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 | 93.8 | ||
Root | \(1.94658 + 1.94658i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.93 |
Dual form | 230.3.f.a.47.8 |
$q$-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 | ||||
\(3\) | 1.94658 | + | 1.94658i | 0.648860 | + | 0.648860i | 0.952717 | − | 0.303858i | \(-0.0982748\pi\) |
−0.303858 | + | 0.952717i | \(0.598275\pi\) | |||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0.283956 | + | 4.99193i | 0.0567911 | + | 0.998386i | ||||
\(6\) | −3.89316 | −0.648860 | ||||||||
\(7\) | 9.76397 | − | 9.76397i | 1.39485 | − | 1.39485i | 0.580822 | − | 0.814031i | \(-0.302731\pi\) |
0.814031 | − | 0.580822i | \(-0.197269\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.42166i | − | 0.157963i | ||||||
\(10\) | −5.27589 | − | 4.70797i | −0.527589 | − | 0.470797i | ||||
\(11\) | 21.6746 | 1.97042 | 0.985208 | − | 0.171364i | \(-0.0548173\pi\) | ||||
0.985208 | + | 0.171364i | \(0.0548173\pi\) | |||||||
\(12\) | 3.89316 | − | 3.89316i | 0.324430 | − | 0.324430i | ||||
\(13\) | −0.532316 | − | 0.532316i | −0.0409474 | − | 0.0409474i | 0.686337 | − | 0.727284i | \(-0.259218\pi\) |
−0.727284 | + | 0.686337i | \(0.759218\pi\) | |||||||
\(14\) | 19.5279i | 1.39485i | ||||||||
\(15\) | −9.16444 | + | 10.2699i | −0.610963 | + | 0.684662i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −18.9142 | + | 18.9142i | −1.11260 | + | 1.11260i | −0.119804 | + | 0.992798i | \(0.538227\pi\) |
−0.992798 | + | 0.119804i | \(0.961773\pi\) | |||||||
\(18\) | 1.42166 | + | 1.42166i | 0.0789813 | + | 0.0789813i | ||||
\(19\) | − | 7.51292i | − | 0.395417i | −0.980261 | − | 0.197708i | \(-0.936650\pi\) | ||
0.980261 | − | 0.197708i | \(-0.0633499\pi\) | |||||||
\(20\) | 9.98386 | − | 0.567911i | 0.499193 | − | 0.0283956i | ||||
\(21\) | 38.0127 | 1.81013 | ||||||||
\(22\) | −21.6746 | + | 21.6746i | −0.985208 | + | 0.985208i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | 7.78631i | 0.324430i | ||||||||
\(25\) | −24.8387 | + | 2.83497i | −0.993550 | + | 0.113399i | ||||
\(26\) | 1.06463 | 0.0409474 | ||||||||
\(27\) | 20.2866 | − | 20.2866i | 0.751355 | − | 0.751355i | ||||
\(28\) | −19.5279 | − | 19.5279i | −0.697426 | − | 0.697426i | ||||
\(29\) | 14.9938i | 0.517026i | 0.966008 | + | 0.258513i | \(0.0832326\pi\) | ||||
−0.966008 | + | 0.258513i | \(0.916767\pi\) | |||||||
\(30\) | −1.10548 | − | 19.4344i | −0.0368495 | − | 0.647812i | ||||
\(31\) | −13.8457 | −0.446635 | −0.223317 | − | 0.974746i | \(-0.571689\pi\) | ||||
−0.223317 | + | 0.974746i | \(0.571689\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 42.1913 | + | 42.1913i | 1.27852 | + | 1.27852i | ||||
\(34\) | − | 37.8285i | − | 1.11260i | ||||||
\(35\) | 51.5136 | + | 45.9685i | 1.47182 | + | 1.31339i | ||||
\(36\) | −2.84333 | −0.0789813 | ||||||||
\(37\) | −34.1988 | + | 34.1988i | −0.924292 | + | 0.924292i | −0.997329 | − | 0.0730376i | \(-0.976731\pi\) |
0.0730376 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(38\) | 7.51292 | + | 7.51292i | 0.197708 | + | 0.197708i | ||||
\(39\) | − | 2.07239i | − | 0.0531382i | ||||||
\(40\) | −9.41595 | + | 10.5518i | −0.235399 | + | 0.263794i | ||||
\(41\) | −34.2921 | −0.836394 | −0.418197 | − | 0.908356i | \(-0.637338\pi\) | ||||
−0.418197 | + | 0.908356i | \(0.637338\pi\) | |||||||
\(42\) | −38.0127 | + | 38.0127i | −0.905063 | + | 0.905063i | ||||
\(43\) | 32.8950 | + | 32.8950i | 0.765000 | + | 0.765000i | 0.977222 | − | 0.212222i | \(-0.0680699\pi\) |
−0.212222 | + | 0.977222i | \(0.568070\pi\) | |||||||
\(44\) | − | 43.3491i | − | 0.985208i | ||||||
\(45\) | 7.09685 | − | 0.403689i | 0.157708 | − | 0.00897088i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 1.95008 | − | 1.95008i | 0.0414911 | − | 0.0414911i | −0.686057 | − | 0.727548i | \(-0.740660\pi\) |
0.727548 | + | 0.686057i | \(0.240660\pi\) | |||||||
\(48\) | −7.78631 | − | 7.78631i | −0.162215 | − | 0.162215i | ||||
\(49\) | − | 141.670i | − | 2.89123i | ||||||
\(50\) | 22.0038 | − | 27.6737i | 0.440075 | − | 0.553474i | ||||
\(51\) | −73.6361 | −1.44384 | ||||||||
\(52\) | −1.06463 | + | 1.06463i | −0.0204737 | + | 0.0204737i | ||||
\(53\) | 29.3946 | + | 29.3946i | 0.554616 | + | 0.554616i | 0.927769 | − | 0.373154i | \(-0.121724\pi\) |
−0.373154 | + | 0.927769i | \(0.621724\pi\) | |||||||
\(54\) | 40.5732i | 0.751355i | ||||||||
\(55\) | 6.15462 | + | 108.198i | 0.111902 | + | 1.96724i | ||||
\(56\) | 39.0559 | 0.697426 | ||||||||
\(57\) | 14.6245 | − | 14.6245i | 0.256570 | − | 0.256570i | ||||
\(58\) | −14.9938 | − | 14.9938i | −0.258513 | − | 0.258513i | ||||
\(59\) | − | 36.8175i | − | 0.624025i | −0.950078 | − | 0.312012i | \(-0.898997\pi\) | ||
0.950078 | − | 0.312012i | \(-0.101003\pi\) | |||||||
\(60\) | 20.5399 | + | 18.3289i | 0.342331 | + | 0.305481i | ||||
\(61\) | 1.40337 | 0.0230061 | 0.0115030 | − | 0.999934i | \(-0.496338\pi\) | ||||
0.0115030 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(62\) | 13.8457 | − | 13.8457i | 0.223317 | − | 0.223317i | ||||
\(63\) | −13.8811 | − | 13.8811i | −0.220335 | − | 0.220335i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 2.50613 | − | 2.80844i | 0.0385558 | − | 0.0432067i | ||||
\(66\) | −84.3825 | −1.27852 | ||||||||
\(67\) | 15.7465 | − | 15.7465i | 0.235022 | − | 0.235022i | −0.579763 | − | 0.814785i | \(-0.696855\pi\) |
0.814785 | + | 0.579763i | \(0.196855\pi\) | |||||||
\(68\) | 37.8285 | + | 37.8285i | 0.556301 | + | 0.556301i | ||||
\(69\) | − | 13.2023i | − | 0.191338i | ||||||
\(70\) | −97.4821 | + | 5.54507i | −1.39260 | + | 0.0792153i | ||||
\(71\) | −56.6402 | −0.797749 | −0.398874 | − | 0.917006i | \(-0.630599\pi\) | ||||
−0.398874 | + | 0.917006i | \(0.630599\pi\) | |||||||
\(72\) | 2.84333 | − | 2.84333i | 0.0394907 | − | 0.0394907i | ||||
\(73\) | 8.98250 | + | 8.98250i | 0.123048 | + | 0.123048i | 0.765949 | − | 0.642901i | \(-0.222269\pi\) |
−0.642901 | + | 0.765949i | \(0.722269\pi\) | |||||||
\(74\) | − | 68.3976i | − | 0.924292i | ||||||
\(75\) | −53.8691 | − | 42.8321i | −0.718254 | − | 0.571094i | ||||
\(76\) | −15.0258 | −0.197708 | ||||||||
\(77\) | 211.630 | − | 211.630i | 2.74844 | − | 2.74844i | ||||
\(78\) | 2.07239 | + | 2.07239i | 0.0265691 | + | 0.0265691i | ||||
\(79\) | − | 78.8377i | − | 0.997946i | −0.866618 | − | 0.498973i | \(-0.833711\pi\) | ||
0.866618 | − | 0.498973i | \(-0.166289\pi\) | |||||||
\(80\) | −1.13582 | − | 19.9677i | −0.0141978 | − | 0.249597i | ||||
\(81\) | 66.1839 | 0.817085 | ||||||||
\(82\) | 34.2921 | − | 34.2921i | 0.418197 | − | 0.418197i | ||||
\(83\) | −61.7870 | − | 61.7870i | −0.744422 | − | 0.744422i | 0.229004 | − | 0.973426i | \(-0.426453\pi\) |
−0.973426 | + | 0.229004i | \(0.926453\pi\) | |||||||
\(84\) | − | 76.0253i | − | 0.905063i | ||||||
\(85\) | −99.7893 | − | 89.0477i | −1.17399 | − | 1.04762i | ||||
\(86\) | −65.7900 | −0.765000 | ||||||||
\(87\) | −29.1865 | + | 29.1865i | −0.335478 | + | 0.335478i | ||||
\(88\) | 43.3491 | + | 43.3491i | 0.492604 | + | 0.492604i | ||||
\(89\) | − | 36.1338i | − | 0.405998i | −0.979179 | − | 0.202999i | \(-0.934931\pi\) | ||
0.979179 | − | 0.202999i | \(-0.0650688\pi\) | |||||||
\(90\) | −6.69316 | + | 7.50053i | −0.0743684 | + | 0.0833393i | ||||
\(91\) | −10.3950 | −0.114231 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | −26.9517 | − | 26.9517i | −0.289803 | − | 0.289803i | ||||
\(94\) | 3.90016i | 0.0414911i | ||||||||
\(95\) | 37.5040 | − | 2.13334i | 0.394779 | − | 0.0224562i | ||||
\(96\) | 15.5726 | 0.162215 | ||||||||
\(97\) | −89.6141 | + | 89.6141i | −0.923857 | + | 0.923857i | −0.997299 | − | 0.0734423i | \(-0.976602\pi\) |
0.0734423 | + | 0.997299i | \(0.476602\pi\) | |||||||
\(98\) | 141.670 | + | 141.670i | 1.44561 | + | 1.44561i | ||||
\(99\) | − | 30.8139i | − | 0.311252i | ||||||
\(100\) | 5.66995 | + | 49.6775i | 0.0566995 | + | 0.496775i | ||||
\(101\) | −92.9192 | −0.919992 | −0.459996 | − | 0.887921i | \(-0.652149\pi\) | ||||
−0.459996 | + | 0.887921i | \(0.652149\pi\) | |||||||
\(102\) | 73.6361 | − | 73.6361i | 0.721922 | − | 0.721922i | ||||
\(103\) | −16.8396 | − | 16.8396i | −0.163491 | − | 0.163491i | 0.620620 | − | 0.784111i | \(-0.286881\pi\) |
−0.784111 | + | 0.620620i | \(0.786881\pi\) | |||||||
\(104\) | − | 2.12926i | − | 0.0204737i | ||||||
\(105\) | 10.7939 | + | 189.757i | 0.102799 | + | 1.80721i | ||||
\(106\) | −58.7893 | −0.554616 | ||||||||
\(107\) | −55.1257 | + | 55.1257i | −0.515194 | + | 0.515194i | −0.916113 | − | 0.400919i | \(-0.868691\pi\) |
0.400919 | + | 0.916113i | \(0.368691\pi\) | |||||||
\(108\) | −40.5732 | − | 40.5732i | −0.375678 | − | 0.375678i | ||||
\(109\) | 3.66113i | 0.0335883i | 0.999859 | + | 0.0167942i | \(0.00534600\pi\) | ||||
−0.999859 | + | 0.0167942i | \(0.994654\pi\) | |||||||
\(110\) | −114.353 | − | 102.043i | −1.03957 | − | 0.927667i | ||||
\(111\) | −133.141 | −1.19947 | ||||||||
\(112\) | −39.0559 | + | 39.0559i | −0.348713 | + | 0.348713i | ||||
\(113\) | 55.5662 | + | 55.5662i | 0.491736 | + | 0.491736i | 0.908853 | − | 0.417117i | \(-0.136959\pi\) |
−0.417117 | + | 0.908853i | \(0.636959\pi\) | |||||||
\(114\) | 29.2490i | 0.256570i | ||||||||
\(115\) | 15.9655 | − | 17.8914i | 0.138831 | − | 0.155577i | ||||
\(116\) | 29.9875 | 0.258513 | ||||||||
\(117\) | −0.756774 | + | 0.756774i | −0.00646815 | + | 0.00646815i | ||||
\(118\) | 36.8175 | + | 36.8175i | 0.312012 | + | 0.312012i | ||||
\(119\) | 369.356i | 3.10383i | ||||||||
\(120\) | −38.8687 | + | 2.21097i | −0.323906 | + | 0.0184247i | ||||
\(121\) | 348.787 | 2.88254 | ||||||||
\(122\) | −1.40337 | + | 1.40337i | −0.0115030 | + | 0.0115030i | ||||
\(123\) | −66.7524 | − | 66.7524i | −0.542702 | − | 0.542702i | ||||
\(124\) | 27.6914i | 0.223317i | ||||||||
\(125\) | −21.2051 | − | 123.188i | −0.169641 | − | 0.985506i | ||||
\(126\) | 27.7622 | 0.220335 | ||||||||
\(127\) | −81.4452 | + | 81.4452i | −0.641301 | + | 0.641301i | −0.950875 | − | 0.309574i | \(-0.899813\pi\) |
0.309574 | + | 0.950875i | \(0.399813\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 128.065i | 0.992755i | ||||||||
\(130\) | 0.302308 | + | 5.31457i | 0.00232545 | + | 0.0408813i | ||||
\(131\) | −36.7271 | −0.280360 | −0.140180 | − | 0.990126i | \(-0.544768\pi\) | ||||
−0.140180 | + | 0.990126i | \(0.544768\pi\) | |||||||
\(132\) | 84.3825 | − | 84.3825i | 0.639262 | − | 0.639262i | ||||
\(133\) | −73.3559 | − | 73.3559i | −0.551548 | − | 0.551548i | ||||
\(134\) | 31.4930i | 0.235022i | ||||||||
\(135\) | 107.030 | + | 95.5087i | 0.792813 | + | 0.707472i | ||||
\(136\) | −75.6569 | −0.556301 | ||||||||
\(137\) | 26.0189 | − | 26.0189i | 0.189919 | − | 0.189919i | −0.605742 | − | 0.795661i | \(-0.707124\pi\) |
0.795661 | + | 0.605742i | \(0.207124\pi\) | |||||||
\(138\) | 13.2023 | + | 13.2023i | 0.0956691 | + | 0.0956691i | ||||
\(139\) | − | 31.2956i | − | 0.225148i | −0.993643 | − | 0.112574i | \(-0.964090\pi\) | ||
0.993643 | − | 0.112574i | \(-0.0359095\pi\) | |||||||
\(140\) | 91.9370 | − | 103.027i | 0.656693 | − | 0.735908i | ||||
\(141\) | 7.59198 | 0.0538438 | ||||||||
\(142\) | 56.6402 | − | 56.6402i | 0.398874 | − | 0.398874i | ||||
\(143\) | −11.5377 | − | 11.5377i | −0.0806833 | − | 0.0806833i | ||||
\(144\) | 5.68665i | 0.0394907i | ||||||||
\(145\) | −74.8478 | + | 4.25757i | −0.516192 | + | 0.0293625i | ||||
\(146\) | −17.9650 | −0.123048 | ||||||||
\(147\) | 275.772 | − | 275.772i | 1.87600 | − | 1.87600i | ||||
\(148\) | 68.3976 | + | 68.3976i | 0.462146 | + | 0.462146i | ||||
\(149\) | − | 129.249i | − | 0.867445i | −0.901046 | − | 0.433723i | \(-0.857200\pi\) | ||
0.901046 | − | 0.433723i | \(-0.142800\pi\) | |||||||
\(150\) | 96.7011 | − | 11.0370i | 0.644674 | − | 0.0735800i | ||||
\(151\) | 23.8722 | 0.158094 | 0.0790470 | − | 0.996871i | \(-0.474812\pi\) | ||||
0.0790470 | + | 0.996871i | \(0.474812\pi\) | |||||||
\(152\) | 15.0258 | − | 15.0258i | 0.0988542 | − | 0.0988542i | ||||
\(153\) | 26.8897 | + | 26.8897i | 0.175749 | + | 0.175749i | ||||
\(154\) | 423.260i | 2.74844i | ||||||||
\(155\) | −3.93156 | − | 69.1167i | −0.0253649 | − | 0.445914i | ||||
\(156\) | −4.14478 | −0.0265691 | ||||||||
\(157\) | 18.8241 | − | 18.8241i | 0.119899 | − | 0.119899i | −0.644612 | − | 0.764510i | \(-0.722981\pi\) |
0.764510 | + | 0.644612i | \(0.222981\pi\) | |||||||
\(158\) | 78.8377 | + | 78.8377i | 0.498973 | + | 0.498973i | ||||
\(159\) | 114.438i | 0.719735i | ||||||||
\(160\) | 21.1035 | + | 18.8319i | 0.131897 | + | 0.117699i | ||||
\(161\) | −66.2224 | −0.411320 | ||||||||
\(162\) | −66.1839 | + | 66.1839i | −0.408543 | + | 0.408543i | ||||
\(163\) | 213.024 | + | 213.024i | 1.30689 | + | 1.30689i | 0.923646 | + | 0.383247i | \(0.125194\pi\) |
0.383247 | + | 0.923646i | \(0.374806\pi\) | |||||||
\(164\) | 68.5843i | 0.418197i | ||||||||
\(165\) | −198.635 | + | 222.596i | −1.20385 | + | 1.34907i | ||||
\(166\) | 123.574 | 0.744422 | ||||||||
\(167\) | −40.3083 | + | 40.3083i | −0.241367 | + | 0.241367i | −0.817416 | − | 0.576048i | \(-0.804594\pi\) |
0.576048 | + | 0.817416i | \(0.304594\pi\) | |||||||
\(168\) | 76.0253 | + | 76.0253i | 0.452532 | + | 0.452532i | ||||
\(169\) | − | 168.433i | − | 0.996647i | ||||||
\(170\) | 188.837 | − | 10.7416i | 1.11081 | − | 0.0631859i | ||||
\(171\) | −10.6808 | −0.0624611 | ||||||||
\(172\) | 65.7900 | − | 65.7900i | 0.382500 | − | 0.382500i | ||||
\(173\) | 108.158 | + | 108.158i | 0.625193 | + | 0.625193i | 0.946855 | − | 0.321661i | \(-0.104241\pi\) |
−0.321661 | + | 0.946855i | \(0.604241\pi\) | |||||||
\(174\) | − | 58.3731i | − | 0.335478i | ||||||
\(175\) | −214.844 | + | 270.205i | −1.22768 | + | 1.54403i | ||||
\(176\) | −86.6983 | −0.492604 | ||||||||
\(177\) | 71.6681 | − | 71.6681i | 0.404904 | − | 0.404904i | ||||
\(178\) | 36.1338 | + | 36.1338i | 0.202999 | + | 0.202999i | ||||
\(179\) | − | 35.3314i | − | 0.197382i | −0.995118 | − | 0.0986912i | \(-0.968534\pi\) | ||
0.995118 | − | 0.0986912i | \(-0.0314656\pi\) | |||||||
\(180\) | −0.807379 | − | 14.1937i | −0.00448544 | − | 0.0788538i | ||||
\(181\) | −220.468 | −1.21805 | −0.609026 | − | 0.793150i | \(-0.708440\pi\) | ||||
−0.609026 | + | 0.793150i | \(0.708440\pi\) | |||||||
\(182\) | 10.3950 | − | 10.3950i | 0.0571155 | − | 0.0571155i | ||||
\(183\) | 2.73177 | + | 2.73177i | 0.0149277 | + | 0.0149277i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | −180.429 | − | 161.007i | −0.975291 | − | 0.870308i | ||||
\(186\) | 53.9034 | 0.289803 | ||||||||
\(187\) | −409.958 | + | 409.958i | −2.19229 | + | 2.19229i | ||||
\(188\) | −3.90016 | − | 3.90016i | −0.0207456 | − | 0.0207456i | ||||
\(189\) | − | 396.155i | − | 2.09606i | ||||||
\(190\) | −35.3706 | + | 39.6373i | −0.186161 | + | 0.208617i | ||||
\(191\) | 288.600 | 1.51100 | 0.755498 | − | 0.655151i | \(-0.227395\pi\) | ||||
0.755498 | + | 0.655151i | \(0.227395\pi\) | |||||||
\(192\) | −15.5726 | + | 15.5726i | −0.0811074 | + | 0.0811074i | ||||
\(193\) | −127.290 | − | 127.290i | −0.659533 | − | 0.659533i | 0.295736 | − | 0.955270i | \(-0.404435\pi\) |
−0.955270 | + | 0.295736i | \(0.904435\pi\) | |||||||
\(194\) | − | 179.228i | − | 0.923857i | ||||||
\(195\) | 10.3452 | − | 0.588467i | 0.0530524 | − | 0.00301778i | ||||
\(196\) | −283.340 | −1.44561 | ||||||||
\(197\) | −134.497 | + | 134.497i | −0.682726 | + | 0.682726i | −0.960613 | − | 0.277888i | \(-0.910366\pi\) |
0.277888 | + | 0.960613i | \(0.410366\pi\) | |||||||
\(198\) | 30.8139 | + | 30.8139i | 0.155626 | + | 0.155626i | ||||
\(199\) | − | 172.813i | − | 0.868409i | −0.900814 | − | 0.434205i | \(-0.857029\pi\) | ||
0.900814 | − | 0.434205i | \(-0.142971\pi\) | |||||||
\(200\) | −55.3474 | − | 44.0075i | −0.276737 | − | 0.220038i | ||||
\(201\) | 61.3035 | 0.304993 | ||||||||
\(202\) | 92.9192 | − | 92.9192i | 0.459996 | − | 0.459996i | ||||
\(203\) | 146.399 | + | 146.399i | 0.721176 | + | 0.721176i | ||||
\(204\) | 147.272i | 0.721922i | ||||||||
\(205\) | −9.73745 | − | 171.184i | −0.0474997 | − | 0.835044i | ||||
\(206\) | 33.6792 | 0.163491 | ||||||||
\(207\) | −4.82110 | + | 4.82110i | −0.0232903 | + | 0.0232903i | ||||
\(208\) | 2.12926 | + | 2.12926i | 0.0102368 | + | 0.0102368i | ||||
\(209\) | − | 162.839i | − | 0.779135i | ||||||
\(210\) | −200.550 | − | 178.963i | −0.955002 | − | 0.852203i | ||||
\(211\) | −264.657 | −1.25430 | −0.627148 | − | 0.778900i | \(-0.715778\pi\) | ||||
−0.627148 | + | 0.778900i | \(0.715778\pi\) | |||||||
\(212\) | 58.7893 | − | 58.7893i | 0.277308 | − | 0.277308i | ||||
\(213\) | −110.255 | − | 110.255i | −0.517627 | − | 0.517627i | ||||
\(214\) | − | 110.251i | − | 0.515194i | ||||||
\(215\) | −154.869 | + | 173.550i | −0.720320 | + | 0.807210i | ||||
\(216\) | 81.1463 | 0.375678 | ||||||||
\(217\) | −135.189 | + | 135.189i | −0.622990 | + | 0.622990i | ||||
\(218\) | −3.66113 | − | 3.66113i | −0.0167942 | − | 0.0167942i | ||||
\(219\) | 34.9703i | 0.159682i | ||||||||
\(220\) | 216.396 | − | 12.3092i | 0.983618 | − | 0.0559511i | ||||
\(221\) | 20.1367 | 0.0911162 | ||||||||
\(222\) | 133.141 | − | 133.141i | 0.599735 | − | 0.599735i | ||||
\(223\) | −177.977 | − | 177.977i | −0.798104 | − | 0.798104i | 0.184692 | − | 0.982796i | \(-0.440871\pi\) |
−0.982796 | + | 0.184692i | \(0.940871\pi\) | |||||||
\(224\) | − | 78.1117i | − | 0.348713i | ||||||
\(225\) | 4.03038 | + | 35.3123i | 0.0179128 | + | 0.156944i | ||||
\(226\) | −111.132 | −0.491736 | ||||||||
\(227\) | 271.031 | − | 271.031i | 1.19397 | − | 1.19397i | 0.218027 | − | 0.975943i | \(-0.430038\pi\) |
0.975943 | − | 0.218027i | \(-0.0699621\pi\) | |||||||
\(228\) | −29.2490 | − | 29.2490i | −0.128285 | − | 0.128285i | ||||
\(229\) | 51.6876i | 0.225710i | 0.993611 | + | 0.112855i | \(0.0359995\pi\) | ||||
−0.993611 | + | 0.112855i | \(0.964000\pi\) | |||||||
\(230\) | 1.92588 | + | 33.8569i | 0.00837340 | + | 0.147204i | ||||
\(231\) | 823.908 | 3.56670 | ||||||||
\(232\) | −29.9875 | + | 29.9875i | −0.129257 | + | 0.129257i | ||||
\(233\) | 251.702 | + | 251.702i | 1.08026 | + | 1.08026i | 0.996484 | + | 0.0837807i | \(0.0266995\pi\) |
0.0837807 | + | 0.996484i | \(0.473300\pi\) | |||||||
\(234\) | − | 1.51355i | − | 0.00646815i | ||||||
\(235\) | 10.2884 | + | 9.18094i | 0.0437805 | + | 0.0390678i | ||||
\(236\) | −73.6349 | −0.312012 | ||||||||
\(237\) | 153.464 | − | 153.464i | 0.647526 | − | 0.647526i | ||||
\(238\) | −369.356 | − | 369.356i | −1.55191 | − | 1.55191i | ||||
\(239\) | 161.182i | 0.674403i | 0.941433 | + | 0.337201i | \(0.109480\pi\) | ||||
−0.941433 | + | 0.337201i | \(0.890520\pi\) | |||||||
\(240\) | 36.6578 | − | 41.0797i | 0.152741 | − | 0.171165i | ||||
\(241\) | −348.731 | −1.44702 | −0.723508 | − | 0.690316i | \(-0.757472\pi\) | ||||
−0.723508 | + | 0.690316i | \(0.757472\pi\) | |||||||
\(242\) | −348.787 | + | 348.787i | −1.44127 | + | 1.44127i | ||||
\(243\) | −53.7471 | − | 53.7471i | −0.221182 | − | 0.221182i | ||||
\(244\) | − | 2.80674i | − | 0.0115030i | ||||||
\(245\) | 707.207 | − | 40.2280i | 2.88656 | − | 0.164196i | ||||
\(246\) | 133.505 | 0.542702 | ||||||||
\(247\) | −3.99925 | + | 3.99925i | −0.0161913 | + | 0.0161913i | ||||
\(248\) | −27.6914 | − | 27.6914i | −0.111659 | − | 0.111659i | ||||
\(249\) | − | 240.547i | − | 0.966051i | ||||||
\(250\) | 144.393 | + | 101.983i | 0.577573 | + | 0.407933i | ||||
\(251\) | 384.369 | 1.53135 | 0.765676 | − | 0.643227i | \(-0.222405\pi\) | ||||
0.765676 | + | 0.643227i | \(0.222405\pi\) | |||||||
\(252\) | −27.7622 | + | 27.7622i | −0.110167 | + | 0.110167i | ||||
\(253\) | −73.5021 | − | 73.5021i | −0.290522 | − | 0.290522i | ||||
\(254\) | − | 162.890i | − | 0.641301i | ||||||
\(255\) | −20.9094 | − | 367.586i | −0.0819976 | − | 1.44151i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −48.2636 | + | 48.2636i | −0.187796 | + | 0.187796i | −0.794743 | − | 0.606947i | \(-0.792394\pi\) |
0.606947 | + | 0.794743i | \(0.292394\pi\) | |||||||
\(258\) | −128.065 | − | 128.065i | −0.496377 | − | 0.496377i | ||||
\(259\) | 667.832i | 2.57850i | ||||||||
\(260\) | −5.61688 | − | 5.01226i | −0.0216034 | − | 0.0192779i | ||||
\(261\) | 21.3161 | 0.0816709 | ||||||||
\(262\) | 36.7271 | − | 36.7271i | 0.140180 | − | 0.140180i | ||||
\(263\) | −177.216 | − | 177.216i | −0.673827 | − | 0.673827i | 0.284769 | − | 0.958596i | \(-0.408083\pi\) |
−0.958596 | + | 0.284769i | \(0.908083\pi\) | |||||||
\(264\) | 168.765i | 0.639262i | ||||||||
\(265\) | −138.389 | + | 155.083i | −0.522223 | + | 0.585218i | ||||
\(266\) | 146.712 | 0.551548 | ||||||||
\(267\) | 70.3373 | − | 70.3373i | 0.263436 | − | 0.263436i | ||||
\(268\) | −31.4930 | − | 31.4930i | −0.117511 | − | 0.117511i | ||||
\(269\) | − | 106.990i | − | 0.397733i | −0.980027 | − | 0.198867i | \(-0.936274\pi\) | ||
0.980027 | − | 0.198867i | \(-0.0637261\pi\) | |||||||
\(270\) | −202.538 | + | 11.5210i | −0.750142 | + | 0.0426703i | ||||
\(271\) | 83.4806 | 0.308046 | 0.154023 | − | 0.988067i | \(-0.450777\pi\) | ||||
0.154023 | + | 0.988067i | \(0.450777\pi\) | |||||||
\(272\) | 75.6569 | − | 75.6569i | 0.278150 | − | 0.278150i | ||||
\(273\) | −20.2347 | − | 20.2347i | −0.0741199 | − | 0.0741199i | ||||
\(274\) | 52.0378i | 0.189919i | ||||||||
\(275\) | −538.369 | + | 61.4469i | −1.95771 | + | 0.223443i | ||||
\(276\) | −26.4047 | −0.0956691 | ||||||||
\(277\) | −210.157 | + | 210.157i | −0.758689 | + | 0.758689i | −0.976084 | − | 0.217394i | \(-0.930244\pi\) |
0.217394 | + | 0.976084i | \(0.430244\pi\) | |||||||
\(278\) | 31.2956 | + | 31.2956i | 0.112574 | + | 0.112574i | ||||
\(279\) | 19.6839i | 0.0705516i | ||||||||
\(280\) | 11.0901 | + | 194.964i | 0.0396076 | + | 0.696301i | ||||
\(281\) | 63.1340 | 0.224676 | 0.112338 | − | 0.993670i | \(-0.464166\pi\) | ||||
0.112338 | + | 0.993670i | \(0.464166\pi\) | |||||||
\(282\) | −7.59198 | + | 7.59198i | −0.0269219 | + | 0.0269219i | ||||
\(283\) | −156.827 | − | 156.827i | −0.554158 | − | 0.554158i | 0.373480 | − | 0.927638i | \(-0.378164\pi\) |
−0.927638 | + | 0.373480i | \(0.878164\pi\) | |||||||
\(284\) | 113.280i | 0.398874i | ||||||||
\(285\) | 77.1571 | + | 68.8517i | 0.270727 | + | 0.241585i | ||||
\(286\) | 23.0754 | 0.0806833 | ||||||||
\(287\) | −334.827 | + | 334.827i | −1.16665 | + | 1.16665i | ||||
\(288\) | −5.68665 | − | 5.68665i | −0.0197453 | − | 0.0197453i | ||||
\(289\) | − | 426.496i | − | 1.47576i | ||||||
\(290\) | 70.5903 | − | 79.1054i | 0.243415 | − | 0.272777i | ||||
\(291\) | −348.882 | −1.19891 | ||||||||
\(292\) | 17.9650 | − | 17.9650i | 0.0615240 | − | 0.0615240i | ||||
\(293\) | −374.813 | − | 374.813i | −1.27923 | − | 1.27923i | −0.941102 | − | 0.338124i | \(-0.890208\pi\) |
−0.338124 | − | 0.941102i | \(-0.609792\pi\) | |||||||
\(294\) | 551.544i | 1.87600i | ||||||||
\(295\) | 183.790 | − | 10.4545i | 0.623017 | − | 0.0354391i | ||||
\(296\) | −136.795 | −0.462146 | ||||||||
\(297\) | 439.703 | − | 439.703i | 1.48048 | − | 1.48048i | ||||
\(298\) | 129.249 | + | 129.249i | 0.433723 | + | 0.433723i | ||||
\(299\) | 3.61034i | 0.0120747i | ||||||||
\(300\) | −85.6641 | + | 107.738i | −0.285547 | + | 0.359127i | ||||
\(301\) | 642.371 | 2.13412 | ||||||||
\(302\) | −23.8722 | + | 23.8722i | −0.0790470 | + | 0.0790470i | ||||
\(303\) | −180.875 | − | 180.875i | −0.596946 | − | 0.596946i | ||||
\(304\) | 30.0517i | 0.0988542i | ||||||||
\(305\) | 0.398495 | + | 7.00553i | 0.00130654 | + | 0.0229690i | ||||
\(306\) | −53.7793 | −0.175749 | ||||||||
\(307\) | 358.957 | − | 358.957i | 1.16924 | − | 1.16924i | 0.186851 | − | 0.982388i | \(-0.440172\pi\) |
0.982388 | − | 0.186851i | \(-0.0598283\pi\) | |||||||
\(308\) | −423.260 | − | 423.260i | −1.37422 | − | 1.37422i | ||||
\(309\) | − | 65.5592i | − | 0.212166i | ||||||
\(310\) | 73.0482 | + | 65.1851i | 0.235639 | + | 0.210275i | ||||
\(311\) | −8.62512 | −0.0277335 | −0.0138668 | − | 0.999904i | \(-0.504414\pi\) | ||||
−0.0138668 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(312\) | 4.14478 | − | 4.14478i | 0.0132845 | − | 0.0132845i | ||||
\(313\) | 234.501 | + | 234.501i | 0.749204 | + | 0.749204i | 0.974330 | − | 0.225126i | \(-0.0722793\pi\) |
−0.225126 | + | 0.974330i | \(0.572279\pi\) | |||||||
\(314\) | 37.6482i | 0.119899i | ||||||||
\(315\) | 65.3518 | − | 73.2350i | 0.207466 | − | 0.232492i | ||||
\(316\) | −157.675 | −0.498973 | ||||||||
\(317\) | −360.256 | + | 360.256i | −1.13645 | + | 1.13645i | −0.147373 | + | 0.989081i | \(0.547082\pi\) |
−0.989081 | + | 0.147373i | \(0.952918\pi\) | |||||||
\(318\) | −114.438 | − | 114.438i | −0.359868 | − | 0.359868i | ||||
\(319\) | 324.984i | 1.01876i | ||||||||
\(320\) | −39.9354 | + | 2.27165i | −0.124798 | + | 0.00709889i | ||||
\(321\) | −214.613 | −0.668577 | ||||||||
\(322\) | 66.2224 | − | 66.2224i | 0.205660 | − | 0.205660i | ||||
\(323\) | 142.101 | + | 142.101i | 0.439941 | + | 0.439941i | ||||
\(324\) | − | 132.368i | − | 0.408543i | ||||||
\(325\) | 14.7312 | + | 11.7130i | 0.0453266 | + | 0.0360399i | ||||
\(326\) | −426.047 | −1.30689 | ||||||||
\(327\) | −7.12667 | + | 7.12667i | −0.0217941 | + | 0.0217941i | ||||
\(328\) | −68.5843 | − | 68.5843i | −0.209098 | − | 0.209098i | ||||
\(329\) | − | 38.0811i | − | 0.115748i | ||||||
\(330\) | −23.9609 | − | 421.232i | −0.0726088 | − | 1.27646i | ||||
\(331\) | 547.667 | 1.65458 | 0.827291 | − | 0.561773i | \(-0.189881\pi\) | ||||
0.827291 | + | 0.561773i | \(0.189881\pi\) | |||||||
\(332\) | −123.574 | + | 123.574i | −0.372211 | + | 0.372211i | ||||
\(333\) | 48.6192 | + | 48.6192i | 0.146004 | + | 0.146004i | ||||
\(334\) | − | 80.6166i | − | 0.241367i | ||||||
\(335\) | 83.0766 | + | 74.1340i | 0.247990 | + | 0.221296i | ||||
\(336\) | −152.051 | −0.452532 | ||||||||
\(337\) | 274.601 | − | 274.601i | 0.814841 | − | 0.814841i | −0.170514 | − | 0.985355i | \(-0.554543\pi\) |
0.985355 | + | 0.170514i | \(0.0545430\pi\) | |||||||
\(338\) | 168.433 | + | 168.433i | 0.498323 | + | 0.498323i | ||||
\(339\) | 216.328i | 0.638135i | ||||||||
\(340\) | −178.095 | + | 199.579i | −0.523810 | + | 0.586996i | ||||
\(341\) | −300.099 | −0.880056 | ||||||||
\(342\) | 10.6808 | − | 10.6808i | 0.0312305 | − | 0.0312305i | ||||
\(343\) | −904.828 | − | 904.828i | −2.63798 | − | 2.63798i | ||||
\(344\) | 131.580i | 0.382500i | ||||||||
\(345\) | 65.9052 | − | 3.74888i | 0.191029 | − | 0.0108663i | ||||
\(346\) | −216.317 | −0.625193 | ||||||||
\(347\) | −257.194 | + | 257.194i | −0.741192 | + | 0.741192i | −0.972807 | − | 0.231616i | \(-0.925599\pi\) |
0.231616 | + | 0.972807i | \(0.425599\pi\) | |||||||
\(348\) | 58.3731 | + | 58.3731i | 0.167739 | + | 0.167739i | ||||
\(349\) | − | 110.553i | − | 0.316772i | −0.987377 | − | 0.158386i | \(-0.949371\pi\) | ||
0.987377 | − | 0.158386i | \(-0.0506290\pi\) | |||||||
\(350\) | −55.3612 | − | 485.049i | −0.158175 | − | 1.38586i | ||||
\(351\) | −21.5977 | −0.0615320 | ||||||||
\(352\) | 86.6983 | − | 86.6983i | 0.246302 | − | 0.246302i | ||||
\(353\) | 203.861 | + | 203.861i | 0.577509 | + | 0.577509i | 0.934216 | − | 0.356707i | \(-0.116101\pi\) |
−0.356707 | + | 0.934216i | \(0.616101\pi\) | |||||||
\(354\) | 143.336i | 0.404904i | ||||||||
\(355\) | −16.0833 | − | 282.744i | −0.0453051 | − | 0.796461i | ||||
\(356\) | −72.2676 | −0.202999 | ||||||||
\(357\) | −718.980 | + | 718.980i | −2.01395 | + | 2.01395i | ||||
\(358\) | 35.3314 | + | 35.3314i | 0.0986912 | + | 0.0986912i | ||||
\(359\) | 358.509i | 0.998634i | 0.866419 | + | 0.499317i | \(0.166416\pi\) | ||||
−0.866419 | + | 0.499317i | \(0.833584\pi\) | |||||||
\(360\) | 15.0011 | + | 13.3863i | 0.0416696 | + | 0.0371842i | ||||
\(361\) | 304.556 | 0.843646 | ||||||||
\(362\) | 220.468 | − | 220.468i | 0.609026 | − | 0.609026i | ||||
\(363\) | 678.942 | + | 678.942i | 1.87036 | + | 1.87036i | ||||
\(364\) | 20.7901i | 0.0571155i | ||||||||
\(365\) | −42.2894 | + | 47.3907i | −0.115861 | + | 0.129837i | ||||
\(366\) | −5.46354 | −0.0149277 | ||||||||
\(367\) | −89.1803 | + | 89.1803i | −0.242998 | + | 0.242998i | −0.818089 | − | 0.575091i | \(-0.804967\pi\) |
0.575091 | + | 0.818089i | \(0.304967\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 48.7519i | 0.132119i | ||||||||
\(370\) | 341.436 | − | 19.4219i | 0.922800 | − | 0.0524916i | ||||
\(371\) | 574.016 | 1.54721 | ||||||||
\(372\) | −53.9034 | + | 53.9034i | −0.144902 | + | 0.144902i | ||||
\(373\) | 311.754 | + | 311.754i | 0.835800 | + | 0.835800i | 0.988303 | − | 0.152503i | \(-0.0487332\pi\) |
−0.152503 | + | 0.988303i | \(0.548733\pi\) | |||||||
\(374\) | − | 819.916i | − | 2.19229i | ||||||
\(375\) | 198.518 | − | 281.073i | 0.529382 | − | 0.749528i | ||||
\(376\) | 7.80033 | 0.0207456 | ||||||||
\(377\) | 7.98142 | − | 7.98142i | 0.0211709 | − | 0.0211709i | ||||
\(378\) | 396.155 | + | 396.155i | 1.04803 | + | 1.04803i | ||||
\(379\) | − | 266.437i | − | 0.703001i | −0.936188 | − | 0.351500i | \(-0.885672\pi\) | ||
0.936188 | − | 0.351500i | \(-0.114328\pi\) | |||||||
\(380\) | −4.26667 | − | 75.0079i | −0.0112281 | − | 0.197389i | ||||
\(381\) | −317.079 | −0.832228 | ||||||||
\(382\) | −288.600 | + | 288.600i | −0.755498 | + | 0.755498i | ||||
\(383\) | −506.226 | − | 506.226i | −1.32174 | − | 1.32174i | −0.912369 | − | 0.409369i | \(-0.865749\pi\) |
−0.409369 | − | 0.912369i | \(-0.634251\pi\) | |||||||
\(384\) | − | 31.1453i | − | 0.0811074i | ||||||
\(385\) | 1116.53 | + | 996.348i | 2.90009 | + | 2.58792i | ||||
\(386\) | 254.580 | 0.659533 | ||||||||
\(387\) | 46.7656 | − | 46.7656i | 0.120841 | − | 0.120841i | ||||
\(388\) | 179.228 | + | 179.228i | 0.461929 | + | 0.461929i | ||||
\(389\) | 373.660i | 0.960566i | 0.877114 | + | 0.480283i | \(0.159466\pi\) | ||||
−0.877114 | + | 0.480283i | \(0.840534\pi\) | |||||||
\(390\) | −9.75676 | + | 10.9337i | −0.0250173 | + | 0.0280351i | ||||
\(391\) | 128.283 | 0.328088 | ||||||||
\(392\) | 283.340 | − | 283.340i | 0.722807 | − | 0.722807i | ||||
\(393\) | −71.4922 | − | 71.4922i | −0.181914 | − | 0.181914i | ||||
\(394\) | − | 268.994i | − | 0.682726i | ||||||
\(395\) | 393.552 | − | 22.3864i | 0.996335 | − | 0.0566745i | ||||
\(396\) | −61.6279 | −0.155626 | ||||||||
\(397\) | 109.812 | − | 109.812i | 0.276605 | − | 0.276605i | −0.555147 | − | 0.831752i | \(-0.687338\pi\) |
0.831752 | + | 0.555147i | \(0.187338\pi\) | |||||||
\(398\) | 172.813 | + | 172.813i | 0.434205 | + | 0.434205i | ||||
\(399\) | − | 285.586i | − | 0.715754i | ||||||
\(400\) | 99.3550 | − | 11.3399i | 0.248387 | − | 0.0283497i | ||||
\(401\) | 304.662 | 0.759755 | 0.379877 | − | 0.925037i | \(-0.375966\pi\) | ||||
0.379877 | + | 0.925037i | \(0.375966\pi\) | |||||||
\(402\) | −61.3035 | + | 61.3035i | −0.152496 | + | 0.152496i | ||||
\(403\) | 7.37027 | + | 7.37027i | 0.0182885 | + | 0.0182885i | ||||
\(404\) | 185.838i | 0.459996i | ||||||||
\(405\) | 18.7933 | + | 330.385i | 0.0464032 | + | 0.815766i | ||||
\(406\) | −292.797 | −0.721176 | ||||||||
\(407\) | −741.244 | + | 741.244i | −1.82124 | + | 1.82124i | ||||
\(408\) | −147.272 | − | 147.272i | −0.360961 | − | 0.360961i | ||||
\(409\) | 228.713i | 0.559201i | 0.960116 | + | 0.279600i | \(0.0902020\pi\) | ||||
−0.960116 | + | 0.279600i | \(0.909798\pi\) | |||||||
\(410\) | 180.921 | + | 161.447i | 0.441272 | + | 0.393772i | ||||
\(411\) | 101.296 | 0.246461 | ||||||||
\(412\) | −33.6792 | + | 33.6792i | −0.0817456 | + | 0.0817456i | ||||
\(413\) | −359.484 | − | 359.484i | −0.870422 | − | 0.870422i | ||||
\(414\) | − | 9.64219i | − | 0.0232903i | ||||||
\(415\) | 290.892 | − | 325.981i | 0.700944 | − | 0.785497i | ||||
\(416\) | −4.25853 | −0.0102368 | ||||||||
\(417\) | 60.9192 | − | 60.9192i | 0.146089 | − | 0.146089i | ||||
\(418\) | 162.839 | + | 162.839i | 0.389568 | + | 0.389568i | ||||
\(419\) | − | 198.319i | − | 0.473316i | −0.971593 | − | 0.236658i | \(-0.923948\pi\) | ||
0.971593 | − | 0.236658i | \(-0.0760521\pi\) | |||||||
\(420\) | 379.513 | − | 21.5878i | 0.903603 | − | 0.0513996i | ||||
\(421\) | −571.167 | −1.35669 | −0.678346 | − | 0.734743i | \(-0.737303\pi\) | ||||
−0.678346 | + | 0.734743i | \(0.737303\pi\) | |||||||
\(422\) | 264.657 | − | 264.657i | 0.627148 | − | 0.627148i | ||||
\(423\) | −2.77236 | − | 2.77236i | −0.00655404 | − | 0.00655404i | ||||
\(424\) | 117.579i | 0.277308i | ||||||||
\(425\) | 416.184 | − | 523.427i | 0.979257 | − | 1.23159i | ||||
\(426\) | 220.509 | 0.517627 | ||||||||
\(427\) | 13.7025 | − | 13.7025i | 0.0320901 | − | 0.0320901i | ||||
\(428\) | 110.251 | + | 110.251i | 0.257597 | + | 0.257597i | ||||
\(429\) | − | 44.9181i | − | 0.104704i | ||||||
\(430\) | −18.6814 | − | 328.419i | −0.0434452 | − | 0.763765i | ||||
\(431\) | −575.249 | −1.33468 | −0.667342 | − | 0.744751i | \(-0.732568\pi\) | ||||
−0.667342 | + | 0.744751i | \(0.732568\pi\) | |||||||
\(432\) | −81.1463 | + | 81.1463i | −0.187839 | + | 0.187839i | ||||
\(433\) | 0.718397 | + | 0.718397i | 0.00165912 | + | 0.00165912i | 0.707936 | − | 0.706277i | \(-0.249627\pi\) |
−0.706277 | + | 0.707936i | \(0.749627\pi\) | |||||||
\(434\) | − | 270.378i | − | 0.622990i | ||||||
\(435\) | −153.985 | − | 137.410i | −0.353988 | − | 0.315884i | ||||
\(436\) | 7.32226 | 0.0167942 | ||||||||
\(437\) | −25.4775 | + | 25.4775i | −0.0583010 | + | 0.0583010i | ||||
\(438\) | −34.9703 | − | 34.9703i | −0.0798409 | − | 0.0798409i | ||||
\(439\) | − | 520.035i | − | 1.18459i | −0.805721 | − | 0.592295i | \(-0.798222\pi\) | ||
0.805721 | − | 0.592295i | \(-0.201778\pi\) | |||||||
\(440\) | −204.087 | + | 228.705i | −0.463833 | + | 0.519784i | ||||
\(441\) | −201.407 | −0.456706 | ||||||||
\(442\) | −20.1367 | + | 20.1367i | −0.0455581 | + | 0.0455581i | ||||
\(443\) | 54.3749 | + | 54.3749i | 0.122742 | + | 0.122742i | 0.765810 | − | 0.643067i | \(-0.222338\pi\) |
−0.643067 | + | 0.765810i | \(0.722338\pi\) | |||||||
\(444\) | 266.283i | 0.599735i | ||||||||
\(445\) | 180.377 | − | 10.2604i | 0.405343 | − | 0.0230571i | ||||
\(446\) | 355.955 | 0.798104 | ||||||||
\(447\) | 251.594 | − | 251.594i | 0.562850 | − | 0.562850i | ||||
\(448\) | 78.1117 | + | 78.1117i | 0.174357 | + | 0.174357i | ||||
\(449\) | 556.320i | 1.23902i | 0.784989 | + | 0.619510i | \(0.212669\pi\) | ||||
−0.784989 | + | 0.619510i | \(0.787331\pi\) | |||||||
\(450\) | −39.3427 | − | 31.2819i | −0.0874282 | − | 0.0695154i | ||||
\(451\) | −743.268 | −1.64804 | ||||||||
\(452\) | 111.132 | − | 111.132i | 0.245868 | − | 0.245868i | ||||
\(453\) | 46.4691 | + | 46.4691i | 0.102581 | + | 0.102581i | ||||
\(454\) | 542.062i | 1.19397i | ||||||||
\(455\) | −2.95173 | − | 51.8913i | −0.00648731 | − | 0.114047i | ||||
\(456\) | 58.4979 | 0.128285 | ||||||||
\(457\) | 257.657 | − | 257.657i | 0.563801 | − | 0.563801i | −0.366584 | − | 0.930385i | \(-0.619473\pi\) |
0.930385 | + | 0.366584i | \(0.119473\pi\) | |||||||
\(458\) | −51.6876 | − | 51.6876i | −0.112855 | − | 0.112855i | ||||
\(459\) | 767.410i | 1.67192i | ||||||||
\(460\) | −35.7828 | − | 31.9310i | −0.0777887 | − | 0.0694153i | ||||
\(461\) | −236.551 | −0.513125 | −0.256563 | − | 0.966528i | \(-0.582590\pi\) | ||||
−0.256563 | + | 0.966528i | \(0.582590\pi\) | |||||||
\(462\) | −823.908 | + | 823.908i | −1.78335 | + | 1.78335i | ||||
\(463\) | 206.954 | + | 206.954i | 0.446984 | + | 0.446984i | 0.894351 | − | 0.447366i | \(-0.147638\pi\) |
−0.447366 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(464\) | − | 59.9751i | − | 0.129257i | ||||||
\(465\) | 126.888 | − | 142.194i | 0.272877 | − | 0.305794i | ||||
\(466\) | −503.403 | −1.08026 | ||||||||
\(467\) | −455.160 | + | 455.160i | −0.974647 | + | 0.974647i | −0.999686 | − | 0.0250398i | \(-0.992029\pi\) |
0.0250398 | + | 0.999686i | \(0.492029\pi\) | |||||||
\(468\) | 1.51355 | + | 1.51355i | 0.00323408 | + | 0.00323408i | ||||
\(469\) | − | 307.496i | − | 0.655642i | ||||||
\(470\) | −19.4694 | + | 1.10747i | −0.0414242 | + | 0.00235633i | ||||
\(471\) | 73.2851 | 0.155595 | ||||||||
\(472\) | 73.6349 | − | 73.6349i | 0.156006 | − | 0.156006i | ||||
\(473\) | 712.985 | + | 712.985i | 1.50737 | + | 1.50737i | ||||
\(474\) | 306.928i | 0.647526i | ||||||||
\(475\) | 21.2989 | + | 186.611i | 0.0448399 | + | 0.392866i | ||||
\(476\) | 738.711 | 1.55191 | ||||||||
\(477\) | 41.7893 | − | 41.7893i | 0.0876085 | − | 0.0876085i | ||||
\(478\) | −161.182 | − | 161.182i | −0.337201 | − | 0.337201i | ||||
\(479\) | − | 15.9362i | − | 0.0332697i | −0.999862 | − | 0.0166349i | \(-0.994705\pi\) | ||
0.999862 | − | 0.0166349i | \(-0.00529528\pi\) | |||||||
\(480\) | 4.42194 | + | 77.7375i | 0.00921237 | + | 0.161953i | ||||
\(481\) | 36.4091 | 0.0756946 | ||||||||
\(482\) | 348.731 | − | 348.731i | 0.723508 | − | 0.723508i | ||||
\(483\) | −128.907 | − | 128.907i | −0.266889 | − | 0.266889i | ||||
\(484\) | − | 697.574i | − | 1.44127i | ||||||
\(485\) | −472.794 | − | 421.901i | −0.974833 | − | 0.869899i | ||||
\(486\) | 107.494 | 0.221182 | ||||||||
\(487\) | 373.443 | − | 373.443i | 0.766824 | − | 0.766824i | −0.210722 | − | 0.977546i | \(-0.567582\pi\) |
0.977546 | + | 0.210722i | \(0.0675815\pi\) | |||||||
\(488\) | 2.80674 | + | 2.80674i | 0.00575152 | + | 0.00575152i | ||||
\(489\) | 829.334i | 1.69598i | ||||||||
\(490\) | −666.979 | + | 747.435i | −1.36118 | + | 1.52538i | ||||
\(491\) | 253.834 | 0.516974 | 0.258487 | − | 0.966015i | \(-0.416776\pi\) | ||||
0.258487 | + | 0.966015i | \(0.416776\pi\) | |||||||
\(492\) | −133.505 | + | 133.505i | −0.271351 | + | 0.271351i | ||||
\(493\) | −283.596 | − | 283.596i | −0.575244 | − | 0.575244i | ||||
\(494\) | − | 7.99849i | − | 0.0161913i | ||||||
\(495\) | 153.821 | − | 8.74980i | 0.310750 | − | 0.0176764i | ||||
\(496\) | 55.3827 | 0.111659 | ||||||||
\(497\) | −553.033 | + | 553.033i | −1.11274 | + | 1.11274i | ||||
\(498\) | 240.547 | + | 240.547i | 0.483025 | + | 0.483025i | ||||
\(499\) | 482.367i | 0.966668i | 0.875436 | + | 0.483334i | \(0.160574\pi\) | ||||
−0.875436 | + | 0.483334i | \(0.839426\pi\) | |||||||
\(500\) | −246.376 | + | 42.4102i | −0.492753 | + | 0.0848204i | ||||
\(501\) | −156.927 | −0.313227 | ||||||||
\(502\) | −384.369 | + | 384.369i | −0.765676 | + | 0.765676i | ||||
\(503\) | −426.820 | − | 426.820i | −0.848549 | − | 0.848549i | 0.141403 | − | 0.989952i | \(-0.454839\pi\) |
−0.989952 | + | 0.141403i | \(0.954839\pi\) | |||||||
\(504\) | − | 55.5243i | − | 0.110167i | ||||||
\(505\) | −26.3849 | − | 463.846i | −0.0522474 | − | 0.918507i | ||||
\(506\) | 147.004 | 0.290522 | ||||||||
\(507\) | 327.869 | − | 327.869i | 0.646684 | − | 0.646684i | ||||
\(508\) | 162.890 | + | 162.890i | 0.320650 | + | 0.320650i | ||||
\(509\) | 850.581i | 1.67108i | 0.549427 | + | 0.835542i | \(0.314846\pi\) | ||||
−0.549427 | + | 0.835542i | \(0.685154\pi\) | |||||||
\(510\) | 388.495 | + | 346.677i | 0.761756 | + | 0.679758i | ||||
\(511\) | 175.410 | 0.343268 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −152.411 | − | 152.411i | −0.297098 | − | 0.297098i | ||||
\(514\) | − | 96.5272i | − | 0.187796i | ||||||
\(515\) | 79.2804 | − | 88.8438i | 0.153943 | − | 0.172512i | ||||
\(516\) | 256.131 | 0.496377 | ||||||||
\(517\) | 42.2672 | − | 42.2672i | 0.0817547 | − | 0.0817547i | ||||
\(518\) | −667.832 | − | 667.832i | −1.28925 | − | 1.28925i | ||||
\(519\) | 421.078i | 0.811325i | ||||||||
\(520\) | 10.6291 | − | 0.604616i | 0.0204406 | − | 0.00116272i | ||||
\(521\) | −98.0266 | −0.188151 | −0.0940755 | − | 0.995565i | \(-0.529990\pi\) | ||||
−0.0940755 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(522\) | −21.3161 | + | 21.3161i | −0.0408354 | + | 0.0408354i | ||||
\(523\) | 212.663 | + | 212.663i | 0.406622 | + | 0.406622i | 0.880559 | − | 0.473937i | \(-0.157167\pi\) |
−0.473937 | + | 0.880559i | \(0.657167\pi\) | |||||||
\(524\) | 73.4542i | 0.140180i | ||||||||
\(525\) | −944.187 | + | 107.765i | −1.79845 | + | 0.205266i | ||||
\(526\) | 354.433 | 0.673827 | ||||||||
\(527\) | 261.880 | − | 261.880i | 0.496927 | − | 0.496927i | ||||
\(528\) | −168.765 | − | 168.765i | −0.319631 | − | 0.319631i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −16.6935 | − | 293.472i | −0.0314973 | − | 0.553721i | ||||
\(531\) | −52.3420 | −0.0985726 | ||||||||
\(532\) | −146.712 | + | 146.712i | −0.275774 | + | 0.275774i | ||||
\(533\) | 18.2542 | + | 18.2542i | 0.0342481 | + | 0.0342481i | ||||
\(534\) | 140.675i | 0.263436i | ||||||||
\(535\) | −290.837 | − | 259.531i | −0.543621 | − | 0.485104i | ||||
\(536\) | 62.9859 | 0.117511 | ||||||||
\(537\) | 68.7754 | − | 68.7754i | 0.128073 | − | 0.128073i | ||||
\(538\) | 106.990 | + | 106.990i | 0.198867 | + | 0.198867i | ||||
\(539\) | − | 3070.64i | − | 5.69692i | ||||||
\(540\) | 191.017 | − | 214.059i | 0.353736 | − | 0.396406i | ||||
\(541\) | 893.808 | 1.65214 | 0.826070 | − | 0.563568i | \(-0.190572\pi\) | ||||
0.826070 | + | 0.563568i | \(0.190572\pi\) | |||||||
\(542\) | −83.4806 | + | 83.4806i | −0.154023 | + | 0.154023i | ||||
\(543\) | −429.157 | − | 429.157i | −0.790345 | − | 0.790345i | ||||
\(544\) | 151.314i | 0.278150i | ||||||||
\(545\) | −18.2761 | + | 1.03960i | −0.0335341 | + | 0.00190752i | ||||
\(546\) | 40.4695 | 0.0741199 | ||||||||
\(547\) | −97.9282 | + | 97.9282i | −0.179028 | + | 0.179028i | −0.790932 | − | 0.611904i | \(-0.790404\pi\) |
0.611904 | + | 0.790932i | \(0.290404\pi\) | |||||||
\(548\) | −52.0378 | − | 52.0378i | −0.0949595 | − | 0.0949595i | ||||
\(549\) | − | 1.99512i | − | 0.00363410i | ||||||
\(550\) | 476.922 | − | 599.816i | 0.867131 | − | 1.09057i | ||||
\(551\) | 112.647 | 0.204441 | ||||||||
\(552\) | 26.4047 | − | 26.4047i | 0.0478346 | − | 0.0478346i | ||||
\(553\) | −769.769 | − | 769.769i | −1.39199 | − | 1.39199i | ||||
\(554\) | − | 420.314i | − | 0.758689i | ||||||
\(555\) | −37.8062 | − | 664.632i | −0.0681193 | − | 1.19753i | ||||
\(556\) | −62.5911 | −0.112574 | ||||||||
\(557\) | 196.243 | − | 196.243i | 0.352321 | − | 0.352321i | −0.508652 | − | 0.860972i | \(-0.669856\pi\) |
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(558\) | −19.6839 | − | 19.6839i | −0.0352758 | − | 0.0352758i | ||||
\(559\) | − | 35.0210i | − | 0.0626495i | ||||||
\(560\) | −206.054 | − | 183.874i | −0.367954 | − | 0.328347i | ||||
\(561\) | −1596.03 | −2.84497 | ||||||||
\(562\) | −63.1340 | + | 63.1340i | −0.112338 | + | 0.112338i | ||||
\(563\) | 524.329 | + | 524.329i | 0.931312 | + | 0.931312i | 0.997788 | − | 0.0664759i | \(-0.0211755\pi\) |
−0.0664759 | + | 0.997788i | \(0.521176\pi\) | |||||||
\(564\) | − | 15.1840i | − | 0.0269219i | ||||||
\(565\) | −261.604 | + | 293.161i | −0.463016 | + | 0.518869i | ||||
\(566\) | 313.653 | 0.554158 | ||||||||
\(567\) | 646.217 | − | 646.217i | 1.13971 | − | 1.13971i | ||||
\(568\) | −113.280 | − | 113.280i | −0.199437 | − | 0.199437i | ||||
\(569\) | 240.822i | 0.423238i | 0.977352 | + | 0.211619i | \(0.0678736\pi\) | ||||
−0.977352 | + | 0.211619i | \(0.932126\pi\) | |||||||
\(570\) | −146.009 | + | 8.30541i | −0.256156 | + | 0.0145709i | ||||
\(571\) | −145.998 | −0.255687 | −0.127844 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127844 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(572\) | −23.0754 | + | 23.0754i | −0.0403417 | + | 0.0403417i | ||||
\(573\) | 561.783 | + | 561.783i | 0.980424 | + | 0.980424i | ||||
\(574\) | − | 669.655i | − | 1.16665i | ||||||
\(575\) | 93.8461 | + | 74.6184i | 0.163211 | + | 0.129771i | ||||
\(576\) | 11.3733 | 0.0197453 | ||||||||
\(577\) | −45.5478 | + | 45.5478i | −0.0789390 | + | 0.0789390i | −0.745474 | − | 0.666535i | \(-0.767777\pi\) |
0.666535 | + | 0.745474i | \(0.267777\pi\) | |||||||
\(578\) | 426.496 | + | 426.496i | 0.737882 | + | 0.737882i | ||||
\(579\) | − | 495.560i | − | 0.855889i | ||||||
\(580\) | 8.51513 | + | 149.696i | 0.0146813 | + | 0.258096i | ||||
\(581\) | −1206.57 | −2.07672 | ||||||||
\(582\) | 348.882 | − | 348.882i | 0.599454 | − | 0.599454i | ||||
\(583\) | 637.116 | + | 637.116i | 1.09282 | + | 1.09282i | ||||
\(584\) | 35.9300i | 0.0615240i | ||||||||
\(585\) | −3.99265 | − | 3.56287i | −0.00682505 | − | 0.00609038i | ||||
\(586\) | 749.626 | 1.27923 | ||||||||
\(587\) | 697.050 | − | 697.050i | 1.18748 | − | 1.18748i | 0.209718 | − | 0.977762i | \(-0.432746\pi\) |
0.977762 | − | 0.209718i | \(-0.0672544\pi\) | |||||||
\(588\) | −551.544 | − | 551.544i | −0.938000 | − | 0.938000i | ||||
\(589\) | 104.021i | 0.176607i | ||||||||
\(590\) | −173.336 | + | 194.245i | −0.293789 | + | 0.329228i | ||||
\(591\) | −523.618 | −0.885986 | ||||||||
\(592\) | 136.795 | − | 136.795i | 0.231073 | − | 0.231073i | ||||
\(593\) | 528.700 | + | 528.700i | 0.891568 | + | 0.891568i | 0.994671 | − | 0.103103i | \(-0.0328771\pi\) |
−0.103103 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(594\) | 879.406i | 1.48048i | ||||||||
\(595\) | −1843.80 | + | 104.881i | −3.09882 | + | 0.176270i | ||||
\(596\) | −258.499 | −0.433723 | ||||||||
\(597\) | 336.395 | − | 336.395i | 0.563476 | − | 0.563476i | ||||
\(598\) | −3.61034 | − | 3.61034i | −0.00603736 | − | 0.00603736i | ||||
\(599\) | 845.156i | 1.41094i | 0.708738 | + | 0.705472i | \(0.249265\pi\) | ||||
−0.708738 | + | 0.705472i | \(0.750735\pi\) | |||||||
\(600\) | −22.0740 | − | 193.402i | −0.0367900 | − | 0.322337i | ||||
\(601\) | −112.831 | −0.187740 | −0.0938698 | − | 0.995584i | \(-0.529924\pi\) | ||||
−0.0938698 | + | 0.995584i | \(0.529924\pi\) | |||||||
\(602\) | −642.371 | + | 642.371i | −1.06706 | + | 1.06706i | ||||
\(603\) | −22.3862 | − | 22.3862i | −0.0371247 | − | 0.0371247i | ||||
\(604\) | − | 47.7444i | − | 0.0790470i | ||||||
\(605\) | 99.0401 | + | 1741.12i | 0.163703 | + | 2.87789i | ||||
\(606\) | 361.749 | 0.596946 | ||||||||
\(607\) | 196.203 | − | 196.203i | 0.323234 | − | 0.323234i | −0.526773 | − | 0.850006i | \(-0.676598\pi\) |
0.850006 | + | 0.526773i | \(0.176598\pi\) | |||||||
\(608\) | −30.0517 | − | 30.0517i | −0.0494271 | − | 0.0494271i | ||||
\(609\) | 569.953i | 0.935883i | ||||||||
\(610\) | −7.40403 | − | 6.60703i | −0.0121377 | − | 0.0108312i | ||||
\(611\) | −2.07612 | −0.00339790 | ||||||||
\(612\) | 53.7793 | − | 53.7793i | 0.0878747 | − | 0.0878747i | ||||
\(613\) | −371.961 | − | 371.961i | −0.606788 | − | 0.606788i | 0.335318 | − | 0.942105i | \(-0.391156\pi\) |
−0.942105 | + | 0.335318i | \(0.891156\pi\) | |||||||
\(614\) | 717.913i | 1.16924i | ||||||||
\(615\) | 314.268 | − | 352.178i | 0.511005 | − | 0.572647i | ||||
\(616\) | 846.519 | 1.37422 | ||||||||
\(617\) | −201.112 | + | 201.112i | −0.325951 | + | 0.325951i | −0.851045 | − | 0.525094i | \(-0.824030\pi\) |
0.525094 | + | 0.851045i | \(0.324030\pi\) | |||||||
\(618\) | 65.5592 | + | 65.5592i | 0.106083 | + | 0.106083i | ||||
\(619\) | − | 294.954i | − | 0.476501i | −0.971204 | − | 0.238250i | \(-0.923426\pi\) | ||
0.971204 | − | 0.238250i | \(-0.0765739\pi\) | |||||||
\(620\) | −138.233 | + | 7.86312i | −0.222957 | + | 0.0126825i | ||||
\(621\) | −137.590 | −0.221563 | ||||||||
\(622\) | 8.62512 | − | 8.62512i | 0.0138668 | − | 0.0138668i | ||||
\(623\) | −352.809 | − | 352.809i | −0.566307 | − | 0.566307i | ||||
\(624\) | 8.28956i | 0.0132845i | ||||||||
\(625\) | 608.926 | − | 140.834i | 0.974281 | − | 0.225335i | ||||
\(626\) | −469.002 | −0.749204 | ||||||||
\(627\) | 316.980 | − | 316.980i | 0.505549 | − | 0.505549i | ||||
\(628\) | −37.6482 | − | 37.6482i | −0.0599493 | − | 0.0599493i | ||||
\(629\) | − | 1293.69i | − | 2.05674i | ||||||
\(630\) | 7.88322 | + | 138.587i | 0.0125130 | + | 0.219979i | ||||
\(631\) | 909.467 | 1.44131 | 0.720655 | − | 0.693294i | \(-0.243841\pi\) | ||||
0.720655 | + | 0.693294i | \(0.243841\pi\) | |||||||
\(632\) | 157.675 | − | 157.675i | 0.249486 | − | 0.249486i | ||||
\(633\) | −515.175 | − | 515.175i | −0.813862 | − | 0.813862i | ||||
\(634\) | − | 720.512i | − | 1.13645i | ||||||
\(635\) | −429.696 | − | 383.442i | −0.676686 | − | 0.603846i | ||||
\(636\) | 228.876 | 0.359868 | ||||||||
\(637\) | −75.4132 | + | 75.4132i | −0.118388 | + | 0.118388i | ||||
\(638\) | −324.984 | − | 324.984i | −0.509379 | − | 0.509379i | ||||
\(639\) | 80.5232i | 0.126014i | ||||||||
\(640\) | 37.6638 | − | 42.2071i | 0.0588497 | − | 0.0659486i | ||||
\(641\) | 794.199 | 1.23900 | 0.619500 | − | 0.784997i | \(-0.287336\pi\) | ||||
0.619500 | + | 0.784997i | \(0.287336\pi\) | |||||||
\(642\) | 214.613 | − | 214.613i | 0.334288 | − | 0.334288i | ||||
\(643\) | 444.052 | + | 444.052i | 0.690594 | + | 0.690594i | 0.962363 | − | 0.271769i | \(-0.0876086\pi\) |
−0.271769 | + | 0.962363i | \(0.587609\pi\) | |||||||
\(644\) | 132.445i | 0.205660i | ||||||||
\(645\) | −639.293 | + | 36.3649i | −0.991153 | + | 0.0563797i | ||||
\(646\) | −284.202 | −0.439941 | ||||||||
\(647\) | −670.308 | + | 670.308i | −1.03603 | + | 1.03603i | −0.0366989 | + | 0.999326i | \(0.511684\pi\) |
−0.999326 | + | 0.0366989i | \(0.988316\pi\) | |||||||
\(648\) | 132.368 | + | 132.368i | 0.204271 | + | 0.204271i | ||||
\(649\) | − | 798.003i | − | 1.22959i | ||||||
\(650\) | −26.4441 | + | 3.01820i | −0.0406832 | + | 0.00464339i | ||||
\(651\) | −526.311 | −0.808466 | ||||||||
\(652\) | 426.047 | − | 426.047i | 0.653447 | − | 0.653447i | ||||
\(653\) | −368.030 | − | 368.030i | −0.563599 | − | 0.563599i | 0.366729 | − | 0.930328i | \(-0.380478\pi\) |
−0.930328 | + | 0.366729i | \(0.880478\pi\) | |||||||
\(654\) | − | 14.2533i | − | 0.0217941i | ||||||
\(655\) | −10.4289 | − | 183.339i | −0.0159219 | − | 0.279907i | ||||
\(656\) | 137.169 | 0.209098 | ||||||||
\(657\) | 12.7701 | − | 12.7701i | 0.0194370 | − | 0.0194370i | ||||
\(658\) | 38.0811 | + | 38.0811i | 0.0578740 | + | 0.0578740i | ||||
\(659\) | 505.833i | 0.767576i | 0.923421 | + | 0.383788i | \(0.125381\pi\) | ||||
−0.923421 | + | 0.383788i | \(0.874619\pi\) | |||||||
\(660\) | 445.193 | + | 397.271i | 0.674534 | + | 0.601925i | ||||
\(661\) | −208.032 | −0.314723 | −0.157362 | − | 0.987541i | \(-0.550299\pi\) | ||||
−0.157362 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(662\) | −547.667 | + | 547.667i | −0.827291 | + | 0.827291i | ||||
\(663\) | 39.1976 | + | 39.1976i | 0.0591216 | + | 0.0591216i | ||||
\(664\) | − | 247.148i | − | 0.372211i | ||||||
\(665\) | 345.358 | − | 387.017i | 0.519335 | − | 0.581981i | ||||
\(666\) | −97.2383 | −0.146004 | ||||||||
\(667\) | 50.8463 | − | 50.8463i | 0.0762314 | − | 0.0762314i | ||||
\(668\) | 80.6166 | + | 80.6166i | 0.120684 | + | 0.120684i | ||||
\(669\) | − | 692.894i | − | 1.03572i | ||||||
\(670\) | −157.211 | + | 8.94260i | −0.234643 | + | 0.0133472i | ||||
\(671\) | 30.4175 | 0.0453315 | ||||||||
\(672\) | 152.051 | − | 152.051i | 0.226266 | − | 0.226266i | ||||
\(673\) | 215.020 | + | 215.020i | 0.319494 | + | 0.319494i | 0.848573 | − | 0.529078i | \(-0.177462\pi\) |
−0.529078 | + | 0.848573i | \(0.677462\pi\) | |||||||
\(674\) | 549.203i | 0.814841i | ||||||||
\(675\) | −446.381 | + | 561.405i | −0.661306 | + | 0.831711i | ||||
\(676\) | −336.867 | −0.498323 | ||||||||
\(677\) | 500.023 | − | 500.023i | 0.738587 | − | 0.738587i | −0.233718 | − | 0.972305i | \(-0.575089\pi\) |
0.972305 | + | 0.233718i | \(0.0750891\pi\) | |||||||
\(678\) | −216.328 | − | 216.328i | −0.319068 | − | 0.319068i | ||||
\(679\) | 1749.98i | 2.57729i | ||||||||
\(680\) | −21.4832 | − | 377.674i | −0.0315930 | − | 0.555403i | ||||
\(681\) | 1055.17 | 1.54944 | ||||||||
\(682\) | 300.099 | − | 300.099i | 0.440028 | − | 0.440028i | ||||
\(683\) | −456.035 | − | 456.035i | −0.667694 | − | 0.667694i | 0.289488 | − | 0.957182i | \(-0.406515\pi\) |
−0.957182 | + | 0.289488i | \(0.906515\pi\) | |||||||
\(684\) | 21.3617i | 0.0312305i | ||||||||
\(685\) | 137.273 | + | 122.496i | 0.200398 | + | 0.178827i | ||||
\(686\) | 1809.66 | 2.63798 | ||||||||
\(687\) | −100.614 | + | 100.614i | −0.146454 | + | 0.146454i | ||||
\(688\) | −131.580 | − | 131.580i | −0.191250 | − | 0.191250i | ||||
\(689\) | − | 31.2944i | − | 0.0454201i | ||||||
\(690\) | −62.1563 | + | 69.6540i | −0.0900816 | + | 0.100948i | ||||
\(691\) | 470.530 | 0.680941 | 0.340470 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340470 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(692\) | 216.317 | − | 216.317i | 0.312597 | − | 0.312597i | ||||
\(693\) | −300.866 | − | 300.866i | −0.434151 | − | 0.434151i | ||||
\(694\) | − | 514.387i | − | 0.741192i | ||||||
\(695\) | 156.225 | − | 8.88655i | 0.224784 | − | 0.0127864i | ||||
\(696\) | −116.746 | −0.167739 | ||||||||
\(697\) | 648.609 | − | 648.609i | 0.930573 | − | 0.930573i | ||||
\(698\) | 110.553 | + | 110.553i | 0.158386 | + | 0.158386i | ||||
\(699\) | 979.914i | 1.40188i | ||||||||
\(700\) | 540.410 | + | 429.688i | 0.772015 | + | 0.613840i | ||||
\(701\) | 98.5546 | 0.140591 | 0.0702957 | − | 0.997526i | \(-0.477606\pi\) | ||||
0.0702957 | + | 0.997526i | \(0.477606\pi\) | |||||||
\(702\) | 21.5977 | − | 21.5977i | 0.0307660 | − | 0.0307660i | ||||
\(703\) | 256.933 | + | 256.933i | 0.365480 | + | 0.365480i | ||||
\(704\) | 173.397i | 0.246302i | ||||||||
\(705\) | 2.15579 | + | 37.8986i | 0.00305785 | + | 0.0537569i | ||||
\(706\) | −407.722 | −0.577509 | ||||||||
\(707\) | −907.260 | + | 907.260i | −1.28325 | + | 1.28325i | ||||
\(708\) | −143.336 | − | 143.336i | −0.202452 | − | 0.202452i | ||||
\(709\) | − | 352.517i | − | 0.497204i | −0.968606 | − | 0.248602i | \(-0.920029\pi\) | ||
0.968606 | − | 0.248602i | \(-0.0799711\pi\) | |||||||
\(710\) | 298.827 | + | 266.660i | 0.420883 | + | 0.375578i | ||||
\(711\) | −112.081 | −0.157638 | ||||||||
\(712\) | 72.2676 | − | 72.2676i | 0.101499 | − | 0.101499i | ||||
\(713\) | 46.9530 | + | 46.9530i | 0.0658527 | + | 0.0658527i | ||||
\(714\) | − | 1437.96i | − | 2.01395i | ||||||
\(715\) | 54.3193 | − | 60.8717i | 0.0759710 | − | 0.0851352i | ||||
\(716\) | −70.6629 | −0.0986912 | ||||||||
\(717\) | −313.754 | + | 313.754i | −0.437593 | + | 0.437593i | ||||
\(718\) | −358.509 | − | 358.509i | −0.499317 | − | 0.499317i | ||||
\(719\) | − | 668.139i | − | 0.929261i | −0.885505 | − | 0.464631i | \(-0.846187\pi\) | ||
0.885505 | − | 0.464631i | \(-0.153813\pi\) | |||||||
\(720\) | −28.3874 | + | 1.61476i | −0.0394269 | + | 0.00224272i | ||||
\(721\) | −328.843 | −0.456092 | ||||||||
\(722\) | −304.556 | + | 304.556i | −0.421823 | + | 0.421823i | ||||
\(723\) | −678.832 | − | 678.832i | −0.938911 | − | 0.938911i | ||||
\(724\) | 440.935i | 0.609026i | ||||||||
\(725\) | −42.5069 | − | 372.426i | −0.0586303 | − | 0.513691i | ||||
\(726\) | −1357.88 | −1.87036 | ||||||||
\(727\) | 364.452 | − | 364.452i | 0.501310 | − | 0.501310i | −0.410535 | − | 0.911845i | \(-0.634658\pi\) |
0.911845 | + | 0.410535i | \(0.134658\pi\) | |||||||
\(728\) | −20.7901 | − | 20.7901i | −0.0285578 | − | 0.0285578i | ||||
\(729\) | − | 804.901i | − | 1.10412i | ||||||
\(730\) | −5.10127 | − | 89.6801i | −0.00698803 | − | 0.122849i | ||||
\(731\) | −1244.37 | −1.70228 | ||||||||
\(732\) | 5.46354 | − | 5.46354i | 0.00746386 | − | 0.00746386i | ||||
\(733\) | 148.455 | + | 148.455i | 0.202531 | + | 0.202531i | 0.801084 | − | 0.598553i | \(-0.204257\pi\) |
−0.598553 | + | 0.801084i | \(0.704257\pi\) | |||||||
\(734\) | − | 178.361i | − | 0.242998i | ||||||
\(735\) | 1454.94 | + | 1298.33i | 1.97951 | + | 1.76643i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 341.298 | − | 341.298i | 0.463091 | − | 0.463091i | ||||
\(738\) | −48.7519 | − | 48.7519i | −0.0660595 | − | 0.0660595i | ||||
\(739\) | − | 106.485i | − | 0.144093i | −0.997401 | − | 0.0720467i | \(-0.977047\pi\) | ||
0.997401 | − | 0.0720467i | \(-0.0229530\pi\) | |||||||
\(740\) | −322.014 | + | 360.858i | −0.435154 | + | 0.487646i | ||||
\(741\) | −15.5697 | −0.0210117 | ||||||||
\(742\) | −574.016 | + | 574.016i | −0.773607 | + | 0.773607i | ||||
\(743\) | 760.415 | + | 760.415i | 1.02344 | + | 1.02344i | 0.999719 | + | 0.0237201i | \(0.00755106\pi\) |
0.0237201 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(744\) | − | 107.807i | − | 0.144902i | ||||||
\(745\) | 645.204 | − | 36.7011i | 0.866045 | − | 0.0492632i | ||||
\(746\) | −623.507 | −0.835800 | ||||||||
\(747\) | −87.8404 | + | 87.8404i | −0.117591 | + | 0.117591i | ||||
\(748\) | 819.916 | + | 819.916i | 1.09614 | + | 1.09614i | ||||
\(749\) | 1076.49i | 1.43724i | ||||||||
\(750\) | 82.5548 | + | 479.591i | 0.110073 | + | 0.639455i | ||||
\(751\) | 665.100 | 0.885619 | 0.442810 | − | 0.896616i | \(-0.353982\pi\) | ||||
0.442810 | + | 0.896616i | \(0.353982\pi\) | |||||||
\(752\) | −7.80033 | + | 7.80033i | −0.0103728 | + | 0.0103728i | ||||
\(753\) | 748.205 | + | 748.205i | 0.993632 | + | 0.993632i | ||||
\(754\) | 15.9628i | 0.0211709i | ||||||||
\(755\) | 6.77865 | + | 119.168i | 0.00897834 | + | 0.157839i | ||||
\(756\) | −792.310 | −1.04803 | ||||||||
\(757\) | −860.269 | + | 860.269i | −1.13642 | + | 1.13642i | −0.147332 | + | 0.989087i | \(0.547068\pi\) |
−0.989087 | + | 0.147332i | \(0.952932\pi\) | |||||||
\(758\) | 266.437 | + | 266.437i | 0.351500 | + | 0.351500i | ||||
\(759\) | − | 286.155i | − | 0.377016i | ||||||
\(760\) | 79.2746 | + | 70.7413i | 0.104309 | + | 0.0930806i | ||||
\(761\) | −66.4693 | −0.0873447 | −0.0436723 | − | 0.999046i | \(-0.513906\pi\) | ||||
−0.0436723 | + | 0.999046i | \(0.513906\pi\) | |||||||
\(762\) | 317.079 | − | 317.079i | 0.416114 | − | 0.416114i | ||||
\(763\) | 35.7471 | + | 35.7471i | 0.0468508 | + | 0.0468508i | ||||
\(764\) | − | 577.200i | − | 0.755498i | ||||||
\(765\) | −126.596 | + | 141.867i | −0.165485 | + | 0.185447i | ||||
\(766\) | 1012.45 | 1.32174 | ||||||||
\(767\) | −19.5985 | + | 19.5985i | −0.0255522 | + | 0.0255522i | ||||
\(768\) | 31.1453 | + | 31.1453i | 0.0405537 | + | 0.0405537i | ||||
\(769\) | 894.516i | 1.16322i | 0.813468 | + | 0.581610i | \(0.197577\pi\) | ||||
−0.813468 | + | 0.581610i | \(0.802423\pi\) | |||||||
\(770\) | −2112.88 | + | 120.187i | −2.74400 | + | 0.156087i | ||||
\(771\) | −187.898 | −0.243707 | ||||||||
\(772\) | −254.580 | + | 254.580i | −0.329767 | + | 0.329767i | ||||
\(773\) | 926.134 | + | 926.134i | 1.19810 | + | 1.19810i | 0.974734 | + | 0.223369i | \(0.0717056\pi\) |
0.223369 | + | 0.974734i | \(0.428294\pi\) | |||||||
\(774\) | 93.5312i | 0.120841i | ||||||||
\(775\) | 343.909 | − | 39.2521i | 0.443754 | − | 0.0506479i | ||||
\(776\) | −358.457 | −0.461929 | ||||||||
\(777\) | −1299.99 | + | 1299.99i | −1.67308 | + | 1.67308i | ||||
\(778\) | −373.660 | − | 373.660i | −0.480283 | − | 0.480283i | ||||
\(779\) | 257.634i | 0.330724i | ||||||||
\(780\) | −1.17693 | − | 20.6904i | −0.00150889 | − | 0.0265262i | ||||
\(781\) | −1227.65 | −1.57190 | ||||||||
\(782\) | −128.283 | + | 128.283i | −0.164044 | + | 0.164044i | ||||
\(783\) | 304.172 | + | 304.172i | 0.388470 | + | 0.388470i | ||||
\(784\) | 566.680i | 0.722807i | ||||||||
\(785\) | 99.3137 | + | 88.6233i | 0.126514 | + | 0.112896i | ||||
\(786\) | 142.984 | 0.181914 | ||||||||
\(787\) | 271.450 | − | 271.450i | 0.344917 | − | 0.344917i | −0.513295 | − | 0.858212i | \(-0.671575\pi\) |
0.858212 | + | 0.513295i | \(0.171575\pi\) | |||||||
\(788\) | 268.994 | + | 268.994i | 0.341363 | + | 0.341363i | ||||
\(789\) | − | 689.932i | − | 0.874438i | ||||||
\(790\) | −371.166 | + | 415.939i | −0.469830 | + | 0.526505i | ||||
\(791\) | 1085.09 | 1.37180 | ||||||||
\(792\) | 61.6279 | − | 61.6279i | 0.0778130 | − | 0.0778130i | ||||
\(793\) | −0.747037 | − | 0.747037i | −0.000942038 | − | 0.000942038i | ||||
\(794\) | 219.624i | 0.276605i | ||||||||
\(795\) | −571.266 | + | 32.4953i | −0.718574 | + | 0.0408746i | ||||
\(796\) | −345.627 | −0.434205 | ||||||||
\(797\) | −89.1775 | + | 89.1775i | −0.111892 | + | 0.111892i | −0.760836 | − | 0.648944i | \(-0.775211\pi\) |
0.648944 | + | 0.760836i | \(0.275211\pi\) | |||||||
\(798\) | 285.586 | + | 285.586i | 0.357877 | + | 0.357877i | ||||
\(799\) | 73.7686i | 0.0923261i | ||||||||
\(800\) | −88.0151 | + | 110.695i | −0.110019 | + | 0.138369i | ||||
\(801\) | −51.3701 | −0.0641325 | ||||||||
\(802\) | −304.662 | + | 304.662i | −0.379877 | + | 0.379877i | ||||
\(803\) | 194.692 | + | 194.692i | 0.242456 | + | 0.242456i | ||||
\(804\) | − | 122.607i | − | 0.152496i | ||||||
\(805\) | −18.8042 | − | 330.578i | −0.0233593 | − | 0.410656i | ||||
\(806\) | −14.7405 | −0.0182885 | ||||||||
\(807\) | 208.265 | − | 208.265i | 0.258073 | − | 0.258073i | ||||
\(808\) | −185.838 | − | 185.838i | −0.229998 | − | 0.229998i | ||||
\(809\) | − | 714.152i | − | 0.882759i | −0.897321 | − | 0.441380i | \(-0.854489\pi\) | ||
0.897321 | − | 0.441380i | \(-0.145511\pi\) | |||||||
\(810\) | −349.179 | − | 311.592i | −0.431085 | − | 0.384682i | ||||
\(811\) | 938.065 | 1.15668 | 0.578339 | − | 0.815797i | \(-0.303701\pi\) | ||||
0.578339 | + | 0.815797i | \(0.303701\pi\) | |||||||
\(812\) | 292.797 | − | 292.797i | 0.360588 | − | 0.360588i | ||||
\(813\) | 162.501 | + | 162.501i | 0.199879 | + | 0.199879i | ||||
\(814\) | − | 1482.49i | − | 1.82124i | ||||||
\(815\) | −1002.91 | + | 1123.89i | −1.23056 | + | 1.37900i | ||||
\(816\) | 294.544 | 0.360961 | ||||||||
\(817\) | 247.137 | − | 247.137i | 0.302494 | − | 0.302494i | ||||
\(818\) | −228.713 | − | 228.713i | −0.279600 | − | 0.279600i | ||||
\(819\) | 14.7782i | 0.0180442i | ||||||||
\(820\) | −342.368 | + | 19.4749i | −0.417522 | + | 0.0237499i | ||||
\(821\) | 1298.50 | 1.58160 | 0.790802 | − | 0.612073i | \(-0.209664\pi\) | ||||
0.790802 | + | 0.612073i | \(0.209664\pi\) | |||||||
\(822\) | −101.296 | + | 101.296i | −0.123231 | + | 0.123231i | ||||
\(823\) | 413.358 | + | 413.358i | 0.502258 | + | 0.502258i | 0.912139 | − | 0.409881i | \(-0.134430\pi\) |
−0.409881 | + | 0.912139i | \(0.634430\pi\) | |||||||
\(824\) | − | 67.3584i | − | 0.0817456i | ||||||
\(825\) | −1167.59 | − | 928.367i | −1.41526 | − | 1.12529i | ||||
\(826\) | 718.969 | 0.870422 | ||||||||
\(827\) | 771.519 | − | 771.519i | 0.932913 | − | 0.932913i | −0.0649739 | − | 0.997887i | \(-0.520696\pi\) |
0.997887 | + | 0.0649739i | \(0.0206964\pi\) | |||||||
\(828\) | 9.64219 | + | 9.64219i | 0.0116452 | + | 0.0116452i | ||||
\(829\) | 645.980i | 0.779228i | 0.920978 | + | 0.389614i | \(0.127392\pi\) | ||||
−0.920978 | + | 0.389614i | \(0.872608\pi\) | |||||||
\(830\) | 35.0896 | + | 616.873i | 0.0422766 | + | 0.743221i | ||||
\(831\) | −818.174 | −0.984566 | ||||||||
\(832\) | 4.25853 | − | 4.25853i | 0.00511842 | − | 0.00511842i | ||||
\(833\) | 2679.58 | + | 2679.58i | 3.21678 | + | 3.21678i | ||||
\(834\) | 121.838i | 0.146089i | ||||||||
\(835\) | −212.662 | − | 189.770i | −0.254685 | − | 0.227270i | ||||
\(836\) | −325.679 | −0.389568 | ||||||||
\(837\) | −280.882 | + | 280.882i | −0.335581 | + | 0.335581i | ||||
\(838\) | 198.319 | + | 198.319i | 0.236658 | + | 0.236658i | ||||
\(839\) | 1586.81i | 1.89131i | 0.325166 | + | 0.945657i | \(0.394580\pi\) | ||||
−0.325166 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(840\) | −357.925 | + | 401.101i | −0.426102 | + | 0.477501i | ||||
\(841\) | 616.187 | 0.732684 | ||||||||
\(842\) | 571.167 | − | 571.167i | 0.678346 | − | 0.678346i | ||||
\(843\) | 122.895 | + | 122.895i | 0.145783 | + | 0.145783i | ||||
\(844\) | 529.313i | 0.627148i | ||||||||
\(845\) | 840.807 | − | 47.8276i | 0.995038 | − | 0.0566007i | ||||
\(846\) | 5.54472 | 0.00655404 | ||||||||
\(847\) | 3405.55 | − | 3405.55i | 4.02072 | − | 4.02072i | ||||
\(848\) | −117.579 | − | 117.579i | −0.138654 | − | 0.138654i | ||||
\(849\) | − | 610.551i | − | 0.719142i | ||||||
\(850\) | 107.243 | + | 939.611i | 0.126168 | + | 1.10542i | ||||
\(851\) | 231.947 | 0.272559 | ||||||||
\(852\) | −220.509 | + | 220.509i | −0.258813 | + | 0.258813i | ||||
\(853\) | −633.942 | − | 633.942i | −0.743192 | − | 0.743192i | 0.229999 | − | 0.973191i | \(-0.426128\pi\) |
−0.973191 | + | 0.229999i | \(0.926128\pi\) | |||||||
\(854\) | 27.4049i | 0.0320901i | ||||||||
\(855\) | −3.03289 | − | 53.3180i | −0.00354723 | − | 0.0623603i | ||||
\(856\) | −220.503 | −0.257597 | ||||||||
\(857\) | −669.720 | + | 669.720i | −0.781470 | + | 0.781470i | −0.980079 | − | 0.198609i | \(-0.936358\pi\) |
0.198609 | + | 0.980079i | \(0.436358\pi\) | |||||||
\(858\) | 44.9181 | + | 44.9181i | 0.0523522 | + | 0.0523522i | ||||
\(859\) | 1076.95i | 1.25372i | 0.779131 | + | 0.626861i | \(0.215661\pi\) | ||||
−0.779131 | + | 0.626861i | \(0.784339\pi\) | |||||||
\(860\) | 347.100 | + | 309.738i | 0.403605 | + | 0.360160i | ||||
\(861\) | −1303.54 | −1.51398 | ||||||||
\(862\) | 575.249 | − | 575.249i | 0.667342 | − | 0.667342i | ||||
\(863\) | −57.6828 | − | 57.6828i | −0.0668399 | − | 0.0668399i | 0.672897 | − | 0.739737i | \(-0.265050\pi\) |
−0.739737 | + | 0.672897i | \(0.765050\pi\) | |||||||
\(864\) | − | 162.293i | − | 0.187839i | ||||||
\(865\) | −509.207 | + | 570.632i | −0.588679 | + | 0.659690i | ||||
\(866\) | −1.43679 | −0.00165912 | ||||||||
\(867\) | 830.208 | − | 830.208i | 0.957564 | − | 0.957564i | ||||
\(868\) | 270.378 | + | 270.378i | 0.311495 | + | 0.311495i | ||||
\(869\) | − | 1708.77i | − | 1.96637i | ||||||
\(870\) | 291.394 | − | 16.5754i | 0.334936 | − | 0.0190522i | ||||
\(871\) | −16.7642 | −0.0192471 | ||||||||
\(872\) | −7.32226 | + | 7.32226i | −0.00839708 | + | 0.00839708i | ||||
\(873\) | 127.401 | + | 127.401i | 0.145935 | + | 0.145935i | ||||
\(874\) | − | 50.9551i | − | 0.0583010i | ||||||
\(875\) | −1409.85 | − | 995.760i | −1.61126 | − | 1.13801i | ||||
\(876\) | 69.9406 | 0.0798409 | ||||||||
\(877\) | −168.052 | + | 168.052i | −0.191621 | + | 0.191621i | −0.796396 | − | 0.604775i | \(-0.793263\pi\) |
0.604775 | + | 0.796396i | \(0.293263\pi\) | |||||||
\(878\) | 520.035 | + | 520.035i | 0.592295 | + | 0.592295i | ||||
\(879\) | − | 1459.21i | − | 1.66008i | ||||||
\(880\) | −24.6185 | − | 432.792i | −0.0279755 | − | 0.491809i | ||||
\(881\) | −302.189 | −0.343007 | −0.171504 | − | 0.985183i | \(-0.554863\pi\) | ||||
−0.171504 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(882\) | 201.407 | − | 201.407i | 0.228353 | − | 0.228353i | ||||
\(883\) | −856.409 | − | 856.409i | −0.969885 | − | 0.969885i | 0.0296745 | − | 0.999560i | \(-0.490553\pi\) |
−0.999560 | + | 0.0296745i | \(0.990553\pi\) | |||||||
\(884\) | − | 40.2734i | − | 0.0455581i | ||||||
\(885\) | 378.113 | + | 337.411i | 0.427246 | + | 0.381256i | ||||
\(886\) | −108.750 | −0.122742 | ||||||||
\(887\) | 302.316 | − | 302.316i | 0.340830 | − | 0.340830i | −0.515849 | − | 0.856679i | \(-0.672524\pi\) |
0.856679 | + | 0.515849i | \(0.172524\pi\) | |||||||
\(888\) | −266.283 | − | 266.283i | −0.299868 | − | 0.299868i | ||||
\(889\) | 1590.46i | 1.78904i | ||||||||
\(890\) | −170.117 | + | 190.638i | −0.191143 | + | 0.214200i | ||||
\(891\) | 1434.51 | 1.61000 | ||||||||
\(892\) | −355.955 | + | 355.955i | −0.399052 | + | 0.399052i | ||||
\(893\) | −14.6508 | − | 14.6508i | −0.0164063 | − | 0.0164063i | ||||
\(894\) | 503.188i | 0.562850i | ||||||||
\(895\) | 176.372 | − | 10.0326i | 0.197064 | − | 0.0112096i | ||||
\(896\) | −156.223 | −0.174357 | ||||||||
\(897\) | −7.02781 | + | 7.02781i | −0.00783480 | + | 0.00783480i | ||||
\(898\) | −556.320 | − | 556.320i | −0.619510 | − | 0.619510i | ||||
\(899\) | − | 207.599i | − | 0.230922i | ||||||
\(900\) | 70.6247 | − | 8.06076i | 0.0784718 | − | 0.00895640i | ||||
\(901\) | −1111.95 | −1.23413 | ||||||||
\(902\) | 743.268 | − | 743.268i | 0.824022 | − | 0.824022i | ||||
\(903\) | 1250.43 | + | 1250.43i | 1.38475 | + | 1.38475i | ||||
\(904\) | 222.265i | 0.245868i | ||||||||
\(905\) | −62.6030 | − | 1100.56i | −0.0691746 | − | 1.21609i | ||||
\(906\) | −92.9382 | −0.102581 | ||||||||
\(907\) | −522.277 | + | 522.277i | −0.575829 | + | 0.575829i | −0.933751 | − | 0.357922i | \(-0.883485\pi\) |
0.357922 | + | 0.933751i | \(0.383485\pi\) | |||||||
\(908\) | −542.062 | − | 542.062i | −0.596985 | − | 0.596985i | ||||
\(909\) | 132.100i | 0.145324i | ||||||||
\(910\) | 54.8430 | + | 48.9395i | 0.0602670 | + | 0.0537797i | ||||
\(911\) | 99.0099 | 0.108683 | 0.0543413 | − | 0.998522i | \(-0.482694\pi\) | ||||
0.0543413 | + | 0.998522i | \(0.482694\pi\) | |||||||
\(912\) | −58.4979 | + | 58.4979i | −0.0641425 | + | 0.0641425i | ||||
\(913\) | −1339.21 | − | 1339.21i | −1.46682 | − | 1.46682i | ||||
\(914\) | 515.314i | 0.563801i | ||||||||
\(915\) | −12.8611 | + | 14.4125i | −0.0140559 | + | 0.0157514i | ||||
\(916\) | 103.375 | 0.112855 | ||||||||
\(917\) | −358.602 | + | 358.602i | −0.391060 | + | 0.391060i | ||||
\(918\) | −767.410 | − | 767.410i | −0.835959 | − | 0.835959i | ||||
\(919\) | − | 648.385i | − | 0.705534i | −0.935711 | − | 0.352767i | \(-0.885241\pi\) | ||
0.935711 | − | 0.352767i | \(-0.114759\pi\) | |||||||
\(920\) | 67.7138 | − | 3.85176i | 0.0736020 | − | 0.00418670i | ||||
\(921\) | 1397.47 | 1.51734 | ||||||||
\(922\) | 236.551 | − | 236.551i | 0.256563 | − | 0.256563i | ||||
\(923\) | 30.1504 | + | 30.1504i | 0.0326657 | + | 0.0326657i | ||||
\(924\) | − | 1647.82i | − | 1.78335i | ||||||
\(925\) | 752.502 | − | 946.407i | 0.813516 | − | 1.02314i | ||||
\(926\) | −413.908 | −0.446984 | ||||||||
\(927\) | −23.9402 | + | 23.9402i | −0.0258255 | + | 0.0258255i | ||||
\(928\) | 59.9751 | + | 59.9751i | 0.0646283 | + | 0.0646283i | ||||
\(929\) | 559.661i | 0.602434i | 0.953556 | + | 0.301217i | \(0.0973929\pi\) | ||||
−0.953556 | + | 0.301217i | \(0.902607\pi\) | |||||||
\(930\) | 15.3062 | + | 269.082i | 0.0164583 | + | 0.289336i | ||||
\(931\) | −1064.36 | −1.14324 | ||||||||
\(932\) | 503.403 | − | 503.403i | 0.540132 | − | 0.540132i | ||||
\(933\) | −16.7895 | − | 16.7895i | −0.0179952 | − | 0.0179952i | ||||
\(934\) | − | 910.320i | − | 0.974647i | ||||||
\(935\) | −2162.89 | − | 1930.07i | −2.31325 | − | 2.06425i | ||||
\(936\) | −3.02710 | −0.00323408 | ||||||||
\(937\) | −490.873 | + | 490.873i | −0.523878 | + | 0.523878i | −0.918740 | − | 0.394863i | \(-0.870792\pi\) |
0.394863 | + | 0.918740i | \(0.370792\pi\) | |||||||
\(938\) | 307.496 | + | 307.496i | 0.327821 | + | 0.327821i | ||||
\(939\) | 912.949i | 0.972256i | ||||||||
\(940\) | 18.3619 | − | 20.5768i | 0.0195339 | − | 0.0218902i | ||||
\(941\) | −375.476 | −0.399018 | −0.199509 | − | 0.979896i | \(-0.563935\pi\) | ||||
−0.199509 | + | 0.979896i | \(0.563935\pi\) | |||||||
\(942\) | −73.2851 | + | 73.2851i | −0.0777974 | + | 0.0777974i | ||||
\(943\) | 116.290 | + | 116.290i | 0.123320 | + | 0.123320i | ||||
\(944\) | 147.270i | 0.156006i | ||||||||
\(945\) | 1977.58 | − | 112.491i | 2.09268 | − | 0.119038i | ||||
\(946\) | −1425.97 | −1.50737 | ||||||||
\(947\) | 284.861 | − | 284.861i | 0.300804 | − | 0.300804i | −0.540525 | − | 0.841328i | \(-0.681774\pi\) |
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(948\) | −306.928 | − | 306.928i | −0.323763 | − | 0.323763i | ||||
\(949\) | − | 9.56306i | − | 0.0100770i | ||||||
\(950\) | −207.910 | − | 165.312i | −0.218853 | − | 0.174013i | ||||
\(951\) | −1402.53 | −1.47480 | ||||||||
\(952\) | −738.711 | + | 738.711i | −0.775957 | + | 0.775957i | ||||
\(953\) | 930.751 | + | 930.751i | 0.976654 | + | 0.976654i | 0.999734 | − | 0.0230796i | \(-0.00734710\pi\) |
−0.0230796 | + | 0.999734i | \(0.507347\pi\) | |||||||
\(954\) | 83.5785i | 0.0876085i | ||||||||
\(955\) | 81.9497 | + | 1440.67i | 0.0858112 | + | 1.50856i | ||||
\(956\) | 322.364 | 0.337201 | ||||||||
\(957\) | −632.606 | + | 632.606i | −0.661030 | + | 0.661030i | ||||
\(958\) | 15.9362 | + | 15.9362i | 0.0166349 | + | 0.0166349i | ||||
\(959\) | − | 508.095i | − | 0.529818i | ||||||
\(960\) | −82.1594 | − | 73.3155i | −0.0855827 | − | 0.0763704i | ||||
\(961\) | −769.297 | −0.800517 | ||||||||
\(962\) | −36.4091 | + | 36.4091i | −0.0378473 | + | 0.0378473i | ||||
\(963\) | 78.3703 | + | 78.3703i | 0.0813814 | + | 0.0813814i | ||||
\(964\) | 697.462i | 0.723508i | ||||||||
\(965\) | 599.278 | − | 671.567i | 0.621013 | − | 0.695925i | ||||
\(966\) | 257.814 | 0.266889 | ||||||||
\(967\) | 317.651 | − | 317.651i | 0.328491 | − | 0.328491i | −0.523521 | − | 0.852013i | \(-0.675382\pi\) |
0.852013 | + | 0.523521i | \(0.175382\pi\) | |||||||
\(968\) | 697.574 | + | 697.574i | 0.720635 | + | 0.720635i | ||||
\(969\) | 553.222i | 0.570920i | ||||||||
\(970\) | 894.695 | − | 50.8929i | 0.922366 | − | 0.0524669i | ||||
\(971\) | −1018.91 | −1.04934 | −0.524672 | − | 0.851305i | \(-0.675812\pi\) | ||||
−0.524672 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(972\) | −107.494 | + | 107.494i | −0.110591 | + | 0.110591i | ||||
\(973\) | −305.569 | − | 305.569i | −0.314048 | − | 0.314048i | ||||
\(974\) | 746.886i | 0.766824i | ||||||||
\(975\) | 5.87517 | + | 51.4755i | 0.00602581 | + | 0.0527954i | ||||
\(976\) | −5.61348 | −0.00575152 | ||||||||
\(977\) | −604.405 | + | 604.405i | −0.618634 | + | 0.618634i | −0.945181 | − | 0.326547i | \(-0.894115\pi\) |
0.326547 | + | 0.945181i | \(0.394115\pi\) | |||||||
\(978\) | −829.334 | − | 829.334i | −0.847990 | − | 0.847990i | ||||
\(979\) | − | 783.185i | − | 0.799984i | ||||||
\(980\) | −80.4561 | − | 1414.41i | −0.0820980 | − | 1.44328i | ||||
\(981\) | 5.20489 | 0.00530570 | ||||||||
\(982\) | −253.834 | + | 253.834i | −0.258487 | + | 0.258487i | ||||
\(983\) | −579.674 | − | 579.674i | −0.589699 | − | 0.589699i | 0.347851 | − | 0.937550i | \(-0.386912\pi\) |
−0.937550 | + | 0.347851i | \(0.886912\pi\) | |||||||
\(984\) | − | 267.009i | − | 0.271351i | ||||||
\(985\) | −709.591 | − | 633.208i | −0.720396 | − | 0.642851i | ||||
\(986\) | 567.191 | 0.575244 | ||||||||
\(987\) | 74.1278 | − | 74.1278i | 0.0751042 | − | 0.0751042i | ||||
\(988\) | 7.99849 | + | 7.99849i | 0.00809564 | + | 0.00809564i | ||||
\(989\) | − | 223.105i | − | 0.225586i | ||||||
\(990\) | −145.071 | + | 162.571i | −0.146537 | + | 0.164213i | ||||
\(991\) | −455.864 | −0.460004 | −0.230002 | − | 0.973190i | \(-0.573873\pi\) | ||||
−0.230002 | + | 0.973190i | \(0.573873\pi\) | |||||||
\(992\) | −55.3827 | + | 55.3827i | −0.0558294 | + | 0.0558294i | ||||
\(993\) | 1066.08 | + | 1066.08i | 1.07359 | + | 1.07359i | ||||
\(994\) | − | 1106.07i | − | 1.11274i | ||||||
\(995\) | 862.673 | − | 49.0714i | 0.867008 | − | 0.0493180i | ||||
\(996\) | −481.093 | −0.483025 | ||||||||
\(997\) | 71.4972 | − | 71.4972i | 0.0717123 | − | 0.0717123i | −0.670341 | − | 0.742053i | \(-0.733852\pi\) |
0.742053 | + | 0.670341i | \(0.233852\pi\) | |||||||
\(998\) | −482.367 | − | 482.367i | −0.483334 | − | 0.483334i | ||||
\(999\) | 1387.55i | 1.38894i |
(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.93.8 | yes | 20 | |
5.2 | odd | 4 | inner | 230.3.f.a.47.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.a.47.8 | ✓ | 20 | 5.2 | odd | 4 | inner | |
230.3.f.a.93.8 | yes | 20 | 1.1 | even | 1 | trivial |