Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11184604443.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 43x^{4} - 210x^{3} + 1849x^{2} - 4515x + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(1.60692 + 2.78326i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.109 |
Dual form | 378.4.g.a.163.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.301070 | + | 0.521469i | 0.0269285 | + | 0.0466416i | 0.879176 | − | 0.476498i | \(-0.158094\pi\) |
−0.852247 | + | 0.523139i | \(0.824761\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.6665 | + | 5.55825i | −0.953902 | + | 0.300117i | ||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.602141 | − | 1.04294i | 0.0190414 | − | 0.0329806i | ||||
\(11\) | −4.52503 | + | 7.83758i | −0.124032 | + | 0.214829i | −0.921354 | − | 0.388725i | \(-0.872916\pi\) |
0.797322 | + | 0.603554i | \(0.206249\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60214 | 0.119520 | 0.0597598 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597598 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(14\) | 27.2937 | + | 25.0411i | 0.521039 | + | 0.478036i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.61646 | − | 11.4601i | 0.0943958 | − | 0.163498i | −0.814960 | − | 0.579517i | \(-0.803241\pi\) |
0.909356 | + | 0.416018i | \(0.136575\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.8134 | − | 42.9780i | −0.299609 | − | 0.518938i | 0.676437 | − | 0.736500i | \(-0.263523\pi\) |
−0.976047 | + | 0.217562i | \(0.930190\pi\) | |||||||
\(20\) | −2.40856 | −0.0269285 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.1001 | 0.175407 | ||||||||
\(23\) | 65.0049 | + | 112.592i | 0.589324 | + | 1.02074i | 0.994321 | + | 0.106422i | \(0.0339393\pi\) |
−0.404997 | + | 0.914318i | \(0.632727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.3187 | − | 107.939i | 0.498550 | − | 0.863513i | ||||
\(26\) | −5.60214 | − | 9.70319i | −0.0422565 | − | 0.0731905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0787 | − | 72.3151i | 0.108521 | − | 0.488081i | ||||
\(29\) | 50.2607 | 0.321834 | 0.160917 | − | 0.986968i | \(-0.448555\pi\) | ||||
0.160917 | + | 0.986968i | \(0.448555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 124.287 | − | 215.272i | 0.720087 | − | 1.24723i | −0.240878 | − | 0.970555i | \(-0.577435\pi\) |
0.960965 | − | 0.276671i | \(-0.0892313\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −26.4659 | −0.133496 | ||||||||
\(35\) | −8.21732 | − | 7.53912i | −0.0396852 | − | 0.0364098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.1176 | − | 26.1845i | −0.0671708 | − | 0.116343i | 0.830484 | − | 0.557042i | \(-0.188064\pi\) |
−0.897655 | + | 0.440699i | \(0.854731\pi\) | |||||||
\(38\) | −49.6267 | + | 85.9560i | −0.211856 | + | 0.366945i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.40856 | + | 4.17175i | 0.00952068 | + | 0.0164903i | ||||
\(41\) | 277.880 | 1.05848 | 0.529239 | − | 0.848473i | \(-0.322478\pi\) | ||||
0.529239 | + | 0.848473i | \(0.322478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.9644 | −0.173651 | −0.0868256 | − | 0.996224i | \(-0.527672\pi\) | ||||
−0.0868256 | + | 0.996224i | \(0.527672\pi\) | |||||||
\(44\) | −18.1001 | − | 31.3503i | −0.0620158 | − | 0.107414i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 130.010 | − | 225.184i | 0.416715 | − | 0.721772i | ||||
\(47\) | 121.813 | + | 210.986i | 0.378048 | + | 0.654798i | 0.990778 | − | 0.135494i | \(-0.0432622\pi\) |
−0.612730 | + | 0.790292i | \(0.709929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 281.212 | − | 196.390i | 0.819859 | − | 0.572565i | ||||
\(50\) | −249.275 | −0.705056 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.2043 | + | 19.4064i | −0.0298799 | + | 0.0517535i | ||||
\(53\) | 243.524 | − | 421.796i | 0.631143 | − | 1.09317i | −0.356176 | − | 0.934419i | \(-0.615919\pi\) |
0.987318 | − | 0.158752i | \(-0.0507472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.44941 | −0.0133600 | ||||||||
\(56\) | −141.332 | + | 44.4660i | −0.337255 | + | 0.106107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −50.2607 | − | 87.0541i | −0.113785 | − | 0.197082i | ||||
\(59\) | 44.7885 | − | 77.5759i | 0.0988299 | − | 0.171178i | −0.812371 | − | 0.583141i | \(-0.801823\pi\) |
0.911201 | + | 0.411963i | \(0.135157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −339.433 | − | 587.916i | −0.712459 | − | 1.23402i | −0.963931 | − | 0.266151i | \(-0.914248\pi\) |
0.251473 | − | 0.967864i | \(-0.419085\pi\) | |||||||
\(62\) | −497.150 | −1.01836 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 1.68664 | + | 2.92134i | 0.00321849 | + | 0.00557458i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 350.562 | − | 607.191i | 0.639223 | − | 1.10717i | −0.346380 | − | 0.938094i | \(-0.612589\pi\) |
0.985604 | − | 0.169073i | \(-0.0540773\pi\) | |||||||
\(68\) | 26.4659 | + | 45.8402i | 0.0471979 | + | 0.0817491i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.84082 | + | 21.7719i | −0.00826555 | + | 0.0371749i | ||||
\(71\) | −376.105 | −0.628669 | −0.314334 | − | 0.949312i | \(-0.601781\pi\) | ||||
−0.314334 | + | 0.949312i | \(0.601781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 134.482 | − | 232.929i | 0.215615 | − | 0.373456i | −0.737848 | − | 0.674967i | \(-0.764158\pi\) |
0.953463 | + | 0.301511i | \(0.0974911\pi\) | |||||||
\(74\) | −30.2352 | + | 52.3689i | −0.0474969 | + | 0.0822671i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 198.507 | 0.299609 | ||||||||
\(77\) | 36.3783 | − | 163.614i | 0.0538401 | − | 0.242150i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.6704 | − | 34.0701i | −0.0280138 | − | 0.0485213i | 0.851679 | − | 0.524064i | \(-0.175585\pi\) |
−0.879692 | + | 0.475543i | \(0.842252\pi\) | |||||||
\(80\) | 4.81712 | − | 8.34351i | 0.00673214 | − | 0.0116604i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −277.880 | − | 481.303i | −0.374228 | − | 0.648183i | ||||
\(83\) | 491.595 | 0.650115 | 0.325058 | − | 0.945694i | \(-0.394616\pi\) | ||||
0.325058 | + | 0.945694i | \(0.394616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.96808 | 0.0101678 | ||||||||
\(86\) | 48.9644 | + | 84.8089i | 0.0613950 | + | 0.106339i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −36.2002 | + | 62.7006i | −0.0438518 | + | 0.0759535i | ||||
\(89\) | −342.378 | − | 593.015i | −0.407775 | − | 0.706286i | 0.586865 | − | 0.809685i | \(-0.300362\pi\) |
−0.994640 | + | 0.103398i | \(0.967028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.9703 | + | 31.1381i | −0.114010 | + | 0.0358699i | ||||
\(92\) | −520.039 | −0.589324 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 243.626 | − | 421.972i | 0.267320 | − | 0.463012i | ||||
\(95\) | 14.9411 | − | 25.8788i | 0.0161361 | − | 0.0279485i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −328.527 | −0.343885 | −0.171942 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171942 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(98\) | −621.369 | − | 290.683i | −0.640487 | − | 0.299627i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 249.275 | + | 431.757i | 0.249275 | + | 0.431757i | ||||
\(101\) | 189.567 | − | 328.339i | 0.186758 | − | 0.323475i | −0.757409 | − | 0.652940i | \(-0.773535\pi\) |
0.944168 | + | 0.329466i | \(0.106869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 130.161 | + | 225.446i | 0.124516 | + | 0.215669i | 0.921544 | − | 0.388274i | \(-0.126929\pi\) |
−0.797027 | + | 0.603943i | \(0.793595\pi\) | |||||||
\(104\) | 44.8171 | 0.0422565 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −974.095 | −0.892571 | ||||||||
\(107\) | −544.146 | − | 942.488i | −0.491631 | − | 0.851530i | 0.508322 | − | 0.861167i | \(-0.330266\pi\) |
−0.999954 | + | 0.00963652i | \(0.996933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −251.781 | + | 436.097i | −0.221250 | + | 0.383216i | −0.955188 | − | 0.296001i | \(-0.904347\pi\) |
0.733938 | + | 0.679217i | \(0.237680\pi\) | |||||||
\(110\) | 5.44941 | + | 9.43865i | 0.00472346 | + | 0.00818127i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 218.349 | + | 200.328i | 0.184215 | + | 0.169011i | ||||
\(113\) | 1280.25 | 1.06580 | 0.532901 | − | 0.846178i | \(-0.321102\pi\) | ||||
0.532901 | + | 0.846178i | \(0.321102\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39.1421 | + | 67.7961i | −0.0317393 | + | 0.0549741i | ||||
\(116\) | −100.521 | + | 174.108i | −0.0804584 | + | 0.139358i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −179.154 | −0.139767 | ||||||||
\(119\) | −53.1921 | + | 239.235i | −0.0409757 | + | 0.184291i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 624.548 | + | 1081.75i | 0.469232 | + | 0.812734i | ||||
\(122\) | −678.867 | + | 1175.83i | −0.503785 | + | 0.872580i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 497.150 | + | 861.089i | 0.360043 | + | 0.623613i | ||||
\(125\) | 150.317 | 0.107558 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −920.069 | −0.642857 | −0.321429 | − | 0.946934i | \(-0.604163\pi\) | ||||
−0.321429 | + | 0.946934i | \(0.604163\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.37328 | − | 5.84269i | 0.00227581 | − | 0.00394183i | ||||
\(131\) | 1392.23 | + | 2411.42i | 0.928551 | + | 1.60830i | 0.785749 | + | 0.618545i | \(0.212278\pi\) |
0.142802 | + | 0.989751i | \(0.454389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 677.248 | + | 621.353i | 0.441540 | + | 0.405099i | ||||
\(134\) | −1402.25 | −0.903998 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 52.9317 | − | 91.6804i | 0.0333740 | − | 0.0578054i | ||||
\(137\) | 1207.94 | − | 2092.22i | 0.753295 | − | 1.30475i | −0.192922 | − | 0.981214i | \(-0.561796\pi\) |
0.946217 | − | 0.323532i | \(-0.104870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −94.5986 | −0.0577248 | −0.0288624 | − | 0.999583i | \(-0.509188\pi\) | ||||
−0.0288624 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(140\) | 42.5509 | − | 13.3874i | 0.0256872 | − | 0.00808172i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 376.105 | + | 651.433i | 0.222268 | + | 0.384979i | ||||
\(143\) | −25.3498 | + | 43.9072i | −0.0148242 | + | 0.0256763i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.1320 | + | 26.2094i | 0.00866651 | + | 0.0150108i | ||||
\(146\) | −537.926 | −0.304925 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 120.941 | 0.0671708 | ||||||||
\(149\) | 1172.33 | + | 2030.53i | 0.644569 | + | 1.11643i | 0.984401 | + | 0.175941i | \(0.0562967\pi\) |
−0.339831 | + | 0.940486i | \(0.610370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 113.816 | − | 197.135i | 0.0613391 | − | 0.106242i | −0.833725 | − | 0.552180i | \(-0.813796\pi\) |
0.895064 | + | 0.445937i | \(0.147130\pi\) | |||||||
\(152\) | −198.507 | − | 343.824i | −0.105928 | − | 0.183472i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −319.766 | + | 100.605i | −0.167321 | + | 0.0526427i | ||||
\(155\) | 149.677 | 0.0775635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −172.605 | + | 298.961i | −0.0877414 | + | 0.151973i | −0.906556 | − | 0.422085i | \(-0.861298\pi\) |
0.818815 | + | 0.574058i | \(0.194632\pi\) | |||||||
\(158\) | −39.3408 | + | 68.1402i | −0.0198088 | + | 0.0343098i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.2685 | −0.00952068 | ||||||||
\(161\) | −1774.22 | − | 1627.79i | −0.868499 | − | 0.796820i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1645.72 | + | 2850.47i | 0.790813 | + | 1.36973i | 0.925464 | + | 0.378836i | \(0.123675\pi\) |
−0.134651 | + | 0.990893i | \(0.542991\pi\) | |||||||
\(164\) | −555.760 | + | 962.605i | −0.264619 | + | 0.458334i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −491.595 | − | 851.468i | −0.229850 | − | 0.398113i | ||||
\(167\) | 3657.31 | 1.69468 | 0.847338 | − | 0.531054i | \(-0.178204\pi\) | ||||
0.847338 | + | 0.531054i | \(0.178204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2165.62 | −0.985715 | ||||||||
\(170\) | −7.96808 | − | 13.8011i | −0.00359485 | − | 0.00622646i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 97.9289 | − | 169.618i | 0.0434128 | − | 0.0751932i | ||||
\(173\) | 1325.61 | + | 2296.03i | 0.582569 | + | 1.00904i | 0.995174 | + | 0.0981286i | \(0.0312857\pi\) |
−0.412605 | + | 0.910910i | \(0.635381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −501.002 | + | 2253.29i | −0.216413 | + | 0.973331i | ||||
\(176\) | 144.801 | 0.0620158 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −684.755 | + | 1186.03i | −0.288340 | + | 0.499420i | ||||
\(179\) | 700.967 | − | 1214.11i | 0.292697 | − | 0.506965i | −0.681750 | − | 0.731585i | \(-0.738781\pi\) |
0.974446 | + | 0.224620i | \(0.0721141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.91675 | −0.00119779 | −0.000598897 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000598897 | 1.00000i | \(0.500191\pi\) | ||||||||
\(182\) | 152.903 | + | 140.284i | 0.0622743 | + | 0.0571347i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 520.039 | + | 900.734i | 0.208358 | + | 0.360886i | ||||
\(185\) | 9.10293 | − | 15.7667i | 0.00361762 | − | 0.00626591i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 59.8794 | + | 103.714i | 0.0234161 | + | 0.0405579i | ||||
\(188\) | −974.503 | −0.378048 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −59.7645 | −0.0228199 | ||||||||
\(191\) | 126.055 | + | 218.334i | 0.0477540 | + | 0.0827124i | 0.888914 | − | 0.458073i | \(-0.151460\pi\) |
−0.841160 | + | 0.540786i | \(0.818127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −986.702 | + | 1709.02i | −0.368002 | + | 0.637398i | −0.989253 | − | 0.146213i | \(-0.953291\pi\) |
0.621251 | + | 0.783612i | \(0.286625\pi\) | |||||||
\(194\) | 328.527 | + | 569.025i | 0.121582 | + | 0.210586i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 117.891 | + | 1366.93i | 0.0429631 | + | 0.498151i | ||||
\(197\) | −1788.56 | −0.646850 | −0.323425 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323425 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −461.066 | + | 798.589i | −0.164242 | + | 0.284475i | −0.936386 | − | 0.350973i | \(-0.885851\pi\) |
0.772144 | + | 0.635447i | \(0.219184\pi\) | |||||||
\(200\) | 498.550 | − | 863.513i | 0.176264 | − | 0.305298i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −758.266 | −0.264116 | ||||||||
\(203\) | −887.931 | + | 279.361i | −0.306998 | + | 0.0965878i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 83.6615 | + | 144.906i | 0.0285033 | + | 0.0493691i | ||||
\(206\) | 260.323 | − | 450.892i | 0.0880464 | − | 0.152501i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −44.8171 | − | 77.6255i | −0.0149399 | − | 0.0258767i | ||||
\(209\) | 449.125 | 0.148644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5130.61 | −1.67396 | −0.836981 | − | 0.547232i | \(-0.815682\pi\) | ||||
−0.836981 | + | 0.547232i | \(0.815682\pi\) | |||||||
\(212\) | 974.095 | + | 1687.18i | 0.315571 | + | 0.546586i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1088.29 | + | 1884.98i | −0.347636 | + | 0.602123i | ||||
\(215\) | −14.7417 | − | 25.5334i | −0.00467618 | − | 0.00809938i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −999.190 | + | 4493.93i | −0.312578 | + | 1.40584i | ||||
\(218\) | 1007.12 | 0.312895 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.8988 | − | 18.8773i | 0.00333999 | − | 0.00578503i | ||||
\(221\) | 37.0664 | − | 64.2008i | 0.0112821 | − | 0.0195412i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3777.82 | 1.13445 | 0.567223 | − | 0.823564i | \(-0.308018\pi\) | ||||
0.567223 | + | 0.823564i | \(0.308018\pi\) | |||||||
\(224\) | 128.630 | − | 578.521i | 0.0383680 | − | 0.172563i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1280.25 | − | 2217.45i | −0.376818 | − | 0.652667i | ||||
\(227\) | −1661.63 | + | 2878.02i | −0.485842 | + | 0.841502i | −0.999868 | − | 0.0162724i | \(-0.994820\pi\) |
0.514026 | + | 0.857775i | \(0.328153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 477.230 | + | 826.587i | 0.137713 | + | 0.238526i | 0.926631 | − | 0.375973i | \(-0.122692\pi\) |
−0.788918 | + | 0.614499i | \(0.789358\pi\) | |||||||
\(230\) | 156.568 | 0.0448861 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 402.086 | 0.113785 | ||||||||
\(233\) | −2002.14 | − | 3467.80i | −0.562937 | − | 0.975035i | −0.997238 | − | 0.0742678i | \(-0.976338\pi\) |
0.434301 | − | 0.900768i | \(-0.356995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −73.3485 | + | 127.043i | −0.0203605 | + | 0.0352655i | ||||
\(236\) | 179.154 | + | 310.304i | 0.0494150 | + | 0.0855892i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 467.560 | − | 147.104i | 0.127342 | − | 0.0400644i | ||||
\(239\) | −2768.29 | −0.749230 | −0.374615 | − | 0.927181i | \(-0.622225\pi\) | ||||
−0.374615 | + | 0.927181i | \(0.622225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3568.69 | − | 6181.15i | 0.953857 | − | 1.65213i | 0.216896 | − | 0.976195i | \(-0.430407\pi\) |
0.736962 | − | 0.675935i | \(-0.236260\pi\) | |||||||
\(242\) | 1249.10 | − | 2163.50i | 0.331797 | − | 0.574690i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2715.47 | 0.712459 | ||||||||
\(245\) | 187.076 | + | 87.5161i | 0.0487830 | + | 0.0228212i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −139.008 | − | 240.769i | −0.0358092 | − | 0.0620233i | ||||
\(248\) | 994.300 | − | 1722.18i | 0.254589 | − | 0.440961i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −150.317 | − | 260.356i | −0.0380275 | − | 0.0658655i | ||||
\(251\) | −3925.58 | −0.987172 | −0.493586 | − | 0.869697i | \(-0.664314\pi\) | ||||
−0.493586 | + | 0.869697i | \(0.664314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1176.60 | −0.292379 | ||||||||
\(254\) | 920.069 | + | 1593.61i | 0.227284 | + | 0.393668i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1123.14 | − | 1945.33i | −0.272605 | − | 0.472165i | 0.696923 | − | 0.717146i | \(-0.254552\pi\) |
−0.969528 | + | 0.244980i | \(0.921218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 412.615 | + | 378.561i | 0.0989910 | + | 0.0908210i | ||||
\(260\) | −13.4931 | −0.00321849 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2784.47 | − | 4822.84i | 0.656584 | − | 1.13724i | ||||
\(263\) | −641.744 | + | 1111.53i | −0.150463 | + | 0.260609i | −0.931398 | − | 0.364003i | \(-0.881410\pi\) |
0.780935 | + | 0.624612i | \(0.214743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 293.271 | 0.0679830 | ||||||||
\(266\) | 398.967 | − | 1794.38i | 0.0919632 | − | 0.413611i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1402.25 | + | 2428.76i | 0.319612 | + | 0.553583i | ||||
\(269\) | 2360.33 | − | 4088.22i | 0.534989 | − | 0.926629i | −0.464174 | − | 0.885744i | \(-0.653649\pi\) |
0.999164 | − | 0.0408850i | \(-0.0130177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2568.52 | − | 4448.81i | −0.575744 | − | 0.997217i | −0.995960 | − | 0.0897933i | \(-0.971379\pi\) |
0.420217 | − | 0.907424i | \(-0.361954\pi\) | |||||||
\(272\) | −211.727 | −0.0471979 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4831.77 | −1.06532 | ||||||||
\(275\) | 563.988 | + | 976.855i | 0.123672 | + | 0.214206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2885.47 | − | 4997.79i | 0.625889 | − | 1.08407i | −0.362479 | − | 0.931992i | \(-0.618070\pi\) |
0.988368 | − | 0.152080i | \(-0.0485971\pi\) | |||||||
\(278\) | 94.5986 | + | 163.850i | 0.0204088 | + | 0.0353491i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −65.7385 | − | 60.3130i | −0.0140308 | − | 0.0128728i | ||||
\(281\) | −3594.63 | −0.763123 | −0.381562 | − | 0.924343i | \(-0.624614\pi\) | ||||
−0.381562 | + | 0.924343i | \(0.624614\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3765.14 | − | 6521.41i | 0.790863 | − | 1.36982i | −0.134570 | − | 0.990904i | \(-0.542965\pi\) |
0.925433 | − | 0.378911i | \(-0.123701\pi\) | |||||||
\(284\) | 752.211 | − | 1302.87i | 0.157167 | − | 0.272222i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 101.399 | 0.0209646 | ||||||||
\(287\) | −4909.18 | + | 1544.53i | −1.00968 | + | 0.317667i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2368.94 | + | 4103.13i | 0.482179 | + | 0.835158i | ||||
\(290\) | 30.2640 | − | 52.4188i | 0.00612815 | − | 0.0106143i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 537.926 | + | 931.716i | 0.107807 | + | 0.186728i | ||||
\(293\) | 4469.73 | 0.891209 | 0.445605 | − | 0.895230i | \(-0.352989\pi\) | ||||
0.445605 | + | 0.895230i | \(0.352989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.9379 | 0.0106454 | ||||||||
\(296\) | −120.941 | − | 209.476i | −0.0237485 | − | 0.0411335i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2344.66 | − | 4061.06i | 0.455779 | − | 0.789433i | ||||
\(299\) | 364.167 | + | 630.755i | 0.0704358 | + | 0.121998i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 865.031 | − | 272.156i | 0.165646 | − | 0.0521157i | ||||
\(302\) | −455.264 | −0.0867466 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −397.014 | + | 687.648i | −0.0749023 | + | 0.129735i | ||||
\(305\) | 204.387 | − | 354.008i | 0.0383710 | − | 0.0664605i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2811.31 | 0.522638 | 0.261319 | − | 0.965252i | \(-0.415843\pi\) | ||||
0.261319 | + | 0.965252i | \(0.415843\pi\) | |||||||
\(308\) | 494.019 | + | 453.246i | 0.0913939 | + | 0.0838509i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −149.677 | − | 259.248i | −0.0274229 | − | 0.0474978i | ||||
\(311\) | −2580.95 | + | 4470.33i | −0.470585 | + | 0.815077i | −0.999434 | − | 0.0336386i | \(-0.989290\pi\) |
0.528849 | + | 0.848716i | \(0.322624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3358.55 | − | 5817.18i | −0.606506 | − | 1.05050i | −0.991812 | − | 0.127710i | \(-0.959237\pi\) |
0.385306 | − | 0.922789i | \(-0.374096\pi\) | |||||||
\(314\) | 690.421 | 0.124085 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 157.363 | 0.0280138 | ||||||||
\(317\) | −4091.97 | − | 7087.51i | −0.725010 | − | 1.25575i | −0.958970 | − | 0.283508i | \(-0.908502\pi\) |
0.233960 | − | 0.972246i | \(-0.424832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −227.431 | + | 393.922i | −0.0399175 | + | 0.0691392i | ||||
\(320\) | 19.2685 | + | 33.3740i | 0.00336607 | + | 0.00583020i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1045.19 | + | 4700.84i | −0.180889 | + | 0.813563i | ||||
\(323\) | −656.707 | −0.113127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 349.118 | − | 604.690i | 0.0595864 | − | 0.103207i | ||||
\(326\) | 3291.44 | − | 5700.93i | 0.559189 | − | 0.968545i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2223.04 | 0.374228 | ||||||||
\(329\) | −3324.72 | − | 3050.32i | −0.557137 | − | 0.511155i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1774.96 | − | 3074.32i | −0.294745 | − | 0.510514i | 0.680180 | − | 0.733045i | \(-0.261902\pi\) |
−0.974926 | + | 0.222531i | \(0.928568\pi\) | |||||||
\(332\) | −983.190 | + | 1702.94i | −0.162529 | + | 0.281508i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3657.31 | − | 6334.64i | −0.599158 | − | 1.03777i | ||||
\(335\) | 422.175 | 0.0688534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7152.10 | −1.15608 | −0.578041 | − | 0.816008i | \(-0.696183\pi\) | ||||
−0.578041 | + | 0.816008i | \(0.696183\pi\) | |||||||
\(338\) | 2165.62 | + | 3750.96i | 0.348503 | + | 0.603625i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.9362 | + | 27.6023i | −0.00254194 | + | 0.00440277i | ||||
\(341\) | 1124.81 | + | 1948.22i | 0.178627 | + | 0.309391i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3876.45 | + | 5032.57i | −0.610229 | + | 0.792225i | ||||
\(344\) | −391.715 | −0.0613950 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2651.22 | − | 4592.05i | 0.411938 | − | 0.713498i | ||||
\(347\) | −3138.58 | + | 5436.18i | −0.485555 | + | 0.841007i | −0.999862 | − | 0.0165996i | \(-0.994716\pi\) |
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5735.43 | 0.879686 | 0.439843 | − | 0.898075i | \(-0.355034\pi\) | ||||
0.439843 | + | 0.898075i | \(0.355034\pi\) | |||||||
\(350\) | 4403.82 | − | 1385.53i | 0.672554 | − | 0.211599i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −144.801 | − | 250.802i | −0.0219259 | − | 0.0379767i | ||||
\(353\) | 1308.40 | − | 2266.21i | 0.197278 | − | 0.341695i | −0.750367 | − | 0.661021i | \(-0.770123\pi\) |
0.947645 | + | 0.319326i | \(0.103457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −113.234 | − | 196.127i | −0.0169291 | − | 0.0293221i | ||||
\(356\) | 2739.02 | 0.407775 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2803.87 | −0.413936 | ||||||||
\(359\) | 5826.07 | + | 10091.0i | 0.856513 | + | 1.48352i | 0.875234 | + | 0.483699i | \(0.160707\pi\) |
−0.0187217 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2198.09 | − | 3807.21i | 0.320469 | − | 0.555068i | ||||
\(362\) | 2.91675 | + | 5.05197i | 0.000423484 | + | 0.000733496i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 90.0751 | − | 405.119i | 0.0129704 | − | 0.0583352i | ||||
\(365\) | 161.954 | 0.0232248 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6237.16 | − | 10803.1i | 0.887132 | − | 1.53656i | 0.0438807 | − | 0.999037i | \(-0.486028\pi\) |
0.843251 | − | 0.537520i | \(-0.180639\pi\) | |||||||
\(368\) | 1040.08 | − | 1801.47i | 0.147331 | − | 0.255185i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −36.4117 | −0.00511609 | ||||||||
\(371\) | −1957.77 | + | 8805.23i | −0.273969 | + | 1.23220i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −963.950 | − | 1669.61i | −0.133811 | − | 0.231767i | 0.791332 | − | 0.611387i | \(-0.209388\pi\) |
−0.925143 | + | 0.379620i | \(0.876055\pi\) | |||||||
\(374\) | 119.759 | − | 207.428i | 0.0165577 | − | 0.0286788i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 974.503 | + | 1687.89i | 0.133660 | + | 0.231506i | ||||
\(377\) | 281.567 | 0.0384654 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2946.20 | −0.399304 | −0.199652 | − | 0.979867i | \(-0.563981\pi\) | ||||
−0.199652 | + | 0.979867i | \(0.563981\pi\) | |||||||
\(380\) | 59.7645 | + | 103.515i | 0.00806804 | + | 0.0139743i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 252.110 | − | 436.667i | 0.0337672 | − | 0.0584865i | ||||
\(383\) | 1558.73 | + | 2699.80i | 0.207956 | + | 0.360191i | 0.951071 | − | 0.308974i | \(-0.0999855\pi\) |
−0.743114 | + | 0.669164i | \(0.766652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 96.2720 | − | 30.2891i | 0.0127441 | − | 0.00400955i | ||||
\(386\) | 3946.81 | 0.520433 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 657.053 | − | 1138.05i | 0.0859712 | − | 0.148906i | ||||
\(389\) | 918.419 | − | 1590.75i | 0.119706 | − | 0.207337i | −0.799945 | − | 0.600073i | \(-0.795138\pi\) |
0.919651 | + | 0.392736i | \(0.128471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1720.41 | 0.222519 | ||||||||
\(392\) | 2249.69 | − | 1571.12i | 0.289864 | − | 0.202432i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1788.56 | + | 3097.87i | 0.228696 | + | 0.396113i | ||||
\(395\) | 11.8443 | − | 20.5150i | 0.00150874 | − | 0.00261322i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −677.402 | − | 1173.30i | −0.0856369 | − | 0.148327i | 0.820026 | − | 0.572327i | \(-0.193959\pi\) |
−0.905662 | + | 0.423999i | \(0.860626\pi\) | |||||||
\(398\) | 1844.26 | 0.232273 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1994.20 | −0.249275 | ||||||||
\(401\) | −6128.83 | − | 10615.4i | −0.763240 | − | 1.32197i | −0.941172 | − | 0.337928i | \(-0.890274\pi\) |
0.177932 | − | 0.984043i | \(-0.443059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 696.276 | − | 1205.98i | 0.0860644 | − | 0.149068i | ||||
\(404\) | 758.266 | + | 1313.36i | 0.0933791 | + | 0.161737i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1371.80 | + | 1258.58i | 0.167688 | + | 0.153848i | ||||
\(407\) | 273.630 | 0.0333252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3807.82 | − | 6595.34i | 0.460354 | − | 0.797356i | −0.538625 | − | 0.842546i | \(-0.681056\pi\) |
0.998978 | + | 0.0451896i | \(0.0143892\pi\) | |||||||
\(410\) | 167.323 | − | 289.812i | 0.0201549 | − | 0.0349092i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1041.29 | −0.124516 | ||||||||
\(413\) | −360.070 | + | 1619.44i | −0.0429005 | + | 0.192948i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 148.005 | + | 256.352i | 0.0175067 | + | 0.0303224i | ||||
\(416\) | −89.6342 | + | 155.251i | −0.0105641 | + | 0.0182976i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −449.125 | − | 777.907i | −0.0525536 | − | 0.0910255i | ||||
\(419\) | −8575.60 | −0.999870 | −0.499935 | − | 0.866063i | \(-0.666643\pi\) | ||||
−0.499935 | + | 0.866063i | \(0.666643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14776.6 | −1.71061 | −0.855303 | − | 0.518128i | \(-0.826629\pi\) | ||||
−0.855303 | + | 0.518128i | \(0.826629\pi\) | |||||||
\(422\) | 5130.61 | + | 8886.48i | 0.591835 | + | 1.02509i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1948.19 | − | 3374.37i | 0.223143 | − | 0.386494i | ||||
\(425\) | −824.659 | − | 1428.35i | −0.0941220 | − | 0.163024i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9264.39 | + | 8499.77i | 1.04997 | + | 0.963309i | ||||
\(428\) | 4353.17 | 0.491631 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −29.4835 | + | 51.0669i | −0.00330656 | + | 0.00572712i | ||||
\(431\) | −8168.58 | + | 14148.4i | −0.912916 | + | 1.58122i | −0.102992 | + | 0.994682i | \(0.532841\pi\) |
−0.809924 | + | 0.586534i | \(0.800492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6150.96 | 0.682670 | 0.341335 | − | 0.939942i | \(-0.389121\pi\) | ||||
0.341335 | + | 0.939942i | \(0.389121\pi\) | |||||||
\(434\) | 8782.91 | − | 2763.28i | 0.971412 | − | 0.305626i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1007.12 | − | 1744.39i | −0.110625 | − | 0.191608i | ||||
\(437\) | 3225.98 | − | 5587.56i | 0.353134 | − | 0.611646i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1299.24 | − | 2250.35i | −0.141252 | − | 0.244655i | 0.786717 | − | 0.617314i | \(-0.211779\pi\) |
−0.927968 | + | 0.372659i | \(0.878446\pi\) | |||||||
\(440\) | −43.5952 | −0.00472346 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −148.265 | −0.0159554 | ||||||||
\(443\) | −4915.60 | − | 8514.08i | −0.527195 | − | 0.913129i | −0.999498 | − | 0.0316922i | \(-0.989910\pi\) |
0.472303 | − | 0.881436i | \(-0.343423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 206.159 | − | 357.079i | 0.0219616 | − | 0.0380385i | ||||
\(446\) | −3777.82 | − | 6543.38i | −0.401088 | − | 0.694704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1130.66 | + | 355.728i | −0.119238 | + | 0.0375146i | ||||
\(449\) | 13649.3 | 1.43463 | 0.717317 | − | 0.696747i | \(-0.245370\pi\) | ||||
0.717317 | + | 0.696747i | \(0.245370\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1257.42 | + | 2177.91i | −0.131285 | + | 0.227392i | ||||
\(452\) | −2560.49 | + | 4434.91i | −0.266450 | + | 0.461505i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6646.51 | 0.687084 | ||||||||
\(455\) | −46.0346 | − | 42.2352i | −0.00474315 | − | 0.00435169i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6155.95 | + | 10662.4i | 0.630117 | + | 1.09139i | 0.987527 | + | 0.157447i | \(0.0503263\pi\) |
−0.357411 | + | 0.933947i | \(0.616340\pi\) | |||||||
\(458\) | 954.461 | − | 1653.17i | 0.0973778 | − | 0.168663i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −156.568 | − | 271.184i | −0.0158696 | − | 0.0274870i | ||||
\(461\) | 6291.03 | 0.635580 | 0.317790 | − | 0.948161i | \(-0.397059\pi\) | ||||
0.317790 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5964.10 | −0.598651 | −0.299326 | − | 0.954151i | \(-0.596762\pi\) | ||||
−0.299326 | + | 0.954151i | \(0.596762\pi\) | |||||||
\(464\) | −402.086 | − | 696.433i | −0.0402292 | − | 0.0696790i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4004.27 | + | 6935.60i | −0.398057 | + | 0.689454i | ||||
\(467\) | 4290.20 | + | 7430.85i | 0.425111 | + | 0.736314i | 0.996431 | − | 0.0844134i | \(-0.0269016\pi\) |
−0.571320 | + | 0.820728i | \(0.693568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2818.29 | + | 12675.5i | −0.277477 | + | 1.24797i | ||||
\(470\) | 293.394 | 0.0287942 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 358.308 | − | 620.608i | 0.0349417 | − | 0.0605207i | ||||
\(473\) | 221.565 | − | 383.762i | 0.0215382 | − | 0.0373053i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6185.35 | −0.597480 | ||||||||
\(476\) | −722.351 | − | 662.733i | −0.0695565 | − | 0.0638158i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2768.29 | + | 4794.82i | 0.264893 | + | 0.458808i | ||||
\(479\) | −7089.88 | + | 12280.0i | −0.676294 | + | 1.17138i | 0.299794 | + | 0.954004i | \(0.403082\pi\) |
−0.976089 | + | 0.217372i | \(0.930251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −84.6910 | − | 146.689i | −0.00802822 | − | 0.0139053i | ||||
\(482\) | −14274.8 | −1.34896 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4996.39 | −0.469232 | ||||||||
\(485\) | −98.9096 | − | 171.316i | −0.00926031 | − | 0.0160393i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2794.43 | + | 4840.09i | −0.260016 | + | 0.450360i | −0.966246 | − | 0.257622i | \(-0.917061\pi\) |
0.706230 | + | 0.707982i | \(0.250394\pi\) | |||||||
\(488\) | −2715.47 | − | 4703.33i | −0.251892 | − | 0.436290i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35.4934 | − | 411.541i | −0.00327230 | − | 0.0379419i | ||||
\(491\) | −9149.11 | −0.840924 | −0.420462 | − | 0.907310i | \(-0.638132\pi\) | ||||
−0.420462 | + | 0.907310i | \(0.638132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 332.548 | − | 575.990i | 0.0303797 | − | 0.0526193i | ||||
\(494\) | −278.016 | + | 481.538i | −0.0253209 | + | 0.0438571i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3977.20 | −0.360043 | ||||||||
\(497\) | 6644.47 | − | 2090.49i | 0.599689 | − | 0.188674i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10709.1 | + | 18548.8i | 0.960735 | + | 1.66404i | 0.720661 | + | 0.693288i | \(0.243839\pi\) |
0.240075 | + | 0.970754i | \(0.422828\pi\) | |||||||
\(500\) | −300.634 | + | 520.713i | −0.0268895 | + | 0.0465740i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3925.58 | + | 6799.30i | 0.349018 | + | 0.604517i | ||||
\(503\) | 11552.6 | 1.02407 | 0.512034 | − | 0.858965i | \(-0.328892\pi\) | ||||
0.512034 | + | 0.858965i | \(0.328892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 228.292 | 0.0201165 | ||||||||
\(506\) | 1176.60 | + | 2037.92i | 0.103372 | + | 0.179045i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1840.14 | − | 3187.21i | 0.160714 | − | 0.278365i | ||||
\(509\) | −9713.19 | − | 16823.7i | −0.845834 | − | 1.46503i | −0.884895 | − | 0.465791i | \(-0.845770\pi\) |
0.0390601 | − | 0.999237i | \(-0.487564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1081.14 | + | 4862.53i | −0.0935950 | + | 0.420950i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2246.28 | + | 3890.66i | −0.192761 | + | 0.333871i | ||||
\(515\) | −78.3755 | + | 135.750i | −0.00670609 | + | 0.0116153i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2204.83 | −0.187559 | ||||||||
\(518\) | 243.072 | − | 1093.23i | 0.0206177 | − | 0.0927294i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.4931 | + | 23.3707i | 0.00113791 | + | 0.00197091i | ||||
\(521\) | 3458.28 | − | 5989.91i | 0.290806 | − | 0.503691i | −0.683195 | − | 0.730236i | \(-0.739410\pi\) |
0.974001 | + | 0.226546i | \(0.0727433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7971.04 | − | 13806.2i | −0.666442 | − | 1.15431i | −0.978892 | − | 0.204377i | \(-0.934483\pi\) |
0.312450 | − | 0.949934i | \(-0.398850\pi\) | |||||||
\(524\) | −11137.9 | −0.928551 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2566.98 | 0.212786 | ||||||||
\(527\) | −1644.69 | − | 2848.68i | −0.135946 | − | 0.235466i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2367.78 | + | 4101.11i | −0.194606 | + | 0.337068i | ||||
\(530\) | −293.271 | − | 507.961i | −0.0240356 | − | 0.0416309i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3506.93 | + | 1103.35i | −0.285798 | + | 0.0899179i | ||||
\(533\) | 1556.72 | 0.126509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 327.652 | − | 567.510i | 0.0264778 | − | 0.0458610i | ||||
\(536\) | 2804.49 | − | 4857.53i | 0.225999 | − | 0.391443i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9441.34 | −0.756589 | ||||||||
\(539\) | 266.729 | + | 3092.69i | 0.0213151 | + | 0.247146i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8881.02 | + | 15382.4i | 0.705776 | + | 1.22244i | 0.966411 | + | 0.257003i | \(0.0827350\pi\) |
−0.260634 | + | 0.965438i | \(0.583932\pi\) | |||||||
\(542\) | −5137.04 | + | 8897.62i | −0.407112 | + | 0.705139i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 211.727 | + | 366.722i | 0.0166870 | + | 0.0289027i | ||||
\(545\) | −303.215 | −0.0238317 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9998.28 | −0.781527 | −0.390764 | − | 0.920491i | \(-0.627789\pi\) | ||||
−0.390764 | + | 0.920491i | \(0.627789\pi\) | |||||||
\(548\) | 4831.77 | + | 8368.87i | 0.376648 | + | 0.652373i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1127.98 | − | 1953.71i | 0.0874492 | − | 0.151466i | ||||
\(551\) | −1247.14 | − | 2160.10i | −0.0964243 | − | 0.167012i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 536.877 | + | 492.567i | 0.0412845 | + | 0.0378772i | ||||
\(554\) | −11541.9 | −0.885141 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 189.197 | − | 327.699i | 0.0144312 | − | 0.0249956i | ||||
\(557\) | −1558.09 | + | 2698.69i | −0.118525 | + | 0.205291i | −0.919183 | − | 0.393830i | \(-0.871150\pi\) |
0.800658 | + | 0.599121i | \(0.204483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −274.306 | −0.0207547 | ||||||||
\(560\) | −38.7266 | + | 174.175i | −0.00292231 | + | 0.0131433i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3594.63 | + | 6226.08i | 0.269805 | + | 0.467316i | ||||
\(563\) | 11072.6 | − | 19178.4i | 0.828875 | − | 1.43565i | −0.0700470 | − | 0.997544i | \(-0.522315\pi\) |
0.898922 | − | 0.438109i | \(-0.144352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 385.444 | + | 667.609i | 0.0287005 | + | 0.0497107i | ||||
\(566\) | −15060.6 | −1.11845 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3008.84 | −0.222268 | ||||||||
\(569\) | −10360.5 | − | 17944.9i | −0.763331 | − | 1.32213i | −0.941125 | − | 0.338060i | \(-0.890229\pi\) |
0.177794 | − | 0.984068i | \(-0.443104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1524.28 | − | 2640.12i | 0.111715 | − | 0.193495i | −0.804747 | − | 0.593618i | \(-0.797699\pi\) |
0.916462 | + | 0.400123i | \(0.131032\pi\) | |||||||
\(572\) | −101.399 | − | 175.629i | −0.00741210 | − | 0.0128381i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7584.37 | + | 6958.41i | 0.551508 | + | 0.505991i | ||||
\(575\) | 16204.1 | 1.17523 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5648.14 | + | 9782.86i | −0.407513 | + | 0.705834i | −0.994610 | − | 0.103683i | \(-0.966937\pi\) |
0.587097 | + | 0.809516i | \(0.300271\pi\) | |||||||
\(578\) | 4737.89 | − | 8206.27i | 0.340952 | − | 0.590546i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −121.056 | −0.00866651 | ||||||||
\(581\) | −8684.77 | + | 2732.41i | −0.620147 | + | 0.195111i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2203.90 | + | 3817.27i | 0.156563 | + | 0.271175i | ||||
\(584\) | 1075.85 | − | 1863.43i | 0.0762314 | − | 0.132037i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4469.73 | − | 7741.79i | −0.315090 | − | 0.545752i | ||||
\(587\) | 5531.46 | 0.388940 | 0.194470 | − | 0.980908i | \(-0.437701\pi\) | ||||
0.194470 | + | 0.980908i | \(0.437701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12336.0 | −0.862978 | ||||||||
\(590\) | −53.9379 | − | 93.4233i | −0.00376371 | − | 0.00651894i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −241.882 | + | 418.951i | −0.0167927 | + | 0.0290858i | ||||
\(593\) | 2880.05 | + | 4988.40i | 0.199443 | + | 0.345445i | 0.948348 | − | 0.317232i | \(-0.102753\pi\) |
−0.748905 | + | 0.662677i | \(0.769420\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −140.768 | + | 44.2886i | −0.00969906 | + | 0.00305152i | ||||
\(596\) | −9378.62 | −0.644569 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 728.333 | − | 1261.51i | 0.0498056 | − | 0.0862659i | ||||
\(599\) | −8560.31 | + | 14826.9i | −0.583915 | + | 1.01137i | 0.411095 | + | 0.911592i | \(0.365146\pi\) |
−0.995010 | + | 0.0997775i | \(0.968187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2611.63 | −0.177255 | −0.0886277 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886277 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(602\) | −1336.42 | − | 1226.12i | −0.0904791 | − | 0.0830116i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 455.264 | + | 788.540i | 0.0306696 | + | 0.0531212i | ||||
\(605\) | −376.066 | + | 651.365i | −0.0252715 | + | 0.0437715i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13815.8 | + | 23929.7i | 0.923831 | + | 1.60012i | 0.793430 | + | 0.608662i | \(0.208293\pi\) |
0.130402 | + | 0.991461i | \(0.458373\pi\) | |||||||
\(608\) | 1588.06 | 0.105928 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −817.547 | −0.0542647 | ||||||||
\(611\) | 682.413 | + | 1181.97i | 0.0451841 | + | 0.0782611i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −823.643 | + | 1426.59i | −0.0542686 | + | 0.0939959i | −0.891883 | − | 0.452265i | \(-0.850616\pi\) |
0.837615 | + | 0.546261i | \(0.183949\pi\) | |||||||
\(614\) | −2811.31 | − | 4869.33i | −0.184780 | − | 0.320049i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 291.026 | − | 1308.91i | 0.0190354 | − | 0.0856129i | ||||
\(617\) | 15808.0 | 1.03145 | 0.515727 | − | 0.856753i | \(-0.327522\pi\) | ||||
0.515727 | + | 0.856753i | \(0.327522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2005.62 | + | 3473.83i | −0.130230 | + | 0.225566i | −0.923765 | − | 0.382959i | \(-0.874905\pi\) |
0.793535 | + | 0.608525i | \(0.208238\pi\) | |||||||
\(620\) | −299.354 | + | 518.496i | −0.0193909 | + | 0.0335860i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10323.8 | 0.665508 | ||||||||
\(623\) | 9344.74 | + | 8573.50i | 0.600946 | + | 0.551348i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7744.58 | − | 13414.0i | −0.495653 | − | 0.858497i | ||||
\(626\) | −6717.10 | + | 11634.4i | −0.428864 | + | 0.742815i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −690.421 | − | 1195.84i | −0.0438707 | − | 0.0759863i | ||||
\(629\) | −400.100 | −0.0253626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11682.4 | −0.737036 | −0.368518 | − | 0.929621i | \(-0.620135\pi\) | ||||
−0.368518 | + | 0.929621i | \(0.620135\pi\) | |||||||
\(632\) | −157.363 | − | 272.561i | −0.00990438 | − | 0.0171549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8183.95 | + | 14175.0i | −0.512659 | + | 0.887952i | ||||
\(635\) | −277.005 | − | 479.787i | −0.0173112 | − | 0.0299839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1575.39 | − | 1100.20i | 0.0979892 | − | 0.0684327i | ||||
\(638\) | 909.724 | 0.0564519 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 38.5370 | − | 66.7480i | 0.00238017 | − | 0.00412257i | ||||
\(641\) | −5405.96 | + | 9363.40i | −0.333109 | + | 0.576961i | −0.983120 | − | 0.182964i | \(-0.941431\pi\) |
0.650011 | + | 0.759925i | \(0.274764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2335.44 | −0.143236 | −0.0716180 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716180 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(644\) | 9187.28 | − | 2890.51i | 0.562158 | − | 0.176866i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 656.707 | + | 1137.45i | 0.0399966 | + | 0.0692761i | ||||
\(647\) | 12753.8 | − | 22090.2i | 0.774965 | − | 1.34228i | −0.159850 | − | 0.987141i | \(-0.551101\pi\) |
0.934814 | − | 0.355137i | \(-0.115566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 405.338 | + | 702.067i | 0.0245161 | + | 0.0424631i | ||||
\(650\) | −1396.47 | −0.0842680 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13165.7 | −0.790813 | ||||||||
\(653\) | −2171.15 | − | 3760.54i | −0.130113 | − | 0.225362i | 0.793607 | − | 0.608431i | \(-0.208201\pi\) |
−0.923720 | + | 0.383069i | \(0.874867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −838.321 | + | 1452.01i | −0.0500090 | + | 0.0866182i | ||||
\(656\) | −2223.04 | − | 3850.42i | −0.132310 | − | 0.229167i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1958.59 | + | 8808.91i | −0.116039 | + | 0.521896i | ||||
\(659\) | −4148.85 | −0.245245 | −0.122622 | − | 0.992453i | \(-0.539130\pi\) | ||||
−0.122622 | + | 0.992453i | \(0.539130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8975.78 | − | 15546.5i | 0.528165 | − | 0.914809i | −0.471296 | − | 0.881975i | \(-0.656213\pi\) |
0.999461 | − | 0.0328337i | \(-0.0104532\pi\) | |||||||
\(662\) | −3549.92 | + | 6148.65i | −0.208417 | + | 0.360988i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3932.76 | 0.229850 | ||||||||
\(665\) | −120.117 | + | 540.235i | −0.00700442 | + | 0.0315029i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3267.19 | + | 5658.94i | 0.189664 | + | 0.328508i | ||||
\(668\) | −7314.61 | + | 12669.3i | −0.423669 | + | 0.733816i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −422.175 | − | 731.229i | −0.0243434 | − | 0.0421639i | ||||
\(671\) | 6143.78 | 0.353470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13667.9 | 0.782850 | 0.391425 | − | 0.920210i | \(-0.371982\pi\) | ||||
0.391425 | + | 0.920210i | \(0.371982\pi\) | |||||||
\(674\) | 7152.10 | + | 12387.8i | 0.408737 | + | 0.707953i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4331.23 | − | 7501.91i | 0.246429 | − | 0.426827i | ||||
\(677\) | −8632.32 | − | 14951.6i | −0.490054 | − | 0.848799i | 0.509880 | − | 0.860246i | \(-0.329690\pi\) |
−0.999934 | + | 0.0114463i | \(0.996356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5803.92 | − | 1826.03i | 0.328032 | − | 0.103206i | ||||
\(680\) | 63.7447 | 0.00359485 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2249.62 | − | 3896.45i | 0.126308 | − | 0.218772i | ||||
\(683\) | −9857.82 | + | 17074.3i | −0.552268 | + | 0.956556i | 0.445842 | + | 0.895112i | \(0.352904\pi\) |
−0.998110 | + | 0.0614450i | \(0.980429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1454.70 | 0.0811406 | ||||||||
\(686\) | 12593.1 | + | 1681.64i | 0.700885 | + | 0.0935937i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 391.715 | + | 678.471i | 0.0217064 | + | 0.0375966i | ||||
\(689\) | 1364.25 | − | 2362.96i | 0.0754339 | − | 0.130655i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5806.90 | − | 10057.8i | −0.319689 | − | 0.553717i | 0.660734 | − | 0.750620i | \(-0.270245\pi\) |
−0.980423 | + | 0.196903i | \(0.936912\pi\) | |||||||
\(692\) | −10604.9 | −0.582569 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12554.3 | 0.686679 | ||||||||
\(695\) | −28.4808 | − | 49.3302i | −0.00155444 | − | 0.00269238i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1838.58 | − | 3184.52i | 0.0999158 | − | 0.173059i | ||||
\(698\) | −5735.43 | − | 9934.05i | −0.311016 | − | 0.538695i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6803.63 | − | 6242.11i | −0.367361 | − | 0.337042i | ||||
\(701\) | 16100.4 | 0.867481 | 0.433740 | − | 0.901038i | \(-0.357194\pi\) | ||||
0.433740 | + | 0.901038i | \(0.357194\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −750.237 | + | 1299.45i | −0.0402500 | + | 0.0697150i | ||||
\(704\) | −289.602 | + | 501.605i | −0.0155039 | + | 0.0268536i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5233.59 | −0.278993 | ||||||||
\(707\) | −1523.99 | + | 6854.27i | −0.0810688 | + | 0.364613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1098.83 | − | 1903.22i | −0.0582049 | − | 0.100814i | 0.835455 | − | 0.549559i | \(-0.185204\pi\) |
−0.893660 | + | 0.448745i | \(0.851871\pi\) | |||||||
\(710\) | −226.468 | + | 392.255i | −0.0119707 | + | 0.0207339i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2739.02 | − | 4744.12i | −0.144170 | − | 0.249710i | ||||
\(713\) | 32317.2 | 1.69746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.5283 | −0.00159678 | ||||||||
\(716\) | 2803.87 | + | 4856.44i | 0.146348 | + | 0.253483i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11652.1 | − | 20182.1i | 0.605646 | − | 1.04901i | ||||
\(719\) | 4950.87 | + | 8575.16i | 0.256796 | + | 0.444784i | 0.965382 | − | 0.260841i | \(-0.0839998\pi\) |
−0.708586 | + | 0.705625i | \(0.750667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3552.58 | − | 3259.38i | −0.183502 | − | 0.168357i | ||||
\(722\) | −8792.38 | −0.453211 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.83351 | − | 10.1039i | 0.000299448 | − | 0.000518660i | ||||
\(725\) | 3132.18 | − | 5425.10i | 0.160450 | − | 0.277908i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24524.8 | 1.25114 | 0.625568 | − | 0.780170i | \(-0.284867\pi\) | ||||
0.625568 | + | 0.780170i | \(0.284867\pi\) | |||||||
\(728\) | −791.763 | + | 249.105i | −0.0403086 | + | 0.0126819i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −161.954 | − | 280.512i | −0.00821120 | − | 0.0142222i | ||||
\(731\) | −323.971 | + | 561.135i | −0.0163920 | + | 0.0283917i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4870.58 | − | 8436.09i | −0.245428 | − | 0.425094i | 0.716824 | − | 0.697255i | \(-0.245595\pi\) |
−0.962252 | + | 0.272160i | \(0.912262\pi\) | |||||||
\(734\) | −24948.7 | −1.25459 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4160.31 | −0.208358 | ||||||||
\(737\) | 3172.60 | + | 5495.11i | 0.158568 | + | 0.274647i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16049.5 | − | 27798.6i | 0.798905 | − | 1.38374i | −0.121426 | − | 0.992601i | \(-0.538747\pi\) |
0.920330 | − | 0.391143i | \(-0.127920\pi\) | |||||||
\(740\) | 36.4117 | + | 63.0669i | 0.00180881 | + | 0.00313295i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17208.9 | − | 5414.26i | 0.851425 | − | 0.267876i | ||||
\(743\) | 21404.8 | 1.05688 | 0.528442 | − | 0.848970i | \(-0.322777\pi\) | ||||
0.528442 | + | 0.848970i | \(0.322777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −705.906 | + | 1222.67i | −0.0347146 | + | 0.0601275i | ||||
\(746\) | −1927.90 | + | 3339.22i | −0.0946186 | + | 0.163884i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −479.035 | −0.0234161 | ||||||||
\(749\) | 14851.7 | + | 13626.0i | 0.724527 | + | 0.664730i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12218.6 | − | 21163.2i | −0.593692 | − | 1.02830i | −0.993730 | − | 0.111806i | \(-0.964337\pi\) |
0.400038 | − | 0.916498i | \(-0.368997\pi\) | |||||||
\(752\) | 1949.01 | − | 3375.78i | 0.0945119 | − | 0.163699i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −281.567 | − | 487.689i | −0.0135996 | − | 0.0235552i | ||||
\(755\) | 137.066 | 0.00660709 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35339.6 | 1.69675 | 0.848375 | − | 0.529395i | \(-0.177581\pi\) | ||||
0.848375 | + | 0.529395i | \(0.177581\pi\) | |||||||
\(758\) | 2946.20 | + | 5102.97i | 0.141175 | + | 0.244523i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 119.529 | − | 207.030i | 0.00570497 | − | 0.00988129i | ||||
\(761\) | 12995.4 | + | 22508.7i | 0.619033 | + | 1.07220i | 0.989663 | + | 0.143415i | \(0.0458084\pi\) |
−0.370630 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2024.15 | − | 9103.78i | 0.0960410 | − | 0.431951i | ||||
\(764\) | −1008.44 | −0.0477540 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3117.46 | − | 5399.59i | 0.147047 | − | 0.254693i | ||||
\(767\) | 250.911 | − | 434.591i | 0.0118121 | − | 0.0204592i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19140.3 | −0.897551 | −0.448776 | − | 0.893645i | \(-0.648140\pi\) | ||||
−0.448776 | + | 0.893645i | \(0.648140\pi\) | |||||||
\(770\) | −148.734 | − | 136.459i | −0.00696106 | − | 0.00638654i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3946.81 | − | 6836.07i | −0.184001 | − | 0.318699i | ||||
\(773\) | 14103.5 | − | 24428.0i | 0.656232 | − | 1.13663i | −0.325351 | − | 0.945593i | \(-0.605483\pi\) |
0.981583 | − | 0.191034i | \(-0.0611841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15490.9 | − | 26831.0i | −0.717998 | − | 1.24361i | ||||
\(776\) | −2628.21 | −0.121582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3673.68 | −0.169290 | ||||||||
\(779\) | −6895.14 | − | 11942.7i | −0.317130 | − | 0.549285i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1701.89 | − | 2947.75i | 0.0779748 | − | 0.135056i | ||||
\(782\) | −1720.41 | − | 2979.84i | −0.0786723 | − | 0.136264i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4970.95 | − | 2325.47i | −0.226446 | − | 0.105934i | ||||
\(785\) | −207.865 | −0.00945099 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2497.97 | − | 4326.62i | 0.113142 | − | 0.195969i | −0.803893 | − | 0.594774i | \(-0.797242\pi\) |
0.917036 | + | 0.398805i | \(0.130575\pi\) | |||||||
\(788\) | 3577.12 | − | 6195.74i | 0.161712 | − | 0.280094i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −47.3773 | −0.00213368 | ||||||||
\(791\) | −22617.5 | + | 7115.93i | −1.01667 | + | 0.319865i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1901.55 | − | 3293.59i | −0.0851528 | − | 0.147489i | ||||
\(794\) | −1354.80 | + | 2346.59i | −0.0605544 | + | 0.104883i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1844.26 | − | 3194.36i | −0.0821208 | − | 0.142237i | ||||
\(797\) | 895.767 | 0.0398114 | 0.0199057 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199057 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3223.88 | 0.142744 | ||||||||
\(800\) | 1994.20 | + | 3454.05i | 0.0881320 | + | 0.152649i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12257.7 | + | 21230.9i | −0.539692 | + | 0.934774i | ||||
\(803\) | 1217.07 | + | 2108.02i | 0.0534861 | + | 0.0926406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 314.677 | − | 1415.28i | 0.0137775 | − | 0.0619654i | ||||
\(806\) | −2785.10 | −0.121713 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1516.53 | − | 2626.71i | 0.0660290 | − | 0.114366i | ||||
\(809\) | −467.063 | + | 808.978i | −0.0202980 | + | 0.0351572i | −0.875996 | − | 0.482318i | \(-0.839795\pi\) |
0.855698 | + | 0.517476i | \(0.173128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8341.06 | −0.361152 | −0.180576 | − | 0.983561i | \(-0.557796\pi\) | ||||
−0.180576 | + | 0.983561i | \(0.557796\pi\) | |||||||
\(812\) | 808.127 | − | 3634.61i | 0.0349257 | − | 0.157081i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −273.630 | − | 473.942i | −0.0117822 | − | 0.0204074i | ||||
\(815\) | −990.954 | + | 1716.38i | −0.0425909 | + | 0.0737696i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1214.97 | + | 2104.39i | 0.0520275 | + | 0.0901143i | ||||
\(818\) | −15231.3 | −0.651039 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −669.292 | −0.0285033 | ||||||||
\(821\) | −15014.9 | − | 26006.5i | −0.638273 | − | 1.10552i | −0.985812 | − | 0.167856i | \(-0.946316\pi\) |
0.347539 | − | 0.937666i | \(-0.387018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1378.74 | + | 2388.04i | −0.0583958 | + | 0.101144i | −0.893745 | − | 0.448575i | \(-0.851932\pi\) |
0.835350 | + | 0.549719i | \(0.185265\pi\) | |||||||
\(824\) | 1041.29 | + | 1803.57i | 0.0440232 | + | 0.0762504i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3165.03 | − | 995.782i | 0.133324 | − | 0.0419464i | ||||
\(827\) | −21128.3 | −0.888394 | −0.444197 | − | 0.895929i | \(-0.646511\pi\) | ||||
−0.444197 | + | 0.895929i | \(0.646511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7810.43 | − | 13528.1i | 0.327223 | − | 0.566766i | −0.654737 | − | 0.755857i | \(-0.727221\pi\) |
0.981960 | + | 0.189091i | \(0.0605540\pi\) | |||||||
\(830\) | 296.009 | − | 512.703i | 0.0123791 | − | 0.0214412i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 358.537 | 0.0149399 | ||||||||
\(833\) | −390.010 | − | 4522.11i | −0.0162221 | − | 0.188093i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1101.11 | + | 1907.17i | 0.0456351 | + | 0.0790424i | ||||
\(836\) | −898.249 | + | 1555.81i | −0.0371610 | + | 0.0643647i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8575.60 | + | 14853.4i | 0.353507 | + | 0.612293i | ||||
\(839\) | 45714.6 | 1.88110 | 0.940550 | − | 0.339655i | \(-0.110310\pi\) | ||||
0.940550 | + | 0.339655i | \(0.110310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21862.9 | −0.896423 | ||||||||
\(842\) | 14776.6 | + | 25593.7i | 0.604791 | + | 1.04753i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10261.2 | − | 17773.0i | 0.418490 | − | 0.724847i | ||||
\(845\) | −652.003 | − | 1129.30i | −0.0265439 | − | 0.0459753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17046.2 | − | 15639.4i | −0.691517 | − | 0.634444i | ||||
\(848\) | −7792.76 | −0.315571 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1649.32 | + | 2856.70i | −0.0665543 | + | 0.115275i | ||||
\(851\) | 1965.44 | − | 3404.24i | 0.0791708 | − | 0.137128i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4539.60 | −0.182219 | −0.0911096 | − | 0.995841i | \(-0.529041\pi\) | ||||
−0.0911096 | + | 0.995841i | \(0.529041\pi\) | |||||||
\(854\) | 5457.65 | − | 24546.2i | 0.218685 | − | 0.983551i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4353.17 | − | 7539.90i | −0.173818 | − | 0.301061i | ||||
\(857\) | −19837.5 | + | 34359.6i | −0.790707 | + | 1.36955i | 0.134822 | + | 0.990870i | \(0.456954\pi\) |
−0.925530 | + | 0.378675i | \(0.876380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16090.6 | + | 27869.7i | 0.639120 | + | 1.10699i | 0.985626 | + | 0.168941i | \(0.0540347\pi\) |
−0.346506 | + | 0.938048i | \(0.612632\pi\) | |||||||
\(860\) | 117.934 | 0.00467618 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32674.3 | 1.29106 | ||||||||
\(863\) | 1201.72 | + | 2081.44i | 0.0474009 | + | 0.0821007i | 0.888752 | − | 0.458388i | \(-0.151573\pi\) |
−0.841352 | + | 0.540488i | \(0.818240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −798.205 | + | 1382.53i | −0.0313755 | + | 0.0543439i | ||||
\(866\) | −6150.96 | − | 10653.8i | −0.241360 | − | 0.418049i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13569.1 | − | 12449.2i | −0.530603 | − | 0.486811i | ||||
\(869\) | 356.036 | 0.0138984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1963.90 | − | 3401.57i | 0.0763997 | − | 0.132328i | ||||
\(872\) | −2014.25 | + | 3488.78i | −0.0782236 | + | 0.135487i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12903.9 | −0.499407 | ||||||||
\(875\) | −2655.58 | + | 835.498i | −0.102600 | + | 0.0322800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6688.04 | − | 11584.0i | −0.257513 | − | 0.446026i | 0.708062 | − | 0.706150i | \(-0.249570\pi\) |
−0.965575 | + | 0.260125i | \(0.916236\pi\) | |||||||
\(878\) | −2598.48 | + | 4500.71i | −0.0998799 | + | 0.172997i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 43.5952 | + | 75.5092i | 0.00166999 | + | 0.00289252i | ||||
\(881\) | −37240.1 | −1.42412 | −0.712060 | − | 0.702119i | \(-0.752238\pi\) | ||||
−0.712060 | + | 0.702119i | \(0.752238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15721.8 | 0.599186 | 0.299593 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299593 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(884\) | 148.265 | + | 256.803i | 0.00564107 | + | 0.00977062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9831.21 | + | 17028.2i | −0.372783 | + | 0.645680i | ||||
\(887\) | 6729.50 | + | 11655.8i | 0.254740 | + | 0.441223i | 0.964825 | − | 0.262893i | \(-0.0846768\pi\) |
−0.710085 | + | 0.704116i | \(0.751343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16254.4 | − | 5113.97i | 0.613223 | − | 0.192933i | ||||
\(890\) | −824.638 | −0.0310583 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7555.64 | + | 13086.8i | −0.283612 | + | 0.491230i | ||||
\(893\) | 6045.18 | − | 10470.6i | 0.226533 | − | 0.392367i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 844.161 | 0.0315276 | ||||||||
\(896\) | 1746.80 | + | 1602.63i | 0.0651299 | + | 0.0597545i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13649.3 | − | 23641.3i | −0.507220 | − | 0.878531i | ||||
\(899\) | 6246.77 | − | 10819.7i | 0.231748 | − | 0.401399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3222.53 | − | 5581.59i | −0.119154 | − | 0.206382i | ||||
\(902\) | 5029.66 | 0.185665 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10242.0 | 0.376818 | ||||||||
\(905\) | −0.878148 | − | 1.52100i | −3.22548e−5 | − | 5.58670e-5i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13519.1 | + | 23415.7i | −0.494921 | + | 0.857229i | −0.999983 | − | 0.00585452i | \(-0.998136\pi\) |
0.505062 | + | 0.863083i | \(0.331470\pi\) | |||||||
\(908\) | −6646.51 | − | 11512.1i | −0.242921 | − | 0.420751i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.1190 | + | 121.969i | −0.000987895 | + | 0.00444313i | ||||
\(911\) | −19883.2 | −0.723116 | −0.361558 | − | 0.932350i | \(-0.617755\pi\) | ||||
−0.361558 | + | 0.932350i | \(0.617755\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2224.48 | + | 3852.91i | −0.0806348 | + | 0.139664i | ||||
\(914\) | 12311.9 | − | 21324.8i | 0.445560 | − | 0.771732i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3817.84 | −0.137713 | ||||||||
\(917\) | −37999.2 | − | 34863.0i | −1.36842 | − | 1.25548i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16676.1 | − | 28883.9i | −0.598579 | − | 1.03677i | −0.993031 | − | 0.117853i | \(-0.962399\pi\) |
0.394452 | − | 0.918916i | \(-0.370934\pi\) | |||||||
\(920\) | −313.137 | + | 542.369i | −0.0112215 | + | 0.0194363i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6291.03 | − | 10896.4i | −0.224711 | − | 0.389212i | ||||
\(923\) | −2106.99 | −0.0751382 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3768.44 | −0.133952 | ||||||||
\(926\) | 5964.10 | + | 10330.1i | 0.211655 | + | 0.366597i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −804.171 | + | 1392.87i | −0.0284463 | + | 0.0492705i | ||||
\(929\) | −494.177 | − | 855.939i | −0.0174525 | − | 0.0302287i | 0.857167 | − | 0.515038i | \(-0.172222\pi\) |
−0.874620 | + | 0.484809i | \(0.838889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15418.2 | − | 7212.83i | −0.542763 | − | 0.253911i | ||||
\(932\) | 16017.1 | 0.562937 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8580.41 | − | 14861.7i | 0.300599 | − | 0.520653i | ||||
\(935\) | −36.0558 | + | 62.4505i | −0.00126112 | + | 0.00218433i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40549.5 | 1.41376 | 0.706880 | − | 0.707333i | \(-0.250102\pi\) | ||||
0.706880 | + | 0.707333i | \(0.250102\pi\) | |||||||
\(938\) | 24772.8 | − | 7794.04i | 0.862326 | − | 0.271305i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −293.394 | − | 508.173i | −0.0101803 | − | 0.0176328i | ||||
\(941\) | 5412.12 | − | 9374.07i | 0.187492 | − | 0.324746i | −0.756921 | − | 0.653506i | \(-0.773297\pi\) |
0.944414 | + | 0.328760i | \(0.106631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18063.6 | + | 31287.0i | 0.623787 | + | 1.08043i | ||||
\(944\) | −1433.23 | −0.0494150 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −886.261 | −0.0304597 | ||||||||
\(947\) | −28695.5 | − | 49702.1i | −0.984667 | − | 1.70549i | −0.643406 | − | 0.765525i | \(-0.722479\pi\) |
−0.341261 | − | 0.939969i | \(-0.610854\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 753.385 | − | 1304.90i | 0.0257702 | − | 0.0446353i | ||||
\(950\) | 6185.35 | + | 10713.3i | 0.211241 | + | 0.365881i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −425.537 | + | 1913.88i | −0.0144871 | + | 0.0651568i | ||||
\(953\) | 1316.06 | 0.0447338 | 0.0223669 | − | 0.999750i | \(-0.492880\pi\) | ||||
0.0223669 | + | 0.999750i | \(0.492880\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −75.9028 | + | 131.467i | −0.00257189 | + | 0.00445465i | ||||
\(956\) | 5536.58 | − | 9589.64i | 0.187307 | − | 0.324426i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28359.5 | 0.956425 | ||||||||
\(959\) | −9711.07 | + | 43676.2i | −0.326994 | + | 1.47068i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15999.2 | − | 27711.5i | −0.537049 | − | 0.930197i | ||||
\(962\) | −169.382 | + | 293.378i | −0.00567681 | + | 0.00983253i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14274.8 | + | 24724.6i | 0.476929 | + | 0.826065i | ||||
\(965\) | −1188.27 | −0.0396390 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49471.0 | 1.64517 | 0.822585 | − | 0.568642i | \(-0.192531\pi\) | ||||
0.822585 | + | 0.568642i | \(0.192531\pi\) | |||||||
\(968\) | 4996.39 | + | 8653.99i | 0.165899 | + | 0.287345i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −197.819 | + | 342.633i | −0.00654803 | + | 0.0113415i | ||||
\(971\) | −25767.5 | − | 44630.6i | −0.851615 | − | 1.47504i | −0.879750 | − | 0.475437i | \(-0.842290\pi\) |
0.0281347 | − | 0.999604i | \(-0.491043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1671.23 | − | 525.802i | 0.0550638 | − | 0.0173242i | ||||
\(974\) | 11177.7 | 0.367718 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5430.93 | + | 9406.65i | −0.178115 | + | 0.308504i | ||||
\(977\) | −11810.8 | + | 20456.9i | −0.386755 | + | 0.669880i | −0.992011 | − | 0.126151i | \(-0.959738\pi\) |
0.605256 | + | 0.796031i | \(0.293071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6197.07 | 0.202308 | ||||||||
\(980\) | −677.316 | + | 473.017i | −0.0220776 | + | 0.0154183i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9149.11 | + | 15846.7i | 0.297311 | + | 0.514959i | ||||
\(983\) | −19303.4 | + | 33434.5i | −0.626330 | + | 1.08484i | 0.361952 | + | 0.932197i | \(0.382111\pi\) |
−0.988282 | + | 0.152639i | \(0.951223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −538.482 | − | 932.677i | −0.0174187 | − | 0.0301701i | ||||
\(986\) | −1330.19 | −0.0429634 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1112.06 | 0.0358092 | ||||||||
\(989\) | −3182.93 | − | 5512.99i | −0.102337 | − | 0.177253i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4966.28 | − | 8601.86i | 0.159192 | − | 0.275729i | −0.775386 | − | 0.631488i | \(-0.782444\pi\) |
0.934578 | + | 0.355760i | \(0.115778\pi\) | |||||||
\(992\) | 3977.20 | + | 6888.71i | 0.127295 | + | 0.220481i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10265.3 | − | 9418.08i | −0.327561 | − | 0.300526i | ||||
\(995\) | −555.253 | −0.0176912 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23598.0 | + | 40872.9i | −0.749604 | + | 1.29835i | 0.198408 | + | 0.980119i | \(0.436423\pi\) |
−0.948012 | + | 0.318233i | \(0.896910\pi\) | |||||||
\(998\) | 21418.3 | − | 37097.5i | 0.679342 | − | 1.17666i | ||||
\(999\) | 0 | 0 |
(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 | 378.4.g.a.109.2 | ✓ | 6 | |
3.2 | odd | 2 | 378.4.g.b.109.2 | yes | 6 | ||
7.2 | even | 3 | inner | 378.4.g.a.163.2 | yes | 6 | |
21.2 | odd | 6 | 378.4.g.b.163.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.a.109.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
378.4.g.a.163.2 | yes | 6 | 7.2 | even | 3 | inner | |
378.4.g.b.109.2 | yes | 6 | 3.2 | odd | 2 | ||
378.4.g.b.163.2 | yes | 6 | 21.2 | odd | 6 |