Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), not 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 126.2 | ||
Root | \(0.0288455i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.126 |
Dual form | 625.2.d.q.501.2 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.326747 | − | 1.00562i | −0.231045 | − | 0.711083i | −0.997621 | − | 0.0689302i | \(-0.978041\pi\) |
0.766577 | − | 0.642153i | \(-0.221959\pi\) | |||||||
\(3\) | −0.556121 | + | 0.404046i | −0.321077 | + | 0.233276i | −0.736635 | − | 0.676291i | \(-0.763586\pi\) |
0.415558 | + | 0.909567i | \(0.363586\pi\) | |||||||
\(4\) | 0.713519 | − | 0.518402i | 0.356760 | − | 0.259201i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.588029 | + | 0.427228i | 0.240062 | + | 0.174415i | ||||
\(7\) | −1.01199 | −0.382498 | −0.191249 | − | 0.981542i | \(-0.561254\pi\) | ||||
−0.191249 | + | 0.981542i | \(0.561254\pi\) | |||||||
\(8\) | −2.46533 | − | 1.79116i | −0.871624 | − | 0.633272i | ||||
\(9\) | −0.781033 | + | 2.40377i | −0.260344 | + | 0.801258i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58239 | + | 4.87011i | 0.477110 | + | 1.46839i | 0.843091 | + | 0.537771i | \(0.180734\pi\) |
−0.365981 | + | 0.930622i | \(0.619266\pi\) | |||||||
\(12\) | −0.187345 | + | 0.576589i | −0.0540819 | + | 0.166447i | ||||
\(13\) | −1.88045 | + | 5.78744i | −0.521544 | + | 1.60515i | 0.249506 | + | 0.968373i | \(0.419732\pi\) |
−0.771050 | + | 0.636775i | \(0.780268\pi\) | |||||||
\(14\) | 0.330666 | + | 1.01769i | 0.0883742 | + | 0.271988i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.450619 | + | 1.38686i | −0.112655 | + | 0.346716i | ||||
\(17\) | 2.58335 | + | 1.87691i | 0.626554 | + | 0.455218i | 0.855205 | − | 0.518290i | \(-0.173431\pi\) |
−0.228651 | + | 0.973509i | \(0.573431\pi\) | |||||||
\(18\) | 2.67249 | 0.629912 | ||||||||
\(19\) | −2.77389 | − | 2.01535i | −0.636374 | − | 0.462352i | 0.222229 | − | 0.974995i | \(-0.428667\pi\) |
−0.858602 | + | 0.512642i | \(0.828667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.562792 | − | 0.408892i | 0.122811 | − | 0.0892276i | ||||
\(22\) | 4.38045 | − | 3.18259i | 0.933916 | − | 0.678530i | ||||
\(23\) | −0.902070 | − | 2.77629i | −0.188095 | − | 0.578896i | 0.811893 | − | 0.583806i | \(-0.198437\pi\) |
−0.999988 | + | 0.00491011i | \(0.998437\pi\) | |||||||
\(24\) | 2.09473 | 0.427585 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.43442 | 1.26189 | ||||||||
\(27\) | −1.17414 | − | 3.61364i | −0.225964 | − | 0.695445i | ||||
\(28\) | −0.722078 | + | 0.524620i | −0.136460 | + | 0.0991439i | ||||
\(29\) | 1.25597 | − | 0.912514i | 0.233227 | − | 0.169450i | −0.465033 | − | 0.885293i | \(-0.653958\pi\) |
0.698261 | + | 0.715844i | \(0.253958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.46970 | + | 4.70051i | 1.16199 | + | 0.844237i | 0.990029 | − | 0.140866i | \(-0.0449888\pi\) |
0.171964 | + | 0.985103i | \(0.444989\pi\) | |||||||
\(32\) | −4.55272 | −0.804815 | ||||||||
\(33\) | −2.84775 | − | 2.06901i | −0.495730 | − | 0.360169i | ||||
\(34\) | 1.04337 | − | 3.21115i | 0.178936 | − | 0.550708i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.688839 | + | 2.12003i | 0.114806 | + | 0.353338i | ||||
\(37\) | −2.59799 | + | 7.99578i | −0.427106 | + | 1.31450i | 0.473857 | + | 0.880602i | \(0.342861\pi\) |
−0.900963 | + | 0.433896i | \(0.857139\pi\) | |||||||
\(38\) | −1.12032 | + | 3.44799i | −0.181740 | + | 0.559339i | ||||
\(39\) | −1.29263 | − | 3.97831i | −0.206987 | − | 0.637039i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.575868 | + | 1.77234i | −0.0899354 | + | 0.276793i | −0.985901 | − | 0.167331i | \(-0.946485\pi\) |
0.895965 | + | 0.444124i | \(0.146485\pi\) | |||||||
\(42\) | −0.595082 | − | 0.432352i | −0.0918231 | − | 0.0667134i | ||||
\(43\) | 5.22402 | 0.796655 | 0.398328 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398328 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(44\) | 3.65374 | + | 2.65460i | 0.550823 | + | 0.400196i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.49715 | + | 1.81429i | −0.368185 | + | 0.267502i | ||||
\(47\) | −3.88393 | + | 2.82184i | −0.566530 | + | 0.411608i | −0.833843 | − | 0.552002i | \(-0.813864\pi\) |
0.267313 | + | 0.963610i | \(0.413864\pi\) | |||||||
\(48\) | −0.309757 | − | 0.953334i | −0.0447096 | − | 0.137602i | ||||
\(49\) | −5.97587 | −0.853695 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.19501 | −0.307363 | ||||||||
\(52\) | 1.65848 | + | 5.10428i | 0.229990 | + | 0.707837i | ||||
\(53\) | 8.13057 | − | 5.90720i | 1.11682 | − | 0.811417i | 0.133095 | − | 0.991103i | \(-0.457508\pi\) |
0.983724 | + | 0.179686i | \(0.0575083\pi\) | |||||||
\(54\) | −3.25031 | + | 2.36149i | −0.442312 | + | 0.321358i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.49490 | + | 1.81265i | 0.333395 | + | 0.242225i | ||||
\(57\) | 2.35691 | 0.312180 | ||||||||
\(58\) | −1.32803 | − | 0.964869i | −0.174379 | − | 0.126694i | ||||
\(59\) | 0.894451 | − | 2.75284i | 0.116448 | − | 0.358389i | −0.875799 | − | 0.482677i | \(-0.839665\pi\) |
0.992246 | + | 0.124288i | \(0.0396646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.713724 | − | 2.19662i | −0.0913830 | − | 0.281248i | 0.894911 | − | 0.446244i | \(-0.147239\pi\) |
−0.986294 | + | 0.164996i | \(0.947239\pi\) | |||||||
\(62\) | 2.61299 | − | 8.04196i | 0.331850 | − | 1.02133i | ||||
\(63\) | 0.790401 | − | 2.43261i | 0.0995812 | − | 0.306479i | ||||
\(64\) | 2.38882 | + | 7.35205i | 0.298603 | + | 0.919006i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.15015 | + | 3.53981i | −0.141574 | + | 0.435720i | ||||
\(67\) | 3.76108 | + | 2.73258i | 0.459489 | + | 0.333838i | 0.793331 | − | 0.608791i | \(-0.208345\pi\) |
−0.333842 | + | 0.942629i | \(0.608345\pi\) | |||||||
\(68\) | 2.81626 | 0.341522 | ||||||||
\(69\) | 1.62341 | + | 1.17947i | 0.195435 | + | 0.141992i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.25945 | − | 4.54776i | 0.742860 | − | 0.539720i | −0.150745 | − | 0.988573i | \(-0.548167\pi\) |
0.893606 | + | 0.448853i | \(0.148167\pi\) | |||||||
\(72\) | 6.23105 | − | 4.52712i | 0.734337 | − | 0.533527i | ||||
\(73\) | 0.184032 | + | 0.566392i | 0.0215393 | + | 0.0662912i | 0.961248 | − | 0.275684i | \(-0.0889042\pi\) |
−0.939709 | + | 0.341975i | \(0.888904\pi\) | |||||||
\(74\) | 8.88962 | 1.03340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.02398 | −0.346875 | ||||||||
\(77\) | −1.60138 | − | 4.92853i | −0.182494 | − | 0.561658i | ||||
\(78\) | −3.57832 | + | 2.59980i | −0.405165 | + | 0.294369i | ||||
\(79\) | −8.94716 | + | 6.50050i | −1.00663 | + | 0.731363i | −0.963501 | − | 0.267706i | \(-0.913734\pi\) |
−0.0431341 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.02127 | − | 2.92163i | −0.446808 | − | 0.324625i | ||||
\(82\) | 1.97047 | 0.217602 | ||||||||
\(83\) | 11.5667 | + | 8.40373i | 1.26961 | + | 0.922429i | 0.999187 | − | 0.0403114i | \(-0.0128350\pi\) |
0.270427 | + | 0.962740i | \(0.412835\pi\) | |||||||
\(84\) | 0.189592 | − | 0.583505i | 0.0206862 | − | 0.0636656i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.70693 | − | 5.25339i | −0.184063 | − | 0.566488i | ||||
\(87\) | −0.329773 | + | 1.01494i | −0.0353554 | + | 0.108813i | ||||
\(88\) | 4.82205 | − | 14.8407i | 0.514032 | − | 1.58203i | ||||
\(89\) | −1.97562 | − | 6.08032i | −0.209415 | − | 0.644513i | −0.999503 | − | 0.0315198i | \(-0.989965\pi\) |
0.790088 | − | 0.612993i | \(-0.210035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.90301 | − | 5.85686i | 0.199490 | − | 0.613966i | ||||
\(92\) | −2.08288 | − | 1.51330i | −0.217155 | − | 0.157772i | ||||
\(93\) | −5.49716 | −0.570029 | ||||||||
\(94\) | 4.10677 | + | 2.98375i | 0.423581 | + | 0.307750i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.53186 | − | 1.83951i | 0.258407 | − | 0.187744i | ||||
\(97\) | −11.3936 | + | 8.27794i | −1.15685 | + | 0.840498i | −0.989376 | − | 0.145379i | \(-0.953560\pi\) |
−0.167470 | + | 0.985877i | \(0.553560\pi\) | |||||||
\(98\) | 1.95260 | + | 6.00947i | 0.197242 | + | 0.607048i | ||||
\(99\) | −12.9425 | −1.30077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5130 | −1.04608 | −0.523040 | − | 0.852308i | \(-0.675202\pi\) | ||||
−0.523040 | + | 0.852308i | \(0.675202\pi\) | |||||||
\(102\) | 0.717214 | + | 2.20736i | 0.0710147 | + | 0.218561i | ||||
\(103\) | −2.48991 | + | 1.80902i | −0.245338 | + | 0.178248i | −0.703658 | − | 0.710539i | \(-0.748451\pi\) |
0.458320 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(104\) | 15.0022 | − | 10.8997i | 1.47109 | − | 1.06881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.59706 | − | 6.24613i | −0.835020 | − | 0.606678i | ||||
\(107\) | 5.24731 | 0.507277 | 0.253638 | − | 0.967299i | \(-0.418373\pi\) | ||||
0.253638 | + | 0.967299i | \(0.418373\pi\) | |||||||
\(108\) | −2.71109 | − | 1.96972i | −0.260875 | − | 0.189537i | ||||
\(109\) | −2.01450 | + | 6.19999i | −0.192954 | + | 0.593852i | 0.807040 | + | 0.590496i | \(0.201068\pi\) |
−0.999994 | + | 0.00335529i | \(0.998932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.78586 | − | 5.49632i | −0.169507 | − | 0.521688i | ||||
\(112\) | 0.456024 | − | 1.40350i | 0.0430902 | − | 0.132618i | ||||
\(113\) | −0.119143 | + | 0.366684i | −0.0112080 | + | 0.0344947i | −0.956504 | − | 0.291719i | \(-0.905773\pi\) |
0.945296 | + | 0.326214i | \(0.105773\pi\) | |||||||
\(114\) | −0.770113 | − | 2.37016i | −0.0721277 | − | 0.221986i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.423108 | − | 1.30219i | 0.0392846 | − | 0.120906i | ||||
\(117\) | −12.4430 | − | 9.04037i | −1.15036 | − | 0.835782i | ||||
\(118\) | −3.06058 | −0.281749 | ||||||||
\(119\) | −2.61434 | − | 1.89943i | −0.239656 | − | 0.174120i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3148 | + | 8.94724i | −1.11953 | + | 0.813385i | ||||
\(122\) | −1.97576 | + | 1.43548i | −0.178877 | + | 0.129962i | ||||
\(123\) | −0.395853 | − | 1.21831i | −0.0356929 | − | 0.109851i | ||||
\(124\) | 7.05301 | 0.633379 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.70455 | −0.240940 | ||||||||
\(127\) | 1.43484 | + | 4.41598i | 0.127321 | + | 0.391855i | 0.994317 | − | 0.106461i | \(-0.0339519\pi\) |
−0.866995 | + | 0.498316i | \(0.833952\pi\) | |||||||
\(128\) | −0.753609 | + | 0.547529i | −0.0666103 | + | 0.0483952i | ||||
\(129\) | −2.90519 | + | 2.11074i | −0.255787 | + | 0.185840i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1233 | − | 9.53462i | −1.14659 | − | 0.833044i | −0.158563 | − | 0.987349i | \(-0.550686\pi\) |
−0.988023 | + | 0.154305i | \(0.950686\pi\) | |||||||
\(132\) | −3.10450 | −0.270212 | ||||||||
\(133\) | 2.80716 | + | 2.03952i | 0.243412 | + | 0.176849i | ||||
\(134\) | 1.51903 | − | 4.67509i | 0.131224 | − | 0.403867i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00694 | − | 9.25440i | −0.257843 | − | 0.793559i | ||||
\(137\) | 5.92699 | − | 18.2414i | 0.506377 | − | 1.55847i | −0.292066 | − | 0.956398i | \(-0.594343\pi\) |
0.798443 | − | 0.602070i | \(-0.205657\pi\) | |||||||
\(138\) | 0.655664 | − | 2.01792i | 0.0558138 | − | 0.171777i | ||||
\(139\) | 1.10864 | + | 3.41206i | 0.0940340 | + | 0.289407i | 0.987001 | − | 0.160716i | \(-0.0513803\pi\) |
−0.892967 | + | 0.450123i | \(0.851380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.01978 | − | 3.13857i | 0.0858813 | − | 0.264316i | ||||
\(142\) | −6.61859 | − | 4.80869i | −0.555420 | − | 0.403536i | ||||
\(143\) | −31.1611 | −2.60582 | ||||||||
\(144\) | −2.98175 | − | 2.16637i | −0.248479 | − | 0.180531i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.509445 | − | 0.370134i | 0.0421620 | − | 0.0306325i | ||||
\(147\) | 3.32331 | − | 2.41452i | 0.274102 | − | 0.199147i | ||||
\(148\) | 2.29131 | + | 7.05194i | 0.188345 | + | 0.579666i | ||||
\(149\) | 1.60192 | 0.131234 | 0.0656170 | − | 0.997845i | \(-0.479098\pi\) | ||||
0.0656170 | + | 0.997845i | \(0.479098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.74218 | 0.548671 | 0.274336 | − | 0.961634i | \(-0.411542\pi\) | ||||
0.274336 | + | 0.961634i | \(0.411542\pi\) | |||||||
\(152\) | 3.22872 | + | 9.93698i | 0.261884 | + | 0.805995i | ||||
\(153\) | −6.52935 | + | 4.74385i | −0.527867 | + | 0.383518i | ||||
\(154\) | −4.43300 | + | 3.22076i | −0.357221 | + | 0.259536i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.98468 | − | 2.16850i | −0.238966 | − | 0.173619i | ||||
\(157\) | 14.2612 | 1.13817 | 0.569083 | − | 0.822280i | \(-0.307298\pi\) | ||||
0.569083 | + | 0.822280i | \(0.307298\pi\) | |||||||
\(158\) | 9.46051 | + | 6.87346i | 0.752638 | + | 0.546823i | ||||
\(159\) | −2.13480 | + | 6.57024i | −0.169301 | + | 0.521054i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.912890 | + | 2.80959i | 0.0719458 | + | 0.221426i | ||||
\(162\) | −1.62412 | + | 4.99852i | −0.127603 | + | 0.392721i | ||||
\(163\) | 3.12542 | − | 9.61904i | 0.244801 | − | 0.753421i | −0.750868 | − | 0.660453i | \(-0.770364\pi\) |
0.995669 | − | 0.0929686i | \(-0.0296356\pi\) | |||||||
\(164\) | 0.507891 | + | 1.56313i | 0.0396596 | + | 0.122060i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.67159 | − | 14.3777i | 0.362586 | − | 1.11592i | ||||
\(167\) | 13.5236 | + | 9.82548i | 1.04649 | + | 0.760318i | 0.971542 | − | 0.236869i | \(-0.0761213\pi\) |
0.0749467 | + | 0.997188i | \(0.476121\pi\) | |||||||
\(168\) | −2.11986 | −0.163551 | ||||||||
\(169\) | −19.4412 | − | 14.1248i | −1.49547 | − | 1.08653i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.01094 | − | 5.09374i | 0.536140 | − | 0.389528i | ||||
\(172\) | 3.72744 | − | 2.70814i | 0.284214 | − | 0.206494i | ||||
\(173\) | −1.99090 | − | 6.12735i | −0.151365 | − | 0.465853i | 0.846410 | − | 0.532533i | \(-0.178760\pi\) |
−0.997774 | + | 0.0666791i | \(0.978760\pi\) | |||||||
\(174\) | 1.12840 | 0.0855435 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.46723 | −0.562864 | ||||||||
\(177\) | 0.614849 | + | 1.89231i | 0.0462149 | + | 0.142235i | ||||
\(178\) | −5.46899 | + | 3.97345i | −0.409918 | + | 0.297823i | ||||
\(179\) | 12.4866 | − | 9.07201i | 0.933289 | − | 0.678074i | −0.0135069 | − | 0.999909i | \(-0.504300\pi\) |
0.946796 | + | 0.321835i | \(0.104300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03388 | − | 0.751154i | −0.0768473 | − | 0.0558329i | 0.548698 | − | 0.836020i | \(-0.315124\pi\) |
−0.625546 | + | 0.780188i | \(0.715124\pi\) | |||||||
\(182\) | −6.51160 | −0.482672 | ||||||||
\(183\) | 1.28445 | + | 0.933208i | 0.0949493 | + | 0.0689847i | ||||
\(184\) | −2.74889 | + | 8.46021i | −0.202651 | + | 0.623695i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.79618 | + | 5.52807i | 0.131702 | + | 0.405338i | ||||
\(187\) | −5.05290 | + | 15.5512i | −0.369504 | + | 1.13722i | ||||
\(188\) | −1.30841 | + | 4.02688i | −0.0954258 | + | 0.293690i | ||||
\(189\) | 1.18823 | + | 3.65699i | 0.0864308 | + | 0.266007i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.80346 | − | 5.55049i | 0.130494 | − | 0.401619i | −0.864368 | − | 0.502860i | \(-0.832281\pi\) |
0.994862 | + | 0.101241i | \(0.0322812\pi\) | |||||||
\(192\) | −4.29904 | − | 3.12343i | −0.310256 | − | 0.225414i | ||||
\(193\) | 4.17773 | 0.300719 | 0.150360 | − | 0.988631i | \(-0.451957\pi\) | ||||
0.150360 | + | 0.988631i | \(0.451957\pi\) | |||||||
\(194\) | 12.0473 | + | 8.75289i | 0.864947 | + | 0.628421i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.26390 | + | 3.09790i | −0.304564 | + | 0.221279i | ||||
\(197\) | −14.1460 | + | 10.2777i | −1.00786 | + | 0.732255i | −0.963760 | − | 0.266772i | \(-0.914043\pi\) |
−0.0441025 | + | 0.999027i | \(0.514043\pi\) | |||||||
\(198\) | 4.22893 | + | 13.0153i | 0.300537 | + | 0.924959i | ||||
\(199\) | 5.89046 | 0.417564 | 0.208782 | − | 0.977962i | \(-0.433050\pi\) | ||||
0.208782 | + | 0.977962i | \(0.433050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.19571 | −0.225408 | ||||||||
\(202\) | 3.43508 | + | 10.5721i | 0.241692 | + | 0.743850i | ||||
\(203\) | −1.27103 | + | 0.923459i | −0.0892090 | + | 0.0648141i | ||||
\(204\) | −1.56618 | + | 1.13790i | −0.109655 | + | 0.0796689i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.63277 | + | 1.91282i | 0.183434 | + | 0.133272i | ||||
\(207\) | 7.37811 | 0.512814 | ||||||||
\(208\) | −7.17902 | − | 5.21586i | −0.497775 | − | 0.361655i | ||||
\(209\) | 5.42558 | − | 16.6982i | 0.375295 | − | 1.15504i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.70118 | − | 11.3911i | −0.254800 | − | 0.784193i | −0.993869 | − | 0.110564i | \(-0.964734\pi\) |
0.739069 | − | 0.673629i | \(-0.235266\pi\) | |||||||
\(212\) | 2.73901 | − | 8.42981i | 0.188116 | − | 0.578962i | ||||
\(213\) | −1.64351 | + | 5.05821i | −0.112612 | + | 0.346583i | ||||
\(214\) | −1.71454 | − | 5.27682i | −0.117204 | − | 0.360716i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.57798 | + | 11.0119i | −0.243451 | + | 0.749264i | ||||
\(217\) | −6.54730 | − | 4.75689i | −0.444460 | − | 0.322919i | ||||
\(218\) | 6.89309 | 0.466859 | ||||||||
\(219\) | −0.331192 | − | 0.240625i | −0.0223799 | − | 0.0162600i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7204 | + | 11.4215i | −1.05747 | + | 0.768296i | ||||
\(222\) | −4.94371 | + | 3.59181i | −0.331800 | + | 0.241067i | ||||
\(223\) | 0.394663 | + | 1.21465i | 0.0264286 | + | 0.0813389i | 0.963401 | − | 0.268065i | \(-0.0863842\pi\) |
−0.936972 | + | 0.349404i | \(0.886384\pi\) | |||||||
\(224\) | 4.60733 | 0.307840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.407676 | 0.0271182 | ||||||||
\(227\) | −8.69517 | − | 26.7610i | −0.577119 | − | 1.77619i | −0.628849 | − | 0.777527i | \(-0.716474\pi\) |
0.0517304 | − | 0.998661i | \(-0.483526\pi\) | |||||||
\(228\) | 1.68170 | − | 1.22183i | 0.111373 | − | 0.0809175i | ||||
\(229\) | −9.12744 | + | 6.63147i | −0.603158 | + | 0.438220i | −0.846998 | − | 0.531595i | \(-0.821593\pi\) |
0.243840 | + | 0.969815i | \(0.421593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.88191 | + | 2.09383i | 0.189616 | + | 0.137764i | ||||
\(232\) | −4.73083 | −0.310594 | ||||||||
\(233\) | −10.8990 | − | 7.91861i | −0.714019 | − | 0.518765i | 0.170448 | − | 0.985367i | \(-0.445478\pi\) |
−0.884468 | + | 0.466601i | \(0.845478\pi\) | |||||||
\(234\) | −5.02550 | + | 15.4669i | −0.328527 | + | 1.01110i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.788868 | − | 2.42789i | −0.0513510 | − | 0.158042i | ||||
\(237\) | 2.34921 | − | 7.23013i | 0.152598 | − | 0.469647i | ||||
\(238\) | −1.05588 | + | 3.24967i | −0.0684426 | + | 0.210645i | ||||
\(239\) | 0.587907 | + | 1.80939i | 0.0380285 | + | 0.117040i | 0.968269 | − | 0.249912i | \(-0.0804015\pi\) |
−0.930240 | + | 0.366951i | \(0.880402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.04699 | + | 18.6107i | −0.389521 | + | 1.19882i | 0.543626 | + | 0.839327i | \(0.317051\pi\) |
−0.933147 | + | 0.359495i | \(0.882949\pi\) | |||||||
\(242\) | 13.0214 | + | 9.46058i | 0.837046 | + | 0.608149i | ||||
\(243\) | 14.8156 | 0.950422 | ||||||||
\(244\) | −1.64799 | − | 1.19733i | −0.105502 | − | 0.0766514i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.09582 | + | 0.796159i | −0.0698668 | + | 0.0507612i | ||||
\(247\) | 16.8799 | − | 12.2639i | 1.07404 | − | 0.780336i | ||||
\(248\) | −7.53053 | − | 23.1766i | −0.478189 | − | 1.47171i | ||||
\(249\) | −9.82800 | −0.622824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7096 | 1.30718 | 0.653590 | − | 0.756849i | \(-0.273262\pi\) | ||||
0.653590 | + | 0.756849i | \(0.273262\pi\) | |||||||
\(252\) | −0.697101 | − | 2.14546i | −0.0439132 | − | 0.135151i | ||||
\(253\) | 12.0934 | − | 8.78636i | 0.760305 | − | 0.552394i | ||||
\(254\) | 3.97199 | − | 2.88582i | 0.249225 | − | 0.181072i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.3049 | + | 9.66657i | 0.831556 | + | 0.604161i | ||||
\(257\) | −15.0730 | −0.940225 | −0.470113 | − | 0.882606i | \(-0.655787\pi\) | ||||
−0.470113 | + | 0.882606i | \(0.655787\pi\) | |||||||
\(258\) | 3.07187 | + | 2.23184i | 0.191246 | + | 0.138949i | ||||
\(259\) | 2.62915 | − | 8.09168i | 0.163367 | − | 0.502793i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.21252 | + | 3.73177i | 0.0750534 | + | 0.230990i | ||||
\(262\) | −5.30025 | + | 16.3125i | −0.327450 | + | 1.00779i | ||||
\(263\) | −1.54609 | + | 4.75839i | −0.0953363 | + | 0.293415i | −0.987341 | − | 0.158611i | \(-0.949298\pi\) |
0.892005 | + | 0.452026i | \(0.149298\pi\) | |||||||
\(264\) | 3.31469 | + | 10.2016i | 0.204005 | + | 0.627864i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.13376 | − | 3.48935i | 0.0695152 | − | 0.213946i | ||||
\(267\) | 3.55541 | + | 2.58316i | 0.217588 | + | 0.158087i | ||||
\(268\) | 4.10018 | 0.250458 | ||||||||
\(269\) | 22.3939 | + | 16.2701i | 1.36538 | + | 0.992007i | 0.998082 | + | 0.0619045i | \(0.0197174\pi\) |
0.367299 | + | 0.930103i | \(0.380283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3522 | − | 15.5133i | 1.29705 | − | 0.942365i | 0.297132 | − | 0.954836i | \(-0.403970\pi\) |
0.999922 | + | 0.0124713i | \(0.00396983\pi\) | |||||||
\(272\) | −3.76713 | + | 2.73698i | −0.228416 | + | 0.165954i | ||||
\(273\) | 1.30814 | + | 4.02603i | 0.0791720 | + | 0.243666i | ||||
\(274\) | −20.2806 | −1.22520 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.76977 | 0.106528 | ||||||||
\(277\) | 2.20106 | + | 6.77415i | 0.132249 | + | 0.407019i | 0.995152 | − | 0.0983496i | \(-0.0313563\pi\) |
−0.862903 | + | 0.505369i | \(0.831356\pi\) | |||||||
\(278\) | 3.06900 | − | 2.22976i | 0.184066 | − | 0.133732i | ||||
\(279\) | −16.3520 | + | 11.8804i | −0.978970 | + | 0.711263i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.35445 | + | 6.06986i | 0.498385 | + | 0.362098i | 0.808400 | − | 0.588634i | \(-0.200334\pi\) |
−0.310015 | + | 0.950732i | \(0.600334\pi\) | |||||||
\(282\) | −3.48943 | −0.207793 | ||||||||
\(283\) | 3.68901 | + | 2.68023i | 0.219289 | + | 0.159323i | 0.692007 | − | 0.721891i | \(-0.256727\pi\) |
−0.472717 | + | 0.881214i | \(0.656727\pi\) | |||||||
\(284\) | 2.10867 | − | 6.48983i | 0.125127 | − | 0.385100i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1818 | + | 31.3363i | 0.602062 | + | 1.85296i | ||||
\(287\) | 0.582775 | − | 1.79360i | 0.0344001 | − | 0.105873i | ||||
\(288\) | 3.55583 | − | 10.9437i | 0.209529 | − | 0.644864i | ||||
\(289\) | −2.10240 | − | 6.47052i | −0.123670 | − | 0.380619i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.99156 | − | 9.20708i | 0.175368 | − | 0.539729i | ||||
\(292\) | 0.424929 | + | 0.308729i | 0.0248671 | + | 0.0180670i | ||||
\(293\) | 20.8237 | 1.21653 | 0.608267 | − | 0.793733i | \(-0.291865\pi\) | ||||
0.608267 | + | 0.793733i | \(0.291865\pi\) | |||||||
\(294\) | −3.51398 | − | 2.55306i | −0.204939 | − | 0.148897i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 20.7266 | − | 15.0588i | 1.20471 | − | 0.875274i | ||||
\(297\) | 15.7409 | − | 11.4364i | 0.913378 | − | 0.663608i | ||||
\(298\) | −0.523421 | − | 1.61092i | −0.0303210 | − | 0.0933183i | ||||
\(299\) | 17.7639 | 1.02731 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.28668 | −0.304719 | ||||||||
\(302\) | −2.20299 | − | 6.78010i | −0.126768 | − | 0.390151i | ||||
\(303\) | 5.84649 | − | 4.24772i | 0.335872 | − | 0.244025i | ||||
\(304\) | 4.04497 | − | 2.93885i | 0.231995 | − | 0.168554i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.90398 | + | 5.01603i | 0.394674 | + | 0.286747i | ||||
\(307\) | −9.44200 | −0.538884 | −0.269442 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269442 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(308\) | −3.69757 | − | 2.68644i | −0.210689 | − | 0.153074i | ||||
\(309\) | 0.653762 | − | 2.01207i | 0.0371912 | − | 0.114463i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.13477 | + | 12.7255i | 0.234461 | + | 0.721597i | 0.997192 | + | 0.0748814i | \(0.0238578\pi\) |
−0.762731 | + | 0.646715i | \(0.776142\pi\) | |||||||
\(312\) | −3.93905 | + | 12.1231i | −0.223005 | + | 0.686338i | ||||
\(313\) | −7.41478 | + | 22.8203i | −0.419108 | + | 1.28988i | 0.489416 | + | 0.872050i | \(0.337210\pi\) |
−0.908524 | + | 0.417832i | \(0.862790\pi\) | |||||||
\(314\) | −4.65979 | − | 14.3414i | −0.262967 | − | 0.809330i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.01410 | + | 9.27646i | −0.169557 | + | 0.521841i | ||||
\(317\) | 11.7806 | + | 8.55911i | 0.661664 | + | 0.480727i | 0.867225 | − | 0.497917i | \(-0.165902\pi\) |
−0.205560 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(318\) | 7.30473 | 0.409629 | ||||||||
\(319\) | 6.43148 | + | 4.67274i | 0.360094 | + | 0.261623i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.91814 | + | 2.12015i | −0.162875 | + | 0.118335i | ||||
\(322\) | 2.52710 | − | 1.83605i | 0.140830 | − | 0.102319i | ||||
\(323\) | −3.38329 | − | 10.4127i | −0.188251 | − | 0.579378i | ||||
\(324\) | −4.38383 | −0.243546 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.6944 | −0.592305 | ||||||||
\(327\) | −1.38477 | − | 4.26190i | −0.0765782 | − | 0.235683i | ||||
\(328\) | 4.59425 | − | 3.33792i | 0.253675 | − | 0.184306i | ||||
\(329\) | 3.93052 | − | 2.85569i | 0.216697 | − | 0.157439i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7601 | + | 14.3566i | 1.08611 | + | 0.789108i | 0.978739 | − | 0.205111i | \(-0.0657555\pi\) |
0.107375 | + | 0.994219i | \(0.465755\pi\) | |||||||
\(332\) | 12.6096 | 0.692042 | ||||||||
\(333\) | −17.1909 | − | 12.4899i | −0.942056 | − | 0.684444i | ||||
\(334\) | 5.46193 | − | 16.8101i | 0.298864 | − | 0.919808i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.313472 | + | 0.964769i | 0.0171013 | + | 0.0526325i | ||||
\(337\) | 2.64896 | − | 8.15266i | 0.144298 | − | 0.444104i | −0.852622 | − | 0.522528i | \(-0.824989\pi\) |
0.996920 | + | 0.0784246i | \(0.0249890\pi\) | |||||||
\(338\) | −7.85192 | + | 24.1657i | −0.427088 | + | 1.31444i | ||||
\(339\) | −0.0818993 | − | 0.252060i | −0.00444816 | − | 0.0136900i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.6544 | + | 38.9462i | −0.685274 | + | 2.10906i | ||||
\(342\) | −7.41319 | − | 5.38600i | −0.400859 | − | 0.291241i | ||||
\(343\) | 13.1315 | 0.709035 | ||||||||
\(344\) | −12.8789 | − | 9.35707i | −0.694384 | − | 0.504499i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.51128 | + | 4.00418i | −0.296288 | + | 0.215266i | ||||
\(347\) | 8.74352 | − | 6.35254i | 0.469377 | − | 0.341022i | −0.327822 | − | 0.944740i | \(-0.606314\pi\) |
0.797198 | + | 0.603717i | \(0.206314\pi\) | |||||||
\(348\) | 0.290846 | + | 0.895132i | 0.0155910 | + | 0.0479841i | ||||
\(349\) | −8.13956 | −0.435701 | −0.217850 | − | 0.975982i | \(-0.569904\pi\) | ||||
−0.217850 | + | 0.975982i | \(0.569904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.1217 | 1.23414 | ||||||||
\(352\) | −7.20420 | − | 22.1723i | −0.383985 | − | 1.18179i | ||||
\(353\) | 17.1237 | − | 12.4411i | 0.911404 | − | 0.662174i | −0.0299652 | − | 0.999551i | \(-0.509540\pi\) |
0.941370 | + | 0.337377i | \(0.109540\pi\) | |||||||
\(354\) | 1.70205 | − | 1.23661i | 0.0904630 | − | 0.0657252i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.56169 | − | 3.31426i | −0.241769 | − | 0.175656i | ||||
\(357\) | 2.22134 | 0.117566 | ||||||||
\(358\) | −13.2030 | − | 9.59252i | −0.697799 | − | 0.506980i | ||||
\(359\) | −1.64578 | + | 5.06518i | −0.0868608 | + | 0.267330i | −0.985047 | − | 0.172285i | \(-0.944885\pi\) |
0.898186 | + | 0.439615i | \(0.144885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.23849 | − | 6.88938i | −0.117816 | − | 0.362599i | ||||
\(362\) | −0.417563 | + | 1.28513i | −0.0219466 | + | 0.0675447i | ||||
\(363\) | 3.23344 | − | 9.95150i | 0.169711 | − | 0.522318i | ||||
\(364\) | −1.67838 | − | 5.16551i | −0.0879708 | − | 0.270746i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.518766 | − | 1.59660i | 0.0271163 | − | 0.0834554i | ||||
\(367\) | −13.7753 | − | 10.0083i | −0.719064 | − | 0.522431i | 0.167021 | − | 0.985953i | \(-0.446585\pi\) |
−0.886085 | + | 0.463523i | \(0.846585\pi\) | |||||||
\(368\) | 4.25682 | 0.221902 | ||||||||
\(369\) | −3.81053 | − | 2.76851i | −0.198368 | − | 0.144123i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.22809 | + | 5.97806i | −0.427181 | + | 0.310365i | ||||
\(372\) | −3.92233 | + | 2.84974i | −0.203363 | + | 0.147752i | ||||
\(373\) | 2.11717 | + | 6.51599i | 0.109623 | + | 0.337385i | 0.990788 | − | 0.135425i | \(-0.0432399\pi\) |
−0.881165 | + | 0.472810i | \(0.843240\pi\) | |||||||
\(374\) | 17.2897 | 0.894028 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.6295 | 0.754461 | ||||||||
\(377\) | 2.91933 | + | 8.98478i | 0.150353 | + | 0.462740i | ||||
\(378\) | 3.28930 | − | 2.38982i | 0.169183 | − | 0.122919i | ||||
\(379\) | 5.97714 | − | 4.34265i | 0.307025 | − | 0.223067i | −0.423594 | − | 0.905852i | \(-0.639232\pi\) |
0.730619 | + | 0.682785i | \(0.239232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.58220 | − | 1.87608i | −0.132290 | − | 0.0961145i | ||||
\(382\) | −6.17097 | −0.315734 | ||||||||
\(383\) | 16.3447 | + | 11.8751i | 0.835175 | + | 0.606790i | 0.921019 | − | 0.389518i | \(-0.127359\pi\) |
−0.0858436 | + | 0.996309i | \(0.527359\pi\) | |||||||
\(384\) | 0.197871 | − | 0.608985i | 0.0100976 | − | 0.0310771i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.36506 | − | 4.20122i | −0.0694797 | − | 0.213836i | ||||
\(387\) | −4.08013 | + | 12.5573i | −0.207405 | + | 0.638326i | ||||
\(388\) | −3.83826 | + | 11.8129i | −0.194858 | + | 0.599711i | ||||
\(389\) | 2.71944 | + | 8.36957i | 0.137881 | + | 0.424354i | 0.996027 | − | 0.0890516i | \(-0.0283836\pi\) |
−0.858146 | + | 0.513406i | \(0.828384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.88049 | − | 8.86522i | 0.145672 | − | 0.448334i | ||||
\(392\) | 14.7325 | + | 10.7038i | 0.744102 | + | 0.540621i | ||||
\(393\) | 11.1506 | 0.562471 | ||||||||
\(394\) | 14.9576 | + | 10.8674i | 0.753555 | + | 0.547490i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.23475 | + | 6.70944i | −0.464064 | + | 0.337162i | ||||
\(397\) | 4.92939 | − | 3.58141i | 0.247399 | − | 0.179746i | −0.457174 | − | 0.889377i | \(-0.651138\pi\) |
0.704573 | + | 0.709631i | \(0.251138\pi\) | |||||||
\(398\) | −1.92469 | − | 5.92358i | −0.0964759 | − | 0.296922i | ||||
\(399\) | −2.38518 | −0.119408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.71924 | −0.0858547 | −0.0429274 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429274 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(402\) | 1.04419 | + | 3.21368i | 0.0520793 | + | 0.160284i | ||||
\(403\) | −39.3699 | + | 28.6039i | −1.96116 | + | 1.42486i | ||||
\(404\) | −7.50121 | + | 5.44995i | −0.373199 | + | 0.271145i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.34396 | + | 0.976443i | 0.0666995 | + | 0.0484600i | ||||
\(407\) | −43.0514 | −2.13398 | ||||||||
\(408\) | 5.41142 | + | 3.93163i | 0.267905 | + | 0.194645i | ||||
\(409\) | −8.57257 | + | 26.3837i | −0.423886 | + | 1.30459i | 0.480170 | + | 0.877175i | \(0.340575\pi\) |
−0.904056 | + | 0.427413i | \(0.859425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.07423 | + | 12.5392i | 0.200967 | + | 0.618513i | ||||
\(412\) | −0.838796 | + | 2.58155i | −0.0413245 | + | 0.127184i | ||||
\(413\) | −0.905180 | + | 2.78586i | −0.0445410 | + | 0.137083i | ||||
\(414\) | −2.41077 | − | 7.41960i | −0.118483 | − | 0.364653i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.56118 | − | 26.3486i | 0.419747 | − | 1.29185i | ||||
\(417\) | −1.99517 | − | 1.44957i | −0.0977037 | − | 0.0709859i | ||||
\(418\) | −18.5649 | −0.908039 | ||||||||
\(419\) | −13.2306 | − | 9.61263i | −0.646359 | − | 0.469608i | 0.215670 | − | 0.976466i | \(-0.430807\pi\) |
−0.862029 | + | 0.506859i | \(0.830807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.04616 | − | 5.84588i | 0.392146 | − | 0.284911i | −0.374188 | − | 0.927353i | \(-0.622079\pi\) |
0.766334 | + | 0.642442i | \(0.222079\pi\) | |||||||
\(422\) | −10.2458 | + | 7.44398i | −0.498756 | + | 0.362367i | ||||
\(423\) | −3.74959 | − | 11.5400i | −0.182311 | − | 0.561096i | ||||
\(424\) | −30.6253 | −1.48729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.62367 | 0.272467 | ||||||||
\(427\) | 0.722285 | + | 2.22296i | 0.0349538 | + | 0.107577i | ||||
\(428\) | 3.74406 | − | 2.72022i | 0.180976 | − | 0.131487i | ||||
\(429\) | 17.3294 | − | 12.5905i | 0.836669 | − | 0.607876i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.6093 | + | 12.0673i | 0.800040 | + | 0.581263i | 0.910926 | − | 0.412570i | \(-0.135369\pi\) |
−0.110886 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(432\) | 5.54071 | 0.266578 | ||||||||
\(433\) | −20.9914 | − | 15.2512i | −1.00878 | − | 0.732925i | −0.0448309 | − | 0.998995i | \(-0.514275\pi\) |
−0.963954 | + | 0.266070i | \(0.914275\pi\) | |||||||
\(434\) | −2.64433 | + | 8.13842i | −0.126932 | + | 0.390657i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.77671 | + | 5.46814i | 0.0850887 | + | 0.261876i | ||||
\(437\) | −3.09294 | + | 9.51909i | −0.147955 | + | 0.455360i | ||||
\(438\) | −0.133762 | + | 0.411678i | −0.00639141 | + | 0.0196708i | ||||
\(439\) | 7.76509 | + | 23.8985i | 0.370608 | + | 1.14061i | 0.946395 | + | 0.323013i | \(0.104696\pi\) |
−0.575787 | + | 0.817600i | \(0.695304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.66735 | − | 14.3646i | 0.222255 | − | 0.684030i | ||||
\(442\) | 16.6224 | + | 12.0768i | 0.790645 | + | 0.574437i | ||||
\(443\) | −27.0262 | −1.28405 | −0.642027 | − | 0.766682i | \(-0.721906\pi\) | ||||
−0.642027 | + | 0.766682i | \(0.721906\pi\) | |||||||
\(444\) | −4.12355 | − | 2.99594i | −0.195695 | − | 0.142181i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.09252 | − | 0.793765i | 0.0517325 | − | 0.0375859i | ||||
\(447\) | −0.890859 | + | 0.647247i | −0.0421362 | + | 0.0306137i | ||||
\(448\) | −2.41748 | − | 7.44023i | −0.114215 | − | 0.351518i | ||||
\(449\) | 37.9871 | 1.79272 | 0.896361 | − | 0.443325i | \(-0.146201\pi\) | ||||
0.896361 | + | 0.443325i | \(0.146201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.54273 | −0.449350 | ||||||||
\(452\) | 0.105079 | + | 0.323400i | 0.00494250 | + | 0.0152115i | ||||
\(453\) | −3.74947 | + | 2.72415i | −0.176166 | + | 0.127992i | ||||
\(454\) | −24.0703 | + | 17.4881i | −1.12968 | + | 0.820759i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.81055 | − | 4.22161i | −0.272104 | − | 0.197695i | ||||
\(457\) | 29.9832 | 1.40256 | 0.701278 | − | 0.712888i | \(-0.252613\pi\) | ||||
0.701278 | + | 0.712888i | \(0.252613\pi\) | |||||||
\(458\) | 9.65113 | + | 7.01195i | 0.450967 | + | 0.327647i | ||||
\(459\) | 3.74927 | − | 11.5391i | 0.175001 | − | 0.538597i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.659330 | − | 2.02921i | −0.0307081 | − | 0.0945097i | 0.934528 | − | 0.355890i | \(-0.115822\pi\) |
−0.965236 | + | 0.261380i | \(0.915822\pi\) | |||||||
\(462\) | 1.16395 | − | 3.58227i | 0.0541518 | − | 0.166662i | ||||
\(463\) | 6.79231 | − | 20.9046i | 0.315665 | − | 0.971518i | −0.659815 | − | 0.751428i | \(-0.729365\pi\) |
0.975480 | − | 0.220089i | \(-0.0706348\pi\) | |||||||
\(464\) | 0.699568 | + | 2.15305i | 0.0324766 | + | 0.0999528i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.40192 | + | 13.5477i | −0.203915 | + | 0.627585i | ||||
\(467\) | 4.29663 | + | 3.12169i | 0.198824 | + | 0.144454i | 0.682743 | − | 0.730659i | \(-0.260787\pi\) |
−0.483918 | + | 0.875113i | \(0.660787\pi\) | |||||||
\(468\) | −13.5649 | −0.627036 | ||||||||
\(469\) | −3.80619 | − | 2.76536i | −0.175754 | − | 0.127693i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.93094 | + | 5.76216i | −0.365438 | + | 0.265507i | ||||
\(472\) | −7.13590 | + | 5.18453i | −0.328456 | + | 0.238637i | ||||
\(473\) | 8.26646 | + | 25.4415i | 0.380092 | + | 1.16980i | ||||
\(474\) | −8.03838 | −0.369215 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.85005 | −0.130632 | ||||||||
\(477\) | 7.84933 | + | 24.1578i | 0.359396 | + | 1.10611i | ||||
\(478\) | 1.62747 | − | 1.18243i | 0.0744387 | − | 0.0540829i | ||||
\(479\) | 17.0603 | − | 12.3950i | 0.779506 | − | 0.566344i | −0.125325 | − | 0.992116i | \(-0.539997\pi\) |
0.904831 | + | 0.425772i | \(0.139997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.3897 | − | 30.0714i | −1.88721 | − | 1.37114i | ||||
\(482\) | 20.6912 | 0.942459 | ||||||||
\(483\) | −1.64288 | − | 1.19362i | −0.0747536 | − | 0.0543116i | ||||
\(484\) | −4.14859 | + | 12.7681i | −0.188572 | + | 0.580366i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.84095 | − | 14.8989i | −0.219590 | − | 0.675829i | ||||
\(487\) | 8.22358 | − | 25.3096i | 0.372646 | − | 1.14689i | −0.572407 | − | 0.819969i | \(-0.693990\pi\) |
0.945053 | − | 0.326917i | \(-0.106010\pi\) | |||||||
\(488\) | −2.17494 | + | 6.69377i | −0.0984549 | + | 0.303013i | ||||
\(489\) | 2.14842 | + | 6.61216i | 0.0971550 | + | 0.299012i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.556442 | − | 1.71255i | 0.0251119 | − | 0.0772865i | −0.937715 | − | 0.347405i | \(-0.887063\pi\) |
0.962827 | + | 0.270119i | \(0.0870629\pi\) | |||||||
\(492\) | −0.914024 | − | 0.664077i | −0.0412074 | − | 0.0299389i | ||||
\(493\) | 4.95731 | 0.223266 | ||||||||
\(494\) | −17.8484 | − | 12.9676i | −0.803036 | − | 0.583440i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.43433 | + | 6.85444i | −0.423614 | + | 0.307774i | ||||
\(497\) | −6.33453 | + | 4.60231i | −0.284143 | + | 0.206442i | ||||
\(498\) | 3.21127 | + | 9.88326i | 0.143900 | + | 0.442880i | ||||
\(499\) | 28.6962 | 1.28462 | 0.642309 | − | 0.766446i | \(-0.277977\pi\) | ||||
0.642309 | + | 0.766446i | \(0.277977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4907 | −0.513367 | ||||||||
\(502\) | −6.76681 | − | 20.8261i | −0.302017 | − | 0.929514i | ||||
\(503\) | −19.1597 | + | 13.9204i | −0.854290 | + | 0.620678i | −0.926326 | − | 0.376724i | \(-0.877051\pi\) |
0.0720355 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(504\) | −6.30579 | + | 4.58143i | −0.280882 | + | 0.204073i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.7872 | − | 9.29048i | −0.568462 | − | 0.413012i | ||||
\(507\) | 16.5187 | 0.733622 | ||||||||
\(508\) | 3.31304 | + | 2.40706i | 0.146992 | + | 0.106796i | ||||
\(509\) | 5.46826 | − | 16.8296i | 0.242376 | − | 0.745958i | −0.753681 | − | 0.657241i | \(-0.771723\pi\) |
0.996057 | − | 0.0887168i | \(-0.0282766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.186239 | − | 0.573186i | −0.00823874 | − | 0.0253562i | ||||
\(512\) | 4.79789 | − | 14.7664i | 0.212039 | − | 0.652589i | ||||
\(513\) | −4.02580 | + | 12.3901i | −0.177743 | + | 0.547038i | ||||
\(514\) | 4.92504 | + | 15.1577i | 0.217234 | + | 0.668578i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.978694 | + | 3.01211i | −0.0430846 | + | 0.132601i | ||||
\(517\) | −19.8886 | − | 14.4499i | −0.874700 | − | 0.635507i | ||||
\(518\) | −8.99625 | −0.395273 | ||||||||
\(519\) | 3.58291 | + | 2.60313i | 0.157272 | + | 0.114265i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.5876 | + | 13.5047i | −0.814338 | + | 0.591651i | −0.915085 | − | 0.403261i | \(-0.867877\pi\) |
0.100747 | + | 0.994912i | \(0.467877\pi\) | |||||||
\(522\) | 3.35656 | − | 2.43868i | 0.146913 | − | 0.106738i | ||||
\(523\) | 8.95447 | + | 27.5590i | 0.391552 | + | 1.20507i | 0.931615 | + | 0.363447i | \(0.118400\pi\) |
−0.540063 | + | 0.841625i | \(0.681600\pi\) | |||||||
\(524\) | −14.3065 | −0.624982 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.29033 | 0.230669 | ||||||||
\(527\) | 7.89104 | + | 24.2861i | 0.343739 | + | 1.05792i | ||||
\(528\) | 4.15268 | − | 3.01710i | 0.180722 | − | 0.131302i | ||||
\(529\) | 11.7134 | − | 8.51025i | 0.509276 | − | 0.370011i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.91860 | + | 4.30011i | 0.256845 | + | 0.186609i | ||||
\(532\) | 3.06025 | 0.132679 | ||||||||
\(533\) | −9.17441 | − | 6.66560i | −0.397388 | − | 0.288719i | ||||
\(534\) | 1.43596 | − | 4.41944i | 0.0621402 | − | 0.191248i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.37778 | − | 13.4734i | −0.189091 | − | 0.581963i | ||||
\(537\) | −3.27853 | + | 10.0903i | −0.141479 | + | 0.435428i | ||||
\(538\) | 9.04448 | − | 27.8361i | 0.389935 | − | 1.20010i | ||||
\(539\) | −9.45618 | − | 29.1031i | −0.407307 | − | 1.25356i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.55563 | − | 23.2538i | 0.324842 | − | 0.999760i | −0.646670 | − | 0.762770i | \(-0.723839\pi\) |
0.971512 | − | 0.236990i | \(-0.0761610\pi\) | |||||||
\(542\) | −22.5773 | − | 16.4034i | −0.969778 | − | 0.704585i | ||||
\(543\) | 0.878460 | 0.0376983 | ||||||||
\(544\) | −11.7613 | − | 8.54506i | −0.504260 | − | 0.366367i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.62124 | − | 2.63098i | 0.154975 | − | 0.112596i | ||||
\(547\) | −5.26131 | + | 3.82257i | −0.224957 | + | 0.163441i | −0.694555 | − | 0.719439i | \(-0.744399\pi\) |
0.469598 | + | 0.882880i | \(0.344399\pi\) | |||||||
\(548\) | −5.22736 | − | 16.0882i | −0.223302 | − | 0.687252i | ||||
\(549\) | 5.83761 | 0.249143 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.32295 | −0.226765 | ||||||||
\(552\) | −1.88959 | − | 5.81558i | −0.0804265 | − | 0.247527i | ||||
\(553\) | 9.05448 | − | 6.57847i | 0.385036 | − | 0.279745i | ||||
\(554\) | 6.09306 | − | 4.42687i | 0.258869 | − | 0.188080i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.55986 | + | 1.85984i | 0.108562 | + | 0.0788749i | ||||
\(557\) | −3.12305 | −0.132328 | −0.0661640 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661640 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(558\) | 17.2902 | + | 12.5621i | 0.731953 | + | 0.531795i | ||||
\(559\) | −9.82352 | + | 30.2337i | −0.415491 | + | 1.27875i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.47338 | − | 10.6900i | −0.146646 | − | 0.451330i | ||||
\(562\) | 3.37421 | − | 10.3847i | 0.142332 | − | 0.438054i | ||||
\(563\) | 11.2869 | − | 34.7376i | 0.475687 | − | 1.46401i | −0.369342 | − | 0.929293i | \(-0.620417\pi\) |
0.845029 | − | 0.534720i | \(-0.179583\pi\) | |||||||
\(564\) | −0.899407 | − | 2.76809i | −0.0378719 | − | 0.116558i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.48992 | − | 4.58551i | 0.0626262 | − | 0.192744i | ||||
\(567\) | 4.06951 | + | 2.95667i | 0.170903 | + | 0.124168i | ||||
\(568\) | −23.5774 | −0.989285 | ||||||||
\(569\) | 30.5546 | + | 22.1992i | 1.28092 | + | 0.930640i | 0.999580 | − | 0.0289691i | \(-0.00922244\pi\) |
0.281336 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.3614 | − | 24.2385i | 1.39613 | − | 1.01435i | 0.400971 | − | 0.916091i | \(-0.368673\pi\) |
0.995161 | − | 0.0982590i | \(-0.0313274\pi\) | |||||||
\(572\) | −22.2340 | + | 16.1540i | −0.929652 | + | 0.675432i | ||||
\(573\) | 1.23971 | + | 3.81542i | 0.0517895 | + | 0.159392i | ||||
\(574\) | −1.99410 | −0.0832322 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −19.5384 | −0.814100 | ||||||||
\(577\) | 1.31928 | + | 4.06033i | 0.0549224 | + | 0.169034i | 0.974755 | − | 0.223277i | \(-0.0716756\pi\) |
−0.919833 | + | 0.392311i | \(0.871676\pi\) | |||||||
\(578\) | −5.81995 | + | 4.22844i | −0.242078 | + | 0.175880i | ||||
\(579\) | −2.32332 | + | 1.68799i | −0.0965540 | + | 0.0701506i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.7055 | − | 8.50453i | −0.485625 | − | 0.352827i | ||||
\(582\) | −10.2363 | −0.424310 | ||||||||
\(583\) | 41.6345 | + | 30.2492i | 1.72432 | + | 1.25280i | ||||
\(584\) | 0.560803 | − | 1.72597i | 0.0232062 | − | 0.0714213i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.80408 | − | 20.9408i | −0.281074 | − | 0.865056i | ||||
\(587\) | −3.53301 | + | 10.8735i | −0.145823 | + | 0.448797i | −0.997116 | − | 0.0758937i | \(-0.975819\pi\) |
0.851293 | + | 0.524691i | \(0.175819\pi\) | |||||||
\(588\) | 1.11955 | − | 3.44562i | 0.0461694 | − | 0.142095i | ||||
\(589\) | −8.47306 | − | 26.0774i | −0.349126 | − | 1.07450i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.71425 | − | 11.4313i | 0.152784 | − | 0.470220i | ||||
\(592\) | −9.91834 | − | 7.20609i | −0.407641 | − | 0.296169i | ||||
\(593\) | −30.9375 | −1.27045 | −0.635225 | − | 0.772327i | \(-0.719092\pi\) | ||||
−0.635225 | + | 0.772327i | \(0.719092\pi\) | |||||||
\(594\) | −16.6440 | − | 12.0926i | −0.682912 | − | 0.496164i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.14300 | − | 0.830436i | 0.0468190 | − | 0.0340160i | ||||
\(597\) | −3.27581 | + | 2.38001i | −0.134070 | + | 0.0974075i | ||||
\(598\) | −5.80430 | − | 17.8638i | −0.237355 | − | 0.730505i | ||||
\(599\) | −46.1912 | −1.88732 | −0.943660 | − | 0.330916i | \(-0.892642\pi\) | ||||
−0.943660 | + | 0.330916i | \(0.892642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.0963 | −1.55398 | −0.776990 | − | 0.629513i | \(-0.783254\pi\) | ||||
−0.776990 | + | 0.629513i | \(0.783254\pi\) | |||||||
\(602\) | 1.72740 | + | 5.31641i | 0.0704038 | + | 0.216681i | ||||
\(603\) | −9.50604 | + | 6.90654i | −0.387116 | + | 0.281256i | ||||
\(604\) | 4.81068 | − | 3.49516i | 0.195744 | − | 0.142216i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.18193 | − | 4.49144i | −0.251124 | − | 0.182452i | ||||
\(607\) | −38.6361 | −1.56819 | −0.784095 | − | 0.620641i | \(-0.786873\pi\) | ||||
−0.784095 | + | 0.620641i | \(0.786873\pi\) | |||||||
\(608\) | 12.6287 | + | 9.17532i | 0.512163 | + | 0.372108i | ||||
\(609\) | 0.333728 | − | 1.02711i | 0.0135234 | − | 0.0416206i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.02770 | − | 27.7844i | −0.365221 | − | 1.12404i | ||||
\(612\) | −2.19960 | + | 6.76966i | −0.0889134 | + | 0.273647i | ||||
\(613\) | 3.32381 | − | 10.2296i | 0.134247 | − | 0.413171i | −0.861225 | − | 0.508224i | \(-0.830302\pi\) |
0.995472 | + | 0.0950531i | \(0.0303021\pi\) | |||||||
\(614\) | 3.08515 | + | 9.49510i | 0.124506 | + | 0.383191i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.87989 | + | 15.0187i | −0.196616 | + | 0.605123i | ||||
\(617\) | −8.74322 | − | 6.35232i | −0.351989 | − | 0.255735i | 0.397714 | − | 0.917509i | \(-0.369804\pi\) |
−0.749703 | + | 0.661775i | \(0.769804\pi\) | |||||||
\(618\) | −2.23700 | −0.0899855 | ||||||||
\(619\) | 29.8477 | + | 21.6856i | 1.19968 | + | 0.871619i | 0.994253 | − | 0.107054i | \(-0.0341417\pi\) |
0.205427 | + | 0.978672i | \(0.434142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.97334 | + | 6.51951i | −0.360088 | + | 0.261619i | ||||
\(622\) | 11.4460 | − | 8.31603i | 0.458944 | − | 0.333443i | ||||
\(623\) | 1.99931 | + | 6.15325i | 0.0801008 | + | 0.246525i | ||||
\(624\) | 6.09985 | 0.244189 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.3714 | 1.01405 | ||||||||
\(627\) | 3.72956 | + | 11.4784i | 0.148944 | + | 0.458404i | ||||
\(628\) | 10.1756 | − | 7.39302i | 0.406051 | − | 0.295014i | ||||
\(629\) | −21.7189 | + | 15.7797i | −0.865988 | + | 0.629177i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7615 | − | 23.0761i | −1.26440 | − | 0.918643i | −0.265439 | − | 0.964128i | \(-0.585517\pi\) |
−0.998965 | + | 0.0454842i | \(0.985517\pi\) | |||||||
\(632\) | 33.7011 | 1.34056 | ||||||||
\(633\) | 6.66081 | + | 4.83936i | 0.264744 | + | 0.192347i | ||||
\(634\) | 4.75796 | − | 14.6435i | 0.188963 | − | 0.581568i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.88281 | + | 5.79468i | 0.0746581 | + | 0.229774i | ||||
\(637\) | 11.2373 | − | 34.5850i | 0.445240 | − | 1.37031i | ||||
\(638\) | 2.59755 | − | 7.99445i | 0.102838 | − | 0.316503i | ||||
\(639\) | 6.04294 | + | 18.5983i | 0.239055 | + | 0.735735i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.57978 | − | 7.93973i | 0.101895 | − | 0.313601i | −0.887094 | − | 0.461589i | \(-0.847280\pi\) |
0.988989 | + | 0.147988i | \(0.0472797\pi\) | |||||||
\(642\) | 3.08557 | + | 2.24180i | 0.121778 | + | 0.0884767i | ||||
\(643\) | 13.1408 | 0.518223 | 0.259112 | − | 0.965847i | \(-0.416570\pi\) | ||||
0.259112 | + | 0.965847i | \(0.416570\pi\) | |||||||
\(644\) | 2.10786 | + | 1.53145i | 0.0830613 | + | 0.0603476i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.36577 | + | 6.80463i | −0.368491 | + | 0.267725i | ||||
\(647\) | 21.0992 | − | 15.3295i | 0.829496 | − | 0.602664i | −0.0899210 | − | 0.995949i | \(-0.528661\pi\) |
0.919417 | + | 0.393285i | \(0.128661\pi\) | |||||||
\(648\) | 4.68064 | + | 14.4055i | 0.183873 | + | 0.565902i | ||||
\(649\) | 14.8220 | 0.581814 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.56310 | 0.218035 | ||||||||
\(652\) | −2.75649 | − | 8.48359i | −0.107952 | − | 0.332243i | ||||
\(653\) | 18.6312 | − | 13.5364i | 0.729097 | − | 0.529720i | −0.160181 | − | 0.987088i | \(-0.551208\pi\) |
0.889278 | + | 0.457368i | \(0.151208\pi\) | |||||||
\(654\) | −3.83339 | + | 2.78512i | −0.149898 | + | 0.108907i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.19849 | − | 1.59730i | −0.0858367 | − | 0.0623640i | ||||
\(657\) | −1.50521 | −0.0587240 | ||||||||
\(658\) | −4.15603 | − | 3.01953i | −0.162019 | − | 0.117714i | ||||
\(659\) | 10.7408 | − | 33.0569i | 0.418403 | − | 1.28771i | −0.490768 | − | 0.871290i | \(-0.663284\pi\) |
0.909171 | − | 0.416422i | \(-0.136716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.56334 | + | 17.1222i | 0.216389 | + | 0.665976i | 0.999052 | + | 0.0435308i | \(0.0138607\pi\) |
−0.782663 | + | 0.622445i | \(0.786139\pi\) | |||||||
\(662\) | 7.98074 | − | 24.5622i | 0.310180 | − | 0.954636i | ||||
\(663\) | 4.12762 | − | 12.7035i | 0.160304 | − | 0.493364i | ||||
\(664\) | −13.4633 | − | 41.4359i | −0.522478 | − | 1.60802i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.94309 | + | 21.3686i | −0.269039 | + | 0.828018i | ||||
\(667\) | −3.66637 | − | 2.66377i | −0.141962 | − | 0.103142i | ||||
\(668\) | 14.7429 | 0.570420 | ||||||||
\(669\) | −0.710254 | − | 0.516030i | −0.0274600 | − | 0.0199509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.56838 | − | 6.95183i | 0.369383 | − | 0.268372i | ||||
\(672\) | −2.56223 | + | 1.86157i | −0.0988403 | + | 0.0718117i | ||||
\(673\) | −4.59267 | − | 14.1348i | −0.177034 | − | 0.544856i | 0.822686 | − | 0.568496i | \(-0.192474\pi\) |
−0.999721 | + | 0.0236399i | \(0.992474\pi\) | |||||||
\(674\) | −9.06404 | −0.349134 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.1940 | −0.815153 | ||||||||
\(677\) | 7.14565 | + | 21.9920i | 0.274629 | + | 0.845223i | 0.989317 | + | 0.145779i | \(0.0465688\pi\) |
−0.714688 | + | 0.699444i | \(0.753431\pi\) | |||||||
\(678\) | −0.226717 | + | 0.164720i | −0.00870702 | + | 0.00632602i | ||||
\(679\) | 11.5303 | − | 8.37723i | 0.442491 | − | 0.321489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6482 | + | 11.3691i | 0.599641 | + | 0.435665i | ||||
\(682\) | 43.3000 | 1.65804 | ||||||||
\(683\) | −15.8848 | − | 11.5410i | −0.607816 | − | 0.441604i | 0.240828 | − | 0.970568i | \(-0.422581\pi\) |
−0.848645 | + | 0.528963i | \(0.822581\pi\) | |||||||
\(684\) | 2.36183 | − | 7.26897i | 0.0903069 | − | 0.277936i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.29068 | − | 13.2054i | −0.163819 | − | 0.504183i | ||||
\(687\) | 2.39654 | − | 7.37580i | 0.0914339 | − | 0.281404i | ||||
\(688\) | −2.35404 | + | 7.24499i | −0.0897469 | + | 0.276213i | ||||
\(689\) | 18.8984 | + | 58.1634i | 0.719973 | + | 2.21585i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.81635 | + | 5.59014i | −0.0690970 | + | 0.212659i | −0.979642 | − | 0.200750i | \(-0.935662\pi\) |
0.910545 | + | 0.413409i | \(0.135662\pi\) | |||||||
\(692\) | −4.59697 | − | 3.33989i | −0.174751 | − | 0.126964i | ||||
\(693\) | 13.0978 | 0.497544 | ||||||||
\(694\) | −9.24518 | − | 6.71702i | −0.350942 | − | 0.254974i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.63092 | − | 1.91147i | 0.0997246 | − | 0.0724542i | ||||
\(697\) | −4.81419 | + | 3.49771i | −0.182351 | + | 0.132485i | ||||
\(698\) | 2.65958 | + | 8.18533i | 0.100666 | + | 0.309819i | ||||
\(699\) | 9.26066 | 0.350270 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.0581 | −1.89067 | −0.945334 | − | 0.326103i | \(-0.894264\pi\) | ||||
−0.945334 | + | 0.326103i | \(0.894264\pi\) | |||||||
\(702\) | −7.55493 | − | 23.2517i | −0.285142 | − | 0.877578i | ||||
\(703\) | 23.3208 | − | 16.9435i | 0.879560 | − | 0.639038i | ||||
\(704\) | −32.0252 | + | 23.2677i | −1.20700 | + | 0.876934i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.1062 | − | 13.1549i | −0.681436 | − | 0.495092i | ||||
\(707\) | 10.6391 | 0.400124 | ||||||||
\(708\) | 1.41968 | + | 1.03146i | 0.0533550 | + | 0.0387647i | ||||
\(709\) | 4.24917 | − | 13.0776i | 0.159581 | − | 0.491139i | −0.839015 | − | 0.544108i | \(-0.816868\pi\) |
0.998596 | + | 0.0529685i | \(0.0168683\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.63768 | − | 26.5841i | −0.323938 | − | 0.996980i | ||||
\(712\) | −6.02032 | + | 18.5286i | −0.225621 | + | 0.694390i | ||||
\(713\) | 7.21384 | − | 22.2019i | 0.270161 | − | 0.831469i | ||||
\(714\) | −0.725816 | − | 2.23383i | −0.0271630 | − | 0.0835991i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.20645 | − | 12.9461i | 0.157202 | − | 0.483819i | ||||
\(717\) | −1.05802 | − | 0.768700i | −0.0395126 | − | 0.0287076i | ||||
\(718\) | 5.63142 | 0.210163 | ||||||||
\(719\) | 8.49464 | + | 6.17172i | 0.316797 | + | 0.230166i | 0.734807 | − | 0.678276i | \(-0.237273\pi\) |
−0.418011 | + | 0.908442i | \(0.637273\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.51977 | − | 1.83072i | 0.0938413 | − | 0.0681797i | ||||
\(722\) | −6.19670 | + | 4.50216i | −0.230617 | + | 0.167553i | ||||
\(723\) | −4.15672 | − | 12.7931i | −0.154590 | − | 0.475780i | ||||
\(724\) | −1.12709 | −0.0418880 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.0640 | −0.410623 | ||||||||
\(727\) | 1.87377 | + | 5.76688i | 0.0694944 | + | 0.213882i | 0.979772 | − | 0.200116i | \(-0.0641320\pi\) |
−0.910278 | + | 0.413998i | \(0.864132\pi\) | |||||||
\(728\) | −15.1821 | + | 11.0305i | −0.562687 | + | 0.408816i | ||||
\(729\) | 3.82455 | − | 2.77870i | 0.141650 | − | 0.102915i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.4955 | + | 9.80503i | 0.499148 | + | 0.362652i | ||||
\(732\) | 1.40026 | 0.0517550 | ||||||||
\(733\) | 1.89367 | + | 1.37583i | 0.0699442 | + | 0.0508174i | 0.622208 | − | 0.782852i | \(-0.286236\pi\) |
−0.552264 | + | 0.833669i | \(0.686236\pi\) | |||||||
\(734\) | −5.56358 | + | 17.1229i | −0.205355 | + | 0.632019i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.10687 | + | 12.6397i | 0.151381 | + | 0.465904i | ||||
\(737\) | −7.35648 | + | 22.6409i | −0.270979 | + | 0.833988i | ||||
\(738\) | −1.53900 | + | 4.73656i | −0.0566514 | + | 0.174355i | ||||
\(739\) | −12.8351 | − | 39.5024i | −0.472147 | − | 1.45312i | −0.849768 | − | 0.527158i | \(-0.823258\pi\) |
0.377621 | − | 0.925960i | \(-0.376742\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.43206 | + | 13.6405i | −0.162816 | + | 0.501096i | ||||
\(742\) | 8.70018 | + | 6.32105i | 0.319394 | + | 0.232053i | ||||
\(743\) | 0.813821 | 0.0298562 | 0.0149281 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149281 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(744\) | 13.5523 | + | 9.84631i | 0.496851 | + | 0.360983i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.86085 | − | 4.25815i | 0.214581 | − | 0.155902i | ||||
\(747\) | −29.2347 | + | 21.2402i | −1.06964 | + | 0.777139i | ||||
\(748\) | 4.45644 | + | 13.7155i | 0.162944 | + | 0.501489i | ||||
\(749\) | −5.31025 | −0.194032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.8919 | 1.16375 | 0.581877 | − | 0.813277i | \(-0.302319\pi\) | ||||
0.581877 | + | 0.813277i | \(0.302319\pi\) | |||||||
\(752\) | −2.16333 | − | 6.65806i | −0.0788886 | − | 0.242794i | ||||
\(753\) | −11.5171 | + | 8.36764i | −0.419705 | + | 0.304934i | ||||
\(754\) | 8.08142 | − | 5.87150i | 0.294308 | − | 0.213827i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.74361 | + | 1.99335i | 0.0997842 | + | 0.0724974i | ||||
\(757\) | −26.7040 | −0.970572 | −0.485286 | − | 0.874355i | \(-0.661285\pi\) | ||||
−0.485286 | + | 0.874355i | \(0.661285\pi\) | |||||||
\(758\) | −6.32008 | − | 4.59181i | −0.229556 | − | 0.166782i | ||||
\(759\) | −3.17530 | + | 9.77256i | −0.115256 | + | 0.354722i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3076 | + | 40.9567i | 0.482402 | + | 1.48468i | 0.835709 | + | 0.549172i | \(0.185057\pi\) |
−0.353307 | + | 0.935507i | \(0.614943\pi\) | |||||||
\(762\) | −1.04290 | + | 3.20973i | −0.0377804 | + | 0.116276i | ||||
\(763\) | 2.03866 | − | 6.27436i | 0.0738046 | − | 0.227147i | ||||
\(764\) | −1.59058 | − | 4.89530i | −0.0575451 | − | 0.177106i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.60132 | − | 20.3168i | 0.238515 | − | 0.734075i | ||||
\(767\) | 14.2499 | + | 10.3532i | 0.514535 | + | 0.373831i | ||||
\(768\) | −11.3049 | −0.407929 | ||||||||
\(769\) | 0.852363 | + | 0.619278i | 0.0307370 | + | 0.0223317i | 0.603048 | − | 0.797705i | \(-0.293953\pi\) |
−0.572311 | + | 0.820037i | \(0.693953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.38239 | − | 6.09016i | 0.301884 | − | 0.219332i | ||||
\(772\) | 2.98089 | − | 2.16574i | 0.107285 | − | 0.0779468i | ||||
\(773\) | 4.08825 | + | 12.5823i | 0.147044 | + | 0.452556i | 0.997268 | − | 0.0738656i | \(-0.0235336\pi\) |
−0.850224 | + | 0.526421i | \(0.823534\pi\) | |||||||
\(774\) | 13.9611 | 0.501823 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 42.9161 | 1.54060 | ||||||||
\(777\) | 1.80728 | + | 5.56225i | 0.0648360 | + | 0.199545i | ||||
\(778\) | 7.52807 | − | 5.46946i | 0.269894 | − | 0.196090i | ||||
\(779\) | 5.16927 | − | 3.75569i | 0.185208 | − | 0.134562i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0530 | + | 23.2879i | 1.14695 | + | 0.833306i | ||||
\(782\) | −9.85627 | −0.352459 | ||||||||
\(783\) | −4.77218 | − | 3.46719i | −0.170544 | − | 0.123907i | ||||
\(784\) | 2.69284 | − | 8.28770i | 0.0961728 | − | 0.295989i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.64341 | − | 11.2133i | −0.129956 | − | 0.399964i | ||||
\(787\) | −10.3946 | + | 31.9914i | −0.370529 | + | 1.14037i | 0.575917 | + | 0.817508i | \(0.304645\pi\) |
−0.946446 | + | 0.322862i | \(0.895355\pi\) | |||||||
\(788\) | −4.76548 | + | 14.6667i | −0.169763 | + | 0.522478i | ||||
\(789\) | −1.06279 | − | 3.27093i | −0.0378364 | − | 0.116448i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.120572 | − | 0.371082i | 0.00428705 | − | 0.0131942i | ||||
\(792\) | 31.9076 | + | 23.1822i | 1.13379 | + | 0.823744i | ||||
\(793\) | 14.0549 | 0.499105 | ||||||||
\(794\) | −5.21221 | − | 3.78689i | −0.184974 | − | 0.134392i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.20296 | − | 3.05363i | 0.148970 | − | 0.108233i | ||||
\(797\) | 5.58012 | − | 4.05419i | 0.197658 | − | 0.143607i | −0.484554 | − | 0.874761i | \(-0.661018\pi\) |
0.682212 | + | 0.731154i | \(0.261018\pi\) | |||||||
\(798\) | 0.779350 | + | 2.39859i | 0.0275887 | + | 0.0849093i | ||||
\(799\) | −15.3299 | −0.542333 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.1587 | 0.570941 | ||||||||
\(802\) | 0.561756 | + | 1.72891i | 0.0198363 | + | 0.0610498i | ||||
\(803\) | −2.46718 | + | 1.79251i | −0.0870649 | + | 0.0632564i | ||||
\(804\) | −2.28020 | + | 1.65666i | −0.0804164 | + | 0.0584259i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 41.6288 | + | 30.2451i | 1.46631 | + | 1.06534i | ||||
\(807\) | −19.0276 | −0.669803 | ||||||||
\(808\) | 25.9179 | + | 18.8305i | 0.911789 | + | 0.662454i | ||||
\(809\) | −10.9185 | + | 33.6037i | −0.383874 | + | 1.18144i | 0.553420 | + | 0.832902i | \(0.313322\pi\) |
−0.937294 | + | 0.348540i | \(0.886678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.22742 | − | 3.77760i | −0.0431005 | − | 0.132650i | 0.927191 | − | 0.374589i | \(-0.122216\pi\) |
−0.970291 | + | 0.241940i | \(0.922216\pi\) | |||||||
\(812\) | −0.428183 | + | 1.31781i | −0.0150263 | + | 0.0462461i | ||||
\(813\) | −5.60634 | + | 17.2545i | −0.196623 | + | 0.605143i | ||||
\(814\) | 14.0669 | + | 43.2934i | 0.493044 | + | 1.51743i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.989114 | − | 3.04418i | 0.0346259 | − | 0.106568i | ||||
\(817\) | −14.4908 | − | 10.5282i | −0.506970 | − | 0.368335i | ||||
\(818\) | 29.3331 | 1.02561 | ||||||||
\(819\) | 12.5923 | + | 9.14881i | 0.440009 | + | 0.319685i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.7204 | + | 14.3277i | −0.688247 | + | 0.500041i | −0.876083 | − | 0.482160i | \(-0.839853\pi\) |
0.187836 | + | 0.982200i | \(0.439853\pi\) | |||||||
\(822\) | 11.2785 | − | 8.19429i | 0.393382 | − | 0.285809i | ||||
\(823\) | −6.87883 | − | 21.1709i | −0.239781 | − | 0.737970i | −0.996451 | − | 0.0841731i | \(-0.973175\pi\) |
0.756670 | − | 0.653797i | \(-0.226825\pi\) | |||||||
\(824\) | 9.37870 | 0.326722 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.09729 | 0.107768 | ||||||||
\(827\) | −8.22592 | − | 25.3168i | −0.286043 | − | 0.880351i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) |
0.700041 | − | 0.714103i | \(-0.253165\pi\) | |||||||
\(828\) | 5.26442 | − | 3.82483i | 0.182951 | − | 0.132922i | ||||
\(829\) | 6.33731 | − | 4.60432i | 0.220104 | − | 0.159915i | −0.472270 | − | 0.881454i | \(-0.656565\pi\) |
0.692373 | + | 0.721539i | \(0.256565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.96112 | − | 2.87792i | −0.137410 | − | 0.0998340i | ||||
\(832\) | −47.0416 | −1.63088 | ||||||||
\(833\) | −15.4378 | − | 11.2162i | −0.534886 | − | 0.388618i | ||||
\(834\) | −0.805810 | + | 2.48003i | −0.0279029 | + | 0.0858764i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.78513 | − | 14.7271i | −0.165497 | − | 0.509348i | ||||
\(837\) | 9.38961 | − | 28.8982i | 0.324552 | − | 0.998870i | ||||
\(838\) | −5.34361 | + | 16.4459i | −0.184592 | + | 0.568116i | ||||
\(839\) | 1.81517 | + | 5.58652i | 0.0626666 | + | 0.192868i | 0.977488 | − | 0.210990i | \(-0.0676689\pi\) |
−0.914822 | + | 0.403858i | \(0.867669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.21672 | + | 25.2885i | −0.283335 | + | 0.872016i | ||||
\(842\) | −8.50781 | − | 6.18129i | −0.293199 | − | 0.213021i | ||||
\(843\) | −7.09859 | −0.244488 | ||||||||
\(844\) | −8.54601 | − | 6.20904i | −0.294166 | − | 0.213724i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.3798 | + | 7.54135i | −0.356864 | + | 0.259277i | ||||
\(847\) | 12.4625 | − | 9.05456i | 0.428218 | − | 0.311118i | ||||
\(848\) | 4.52869 | + | 13.9379i | 0.155516 | + | 0.478629i | ||||
\(849\) | −3.13447 | −0.107575 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5421 | 0.841293 | ||||||||
\(852\) | 1.44951 | + | 4.46113i | 0.0496594 | + | 0.152836i | ||||
\(853\) | −22.7695 | + | 16.5430i | −0.779613 | + | 0.566422i | −0.904863 | − | 0.425703i | \(-0.860027\pi\) |
0.125250 | + | 0.992125i | \(0.460027\pi\) | |||||||
\(854\) | 1.99946 | − | 1.45269i | 0.0684201 | − | 0.0497101i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.9363 | − | 9.39880i | −0.442155 | − | 0.321244i | ||||
\(857\) | 36.2976 | 1.23990 | 0.619951 | − | 0.784640i | \(-0.287152\pi\) | ||||
0.619951 | + | 0.784640i | \(0.287152\pi\) | |||||||
\(858\) | −18.3236 | − | 13.3129i | −0.625558 | − | 0.454495i | ||||
\(859\) | 1.18168 | − | 3.63684i | 0.0403185 | − | 0.124087i | −0.928871 | − | 0.370402i | \(-0.879220\pi\) |
0.969190 | + | 0.246315i | \(0.0792198\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.400602 | + | 1.23292i | 0.0136525 | + | 0.0420180i | ||||
\(862\) | 6.70817 | − | 20.6456i | 0.228481 | − | 0.703192i | ||||
\(863\) | −7.90944 | + | 24.3428i | −0.269240 | + | 0.828637i | 0.721446 | + | 0.692471i | \(0.243478\pi\) |
−0.990686 | + | 0.136166i | \(0.956522\pi\) | |||||||
\(864\) | 5.34555 | + | 16.4519i | 0.181859 | + | 0.559705i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.47805 | + | 26.0928i | −0.288096 | + | 0.886668i | ||||
\(867\) | 3.78357 | + | 2.74893i | 0.128497 | + | 0.0933584i | ||||
\(868\) | −7.13761 | −0.242266 | ||||||||
\(869\) | −45.8161 | − | 33.2873i | −1.55420 | − | 1.12920i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.8872 | + | 16.6285i | −0.775504 | + | 0.563437i | ||||
\(872\) | 16.0716 | − | 11.6767i | 0.544253 | − | 0.395423i | ||||
\(873\) | −10.9995 | − | 33.8530i | −0.372277 | − | 1.14575i | ||||
\(874\) | 10.5832 | 0.357983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.361053 | −0.0121988 | ||||||||
\(877\) | −4.59134 | − | 14.1307i | −0.155038 | − | 0.477159i | 0.843126 | − | 0.537716i | \(-0.180713\pi\) |
−0.998165 | + | 0.0605562i | \(0.980713\pi\) | |||||||
\(878\) | 21.4957 | − | 15.6175i | 0.725443 | − | 0.527066i | ||||
\(879\) | −11.5805 | + | 8.41373i | −0.390601 | + | 0.283788i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.70995 | − | 1.24235i | −0.0576098 | − | 0.0418560i | 0.558608 | − | 0.829432i | \(-0.311336\pi\) |
−0.616217 | + | 0.787576i | \(0.711336\pi\) | |||||||
\(882\) | −15.9704 | −0.537753 | ||||||||
\(883\) | −41.3269 | − | 30.0257i | −1.39076 | − | 1.01045i | −0.995782 | − | 0.0917559i | \(-0.970752\pi\) |
−0.394978 | − | 0.918690i | \(-0.629248\pi\) | |||||||
\(884\) | −5.29586 | + | 16.2990i | −0.178119 | + | 0.548194i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.83073 | + | 27.1782i | 0.296674 | + | 0.913069i | ||||
\(887\) | −14.0850 | + | 43.3491i | −0.472927 | + | 1.45552i | 0.375807 | + | 0.926698i | \(0.377366\pi\) |
−0.848733 | + | 0.528821i | \(0.822634\pi\) | |||||||
\(888\) | −5.44208 | + | 16.7490i | −0.182624 | + | 0.562060i | ||||
\(889\) | −1.45205 | − | 4.46895i | −0.0487002 | − | 0.149884i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.86540 | − | 24.2072i | 0.263501 | − | 0.810972i | ||||
\(892\) | 0.911277 | + | 0.662081i | 0.0305118 | + | 0.0221681i | ||||
\(893\) | 16.4606 | 0.550833 | ||||||||
\(894\) | 0.941972 | + | 0.684383i | 0.0315043 | + | 0.0228892i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.762649 | − | 0.554097i | 0.0254783 | − | 0.0185111i | ||||
\(897\) | −9.87888 | + | 7.17743i | −0.329846 | + | 0.239647i | ||||
\(898\) | −12.4122 | − | 38.2007i | −0.414199 | − | 1.27477i | ||||
\(899\) | 12.4150 | 0.414064 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0914 | 1.06912 | ||||||||
\(902\) | 3.11806 | + | 9.59639i | 0.103820 | + | 0.319525i | ||||
\(903\) | 2.94003 | − | 2.13606i | 0.0978382 | − | 0.0710836i | ||||
\(904\) | 0.950518 | − | 0.690592i | 0.0316137 | − | 0.0229687i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.96460 | + | 2.88045i | 0.131715 | + | 0.0956965i | ||||
\(907\) | 27.5215 | 0.913837 | 0.456919 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456919 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(908\) | −20.0771 | − | 14.5869i | −0.666283 | − | 0.484083i | ||||
\(909\) | 8.21099 | − | 25.2708i | 0.272341 | − | 0.838180i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5779 | + | 47.9437i | 0.516118 | + | 1.58845i | 0.781239 | + | 0.624232i | \(0.214588\pi\) |
−0.265121 | + | 0.964215i | \(0.585412\pi\) | |||||||
\(912\) | −1.06207 | + | 3.26871i | −0.0351686 | + | 0.108238i | ||||
\(913\) | −22.6239 | + | 69.6293i | −0.748743 | + | 2.30439i | ||||
\(914\) | −9.79692 | − | 30.1518i | −0.324053 | − | 0.997334i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.07483 | + | 9.46337i | −0.101595 | + | 0.312678i | ||||
\(917\) | 13.2807 | + | 9.64899i | 0.438567 | + | 0.318638i | ||||
\(918\) | −12.8290 | −0.423420 | ||||||||
\(919\) | −10.2376 | − | 7.43802i | −0.337706 | − | 0.245358i | 0.405988 | − | 0.913879i | \(-0.366928\pi\) |
−0.743693 | + | 0.668521i | \(0.766928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.25090 | − | 3.81500i | 0.173023 | − | 0.125709i | ||||
\(922\) | −1.82519 | + | 1.32608i | −0.0601093 | + | 0.0436720i | ||||
\(923\) | 14.5493 | + | 44.7781i | 0.478895 | + | 1.47389i | ||||
\(924\) | 3.14174 | 0.103356 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.2415 | −0.763763 | ||||||||
\(927\) | −2.40378 | − | 7.39808i | −0.0789506 | − | 0.242985i | ||||
\(928\) | −5.71807 | + | 4.15442i | −0.187705 | + | 0.136376i | ||||
\(929\) | 2.45910 | − | 1.78664i | 0.0806805 | − | 0.0586178i | −0.546714 | − | 0.837320i | \(-0.684121\pi\) |
0.627394 | + | 0.778702i | \(0.284121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5764 | + | 12.0434i | 0.543269 | + | 0.394708i | ||||
\(932\) | −11.8817 | −0.389198 | ||||||||
\(933\) | −7.44111 | − | 5.40628i | −0.243611 | − | 0.176994i | ||||
\(934\) | 1.73533 | − | 5.34080i | 0.0567817 | − | 0.174756i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.4833 | + | 44.5749i | 0.473400 | + | 1.45698i | ||||
\(937\) | −0.0148559 | + | 0.0457219i | −0.000485323 | + | 0.00149367i | −0.951299 | − | 0.308270i | \(-0.900250\pi\) |
0.950814 | + | 0.309764i | \(0.100250\pi\) | |||||||
\(938\) | −1.53725 | + | 4.73117i | −0.0501930 | + | 0.154478i | ||||
\(939\) | −5.09694 | − | 15.6868i | −0.166332 | − | 0.511919i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.387485 | + | 1.19256i | −0.0126316 | + | 0.0388762i | −0.957174 | − | 0.289514i | \(-0.906506\pi\) |
0.944542 | + | 0.328391i | \(0.106506\pi\) | |||||||
\(942\) | 8.38598 | + | 6.09277i | 0.273230 | + | 0.198513i | ||||
\(943\) | 5.43999 | 0.177150 | ||||||||
\(944\) | 3.41475 | + | 2.48096i | 0.111141 | + | 0.0807484i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.8836 | − | 16.6259i | 0.744009 | − | 0.540554i | ||||
\(947\) | 36.0810 | − | 26.2143i | 1.17247 | − | 0.851852i | 0.181171 | − | 0.983452i | \(-0.442011\pi\) |
0.991303 | + | 0.131600i | \(0.0420114\pi\) | |||||||
\(948\) | −2.07191 | − | 6.37667i | −0.0672924 | − | 0.207105i | ||||
\(949\) | −3.62403 | −0.117641 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0097 | −0.324587 | ||||||||
\(952\) | 3.04301 | + | 9.36541i | 0.0986244 | + | 0.303535i | ||||
\(953\) | −33.8353 | + | 24.5828i | −1.09603 | + | 0.796314i | −0.980408 | − | 0.196980i | \(-0.936887\pi\) |
−0.115624 | + | 0.993293i | \(0.536887\pi\) | |||||||
\(954\) | 21.7289 | − | 15.7869i | 0.703498 | − | 0.511121i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.35748 | + | 0.986264i | 0.0439039 | + | 0.0318980i | ||||
\(957\) | −5.46469 | −0.176648 | ||||||||
\(958\) | −18.0392 | − | 13.1062i | −0.582819 | − | 0.423443i | ||||
\(959\) | −5.99808 | + | 18.4602i | −0.193688 | + | 0.596111i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1827 | + | 31.3391i | 0.328474 | + | 1.01094i | ||||
\(962\) | −16.7165 | + | 51.4482i | −0.538962 | + | 1.65876i | ||||
\(963\) | −4.09833 | + | 12.6134i | −0.132067 | + | 0.406460i | ||||
\(964\) | 5.33319 | + | 16.4139i | 0.171771 | + | 0.528656i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.663528 | + | 2.04213i | −0.0213487 | + | 0.0657044i | ||||
\(967\) | 36.0001 | + | 26.1556i | 1.15769 | + | 0.841109i | 0.989484 | − | 0.144644i | \(-0.0462037\pi\) |
0.168203 | + | 0.985752i | \(0.446204\pi\) | |||||||
\(968\) | 46.3860 | 1.49090 | ||||||||
\(969\) | 6.08872 | + | 4.42372i | 0.195598 | + | 0.142110i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.96504 | + | 2.15423i | −0.0951526 | + | 0.0691324i | −0.634344 | − | 0.773051i | \(-0.718730\pi\) |
0.539192 | + | 0.842183i | \(0.318730\pi\) | |||||||
\(972\) | 10.5712 | − | 7.68044i | 0.339072 | − | 0.246350i | ||||
\(973\) | −1.12194 | − | 3.45298i | −0.0359678 | − | 0.110698i | ||||
\(974\) | −28.1389 | −0.901629 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.36802 | 0.107808 | ||||||||
\(977\) | −4.86869 | − | 14.9843i | −0.155763 | − | 0.479389i | 0.842474 | − | 0.538736i | \(-0.181098\pi\) |
−0.998237 | + | 0.0593470i | \(0.981098\pi\) | |||||||
\(978\) | 5.94735 | − | 4.32101i | 0.190175 | − | 0.138171i | ||||
\(979\) | 26.4856 | − | 19.2429i | 0.846485 | − | 0.615007i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3300 | − | 9.68480i | −0.425594 | − | 0.309212i | ||||
\(982\) | −1.90400 | −0.0607591 | ||||||||
\(983\) | 21.7641 | + | 15.8125i | 0.694166 | + | 0.504341i | 0.878027 | − | 0.478611i | \(-0.158860\pi\) |
−0.183861 | + | 0.982952i | \(0.558860\pi\) | |||||||
\(984\) | −1.20629 | + | 3.71257i | −0.0384551 | + | 0.118353i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.61979 | − | 4.98519i | −0.0515845 | − | 0.158761i | ||||
\(987\) | −1.03202 | + | 3.17622i | −0.0328494 | + | 0.101100i | ||||
\(988\) | 5.68646 | − | 17.5011i | 0.180910 | − | 0.556785i | ||||
\(989\) | −4.71243 | − | 14.5034i | −0.149847 | − | 0.461180i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34725 | − | 13.3795i | 0.138095 | − | 0.425013i | −0.857964 | − | 0.513710i | \(-0.828271\pi\) |
0.996059 | + | 0.0886979i | \(0.0282706\pi\) | |||||||
\(992\) | −29.4547 | − | 21.4001i | −0.935189 | − | 0.679455i | ||||
\(993\) | −16.7897 | −0.532806 | ||||||||
\(994\) | 6.69798 | + | 4.86636i | 0.212447 | + | 0.154352i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.01247 | + | 5.09485i | −0.222198 | + | 0.161437i | ||||
\(997\) | 0.500493 | − | 0.363630i | 0.0158508 | − | 0.0115163i | −0.579832 | − | 0.814736i | \(-0.696882\pi\) |
0.595682 | + | 0.803220i | \(0.296882\pi\) | |||||||
\(998\) | −9.37639 | − | 28.8575i | −0.296804 | − | 0.913470i | ||||
\(999\) | 31.9443 | 1.01067 |
(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 | 625.2.d.q.126.2 | 16 | ||
5.2 | odd | 4 | 625.2.e.j.499.6 | 32 | |||
5.3 | odd | 4 | 625.2.e.j.499.3 | 32 | |||
5.4 | even | 2 | 625.2.d.m.126.3 | 16 | |||
25.2 | odd | 20 | 625.2.b.d.624.6 | 16 | |||
25.3 | odd | 20 | 625.2.e.j.124.6 | 32 | |||
25.4 | even | 10 | 625.2.d.m.501.3 | 16 | |||
25.6 | even | 5 | 625.2.d.p.376.3 | 16 | |||
25.8 | odd | 20 | 625.2.e.k.249.6 | 32 | |||
25.9 | even | 10 | 625.2.d.n.251.2 | 16 | |||
25.11 | even | 5 | 625.2.a.e.1.4 | ✓ | 8 | ||
25.12 | odd | 20 | 625.2.e.k.374.6 | 32 | |||
25.13 | odd | 20 | 625.2.e.k.374.3 | 32 | |||
25.14 | even | 10 | 625.2.a.g.1.5 | yes | 8 | ||
25.16 | even | 5 | 625.2.d.p.251.3 | 16 | |||
25.17 | odd | 20 | 625.2.e.k.249.3 | 32 | |||
25.19 | even | 10 | 625.2.d.n.376.2 | 16 | |||
25.21 | even | 5 | inner | 625.2.d.q.501.2 | 16 | ||
25.22 | odd | 20 | 625.2.e.j.124.3 | 32 | |||
25.23 | odd | 20 | 625.2.b.d.624.11 | 16 | |||
75.11 | odd | 10 | 5625.2.a.be.1.5 | 8 | |||
75.14 | odd | 10 | 5625.2.a.s.1.4 | 8 | |||
100.11 | odd | 10 | 10000.2.a.bn.1.3 | 8 | |||
100.39 | odd | 10 | 10000.2.a.be.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.4 | ✓ | 8 | 25.11 | even | 5 | ||
625.2.a.g.1.5 | yes | 8 | 25.14 | even | 10 | ||
625.2.b.d.624.6 | 16 | 25.2 | odd | 20 | |||
625.2.b.d.624.11 | 16 | 25.23 | odd | 20 | |||
625.2.d.m.126.3 | 16 | 5.4 | even | 2 | |||
625.2.d.m.501.3 | 16 | 25.4 | even | 10 | |||
625.2.d.n.251.2 | 16 | 25.9 | even | 10 | |||
625.2.d.n.376.2 | 16 | 25.19 | even | 10 | |||
625.2.d.p.251.3 | 16 | 25.16 | even | 5 | |||
625.2.d.p.376.3 | 16 | 25.6 | even | 5 | |||
625.2.d.q.126.2 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.q.501.2 | 16 | 25.21 | even | 5 | inner | ||
625.2.e.j.124.3 | 32 | 25.22 | odd | 20 | |||
625.2.e.j.124.6 | 32 | 25.3 | odd | 20 | |||
625.2.e.j.499.3 | 32 | 5.3 | odd | 4 | |||
625.2.e.j.499.6 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.249.3 | 32 | 25.17 | odd | 20 | |||
625.2.e.k.249.6 | 32 | 25.8 | odd | 20 | |||
625.2.e.k.374.3 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.374.6 | 32 | 25.12 | odd | 20 | |||
5625.2.a.s.1.4 | 8 | 75.14 | odd | 10 | |||
5625.2.a.be.1.5 | 8 | 75.11 | odd | 10 | |||
10000.2.a.be.1.6 | 8 | 100.39 | odd | 10 | |||
10000.2.a.bn.1.3 | 8 | 100.11 | odd | 10 |