\(687\) | −201.421 | + | 201.421i | −0.293189 | + | 0.293189i | ||||
\(688\) | 142.212 | + | 142.212i | 0.206703 | + | 0.206703i | ||||
\(689\) | 747.297i | 1.08461i | ||||||||
\(690\) | −61.7485 | − | 98.1663i | −0.0894906 | − | 0.142270i | ||||
\(691\) | 1025.93 | 1.48470 | 0.742350 | − | 0.670012i | \(-0.233711\pi\) | ||||
0.742350 | + | 0.670012i | \(0.233711\pi\) | |||||||
\(692\) | 310.193 | − | 310.193i | 0.448256 | − | 0.448256i | ||||
\(693\) | 56.7521 | + | 56.7521i | 0.0818934 | + | 0.0818934i | ||||
\(694\) | − | 779.832i | − | 1.12368i | ||||||
\(695\) | −53.1784 | + | 233.513i | −0.0765157 | + | 0.335990i | ||||
\(696\) | 376.771 | 0.541338 | ||||||||
\(697\) | −1283.94 | + | 1283.94i | −1.84210 | + | 1.84210i | ||||
\(698\) | −459.513 | − | 459.513i | −0.658329 | − | 0.658329i | ||||
\(699\) | − | 1162.15i | − | 1.66259i | ||||||
\(700\) | −87.0618 | − | 248.035i | −0.124374 | − | 0.354336i | ||||
\(701\) | 289.331 | 0.412740 | 0.206370 | − | 0.978474i | \(-0.433835\pi\) | ||||
0.206370 | + | 0.978474i | \(0.433835\pi\) | |||||||
\(702\) | −343.624 | + | 343.624i | −0.489493 | + | 0.489493i | ||||
\(703\) | 747.601 | + | 747.601i | 1.06344 | + | 1.06344i | ||||
\(704\) | 45.3129i | 0.0643649i | ||||||||
\(705\) | −1074.18 | − | 244.626i | −1.52366 | − | 0.346987i | ||||
\(706\) | 80.9737 | 0.114694 | ||||||||
\(707\) | −572.233 | + | 572.233i | −0.809382 | + | 0.809382i | ||||
\(708\) | 157.446 | + | 157.446i | 0.222381 | + | 0.222381i | ||||
\(709\) | 741.084i | 1.04525i | 0.852562 | + | 0.522626i | \(0.175048\pi\) | ||||
−0.852562 | + | 0.522626i | \(0.824952\pi\) | |||||||
\(710\) | 230.007 | − | 144.679i | 0.323953 | − | 0.203773i | ||||
\(711\) | −88.3228 | −0.124223 | ||||||||
\(712\) | −261.270 | + | 261.270i | −0.366952 | + | 0.366952i | ||||
\(713\) | −135.554 | − | 135.554i | −0.190117 | − | 0.190117i | ||||
\(714\) | 701.377i | 0.982320i | ||||||||
\(715\) | 240.317 | + | 382.050i | 0.336107 | + | 0.534335i | ||||
\(716\) | −336.762 | −0.470338 | ||||||||
\(717\) | −767.140 | + | 767.140i | −1.06993 | + | 1.06993i | ||||
\(718\) | −433.495 | − | 433.495i | −0.603753 | − | 0.603753i | ||||
\(719\) | − | 894.494i | − | 1.24408i | −0.782985 | − | 0.622040i | \(-0.786304\pi\) | ||
0.782985 | − | 0.622040i | \(-0.213696\pi\) | |||||||
\(720\) | −11.9693 | + | 52.5586i | −0.0166240 | + | 0.0729980i | ||||
\(721\) | 95.0787 | 0.131871 | ||||||||
\(722\) | 104.846 | − | 104.846i | 0.145216 | − | 0.145216i | ||||
\(723\) | 73.7382 | + | 73.7382i | 0.101989 | + | 0.101989i | ||||
\(724\) | 486.480i | 0.671933i | ||||||||
\(725\) | −421.662 | + | 877.772i | −0.581603 | + | 1.21072i | ||||
\(726\) | −430.039 | −0.592341 | ||||||||
\(727\) | −91.2326 | + | 91.2326i | −0.125492 | + | 0.125492i | −0.767063 | − | 0.641571i | \(-0.778283\pi\) |
0.641571 | + | 0.767063i | \(0.278283\pi\) | |||||||
\(728\) | −167.576 | − | 167.576i | −0.230186 | − | 0.230186i | ||||
\(729\) | − | 399.511i | − | 0.548026i | ||||||
\(730\) | −143.648 | − | 32.7134i | −0.196779 | − | 0.0448129i | ||||
\(731\) | 1386.92 | 1.89728 | ||||||||
\(732\) | 82.5986 | − | 82.5986i | 0.112840 | − | 0.112840i | ||||
\(733\) | 830.074 | + | 830.074i | 1.13243 | + | 1.13243i | 0.989771 | + | 0.142663i | \(0.0455666\pi\) |
0.142663 | + | 0.989771i | \(0.454433\pi\) | |||||||
\(734\) | − | 47.4976i | − | 0.0647106i | ||||||
\(735\) | −309.155 | + | 194.464i | −0.420619 | + | 0.264577i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −86.8138 | + | 86.8138i | −0.117793 | + | 0.117793i | ||||
\(738\) | −177.416 | − | 177.416i | −0.240401 | − | 0.240401i | ||||
\(739\) | 980.834i | 1.32725i | 0.748067 | + | 0.663623i | \(0.230982\pi\) | ||||
−0.748067 | + | 0.663623i | \(0.769018\pi\) | |||||||
\(740\) | 260.818 | + | 414.642i | 0.352457 | + | 0.560327i | ||||
\(741\) | −1176.34 | −1.58751 | ||||||||
\(742\) | 246.523 | − | 246.523i | 0.332241 | − | 0.332241i | ||||
\(743\) | −752.792 | − | 752.792i | −1.01318 | − | 1.01318i | −0.999912 | − | 0.0132664i | \(-0.995777\pi\) |
−0.0132664 | − | 0.999912i | \(-0.504223\pi\) | |||||||
\(744\) | 386.644i | 0.519683i | ||||||||
\(745\) | −161.479 | + | 709.073i | −0.216750 | + | 0.951775i | ||||
\(746\) | −133.046 | −0.178345 | ||||||||
\(747\) | 4.85137 | − | 4.85137i | 0.00649446 | − | 0.00649446i | ||||
\(748\) | 220.956 | + | 220.956i | 0.295396 | + | 0.295396i | ||||
\(749\) | 937.304i | 1.25141i | ||||||||
\(750\) | −473.202 | − | 376.239i | −0.630936 | − | 0.501652i | ||||
\(751\) | −121.843 | −0.162241 | −0.0811207 | − | 0.996704i | \(-0.525850\pi\) | ||||
−0.0811207 | + | 0.996704i | \(0.525850\pi\) | |||||||
\(752\) | 182.233 | − | 182.233i | 0.242332 | − | 0.242332i | ||||
\(753\) | 283.074 | + | 283.074i | 0.375928 | + | 0.375928i | ||||
\(754\) | 877.915i | 1.16434i | ||||||||
\(755\) | 713.929 | + | 162.585i | 0.945602 | + | 0.215344i | ||||
\(756\) | 226.713 | 0.299885 | ||||||||
\(757\) | 257.331 | − | 257.331i | 0.339936 | − | 0.339936i | −0.516407 | − | 0.856343i | \(-0.672731\pi\) |
0.856343 | + | 0.516407i | \(0.172731\pi\) | |||||||
\(758\) | −323.563 | − | 323.563i | −0.426864 | − | 0.426864i | ||||
\(759\) | − | 92.8965i | − | 0.122393i | ||||||
\(760\) | 258.372 | − | 162.521i | 0.339963 | − | 0.213843i | ||||
\(761\) | −232.530 | −0.305558 | −0.152779 | − | 0.988260i | \(-0.548822\pi\) | ||||
−0.152779 | + | 0.988260i | \(0.548822\pi\) | |||||||
\(762\) | −412.698 | + | 412.698i | −0.541598 | + | 0.541598i | ||||
\(763\) | −628.561 | − | 628.561i | −0.823802 | − | 0.823802i | ||||
\(764\) | − | 80.7778i | − | 0.105730i | ||||||
\(765\) | 197.923 | + | 314.653i | 0.258723 | + | 0.411311i | ||||
\(766\) | 599.714 | 0.782917 | ||||||||
\(767\) | −366.865 | + | 366.865i | −0.478311 | + | 0.478311i | ||||
\(768\) | −38.6909 | − | 38.6909i | −0.0503788 | − | 0.0503788i | ||||
\(769\) | 949.124i | 1.23423i | 0.786872 | + | 0.617116i | \(0.211699\pi\) | ||||
−0.786872 | + | 0.617116i | \(0.788301\pi\) | |||||||
\(770\) | 46.7557 | − | 205.310i | 0.0607217 | − | 0.266636i | ||||
\(771\) | −714.492 | −0.926708 | ||||||||
\(772\) | 21.0501 | − | 21.0501i | 0.0272670 | − | 0.0272670i | ||||
\(773\) | −502.010 | − | 502.010i | −0.649431 | − | 0.649431i | 0.303425 | − | 0.952855i | \(-0.401870\pi\) |
−0.952855 | + | 0.303425i | \(0.901870\pi\) | |||||||
\(774\) | 191.645i | 0.247604i | ||||||||
\(775\) | −900.773 | − | 432.712i | −1.16229 | − | 0.558338i | ||||
\(776\) | 187.257 | 0.241311 | ||||||||
\(777\) | −622.767 | + | 622.767i | −0.801501 | + | 0.801501i | ||||
\(778\) | −64.2288 | − | 64.2288i | −0.0825563 | − | 0.0825563i | ||||
\(779\) | 1420.76i | 1.82383i | ||||||||
\(780\) | −531.415 | − | 121.020i | −0.681301 | − | 0.155154i | ||||
\(781\) | 217.659 | 0.278693 | ||||||||
\(782\) | 132.289 | − | 132.289i | 0.169168 | − | 0.169168i | ||||
\(783\) | −593.866 | − | 593.866i | −0.758450 | − | 0.758450i | ||||
\(784\) | − | 85.4383i | − | 0.108977i | ||||||
\(785\) | −345.969 | + | 217.621i | −0.440724 | + | 0.277224i | ||||
\(786\) | −651.887 | −0.829372 | ||||||||
\(787\) | −846.737 | + | 846.737i | −1.07591 | + | 1.07591i | −0.0790333 | + | 0.996872i | \(0.525183\pi\) |
−0.996872 | + | 0.0790333i | \(0.974817\pi\) | |||||||
\(788\) | −413.159 | − | 413.159i | −0.524313 | − | 0.524313i | ||||
\(789\) | 570.938i | 0.723623i | ||||||||
\(790\) | 123.378 | + | 196.144i | 0.156175 | + | 0.248283i | ||||
\(791\) | −328.385 | −0.415152 | ||||||||
\(792\) | −30.5319 | + | 30.5319i | −0.0385504 | + | 0.0385504i | ||||
\(793\) | 192.463 | + | 192.463i | 0.242702 | + | 0.242702i | ||||
\(794\) | 978.582i | 1.23247i | ||||||||
\(795\) | 178.034 | − | 781.770i | 0.223943 | − | 0.983358i | ||||
\(796\) | 107.741 | 0.135353 | ||||||||
\(797\) | 119.516 | − | 119.516i | 0.149957 | − | 0.149957i | −0.628142 | − | 0.778099i | \(-0.716184\pi\) |
0.778099 | + | 0.628142i | \(0.216184\pi\) | |||||||
\(798\) | 388.059 | + | 388.059i | 0.486289 | + | 0.486289i | ||||
\(799\) | − | 1777.23i | − | 2.22431i | ||||||
\(800\) | 133.440 | − | 46.8382i | 0.166800 | − | 0.0585477i | ||||
\(801\) | −352.089 | −0.439562 | ||||||||
\(802\) | 615.748 | − | 615.748i | 0.767765 | − | 0.767765i | ||||
\(803\) | −83.4472 | − | 83.4472i | −0.103919 | − | 0.103919i | ||||
\(804\) | − | 148.254i | − | 0.184395i | ||||||
\(805\) | −122.921 | − | 27.9931i | −0.152697 | − | 0.0347741i | ||||
\(806\) | −900.920 | −1.11777 | ||||||||
\(807\) | −869.622 | + | 869.622i | −1.07760 | + | 1.07760i | ||||
\(808\) | −307.855 | − | 307.855i | −0.381008 | − | 0.381008i | ||||
\(809\) | − | 305.296i | − | 0.377374i | −0.982037 | − | 0.188687i | \(-0.939577\pi\) | ||
0.982037 | − | 0.188687i | \(-0.0604232\pi\) | |||||||
\(810\) | 586.527 | − | 368.937i | 0.724108 | − | 0.455478i | ||||
\(811\) | −499.487 | −0.615890 | −0.307945 | − | 0.951404i | \(-0.599641\pi\) | ||||
−0.307945 | + | 0.951404i | \(0.599641\pi\) | |||||||
\(812\) | 289.612 | − | 289.612i | 0.356665 | − | 0.356665i | ||||
\(813\) | −859.779 | − | 859.779i | −1.05754 | − | 1.05754i | ||||
\(814\) | 392.383i | 0.482043i | ||||||||
\(815\) | 352.846 | + | 560.946i | 0.432940 | + | 0.688277i | ||||
\(816\) | −377.332 | −0.462417 | ||||||||
\(817\) | 767.355 | − | 767.355i | 0.939235 | − | 0.939235i | ||||
\(818\) | 43.1536 | + | 43.1536i | 0.0527551 | + | 0.0527551i | ||||
\(819\) | − | 225.826i | − | 0.275734i | ||||||
\(820\) | −146.166 | + | 641.831i | −0.178251 | + | 0.782721i | ||||
\(821\) | 202.465 | 0.246608 | 0.123304 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123304 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(822\) | −151.480 | + | 151.480i | −0.184282 | + | 0.184282i | ||||
\(823\) | 740.027 | + | 740.027i | 0.899182 | + | 0.899182i | 0.995364 | − | 0.0961816i | \(-0.0306630\pi\) |
−0.0961816 | + | 0.995364i | \(0.530663\pi\) | |||||||
\(824\) | 51.1512i | 0.0620767i | ||||||||
\(825\) | −160.384 | − | 456.926i | −0.194405 | − | 0.553850i | ||||
\(826\) | 242.047 | 0.293035 | ||||||||
\(827\) | 544.959 | − | 544.959i | 0.658959 | − | 0.658959i | −0.296175 | − | 0.955134i | \(-0.595711\pi\) |
0.955134 | + | 0.296175i | \(0.0957111\pi\) | |||||||
\(828\) | 18.2798 | + | 18.2798i | 0.0220771 | + | 0.0220771i | ||||
\(829\) | − | 736.438i | − | 0.888345i | −0.895941 | − | 0.444173i | \(-0.853498\pi\) | ||
0.895941 | − | 0.444173i | \(-0.146502\pi\) | |||||||
\(830\) | −17.5506 | − | 3.99684i | −0.0211453 | − | 0.00481547i | ||||
\(831\) | 884.911 | 1.06487 | ||||||||
\(832\) | 90.1537 | − | 90.1537i | 0.108358 | − | 0.108358i | ||||
\(833\) | −416.617 | − | 416.617i | −0.500141 | − | 0.500141i | ||||
\(834\) | − | 231.654i | − | 0.277762i | ||||||
\(835\) | 471.212 | − | 296.401i | 0.564325 | − | 0.354972i | ||||
\(836\) | 244.502 | 0.292467 | ||||||||
\(837\) | 609.428 | − | 609.428i | 0.728109 | − | 0.728109i | ||||
\(838\) | 49.6628 | + | 49.6628i | 0.0592635 | + | 0.0592635i | ||||
\(839\) | 1022.72i | 1.21897i | 0.792797 | + | 0.609485i | \(0.208624\pi\) | ||||
−0.792797 | + | 0.609485i | \(0.791376\pi\) | |||||||
\(840\) | 135.383 | + | 215.229i | 0.161171 | + | 0.256225i | ||||
\(841\) | −676.252 | −0.804105 | ||||||||
\(842\) | 95.0400 | − | 95.0400i | 0.112874 | − | 0.112874i | ||||
\(843\) | 1041.68 | + | 1041.68i | 1.23569 | + | 1.23569i | ||||
\(844\) | − | 283.867i | − | 0.336335i | ||||||
\(845\) | 94.3596 | − | 414.344i | 0.111668 | − | 0.490348i | ||||
\(846\) | 245.579 | 0.290282 | ||||||||
\(847\) | −330.557 | + | 330.557i | −0.390268 | + | 0.390268i | ||||
\(848\) | 132.626 | + | 132.626i | 0.156399 | + | 0.156399i | ||||
\(849\) | 849.304i | 1.00036i | ||||||||
\(850\) | 422.290 | − | 879.078i | 0.496812 | − | 1.03421i | ||||
\(851\) | 234.924 | 0.276057 | ||||||||
\(852\) | −185.851 | + | 185.851i | −0.218135 | + | 0.218135i | ||||
\(853\) | 393.306 | + | 393.306i | 0.461085 | + | 0.461085i | 0.899011 | − | 0.437926i | \(-0.144287\pi\) |
−0.437926 | + | 0.899011i | \(0.644287\pi\) | |||||||
\(854\) | − | 126.982i | − | 0.148690i | ||||||
\(855\) | 283.599 | + | 64.5847i | 0.331695 | + | 0.0755376i | ||||
\(856\) | −504.259 | −0.589087 | ||||||||
\(857\) | −280.421 | + | 280.421i | −0.327213 | + | 0.327213i | −0.851526 | − | 0.524313i | \(-0.824322\pi\) |
0.524313 | + | 0.851526i | \(0.324322\pi\) | |||||||
\(858\) | −308.706 | − | 308.706i | −0.359797 | − | 0.359797i | ||||
\(859\) | − | 777.697i | − | 0.905351i | −0.891675 | − | 0.452676i | \(-0.850470\pi\) | ||
0.891675 | − | 0.452676i | \(-0.149530\pi\) | |||||||
\(860\) | 425.598 | − | 267.709i | 0.494881 | − | 0.311290i | ||||
\(861\) | −1183.52 | −1.37459 | ||||||||
\(862\) | 697.801 | − | 697.801i | 0.809514 | − | 0.809514i | ||||
\(863\) | −641.227 | − | 641.227i | −0.743021 | − | 0.743021i | 0.230137 | − | 0.973158i | \(-0.426083\pi\) |
−0.973158 | + | 0.230137i | \(0.926083\pi\) | |||||||
\(864\) | 121.969i | 0.141168i | ||||||||
\(865\) | −583.929 | − | 928.317i | −0.675063 | − | 1.07320i | ||||
\(866\) | −774.735 | −0.894614 | ||||||||
\(867\) | −1141.11 | + | 1141.11i | −1.31616 | + | 1.31616i | ||||
\(868\) | 297.201 | + | 297.201i | 0.342397 | + | 0.342397i | ||||
\(869\) | 185.614i | 0.213595i | ||||||||
\(870\) | 209.153 | − | 918.414i | 0.240405 | − | 1.05565i | ||||
\(871\) | 345.447 | 0.396609 | ||||||||
\(872\) | 338.158 | − | 338.158i | 0.387796 | − | 0.387796i | ||||
\(873\) | 126.175 | + | 126.175i | 0.144530 | + | 0.144530i | ||||
\(874\) | − | 146.386i | − | 0.167490i | ||||||
\(875\) | −652.937 | + | 74.5323i | −0.746214 | + | 0.0851797i | ||||
\(876\) | 142.505 | 0.162677 | ||||||||
\(877\) | 661.294 | − | 661.294i | 0.754041 | − | 0.754041i | −0.221190 | − | 0.975231i | \(-0.570994\pi\) |
0.975231 | + | 0.221190i | \(0.0709941\pi\) | |||||||
\(878\) | 186.351 | + | 186.351i | 0.212245 | + | 0.212245i | ||||
\(879\) | − | 1000.72i | − | 1.13847i | ||||||
\(880\) | 110.454 | + | 25.1540i | 0.125516 | + | 0.0285841i | ||||
\(881\) | 486.151 | 0.551817 | 0.275909 | − | 0.961184i | \(-0.411021\pi\) | ||||
0.275909 | + | 0.961184i | \(0.411021\pi\) | |||||||
\(882\) | 57.5686 | − | 57.5686i | 0.0652705 | − | 0.0652705i | ||||
\(883\) | 756.733 | + | 756.733i | 0.857003 | + | 0.857003i | 0.990984 | − | 0.133981i | \(-0.0427761\pi\) |
−0.133981 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(884\) | − | 879.222i | − | 0.994595i | ||||||
\(885\) | 471.190 | − | 296.387i | 0.532418 | − | 0.334901i | ||||
\(886\) | −688.783 | −0.777407 | ||||||||
\(887\) | 545.935 | − | 545.935i | 0.615485 | − | 0.615485i | −0.328885 | − | 0.944370i | \(-0.606673\pi\) |
0.944370 | + | 0.328885i | \(0.106673\pi\) | |||||||
\(888\) | −335.041 | − | 335.041i | −0.377298 | − | 0.377298i | ||||
\(889\) | 634.454i | 0.713672i | ||||||||
\(890\) | 491.833 | + | 781.905i | 0.552622 | + | 0.878545i | ||||
\(891\) | 555.042 | 0.622942 | ||||||||
\(892\) | 195.295 | − | 195.295i | 0.218940 | − | 0.218940i | ||||
\(893\) | −983.308 | − | 983.308i | −1.10113 | − | 1.10113i | ||||
\(894\) | − | 703.427i | − | 0.786831i | ||||||
\(895\) | −186.943 | + | 820.888i | −0.208875 | + | 0.917194i | ||||
\(896\) | −59.4809 | −0.0663849 | ||||||||
\(897\) | −184.825 | + | 184.825i | −0.206048 | + | 0.206048i | ||||
\(898\) | −85.4403 | − | 85.4403i | −0.0951451 | − | 0.0951451i | ||||
\(899\) | − | 1557.01i | − | 1.73194i | ||||||
\(900\) | 121.472 | + | 58.3524i | 0.134969 | + | 0.0648360i | ||||
\(901\) | 1293.43 | 1.43555 | ||||||||
\(902\) | −372.848 | + | 372.848i | −0.413357 | + | 0.413357i | ||||
\(903\) | 639.222 | + | 639.222i | 0.707887 | + | 0.707887i | ||||
\(904\) | − | 176.667i | − | 0.195428i | ||||||
\(905\) | 1185.84 | + | 270.054i | 1.31032 | + | 0.298402i | ||||
\(906\) | −708.245 | −0.781728 | ||||||||
\(907\) | −591.187 | + | 591.187i | −0.651805 | + | 0.651805i | −0.953427 | − | 0.301623i | \(-0.902472\pi\) |
0.301623 | + | 0.953427i | \(0.402472\pi\) | |||||||
\(908\) | 514.947 | + | 514.947i | 0.567122 | + | 0.567122i | ||||
\(909\) | − | 414.867i | − | 0.456399i | ||||||
\(910\) | −501.505 | + | 315.457i | −0.551105 | + | 0.346656i | ||||
\(911\) | −1015.60 | −1.11482 | −0.557409 | − | 0.830238i | \(-0.688204\pi\) | ||||
−0.557409 | + | 0.830238i | \(0.688204\pi\) | |||||||
\(912\) | −208.771 | + | 208.771i | −0.228916 | + | 0.228916i | ||||
\(913\) | −10.1954 | − | 10.1954i | −0.0111669 | − | 0.0111669i | ||||
\(914\) | 476.910i | 0.521784i | ||||||||
\(915\) | −155.489 | − | 247.193i | −0.169934 | − | 0.270157i | ||||
\(916\) | −166.588 | −0.181865 | ||||||||
\(917\) | −501.084 | + | 501.084i | −0.546438 | + | 0.546438i | ||||
\(918\) | 594.750 | + | 594.750i | 0.647876 | + | 0.647876i | ||||
\(919\) | 621.488i | 0.676266i | 0.941098 | + | 0.338133i | \(0.109795\pi\) | ||||
−0.941098 | + | 0.338133i | \(0.890205\pi\) | |||||||
\(920\) | 15.0600 | − | 66.1302i | 0.0163695 | − | 0.0718806i | ||||
\(921\) | 1894.15 | 2.05662 | ||||||||
\(922\) | −278.593 | + | 278.593i | −0.302161 | + | 0.302161i | ||||
\(923\) | −433.052 | − | 433.052i | −0.469178 | − | 0.469178i | ||||
\(924\) | 203.675i | 0.220428i | ||||||||
\(925\) | 1155.51 | − | 405.592i | 1.24920 | − | 0.438478i | ||||
\(926\) | −635.954 | −0.686775 | ||||||||
\(927\) | −34.4658 | + | 34.4658i | −0.0371800 | + | 0.0371800i | ||||
\(928\) | 155.808 | + | 155.808i | 0.167896 | + | 0.167896i | ||||
\(929\) | 812.510i | 0.874607i | 0.899314 | + | 0.437304i | \(0.144067\pi\) | ||||
−0.899314 | + | 0.437304i | \(0.855933\pi\) | |||||||
\(930\) | 942.480 | + | 214.633i | 1.01342 | + | 0.230788i | ||||
\(931\) | −461.013 | −0.495181 | ||||||||
\(932\) | 480.588 | − | 480.588i | 0.515652 | − | 0.515652i | ||||
\(933\) | −518.603 | − | 518.603i | −0.555844 | − | 0.555844i | ||||
\(934\) | 328.639i | 0.351861i | ||||||||
\(935\) | 661.258 | − | 415.944i | 0.707228 | − | 0.444860i | ||||
\(936\) | 121.492 | 0.129799 | ||||||||
\(937\) | 443.029 | − | 443.029i | 0.472816 | − | 0.472816i | −0.430008 | − | 0.902825i | \(-0.641489\pi\) |
0.902825 | + | 0.430008i | \(0.141489\pi\) | |||||||
\(938\) | −113.958 | − | 113.958i | −0.121490 | − | 0.121490i | ||||
\(939\) | 181.390i | 0.193174i | ||||||||
\(940\) | −343.049 | − | 545.372i | −0.364946 | − | 0.580183i | ||||
\(941\) | −751.943 | −0.799090 | −0.399545 | − | 0.916714i | \(-0.630832\pi\) | ||||
−0.399545 | + | 0.916714i | \(0.630832\pi\) | |||||||
\(942\) | 279.551 | − | 279.551i | 0.296763 | − | 0.296763i | ||||
\(943\) | 223.228 | + | 223.228i | 0.236721 | + | 0.236721i | ||||
\(944\) | 130.218i | 0.137943i | ||||||||
\(945\) | 125.853 | − | 552.634i | 0.133177 | − | 0.584798i | ||||
\(946\) | 402.751 | 0.425741 | ||||||||
\(947\) | −1086.68 | + | 1086.68i | −1.14750 | + | 1.14750i | −0.160460 | + | 0.987042i | \(0.551298\pi\) |
−0.987042 | + | 0.160460i | \(0.948702\pi\) | |||||||
\(948\) | −158.489 | − | 158.489i | −0.167183 | − | 0.167183i | ||||
\(949\) | 332.050i | 0.349895i | ||||||||
\(950\) | −252.733 | − | 720.023i | −0.266034 | − | 0.757919i | ||||
\(951\) | 679.255 | 0.714254 | ||||||||
\(952\) | −290.043 | + | 290.043i | −0.304667 | + | 0.304667i | ||||
\(953\) | −58.8145 | − | 58.8145i | −0.0617151 | − | 0.0617151i | 0.675576 | − | 0.737291i | \(-0.263895\pi\) |
−0.737291 | + | 0.675576i | \(0.763895\pi\) | |||||||
\(954\) | 178.728i | 0.187346i | ||||||||
\(955\) | −196.903 | − | 44.8412i | −0.206181 | − | 0.0469542i | ||||
\(956\) | −634.476 | −0.663678 | ||||||||
\(957\) | 533.519 | − | 533.519i | 0.557491 | − | 0.557491i | ||||
\(958\) | 55.2512 | + | 55.2512i | 0.0576735 | + | 0.0576735i | ||||
\(959\) | 232.876i | 0.242832i | ||||||||
\(960\) | −115.791 | + | 72.8346i | −0.120615 | + | 0.0758693i | ||||
\(961\) | 636.810 | 0.662654 | ||||||||
\(962\) | 780.679 | − | 780.679i | 0.811517 | − | 0.811517i | ||||
\(963\) | −339.771 | − | 339.771i | −0.352825 | − | 0.352825i | ||||
\(964\) | 60.9865i | 0.0632640i | ||||||||
\(965\) | −39.6262 | − | 62.9968i | −0.0410634 | − | 0.0652817i | ||||
\(966\) | 121.943 | 0.126235 | ||||||||
\(967\) | −280.533 | + | 280.533i | −0.290107 | + | 0.290107i | −0.837122 | − | 0.547016i | \(-0.815764\pi\) |
0.547016 | + | 0.837122i | \(0.315764\pi\) | |||||||
\(968\) | −177.836 | − | 177.836i | −0.183715 | − | 0.183715i | ||||
\(969\) | 2036.03i | 2.10117i | ||||||||
\(970\) | 103.950 | − | 456.457i | 0.107165 | − | 0.470574i | ||||
\(971\) | 1572.33 | 1.61929 | 0.809644 | − | 0.586922i | \(-0.199660\pi\) | ||||
0.809644 | + | 0.586922i | \(0.199660\pi\) | |||||||
\(972\) | −199.498 | + | 199.498i | −0.205245 | + | 0.205245i | ||||
\(973\) | −178.065 | − | 178.065i | −0.183006 | − | 0.183006i | ||||
\(974\) | 707.958i | 0.726857i | ||||||||
\(975\) | −589.996 | + | 1228.19i | −0.605124 | + | 1.25968i | ||||
\(976\) | 68.3146 | 0.0699945 | ||||||||
\(977\) | 411.650 | − | 411.650i | 0.421341 | − | 0.421341i | −0.464324 | − | 0.885665i | \(-0.653703\pi\) |
0.885665 | + | 0.464324i | \(0.153703\pi\) | |||||||
\(978\) | −453.258 | − | 453.258i | −0.463454 | − | 0.463454i | ||||
\(979\) | 739.931i | 0.755803i | ||||||||
\(980\) | −208.263 | − | 47.4283i | −0.212514 | − | 0.0483963i | ||||
\(981\) | 455.704 | 0.464530 | ||||||||
\(982\) | 698.356 | − | 698.356i | 0.711157 | − | 0.711157i | ||||
\(983\) | 583.376 | + | 583.376i | 0.593465 | + | 0.593465i | 0.938566 | − | 0.345100i | \(-0.112155\pi\) |
−0.345100 | + | 0.938566i | \(0.612155\pi\) | |||||||
\(984\) | − | 636.721i | − | 0.647074i | ||||||
\(985\) | −1236.46 | + | 777.759i | −1.25529 | + | 0.789603i | ||||
\(986\) | 1519.51 | 1.54109 | ||||||||
\(987\) | 819.115 | − | 819.115i | 0.829903 | − | 0.829903i | ||||
\(988\) | −486.458 | − | 486.458i | −0.492366 | − | 0.492366i | ||||
\(989\) | − | 241.131i | − | 0.243813i | ||||||
\(990\) | 57.4755 | + | 91.3732i | 0.0580561 | + | 0.0922962i | ||||
\(991\) | −1102.34 | −1.11235 | −0.556174 | − | 0.831066i | \(-0.687731\pi\) | ||||
−0.556174 | + | 0.831066i | \(0.687731\pi\) | |||||||
\(992\) | −159.890 | + | 159.890i | −0.161180 | + | 0.161180i | ||||
\(993\) | 217.551 | + | 217.551i | 0.219084 | + | 0.219084i | ||||
\(994\) | 285.715i | 0.287440i | ||||||||
\(995\) | 59.8088 | − | 262.627i | 0.0601093 | − | 0.263947i | ||||
\(996\) | 17.4109 | 0.0174808 | ||||||||
\(997\) | 1326.04 | − | 1326.04i | 1.33003 | − | 1.33003i | 0.424696 | − | 0.905336i | \(-0.360381\pi\) |
0.905336 | − | 0.424696i | \(-0.139619\pi\) | |||||||
\(998\) | 27.0217 | + | 27.0217i | 0.0270759 | + | 0.0270759i | ||||
\(999\) | 1056.18i | 1.05724i |
(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 | 230.3.f.a.93.3 | yes | 20 | |
5.2 | odd | 4 | inner | 230.3.f.a.47.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.a.47.3 | ✓ | 20 | 5.2 | odd | 4 | inner | |
230.3.f.a.93.3 | yes | 20 | 1.1 | even | 1 | trivial |