Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(1.65391940934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(0.153862 - 2.82424i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.3 |
Dual form | 16.5.f.a.11.2 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.97810 | − | 2.67038i | −0.744525 | − | 0.667594i | ||||
\(3\) | −9.42589 | + | 9.42589i | −1.04732 | + | 1.04732i | −0.0484980 | + | 0.998823i | \(0.515443\pi\) |
−0.998823 | + | 0.0484980i | \(0.984557\pi\) | |||||||
\(4\) | 1.73818 | + | 15.9053i | 0.108636 | + | 0.994082i | ||||
\(5\) | −2.84710 | + | 2.84710i | −0.113884 | + | 0.113884i | −0.761752 | − | 0.647868i | \(-0.775661\pi\) |
0.647868 | + | 0.761752i | \(0.275661\pi\) | |||||||
\(6\) | 53.2419 | − | 2.90058i | 1.47894 | − | 0.0805716i | ||||
\(7\) | −76.7794 | −1.56693 | −0.783463 | − | 0.621439i | \(-0.786549\pi\) | ||||
−0.783463 | + | 0.621439i | \(0.786549\pi\) | |||||||
\(8\) | 37.2967 | − | 52.0092i | 0.582761 | − | 0.812644i | ||||
\(9\) | − | 96.6949i | − | 1.19376i | ||||||
\(10\) | 16.0818 | − | 0.876123i | 0.160818 | − | 0.00876123i | ||||
\(11\) | 121.488 | + | 121.488i | 1.00403 | + | 1.00403i | 0.999992 | + | 0.00403849i | \(0.00128549\pi\) |
0.00403849 | + | 0.999992i | \(0.498715\pi\) | |||||||
\(12\) | −166.306 | − | 133.538i | −1.15490 | − | 0.927346i | ||||
\(13\) | 27.1604 | + | 27.1604i | 0.160712 | + | 0.160712i | 0.782882 | − | 0.622170i | \(-0.213749\pi\) |
−0.622170 | + | 0.782882i | \(0.713749\pi\) | |||||||
\(14\) | 228.657 | + | 205.030i | 1.16662 | + | 1.04607i | ||||
\(15\) | − | 53.6729i | − | 0.238546i | ||||||
\(16\) | −249.957 | + | 55.2924i | −0.976396 | + | 0.215986i | ||||
\(17\) | −88.0613 | −0.304710 | −0.152355 | − | 0.988326i | \(-0.548686\pi\) | ||||
−0.152355 | + | 0.988326i | \(0.548686\pi\) | |||||||
\(18\) | −258.212 | + | 287.967i | −0.796950 | + | 0.888787i | ||||
\(19\) | −261.112 | + | 261.112i | −0.723302 | + | 0.723302i | −0.969276 | − | 0.245974i | \(-0.920892\pi\) |
0.245974 | + | 0.969276i | \(0.420892\pi\) | |||||||
\(20\) | −50.2328 | − | 40.3352i | −0.125582 | − | 0.100838i | ||||
\(21\) | 723.714 | − | 723.714i | 1.64107 | − | 1.64107i | ||||
\(22\) | −37.3847 | − | 686.220i | −0.0772412 | − | 1.41781i | ||||
\(23\) | 93.4210 | 0.176599 | 0.0882996 | − | 0.996094i | \(-0.471857\pi\) | ||||
0.0882996 | + | 0.996094i | \(0.471857\pi\) | |||||||
\(24\) | 138.678 | + | 841.788i | 0.240761 | + | 1.46144i | ||||
\(25\) | 608.788i | 0.974061i | ||||||||
\(26\) | −8.35791 | − | 153.415i | −0.0123638 | − | 0.226945i | ||||
\(27\) | 147.938 | + | 147.938i | 0.202933 | + | 0.202933i | ||||
\(28\) | −133.456 | − | 1221.20i | −0.170224 | − | 1.55765i | ||||
\(29\) | 272.522 | + | 272.522i | 0.324045 | + | 0.324045i | 0.850316 | − | 0.526272i | \(-0.176410\pi\) |
−0.526272 | + | 0.850316i | \(0.676410\pi\) | |||||||
\(30\) | −143.327 | + | 159.843i | −0.159252 | + | 0.177604i | ||||
\(31\) | − | 1232.20i | − | 1.28220i | −0.767455 | − | 0.641102i | \(-0.778477\pi\) | ||
0.767455 | − | 0.641102i | \(-0.221523\pi\) | |||||||
\(32\) | 892.050 | + | 502.814i | 0.871143 | + | 0.491030i | ||||
\(33\) | −2290.26 | −2.10308 | ||||||||
\(34\) | 262.256 | + | 235.157i | 0.226865 | + | 0.203423i | ||||
\(35\) | 218.599 | − | 218.599i | 0.178448 | − | 0.178448i | ||||
\(36\) | 1537.96 | − | 168.073i | 1.18670 | − | 0.129686i | ||||
\(37\) | −1046.16 | + | 1046.16i | −0.764177 | + | 0.764177i | −0.977075 | − | 0.212898i | \(-0.931710\pi\) |
0.212898 | + | 0.977075i | \(0.431710\pi\) | |||||||
\(38\) | 1474.89 | − | 80.3506i | 1.02139 | − | 0.0556445i | ||||
\(39\) | −512.021 | −0.336635 | ||||||||
\(40\) | 41.8880 | + | 254.263i | 0.0261800 | + | 0.158914i | ||||
\(41\) | 915.267i | 0.544478i | 0.962230 | + | 0.272239i | \(0.0877641\pi\) | ||||
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(42\) | −4087.88 | + | 222.705i | −2.31739 | + | 0.126250i | ||||
\(43\) | 1116.82 | + | 1116.82i | 0.604013 | + | 0.604013i | 0.941375 | − | 0.337362i | \(-0.109535\pi\) |
−0.337362 | + | 0.941375i | \(0.609535\pi\) | |||||||
\(44\) | −1721.13 | + | 2143.47i | −0.889014 | + | 1.10716i | ||||
\(45\) | 275.300 | + | 275.300i | 0.135951 | + | 0.135951i | ||||
\(46\) | −278.217 | − | 249.469i | −0.131483 | − | 0.117897i | ||||
\(47\) | − | 1720.70i | − | 0.778949i | −0.921037 | − | 0.389475i | \(-0.872657\pi\) | ||
0.921037 | − | 0.389475i | \(-0.127343\pi\) | |||||||
\(48\) | 1834.89 | − | 2877.25i | 0.796394 | − | 1.24881i | ||||
\(49\) | 3494.07 | 1.45526 | ||||||||
\(50\) | 1625.69 | − | 1813.03i | 0.650277 | − | 0.725213i | ||||
\(51\) | 830.056 | − | 830.056i | 0.319130 | − | 0.319130i | ||||
\(52\) | −384.784 | + | 479.203i | −0.142302 | + | 0.177220i | ||||
\(53\) | 734.019 | − | 734.019i | 0.261310 | − | 0.261310i | −0.564276 | − | 0.825586i | \(-0.690845\pi\) |
0.825586 | + | 0.564276i | \(0.190845\pi\) | |||||||
\(54\) | −45.5242 | − | 835.626i | −0.0156119 | − | 0.286566i | ||||
\(55\) | −691.775 | −0.228686 | ||||||||
\(56\) | −2863.62 | + | 3993.23i | −0.913143 | + | 1.27335i | ||||
\(57\) | − | 4922.43i | − | 1.51506i | ||||||
\(58\) | −83.8616 | − | 1539.33i | −0.0249291 | − | 0.457590i | ||||
\(59\) | −1202.73 | − | 1202.73i | −0.345512 | − | 0.345512i | 0.512923 | − | 0.858435i | \(-0.328563\pi\) |
−0.858435 | + | 0.512923i | \(0.828563\pi\) | |||||||
\(60\) | 853.684 | − | 93.2930i | 0.237135 | − | 0.0259147i | ||||
\(61\) | 580.221 | + | 580.221i | 0.155932 | + | 0.155932i | 0.780761 | − | 0.624830i | \(-0.214832\pi\) |
−0.624830 | + | 0.780761i | \(0.714832\pi\) | |||||||
\(62\) | −3290.44 | + | 3669.61i | −0.855993 | + | 0.954634i | ||||
\(63\) | 7424.17i | 1.87054i | ||||||||
\(64\) | −1313.91 | − | 3879.54i | −0.320779 | − | 0.947154i | ||||
\(65\) | −154.657 | −0.0366051 | ||||||||
\(66\) | 6820.62 | + | 6115.86i | 1.56580 | + | 1.40401i | ||||
\(67\) | −1483.97 | + | 1483.97i | −0.330580 | + | 0.330580i | −0.852807 | − | 0.522227i | \(-0.825101\pi\) |
0.522227 | + | 0.852807i | \(0.325101\pi\) | |||||||
\(68\) | −153.066 | − | 1400.64i | −0.0331025 | − | 0.302907i | ||||
\(69\) | −880.576 | + | 880.576i | −0.184956 | + | 0.184956i | ||||
\(70\) | −1234.75 | + | 67.2681i | −0.251990 | + | 0.0137282i | ||||
\(71\) | 5571.73 | 1.10528 | 0.552641 | − | 0.833419i | \(-0.313620\pi\) | ||||
0.552641 | + | 0.833419i | \(0.313620\pi\) | |||||||
\(72\) | −5029.02 | − | 3606.40i | −0.970105 | − | 0.695679i | ||||
\(73\) | 6615.21i | 1.24136i | 0.784064 | + | 0.620681i | \(0.213144\pi\) | ||||
−0.784064 | + | 0.620681i | \(0.786856\pi\) | |||||||
\(74\) | 5909.20 | − | 321.929i | 1.07911 | − | 0.0587890i | ||||
\(75\) | −5738.37 | − | 5738.37i | −1.02015 | − | 1.02015i | ||||
\(76\) | −4606.93 | − | 3699.21i | −0.797598 | − | 0.640445i | ||||
\(77\) | −9327.75 | − | 9327.75i | −1.57324 | − | 1.57324i | ||||
\(78\) | 1524.85 | + | 1367.29i | 0.250633 | + | 0.224735i | ||||
\(79\) | 5391.66i | 0.863910i | 0.901895 | + | 0.431955i | \(0.142176\pi\) | ||||
−0.901895 | + | 0.431955i | \(0.857824\pi\) | |||||||
\(80\) | 554.231 | − | 869.077i | 0.0865986 | − | 0.135793i | ||||
\(81\) | 5043.39 | 0.768692 | ||||||||
\(82\) | 2444.11 | − | 2725.76i | 0.363490 | − | 0.405378i | ||||
\(83\) | −2554.07 | + | 2554.07i | −0.370747 | + | 0.370747i | −0.867749 | − | 0.497002i | \(-0.834434\pi\) |
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(84\) | 12768.8 | + | 10252.9i | 1.80964 | + | 1.45308i | ||||
\(85\) | 250.719 | − | 250.719i | 0.0347017 | − | 0.0347017i | ||||
\(86\) | −343.673 | − | 6308.34i | −0.0464674 | − | 0.852939i | ||||
\(87\) | −5137.52 | −0.678758 | ||||||||
\(88\) | 10849.6 | − | 1787.39i | 1.40103 | − | 0.230809i | ||||
\(89\) | − | 10962.7i | − | 1.38400i | −0.721898 | − | 0.691999i | \(-0.756730\pi\) | ||
0.721898 | − | 0.691999i | \(-0.243270\pi\) | |||||||
\(90\) | −84.7166 | − | 1555.03i | −0.0104588 | − | 0.191979i | ||||
\(91\) | −2085.35 | − | 2085.35i | −0.251824 | − | 0.251824i | ||||
\(92\) | 162.382 | + | 1485.89i | 0.0191850 | + | 0.175554i | ||||
\(93\) | 11614.6 | + | 11614.6i | 1.34288 | + | 1.34288i | ||||
\(94\) | −4594.92 | + | 5124.42i | −0.520022 | + | 0.579948i | ||||
\(95\) | − | 1486.83i | − | 0.164745i | ||||||
\(96\) | −13147.8 | + | 3668.90i | −1.42663 | + | 0.398101i | ||||
\(97\) | 4713.20 | 0.500925 | 0.250462 | − | 0.968126i | \(-0.419417\pi\) | ||||
0.250462 | + | 0.968126i | \(0.419417\pi\) | |||||||
\(98\) | −10405.7 | − | 9330.48i | −1.08347 | − | 0.971520i | ||||
\(99\) | 11747.2 | − | 11747.2i | 1.19858 | − | 1.19858i | ||||
\(100\) | −9682.96 | + | 1058.18i | −0.968296 | + | 0.105818i | ||||
\(101\) | −11381.0 | + | 11381.0i | −1.11568 | + | 1.11568i | −0.123307 | + | 0.992369i | \(0.539350\pi\) |
−0.992369 | + | 0.123307i | \(0.960650\pi\) | |||||||
\(102\) | −4688.56 | + | 255.429i | −0.450649 | + | 0.0245510i | ||||
\(103\) | 175.758 | 0.0165668 | 0.00828342 | − | 0.999966i | \(-0.497363\pi\) | ||||
0.00828342 | + | 0.999966i | \(0.497363\pi\) | |||||||
\(104\) | 2425.58 | − | 399.597i | 0.224258 | − | 0.0369450i | ||||
\(105\) | 4120.97i | 0.373784i | ||||||||
\(106\) | −4146.09 | + | 225.876i | −0.369000 | + | 0.0201028i | ||||
\(107\) | 15151.8 | + | 15151.8i | 1.32342 | + | 1.32342i | 0.910988 | + | 0.412432i | \(0.135321\pi\) |
0.412432 | + | 0.910988i | \(0.364679\pi\) | |||||||
\(108\) | −2095.86 | + | 2610.14i | −0.179686 | + | 0.223778i | ||||
\(109\) | −2349.51 | − | 2349.51i | −0.197754 | − | 0.197754i | 0.601283 | − | 0.799036i | \(-0.294657\pi\) |
−0.799036 | + | 0.601283i | \(0.794657\pi\) | |||||||
\(110\) | 2060.18 | + | 1847.30i | 0.170263 | + | 0.152669i | ||||
\(111\) | − | 19721.9i | − | 1.60068i | ||||||
\(112\) | 19191.6 | − | 4245.32i | 1.52994 | − | 0.338434i | ||||
\(113\) | −8526.30 | −0.667734 | −0.333867 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333867 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(114\) | −13144.7 | + | 14659.5i | −1.01145 | + | 1.12800i | ||||
\(115\) | −265.979 | + | 265.979i | −0.0201118 | + | 0.0201118i | ||||
\(116\) | −3860.85 | + | 4808.23i | −0.286924 | + | 0.357330i | ||||
\(117\) | 2626.27 | − | 2626.27i | 0.191852 | − | 0.191852i | ||||
\(118\) | 370.108 | + | 6793.57i | 0.0265806 | + | 0.487904i | ||||
\(119\) | 6761.29 | 0.477459 | ||||||||
\(120\) | −2791.49 | − | 2001.82i | −0.193853 | − | 0.139015i | ||||
\(121\) | 14877.5i | 1.01615i | ||||||||
\(122\) | −178.548 | − | 3277.37i | −0.0119960 | − | 0.220194i | ||||
\(123\) | −8627.21 | − | 8627.21i | −0.570243 | − | 0.570243i | ||||
\(124\) | 19598.5 | − | 2141.78i | 1.27462 | − | 0.139294i | ||||
\(125\) | −3512.72 | − | 3512.72i | −0.224814 | − | 0.224814i | ||||
\(126\) | 19825.3 | − | 22109.9i | 1.24876 | − | 1.39266i | ||||
\(127\) | − | 2844.31i | − | 0.176347i | −0.996105 | − | 0.0881737i | \(-0.971897\pi\) | ||
0.996105 | − | 0.0881737i | \(-0.0281031\pi\) | |||||||
\(128\) | −6446.87 | + | 15062.3i | −0.393486 | + | 0.919331i | ||||
\(129\) | −21054.1 | −1.26519 | ||||||||
\(130\) | 460.583 | + | 412.991i | 0.0272534 | + | 0.0244373i | ||||
\(131\) | −6989.87 | + | 6989.87i | −0.407311 | + | 0.407311i | −0.880800 | − | 0.473489i | \(-0.842994\pi\) |
0.473489 | + | 0.880800i | \(0.342994\pi\) | |||||||
\(132\) | −3980.87 | − | 36427.3i | −0.228471 | − | 2.09064i | ||||
\(133\) | 20048.0 | − | 20048.0i | 1.13336 | − | 1.13336i | ||||
\(134\) | 8382.19 | − | 456.655i | 0.466818 | − | 0.0254319i | ||||
\(135\) | −842.390 | −0.0462217 | ||||||||
\(136\) | −3284.40 | + | 4580.00i | −0.177573 | + | 0.247621i | ||||
\(137\) | − | 3669.69i | − | 0.195519i | −0.995210 | − | 0.0977594i | \(-0.968832\pi\) | ||
0.995210 | − | 0.0977594i | \(-0.0311676\pi\) | |||||||
\(138\) | 4973.92 | − | 270.975i | 0.261180 | − | 0.0142289i | ||||
\(139\) | 4401.33 | + | 4401.33i | 0.227800 | + | 0.227800i | 0.811773 | − | 0.583973i | \(-0.198503\pi\) |
−0.583973 | + | 0.811773i | \(0.698503\pi\) | |||||||
\(140\) | 3856.84 | + | 3096.91i | 0.196778 | + | 0.158006i | ||||
\(141\) | 16219.1 | + | 16219.1i | 0.815810 | + | 0.815810i | ||||
\(142\) | −16593.2 | − | 14878.6i | −0.822911 | − | 0.737880i | ||||
\(143\) | 6599.30i | 0.322720i | ||||||||
\(144\) | 5346.49 | + | 24169.6i | 0.257836 | + | 1.16559i | ||||
\(145\) | −1551.79 | −0.0738071 | ||||||||
\(146\) | 17665.1 | − | 19700.8i | 0.828725 | − | 0.924225i | ||||
\(147\) | −32934.7 | + | 32934.7i | −1.52412 | + | 1.52412i | ||||
\(148\) | −18457.9 | − | 14821.1i | −0.842671 | − | 0.676637i | ||||
\(149\) | 15737.5 | − | 15737.5i | 0.708863 | − | 0.708863i | −0.257433 | − | 0.966296i | \(-0.582877\pi\) |
0.966296 | + | 0.257433i | \(0.0828766\pi\) | |||||||
\(150\) | 1765.84 | + | 32413.1i | 0.0784817 | + | 1.44058i | ||||
\(151\) | −41972.2 | −1.84080 | −0.920402 | − | 0.390974i | \(-0.872138\pi\) | ||||
−0.920402 | + | 0.390974i | \(0.872138\pi\) | |||||||
\(152\) | 3841.61 | + | 23318.9i | 0.166275 | + | 1.00930i | ||||
\(153\) | 8515.08i | 0.363752i | ||||||||
\(154\) | 2870.38 | + | 52687.6i | 0.121031 | + | 2.22160i | ||||
\(155\) | 3508.19 | + | 3508.19i | 0.146023 | + | 0.146023i | ||||
\(156\) | −889.982 | − | 8143.85i | −0.0365706 | − | 0.334642i | ||||
\(157\) | −24735.4 | − | 24735.4i | −1.00351 | − | 1.00351i | −0.999994 | − | 0.00351271i | \(-0.998882\pi\) |
−0.00351271 | − | 0.999994i | \(-0.501118\pi\) | |||||||
\(158\) | 14397.8 | − | 16056.9i | 0.576741 | − | 0.643203i | ||||
\(159\) | 13837.6i | 0.547350i | ||||||||
\(160\) | −3971.32 | + | 1108.19i | −0.155130 | + | 0.0432888i | ||||
\(161\) | −7172.80 | −0.276718 | ||||||||
\(162\) | −15019.7 | − | 13467.7i | −0.572310 | − | 0.513174i | ||||
\(163\) | 24429.8 | − | 24429.8i | 0.919483 | − | 0.919483i | −0.0775084 | − | 0.996992i | \(-0.524696\pi\) |
0.996992 | + | 0.0775084i | \(0.0246965\pi\) | |||||||
\(164\) | −14557.6 | + | 1590.90i | −0.541255 | + | 0.0591499i | ||||
\(165\) | 6520.60 | − | 6520.60i | 0.239508 | − | 0.239508i | ||||
\(166\) | 14426.6 | − | 785.951i | 0.523539 | − | 0.0285220i | ||||
\(167\) | 52178.2 | 1.87093 | 0.935463 | − | 0.353425i | \(-0.114983\pi\) | ||||
0.935463 | + | 0.353425i | \(0.114983\pi\) | |||||||
\(168\) | −10647.6 | − | 64631.9i | −0.377255 | − | 2.28996i | ||||
\(169\) | − | 27085.6i | − | 0.948343i | ||||||
\(170\) | −1416.18 | + | 77.1525i | −0.0490029 | + | 0.00266964i | ||||
\(171\) | 25248.2 | + | 25248.2i | 0.863452 | + | 0.863452i | ||||
\(172\) | −15822.1 | + | 19704.6i | −0.534821 | + | 0.666056i | ||||
\(173\) | 26316.2 | + | 26316.2i | 0.879289 | + | 0.879289i | 0.993461 | − | 0.114172i | \(-0.0364216\pi\) |
−0.114172 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(174\) | 15300.1 | + | 13719.1i | 0.505353 | + | 0.453135i | ||||
\(175\) | − | 46742.4i | − | 1.52628i | ||||||
\(176\) | −37084.1 | − | 23649.4i | −1.19719 | − | 0.763475i | ||||
\(177\) | 22673.5 | 0.723723 | ||||||||
\(178\) | −29274.4 | + | 32647.9i | −0.923949 | + | 1.03042i | ||||
\(179\) | 4815.78 | − | 4815.78i | 0.150301 | − | 0.150301i | −0.627952 | − | 0.778252i | \(-0.716106\pi\) |
0.778252 | + | 0.627952i | \(0.216106\pi\) | |||||||
\(180\) | −3900.21 | + | 4857.25i | −0.120377 | + | 0.149915i | ||||
\(181\) | −23924.9 | + | 23924.9i | −0.730286 | + | 0.730286i | −0.970676 | − | 0.240391i | \(-0.922724\pi\) |
0.240391 | + | 0.970676i | \(0.422724\pi\) | |||||||
\(182\) | 641.715 | + | 11779.1i | 0.0193731 | + | 0.355606i | ||||
\(183\) | −10938.2 | −0.326621 | ||||||||
\(184\) | 3484.29 | − | 4858.75i | 0.102915 | − | 0.143512i | ||||
\(185\) | − | 5957.04i | − | 0.174055i | ||||||
\(186\) | −3574.09 | − | 65604.7i | −0.103309 | − | 1.89631i | ||||
\(187\) | −10698.4 | − | 10698.4i | −0.305939 | − | 0.305939i | ||||
\(188\) | 27368.2 | − | 2990.88i | 0.774339 | − | 0.0846219i | ||||
\(189\) | −11358.6 | − | 11358.6i | −0.317981 | − | 0.317981i | ||||
\(190\) | −3970.38 | + | 4427.92i | −0.109983 | + | 0.122657i | ||||
\(191\) | 45079.4i | 1.23569i | 0.786298 | + | 0.617847i | \(0.211995\pi\) | ||||
−0.786298 | + | 0.617847i | \(0.788005\pi\) | |||||||
\(192\) | 48952.9 | + | 24183.3i | 1.32793 | + | 0.656015i | ||||
\(193\) | 50286.0 | 1.34999 | 0.674997 | − | 0.737820i | \(-0.264145\pi\) | ||||
0.674997 | + | 0.737820i | \(0.264145\pi\) | |||||||
\(194\) | −14036.4 | − | 12586.0i | −0.372951 | − | 0.334415i | ||||
\(195\) | 1457.78 | − | 1457.78i | 0.0383373 | − | 0.0383373i | ||||
\(196\) | 6073.31 | + | 55574.2i | 0.158093 | + | 1.44664i | ||||
\(197\) | −25662.2 | + | 25662.2i | −0.661243 | + | 0.661243i | −0.955673 | − | 0.294430i | \(-0.904870\pi\) |
0.294430 | + | 0.955673i | \(0.404870\pi\) | |||||||
\(198\) | −66354.0 | + | 3614.91i | −1.69253 | + | 0.0922077i | ||||
\(199\) | −44599.1 | −1.12621 | −0.563106 | − | 0.826385i | \(-0.690394\pi\) | ||||
−0.563106 | + | 0.826385i | \(0.690394\pi\) | |||||||
\(200\) | 31662.6 | + | 22705.8i | 0.791564 | + | 0.567645i | ||||
\(201\) | − | 27975.5i | − | 0.692447i | ||||||
\(202\) | 64285.4 | − | 3502.21i | 1.57547 | − | 0.0858302i | ||||
\(203\) | −20924.0 | − | 20924.0i | −0.507754 | − | 0.507754i | ||||
\(204\) | 14645.1 | + | 11759.5i | 0.351910 | + | 0.282572i | ||||
\(205\) | −2605.86 | − | 2605.86i | −0.0620073 | − | 0.0620073i | ||||
\(206\) | −523.424 | − | 469.339i | −0.0123344 | − | 0.0110599i | ||||
\(207\) | − | 9033.33i | − | 0.210818i | ||||||
\(208\) | −8290.70 | − | 5287.17i | −0.191630 | − | 0.122207i | ||||
\(209\) | −63443.8 | −1.45244 | ||||||||
\(210\) | 11004.6 | − | 12272.7i | 0.249536 | − | 0.278292i | ||||
\(211\) | 25828.5 | − | 25828.5i | 0.580143 | − | 0.580143i | −0.354800 | − | 0.934942i | \(-0.615451\pi\) |
0.934942 | + | 0.354800i | \(0.115451\pi\) | |||||||
\(212\) | 12950.6 | + | 10398.9i | 0.288151 | + | 0.231375i | ||||
\(213\) | −52518.5 | + | 52518.5i | −1.15759 | + | 1.15759i | ||||
\(214\) | −4662.59 | − | 85584.8i | −0.101812 | − | 1.86883i | ||||
\(215\) | −6359.40 | −0.137575 | ||||||||
\(216\) | 13211.8 | − | 2176.54i | 0.283174 | − | 0.0466508i | ||||
\(217\) | 94607.4i | 2.00912i | ||||||||
\(218\) | 723.003 | + | 13271.2i | 0.0152134 | + | 0.279252i | ||||
\(219\) | −62354.3 | − | 62354.3i | −1.30010 | − | 1.30010i | ||||
\(220\) | −1202.43 | − | 11002.9i | −0.0248435 | − | 0.227333i | ||||
\(221\) | −2391.78 | − | 2391.78i | −0.0489707 | − | 0.0489707i | ||||
\(222\) | −52665.0 | + | 58734.0i | −1.06860 | + | 1.19175i | ||||
\(223\) | 72650.0i | 1.46092i | 0.682957 | + | 0.730459i | \(0.260694\pi\) | ||||
−0.682957 | + | 0.730459i | \(0.739306\pi\) | |||||||
\(224\) | −68491.1 | − | 38605.8i | −1.36502 | − | 0.769407i | ||||
\(225\) | 58866.7 | 1.16280 | ||||||||
\(226\) | 25392.2 | + | 22768.4i | 0.497145 | + | 0.445776i | ||||
\(227\) | 18858.2 | − | 18858.2i | 0.365972 | − | 0.365972i | −0.500034 | − | 0.866006i | \(-0.666679\pi\) |
0.866006 | + | 0.500034i | \(0.166679\pi\) | |||||||
\(228\) | 78292.8 | − | 8556.05i | 1.50609 | − | 0.164590i | ||||
\(229\) | 41675.9 | − | 41675.9i | 0.794721 | − | 0.794721i | −0.187537 | − | 0.982258i | \(-0.560050\pi\) |
0.982258 | + | 0.187537i | \(0.0600504\pi\) | |||||||
\(230\) | 1502.38 | − | 81.8483i | 0.0284003 | − | 0.00154723i | ||||
\(231\) | 175845. | 3.29538 | ||||||||
\(232\) | 24337.8 | − | 4009.48i | 0.452174 | − | 0.0744923i | ||||
\(233\) | − | 2767.61i | − | 0.0509792i | −0.999675 | − | 0.0254896i | \(-0.991886\pi\) | ||
0.999675 | − | 0.0254896i | \(-0.00811447\pi\) | |||||||
\(234\) | −14834.4 | + | 808.167i | −0.270918 | + | 0.0147594i | ||||
\(235\) | 4899.00 | + | 4899.00i | 0.0887099 | + | 0.0887099i | ||||
\(236\) | 17039.2 | − | 21220.3i | 0.305932 | − | 0.381002i | ||||
\(237\) | −50821.2 | − | 50821.2i | −0.904791 | − | 0.904791i | ||||
\(238\) | −20135.8 | − | 18055.2i | −0.355480 | − | 0.318749i | ||||
\(239\) | − | 49981.8i | − | 0.875016i | −0.899215 | − | 0.437508i | \(-0.855861\pi\) | ||
0.899215 | − | 0.437508i | \(-0.144139\pi\) | |||||||
\(240\) | 2967.71 | + | 13416.0i | 0.0515227 | + | 0.232916i | ||||
\(241\) | −44076.0 | −0.758872 | −0.379436 | − | 0.925218i | \(-0.623882\pi\) | ||||
−0.379436 | + | 0.925218i | \(0.623882\pi\) | |||||||
\(242\) | 39728.6 | − | 44306.7i | 0.678378 | − | 0.756552i | ||||
\(243\) | −59521.4 | + | 59521.4i | −1.00800 | + | 1.00800i | ||||
\(244\) | −8220.07 | + | 10237.1i | −0.138069 | + | 0.171948i | ||||
\(245\) | −9947.97 | + | 9947.97i | −0.165730 | + | 0.165730i | ||||
\(246\) | 2654.80 | + | 48730.6i | 0.0438695 | + | 0.805252i | ||||
\(247\) | −14183.8 | −0.232487 | ||||||||
\(248\) | −64085.7 | − | 45957.0i | −1.04198 | − | 0.747219i | ||||
\(249\) | − | 48148.8i | − | 0.776582i | ||||||
\(250\) | 1080.95 | + | 19841.5i | 0.0172952 | + | 0.317464i | ||||
\(251\) | −31786.2 | − | 31786.2i | −0.504534 | − | 0.504534i | 0.408309 | − | 0.912844i | \(-0.366119\pi\) |
−0.912844 | + | 0.408309i | \(0.866119\pi\) | |||||||
\(252\) | −118084. | + | 12904.5i | −1.85947 | + | 0.203208i | ||||
\(253\) | 11349.5 | + | 11349.5i | 0.177311 | + | 0.177311i | ||||
\(254\) | −7595.38 | + | 8470.64i | −0.117729 | + | 0.131295i | ||||
\(255\) | 4726.51i | 0.0726876i | ||||||||
\(256\) | 59421.5 | − | 27641.5i | 0.906700 | − | 0.421776i | ||||
\(257\) | 70865.6 | 1.07292 | 0.536462 | − | 0.843924i | \(-0.319760\pi\) | ||||
0.536462 | + | 0.843924i | \(0.319760\pi\) | |||||||
\(258\) | 62701.1 | + | 56222.3i | 0.941968 | + | 0.844635i | ||||
\(259\) | 80323.4 | − | 80323.4i | 1.19741 | − | 1.19741i | ||||
\(260\) | −268.820 | − | 2459.86i | −0.00397663 | − | 0.0363885i | ||||
\(261\) | 26351.5 | − | 26351.5i | 0.386833 | − | 0.386833i | ||||
\(262\) | 39482.1 | − | 2150.95i | 0.575172 | − | 0.0313349i | ||||
\(263\) | −113289. | −1.63786 | −0.818929 | − | 0.573894i | \(-0.805432\pi\) | ||||
−0.818929 | + | 0.573894i | \(0.805432\pi\) | |||||||
\(264\) | −85419.1 | + | 119115.i | −1.22560 | + | 1.70906i | ||||
\(265\) | 4179.65i | 0.0595180i | ||||||||
\(266\) | −113241. | + | 6169.27i | −1.60044 | + | 0.0871908i | ||||
\(267\) | 103333. | + | 103333.i | 1.44949 | + | 1.44949i | ||||
\(268\) | −26182.5 | − | 21023.6i | −0.364536 | − | 0.292711i | ||||
\(269\) | 70652.7 | + | 70652.7i | 0.976393 | + | 0.976393i | 0.999728 | − | 0.0233352i | \(-0.00742850\pi\) |
−0.0233352 | + | 0.999728i | \(0.507428\pi\) | |||||||
\(270\) | 2508.72 | + | 2249.50i | 0.0344132 | + | 0.0308573i | ||||
\(271\) | 110180.i | 1.50025i | 0.661294 | + | 0.750126i | \(0.270007\pi\) | ||||
−0.661294 | + | 0.750126i | \(0.729993\pi\) | |||||||
\(272\) | 22011.6 | − | 4869.12i | 0.297518 | − | 0.0658132i | ||||
\(273\) | 39312.7 | 0.527481 | ||||||||
\(274\) | −9799.47 | + | 10928.7i | −0.130527 | + | 0.145569i | ||||
\(275\) | −73960.2 | + | 73960.2i | −0.977987 | + | 0.977987i | ||||
\(276\) | −15536.4 | − | 12475.2i | −0.203954 | − | 0.163769i | ||||
\(277\) | 34611.0 | − | 34611.0i | 0.451081 | − | 0.451081i | −0.444632 | − | 0.895713i | \(-0.646666\pi\) |
0.895713 | + | 0.444632i | \(0.146666\pi\) | |||||||
\(278\) | −1354.40 | − | 24860.8i | −0.0175249 | − | 0.321681i | ||||
\(279\) | −119147. | −1.53065 | ||||||||
\(280\) | −3216.13 | − | 19522.1i | −0.0410221 | − | 0.249007i | ||||
\(281\) | − | 147980.i | − | 1.87408i | −0.349216 | − | 0.937042i | \(-0.613552\pi\) | ||
0.349216 | − | 0.937042i | \(-0.386448\pi\) | |||||||
\(282\) | −4991.02 | − | 91613.4i | −0.0627612 | − | 1.15202i | ||||
\(283\) | 39761.2 | + | 39761.2i | 0.496463 | + | 0.496463i | 0.910335 | − | 0.413872i | \(-0.135824\pi\) |
−0.413872 | + | 0.910335i | \(0.635824\pi\) | |||||||
\(284\) | 9684.65 | + | 88620.1i | 0.120073 | + | 1.09874i | ||||
\(285\) | 14014.7 | + | 14014.7i | 0.172541 | + | 0.172541i | ||||
\(286\) | 17622.6 | − | 19653.4i | 0.215446 | − | 0.240273i | ||||
\(287\) | − | 70273.6i | − | 0.853156i | ||||||
\(288\) | 48619.6 | − | 86256.7i | 0.586173 | − | 1.03994i | ||||
\(289\) | −75766.2 | −0.907152 | ||||||||
\(290\) | 4621.40 | + | 4143.87i | 0.0549512 | + | 0.0492732i | ||||
\(291\) | −44426.1 | + | 44426.1i | −0.524629 | + | 0.524629i | ||||
\(292\) | −105217. | + | 11498.4i | −1.23401 | + | 0.134856i | ||||
\(293\) | −708.909 | + | 708.909i | −0.00825763 | + | 0.00825763i | −0.711224 | − | 0.702966i | \(-0.751859\pi\) |
0.702966 | + | 0.711224i | \(0.251859\pi\) | |||||||
\(294\) | 186031. | − | 10134.8i | 2.15224 | − | 0.117252i | ||||
\(295\) | 6848.56 | 0.0786965 | ||||||||
\(296\) | 15391.6 | + | 93428.1i | 0.175671 | + | 1.06634i | ||||
\(297\) | 35945.3i | 0.407502i | ||||||||
\(298\) | −88892.8 | + | 4842.81i | −1.00100 | + | 0.0545337i | ||||
\(299\) | 2537.35 | + | 2537.35i | 0.0283816 | + | 0.0283816i | ||||
\(300\) | 81296.2 | − | 101245.i | 0.903292 | − | 1.12494i | ||||
\(301\) | −85748.8 | − | 85748.8i | −0.946444 | − | 0.946444i | ||||
\(302\) | 124997. | + | 112081.i | 1.37052 | + | 1.22891i | ||||
\(303\) | − | 214552.i | − | 2.33694i | ||||||
\(304\) | 50829.4 | − | 79704.5i | 0.550007 | − | 0.862453i | ||||
\(305\) | −3303.90 | −0.0355162 | ||||||||
\(306\) | 22738.5 | − | 25358.8i | 0.242839 | − | 0.270823i | ||||
\(307\) | −20597.1 | + | 20597.1i | −0.218539 | + | 0.218539i | −0.807883 | − | 0.589344i | \(-0.799386\pi\) |
0.589344 | + | 0.807883i | \(0.299386\pi\) | |||||||
\(308\) | 132147. | − | 164574.i | 1.39302 | − | 1.73484i | ||||
\(309\) | −1656.67 | + | 1656.67i | −0.0173508 | + | 0.0173508i | ||||
\(310\) | −1079.56 | − | 19816.0i | −0.0112337 | − | 0.206201i | ||||
\(311\) | 82310.6 | 0.851011 | 0.425505 | − | 0.904956i | \(-0.360096\pi\) | ||||
0.425505 | + | 0.904956i | \(0.360096\pi\) | |||||||
\(312\) | −19096.7 | + | 26629.8i | −0.196177 | + | 0.273564i | ||||
\(313\) | 120415.i | 1.22911i | 0.788872 | + | 0.614557i | \(0.210665\pi\) | ||||
−0.788872 | + | 0.614557i | \(0.789335\pi\) | |||||||
\(314\) | 7611.70 | + | 139718.i | 0.0772009 | + | 1.41707i | ||||
\(315\) | −21137.4 | − | 21137.4i | −0.213025 | − | 0.213025i | ||||
\(316\) | −85756.0 | + | 9371.65i | −0.858797 | + | 0.0938517i | ||||
\(317\) | 14795.3 | + | 14795.3i | 0.147233 | + | 0.147233i | 0.776881 | − | 0.629648i | \(-0.216801\pi\) |
−0.629648 | + | 0.776881i | \(0.716801\pi\) | |||||||
\(318\) | 36951.5 | − | 41209.7i | 0.365408 | − | 0.407516i | ||||
\(319\) | 66216.1i | 0.650702i | ||||||||
\(320\) | 14786.3 | + | 7304.61i | 0.144397 | + | 0.0713340i | ||||
\(321\) | −285639. | −2.77209 | ||||||||
\(322\) | 21361.3 | + | 19154.1i | 0.206023 | + | 0.184735i | ||||
\(323\) | 22993.9 | − | 22993.9i | 0.220398 | − | 0.220398i | ||||
\(324\) | 8766.29 | + | 80216.6i | 0.0835076 | + | 0.764142i | ||||
\(325\) | −16534.9 | + | 16534.9i | −0.156543 | + | 0.156543i | ||||
\(326\) | −137991. | + | 7517.63i | −1.29842 | + | 0.0707369i | ||||
\(327\) | 44292.5 | 0.414224 | ||||||||
\(328\) | 47602.3 | + | 34136.4i | 0.442467 | + | 0.317300i | ||||
\(329\) | 132114.i | 1.22056i | ||||||||
\(330\) | −36831.5 | + | 2006.55i | −0.338214 | + | 0.0184256i | ||||
\(331\) | 82868.2 | + | 82868.2i | 0.756366 | + | 0.756366i | 0.975659 | − | 0.219293i | \(-0.0703752\pi\) |
−0.219293 | + | 0.975659i | \(0.570375\pi\) | |||||||
\(332\) | −45062.8 | − | 36183.9i | −0.408829 | − | 0.328276i | ||||
\(333\) | 101158. | + | 101158.i | 0.912247 | + | 0.912247i | ||||
\(334\) | −155392. | − | 139336.i | −1.39295 | − | 1.24902i | ||||
\(335\) | − | 8450.04i | − | 0.0752955i | ||||||
\(336\) | −140882. | + | 220914.i | −1.24789 | + | 1.95679i | ||||
\(337\) | 78854.4 | 0.694331 | 0.347165 | − | 0.937804i | \(-0.387144\pi\) | ||||
0.347165 | + | 0.937804i | \(0.387144\pi\) | |||||||
\(338\) | −72328.8 | + | 80663.8i | −0.633108 | + | 0.706066i | ||||
\(339\) | 80368.0 | − | 80368.0i | 0.699332 | − | 0.699332i | ||||
\(340\) | 4423.56 | + | 3551.98i | 0.0382661 | + | 0.0307264i | ||||
\(341\) | 149697. | − | 149697.i | 1.28737 | − | 1.28737i | ||||
\(342\) | −7769.49 | − | 142614.i | −0.0664264 | − | 1.21930i | ||||
\(343\) | −83925.2 | −0.713352 | ||||||||
\(344\) | 99738.7 | − | 16431.2i | 0.842843 | − | 0.138852i | ||||
\(345\) | − | 5014.18i | − | 0.0421271i | ||||||
\(346\) | −8098.15 | − | 148647.i | −0.0676447 | − | 1.24166i | ||||
\(347\) | −59543.0 | − | 59543.0i | −0.494506 | − | 0.494506i | 0.415216 | − | 0.909723i | \(-0.363706\pi\) |
−0.909723 | + | 0.415216i | \(0.863706\pi\) | |||||||
\(348\) | −8929.91 | − | 81713.8i | −0.0737375 | − | 0.674741i | ||||
\(349\) | −756.172 | − | 756.172i | −0.00620826 | − | 0.00620826i | 0.703996 | − | 0.710204i | \(-0.251397\pi\) |
−0.710204 | + | 0.703996i | \(0.751397\pi\) | |||||||
\(350\) | −124820. | + | 139203.i | −1.01894 | + | 1.13635i | ||||
\(351\) | 8036.11i | 0.0652276i | ||||||||
\(352\) | 47287.4 | + | 169459.i | 0.381645 | + | 1.36766i | ||||
\(353\) | 23723.5 | 0.190384 | 0.0951918 | − | 0.995459i | \(-0.469654\pi\) | ||||
0.0951918 | + | 0.995459i | \(0.469654\pi\) | |||||||
\(354\) | −67524.1 | − | 60546.9i | −0.538830 | − | 0.483154i | ||||
\(355\) | −15863.3 | + | 15863.3i | −0.125874 | + | 0.125874i | ||||
\(356\) | 174364. | − | 19055.0i | 1.37581 | − | 0.150352i | ||||
\(357\) | −63731.2 | + | 63731.2i | −0.500053 | + | 0.500053i | ||||
\(358\) | −27201.8 | + | 1481.93i | −0.212242 | + | 0.0115628i | ||||
\(359\) | 146064. | 1.13333 | 0.566663 | − | 0.823950i | \(-0.308234\pi\) | ||||
0.566663 | + | 0.823950i | \(0.308234\pi\) | |||||||
\(360\) | 24585.9 | − | 4050.35i | 0.189706 | − | 0.0312527i | ||||
\(361\) | − | 6038.12i | − | 0.0463327i | ||||||
\(362\) | 135139. | − | 7362.28i | 1.03125 | − | 0.0561817i | ||||
\(363\) | −140234. | − | 140234.i | −1.06424 | − | 1.06424i | ||||
\(364\) | 29543.5 | − | 36792.9i | 0.222976 | − | 0.277691i | ||||
\(365\) | −18834.2 | − | 18834.2i | −0.141371 | − | 0.141371i | ||||
\(366\) | 32575.1 | + | 29209.1i | 0.243177 | + | 0.218050i | ||||
\(367\) | − | 151129.i | − | 1.12206i | −0.827797 | − | 0.561028i | \(-0.810406\pi\) | ||
0.827797 | − | 0.561028i | \(-0.189594\pi\) | |||||||
\(368\) | −23351.3 | + | 5165.47i | −0.172431 | + | 0.0381430i | ||||
\(369\) | 88501.7 | 0.649978 | ||||||||
\(370\) | −15907.5 | + | 17740.7i | −0.116198 | + | 0.129588i | ||||
\(371\) | −56357.5 | + | 56357.5i | −0.409453 | + | 0.409453i | ||||
\(372\) | −164545. | + | 204922.i | −1.18905 | + | 1.48082i | ||||
\(373\) | 26207.7 | − | 26207.7i | 0.188370 | − | 0.188370i | −0.606621 | − | 0.794991i | \(-0.707476\pi\) |
0.794991 | + | 0.606621i | \(0.207476\pi\) | |||||||
\(374\) | 3292.15 | + | 60429.5i | 0.0235362 | + | 0.432022i | ||||
\(375\) | 66221.0 | 0.470905 | ||||||||
\(376\) | −89492.2 | − | 64176.4i | −0.633008 | − | 0.453941i | ||||
\(377\) | 14803.6i | 0.104156i | ||||||||
\(378\) | 3495.32 | + | 64158.8i | 0.0244626 | + | 0.449027i | ||||
\(379\) | 110424. | + | 110424.i | 0.768752 | + | 0.768752i | 0.977887 | − | 0.209135i | \(-0.0670647\pi\) |
−0.209135 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(380\) | 23648.4 | − | 2584.36i | 0.163770 | − | 0.0178973i | ||||
\(381\) | 26810.1 | + | 26810.1i | 0.184692 | + | 0.184692i | ||||
\(382\) | 120379. | − | 134251.i | 0.824942 | − | 0.920006i | ||||
\(383\) | 10514.9i | 0.0716819i | 0.999358 | + | 0.0358409i | \(0.0114110\pi\) | ||||
−0.999358 | + | 0.0358409i | \(0.988589\pi\) | |||||||
\(384\) | −81208.2 | − | 202743.i | −0.550728 | − | 1.37494i | ||||
\(385\) | 53114.1 | 0.358334 | ||||||||
\(386\) | −149757. | − | 134282.i | −1.00511 | − | 0.901249i | ||||
\(387\) | 107991. | − | 107991.i | 0.721049 | − | 0.721049i | ||||
\(388\) | 8192.37 | + | 74964.9i | 0.0544185 | + | 0.497960i | ||||
\(389\) | −166762. | + | 166762.i | −1.10204 | + | 1.10204i | −0.107877 | + | 0.994164i | \(0.534405\pi\) |
−0.994164 | + | 0.107877i | \(0.965595\pi\) | |||||||
\(390\) | −8234.21 | + | 448.593i | −0.0541368 | + | 0.00294933i | ||||
\(391\) | −8226.78 | −0.0538116 | ||||||||
\(392\) | 130317. | − | 181724.i | 0.848066 | − | 1.18260i | ||||
\(393\) | − | 131772.i | − | 0.853172i | ||||||
\(394\) | 144952. | − | 7896.89i | 0.933755 | − | 0.0508702i | ||||
\(395\) | −15350.6 | − | 15350.6i | −0.0983855 | − | 0.0983855i | ||||
\(396\) | 207262. | + | 166425.i | 1.32169 | + | 1.06127i | ||||
\(397\) | −192542. | − | 192542.i | −1.22164 | − | 1.22164i | −0.967048 | − | 0.254594i | \(-0.918058\pi\) |
−0.254594 | − | 0.967048i | \(-0.581942\pi\) | |||||||
\(398\) | 132821. | + | 119096.i | 0.838494 | + | 0.751853i | ||||
\(399\) | 377941.i | 2.37399i | ||||||||
\(400\) | −33661.4 | − | 152171.i | −0.210384 | − | 0.951070i | ||||
\(401\) | 91157.6 | 0.566897 | 0.283448 | − | 0.958987i | \(-0.408522\pi\) | ||||
0.283448 | + | 0.958987i | \(0.408522\pi\) | |||||||
\(402\) | −74705.2 | + | 83314.0i | −0.462273 | + | 0.515544i | ||||
\(403\) | 33467.0 | − | 33467.0i | 0.206066 | − | 0.206066i | ||||
\(404\) | −200801. | − | 161236.i | −1.23027 | − | 0.987870i | ||||
\(405\) | −14359.0 | + | 14359.0i | −0.0875417 | + | 0.0875417i | ||||
\(406\) | 6438.84 | + | 118189.i | 0.0390621 | + | 0.717010i | ||||
\(407\) | −254191. | −1.53451 | ||||||||
\(408\) | −12212.2 | − | 74128.9i | −0.0733624 | − | 0.445315i | ||||
\(409\) | − | 107774.i | − | 0.644272i | −0.946693 | − | 0.322136i | \(-0.895599\pi\) | ||
0.946693 | − | 0.322136i | \(-0.104401\pi\) | |||||||
\(410\) | 801.887 | + | 14719.1i | 0.00477029 | + | 0.0875618i | ||||
\(411\) | 34590.1 | + | 34590.1i | 0.204771 | + | 0.204771i | ||||
\(412\) | 305.497 | + | 2795.48i | 0.00179975 | + | 0.0164688i | ||||
\(413\) | 92344.5 | + | 92344.5i | 0.541391 | + | 0.541391i | ||||
\(414\) | −24122.4 | + | 26902.2i | −0.140741 | + | 0.156959i | ||||
\(415\) | − | 14543.4i | − | 0.0844442i | ||||||
\(416\) | 10571.8 | + | 37885.0i | 0.0610888 | + | 0.218918i | ||||
\(417\) | −82972.9 | −0.477160 | ||||||||
\(418\) | 188942. | + | 169419.i | 1.08137 | + | 0.969637i | ||||
\(419\) | −118524. | + | 118524.i | −0.675115 | + | 0.675115i | −0.958891 | − | 0.283776i | \(-0.908413\pi\) |
0.283776 | + | 0.958891i | \(0.408413\pi\) | |||||||
\(420\) | −65545.3 | + | 7162.97i | −0.371572 | + | 0.0406064i | ||||
\(421\) | −226616. | + | 226616.i | −1.27858 | + | 1.27858i | −0.337113 | + | 0.941464i | \(0.609451\pi\) |
−0.941464 | + | 0.337113i | \(0.890549\pi\) | |||||||
\(422\) | −145892. | + | 7948.08i | −0.819231 | + | 0.0446310i | ||||
\(423\) | −166383. | −0.929882 | ||||||||
\(424\) | −10799.2 | − | 65552.2i | −0.0600706 | − | 0.364633i | ||||
\(425\) | − | 53610.7i | − | 0.296807i | ||||||
\(426\) | 296650. | − | 16161.2i | 1.63465 | − | 0.0890544i | ||||
\(427\) | −44549.0 | − | 44549.0i | −0.244333 | − | 0.244333i | ||||
\(428\) | −214658. | + | 267331.i | −1.17182 | + | 1.45936i | ||||
\(429\) | −62204.3 | − | 62204.3i | −0.337991 | − | 0.337991i | ||||
\(430\) | 18938.9 | + | 16982.0i | 0.102428 | + | 0.0918442i | ||||
\(431\) | − | 5397.51i | − | 0.0290562i | −0.999894 | − | 0.0145281i | \(-0.995375\pi\) | ||
0.999894 | − | 0.0145281i | \(-0.00462460\pi\) | |||||||
\(432\) | −45158.1 | − | 28798.4i | −0.241974 | − | 0.154312i | ||||
\(433\) | 163835. | 0.873840 | 0.436920 | − | 0.899500i | \(-0.356069\pi\) | ||||
0.436920 | + | 0.899500i | \(0.356069\pi\) | |||||||
\(434\) | 252638. | − | 281751.i | 1.34128 | − | 1.49584i | ||||
\(435\) | 14627.0 | − | 14627.0i | 0.0772997 | − | 0.0772997i | ||||
\(436\) | 33285.9 | − | 41453.6i | 0.175100 | − | 0.218067i | ||||
\(437\) | −24393.4 | + | 24393.4i | −0.127735 | + | 0.127735i | ||||
\(438\) | 19187.9 | + | 352207.i | 0.100018 | + | 1.83590i | ||||
\(439\) | 158472. | 0.822289 | 0.411144 | − | 0.911570i | \(-0.365129\pi\) | ||||
0.411144 | + | 0.911570i | \(0.365129\pi\) | |||||||
\(440\) | −25800.9 | + | 35978.7i | −0.133269 | + | 0.185840i | ||||
\(441\) | − | 337859.i | − | 1.73723i | ||||||
\(442\) | 736.008 | + | 13509.9i | 0.00376737 | + | 0.0691524i | ||||
\(443\) | −137929. | − | 137929.i | −0.702826 | − | 0.702826i | 0.262190 | − | 0.965016i | \(-0.415555\pi\) |
−0.965016 | + | 0.262190i | \(0.915555\pi\) | |||||||
\(444\) | 313684. | − | 34280.2i | 1.59120 | − | 0.173891i | ||||
\(445\) | 31211.8 | + | 31211.8i | 0.157615 | + | 0.157615i | ||||
\(446\) | 194003. | − | 216359.i | 0.975300 | − | 1.08769i | ||||
\(447\) | 296680.i | 1.48482i | ||||||||
\(448\) | 100881. | + | 297869.i | 0.502638 | + | 1.48412i | ||||
\(449\) | 327336. | 1.62368 | 0.811841 | − | 0.583879i | \(-0.198466\pi\) | ||||
0.811841 | + | 0.583879i | \(0.198466\pi\) | |||||||
\(450\) | −175311. | − | 157196.i | −0.865733 | − | 0.776278i | ||||
\(451\) | −111194. | + | 111194.i | −0.546672 | + | 0.546672i | ||||
\(452\) | −14820.2 | − | 135613.i | −0.0725400 | − | 0.663782i | ||||
\(453\) | 395625. | − | 395625.i | 1.92791 | − | 1.92791i | ||||
\(454\) | −106520. | + | 5803.13i | −0.516797 | + | 0.0281547i | ||||
\(455\) | 11874.4 | 0.0573575 | ||||||||
\(456\) | −256012. | − | 183590.i | −1.23120 | − | 0.882918i | ||||
\(457\) | 154510.i | 0.739817i | 0.929068 | + | 0.369909i | \(0.120611\pi\) | ||||
−0.929068 | + | 0.369909i | \(0.879389\pi\) | |||||||
\(458\) | −235406. | + | 12824.7i | −1.12224 | + | 0.0611388i | ||||
\(459\) | −13027.6 | − | 13027.6i | −0.0618358 | − | 0.0618358i | ||||
\(460\) | −4692.80 | − | 3768.16i | −0.0221777 | − | 0.0178079i | ||||
\(461\) | 19296.3 | + | 19296.3i | 0.0907971 | + | 0.0907971i | 0.751046 | − | 0.660249i | \(-0.229549\pi\) |
−0.660249 | + | 0.751046i | \(0.729549\pi\) | |||||||
\(462\) | −523683. | − | 469571.i | −2.45349 | − | 2.19997i | ||||
\(463\) | 26503.6i | 0.123635i | 0.998087 | + | 0.0618176i | \(0.0196897\pi\) | ||||
−0.998087 | + | 0.0618176i | \(0.980310\pi\) | |||||||
\(464\) | −83187.2 | − | 53050.5i | −0.386385 | − | 0.246407i | ||||
\(465\) | −66135.7 | −0.305865 | ||||||||
\(466\) | −7390.56 | + | 8242.22i | −0.0340334 | + | 0.0379553i | ||||
\(467\) | 111797. | − | 111797.i | 0.512622 | − | 0.512622i | −0.402707 | − | 0.915329i | \(-0.631931\pi\) |
0.915329 | + | 0.402707i | \(0.131931\pi\) | |||||||
\(468\) | 46336.5 | + | 37206.7i | 0.211559 | + | 0.169875i | ||||
\(469\) | 113939. | − | 113939.i | 0.517994 | − | 0.517994i | ||||
\(470\) | −1507.54 | − | 27671.9i | −0.00682455 | − | 0.125269i | ||||
\(471\) | 466307. | 2.10199 | ||||||||
\(472\) | −107411. | + | 17695.1i | −0.482129 | + | 0.0794272i | ||||
\(473\) | 271360.i | 1.21290i | ||||||||
\(474\) | 15638.9 | + | 287063.i | 0.0696066 | + | 1.27767i | ||||
\(475\) | −158962. | − | 158962.i | −0.704541 | − | 0.704541i | ||||
\(476\) | 11752.3 | + | 107540.i | 0.0518692 | + | 0.474633i | ||||
\(477\) | −70975.8 | − | 70975.8i | −0.311942 | − | 0.311942i | ||||
\(478\) | −133470. | + | 148851.i | −0.584155 | + | 0.651471i | ||||
\(479\) | − | 225380.i | − | 0.982301i | −0.871075 | − | 0.491150i | \(-0.836577\pi\) | ||
0.871075 | − | 0.491150i | \(-0.163423\pi\) | |||||||
\(480\) | 26987.5 | − | 47879.0i | 0.117133 | − | 0.207808i | ||||
\(481\) | −56828.1 | −0.245625 | ||||||||
\(482\) | 131263. | + | 117700.i | 0.564999 | + | 0.506618i | ||||
\(483\) | 67610.1 | − | 67610.1i | 0.289813 | − | 0.289813i | ||||
\(484\) | −236631. | + | 25859.7i | −1.01014 | + | 0.110391i | ||||
\(485\) | −13419.0 | + | 13419.0i | −0.0570473 | + | 0.0570473i | ||||
\(486\) | 336205. | − | 18316.2i | 1.42342 | − | 0.0775466i | ||||
\(487\) | 8483.58 | 0.0357702 | 0.0178851 | − | 0.999840i | \(-0.494307\pi\) | ||||
0.0178851 | + | 0.999840i | \(0.494307\pi\) | |||||||
\(488\) | 51817.2 | − | 8536.50i | 0.217588 | − | 0.0358460i | ||||
\(489\) | 460544.i | 1.92599i | ||||||||
\(490\) | 56190.9 | − | 3061.23i | 0.234031 | − | 0.0127498i | ||||
\(491\) | 69265.0 | + | 69265.0i | 0.287310 | + | 0.287310i | 0.836016 | − | 0.548706i | \(-0.184879\pi\) |
−0.548706 | + | 0.836016i | \(0.684879\pi\) | |||||||
\(492\) | 122223. | − | 152214.i | 0.504919 | − | 0.628817i | ||||
\(493\) | −23998.6 | − | 23998.6i | −0.0987399 | − | 0.0987399i | ||||
\(494\) | 42240.8 | + | 37876.1i | 0.173092 | + | 0.155207i | ||||
\(495\) | 66891.1i | 0.272997i | ||||||||
\(496\) | 68131.3 | + | 307997.i | 0.276938 | + | 1.25194i | ||||
\(497\) | −427794. | −1.73190 | ||||||||
\(498\) | −128576. | + | 143392.i | −0.518441 | + | 0.578185i | ||||
\(499\) | 86869.4 | − | 86869.4i | 0.348872 | − | 0.348872i | −0.510817 | − | 0.859689i | \(-0.670657\pi\) |
0.859689 | + | 0.510817i | \(0.170657\pi\) | |||||||
\(500\) | 49765.1 | − | 61976.6i | 0.199061 | − | 0.247906i | ||||
\(501\) | −491827. | + | 491827.i | −1.95946 | + | 1.95946i | ||||
\(502\) | 9781.39 | + | 179544.i | 0.0388144 | + | 0.712463i | ||||
\(503\) | 112271. | 0.443745 | 0.221872 | − | 0.975076i | \(-0.428783\pi\) | ||||
0.221872 | + | 0.975076i | \(0.428783\pi\) | |||||||
\(504\) | 386125. | + | 276897.i | 1.52008 | + | 1.09008i | ||||
\(505\) | − | 64805.7i | − | 0.254115i | ||||||
\(506\) | −3492.52 | − | 64107.4i | −0.0136407 | − | 0.250384i | ||||
\(507\) | 255306. | + | 255306.i | 0.993220 | + | 0.993220i | ||||
\(508\) | 45239.6 | − | 4943.91i | 0.175304 | − | 0.0191577i | ||||
\(509\) | −167589. | − | 167589.i | −0.646861 | − | 0.646861i | 0.305372 | − | 0.952233i | \(-0.401219\pi\) |
−0.952233 | + | 0.305372i | \(0.901219\pi\) | |||||||
\(510\) | 12621.6 | − | 14076.0i | 0.0485258 | − | 0.0541177i | ||||
\(511\) | − | 507912.i | − | 1.94512i | ||||||
\(512\) | −250776. | − | 76358.6i | −0.956636 | − | 0.291285i | ||||
\(513\) | −77256.9 | −0.293564 | ||||||||
\(514\) | −211045. | − | 189238.i | −0.798820 | − | 0.716278i | ||||
\(515\) | −500.399 | + | 500.399i | −0.00188670 | + | 0.00188670i | ||||
\(516\) | −36595.7 | − | 334871.i | −0.137445 | − | 1.25770i | ||||
\(517\) | 209044. | − | 209044.i | 0.782089 | − | 0.782089i | ||||
\(518\) | −453705. | + | 24717.5i | −1.69088 | + | 0.0921180i | ||||
\(519\) | −496108. | −1.84180 | ||||||||
\(520\) | −5768.18 | + | 8043.56i | −0.0213320 | + | 0.0297469i | ||||
\(521\) | − | 287463.i | − | 1.05903i | −0.848302 | − | 0.529513i | \(-0.822375\pi\) | ||
0.848302 | − | 0.529513i | \(-0.177625\pi\) | |||||||
\(522\) | −148846. | + | 8108.99i | −0.546254 | + | 0.0297595i | ||||
\(523\) | −203069. | − | 203069.i | −0.742404 | − | 0.742404i | 0.230636 | − | 0.973040i | \(-0.425919\pi\) |
−0.973040 | + | 0.230636i | \(0.925919\pi\) | |||||||
\(524\) | −123326. | − | 99026.4i | −0.449149 | − | 0.360652i | ||||
\(525\) | 440588. | + | 440588.i | 1.59851 | + | 1.59851i | ||||
\(526\) | 337386. | + | 302524.i | 1.21943 | + | 1.09343i | ||||
\(527\) | 108509.i | 0.390701i | ||||||||
\(528\) | 572467. | − | 126634.i | 2.05344 | − | 0.454237i | ||||
\(529\) | −271114. | −0.968813 | ||||||||
\(530\) | 11161.2 | − | 12447.4i | 0.0397339 | − | 0.0443126i | ||||
\(531\) | −116297. | + | 116297.i | −0.412459 | + | 0.412459i | ||||
\(532\) | 353717. | + | 284023.i | 1.24978 | + | 1.00353i | ||||
\(533\) | −24859.0 | + | 24859.0i | −0.0875042 | + | 0.0875042i | ||||
\(534\) | −31798.0 | − | 583673.i | −0.111511 | − | 2.04685i | ||||
\(535\) | −86277.6 | −0.301433 | ||||||||
\(536\) | 21833.0 | + | 132528.i | 0.0759946 | + | 0.461293i | ||||
\(537\) | 90786.1i | 0.314826i | ||||||||
\(538\) | −21741.6 | − | 399080.i | −0.0751150 | − | 1.37878i | ||||
\(539\) | 424486. | + | 424486.i | 1.46112 | + | 1.46112i | ||||
\(540\) | −1464.22 | − | 13398.5i | −0.00502134 | − | 0.0459481i | ||||
\(541\) | 308972. | + | 308972.i | 1.05566 | + | 1.05566i | 0.998357 | + | 0.0573036i | \(0.0182503\pi\) |
0.0573036 | + | 0.998357i | \(0.481750\pi\) | |||||||
\(542\) | 294222. | − | 328127.i | 1.00156 | − | 1.11698i | ||||
\(543\) | − | 451027.i | − | 1.52969i | ||||||
\(544\) | −78555.1 | − | 44278.5i | −0.265446 | − | 0.149622i | ||||
\(545\) | 13378.6 | 0.0450420 | ||||||||
\(546\) | −117077. | − | 104980.i | −0.392723 | − | 0.352143i | ||||
\(547\) | −8623.13 | + | 8623.13i | −0.0288198 | + | 0.0288198i | −0.721370 | − | 0.692550i | \(-0.756487\pi\) |
0.692550 | + | 0.721370i | \(0.256487\pi\) | |||||||
\(548\) | 58367.6 | − | 6378.57i | 0.194362 | − | 0.0212404i | ||||
\(549\) | 56104.4 | − | 56104.4i | 0.186145 | − | 0.186145i | ||||
\(550\) | 417763. | − | 22759.4i | 1.38103 | − | 0.0752376i | ||||
\(551\) | −142317. | −0.468765 | ||||||||
\(552\) | 12955.5 | + | 78640.6i | 0.0425182 | + | 0.258089i | ||||
\(553\) | − | 413968.i | − | 1.35368i | ||||||
\(554\) | −195499. | + | 10650.6i | −0.636980 | + | 0.0347022i | ||||
\(555\) | 56150.4 | + | 56150.4i | 0.182292 | + | 0.182292i | ||||
\(556\) | −62354.2 | + | 77654.8i | −0.201705 | + | 0.251199i | ||||
\(557\) | −208785. | − | 208785.i | −0.672961 | − | 0.672961i | 0.285437 | − | 0.958398i | \(-0.407861\pi\) |
−0.958398 | + | 0.285437i | \(0.907861\pi\) | |||||||
\(558\) | 354833. | + | 318168.i | 1.13961 | + | 1.02185i | ||||
\(559\) | 60666.5i | 0.194145i | ||||||||
\(560\) | −42553.5 | + | 66727.2i | −0.135694 | + | 0.212778i | ||||
\(561\) | 201683. | 0.640832 | ||||||||
\(562\) | −395161. | + | 440698.i | −1.25113 | + | 1.39530i | ||||
\(563\) | 127891. | − | 127891.i | 0.403480 | − | 0.403480i | −0.475977 | − | 0.879458i | \(-0.657906\pi\) |
0.879458 | + | 0.475977i | \(0.157906\pi\) | |||||||
\(564\) | −229778. | + | 286162.i | −0.722356 | + | 0.899608i | ||||
\(565\) | 24275.2 | − | 24275.2i | 0.0760443 | − | 0.0760443i | ||||
\(566\) | −12235.5 | − | 224590.i | −0.0381935 | − | 0.701065i | ||||
\(567\) | −387228. | −1.20448 | ||||||||
\(568\) | 207807. | − | 289781.i | 0.644116 | − | 0.898201i | ||||
\(569\) | 488561.i | 1.50902i | 0.656290 | + | 0.754509i | \(0.272125\pi\) | ||||
−0.656290 | + | 0.754509i | \(0.727875\pi\) | |||||||
\(570\) | −4312.65 | − | 79161.5i | −0.0132738 | − | 0.243649i | ||||
\(571\) | −17324.2 | − | 17324.2i | −0.0531352 | − | 0.0531352i | 0.680040 | − | 0.733175i | \(-0.261962\pi\) |
−0.733175 | + | 0.680040i | \(0.761962\pi\) | |||||||
\(572\) | −104964. | + | 11470.7i | −0.320810 | + | 0.0350590i | ||||
\(573\) | −424913. | − | 424913.i | −1.29417 | − | 1.29417i | ||||
\(574\) | −187657. | + | 209282.i | −0.569562 | + | 0.635197i | ||||
\(575\) | 56873.6i | 0.172018i | ||||||||
\(576\) | −375132. | + | 127049.i | −1.13068 | + | 0.382935i | ||||
\(577\) | −9362.93 | −0.0281229 | −0.0140615 | − | 0.999901i | \(-0.504476\pi\) | ||||
−0.0140615 | + | 0.999901i | \(0.504476\pi\) | |||||||
\(578\) | 225639. | + | 202324.i | 0.675397 | + | 0.605609i | ||||
\(579\) | −473990. | + | 473990.i | −1.41388 | + | 1.41388i | ||||
\(580\) | −2697.29 | − | 24681.8i | −0.00801810 | − | 0.0733702i | ||||
\(581\) | 196100. | − | 196100.i | 0.580932 | − | 0.580932i | ||||
\(582\) | 250940. | − | 13671.0i | 0.740839 | − | 0.0403603i | ||||
\(583\) | 178348. | 0.524725 | ||||||||
\(584\) | 344052. | + | 246726.i | 1.00878 | + | 0.723417i | ||||
\(585\) | 14954.5i | 0.0436978i | ||||||||
\(586\) | 4004.26 | − | 218.149i | 0.0116608 | − | 0.000635268i | ||||
\(587\) | 46301.5 | + | 46301.5i | 0.134375 | + | 0.134375i | 0.771095 | − | 0.636720i | \(-0.219709\pi\) |
−0.636720 | + | 0.771095i | \(0.719709\pi\) | |||||||
\(588\) | −581083. | − | 466590.i | −1.68067 | − | 1.34953i | ||||
\(589\) | 321742. | + | 321742.i | 0.927422 | + | 0.927422i | ||||
\(590\) | −20395.7 | − | 18288.2i | −0.0585916 | − | 0.0525373i | ||||
\(591\) | − | 483778.i | − | 1.38507i | ||||||
\(592\) | 203650. | − | 319340.i | 0.581088 | − | 0.911191i | ||||
\(593\) | −194145. | −0.552099 | −0.276049 | − | 0.961143i | \(-0.589025\pi\) | ||||
−0.276049 | + | 0.961143i | \(0.589025\pi\) | |||||||
\(594\) | 95987.6 | − | 107049.i | 0.272046 | − | 0.303395i | ||||
\(595\) | −19250.1 | + | 19250.1i | −0.0543749 | + | 0.0543749i | ||||
\(596\) | 277664. | + | 222955.i | 0.781676 | + | 0.627660i | ||||
\(597\) | 420387. | − | 420387.i | 1.17951 | − | 1.17951i | ||||
\(598\) | −780.804 | − | 14332.2i | −0.00218343 | − | 0.0400783i | ||||
\(599\) | 474516. | 1.32250 | 0.661252 | − | 0.750164i | \(-0.270025\pi\) | ||||
0.661252 | + | 0.750164i | \(0.270025\pi\) | |||||||
\(600\) | −512470. | + | 84425.8i | −1.42353 | + | 0.234516i | ||||
\(601\) | − | 87515.3i | − | 0.242290i | −0.992635 | − | 0.121145i | \(-0.961343\pi\) | ||
0.992635 | − | 0.121145i | \(-0.0386566\pi\) | |||||||
\(602\) | 26387.0 | + | 484350.i | 0.0728110 | + | 1.33649i | ||||
\(603\) | 143493. | + | 143493.i | 0.394634 | + | 0.394634i | ||||
\(604\) | −72955.0 | − | 667580.i | −0.199977 | − | 1.82991i | ||||
\(605\) | −42357.8 | − | 42357.8i | −0.115724 | − | 0.115724i | ||||
\(606\) | −572935. | + | 638958.i | −1.56013 | + | 1.73991i | ||||
\(607\) | 687260.i | 1.86528i | 0.360808 | + | 0.932640i | \(0.382501\pi\) | ||||
−0.360808 | + | 0.932640i | \(0.617499\pi\) | |||||||
\(608\) | −364216. | + | 101634.i | −0.985263 | + | 0.274937i | ||||
\(609\) | 394456. | 1.06356 | ||||||||
\(610\) | 9839.34 | + | 8822.65i | 0.0264427 | + | 0.0237104i | ||||
\(611\) | 46734.8 | − | 46734.8i | 0.125187 | − | 0.125187i | ||||
\(612\) | −135435. | + | 14800.7i | −0.361600 | + | 0.0395166i | ||||
\(613\) | −220862. | + | 220862.i | −0.587761 | + | 0.587761i | −0.937025 | − | 0.349263i | \(-0.886432\pi\) |
0.349263 | + | 0.937025i | \(0.386432\pi\) | |||||||
\(614\) | 116342. | − | 6338.23i | 0.308603 | − | 0.0168124i | ||||
\(615\) | 49125.1 | 0.129883 | ||||||||
\(616\) | −833023. | + | 137234.i | −2.19531 | + | 0.361661i | ||||
\(617\) | − | 518967.i | − | 1.36323i | −0.731711 | − | 0.681615i | \(-0.761278\pi\) | ||
0.731711 | − | 0.681615i | \(-0.238722\pi\) | |||||||
\(618\) | 9357.67 | − | 509.798i | 0.0245014 | − | 0.00133482i | ||||
\(619\) | −77555.3 | − | 77555.3i | −0.202409 | − | 0.202409i | 0.598622 | − | 0.801031i | \(-0.295715\pi\) |
−0.801031 | + | 0.598622i | \(0.795715\pi\) | |||||||
\(620\) | −49701.1 | + | 61896.8i | −0.129295 | + | 0.161022i | ||||
\(621\) | 13820.5 | + | 13820.5i | 0.0358378 | + | 0.0358378i | ||||
\(622\) | −245129. | − | 219800.i | −0.633599 | − | 0.568130i | ||||
\(623\) | 841705.i | 2.16862i | ||||||||
\(624\) | 127984. | − | 28310.9i | 0.328689 | − | 0.0727084i | ||||
\(625\) | −360490. | −0.922855 | ||||||||
\(626\) | 321554. | − | 358609.i | 0.820550 | − | 0.915107i | ||||
\(627\) | 598015. | − | 598015.i | 1.52117 | − | 1.52117i | ||||
\(628\) | 350430. | − | 436419.i | 0.888550 | − | 1.10658i | ||||
\(629\) | 92126.1 | − | 92126.1i | 0.232853 | − | 0.232853i | ||||
\(630\) | 6504.48 | + | 119394.i | 0.0163882 | + | 0.300816i | ||||
\(631\) | 344653. | 0.865612 | 0.432806 | − | 0.901487i | \(-0.357523\pi\) | ||||
0.432806 | + | 0.901487i | \(0.357523\pi\) | |||||||
\(632\) | 280416. | + | 201091.i | 0.702051 | + | 0.503453i | ||||
\(633\) | 486914.i | 1.21519i | ||||||||
\(634\) | −4552.88 | − | 83571.0i | −0.0113268 | − | 0.207911i | ||||
\(635\) | 8098.03 | + | 8098.03i | 0.0200832 | + | 0.0200832i | ||||
\(636\) | −220091. | + | 24052.1i | −0.544111 | + | 0.0594619i | ||||
\(637\) | 94900.2 | + | 94900.2i | 0.233877 | + | 0.233877i | ||||
\(638\) | 176822. | − | 197198.i | 0.434405 | − | 0.484464i | ||||
\(639\) | − | 538758.i | − | 1.31945i | ||||||
\(640\) | −24529.0 | − | 61238.8i | −0.0598853 | − | 0.149509i | ||||
\(641\) | −183353. | −0.446243 | −0.223122 | − | 0.974791i | \(-0.571625\pi\) | ||||
−0.223122 | + | 0.974791i | \(0.571625\pi\) | |||||||
\(642\) | 850662. | + | 762764.i | 2.06389 | + | 1.85063i | ||||
\(643\) | −541900. | + | 541900.i | −1.31068 | + | 1.31068i | −0.389768 | + | 0.920913i | \(0.627445\pi\) |
−0.920913 | + | 0.389768i | \(0.872555\pi\) | |||||||
\(644\) | −12467.6 | − | 114086.i | −0.0300615 | − | 0.275080i | ||||
\(645\) | 59943.0 | − | 59943.0i | 0.144085 | − | 0.144085i | ||||
\(646\) | −129880. | + | 7075.78i | −0.311228 | + | 0.0169555i | ||||
\(647\) | −358562. | −0.856555 | −0.428278 | − | 0.903647i | \(-0.640879\pi\) | ||||
−0.428278 | + | 0.903647i | \(0.640879\pi\) | |||||||
\(648\) | 188102. | − | 262302.i | 0.447963 | − | 0.624672i | ||||
\(649\) | − | 292233.i | − | 0.693808i | ||||||
\(650\) | 93397.0 | − | 5088.19i | 0.221058 | − | 0.0120431i | ||||
\(651\) | −891760. | − | 891760.i | −2.10419 | − | 2.10419i | ||||
\(652\) | 431026. | + | 346099.i | 1.01393 | + | 0.814152i | ||||
\(653\) | −73642.4 | − | 73642.4i | −0.172704 | − | 0.172704i | 0.615463 | − | 0.788166i | \(-0.288969\pi\) |
−0.788166 | + | 0.615463i | \(0.788969\pi\) | |||||||
\(654\) | −131908. | − | 118278.i | −0.308400 | − | 0.276533i | ||||
\(655\) | − | 39801.7i | − | 0.0927725i | ||||||
\(656\) | −50607.3 | − | 228778.i | −0.117600 | − | 0.531626i | ||||
\(657\) | 639657. | 1.48189 | ||||||||
\(658\) | 352795. | − | 393449.i | 0.814836 | − | 0.908735i | ||||
\(659\) | 22081.7 | − | 22081.7i | 0.0508467 | − | 0.0508467i | −0.681226 | − | 0.732073i | \(-0.738553\pi\) |
0.732073 | + | 0.681226i | \(0.238553\pi\) | |||||||
\(660\) | 115046. | + | 92378.2i | 0.264109 | + | 0.212071i | ||||
\(661\) | 20869.3 | − | 20869.3i | 0.0477644 | − | 0.0477644i | −0.682821 | − | 0.730586i | \(-0.739247\pi\) |
0.730586 | + | 0.682821i | \(0.239247\pi\) | |||||||
\(662\) | −25500.6 | − | 468079.i | −0.0581881 | − | 1.06808i | ||||
\(663\) | 45089.3 | 0.102576 | ||||||||
\(664\) | 37576.8 | + | 228094.i | 0.0852283 | + | 0.517342i | ||||
\(665\) | 114157.i | 0.258143i | ||||||||
\(666\) | −31128.8 | − | 571390.i | −0.0701802 | − | 1.28820i | ||||
\(667\) | 25459.3 | + | 25459.3i | 0.0572261 | + | 0.0572261i | ||||
\(668\) | 90694.9 | + | 829911.i | 0.203250 | + | 1.85985i | ||||
\(669\) | −684791. | − | 684791.i | −1.53005 | − | 1.53005i | ||||
\(670\) | −22564.8 | + | 25165.1i | −0.0502669 | + | 0.0560594i | ||||
\(671\) | 140979.i | 0.313120i | ||||||||
\(672\) | 1.00948e6 | − | 281696.i | 2.23543 | − | 0.623794i | ||||
\(673\) | 379771. | 0.838479 | 0.419239 | − | 0.907876i | \(-0.362297\pi\) | ||||
0.419239 | + | 0.907876i | \(0.362297\pi\) | |||||||
\(674\) | −234837. | − | 210571.i | −0.516947 | − | 0.463531i | ||||
\(675\) | −90063.0 | + | 90063.0i | −0.197669 | + | 0.197669i | ||||
\(676\) | 430805. | − | 47079.6i | 0.942731 | − | 0.103024i | ||||
\(677\) | −156167. | + | 156167.i | −0.340731 | + | 0.340731i | −0.856642 | − | 0.515911i | \(-0.827454\pi\) |
0.515911 | + | 0.856642i | \(0.327454\pi\) | |||||||
\(678\) | −453957. | + | 24731.2i | −0.987541 | + | 0.0538004i | ||||
\(679\) | −361877. | −0.784912 | ||||||||
\(680\) | −3688.71 | − | 22390.7i | −0.00797731 | − | 0.0484228i | ||||
\(681\) | 355511.i | 0.766581i | ||||||||
\(682\) | −845560. | + | 46065.4i | −1.81792 | + | 0.0990390i | ||||
\(683\) | 164044. | + | 164044.i | 0.351656 | + | 0.351656i | 0.860725 | − | 0.509070i | \(-0.170010\pi\) |
−0.509070 | + | 0.860725i | \(0.670010\pi\) | |||||||
\(684\) | −357695. | + | 445466.i | −0.764540 | + | 0.952144i | ||||
\(685\) | 10448.0 | + | 10448.0i | 0.0222665 | + | 0.0222665i | ||||
\(686\) | 249938. | + | 224112.i | 0.531109 | + | 0.476230i | ||||
\(687\) | 785666.i | 1.66466i | ||||||||
\(688\) | −340909. | − | 217406.i | −0.720215 | − | 0.459298i | ||||
\(689\) | 39872.4 | 0.0839912 | ||||||||
\(690\) | −13389.7 | + | 14932.7i | −0.0281238 | + | 0.0313647i | ||||
\(691\) | −288207. | + | 288207.i | −0.603599 | + | 0.603599i | −0.941266 | − | 0.337667i | \(-0.890362\pi\) |
0.337667 | + | 0.941266i | \(0.390362\pi\) | |||||||
\(692\) | −372825. | + | 464310.i | −0.778562 | + | 0.969607i | ||||
\(693\) | −901945. | + | 901945.i | −1.87808 | + | 1.87808i | ||||
\(694\) | 18322.8 | + | 336327.i | 0.0380429 | + | 0.698302i | ||||
\(695\) | −25062.1 | −0.0518856 | ||||||||
\(696\) | −191613. | + | 267198.i | −0.395554 | + | 0.551589i | ||||
\(697\) | − | 80599.7i | − | 0.165908i | ||||||
\(698\) | 232.693 | + | 4271.22i | 0.000477608 | + | 0.00876681i | ||||
\(699\) | 26087.2 | + | 26087.2i | 0.0533916 | + | 0.0533916i | ||||
\(700\) | 743451. | − | 81246.4i | 1.51725 | − | 0.165809i | ||||
\(701\) | 323248. | + | 323248.i | 0.657808 | + | 0.657808i | 0.954861 | − | 0.297053i | \(-0.0960038\pi\) |
−0.297053 | + | 0.954861i | \(0.596004\pi\) | |||||||
\(702\) | 21459.4 | − | 23932.3i | 0.0435456 | − | 0.0485636i | ||||
\(703\) | − | 546329.i | − | 1.10546i | ||||||
\(704\) | 311692. | − | 630941.i | 0.628899 | − | 1.27304i | ||||
\(705\) | −92355.0 | −0.185816 | ||||||||
\(706\) | −70651.0 | − | 63350.7i | −0.141745 | − | 0.127099i | ||||
\(707\) | 873826. | − | 873826.i | 1.74818 | − | 1.74818i | ||||
\(708\) | 39410.6 | + | 360629.i | 0.0786224 | + | 0.719440i | ||||
\(709\) | −580085. | + | 580085.i | −1.15398 | + | 1.15398i | −0.168235 | + | 0.985747i | \(0.553807\pi\) |
−0.985747 | + | 0.168235i | \(0.946193\pi\) | |||||||
\(710\) | 89603.4 | − | 4881.52i | 0.177749 | − | 0.00968364i | ||||
\(711\) | 521346. | 1.03130 | ||||||||
\(712\) | −570159. | − | 408871.i | −1.12470 | − | 0.806540i | ||||
\(713\) | − | 115113.i | − | 0.226436i | ||||||
\(714\) | 359984. | − | 19611.7i | 0.706134 | − | 0.0384696i | ||||
\(715\) | −18788.9 | − | 18788.9i | −0.0367526 | − | 0.0367526i | ||||
\(716\) | 84967.2 | + | 68225.8i | 0.165739 | + | 0.133083i | ||||
\(717\) | 471123. | + | 471123.i | 0.916423 | + | 0.916423i | ||||
\(718\) | −434994. | − | 390046.i | −0.843789 | − | 0.756601i | ||||
\(719\) | − | 332243.i | − | 0.642684i | −0.946963 | − | 0.321342i | \(-0.895866\pi\) | ||
0.946963 | − | 0.321342i | \(-0.104134\pi\) | |||||||
\(720\) | −84035.3 | − | 53591.3i | −0.162105 | − | 0.103378i | ||||
\(721\) | −13494.5 | −0.0259590 | ||||||||
\(722\) | −16124.1 | + | 17982.1i | −0.0309314 | + | 0.0344959i | ||||
\(723\) | 415456. | − | 415456.i | 0.794783 | − | 0.794783i | ||||
\(724\) | −422118. | − | 338947.i | −0.805299 | − | 0.646628i | ||||
\(725\) | −165908. | + | 165908.i | −0.315639 | + | 0.315639i | ||||
\(726\) | 43153.4 | + | 792107.i | 0.0818732 | + | 1.50283i | ||||
\(727\) | 362311. | 0.685508 | 0.342754 | − | 0.939425i | \(-0.388640\pi\) | ||||
0.342754 | + | 0.939425i | \(0.388640\pi\) | |||||||
\(728\) | −186234. | + | 30680.8i | −0.351396 | + | 0.0578900i | ||||
\(729\) | − | 713570.i | − | 1.34271i | ||||||
\(730\) | 5795.74 | + | 106384.i | 0.0108758 | + | 0.199633i | ||||
\(731\) | −98348.7 | − | 98348.7i | −0.184049 | − | 0.184049i | ||||
\(732\) | −19012.5 | − | 173975.i | −0.0354828 | − | 0.324688i | ||||
\(733\) | 377844. | + | 377844.i | 0.703242 | + | 0.703242i | 0.965105 | − | 0.261863i | \(-0.0843369\pi\) |
−0.261863 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(734\) | −403570. | + | 450076.i | −0.749078 | + | 0.835399i | ||||
\(735\) | − | 187537.i | − | 0.347146i | ||||||
\(736\) | 83336.2 | + | 46973.4i | 0.153843 | + | 0.0867155i | ||||
\(737\) | −360569. | −0.663825 | ||||||||
\(738\) | −263567. | − | 236333.i | −0.483925 | − | 0.433922i | ||||
\(739\) | 467502. | − | 467502.i | 0.856042 | − | 0.856042i | −0.134828 | − | 0.990869i | \(-0.543048\pi\) |
0.990869 | + | 0.134828i | \(0.0430480\pi\) | |||||||
\(740\) | 94748.5 | − | 10354.4i | 0.173025 | − | 0.0189086i | ||||
\(741\) | 133695. | − | 133695.i | 0.243489 | − | 0.243489i | ||||
\(742\) | 318334. | − | 17342.6i | 0.578196 | − | 0.0314997i | ||||
\(743\) | −555820. | −1.00683 | −0.503415 | − | 0.864045i | \(-0.667923\pi\) | ||||
−0.503415 | + | 0.864045i | \(0.667923\pi\) | |||||||
\(744\) | 1.03725e6 | − | 170879.i | 1.87386 | − | 0.308705i | ||||
\(745\) | 89612.4i | 0.161456i | ||||||||
\(746\) | −148034. | + | 8064.75i | −0.266001 | + | 0.0144915i | ||||
\(747\) | 246966. | + | 246966.i | 0.442584 | + | 0.442584i | ||||
\(748\) | 151565. | − | 188756.i | 0.270892 | − | 0.337364i | ||||
\(749\) | −1.16335e6 | − | 1.16335e6i | −2.07370 | − | 2.07370i | ||||
\(750\) | −197213. | − | 176835.i | −0.350601 | − | 0.314373i | ||||
\(751\) | 308308.i | 0.546644i | 0.961923 | + | 0.273322i | \(0.0881224\pi\) | ||||
−0.961923 | + | 0.273322i | \(0.911878\pi\) | |||||||
\(752\) | 95141.6 | + | 430102.i | 0.168242 | + | 0.760563i | ||||
\(753\) | 599226. | 1.05682 | ||||||||
\(754\) | 39531.1 | − | 44086.5i | 0.0695339 | − | 0.0775467i | ||||
\(755\) | 119499. | − | 119499.i | 0.209638 | − | 0.209638i | ||||
\(756\) | 160919. | − | 200405.i | 0.281555 | − | 0.350643i | ||||
\(757\) | 34980.2 | − | 34980.2i | 0.0610423 | − | 0.0610423i | −0.675927 | − | 0.736969i | \(-0.736256\pi\) |
0.736969 | + | 0.675927i | \(0.236256\pi\) | |||||||
\(758\) | −33980.3 | − | 623729.i | −0.0591410 | − | 1.08557i | ||||
\(759\) | −213958. | −0.371403 | ||||||||
\(760\) | −77328.6 | − | 55453.7i | −0.133879 | − | 0.0960070i | ||||
\(761\) | − | 545745.i | − | 0.942368i | −0.882035 | − | 0.471184i | \(-0.843827\pi\) | ||
0.882035 | − | 0.471184i | \(-0.156173\pi\) | |||||||
\(762\) | −8250.14 | − | 151437.i | −0.0142086 | − | 0.260808i | ||||
\(763\) | 180394. | + | 180394.i | 0.309866 | + | 0.309866i | ||||
\(764\) | −717001. | + | 78355.8i | −1.22838 | + | 0.134241i | ||||
\(765\) | −24243.3 | − | 24243.3i | −0.0414256 | − | 0.0414256i | ||||
\(766\) | 28078.9 | − | 31314.6i | 0.0478544 | − | 0.0533690i | ||||
\(767\) | − | 65332.9i | − | 0.111056i | ||||||
\(768\) | −299555. | + | 820646.i | −0.507871 | + | 1.39134i | ||||
\(769\) | 510362. | 0.863030 | 0.431515 | − | 0.902106i | \(-0.357979\pi\) | ||||
0.431515 | + | 0.902106i | \(0.357979\pi\) | |||||||
\(770\) | −158179. | − | 141835.i | −0.266789 | − | 0.239222i | ||||
\(771\) | −667972. | + | 667972.i | −1.12370 | + | 1.12370i | ||||
\(772\) | 87405.8 | + | 799814.i | 0.146658 | + | 1.34200i | ||||
\(773\) | 596763. | − | 596763.i | 0.998718 | − | 0.998718i | −0.00128103 | − | 0.999999i | \(-0.500408\pi\) |
0.999999 | + | 0.00128103i | \(0.000407764\pi\) | |||||||
\(774\) | −609984. | + | 33231.4i | −1.01821 | + | 0.0554711i | ||||
\(775\) | 750148. | 1.24895 | ||||||||
\(776\) | 175787. | − | 245130.i | 0.291919 | − | 0.407073i | ||||
\(777\) | 1.51424e6i | 2.50814i | ||||||||
\(778\) | 941952. | − | 51316.8i | 1.55621 | − | 0.0847813i | ||||
\(779\) | −238987. | − | 238987.i | −0.393822 | − | 0.393822i | ||||
\(780\) | 25720.2 | + | 20652.5i | 0.0422752 | + | 0.0339456i | ||||
\(781\) | 676897. | + | 676897.i | 1.10974 | + | 1.10974i | ||||
\(782\) | 24500.2 | + | 21968.6i | 0.0400641 | + | 0.0359243i | ||||
\(783\) | 80632.7i | 0.131519i | ||||||||
\(784\) | −873369. | + | 193196.i | −1.42091 | + | 0.314315i | ||||
\(785\) | 140849. | 0.228567 | ||||||||
\(786\) | −351880. | + | 392429.i | −0.569572 | + | 0.635208i | ||||
\(787\) | −463254. | + | 463254.i | −0.747945 | + | 0.747945i | −0.974093 | − | 0.226148i | \(-0.927387\pi\) |
0.226148 | + | 0.974093i | \(0.427387\pi\) | |||||||
\(788\) | −452770. | − | 363560.i | −0.729165 | − | 0.585495i | ||||
\(789\) | 1.06785e6 | − | 1.06785e6i | 1.71536 | − | 1.71536i | ||||
\(790\) | 4723.76 | + | 86707.5i | 0.00756891 | + | 0.138932i | ||||
\(791\) | 654644. | 1.04629 | ||||||||
\(792\) | −172831. | − | 1.04910e6i | −0.275532 | − | 1.67250i | ||||
\(793\) | 31518.0i | 0.0501202i | ||||||||
\(794\) | 59249.8 | + | 1.08757e6i | 0.0939823 | + | 1.72510i | ||||
\(795\) | −39396.9 | − | 39396.9i | −0.0623344 | − | 0.0623344i | ||||
\(796\) | −77521.1 | − | 709363.i | −0.122347 | − | 1.11955i | ||||
\(797\) | 406283. | + | 406283.i | 0.639605 | + | 0.639605i | 0.950458 | − | 0.310853i | \(-0.100615\pi\) |
−0.310853 | + | 0.950458i | \(0.600615\pi\) | |||||||
\(798\) | 1.00924e6 | − | 1.12555e6i | 1.58486 | − | 1.76749i | ||||
\(799\) | 151527.i | 0.237354i | ||||||||
\(800\) | −306107. | + | 543070.i | −0.478293 | + | 0.848546i | ||||
\(801\) | −1.06003e6 | −1.65217 | ||||||||
\(802\) | −271476. | − | 243425.i | −0.422069 | − | 0.378457i | ||||
\(803\) | −803667. | + | 803667.i | −1.24636 | + | 1.24636i | ||||
\(804\) | 444960. | − | 48626.4i | 0.688349 | − | 0.0752246i | ||||
\(805\) | 20421.7 | − | 20421.7i | 0.0315137 | − | 0.0315137i | ||||
\(806\) | −189037. | + | 10298.6i | −0.290990 | + | 0.0158529i | ||||
\(807\) | −1.33193e6 | −2.04519 | ||||||||
\(808\) | 167443. | + | 1.01639e6i | 0.256475 | + | 1.55682i | ||||
\(809\) | 766553.i | 1.17124i | 0.810587 | + | 0.585619i | \(0.199148\pi\) | ||||
−0.810587 | + | 0.585619i | \(0.800852\pi\) | |||||||
\(810\) | 81106.7 | − | 4418.63i | 0.123619 | − | 0.00673468i | ||||
\(811\) | −418641. | − | 418641.i | −0.636503 | − | 0.636503i | 0.313188 | − | 0.949691i | \(-0.398603\pi\) |
−0.949691 | + | 0.313188i | \(0.898603\pi\) | |||||||
\(812\) | 296434. | − | 369173.i | 0.449589 | − | 0.559909i | ||||
\(813\) | −1.03855e6 | − | 1.03855e6i | −1.57125 | − | 1.57125i | ||||
\(814\) | 757006. | + | 678785.i | 1.14248 | + | 1.02443i | ||||
\(815\) | 139108.i | 0.209429i | ||||||||
\(816\) | −161583. | + | 253375.i | −0.242670 | + | 0.380525i | ||||
\(817\) | −583231. | −0.873769 | ||||||||
\(818\) | −287798. | + | 320963.i | −0.430112 | + | 0.479677i | ||||
\(819\) | −201643. | + | 201643.i | −0.300618 | + | 0.300618i | ||||
\(820\) | 36917.5 | − | 45976.4i | 0.0549041 | − | 0.0683766i | ||||
\(821\) | −23229.7 | + | 23229.7i | −0.0344633 | + | 0.0344633i | −0.724128 | − | 0.689665i | \(-0.757758\pi\) |
0.689665 | + | 0.724128i | \(0.257758\pi\) | |||||||
\(822\) | −10644.2 | − | 195382.i | −0.0157533 | − | 0.289161i | ||||
\(823\) | −41797.3 | −0.0617090 | −0.0308545 | − | 0.999524i | \(-0.509823\pi\) | ||||
−0.0308545 | + | 0.999524i | \(0.509823\pi\) | |||||||
\(824\) | 6555.17 | − | 9141.01i | 0.00965450 | − | 0.0134629i | ||||
\(825\) | − | 1.39428e6i | − | 2.04853i | ||||||
\(826\) | −28416.7 | − | 521606.i | −0.0416498 | − | 0.764509i | ||||
\(827\) | −349889. | − | 349889.i | −0.511587 | − | 0.511587i | 0.403425 | − | 0.915013i | \(-0.367820\pi\) |
−0.915013 | + | 0.403425i | \(0.867820\pi\) | |||||||
\(828\) | 143678. | − | 15701.5i | 0.209570 | − | 0.0229024i | ||||
\(829\) | 213369. | + | 213369.i | 0.310472 | + | 0.310472i | 0.845092 | − | 0.534621i | \(-0.179545\pi\) |
−0.534621 | + | 0.845092i | \(0.679545\pi\) | |||||||
\(830\) | −38836.4 | + | 43311.8i | −0.0563745 | + | 0.0628709i | ||||
\(831\) | 652479.i | 0.944853i | ||||||||
\(832\) | 69683.4 | − | 141056.i | 0.100666 | − | 0.203772i | ||||
\(833\) | −307692. | −0.443432 | ||||||||
\(834\) | 247102. | + | 221569.i | 0.355258 | + | 0.318549i | ||||
\(835\) | −148557. | + | 148557.i | −0.213069 | + | 0.213069i | ||||
\(836\) | −110276. | − | 1.00909e6i | −0.157787 | − | 1.44384i | ||||
\(837\) | 182289. | − | 182289.i | 0.260202 | − | 0.260202i | ||||
\(838\) | 669479. | − | 36472.7i | 0.953343 | − | 0.0519374i | ||||
\(839\) | −7789.74 | −0.0110662 | −0.00553311 | − | 0.999985i | \(-0.501761\pi\) | ||||
−0.00553311 | + | 0.999985i | \(0.501761\pi\) | |||||||
\(840\) | 214328. | + | 153699.i | 0.303754 | + | 0.217827i | ||||
\(841\) | − | 558745.i | − | 0.789990i | ||||||
\(842\) | 1.28004e6 | − | 69735.4i | 1.80550 | − | 0.0983624i | ||||
\(843\) | 1.39484e6 | + | 1.39484e6i | 1.96277 | + | 1.96277i | ||||
\(844\) | 455705. | + | 365916.i | 0.639734 | + | 0.513685i | ||||
\(845\) | 77115.5 | + | 77115.5i | 0.108001 | + | 0.108001i | ||||
\(846\) | 495505. | + | 444305.i | 0.692320 | + | 0.620784i | ||||
\(847\) | − | 1.14229e6i | − | 1.59224i | ||||||
\(848\) | −142888. | + | 224059.i | −0.198703 | + | 0.311581i | ||||
\(849\) | −749570. | −1.03991 | ||||||||
\(850\) | −143161. | + | 159658.i | −0.198146 | + | 0.220980i | ||||
\(851\) | −97733.2 | + | 97733.2i | −0.134953 | + | 0.134953i | ||||
\(852\) | −926610. | − | 744037.i | −1.27649 | − | 1.02498i | ||||
\(853\) | 485860. | − | 485860.i | 0.667749 | − | 0.667749i | −0.289445 | − | 0.957195i | \(-0.593471\pi\) |
0.957195 | + | 0.289445i | \(0.0934708\pi\) | |||||||
\(854\) | 13708.8 | + | 251634.i | 0.0187968 | + | 0.345028i | ||||
\(855\) | −143768. | −0.196667 | ||||||||
\(856\) | 1.35315e6 | − | 222921.i | 1.84671 | − | 0.304232i | ||||
\(857\) | 1.01914e6i | 1.38763i | 0.720154 | + | 0.693814i | \(0.244071\pi\) | ||||
−0.720154 | + | 0.693814i | \(0.755929\pi\) | |||||||
\(858\) | 19141.8 | + | 351359.i | 0.0260021 | + | 0.477284i | ||||
\(859\) | 232567. | + | 232567.i | 0.315182 | + | 0.315182i | 0.846913 | − | 0.531731i | \(-0.178458\pi\) |
−0.531731 | + | 0.846913i | \(0.678458\pi\) | |||||||
\(860\) | −11053.8 | − | 101148.i | −0.0149456 | − | 0.136761i | ||||
\(861\) | 662392. | + | 662392.i | 0.893529 | + | 0.893529i | ||||
\(862\) | −14413.4 | + | 16074.3i | −0.0193978 | + | 0.0216331i | ||||
\(863\) | − | 739852.i | − | 0.993398i | −0.867923 | − | 0.496699i | \(-0.834545\pi\) | ||
0.867923 | − | 0.496699i | \(-0.165455\pi\) | |||||||
\(864\) | 57582.9 | + | 206354.i | 0.0771376 | + | 0.276430i | ||||
\(865\) | −149850. | −0.200274 | ||||||||
\(866\) | −487919. | − | 437502.i | −0.650596 | − | 0.583371i | ||||
\(867\) | 714164. | − | 714164.i | 0.950079 | − | 0.950079i | ||||
\(868\) | −1.50476e6 | + | 164444.i | −1.99723 | + | 0.218263i | ||||
\(869\) | −655020. | + | 655020.i | −0.867392 | + | 0.867392i | ||||
\(870\) | −82620.5 | + | 4501.10i | −0.109156 | + | 0.00594675i | ||||
\(871\) | −80610.5 | −0.106256 | ||||||||
\(872\) | −209825. | + | 34567.2i | −0.275947 | + | 0.0454602i | ||||
\(873\) | − | 455742.i | − | 0.597986i | ||||||
\(874\) | 137785. | − | 7506.44i | 0.180377 | − | 0.00982677i | ||||
\(875\) | 269704. | + | 269704.i | 0.352267 | + | 0.352267i | ||||
\(876\) | 883381. | − | 1.10015e6i | 1.15117 | − | 1.43365i | ||||
\(877\) | −828805. | − | 828805.i | −1.07759 | − | 1.07759i | −0.996725 | − | 0.0808636i | \(-0.974232\pi\) |
−0.0808636 | − | 0.996725i | \(-0.525768\pi\) | |||||||
\(878\) | −471947. | − | 423181.i | −0.612215 | − | 0.548955i | ||||
\(879\) | − | 13364.2i | − | 0.0172968i | ||||||
\(880\) | 172914. | − | 38249.9i | 0.223288 | − | 0.0493930i | ||||
\(881\) | 1.20631e6 | 1.55420 | 0.777099 | − | 0.629379i | \(-0.216690\pi\) | ||||
0.777099 | + | 0.629379i | \(0.216690\pi\) | |||||||
\(882\) | −902210. | + | 1.00618e6i | −1.15977 | + | 1.29341i | ||||
\(883\) | 381765. | − | 381765.i | 0.489637 | − | 0.489637i | −0.418555 | − | 0.908192i | \(-0.637463\pi\) |
0.908192 | + | 0.418555i | \(0.137463\pi\) | |||||||
\(884\) | 33884.6 | − | 42199.3i | 0.0433609 | − | 0.0540008i | ||||
\(885\) | −64553.8 | + | 64553.8i | −0.0824205 | + | 0.0824205i | ||||
\(886\) | 42444.1 | + | 779088.i | 0.0540692 | + | 0.992474i | ||||
\(887\) | −1.44154e6 | −1.83223 | −0.916113 | − | 0.400919i | \(-0.868691\pi\) | ||||
−0.916113 | + | 0.400919i | \(0.868691\pi\) | |||||||
\(888\) | −1.02572e6 | − | 735564.i | −1.30078 | − | 0.932812i | ||||
\(889\) | 218384.i | 0.276323i | ||||||||
\(890\) | −9604.63 | − | 176299.i | −0.0121255 | − | 0.222572i | ||||
\(891\) | 612709. | + | 612709.i | 0.771790 | + | 0.771790i | ||||
\(892\) | −1.15552e6 | + | 126278.i | −1.45227 | + | 0.158708i | ||||
\(893\) | 449295. | + | 449295.i | 0.563416 | + | 0.563416i | ||||
\(894\) | 792246. | − | 883542.i | 0.991254 | − | 1.10548i | ||||
\(895\) | 27422.0i | 0.0342337i | ||||||||
\(896\) | 494987. | − | 1.15647e6i | 0.616563 | − | 1.44052i | ||||
\(897\) | −47833.5 | −0.0594494 | ||||||||
\(898\) | −974840. | − | 874110.i | −1.20887 | − | 1.08396i | ||||
\(899\) | 335801. | − | 335801.i | 0.415492 | − | 0.415492i | ||||
\(900\) | 102321. | + | 936293.i | 0.126322 | + | 1.15592i | ||||
\(901\) | −64638.6 | + | 64638.6i | −0.0796238 | + | 0.0796238i | ||||
\(902\) | 628075. | − | 34217.0i | 0.771967 | − | 0.0420561i | ||||
\(903\) | 1.61652e6 | 1.98246 | ||||||||
\(904\) | −318003. | + | 443446.i | −0.389129 | + | 0.542630i | ||||
\(905\) | − | 136233.i | − | 0.166336i | ||||||
\(906\) | −2.23468e6 | + | 121744.i | −2.72244 | + | 0.148316i | ||||
\(907\) | −208093. | − | 208093.i | −0.252955 | − | 0.252955i | 0.569226 | − | 0.822181i | \(-0.307243\pi\) |
−0.822181 | + | 0.569226i | \(0.807243\pi\) | |||||||
\(908\) | 332724. | + | 267166.i | 0.403564 | + | 0.324049i | ||||
\(909\) | 1.10048e6 | + | 1.10048e6i | 1.33185 | + | 1.33185i | ||||
\(910\) | −35363.3 | − | 31709.2i | −0.0427041 | − | 0.0382915i | ||||
\(911\) | − | 861726.i | − | 1.03832i | −0.854676 | − | 0.519162i | \(-0.826244\pi\) | ||
0.854676 | − | 0.519162i | \(-0.173756\pi\) | |||||||
\(912\) | 272173. | + | 1.23040e6i | 0.327232 | + | 1.47930i | ||||
\(913\) | −620577. | −0.744482 | ||||||||
\(914\) | 412600. | − | 460147.i | 0.493898 | − | 0.550813i | ||||
\(915\) | 31142.2 | − | 31142.2i | 0.0371969 | − | 0.0371969i | ||||
\(916\) | 735309. | + | 590429.i | 0.876353 | + | 0.703682i | ||||
\(917\) | 536678. | − | 536678.i | 0.638227 | − | 0.638227i | ||||
\(918\) | 4008.92 | + | 73586.3i | 0.00475710 | + | 0.0873196i | ||||
\(919\) | −368829. | −0.436711 | −0.218355 | − | 0.975869i | \(-0.570069\pi\) | ||||
−0.218355 | + | 0.975869i | \(0.570069\pi\) | |||||||
\(920\) | 3913.22 | + | 23753.5i | 0.00462336 | + | 0.0280641i | ||||
\(921\) | − | 388292.i | − | 0.457761i | ||||||
\(922\) | −5937.94 | − | 108995.i | −0.00698512 | − | 0.128216i | ||||
\(923\) | 151330. | + | 151330.i | 0.177632 | + | 0.177632i | ||||
\(924\) | 305649. | + | 2.79686e6i | 0.357996 | + | 3.27587i | ||||
\(925\) | −636889. | − | 636889.i | −0.744355 | − | 0.744355i | ||||
\(926\) | 70774.5 | − | 78930.3i | 0.0825382 | − | 0.0920496i | ||||
\(927\) | − | 16994.8i | − | 0.0197769i | ||||||
\(928\) | 106075. | + | 380131.i | 0.123174 | + | 0.441405i | ||||
\(929\) | 842458. | 0.976151 | 0.488076 | − | 0.872801i | \(-0.337699\pi\) | ||||
0.488076 | + | 0.872801i | \(0.337699\pi\) | |||||||
\(930\) | 196959. | + | 176607.i | 0.227724 | + | 0.204194i | ||||
\(931\) | −912344. | + | 912344.i | −1.05259 | + | 1.05259i | ||||
\(932\) | 44019.7 | − | 4810.59i | 0.0506775 | − | 0.00553817i | ||||
\(933\) | −775851. | + | 775851.i | −0.891282 | + | 0.891282i | ||||
\(934\) | −631484. | + | 34402.7i | −0.723883 | + | 0.0394366i | ||||
\(935\) | 60918.6 | 0.0696830 | ||||||||
\(936\) | −38638.9 | − | 234541.i | −0.0441036 | − | 0.267712i | ||||
\(937\) | 41186.1i | 0.0469107i | 0.999725 | + | 0.0234553i | \(0.00746675\pi\) | ||||
−0.999725 | + | 0.0234553i | \(0.992533\pi\) | |||||||
\(938\) | −643579. | + | 35061.7i | −0.731470 | + | 0.0398499i | ||||
\(939\) | −1.13502e6 | − | 1.13502e6i | −1.28728 | − | 1.28728i | ||||
\(940\) | −69404.8 | + | 86435.5i | −0.0785478 | + | 0.0978220i | ||||
\(941\) | 495362. | + | 495362.i | 0.559427 | + | 0.559427i | 0.929144 | − | 0.369717i | \(-0.120546\pi\) |
−0.369717 | + | 0.929144i | \(0.620546\pi\) | |||||||
\(942\) | −1.38871e6 | − | 1.24522e6i | −1.56498 | − | 1.40327i | ||||
\(943\) | 85505.2i | 0.0961544i | ||||||||
\(944\) | 367132. | + | 234129.i | 0.411982 | + | 0.262731i | ||||
\(945\) | 64678.2 | 0.0724259 | ||||||||
\(946\) | 724633. | − | 808137.i | 0.809722 | − | 0.903031i | ||||
\(947\) | −825578. | + | 825578.i | −0.920573 | + | 0.920573i | −0.997070 | − | 0.0764965i | \(-0.975627\pi\) |
0.0764965 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(948\) | 719991. | − | 896663.i | 0.801143 | − | 0.997729i | ||||
\(949\) | −179672. | + | 179672.i | −0.199502 | + | 0.199502i | ||||
\(950\) | 48916.5 | + | 897893.i | 0.0542011 | + | 0.994895i | ||||
\(951\) | −278918. | −0.308401 | ||||||||
\(952\) | 252174. | − | 351649.i | 0.278244 | − | 0.388004i | ||||
\(953\) | 1.06311e6i | 1.17055i | 0.810834 | + | 0.585276i | \(0.199014\pi\) | ||||
−0.810834 | + | 0.585276i | \(0.800986\pi\) | |||||||
\(954\) | 21841.0 | + | 400905.i | 0.0239980 | + | 0.440499i | ||||
\(955\) | −128345. | − | 128345.i | −0.140726 | − | 0.140726i | ||||
\(956\) | 794975. | − | 86877.1i | 0.869837 | − | 0.0950582i | ||||
\(957\) | −624145. | − | 624145.i | −0.681494 | − | 0.681494i | ||||
\(958\) | −601850. | + | 671205.i | −0.655778 | + | 0.731348i | ||||
\(959\) | 281757.i | 0.306364i | ||||||||
\(960\) | −208226. | + | 70521.5i | −0.225940 | + | 0.0765208i | ||||
\(961\) | −594793. | −0.644050 | ||||||||
\(962\) | 169240. | + | 151752.i | 0.182874 | + | 0.163978i | ||||
\(963\) | 1.46511e6 | − | 1.46511e6i | 1.57985 | − | 1.57985i | ||||
\(964\) | −76611.9 | − | 701043.i | −0.0824408 | − | 0.754381i | ||||
\(965\) | −143169. | + | 143169.i | −0.153743 | + | 0.153743i | ||||
\(966\) | −381894. | + | 20805.3i | −0.409250 | + | 0.0222956i | ||||
\(967\) | 1.03910e6 | 1.11123 | 0.555615 | − | 0.831440i | \(-0.312483\pi\) | ||||
0.555615 | + | 0.831440i | \(0.312483\pi\) | |||||||
\(968\) | 773767. | + | 554882.i | 0.825771 | + | 0.592175i | ||||
\(969\) | 433476.i | 0.461655i | ||||||||
\(970\) | 75796.7 | − | 4129.34i | 0.0805577 | − | 0.00438872i | ||||
\(971\) | 624932. | + | 624932.i | 0.662818 | + | 0.662818i | 0.956043 | − | 0.293225i | \(-0.0947285\pi\) |
−0.293225 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(972\) | −1.05016e6 | − | 843247.i | −1.11154 | − | 0.892529i | ||||
\(973\) | −337931. | − | 337931.i | −0.356946 | − | 0.356946i | ||||
\(974\) | −25265.0 | − | 22654.4i | −0.0266318 | − | 0.0238800i | ||||
\(975\) | − | 311712.i | − | 0.327903i | ||||||
\(976\) | −177112. | − | 112949.i | −0.185930 | − | 0.118572i | ||||
\(977\) | 1.37121e6 | 1.43653 | 0.718264 | − | 0.695771i | \(-0.244937\pi\) | ||||
0.718264 | + | 0.695771i | \(0.244937\pi\) | |||||||
\(978\) | 1.22983e6 | − | 1.37155e6i | 1.28578 | − | 1.43395i | ||||
\(979\) | 1.33183e6 | − | 1.33183e6i | 1.38958 | − | 1.38958i | ||||
\(980\) | −175517. | − | 140934.i | −0.182754 | − | 0.146745i | ||||
\(981\) | −227186. | + | 227186.i | −0.236071 | + | 0.236071i | ||||
\(982\) | −21314.5 | − | 391242.i | −0.0221031 | − | 0.405716i | ||||
\(983\) | 838159. | 0.867400 | 0.433700 | − | 0.901057i | \(-0.357208\pi\) | ||||
0.433700 | + | 0.901057i | \(0.357208\pi\) | |||||||
\(984\) | −770461. | + | 126928.i | −0.795720 | + | 0.131089i | ||||
\(985\) | − | 146126.i | − | 0.150610i | ||||||
\(986\) | 7384.97 | + | 135556.i | 0.00759617 | + | 0.139432i | ||||
\(987\) | −1.24529e6 | − | 1.24529e6i | −1.27831 | − | 1.27831i | ||||
\(988\) | −24653.9 | − | 225598.i | −0.0252564 | − | 0.231111i | ||||
\(989\) | 104335. | + | 104335.i | 0.106668 | + | 0.106668i | ||||
\(990\) | 178625. | − | 199209.i | 0.182251 | − | 0.203253i | ||||
\(991\) | 817540.i | 0.832457i | 0.909260 | + | 0.416228i | \(0.136648\pi\) | ||||
−0.909260 | + | 0.416228i | \(0.863352\pi\) | |||||||
\(992\) | 619567. | − | 1.09918e6i | 0.629601 | − | 1.11698i | ||||
\(993\) | −1.56221e6 | −1.58432 | ||||||||
\(994\) | 1.27401e6 | + | 1.14237e6i | 1.28944 | + | 1.15620i | ||||
\(995\) | 126978. | − | 126978.i | 0.128258 | − | 0.128258i | ||||
\(996\) | 765822. | − | 83691.1i | 0.771986 | − | 0.0843647i | ||||
\(997\) | −243046. | + | 243046.i | −0.244511 | + | 0.244511i | −0.818713 | − | 0.574203i | \(-0.805312\pi\) |
0.574203 | + | 0.818713i | \(0.305312\pi\) | |||||||
\(998\) | −490680. | + | 26731.9i | −0.492649 | + | 0.0268391i | ||||
\(999\) | −309534. | −0.310154 |
(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 | 16.5.f.a.3.2 | ✓ | 14 | |
3.2 | odd | 2 | 144.5.m.a.19.6 | 14 | |||
4.3 | odd | 2 | 64.5.f.a.47.7 | 14 | |||
8.3 | odd | 2 | 128.5.f.a.95.1 | 14 | |||
8.5 | even | 2 | 128.5.f.b.95.7 | 14 | |||
12.11 | even | 2 | 576.5.m.a.559.4 | 14 | |||
16.3 | odd | 4 | 128.5.f.b.31.7 | 14 | |||
16.5 | even | 4 | 64.5.f.a.15.7 | 14 | |||
16.11 | odd | 4 | inner | 16.5.f.a.11.2 | yes | 14 | |
16.13 | even | 4 | 128.5.f.a.31.1 | 14 | |||
48.5 | odd | 4 | 576.5.m.a.271.4 | 14 | |||
48.11 | even | 4 | 144.5.m.a.91.6 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.2 | ✓ | 14 | 1.1 | even | 1 | trivial | |
16.5.f.a.11.2 | yes | 14 | 16.11 | odd | 4 | inner | |
64.5.f.a.15.7 | 14 | 16.5 | even | 4 | |||
64.5.f.a.47.7 | 14 | 4.3 | odd | 2 | |||
128.5.f.a.31.1 | 14 | 16.13 | even | 4 | |||
128.5.f.a.95.1 | 14 | 8.3 | odd | 2 | |||
128.5.f.b.31.7 | 14 | 16.3 | odd | 4 | |||
128.5.f.b.95.7 | 14 | 8.5 | even | 2 | |||
144.5.m.a.19.6 | 14 | 3.2 | odd | 2 | |||
144.5.m.a.91.6 | 14 | 48.11 | even | 4 | |||
576.5.m.a.271.4 | 14 | 48.5 | odd | 4 | |||
576.5.m.a.559.4 | 14 | 12.11 | even | 2 |